Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(1,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.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: | \(48.2935231425\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.1 |
$q$-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 | ||||||||
\(5\) | 2.56155 | 1.14556 | 0.572781 | − | 0.819709i | \(-0.305865\pi\) | ||||
0.572781 | + | 0.819709i | \(0.305865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.12311 | −1.54467 | −0.772337 | − | 0.635213i | \(-0.780912\pi\) | ||||
−0.772337 | + | 0.635213i | \(0.780912\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.43845 | −0.676304 | −0.338152 | − | 0.941092i | \(-0.609802\pi\) | ||||
−0.338152 | + | 0.941092i | \(0.609802\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.12311 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12311 | −0.716490 | −0.358245 | − | 0.933628i | \(-0.616625\pi\) | ||||
−0.358245 | + | 0.933628i | \(0.616625\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.68466 | −1.81088 | −0.905438 | − | 0.424478i | \(-0.860458\pi\) | ||||
−0.905438 | + | 0.424478i | \(0.860458\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.56155 | 0.312311 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.56155 | 1.77554 | 0.887768 | − | 0.460291i | \(-0.152255\pi\) | ||||
0.887768 | + | 0.460291i | \(0.152255\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.56155 | −0.280463 | −0.140232 | − | 0.990119i | \(-0.544785\pi\) | ||||
−0.140232 | + | 0.990119i | \(0.544785\pi\) | |||||||
\(32\) | 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 | \(-0.514698\pi\) | ||||
−0.0461594 | + | 0.998934i | \(0.514698\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.43845 | −1.16169 | −0.580845 | − | 0.814014i | \(-0.697278\pi\) | ||||
−0.580845 | + | 0.814014i | \(0.697278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.24621 | 1.10504 | 0.552518 | − | 0.833501i | \(-0.313667\pi\) | ||||
0.552518 | + | 0.833501i | \(0.313667\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.561553 | −0.0819109 | −0.0409554 | − | 0.999161i | \(-0.513040\pi\) | ||||
−0.0409554 | + | 0.999161i | \(0.513040\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.68466 | −0.918208 | −0.459104 | − | 0.888382i | \(-0.651830\pi\) | ||||
−0.459104 | + | 0.888382i | \(0.651830\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −13.1231 | −1.76952 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.12311 | 1.05754 | 0.528769 | − | 0.848766i | \(-0.322654\pi\) | ||||
0.528769 | + | 0.848766i | \(0.322654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.24621 | −1.05582 | −0.527910 | − | 0.849301i | \(-0.677024\pi\) | ||||
−0.527910 | + | 0.849301i | \(0.677024\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.24621 | −0.774747 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.31534 | −0.405033 | −0.202517 | − | 0.979279i | \(-0.564912\pi\) | ||||
−0.202517 | + | 0.979279i | \(0.564912\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.56155 | −0.185322 | −0.0926611 | − | 0.995698i | \(-0.529537\pi\) | ||||
−0.0926611 | + | 0.995698i | \(0.529537\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.12311 | −0.833696 | −0.416848 | − | 0.908976i | \(-0.636865\pi\) | ||||
−0.416848 | + | 0.908976i | \(0.636865\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.12311 | −0.583832 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.56155 | −0.963250 | −0.481625 | − | 0.876377i | \(-0.659953\pi\) | ||||
−0.481625 | + | 0.876377i | \(0.659953\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.56155 | −0.281167 | −0.140583 | − | 0.990069i | \(-0.544898\pi\) | ||||
−0.140583 | + | 0.990069i | \(0.544898\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.5616 | 1.14556 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.31534 | −0.139426 | −0.0697130 | − | 0.997567i | \(-0.522208\pi\) | ||||
−0.0697130 | + | 0.997567i | \(0.522208\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.43845 | −0.255619 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.00000 | −0.820783 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.75379 | −0.178070 | −0.0890351 | − | 0.996028i | \(-0.528378\pi\) | ||||
−0.0890351 | + | 0.996028i | \(0.528378\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.43845 | −0.634399 | −0.317200 | − | 0.948359i | \(-0.602742\pi\) | ||||
−0.317200 | + | 0.948359i | \(0.602742\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.4924 | −1.59438 | −0.797191 | − | 0.603727i | \(-0.793682\pi\) | ||||
−0.797191 | + | 0.603727i | \(0.793682\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.8078 | −1.60989 | −0.804946 | − | 0.593348i | \(-0.797806\pi\) | ||||
−0.804946 | + | 0.593348i | \(0.797806\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.12311 | −0.481941 | −0.240971 | − | 0.970532i | \(-0.577466\pi\) | ||||
