Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4032,2,Mod(1889,4032)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4032, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4032.1889");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4032 = 2^{6} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4032.i (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.1956820950\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1889.5 | ||
Root | \(-0.437016 + 0.437016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4032.1889 |
Dual form | 4032.2.i.a.1889.2 |
$q$-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 \(\left(\mathbb{Z}/4032\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(1793\) | \(3781\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000i | 0.894427i | 0.894427 | + | 0.447214i | \(0.147584\pi\) | ||||
−0.894427 | + | 0.447214i | \(0.852416\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | − | 1.41421i | −0.845154 | − | 0.534522i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.41421 | 0.426401 | 0.213201 | − | 0.977008i | \(-0.431611\pi\) | ||||
0.213201 | + | 0.977008i | \(0.431611\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.47214 | 1.08465 | 0.542326 | − | 0.840168i | \(-0.317544\pi\) | ||||
0.542326 | + | 0.840168i | \(0.317544\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.32456 | −1.45095 | −0.725476 | − | 0.688247i | \(-0.758380\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.16228i | − | 0.659380i | −0.944089 | − | 0.329690i | \(-0.893056\pi\) | ||
0.944089 | − | 0.329690i | \(-0.106944\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.16228 | −0.587220 | −0.293610 | − | 0.955925i | \(-0.594857\pi\) | ||||
−0.293610 | + | 0.955925i | \(0.594857\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685i | 1.01600i | 0.861357 | + | 0.508001i | \(0.169615\pi\) | ||||
−0.861357 | + | 0.508001i | \(0.830385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.82843 | − | 4.47214i | 0.478091 | − | 0.755929i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.47214i | 0.735215i | 0.929981 | + | 0.367607i | \(0.119823\pi\) | ||||
−0.929981 | + | 0.367607i | \(0.880177\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47214 | 0.698430 | 0.349215 | − | 0.937043i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937043i | \(0.386448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.00000i | 0.609994i | 0.952353 | + | 0.304997i | \(0.0986555\pi\) | ||||
−0.952353 | + | 0.304997i | \(0.901344\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | + | 6.32456i | 0.428571 | + | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.48683 | −1.30312 | −0.651558 | − | 0.758599i | \(-0.725884\pi\) | ||||
−0.651558 | + | 0.758599i | \(0.725884\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.82843i | 0.381385i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.94427i | 1.16445i | 0.813029 | + | 0.582223i | \(0.197817\pi\) | ||||
−0.813029 | + | 0.582223i | \(0.802183\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.48528 | 1.08643 | 0.543214 | − | 0.839594i | \(-0.317207\pi\) | ||||
0.543214 | + | 0.839594i | \(0.317207\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.00000i | − | 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 9.48683i | − | 1.12588i | −0.826498 | − | 0.562940i | \(-0.809670\pi\) | ||
0.826498 | − | 0.562940i | \(-0.190330\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.32456i | − | 0.740233i | −0.928985 | − | 0.370117i | \(-0.879318\pi\) | ||
0.928985 | − | 0.370117i | \(-0.120682\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.16228 | − | 2.00000i | −0.360375 | − | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.94427 | −1.00631 | −0.503155 | − | 0.864196i | \(-0.667827\pi\) | ||||
−0.503155 | + | 0.864196i | \(0.667827\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.94427i | 0.970143i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.4164 | −1.42214 | −0.711068 | − | 0.703123i | \(-0.751788\pi\) | ||||
−0.711068 | + | 0.703123i | \(0.751788\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 12.6491i | − | 1.29777i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.32456i | 0.642161i | 0.947052 | + | 0.321081i | \(0.104046\pi\) | ||||
−0.947052 | + | 0.321081i | \(0.895954\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.0000i | 1.79107i | 0.444994 | + | 0.895533i | \(0.353206\pi\) | ||||
−0.444994 | + | 0.895533i | \(0.646794\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.07107 | −0.683586 | −0.341793 | − | 0.939775i | \(-0.611034\pi\) | ||||
−0.341793 | + | 0.939775i | \(0.611034\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.47214i | 0.428353i | 0.976795 | + | 0.214176i | \(0.0687068\pi\) | ||||
