Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,2,Mod(97,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.97");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.j (of order \(4\), degree \(2\), 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: | \(3.06625543762\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.18939904.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 289.4 | ||
Root | \(0.500000 - 0.0297061i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.289 |
Dual form | 384.2.j.b.97.4 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.707107 | + | 0.707107i | 0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.334904 | − | 0.334904i | 0.149774 | − | 0.149774i | −0.628243 | − | 0.778017i | \(-0.716226\pi\) |
0.778017 | + | 0.628243i | \(0.216226\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.55765i | − | 1.72263i | −0.508072 | − | 0.861314i | \(-0.669642\pi\) | ||
0.508072 | − | 0.861314i | \(-0.330358\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.47363 | − | 2.47363i | 0.745826 | − | 0.745826i | −0.227866 | − | 0.973692i | \(-0.573175\pi\) |
0.973692 | + | 0.227866i | \(0.0731749\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.0594122 | + | 0.0594122i | 0.0164780 | + | 0.0164780i | 0.715298 | − | 0.698820i | \(-0.246291\pi\) |
−0.698820 | + | 0.715298i | \(0.746291\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.473626 | 0.122290 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.61706 | 0.877266 | 0.438633 | − | 0.898666i | \(-0.355463\pi\) | ||||
0.438633 | + | 0.898666i | \(0.355463\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.55765 | − | 2.55765i | −0.586765 | − | 0.586765i | 0.349989 | − | 0.936754i | \(-0.386185\pi\) |
−0.936754 | + | 0.349989i | \(0.886185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.22274 | − | 3.22274i | 0.703260 | − | 0.703260i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.82843i | 0.589768i | 0.955533 | + | 0.294884i | \(0.0952810\pi\) | ||||
−0.955533 | + | 0.294884i | \(0.904719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.77568i | 0.955136i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.707107 | + | 0.707107i | −0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.16333 | + | 5.16333i | 0.958807 | + | 0.958807i | 0.999184 | − | 0.0403780i | \(-0.0128562\pi\) |
−0.0403780 | + | 0.999184i | \(0.512856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.557647 | −0.100156 | −0.0500782 | − | 0.998745i | \(-0.515947\pi\) | ||||
−0.0500782 | + | 0.998745i | \(0.515947\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.49824 | 0.608965 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.52637 | − | 1.52637i | −0.258004 | − | 0.258004i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.38607 | + | 4.38607i | −0.721066 | + | 0.721066i | −0.968822 | − | 0.247756i | \(-0.920307\pi\) |
0.247756 | + | 0.968822i | \(0.420307\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.0840215i | 0.0134542i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.27391i | − | 1.44834i | −0.689620 | − | 0.724171i | \(-0.742223\pi\) | ||
0.689620 | − | 0.724171i | \(-0.257777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.61040 | − | 1.61040i | 0.245583 | − | 0.245583i | −0.573572 | − | 0.819155i | \(-0.694443\pi\) |
0.819155 | + | 0.573572i | \(0.194443\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.334904 | + | 0.334904i | 0.0499245 | + | 0.0499245i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.82843 | 0.412568 | 0.206284 | − | 0.978492i | \(-0.433863\pi\) | ||||
0.206284 | + | 0.978492i | \(0.433863\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.7721 | −1.96745 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.55765 | + | 2.55765i | 0.358142 | + | 0.358142i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.493523 | − | 0.493523i | 0.0677906 | − | 0.0677906i | −0.672399 | − | 0.740189i | \(-0.734736\pi\) |
0.740189 | + | 0.672399i | \(0.234736\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.65685i | − | 0.223410i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 3.61706i | − | 0.479091i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.00000 | + | 4.00000i | −0.520756 | + | 0.520756i | −0.917800 | − | 0.397044i | \(-0.870036\pi\) |
0.397044 | + | 0.917800i | \(0.370036\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.72922 | − | 2.72922i | −0.349441 | − | 0.349441i | 0.510460 | − | 0.859901i | \(-0.329475\pi\) |
−0.859901 | + | 0.510460i | \(0.829475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 4.55765 | 0.574210 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0397948 | 0.00493593 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.77568 | − | 3.77568i | −0.461273 | − | 0.461273i | 0.437800 | − | 0.899072i | \(-0.355758\pi\) |
−0.899072 | + | 0.437800i | \(0.855758\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | + | 2.00000i | −0.240772 | + | 0.240772i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.11529i | 1.08179i | 0.841091 | + | 0.540893i | \(0.181914\pi\) | ||||
−0.841091 | + | 0.540893i | \(0.818086\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.541560i | − | 0.0633848i | −0.999498 | − | 0.0316924i | \(-0.989910\pi\) | ||
0.999498 | − | 0.0316924i | \(-0.0100897\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.37691 | + | 3.37691i | −0.389933 | + | 0.389933i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11.2739 | − | 11.2739i | −1.28478 | − | 1.28478i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.9937 | −1.23689 | −0.618445 | − | 0.785828i | \(-0.712237\pi\) | ||||
−0.618445 | + | 0.785828i | \(0.712237\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.6417 | + | 10.6417i | 1.16807 | + | 1.16807i | 0.982660 | + | 0.185415i | \(0.0593628\pi\) |
0.185415 | + | 0.982660i | \(0.440637\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.21137 | − | 1.21137i | 0.131391 | − | 0.131391i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.30205i | 0.782862i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 14.6533i | 1.55325i | 0.629964 | + | 0.776625i | \(0.283070\pi\) | ||||
−0.629964 | + | 0.776625i | \(0.716930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.270780 | − | 0.270780i | 0.0283854 | − | 0.0283854i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.394316 | − | 0.394316i | −0.0408887 | − | 0.0408887i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.71313 | −0.175764 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.31724 | 0.438349 | 0.219175 | − | 0.975686i | \(-0.429664\pi\) | ||||
0.219175 | + | 0.975686i | \(0.429664\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.47363 | + | 2.47363i | 0.248609 | + | 0.248609i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.453728 | − | 0.453728i | 0.0451477 | − | 0.0451477i | −0.684173 | − | 0.729320i | \(-0.739836\pi\) |
0.729320 | + | 0.684173i | \(0.239836\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.33686i | 0.131724i | 0.997829 | + | 0.0658622i | \(0.0209798\pi\) | ||||
−0.997829 | + | 0.0658622i | \(0.979020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 2.15862i | − | 0.210660i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.06255 | + | 6.06255i | −0.586088 | + | 0.586088i | −0.936570 | − | 0.350481i | \(-0.886018\pi\) |
0.350481 | + | 0.936570i | \(0.386018\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.71627 | − | 5.71627i | −0.547519 | − | 0.547519i | 0.378203 | − | 0.925722i | \(-0.376542\pi\) |
−0.925722 | + | 0.378203i | \(0.876542\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.20285 | −0.588748 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.55136 | −0.898516 | −0.449258 | − | 0.893402i | \(-0.648312\pi\) | ||||
