Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(721,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.721");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.t (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 2161.4 | ||
Root | \(-0.966675 + 1.03225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.2161 |
Dual form | 2880.2.t.c.721.1 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.707107 | − | 0.707107i | −0.316228 | − | 0.316228i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73696i | 0.656511i | 0.944589 | + | 0.328255i | \(0.106461\pi\) | ||||
−0.944589 | + | 0.328255i | \(0.893539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.505430 | + | 0.505430i | 0.152393 | + | 0.152393i | 0.779186 | − | 0.626793i | \(-0.215633\pi\) |
−0.626793 | + | 0.779186i | \(0.715633\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88750 | + | 1.88750i | −0.523498 | + | 0.523498i | −0.918626 | − | 0.395128i | \(-0.870700\pi\) |
0.395128 | + | 0.918626i | \(0.370700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.53524 | −1.09996 | −0.549979 | − | 0.835178i | \(-0.685364\pi\) | ||||
−0.549979 | + | 0.835178i | \(0.685364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.22022 | − | 3.22022i | 0.738768 | − | 0.738768i | −0.233571 | − | 0.972340i | \(-0.575041\pi\) |
0.972340 | + | 0.233571i | \(0.0750413\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 8.85045i | − | 1.84545i | −0.385463 | − | 0.922723i | \(-0.625958\pi\) | ||
0.385463 | − | 0.922723i | \(-0.374042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000i | 0.200000i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44059 | − | 2.44059i | 0.453205 | − | 0.453205i | −0.443212 | − | 0.896417i | \(-0.646161\pi\) |
0.896417 | + | 0.443212i | \(0.146161\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.70401 | 1.02447 | 0.512235 | − | 0.858845i | \(-0.328818\pi\) | ||||
0.512235 | + | 0.858845i | \(0.328818\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.22822 | − | 1.22822i | 0.207607 | − | 0.207607i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.35670 | − | 5.35670i | −0.880636 | − | 0.880636i | 0.112963 | − | 0.993599i | \(-0.463966\pi\) |
−0.993599 | + | 0.112963i | \(0.963966\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.0343i | 1.56709i | 0.621335 | + | 0.783545i | \(0.286591\pi\) | ||||
−0.621335 | + | 0.783545i | \(0.713409\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.10564 | + | 2.10564i | 0.321107 | + | 0.321107i | 0.849192 | − | 0.528085i | \(-0.177090\pi\) |
−0.528085 | + | 0.849192i | \(0.677090\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.32303 | 0.630578 | 0.315289 | − | 0.948996i | \(-0.397899\pi\) | ||||
0.315289 | + | 0.948996i | \(0.397899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.98295 | 0.568993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37458 | + | 1.37458i | 0.188814 | + | 0.188814i | 0.795183 | − | 0.606369i | \(-0.207375\pi\) |
−0.606369 | + | 0.795183i | \(0.707375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.714786i | − | 0.0963817i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.64140 | + | 6.64140i | 0.864637 | + | 0.864637i | 0.991872 | − | 0.127236i | \(-0.0406105\pi\) |
−0.127236 | + | 0.991872i | \(0.540611\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.26208 | − | 5.26208i | 0.673741 | − | 0.673741i | −0.284836 | − | 0.958576i | \(-0.591939\pi\) |
0.958576 | + | 0.284836i | \(0.0919391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.66933 | 0.331089 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5578 | − | 10.5578i | 1.28984 | − | 1.28984i | 0.354954 | − | 0.934884i | \(-0.384497\pi\) |
0.934884 | − | 0.354954i | \(-0.115503\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0437i | 1.66668i | 0.552764 | + | 0.833338i | \(0.313573\pi\) | ||||
−0.552764 | + | 0.833338i | \(0.686427\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.63830i | 0.776954i | 0.921458 | + | 0.388477i | \(0.126999\pi\) | ||||
−0.921458 | + | 0.388477i | \(0.873001\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.877914 | + | 0.877914i | −0.100048 | + | 0.100048i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.27297 | −0.480746 | −0.240373 | − | 0.970681i | \(-0.577270\pi\) | ||||
−0.240373 | + | 0.970681i | \(0.577270\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.15483 | − | 9.15483i | 1.00487 | − | 1.00487i | 0.00488547 | − | 0.999988i | \(-0.498445\pi\) |
0.999988 | − | 0.00488547i | \(-0.00155510\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.20690 | + | 3.20690i | 0.347837 | + | 0.347837i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.23826i | 0.343255i | 0.985162 | + | 0.171627i | \(0.0549025\pi\) | ||||
−0.985162 | + | 0.171627i | \(0.945097\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.27852 | − | 3.27852i | −0.343682 | − | 0.343682i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.55407 | −0.467238 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.94129 | 0.197108 | 0.0985541 | − | 0.995132i | \(-0.468578\pi\) | ||||
0.0985541 | + | 0.995132i | \(0.468578\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3395 | − | 10.3395i | −1.02882 | − | 1.02882i | −0.999572 | − | 0.0292464i | \(-0.990689\pi\) |
−0.0292464 | − | 0.999572i | \(-0.509311\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 4.96401i | − | 0.489118i | −0.969634 | − | 0.244559i | \(-0.921357\pi\) | ||
0.969634 | − | 0.244559i | \(-0.0786433\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.74631 | − | 2.74631i | −0.265496 | − | 0.265496i | 0.561787 | − | 0.827282i | \(-0.310114\pi\) |
−0.827282 | + | 0.561787i | \(0.810114\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.99959 | − | 6.99959i | 0.670439 | − | 0.670439i | −0.287378 | − | 0.957817i | \(-0.592784\pi\) |
