Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1600,2,Mod(49,1600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1600.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1600 = 2^{6} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1600.q (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: | \(12.7760643234\) |
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: | \( 2^{14} \) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Root | \(-0.966675 + 1.03225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1600.49 |
Dual form | 1600.2.q.g.849.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1151\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.209571 | − | 0.209571i | −0.120996 | − | 0.120996i | 0.644016 | − | 0.765012i | \(-0.277267\pi\) |
−0.765012 | + | 0.644016i | \(0.777267\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73696 | 0.656511 | 0.328255 | − | 0.944589i | \(-0.393539\pi\) | ||||
0.328255 | + | 0.944589i | \(0.393539\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2.91216i | − | 0.970720i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.505430 | − | 0.505430i | −0.152393 | − | 0.152393i | 0.626793 | − | 0.779186i | \(-0.284367\pi\) |
−0.779186 | + | 0.626793i | \(0.784367\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.88750 | − | 1.88750i | −0.523498 | − | 0.523498i | 0.395128 | − | 0.918626i | \(-0.370700\pi\) |
−0.918626 | + | 0.395128i | \(0.870700\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 4.53524i | − | 1.09996i | −0.835178 | − | 0.549979i | \(-0.814636\pi\) | ||
0.835178 | − | 0.549979i | \(-0.185364\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.22022 | + | 3.22022i | −0.738768 | + | 0.738768i | −0.972340 | − | 0.233571i | \(-0.924959\pi\) |
0.233571 | + | 0.972340i | \(0.424959\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.364018 | − | 0.364018i | −0.0794352 | − | 0.0794352i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.85045 | −1.84545 | −0.922723 | − | 0.385463i | \(-0.874042\pi\) | ||||
−0.922723 | + | 0.385463i | \(0.874042\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.23902 | + | 1.23902i | −0.238449 | + | 0.238449i | ||||
\(28\) | 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 | ||||||||
\(33\) | 0.211847i | 0.0368779i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.35670 | + | 5.35670i | −0.880636 | + | 0.880636i | −0.993599 | − | 0.112963i | \(-0.963966\pi\) |
0.112963 | + | 0.993599i | \(0.463966\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.791130i | 0.126682i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.0343i | − | 1.56709i | −0.621335 | − | 0.783545i | \(-0.713409\pi\) | ||
0.621335 | − | 0.783545i | \(-0.286591\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.10564 | + | 2.10564i | −0.321107 | + | 0.321107i | −0.849192 | − | 0.528085i | \(-0.822910\pi\) |
0.528085 | + | 0.849192i | \(0.322910\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.32303i | 0.630578i | 0.948996 | + | 0.315289i | \(0.102101\pi\) | ||||
−0.948996 | + | 0.315289i | \(0.897899\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.98295 | −0.568993 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.950456 | + | 0.950456i | −0.133091 | + | 0.133091i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.37458 | − | 1.37458i | 0.188814 | − | 0.188814i | −0.606369 | − | 0.795183i | \(-0.707375\pi\) |
0.795183 | + | 0.606369i | \(0.207375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.34973 | 0.178776 | ||||||||
\(58\) | 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 | ||||||||
\(63\) | − | 5.05832i | − | 0.637288i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5578 | − | 10.5578i | −1.28984 | − | 1.28984i | −0.934884 | − | 0.354954i | \(-0.884497\pi\) |
−0.354954 | − | 0.934884i | \(-0.615503\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.85480 | + | 1.85480i | 0.223292 | + | 0.223292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.0437i | − | 1.66668i | −0.552764 | − | 0.833338i | \(-0.686427\pi\) | ||
0.552764 | − | 0.833338i | \(-0.313573\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.63830 | −0.776954 | −0.388477 | − | 0.921458i | \(-0.626999\pi\) | ||||
−0.388477 | + | 0.921458i | \(0.626999\pi\) | |||||||
\(74\) | 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 | \(-0.422730\pi\) | ||||
0.240373 | + | 0.970681i | \(0.422730\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.21715 | −0.913017 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.15483 | − | 9.15483i | −1.00487 | − | 1.00487i | −0.999988 | − | 0.00488547i | \(-0.998445\pi\) |
−0.00488547 | − | 0.999988i | \(-0.501555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.02295 | −0.109672 | ||||||||
\(88\) | 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 | ||||||||
\(93\) | −1.19540 | − | 1.19540i | −0.123957 | − | 0.123957i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.94129i | − | 0.197108i | −0.995132 | − | 0.0985541i | \(-0.968578\pi\) | ||
0.995132 | − | 0.0985541i | \(-0.0314217\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.47189 | + | 1.47189i | −0.147931 | + | 0.147931i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3395 | + | 10.3395i | 1.02882 | + | 1.02882i | 0.999572 | + | 0.0292464i | \(0.00931074\pi\) |
0.0292464 | + | 0.999572i | \(0.490689\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.96401 | 0.489118 | 0.244559 | − | 0.969634i | \(-0.421357\pi\) | ||||
0.244559 | + | 0.969634i | \(0.421357\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.74631 | − | 2.74631i | 0.265496 | − | 0.265496i | −0.561787 | − | 0.827282i | \(-0.689886\pi\) |
