Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4752,2,Mod(1,4752)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4752, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4752.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4752 = 2^{4} \cdot 3^{3} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4752.a (trivial) |
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: | yes |
Analytic conductor: | \(37.9449110405\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 297) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4752.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | ||||||||
\(5\) | 0.732051 | 0.327383 | 0.163692 | − | 0.986512i | \(-0.447660\pi\) | ||||
0.163692 | + | 0.986512i | \(0.447660\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.73205 | 1.41058 | 0.705291 | − | 0.708918i | \(-0.250816\pi\) | ||||
0.705291 | + | 0.708918i | \(0.250816\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.267949 | −0.0743157 | −0.0371579 | − | 0.999309i | \(-0.511830\pi\) | ||||
−0.0371579 | + | 0.999309i | \(0.511830\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.19615 | 1.01772 | 0.508858 | − | 0.860850i | \(-0.330068\pi\) | ||||
0.508858 | + | 0.860850i | \(0.330068\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.19615 | 1.19208 | 0.596040 | − | 0.802955i | \(-0.296740\pi\) | ||||
0.596040 | + | 0.802955i | \(0.296740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.00000 | 1.66812 | 0.834058 | − | 0.551677i | \(-0.186012\pi\) | ||||
0.834058 | + | 0.551677i | \(0.186012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.46410 | −0.892820 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.26795 | 0.235452 | 0.117726 | − | 0.993046i | \(-0.462440\pi\) | ||||
0.117726 | + | 0.993046i | \(0.462440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.535898 | −0.0962502 | −0.0481251 | − | 0.998841i | \(-0.515325\pi\) | ||||
−0.0481251 | + | 0.998841i | \(0.515325\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.73205 | 0.461801 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.46410 | −1.06269 | −0.531346 | − | 0.847155i | \(-0.678314\pi\) | ||||
−0.531346 | + | 0.847155i | \(0.678314\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.46410 | −0.228654 | −0.114327 | − | 0.993443i | \(-0.536471\pi\) | ||||
−0.114327 | + | 0.993443i | \(0.536471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.46410 | −0.528271 | −0.264135 | − | 0.964486i | \(-0.585087\pi\) | ||||
−0.264135 | + | 0.964486i | \(0.585087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.1962 | 1.48726 | 0.743631 | − | 0.668590i | \(-0.233102\pi\) | ||||
0.743631 | + | 0.668590i | \(0.233102\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | 0.989743 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.73205 | −0.649997 | −0.324999 | − | 0.945715i | \(-0.605364\pi\) | ||||
−0.324999 | + | 0.945715i | \(0.605364\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.732051 | 0.0987097 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.1962 | 1.32743 | 0.663713 | − | 0.747987i | \(-0.268980\pi\) | ||||
0.663713 | + | 0.747987i | \(0.268980\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.26795 | −0.546455 | −0.273227 | − | 0.961949i | \(-0.588091\pi\) | ||||
−0.273227 | + | 0.961949i | \(0.588091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.196152 | −0.0243297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.92820 | −0.724245 | −0.362123 | − | 0.932130i | \(-0.617948\pi\) | ||||
−0.362123 | + | 0.932130i | \(0.617948\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.8564 | −1.64445 | −0.822226 | − | 0.569160i | \(-0.807268\pi\) | ||||
−0.822226 | + | 0.569160i | \(0.807268\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.19615 | 0.374081 | 0.187041 | − | 0.982352i | \(-0.440110\pi\) | ||||
0.187041 | + | 0.982352i | \(0.440110\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.73205 | 0.425307 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.73205 | 0.644906 | 0.322453 | − | 0.946585i | \(-0.395493\pi\) | ||||
0.322453 | + | 0.946585i | \(0.395493\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.07180 | 0.333183 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.339746 | 0.0360130 | 0.0180065 | − | 0.999838i | \(-0.494268\pi\) | ||||
0.0180065 | + | 0.999838i | \(0.494268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.00000 | −0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.80385 | 0.390267 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.39230 | −0.547506 | −0.273753 | − | 0.961800i | \(-0.588265\pi\) | ||||
−0.273753 | + | 0.961800i | \(0.588265\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.196152 | 0.0195179 | 0.00975895 | − | 0.999952i | \(-0.496894\pi\) | ||||
0.00975895 | + | 0.999952i | \(0.496894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8564 | −1.26678 | −0.633390 | − | 0.773833i | \(-0.718337\pi\) | ||||
