Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2925,2,Mod(2224,2925)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2925, base_ring=CyclotomicField(2))
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("2925.2224");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2925 = 3^{2} \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2925.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.3562425912\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 65) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2224.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2925.2224 |
Dual form | 2925.2.c.r.2224.2 |
$q$-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 \(\left(\mathbb{Z}/2925\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) | \(2251\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214i | 0.292893i | 0.989219 | + | 0.146447i | \(0.0467837\pi\) | ||||
−0.989219 | + | 0.146447i | \(0.953216\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.82843 | 0.914214 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.828427i | 0.313116i | 0.987669 | + | 0.156558i | \(0.0500398\pi\) | ||||
−0.987669 | + | 0.156558i | \(0.949960\pi\) | |||||||
\(8\) | 1.58579i | 0.560660i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.585786 | −0.176621 | −0.0883106 | − | 0.996093i | \(-0.528147\pi\) | ||||
−0.0883106 | + | 0.996093i | \(0.528147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −0.343146 | −0.0917096 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | − 4.82843i | − 1.17107i | −0.810649 | − | 0.585533i | \(-0.800885\pi\) | ||||
0.810649 | − | 0.585533i | \(-0.199115\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.41421 | −0.783274 | −0.391637 | − | 0.920120i | \(-0.628091\pi\) | ||||
−0.391637 | + | 0.920120i | \(0.628091\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − 0.242641i | − 0.0517312i | ||||||||
\(23\) | 1.41421i | 0.294884i | 0.989071 | + | 0.147442i | \(0.0471040\pi\) | ||||
−0.989071 | + | 0.147442i | \(0.952896\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.414214 | 0.0812340 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.51472i | 0.286255i | ||||||||
\(29\) | 5.65685 | 1.05045 | 0.525226 | − | 0.850963i | \(-0.323981\pi\) | ||||
0.525226 | + | 0.850963i | \(0.323981\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2426 | 1.83963 | 0.919816 | − | 0.392349i | \(-0.128338\pi\) | ||||
0.919816 | + | 0.392349i | \(0.128338\pi\) | |||||||
\(32\) | 4.41421i | 0.780330i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | 0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 8.48528i | − 1.39497i | −0.716599 | − | 0.697486i | \(-0.754302\pi\) | ||||
0.716599 | − | 0.697486i | \(-0.245698\pi\) | |||||||
\(38\) | − 1.41421i | − 0.229416i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.82843 | 1.37877 | 0.689384 | − | 0.724396i | \(-0.257881\pi\) | ||||
0.689384 | + | 0.724396i | \(0.257881\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.07107i | 0.468333i | 0.972196 | + | 0.234167i | \(0.0752362\pi\) | ||||
−0.972196 | + | 0.234167i | \(0.924764\pi\) | |||||||
\(44\) | −1.07107 | −0.161470 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.585786 | −0.0863695 | ||||||||
\(47\) | 0.828427i | 0.120839i | 0.998173 | + | 0.0604193i | \(0.0192438\pi\) | ||||
−0.998173 | + | 0.0604193i | \(0.980756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.31371 | 0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 1.82843i | − 0.253557i | ||||||||
\(53\) | 14.4853i | 1.98971i | 0.101327 | + | 0.994853i | \(0.467691\pi\) | ||||
−0.101327 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.31371 | −0.175552 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.34315i | 0.307670i | ||||||||
\(59\) | 10.2426 | 1.33348 | 0.666739 | − | 0.745291i | \(-0.267690\pi\) | ||||
0.666739 | + | 0.745291i | \(0.267690\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.00000 | −1.02430 | −0.512148 | − | 0.858898i | \(-0.671150\pi\) | ||||
−0.512148 | + | 0.858898i | \(0.671150\pi\) | |||||||
\(62\) | 4.24264i | 0.538816i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.17157 | 0.521447 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.00000i | 0.244339i | 0.992509 | + | 0.122169i | \(0.0389851\pi\) | ||||
−0.992509 | + | 0.122169i | \(0.961015\pi\) | |||||||
\(68\) | − 8.82843i | − 1.07060i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.89949 | 0.937498 | 0.468749 | − | 0.883332i | \(-0.344705\pi\) | ||||
0.468749 | + | 0.883332i | \(0.344705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 8.48528i | − 0.993127i | −0.868000 | − | 0.496564i | \(-0.834595\pi\) | ||||
0.868000 | − | 0.496564i | \(-0.165405\pi\) | |||||||
\(74\) | 3.51472 | 0.408578 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −6.24264 | −0.716080 | ||||||||
\(77\) | − 0.485281i | − 0.0553029i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.48528 | −0.954669 | −0.477334 | − | 0.878722i | \(-0.658397\pi\) | ||||
−0.477334 | + | 0.878722i | \(0.658397\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.65685i | 0.403832i | ||||||||
\(83\) | 8.82843i | 0.969046i | 0.874779 | + | 0.484523i | \(0.161007\pi\) | ||||
−0.874779 | + | 0.484523i | \(0.838993\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.27208 | −0.137172 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − 0.928932i | − 0.0990245i | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.828427 | 0.0868428 | ||||||||
\(92\) | 2.58579i | 0.269587i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.343146 | −0.0353928 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 3.65685i | − 0.371297i | −0.982616 | − | 0.185649i | \(-0.940561\pi\) | ||||
0.982616 | − | 0.185649i | \(-0.0594386\pi\) | |||||||
\(98\) | 2.61522i | 0.264177i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.65685 | −0.761885 | −0.380943 | − | 0.924599i | \(-0.624401\pi\) | ||||
−0.380943 | + | 0.924599i | \(0.624401\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.4142i | 1.71587i | 0.513755 | + | 0.857937i | \(0.328254\pi\) | ||||
−0.513755 | + | 0.857937i | \(0.671746\pi\) | |||||||
\(104\) | 1.58579 | 0.155499 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | − 6.58579i | − 0.636672i | −0.947978 | − | 0.318336i | \(-0.896876\pi\) | ||||