−0.976795 | + | 0.214176i | \(0.931293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 12.7279i | − | 1.19734i | −0.800995 | − | 0.598671i | \(-0.795696\pi\) | ||
0.800995 | − | 0.598671i | \(-0.204304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.32456 | 0.589768 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −10.0000 | − | 6.32456i | −0.916698 | − | 0.579771i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.00000 | −0.818182 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000i | 1.07331i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.94427 | −0.793676 | −0.396838 | − | 0.917889i | \(-0.629892\pi\) | ||||
−0.396838 | + | 0.917889i | \(0.629892\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 14.1421 | + | 8.94427i | 1.22628 | + | 0.775567i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.89949i | 0.845771i | 0.906183 | + | 0.422885i | \(0.138983\pi\) | ||||
−0.906183 | + | 0.422885i | \(0.861017\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.6491 | 1.07288 | 0.536442 | − | 0.843937i | \(-0.319768\pi\) | ||||
0.536442 | + | 0.843937i | \(0.319768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.32456i | − | 0.525226i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −22.1359 | −1.81345 | −0.906724 | − | 0.421725i | \(-0.861425\pi\) | ||||
−0.906724 | + | 0.421725i | \(0.861425\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.4164 | −1.09181 | −0.545906 | − | 0.837846i | \(-0.683814\pi\) | ||||
−0.545906 | + | 0.837846i | \(0.683814\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.3137 | −0.908739 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.1421 | −1.12867 | −0.564333 | − | 0.825547i | \(-0.690866\pi\) | ||||
−0.564333 | + | 0.825547i | \(0.690866\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.47214 | + | 7.07107i | −0.352454 | + | 0.557278i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.00000i | − | 0.469956i | −0.972001 | − | 0.234978i | \(-0.924498\pi\) | ||
0.972001 | − | 0.234978i | \(-0.0755019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 6.00000i | − | 0.456172i | −0.973641 | − | 0.228086i | \(-0.926753\pi\) | ||
0.973641 | − | 0.228086i | \(-0.0732467\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.23607 | − | 1.41421i | −0.169031 | − | 0.106904i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.24264 | 0.317110 | 0.158555 | − | 0.987350i | \(-0.449317\pi\) | ||||
0.158555 | + | 0.987350i | \(0.449317\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.65685 | 0.420471 | 0.210235 | − | 0.977651i | \(-0.432577\pi\) | ||||
0.210235 | + | 0.977651i | \(0.432577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.94427 | −0.657596 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.32456 | 0.462497 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 15.8114i | − | 1.14407i | −0.820229 | − | 0.572036i | \(-0.806154\pi\) | ||
0.820229 | − | 0.572036i | \(-0.193846\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −22.1359 | −1.57712 | −0.788560 | − | 0.614957i | \(-0.789173\pi\) | ||||
−0.788560 | + | 0.614957i | \(0.789173\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.4558i | 1.80452i | 0.431196 | + | 0.902258i | \(0.358092\pi\) | ||||
−0.431196 | + | 0.902258i | \(0.641908\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 7.07107 | + | 4.47214i | 0.496292 | + | 0.313882i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.94427i | 0.624695i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.94427 | −0.618688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 12.0000i | 0.826114i | 0.910705 | + | 0.413057i | \(0.135539\pi\) | ||||
−0.910705 | + | 0.413057i | \(0.864461\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.00000 | −0.545595 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.00000 | − | 12.6491i | 0.543075 | − | 0.858678i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.7990i | 1.32584i | 0.748691 | + | 0.662919i | \(0.230683\pi\) | ||||
−0.748691 | + | 0.662919i | \(0.769317\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 17.8885i | − | 1.18730i | −0.804722 | − | 0.593652i | \(-0.797686\pi\) | ||
0.804722 | − | 0.593652i | \(-0.202314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9706 | 1.12145 | 0.560723 | − | 0.828003i | \(-0.310523\pi\) | ||||
0.560723 | + | 0.828003i | \(0.310523\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.41421i | 0.0926482i | 0.998926 | + | 0.0463241i | \(0.0147507\pi\) | ||||
−0.998926 | + | 0.0463241i | \(0.985249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 16.0000i | − | 1.04372i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.48683i | − | 0.613652i | −0.951766 | − | 0.306826i | \(-0.900733\pi\) | ||
0.951766 | − | 0.306826i | \(-0.0992670\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.32456i | 0.407400i | 0.979033 | + | 0.203700i | \(0.0652968\pi\) | ||||
