Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7800,2,Mod(1,7800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("7800.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7800.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: | \(62.2833135766\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1560) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.76156\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7800.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.86464 | −0.863722 | −0.431861 | − | 0.901940i | \(-0.642143\pi\) | ||||
−0.431861 | + | 0.901940i | \(0.642143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.52311 | −1.33955 | −0.669776 | − | 0.742563i | \(-0.733610\pi\) | ||||
−0.669776 | + | 0.742563i | \(0.733610\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.52311 | 0.808258 | 0.404129 | − | 0.914702i | \(-0.367575\pi\) | ||||
0.404129 | + | 0.914702i | \(0.367575\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.52311 | −1.56868 | −0.784339 | − | 0.620333i | \(-0.786998\pi\) | ||||
−0.784339 | + | 0.620333i | \(0.786998\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.77551 | 1.25818 | 0.629090 | − | 0.777332i | \(-0.283428\pi\) | ||||
0.629090 | + | 0.777332i | \(0.283428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.72928 | 1.02901 | 0.514505 | − | 0.857488i | \(-0.327976\pi\) | ||||
0.514505 | + | 0.857488i | \(0.327976\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.86464 | −0.498670 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.72928 | 0.613090 | 0.306545 | − | 0.951856i | \(-0.400827\pi\) | ||||
0.306545 | + | 0.951856i | \(0.400827\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.1170 | −1.58002 | −0.790008 | − | 0.613097i | \(-0.789924\pi\) | ||||
−0.790008 | + | 0.613097i | \(0.789924\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5.52311 | 0.842267 | 0.421134 | − | 0.906999i | \(-0.361632\pi\) | ||||
0.421134 | + | 0.906999i | \(0.361632\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.65847 | −1.26297 | −0.631484 | − | 0.775389i | \(-0.717554\pi\) | ||||
−0.631484 | + | 0.775389i | \(0.717554\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −7.00000 | −1.00000 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.52311 | −0.773391 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.77551 | 0.930688 | 0.465344 | − | 0.885130i | \(-0.345931\pi\) | ||||
0.465344 | + | 0.885130i | \(0.345931\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.52311 | 0.466648 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.593923 | 0.0773221 | 0.0386611 | − | 0.999252i | \(-0.487691\pi\) | ||||
0.0386611 | + | 0.999252i | \(0.487691\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.25240 | −0.672500 | −0.336250 | − | 0.941773i | \(-0.609159\pi\) | ||||
−0.336250 | + | 0.941773i | \(0.609159\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.5048 | 1.28336 | 0.641682 | − | 0.766971i | \(-0.278237\pi\) | ||||
0.641682 | + | 0.766971i | \(0.278237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.52311 | −0.905677 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.38776 | −0.283374 | −0.141687 | − | 0.989911i | \(-0.545253\pi\) | ||||
−0.141687 | + | 0.989911i | \(0.545253\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.45856 | −0.638877 | −0.319438 | − | 0.947607i | \(-0.603494\pi\) | ||||
−0.319438 | + | 0.947607i | \(0.603494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.47689 | 0.278671 | 0.139336 | − | 0.990245i | \(-0.455503\pi\) | ||||
0.139336 | + | 0.990245i | \(0.455503\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.11704 | −0.890961 | −0.445480 | − | 0.895292i | \(-0.646967\pi\) | ||||
−0.445480 | + | 0.895292i | \(0.646967\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.77551 | 0.726411 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.1170 | −1.49640 | −0.748201 | − | 0.663472i | \(-0.769082\pi\) | ||||
−0.748201 | + | 0.663472i | \(0.769082\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.72928 | 0.594099 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.86464 | −0.287907 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.7293 | −1.16711 | −0.583554 | − | 0.812075i | \(-0.698338\pi\) | ||||
−0.583554 | + | 0.812075i | \(0.698338\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.7755 | −1.45587 | −0.727937 | − | 0.685644i | \(-0.759521\pi\) | ||||
−0.727937 | + | 0.685644i | \(0.759521\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.72928 | −0.167176 | −0.0835880 | − | 0.996500i | \(-0.526638\pi\) | ||||
−0.0835880 | + | 0.996500i | \(0.526638\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.0279 | 1.15206 | 0.576032 | − | 0.817427i | \(-0.304600\pi\) | ||||
0.576032 | + | 0.817427i | \(0.304600\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.72928 | 0.353968 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 7.25240 | 0.682248 | 0.341124 | − | 0.940018i | \(-0.389192\pi\) | ||||