−0.633390 | + | 0.773833i | \(0.718337\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.66025 | 0.547197 | 0.273599 | − | 0.961844i | \(-0.411786\pi\) | ||||
0.273599 | + | 0.961844i | \(0.411786\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.8564 | 1.13564 | 0.567819 | − | 0.823154i | \(-0.307787\pi\) | ||||
0.567819 | + | 0.823154i | \(0.307787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.6603 | 1.09690 | 0.548452 | − | 0.836182i | \(-0.315217\pi\) | ||||
0.548452 | + | 0.836182i | \(0.315217\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.85641 | 0.546113 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.6603 | 1.43557 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.92820 | −0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.46410 | −0.484861 | −0.242430 | − | 0.970169i | \(-0.577945\pi\) | ||||
−0.242430 | + | 0.970169i | \(0.577945\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.1244 | −1.32142 | −0.660711 | − | 0.750641i | \(-0.729745\pi\) | ||||
−0.660711 | + | 0.750641i | \(0.729745\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.3923 | 1.68153 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.39230 | 0.717003 | 0.358501 | − | 0.933529i | \(-0.383288\pi\) | ||||
0.358501 | + | 0.933529i | \(0.383288\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.19615 | 0.610370 | 0.305185 | − | 0.952293i | \(-0.401282\pi\) | ||||
0.305185 | + | 0.952293i | \(0.401282\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.267949 | −0.0224070 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.928203 | 0.0770831 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −9.85641 | −0.807468 | −0.403734 | − | 0.914876i | \(-0.632288\pi\) | ||||
−0.403734 | + | 0.914876i | \(0.632288\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.80385 | 0.390932 | 0.195466 | − | 0.980711i | \(-0.437378\pi\) | ||||
0.195466 | + | 0.980711i | \(0.437378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.392305 | −0.0315107 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.5359 | 0.840856 | 0.420428 | − | 0.907326i | \(-0.361880\pi\) | ||||
0.420428 | + | 0.907326i | \(0.361880\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 29.8564 | 2.35301 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −19.0000 | −1.48819 | −0.744097 | − | 0.668071i | \(-0.767120\pi\) | ||||
−0.744097 | + | 0.668071i | \(0.767120\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 22.7321 | 1.75906 | 0.879529 | − | 0.475844i | \(-0.157857\pi\) | ||||
0.879529 | + | 0.475844i | \(0.157857\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9282 | −0.994477 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.39230 | 0.333941 | 0.166970 | − | 0.985962i | \(-0.446602\pi\) | ||||
0.166970 | + | 0.985962i | \(0.446602\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.6603 | −1.25940 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −14.1962 | −1.06107 | −0.530535 | − | 0.847663i | \(-0.678009\pi\) | ||||
−0.530535 | + | 0.847663i | \(0.678009\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.3205 | −1.21309 | −0.606547 | − | 0.795048i | \(-0.707446\pi\) | ||||
−0.606547 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.73205 | −0.347907 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 4.19615 | 0.306853 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.00000 | −0.289430 | −0.144715 | − | 0.989473i | \(-0.546227\pi\) | ||||
−0.144715 | + | 0.989473i | \(0.546227\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.80385 | −0.201825 | −0.100913 | − | 0.994895i | \(-0.532176\pi\) | ||||
−0.100913 | + | 0.994895i | \(0.532176\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.66025 | −0.688265 | −0.344132 | − | 0.938921i | \(-0.611827\pi\) | ||||
−0.344132 | + | 0.938921i | \(0.611827\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 15.0000 | 1.06332 | 0.531661 | − | 0.846957i | \(-0.321568\pi\) | ||||
0.531661 | + | 0.846957i | \(0.321568\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.73205 | 0.332125 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.07180 | −0.0748575 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.19615 | 0.359425 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.33975 | 0.642975 | 0.321487 | − | 0.946914i | \(-0.395817\pi\) | ||||
0.321487 | + | 0.946914i | \(0.395817\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.53590 | −0.172947 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.00000 | −0.135769 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.12436 | −0.0756323 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −17.8564 | −1.19575 | −0.597877 | − | 0.801588i | \(-0.703989\pi\) | ||||
−0.597877 | + | 0.801588i | \(0.703989\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −29.6603 | −1.96862 | −0.984310 | − | 0.176447i | \(-0.943540\pi\) | ||||
−0.984310 | + | 0.176447i | \(0.943540\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −16.3923 | −1.08323 | −0.541617 | − | 0.840625i | \(-0.682188\pi\) | ||||