−0.449258 | + | 0.893402i | \(0.648312\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.947252 | + | 0.947252i | 0.0883317 | + | 0.0883317i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0594122 | + | 0.0594122i | −0.00549266 | + | 0.00549266i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 16.4853i | − | 1.51120i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.23765i | − | 0.112514i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.55765 | − | 6.55765i | 0.591283 | − | 0.591283i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.27391 | + | 3.27391i | 0.292828 | + | 0.292828i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.09921 | 0.452481 | 0.226241 | − | 0.974071i | \(-0.427356\pi\) | ||||
0.226241 | + | 0.974071i | \(0.427356\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.27744 | 0.200518 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.11882 | − | 2.11882i | −0.185123 | − | 0.185123i | 0.608461 | − | 0.793584i | \(-0.291787\pi\) |
−0.793584 | + | 0.608461i | \(0.791787\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −11.6569 | + | 11.6569i | −1.01078 | + | 1.01078i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.473626i | 0.0407632i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.37941i | − | 0.288723i | −0.989525 | − | 0.144361i | \(-0.953887\pi\) | ||
0.989525 | − | 0.144361i | \(-0.0461127\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.88118 | + | 5.88118i | −0.498835 | + | 0.498835i | −0.911075 | − | 0.412240i | \(-0.864746\pi\) |
0.412240 | + | 0.911075i | \(0.364746\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.00000 | + | 2.00000i | 0.168430 | + | 0.168430i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.293927 | 0.0245794 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.45844 | 0.287208 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −9.73838 | − | 9.73838i | −0.803208 | − | 0.803208i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.99176 | − | 9.99176i | 0.818557 | − | 0.818557i | −0.167342 | − | 0.985899i | \(-0.553518\pi\) |
0.985899 | + | 0.167342i | \(0.0535185\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.97685i | 0.811905i | 0.913894 | + | 0.405952i | \(0.133060\pi\) | ||||
−0.913894 | + | 0.405952i | \(0.866940\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.61706i | 0.292422i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.186758 | + | 0.186758i | −0.0150008 | + | 0.0150008i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.1618 | + | 16.1618i | 1.28985 | + | 1.28985i | 0.934877 | + | 0.354971i | \(0.115509\pi\) |
0.354971 | + | 0.934877i | \(0.384491\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.697947 | 0.0553508 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8910 | 1.01595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.50490 | + | 7.50490i | 0.587829 | + | 0.587829i | 0.937043 | − | 0.349214i | \(-0.113551\pi\) |
−0.349214 | + | 0.937043i | \(0.613551\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.17157 | − | 1.17157i | 0.0912068 | − | 0.0912068i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 5.83822i | − | 0.451775i | −0.974153 | − | 0.225888i | \(-0.927472\pi\) | ||
0.974153 | − | 0.225888i | \(-0.0725282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 12.9929i | − | 0.999457i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.55765 | − | 2.55765i | 0.195588 | − | 0.195588i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.62530 | + | 3.62530i | 0.275627 | + | 0.275627i | 0.831360 | − | 0.555734i | \(-0.187563\pi\) |
−0.555734 | + | 0.831360i | \(0.687563\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.7659 | 1.64534 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.65685 | −0.425195 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.28334 | − | 9.28334i | −0.693869 | − | 0.693869i | 0.269212 | − | 0.963081i | \(-0.413237\pi\) |
−0.963081 | + | 0.269212i | \(0.913237\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.8316 | − | 10.8316i | 0.805104 | − | 0.805104i | −0.178785 | − | 0.983888i | \(-0.557217\pi\) |
0.983888 | + | 0.178785i | \(0.0572165\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.85970i | − | 0.285317i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.93783i | 0.215993i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.94725 | − | 8.94725i | 0.654288 | − | 0.654288i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.22274 | + | 3.22274i | 0.234420 | + | 0.234420i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.63001 | −0.624446 | −0.312223 | − | 0.950009i | \(-0.601074\pi\) | ||||
−0.312223 | + | 0.950009i | \(0.601074\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4514 | 0.824288 | 0.412144 | − | 0.911119i | \(-0.364780\pi\) | ||||
0.412144 | + | 0.911119i | \(0.364780\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.0281391 | + | 0.0281391i | 0.00201509 | + | 0.00201509i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.48999 | + | 7.48999i | −0.533640 | + | 0.533640i | −0.921654 | − | 0.388014i | \(-0.873161\pi\) |
0.388014 | + | 0.921654i | \(0.373161\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 3.68000i | − | 0.260868i | −0.991457 | − | 0.130434i | \(-0.958363\pi\) | ||
0.991457 | − | 0.130434i | \(-0.0416371\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 5.33962i | − | 0.376627i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 23.5326 | − | 23.5326i | 1.65167 | − | 1.65167i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.10587 | − | 3.10587i | −0.216923 | − | 0.216923i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.82843 | −0.196589 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.6533 | −0.875249 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1188 | − | 10.1188i | −0.696609 | − | 0.696609i | 0.267069 | − | 0.963677i | \(-0.413945\pi\) |
−0.963677 | + | 0.267069i | \(0.913945\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −6.44549 | + | 6.44549i | −0.441637 | + | 0.441637i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 1.07866i | − | 0.0735637i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.54156i | 0.172532i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.382941 | − | 0.382941i | 0.0258767 | − | 0.0258767i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.214897 | + | 0.214897i | 0.0144556 | + | 0.0144556i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.86156 | −0.325554 | −0.162777 | − | 0.986663i | \(-0.552045\pi\) | ||||
−0.162777 | + | 0.986663i | \(0.552045\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.77568 | −0.318379 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.6417 | − | 10.6417i | −0.706312 | − | 0.706312i | 0.259445 | − | 0.965758i | \(-0.416460\pi\) |
−0.965758 | + | 0.259445i | \(0.916460\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1712 | − | 20.1712i | 1.33295 | − | 1.33295i | 0.430229 | − | 0.902720i | \(-0.358433\pi\) |
0.902720 | − | 0.430229i | \(-0.141567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 15.9437i | − | 1.04902i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 13.5702i | 0.889014i | 0.895775 | + | 0.444507i | \(0.146621\pi\) | ||||
−0.895775 | + | 0.444507i | \(0.853379\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.947252 | − | 0.947252i | 0.0617919 | − | 0.0617919i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −7.77373 | − | 7.77373i | −0.504958 | − | 0.504958i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 29.3629 | 1.89933 | 0.949665 | − | 0.313267i | \(-0.101424\pi\) | ||||
0.949665 | + | 0.313267i | \(0.101424\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.0063 | 1.54638 | 0.773190 | − | 0.634175i | \(-0.218660\pi\) | ||||