0.957817 | + | 0.287378i | \(0.0927837\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.53194 | 0.614474 | 0.307237 | − | 0.951633i | \(-0.400596\pi\) | ||||
0.307237 | + | 0.951633i | \(0.400596\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.25821 | + | 6.25821i | −0.583582 | + | 0.583582i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.87756i | − | 0.722134i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.4891i | − | 0.953553i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.707107 | − | 0.707107i | 0.0632456 | − | 0.0632456i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.50861 | 0.222603 | 0.111302 | − | 0.993787i | \(-0.464498\pi\) | ||||
0.111302 | + | 0.993787i | \(0.464498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.55783 | − | 8.55783i | 0.747701 | − | 0.747701i | −0.226346 | − | 0.974047i | \(-0.572678\pi\) |
0.974047 | + | 0.226346i | \(0.0726780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.59340 | + | 5.59340i | 0.485009 | + | 0.485009i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.47131i | − | 0.552881i | −0.961031 | − | 0.276440i | \(-0.910845\pi\) | ||
0.961031 | − | 0.276440i | \(-0.0891549\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.4430 | + | 16.4430i | 1.39468 | + | 1.39468i | 0.814458 | + | 0.580223i | \(0.197035\pi\) |
0.580223 | + | 0.814458i | \(0.302965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.90800 | −0.159555 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.45151 | −0.286632 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.72803 | + | 2.72803i | 0.223489 | + | 0.223489i | 0.809966 | − | 0.586477i | \(-0.199486\pi\) |
−0.586477 | + | 0.809966i | \(0.699486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 11.5196i | − | 0.937453i | −0.883343 | − | 0.468726i | \(-0.844713\pi\) | ||
0.883343 | − | 0.468726i | \(-0.155287\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.03334 | − | 4.03334i | −0.323966 | − | 0.323966i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.28013 | − | 3.28013i | 0.261783 | − | 0.261783i | −0.563995 | − | 0.825778i | \(-0.690736\pi\) |
0.825778 | + | 0.563995i | \(0.190736\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.3729 | 1.21156 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.27367 | − | 9.27367i | 0.726370 | − | 0.726370i | −0.243525 | − | 0.969895i | \(-0.578304\pi\) |
0.969895 | + | 0.243525i | \(0.0783037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 7.08065i | − | 0.547917i | −0.961742 | − | 0.273958i | \(-0.911667\pi\) | ||
0.961742 | − | 0.273958i | \(-0.0883331\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.87470i | 0.451900i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.21471 | − | 5.21471i | 0.396467 | − | 0.396467i | −0.480518 | − | 0.876985i | \(-0.659551\pi\) |
0.876985 | + | 0.480518i | \(0.159551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.73696 | −0.131302 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.32196 | − | 6.32196i | 0.472525 | − | 0.472525i | −0.430206 | − | 0.902731i | \(-0.641559\pi\) |
0.902731 | + | 0.430206i | \(0.141559\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.0695 | + | 13.0695i | 0.971448 | + | 0.971448i | 0.999604 | − | 0.0281553i | \(-0.00896329\pi\) |
−0.0281553 | + | 0.999604i | \(0.508963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.57552i | 0.556963i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.29225 | − | 2.29225i | −0.167626 | − | 0.167626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1722 | −1.60433 | −0.802164 | − | 0.597104i | \(-0.796318\pi\) | ||||
−0.802164 | + | 0.597104i | \(0.796318\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.97695 | 0.574193 | 0.287097 | − | 0.957902i | \(-0.407310\pi\) | ||||
0.287097 | + | 0.957902i | \(0.407310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.76327 | − | 5.76327i | −0.410616 | − | 0.410616i | 0.471337 | − | 0.881953i | \(-0.343772\pi\) |
−0.881953 | + | 0.471337i | \(0.843772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.38869i | − | 0.381994i | −0.981591 | − | 0.190997i | \(-0.938828\pi\) | ||
0.981591 | − | 0.190997i | \(-0.0611721\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.23921 | + | 4.23921i | 0.297534 | + | 0.297534i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.09530 | − | 7.09530i | 0.495557 | − | 0.495557i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.25519 | 0.225166 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.7547 | + | 10.7547i | −0.740384 | + | 0.740384i | −0.972652 | − | 0.232268i | \(-0.925385\pi\) |
0.232268 | + | 0.972652i | \(0.425385\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 2.97782i | − | 0.203086i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.90766i | 0.672576i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.56026 | − | 8.56026i | 0.575826 | − | 0.575826i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.98714 | 0.266998 | 0.133499 | − | 0.991049i | \(-0.457379\pi\) | ||||
0.133499 | + | 0.991049i | \(0.457379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.82103 | + | 3.82103i | −0.253611 | + | 0.253611i | −0.822449 | − | 0.568839i | \(-0.807393\pi\) |
0.568839 | + | 0.822449i | \(0.307393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.80687 | − | 8.80687i | −0.581974 | − | 0.581974i | 0.353471 | − | 0.935445i | \(-0.385001\pi\) |
−0.935445 | + | 0.353471i | \(0.885001\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6042i | 1.08778i | 0.839157 | + | 0.543889i | \(0.183049\pi\) | ||||
−0.839157 | + | 0.543889i | \(0.816951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.05684 | − | 3.05684i | −0.199406 | − | 0.199406i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.81234 | 0.246600 | 0.123300 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123300 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.54985 | 0.615160 | 0.307580 | − | 0.951522i | \(-0.400481\pi\) | ||||