0.827282 | + | 0.561787i | \(0.189886\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.99959 | + | 6.99959i | −0.670439 | + | 0.670439i | −0.957817 | − | 0.287378i | \(-0.907216\pi\) |
0.287378 | + | 0.957817i | \(0.407216\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.24522 | 0.213107 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.53194i | − | 0.614474i | −0.951633 | − | 0.307237i | \(-0.900596\pi\) | ||
0.951633 | − | 0.307237i | \(-0.0994044\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.49670 | + | 5.49670i | −0.508170 | + | 0.508170i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 7.87756i | − | 0.722134i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 10.4891i | − | 0.953553i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.10289 | + | 2.10289i | −0.189612 | + | 0.189612i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.50861i | − | 0.222603i | −0.993787 | − | 0.111302i | \(-0.964498\pi\) | ||
0.993787 | − | 0.111302i | \(-0.0355020\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.882562 | 0.0777053 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.55783 | + | 8.55783i | −0.747701 | + | 0.747701i | −0.974047 | − | 0.226346i | \(-0.927322\pi\) |
0.226346 | + | 0.974047i | \(0.427322\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.59340 | + | 5.59340i | −0.485009 | + | 0.485009i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.47131 | 0.552881 | 0.276440 | − | 0.961031i | \(-0.410845\pi\) | ||||
0.276440 | + | 0.961031i | \(0.410845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.4430 | − | 16.4430i | −1.39468 | − | 1.39468i | −0.814458 | − | 0.580223i | \(-0.802965\pi\) |
−0.580223 | − | 0.814458i | \(-0.697035\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.905982 | − | 0.905982i | 0.0762974 | − | 0.0762974i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.90800i | 0.159555i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.834712 | + | 0.834712i | 0.0688459 | + | 0.0688459i | ||||
\(148\) | 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 | ||||||||
\(153\) | −13.2074 | −1.06775 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.28013 | − | 3.28013i | −0.261783 | − | 0.261783i | 0.563995 | − | 0.825778i | \(-0.309264\pi\) |
−0.825778 | + | 0.563995i | \(0.809264\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.576147 | −0.0456914 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.3729 | −1.21156 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.27367 | + | 9.27367i | 0.726370 | + | 0.726370i | 0.969895 | − | 0.243525i | \(-0.0783037\pi\) |
−0.243525 | + | 0.969895i | \(0.578304\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.08065 | 0.547917 | 0.273958 | − | 0.961742i | \(-0.411667\pi\) | ||||
0.273958 | + | 0.961742i | \(0.411667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.87470i | − | 0.451900i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 9.37778 | + | 9.37778i | 0.717137 | + | 0.717137i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.21471 | − | 5.21471i | −0.396467 | − | 0.396467i | 0.480518 | − | 0.876985i | \(-0.340449\pi\) |
−0.876985 | + | 0.480518i | \(0.840449\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2.78369i | − | 0.209235i | ||||||
\(178\) | 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 | ||||||||
\(183\) | −2.20556 | −0.163040 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.29225 | + | 2.29225i | −0.167626 | + | 0.167626i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.15213 | + | 2.15213i | −0.156545 | + | 0.156545i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.1722 | 1.60433 | 0.802164 | − | 0.597104i | \(-0.203682\pi\) | ||||
0.802164 | + | 0.597104i | \(0.203682\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.97695i | 0.574193i | 0.957902 | + | 0.287097i | \(0.0926901\pi\) | ||||
−0.957902 | + | 0.287097i | \(0.907310\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.76327 | − | 5.76327i | 0.410616 | − | 0.410616i | −0.471337 | − | 0.881953i | \(-0.656228\pi\) |
0.881953 | + | 0.471337i | \(0.156228\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.38869i | 0.381994i | 0.981591 | + | 0.190997i | \(0.0611721\pi\) | ||||
−0.981591 | + | 0.190997i | \(0.938828\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.42521i | 0.312130i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.23921 | − | 4.23921i | 0.297534 | − | 0.297534i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 25.7739i | 1.79141i | ||||||||
\(208\) | 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 | ||||||||
\(213\) | −2.94315 | + | 2.94315i | −0.201661 | + | 0.201661i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.90766 | 0.672576 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.39120 | + | 1.39120i | 0.0940084 | + | 0.0940084i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.56026 | + | 8.56026i | −0.575826 | + | 0.575826i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.98714i | 0.266998i | 0.991049 | + | 0.133499i | \(0.0426214\pi\) | ||||
−0.991049 | + | 0.133499i | \(0.957379\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.82103 | − | 3.82103i | −0.253611 | − | 0.253611i | 0.568839 | − | 0.822449i | \(-0.307393\pi\) |
−0.822449 | + | 0.568839i | \(0.807393\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 8.80687 | + | 8.80687i | 0.581974 | + | 0.581974i | 0.935445 | − | 0.353471i | \(-0.114999\pi\) |