0.773190 | + | 0.634175i | \(0.218660\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.707107 | − | 0.707107i | −0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.61235 | + | 4.61235i | −0.294672 | + | 0.294672i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 0.303911i | − | 0.0193374i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0496i | 0.953729i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.7570 | + | 15.7570i | −0.994571 | + | 0.994571i | −0.999985 | − | 0.00541463i | \(-0.998276\pi\) |
0.00541463 | + | 0.999985i | \(0.498276\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.99647 | + | 6.99647i | 0.439864 | + | 0.439864i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.71313 | 0.107281 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 8.66038 | 0.540220 | 0.270110 | − | 0.962829i | \(-0.412940\pi\) | ||||
0.270110 | + | 0.962829i | \(0.412940\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.9902 | + | 19.9902i | 1.24213 | + | 1.24213i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.16333 | + | 5.16333i | −0.319602 | + | 0.319602i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.3208i | 0.821394i | 0.911772 | + | 0.410697i | \(0.134715\pi\) | ||||
−0.911772 | + | 0.410697i | \(0.865285\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 0.330566i | − | 0.0203065i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.3615 | + | 10.3615i | −0.634111 | + | 0.634111i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.6714 | + | 11.6714i | 0.711616 | + | 0.711616i | 0.966873 | − | 0.255257i | \(-0.0821602\pi\) |
−0.255257 | + | 0.966873i | \(0.582160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.9769 | −1.33500 | −0.667499 | − | 0.744610i | \(-0.732635\pi\) | ||||
−0.667499 | + | 0.744610i | \(0.732635\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.382941 | 0.0231766 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.8132 | + | 11.8132i | 0.712365 | + | 0.712365i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.9504 | − | 10.9504i | 0.657945 | − | 0.657945i | −0.296949 | − | 0.954893i | \(-0.595969\pi\) |
0.954893 | + | 0.296949i | \(0.0959690\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 0.557647i | − | 0.0333855i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 22.8910i | − | 1.36556i | −0.730624 | − | 0.682780i | \(-0.760771\pi\) | ||
0.730624 | − | 0.682780i | \(-0.239229\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.48528 | + | 4.48528i | −0.266622 | + | 0.266622i | −0.827738 | − | 0.561115i | \(-0.810372\pi\) |
0.561115 | + | 0.827738i | \(0.310372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.21137 | − | 1.21137i | −0.0717552 | − | 0.0717552i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.2672 | −2.49496 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.91688 | −0.230405 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.05275 | + | 3.05275i | 0.178955 | + | 0.178955i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.6221 | + | 21.6221i | −1.26318 | + | 1.26318i | −0.313636 | + | 0.949543i | \(0.601547\pi\) |
−0.949543 | + | 0.313636i | \(0.898453\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.67923i | 0.155991i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.49824i | 0.202988i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.168043 | + | 0.168043i | −0.00971818 | + | 0.00971818i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.33962 | − | 7.33962i | −0.423048 | − | 0.423048i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.641669 | 0.0368629 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.82805 | −0.104674 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.1118 | + | 12.1118i | 0.691255 | + | 0.691255i | 0.962508 | − | 0.271253i | \(-0.0874380\pi\) |
−0.271253 | + | 0.962508i | \(0.587438\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.945300 | + | 0.945300i | −0.0537762 | + | 0.0537762i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 26.8651i | − | 1.52338i | −0.647943 | − | 0.761689i | \(-0.724370\pi\) | ||
0.647943 | − | 0.761689i | \(-0.275630\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.6890i | 1.11289i | 0.830885 | + | 0.556445i | \(0.187835\pi\) | ||||
−0.830885 | + | 0.556445i | \(0.812165\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.52637 | − | 1.52637i | 0.0860014 | − | 0.0860014i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −21.3447 | − | 21.3447i | −1.19884 | − | 1.19884i | −0.974515 | − | 0.224323i | \(-0.927983\pi\) |
−0.224323 | − | 0.974515i | \(-0.572017\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.5443 | 1.43021 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.57373 | −0.478539 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.25116 | − | 9.25116i | −0.514748 | − | 0.514748i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.283734 | + | 0.283734i | −0.0157387 | + | 0.0157387i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 8.08402i | − | 0.447047i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 12.8910i | − | 0.710702i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −14.6926 | + | 14.6926i | −0.807576 | + | 0.807576i | −0.984266 | − | 0.176690i | \(-0.943461\pi\) |
0.176690 | + | 0.984266i | \(0.443461\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.38607 | − | 4.38607i | −0.240355 | − | 0.240355i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.52898 | −0.138173 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.0098 | −1.25342 | −0.626712 | − | 0.779251i | \(-0.715600\pi\) | ||||
−0.626712 | + | 0.779251i | \(0.715600\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −6.75383 | − | 6.75383i | −0.366818 | − | 0.366818i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.37941 | + | 1.37941i | −0.0746993 | + | 0.0746993i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 30.8651i | 1.66656i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.33962i | 0.0721225i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.9026 | − | 10.9026i | 0.585284 | − | 0.585284i | −0.351067 | − | 0.936350i | \(-0.614181\pi\) |
0.936350 | + | 0.351067i | \(0.114181\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −20.0563 | − | 20.0563i | −1.07359 | − | 1.07359i | −0.997068 | − | 0.0765186i | \(-0.975620\pi\) |
−0.0765186 | − | 0.997068i | \(-0.524380\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.0840215 | −0.00448474 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.2117 | −0.649965 | −0.324983 | − | 0.945720i | \(-0.605358\pi\) | ||||
−0.324983 | + | 0.945720i | \(0.605358\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.05275 | + | 3.05275i | 0.162023 | + | 0.162023i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 11.6569 | − | 11.6569i | 0.616946 | − | 0.616946i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 33.4780i | 1.76690i | 0.468522 | + | 0.883452i | \(0.344786\pi\) | ||||
−0.468522 | + | 0.883452i | \(0.655214\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 5.91688i | − | 0.311415i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.875150 | − | 0.875150i | 0.0459335 | − | 0.0459335i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.181370 | − | 0.181370i | −0.00949337 | − | 0.00949337i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.702379 | −0.0366639 | −0.0183319 | − | 0.999832i | \(-0.505836\pi\) | ||||
−0.0183319 | + | 0.999832i | \(0.505836\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.27391 | 0.482781 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.24930 | − | 2.24930i | −0.116778 | − | 0.116778i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.9598 | + | 18.9598i | −0.981702 | + | 0.981702i | −0.999836 | − | 0.0181339i | \(-0.994227\pi\) |