0.307580 | + | 0.951522i | \(0.400481\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.81637 | − | 2.81637i | −0.179932 | − | 0.179932i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1563i | 0.773487i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.9933 | + | 11.9933i | 0.757010 | + | 0.757010i | 0.975777 | − | 0.218767i | \(-0.0702034\pi\) |
−0.218767 | + | 0.975777i | \(0.570203\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.47328 | − | 4.47328i | 0.281233 | − | 0.281233i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.8752 | −1.17740 | −0.588702 | − | 0.808350i | \(-0.700361\pi\) | ||||
−0.588702 | + | 0.808350i | \(0.700361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.30440 | − | 9.30440i | 0.578147 | − | 0.578147i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.1398i | 1.42686i | 0.700727 | + | 0.713429i | \(0.252859\pi\) | ||||
−0.700727 | + | 0.713429i | \(0.747141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.94396i | − | 0.119416i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.6368 | − | 10.6368i | 0.648539 | − | 0.648539i | −0.304101 | − | 0.952640i | \(-0.598356\pi\) |
0.952640 | + | 0.304101i | \(0.0983560\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.9763 | −1.21348 | −0.606738 | − | 0.794902i | \(-0.707522\pi\) | ||||
−0.606738 | + | 0.794902i | \(0.707522\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.505430 | + | 0.505430i | −0.0304786 | + | 0.0304786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1534 | − | 16.1534i | −0.970563 | − | 0.970563i | 0.0290160 | − | 0.999579i | \(-0.490763\pi\) |
−0.999579 | + | 0.0290160i | \(0.990763\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 9.43520i | − | 0.562857i | −0.959582 | − | 0.281429i | \(-0.909192\pi\) | ||
0.959582 | − | 0.281429i | \(-0.0908082\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.71287 | − | 8.71287i | −0.517926 | − | 0.517926i | 0.399017 | − | 0.916943i | \(-0.369351\pi\) |
−0.916943 | + | 0.399017i | \(0.869351\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.4292 | −1.02881 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.56843 | 0.209908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1045 | + | 11.1045i | 0.648729 | + | 0.648729i | 0.952686 | − | 0.303957i | \(-0.0983079\pi\) |
−0.303957 | + | 0.952686i | \(0.598308\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.39236i | − | 0.546844i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 16.7052 | + | 16.7052i | 0.966087 | + | 0.966087i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.65742 | + | 3.65742i | −0.210810 | + | 0.210810i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −7.44171 | −0.426111 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.99854 | − | 2.99854i | 0.171136 | − | 0.171136i | −0.616343 | − | 0.787478i | \(-0.711386\pi\) |
0.787478 | + | 0.616343i | \(0.211386\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 9.06099i | − | 0.513802i | −0.966438 | − | 0.256901i | \(-0.917299\pi\) | ||
0.966438 | − | 0.256901i | \(-0.0827014\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.5699i | − | 1.10616i | −0.833129 | − | 0.553078i | \(-0.813453\pi\) | ||
0.833129 | − | 0.553078i | \(-0.186547\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.1019 | − | 11.1019i | 0.623546 | − | 0.623546i | −0.322890 | − | 0.946436i | \(-0.604654\pi\) |
0.946436 | + | 0.322890i | \(0.104654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.46709 | 0.138131 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.6045 | + | 14.6045i | −0.812614 | + | 0.812614i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.88750 | − | 1.88750i | −0.104700 | − | 0.104700i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.50894i | 0.413981i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.14718 | + | 8.14718i | 0.447810 | + | 0.447810i | 0.894626 | − | 0.446816i | \(-0.147442\pi\) |
−0.446816 | + | 0.894626i | \(0.647442\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −14.9309 | −0.815765 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.1380 | −1.36935 | −0.684677 | − | 0.728847i | \(-0.740057\pi\) | ||||
−0.684677 | + | 0.728847i | \(0.740057\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.88298 | + | 2.88298i | 0.156122 | + | 0.156122i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0770i | 1.03006i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7.36719 | + | 7.36719i | 0.395491 | + | 0.395491i | 0.876639 | − | 0.481148i | \(-0.159780\pi\) |
−0.481148 | + | 0.876639i | \(0.659780\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.25982 | + | 3.25982i | −0.174494 | + | 0.174494i | −0.788951 | − | 0.614457i | \(-0.789375\pi\) |
0.614457 | + | 0.788951i | \(0.289375\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −0.502832 | −0.0267630 | −0.0133815 | − | 0.999910i | \(-0.504260\pi\) | ||||
−0.0133815 | + | 0.999910i | \(0.504260\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.93037 | − | 9.93037i | 0.527049 | − | 0.527049i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 5.95161i | 0.314114i | 0.987590 | + | 0.157057i | \(0.0502007\pi\) | ||||
−0.987590 | + | 0.157057i | \(0.949799\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 1.73958i | − | 0.0915571i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.69399 | − | 4.69399i | 0.245695 | − | 0.245695i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.95365 | −0.101980 | −0.0509898 | − | 0.998699i | \(-0.516238\pi\) | ||||
−0.0509898 | + | 0.998699i | \(0.516238\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.38760 | + | 2.38760i | −0.123958 | + | 0.123958i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.6509 | − | 18.6509i | −0.965708 | − | 0.965708i | 0.0337233 | − | 0.999431i | \(-0.489264\pi\) |