−0.353471 | + | 0.935445i | \(0.614999\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.367971i | 0.0242107i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.6042 | 1.08778 | 0.543889 | − | 0.839157i | \(-0.316951\pi\) | ||||
0.543889 | + | 0.839157i | \(0.316951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.895491 | − | 0.895491i | −0.0581684 | − | 0.0581684i | ||||
\(238\) | 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 | ||||||||
\(243\) | 5.43913 | + | 5.43913i | 0.348921 | + | 0.348921i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1563 | 0.773487 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.83718i | 0.243171i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −11.9933 | − | 11.9933i | −0.757010 | − | 0.757010i | 0.218767 | − | 0.975777i | \(-0.429797\pi\) |
−0.975777 | + | 0.218767i | \(0.929797\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.47328 | + | 4.47328i | 0.281233 | + | 0.281233i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 18.8752i | − | 1.17740i | −0.808350 | − | 0.588702i | \(-0.799639\pi\) | ||
0.808350 | − | 0.588702i | \(-0.200361\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.30440 | + | 9.30440i | −0.578147 | + | 0.578147i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.10738 | − | 7.10738i | −0.439936 | − | 0.439936i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 23.1398 | 1.42686 | 0.713429 | − | 0.700727i | \(-0.247141\pi\) | ||||
0.713429 | + | 0.700727i | \(0.247141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.678646 | − | 0.678646i | 0.0415325 | − | 0.0415325i | ||||
\(268\) | 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 | ||||||||
\(273\) | 1.37417i | 0.0831683i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.1534 | + | 16.1534i | −0.970563 | + | 0.970563i | −0.999579 | − | 0.0290160i | \(-0.990763\pi\) |
0.0290160 | + | 0.999579i | \(0.490763\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 16.6110i | − | 0.994474i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.43520i | 0.562857i | 0.959582 | + | 0.281429i | \(0.0908082\pi\) | ||||
−0.959582 | + | 0.281429i | \(0.909192\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.71287 | − | 8.71287i | 0.517926 | − | 0.517926i | −0.399017 | − | 0.916943i | \(-0.630649\pi\) |
0.916943 | + | 0.399017i | \(0.130649\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 17.4292i | − | 1.02881i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.56843 | −0.209908 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.406838 | + | 0.406838i | −0.0238493 | + | 0.0238493i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 11.1045 | − | 11.1045i | 0.648729 | − | 0.648729i | −0.303957 | − | 0.952686i | \(-0.598308\pi\) |
0.952686 | + | 0.303957i | \(0.0983079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.25247 | 0.0726759 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | − | 4.33372i | − | 0.248966i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.99854 | − | 2.99854i | −0.171136 | − | 0.171136i | 0.616343 | − | 0.787478i | \(-0.288614\pi\) |
−0.787478 | + | 0.616343i | \(0.788614\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.04031 | − | 1.04031i | −0.0591814 | − | 0.0591814i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.06099i | 0.513802i | 0.966438 | + | 0.256901i | \(0.0827014\pi\) | ||||
−0.966438 | + | 0.256901i | \(0.917299\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 19.5699 | 1.10616 | 0.553078 | − | 0.833129i | \(-0.313453\pi\) | ||||
0.553078 | + | 0.833129i | \(0.313453\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.1019 | + | 11.1019i | 0.623546 | + | 0.623546i | 0.946436 | − | 0.322890i | \(-0.104654\pi\) |
−0.322890 | + | 0.946436i | \(0.604654\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.46709 | −0.138131 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.15109 | −0.0642478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6045 | + | 14.6045i | 0.812614 | + | 0.812614i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.93382 | 0.162241 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 15.5996 | + | 15.5996i | 0.854851 | + | 0.854851i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.1380i | 1.36935i | 0.728847 | + | 0.684677i | \(0.240057\pi\) | ||||
−0.728847 | + | 0.684677i | \(0.759943\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.36891 | + | 1.36891i | −0.0743488 | + | 0.0743488i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.88298 | − | 2.88298i | −0.156122 | − | 0.156122i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.0770 | −1.03006 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −7.36719 | + | 7.36719i | −0.395491 | + | 0.395491i | −0.876639 | − | 0.481148i | \(-0.840220\pi\) |
0.481148 | + | 0.876639i | \(0.340220\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.25982 | − | 3.25982i | 0.174494 | − | 0.174494i | −0.614457 | − | 0.788951i | \(-0.710625\pi\) |
0.788951 | + | 0.614457i | \(0.210625\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.67729 | 0.249655 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0.502832i | 0.0267630i | 0.999910 | + | 0.0133815i | \(0.00425960\pi\) | ||||
−0.999910 | + | 0.0133815i | \(0.995740\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.65091 | + | 1.65091i | −0.0873754 | + | 0.0873754i | ||||
\(358\) | 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 | ||||||||
\(363\) | −2.19821 | + | 2.19821i | −0.115376 | + | 0.115376i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.95365i | 0.101980i | 0.998699 | + | 0.0509898i | \(0.0162376\pi\) | ||||
−0.998699 | + | 0.0509898i | \(0.983762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −29.2214 | −1.52121 | ||||||||