0.0181339 | + | 0.999836i | \(0.494227\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.63001i | 0.239093i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.613530i | 0.0315984i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.77844 | − | 1.77844i | 0.0913523 | − | 0.0913523i | −0.659954 | − | 0.751306i | \(-0.729424\pi\) |
0.751306 | + | 0.659954i | \(0.229424\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.60568 | + | 3.60568i | 0.184725 | + | 0.184725i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 25.4880 | 1.30238 | 0.651188 | − | 0.758916i | \(-0.274271\pi\) | ||||
0.651188 | + | 0.758916i | \(0.274271\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.55136 | −0.384853 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.61040 | + | 1.61040i | 0.0818610 | + | 0.0818610i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.7049 | − | 11.7049i | 0.593462 | − | 0.593462i | −0.345103 | − | 0.938565i | \(-0.612156\pi\) |
0.938565 | + | 0.345103i | \(0.112156\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2306i | 0.517383i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 2.99647i | − | 0.151152i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.68184 | + | 3.68184i | −0.185253 | + | 0.185253i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 9.04646 | + | 9.04646i | 0.454029 | + | 0.454029i | 0.896689 | − | 0.442661i | \(-0.145965\pi\) |
−0.442661 | + | 0.896689i | \(0.645965\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.4853 | −0.825296 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0853 | −0.903137 | −0.451568 | − | 0.892237i | \(-0.649135\pi\) | ||||
−0.451568 | + | 0.892237i | \(0.649135\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0331311 | − | 0.0331311i | −0.00165038 | − | 0.00165038i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.334904 | + | 0.334904i | −0.0166415 | + | 0.0166415i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.6990i | 1.07558i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 25.2271i | − | 1.24740i | −0.781665 | − | 0.623699i | \(-0.785629\pi\) | ||
0.781665 | − | 0.623699i | \(-0.214371\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.38960 | − | 2.38960i | 0.117870 | − | 0.117870i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.2306 | + | 18.2306i | 0.897069 | + | 0.897069i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.12787 | 0.349894 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.31724 | −0.407297 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.25283 | − | 7.25283i | −0.354324 | − | 0.354324i | 0.507392 | − | 0.861716i | \(-0.330610\pi\) |
−0.861716 | + | 0.507392i | \(0.830610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.39550 | + | 2.39550i | −0.116749 | + | 0.116749i | −0.763068 | − | 0.646318i | \(-0.776308\pi\) |
0.646318 | + | 0.763068i | \(0.276308\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.82843i | 0.137523i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 17.2739i | 0.837908i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.4388 | + | 12.4388i | −0.601957 | + | 0.601957i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.207838 | + | 0.207838i | 0.0100345 | + | 0.0100345i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.42454 | −0.213123 | −0.106561 | − | 0.994306i | \(-0.533984\pi\) | ||||
−0.106561 | + | 0.994306i | \(0.533984\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.31371 | 0.351474 | 0.175737 | − | 0.984437i | \(-0.443769\pi\) | ||||
0.175737 | + | 0.984437i | \(0.443769\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.44549 | + | 2.44549i | 0.117252 | + | 0.117252i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.23412 | − | 7.23412i | 0.346055 | − | 0.346055i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 29.6533i | − | 1.41527i | −0.706576 | − | 0.707637i | \(-0.749761\pi\) | ||
0.706576 | − | 0.707637i | \(-0.250239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 13.7721i | − | 0.655817i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.3056 | + | 10.3056i | −0.489633 | + | 0.489633i | −0.908190 | − | 0.418557i | \(-0.862536\pi\) |
0.418557 | + | 0.908190i | \(0.362536\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.90746 | + | 4.90746i | 0.232636 | + | 0.232636i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.1305 | 0.668349 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.48844 | −0.306208 | −0.153104 | − | 0.988210i | \(-0.548927\pi\) | ||||
−0.153104 | + | 0.988210i | \(0.548927\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.9402 | − | 22.9402i | −1.08021 | − | 1.08021i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −7.05470 | + | 7.05470i | −0.331459 | + | 0.331459i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 0.181370i | − | 0.00850278i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 9.00353i | − | 0.421167i | −0.977576 | − | 0.210584i | \(-0.932464\pi\) | ||
0.977576 | − | 0.210584i | \(-0.0675364\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.55765 | + | 2.55765i | −0.119381 | + | 0.119381i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −14.6218 | − | 14.6218i | −0.681004 | − | 0.681004i | 0.279223 | − | 0.960226i | \(-0.409923\pi\) |
−0.960226 | + | 0.279223i | \(0.909923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6435 | −0.866437 | −0.433219 | − | 0.901289i | \(-0.642622\pi\) | ||||
−0.433219 | + | 0.901289i | \(0.642622\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.264116 | −0.0122481 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.5138 | + | 23.5138i | 1.08809 | + | 1.08809i | 0.995725 | + | 0.0923633i | \(0.0294421\pi\) |
0.0923633 | + | 0.995725i | \(0.470558\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −17.2082 | + | 17.2082i | −0.794601 | + | 0.794601i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 22.8562i | 1.05316i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.96703i | − | 0.366325i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.2145 | − | 12.2145i | 0.560440 | − | 0.560440i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.493523 | + | 0.493523i | 0.0225969 | + | 0.0225969i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.08864 | −0.0497412 | −0.0248706 | − | 0.999691i | \(-0.507917\pi\) | ||||
−0.0248706 | + | 0.999691i | \(0.507917\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.521173 | −0.0237634 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 9.11529 | + | 9.11529i | 0.414760 | + | 0.414760i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.44586 | − | 1.44586i | 0.0656531 | − | 0.0656531i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 35.3298i | − | 1.60095i | −0.599369 | − | 0.800473i | \(-0.704582\pi\) | ||
0.599369 | − | 0.800473i | \(-0.295418\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.6135i | 0.479960i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.8910 | − | 12.8910i | 0.581761 | − | 0.581761i | −0.353626 | − | 0.935387i | \(-0.615051\pi\) |
0.935387 | + | 0.353626i | \(0.115051\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.6761 | + | 18.6761i | 0.841128 | + | 0.841128i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.65685 | 0.0744701 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 41.5443 | 1.86352 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.3798 | − | 14.3798i | −0.643728 | − | 0.643728i | 0.307742 | − | 0.951470i | \(-0.400427\pi\) |
−0.951470 | + | 0.307742i | \(0.900427\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.12825 | − | 4.12825i | 0.184437 | − | 0.184437i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.2969i | − | 1.35087i | −0.737420 | − | 0.675435i | \(-0.763956\pi\) | ||
