Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8280,2,Mod(1,8280)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8280, 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("8280.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8280 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8280.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: | \(66.1161328736\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 2760) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8280.1 |
$q$-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 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.56155 | −0.968176 | −0.484088 | − | 0.875019i | \(-0.660849\pi\) | ||||
−0.484088 | + | 0.875019i | \(0.660849\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.12311 | 1.54467 | 0.772337 | − | 0.635213i | \(-0.219088\pi\) | ||||
0.772337 | + | 0.635213i | \(0.219088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.56155 | −1.10634 | −0.553170 | − | 0.833069i | \(-0.686582\pi\) | ||||
−0.553170 | + | 0.833069i | \(0.686582\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.12311 | 0.257658 | 0.128829 | − | 0.991667i | \(-0.458878\pi\) | ||||
0.128829 | + | 0.991667i | \(0.458878\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.56155 | −1.58984 | −0.794920 | − | 0.606714i | \(-0.792487\pi\) | ||||
−0.794920 | + | 0.606714i | \(0.792487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.68466 | −0.661784 | −0.330892 | − | 0.943669i | \(-0.607350\pi\) | ||||
−0.330892 | + | 0.943669i | \(0.607350\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.56155 | −0.432981 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.561553 | 0.0923187 | 0.0461594 | − | 0.998934i | \(-0.485302\pi\) | ||||
0.0461594 | + | 0.998934i | \(0.485302\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.43845 | −0.536995 | −0.268498 | − | 0.963280i | \(-0.586527\pi\) | ||||
−0.268498 | + | 0.963280i | \(0.586527\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.24621 | −0.952538 | −0.476269 | − | 0.879300i | \(-0.658011\pi\) | ||||
−0.476269 | + | 0.879300i | \(0.658011\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.00000 | −1.16692 | −0.583460 | − | 0.812142i | \(-0.698301\pi\) | ||||
−0.583460 | + | 0.812142i | \(0.698301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.438447 | −0.0626353 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.561553 | −0.0771352 | −0.0385676 | − | 0.999256i | \(-0.512279\pi\) | ||||
−0.0385676 | + | 0.999256i | \(0.512279\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.12311 | 0.690799 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.56155 | −0.854241 | −0.427121 | − | 0.904195i | \(-0.640472\pi\) | ||||
−0.427121 | + | 0.904195i | \(0.640472\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.3693 | 1.71177 | 0.855883 | − | 0.517170i | \(-0.173014\pi\) | ||||
0.855883 | + | 0.517170i | \(0.173014\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.00000 | 0.248069 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.56155 | −0.312943 | −0.156472 | − | 0.987682i | \(-0.550012\pi\) | ||||
−0.156472 | + | 0.987682i | \(0.550012\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.6847 | −1.38671 | −0.693357 | − | 0.720594i | \(-0.743869\pi\) | ||||
−0.693357 | + | 0.720594i | \(0.743869\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −13.1231 | −1.49552 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.2462 | 1.15279 | 0.576394 | − | 0.817172i | \(-0.304459\pi\) | ||||
0.576394 | + | 0.817172i | \(0.304459\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.315342 | 0.0346132 | 0.0173066 | − | 0.999850i | \(-0.494491\pi\) | ||||
0.0173066 | + | 0.999850i | \(0.494491\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.56155 | −0.494770 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.12311 | 0.331049 | 0.165524 | − | 0.986206i | \(-0.447068\pi\) | ||||
0.165524 | + | 0.986206i | \(0.447068\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.12311 | −0.537047 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.12311 | 0.115228 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.31534 | −0.628400 | −0.314200 | − | 0.949357i | \(-0.601736\pi\) | ||||
−0.314200 | + | 0.949357i | \(0.601736\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 14.2462 | 1.40372 | 0.701860 | − | 0.712314i | \(-0.252353\pi\) | ||||
0.701860 | + | 0.712314i | \(0.252353\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.68466 | −0.742904 | −0.371452 | − | 0.928452i | \(-0.621140\pi\) | ||||
−0.371452 | + | 0.928452i | \(0.621140\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.24621 | −0.406713 | −0.203357 | − | 0.979105i | \(-0.565185\pi\) | ||||