−0.541617 | + | 0.840625i | \(0.682188\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.33975 | 0.415331 | 0.207665 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207665 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.46410 | 0.486904 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.3923 | 1.06033 | 0.530165 | − | 0.847894i | \(-0.322130\pi\) | ||||
0.530165 | + | 0.847894i | \(0.322130\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.1962 | 0.978870 | 0.489435 | − | 0.872040i | \(-0.337203\pi\) | ||||
0.489435 | + | 0.872040i | \(0.337203\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.07180 | 0.324025 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.39230 | −0.0885902 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5885 | 0.668337 | 0.334169 | − | 0.942513i | \(-0.391544\pi\) | ||||
0.334169 | + | 0.942513i | \(0.391544\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.7321 | 0.794204 | 0.397102 | − | 0.917775i | \(-0.370016\pi\) | ||||
0.397102 | + | 0.917775i | \(0.370016\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −24.1244 | −1.49901 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.87564 | 0.300645 | 0.150323 | − | 0.988637i | \(-0.451969\pi\) | ||||
0.150323 | + | 0.988637i | \(0.451969\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.46410 | −0.212798 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.9282 | 1.64184 | 0.820921 | − | 0.571042i | \(-0.193461\pi\) | ||||
0.820921 | + | 0.571042i | \(0.193461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.26795 | 0.137768 | 0.0688841 | − | 0.997625i | \(-0.478056\pi\) | ||||
0.0688841 | + | 0.997625i | \(0.478056\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.46410 | −0.269195 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.85641 | −0.592214 | −0.296107 | − | 0.955155i | \(-0.595689\pi\) | ||||
−0.296107 | + | 0.955155i | \(0.595689\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.2487 | 1.56032 | 0.780162 | − | 0.625578i | \(-0.215137\pi\) | ||||
0.780162 | + | 0.625578i | \(0.215137\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.46410 | −0.322536 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.607695 | 0.0357468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 27.1244 | 1.58462 | 0.792311 | − | 0.610118i | \(-0.208878\pi\) | ||||
0.792311 | + | 0.610118i | \(0.208878\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.46410 | 0.434577 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.14359 | −0.123967 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9282 | −0.745169 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.12436 | −0.178900 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.3205 | 1.55926 | 0.779632 | − | 0.626238i | \(-0.215406\pi\) | ||||
0.779632 | + | 0.626238i | \(0.215406\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.5885 | 1.73451 | 0.867256 | − | 0.497862i | \(-0.165881\pi\) | ||||
0.867256 | + | 0.497862i | \(0.165881\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.92820 | −0.108988 | −0.0544942 | − | 0.998514i | \(-0.517355\pi\) | ||||
−0.0544942 | + | 0.998514i | \(0.517355\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.5885 | −0.594707 | −0.297354 | − | 0.954767i | \(-0.596104\pi\) | ||||
−0.297354 | + | 0.954767i | \(0.596104\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.26795 | 0.0709915 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 21.8038 | 1.21320 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.19615 | 0.0663506 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 38.0526 | 2.09791 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 27.3923 | 1.50562 | 0.752809 | − | 0.658239i | \(-0.228699\pi\) | ||||
0.752809 | + | 0.658239i | \(0.228699\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.33975 | −0.237106 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −29.9808 | −1.63316 | −0.816578 | − | 0.577235i | \(-0.804132\pi\) | ||||
−0.816578 | + | 0.577235i | \(0.804132\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.535898 | −0.0290205 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.267949 | −0.0144679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.3397 | 0.555067 | 0.277533 | − | 0.960716i | \(-0.410483\pi\) | ||||
0.277533 | + | 0.960716i | \(0.410483\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.87564 | −0.314516 | −0.157258 | − | 0.987558i | \(-0.550265\pi\) | ||||
−0.157258 | + | 0.987558i | \(0.550265\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −21.1244 | −1.12434 | −0.562168 | − | 0.827023i | \(-0.690033\pi\) | ||||
−0.562168 | + | 0.827023i | \(0.690033\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1436 | −0.538366 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.53590 | 0.344952 | 0.172476 | − | 0.985014i | \(-0.444823\pi\) | ||||
