Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [72,2,Mod(11,72)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(72, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("72.11");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 72 = 2^{3} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 72.l (of order \(6\), degree \(2\), 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: | \(0.574922894553\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 11.2 | ||
Root | \(1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 72.11 |
Dual form | 72.2.l.a.59.2 |
$q$-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 \(\left(\mathbb{Z}/72\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(55\) | \(65\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.22474 | + | 0.707107i | 0.866025 | + | 0.500000i | ||||
\(3\) | −0.724745 | − | 1.57313i | −0.418432 | − | 0.908248i | ||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 0.224745 | − | 2.43916i | 0.0917517 | − | 0.995782i | ||||
\(7\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(8\) | 2.82843i | 1.00000i | ||||||||
\(9\) | −1.94949 | + | 2.28024i | −0.649830 | + | 0.760080i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.72474 | − | 3.30518i | −1.72608 | − | 0.996550i | −0.904534 | − | 0.426401i | \(-0.859781\pi\) |
−0.821541 | − | 0.570149i | \(-0.806886\pi\) | |||||||
\(12\) | 2.00000 | − | 2.82843i | 0.577350 | − | 0.816497i | ||||
\(13\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | 2.36773i | 0.574258i | 0.957892 | + | 0.287129i | \(0.0927008\pi\) | ||||
−0.957892 | + | 0.287129i | \(0.907299\pi\) | |||||||
\(18\) | −4.00000 | + | 1.41421i | −0.942809 | + | 0.333333i | ||||
\(19\) | 6.34847 | 1.45644 | 0.728219 | − | 0.685344i | \(-0.240348\pi\) | ||||
0.728219 | + | 0.685344i | \(0.240348\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.67423 | − | 8.09601i | −0.996550 | − | 1.72608i | ||||
\(23\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(24\) | 4.44949 | − | 2.04989i | 0.908248 | − | 0.418432i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000 | + | 1.41421i | 0.962250 | + | 0.272166i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(32\) | −4.89898 | + | 2.82843i | −0.866025 | + | 0.500000i | ||||
\(33\) | −1.05051 | + | 11.4012i | −0.182870 | + | 1.98469i | ||||
\(34\) | −1.67423 | + | 2.89986i | −0.287129 | + | 0.497322i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.89898 | − | 1.09638i | −0.983163 | − | 0.182729i | ||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 7.77526 | + | 4.48905i | 1.26131 | + | 0.728219i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.39898 | − | 5.42650i | 1.46787 | − | 0.847477i | 0.468521 | − | 0.883452i | \(-0.344787\pi\) |
0.999353 | + | 0.0359748i | \(0.0114536\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.17423 | + | 10.6941i | −0.941562 | + | 1.63083i | −0.179069 | + | 0.983836i | \(0.557309\pi\) |
−0.762493 | + | 0.646997i | \(0.776025\pi\) | |||||||
\(44\) | − | 13.2207i | − | 1.99310i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | 6.89898 | + | 0.635674i | 0.995782 | + | 0.0917517i | ||||
\(49\) | −3.50000 | − | 6.06218i | −0.500000 | − | 0.866025i | ||||
\(50\) | 6.12372 | − | 3.53553i | 0.866025 | − | 0.500000i | ||||
\(51\) | 3.72474 | − | 1.71600i | 0.521569 | − | 0.240288i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(54\) | 5.12372 | + | 5.26758i | 0.697251 | + | 0.716827i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.60102 | − | 9.98698i | −0.609420 | − | 1.32281i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.62372 | + | 0.937458i | −0.211391 | + | 0.122047i | −0.601958 | − | 0.798528i | \(-0.705612\pi\) |
0.390567 | + | 0.920575i | \(0.372279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −9.34847 | + | 13.2207i | −1.15072 | + | 1.62736i | ||||
\(67\) | −0.174235 | − | 0.301783i | −0.0212861 | − | 0.0368687i | 0.855186 | − | 0.518321i | \(-0.173443\pi\) |
−0.876472 | + | 0.481452i | \(0.840109\pi\) | |||||||
\(68\) | −4.10102 | + | 2.36773i | −0.497322 | + | 0.287129i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | −6.44949 | − | 5.51399i | −0.760080 | − | 0.649830i | ||||
\(73\) | −15.6969 | −1.83719 | −0.918594 | − | 0.395203i | \(-0.870674\pi\) | ||||
−0.918594 | + | 0.395203i | \(0.870674\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.62372 | − | 0.794593i | −0.995782 | − | 0.0917517i | ||||
\(76\) | 6.34847 | + | 10.9959i | 0.728219 | + | 1.26131i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.39898 | − | 8.89060i | −0.155442 | − | 0.987845i | ||||
\(82\) | 15.3485 | 1.69495 | ||||||||
\(83\) | 2.44949 | + | 1.41421i | 0.268866 | + | 0.155230i | 0.628372 | − | 0.777913i | \(-0.283721\pi\) |
−0.359506 | + | 0.933143i | \(0.617055\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −15.1237 | + | 8.73169i | −1.63083 | + | 0.941562i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.34847 | − | 16.1920i | 0.996550 | − | 1.72608i | ||||
\(89\) | 5.65685i | 0.599625i | 0.953998 | + | 0.299813i | \(0.0969242\pi\) | ||||
−0.953998 | + | 0.299813i | \(0.903076\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 8.00000 | + | 5.65685i | 0.816497 | + | 0.577350i | ||||