−0.999431 | + | 0.0337233i | \(0.989264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.21320i | 0.474504i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.85143 | + | 3.85143i | 0.197835 | + | 0.197835i | 0.799071 | − | 0.601236i | \(-0.205325\pi\) |
−0.601236 | + | 0.799071i | \(0.705325\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.29258 | 0.117145 | 0.0585726 | − | 0.998283i | \(-0.481345\pi\) | ||||
0.0585726 | + | 0.998283i | \(0.481345\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.24156 | 0.0632757 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.90500 | − | 4.90500i | −0.248693 | − | 0.248693i | 0.571741 | − | 0.820434i | \(-0.306268\pi\) |
−0.820434 | + | 0.571741i | \(0.806268\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 40.1389i | 2.02991i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.02144 | + | 3.02144i | 0.152025 | + | 0.152025i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.8616 | + | 10.8616i | −0.545126 | + | 0.545126i | −0.925027 | − | 0.379901i | \(-0.875958\pi\) |
0.379901 | + | 0.925027i | \(0.375958\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.10783 | 0.354948 | 0.177474 | − | 0.984125i | \(-0.443207\pi\) | ||||
0.177474 | + | 0.984125i | \(0.443207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.7663 | + | 10.7663i | −0.536308 | + | 0.536308i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5.41487i | − | 0.268405i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 29.1697i | 1.44235i | 0.692752 | + | 0.721176i | \(0.256398\pi\) | ||||
−0.692752 | + | 0.721176i | \(0.743602\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11.5359 | + | 11.5359i | −0.567643 | + | 0.567643i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −12.9469 | −0.635538 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.06616 | − | 3.06616i | 0.149792 | − | 0.149792i | −0.628233 | − | 0.778025i | \(-0.716222\pi\) |
0.778025 | + | 0.628233i | \(0.216222\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.532242 | − | 0.532242i | −0.0259399 | − | 0.0259399i | 0.694018 | − | 0.719958i | \(-0.255839\pi\) |
−0.719958 | + | 0.694018i | \(0.755839\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 4.53524i | − | 0.219992i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.14005 | + | 9.14005i | 0.442318 | + | 0.442318i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.7237 | 0.805555 | 0.402777 | − | 0.915298i | \(-0.368045\pi\) | ||||
0.402777 | + | 0.915298i | \(0.368045\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.3675 | 1.36326 | 0.681628 | − | 0.731699i | \(-0.261272\pi\) | ||||
0.681628 | + | 0.731699i | \(0.261272\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.5004 | − | 28.5004i | −1.36336 | − | 1.36336i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 13.5018i | − | 0.644405i | −0.946671 | − | 0.322203i | \(-0.895577\pi\) | ||
0.946671 | − | 0.322203i | \(-0.104423\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.55246 | − | 9.55246i | −0.453851 | − | 0.453851i | 0.442780 | − | 0.896630i | \(-0.353992\pi\) |
−0.896630 | + | 0.442780i | \(0.853992\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.28980 | − | 2.28980i | 0.108547 | − | 0.108547i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.35573 | 0.441524 | 0.220762 | − | 0.975328i | \(-0.429146\pi\) | ||||
0.220762 | + | 0.975328i | \(0.429146\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.07162 | + | 5.07162i | −0.238813 | + | 0.238813i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.63652i | 0.217364i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.84779i | 0.320326i | 0.987091 | + | 0.160163i | \(0.0512020\pi\) | ||||
−0.987091 | + | 0.160163i | \(0.948798\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7403 | − | 11.7403i | 0.546801 | − | 0.546801i | −0.378713 | − | 0.925514i | \(-0.623633\pi\) |
0.925514 | + | 0.378713i | \(0.123633\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.6096 | 1.23665 | 0.618326 | − | 0.785922i | \(-0.287811\pi\) | ||||
0.618326 | + | 0.785922i | \(0.287811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.47583 | − | 1.47583i | 0.0682933 | − | 0.0682933i | −0.672135 | − | 0.740428i | \(-0.734623\pi\) |
0.740428 | + | 0.672135i | \(0.234623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.3385 | + | 18.3385i | 0.846792 | + | 0.846792i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.12851i | 0.0978688i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.22022 | + | 3.22022i | 0.147754 | + | 0.147754i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.78600 | −0.127296 | −0.0636479 | − | 0.997972i | \(-0.520273\pi\) | ||||
−0.0636479 | + | 0.997972i | \(0.520273\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.2215 | 0.922022 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.37270 | − | 1.37270i | −0.0623311 | − | 0.0623311i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.9499i | − | 0.768073i | −0.923318 | − | 0.384036i | \(-0.874534\pi\) | ||
0.923318 | − | 0.384036i | \(-0.125466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.8390 | − | 22.8390i | −1.03071 | − | 1.03071i | −0.999513 | − | 0.0311972i | \(-0.990068\pi\) |
−0.0311972 | − | 0.999513i | \(-0.509932\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.0687 | + | 11.0687i | −0.498507 | + | 0.498507i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.3933 | −1.09419 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.33906 | + | 2.33906i | −0.104711 | + | 0.104711i | −0.757521 | − | 0.652811i | \(-0.773590\pi\) |
0.652811 | + | 0.757521i | \(0.273590\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.58801i | − | 0.0708057i | −0.999373 | − | 0.0354029i | \(-0.988729\pi\) | ||
0.999373 | − | 0.0354029i | \(-0.0112714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.6223i | 0.650682i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.61613 | − | 3.61613i | 0.160282 | − | 0.160282i | −0.622410 | − | 0.782692i | \(-0.713846\pi\) |