0.947978 | − | 0.318336i | \(-0.103124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.00000 | 0.191565 | 0.0957826 | − | 0.995402i | \(-0.469465\pi\) | ||||
0.0957826 | + | 0.995402i | \(0.469465\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.48528i | 0.234837i | ||||||||
\(113\) | 3.17157i | 0.298356i | 0.988810 | + | 0.149178i | \(0.0476628\pi\) | ||||
−0.988810 | + | 0.149178i | \(0.952337\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 10.3431 | 0.960337 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.24264i | 0.390567i | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | − 3.31371i | − 0.300009i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 18.7279 | 1.68182 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.41421i | 0.835376i | 0.908590 | + | 0.417688i | \(0.137160\pi\) | ||||
−0.908590 | + | 0.417688i | \(0.862840\pi\) | |||||||
\(128\) | 10.5563i | 0.933058i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.9706 | −1.48272 | −0.741362 | − | 0.671105i | \(-0.765820\pi\) | ||||
−0.741362 | + | 0.671105i | \(0.765820\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 2.82843i | − 0.245256i | ||||||||
\(134\) | −0.828427 | −0.0715652 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.65685 | 0.656570 | ||||||||
\(137\) | 5.31371i | 0.453981i | 0.973897 | + | 0.226990i | \(0.0728886\pi\) | ||||
−0.973897 | + | 0.226990i | \(0.927111\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4853 | 1.05899 | 0.529494 | − | 0.848314i | \(-0.322382\pi\) | ||||
0.529494 | + | 0.848314i | \(0.322382\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.27208i | 0.274587i | ||||||||
\(143\) | 0.585786i | 0.0489859i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.51472 | 0.290880 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − 15.5147i | − 1.27530i | ||||||||
\(149\) | −0.343146 | −0.0281116 | −0.0140558 | − | 0.999901i | \(-0.504474\pi\) | ||||
−0.0140558 | + | 0.999901i | \(0.504474\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 18.2426 | 1.48457 | 0.742283 | − | 0.670087i | \(-0.233743\pi\) | ||||
0.742283 | + | 0.670087i | \(0.233743\pi\) | |||||||
\(152\) | − 5.41421i | − 0.439151i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.201010 | 0.0161979 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 18.0000i | − 1.43656i | −0.695756 | − | 0.718278i | \(-0.744931\pi\) | ||||
0.695756 | − | 0.718278i | \(-0.255069\pi\) | |||||||
\(158\) | − 3.51472i | − 0.279616i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.17157 | −0.0923329 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 14.9706i | − 1.17258i | −0.810099 | − | 0.586292i | \(-0.800587\pi\) | ||||
0.810099 | − | 0.586292i | \(-0.199413\pi\) | |||||||
\(164\) | 16.1421 | 1.26049 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.65685 | −0.283827 | ||||||||
\(167\) | − 8.82843i | − 0.683164i | −0.939852 | − | 0.341582i | \(-0.889037\pi\) | ||||
0.939852 | − | 0.341582i | \(-0.110963\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.61522i | 0.428157i | ||||||||
\(173\) | − 11.1716i | − 0.849359i | −0.905344 | − | 0.424679i | \(-0.860387\pi\) | ||||
0.905344 | − | 0.424679i | \(-0.139613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.75736 | −0.132466 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.48528i | 0.186280i | ||||||||
\(179\) | −5.65685 | −0.422813 | −0.211407 | − | 0.977398i | \(-0.567804\pi\) | ||||
−0.211407 | + | 0.977398i | \(0.567804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(182\) | 0.343146i | 0.0254357i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.24264 | −0.165330 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.82843i | 0.206835i | ||||||||
\(188\) | 1.51472i | 0.110472i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6569 | −0.988175 | −0.494088 | − | 0.869412i | \(-0.664498\pi\) | ||||
−0.494088 | + | 0.869412i | \(0.664498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.6569i | 1.12701i | 0.826114 | + | 0.563503i | \(0.190546\pi\) | ||||
−0.826114 | + | 0.563503i | \(0.809454\pi\) | |||||||
\(194\) | 1.51472 | 0.108750 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.5442 | 0.824583 | ||||||||
\(197\) | − 22.9706i | − 1.63658i | −0.574802 | − | 0.818292i | \(-0.694921\pi\) | ||||
0.574802 | − | 0.818292i | \(-0.305079\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 3.17157i | − 0.223151i | ||||||||
\(203\) | 4.68629i | 0.328913i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.21320 | −0.502568 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 3.00000i | − 0.208013i | ||||||||
\(209\) | 2.00000 | 0.138343 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.3137 | −1.32961 | −0.664805 | − | 0.747017i | \(-0.731485\pi\) | ||||
−0.664805 | + | 0.747017i | \(0.731485\pi\) | |||||||
\(212\) | 26.4853i | 1.81902i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.72792 | 0.186477 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.48528i | 0.576018i | ||||||||
\(218\) | 0.828427i | 0.0561082i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.82843 | −0.324795 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.4853i | 1.77359i | 0.462167 | + | 0.886793i | \(0.347072\pi\) | ||||
−0.462167 | + | 0.886793i | \(0.652928\pi\) | |||||||
\(224\) | −3.65685 | −0.244334 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.31371 | −0.0873866 | ||||||||
\(227\) | − 27.6569i | − 1.83565i | −0.396985 | − | 0.917825i | \(-0.629944\pi\) | ||||
0.396985 | − | 0.917825i | \(-0.370056\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.828427 | −0.0547440 | −0.0273720 | − | 0.999625i | \(-0.508714\pi\) | ||||
−0.0273720 | + | 0.999625i | \(0.508714\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.97056i | 0.588946i | ||||||||
\(233\) | − 24.6274i | − 1.61340i | −0.590964 | − | 0.806698i | \(-0.701253\pi\) | ||||
0.590964 | − | 0.806698i | \(-0.298747\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 18.7279 | 1.21908 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.65685i | 0.107398i | ||||||||
\(239\) | −0.585786 | −0.0378914 | −0.0189457 | − | 0.999821i | \(-0.506031\pi\) | ||||
−0.0189457 | + | 0.999821i | \(0.506031\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.48528 | 0.160091 | 0.0800455 | − | 0.996791i | \(-0.474493\pi\) | ||||
0.0800455 | + | 0.996791i | \(0.474493\pi\) | |||||||