\(97\) | 4.84847 | − | 8.39780i | 0.492287 | − | 0.852667i | −0.507673 | − | 0.861550i | \(-0.669494\pi\) |
0.999961 | + | 0.00888289i | \(0.00282755\pi\) | |||||||
\(98\) | − | 9.89949i | − | 1.00000i | ||||||
\(99\) | 18.6969 | − | 6.61037i | 1.87911 | − | 0.664367i | ||||
\(100\) | 10.0000 | 1.00000 | ||||||||
\(101\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(102\) | 5.77526 | + | 0.532134i | 0.571835 | + | 0.0526891i | ||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.0956i | 1.45935i | 0.683793 | + | 0.729676i | \(0.260329\pi\) | ||||
−0.683793 | + | 0.729676i | \(0.739671\pi\) | |||||||
\(108\) | 2.55051 | + | 10.0745i | 0.245423 | + | 0.969416i | ||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.79796 | + | 5.65685i | −0.921714 | + | 0.532152i | −0.884182 | − | 0.467143i | \(-0.845283\pi\) |
−0.0375328 | + | 0.999295i | \(0.511950\pi\) | |||||||
\(114\) | 1.42679 | − | 15.4849i | 0.133631 | − | 1.45030i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.65153 | −0.244093 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.3485 | + | 28.3164i | 1.48622 | + | 2.57422i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −15.3485 | − | 10.8530i | −1.38392 | − | 0.978583i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −9.79796 | − | 5.65685i | −0.866025 | − | 0.500000i | ||||
\(129\) | 21.2980 | + | 1.96240i | 1.87518 | + | 0.172780i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.2474 | − | 7.07107i | 1.07006 | − | 0.617802i | 0.141865 | − | 0.989886i | \(-0.454690\pi\) |
0.928199 | + | 0.372084i | \(0.121357\pi\) | |||||||
\(132\) | −20.7980 | + | 9.58166i | −1.81023 | + | 0.833976i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 0.492810i | − | 0.0425723i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.69694 | −0.574258 | ||||||||
\(137\) | 5.29796 | + | 3.05878i | 0.452635 | + | 0.261329i | 0.708942 | − | 0.705266i | \(-0.249173\pi\) |
−0.256307 | + | 0.966595i | \(0.582506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −9.17423 | − | 15.8902i | −0.778148 | − | 1.34779i | −0.933008 | − | 0.359856i | \(-0.882826\pi\) |
0.154859 | − | 0.987937i | \(-0.450508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −4.00000 | − | 11.3137i | −0.333333 | − | 0.942809i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −19.2247 | − | 11.0994i | −1.59105 | − | 0.918594i | ||||
\(147\) | −7.00000 | + | 9.89949i | −0.577350 | + | 0.816497i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(150\) | −10.0000 | − | 7.07107i | −0.816497 | − | 0.577350i | ||||
\(151\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(152\) | 17.9562i | 1.45644i | ||||||||
\(153\) | −5.39898 | − | 4.61586i | −0.436482 | − | 0.373170i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 4.57321 | − | 11.8780i | 0.359306 | − | 0.933220i | ||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | 18.7980 | + | 10.8530i | 1.46787 | + | 0.847477i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.00000 | + | 3.46410i | 0.155230 | + | 0.268866i | ||||
\(167\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | + | 11.2583i | −0.500000 | + | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.3763 | + | 14.4760i | −0.946437 | + | 1.10701i | ||||
\(172\) | −24.6969 | −1.88312 | ||||||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 22.8990 | − | 13.2207i | 1.72608 | − | 0.996550i | ||||
\(177\) | 2.65153 | + | 1.87492i | 0.199301 | + | 0.140927i | ||||
\(178\) | −4.00000 | + | 6.92820i | −0.299813 | + | 0.519291i | ||||
\(179\) | − | 19.7990i | − | 1.47985i | −0.672692 | − | 0.739923i | \(-0.734862\pi\) | ||
0.672692 | − | 0.739923i | \(-0.265138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.82577 | − | 13.5546i | 0.572277 | − | 0.991212i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(192\) | 5.79796 | + | 12.5851i | 0.418432 | + | 0.908248i | ||||
\(193\) | 1.84847 | + | 3.20164i | 0.133056 | + | 0.230459i | 0.924853 | − | 0.380325i | \(-0.124188\pi\) |
−0.791797 | + | 0.610784i | \(0.790854\pi\) | |||||||
\(194\) | 11.8763 | − | 6.85677i | 0.852667 | − | 0.492287i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.00000 | − | 12.1244i | 0.500000 | − | 0.866025i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 27.5732 | + | 5.12472i | 1.95954 | + | 0.364198i | ||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 12.2474 | + | 7.07107i | 0.866025 | + | 0.500000i | ||||
\(201\) | −0.348469 | + | 0.492810i | −0.0245791 | + | 0.0347601i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.69694 | + | 4.73545i | 0.468879 | + | 0.331548i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −36.3434 | − | 20.9829i | −2.51392 | − | 1.45141i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.00000 | − | 12.1244i | −0.481900 | − | 0.834675i | 0.517884 | − | 0.855451i | \(-0.326720\pi\) |
−0.999784 | + | 0.0207756i | \(0.993386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −10.6742 | + | 18.4883i | −0.729676 | + | 1.26384i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −4.00000 | + | 14.1421i | −0.272166 | + | 0.962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.3763 | + | 24.6934i | 0.768737 | + | 1.66862i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.00000 | + | 14.1421i | 0.333333 | + | 0.942809i | ||||
\(226\) | −16.0000 | −1.06430 | ||||||||