0.782692 | + | 0.622410i | \(0.213846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.5305 | −0.510079 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.51009 | + | 3.51009i | −0.154673 | + | 0.154673i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18499 | + | 2.18499i | 0.0960956 | + | 0.0960956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.93031i | − | 0.391244i | −0.980679 | − | 0.195622i | \(-0.937327\pi\) | ||
0.980679 | − | 0.195622i | \(-0.0626725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.0355 | − | 15.0355i | −0.657455 | − | 0.657455i | 0.297323 | − | 0.954777i | \(-0.403906\pi\) |
−0.954777 | + | 0.297323i | \(0.903906\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −25.8691 | −1.12687 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −55.3305 | −2.40567 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.9397 | − | 18.9397i | −0.820368 | − | 0.820368i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.88387i | 0.167914i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.01310 | + | 2.01310i | 0.0867106 | + | 0.0867106i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.57591 | − | 5.57591i | 0.239727 | − | 0.239727i | −0.577010 | − | 0.816737i | \(-0.695781\pi\) |
0.816737 | + | 0.577010i | \(0.195781\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.89891 | −0.424023 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.8366 | + | 32.8366i | −1.40399 | + | 1.40399i | −0.617136 | + | 0.786856i | \(0.711707\pi\) |
−0.786856 | + | 0.617136i | \(0.788293\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 15.7184i | − | 0.669628i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7.42199i | − | 0.315615i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2077 | + | 24.2077i | −1.02571 | + | 1.02571i | −0.0260537 | + | 0.999661i | \(0.508294\pi\) |
−0.999661 | + | 0.0260537i | \(0.991706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.94877 | −0.336197 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.3407 | − | 22.3407i | 0.941547 | − | 0.941547i | −0.0568365 | − | 0.998384i | \(-0.518101\pi\) |
0.998384 | + | 0.0568365i | \(0.0181014\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.61878 | − | 4.61878i | −0.194314 | − | 0.194314i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.3339i | 1.22974i | 0.788629 | + | 0.614870i | \(0.210791\pi\) | ||||
−0.788629 | + | 0.614870i | \(0.789209\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −23.9934 | − | 23.9934i | −1.00409 | − | 1.00409i | −0.999992 | − | 0.00410070i | \(-0.998695\pi\) |
−0.00410070 | − | 0.999992i | \(-0.501305\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.85045 | 0.369089 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −31.9232 | −1.32898 | −0.664490 | − | 0.747297i | \(-0.731351\pi\) | ||||
−0.664490 | + | 0.747297i | \(0.731351\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 15.9016 | + | 15.9016i | 0.659710 | + | 0.659710i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.38951i | 0.0575477i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −26.2847 | − | 26.2847i | −1.08488 | − | 1.08488i | −0.996046 | − | 0.0888379i | \(-0.971685\pi\) |
−0.0888379 | − | 0.996046i | \(-0.528315\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.3681 | − | 18.3681i | 0.756846 | − | 0.756846i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 38.2085 | 1.56904 | 0.784518 | − | 0.620106i | \(-0.212910\pi\) | ||||
0.784518 | + | 0.620106i | \(0.212910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.57027 | + | 5.57027i | −0.228359 | + | 0.228359i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 25.1150i | 1.02617i | 0.858337 | + | 0.513086i | \(0.171498\pi\) | ||||
−0.858337 | + | 0.513086i | \(0.828502\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.2022i | 0.905647i | 0.891600 | + | 0.452823i | \(0.149583\pi\) | ||||
−0.891600 | + | 0.452823i | \(0.850417\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.41690 | + | 7.41690i | −0.301540 | + | 0.301540i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.9648 | −0.526226 | −0.263113 | − | 0.964765i | \(-0.584749\pi\) | ||||
−0.263113 | + | 0.964765i | \(0.584749\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.15970 | + | 8.15970i | −0.330106 | + | 0.330106i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.42804 | + | 7.42804i | 0.300016 | + | 0.300016i | 0.841020 | − | 0.541004i | \(-0.181956\pi\) |
−0.541004 | + | 0.841020i | \(0.681956\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.2743i | 0.936989i | 0.883467 | + | 0.468494i | \(0.155203\pi\) | ||||
−0.883467 | + | 0.468494i | \(0.844797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.6213 | + | 31.6213i | 1.27097 | + | 1.27097i | 0.945581 | + | 0.325386i | \(0.105494\pi\) |
0.325386 | + | 0.945581i | \(0.394506\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.62474 | −0.225351 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.00000 | −0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 24.2939 | + | 24.2939i | 0.968663 | + | 0.968663i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 29.9258i | − | 1.19133i | −0.803234 | − | 0.595663i | \(-0.796889\pi\) | ||
0.803234 | − | 0.595663i | \(-0.203111\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.77386 | − | 1.77386i | −0.0703933 | − | 0.0703933i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.51782 | + | 7.51782i | −0.297867 | + | 0.297867i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2240 | −0.403825 | −0.201912 | − | 0.979404i | \(-0.564716\pi\) | ||||
−0.201912 | + | 0.979404i | \(0.564716\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7202 | − | 13.7202i | 0.541074 | − | 0.541074i | −0.382770 | − | 0.923844i | \(-0.625030\pi\) |