\(242\) | − 4.41421i | − 0.283756i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −14.6274 | −0.936424 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.41421i | 0.217241i | ||||||||
\(248\) | 16.2426i | 1.03141i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.7990 | 1.24970 | 0.624851 | − | 0.780744i | \(-0.285160\pi\) | ||||
0.624851 | + | 0.780744i | \(0.285160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 0.828427i | − 0.0520828i | ||||||||
\(254\) | −3.89949 | −0.244676 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | 16.3431i | 1.01946i | 0.860335 | + | 0.509729i | \(0.170254\pi\) | ||||
−0.860335 | + | 0.509729i | \(0.829746\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.02944 | 0.436788 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − 7.02944i | − 0.434280i | ||||||||
\(263\) | 13.4142i | 0.827156i | 0.910469 | + | 0.413578i | \(0.135721\pi\) | ||||
−0.910469 | + | 0.413578i | \(0.864279\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.17157 | 0.0718337 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.65685i | 0.223378i | ||||||||
\(269\) | −2.68629 | −0.163786 | −0.0818930 | − | 0.996641i | \(-0.526097\pi\) | ||||
−0.0818930 | + | 0.996641i | \(0.526097\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.27208 | 0.0772732 | 0.0386366 | − | 0.999253i | \(-0.487699\pi\) | ||||
0.0386366 | + | 0.999253i | \(0.487699\pi\) | |||||||
\(272\) | − 14.4853i | − 0.878299i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.20101 | −0.132968 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.17157i | 0.430898i | 0.976515 | + | 0.215449i | \(0.0691215\pi\) | ||||
−0.976515 | + | 0.215449i | \(0.930878\pi\) | |||||||
\(278\) | 5.17157i | 0.310170i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7990 | 1.06180 | 0.530899 | − | 0.847435i | \(-0.321854\pi\) | ||||
0.530899 | + | 0.847435i | \(0.321854\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.72792i | 0.518821i | 0.965767 | + | 0.259411i | \(0.0835283\pi\) | ||||
−0.965767 | + | 0.259411i | \(0.916472\pi\) | |||||||
\(284\) | 14.4437 | 0.857073 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.242641 | −0.0143476 | ||||||||
\(287\) | 7.31371i | 0.431715i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.31371 | −0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 15.5147i | − 0.907930i | ||||||||
\(293\) | 2.14214i | 0.125145i | 0.998040 | + | 0.0625724i | \(0.0199304\pi\) | ||||
−0.998040 | + | 0.0625724i | \(0.980070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.4558 | 0.782105 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − 0.142136i | − 0.00823370i | ||||||||
\(299\) | 1.41421 | 0.0817861 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.54416 | −0.146643 | ||||||||
\(302\) | 7.55635i | 0.434819i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −10.2426 | −0.587456 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 19.1716i | − 1.09418i | −0.837074 | − | 0.547090i | \(-0.815736\pi\) | ||||
0.837074 | − | 0.547090i | \(-0.184264\pi\) | |||||||
\(308\) | − 0.887302i | − 0.0505587i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.48528 | 0.481156 | 0.240578 | − | 0.970630i | \(-0.422663\pi\) | ||||
0.240578 | + | 0.970630i | \(0.422663\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.828427i | 0.0468255i | 0.999726 | + | 0.0234127i | \(0.00745319\pi\) | ||||
−0.999726 | + | 0.0234127i | \(0.992547\pi\) | |||||||
\(314\) | 7.45584 | 0.420758 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −15.5147 | −0.872771 | ||||||||
\(317\) | 26.1421i | 1.46829i | 0.678993 | + | 0.734144i | \(0.262416\pi\) | ||||
−0.678993 | + | 0.734144i | \(0.737584\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.31371 | −0.185532 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − 0.485281i | − 0.0270437i | ||||||||
\(323\) | 16.4853i | 0.917266i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.20101 | 0.343442 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 14.0000i | 0.773021i | ||||||||
\(329\) | −0.686292 | −0.0378365 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.0416 | 1.21152 | 0.605759 | − | 0.795648i | \(-0.292870\pi\) | ||||
0.605759 | + | 0.795648i | \(0.292870\pi\) | |||||||
\(332\) | 16.1421i | 0.885915i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.65685 | 0.200094 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 7.17157i | − 0.390660i | −0.980738 | − | 0.195330i | \(-0.937422\pi\) | ||||
0.980738 | − | 0.195330i | \(-0.0625779\pi\) | |||||||
\(338\) | − 0.414214i | − 0.0225302i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.00000 | −0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.0294i | 0.595534i | ||||||||
\(344\) | −4.87006 | −0.262576 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.62742 | 0.248771 | ||||||||
\(347\) | 4.24264i | 0.227757i | 0.993495 | + | 0.113878i | \(0.0363274\pi\) | ||||
−0.993495 | + | 0.113878i | \(0.963673\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.51472 | −0.0810810 | −0.0405405 | − | 0.999178i | \(-0.512908\pi\) | ||||
−0.0405405 | + | 0.999178i | \(0.512908\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | − 2.58579i | − 0.137823i | ||||||||
\(353\) | − 9.17157i | − 0.488154i | −0.969756 | − | 0.244077i | \(-0.921515\pi\) | ||||
0.969756 | − | 0.244077i | \(-0.0784849\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.9706 | 0.581439 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 2.34315i | − 0.123839i | ||||||||
\(359\) | −27.8995 | −1.47248 | −0.736240 | − | 0.676721i | \(-0.763400\pi\) | ||||
−0.736240 | + | 0.676721i | \(0.763400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.34315 | −0.386481 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.51472 | 0.0793928 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 4.44365i | − 0.231957i | −0.993252 | − | 0.115978i | \(-0.963000\pi\) | ||||
0.993252 | − | 0.115978i | \(-0.0370003\pi\) | |||||||
\(368\) | 4.24264i | 0.221163i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.0000 | −0.623009 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 25.3137i | − 1.31069i | −0.755328 | − | 0.655347i | \(-0.772522\pi\) | ||||
0.755328 | − | 0.655347i | \(-0.227478\pi\) | |||||||
\(374\) | −1.17157 | −0.0605806 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.31371 | −0.0677493 | ||||||||