0.737420 | − | 0.675435i | \(-0.236044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 0.303911i | − | 0.0135239i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 9.18740 | − | 9.18740i | 0.408027 | − | 0.408027i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5825 | − | 10.5825i | −0.469063 | − | 0.469063i | 0.432548 | − | 0.901611i | \(-0.357615\pi\) |
−0.901611 | + | 0.432548i | \(0.857615\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.46824 | −0.109188 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.61706 | 0.159697 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.447718 | + | 0.447718i | 0.0197288 | + | 0.0197288i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.99647 | − | 6.99647i | 0.307704 | − | 0.307704i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.12695i | 0.225048i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.9049i | 1.09110i | 0.838078 | + | 0.545551i | \(0.183680\pi\) | ||||
−0.838078 | + | 0.545551i | \(0.816320\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.9008 | − | 12.9008i | 0.564112 | − | 0.564112i | −0.366361 | − | 0.930473i | \(-0.619396\pi\) |
0.930473 | + | 0.366361i | \(0.119396\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 15.3908 | + | 15.3908i | 0.671709 | + | 0.671709i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.01704 | −0.0878638 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 15.0000 | 0.652174 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.00000 | − | 4.00000i | −0.173585 | − | 0.173585i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.550984 | − | 0.550984i | 0.0238657 | − | 0.0238657i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.06074i | 0.175561i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 13.1286i | − | 0.566542i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −34.0671 | + | 34.0671i | −1.46738 | + | 1.46738i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.2767 | − | 18.2767i | −0.785776 | − | 0.785776i | 0.195023 | − | 0.980799i | \(-0.437522\pi\) |
−0.980799 | + | 0.195023i | \(0.937522\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.3181 | 0.657364 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.82880 | −0.164008 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13.7355 | − | 13.7355i | −0.587287 | − | 0.587287i | 0.349609 | − | 0.936896i | \(-0.386315\pi\) |
−0.936896 | + | 0.349609i | \(0.886315\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.72922 | − | 2.72922i | 0.116480 | − | 0.116480i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 26.4120i | − | 1.12519i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 50.1055i | 2.13070i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.07736 | + | 2.07736i | −0.0881789 | + | 0.0881789i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.5525 | + | 27.5525i | 1.16744 | + | 1.16744i | 0.982808 | + | 0.184631i | \(0.0591089\pi\) |
0.184631 | + | 0.982808i | \(0.440891\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.191354 | 0.00809342 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.6533 | 0.534224 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 19.8928 | + | 19.8928i | 0.838383 | + | 0.838383i | 0.988646 | − | 0.150263i | \(-0.0480121\pi\) |
−0.150263 | + | 0.988646i | \(0.548012\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.19879 | + | 3.19879i | −0.134574 | + | 0.134574i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.55765i | 0.191403i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.4849i | 0.565317i | 0.959221 | + | 0.282658i | \(0.0912163\pi\) | ||||
−0.959221 | + | 0.282658i | \(0.908784\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 14.8284 | − | 14.8284i | 0.620550 | − | 0.620550i | −0.325122 | − | 0.945672i | \(-0.605405\pi\) |
0.945672 | + | 0.325122i | \(0.105405\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.10234 | − | 6.10234i | −0.254929 | − | 0.254929i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5077 | −0.563308 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11.6176 | −0.483648 | −0.241824 | − | 0.970320i | \(-0.577746\pi\) | ||||
−0.241824 | + | 0.970320i | \(0.577746\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.09735 | + | 8.09735i | 0.336514 | + | 0.336514i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 48.5010 | − | 48.5010i | 2.01216 | − | 2.01216i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 2.44158i | − | 0.101120i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0397948i | 0.00164531i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0268 | − | 17.0268i | 0.702773 | − | 0.702773i | −0.262232 | − | 0.965005i | \(-0.584459\pi\) |
0.965005 | + | 0.262232i | \(0.0844585\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.42627 | + | 1.42627i | 0.0587682 | + | 0.0587682i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10.5925 | −0.435715 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 41.5372 | 1.70573 | 0.852865 | − | 0.522132i | \(-0.174863\pi\) | ||||
0.852865 | + | 0.522132i | \(0.174863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.52099 | − | 5.52099i | −0.226338 | − | 0.226338i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.60215 | − | 2.60215i | 0.106499 | − | 0.106499i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.43160i | − | 0.262788i | −0.991330 | − | 0.131394i | \(-0.958055\pi\) | ||
0.991330 | − | 0.131394i | \(-0.0419453\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.45844i | 0.141073i | 0.997509 | + | 0.0705364i | \(0.0224711\pi\) | ||||
−0.997509 | + | 0.0705364i | \(0.977529\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.77568 | − | 3.77568i | 0.153758 | − | 0.153758i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.414494 | − | 0.414494i | −0.0168516 | − | 0.0168516i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −30.1019 | −1.22180 | −0.610900 | − | 0.791708i | \(-0.709192\pi\) | ||||
−0.610900 | + | 0.791708i | \(0.709192\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.2802 | 1.34858 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.168043 | + | 0.168043i | 0.00679829 | + | 0.00679829i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.50490 | + | 2.50490i | −0.101172 | + | 0.101172i | −0.755881 | − | 0.654709i | \(-0.772791\pi\) |
0.654709 | + | 0.755881i | \(0.272791\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 4.39236i | − | 0.177117i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 22.9098i | − | 0.922315i | −0.887318 | − | 0.461157i | \(-0.847434\pi\) | ||
0.887318 | − | 0.461157i | \(-0.152566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.6104 | − | 28.6104i | 1.14995 | − | 1.14995i | 0.163386 | − | 0.986562i | \(-0.447758\pi\) |
0.986562 | − | 0.163386i | \(-0.0522415\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 2.00000i | −0.0802572 | − | 0.0802572i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 66.7847 | 2.67567 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.6855 | −0.867420 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −8.94725 | − | 8.94725i | −0.357319 | − | 0.357319i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.8647 | + | 15.8647i | −0.632567 | + | 0.632567i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 11.1851i | − | 0.445270i | −0.974902 | − | 0.222635i | \(-0.928534\pi\) | ||
0.974902 | − | 0.222635i | \(-0.0714659\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 14.3102i | − | 0.568779i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.70774 | − | 1.70774i | 0.0677698 | − | 0.0677698i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.818234 | − | 0.818234i | −0.0324196 | − | 0.0324196i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.11529 | −0.360595 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.69312 | −0.264362 | −0.132181 | − | 0.991226i | \(-0.542198\pi\) | ||||