0.923844 | + | 0.382770i | \(0.125030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.6767i | 0.734255i | 0.930171 | + | 0.367128i | \(0.119659\pi\) | ||||
−0.930171 | + | 0.367128i | \(0.880341\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.71353i | 0.263529i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7935 | + | 12.7935i | −0.500647 | + | 0.500647i | −0.911639 | − | 0.410992i | \(-0.865183\pi\) |
0.410992 | + | 0.911639i | \(0.365183\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1026 | −0.472888 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.3193 | − | 12.3193i | 0.479893 | − | 0.479893i | −0.425204 | − | 0.905097i | \(-0.639798\pi\) |
0.905097 | + | 0.425204i | \(0.139798\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0352 | − | 24.0352i | −0.934862 | − | 0.934862i | 0.0631421 | − | 0.998005i | \(-0.479888\pi\) |
−0.998005 | + | 0.0631421i | \(0.979888\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 7.91026i | − | 0.306747i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.6003 | − | 21.6003i | −0.836367 | − | 0.836367i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.31923 | 0.205347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −21.5360 | −0.830150 | −0.415075 | − | 0.909787i | \(-0.636245\pi\) | ||||
−0.415075 | + | 0.909787i | \(0.636245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −13.1852 | − | 13.1852i | −0.506750 | − | 0.506750i | 0.406778 | − | 0.913527i | \(-0.366652\pi\) |
−0.913527 | + | 0.406778i | \(0.866652\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.37195i | 0.129404i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.6011 | + | 30.6011i | 1.17092 | + | 1.17092i | 0.981991 | + | 0.188926i | \(0.0605008\pi\) |
0.188926 | + | 0.981991i | \(0.439499\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.57590 | + | 4.57590i | −0.174836 | + | 0.174836i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.18905 | −0.197687 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.2675 | − | 25.2675i | 0.961220 | − | 0.961220i | −0.0380558 | − | 0.999276i | \(-0.512116\pi\) |
0.999276 | + | 0.0380558i | \(0.0121165\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 23.2540i | − | 0.882074i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 45.5079i | − | 1.72373i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18.5583 | + | 18.5583i | −0.700937 | + | 0.700937i | −0.964612 | − | 0.263675i | \(-0.915065\pi\) |
0.263675 | + | 0.964612i | \(0.415065\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.4995 | −1.30117 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 17.9593 | − | 17.9593i | 0.675431 | − | 0.675431i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.38093 | + | 4.38093i | 0.164529 | + | 0.164529i | 0.784570 | − | 0.620040i | \(-0.212884\pi\) |
−0.620040 | + | 0.784570i | \(0.712884\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 50.4831i | − | 1.89061i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.34916 | + | 1.34916i | 0.0504556 | + | 0.0504556i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.61691 | 0.0603007 | 0.0301503 | − | 0.999545i | \(-0.490401\pi\) | ||||
0.0301503 | + | 0.999545i | \(0.490401\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.62231 | 0.321112 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.44059 | + | 2.44059i | 0.0906411 | + | 0.0906411i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 39.3600i | − | 1.45978i | −0.683563 | − | 0.729891i | \(-0.739571\pi\) | ||
0.683563 | − | 0.729891i | \(-0.260429\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.54958 | − | 9.54958i | −0.353204 | − | 0.353204i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0787 | + | 34.0787i | −1.25873 | + | 1.25873i | −0.307026 | + | 0.951701i | \(0.599334\pi\) |
−0.951701 | + | 0.307026i | \(0.900666\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.6724 | 0.393124 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.4278 | + | 15.4278i | −0.567520 | + | 0.567520i | −0.931433 | − | 0.363913i | \(-0.881441\pi\) |
0.363913 | + | 0.931433i | \(0.381441\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5004i | 0.862147i | 0.902317 | + | 0.431074i | \(0.141865\pi\) | ||||
−0.902317 | + | 0.431074i | \(0.858135\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 3.85801i | − | 0.141347i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.77024 | − | 4.77024i | 0.174301 | − | 0.174301i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.8586 | −0.396236 | −0.198118 | − | 0.980178i | \(-0.563483\pi\) | ||||
−0.198118 | + | 0.980178i | \(0.563483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.14560 | + | 8.14560i | −0.296449 | + | 0.296449i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8434 | + | 18.8434i | 0.684874 | + | 0.684874i | 0.961094 | − | 0.276220i | \(-0.0890819\pi\) |
−0.276220 | + | 0.961094i | \(0.589082\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.2837i | 0.807783i | 0.914807 | + | 0.403891i | \(0.132343\pi\) | ||||
−0.914807 | + | 0.403891i | \(0.867657\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.1580 | + | 12.1580i | 0.440151 | + | 0.440151i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −25.0713 | −0.905271 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.5399 | 0.380077 | 0.190039 | − | 0.981777i | \(-0.439139\pi\) | ||||
0.190039 | + | 0.981777i | \(0.439139\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.07768 | − | 4.07768i | −0.146664 | − | 0.146664i | 0.629962 | − | 0.776626i | \(-0.283070\pi\) |
−0.776626 | + | 0.629962i | \(0.783070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.70401i | 0.204894i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 32.3125 | + | 32.3125i | 1.15772 | + | 1.15772i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.09809 | + | 7.09809i | −0.253990 | + | 0.253990i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.63881 | −0.165566 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.16669 | − | 8.16669i | 0.291111 | − | 0.291111i | −0.546408 | − | 0.837519i | \(-0.684005\pi\) |