\(377\) | − 5.65685i | − 0.291343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.9289 | −0.766848 | −0.383424 | − | 0.923572i | \(-0.625255\pi\) | ||||
−0.383424 | + | 0.923572i | \(0.625255\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − 5.65685i | − 0.289430i | ||||||||
\(383\) | − 33.1127i | − 1.69198i | −0.533199 | − | 0.845990i | \(-0.679010\pi\) | ||||
0.533199 | − | 0.845990i | \(-0.320990\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.48528 | −0.330092 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 6.68629i | − 0.339445i | ||||||||
\(389\) | −16.6274 | −0.843044 | −0.421522 | − | 0.906818i | \(-0.638504\pi\) | ||||
−0.421522 | + | 0.906818i | \(0.638504\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.82843 | 0.345328 | ||||||||
\(392\) | 10.0122i | 0.505692i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 9.51472 | 0.479345 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 27.7990i | 1.39519i | 0.716492 | + | 0.697596i | \(0.245747\pi\) | ||||
−0.716492 | + | 0.697596i | \(0.754253\pi\) | |||||||
\(398\) | − 1.65685i | − 0.0830506i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.3137 | −0.864605 | −0.432303 | − | 0.901729i | \(-0.642299\pi\) | ||||
−0.432303 | + | 0.901729i | \(0.642299\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 10.2426i | − 0.510222i | ||||||||
\(404\) | −14.0000 | −0.696526 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.94113 | −0.0963364 | ||||||||
\(407\) | 4.97056i | 0.246382i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.8284 | −0.634325 | −0.317162 | − | 0.948371i | \(-0.602730\pi\) | ||||
−0.317162 | + | 0.948371i | \(0.602730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 31.8406i | 1.56867i | ||||||||
\(413\) | 8.48528i | 0.417533i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.41421 | 0.216425 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0.828427i | 0.0405197i | ||||||||
\(419\) | 5.17157 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.02944 | −0.0501717 | −0.0250859 | − | 0.999685i | \(-0.507986\pi\) | ||||
−0.0250859 | + | 0.999685i | \(0.507986\pi\) | |||||||
\(422\) | − 8.00000i | − 0.389434i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −22.9706 | −1.11555 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 6.62742i | − 0.320723i | ||||||||
\(428\) | − 12.0416i | − 0.582054i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.61522 | −0.174139 | −0.0870696 | − | 0.996202i | \(-0.527750\pi\) | ||||
−0.0870696 | + | 0.996202i | \(0.527750\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 3.65685i | − 0.175737i | −0.996132 | − | 0.0878686i | \(-0.971994\pi\) | ||||
0.996132 | − | 0.0878686i | \(-0.0280056\pi\) | |||||||
\(434\) | −3.51472 | −0.168712 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.65685 | 0.175132 | ||||||||
\(437\) | − 4.82843i | − 0.230975i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.9706 | 1.57360 | 0.786800 | − | 0.617209i | \(-0.211737\pi\) | ||||
0.786800 | + | 0.617209i | \(0.211737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 2.00000i | − 0.0951303i | ||||||||
\(443\) | 6.58579i | 0.312900i | 0.987686 | + | 0.156450i | \(0.0500050\pi\) | ||||
−0.987686 | + | 0.156450i | \(0.949995\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −10.9706 | −0.519471 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.45584i | 0.163273i | ||||||||
\(449\) | 29.1127 | 1.37391 | 0.686957 | − | 0.726698i | \(-0.258946\pi\) | ||||
0.686957 | + | 0.726698i | \(0.258946\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.17157 | −0.243520 | ||||||||
\(452\) | 5.79899i | 0.272762i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.4558 | 0.537649 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.0000i | 0.842004i | 0.907060 | + | 0.421002i | \(0.138322\pi\) | ||||
−0.907060 | + | 0.421002i | \(0.861678\pi\) | |||||||
\(458\) | − 0.343146i | − 0.0160341i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4853 | −1.23354 | −0.616771 | − | 0.787142i | \(-0.711560\pi\) | ||||
−0.616771 | + | 0.787142i | \(0.711560\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 15.6569i | − 0.727636i | −0.931470 | − | 0.363818i | \(-0.881473\pi\) | ||||
0.931470 | − | 0.363818i | \(-0.118527\pi\) | |||||||
\(464\) | 16.9706 | 0.787839 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 10.2010 | 0.472553 | ||||||||
\(467\) | − 10.5858i | − 0.489852i | −0.969542 | − | 0.244926i | \(-0.921236\pi\) | ||||
0.969542 | − | 0.244926i | \(-0.0787636\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.65685 | −0.0765064 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 16.2426i | 0.747628i | ||||||||
\(473\) | − 1.79899i | − 0.0827176i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.31371 | 0.335223 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − 0.242641i | − 0.0110981i | ||||||||
\(479\) | −5.27208 | −0.240887 | −0.120444 | − | 0.992720i | \(-0.538432\pi\) | ||||
−0.120444 | + | 0.992720i | \(0.538432\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.48528 | −0.386896 | ||||||||
\(482\) | 1.02944i | 0.0468896i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −19.4853 | −0.885695 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 22.9706i | − 1.04090i | −0.853894 | − | 0.520448i | \(-0.825765\pi\) | ||||
0.853894 | − | 0.520448i | \(-0.174235\pi\) | |||||||
\(488\) | − 12.6863i | − 0.574281i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.8284 | −0.488680 | −0.244340 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244340 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 27.3137i | − 1.23015i | ||||||||
\(494\) | −1.41421 | −0.0636285 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 30.7279 | 1.37972 | ||||||||
\(497\) | 6.54416i | 0.293546i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −10.4437 | −0.467522 | −0.233761 | − | 0.972294i | \(-0.575103\pi\) | ||||
−0.233761 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.20101i | 0.366029i | ||||||||
\(503\) | − 18.1005i | − 0.807062i | −0.914966 | − | 0.403531i | \(-0.867783\pi\) | ||||
0.914966 | − | 0.403531i | \(-0.132217\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.343146 | 0.0152547 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.2132i | 0.763712i | ||||||||