0.172476 | + | 0.985014i | \(0.444823\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.00000 | 0.421053 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.33975 | 0.122468 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.9282 | −0.727046 | −0.363523 | − | 0.931585i | \(-0.618426\pi\) | ||||
−0.363523 | + | 0.931585i | \(0.618426\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.6603 | −0.916875 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.1244 | −1.04200 | −0.521000 | − | 0.853557i | \(-0.674441\pi\) | ||||
−0.521000 | + | 0.853557i | \(0.674441\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.339746 | −0.0174978 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.8564 | −0.763122 | −0.381561 | − | 0.924344i | \(-0.624613\pi\) | ||||
−0.381561 | + | 0.924344i | \(0.624613\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 24.7321 | 1.26375 | 0.631874 | − | 0.775071i | \(-0.282286\pi\) | ||||
0.631874 | + | 0.775071i | \(0.282286\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.73205 | 0.139238 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −21.4641 | −1.08827 | −0.544137 | − | 0.838997i | \(-0.683143\pi\) | ||||
−0.544137 | + | 0.838997i | \(0.683143\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 33.5692 | 1.69767 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.19615 | 0.211131 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.3923 | 1.02346 | 0.511730 | − | 0.859146i | \(-0.329005\pi\) | ||||
0.511730 | + | 0.859146i | \(0.329005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.53590 | 0.326387 | 0.163194 | − | 0.986594i | \(-0.447820\pi\) | ||||
0.163194 | + | 0.986594i | \(0.447820\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.143594 | 0.00715290 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.46410 | −0.320414 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.9090 | 1.62724 | 0.813622 | − | 0.581394i | \(-0.197493\pi\) | ||||
0.813622 | + | 0.581394i | \(0.197493\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 38.0526 | 1.87244 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 23.7128 | 1.15845 | 0.579223 | − | 0.815169i | \(-0.303356\pi\) | ||||
0.579223 | + | 0.815169i | \(0.303356\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.8564 | 1.01648 | 0.508240 | − | 0.861216i | \(-0.330296\pi\) | ||||
0.508240 | + | 0.861216i | \(0.330296\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −18.7321 | −0.908638 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.9282 | −0.770820 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.5359 | 0.700170 | 0.350085 | − | 0.936718i | \(-0.386153\pi\) | ||||
0.350085 | + | 0.936718i | \(0.386153\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.60770 | −0.173375 | −0.0866874 | − | 0.996236i | \(-0.527628\pi\) | ||||
−0.0866874 | + | 0.996236i | \(0.527628\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 41.5692 | 1.98853 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.5359 | −1.45740 | −0.728699 | − | 0.684834i | \(-0.759875\pi\) | ||||
−0.728699 | + | 0.684834i | \(0.759875\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.26795 | −0.155265 | −0.0776325 | − | 0.996982i | \(-0.524736\pi\) | ||||
−0.0776325 | + | 0.996982i | \(0.524736\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.248711 | 0.0117900 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.2487 | 0.483667 | 0.241833 | − | 0.970318i | \(-0.422251\pi\) | ||||
0.241833 | + | 0.970318i | \(0.422251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.46410 | −0.0689419 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.732051 | −0.0343191 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.0718 | −0.517917 | −0.258958 | − | 0.965888i | \(-0.583379\pi\) | ||||
−0.258958 | + | 0.965888i | \(0.583379\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 29.6603 | 1.38142 | 0.690708 | − | 0.723134i | \(-0.257299\pi\) | ||||
0.690708 | + | 0.723134i | \(0.257299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.7846 | 1.19831 | 0.599156 | − | 0.800632i | \(-0.295503\pi\) | ||||
0.599156 | + | 0.800632i | \(0.295503\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.9282 | −0.875893 | −0.437946 | − | 0.899001i | \(-0.644294\pi\) | ||||
−0.437946 | + | 0.899001i | \(0.644294\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −22.1244 | −1.02161 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.46410 | −0.159280 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.1962 | −1.06431 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.5167 | −0.526210 | −0.263105 | − | 0.964767i | \(-0.584747\pi\) | ||||
−0.263105 | + | 0.964767i | \(0.584747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.73205 | 0.0789747 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.94744 | −0.179244 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.8564 | −0.854465 | −0.427233 | − | 0.904142i | \(-0.640511\pi\) | ||||
−0.427233 | + | 0.904142i | \(0.640511\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −30.0526 | −1.35625 | −0.678126 | − | 0.734945i | \(-0.737208\pi\) | ||||