−0.240971 | + | 0.970532i | \(0.577466\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.2462 | −2.07447 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.12311 | 0.377964 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.2462 | 1.38602 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −8.80776 | −0.787790 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.5616 | −1.64707 | −0.823536 | − | 0.567264i | \(-0.808002\pi\) | ||||
−0.823536 | + | 0.567264i | \(0.808002\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.31534 | −0.289663 | −0.144831 | − | 0.989456i | \(-0.546264\pi\) | ||||
−0.144831 | + | 0.989456i | \(0.546264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.12311 | −0.270808 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.12311 | −0.608568 | −0.304284 | − | 0.952581i | \(-0.598417\pi\) | ||||
−0.304284 | + | 0.952581i | \(0.598417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 18.4924 | 1.56851 | 0.784253 | − | 0.620441i | \(-0.213046\pi\) | ||||
0.784253 | + | 0.620441i | \(0.213046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.4924 | 1.04467 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.4924 | 2.03398 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.9309 | 1.05934 | 0.529669 | − | 0.848204i | \(-0.322316\pi\) | ||||
0.529669 | + | 0.848204i | \(0.322316\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.561553 | 0.0456985 | 0.0228493 | − | 0.999739i | \(-0.492726\pi\) | ||||
0.0228493 | + | 0.999739i | \(0.492726\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.9309 | 1.51085 | 0.755424 | − | 0.655236i | \(-0.227431\pi\) | ||||
0.755424 | + | 0.655236i | \(0.227431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.68466 | −0.684447 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.3693 | −1.12549 | −0.562746 | − | 0.826630i | \(-0.690255\pi\) | ||||
−0.562746 | + | 0.826630i | \(0.690255\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.315342 | 0.0244019 | 0.0122009 | − | 0.999926i | \(-0.496116\pi\) | ||||
0.0122009 | + | 0.999926i | \(0.496116\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.05398 | −0.542613 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 19.3693 | 1.47262 | 0.736311 | − | 0.676643i | \(-0.236566\pi\) | ||||
0.736311 | + | 0.676643i | \(0.236566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.56155 | 0.118042 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 14.8769 | 1.11195 | 0.555976 | − | 0.831199i | \(-0.312345\pi\) | ||||
0.555976 | + | 0.831199i | \(0.312345\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.5616 | −1.45400 | −0.726999 | − | 0.686638i | \(-0.759086\pi\) | ||||
−0.726999 | + | 0.686638i | \(0.759086\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.43845 | −0.105757 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.1231 | −1.54467 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.12311 | −0.660125 | −0.330062 | − | 0.943959i | \(-0.607070\pi\) | ||||
−0.330062 | + | 0.943959i | \(0.607070\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.6155 | 1.62790 | 0.813951 | − | 0.580934i | \(-0.197313\pi\) | ||||
0.813951 | + | 0.580934i | \(0.197313\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −15.1231 | −1.07748 | −0.538738 | − | 0.842473i | \(-0.681099\pi\) | ||||
−0.538738 | + | 0.842473i | \(0.681099\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.68466 | 0.473863 | 0.236931 | − | 0.971526i | \(-0.423858\pi\) | ||||
0.236931 | + | 0.971526i | \(0.423858\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.56155 | 0.671089 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0540 | −1.33079 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.0000 | 1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0540 | −1.79363 | −0.896815 | − | 0.442406i | \(-0.854125\pi\) | ||||
−0.896815 | + | 0.442406i | \(0.854125\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.5616 | 1.26589 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.56155 | −0.106005 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.0540 | −0.676304 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.2462 | −0.686137 | −0.343069 | − | 0.939310i | \(-0.611466\pi\) | ||||
−0.343069 | + | 0.939310i | \(0.611466\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.8078 | 1.58018 | 0.790088 | − | 0.612993i | \(-0.210035\pi\) | ||||
0.790088 | + | 0.612993i | \(0.210035\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −26.4924 | −1.75067 | −0.875334 | − | 0.483518i | \(-0.839359\pi\) | ||||
−0.875334 | + | 0.483518i | \(0.839359\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −5.75379 | −0.376943 | −0.188472 | − | 0.982079i | \(-0.560353\pi\) | ||||
−0.188472 | + | 0.982079i | \(0.560353\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.43845 | −0.0938339 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.87689 | 0.444829 | 0.222415 | − | 0.974952i | \(-0.428606\pi\) | ||||
