Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9216,2,Mod(1,9216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9216.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9216 = 2^{10} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9216.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: | \(73.5901305028\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{24})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 256) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(0.517638\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9216.1 |
$q$-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 | ||||||||
\(5\) | 2.44949 | 1.09545 | 0.547723 | − | 0.836660i | \(-0.315495\pi\) | ||||
0.547723 | + | 0.836660i | \(0.315495\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.03528 | 0.391298 | 0.195649 | − | 0.980674i | \(-0.437319\pi\) | ||||
0.195649 | + | 0.980674i | \(0.437319\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.26795 | 0.382301 | 0.191151 | − | 0.981561i | \(-0.438778\pi\) | ||||
0.191151 | + | 0.981561i | \(0.438778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.27792 | 1.46383 | 0.731915 | − | 0.681396i | \(-0.238627\pi\) | ||||
0.731915 | + | 0.681396i | \(0.238627\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.46410 | −0.840168 | −0.420084 | − | 0.907485i | \(-0.637999\pi\) | ||||
−0.420084 | + | 0.907485i | \(0.637999\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.26795 | −0.290887 | −0.145444 | − | 0.989367i | \(-0.546461\pi\) | ||||
−0.145444 | + | 0.989367i | \(0.546461\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.69213 | 1.39541 | 0.697703 | − | 0.716387i | \(-0.254206\pi\) | ||||
0.697703 | + | 0.716387i | \(0.254206\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.44949 | −0.454859 | −0.227429 | − | 0.973795i | \(-0.573032\pi\) | ||||
−0.227429 | + | 0.973795i | \(0.573032\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.65685 | 1.01600 | 0.508001 | − | 0.861357i | \(-0.330385\pi\) | ||||
0.508001 | + | 0.861357i | \(0.330385\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.53590 | 0.428645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.378937 | −0.0622969 | −0.0311485 | − | 0.999515i | \(-0.509916\pi\) | ||||
−0.0311485 | + | 0.999515i | \(0.509916\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.92820 | 1.08200 | 0.541002 | − | 0.841021i | \(-0.318045\pi\) | ||||
0.541002 | + | 0.841021i | \(0.318045\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.19615 | −1.24990 | −0.624951 | − | 0.780664i | \(-0.714881\pi\) | ||||
−0.624951 | + | 0.780664i | \(0.714881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.79796 | 1.42918 | 0.714590 | − | 0.699544i | \(-0.246613\pi\) | ||||
0.714590 | + | 0.699544i | \(0.246613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.92820 | −0.846886 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.03579 | −0.829080 | −0.414540 | − | 0.910031i | \(-0.636057\pi\) | ||||
−0.414540 | + | 0.910031i | \(0.636057\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.10583 | 0.418790 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 10.7321 | 1.39719 | 0.698597 | − | 0.715515i | \(-0.253808\pi\) | ||||
0.698597 | + | 0.715515i | \(0.253808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.378937 | 0.0485180 | 0.0242590 | − | 0.999706i | \(-0.492277\pi\) | ||||
0.0242590 | + | 0.999706i | \(0.492277\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 12.9282 | 1.60355 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.19615 | 0.512642 | 0.256321 | − | 0.966592i | \(-0.417490\pi\) | ||||
0.256321 | + | 0.966592i | \(0.417490\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.69213 | −0.794210 | −0.397105 | − | 0.917773i | \(-0.629985\pi\) | ||||
−0.397105 | + | 0.917773i | \(0.629985\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.46410 | −1.10769 | −0.553845 | − | 0.832620i | \(-0.686840\pi\) | ||||
−0.553845 | + | 0.832620i | \(0.686840\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.31268 | 0.149593 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.4548 | 1.73880 | 0.869401 | − | 0.494107i | \(-0.164505\pi\) | ||||
0.869401 | + | 0.494107i | \(0.164505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.19615 | 0.899645 | 0.449822 | − | 0.893118i | \(-0.351487\pi\) | ||||
0.449822 | + | 0.893118i | \(0.351487\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.48528 | −0.920358 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.46410 | 1.00319 | 0.501596 | − | 0.865102i | \(-0.332746\pi\) | ||||