−0.678126 | + | 0.734945i | \(0.737208\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.32051 | 0.239624 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −51.7128 | −2.31964 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.4641 | 0.871333 | 0.435666 | − | 0.900108i | \(-0.356513\pi\) | ||||
0.435666 | + | 0.900108i | \(0.356513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 22.9282 | 1.02232 | 0.511159 | − | 0.859486i | \(-0.329216\pi\) | ||||
0.511159 | + | 0.859486i | \(0.329216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.143594 | 0.00638983 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −16.0526 | −0.711517 | −0.355759 | − | 0.934578i | \(-0.615777\pi\) | ||||
−0.355759 | + | 0.934578i | \(0.615777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11.9282 | 0.527673 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.41154 | −0.414722 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1962 | 0.448426 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.7846 | −0.910590 | −0.455295 | − | 0.890341i | \(-0.650466\pi\) | ||||
−0.455295 | + | 0.890341i | \(0.650466\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −39.9808 | −1.74824 | −0.874118 | − | 0.485713i | \(-0.838560\pi\) | ||||
−0.874118 | + | 0.485713i | \(0.838560\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.24871 | −0.0979554 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 41.0000 | 1.78261 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.392305 | 0.0169926 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.14359 | 0.179143 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 6.92820 | 0.298419 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.5885 | −1.01415 | −0.507073 | − | 0.861903i | \(-0.669273\pi\) | ||||
−0.507073 | + | 0.861903i | \(0.669273\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.67949 | 0.371789 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.8038 | 0.718481 | 0.359240 | − | 0.933245i | \(-0.383036\pi\) | ||||
0.359240 | + | 0.933245i | \(0.383036\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.58846 | 0.280678 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 21.3923 | 0.909693 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −29.2679 | −1.24012 | −0.620061 | − | 0.784553i | \(-0.712892\pi\) | ||||
−0.620061 | + | 0.784553i | \(0.712892\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.928203 | 0.0392588 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −35.7128 | −1.50512 | −0.752558 | − | 0.658526i | \(-0.771180\pi\) | ||||
−0.752558 | + | 0.658526i | \(0.771180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.53590 | 0.359108 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −35.3205 | −1.48071 | −0.740356 | − | 0.672215i | \(-0.765343\pi\) | ||||
−0.740356 | + | 0.672215i | \(0.765343\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.1244 | −1.34436 | −0.672181 | − | 0.740387i | \(-0.734642\pi\) | ||||
−0.672181 | + | 0.740387i | \(0.734642\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −35.7128 | −1.48933 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.00000 | −0.124892 | −0.0624458 | − | 0.998048i | \(-0.519890\pi\) | ||||
−0.0624458 | + | 0.998048i | \(0.519890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.73205 | −0.195982 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.41154 | −0.0582606 | −0.0291303 | − | 0.999576i | \(-0.509274\pi\) | ||||
−0.0291303 | + | 0.999576i | \(0.509274\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.78461 | −0.114738 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −47.7128 | −1.95933 | −0.979665 | − | 0.200639i | \(-0.935698\pi\) | ||||
−0.979665 | + | 0.200639i | \(0.935698\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.4641 | 0.469982 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 46.2487 | 1.88967 | 0.944836 | − | 0.327545i | \(-0.106221\pi\) | ||||
0.944836 | + | 0.327545i | \(0.106221\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.85641 | 0.157306 | 0.0786531 | − | 0.996902i | \(-0.474938\pi\) | ||||
0.0786531 | + | 0.996902i | \(0.474938\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.732051 | 0.0297621 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 37.5885 | 1.52567 | 0.762834 | − | 0.646594i | \(-0.223807\pi\) | ||||
0.762834 | + | 0.646594i | \(0.223807\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.73205 | −0.110527 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.9090 | 0.925284 | 0.462642 | − | 0.886545i | \(-0.346901\pi\) | ||||
0.462642 | + | 0.886545i | \(0.346901\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −37.8564 | −1.52404 | −0.762021 | − | 0.647553i | \(-0.775793\pi\) | ||||
−0.762021 | + | 0.647553i | \(0.775793\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −20.4641 | −0.822522 | −0.411261 | − | 0.911518i | \(-0.634911\pi\) | ||||