0.222415 | + | 0.974952i | \(0.428606\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.876894 | 0.0564857 | 0.0282429 | − | 0.999601i | \(-0.491009\pi\) | ||||
0.0282429 | + | 0.999601i | \(0.491009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.56155 | 0.163652 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.61553 | 0.484564 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3153 | −0.777337 | −0.388669 | − | 0.921378i | \(-0.627065\pi\) | ||||
−0.388669 | + | 0.921378i | \(0.627065\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 44.4924 | 2.79721 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.00000 | 0.124757 | 0.0623783 | − | 0.998053i | \(-0.480131\pi\) | ||||
0.0623783 | + | 0.998053i | \(0.480131\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.561553 | −0.0348932 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.1771 | 0.812534 | 0.406267 | − | 0.913754i | \(-0.366830\pi\) | ||||
0.406267 | + | 0.913754i | \(0.366830\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.1231 | −1.05186 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 21.3002 | 1.29870 | 0.649348 | − | 0.760492i | \(-0.275042\pi\) | ||||
0.649348 | + | 0.760492i | \(0.275042\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.0540 | 1.21819 | 0.609096 | − | 0.793096i | \(-0.291532\pi\) | ||||
0.609096 | + | 0.793096i | \(0.291532\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.00000 | −0.482418 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.56155 | 0.153909 | 0.0769544 | − | 0.997035i | \(-0.475480\pi\) | ||||
0.0769544 | + | 0.997035i | \(0.475480\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −29.3693 | −1.75203 | −0.876013 | − | 0.482287i | \(-0.839806\pi\) | ||||
−0.876013 | + | 0.482287i | \(0.839806\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −21.6155 | −1.28491 | −0.642455 | − | 0.766324i | \(-0.722084\pi\) | ||||
−0.642455 | + | 0.766324i | \(0.722084\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.43845 | −0.439078 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.5616 | 1.43490 | 0.717451 | − | 0.696609i | \(-0.245309\pi\) | ||||
0.717451 | + | 0.696609i | \(0.245309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.8078 | 1.21147 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.1771 | 1.22470 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.24621 | 0.417665 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.1231 | −1.20951 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.8769 | −0.734923 | −0.367462 | − | 0.930039i | \(-0.619773\pi\) | ||||
−0.367462 | + | 0.930039i | \(0.619773\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.6847 | −0.889395 | −0.444698 | − | 0.895681i | \(-0.646689\pi\) | ||||
−0.444698 | + | 0.895681i | \(0.646689\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −24.2462 | −1.37048 | −0.685238 | − | 0.728319i | \(-0.740302\pi\) | ||||
−0.685238 | + | 0.728319i | \(0.740302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 31.1231 | 1.74805 | 0.874024 | − | 0.485883i | \(-0.161502\pi\) | ||||
0.874024 | + | 0.485883i | \(0.161502\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.9848 | −2.74262 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.8769 | −0.716490 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.80776 | −0.211217 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.561553 | −0.0309594 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.1231 | −1.21600 | −0.607998 | − | 0.793939i | \(-0.708027\pi\) | ||||
−0.607998 | + | 0.793939i | \(0.708027\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.49242 | −0.463991 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.753789 | 0.0410615 | 0.0205307 | − | 0.999789i | \(-0.493464\pi\) | ||||
0.0205307 | + | 0.999789i | \(0.493464\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.00000 | 0.433224 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 29.8617 | 1.60306 | 0.801531 | − | 0.597953i | \(-0.204019\pi\) | ||||
0.801531 | + | 0.597953i | \(0.204019\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 29.1771 | 1.56181 | 0.780907 | − | 0.624648i | \(-0.214757\pi\) | ||||
0.780907 | + | 0.624648i | \(0.214757\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 33.9848 | 1.80883 | 0.904415 | − | 0.426653i | \(-0.140307\pi\) | ||||
0.904415 | + | 0.426653i | \(0.140307\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | −0.212298 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.8078 | 1.36208 | 0.681041 | − | 0.732245i | \(-0.261528\pi\) | ||||
0.681041 | + | 0.732245i | \(0.261528\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.24621 | −0.486643 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.2462 | −0.955050 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.0539753 | 0.00281749 | 0.00140874 | − | 0.999999i | \(-0.499552\pi\) | ||||