0.341124 | + | 0.940018i | \(0.389192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.79383 | −0.253985 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.1170 | −0.912223 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.2524 | −1.53090 | −0.765451 | − | 0.643494i | \(-0.777484\pi\) | ||||
−0.765451 | + | 0.643494i | \(0.777484\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.52311 | 0.486283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.77551 | −0.766720 | −0.383360 | − | 0.923599i | \(-0.625233\pi\) | ||||
−0.383360 | + | 0.923599i | \(0.625233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.4340 | −1.66036 | −0.830179 | − | 0.557497i | \(-0.811762\pi\) | ||||
−0.830179 | + | 0.557497i | \(0.811762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.58767 | 0.643577 | 0.321789 | − | 0.946812i | \(-0.395716\pi\) | ||||
0.321789 | + | 0.946812i | \(0.395716\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.65847 | −0.729175 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.86464 | −0.239553 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.00000 | −0.577350 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.40608 | −0.115190 | −0.0575952 | − | 0.998340i | \(-0.518343\pi\) | ||||
−0.0575952 | + | 0.998340i | \(0.518343\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.31695 | −0.107172 | −0.0535858 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535858 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5.52311 | −0.446517 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −20.7110 | −1.65291 | −0.826457 | − | 0.562999i | \(-0.809647\pi\) | ||||
−0.826457 | + | 0.562999i | \(0.809647\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.77551 | 0.537333 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.27072 | −0.177856 | −0.0889282 | − | 0.996038i | \(-0.528344\pi\) | ||||
−0.0889282 | + | 0.996038i | \(0.528344\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.34153 | −0.568104 | −0.284052 | − | 0.958809i | \(-0.591679\pi\) | ||||
−0.284052 | + | 0.958809i | \(0.591679\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.52311 | 0.269419 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 16.0925 | 1.22349 | 0.611743 | − | 0.791056i | \(-0.290468\pi\) | ||||
0.611743 | + | 0.791056i | \(0.290468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.593923 | 0.0446420 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.0462 | 1.12461 | 0.562304 | − | 0.826931i | \(-0.309915\pi\) | ||||
0.562304 | + | 0.826931i | \(0.309915\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.58767 | 0.415328 | 0.207664 | − | 0.978200i | \(-0.433414\pi\) | ||||
0.207664 | + | 0.978200i | \(0.433414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.25240 | −0.388268 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.8217 | 1.15700 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 17.5510 | 1.26995 | 0.634974 | − | 0.772534i | \(-0.281011\pi\) | ||||
0.634974 | + | 0.772534i | \(0.281011\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.8217 | −0.994911 | −0.497455 | − | 0.867490i | \(-0.665732\pi\) | ||||
−0.497455 | + | 0.867490i | \(0.665732\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −26.3511 | −1.87744 | −0.938719 | − | 0.344682i | \(-0.887987\pi\) | ||||
−0.938719 | + | 0.344682i | \(0.887987\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.0741 | −1.63568 | −0.817841 | − | 0.575444i | \(-0.804829\pi\) | ||||
−0.817841 | + | 0.575444i | \(0.804829\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5048 | 0.740951 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.52311 | −0.522893 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0925 | −0.698110 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.52311 | 0.104856 | 0.0524278 | − | 0.998625i | \(-0.483304\pi\) | ||||
0.0524278 | + | 0.998625i | \(0.483304\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.38776 | −0.163606 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.45856 | −0.368856 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.52311 | −0.371525 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.3169 | −0.891769 | −0.445884 | − | 0.895091i | \(-0.647111\pi\) | ||||
−0.445884 | + | 0.895091i | \(0.647111\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.80009 | 0.451338 | 0.225669 | − | 0.974204i | \(-0.427543\pi\) | ||||
0.225669 | + | 0.974204i | \(0.427543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.52311 | 0.100650 | 0.0503251 | − | 0.998733i | \(-0.483974\pi\) | ||||
0.0503251 | + | 0.998733i | \(0.483974\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7110 | 0.701698 | 0.350849 | − | 0.936432i | \(-0.385893\pi\) | ||||
0.350849 | + | 0.936432i | \(0.385893\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.47689 | 0.160891 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4.65847 | 0.301332 | 0.150666 | − | 0.988585i | \(-0.451858\pi\) | ||||
0.150666 | + | 0.988585i | \(0.451858\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.22449 | 0.336539 | 0.168269 | − | 0.985741i | \(-0.446182\pi\) | ||||