−0.132181 | + | 0.991226i | \(0.542198\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.9410 | + | 17.9410i | 0.707522 | + | 0.707522i | 0.966014 | − | 0.258491i | \(-0.0832253\pi\) |
−0.258491 | + | 0.966014i | \(0.583225\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.762725 | − | 0.762725i | 0.0300323 | − | 0.0300323i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6.72999i | − | 0.264583i | −0.991211 | − | 0.132292i | \(-0.957766\pi\) | ||
0.991211 | − | 0.132292i | \(-0.0422335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.7890i | 0.776786i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.79715 | + | 1.79715i | −0.0704360 | + | 0.0704360i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.1731 | − | 26.1731i | −1.02423 | − | 1.02423i | −0.999699 | − | 0.0245347i | \(-0.992190\pi\) |
−0.0245347 | − | 0.999699i | \(-0.507810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.41921 | −0.0554529 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.541560 | 0.0211283 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13.9741 | − | 13.9741i | −0.544353 | − | 0.544353i | 0.380449 | − | 0.924802i | \(-0.375770\pi\) |
−0.924802 | + | 0.380449i | \(0.875770\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.9241 | + | 11.9241i | −0.463794 | + | 0.463794i | −0.899897 | − | 0.436103i | \(-0.856358\pi\) |
0.436103 | + | 0.899897i | \(0.356358\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.303911i | 0.0118029i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.80785i | 0.302776i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.6041 | + | 14.6041i | −0.565473 | + | 0.565473i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.43764 | − | 3.43764i | −0.132907 | − | 0.132907i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −13.5021 | −0.521244 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.3066 | −1.43807 | −0.719033 | − | 0.694976i | \(-0.755415\pi\) | ||||
−0.719033 | + | 0.694976i | \(0.755415\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.37691 | − | 3.37691i | −0.129978 | − | 0.129978i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.447461 | + | 0.447461i | −0.0171973 | + | 0.0171973i | −0.715653 | − | 0.698456i | \(-0.753871\pi\) |
0.698456 | + | 0.715653i | \(0.253871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 19.6764i | − | 0.755113i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 15.0496i | − | 0.576702i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.27521 | − | 4.27521i | 0.163586 | − | 0.163586i | −0.620567 | − | 0.784153i | \(-0.713098\pi\) |
0.784153 | + | 0.620567i | \(0.213098\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.13178 | − | 1.13178i | −0.0432430 | − | 0.0432430i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.5264 | 1.08835 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.0586426 | 0.00223410 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.0786 | − | 20.0786i | −0.763827 | − | 0.763827i | 0.213185 | − | 0.977012i | \(-0.431616\pi\) |
−0.977012 | + | 0.213185i | \(0.931616\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 11.2739 | − | 11.2739i | 0.428261 | − | 0.428261i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.93926i | 0.149425i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.5443i | − | 1.27058i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.59558 | + | 9.59558i | −0.362938 | + | 0.362938i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.4467 | + | 10.4467i | 0.394565 | + | 0.394565i | 0.876311 | − | 0.481746i | \(-0.159997\pi\) |
−0.481746 | + | 0.876311i | \(0.659997\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 22.4361 | 0.846192 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.33962 | 0.0504529 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.06793 | − | 2.06793i | −0.0777727 | − | 0.0777727i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −16.0916 | + | 16.0916i | −0.604332 | + | 0.604332i | −0.941459 | − | 0.337127i | \(-0.890545\pi\) |
0.337127 | + | 0.941459i | \(0.390545\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 10.9937i | − | 0.412296i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.57726i | − | 0.0590690i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.0984373 | − | 0.0984373i | 0.00368135 | − | 0.00368135i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.7627 | + | 20.7627i | 0.775398 | + | 0.775398i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −30.9957 | −1.15594 | −0.577972 | − | 0.816057i | \(-0.696156\pi\) | ||||
−0.577972 | + | 0.816057i | \(0.696156\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.09292 | 0.226912 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.9750 | + | 16.9750i | 0.631307 | + | 0.631307i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.6584 | + | 24.6584i | −0.915790 | + | 0.915790i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 41.1117i | 1.52475i | 0.647135 | + | 0.762375i | \(0.275967\pi\) | ||||
−0.647135 | + | 0.762375i | \(0.724033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.82490 | − | 5.82490i | 0.215442 | − | 0.215442i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.146061 | − | 0.146061i | −0.00539490 | − | 0.00539490i | 0.704404 | − | 0.709799i | \(-0.251214\pi\) |
−0.709799 | + | 0.704404i | \(0.751214\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.52284 | −0.240599 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18.6792 | −0.688058 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.50766 | + | 1.50766i | 0.0554601 | + | 0.0554601i | 0.734293 | − | 0.678833i | \(-0.237514\pi\) |
−0.678833 | + | 0.734293i | \(0.737514\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.214897 | − | 0.214897i | 0.00789445 | − | 0.00789445i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.5175i | 1.48644i | 0.669046 | + | 0.743221i | \(0.266703\pi\) | ||||
−0.669046 | + | 0.743221i | \(0.733297\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 6.69256i | − | 0.245196i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −10.6417 | + | 10.6417i | −0.389358 | + | 0.389358i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 27.6309 | + | 27.6309i | 1.00961 | + | 1.00961i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −12.5843 | −0.459208 | −0.229604 | − | 0.973284i | \(-0.573743\pi\) | ||||
−0.229604 | + | 0.973284i | \(0.573743\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −22.2837 | −0.812064 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.34129 | + | 3.34129i | 0.121602 | + | 0.121602i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.49900 | − | 7.49900i | 0.272556 | − | 0.272556i | −0.557572 | − | 0.830128i | \(-0.688267\pi\) |
0.830128 | + | 0.557572i | \(0.188267\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 9.89450i | 0.359148i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 42.8182i | − | 1.55216i | −0.630635 | − | 0.776079i | \(-0.717206\pi\) | ||
0.630635 | − | 0.776079i | \(-0.282794\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.0527 | + | 26.0527i | −0.943172 | + | 0.943172i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.21137 | + | 1.21137i | 0.0437971 | + | 0.0437971i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.475298 | −0.0171620 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.7455 | 0.459614 | 0.229807 | − | 0.973236i | \(-0.426190\pi\) | ||||
0.229807 | + | 0.973236i | \(0.426190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.12382 | + | 6.12382i | 0.220544 | + | 0.220544i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.8765 | − | 22.8765i | 0.822809 | − | 0.822809i | −0.163701 | − | 0.986510i | \(-0.552343\pi\) |