0.00140874 | + | 0.999999i | \(0.499552\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.68466 | −0.347050 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.80776 | 0.145381 | 0.0726903 | − | 0.997355i | \(-0.476842\pi\) | ||||
0.0726903 | + | 0.997355i | \(0.476842\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −23.3153 | −1.20080 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.31534 | −0.221664 | −0.110832 | − | 0.993839i | \(-0.535352\pi\) | ||||
−0.110832 | + | 0.993839i | \(0.535352\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.0540 | 0.973613 | 0.486806 | − | 0.873510i | \(-0.338162\pi\) | ||||
0.486806 | + | 0.873510i | \(0.338162\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.1231 | −0.668815 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 32.2462 | 1.63495 | 0.817474 | − | 0.575966i | \(-0.195374\pi\) | ||||
0.817474 | + | 0.575966i | \(0.195374\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.8078 | −1.81088 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −21.9309 | −1.10346 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.61553 | 0.382212 | 0.191106 | − | 0.981569i | \(-0.438793\pi\) | ||||
0.191106 | + | 0.981569i | \(0.438793\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4924 | 0.723717 | 0.361859 | − | 0.932233i | \(-0.382142\pi\) | ||||
0.361859 | + | 0.932233i | \(0.382142\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.80776 | 0.189678 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.87689 | 0.142602 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.36932 | −0.265496 | −0.132748 | − | 0.991150i | \(-0.542380\pi\) | ||||
−0.132748 | + | 0.991150i | \(0.542380\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.12311 | 0.399712 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.56155 | −0.322094 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 4.75379 | 0.232238 | 0.116119 | − | 0.993235i | \(-0.462955\pi\) | ||||
0.116119 | + | 0.993235i | \(0.462955\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.00000 | −0.0974740 | −0.0487370 | − | 0.998812i | \(-0.515520\pi\) | ||||
−0.0487370 | + | 0.998812i | \(0.515520\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.43845 | 0.312311 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.24621 | −0.399062 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 16.0000 | 0.770693 | 0.385346 | − | 0.922772i | \(-0.374082\pi\) | ||||
0.385346 | + | 0.922772i | \(0.374082\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.1080 | −1.83135 | −0.915676 | − | 0.401918i | \(-0.868344\pi\) | ||||
−0.915676 | + | 0.401918i | \(0.868344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 27.1231 | 1.29747 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0540 | −0.766214 | −0.383107 | − | 0.923704i | \(-0.625146\pi\) | ||||
−0.383107 | + | 0.923704i | \(0.625146\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0.876894 | 0.0416625 | 0.0208313 | − | 0.999783i | \(-0.493369\pi\) | ||||
0.0208313 | + | 0.999783i | \(0.493369\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.36932 | −0.159721 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.4924 | −1.53341 | −0.766706 | − | 0.641998i | \(-0.778106\pi\) | ||||
−0.766706 | + | 0.641998i | \(0.778106\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 38.1080 | 1.79443 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.24621 | −0.292827 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −29.8078 | −1.39435 | −0.697174 | − | 0.716902i | \(-0.745560\pi\) | ||||
−0.697174 | + | 0.716902i | \(0.745560\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −32.4233 | −1.51010 | −0.755052 | − | 0.655665i | \(-0.772388\pi\) | ||||
−0.755052 | + | 0.655665i | \(0.772388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.4384 | −0.531590 | −0.265795 | − | 0.964030i | \(-0.585634\pi\) | ||||
−0.265795 | + | 0.964030i | \(0.585634\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.24621 | −0.103942 | −0.0519711 | − | 0.998649i | \(-0.516550\pi\) | ||||
−0.0519711 | + | 0.998649i | \(0.516550\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.31534 | −0.153088 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −37.1231 | −1.70692 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.87689 | −0.223767 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.0540 | −0.870598 | −0.435299 | − | 0.900286i | \(-0.643357\pi\) | ||||
−0.435299 | + | 0.900286i | \(0.643357\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.36932 | 0.0624355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.49242 | −0.203990 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.63068 | −0.300465 | −0.150232 | − | 0.988651i | \(-0.548002\pi\) | ||||