\(370\) | 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 | \(-0.510736\pi\) |
0.999431 | + | 0.0337233i | \(0.0107365\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9.21320 | −0.474504 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.85143 | − | 3.85143i | −0.197835 | − | 0.197835i | 0.601236 | − | 0.799071i | \(-0.294675\pi\) |
−0.799071 | + | 0.601236i | \(0.794675\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.525732 | + | 0.525732i | −0.0269341 | + | 0.0269341i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 2.29258i | − | 0.117145i | −0.998283 | − | 0.0585726i | \(-0.981345\pi\) | ||
0.998283 | − | 0.0585726i | \(-0.0186549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.13195 | + | 6.13195i | 0.311705 | + | 0.311705i | ||||
\(388\) | 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 | ||||||||
\(393\) | 3.58695 | 0.180938 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.8616 | + | 10.8616i | 0.545126 | + | 0.545126i | 0.925027 | − | 0.379901i | \(-0.124042\pi\) |
−0.379901 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 2.34443 | 0.117368 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.10783 | −0.354948 | −0.177474 | − | 0.984125i | \(-0.556793\pi\) | ||||
−0.177474 | + | 0.984125i | \(0.556793\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −10.7663 | − | 10.7663i | −0.536308 | − | 0.536308i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.41487 | 0.268405 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 29.1697i | − | 1.44235i | −0.692752 | − | 0.721176i | \(-0.743602\pi\) | ||
0.692752 | − | 0.721176i | \(-0.256398\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.35620 | − | 1.35620i | −0.0668964 | − | 0.0668964i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.5359 | + | 11.5359i | 0.567643 | + | 0.567643i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.89198i | 0.337502i | ||||||||
\(418\) | 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 | ||||||||
\(423\) | 12.5893 | 0.612115 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.14005 | − | 9.14005i | 0.442318 | − | 0.442318i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.399861 | − | 0.399861i | 0.0193055 | − | 0.0193055i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.7237 | −0.805555 | −0.402777 | − | 0.915298i | \(-0.631955\pi\) | ||||
−0.402777 | + | 0.915298i | \(0.631955\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 28.3675i | 1.36326i | 0.731699 | + | 0.681628i | \(0.238728\pi\) | ||||
−0.731699 | + | 0.681628i | \(0.761272\pi\) | |||||||
\(434\) | 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 | \(0.104423\pi\) | ||||
−0.946671 | + | 0.322203i | \(0.895577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.5990i | 0.552333i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.55246 | + | 9.55246i | −0.453851 | + | 0.453851i | −0.896630 | − | 0.442780i | \(-0.853992\pi\) |
0.442780 | + | 0.896630i | \(0.353992\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.14343i | − | 0.0540824i | ||||||
\(448\) | 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 | ||||||||
\(453\) | −2.41418 | + | 2.41418i | −0.113428 | + | 0.113428i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.84779 | 0.320326 | 0.160163 | − | 0.987091i | \(-0.448798\pi\) | ||||
0.160163 | + | 0.987091i | \(0.448798\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.61925 | + | 5.61925i | 0.262284 | + | 0.262284i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −11.7403 | + | 11.7403i | −0.546801 | + | 0.546801i | −0.925514 | − | 0.378713i | \(-0.876367\pi\) |
0.378713 | + | 0.925514i | \(0.376367\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.6096i | 1.23665i | 0.785922 | + | 0.618326i | \(0.212189\pi\) | ||||
−0.785922 | + | 0.618326i | \(0.787811\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.47583 | + | 1.47583i | 0.0682933 | + | 0.0682933i | 0.740428 | − | 0.672135i | \(-0.234623\pi\) |
−0.672135 | + | 0.740428i | \(0.734623\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.3385 | − | 18.3385i | −0.846792 | − | 0.846792i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.37484i | 0.0633494i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.12851 | 0.0978688 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.00301 | − | 4.00301i | −0.183285 | − | 0.183285i | ||||
\(478\) | 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 | ||||||||
\(483\) | 3.22172 | + | 3.22172i | 0.146593 | + | 0.146593i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.9499 | −0.768073 | −0.384036 | − | 0.923318i | \(-0.625466\pi\) | ||||
−0.384036 | + | 0.923318i | \(0.625466\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 3.88699i | − | 0.175776i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 22.8390 | + | 22.8390i | 1.03071 | + | 1.03071i | 0.999513 | + | 0.0311972i | \(0.00993197\pi\) |
0.0311972 | + | 0.999513i | \(0.490068\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11.0687 | − | 11.0687i | −0.498507 | − | 0.498507i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 24.3933i | − | 1.09419i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.33906 | − | 2.33906i | 0.104711 | − | 0.104711i | −0.652811 | − | 0.757521i | \(-0.726410\pi\) |
0.757521 | + | 0.652811i | \(0.226410\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.48390 | − | 1.48390i | −0.0662958 | − | 0.0662958i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.58801 | −0.0708057 | −0.0354029 | − | 0.999373i | \(-0.511271\pi\) | ||||