0.168269 | + | 0.985741i | \(0.446182\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.52311 | 0.224170 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.11704 | −0.514396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.85838 | 0.369778 | 0.184889 | − | 0.982759i | \(-0.440807\pi\) | ||||
0.184889 | + | 0.982759i | \(0.440807\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 21.5510 | 1.35490 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.29862 | 0.143384 | 0.0716921 | − | 0.997427i | \(-0.477160\pi\) | ||||
0.0716921 | + | 0.997427i | \(0.477160\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.77551 | 0.419394 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.5789 | 1.94724 | 0.973620 | − | 0.228175i | \(-0.0732760\pi\) | ||||
0.973620 | + | 0.228175i | \(0.0732760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.1170 | −0.863949 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.3632 | −1.85128 | −0.925638 | − | 0.378411i | \(-0.876471\pi\) | ||||
−0.925638 | + | 0.378411i | \(0.876471\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 28.5972 | 1.73716 | 0.868580 | − | 0.495550i | \(-0.165033\pi\) | ||||
0.868580 | + | 0.495550i | \(0.165033\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.79383 | −0.107781 | −0.0538905 | − | 0.998547i | \(-0.517162\pi\) | ||||
−0.0538905 | + | 0.998547i | \(0.517162\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.72928 | 0.343003 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 32.2095 | 1.92146 | 0.960729 | − | 0.277489i | \(-0.0895024\pi\) | ||||
0.960729 | + | 0.277489i | \(0.0895024\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.0925 | −1.07548 | −0.537742 | − | 0.843109i | \(-0.680723\pi\) | ||||
−0.537742 | + | 0.843109i | \(0.680723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5048 | 0.794400 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6218 | 0.737375 | 0.368688 | − | 0.929553i | \(-0.379807\pi\) | ||||
0.368688 | + | 0.929553i | \(0.379807\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.86464 | −0.166223 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.52311 | −0.435073 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.7293 | −0.673830 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.7755 | −0.840549 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.8217 | −1.80445 | −0.902223 | − | 0.431271i | \(-0.858065\pi\) | ||||
−0.902223 | + | 0.431271i | \(0.858065\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.7938 | −0.666627 | −0.333313 | − | 0.942816i | \(-0.608167\pi\) | ||||
−0.333313 | + | 0.942816i | \(0.608167\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.4340 | −0.642197 | −0.321098 | − | 0.947046i | \(-0.604052\pi\) | ||||
−0.321098 | + | 0.947046i | \(0.604052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −19.4094 | −1.08672 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.72928 | −0.0965191 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −19.4586 | −1.08270 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 12.0279 | 0.665145 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.20617 | 0.121262 | 0.0606310 | − | 0.998160i | \(-0.480689\pi\) | ||||
0.0606310 | + | 0.998160i | \(0.480689\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.72928 | 0.204363 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8034 | 0.915340 | 0.457670 | − | 0.889122i | \(-0.348684\pi\) | ||||
0.457670 | + | 0.889122i | \(0.348684\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.25240 | 0.393896 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4123 | −0.888778 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9.96336 | −0.534861 | −0.267430 | − | 0.963577i | \(-0.586175\pi\) | ||||
−0.267430 | + | 0.963577i | \(0.586175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −21.3449 | −1.14256 | −0.571282 | − | 0.820754i | \(-0.693554\pi\) | ||||
−0.571282 | + | 0.820754i | \(0.693554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.3973 | −1.77756 | −0.888781 | − | 0.458333i | \(-0.848447\pi\) | ||||
−0.888781 | + | 0.458333i | \(0.848447\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.9754 | 1.15982 | 0.579909 | − | 0.814681i | \(-0.303088\pi\) | ||||
0.579909 | + | 0.814681i | \(0.303088\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.58767 | −0.346719 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.79383 | −0.146638 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −29.2803 | −1.52842 | −0.764210 | − | 0.644968i | \(-0.776871\pi\) | ||||
−0.764210 | + | 0.644968i | \(0.776871\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −10.1170 | −0.526672 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.41233 | −0.124906 | −0.0624530 | − | 0.998048i | \(-0.519892\pi\) | ||||
−0.0624530 | + | 0.998048i | \(0.519892\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.77551 | 0.348957 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.5231 | 1.00284 | 0.501418 | − | 0.865205i | \(-0.332812\pi\) | ||||