−0.203357 | + | 0.979105i | \(0.565185\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.31534 | −0.217809 | −0.108905 | − | 0.994052i | \(-0.534734\pi\) | ||||
−0.108905 | + | 0.994052i | \(0.534734\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.6847 | 1.07113 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.2462 | 1.26415 | 0.632073 | − | 0.774909i | \(-0.282204\pi\) | ||||
0.632073 | + | 0.774909i | \(0.282204\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2462 | 0.895216 | 0.447608 | − | 0.894230i | \(-0.352276\pi\) | ||||
0.447608 | + | 0.894230i | \(0.352276\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.87689 | −0.249458 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −14.0000 | −1.19610 | −0.598050 | − | 0.801459i | \(-0.704058\pi\) | ||||
−0.598050 | + | 0.801459i | \(0.704058\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.8078 | −1.08634 | −0.543170 | − | 0.839623i | \(-0.682776\pi\) | ||||
−0.543170 | + | 0.839623i | \(0.682776\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 10.2462 | 0.856831 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.56155 | −0.710998 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3693 | 1.09526 | 0.547629 | − | 0.836722i | \(-0.315531\pi\) | ||||
0.547629 | + | 0.836722i | \(0.315531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2462 | 0.833825 | 0.416912 | − | 0.908947i | \(-0.363112\pi\) | ||||
0.416912 | + | 0.908947i | \(0.363112\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.68466 | −0.295959 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.0540 | −1.36106 | −0.680528 | − | 0.732722i | \(-0.738249\pi\) | ||||
−0.680528 | + | 0.732722i | \(0.738249\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.56155 | −0.201879 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.3693 | 1.51712 | 0.758561 | − | 0.651602i | \(-0.225903\pi\) | ||||
0.758561 | + | 0.651602i | \(0.225903\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.4924 | 0.966693 | 0.483346 | − | 0.875429i | \(-0.339421\pi\) | ||||
0.483346 | + | 0.875429i | \(0.339421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −15.1231 | −1.14979 | −0.574894 | − | 0.818228i | \(-0.694957\pi\) | ||||
−0.574894 | + | 0.818228i | \(0.694957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.56155 | −0.193635 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.4924 | −0.933727 | −0.466864 | − | 0.884329i | \(-0.654616\pi\) | ||||
−0.466864 | + | 0.884329i | \(0.654616\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.876894 | 0.0651790 | 0.0325895 | − | 0.999469i | \(-0.489625\pi\) | ||||
0.0325895 | + | 0.999469i | \(0.489625\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.561553 | 0.0412862 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −23.3693 | −1.70893 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.4924 | 0.903920 | 0.451960 | − | 0.892038i | \(-0.350725\pi\) | ||||
0.451960 | + | 0.892038i | \(0.350725\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −13.3693 | −0.962344 | −0.481172 | − | 0.876626i | \(-0.659789\pi\) | ||||
−0.481172 | + | 0.876626i | \(0.659789\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.2462 | −1.44248 | −0.721241 | − | 0.692684i | \(-0.756428\pi\) | ||||
−0.721241 | + | 0.692684i | \(0.756428\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.87689 | −0.203938 | −0.101969 | − | 0.994788i | \(-0.532514\pi\) | ||||
−0.101969 | + | 0.994788i | \(0.532514\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.9309 | 1.53925 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.43845 | −0.240152 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.75379 | 0.397998 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4384 | −0.925141 | −0.462570 | − | 0.886583i | \(-0.653073\pi\) | ||||
−0.462570 | + | 0.886583i | \(0.653073\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.24621 | −0.425988 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.43845 | 0.640724 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.12311 | −0.613686 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.3693 | −1.29707 | −0.648533 | − | 0.761187i | \(-0.724617\pi\) | ||||
−0.648533 | + | 0.761187i | \(0.724617\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.49242 | −0.563662 | −0.281831 | − | 0.959464i | \(-0.590942\pi\) | ||||
−0.281831 | + | 0.959464i | \(0.590942\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.12311 | −0.470708 | −0.235354 | − | 0.971910i | \(-0.575625\pi\) | ||||
−0.235354 | + | 0.971910i | \(0.575625\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.3693 | −0.875853 | −0.437927 | − | 0.899011i | \(-0.644287\pi\) | ||||
−0.437927 | + | 0.899011i | \(0.644287\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.6847 | 1.27329 | 0.636647 | − | 0.771155i | \(-0.280321\pi\) | ||||