−0.150232 | + | 0.988651i | \(0.548002\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.75379 | 0.0791474 | 0.0395737 | − | 0.999217i | \(-0.487400\pi\) | ||||
0.0395737 | + | 0.999217i | \(0.487400\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.4233 | 1.77554 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.56155 | −0.0700452 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 25.9309 | 1.16083 | 0.580413 | − | 0.814323i | \(-0.302891\pi\) | ||||
0.580413 | + | 0.814323i | \(0.302891\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.19224 | −0.320686 | −0.160343 | − | 0.987061i | \(-0.551260\pi\) | ||||
−0.160343 | + | 0.987061i | \(0.551260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.6155 | 1.13988 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.0540 | −0.755904 | −0.377952 | − | 0.925825i | \(-0.623372\pi\) | ||||
−0.377952 | + | 0.925825i | \(0.623372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.12311 | −0.315108 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.4924 | −0.726743 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.87689 | 0.126526 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.3693 | −1.76861 | −0.884306 | − | 0.466908i | \(-0.845368\pi\) | ||||
−0.884306 | + | 0.466908i | \(0.845368\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.63068 | −0.202486 | −0.101243 | − | 0.994862i | \(-0.532282\pi\) | ||||
−0.101243 | + | 0.994862i | \(0.532282\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.43845 | −0.280463 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 52.4233 | 2.27927 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.1383 | 0.785655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −42.2462 | −1.82646 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.12311 | −0.220668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.1922 | −0.481192 | −0.240596 | − | 0.970625i | \(-0.577343\pi\) | ||||
−0.240596 | + | 0.970625i | \(0.577343\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −43.0540 | −1.84423 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −31.6847 | −1.35474 | −0.677369 | − | 0.735643i | \(-0.736880\pi\) | ||||
−0.677369 | + | 0.735643i | \(0.736880\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −29.8617 | −1.27215 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.56155 | −0.364074 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.1922 | −0.516602 | −0.258301 | − | 0.966065i | \(-0.583163\pi\) | ||||
−0.258301 | + | 0.966065i | \(0.583163\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.6695 | −0.747340 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.9309 | −0.460681 | −0.230341 | − | 0.973110i | \(-0.573984\pi\) | ||||
−0.230341 | + | 0.973110i | \(0.573984\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1231 | −0.552093 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 10.2462 | 0.429544 | 0.214772 | − | 0.976664i | \(-0.431099\pi\) | ||||
0.214772 | + | 0.976664i | \(0.431099\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 36.1231 | 1.51170 | 0.755852 | − | 0.654742i | \(-0.227223\pi\) | ||||
0.755852 | + | 0.654742i | \(0.227223\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5616 | −0.565556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.00000 | 0.249783 | 0.124892 | − | 0.992170i | \(-0.460142\pi\) | ||||
0.124892 | + | 0.992170i | \(0.460142\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.56155 | −0.106271 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.2462 | 1.41833 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −28.6847 | −1.18394 | −0.591971 | − | 0.805959i | \(-0.701650\pi\) | ||||
−0.591971 | + | 0.805959i | \(0.701650\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.87689 | 0.200949 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −41.0540 | −1.68588 | −0.842942 | − | 0.538004i | \(-0.819179\pi\) | ||||
−0.842942 | + | 0.538004i | \(0.819179\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.5616 | 0.432981 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −36.9309 | −1.50895 | −0.754477 | − | 0.656326i | \(-0.772110\pi\) | ||||
−0.754477 | + | 0.656326i | \(0.772110\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.4924 | 0.672740 | 0.336370 | − | 0.941730i | \(-0.390801\pi\) | ||||
0.336370 | + | 0.941730i | \(0.390801\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 39.0540 | 1.58777 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.43845 | −0.180151 | −0.0900755 | − | 0.995935i | \(-0.528711\pi\) | ||||
−0.0900755 | + | 0.995935i | \(0.528711\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.36932 | 0.0553966 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.73863 | −0.352950 | −0.176475 | − | 0.984305i | \(-0.556469\pi\) | ||||
−0.176475 | + | 0.984305i | \(0.556469\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.12311 | −0.286765 | −0.143383 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143383 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.6155 | 1.27074 | 0.635368 | − | 0.772210i | \(-0.280849\pi\) | ||||