\(509\) | −21.1127 | −0.935804 | −0.467902 | − | 0.883780i | \(-0.654990\pi\) | ||||
−0.467902 | + | 0.883780i | \(0.654990\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.02944 | 0.310964 | ||||||||
\(512\) | 22.7574i | 1.00574i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.76955 | −0.298592 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 0.485281i | − 0.0213427i | ||||||||
\(518\) | 2.91169i | 0.127932i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.34315 | 0.277898 | 0.138949 | − | 0.990300i | \(-0.455628\pi\) | ||||
0.138949 | + | 0.990300i | \(0.455628\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 28.2426i | − 1.23496i | −0.786585 | − | 0.617482i | \(-0.788153\pi\) | ||||
0.786585 | − | 0.617482i | \(-0.211847\pi\) | |||||||
\(524\) | −31.0294 | −1.35553 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.55635 | −0.242268 | ||||||||
\(527\) | − 49.4558i | − 2.15433i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.0000 | 0.913043 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − 5.17157i | − 0.224216i | ||||||||
\(533\) | − 8.82843i | − 0.382402i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −3.17157 | −0.136991 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 1.11270i | − 0.0479718i | ||||||||
\(539\) | −3.69848 | −0.159305 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.8284 | −0.551537 | −0.275769 | − | 0.961224i | \(-0.588932\pi\) | ||||
−0.275769 | + | 0.961224i | \(0.588932\pi\) | |||||||
\(542\) | 0.526912i | 0.0226328i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 21.3137 | 0.913818 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.2132i | 1.24907i | 0.780998 | + | 0.624533i | \(0.214711\pi\) | ||||
−0.780998 | + | 0.624533i | \(0.785289\pi\) | |||||||
\(548\) | 9.71573i | 0.415035i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.3137 | −0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 7.02944i | − 0.298922i | ||||||||
\(554\) | −2.97056 | −0.126207 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 22.8284 | 0.968141 | ||||||||
\(557\) | 3.79899i | 0.160968i | 0.996756 | + | 0.0804842i | \(0.0256467\pi\) | ||||
−0.996756 | + | 0.0804842i | \(0.974353\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.07107 | 0.129892 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.37258i | 0.310994i | ||||||||
\(563\) | 16.2426i | 0.684546i | 0.939601 | + | 0.342273i | \(0.111197\pi\) | ||||
−0.939601 | + | 0.342273i | \(0.888803\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −3.61522 | −0.151959 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.5269i | 0.525618i | ||||||||
\(569\) | −21.6569 | −0.907903 | −0.453951 | − | 0.891027i | \(-0.649986\pi\) | ||||
−0.453951 | + | 0.891027i | \(0.649986\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −28.4853 | −1.19207 | −0.596036 | − | 0.802958i | \(-0.703258\pi\) | ||||
−0.596036 | + | 0.802958i | \(0.703258\pi\) | |||||||
\(572\) | 1.07107i | 0.0447836i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.02944 | −0.126446 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.1716i | 1.21443i | 0.794538 | + | 0.607214i | \(0.207713\pi\) | ||||
−0.794538 | + | 0.607214i | \(0.792287\pi\) | |||||||
\(578\) | − 2.61522i | − 0.108779i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.31371 | −0.303424 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 8.48528i | − 0.351424i | ||||||||
\(584\) | 13.4558 | 0.556807 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.887302 | −0.0366541 | ||||||||
\(587\) | 31.6569i | 1.30662i | 0.757091 | + | 0.653309i | \(0.226620\pi\) | ||||
−0.757091 | + | 0.653309i | \(0.773380\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −34.9706 | −1.44094 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − 25.4558i | − 1.04623i | ||||||||
\(593\) | − 20.6274i | − 0.847066i | −0.905881 | − | 0.423533i | \(-0.860790\pi\) | ||||
0.905881 | − | 0.423533i | \(-0.139210\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.627417 | −0.0257000 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.585786i | 0.0239546i | ||||||||
\(599\) | −25.4558 | −1.04010 | −0.520049 | − | 0.854137i | \(-0.674086\pi\) | ||||
−0.520049 | + | 0.854137i | \(0.674086\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.627417 | 0.0255929 | 0.0127964 | − | 0.999918i | \(-0.495927\pi\) | ||||
0.0127964 | + | 0.999918i | \(0.495927\pi\) | |||||||
\(602\) | − 1.05382i | − 0.0429507i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 33.3553 | 1.35721 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 40.2426i | − 1.63340i | −0.577064 | − | 0.816699i | \(-0.695802\pi\) | ||||
0.577064 | − | 0.816699i | \(-0.304198\pi\) | |||||||
\(608\) | − 15.0711i | − 0.611213i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.828427 | 0.0335146 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 37.3137i | − 1.50709i | −0.657398 | − | 0.753543i | \(-0.728343\pi\) | ||||
0.657398 | − | 0.753543i | \(-0.271657\pi\) | |||||||
\(614\) | 7.94113 | 0.320478 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.769553 | 0.0310062 | ||||||||
\(617\) | − 22.9706i | − 0.924760i | −0.886682 | − | 0.462380i | \(-0.846996\pi\) | ||||
0.886682 | − | 0.462380i | \(-0.153004\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.2426 | −0.411686 | −0.205843 | − | 0.978585i | \(-0.565994\pi\) | ||||
−0.205843 | + | 0.978585i | \(0.565994\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.51472i | 0.140927i | ||||||||
\(623\) | 4.97056i | 0.199141i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −0.343146 | −0.0137149 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 32.9117i | − 1.31332i | ||||||||
\(629\) | −40.9706 | −1.63360 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.2426 | −0.726228 | −0.363114 | − | 0.931745i | \(-0.618286\pi\) | ||||
−0.363114 | + | 0.931745i | \(0.618286\pi\) | |||||||
\(632\) | − 13.4558i | − 0.535245i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −10.8284 | −0.430052 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.31371i | − 0.250158i | ||||||||
\(638\) | − 1.37258i | − 0.0543411i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.3431 | −1.43547 | −0.717734 | − | 0.696317i | \(-0.754821\pi\) | ||||
−0.717734 | + | 0.696317i | \(0.754821\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.4853i | 1.04448i | 0.852799 | + | 0.522239i | \(0.174903\pi\) | ||||