0.501418 | + | 0.865205i | \(0.332812\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.2524 | −0.883867 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 23.7047 | 1.21125 | 0.605627 | − | 0.795749i | \(-0.292922\pi\) | ||||
0.605627 | + | 0.795749i | \(0.292922\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.52311 | 0.280756 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.0000 | −0.709828 | −0.354914 | − | 0.934899i | \(-0.615490\pi\) | ||||
−0.354914 | + | 0.934899i | \(0.615490\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.5510 | 2.10133 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.77551 | −0.442666 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −28.8680 | −1.44884 | −0.724421 | − | 0.689358i | \(-0.757893\pi\) | ||||
−0.724421 | + | 0.689358i | \(0.757893\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 20.0804 | 1.00277 | 0.501383 | − | 0.865225i | \(-0.332825\pi\) | ||||
0.501383 | + | 0.865225i | \(0.332825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.72928 | 0.285396 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.6831 | −0.529539 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.6926 | −0.677057 | −0.338529 | − | 0.940956i | \(-0.609929\pi\) | ||||
−0.338529 | + | 0.940956i | \(0.609929\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.4340 | −0.958608 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.58767 | 0.371570 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.3632 | −0.799393 | −0.399697 | − | 0.916647i | \(-0.630885\pi\) | ||||
−0.399697 | + | 0.916647i | \(0.630885\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.9817 | 1.21753 | 0.608766 | − | 0.793350i | \(-0.291665\pi\) | ||||
0.608766 | + | 0.793350i | \(0.291665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.65847 | −0.420989 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.86464 | −0.138306 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.9388 | −1.34576 | −0.672882 | − | 0.739750i | \(-0.734944\pi\) | ||||
−0.672882 | + | 0.739750i | \(0.734944\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.7110 | 1.28365 | 0.641823 | − | 0.766852i | \(-0.278178\pi\) | ||||
0.641823 | + | 0.766852i | \(0.278178\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −26.5048 | −1.26790 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.00958 | −0.239094 | −0.119547 | − | 0.992829i | \(-0.538144\pi\) | ||||
−0.119547 | + | 0.992829i | \(0.538144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.6926 | 0.935625 | 0.467813 | − | 0.883828i | \(-0.345042\pi\) | ||||
0.467813 | + | 0.883828i | \(0.345042\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.40608 | −0.0665052 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.7143 | 1.82704 | 0.913520 | − | 0.406794i | \(-0.133353\pi\) | ||||
0.913520 | + | 0.406794i | \(0.133353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 28.9817 | 1.36469 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.31695 | −0.0618756 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.9538 | −0.512396 | −0.256198 | − | 0.966624i | \(-0.582470\pi\) | ||||
−0.256198 | + | 0.966624i | \(0.582470\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.52311 | −0.257797 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.864641 | −0.0402703 | −0.0201352 | − | 0.999797i | \(-0.506410\pi\) | ||||
−0.0201352 | + | 0.999797i | \(0.506410\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −16.0000 | −0.743583 | −0.371792 | − | 0.928316i | \(-0.621256\pi\) | ||||
−0.371792 | + | 0.928316i | \(0.621256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.7755 | −0.961376 | −0.480688 | − | 0.876892i | \(-0.659613\pi\) | ||||
−0.480688 | + | 0.876892i | \(0.659613\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20.7110 | −0.954311 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.8217 | −0.727484 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.77551 | 0.310229 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 20.6585 | 0.943910 | 0.471955 | − | 0.881623i | \(-0.343549\pi\) | ||||
0.471955 | + | 0.881623i | \(0.343549\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.72928 | 0.170041 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 16.3632 | 0.741486 | 0.370743 | − | 0.928735i | \(-0.379103\pi\) | ||||
0.370743 | + | 0.928735i | \(0.379103\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.27072 | −0.102685 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.7389 | 1.20671 | 0.603354 | − | 0.797473i | \(-0.293831\pi\) | ||||
0.603354 | + | 0.797473i | \(0.293831\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −37.4219 | −1.68540 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.24281 | 0.189934 | 0.0949672 | − | 0.995480i | \(-0.469725\pi\) | ||||
0.0949672 | + | 0.995480i | \(0.469725\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −7.34153 | −0.327995 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.889220 | 0.0396484 | 0.0198242 | − | 0.999803i | \(-0.493689\pi\) | ||||