−0.411261 | + | 0.911518i | \(0.634911\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.26795 | 0.0507993 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 17.2487 | 0.689948 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −27.1244 | −1.08152 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.39230 | 0.135046 | 0.0675228 | − | 0.997718i | \(-0.478490\pi\) | ||||
0.0675228 | + | 0.997718i | \(0.478490\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00000 | −0.158735 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85641 | −0.0735535 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.87564 | −0.113581 | −0.0567906 | − | 0.998386i | \(-0.518087\pi\) | ||||
−0.0567906 | + | 0.998386i | \(0.518087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.3923 | −1.19856 | −0.599278 | − | 0.800541i | \(-0.704545\pi\) | ||||
−0.599278 | + | 0.800541i | \(0.704545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 26.2487 | 1.03194 | 0.515972 | − | 0.856606i | \(-0.327431\pi\) | ||||
0.515972 | + | 0.856606i | \(0.327431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1962 | 0.400234 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 29.4641 | 1.15302 | 0.576510 | − | 0.817090i | \(-0.304414\pi\) | ||||
0.576510 | + | 0.817090i | \(0.304414\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.0718 | −0.432611 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −37.6603 | −1.46704 | −0.733518 | − | 0.679670i | \(-0.762123\pi\) | ||||
−0.733518 | + | 0.679670i | \(0.762123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.60770 | 0.101428 | 0.0507138 | − | 0.998713i | \(-0.483850\pi\) | ||||
0.0507138 | + | 0.998713i | \(0.483850\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.1962 | 0.550503 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.1436 | 0.392762 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.26795 | −0.164762 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.44486 | −0.364073 | −0.182036 | − | 0.983292i | \(-0.558269\pi\) | ||||
−0.182036 | + | 0.983292i | \(0.558269\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −30.2487 | −1.16255 | −0.581276 | − | 0.813706i | \(-0.697446\pi\) | ||||
−0.581276 | + | 0.813706i | \(0.697446\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.1244 | −0.772302 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.5885 | −0.864323 | −0.432162 | − | 0.901796i | \(-0.642249\pi\) | ||||
−0.432162 | + | 0.901796i | \(0.642249\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.14359 | 0.234735 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.26795 | 0.0483050 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.21539 | 0.274486 | 0.137243 | − | 0.990537i | \(-0.456176\pi\) | ||||
0.137243 | + | 0.990537i | \(0.456176\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.26795 | 0.199825 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.14359 | −0.232705 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.94744 | −0.375710 | −0.187855 | − | 0.982197i | \(-0.560153\pi\) | ||||
−0.187855 | + | 0.982197i | \(0.560153\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −33.5885 | −1.26681 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.732051 | 0.0275316 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.3923 | −1.32919 | −0.664593 | − | 0.747206i | \(-0.731395\pi\) | ||||
−0.664593 | + | 0.747206i | \(0.731395\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.28719 | −0.160556 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.196152 | −0.00733568 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.9808 | 0.857038 | 0.428519 | − | 0.903533i | \(-0.359036\pi\) | ||||
0.428519 | + | 0.903533i | \(0.359036\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −47.9808 | −1.78690 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.66025 | −0.210217 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 29.3205 | 1.08744 | 0.543719 | − | 0.839268i | \(-0.317016\pi\) | ||||
0.543719 | + | 0.839268i | \(0.317016\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −14.5359 | −0.537630 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.9282 | 0.920744 | 0.460372 | − | 0.887726i | \(-0.347716\pi\) | ||||
0.460372 | + | 0.887726i | \(0.347716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.92820 | −0.218368 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 34.2487 | 1.25986 | 0.629930 | − | 0.776652i | \(-0.283084\pi\) | ||||
0.629930 | + | 0.776652i | \(0.283084\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 28.5885 | 1.04881 | 0.524404 | − | 0.851469i | \(-0.324288\pi\) | ||||
0.524404 | + | 0.851469i | \(0.324288\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.21539 | −0.264351 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.1244 | 0.771867 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.3205 | 0.814487 | 0.407243 | − | 0.913320i | \(-0.366490\pi\) | ||||
0.407243 | + | 0.913320i | \(0.366490\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.51666 | 0.127984 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.3205 | 1.02933 | 0.514663 | − | 0.857392i | \(-0.327917\pi\) | ||||