−0.852799 | + | 0.522239i | \(0.825097\pi\) | |||||||
\(644\) | −2.14214 | −0.0844120 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.82843 | −0.268661 | ||||||||
\(647\) | 6.58579i | 0.258914i | 0.991585 | + | 0.129457i | \(0.0413234\pi\) | ||||
−0.991585 | + | 0.129457i | \(0.958677\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.00000 | −0.235521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 27.3726i | − 1.07199i | ||||||||
\(653\) | − 13.0294i | − 0.509881i | −0.966957 | − | 0.254941i | \(-0.917944\pi\) | ||||
0.966957 | − | 0.254941i | \(-0.0820559\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 26.4853 | 1.03408 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − 0.284271i | − 0.0110820i | ||||||||
\(659\) | 46.1421 | 1.79744 | 0.898721 | − | 0.438520i | \(-0.144497\pi\) | ||||
0.898721 | + | 0.438520i | \(0.144497\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.5980 | −1.92914 | −0.964569 | − | 0.263831i | \(-0.915014\pi\) | ||||
−0.964569 | + | 0.263831i | \(0.915014\pi\) | |||||||
\(662\) | 9.12994i | 0.354845i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −14.0000 | −0.543305 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.00000i | 0.309761i | ||||||||
\(668\) | − 16.1421i | − 0.624558i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.68629 | 0.180912 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 10.4853i | − 0.404178i | −0.979367 | − | 0.202089i | \(-0.935227\pi\) | ||||
0.979367 | − | 0.202089i | \(-0.0647730\pi\) | |||||||
\(674\) | 2.97056 | 0.114422 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.82843 | −0.0703241 | ||||||||
\(677\) | 8.14214i | 0.312928i | 0.987684 | + | 0.156464i | \(0.0500095\pi\) | ||||
−0.987684 | + | 0.156464i | \(0.949991\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.02944 | 0.116259 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 2.48528i | − 0.0951663i | ||||||||
\(683\) | − 33.3137i | − 1.27471i | −0.770569 | − | 0.637357i | \(-0.780028\pi\) | ||||
0.770569 | − | 0.637357i | \(-0.219972\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.56854 | −0.174428 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 9.21320i | 0.351250i | ||||||||
\(689\) | 14.4853 | 0.551845 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 21.0711 | 0.801581 | 0.400791 | − | 0.916170i | \(-0.368735\pi\) | ||||
0.400791 | + | 0.916170i | \(0.368735\pi\) | |||||||
\(692\) | − 20.4264i | − 0.776495i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.75736 | −0.0667084 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 42.6274i | − 1.61463i | ||||||||
\(698\) | − 0.627417i | − 0.0237481i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.3137 | −1.40932 | −0.704660 | − | 0.709545i | \(-0.748900\pi\) | ||||
−0.704660 | + | 0.709545i | \(0.748900\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.9706i | 1.09265i | ||||||||
\(704\) | −2.44365 | −0.0920986 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.79899 | 0.142977 | ||||||||
\(707\) | − 6.34315i | − 0.238559i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.1127 | 0.642681 | 0.321340 | − | 0.946964i | \(-0.395867\pi\) | ||||
0.321340 | + | 0.946964i | \(0.395867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.51472i | 0.356579i | ||||||||
\(713\) | 14.4853i | 0.542478i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.3431 | −0.386542 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − 11.5563i | − 0.431279i | ||||||||
\(719\) | −4.97056 | −0.185371 | −0.0926854 | − | 0.995695i | \(-0.529545\pi\) | ||||
−0.0926854 | + | 0.995695i | \(0.529545\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −14.4264 | −0.537267 | ||||||||
\(722\) | − 3.04163i | − 0.113198i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 19.3553i | − 0.717850i | −0.933366 | − | 0.358925i | \(-0.883143\pi\) | ||||
0.933366 | − | 0.358925i | \(-0.116857\pi\) | |||||||
\(728\) | 1.31371i | 0.0486893i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 14.8284 | 0.548449 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 1.31371i | − 0.0485229i | −0.999706 | − | 0.0242615i | \(-0.992277\pi\) | ||||
0.999706 | − | 0.0242615i | \(-0.00772342\pi\) | |||||||
\(734\) | 1.84062 | 0.0679385 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.24264 | −0.230107 | ||||||||
\(737\) | − 1.17157i | − 0.0431554i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.7279 | −1.13034 | −0.565172 | − | 0.824973i | \(-0.691190\pi\) | ||||
−0.565172 | + | 0.824973i | \(0.691190\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − 4.97056i | − 0.182475i | ||||||||
\(743\) | 38.4853i | 1.41189i | 0.708268 | + | 0.705944i | \(0.249477\pi\) | ||||
−0.708268 | + | 0.705944i | \(0.750523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.4853 | 0.383893 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5.17157i | 0.189091i | ||||||||
\(749\) | 5.45584 | 0.199352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.4853 | −1.62329 | −0.811645 | − | 0.584150i | \(-0.801428\pi\) | ||||
−0.811645 | + | 0.584150i | \(0.801428\pi\) | |||||||
\(752\) | 2.48528i | 0.0906289i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.34315 | 0.0853323 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 4.14214i | − 0.150548i | −0.997163 | − | 0.0752742i | \(-0.976017\pi\) | ||||
0.997163 | − | 0.0752742i | \(-0.0239832\pi\) | |||||||
\(758\) | − 6.18377i | − 0.224605i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 36.6274 | 1.32774 | 0.663871 | − | 0.747847i | \(-0.268912\pi\) | ||||
0.663871 | + | 0.747847i | \(0.268912\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.65685i | 0.0599822i | ||||||||
\(764\) | −24.9706 | −0.903403 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.7157 | 0.495569 | ||||||||
\(767\) | − 10.2426i | − 0.369840i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.9706 | −0.395609 | −0.197804 | − | 0.980242i | \(-0.563381\pi\) | ||||
−0.197804 | + | 0.980242i | \(0.563381\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 28.6274i | 1.03032i | ||||||||
\(773\) | − 6.14214i | − 0.220917i | −0.993881 | − | 0.110459i | \(-0.964768\pi\) | ||||
0.993881 | − | 0.110459i | \(-0.0352320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 5.79899 | 0.208172 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − 6.88730i | − 0.246922i | ||||||||