0.636647 | + | 0.771155i | \(0.280321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.438447 | −0.0280114 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.24621 | 0.142923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.1231 | 1.83823 | 0.919117 | − | 0.393985i | \(-0.128904\pi\) | ||||
0.919117 | + | 0.393985i | \(0.128904\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.12311 | 0.322087 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.6155 | −1.47310 | −0.736548 | − | 0.676385i | \(-0.763545\pi\) | ||||
−0.736548 | + | 0.676385i | \(0.763545\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.43845 | −0.0893808 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.5616 | −1.88451 | −0.942253 | − | 0.334902i | \(-0.891297\pi\) | ||||
−0.942253 | + | 0.334902i | \(0.891297\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.561553 | −0.0344959 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −11.4384 | −0.697414 | −0.348707 | − | 0.937232i | \(-0.613379\pi\) | ||||
−0.348707 | + | 0.937232i | \(0.613379\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6847 | 0.709792 | 0.354896 | − | 0.934906i | \(-0.384516\pi\) | ||||
0.354896 | + | 0.934906i | \(0.384516\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.12311 | 0.308935 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.24621 | −0.495467 | −0.247733 | − | 0.968828i | \(-0.579686\pi\) | ||||
−0.247733 | + | 0.968828i | \(0.579686\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0000 | −0.596550 | −0.298275 | − | 0.954480i | \(-0.596411\pi\) | ||||
−0.298275 | + | 0.954480i | \(0.596411\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.56155 | 0.152269 | 0.0761343 | − | 0.997098i | \(-0.475742\pi\) | ||||
0.0761343 | + | 0.997098i | \(0.475742\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.80776 | 0.519906 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.80776 | 0.223986 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.93087 | −0.463326 | −0.231663 | − | 0.972796i | \(-0.574417\pi\) | ||||
−0.231663 | + | 0.972796i | \(0.574417\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.56155 | −0.382028 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.00000 | 0.115663 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 16.0000 | 0.922225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.3693 | 0.765525 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.6155 | −1.69025 | −0.845124 | − | 0.534571i | \(-0.820473\pi\) | ||||
−0.845124 | + | 0.534571i | \(0.820473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.00000 | 0.453638 | 0.226819 | − | 0.973937i | \(-0.427167\pi\) | ||||
0.226819 | + | 0.973937i | \(0.427167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.43845 | 0.194353 | 0.0971763 | − | 0.995267i | \(-0.469019\pi\) | ||||
0.0971763 | + | 0.995267i | \(0.469019\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.1231 | 0.624736 | 0.312368 | − | 0.949961i | \(-0.398878\pi\) | ||||
0.312368 | + | 0.949961i | \(0.398878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −43.8617 | −2.45579 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.12311 | −0.285057 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00000 | 0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.4924 | 1.12978 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.19224 | −0.175461 | −0.0877306 | − | 0.996144i | \(-0.527961\pi\) | ||||
−0.0877306 | + | 0.996144i | \(0.527961\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −2.56155 | −0.139953 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.0000 | −0.762629 | −0.381314 | − | 0.924445i | \(-0.624528\pi\) | ||||
−0.381314 | + | 0.924445i | \(0.624528\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.8769 | −1.02224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.0540 | 1.02882 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −26.7386 | −1.43541 | −0.717703 | − | 0.696350i | \(-0.754806\pi\) | ||||
−0.717703 | + | 0.696350i | \(0.754806\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.05398 | 0.0564180 | 0.0282090 | − | 0.999602i | \(-0.491020\pi\) | ||||
0.0282090 | + | 0.999602i | \(0.491020\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1231 | −0.592023 | −0.296012 | − | 0.955184i | \(-0.595657\pi\) | ||||
−0.296012 | + | 0.955184i | \(0.595657\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.6847 | −0.620157 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.0000 | 1.26667 | 0.633336 | − | 0.773877i | \(-0.281685\pi\) | ||||