0.986510 | + | 0.163701i | \(0.0523432\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 2.66314i | − | 0.0956630i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 28.2704i | 1.01419i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.7194 | + | 23.7194i | −0.849836 | + | 0.849836i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.5478 | + | 22.5478i | 0.806825 | + | 0.806825i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −7.30205 | −0.260954 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.8253 | 0.386370 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.20470 | − | 5.20470i | −0.185528 | − | 0.185528i | 0.608232 | − | 0.793759i | \(-0.291879\pi\) |
−0.793759 | + | 0.608232i | \(0.791879\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.41921 | + | 9.41921i | −0.335333 | + | 0.335333i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.5317i | 1.54781i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 0.324298i | − | 0.0115162i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.233745 | − | 0.233745i | 0.00829009 | − | 0.00829009i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0149 | − | 17.0149i | −0.602698 | − | 0.602698i | 0.338330 | − | 0.941028i | \(-0.390138\pi\) |
−0.941028 | + | 0.338330i | \(0.890138\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.2306 | 0.361932 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.6533 | −0.517750 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.33962 | − | 1.33962i | −0.0472740 | − | 0.0472740i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.31724 | − | 4.31724i | 0.152163 | − | 0.152163i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 16.5058i | 0.581032i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7.83586i | − | 0.275494i | −0.990467 | − | 0.137747i | \(-0.956014\pi\) | ||
0.990467 | − | 0.137747i | \(-0.0439861\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −32.3396 | + | 32.3396i | −1.13560 | + | 1.13560i | −0.146366 | + | 0.989230i | \(0.546758\pi\) |
−0.989230 | + | 0.146366i | \(0.953242\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15.5400 | − | 15.5400i | −0.545011 | − | 0.545011i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.02684 | 0.176083 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.23765 | −0.288199 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.270780 | + | 0.270780i | 0.00946181 | + | 0.00946181i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −19.3541 | + | 19.3541i | −0.675464 | + | 0.675464i | −0.958970 | − | 0.283507i | \(-0.908502\pi\) |
0.283507 | + | 0.958970i | \(0.408502\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.8560i | − | 1.00586i | −0.864328 | − | 0.502929i | \(-0.832256\pi\) | ||
0.864328 | − | 0.502929i | \(-0.167744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.7064i | 0.581644i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.1984 | − | 10.1984i | 0.354634 | − | 0.354634i | −0.507197 | − | 0.861830i | \(-0.669318\pi\) |
0.861830 | + | 0.507197i | \(0.169318\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.3794 | − | 15.3794i | −0.534148 | − | 0.534148i | 0.387656 | − | 0.921804i | \(-0.373285\pi\) |
−0.921804 | + | 0.387656i | \(0.873285\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.4862 | 0.537210 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −49.8147 | −1.72598 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.95524 | − | 1.95524i | −0.0676640 | − | 0.0676640i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.394316 | − | 0.394316i | 0.0136296 | − | 0.0136296i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.4557i | 1.53478i | 0.641181 | + | 0.767390i | \(0.278445\pi\) | ||||
−0.641181 | + | 0.767390i | \(0.721555\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.3200i | 0.838620i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.1864 | − | 16.1864i | 0.557488 | − | 0.557488i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.35139 | − | 4.35139i | −0.149692 | − | 0.149692i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.64077 | −0.193819 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.34315 | −0.217696 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −12.4057 | − | 12.4057i | −0.425262 | − | 0.425262i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.7131 | − | 11.7131i | 0.401049 | − | 0.401049i | −0.477553 | − | 0.878603i | \(-0.658476\pi\) |
0.878603 | + | 0.477553i | \(0.158476\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.71313i | − | 0.0585879i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.0888i | 0.652062i | 0.945359 | + | 0.326031i | \(0.105711\pi\) | ||||
−0.945359 | + | 0.326031i | \(0.894289\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.1323 | − | 38.1323i | 1.30106 | − | 1.30106i | 0.373379 | − | 0.927679i | \(-0.378199\pi\) |
0.927679 | − | 0.373379i | \(-0.121801\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −29.8874 | − | 29.8874i | −1.01856 | − | 1.01856i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.64533 | 0.124089 | 0.0620443 | − | 0.998073i | \(-0.480238\pi\) | ||||
0.0620443 | + | 0.998073i | \(0.480238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.42826 | 0.0825632 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.76965 | − | 2.76965i | −0.0940623 | − | 0.0940623i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.1943 | + | 27.1943i | −0.922504 | + | 0.922504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 0.448643i | − | 0.0152017i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.31724i | 0.146116i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.9213 | − | 14.9213i | 0.504433 | − | 0.504433i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.0563 | − | 40.0563i | −1.35260 | − | 1.35260i | −0.882738 | − | 0.469866i | \(-0.844302\pi\) |
−0.469866 | − | 0.882738i | \(-0.655698\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −30.5783 | −1.03138 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.0118 | −0.674214 | −0.337107 | − | 0.941466i | \(-0.609448\pi\) | ||||
−0.337107 | + | 0.941466i | \(0.609448\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6273 | + | 10.6273i | 0.357636 | + | 0.357636i | 0.862941 | − | 0.505305i | \(-0.168620\pi\) |
−0.505305 | + | 0.862941i | \(0.668620\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.89450 | + | 1.89450i | −0.0636830 | + | 0.0636830i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 26.1180i | − | 0.876958i | −0.898742 | − | 0.438479i | \(-0.855517\pi\) | ||
0.898742 | − | 0.438479i | \(-0.144483\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 23.2404i | − | 0.779458i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.47363 | + | 2.47363i | −0.0828696 | + | 0.0828696i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.23412 | − | 7.23412i | −0.242081 | − | 0.242081i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.21805 | −0.207847 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.237649 | −0.00793486 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.87932 | − | 2.87932i | −0.0960306 | − | 0.0960306i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.78510 | − | 1.78510i | 0.0594704 | − | 0.0594704i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 10.3798i | − | 0.345418i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 7.25507i | − | 0.241167i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.2378 | + | 36.2378i | −1.20326 | + | 1.20326i | −0.230087 | + | 0.973170i | \(0.573901\pi\) |