\(779\) | −30.1421 | −1.07995 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.62742 | −0.165582 | ||||||||
\(782\) | 2.82843i | 0.101144i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 18.9411 | 0.676469 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 5.51472i | − 0.196578i | −0.995158 | − | 0.0982892i | \(-0.968663\pi\) | ||||
0.995158 | − | 0.0982892i | \(-0.0313370\pi\) | |||||||
\(788\) | − 42.0000i | − 1.49619i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.62742 | −0.0934202 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000i | 0.284088i | ||||||||
\(794\) | −11.5147 | −0.408642 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.31371 | −0.259228 | ||||||||
\(797\) | 10.9706i | 0.388597i | 0.980942 | + | 0.194299i | \(0.0622431\pi\) | ||||
−0.980942 | + | 0.194299i | \(0.937757\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 7.17157i | − 0.253237i | ||||||||
\(803\) | 4.97056i | 0.175407i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.24264 | 0.149441 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 12.1421i | − 0.427159i | ||||||||
\(809\) | −45.2548 | −1.59108 | −0.795538 | − | 0.605904i | \(-0.792811\pi\) | ||||
−0.795538 | + | 0.605904i | \(0.792811\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.38478 | 0.294429 | 0.147215 | − | 0.989105i | \(-0.452969\pi\) | ||||
0.147215 | + | 0.989105i | \(0.452969\pi\) | |||||||
\(812\) | 8.56854i | 0.300697i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.05887 | −0.0721635 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 10.4853i | − 0.366834i | ||||||||
\(818\) | − 5.31371i | − 0.185789i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −39.2548 | −1.37000 | −0.685002 | − | 0.728542i | \(-0.740199\pi\) | ||||
−0.685002 | + | 0.728542i | \(0.740199\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.3848i | 1.19858i | 0.800533 | + | 0.599289i | \(0.204550\pi\) | ||||
−0.800533 | + | 0.599289i | \(0.795450\pi\) | |||||||
\(824\) | −27.6152 | −0.962022 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.51472 | −0.122293 | ||||||||
\(827\) | 27.8579i | 0.968713i | 0.874871 | + | 0.484356i | \(0.160946\pi\) | ||||
−0.874871 | + | 0.484356i | \(0.839054\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.02944 | −0.244142 | −0.122071 | − | 0.992521i | \(-0.538954\pi\) | ||||
−0.122071 | + | 0.992521i | \(0.538954\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 4.17157i | − 0.144623i | ||||||||
\(833\) | − 30.4853i | − 1.05625i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.65685 | 0.126475 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.14214i | 0.0739988i | ||||||||
\(839\) | −18.7279 | −0.646560 | −0.323280 | − | 0.946303i | \(-0.604786\pi\) | ||||
−0.323280 | + | 0.946303i | \(0.604786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.00000 | 0.103448 | ||||||||
\(842\) | − 0.426407i | − 0.0146950i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −35.3137 | −1.21555 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 8.82843i | − 0.303348i | ||||||||
\(848\) | 43.4558i | 1.49228i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.0000 | 0.411355 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.4558i | 1.28246i | 0.767347 | + | 0.641232i | \(0.221576\pi\) | ||||
−0.767347 | + | 0.641232i | \(0.778424\pi\) | |||||||
\(854\) | 2.74517 | 0.0939376 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.4437 | 0.356957 | ||||||||
\(857\) | 0.343146i | 0.0117216i | 0.999983 | + | 0.00586082i | \(0.00186557\pi\) | ||||
−0.999983 | + | 0.00586082i | \(0.998134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.7990 | −0.402576 | −0.201288 | − | 0.979532i | \(-0.564513\pi\) | ||||
−0.201288 | + | 0.979532i | \(0.564513\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − 1.49747i | − 0.0510042i | ||||||||
\(863\) | − 19.4558i | − 0.662285i | −0.943581 | − | 0.331142i | \(-0.892566\pi\) | ||||
0.943581 | − | 0.331142i | \(-0.107434\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.51472 | 0.0514722 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.5147i | 0.526604i | ||||||||
\(869\) | 4.97056 | 0.168615 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.00000 | 0.0677674 | ||||||||
\(872\) | 3.17157i | 0.107403i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.00000 | 0.0676510 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 2.68629i | − 0.0907096i | −0.998971 | − | 0.0453548i | \(-0.985558\pi\) | ||||
0.998971 | − | 0.0453548i | \(-0.0144418\pi\) | |||||||
\(878\) | 13.6569i | 0.460897i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.9706 | −1.78462 | −0.892312 | − | 0.451420i | \(-0.850918\pi\) | ||||
−0.892312 | + | 0.451420i | \(0.850918\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 32.2426i | − 1.08505i | −0.840039 | − | 0.542526i | \(-0.817468\pi\) | ||||
0.840039 | − | 0.542526i | \(-0.182532\pi\) | |||||||
\(884\) | −8.82843 | −0.296932 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.72792 | −0.0916463 | ||||||||
\(887\) | 14.3848i | 0.482994i | 0.970402 | + | 0.241497i | \(0.0776383\pi\) | ||||
−0.970402 | + | 0.241497i | \(0.922362\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.79899 | −0.261570 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 48.4264i | 1.62144i | ||||||||
\(893\) | − 2.82843i | − 0.0946497i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.74517 | −0.292155 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 12.0589i | 0.402410i | ||||||||
\(899\) | 57.9411 | 1.93244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 69.9411 | 2.33008 | ||||||||
\(902\) | − 2.14214i | − 0.0713253i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.02944 | −0.167277 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 33.2132i | 1.10283i | 0.834232 | + | 0.551413i | \(0.185911\pi\) | ||||
−0.834232 | + | 0.551413i | \(0.814089\pi\) | |||||||
\(908\) | − 50.5685i | − 1.67818i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 5.17157i | − 0.171154i | ||||||||
\(914\) | −7.45584 | −0.246617 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.51472 | −0.0500477 | ||||||||
\(917\) | − 14.0589i | − 0.464265i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.4853 | 0.543799 | 0.271900 | − | 0.962326i | \(-0.412348\pi\) | ||||