0.514663 | + | 0.857392i | \(0.327917\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.679492 | 0.0246316 | 0.0123158 | − | 0.999924i | \(-0.496080\pi\) | ||||
0.0123158 | + | 0.999924i | \(0.496080\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.2487 | 1.60191 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.73205 | −0.0986486 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.5885 | −0.922743 | −0.461372 | − | 0.887207i | \(-0.652643\pi\) | ||||
−0.461372 | + | 0.887207i | \(0.652643\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.1244 | −0.759790 | −0.379895 | − | 0.925030i | \(-0.624040\pi\) | ||||
−0.379895 | + | 0.925030i | \(0.624040\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.39230 | 0.0859341 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.60770 | −0.272574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8564 | −0.495821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.71281 | 0.275282 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −23.0526 | −0.821735 | −0.410867 | − | 0.911695i | \(-0.634774\pi\) | ||||
−0.410867 | + | 0.911695i | \(0.634774\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 43.5167 | 1.54727 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.14359 | 0.0406102 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.00000 | −0.283375 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 42.7846 | 1.51361 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.19615 | 0.112790 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 21.8564 | 0.770337 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.4115 | −0.823106 | −0.411553 | − | 0.911386i | \(-0.635013\pi\) | ||||
−0.411553 | + | 0.911386i | \(0.635013\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.3923 | −0.716071 | −0.358035 | − | 0.933708i | \(-0.616553\pi\) | ||||
−0.358035 | + | 0.933708i | \(0.616553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.9090 | −0.487210 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.0000 | −0.629740 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12.3923 | 0.432494 | 0.216247 | − | 0.976339i | \(-0.430618\pi\) | ||||
0.216247 | + | 0.976339i | \(0.430618\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −48.7128 | −1.69802 | −0.849011 | − | 0.528375i | \(-0.822801\pi\) | ||||
−0.849011 | + | 0.528375i | \(0.822801\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −44.9808 | −1.56413 | −0.782067 | − | 0.623194i | \(-0.785835\pi\) | ||||
−0.782067 | + | 0.623194i | \(0.785835\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.607695 | −0.0211061 | −0.0105531 | − | 0.999944i | \(-0.503359\pi\) | ||||
−0.0105531 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.0718 | 1.00728 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.6410 | 0.575886 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −35.0333 | −1.20948 | −0.604742 | − | 0.796421i | \(-0.706724\pi\) | ||||
−0.604742 | + | 0.796421i | \(0.706724\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.3923 | −0.944562 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.46410 | −0.325575 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.73205 | 0.128235 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −51.7128 | −1.77269 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.2679 | 0.420047 | 0.210023 | − | 0.977696i | \(-0.432646\pi\) | ||||
0.210023 | + | 0.977696i | \(0.432646\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.8038 | −0.813124 | −0.406562 | − | 0.913623i | \(-0.633272\pi\) | ||||
−0.406562 | + | 0.913623i | \(0.633272\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −28.8564 | −0.984568 | −0.492284 | − | 0.870435i | \(-0.663838\pi\) | ||||
−0.492284 | + | 0.870435i | \(0.663838\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −17.9090 | −0.609628 | −0.304814 | − | 0.952412i | \(-0.598594\pi\) | ||||
−0.304814 | + | 0.952412i | \(0.598594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.21539 | 0.109327 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.73205 | 0.194447 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.58846 | 0.0538228 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.8564 | −0.874106 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.1962 | −0.378067 | −0.189034 | − | 0.981971i | \(-0.560536\pi\) | ||||
−0.189034 | + | 0.981971i | \(0.560536\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.3205 | 1.72903 | 0.864516 | − | 0.502605i | \(-0.167625\pi\) | ||||
0.864516 | + | 0.502605i | \(0.167625\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.67949 | 0.191130 | 0.0955651 | − | 0.995423i | \(-0.469534\pi\) | ||||
0.0955651 | + | 0.995423i | \(0.469534\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 6.73205 | 0.226040 | 0.113020 | − | 0.993593i | \(-0.463948\pi\) | ||||