−0.973170 | + | 0.230087i | \(0.926099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.453728 | + | 0.453728i | 0.0150492 | + | 0.0150492i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0535 | −0.697533 | −0.348767 | − | 0.937210i | \(-0.613399\pi\) | ||||
−0.348767 | + | 0.937210i | \(0.613399\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.6470 | 1.74236 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.29263 | − | 1.29263i | −0.0427330 | − | 0.0427330i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.65685 | + | 9.65685i | −0.318897 | + | 0.318897i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17.8839i | 0.589937i | 0.955507 | + | 0.294968i | \(0.0953091\pi\) | ||||
−0.955507 | + | 0.294968i | \(0.904691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.1286i | 0.564407i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −0.541560 | + | 0.541560i | −0.0178257 | + | 0.0178257i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −20.9465 | − | 20.9465i | −0.688716 | − | 0.688716i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.33686 | −0.0439081 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 10.2774 | 0.337192 | 0.168596 | − | 0.985685i | \(-0.446077\pi\) | ||||
0.168596 | + | 0.985685i | \(0.446077\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 35.2243 | + | 35.2243i | 1.15443 | + | 1.15443i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 18.9965 | − | 18.9965i | 0.621917 | − | 0.621917i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 5.99294i | − | 0.195990i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.5780i | − | 0.443574i | −0.975095 | − | 0.221787i | \(-0.928811\pi\) | ||
0.975095 | − | 0.221787i | \(-0.0711890\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −13.9222 | + | 13.9222i | −0.454335 | + | 0.454335i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.95902 | + | 3.95902i | 0.129060 | + | 0.129060i | 0.768686 | − | 0.639626i | \(-0.220911\pi\) |
−0.639626 | + | 0.768686i | \(0.720911\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.2306 | 0.854186 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.15862 | 0.0702199 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 33.1708 | + | 33.1708i | 1.07791 | + | 1.07791i | 0.996697 | + | 0.0812084i | \(0.0258779\pi\) |
0.0812084 | + | 0.996697i | \(0.474122\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.0321752 | − | 0.0321752i | 0.00104445 | − | 0.00104445i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 30.1860i | − | 0.978847i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.59115i | − | 0.181115i | −0.995891 | − | 0.0905576i | \(-0.971135\pi\) | ||
0.995891 | − | 0.0905576i | \(-0.0288649\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.89023 | + | 2.89023i | −0.0935255 | + | 0.0935255i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 18.0625 | + | 18.0625i | 0.583879 | + | 0.583879i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.4022 | −0.497362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.6890 | −0.989969 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.06255 | − | 6.06255i | −0.195363 | − | 0.195363i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.83511 | − | 3.83511i | 0.123457 | − | 0.123457i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.7561i | 0.989048i | 0.869164 | + | 0.494524i | \(0.164658\pi\) | ||||
−0.869164 | + | 0.494524i | \(0.835342\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 13.0831i | − | 0.420290i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8.03756 | + | 8.03756i | −0.257938 | + | 0.257938i | −0.824215 | − | 0.566277i | \(-0.808383\pi\) |
0.566277 | + | 0.824215i | \(0.308383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.8043 | + | 26.8043i | 0.859307 | + | 0.859307i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.401260 | −0.0128506 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.8323 | 0.730471 | 0.365235 | − | 0.930915i | \(-0.380988\pi\) | ||||
0.365235 | + | 0.930915i | \(0.380988\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.2468 | + | 36.2468i | 1.15845 | + | 1.15845i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.71627 | − | 5.71627i | 0.182506 | − | 0.182506i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 46.3557i | − | 1.47852i | −0.673422 | − | 0.739258i | \(-0.735176\pi\) | ||
0.673422 | − | 0.739258i | \(-0.264824\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.01686i | 0.159850i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.11529 | − | 9.11529i | 0.290143 | − | 0.290143i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.55489 | + | 4.55489i | 0.144837 | + | 0.144837i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.43683 | 0.109175 | 0.0545873 | − | 0.998509i | \(-0.482616\pi\) | ||||
0.0545873 | + | 0.998509i | \(0.482616\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −20.7784 | −0.659383 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.23245 | − | 1.23245i | −0.0390712 | − | 0.0390712i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.9430 | − | 21.9430i | 0.694940 | − | 0.694940i | −0.268374 | − | 0.963315i | \(-0.586486\pi\) |
0.963315 | + | 0.268374i | \(0.0864864\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 6.20285i | − | 0.196249i |
(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 | 384.2.j.b.289.4 | 8 | ||
3.2 | odd | 2 | 1152.2.k.c.289.2 | 8 | |||
4.3 | odd | 2 | 384.2.j.a.289.2 | 8 | |||
8.3 | odd | 2 | 192.2.j.a.145.3 | 8 | |||
8.5 | even | 2 | 48.2.j.a.13.4 | ✓ | 8 | ||
12.11 | even | 2 | 1152.2.k.f.289.2 | 8 | |||
16.3 | odd | 4 | 192.2.j.a.49.3 | 8 | |||
16.5 | even | 4 | inner | 384.2.j.b.97.4 | 8 | ||
16.11 | odd | 4 | 384.2.j.a.97.2 | 8 | |||
16.13 | even | 4 | 48.2.j.a.37.4 | yes | 8 | ||
24.5 | odd | 2 | 144.2.k.b.109.1 | 8 | |||
24.11 | even | 2 | 576.2.k.b.145.3 | 8 | |||
32.3 | odd | 8 | 3072.2.d.i.1537.3 | 8 | |||
32.5 | even | 8 | 3072.2.a.i.1.3 | 4 | |||
32.11 | odd | 8 | 3072.2.a.n.1.2 | 4 | |||
32.13 | even | 8 | 3072.2.d.f.1537.2 | 8 | |||
32.19 | odd | 8 | 3072.2.d.i.1537.6 | 8 | |||
32.21 | even | 8 | 3072.2.a.t.1.2 | 4 | |||
32.27 | odd | 8 | 3072.2.a.o.1.3 | 4 | |||
32.29 | even | 8 | 3072.2.d.f.1537.7 | 8 | |||
48.5 | odd | 4 | 1152.2.k.c.865.2 | 8 | |||
48.11 | even | 4 | 1152.2.k.f.865.2 | 8 | |||
48.29 | odd | 4 | 144.2.k.b.37.1 | 8 | |||
48.35 | even | 4 | 576.2.k.b.433.3 | 8 | |||
96.5 | odd | 8 | 9216.2.a.bo.1.2 | 4 | |||
96.11 | even | 8 | 9216.2.a.x.1.3 | 4 | |||
96.53 | odd | 8 | 9216.2.a.y.1.3 | 4 | |||
96.59 | even | 8 | 9216.2.a.bn.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.2.j.a.13.4 | ✓ | 8 | 8.5 | even | 2 | ||
48.2.j.a.37.4 | yes | 8 | 16.13 | even | 4 | ||
144.2.k.b.37.1 | 8 | 48.29 | odd | 4 | |||
144.2.k.b.109.1 | 8 | 24.5 | odd | 2 | |||
192.2.j.a.49.3 | 8 | 16.3 | odd | 4 | |||
192.2.j.a.145.3 | 8 | 8.3 | odd | 2 | |||
384.2.j.a.97.2 | 8 | 16.11 | odd | 4 | |||
384.2.j.a.289.2 | 8 | 4.3 | odd | 2 | |||
384.2.j.b.97.4 | 8 | 16.5 | even | 4 | inner | ||
384.2.j.b.289.4 | 8 | 1.1 | even | 1 | trivial | ||
576.2.k.b.145.3 | 8 | 24.11 | even | 2 | |||
576.2.k.b.433.3 | 8 | 48.35 | even | 4 | |||
1152.2.k.c.289.2 | 8 | 3.2 | odd | 2 | |||
1152.2.k.c.865.2 | 8 | 48.5 | odd | 4 | |||
1152.2.k.f.289.2 | 8 | 12.11 | even | 2 | |||
1152.2.k.f.865.2 | 8 | 48.11 | even | 4 | |||
3072.2.a.i.1.3 | 4 | 32.5 | even | 8 | |||
3072.2.a.n.1.2 | 4 | 32.11 | odd | 8 | |||
3072.2.a.o.1.3 | 4 | 32.27 | odd | 8 | |||
3072.2.a.t.1.2 | 4 | 32.21 | even | 8 | |||
3072.2.d.f.1537.2 | 8 | 32.13 | even | 8 | |||
3072.2.d.f.1537.7 | 8 | 32.29 | even | 8 | |||
3072.2.d.i.1537.3 | 8 | 32.3 | odd | 8 | |||
3072.2.d.i.1537.6 | 8 | 32.19 | odd | 8 | |||
9216.2.a.x.1.3 | 4 | 96.11 | even | 8 | |||
9216.2.a.y.1.3 | 4 | 96.53 | odd | 8 | |||
9216.2.a.bn.1.2 | 4 | 96.59 | even | 8 | |||
9216.2.a.bo.1.2 | 4 | 96.5 | odd | 8 |