−0.979033 | + | 0.203700i | \(0.934703\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.6491 | + | 6.00000i | −0.808122 | + | 0.383326i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 8.94427i | − | 0.564557i | −0.959332 | − | 0.282279i | \(-0.908910\pi\) | ||
0.959332 | − | 0.282279i | \(-0.0910903\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.47214i | − | 0.281161i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 31.3050 | 1.95275 | 0.976375 | − | 0.216085i | \(-0.0693287\pi\) | ||||
0.976375 | + | 0.216085i | \(0.0693287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.32456 | − | 10.0000i | 0.392989 | − | 0.621370i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 9.48683i | − | 0.584983i | −0.956268 | − | 0.292492i | \(-0.905516\pi\) | ||
0.956268 | − | 0.292492i | \(-0.0944843\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 18.9737i | − | 1.16554i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.00000i | 0.365826i | 0.983129 | + | 0.182913i | \(0.0585527\pi\) | ||||
−0.983129 | + | 0.182913i | \(0.941447\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 22.6274i | − | 1.37452i | −0.726413 | − | 0.687259i | \(-0.758814\pi\) | ||
0.726413 | − | 0.687259i | \(-0.241186\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.41421 | 0.0852803 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8328i | 1.61223i | 0.591761 | + | 0.806114i | \(0.298433\pi\) | ||||
−0.591761 | + | 0.806114i | \(0.701567\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 15.5563i | − | 0.928014i | −0.885832 | − | 0.464007i | \(-0.846411\pi\) | ||
0.885832 | − | 0.464007i | \(-0.153589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.9737 | −1.12787 | −0.563934 | − | 0.825820i | \(-0.690713\pi\) | ||||
−0.563934 | + | 0.825820i | \(0.690713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −10.0000 | − | 6.32456i | −0.590281 | − | 0.373327i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.00000 | 0.176471 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.0000i | 0.817889i | 0.912559 | + | 0.408944i | \(0.134103\pi\) | ||||
−0.912559 | + | 0.408944i | \(0.865897\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −17.8885 | −1.04151 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.65685 | − | 8.94427i | 0.326056 | − | 0.515539i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 16.9706i | 0.971732i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −31.6228 | −1.80481 | −0.902404 | − | 0.430892i | \(-0.858199\pi\) | ||||
−0.902404 | + | 0.430892i | \(0.858199\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.0000 | 0.680458 | 0.340229 | − | 0.940343i | \(-0.389495\pi\) | ||||
0.340229 | + | 0.940343i | \(0.389495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6491i | 0.714970i | 0.933919 | + | 0.357485i | \(0.116366\pi\) | ||||
−0.933919 | + | 0.357485i | \(0.883634\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.48683 | 0.532834 | 0.266417 | − | 0.963858i | \(-0.414160\pi\) | ||||
0.266417 | + | 0.963858i | \(0.414160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.47214 | −0.250392 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −28.2843 | −1.57378 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.8885 | + | 11.3137i | 0.986227 | + | 0.623745i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.0000i | 0.659580i | 0.944054 | + | 0.329790i | \(0.106978\pi\) | ||||
−0.944054 | + | 0.329790i | \(0.893022\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000i | 0.433224i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23607 | − | 18.3848i | 0.120736 | − | 0.992685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 35.3553 | 1.89797 | 0.948987 | − | 0.315315i | \(-0.102110\pi\) | ||||
0.948987 | + | 0.315315i | \(0.102110\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.82843 | −0.151402 | −0.0757011 | − | 0.997131i | \(-0.524119\pi\) | ||||
−0.0757011 | + | 0.997131i | \(0.524119\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.47214 | −0.238028 | −0.119014 | − | 0.992893i | \(-0.537973\pi\) | ||||
−0.119014 | + | 0.992893i | \(0.537973\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 18.9737 | 1.00702 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.48683i | − | 0.500696i | −0.968156 | − | 0.250348i | \(-0.919455\pi\) | ||
0.968156 | − | 0.250348i | \(-0.0805450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.0000 | 1.10526 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 12.6491 | 0.662085 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.1421i | 0.738213i | 0.929387 | + | 0.369107i | \(0.120336\pi\) | ||||
−0.929387 | + | 0.369107i | \(0.879664\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.2132 | + | 13.4164i | 1.10133 | + | 0.696545i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000i | 1.02733i | 0.857991 | + | 0.513665i | \(0.171713\pi\) | ||||