0.633336 | + | 0.773877i | \(0.281685\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.7386 | −0.933612 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.00000 | 0.104685 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.3002 | 0.903062 | 0.451531 | − | 0.892255i | \(-0.350878\pi\) | ||||
0.451531 | + | 0.892255i | \(0.350878\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.43845 | 0.0746805 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −19.7538 | −1.02281 | −0.511406 | − | 0.859339i | \(-0.670875\pi\) | ||||
−0.511406 | + | 0.859339i | \(0.670875\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17.1231 | −0.881885 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.75379 | −0.0900861 | −0.0450430 | − | 0.998985i | \(-0.514342\pi\) | ||||
−0.0450430 | + | 0.998985i | \(0.514342\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.9309 | 1.12062 | 0.560308 | − | 0.828285i | \(-0.310683\pi\) | ||||
0.560308 | + | 0.828285i | \(0.310683\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1231 | −0.668815 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −30.4924 | −1.54603 | −0.773014 | − | 0.634389i | \(-0.781252\pi\) | ||||
−0.773014 | + | 0.634389i | \(0.781252\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.56155 | −0.230688 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.2462 | 0.515543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −23.6155 | −1.18523 | −0.592615 | − | 0.805486i | \(-0.701904\pi\) | ||||
−0.592615 | + | 0.805486i | \(0.701904\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.0000 | −0.898877 | −0.449439 | − | 0.893311i | \(-0.648376\pi\) | ||||
−0.449439 | + | 0.893311i | \(0.648376\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.36932 | −0.367092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.87689 | 0.142602 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.31534 | −0.114486 | −0.0572431 | − | 0.998360i | \(-0.518231\pi\) | ||||
−0.0572431 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.8078 | 0.827056 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.315342 | 0.0154795 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.8769 | 1.31302 | 0.656511 | − | 0.754316i | \(-0.272032\pi\) | ||||
0.656511 | + | 0.754316i | \(0.272032\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4924 | 1.29116 | 0.645581 | − | 0.763692i | \(-0.276615\pi\) | ||||
0.645581 | + | 0.763692i | \(0.276615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.56155 | −0.221268 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −34.2462 | −1.65729 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.4924 | −0.987085 | −0.493543 | − | 0.869722i | \(-0.664298\pi\) | ||||
−0.493543 | + | 0.869722i | \(0.664298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −7.43845 | −0.357469 | −0.178734 | − | 0.983897i | \(-0.557200\pi\) | ||||
−0.178734 | + | 0.983897i | \(0.557200\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.12311 | 0.0537254 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.4924 | −0.783579 | −0.391789 | − | 0.920055i | \(-0.628144\pi\) | ||||
−0.391789 | + | 0.920055i | \(0.628144\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.12311 | 0.148049 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.4233 | 1.90769 | 0.953847 | − | 0.300294i | \(-0.0970849\pi\) | ||||
0.953847 | + | 0.300294i | \(0.0970849\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.6155 | −0.829483 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.12311 | −0.240175 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3153 | −0.482531 | −0.241266 | − | 0.970459i | \(-0.577563\pi\) | ||||
−0.241266 | + | 0.970459i | \(0.577563\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −20.2462 | −0.942960 | −0.471480 | − | 0.881877i | \(-0.656280\pi\) | ||||
−0.471480 | + | 0.881877i | \(0.656280\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.63068 | 0.215206 | 0.107603 | − | 0.994194i | \(-0.465682\pi\) | ||||
0.107603 | + | 0.994194i | \(0.465682\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −31.6847 | −1.46619 | −0.733096 | − | 0.680126i | \(-0.761925\pi\) | ||||
−0.733096 | + | 0.680126i | \(0.761925\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.56155 | 0.302984 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −32.0000 | −1.47136 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.12311 | 0.0515316 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.7386 | −1.03895 | −0.519477 | − | 0.854484i | \(-0.673873\pi\) | ||||
−0.519477 | + | 0.854484i | \(0.673873\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.12311 | 0.0512092 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.00000 | −0.272446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.7386 | 0.849129 | 0.424564 | − | 0.905398i | \(-0.360427\pi\) | ||||