\(227\) | 21.2753 | + | 12.2833i | 1.41209 | + | 0.815270i | 0.995585 | − | 0.0938647i | \(-0.0299221\pi\) |
0.416503 | + | 0.909134i | \(0.363255\pi\) | |||||||
\(228\) | 12.6969 | − | 17.9562i | 0.840875 | − | 1.18918i | ||||
\(229\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 28.8092i | − | 1.88735i | −0.330870 | − | 0.943676i | \(-0.607342\pi\) | ||
0.330870 | − | 0.943676i | \(-0.392658\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.24745 | − | 1.87492i | −0.211391 | − | 0.122047i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.8485 | − | 23.9863i | 0.892058 | − | 1.54509i | 0.0546547 | − | 0.998505i | \(-0.482594\pi\) |
0.837404 | − | 0.546585i | \(-0.184072\pi\) | |||||||
\(242\) | 46.2405i | 2.97245i | ||||||||
\(243\) | −12.9722 | + | 8.64420i | −0.832167 | + | 0.554526i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −11.1237 | − | 24.1452i | −0.709223 | − | 1.53944i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.449490 | − | 4.87832i | 0.0284853 | − | 0.309151i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 10.3602i | − | 0.653930i | −0.945036 | − | 0.326965i | \(-0.893974\pi\) | ||
0.945036 | − | 0.326965i | \(-0.106026\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | −17.6010 | + | 10.1620i | −1.09792 | + | 0.633885i | −0.935674 | − | 0.352865i | \(-0.885208\pi\) |
−0.162247 | + | 0.986750i | \(0.551874\pi\) | |||||||
\(258\) | 24.6969 | + | 17.4634i | 1.53756 | + | 1.08722i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.0000 | 1.23560 | ||||||||
\(263\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(264\) | −32.2474 | − | 2.97129i | −1.98469 | − | 0.182870i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.89898 | − | 4.09978i | 0.544609 | − | 0.250902i | ||||
\(268\) | 0.348469 | − | 0.603566i | 0.0212861 | − | 0.0368687i | ||||
\(269\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(272\) | −8.20204 | − | 4.73545i | −0.497322 | − | 0.287129i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.32577 | + | 7.49245i | 0.261329 | + | 0.452635i | ||||
\(275\) | −28.6237 | + | 16.5259i | −1.72608 | + | 0.996550i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(278\) | − | 25.9487i | − | 1.55630i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.4949 | + | 14.1421i | 1.46124 | + | 0.843649i | 0.999069 | − | 0.0431402i | \(-0.0137362\pi\) |
0.462174 | + | 0.886789i | \(0.347070\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.0000 | + | 19.0526i | 0.653882 | + | 1.13256i | 0.982173 | + | 0.187980i | \(0.0601941\pi\) |
−0.328291 | + | 0.944577i | \(0.606473\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 3.10102 | − | 16.6848i | 0.182729 | − | 0.983163i | ||||
\(289\) | 11.3939 | 0.670228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.7247 | − | 1.54102i | −0.980422 | − | 0.0903364i | ||||
\(292\) | −15.6969 | − | 27.1879i | −0.918594 | − | 1.59105i | ||||
\(293\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(294\) | −15.5732 | + | 7.17461i | −0.908248 | + | 0.418432i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −23.9495 | − | 24.6219i | −1.38969 | − | 1.42871i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −7.24745 | − | 15.7313i | −0.418432 | − | 0.908248i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −12.6969 | + | 21.9917i | −0.728219 | + | 1.26131i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.34847 | − | 9.47090i | −0.191419 | − | 0.541415i | ||||
\(307\) | 24.3485 | 1.38964 | 0.694820 | − | 0.719183i | \(-0.255484\pi\) | ||||
0.694820 | + | 0.719183i | \(0.255484\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.1969 | + | 29.7860i | −0.972028 | + | 1.68360i | −0.282617 | + | 0.959233i | \(0.591202\pi\) |
−0.689412 | + | 0.724370i | \(0.742131\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 23.7474 | − | 10.9405i | 1.32545 | − | 0.610639i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 15.0314i | 0.836371i | ||||||||
\(324\) | 14.0000 | − | 11.3137i | 0.777778 | − | 0.628539i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.44949 | + | 1.41421i | 0.135665 | + | 0.0783260i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 15.3485 | + | 26.5843i | 0.847477 | + | 1.46787i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.0000 | + | 22.5167i | −0.714545 | + | 1.23763i | 0.248590 | + | 0.968609i | \(0.420033\pi\) |
−0.963135 | + | 0.269019i | \(0.913301\pi\) | |||||||
\(332\) | 5.65685i | 0.310460i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.1969 | − | 19.3937i | −0.609936 | − | 1.05644i | −0.991250 | − | 0.131995i | \(-0.957862\pi\) |
0.381314 | − | 0.924445i | \(-0.375472\pi\) | |||||||
\(338\) | −15.9217 | + | 9.19239i | −0.866025 | + | 0.500000i | ||||
\(339\) | 16.0000 | + | 11.3137i | 0.869001 | + | 0.614476i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −25.3939 | + | 8.97809i | −1.37314 | + | 0.485480i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −30.2474 | − | 17.4634i | −1.63083 | − | 0.941562i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.4217 | − | 11.7905i | 1.09629 | − | 0.632945i | 0.161048 | − | 0.986947i | \(-0.448512\pi\) |
0.935245 | + | 0.354001i | \(0.115179\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 37.3939 | 1.99310 | ||||||||