−0.857991 | + | 0.513665i | \(0.828287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −24.0000 | −1.22634 | −0.613171 | − | 0.789950i | \(-0.710106\pi\) | ||||
−0.613171 | + | 0.789950i | \(0.710106\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | − | 6.32456i | 0.203859 | − | 0.322329i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −22.1359 | −1.12234 | −0.561168 | − | 0.827702i | \(-0.689648\pi\) | ||||
−0.561168 | + | 0.827702i | \(0.689648\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 14.1421i | − | 0.715199i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 17.8885i | − | 0.900070i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.82843 | −0.141955 | −0.0709773 | − | 0.997478i | \(-0.522612\pi\) | ||||
−0.0709773 | + | 0.997478i | \(0.522612\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 15.5563i | − | 0.776847i | −0.921481 | − | 0.388424i | \(-0.873020\pi\) | ||
0.921481 | − | 0.388424i | \(-0.126980\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.32456i | 0.313497i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.6228i | 1.56365i | 0.623501 | + | 0.781823i | \(0.285710\pi\) | ||||
−0.623501 | + | 0.781823i | \(0.714290\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.6491 | − | 20.0000i | 0.622422 | − | 0.984136i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8328i | 1.31087i | 0.755252 | + | 0.655434i | \(0.227514\pi\) | ||||
−0.755252 | + | 0.655434i | \(0.772486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8328i | 1.30775i | 0.756602 | + | 0.653876i | \(0.226858\pi\) | ||||
−0.756602 | + | 0.653876i | \(0.773142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.47214 | 0.216930 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −18.9737 | − | 12.0000i | −0.918200 | − | 0.580721i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.8114i | 0.761608i | 0.924656 | + | 0.380804i | \(0.124353\pi\) | ||||
−0.924656 | + | 0.380804i | \(0.875647\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.6491i | 0.607877i | 0.952692 | + | 0.303939i | \(0.0983018\pi\) | ||||
−0.952692 | + | 0.303939i | \(0.901698\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 20.0000i | 0.956730i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4558i | 1.21494i | 0.794342 | + | 0.607471i | \(0.207816\pi\) | ||||
−0.794342 | + | 0.607471i | \(0.792184\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.07107 | −0.335957 | −0.167978 | − | 0.985791i | \(-0.553724\pi\) | ||||
−0.167978 | + | 0.985791i | \(0.553724\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 26.8328i | − | 1.27200i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.5269i | − | 1.53504i | −0.641025 | − | 0.767520i | \(-0.721491\pi\) | ||
0.641025 | − | 0.767520i | \(-0.278509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.32456 | 0.297812 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.00000 | 0.374224 | 0.187112 | − | 0.982339i | \(-0.440087\pi\) | ||||
0.187112 | + | 0.982339i | \(0.440087\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 30.0000i | − | 1.39724i | −0.715493 | − | 0.698620i | \(-0.753798\pi\) | ||
0.715493 | − | 0.698620i | \(-0.246202\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.8328 | 1.24703 | 0.623513 | − | 0.781813i | \(-0.285705\pi\) | ||||
0.623513 | + | 0.781813i | \(0.285705\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.94427i | 0.413892i | 0.978352 | + | 0.206946i | \(0.0663524\pi\) | ||||
−0.978352 | + | 0.206946i | \(0.933648\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.82843 | + | 4.47214i | −0.130605 | + | 0.206504i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.65685i | 0.260102i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.32456 | −0.290191 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.00000 | 0.182765 | 0.0913823 | − | 0.995816i | \(-0.470871\pi\) | ||||
0.0913823 | + | 0.995816i | \(0.470871\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −12.6491 | −0.574367 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.4164 | 0.607955 | 0.303978 | − | 0.952679i | \(-0.401685\pi\) | ||||
0.303978 | + | 0.952679i | \(0.401685\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −26.8701 | −1.21263 | −0.606314 | − | 0.795225i | \(-0.707353\pi\) | ||||
−0.606314 | + | 0.795225i | \(0.707353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.1421 | −0.636930 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −13.4164 | + | 21.2132i | −0.601808 | + | 0.951542i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000i | 0.895323i | 0.894203 | + | 0.447661i | \(0.147743\pi\) | ||||
−0.894203 | + | 0.447661i | \(0.852257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.0000 | 0.713405 | 0.356702 | − | 0.934218i | \(-0.383901\pi\) | ||||