0.424564 | + | 0.905398i | \(0.360427\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.31534 | 0.194749 | 0.0973743 | − | 0.995248i | \(-0.468956\pi\) | ||||
0.0973743 | + | 0.995248i | \(0.468956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.0540 | 1.75890 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 29.9309 | 1.34258 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 22.4233 | 1.00380 | 0.501902 | − | 0.864924i | \(-0.332634\pi\) | ||||
0.501902 | + | 0.864924i | \(0.332634\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.3153 | −0.549114 | −0.274557 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274557 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.31534 | −0.281029 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −6.49242 | −0.287772 | −0.143886 | − | 0.989594i | \(-0.545960\pi\) | ||||
−0.143886 | + | 0.989594i | \(0.545960\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.12311 | −0.226633 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 14.2462 | 0.627763 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −40.9848 | −1.80251 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.50758 | −0.241291 | −0.120646 | − | 0.992696i | \(-0.538496\pi\) | ||||
−0.120646 | + | 0.992696i | \(0.538496\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.492423 | 0.0215321 | 0.0107661 | − | 0.999942i | \(-0.496573\pi\) | ||||
0.0107661 | + | 0.999942i | \(0.496573\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 16.8078 | 0.732158 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.87689 | −0.297871 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.68466 | −0.332237 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.24621 | −0.0967512 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.00000 | 0.257960 | 0.128980 | − | 0.991647i | \(-0.458830\pi\) | ||||
0.128980 | + | 0.991647i | \(0.458830\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.24621 | −0.181888 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.75379 | 0.417042 | 0.208521 | − | 0.978018i | \(-0.433135\pi\) | ||||
0.208521 | + | 0.978018i | \(0.433135\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.61553 | −0.409635 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −26.2462 | −1.11610 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.9309 | 0.505527 | 0.252764 | − | 0.967528i | \(-0.418661\pi\) | ||||
0.252764 | + | 0.967528i | \(0.418661\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.4924 | −0.528373 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.6847 | 0.661030 | 0.330515 | − | 0.943801i | \(-0.392778\pi\) | ||||
0.330515 | + | 0.943801i | \(0.392778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.31534 | −0.0974072 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 22.0000 | 0.922288 | 0.461144 | − | 0.887325i | \(-0.347439\pi\) | ||||
0.461144 | + | 0.887325i | \(0.347439\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 45.8617 | 1.90925 | 0.954625 | − | 0.297812i | \(-0.0962568\pi\) | ||||
0.954625 | + | 0.297812i | \(0.0962568\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.807764 | −0.0335117 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.87689 | −0.119149 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 39.8617 | 1.64527 | 0.822635 | − | 0.568570i | \(-0.192503\pi\) | ||||
0.822635 | + | 0.568570i | \(0.192503\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.13826 | −0.170514 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.8769 | 0.528791 | 0.264395 | − | 0.964414i | \(-0.414828\pi\) | ||||
0.264395 | + | 0.964414i | \(0.414828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.6847 | 0.479024 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.0000 | 1.30748 | 0.653742 | − | 0.756717i | \(-0.273198\pi\) | ||||
0.653742 | + | 0.756717i | \(0.273198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.561553 | 0.0229062 | 0.0114531 | − | 0.999934i | \(-0.496354\pi\) | ||||
0.0114531 | + | 0.999934i | \(0.496354\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.2462 | 0.619847 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.0000 | 1.13648 | 0.568242 | − | 0.822861i | \(-0.307624\pi\) | ||||
0.568242 | + | 0.822861i | \(0.307624\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.0000 | −0.647291 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 20.2462 | 0.817737 | 0.408868 | − | 0.912593i | \(-0.365924\pi\) | ||||
0.408868 | + | 0.912593i | \(0.365924\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −25.6847 | −1.03403 | −0.517013 | − | 0.855978i | \(-0.672956\pi\) | ||||
−0.517013 | + | 0.855978i | \(0.672956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −47.2311 | −1.89838 | −0.949188 | − | 0.314709i | \(-0.898093\pi\) | ||||