0.0198242 | + | 0.999803i | \(0.493689\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.00000 | 0.0444116 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.3694 | −0.503941 | −0.251971 | − | 0.967735i | \(-0.581079\pi\) | ||||
−0.251971 | + | 0.967735i | \(0.581079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.52311 | 0.155549 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.8034 | 1.09085 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.0925 | 0.706380 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3.18785 | 0.139662 | 0.0698310 | − | 0.997559i | \(-0.477754\pi\) | ||||
0.0698310 | + | 0.997559i | \(0.477754\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.1666 | 1.62518 | 0.812591 | − | 0.582835i | \(-0.198056\pi\) | ||||
0.812591 | + | 0.582835i | \(0.198056\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −31.6435 | −1.37841 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 33.5972 | 1.46075 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.593923 | 0.0257740 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.1170 | −0.438218 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 15.0462 | 0.649293 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 20.0525 | 0.863722 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.02791 | −0.345147 | −0.172573 | − | 0.984997i | \(-0.555208\pi\) | ||||
−0.172573 | + | 0.984997i | \(0.555208\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.58767 | 0.239790 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.2032 | −1.33415 | −0.667077 | − | 0.744989i | \(-0.732455\pi\) | ||||
−0.667077 | + | 0.744989i | \(0.732455\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.25240 | −0.224167 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 23.8709 | 1.01693 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 29.2191 | 1.23805 | 0.619026 | − | 0.785370i | \(-0.287528\pi\) | ||||
0.619026 | + | 0.785370i | \(0.287528\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.52311 | 0.233603 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8217 | 0.667994 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −30.5048 | −1.28562 | −0.642812 | − | 0.766024i | \(-0.722232\pi\) | ||||
−0.642812 | + | 0.766024i | \(0.722232\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.1416 | −0.509003 | −0.254502 | − | 0.967072i | \(-0.581911\pi\) | ||||
−0.254502 | + | 0.967072i | \(0.581911\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.85258 | −0.370469 | −0.185234 | − | 0.982694i | \(-0.559304\pi\) | ||||
−0.185234 | + | 0.982694i | \(0.559304\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.5510 | 0.733204 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 30.2341 | 1.25866 | 0.629330 | − | 0.777138i | \(-0.283329\pi\) | ||||
0.629330 | + | 0.777138i | \(0.283329\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.8217 | −0.574412 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.4094 | −0.803855 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.0342 | 0.950722 | 0.475361 | − | 0.879791i | \(-0.342318\pi\) | ||||
0.475361 | + | 0.879791i | \(0.342318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.1849 | 0.831705 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −26.3511 | −1.08394 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −27.9754 | −1.14881 | −0.574406 | − | 0.818570i | \(-0.694767\pi\) | ||||
−0.574406 | + | 0.818570i | \(0.694767\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −23.0741 | −0.944361 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.7389 | 0.929085 | 0.464542 | − | 0.885551i | \(-0.346219\pi\) | ||||
0.464542 | + | 0.885551i | \(0.346219\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2158 | −0.457500 | −0.228750 | − | 0.973485i | \(-0.573464\pi\) | ||||
−0.228750 | + | 0.973485i | \(0.573464\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 10.5048 | 0.427788 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −23.7293 | −0.963142 | −0.481571 | − | 0.876407i | \(-0.659934\pi\) | ||||
−0.481571 | + | 0.876407i | \(0.659934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.65847 | −0.350284 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.2341 | 0.736467 | 0.368234 | − | 0.929733i | \(-0.379963\pi\) | ||||
0.368234 | + | 0.929733i | \(0.379963\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.0245796 | −0.000989536 0 | −0.000494768 | − | 1.00000i | \(-0.500157\pi\) | ||||
−0.000494768 | 1.00000i | \(0.500157\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.2158 | 1.25467 | 0.627334 | − | 0.778751i | \(-0.284146\pi\) | ||||
0.627334 | + | 0.778751i | \(0.284146\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.52311 | −0.301892 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.0925 | −0.403054 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −20.5972 | −0.821266 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.4460 | 0.535279 | 0.267639 | − | 0.963519i | \(-0.413756\pi\) | ||||