0.635368 | + | 0.772210i | \(0.280849\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.31534 | −0.0526980 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.3693 | −1.21477 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.31534 | −0.0923187 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 27.1922 | 1.08251 | 0.541253 | − | 0.840860i | \(-0.317950\pi\) | ||||
0.541253 | + | 0.840860i | \(0.317950\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −47.5464 | −1.88682 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.43845 | −0.0966148 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6307 | 0.656872 | 0.328436 | − | 0.944526i | \(-0.393478\pi\) | ||||
0.328436 | + | 0.944526i | \(0.393478\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 35.3693 | 1.39483 | 0.697415 | − | 0.716668i | \(-0.254334\pi\) | ||||
0.697415 | + | 0.716668i | \(0.254334\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.8769 | −0.506243 | −0.253121 | − | 0.967435i | \(-0.581457\pi\) | ||||
−0.253121 | + | 0.967435i | \(0.581457\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.6155 | −1.63355 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 4.05398 | 0.158644 | 0.0793222 | − | 0.996849i | \(-0.474724\pi\) | ||||
0.0793222 | + | 0.996849i | \(0.474724\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.49242 | −0.331826 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.8769 | −0.891157 | −0.445579 | − | 0.895243i | \(-0.647002\pi\) | ||||
−0.445579 | + | 0.895243i | \(0.647002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.49242 | −0.0969440 | −0.0484720 | − | 0.998825i | \(-0.515435\pi\) | ||||
−0.0484720 | + | 0.998825i | \(0.515435\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −8.00000 | −0.310227 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −83.0388 | −3.21528 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.2462 | 1.63090 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.1922 | 1.16383 | 0.581913 | − | 0.813251i | \(-0.302305\pi\) | ||||
0.581913 | + | 0.813251i | \(0.302305\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.8769 | 1.18670 | 0.593348 | − | 0.804946i | \(-0.297806\pi\) | ||||
0.593348 | + | 0.804946i | \(0.297806\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.75379 | −0.0673042 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.49242 | −0.171898 | −0.0859489 | − | 0.996300i | \(-0.527392\pi\) | ||||
−0.0859489 | + | 0.996300i | \(0.527392\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.2462 | −0.697152 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.3002 | 0.620988 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.61553 | −0.213625 | −0.106812 | − | 0.994279i | \(-0.534064\pi\) | ||||
−0.106812 | + | 0.994279i | \(0.534064\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 47.3693 | 1.79682 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −30.6695 | −1.16169 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0000 | 0.377695 | 0.188847 | − | 0.982006i | \(-0.439525\pi\) | ||||
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.75379 | 0.0661454 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.0000 | 0.376089 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.93087 | 0.372962 | 0.186481 | − | 0.982459i | \(-0.440292\pi\) | ||||
0.186481 | + | 0.982459i | \(0.440292\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.5616 | 0.507884 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.0000 | 1.19673 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −44.1771 | −1.64753 | −0.823764 | − | 0.566934i | \(-0.808130\pi\) | ||||
−0.823764 | + | 0.566934i | \(0.808130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.43845 | −0.239780 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 14.9309 | 0.554519 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.4384 | 0.387141 | 0.193570 | − | 0.981086i | \(-0.437993\pi\) | ||||
0.193570 | + | 0.981086i | \(0.437993\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.8769 | 1.10504 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.1922 | −0.376459 | −0.188229 | − | 0.982125i | \(-0.560275\pi\) | ||||
−0.188229 | + | 0.982125i | \(0.560275\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 16.9848 | 0.625645 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.00000 | 0.147142 | 0.0735712 | − | 0.997290i | \(-0.476560\pi\) | ||||
0.0735712 | + | 0.997290i | \(0.476560\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.5616 | 1.08451 | 0.542254 | − | 0.840215i | \(-0.317571\pi\) | ||||
0.542254 | + | 0.840215i | \(0.317571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 33.1231 | 1.21354 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16.4924 | −0.602620 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 52.1080 | 1.90145 | 0.950723 | − | 0.310041i | \(-0.100343\pi\) | ||||