0.501596 | + | 0.865102i | \(0.332746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.46410 | 0.572793 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.10583 | −0.318651 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.46410 | −0.351726 | −0.175863 | − | 0.984415i | \(-0.556272\pi\) | ||||
−0.175863 | + | 0.984415i | \(0.556272\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.8338 | 1.57552 | 0.787759 | − | 0.615984i | \(-0.211241\pi\) | ||||
0.787759 | + | 0.615984i | \(0.211241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.62158 | −0.455378 | −0.227689 | − | 0.973734i | \(-0.573117\pi\) | ||||
−0.227689 | + | 0.973734i | \(0.573117\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.5885 | −1.21697 | −0.608486 | − | 0.793565i | \(-0.708223\pi\) | ||||
−0.608486 | + | 0.793565i | \(0.708223\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.96524 | −0.379801 | −0.189901 | − | 0.981803i | \(-0.560817\pi\) | ||||
−0.189901 | + | 0.981803i | \(0.560817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.928203 | −0.0873180 | −0.0436590 | − | 0.999046i | \(-0.513902\pi\) | ||||
−0.0436590 | + | 0.999046i | \(0.513902\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 16.3923 | 1.52859 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.58630 | −0.328756 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.39230 | −0.853846 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −9.79796 | −0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.65685 | −0.501965 | −0.250982 | − | 0.967992i | \(-0.580754\pi\) | ||||
−0.250982 | + | 0.967992i | \(0.580754\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.6603 | 1.54298 | 0.771492 | − | 0.636239i | \(-0.219511\pi\) | ||||
0.771492 | + | 0.636239i | \(0.219511\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.31268 | −0.113824 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.196152 | −0.0166374 | −0.00831872 | − | 0.999965i | \(-0.502648\pi\) | ||||
−0.00831872 | + | 0.999965i | \(0.502648\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.69213 | 0.559624 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | −0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5211 | 1.18961 | 0.594806 | − | 0.803869i | \(-0.297229\pi\) | ||||
0.594806 | + | 0.803869i | \(0.297229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.62158 | 0.376099 | 0.188049 | − | 0.982160i | \(-0.439784\pi\) | ||||
0.188049 | + | 0.982160i | \(0.439784\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.8564 | 1.11297 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.52004 | 0.360739 | 0.180369 | − | 0.983599i | \(-0.442271\pi\) | ||||
0.180369 | + | 0.983599i | \(0.442271\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.92820 | 0.546019 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2679 | 1.03923 | 0.519613 | − | 0.854402i | \(-0.326076\pi\) | ||||
0.519613 | + | 0.854402i | \(0.326076\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −23.6627 | −1.83107 | −0.915537 | − | 0.402234i | \(-0.868234\pi\) | ||||
−0.915537 | + | 0.402234i | \(0.868234\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.8564 | 1.14280 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.03579 | 0.458893 | 0.229446 | − | 0.973321i | \(-0.426308\pi\) | ||||
0.229446 | + | 0.973321i | \(0.426308\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.03528 | 0.0782595 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.19615 | 0.612609 | 0.306305 | − | 0.951934i | \(-0.400907\pi\) | ||||
0.306305 | + | 0.951934i | \(0.400907\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.4896 | −0.854013 | −0.427007 | − | 0.904248i | \(-0.640432\pi\) | ||||
−0.427007 | + | 0.904248i | \(0.640432\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.928203 | −0.0682429 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.39230 | −0.321197 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.9706 | 1.22795 | 0.613973 | − | 0.789327i | \(-0.289570\pi\) | ||||
0.613973 | + | 0.789327i | \(0.289570\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.39230 | 0.172202 | 0.0861009 | − | 0.996286i | \(-0.472559\pi\) | ||||
0.0861009 | + | 0.996286i | \(0.472559\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.44949 | 0.174519 | 0.0872595 | − | 0.996186i | \(-0.472189\pi\) | ||||
0.0872595 | + | 0.996186i | \(0.472189\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.5606 | −1.31573 | −0.657865 | − | 0.753136i | \(-0.728540\pi\) | ||||
−0.657865 | + | 0.753136i | \(0.728540\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.53590 | −0.177985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.9706 | 1.18528 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.60770 | −0.111207 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.196152 | −0.0135037 | −0.00675184 | − | 0.999977i | \(-0.502149\pi\) | ||||