0.356702 | + | 0.934218i | \(0.383901\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0000 | −1.60198 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 14.0000i | − | 0.620539i | −0.950649 | − | 0.310270i | \(-0.899581\pi\) | ||
0.950649 | − | 0.310270i | \(-0.100419\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.94427 | + | 14.1421i | −0.395671 | + | 0.625611i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.3137 | −0.497576 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.47214 | 0.195928 | 0.0979639 | − | 0.995190i | \(-0.468767\pi\) | ||||
0.0979639 | + | 0.995190i | \(0.468767\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.2982i | 1.10201i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.0000 | 0.565217 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 14.1421i | − | 0.611418i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.24264 | + | 8.94427i | 0.182743 | + | 0.385257i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 26.8328i | − | 1.15363i | −0.816874 | − | 0.576816i | \(-0.804295\pi\) | ||
0.816874 | − | 0.576816i | \(-0.195705\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −8.94427 | −0.383131 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.0000i | 0.940652i | 0.882493 | + | 0.470326i | \(0.155864\pi\) | ||||
−0.882493 | + | 0.470326i | \(0.844136\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 20.0000 | 0.852029 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 20.0000 | + | 12.6491i | 0.850487 | + | 0.537895i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.7851 | 1.47389 | 0.736945 | − | 0.675953i | \(-0.236268\pi\) | ||||
0.736945 | + | 0.675953i | \(0.236268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 35.7771i | 1.50782i | 0.656975 | + | 0.753912i | \(0.271836\pi\) | ||||
−0.656975 | + | 0.753912i | \(0.728164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.4558 | 1.07094 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 24.0416i | − | 1.00788i | −0.863739 | − | 0.503939i | \(-0.831884\pi\) | ||
0.863739 | − | 0.503939i | \(-0.168116\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 22.0000i | − | 0.920671i | −0.887745 | − | 0.460336i | \(-0.847729\pi\) | ||
0.887745 | − | 0.460336i | \(-0.152271\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.16228i | − | 0.131876i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 25.2982i | − | 1.05318i | −0.850120 | − | 0.526589i | \(-0.823471\pi\) | ||
0.850120 | − | 0.526589i | \(-0.176529\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.4164 | −0.555651 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 8.94427i | − | 0.369170i | −0.982817 | − | 0.184585i | \(-0.940906\pi\) | ||
0.982817 | − | 0.184585i | \(-0.0590940\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 35.7771i | − | 1.47417i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.3607 | −0.918243 | −0.459122 | − | 0.888373i | \(-0.651836\pi\) | ||||
−0.459122 | + | 0.888373i | \(0.651836\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.6491 | − | 20.0000i | 0.518563 | − | 0.819920i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.48683i | 0.387621i | 0.981039 | + | 0.193811i | \(0.0620848\pi\) | ||||
−0.981039 | + | 0.193811i | \(0.937915\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.6491i | 0.515968i | 0.966149 | + | 0.257984i | \(0.0830582\pi\) | ||||
−0.966149 | + | 0.257984i | \(0.916942\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 18.0000i | − | 0.731804i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 25.4558i | − | 1.03322i | −0.856221 | − | 0.516610i | \(-0.827194\pi\) | ||
0.856221 | − | 0.516610i | \(-0.172806\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 17.8885i | − | 0.722511i | −0.932467 | − | 0.361256i | \(-0.882348\pi\) | ||
0.932467 | − | 0.361256i | \(-0.117652\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 35.3553i | − | 1.42335i | −0.702508 | − | 0.711676i | \(-0.747936\pi\) | ||
0.702508 | − | 0.711676i | \(-0.252064\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 12.6491 | 0.508411 | 0.254205 | − | 0.967150i | \(-0.418186\pi\) | ||||
0.254205 | + | 0.967150i | \(0.418186\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 30.0000 | + | 18.9737i | 1.20192 | + | 0.760164i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 20.0000i | 0.797452i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.8328 | 1.06820 | 0.534099 | − | 0.845422i | \(-0.320651\pi\) | ||||
0.534099 | + | 0.845422i | \(0.320651\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 17.8885i | − | 0.709885i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 43.8406i | 1.73160i | 0.500390 | + | 0.865800i | \(0.333190\pi\) | ||||
−0.500390 | + | 0.865800i | \(0.666810\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.2719 | 1.74591 | 0.872956 | − | 0.487798i | \(-0.162200\pi\) | ||||