0.267639 | + | 0.963519i | \(0.413756\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.52311 | 0.0605384 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.00000 | −0.277350 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.38776 | −0.0944581 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.54144 | 0.100381 | 0.0501904 | − | 0.998740i | \(-0.484017\pi\) | ||||
0.0501904 | + | 0.998740i | \(0.484017\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.9634 | −0.550661 | −0.275330 | − | 0.961350i | \(-0.588787\pi\) | ||||
−0.275330 | + | 0.961350i | \(0.588787\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 30.8034 | 1.21101 | 0.605504 | − | 0.795843i | \(-0.292972\pi\) | ||||
0.605504 | + | 0.795843i | \(0.292972\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.70138 | −0.0667848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.00000 | −0.0782660 | −0.0391330 | − | 0.999234i | \(-0.512460\pi\) | ||||
−0.0391330 | + | 0.999234i | \(0.512460\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.45856 | −0.212959 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.05581 | −0.157992 | −0.0789960 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789960 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −32.9325 | −1.28093 | −0.640463 | − | 0.767989i | \(-0.721258\pi\) | ||||
−0.640463 | + | 0.767989i | \(0.721258\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.52311 | −0.214500 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.9729 | −1.97368 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.3169 | −0.514863 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.0462 | 0.580853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.42192 | −0.363188 | −0.181594 | − | 0.983374i | \(-0.558126\pi\) | ||||
−0.181594 | + | 0.983374i | \(0.558126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −42.2341 | −1.62319 | −0.811594 | − | 0.584222i | \(-0.801400\pi\) | ||||
−0.811594 | + | 0.584222i | \(0.801400\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.80009 | 0.260580 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 18.7509 | 0.717484 | 0.358742 | − | 0.933437i | \(-0.383206\pi\) | ||||
0.358742 | + | 0.933437i | \(0.383206\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.52311 | 0.0581104 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.77551 | 0.258126 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 45.2524 | 1.72148 | 0.860741 | − | 0.509043i | \(-0.170001\pi\) | ||||
0.860741 | + | 0.509043i | \(0.170001\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 55.8776 | 2.11651 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10.7110 | 0.405126 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.4586 | −1.41479 | −0.707395 | − | 0.706818i | \(-0.750130\pi\) | ||||
−0.707395 | + | 0.706818i | \(0.750130\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.1387 | 0.495535 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.8988 | 0.446869 | 0.223435 | − | 0.974719i | \(-0.428273\pi\) | ||||
0.223435 | + | 0.974719i | \(0.428273\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.47689 | 0.0928905 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −43.1020 | −1.61418 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.65847 | 0.173974 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.7851 | 0.961622 | 0.480811 | − | 0.876824i | \(-0.340342\pi\) | ||||
0.480811 | + | 0.876824i | \(0.340342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.22449 | 0.194301 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −34.8034 | −1.29079 | −0.645394 | − | 0.763850i | \(-0.723307\pi\) | ||||
−0.645394 | + | 0.763850i | \(0.723307\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −30.5048 | −1.12826 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.5510 | −0.722133 | −0.361067 | − | 0.932540i | \(-0.617587\pi\) | ||||
−0.361067 | + | 0.932540i | \(0.617587\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −30.0925 | −1.10847 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2986 | 0.452412 | 0.226206 | − | 0.974079i | \(-0.427368\pi\) | ||||
0.226206 | + | 0.974079i | \(0.427368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.52311 | 0.129425 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −40.9975 | −1.50405 | −0.752027 | − | 0.659133i | \(-0.770924\pi\) | ||||
−0.752027 | + | 0.659133i | \(0.770924\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8.11704 | −0.296987 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.5510 | 1.22429 | 0.612147 | − | 0.790744i | \(-0.290306\pi\) | ||||
0.612147 | + | 0.790744i | \(0.290306\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.85838 | 0.213491 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.1020 | −0.912349 | −0.456175 | − | 0.889890i | \(-0.650781\pi\) | ||||