−0.00675184 | + | 0.999977i | \(0.502149\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.0764 | −1.36920 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.85641 | 0.397559 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.2832 | −1.22986 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.65685 | 0.378811 | 0.189405 | − | 0.981899i | \(-0.439344\pi\) | ||||
0.189405 | + | 0.981899i | \(0.439344\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.12436 | −0.207371 | −0.103685 | − | 0.994610i | \(-0.533064\pi\) | ||||
−0.103685 | + | 0.994610i | \(0.533064\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.69161 | 0.111785 | 0.0558925 | − | 0.998437i | \(-0.482200\pi\) | ||||
0.0558925 | + | 0.998437i | \(0.482200\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.46410 | 0.620014 | 0.310007 | − | 0.950734i | \(-0.399669\pi\) | ||||
0.310007 | + | 0.950734i | \(0.399669\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.0000 | 1.56559 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.17260 | 0.463957 | 0.231979 | − | 0.972721i | \(-0.425480\pi\) | ||||
0.231979 | + | 0.972721i | \(0.425480\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.3923 | −1.18475 | −0.592376 | − | 0.805661i | \(-0.701810\pi\) | ||||
−0.592376 | + | 0.805661i | \(0.701810\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.5211 | −0.927717 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.69213 | −0.425810 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.12436 | −0.197208 | −0.0986038 | − | 0.995127i | \(-0.531438\pi\) | ||||
−0.0986038 | + | 0.995127i | \(0.531438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.48528 | 0.533465 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.928203 | 0.0578997 | 0.0289499 | − | 0.999581i | \(-0.490784\pi\) | ||||
0.0289499 | + | 0.999581i | \(0.490784\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.392305 | −0.0243766 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.9038 | 0.795682 | 0.397841 | − | 0.917454i | \(-0.369760\pi\) | ||||
0.397841 | + | 0.917454i | \(0.369760\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −14.7846 | −0.908211 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.34847 | −0.448044 | −0.224022 | − | 0.974584i | \(-0.571919\pi\) | ||||
−0.224022 | + | 0.974584i | \(0.571919\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −21.1117 | −1.28244 | −0.641221 | − | 0.767356i | \(-0.721572\pi\) | ||||
−0.641221 | + | 0.767356i | \(0.721572\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.26795 | 0.0764602 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1769 | 0.611470 | 0.305735 | − | 0.952117i | \(-0.401098\pi\) | ||||
0.305735 | + | 0.952117i | \(0.401098\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.39230 | 0.262023 | 0.131011 | − | 0.991381i | \(-0.458178\pi\) | ||||
0.131011 | + | 0.991381i | \(0.458178\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.1962 | 0.724986 | 0.362493 | − | 0.931986i | \(-0.381926\pi\) | ||||
0.362493 | + | 0.931986i | \(0.381926\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.17260 | 0.423385 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.00000 | −0.294118 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.1464 | −1.00171 | −0.500853 | − | 0.865533i | \(-0.666980\pi\) | ||||
−0.500853 | + | 0.865533i | \(0.666980\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 26.2880 | 1.53055 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 35.3205 | 2.04264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.48528 | −0.489083 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.928203 | 0.0531488 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9808 | −1.19744 | −0.598718 | − | 0.800960i | \(-0.704323\pi\) | ||||
−0.598718 | + | 0.800960i | \(0.704323\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.2784 | −0.582836 | −0.291418 | − | 0.956596i | \(-0.594127\pi\) | ||||
−0.291418 | + | 0.956596i | \(0.594127\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.7846 | −1.62700 | −0.813501 | − | 0.581563i | \(-0.802441\pi\) | ||||
−0.813501 | + | 0.581563i | \(0.802441\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.3190 | 1.36589 | 0.682946 | − | 0.730468i | \(-0.260698\pi\) | ||||
0.682946 | + | 0.730468i | \(0.260698\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.10583 | −0.173893 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.39230 | 0.244394 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.27792 | 0.292766 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 10.1436 | 0.559234 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.58846 | 0.252204 | 0.126102 | − | 0.992017i | \(-0.459753\pi\) | ||||