0.950723 | + | 0.310041i | \(0.100343\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.43845 | 0.0523505 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.1922 | 0.842936 | 0.421468 | − | 0.906843i | \(-0.361515\pi\) | ||||
0.421468 | + | 0.906843i | \(0.361515\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −29.8769 | −1.08304 | −0.541518 | − | 0.840689i | \(-0.682150\pi\) | ||||
−0.541518 | + | 0.840689i | \(0.682150\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −16.8078 | −0.608482 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −19.8078 | −0.715217 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.8617 | −1.43745 | −0.718726 | − | 0.695294i | \(-0.755274\pi\) | ||||
−0.718726 | + | 0.695294i | \(0.755274\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.43845 | 0.339477 | 0.169739 | − | 0.985489i | \(-0.445708\pi\) | ||||
0.169739 | + | 0.985489i | \(0.445708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.43845 | −0.0875916 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.2311 | 0.832339 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.00000 | 0.286263 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 48.4924 | 1.73077 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.3693 | 1.04690 | 0.523452 | − | 0.852055i | \(-0.324644\pi\) | ||||
0.523452 | + | 0.852055i | \(0.324644\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.12311 | −0.182157 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 20.1080 | 0.714054 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 22.9848 | 0.814165 | 0.407082 | − | 0.913391i | \(-0.366546\pi\) | ||||
0.407082 | + | 0.913391i | \(0.366546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.31534 | −0.0819109 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.4924 | 1.28779 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.2462 | −0.784076 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.3693 | 0.680989 | 0.340494 | − | 0.940247i | \(-0.389406\pi\) | ||||
0.340494 | + | 0.940247i | \(0.389406\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.4924 | 1.21119 | 0.605596 | − | 0.795772i | \(-0.292935\pi\) | ||||
0.605596 | + | 0.795772i | \(0.292935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −36.8078 | −1.28932 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −22.6307 | −0.791747 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.9309 | 1.35870 | 0.679348 | − | 0.733816i | \(-0.262263\pi\) | ||||
0.679348 | + | 0.733816i | \(0.262263\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.56155 | 0.159006 | 0.0795029 | − | 0.996835i | \(-0.474667\pi\) | ||||
0.0795029 | + | 0.996835i | \(0.474667\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 34.4924 | 1.19942 | 0.599710 | − | 0.800218i | \(-0.295283\pi\) | ||||
0.599710 | + | 0.800218i | \(0.295283\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.1231 | 1.49773 | 0.748864 | − | 0.662724i | \(-0.230600\pi\) | ||||
0.748864 | + | 0.662724i | \(0.230600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.12311 | 0.142857 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.807764 | 0.0279538 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 44.9157 | 1.55066 | 0.775331 | − | 0.631555i | \(-0.217583\pi\) | ||||
0.775331 | + | 0.631555i | \(0.217583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 62.4233 | 2.15253 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −18.0691 | −0.621597 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 15.2462 | 0.523866 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.87689 | 0.167178 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 36.0540 | 1.23446 | 0.617232 | − | 0.786781i | \(-0.288254\pi\) | ||||
0.617232 | + | 0.786781i | \(0.288254\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.1231 | 1.43890 | 0.719449 | − | 0.694545i | \(-0.244394\pi\) | ||||
0.719449 | + | 0.694545i | \(0.244394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.5076 | 0.460873 | 0.230436 | − | 0.973087i | \(-0.425985\pi\) | ||||
0.230436 | + | 0.973087i | \(0.425985\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.8078 | 1.01467 | 0.507334 | − | 0.861749i | \(-0.330631\pi\) | ||||
0.507334 | + | 0.861749i | \(0.330631\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.6155 | 1.68698 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 43.8617 | 1.48791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.08429 | 0.273926 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −8.80776 | −0.297757 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −31.6847 | −1.06991 | −0.534957 | − | 0.844879i | \(-0.679672\pi\) | ||||
−0.534957 | + | 0.844879i | \(0.679672\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −33.4233 | −1.12606 | −0.563030 | − | 0.826437i | \(-0.690364\pi\) | ||||