\(353\) | 32.2980 | + | 18.6472i | 1.71905 | + | 0.992492i | 0.920677 | + | 0.390324i | \(0.127637\pi\) |
0.798369 | + | 0.602168i | \(0.205696\pi\) | |||||||
\(354\) | 1.92168 | + | 4.17121i | 0.102136 | + | 0.221697i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.79796 | + | 5.65685i | −0.519291 | + | 0.299813i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.0000 | − | 24.2487i | 0.739923 | − | 1.28158i | ||||
\(359\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.3031 | 1.12121 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.6969 | − | 46.2405i | 1.71614 | − | 2.42699i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.94949 | + | 32.0108i | −0.309718 | + | 1.66642i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 19.1691 | − | 11.0673i | 0.991212 | − | 0.572277i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.6515 | −0.598499 | −0.299249 | − | 0.954175i | \(-0.596736\pi\) | ||||
−0.299249 | + | 0.954175i | \(0.596736\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(384\) | −1.79796 | + | 19.5133i | −0.0917517 | + | 0.995782i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 5.22826i | 0.266111i | ||||||||
\(387\) | −12.3485 | − | 34.9267i | −0.627708 | − | 1.77543i | ||||
\(388\) | 19.3939 | 0.984575 | ||||||||
\(389\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 17.1464 | − | 9.89949i | 0.866025 | − | 0.500000i | ||||
\(393\) | −20.0000 | − | 14.1421i | −1.00887 | − | 0.713376i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 30.1464 | + | 25.7737i | 1.51492 | + | 1.29518i | ||||
\(397\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 10.0000 | + | 17.3205i | 0.500000 | + | 0.866025i | ||||
\(401\) | −12.6464 | + | 7.30142i | −0.631532 | + | 0.364615i | −0.781345 | − | 0.624099i | \(-0.785466\pi\) |
0.149813 | + | 0.988714i | \(0.452133\pi\) | |||||||
\(402\) | −0.775255 | + | 0.357161i | −0.0386662 | + | 0.0178136i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 4.85357 | + | 10.5352i | 0.240288 | + | 0.521569i | ||||
\(409\) | −20.1969 | − | 34.9821i | −0.998674 | − | 1.72975i | −0.543915 | − | 0.839140i | \(-0.683059\pi\) |
−0.454759 | − | 0.890614i | \(-0.650275\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.972194 | − | 10.5512i | 0.0479548 | − | 0.520453i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −18.3485 | + | 25.9487i | −0.898528 | + | 1.27071i | ||||
\(418\) | −29.6742 | − | 51.3973i | −1.45141 | − | 2.51392i | ||||
\(419\) | −31.8434 | + | 18.3848i | −1.55565 | + | 0.898155i | −0.557986 | + | 0.829851i | \(0.688426\pi\) |
−0.997665 | + | 0.0683046i | \(0.978241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(422\) | − | 19.7990i | − | 0.963800i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.2526 | + | 5.91931i | 0.497322 | + | 0.287129i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −26.1464 | + | 15.0956i | −1.26384 | + | 0.729676i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(432\) | −14.8990 | + | 14.4921i | −0.716827 | + | 0.697251i | ||||
\(433\) | −33.6969 | −1.61937 | −0.809686 | − | 0.586864i | \(-0.800362\pi\) | ||||
−0.809686 | + | 0.586864i | \(0.800362\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −3.52781 | + | 38.2873i | −0.168565 | + | 1.82944i | ||||
\(439\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.6464 | + | 3.83732i | 0.983163 | + | 0.182729i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −32.7247 | − | 18.8936i | −1.55480 | − | 0.897664i | −0.997740 | − | 0.0671913i | \(-0.978596\pi\) |
−0.557059 | − | 0.830473i | \(-0.688070\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.5446i | 1.58307i | 0.611124 | + | 0.791535i | \(0.290718\pi\) | ||||
−0.611124 | + | 0.791535i | \(0.709282\pi\) | |||||||
\(450\) | −3.87628 | + | 20.8560i | −0.182729 | + | 0.983163i | ||||
\(451\) | −71.7423 | −3.37822 | ||||||||
\(452\) | −19.5959 | − | 11.3137i | −0.921714 | − | 0.532152i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.3712 | + | 30.0878i | 0.815270 | + | 1.41209i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 28.2474 | − | 13.0137i | 1.32281 | − | 0.609420i | ||||
\(457\) | −8.19694 | + | 14.1975i | −0.383437 | + | 0.664132i | −0.991551 | − | 0.129718i | \(-0.958593\pi\) |
0.608114 | + | 0.793849i | \(0.291926\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.34847 | + | 11.8386i | −0.156293 | + | 0.552580i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.3712 | − | 35.2839i | 0.943676 | − | 1.63450i | ||||
\(467\) | − | 41.5371i | − | 1.92211i | −0.276360 | − | 0.961054i | \(-0.589128\pi\) | ||
0.276360 | − | 0.961054i | \(-0.410872\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.65153 | − | 4.59259i | −0.122047 | − | 0.211391i | ||||
\(473\) | 70.6918 | − | 40.8140i | 3.25041 | − | 1.87663i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8712 | − | 27.4897i | 0.728219 | − | 1.26131i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 33.9217 | − | 19.5847i | 1.54509 | − | 0.892058i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −32.6969 | + | 56.6328i | −1.48622 | + | 2.57422i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0000 | + | 1.41421i | −0.997940 | + | 0.0641500i | ||||