0.126102 | + | 0.992017i | \(0.459753\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.2784 | 0.561571 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.7128 | 1.83645 | 0.918227 | − | 0.396055i | \(-0.129621\pi\) | ||||
0.918227 | + | 0.396055i | \(0.129621\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.17260 | 0.388418 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.3843 | −0.722682 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.7321 | 0.576127 | 0.288063 | − | 0.957611i | \(-0.406989\pi\) | ||||
0.288063 | + | 0.957611i | \(0.406989\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −28.4601 | −1.52344 | −0.761718 | − | 0.647909i | \(-0.775644\pi\) | ||||
−0.761718 | + | 0.647909i | \(0.775644\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.9282 | −0.688099 | −0.344049 | − | 0.938952i | \(-0.611799\pi\) | ||||
−0.344049 | + | 0.938952i | \(0.611799\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −16.3923 | −0.870013 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.2880 | −1.38743 | −0.693715 | − | 0.720250i | \(-0.744027\pi\) | ||||
−0.693715 | + | 0.720250i | \(0.744027\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3923 | −0.915384 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −23.1822 | −1.21341 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8295 | 0.669692 | 0.334846 | − | 0.942273i | \(-0.391316\pi\) | ||||
0.334846 | + | 0.942273i | \(0.391316\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.24871 | −0.324417 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.3180 | 0.741358 | 0.370679 | − | 0.928761i | \(-0.379125\pi\) | ||||
0.370679 | + | 0.928761i | \(0.379125\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −12.9282 | −0.665836 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 27.1244 | 1.39328 | 0.696642 | − | 0.717419i | \(-0.254676\pi\) | ||||
0.696642 | + | 0.717419i | \(0.254676\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 19.5959 | 1.00130 | 0.500652 | − | 0.865648i | \(-0.333094\pi\) | ||||
0.500652 | + | 0.865648i | \(0.333094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.21539 | 0.163871 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.9348 | −0.554415 | −0.277207 | − | 0.960810i | \(-0.589409\pi\) | ||||
−0.277207 | + | 0.960810i | \(0.589409\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.1822 | −1.17238 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 37.8564 | 1.90476 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.3886 | −0.822518 | −0.411259 | − | 0.911519i | \(-0.634911\pi\) | ||||
−0.411259 | + | 0.911519i | \(0.634911\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 34.3923 | 1.71747 | 0.858735 | − | 0.512420i | \(-0.171251\pi\) | ||||
0.858735 | + | 0.512420i | \(0.171251\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.8564 | 1.48725 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.480473 | −0.0238162 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 30.9282 | 1.52930 | 0.764651 | − | 0.644445i | \(-0.222912\pi\) | ||||
0.764651 | + | 0.644445i | \(0.222912\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 11.1106 | 0.546719 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0764 | 0.985511 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.80385 | 0.185830 | 0.0929151 | − | 0.995674i | \(-0.470381\pi\) | ||||
0.0929151 | + | 0.995674i | \(0.470381\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.5002 | −1.82765 | −0.913824 | − | 0.406109i | \(-0.866885\pi\) | ||||
−0.913824 | + | 0.406109i | \(0.866885\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.46410 | −0.168034 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.392305 | 0.0189850 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.17260 | 0.345492 | 0.172746 | − | 0.984966i | \(-0.444736\pi\) | ||||
0.172746 | + | 0.984966i | \(0.444736\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.6077 | 0.653944 | 0.326972 | − | 0.945034i | \(-0.393972\pi\) | ||||
0.326972 | + | 0.945034i | \(0.393972\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.48528 | −0.405906 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.9449 | −1.52465 | −0.762324 | − | 0.647196i | \(-0.775941\pi\) | ||||
−0.762324 | + | 0.647196i | \(0.775941\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.80385 | 0.180726 | 0.0903631 | − | 0.995909i | \(-0.471197\pi\) | ||||