0.872956 | + | 0.487798i | \(0.162200\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.00000 | −0.314512 | −0.157256 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157256 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 12.6491i | 0.496521i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 47.4342 | 1.85624 | 0.928121 | − | 0.372278i | \(-0.121423\pi\) | ||||
0.928121 | + | 0.372278i | \(0.121423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −46.6690 | −1.81797 | −0.908984 | − | 0.416831i | \(-0.863141\pi\) | ||||
−0.908984 | + | 0.416831i | \(0.863141\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.48528 | −0.330039 | −0.165020 | − | 0.986290i | \(-0.552769\pi\) | ||||
−0.165020 | + | 0.986290i | \(0.552769\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −17.8885 | + | 28.2843i | −0.693688 | + | 1.09682i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.0000i | 0.387202i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000 | 0.463255 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −36.0000 | −1.38770 | −0.693849 | − | 0.720121i | \(-0.744086\pi\) | ||||
−0.693849 | + | 0.720121i | \(0.744086\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.00000i | 0.0768662i | 0.999261 | + | 0.0384331i | \(0.0122367\pi\) | ||||
−0.999261 | + | 0.0384331i | \(0.987763\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.94427 | − | 14.1421i | 0.343250 | − | 0.542725i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 41.0122 | 1.56929 | 0.784644 | − | 0.619947i | \(-0.212846\pi\) | ||||
0.784644 | + | 0.619947i | \(0.212846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −19.7990 | −0.756481 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.2982 | −0.962390 | −0.481195 | − | 0.876614i | \(-0.659797\pi\) | ||||
−0.481195 | + | 0.876614i | \(0.659797\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.2982i | 0.959616i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.0000 | 0.757554 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 41.1096 | 1.55269 | 0.776344 | − | 0.630309i | \(-0.217072\pi\) | ||||
0.776344 | + | 0.630309i | \(0.217072\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 28.2843i | − | 1.06676i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.4558 | − | 40.2492i | 0.957366 | − | 1.51373i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 40.2492i | 1.51159i | 0.654808 | + | 0.755796i | \(0.272750\pi\) | ||||
−0.654808 | + | 0.755796i | \(0.727250\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 17.8885 | 0.669931 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 20.0000 | 0.745874 | 0.372937 | − | 0.927857i | \(-0.378351\pi\) | ||||
0.372937 | + | 0.927857i | \(0.378351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.16228 | −0.117444 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 16.9706i | − | 0.629403i | −0.949191 | − | 0.314702i | \(-0.898096\pi\) | ||
0.949191 | − | 0.314702i | \(-0.101904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 17.8885i | 0.661632i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −50.9117 | −1.88047 | −0.940233 | − | 0.340532i | \(-0.889393\pi\) | ||||
−0.940233 | + | 0.340532i | \(0.889393\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2.82843i | − | 0.104186i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 10.0000i | − | 0.367856i | −0.982940 | − | 0.183928i | \(-0.941119\pi\) | ||
0.982940 | − | 0.183928i | \(-0.0588813\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.4605i | 1.04411i | 0.852910 | + | 0.522057i | \(0.174835\pi\) | ||||
−0.852910 | + | 0.522057i | \(0.825165\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 44.2719i | − | 1.62200i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 15.8114 | + | 10.0000i | 0.577736 | + | 0.365392i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.1935 | 1.79510 | 0.897548 | − | 0.440917i | \(-0.145347\pi\) | ||||
0.897548 | + | 0.440917i | \(0.145347\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 26.8328i | − | 0.976546i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 22.3607i | − | 0.812713i | −0.913715 | − | 0.406356i | \(-0.866799\pi\) | ||
0.913715 | − | 0.406356i | \(-0.133201\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13.4164 | −0.486344 | −0.243172 | − | 0.969983i | \(-0.578188\pi\) | ||||
−0.243172 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.32456 | − | 10.0000i | 0.228964 | − | 0.362024i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 37.9473i | − | 1.36842i | −0.729287 | − | 0.684208i | \(-0.760148\pi\) | ||
0.729287 | − | 0.684208i | \(-0.239852\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 46.0000i | − | 1.65451i | −0.561830 | − | 0.827253i | \(-0.689903\pi\) | ||