\(487\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.44949 | − | 3.14626i | −0.0655482 | − | 0.142279i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 25.3763 | − | 14.6510i | 1.14522 | − | 0.661190i | 0.197499 | − | 0.980303i | \(-0.436718\pi\) |
0.947717 | + | 0.319113i | \(0.103385\pi\) | |||||||
\(492\) | 3.44949 | − | 37.4373i | 0.155515 | − | 1.68781i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 4.00000 | − | 5.65685i | 0.179244 | − | 0.253490i | ||||
\(499\) | 21.8712 | + | 37.8820i | 0.979088 | + | 1.69583i | 0.665725 | + | 0.746197i | \(0.268122\pi\) |
0.313363 | + | 0.949633i | \(0.398544\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.32577 | − | 12.6886i | 0.326965 | − | 0.566320i | ||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.4217 | + | 2.06594i | 0.995782 | + | 0.0917517i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 22.6274i | − | 1.00000i | ||||||
\(513\) | 31.7423 | + | 8.97809i | 1.40146 | + | 0.396392i | ||||
\(514\) | −28.7423 | −1.26777 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17.8990 | + | 38.8515i | 0.787959 | + | 1.71034i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.8236i | 1.21897i | 0.792797 | + | 0.609486i | \(0.208624\pi\) | ||||
−0.792797 | + | 0.609486i | \(0.791376\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.0000 | 1.66162 | 0.830812 | − | 0.556553i | \(-0.187876\pi\) | ||||
0.830812 | + | 0.556553i | \(0.187876\pi\) | |||||||
\(524\) | 24.4949 | + | 14.1421i | 1.07006 | + | 0.617802i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −37.3939 | − | 26.4415i | −1.62736 | − | 1.15072i | ||||
\(529\) | 11.5000 | − | 19.9186i | 0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.02781 | − | 5.53004i | 0.0446030 | − | 0.239983i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 13.7980 | + | 1.27135i | 0.597096 | + | 0.0550167i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.853572 | − | 0.492810i | 0.0368687 | − | 0.0212861i | ||||
\(537\) | −31.1464 | + | 14.3492i | −1.34407 | + | 0.619214i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 46.2726i | 1.99310i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.69694 | − | 11.5994i | −0.287129 | − | 0.497322i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.1742 | + | 26.2825i | −0.648803 | + | 1.12376i | 0.334606 | + | 0.942358i | \(0.391397\pi\) |
−0.983409 | + | 0.181402i | \(0.941936\pi\) | |||||||
\(548\) | 12.2351i | 0.522658i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −46.7423 | −1.99310 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.3485 | − | 31.7805i | 0.778148 | − | 1.34779i | ||||
\(557\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −26.9949 | − | 2.48732i | −1.13973 | − | 0.105015i | ||||
\(562\) | 20.0000 | + | 34.6410i | 0.843649 | + | 1.46124i | ||||
\(563\) | −6.57832 | + | 3.79799i | −0.277243 | + | 0.160066i | −0.632175 | − | 0.774826i | \(-0.717837\pi\) |
0.354932 | + | 0.934892i | \(0.384504\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 31.1127i | 1.30776i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −21.7020 | − | 12.5297i | −0.909797 | − | 0.525271i | −0.0294311 | − | 0.999567i | \(-0.509370\pi\) |
−0.880366 | + | 0.474295i | \(0.842703\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.8712 | + | 22.2935i | 0.538642 | + | 0.932955i | 0.998978 | + | 0.0452101i | \(0.0143957\pi\) |
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 15.5959 | − | 18.2419i | 0.649830 | − | 0.760080i | ||||
\(577\) | 46.3939 | 1.93140 | 0.965701 | − | 0.259656i | \(-0.0836092\pi\) | ||||
0.965701 | + | 0.259656i | \(0.0836092\pi\) | |||||||
\(578\) | 13.9546 | + | 8.05669i | 0.580435 | + | 0.335114i | ||||
\(579\) | 3.69694 | − | 5.22826i | 0.153640 | − | 0.217279i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −19.3939 | − | 13.7135i | −0.803902 | − | 0.568445i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 44.3976i | − | 1.83719i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 16.3207 | + | 9.42274i | 0.673626 | + | 0.388918i | 0.797449 | − | 0.603386i | \(-0.206182\pi\) |
−0.123823 | + | 0.992304i | \(0.539516\pi\) | |||||||
\(588\) | −24.1464 | − | 2.22486i | −0.995782 | − | 0.0917517i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 45.2548i | − | 1.85839i | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||
0.369586 | − | 0.929197i | \(-0.379500\pi\) | |||||||
\(594\) | −11.9217 | − | 47.0904i | −0.489153 | − | 1.93214i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(600\) | 2.24745 | − | 24.3916i | 0.0917517 | − | 0.995782i | ||||
\(601\) | −4.15153 | + | 7.19066i | −0.169344 | + | 0.293313i | −0.938190 | − | 0.346122i | \(-0.887498\pi\) |
0.768845 | + | 0.639435i | \(0.220832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.02781 | + | 0.191027i | 0.0418555 | + | 0.00777921i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(608\) | −31.1010 | + | 17.9562i | −1.26131 | + | 0.728219i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.59592 | − | 13.9672i | 0.104934 | − | 0.564589i | ||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | 29.8207 | + | 17.2170i | 1.20346 | + | 0.694820i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −39.6464 | + | 22.8899i | −1.59611 | + | 0.921512i | −0.603877 | + | 0.797077i | \(0.706378\pi\) |