0.0903631 | + | 0.995909i | \(0.471197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 23.1822 | 1.09894 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.2487 | −1.14437 | −0.572184 | − | 0.820125i | \(-0.693904\pi\) | ||||
−0.572184 | + | 0.820125i | \(0.693904\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.78461 | 0.413651 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.3843 | 0.627464 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.7846 | 0.972263 | 0.486132 | − | 0.873886i | \(-0.338408\pi\) | ||||
0.486132 | + | 0.873886i | \(0.338408\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.175865 | −0.00819087 | −0.00409544 | − | 0.999992i | \(-0.501304\pi\) | ||||
−0.00409544 | + | 0.999992i | \(0.501304\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.4863 | 0.859132 | 0.429566 | − | 0.903036i | \(-0.358667\pi\) | ||||
0.429566 | + | 0.903036i | \(0.358667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.2679 | 1.16926 | 0.584631 | − | 0.811300i | \(-0.301239\pi\) | ||||
0.584631 | + | 0.811300i | \(0.301239\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.34418 | 0.200595 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −10.3923 | −0.477839 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.26795 | −0.0581775 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.62536 | 0.119956 | 0.0599778 | − | 0.998200i | \(-0.480897\pi\) | ||||
0.0599778 | + | 0.998200i | \(0.480897\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.00000 | −0.0911922 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.48528 | −0.385297 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.24693 | −0.328390 | −0.164195 | − | 0.986428i | \(-0.552503\pi\) | ||||
−0.164195 | + | 0.986428i | \(0.552503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1962 | 1.45299 | 0.726496 | − | 0.687171i | \(-0.241148\pi\) | ||||
0.726496 | + | 0.687171i | \(0.241148\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.48528 | 0.382158 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.92820 | −0.310772 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.1962 | −0.725039 | −0.362520 | − | 0.931976i | \(-0.618083\pi\) | ||||
−0.362520 | + | 0.931976i | \(0.618083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −32.4997 | −1.44909 | −0.724545 | − | 0.689227i | \(-0.757950\pi\) | ||||
−0.724545 | + | 0.689227i | \(0.757950\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 38.7846 | 1.72589 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 30.5307 | 1.35325 | 0.676625 | − | 0.736328i | \(-0.263442\pi\) | ||||
0.676625 | + | 0.736328i | \(0.263442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.79796 | −0.433436 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.3205 | −0.498841 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.4233 | 0.546377 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12.0000 | −0.525730 | −0.262865 | − | 0.964833i | \(-0.584667\pi\) | ||||
−0.262865 | + | 0.964833i | \(0.584667\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.7321 | 0.994003 | 0.497002 | − | 0.867750i | \(-0.334434\pi\) | ||||
0.497002 | + | 0.867750i | \(0.334434\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.5959 | −0.853612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.7846 | 0.947157 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 36.5665 | 1.58387 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.8353 | −1.33313 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.51666 | −0.323765 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 19.9749 | 0.858786 | 0.429393 | − | 0.903118i | \(-0.358728\pi\) | ||||
0.429393 | + | 0.903118i | \(0.358728\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.71281 | −0.416051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.6603 | −0.755098 | −0.377549 | − | 0.925990i | \(-0.623233\pi\) | ||||
−0.377549 | + | 0.925990i | \(0.623233\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.10583 | 0.132313 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.0000 | 0.680389 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.13681 | −0.0481683 | −0.0240841 | − | 0.999710i | \(-0.507667\pi\) | ||||
−0.0240841 | + | 0.999710i | \(0.507667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −43.2586 | −1.82964 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 39.1244 | 1.64889 | 0.824447 | − | 0.565938i | \(-0.191486\pi\) | ||||
0.824447 | + | 0.565938i | \(0.191486\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.27362 | −0.0956521 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.0000 | −0.503066 | −0.251533 | − | 0.967849i | \(-0.580935\pi\) | ||||
−0.251533 | + | 0.967849i | \(0.580935\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19.8038 | −0.828765 | −0.414383 | − | 0.910103i | \(-0.636002\pi\) | ||||