0.837519 | + | 0.546408i | \(0.184005\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3458i | 0.403409i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.8643i | 0.705403i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.9971 | + | 17.9971i | −0.637491 | + | 0.637491i | −0.949936 | − | 0.312445i | \(-0.898852\pi\) |
0.312445 | + | 0.949936i | \(0.398852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.6060 | −0.693609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.35520 | + | 3.35520i | −0.118402 | + | 0.118402i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.8703 | − | 10.8703i | −0.383128 | − | 0.383128i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.0296i | 1.47768i | 0.673879 | + | 0.738841i | \(0.264627\pi\) | ||||
−0.673879 | + | 0.738841i | \(0.735373\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.7601 | − | 18.7601i | −0.658757 | − | 0.658757i | 0.296329 | − | 0.955086i | \(-0.404238\pi\) |
−0.955086 | + | 0.296329i | \(0.904238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.1149 | −0.459397 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.5612 | 0.474447 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.4050 | + | 21.4050i | 0.747038 | + | 0.747038i | 0.973922 | − | 0.226884i | \(-0.0728538\pi\) |
−0.226884 | + | 0.973922i | \(0.572854\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 43.7323i | 1.52441i | 0.647334 | + | 0.762206i | \(0.275884\pi\) | ||||
−0.647334 | + | 0.762206i | \(0.724116\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.9621 | − | 19.9621i | −0.694149 | − | 0.694149i | 0.268993 | − | 0.963142i | \(-0.413309\pi\) |
−0.963142 | + | 0.268993i | \(0.913309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.3869 | − | 31.3869i | 1.09011 | − | 1.09011i | 0.0945964 | − | 0.995516i | \(-0.469844\pi\) |
0.995516 | − | 0.0945964i | \(-0.0301561\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.0637 | −0.625869 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.00677 | + | 5.00677i | −0.173267 | + | 0.173267i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 54.5335i | − | 1.88271i | −0.337423 | − | 0.941353i | \(-0.609555\pi\) | ||
0.337423 | − | 0.941353i | \(-0.390445\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0871i | 0.589210i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.15404 | − | 4.15404i | 0.142903 | − | 0.142903i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 18.2192 | 0.626018 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −47.4092 | + | 47.4092i | −1.62517 | + | 1.62517i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 21.5932 | + | 21.5932i | 0.739336 | + | 0.739336i | 0.972449 | − | 0.233114i | \(-0.0748914\pi\) |
−0.233114 | + | 0.972449i | \(0.574891\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 41.3609i | − | 1.41286i | −0.707782 | − | 0.706431i | \(-0.750304\pi\) | ||
0.707782 | − | 0.706431i | \(-0.249696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.700596 | + | 0.700596i | 0.0239040 | + | 0.0239040i | 0.718958 | − | 0.695054i | \(-0.244619\pi\) |
−0.695054 | + | 0.718958i | \(0.744619\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 55.0780 | 1.87488 | 0.937439 | − | 0.348150i | \(-0.113190\pi\) | ||||
0.937439 | + | 0.348150i | \(0.113190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.37471 | −0.250748 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.15969 | − | 2.15969i | −0.0732623 | − | 0.0732623i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.8556i | 1.35045i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.22822 | + | 1.22822i | 0.0415214 | + | 0.0415214i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −36.5100 | + | 36.5100i | −1.23285 | + | 1.23285i | −0.269992 | + | 0.962863i | \(0.587021\pi\) |
−0.962863 | + | 0.269992i | \(0.912979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.3503 | −1.83111 | −0.915554 | − | 0.402196i | \(-0.868247\pi\) | ||||
−0.915554 | + | 0.402196i | \(0.868247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.5476 | + | 35.5476i | −1.19627 | + | 1.19627i | −0.220999 | + | 0.975274i | \(0.570932\pi\) |
−0.975274 | + | 0.220999i | \(0.929068\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.817003i | 0.0274323i | 0.999906 | + | 0.0137161i | \(0.00436612\pi\) | ||||
−0.999906 | + | 0.0137161i | \(0.995634\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.35737i | 0.146141i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.9211 | − | 13.9211i | 0.465851 | − | 0.465851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.94060 | −0.298851 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 13.9211 | − | 13.9211i | 0.464296 | − | 0.464296i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.23407 | − | 6.23407i | −0.207687 | − | 0.207687i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 18.4831i | − | 0.614398i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.36159 | + | 3.36159i | 0.111620 | + | 0.111620i | 0.760711 | − | 0.649091i | \(-0.224851\pi\) |
−0.649091 | + | 0.760711i | \(0.724851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.6568 | 1.14823 | 0.574116 | − | 0.818774i | \(-0.305346\pi\) | ||||
0.574116 | + | 0.818774i | \(0.305346\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.25426 | 0.306271 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.8646 | + | 14.8646i | 0.490874 | + | 0.490874i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 24.3452i | − | 0.803074i | −0.915843 | − | 0.401537i | \(-0.868476\pi\) | ||