−0.0354029 | + | 0.999373i | \(0.511271\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.23117 | + | 1.23117i | −0.0546781 | + | 0.0546781i | ||||
\(508\) | 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 | ||||||||
\(513\) | − | 7.97981i | − | 0.352317i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18499 | − | 2.18499i | 0.0960956 | − | 0.0960956i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.18571i | 0.0959419i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.93031i | 0.391244i | 0.980679 | + | 0.195622i | \(0.0626725\pi\) | ||||
−0.980679 | + | 0.195622i | \(0.937327\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.0355 | − | 15.0355i | 0.657455 | − | 0.657455i | −0.297323 | − | 0.954777i | \(-0.596094\pi\) |
0.954777 | + | 0.297323i | \(0.0960937\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 25.8691i | − | 1.12687i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 55.3305 | 2.40567 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 19.3408 | − | 19.3408i | 0.839320 | − | 0.839320i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −18.9397 | + | 18.9397i | −0.820368 | + | 0.820368i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.64980 | −0.114347 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | − | 5.47798i | − | 0.235083i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.8366 | + | 32.8366i | 1.40399 | + | 1.40399i | 0.786856 | + | 0.617136i | \(0.211707\pi\) |
0.617136 | + | 0.786856i | \(0.288293\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.3240 | − | 15.3240i | −0.654013 | − | 0.654013i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.7184i | 0.669628i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.42199 | 0.315615 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.2077 | − | 24.2077i | −1.02571 | − | 1.02571i | −0.999661 | − | 0.0260537i | \(-0.991706\pi\) |
−0.0260537 | − | 0.999661i | \(-0.508294\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.94877 | 0.336197 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.960778 | 0.0405641 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.3407 | − | 22.3407i | −0.941547 | − | 0.941547i | 0.0568365 | − | 0.998384i | \(-0.481899\pi\) |
−0.998384 | + | 0.0568365i | \(0.981899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.2729 | −0.599406 | ||||||||
\(568\) | 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 | ||||||||
\(573\) | −4.64666 | − | 4.64666i | −0.194117 | − | 0.194117i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31.9232i | 1.32898i | 0.747297 | + | 0.664490i | \(0.231351\pi\) | ||||
−0.747297 | + | 0.664490i | \(0.768649\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.67174 | − | 1.67174i | 0.0694751 | − | 0.0694751i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −15.9016 | − | 15.9016i | −0.659710 | − | 0.659710i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.38951 | −0.0575477 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 26.2847 | − | 26.2847i | 1.08488 | − | 1.08488i | 0.0888379 | − | 0.996046i | \(-0.471685\pi\) |
0.996046 | − | 0.0888379i | \(-0.0283153\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.3681 | + | 18.3681i | −0.756846 | + | 0.756846i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.41563 | −0.0993658 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 38.2085i | − | 1.56904i | −0.620106 | − | 0.784518i | \(-0.712910\pi\) | ||
0.620106 | − | 0.784518i | \(-0.287090\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.12931 | − | 1.12931i | 0.0462197 | − | 0.0462197i | ||||
\(598\) | 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 | ||||||||
\(603\) | −30.7459 | + | 30.7459i | −1.25207 | + | 1.25207i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 12.9648i | 0.526226i | 0.964765 | + | 0.263113i | \(0.0847492\pi\) | ||||
−0.964765 | + | 0.263113i | \(0.915251\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.77683 | −0.0720009 | ||||||||
\(610\) | 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 | \(-0.818044\pi\) |
0.541004 | + | 0.841020i | \(0.318044\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2743 | −0.936989 | −0.468494 | − | 0.883467i | \(-0.655203\pi\) | ||||
−0.468494 | + | 0.883467i | \(0.655203\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −31.6213 | − | 31.6213i | −1.27097 | − | 1.27097i | −0.945581 | − | 0.325386i | \(-0.894506\pi\) |
−0.325386 | − | 0.945581i | \(-0.605494\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.9659 | − | 10.9659i | 0.440045 | − | 0.440045i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.62474i | 0.225351i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.682194 | − | 0.682194i | −0.0272442 | − | 0.0272442i | ||||
\(628\) | 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 | ||||||||
\(633\) | 4.50775 | 0.179167 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.51782 | + | 7.51782i | 0.297867 | + | 0.297867i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −40.8974 | −1.61788 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.2240 | 0.403825 | 0.201912 | − | 0.979404i | \(-0.435284\pi\) | ||||
0.201912 | + | 0.979404i | \(0.435284\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.7202 | + | 13.7202i | 0.541074 | + | 0.541074i | 0.923844 | − | 0.382770i | \(-0.125030\pi\) |
−0.382770 | + | 0.923844i | \(0.625030\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.6767 | −0.734255 | −0.367128 | − | 0.930171i | \(-0.619659\pi\) | ||||