−0.456175 | + | 0.889890i | \(0.650781\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 21.5510 | 0.782253 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −39.9021 | −1.44645 | −0.723226 | − | 0.690612i | \(-0.757341\pi\) | ||||
−0.723226 | + | 0.690612i | \(0.757341\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.593923 | 0.0214453 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.5510 | −0.560784 | −0.280392 | − | 0.959886i | \(-0.590464\pi\) | ||||
−0.280392 | + | 0.959886i | \(0.590464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.29862 | 0.0827830 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −27.7972 | −0.999794 | −0.499897 | − | 0.866085i | \(-0.666629\pi\) | ||||
−0.499897 | + | 0.866085i | \(0.666629\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −35.6435 | −1.27706 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.84006 | 0.244757 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6.77551 | 0.242137 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.6339 | 1.09198 | 0.545990 | − | 0.837792i | \(-0.316154\pi\) | ||||
0.545990 | + | 0.837792i | \(0.316154\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.5789 | 1.12424 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.25240 | −0.186518 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.6464 | 0.660490 | 0.330245 | − | 0.943895i | \(-0.392869\pi\) | ||||
0.330245 | + | 0.943895i | \(0.392869\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.8217 | 1.69181 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −14.1170 | −0.498801 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 15.6368 | 0.551812 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.3632 | −1.06883 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −54.8313 | −1.92777 | −0.963883 | − | 0.266325i | \(-0.914191\pi\) | ||||
−0.963883 | + | 0.266325i | \(0.914191\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.97209 | 0.209709 | 0.104854 | − | 0.994488i | \(-0.466562\pi\) | ||||
0.104854 | + | 0.994488i | \(0.466562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.5972 | 1.00295 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.4586 | 0.680769 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.2866 | 1.05701 | 0.528504 | − | 0.848931i | \(-0.322753\pi\) | ||||
0.528504 | + | 0.848931i | \(0.322753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 31.2437 | 1.08909 | 0.544543 | − | 0.838733i | \(-0.316703\pi\) | ||||
0.544543 | + | 0.838733i | \(0.316703\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.9754 | 0.764160 | 0.382080 | − | 0.924129i | \(-0.375208\pi\) | ||||
0.382080 | + | 0.924129i | \(0.375208\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.7014 | −0.406406 | −0.203203 | − | 0.979137i | \(-0.565135\pi\) | ||||
−0.203203 | + | 0.979137i | \(0.565135\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.79383 | −0.0622274 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 38.6618 | 1.33955 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.72928 | 0.198033 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.7047 | 0.404091 | 0.202046 | − | 0.979376i | \(-0.435241\pi\) | ||||
0.202046 | + | 0.979376i | \(0.435241\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 16.9075 | 0.583019 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 32.2095 | 1.10935 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.0925 | −0.620932 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.0558 | −0.961741 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15.3169 | 0.524442 | 0.262221 | − | 0.965008i | \(-0.415545\pi\) | ||||
0.262221 | + | 0.965008i | \(0.415545\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −20.7476 | −0.708725 | −0.354362 | − | 0.935108i | \(-0.615302\pi\) | ||||
−0.354362 | + | 0.935108i | \(0.615302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 53.0375 | 1.80962 | 0.904808 | − | 0.425820i | \(-0.140014\pi\) | ||||
0.904808 | + | 0.425820i | \(0.140014\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10.2095 | −0.347535 | −0.173768 | − | 0.984787i | \(-0.555594\pi\) | ||||
−0.173768 | + | 0.984787i | \(0.555594\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.5048 | 0.458647 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.09539 | −0.240695 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.5048 | 0.355941 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −6.00000 | −0.203069 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.28030 | −0.313374 | −0.156687 | − | 0.987648i | \(-0.550081\pi\) | ||||
−0.156687 | + | 0.987648i | \(0.550081\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.6218 | 0.425724 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −22.4923 | −0.757784 | −0.378892 | − | 0.925441i | \(-0.623695\pi\) | ||||
−0.378892 | + | 0.925441i | \(0.623695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 28.5972 | 0.962374 | 0.481187 | − | 0.876618i | \(-0.340206\pi\) | ||||
0.481187 | + | 0.876618i | \(0.340206\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.2062 | 1.14853 | 0.574265 | − | 0.818669i | \(-0.305288\pi\) | ||||