−0.414383 | + | 0.910103i | \(0.636002\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.69213 | 0.279081 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.1436 | −0.672067 | −0.336033 | − | 0.941850i | \(-0.609085\pi\) | ||||
−0.336033 | + | 0.941850i | \(0.609085\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.48528 | 0.352029 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.65308 | −0.316958 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.1244 | 0.624249 | 0.312124 | − | 0.950041i | \(-0.398959\pi\) | ||||
0.312124 | + | 0.950041i | \(0.398959\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.17260 | −0.295542 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.85641 | 0.322624 | 0.161312 | − | 0.986903i | \(-0.448427\pi\) | ||||
0.161312 | + | 0.986903i | \(0.448427\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.78461 | −0.360134 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.8744 | −1.22063 | −0.610316 | − | 0.792158i | \(-0.708958\pi\) | ||||
−0.610316 | + | 0.792158i | \(0.708958\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −19.6077 | −0.799815 | −0.399907 | − | 0.916556i | \(-0.630958\pi\) | ||||
−0.399907 | + | 0.916556i | \(0.630958\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −23.0064 | −0.935341 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.9096 | 1.25458 | 0.627292 | − | 0.778785i | \(-0.284163\pi\) | ||||
0.627292 | + | 0.778785i | \(0.284163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 51.7128 | 2.09208 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.6012 | 1.31675 | 0.658376 | − | 0.752689i | \(-0.271244\pi\) | ||||
0.658376 | + | 0.752689i | \(0.271244\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.3205 | −0.938848 | −0.469424 | − | 0.882973i | \(-0.655538\pi\) | ||||
−0.469424 | + | 0.882973i | \(0.655538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.58846 | 0.184426 | 0.0922128 | − | 0.995739i | \(-0.470606\pi\) | ||||
0.0922128 | + | 0.995739i | \(0.470606\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.79796 | 0.392547 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.31268 | 0.0523399 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.5312 | 1.41447 | 0.707237 | − | 0.706976i | \(-0.249941\pi\) | ||||
0.707237 | + | 0.706976i | \(0.249941\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.8564 | −0.549875 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −31.2886 | −1.23970 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.3923 | −1.35841 | −0.679207 | − | 0.733947i | \(-0.737676\pi\) | ||||
−0.679207 | + | 0.733947i | \(0.737676\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.1962 | 0.796459 | 0.398229 | − | 0.917286i | \(-0.369625\pi\) | ||||
0.398229 | + | 0.917286i | \(0.369625\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.69213 | −0.263095 | −0.131547 | − | 0.991310i | \(-0.541995\pi\) | ||||
−0.131547 | + | 0.991310i | \(0.541995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.6077 | 0.534149 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 46.1886 | 1.80750 | 0.903749 | − | 0.428062i | \(-0.140804\pi\) | ||||
0.903749 | + | 0.428062i | \(0.140804\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 43.2586 | 1.69025 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.5167 | −0.760261 | −0.380131 | − | 0.924933i | \(-0.624121\pi\) | ||||
−0.380131 | + | 0.924933i | \(0.624121\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.7338 | 1.19540 | 0.597702 | − | 0.801718i | \(-0.296080\pi\) | ||||
0.597702 | + | 0.801718i | \(0.296080\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.21539 | −0.124687 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −16.3923 | −0.634713 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.480473 | 0.0185485 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.67949 | 0.257475 | 0.128738 | − | 0.991679i | \(-0.458907\pi\) | ||||
0.128738 | + | 0.991679i | \(0.458907\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −44.8759 | −1.72472 | −0.862360 | − | 0.506295i | \(-0.831015\pi\) | ||||
−0.862360 | + | 0.506295i | \(0.831015\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.58630 | −0.137630 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −29.6603 | −1.13492 | −0.567459 | − | 0.823402i | \(-0.692073\pi\) | ||||
−0.567459 | + | 0.823402i | \(0.692073\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −29.3939 | −1.12308 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −31.8564 | −1.21363 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.3731 | 1.26957 | 0.634786 | − | 0.772688i | \(-0.281088\pi\) | ||||