−0.367128 | + | 0.930171i | \(0.619659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.71353i | − | 0.263529i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.07636 | − | 2.07636i | −0.0813790 | − | 0.0813790i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 12.7935 | + | 12.7935i | 0.500647 | + | 0.500647i | 0.911639 | − | 0.410992i | \(-0.134817\pi\) |
−0.410992 | + | 0.911639i | \(0.634817\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 19.3318i | 0.754205i | ||||||||
\(658\) | 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 | ||||||||
\(663\) | 3.58797 | 0.139345 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −21.6003 | + | 21.6003i | −0.836367 | + | 0.836367i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.835589 | − | 0.835589i | 0.0323057 | − | 0.0323057i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.31923 | −0.205347 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 21.5360i | − | 0.830150i | −0.909787 | − | 0.415075i | \(-0.863755\pi\) | ||
0.909787 | − | 0.415075i | \(-0.136245\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 13.1852 | − | 13.1852i | 0.506750 | − | 0.506750i | −0.406778 | − | 0.913527i | \(-0.633348\pi\) |
0.913527 | + | 0.406778i | \(0.133348\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 3.37195i | − | 0.129404i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.60156i | 0.0613717i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 30.6011 | − | 30.6011i | 1.17092 | − | 1.17092i | 0.188926 | − | 0.981991i | \(-0.439499\pi\) |
0.981991 | − | 0.188926i | \(-0.0605008\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.69133i | − | 0.140833i | ||||||
\(688\) | 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 | ||||||||
\(693\) | −2.55663 | + | 2.55663i | −0.0971182 | + | 0.0971182i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −45.5079 | −1.72373 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.47976 | − | 3.47976i | −0.131617 | − | 0.131617i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.5583 | − | 18.5583i | 0.700937 | − | 0.700937i | −0.263675 | − | 0.964612i | \(-0.584935\pi\) |
0.964612 | + | 0.263675i | \(0.0849345\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 34.4995i | − | 1.30117i | ||||||
\(704\) | 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 | 0.620040 | − | 0.784570i | \(-0.287116\pi\) |
−0.784570 | + | 0.620040i | \(0.787116\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 12.4436i | − | 0.466670i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −50.4831 | −1.89061 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.798957 | − | 0.798957i | −0.0298376 | − | 0.0298376i | ||||
\(718\) | 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 | ||||||||
\(723\) | −2.00137 | − | 2.00137i | −0.0744319 | − | 0.0744319i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −39.3600 | −1.45978 | −0.729891 | − | 0.683563i | \(-0.760429\pi\) | ||||
−0.729891 | + | 0.683563i | \(0.760429\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.3717i | 0.828581i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 9.54958 | + | 9.54958i | 0.353204 | + | 0.353204i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −34.0787 | − | 34.0787i | −1.25873 | − | 1.25873i | −0.951701 | − | 0.307026i | \(-0.900666\pi\) |
−0.307026 | − | 0.951701i | \(-0.599334\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.6724i | 0.393124i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 15.4278 | − | 15.4278i | 0.567520 | − | 0.567520i | −0.363913 | − | 0.931433i | \(-0.618559\pi\) |
0.931433 | + | 0.363913i | \(0.118559\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.54761 | − | 2.54761i | −0.0935888 | − | 0.0935888i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.5004 | 0.862147 | 0.431074 | − | 0.902317i | \(-0.358135\pi\) | ||||
0.431074 | + | 0.902317i | \(0.358135\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −26.6603 | + | 26.6603i | −0.975451 | + | 0.975451i | ||||
\(748\) | 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 | ||||||||
\(753\) | 5.02690i | 0.183190i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.8434 | − | 18.8434i | 0.684874 | − | 0.684874i | −0.276220 | − | 0.961094i | \(-0.589082\pi\) |
0.961094 | + | 0.276220i | \(0.0890819\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 1.87494i | − | 0.0680561i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 22.2837i | − | 0.807783i | −0.914807 | − | 0.403891i | \(-0.867657\pi\) | ||
0.914807 | − | 0.403891i | \(-0.132343\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −12.1580 | + | 12.1580i | −0.440151 | + | 0.440151i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 25.0713i | − | 0.905271i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −10.5399 | −0.380077 | −0.190039 | − | 0.981777i | \(-0.560861\pi\) | ||||
−0.190039 | + | 0.981777i | \(0.560861\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.95571 | + | 3.95571i | −0.142461 | + | 0.142461i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.07768 | + | 4.07768i | −0.146664 | + | 0.146664i | −0.776626 | − | 0.629962i | \(-0.783070\pi\) |
0.629962 | + | 0.776626i | \(0.283070\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.89987 | 0.139907 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 6.04786i | 0.216133i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.16669 | − | 8.16669i | −0.291111 | − | 0.291111i | 0.546408 | − | 0.837519i | \(-0.315995\pi\) |
−0.837519 | + | 0.546408i | \(0.815995\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.84943 | − | 4.84943i | −0.172644 | − | 0.172644i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 11.3458i | − | 0.403409i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.8643 | −0.705403 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.9971 | − | 17.9971i | −0.637491 | − | 0.637491i | 0.312445 | − | 0.949936i | \(-0.398852\pi\) |