−0.949188 | + | 0.314709i | \(0.898093\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.00000 | −0.320513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.56155 | −0.102136 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.2462 | −0.726370 | −0.363185 | − | 0.931717i | \(-0.618311\pi\) | ||||
−0.363185 | + | 0.931717i | \(0.618311\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.2462 | 0.565344 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.876894 | −0.0347438 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 32.2462 | 1.27365 | 0.636824 | − | 0.771009i | \(-0.280248\pi\) | ||||
0.636824 | + | 0.771009i | \(0.280248\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.3002 | −1.31323 | −0.656616 | − | 0.754225i | \(-0.728013\pi\) | ||||
−0.656616 | + | 0.754225i | \(0.728013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −34.8769 | −1.37115 | −0.685576 | − | 0.728001i | \(-0.740450\pi\) | ||||
−0.685576 | + | 0.728001i | \(0.740450\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −33.6155 | −1.31952 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.4924 | 1.34979 | 0.674896 | − | 0.737912i | \(-0.264188\pi\) | ||||
0.674896 | + | 0.737912i | \(0.264188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.2462 | 0.400353 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3693 | 0.598704 | 0.299352 | − | 0.954143i | \(-0.403230\pi\) | ||||
0.299352 | + | 0.954143i | \(0.403230\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7386 | −0.651057 | −0.325529 | − | 0.945532i | \(-0.605542\pi\) | ||||
−0.325529 | + | 0.945532i | \(0.605542\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.87689 | −0.111561 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.56155 | −0.331505 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 68.4924 | 2.64412 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6307 | 0.718160 | 0.359080 | − | 0.933307i | \(-0.383091\pi\) | ||||
0.359080 | + | 0.933307i | \(0.383091\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.3002 | 0.434301 | 0.217151 | − | 0.976138i | \(-0.430324\pi\) | ||||
0.217151 | + | 0.976138i | \(0.430324\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.3693 | 0.589820 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6.24621 | 0.239005 | 0.119502 | − | 0.992834i | \(-0.461870\pi\) | ||||
0.119502 | + | 0.992834i | \(0.461870\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.0000 | −0.534913 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.12311 | −0.0427869 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.50758 | −0.285602 | −0.142801 | − | 0.989751i | \(-0.545611\pi\) | ||||
−0.142801 | + | 0.989751i | \(0.545611\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.8078 | −0.485826 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.6847 | 0.594099 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −37.8617 | −1.43002 | −0.715009 | − | 0.699115i | \(-0.753577\pi\) | ||||
−0.715009 | + | 0.699115i | \(0.753577\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.630683 | 0.0237867 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.1771 | 0.608402 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −28.8769 | −1.08449 | −0.542247 | − | 0.840219i | \(-0.682426\pi\) | ||||
−0.542247 | + | 0.840219i | \(0.682426\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.68466 | −0.137992 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.2462 | 0.383187 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −13.3002 | −0.496013 | −0.248007 | − | 0.968758i | \(-0.579775\pi\) | ||||
−0.248007 | + | 0.968758i | \(0.579775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −36.4924 | −1.35905 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.56155 | −0.317968 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.8078 | 0.475014 | 0.237507 | − | 0.971386i | \(-0.423670\pi\) | ||||
0.237507 | + | 0.971386i | \(0.423670\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.4924 | 1.05383 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.9309 | −1.03165 | −0.515825 | − | 0.856694i | \(-0.672515\pi\) | ||||
−0.515825 | + | 0.856694i | \(0.672515\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −13.1231 | −0.483396 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.9309 | −0.953882 | −0.476941 | − | 0.878935i | \(-0.658255\pi\) | ||||
−0.476941 | + | 0.878935i | \(0.658255\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −52.4924 | −1.92576 | −0.962880 | − | 0.269929i | \(-0.913000\pi\) | ||||
−0.962880 | + | 0.269929i | \(0.913000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 13.3693 | 0.489814 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 19.6847 | 0.719262 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.61553 | 0.0589515 | 0.0294757 | − | 0.999565i | \(-0.490616\pi\) | ||||