−0.992228 | + | 0.124434i | \(0.960288\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8712 | − | 43.0781i | 0.999657 | − | 1.73146i | 0.477143 | − | 0.878826i | \(-0.341672\pi\) |
0.522514 | − | 0.852631i | \(-0.324994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −42.1237 | + | 24.3201i | −1.68360 | + | 0.972028i | ||||
\(627\) | −6.66913 | + | 72.3801i | −0.266339 | + | 2.89058i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.0000 | + | 19.7990i | −0.556450 | + | 0.786939i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.7474 | − | 25.2576i | −1.72792 | − | 0.997615i | −0.898470 | − | 0.439034i | \(-0.855321\pi\) |
−0.829450 | − | 0.558581i | \(-0.811346\pi\) | |||||||
\(642\) | 36.8207 | + | 3.39267i | 1.45320 | + | 0.133898i | ||||
\(643\) | 8.82577 | + | 15.2867i | 0.348054 | + | 0.602848i | 0.985904 | − | 0.167313i | \(-0.0535092\pi\) |
−0.637850 | + | 0.770161i | \(0.720176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.6288 | + | 18.4097i | −0.418186 | + | 0.724319i | ||||
\(647\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(648\) | 25.1464 | − | 3.95691i | 0.987845 | − | 0.155442i | ||||
\(649\) | 12.3939 | 0.486502 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.00000 | + | 3.46410i | 0.0783260 | + | 0.135665i | ||||
\(653\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 43.4120i | 1.69495i | ||||||||
\(657\) | 30.6010 | − | 35.7928i | 1.19386 | − | 1.39641i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.6413 | − | 24.0416i | −1.62212 | − | 0.936529i | −0.986353 | − | 0.164644i | \(-0.947352\pi\) |
−0.635763 | − | 0.771885i | \(-0.719314\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(662\) | −31.8434 | + | 18.3848i | −1.23763 | + | 0.714545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.00000 | + | 6.92820i | −0.155230 | + | 0.268866i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.00000 | − | 8.66025i | 0.192736 | − | 0.333828i | −0.753420 | − | 0.657539i | \(-0.771597\pi\) |
0.946156 | + | 0.323711i | \(0.104931\pi\) | |||||||
\(674\) | − | 31.6697i | − | 1.21987i | ||||||
\(675\) | 18.6237 | − | 18.1151i | 0.716827 | − | 0.697251i | ||||
\(676\) | −26.0000 | −1.00000 | ||||||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 11.5959 | + | 25.1701i | 0.445339 | + | 0.966652i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 3.90408 | − | 42.3710i | 0.149605 | − | 1.62366i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.8167i | 0.796530i | 0.917270 | + | 0.398265i | \(0.130387\pi\) | ||||
−0.917270 | + | 0.398265i | \(0.869613\pi\) | |||||||
\(684\) | −37.4495 | − | 6.96031i | −1.43192 | − | 0.266134i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24.6969 | − | 42.7764i | −0.941562 | − | 1.63083i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.0000 | − | 39.8372i | 0.874961 | − | 1.51548i | 0.0181572 | − | 0.999835i | \(-0.494220\pi\) |
0.856804 | − | 0.515642i | \(-0.172447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 33.3485 | 1.26589 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8485 | + | 22.2542i | 0.486670 | + | 0.842938i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −45.3207 | + | 20.8793i | −1.71418 | + | 0.789728i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 45.7980 | + | 26.4415i | 1.72608 | + | 0.996550i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 26.3712 | + | 45.6762i | 0.992492 | + | 1.71905i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −0.595918 | + | 6.46750i | −0.0223960 | + | 0.243064i | ||||
\(709\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −16.0000 | −0.599625 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 34.2929 | − | 19.7990i | 1.28158 | − | 0.739923i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 26.0908 | + | 15.0635i | 0.971000 | + | 0.560607i | ||||
\(723\) | −47.7702 | − | 4.40156i | −1.77659 | − | 0.163696i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 72.7423 | − | 33.5125i | 2.69972 | − | 1.24377i | ||||
\(727\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.0000 | + | 14.1421i | 0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −25.3207 | − | 14.6189i | −0.936519 | − | 0.540699i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.30351i | 0.0848508i | ||||||||
\(738\) | −29.9217 | + | 34.9982i | −1.10143 | + | 1.28830i | ||||
\(739\) | −19.7423 | −0.726234 | −0.363117 | − | 0.931744i | \(-0.618287\pi\) | ||||
−0.363117 | + | 0.931744i | \(0.618287\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.00000 | + | 2.82843i | −0.292705 | + | 0.103487i | ||||
\(748\) | 31.3031 | 1.14455 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.2980 | + | 7.50850i | −0.593931 | + | 0.273625i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(758\) | −14.2702 | − | 8.23888i | −0.518315 | − | 0.299249i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.79796 | + | 5.65685i | −0.355176 | + | 0.205061i | −0.666962 | − | 0.745091i | \(-0.732406\pi\) |
0.311787 | + | 0.950152i | \(0.399073\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −16.0000 | + | 22.6274i | −0.577350 | + | 0.816497i | ||||
\(769\) | 11.0000 | + | 19.0526i | 0.396670 | + | 0.687053i | 0.993313 | − | 0.115454i | \(-0.0368323\pi\) |
−0.596643 | + | 0.802507i | \(0.703499\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 28.7423 | + | 20.3239i | 1.03513 | + | 0.731948i | ||||