−0.949936 | + | 0.312445i | \(0.898852\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.6060 | 0.693609 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 9.43033 | 0.333204 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.35520 | + | 3.35520i | 0.118402 | + | 0.118402i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.45835 | −0.156941 | ||||||||
\(808\) | 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 | ||||||||
\(813\) | 4.18646 | + | 4.18646i | 0.146826 | + | 0.146826i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 13.5612i | − | 0.474447i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.54757 | + | 9.54757i | −0.333619 | + | 0.333619i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −21.4050 | − | 21.4050i | −0.747038 | − | 0.747038i | 0.226884 | − | 0.973922i | \(-0.427146\pi\) |
−0.973922 | + | 0.226884i | \(0.927146\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −43.7323 | −1.52441 | −0.762206 | − | 0.647334i | \(-0.775884\pi\) | ||||
−0.762206 | + | 0.647334i | \(0.775884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.9621 | − | 19.9621i | 0.694149 | − | 0.694149i | −0.268993 | − | 0.963142i | \(-0.586691\pi\) |
0.963142 | + | 0.268993i | \(0.0866908\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.3869 | + | 31.3869i | −1.09011 | + | 1.09011i | −0.0945964 | + | 0.995516i | \(0.530156\pi\) |
−0.995516 | + | 0.0945964i | \(0.969844\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.77057 | 0.234868 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 18.0637i | 0.625869i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.06737 | + | 7.06737i | −0.244284 | + | 0.244284i | ||||
\(838\) | 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 | ||||||||
\(843\) | 1.97735 | − | 1.97735i | 0.0681035 | − | 0.0681035i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 18.2192i | − | 0.626018i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.65193 | −0.125334 | ||||||||
\(850\) | 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 | \(-0.925109\pi\) |
0.233114 | + | 0.972449i | \(0.425109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 41.3609 | 1.41286 | 0.706431 | − | 0.707782i | \(-0.250304\pi\) | ||||
0.706431 | + | 0.707782i | \(0.250304\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.700596 | − | 0.700596i | −0.0239040 | − | 0.0239040i | 0.695054 | − | 0.718958i | \(-0.255381\pi\) |
−0.718958 | + | 0.695054i | \(0.755381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.65265 | + | 3.65265i | −0.124482 | + | 0.124482i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 55.0780i | − | 1.87488i | −0.348150 | − | 0.937439i | \(-0.613190\pi\) | ||
0.348150 | − | 0.937439i | \(-0.386810\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.747840 | + | 0.747840i | 0.0253980 | + | 0.0253980i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.15969 | − | 2.15969i | −0.0732623 | − | 0.0732623i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 39.8556i | 1.35045i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.65335 | −0.191337 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 36.5100 | + | 36.5100i | 1.23285 | + | 1.23285i | 0.962863 | + | 0.269992i | \(0.0870211\pi\) |
0.269992 | + | 0.962863i | \(0.412979\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.65435 | −0.156987 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.3503 | 1.83111 | 0.915554 | − | 0.402196i | \(-0.131753\pi\) | ||||
0.915554 | + | 0.402196i | \(0.131753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.5476 | − | 35.5476i | −1.19627 | − | 1.19627i | −0.975274 | − | 0.220999i | \(-0.929068\pi\) |
−0.220999 | − | 0.975274i | \(-0.570932\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.817003 | −0.0274323 | −0.0137161 | − | 0.999906i | \(-0.504366\pi\) | ||||
−0.0137161 | + | 0.999906i | \(0.504366\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 4.35737i | − | 0.146141i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.15320 | + | 4.15320i | 0.139137 | + | 0.139137i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.9211 | − | 13.9211i | −0.465851 | − | 0.465851i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 7.00186i | − | 0.233785i | ||||||
\(898\) | 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 | ||||||||
\(903\) | 1.53298 | 0.0510144 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.36159 | − | 3.36159i | 0.111620 | − | 0.111620i | −0.649091 | − | 0.760711i | \(-0.724851\pi\) |
0.760711 | + | 0.649091i | \(0.224851\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 30.1103 | − | 30.1103i | 0.998695 | − | 0.998695i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −34.6568 | −1.14823 | −0.574116 | − | 0.818774i | \(-0.694654\pi\) | ||||
−0.574116 | + | 0.818774i | \(0.694654\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.25426i | 0.306271i | ||||||||
\(914\) | 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 | \(0.131524\pi\) | ||||
−0.915843 | + | 0.401537i | \(0.868476\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.25681i | 0.0414135i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −26.5074 | + | 26.5074i | −0.872501 | + | 0.872501i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 14.4560i | − | 0.474797i | ||||||
\(928\) | 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 | ||||||||
\(933\) | 1.89892 | − | 1.89892i | 0.0621680 | − | 0.0621680i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.4847 | −0.767211 | −0.383606 | − | 0.923497i | \(-0.625318\pi\) | ||||