0.561830 | − | 0.827253i | \(-0.310097\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685i | 0.203200i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.2843 | −1.01339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 13.4164i | − | 0.480077i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 28.2843i | − | 1.00951i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.0000 | + | 28.4605i | −0.640006 | + | 1.01194i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 42.0000i | − | 1.48772i | −0.668338 | − | 0.743858i | \(-0.732994\pi\) | ||
0.668338 | − | 0.743858i | \(-0.267006\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −35.7771 | −1.26570 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 8.94427i | − | 0.315637i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.1421 | − | 8.94427i | −0.498445 | − | 0.315244i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0416i | 0.845259i | 0.906303 | + | 0.422629i | \(0.138893\pi\) | ||||
−0.906303 | + | 0.422629i | \(0.861107\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.6491 | 0.444170 | 0.222085 | − | 0.975027i | \(-0.428714\pi\) | ||||
0.222085 | + | 0.975027i | \(0.428714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 25.2982i | − | 0.885073i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.48683 | 0.331093 | 0.165546 | − | 0.986202i | \(-0.447061\pi\) | ||||
0.165546 | + | 0.986202i | \(0.447061\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 44.7214 | 1.55889 | 0.779444 | − | 0.626472i | \(-0.215502\pi\) | ||||
0.779444 | + | 0.626472i | \(0.215502\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.5269 | −1.13107 | −0.565536 | − | 0.824724i | \(-0.691331\pi\) | ||||
−0.565536 | + | 0.824724i | \(0.691331\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.3137 | 0.392941 | 0.196471 | − | 0.980510i | \(-0.437052\pi\) | ||||
0.196471 | + | 0.980510i | \(0.437052\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 13.4164 | + | 28.2843i | 0.464851 | + | 0.979992i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 24.0000i | − | 0.830554i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −36.0000 | −1.24286 | −0.621429 | − | 0.783470i | \(-0.713448\pi\) | ||||
−0.621429 | + | 0.783470i | \(0.713448\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.0000 | −0.655172 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 26.0000i | − | 0.894427i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.1246 | + | 12.7279i | 0.691490 | + | 0.437337i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.1421 | 0.484786 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.0833 | 1.64634 | 0.823170 | − | 0.567795i | \(-0.192204\pi\) | ||||
0.823170 | + | 0.567795i | \(0.192204\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 40.2492 | 1.37489 | 0.687444 | − | 0.726238i | \(-0.258733\pi\) | ||||
0.687444 | + | 0.726238i | \(0.258733\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.6228 | −1.07896 | −0.539478 | − | 0.842000i | \(-0.681378\pi\) | ||||
−0.539478 | + | 0.842000i | \(0.681378\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.8114i | 0.538226i | 0.963109 | + | 0.269113i | \(0.0867305\pi\) | ||||
−0.963109 | + | 0.269113i | \(0.913270\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0000 | 0.408012 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.6491 | −0.429092 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.9706 | − | 26.8328i | 0.573710 | − | 0.907115i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 53.6656i | − | 1.81216i | −0.423107 | − | 0.906080i | \(-0.639061\pi\) | ||
0.423107 | − | 0.906080i | \(-0.360939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 22.3607 | 0.753350 | 0.376675 | − | 0.926345i | \(-0.377067\pi\) | ||||
0.376675 | + | 0.926345i | \(0.377067\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.0000i | 1.48072i | 0.672212 | + | 0.740359i | \(0.265344\pi\) | ||||
−0.672212 | + | 0.740359i | \(0.734656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 52.0000 | 1.74599 | 0.872995 | − | 0.487730i | \(-0.162175\pi\) | ||||
0.872995 | + | 0.487730i | \(0.162175\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | + | 12.6491i | 0.670778 | + | 0.424238i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 50.5964 | 1.69315 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.48528i | 0.283632i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 17.8885i | − | 0.596616i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.4264 | −1.41343 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.3137i | 0.376080i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 52.0000i | − | 1.72663i | −0.504664 | − | 0.863316i | \(-0.668384\pi\) | ||
0.504664 | − | 0.863316i | \(-0.331616\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47.4342i | 1.57156i | 0.618504 | + | 0.785782i | \(0.287739\pi\) | ||||