0.113020 | + | 0.993593i | \(0.463948\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.3923 | −0.683936 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 52.9808 | 1.77293 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −10.3923 | −0.347376 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.679492 | −0.0226623 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −19.8564 | −0.661513 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −11.9474 | −0.397146 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.4641 | −0.413864 | −0.206932 | − | 0.978355i | \(-0.566348\pi\) | ||||
−0.206932 | + | 0.978355i | \(0.566348\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.46410 | −0.313560 | −0.156780 | − | 0.987634i | \(-0.550111\pi\) | ||||
−0.156780 | + | 0.987634i | \(0.550111\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −56.4449 | −1.86397 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.3205 | 1.42901 | 0.714506 | − | 0.699629i | \(-0.246652\pi\) | ||||
0.714506 | + | 0.699629i | \(0.246652\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.71281 | 0.122209 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 28.8564 | 0.948793 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −43.2679 | −1.41958 | −0.709788 | − | 0.704416i | \(-0.751209\pi\) | ||||
−0.709788 | + | 0.704416i | \(0.751209\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 36.0000 | 1.17985 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.07180 | 0.100458 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −45.1962 | −1.47649 | −0.738247 | − | 0.674531i | \(-0.764346\pi\) | ||||
−0.738247 | + | 0.674531i | \(0.764346\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.5359 | −0.865046 | −0.432523 | − | 0.901623i | \(-0.642376\pi\) | ||||
−0.432523 | + | 0.901623i | \(0.642376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −11.7128 | −0.381422 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.6603 | −0.768855 | −0.384427 | − | 0.923155i | \(-0.625601\pi\) | ||||
−0.384427 | + | 0.923155i | \(0.625601\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.856406 | −0.0278001 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.14359 | 0.199011 | 0.0995053 | − | 0.995037i | \(-0.468274\pi\) | ||||
0.0995053 | + | 0.995037i | \(0.468274\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.92820 | −0.0947544 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 31.3205 | 1.01139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7128 | −0.990736 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.05256 | −0.0660742 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −30.4115 | −0.977969 | −0.488985 | − | 0.872292i | \(-0.662633\pi\) | ||||
−0.488985 | + | 0.872292i | \(0.662633\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.58846 | 0.0830675 | 0.0415338 | − | 0.999137i | \(-0.486776\pi\) | ||||
0.0415338 | + | 0.999137i | \(0.486776\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.8564 | 0.860977 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 35.6603 | 1.14087 | 0.570436 | − | 0.821342i | \(-0.306774\pi\) | ||||
0.570436 | + | 0.821342i | \(0.306774\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.339746 | 0.0108583 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.0526 | −0.511997 | −0.255999 | − | 0.966677i | \(-0.582404\pi\) | ||||
−0.255999 | + | 0.966677i | \(0.582404\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.07180 | −0.225326 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.7128 | −0.881216 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4641 | 0.840660 | 0.420330 | − | 0.907371i | \(-0.361914\pi\) | ||||
0.420330 | + | 0.907371i | \(0.361914\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.9808 | 0.348114 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.143594 | 0.00454765 | 0.00227383 | − | 0.999997i | \(-0.499276\pi\) | ||||
0.00227383 | + | 0.999997i | \(0.499276\pi\) | |||||||
\(998\) | 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 | 4752.2.a.w.1.2 | 2 | ||
3.2 | odd | 2 | 4752.2.a.bf.1.1 | 2 | |||
4.3 | odd | 2 | 297.2.a.e.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 297.2.a.f.1.2 | yes | 2 | ||
20.19 | odd | 2 | 7425.2.a.bl.1.2 | 2 | |||
36.7 | odd | 6 | 891.2.e.p.595.2 | 4 | |||
36.11 | even | 6 | 891.2.e.m.595.1 | 4 | |||
36.23 | even | 6 | 891.2.e.m.298.1 | 4 | |||
36.31 | odd | 6 | 891.2.e.p.298.2 | 4 | |||
44.43 | even | 2 | 3267.2.a.q.1.2 | 2 | |||
60.59 | even | 2 | 7425.2.a.z.1.1 | 2 | |||
132.131 | odd | 2 | 3267.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
297.2.a.e.1.1 | ✓ | 2 | 4.3 | odd | 2 | ||
297.2.a.f.1.2 | yes | 2 | 12.11 | even | 2 | ||
891.2.e.m.298.1 | 4 | 36.23 | even | 6 | |||
891.2.e.m.595.1 | 4 | 36.11 | even | 6 | |||
891.2.e.p.298.2 | 4 | 36.31 | odd | 6 | |||
891.2.e.p.595.2 | 4 | 36.7 | odd | 6 | |||
3267.2.a.l.1.1 | 2 | 132.131 | odd | 2 | |||
3267.2.a.q.1.2 | 2 | 44.43 | even | 2 | |||
4752.2.a.w.1.2 | 2 | 1.1 | even | 1 | trivial | ||
4752.2.a.bf.1.1 | 2 | 3.2 | odd | 2 | |||
7425.2.a.z.1.1 | 2 | 60.59 | even | 2 | |||
7425.2.a.bl.1.2 | 2 | 20.19 | odd | 2 |