0.0294757 | + | 0.999565i | \(0.490616\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.2462 | 0.372898 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.17708 | 0.0791274 | 0.0395637 | − | 0.999217i | \(-0.487403\pi\) | ||||
0.0395637 | + | 0.999217i | \(0.487403\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.19224 | −0.0432185 | −0.0216093 | − | 0.999766i | \(-0.506879\pi\) | ||||
−0.0216093 | + | 0.999766i | \(0.506879\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.8769 | 0.393770 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.1231 | −0.473848 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 25.3693 | 0.914841 | 0.457420 | − | 0.889251i | \(-0.348773\pi\) | ||||
0.457420 | + | 0.889251i | \(0.348773\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 52.7386 | 1.89688 | 0.948438 | − | 0.316961i | \(-0.102663\pi\) | ||||
0.948438 | + | 0.316961i | \(0.102663\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.68466 | −0.132357 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.86174 | −0.138361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −59.8617 | −2.14202 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.0540 | −0.608682 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 32.6695 | 1.16454 | 0.582271 | − | 0.812995i | \(-0.302164\pi\) | ||||
0.582271 | + | 0.812995i | \(0.302164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.93087 | 0.210877 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 26.7386 | 0.949517 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 55.7926 | 1.97628 | 0.988138 | − | 0.153570i | \(-0.0490770\pi\) | ||||
0.988138 | + | 0.153570i | \(0.0490770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.4924 | 1.29101 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.2462 | 0.361581 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56155 | −0.0902829 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.1922 | 0.745079 | 0.372540 | − | 0.928016i | \(-0.378487\pi\) | ||||
0.372540 | + | 0.928016i | \(0.378487\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5464 | 0.686367 | 0.343183 | − | 0.939268i | \(-0.388495\pi\) | ||||
0.343183 | + | 0.939268i | \(0.388495\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 19.3693 | 0.678478 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.01515 | −0.245429 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.0000 | 1.32621 | 0.663105 | − | 0.748527i | \(-0.269238\pi\) | ||||
0.663105 | + | 0.748527i | \(0.269238\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.0000 | 1.81261 | 0.906303 | − | 0.422628i | \(-0.138892\pi\) | ||||
0.906303 | + | 0.422628i | \(0.138892\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.94602 | 0.311084 | 0.155542 | − | 0.987829i | \(-0.450288\pi\) | ||||
0.155542 | + | 0.987829i | \(0.450288\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.19224 | 0.180334 | 0.0901669 | − | 0.995927i | \(-0.471260\pi\) | ||||
0.0901669 | + | 0.995927i | \(0.471260\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 12.4924 | 0.432318 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.12311 | 0.176869 | 0.0884346 | − | 0.996082i | \(-0.471814\pi\) | ||||
0.0884346 | + | 0.996082i | \(0.471814\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.3002 | 1.52759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.00000 | −0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −39.0540 | −1.34191 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.561553 | 0.0192498 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.2311 | −1.68564 | −0.842820 | − | 0.538196i | \(-0.819106\pi\) | ||||
−0.842820 | + | 0.538196i | \(0.819106\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −42.4924 | −1.45151 | −0.725757 | − | 0.687951i | \(-0.758510\pi\) | ||||
−0.725757 | + | 0.687951i | \(0.758510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.1771 | −0.688433 | −0.344217 | − | 0.938890i | \(-0.611855\pi\) | ||||
−0.344217 | + | 0.938890i | \(0.611855\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 11.8617 | 0.403778 | 0.201889 | − | 0.979408i | \(-0.435292\pi\) | ||||
0.201889 | + | 0.979408i | \(0.435292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.1231 | −0.514201 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 52.4924 | 1.78068 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.12311 | −0.173590 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.56155 | −0.0865963 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 53.2311 | 1.79749 | 0.898743 | − | 0.438477i | \(-0.144482\pi\) | ||||
0.898743 | + | 0.438477i | \(0.144482\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.6307 | −0.897211 | −0.448605 | − | 0.893730i | \(-0.648079\pi\) | ||||