\(772\) | −3.69694 | + | 6.40329i | −0.133056 | + | 0.230459i | ||||
\(773\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(774\) | 9.57321 | − | 51.5080i | 0.344102 | − | 1.85142i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 23.7526 | + | 13.7135i | 0.852667 | + | 0.492287i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 59.6691 | − | 34.4500i | 2.13787 | − | 1.23430i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 28.0000 | 1.00000 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −14.4949 | − | 31.4626i | −0.517016 | − | 1.12224i | ||||
\(787\) | −25.0000 | − | 43.3013i | −0.891154 | − | 1.54352i | −0.838494 | − | 0.544911i | \(-0.816563\pi\) |
−0.0526599 | − | 0.998613i | \(-0.516770\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 18.6969 | + | 52.8829i | 0.664367 | + | 1.87911i | ||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 28.2843i | 1.00000i | ||||||||
\(801\) | −12.8990 | − | 11.0280i | −0.455763 | − | 0.389654i | ||||
\(802\) | −20.6515 | −0.729231 | ||||||||
\(803\) | 89.8610 | + | 51.8813i | 3.17112 | + | 1.83085i | ||||
\(804\) | −1.20204 | − | 0.110756i | −0.0423927 | − | 0.00390608i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 23.0881i | − | 0.811735i | −0.913932 | − | 0.405868i | \(-0.866969\pi\) | ||
0.913932 | − | 0.405868i | \(-0.133031\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −55.7423 | −1.95738 | −0.978689 | − | 0.205347i | \(-0.934168\pi\) | ||||
−0.978689 | + | 0.205347i | \(0.934168\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.50510 | + | 16.3349i | −0.0526891 | + | 0.571835i | ||||
\(817\) | −39.1969 | + | 67.8911i | −1.37133 | + | 2.37521i | ||||
\(818\) | − | 57.1256i | − | 1.99735i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(822\) | 8.65153 | − | 12.2351i | 0.301757 | − | 0.426749i | ||||
\(823\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 46.7423 | + | 33.0518i | 1.62736 | + | 1.15072i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 19.7990i | − | 0.688478i | −0.938882 | − | 0.344239i | \(-0.888137\pi\) | ||
0.938882 | − | 0.344239i | \(-0.111863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14.3536 | − | 8.28704i | 0.497322 | − | 0.287129i | ||||
\(834\) | −40.8207 | + | 18.8062i | −1.41350 | + | 0.651204i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 83.9314i | − | 2.90283i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −52.0000 | −1.79631 | ||||||||
\(839\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.5000 | + | 25.1147i | 0.500000 | + | 0.866025i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.49490 | − | 48.7832i | 0.154812 | − | 1.68018i | ||||
\(844\) | 14.0000 | − | 24.2487i | 0.481900 | − | 0.834675i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.0000 | − | 31.1127i | 0.755038 | − | 1.06779i | ||||
\(850\) | 8.37117 | + | 14.4993i | 0.287129 | + | 0.497322i | ||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −42.6969 | −1.45935 | ||||||||
\(857\) | −19.5959 | − | 11.3137i | −0.669384 | − | 0.386469i | 0.126459 | − | 0.991972i | \(-0.459639\pi\) |
−0.795843 | + | 0.605503i | \(0.792972\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.1742 | − | 31.4787i | −0.620097 | − | 1.07404i | −0.989467 | − | 0.144757i | \(-0.953760\pi\) |
0.369370 | − | 0.929282i | \(-0.379573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | −28.4949 | + | 7.21393i | −0.969416 | + | 0.245423i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −41.2702 | − | 23.8273i | −1.40242 | − | 0.809686i | ||||
\(867\) | −8.25765 | − | 17.9241i | −0.280445 | − | 0.608733i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.69694 | + | 27.4271i | 0.328192 | + | 0.928266i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −31.3939 | + | 44.3976i | −1.06070 | + | 1.50006i | ||||
\(877\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 56.5685i | 1.90584i | 0.303218 | + | 0.952921i | \(0.401939\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 22.5732 | + | 19.2990i | 0.760080 | + | 0.649830i | ||||
\(883\) | 50.4393 | 1.69742 | 0.848709 | − | 0.528861i | \(-0.177381\pi\) | ||||
0.848709 | + | 0.528861i | \(0.177381\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −26.7196 | − | 46.2798i | −0.897664 | − | 1.55480i | ||||
\(887\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.3763 | + | 55.5203i | −0.716132 | + | 1.86000i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −23.7196 | + | 41.0836i | −0.791535 | + | 1.37098i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −19.4949 | + | 22.8024i | −0.649830 | + | 0.760080i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −87.8661 | − | 50.7295i | −2.92562 | − | 1.68911i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −16.0000 | − | 27.7128i | −0.532152 | − | 0.921714i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.2196 | + | 48.8779i | −0.937018 | + | 1.62296i | −0.166022 | + | 0.986122i | \(0.553092\pi\) |
−0.770996 | + | 0.636841i | \(0.780241\pi\) | |||||||
\(908\) | 49.1331i | 1.63054i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(912\) | 43.7980 | + | 4.03556i | 1.45030 | + | 0.133631i | ||||
\(913\) | −9.34847 | − | 16.1920i | −0.309389 | − | 0.535878i | ||||