0.915843 | − | 0.401537i | \(-0.131524\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.5074 | − | 26.5074i | −0.872501 | − | 0.872501i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.35670 | − | 5.35670i | 0.176127 | − | 0.176127i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.16600 | −0.103873 | −0.0519366 | − | 0.998650i | \(-0.516539\pi\) | ||||
−0.0519366 | + | 0.998650i | \(0.516539\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.8260 | − | 12.8260i | 0.420354 | − | 0.420354i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.24173i | 0.106016i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.4847i | − | 0.767211i | −0.923497 | − | 0.383606i | \(-0.874682\pi\) | ||
0.923497 | − | 0.383606i | \(-0.125318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.7583 | + | 27.7583i | −0.904896 | + | 0.904896i | −0.995855 | − | 0.0909585i | \(-0.971007\pi\) |
0.0909585 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 88.8078 | 2.89198 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2916 | + | 27.2916i | −0.886857 | + | 0.886857i | −0.994220 | − | 0.107363i | \(-0.965759\pi\) |
0.107363 | + | 0.994220i | \(0.465759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.5298 | − | 12.5298i | −0.406734 | − | 0.406734i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 12.1516i | − | 0.393630i | −0.980441 | − | 0.196815i | \(-0.936940\pi\) | ||
0.980441 | − | 0.196815i | \(-0.0630598\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.6781 | + | 15.6781i | 0.507333 | + | 0.507333i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2404 | 0.362972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.53571 | 0.0495392 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.64056 | − | 5.64056i | −0.181576 | − | 0.181576i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2694i | 1.55224i | 0.630585 | + | 0.776120i | \(0.282815\pi\) | ||||
−0.630585 | + | 0.776120i | \(0.717185\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.92047 | + | 5.92047i | 0.189997 | + | 0.189997i | 0.795695 | − | 0.605698i | \(-0.207106\pi\) |
−0.605698 | + | 0.795695i | \(0.707106\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.5610 | + | 28.5610i | −0.915623 | + | 0.915623i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.7522 | 0.887872 | 0.443936 | − | 0.896059i | \(-0.353582\pi\) | ||||
0.443936 | + | 0.896059i | \(0.353582\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.63671 | + | 1.63671i | −0.0523096 | + | 0.0523096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 28.3604i | − | 0.904556i | −0.891877 | − | 0.452278i | \(-0.850611\pi\) | ||
0.891877 | − | 0.452278i | \(-0.149389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.15050i | 0.259697i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 18.6358 | − | 18.6358i | 0.592585 | − | 0.592585i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 43.7506 | 1.38979 | 0.694893 | − | 0.719114i | \(-0.255452\pi\) | ||||
0.694893 | + | 0.719114i | \(0.255452\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.81038 | + | 3.81038i | −0.120797 | + | 0.120797i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5572 | + | 10.5572i | 0.334349 | + | 0.334349i | 0.854235 | − | 0.519887i | \(-0.174026\pi\) |
−0.519887 | + | 0.854235i | \(0.674026\pi\) | |||||||
\(998\) | 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 | 2880.2.t.c.2161.4 | 16 | ||
3.2 | odd | 2 | 320.2.l.a.241.4 | 16 | |||
4.3 | odd | 2 | 720.2.t.c.181.3 | 16 | |||
12.11 | even | 2 | 80.2.l.a.21.6 | ✓ | 16 | ||
15.2 | even | 4 | 1600.2.q.h.49.5 | 16 | |||
15.8 | even | 4 | 1600.2.q.g.49.4 | 16 | |||
15.14 | odd | 2 | 1600.2.l.i.1201.5 | 16 | |||
16.3 | odd | 4 | 720.2.t.c.541.3 | 16 | |||
16.13 | even | 4 | inner | 2880.2.t.c.721.1 | 16 | ||
24.5 | odd | 2 | 640.2.l.a.481.5 | 16 | |||
24.11 | even | 2 | 640.2.l.b.481.4 | 16 | |||
48.5 | odd | 4 | 640.2.l.a.161.5 | 16 | |||
48.11 | even | 4 | 640.2.l.b.161.4 | 16 | |||
48.29 | odd | 4 | 320.2.l.a.81.4 | 16 | |||
48.35 | even | 4 | 80.2.l.a.61.6 | yes | 16 | ||
60.23 | odd | 4 | 400.2.q.h.149.2 | 16 | |||
60.47 | odd | 4 | 400.2.q.g.149.7 | 16 | |||
60.59 | even | 2 | 400.2.l.h.101.3 | 16 | |||
96.29 | odd | 8 | 5120.2.a.u.1.3 | 8 | |||
96.35 | even | 8 | 5120.2.a.s.1.6 | 8 | |||
96.77 | odd | 8 | 5120.2.a.t.1.6 | 8 | |||
96.83 | even | 8 | 5120.2.a.v.1.3 | 8 | |||
240.29 | odd | 4 | 1600.2.l.i.401.5 | 16 | |||
240.77 | even | 4 | 1600.2.q.g.849.4 | 16 | |||
240.83 | odd | 4 | 400.2.q.g.349.7 | 16 | |||
240.173 | even | 4 | 1600.2.q.h.849.5 | 16 | |||
240.179 | even | 4 | 400.2.l.h.301.3 | 16 | |||
240.227 | odd | 4 | 400.2.q.h.349.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.6 | ✓ | 16 | 12.11 | even | 2 | ||
80.2.l.a.61.6 | yes | 16 | 48.35 | even | 4 | ||
320.2.l.a.81.4 | 16 | 48.29 | odd | 4 | |||
320.2.l.a.241.4 | 16 | 3.2 | odd | 2 | |||
400.2.l.h.101.3 | 16 | 60.59 | even | 2 | |||
400.2.l.h.301.3 | 16 | 240.179 | even | 4 | |||
400.2.q.g.149.7 | 16 | 60.47 | odd | 4 | |||
400.2.q.g.349.7 | 16 | 240.83 | odd | 4 | |||
400.2.q.h.149.2 | 16 | 60.23 | odd | 4 | |||
400.2.q.h.349.2 | 16 | 240.227 | odd | 4 | |||
640.2.l.a.161.5 | 16 | 48.5 | odd | 4 | |||
640.2.l.a.481.5 | 16 | 24.5 | odd | 2 | |||
640.2.l.b.161.4 | 16 | 48.11 | even | 4 | |||
640.2.l.b.481.4 | 16 | 24.11 | even | 2 | |||
720.2.t.c.181.3 | 16 | 4.3 | odd | 2 | |||
720.2.t.c.541.3 | 16 | 16.3 | odd | 4 | |||
1600.2.l.i.401.5 | 16 | 240.29 | odd | 4 | |||
1600.2.l.i.1201.5 | 16 | 15.14 | odd | 2 | |||
1600.2.q.g.49.4 | 16 | 15.8 | even | 4 | |||
1600.2.q.g.849.4 | 16 | 240.77 | even | 4 | |||
1600.2.q.h.49.5 | 16 | 15.2 | even | 4 | |||
1600.2.q.h.849.5 | 16 | 240.173 | even | 4 | |||
2880.2.t.c.721.1 | 16 | 16.13 | even | 4 | inner | ||
2880.2.t.c.2161.4 | 16 | 1.1 | even | 1 | trivial | ||
5120.2.a.s.1.6 | 8 | 96.35 | even | 8 | |||
5120.2.a.t.1.6 | 8 | 96.77 | odd | 8 | |||
5120.2.a.u.1.3 | 8 | 96.29 | odd | 8 | |||
5120.2.a.v.1.3 | 8 | 96.83 | even | 8 |