−0.618504 | + | 0.785782i | \(0.712261\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.3607 | 0.737611 | 0.368805 | − | 0.929507i | \(-0.379767\pi\) | ||||
0.368805 | + | 0.929507i | \(0.379767\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.47214i | 0.147043i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −49.1935 | −1.61399 | −0.806993 | − | 0.590561i | \(-0.798907\pi\) | ||||
−0.806993 | + | 0.590561i | \(0.798907\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −18.9737 | − | 40.0000i | −0.621837 | − | 1.31095i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.6491i | 0.413670i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.9473i | 1.23969i | 0.784726 | + | 0.619843i | \(0.212804\pi\) | ||||
−0.784726 | + | 0.619843i | \(0.787196\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 30.0000i | − | 0.977972i | −0.872292 | − | 0.488986i | \(-0.837367\pi\) | ||
0.872292 | − | 0.488986i | \(-0.162633\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 14.1421i | − | 0.460531i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.3848 | 0.597425 | 0.298712 | − | 0.954343i | \(-0.403443\pi\) | ||||
0.298712 | + | 0.954343i | \(0.403443\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 35.3553i | − | 1.14527i | −0.819810 | − | 0.572636i | \(-0.805921\pi\) | ||
0.819810 | − | 0.572636i | \(-0.194079\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 31.6228 | 1.02329 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0000 | − | 22.1359i | 0.452084 | − | 0.714807i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.00000i | 0.257529i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.8328 | 0.862885 | 0.431443 | − | 0.902140i | \(-0.358005\pi\) | ||||
0.431443 | + | 0.902140i | \(0.358005\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.8885i | 0.574071i | 0.957920 | + | 0.287035i | \(0.0926697\pi\) | ||||
−0.957920 | + | 0.287035i | \(0.907330\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.2843 | − | 17.8885i | −0.906752 | − | 0.573480i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 24.0416i | 0.769160i | 0.923092 | + | 0.384580i | \(0.125654\pi\) | ||||
−0.923092 | + | 0.384580i | \(0.874346\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.9737 | −0.606401 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 36.0000 | 1.14822 | 0.574111 | − | 0.818778i | \(-0.305348\pi\) | ||||
0.574111 | + | 0.818778i | \(0.305348\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 44.2719i | − | 1.41062i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.6491 | 0.402218 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.4164 | 0.426186 | 0.213093 | − | 0.977032i | \(-0.431646\pi\) | ||||
0.213093 | + | 0.977032i | \(0.431646\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −50.9117 | −1.61401 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 53.7401 | 1.70197 | 0.850983 | − | 0.525193i | \(-0.176007\pi\) | ||||
0.850983 | + | 0.525193i | \(0.176007\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 4032.2.i.a.1889.5 | yes | 8 | |
3.2 | odd | 2 | 4032.2.i.b.1889.1 | yes | 8 | ||
4.3 | odd | 2 | 4032.2.i.b.1889.8 | yes | 8 | ||
7.6 | odd | 2 | 4032.2.i.b.1889.2 | yes | 8 | ||
8.3 | odd | 2 | 4032.2.i.b.1889.4 | yes | 8 | ||
8.5 | even | 2 | inner | 4032.2.i.a.1889.1 | ✓ | 8 | |
12.11 | even | 2 | inner | 4032.2.i.a.1889.4 | yes | 8 | |
21.20 | even | 2 | inner | 4032.2.i.a.1889.6 | yes | 8 | |
24.5 | odd | 2 | 4032.2.i.b.1889.5 | yes | 8 | ||
24.11 | even | 2 | inner | 4032.2.i.a.1889.8 | yes | 8 | |
28.27 | even | 2 | inner | 4032.2.i.a.1889.3 | yes | 8 | |
56.13 | odd | 2 | 4032.2.i.b.1889.6 | yes | 8 | ||
56.27 | even | 2 | inner | 4032.2.i.a.1889.7 | yes | 8 | |
84.83 | odd | 2 | 4032.2.i.b.1889.7 | yes | 8 | ||
168.83 | odd | 2 | 4032.2.i.b.1889.3 | yes | 8 | ||
168.125 | even | 2 | inner | 4032.2.i.a.1889.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4032.2.i.a.1889.1 | ✓ | 8 | 8.5 | even | 2 | inner | |
4032.2.i.a.1889.2 | yes | 8 | 168.125 | even | 2 | inner | |
4032.2.i.a.1889.3 | yes | 8 | 28.27 | even | 2 | inner | |
4032.2.i.a.1889.4 | yes | 8 | 12.11 | even | 2 | inner | |
4032.2.i.a.1889.5 | yes | 8 | 1.1 | even | 1 | trivial | |
4032.2.i.a.1889.6 | yes | 8 | 21.20 | even | 2 | inner | |
4032.2.i.a.1889.7 | yes | 8 | 56.27 | even | 2 | inner | |
4032.2.i.a.1889.8 | yes | 8 | 24.11 | even | 2 | inner | |
4032.2.i.b.1889.1 | yes | 8 | 3.2 | odd | 2 | ||
4032.2.i.b.1889.2 | yes | 8 | 7.6 | odd | 2 | ||
4032.2.i.b.1889.3 | yes | 8 | 168.83 | odd | 2 | ||
4032.2.i.b.1889.4 | yes | 8 | 8.3 | odd | 2 | ||
4032.2.i.b.1889.5 | yes | 8 | 24.5 | odd | 2 | ||
4032.2.i.b.1889.6 | yes | 8 | 56.13 | odd | 2 | ||
4032.2.i.b.1889.7 | yes | 8 | 84.83 | odd | 2 | ||
4032.2.i.b.1889.8 | yes | 8 | 4.3 | odd | 2 |