\(914\) | −20.0783 | + | 11.5922i | −0.664132 | + | 0.383437i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −12.4722 | + | 12.1316i | −0.411644 | + | 0.400402i | ||||
\(919\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.6464 | − | 38.3034i | −0.581470 | − | 1.26214i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.4949 | + | 14.1421i | 0.803652 | + | 0.463988i | 0.844746 | − | 0.535167i | \(-0.179751\pi\) |
−0.0410949 | + | 0.999155i | \(0.513085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.2196 | − | 38.4855i | −0.728219 | − | 1.26131i | ||||
\(932\) | 49.8990 | − | 28.8092i | 1.63450 | − | 0.943676i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.3712 | − | 50.8724i | 0.961054 | − | 1.66459i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.0000 | −1.11073 | −0.555366 | − | 0.831606i | \(-0.687422\pi\) | ||||
−0.555366 | + | 0.831606i | \(0.687422\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 59.3207 | + | 5.46583i | 1.93586 | + | 0.178371i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | − | 7.49966i | − | 0.244093i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 115.439 | 3.75325 | ||||||||
\(947\) | −0.770153 | − | 0.444648i | −0.0250266 | − | 0.0144491i | 0.487435 | − | 0.873160i | \(-0.337933\pi\) |
−0.512461 | + | 0.858710i | \(0.671266\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 38.8763 | − | 22.4452i | 1.26131 | − | 0.728219i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 59.0005i | 1.91121i | 0.294646 | + | 0.955607i | \(0.404798\pi\) | ||||
−0.294646 | + | 0.955607i | \(0.595202\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.5000 | + | 26.8468i | −0.500000 | + | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −34.4217 | − | 29.4288i | −1.10922 | − | 0.948330i | ||||
\(964\) | 55.3939 | 1.78412 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(968\) | −80.0908 | + | 46.2405i | −2.57422 | + | 1.48622i | ||||
\(969\) | 23.6464 | − | 10.8940i | 0.759633 | − | 0.349964i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 31.1127i | 0.998454i | 0.866471 | + | 0.499227i | \(0.166383\pi\) | ||||
−0.866471 | + | 0.499227i | \(0.833617\pi\) | |||||||
\(972\) | −27.9444 | − | 13.8243i | −0.896317 | − | 0.443415i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 31.4444 | − | 18.1544i | 1.00600 | − | 0.580812i | 0.0959785 | − | 0.995383i | \(-0.469402\pi\) |
0.910017 | + | 0.414572i | \(0.136069\pi\) | |||||||
\(978\) | 0.449490 | − | 4.87832i | 0.0143731 | − | 0.155991i | ||||
\(979\) | 18.6969 | − | 32.3840i | 0.597557 | − | 1.03500i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 41.4393 | 1.32238 | ||||||||
\(983\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(984\) | 30.6969 | − | 43.4120i | 0.978583 | − | 1.38392i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.8434 | + | 4.13188i | 1.42306 | + | 0.131121i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.89898 | − | 4.09978i | 0.281975 | − | 0.129906i | ||||
\(997\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(998\) | 61.8610i | 1.95818i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 72.2.l.a.11.2 | ✓ | 4 | |
3.2 | odd | 2 | 216.2.l.a.35.1 | 4 | |||
4.3 | odd | 2 | 288.2.p.a.47.2 | 4 | |||
8.3 | odd | 2 | CM | 72.2.l.a.11.2 | ✓ | 4 | |
8.5 | even | 2 | 288.2.p.a.47.2 | 4 | |||
9.2 | odd | 6 | 648.2.f.a.323.3 | 4 | |||
9.4 | even | 3 | 216.2.l.a.179.1 | 4 | |||
9.5 | odd | 6 | inner | 72.2.l.a.59.2 | yes | 4 | |
9.7 | even | 3 | 648.2.f.a.323.2 | 4 | |||
12.11 | even | 2 | 864.2.p.a.143.1 | 4 | |||
24.5 | odd | 2 | 864.2.p.a.143.1 | 4 | |||
24.11 | even | 2 | 216.2.l.a.35.1 | 4 | |||
36.7 | odd | 6 | 2592.2.f.a.1295.1 | 4 | |||
36.11 | even | 6 | 2592.2.f.a.1295.4 | 4 | |||
36.23 | even | 6 | 288.2.p.a.239.2 | 4 | |||
36.31 | odd | 6 | 864.2.p.a.719.1 | 4 | |||
72.5 | odd | 6 | 288.2.p.a.239.2 | 4 | |||
72.11 | even | 6 | 648.2.f.a.323.3 | 4 | |||
72.13 | even | 6 | 864.2.p.a.719.1 | 4 | |||
72.29 | odd | 6 | 2592.2.f.a.1295.4 | 4 | |||
72.43 | odd | 6 | 648.2.f.a.323.2 | 4 | |||
72.59 | even | 6 | inner | 72.2.l.a.59.2 | yes | 4 | |
72.61 | even | 6 | 2592.2.f.a.1295.1 | 4 | |||
72.67 | odd | 6 | 216.2.l.a.179.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.l.a.11.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
72.2.l.a.11.2 | ✓ | 4 | 8.3 | odd | 2 | CM | |
72.2.l.a.59.2 | yes | 4 | 9.5 | odd | 6 | inner | |
72.2.l.a.59.2 | yes | 4 | 72.59 | even | 6 | inner | |
216.2.l.a.35.1 | 4 | 3.2 | odd | 2 | |||
216.2.l.a.35.1 | 4 | 24.11 | even | 2 | |||
216.2.l.a.179.1 | 4 | 9.4 | even | 3 | |||
216.2.l.a.179.1 | 4 | 72.67 | odd | 6 | |||
288.2.p.a.47.2 | 4 | 4.3 | odd | 2 | |||
288.2.p.a.47.2 | 4 | 8.5 | even | 2 | |||
288.2.p.a.239.2 | 4 | 36.23 | even | 6 | |||
288.2.p.a.239.2 | 4 | 72.5 | odd | 6 | |||
648.2.f.a.323.2 | 4 | 9.7 | even | 3 | |||
648.2.f.a.323.2 | 4 | 72.43 | odd | 6 | |||
648.2.f.a.323.3 | 4 | 9.2 | odd | 6 | |||
648.2.f.a.323.3 | 4 | 72.11 | even | 6 | |||
864.2.p.a.143.1 | 4 | 12.11 | even | 2 | |||
864.2.p.a.143.1 | 4 | 24.5 | odd | 2 | |||
864.2.p.a.719.1 | 4 | 36.31 | odd | 6 | |||
864.2.p.a.719.1 | 4 | 72.13 | even | 6 | |||
2592.2.f.a.1295.1 | 4 | 36.7 | odd | 6 | |||
2592.2.f.a.1295.1 | 4 | 72.61 | even | 6 | |||
2592.2.f.a.1295.4 | 4 | 36.11 | even | 6 | |||
2592.2.f.a.1295.4 | 4 | 72.29 | odd | 6 |