−0.383606 | + | 0.923497i | \(0.625318\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.10129 | − | 4.10129i | −0.133840 | − | 0.133840i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 27.7583 | − | 27.7583i | 0.904896 | − | 0.904896i | −0.0909585 | − | 0.995855i | \(-0.528993\pi\) |
0.995855 | + | 0.0909585i | \(0.0289931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 88.8078i | 2.89198i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −27.2916 | − | 27.2916i | −0.886857 | − | 0.886857i | 0.107363 | − | 0.994220i | \(-0.465759\pi\) |
−0.994220 | + | 0.107363i | \(0.965759\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.5298 | + | 12.5298i | 0.406734 | + | 0.406734i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 4.65329i | − | 0.150893i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −12.1516 | −0.393630 | −0.196815 | − | 0.980441i | \(-0.563060\pi\) | ||||
−0.196815 | + | 0.980441i | \(0.563060\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.517031 | + | 0.517031i | 0.0167132 | + | 0.0167132i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 11.2404 | 0.362972 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.53571 | 0.0495392 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.99769 | − | 7.99769i | −0.257722 | − | 0.257722i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.2694 | 1.55224 | 0.776120 | − | 0.630585i | \(-0.217185\pi\) | ||||
0.776120 | + | 0.630585i | \(0.217185\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 6.12135i | − | 0.196646i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −5.92047 | − | 5.92047i | −0.189997 | − | 0.189997i | 0.605698 | − | 0.795695i | \(-0.292894\pi\) |
−0.795695 | + | 0.605698i | \(0.792894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.5610 | − | 28.5610i | −0.915623 | − | 0.915623i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 27.7522i | 0.887872i | 0.896059 | + | 0.443936i | \(0.146418\pi\) | ||||
−0.896059 | + | 0.443936i | \(0.853582\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.63671 | − | 1.63671i | 0.0523096 | − | 0.0523096i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 20.3839 | + | 20.3839i | 0.650808 | + | 0.650808i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.3604 | −0.904556 | −0.452278 | − | 0.891877i | \(-0.649389\pi\) | ||||
−0.452278 | + | 0.891877i | \(0.649389\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.57366 | − | 1.57366i | 0.0500901 | − | 0.0500901i | ||||
\(988\) | 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 | ||||||||
\(993\) | − | 3.41483i | − | 0.108366i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.5572 | − | 10.5572i | 0.334349 | − | 0.334349i | −0.519887 | − | 0.854235i | \(-0.674026\pi\) |
0.854235 | + | 0.519887i | \(0.174026\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 13.2741i | − | 0.419974i |
(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 | 1600.2.q.g.49.4 | 16 | ||
4.3 | odd | 2 | 400.2.q.h.149.2 | 16 | |||
5.2 | odd | 4 | 320.2.l.a.241.4 | 16 | |||
5.3 | odd | 4 | 1600.2.l.i.1201.5 | 16 | |||
5.4 | even | 2 | 1600.2.q.h.49.5 | 16 | |||
15.2 | even | 4 | 2880.2.t.c.2161.4 | 16 | |||
16.3 | odd | 4 | 400.2.q.g.349.7 | 16 | |||
16.13 | even | 4 | 1600.2.q.h.849.5 | 16 | |||
20.3 | even | 4 | 400.2.l.h.101.3 | 16 | |||
20.7 | even | 4 | 80.2.l.a.21.6 | ✓ | 16 | ||
20.19 | odd | 2 | 400.2.q.g.149.7 | 16 | |||
40.27 | even | 4 | 640.2.l.b.481.4 | 16 | |||
40.37 | odd | 4 | 640.2.l.a.481.5 | 16 | |||
60.47 | odd | 4 | 720.2.t.c.181.3 | 16 | |||
80.3 | even | 4 | 400.2.l.h.301.3 | 16 | |||
80.13 | odd | 4 | 1600.2.l.i.401.5 | 16 | |||
80.19 | odd | 4 | 400.2.q.h.349.2 | 16 | |||
80.27 | even | 4 | 640.2.l.b.161.4 | 16 | |||
80.29 | even | 4 | inner | 1600.2.q.g.849.4 | 16 | ||
80.37 | odd | 4 | 640.2.l.a.161.5 | 16 | |||
80.67 | even | 4 | 80.2.l.a.61.6 | yes | 16 | ||
80.77 | odd | 4 | 320.2.l.a.81.4 | 16 | |||
160.67 | even | 8 | 5120.2.a.s.1.6 | 8 | |||
160.77 | odd | 8 | 5120.2.a.t.1.6 | 8 | |||
160.147 | even | 8 | 5120.2.a.v.1.3 | 8 | |||
160.157 | odd | 8 | 5120.2.a.u.1.3 | 8 | |||
240.77 | even | 4 | 2880.2.t.c.721.1 | 16 | |||
240.227 | odd | 4 | 720.2.t.c.541.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.2.l.a.21.6 | ✓ | 16 | 20.7 | even | 4 | ||
80.2.l.a.61.6 | yes | 16 | 80.67 | even | 4 | ||
320.2.l.a.81.4 | 16 | 80.77 | odd | 4 | |||
320.2.l.a.241.4 | 16 | 5.2 | odd | 4 | |||
400.2.l.h.101.3 | 16 | 20.3 | even | 4 | |||
400.2.l.h.301.3 | 16 | 80.3 | even | 4 | |||
400.2.q.g.149.7 | 16 | 20.19 | odd | 2 | |||
400.2.q.g.349.7 | 16 | 16.3 | odd | 4 | |||
400.2.q.h.149.2 | 16 | 4.3 | odd | 2 | |||
400.2.q.h.349.2 | 16 | 80.19 | odd | 4 | |||
640.2.l.a.161.5 | 16 | 80.37 | odd | 4 | |||
640.2.l.a.481.5 | 16 | 40.37 | odd | 4 | |||
640.2.l.b.161.4 | 16 | 80.27 | even | 4 | |||
640.2.l.b.481.4 | 16 | 40.27 | even | 4 | |||
720.2.t.c.181.3 | 16 | 60.47 | odd | 4 | |||
720.2.t.c.541.3 | 16 | 240.227 | odd | 4 | |||
1600.2.l.i.401.5 | 16 | 80.13 | odd | 4 | |||
1600.2.l.i.1201.5 | 16 | 5.3 | odd | 4 | |||
1600.2.q.g.49.4 | 16 | 1.1 | even | 1 | trivial | ||
1600.2.q.g.849.4 | 16 | 80.29 | even | 4 | inner | ||
1600.2.q.h.49.5 | 16 | 5.4 | even | 2 | |||
1600.2.q.h.849.5 | 16 | 16.13 | even | 4 | |||
2880.2.t.c.721.1 | 16 | 240.77 | even | 4 | |||
2880.2.t.c.2161.4 | 16 | 15.2 | even | 4 | |||
5120.2.a.s.1.6 | 8 | 160.67 | even | 8 | |||
5120.2.a.t.1.6 | 8 | 160.77 | odd | 8 | |||
5120.2.a.u.1.3 | 8 | 160.157 | odd | 8 | |||
5120.2.a.v.1.3 | 8 | 160.147 | even | 8 |