0.574265 | + | 0.818669i | \(0.305288\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.86464 | −0.0959691 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −30.5048 | −1.02080 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.52311 | −0.251189 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.8188 | 1.29468 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.4219 | −1.24670 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 25.9634 | 0.862099 | 0.431050 | − | 0.902328i | \(-0.358143\pi\) | ||||
0.431050 | + | 0.902328i | \(0.358143\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −11.7293 | −0.389036 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −51.9267 | −1.72041 | −0.860204 | − | 0.509949i | \(-0.829664\pi\) | ||||
−0.860204 | + | 0.509949i | \(0.829664\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.2524 | 0.769542 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.6156 | −0.383162 | −0.191581 | − | 0.981477i | \(-0.561362\pi\) | ||||
−0.191581 | + | 0.981477i | \(0.561362\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −20.0000 | −0.659022 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.38776 | −0.0785939 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.7755 | −0.485291 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 5.83380 | 0.191401 | 0.0957004 | − | 0.995410i | \(-0.469491\pi\) | ||||
0.0957004 | + | 0.995410i | \(0.469491\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −24.6618 | −0.808258 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −31.8217 | −1.04180 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −27.4373 | −0.896338 | −0.448169 | − | 0.893949i | \(-0.647924\pi\) | ||||
−0.448169 | + | 0.893949i | \(0.647924\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11.7938 | −0.384877 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −34.9571 | −1.13957 | −0.569784 | − | 0.821794i | \(-0.692973\pi\) | ||||
−0.569784 | + | 0.821794i | \(0.692973\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 76.1116 | 2.47854 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 53.3848 | 1.73477 | 0.867387 | − | 0.497634i | \(-0.165798\pi\) | ||||
0.867387 | + | 0.497634i | \(0.165798\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.45856 | −0.177192 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.4340 | −0.370772 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.7110 | −0.735680 | −0.367840 | − | 0.929889i | \(-0.619903\pi\) | ||||
−0.367840 | + | 0.929889i | \(0.619903\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −19.4094 | −0.627417 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.82467 | 0.0588603 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.72928 | −0.0557253 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8313 | 0.927153 | 0.463576 | − | 0.886057i | \(-0.346566\pi\) | ||||
0.463576 | + | 0.886057i | \(0.346566\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −19.4586 | −0.625099 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.0462 | 0.611223 | 0.305611 | − | 0.952156i | \(-0.401139\pi\) | ||||
0.305611 | + | 0.952156i | \(0.401139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 30.1729 | 0.965315 | 0.482658 | − | 0.875809i | \(-0.339672\pi\) | ||||
0.482658 | + | 0.875809i | \(0.339672\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.4402 | 1.29248 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12.0279 | 0.384022 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 18.9292 | 0.603747 | 0.301874 | − | 0.953348i | \(-0.402388\pi\) | ||||
0.301874 | + | 0.953348i | \(0.402388\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −41.5510 | −1.32125 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.5510 | −0.811655 | −0.405827 | − | 0.913950i | \(-0.633017\pi\) | ||||
−0.405827 | + | 0.913950i | \(0.633017\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.20617 | 0.0700106 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.16952 | 0.132050 | 0.0660251 | − | 0.997818i | \(-0.478968\pi\) | ||||
0.0660251 | + | 0.997818i | \(0.478968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.72928 | 0.117989 |
(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 | 7800.2.a.bp.1.2 | 3 | ||
5.2 | odd | 4 | 1560.2.l.c.1249.2 | ✓ | 6 | ||
5.3 | odd | 4 | 1560.2.l.c.1249.5 | yes | 6 | ||
5.4 | even | 2 | 7800.2.a.bj.1.2 | 3 | |||
15.2 | even | 4 | 4680.2.l.e.2809.4 | 6 | |||
15.8 | even | 4 | 4680.2.l.e.2809.3 | 6 | |||
20.3 | even | 4 | 3120.2.l.m.1249.2 | 6 | |||
20.7 | even | 4 | 3120.2.l.m.1249.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.c.1249.2 | ✓ | 6 | 5.2 | odd | 4 | ||
1560.2.l.c.1249.5 | yes | 6 | 5.3 | odd | 4 | ||
3120.2.l.m.1249.2 | 6 | 20.3 | even | 4 | |||
3120.2.l.m.1249.5 | 6 | 20.7 | even | 4 | |||
4680.2.l.e.2809.3 | 6 | 15.8 | even | 4 | |||
4680.2.l.e.2809.4 | 6 | 15.2 | even | 4 | |||
7800.2.a.bj.1.2 | 3 | 5.4 | even | 2 | |||
7800.2.a.bp.1.2 | 3 | 1.1 | even | 1 | trivial |