−0.448605 | + | 0.893730i | \(0.648079\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0000 | 0.403832 | 0.201916 | − | 0.979403i | \(-0.435283\pi\) | ||||
0.201916 | + | 0.979403i | \(0.435283\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.1231 | 0.709244 | 0.354622 | − | 0.935010i | \(-0.384609\pi\) | ||||
0.354622 | + | 0.935010i | \(0.384609\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.4924 | −1.22392 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.98485 | −0.300666 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.4924 | −0.417576 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 31.5464 | 1.05213 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.56155 | 0.0853377 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.876894 | 0.0291490 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0691 | −0.467158 | −0.233579 | − | 0.972338i | \(-0.575044\pi\) | ||||
−0.233579 | + | 0.972338i | \(0.575044\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.7386 | −1.01842 | −0.509208 | − | 0.860643i | \(-0.670062\pi\) | ||||
−0.509208 | + | 0.860643i | \(0.670062\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.61553 | 0.0534662 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −26.2462 | −0.866726 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −48.9848 | −1.61586 | −0.807930 | − | 0.589278i | \(-0.799412\pi\) | ||||
−0.807930 | + | 0.589278i | \(0.799412\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.3693 | −0.769210 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.561553 | 0.0184637 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −21.0540 | −0.690759 | −0.345379 | − | 0.938463i | \(-0.612250\pi\) | ||||
−0.345379 | + | 0.938463i | \(0.612250\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.492423 | −0.0161385 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −23.3693 | −0.764258 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4924 | −1.12682 | −0.563409 | − | 0.826178i | \(-0.690511\pi\) | ||||
−0.563409 | + | 0.826178i | \(0.690511\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.3693 | 0.696620 | 0.348310 | − | 0.937379i | \(-0.386756\pi\) | ||||
0.348310 | + | 0.937379i | \(0.386756\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.43845 | −0.111971 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.0000 | 0.389948 | 0.194974 | − | 0.980808i | \(-0.437538\pi\) | ||||
0.194974 | + | 0.980808i | \(0.437538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.00000 | 0.129845 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −19.7538 | −0.639888 | −0.319944 | − | 0.947436i | \(-0.603664\pi\) | ||||
−0.319944 | + | 0.947436i | \(0.603664\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4924 | 0.404245 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 35.8617 | 1.15804 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.4233 | −0.562042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.3693 | −0.430374 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.9848 | −0.417564 | −0.208782 | − | 0.977962i | \(-0.566950\pi\) | ||||
−0.208782 | + | 0.977962i | \(0.566950\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −46.7386 | −1.49991 | −0.749957 | − | 0.661487i | \(-0.769926\pi\) | ||||
−0.749957 | + | 0.661487i | \(0.769926\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.8078 | 1.05177 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −48.4233 | −1.54920 | −0.774599 | − | 0.632452i | \(-0.782048\pi\) | ||||
−0.774599 | + | 0.632452i | \(0.782048\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 16.0000 | 0.511362 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.1771 | −0.771129 | −0.385565 | − | 0.922681i | \(-0.625993\pi\) | ||||
−0.385565 | + | 0.922681i | \(0.625993\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.2462 | −0.645098 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.24621 | −0.198618 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.9460 | −0.411244 | −0.205622 | − | 0.978631i | \(-0.565922\pi\) | ||||
−0.205622 | + | 0.978631i | \(0.565922\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.87689 | −0.0912037 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.8617 | 1.19909 | 0.599547 | − | 0.800340i | \(-0.295348\pi\) | ||||
0.599547 | + | 0.800340i | \(0.295348\pi\) | |||||||
\(998\) | 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 | 8280.2.a.be.1.1 | 2 | ||
3.2 | odd | 2 | 2760.2.a.p.1.1 | ✓ | 2 | ||
12.11 | even | 2 | 5520.2.a.bh.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2760.2.a.p.1.1 | ✓ | 2 | 3.2 | odd | 2 | ||
5520.2.a.bh.1.2 | 2 | 12.11 | even | 2 | |||
8280.2.a.be.1.1 | 2 | 1.1 | even | 1 | trivial |