0.271900 | + | 0.962326i | \(0.412348\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 10.9706i | − 0.361296i | ||||||||
\(923\) | − 7.89949i | − 0.260015i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 6.48528 | 0.213120 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 24.9706i | 0.819699i | ||||||||
\(929\) | 11.1716 | 0.366527 | 0.183264 | − | 0.983064i | \(-0.441334\pi\) | ||||
0.183264 | + | 0.983064i | \(0.441334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −21.5563 | −0.706481 | ||||||||
\(932\) | − 45.0294i | − 1.47499i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.38478 | 0.143474 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 10.9706i | − 0.358393i | −0.983813 | − | 0.179196i | \(-0.942650\pi\) | ||||
0.983813 | − | 0.179196i | \(-0.0573497\pi\) | |||||||
\(938\) | − 0.686292i | − 0.0224082i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 54.7696 | 1.78544 | 0.892718 | − | 0.450615i | \(-0.148795\pi\) | ||||
0.892718 | + | 0.450615i | \(0.148795\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.4853i | 0.406577i | ||||||||
\(944\) | 30.7279 | 1.00011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.745166 | 0.0242274 | ||||||||
\(947\) | − 45.1127i | − 1.46597i | −0.680247 | − | 0.732983i | \(-0.738128\pi\) | ||||
0.680247 | − | 0.732983i | \(-0.261872\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.48528 | −0.275444 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.34315i | 0.205583i | ||||||||
\(953\) | 55.2548i | 1.78988i | 0.446187 | + | 0.894940i | \(0.352782\pi\) | ||||
−0.446187 | + | 0.894940i | \(0.647218\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.07107 | −0.0346408 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 2.18377i | − 0.0705543i | ||||||||
\(959\) | −4.40202 | −0.142149 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9117 | 2.38425 | ||||||||
\(962\) | − 3.51472i | − 0.113319i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.54416 | 0.146357 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 19.9411i | 0.641263i | 0.947204 | + | 0.320632i | \(0.103895\pi\) | ||||
−0.947204 | + | 0.320632i | \(0.896105\pi\) | |||||||
\(968\) | − 16.8995i | − 0.543170i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 12.2843 | 0.394221 | 0.197111 | − | 0.980381i | \(-0.436844\pi\) | ||||
0.197111 | + | 0.980381i | \(0.436844\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3431i | 0.331586i | ||||||||
\(974\) | 9.51472 | 0.304871 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −24.0000 | −0.768221 | ||||||||
\(977\) | − 56.4853i | − 1.80712i | −0.428457 | − | 0.903562i | \(-0.640943\pi\) | ||||
0.428457 | − | 0.903562i | \(-0.359057\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.51472 | −0.112331 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 4.48528i | − 0.143131i | ||||||||
\(983\) | 34.9706i | 1.11539i | 0.830047 | + | 0.557694i | \(0.188314\pi\) | ||||
−0.830047 | + | 0.557694i | \(0.811686\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 11.3137 | 0.360302 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.24264i | 0.198605i | ||||||||
\(989\) | −4.34315 | −0.138104 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.0294 | 0.477426 | 0.238713 | − | 0.971090i | \(-0.423275\pi\) | ||||
0.238713 | + | 0.971090i | \(0.423275\pi\) | |||||||
\(992\) | 45.2132i | 1.43552i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.71068 | −0.0859775 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 23.1716i | − 0.733851i | −0.930250 | − | 0.366926i | \(-0.880410\pi\) | ||||
0.930250 | − | 0.366926i | \(-0.119590\pi\) | |||||||
\(998\) | − 4.32590i | − 0.136934i | ||||||||
\(999\) | 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 | 2925.2.c.r.2224.3 | 4 | ||
3.2 | odd | 2 | 325.2.b.f.274.2 | 4 | |||
5.2 | odd | 4 | 585.2.a.m.1.1 | 2 | |||
5.3 | odd | 4 | 2925.2.a.u.1.2 | 2 | |||
5.4 | even | 2 | inner | 2925.2.c.r.2224.2 | 4 | ||
15.2 | even | 4 | 65.2.a.b.1.2 | ✓ | 2 | ||
15.8 | even | 4 | 325.2.a.i.1.1 | 2 | |||
15.14 | odd | 2 | 325.2.b.f.274.3 | 4 | |||
20.7 | even | 4 | 9360.2.a.cd.1.2 | 2 | |||
60.23 | odd | 4 | 5200.2.a.bu.1.2 | 2 | |||
60.47 | odd | 4 | 1040.2.a.j.1.1 | 2 | |||
65.12 | odd | 4 | 7605.2.a.x.1.2 | 2 | |||
105.62 | odd | 4 | 3185.2.a.j.1.2 | 2 | |||
120.77 | even | 4 | 4160.2.a.bf.1.1 | 2 | |||
120.107 | odd | 4 | 4160.2.a.z.1.2 | 2 | |||
165.32 | odd | 4 | 7865.2.a.j.1.1 | 2 | |||
195.2 | odd | 12 | 845.2.m.f.316.3 | 8 | |||
195.17 | even | 12 | 845.2.e.c.146.2 | 4 | |||
195.32 | odd | 12 | 845.2.m.f.361.2 | 8 | |||
195.38 | even | 4 | 4225.2.a.r.1.2 | 2 | |||
195.47 | odd | 4 | 845.2.c.b.506.3 | 4 | |||
195.62 | even | 12 | 845.2.e.c.191.2 | 4 | |||
195.77 | even | 4 | 845.2.a.g.1.1 | 2 | |||
195.107 | even | 12 | 845.2.e.h.191.1 | 4 | |||
195.122 | odd | 4 | 845.2.c.b.506.2 | 4 | |||
195.137 | odd | 12 | 845.2.m.f.361.3 | 8 | |||
195.152 | even | 12 | 845.2.e.h.146.1 | 4 | |||
195.167 | odd | 12 | 845.2.m.f.316.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
65.2.a.b.1.2 | ✓ | 2 | 15.2 | even | 4 | ||
325.2.a.i.1.1 | 2 | 15.8 | even | 4 | |||
325.2.b.f.274.2 | 4 | 3.2 | odd | 2 | |||
325.2.b.f.274.3 | 4 | 15.14 | odd | 2 | |||
585.2.a.m.1.1 | 2 | 5.2 | odd | 4 | |||
845.2.a.g.1.1 | 2 | 195.77 | even | 4 | |||
845.2.c.b.506.2 | 4 | 195.122 | odd | 4 | |||
845.2.c.b.506.3 | 4 | 195.47 | odd | 4 | |||
845.2.e.c.146.2 | 4 | 195.17 | even | 12 | |||
845.2.e.c.191.2 | 4 | 195.62 | even | 12 | |||
845.2.e.h.146.1 | 4 | 195.152 | even | 12 | |||
845.2.e.h.191.1 | 4 | 195.107 | even | 12 | |||
845.2.m.f.316.2 | 8 | 195.167 | odd | 12 | |||
845.2.m.f.316.3 | 8 | 195.2 | odd | 12 | |||
845.2.m.f.361.2 | 8 | 195.32 | odd | 12 | |||
845.2.m.f.361.3 | 8 | 195.137 | odd | 12 | |||
1040.2.a.j.1.1 | 2 | 60.47 | odd | 4 | |||
2925.2.a.u.1.2 | 2 | 5.3 | odd | 4 | |||
2925.2.c.r.2224.2 | 4 | 5.4 | even | 2 | inner | ||
2925.2.c.r.2224.3 | 4 | 1.1 | even | 1 | trivial | ||
3185.2.a.j.1.2 | 2 | 105.62 | odd | 4 | |||
4160.2.a.z.1.2 | 2 | 120.107 | odd | 4 | |||
4160.2.a.bf.1.1 | 2 | 120.77 | even | 4 | |||
4225.2.a.r.1.2 | 2 | 195.38 | even | 4 | |||
5200.2.a.bu.1.2 | 2 | 60.23 | odd | 4 | |||
7605.2.a.x.1.2 | 2 | 65.12 | odd | 4 | |||
7865.2.a.j.1.1 | 2 | 165.32 | odd | 4 | |||
9360.2.a.cd.1.2 | 2 | 20.7 | even | 4 |