−0.563030 | + | 0.826437i | \(0.690364\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −48.2311 | −1.62310 | −0.811552 | − | 0.584280i | \(-0.801377\pi\) | ||||
−0.811552 | + | 0.584280i | \(0.801377\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.4384 | −0.719833 | −0.359916 | − | 0.932985i | \(-0.617195\pi\) | ||||
−0.359916 | + | 0.932985i | \(0.617195\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.5616 | −0.622535 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.75379 | 0.0586883 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 38.1080 | 1.27381 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14.9309 | −0.497972 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −27.5616 | −0.918208 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −50.1080 | −1.66564 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.5616 | −0.881962 | −0.440981 | − | 0.897516i | \(-0.645369\pi\) | ||||
−0.440981 | + | 0.897516i | \(0.645369\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.630683 | −0.0208955 | −0.0104477 | − | 0.999945i | \(-0.503326\pi\) | ||||
−0.0104477 | + | 0.999945i | \(0.503326\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.1231 | 0.434311 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.31534 | −0.109482 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −30.1771 | −0.995450 | −0.497725 | − | 0.867335i | \(-0.665831\pi\) | ||||
−0.497725 | + | 0.867335i | \(0.665831\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.80776 | 0.125334 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.876894 | −0.0288321 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.56155 | 0.149660 | 0.0748298 | − | 0.997196i | \(-0.476159\pi\) | ||||
0.0748298 | + | 0.997196i | \(0.476159\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.12311 | −0.102356 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −54.1080 | −1.76952 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.75379 | 0.318642 | 0.159321 | − | 0.987227i | \(-0.449069\pi\) | ||||
0.159321 | + | 0.987227i | \(0.449069\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.8078 | −1.00430 | −0.502152 | − | 0.864779i | \(-0.667458\pi\) | ||||
−0.502152 | + | 0.864779i | \(0.667458\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 64.6004 | 2.10368 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −14.6307 | −0.475433 | −0.237717 | − | 0.971335i | \(-0.576399\pi\) | ||||
−0.237717 | + | 0.971335i | \(0.576399\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 17.3693 | 0.563832 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −23.5076 | −0.761485 | −0.380743 | − | 0.924681i | \(-0.624332\pi\) | ||||
−0.380743 | + | 0.924681i | \(0.624332\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −23.3693 | −0.756213 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.12311 | −0.230017 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.5616 | −0.921340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 57.9309 | 1.86486 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.98485 | 0.288933 | 0.144467 | − | 0.989510i | \(-0.453853\pi\) | ||||
0.144467 | + | 0.989510i | \(0.453853\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.1231 | 0.966696 | 0.483348 | − | 0.875428i | \(-0.339421\pi\) | ||||
0.483348 | + | 0.875428i | \(0.339421\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 18.4924 | 0.592840 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.0000 | 0.703842 | 0.351921 | − | 0.936030i | \(-0.385529\pi\) | ||||
0.351921 | + | 0.936030i | \(0.385529\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.73863 | 0.215368 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.8078 | 0.408504 | 0.204252 | − | 0.978918i | \(-0.434524\pi\) | ||||
0.204252 | + | 0.978918i | \(0.434524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.7386 | −1.23432 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62.9309 | −2.00109 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 56.4233 | 1.79234 | 0.896172 | − | 0.443706i | \(-0.146337\pi\) | ||||
0.896172 | + | 0.443706i | \(0.146337\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 17.1231 | 0.542839 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.6695 | −1.44637 | −0.723184 | − | 0.690656i | \(-0.757322\pi\) | ||||
−0.723184 | + | 0.690656i | \(0.757322\pi\) | |||||||
\(998\) | 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 | 6048.2.a.bf.1.2 | yes | 2 | |
3.2 | odd | 2 | 6048.2.a.bd.1.1 | yes | 2 | ||
4.3 | odd | 2 | 6048.2.a.be.1.2 | yes | 2 | ||
12.11 | even | 2 | 6048.2.a.bc.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6048.2.a.bc.1.1 | ✓ | 2 | 12.11 | even | 2 | ||
6048.2.a.bd.1.1 | yes | 2 | 3.2 | odd | 2 | ||
6048.2.a.be.1.2 | yes | 2 | 4.3 | odd | 2 | ||
6048.2.a.bf.1.2 | yes | 2 | 1.1 | even | 1 | trivial |