0.634786 | + | 0.772688i | \(0.281088\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.480473 | −0.0182254 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0000 | −0.909065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 37.7033 | 1.42403 | 0.712017 | − | 0.702162i | \(-0.247782\pi\) | ||||
0.712017 | + | 0.702162i | \(0.247782\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.480473 | 0.0181214 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16.3923 | 0.616496 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −12.8023 | −0.480799 | −0.240399 | − | 0.970674i | \(-0.577278\pi\) | ||||
−0.240399 | + | 0.970674i | \(0.577278\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 37.8564 | 1.41773 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.3923 | 0.613037 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.3644 | −1.72910 | −0.864551 | − | 0.502545i | \(-0.832397\pi\) | ||||
−0.864551 | + | 0.502545i | \(0.832397\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.78461 | −0.178188 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.44949 | −0.0909718 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20.6312 | −0.765169 | −0.382584 | − | 0.923921i | \(-0.624966\pi\) | ||||
−0.382584 | + | 0.923921i | \(0.624966\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.3923 | 1.05013 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −35.6327 | −1.31613 | −0.658063 | − | 0.752963i | \(-0.728624\pi\) | ||||
−0.658063 | + | 0.752963i | \(0.728624\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.32051 | 0.195983 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.9808 | 1.80179 | 0.900893 | − | 0.434041i | \(-0.142913\pi\) | ||||
0.900893 | + | 0.434041i | \(0.142913\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 10.2784 | 0.377079 | 0.188540 | − | 0.982066i | \(-0.439625\pi\) | ||||
0.188540 | + | 0.982066i | \(0.439625\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.5692 | 1.30316 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13.0325 | −0.476198 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.4548 | −0.563954 | −0.281977 | − | 0.959421i | \(-0.590990\pi\) | ||||
−0.281977 | + | 0.959421i | \(0.590990\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.3205 | 0.411995 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −25.8348 | −0.938981 | −0.469491 | − | 0.882937i | \(-0.655562\pi\) | ||||
−0.469491 | + | 0.882937i | \(0.655562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.6410 | 1.25574 | 0.627868 | − | 0.778320i | \(-0.283928\pi\) | ||||
0.627868 | + | 0.778320i | \(0.283928\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.10512 | −0.148615 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 56.6429 | 2.04526 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.3923 | 0.663243 | 0.331622 | − | 0.943412i | \(-0.392404\pi\) | ||||
0.331622 | + | 0.943412i | \(0.392404\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.76217 | −0.135316 | −0.0676579 | − | 0.997709i | \(-0.521553\pi\) | ||||
−0.0676579 | + | 0.997709i | \(0.521553\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.65685 | 0.203200 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.78461 | −0.314741 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.48528 | −0.303627 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 11.0718 | 0.395169 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.3397 | −0.653741 | −0.326871 | − | 0.945069i | \(-0.605994\pi\) | ||||
−0.326871 | + | 0.945069i | \(0.605994\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.960947 | −0.0341673 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.00000 | 0.0710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.41044 | −0.120804 | −0.0604019 | − | 0.998174i | \(-0.519238\pi\) | ||||
−0.0604019 | + | 0.998174i | \(0.519238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −33.9411 | −1.20075 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.0000 | −0.423471 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 16.9706 | 0.598134 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −30.9282 | −1.08738 | −0.543689 | − | 0.839287i | \(-0.682973\pi\) | ||||
−0.543689 | + | 0.839287i | \(0.682973\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.98076 | −0.174898 | −0.0874491 | − | 0.996169i | \(-0.527872\pi\) | ||||
−0.0874491 | + | 0.996169i | \(0.527872\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.4997 | 1.13842 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.3923 | 0.363581 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.2276 | −1.57846 | −0.789228 | − | 0.614101i | \(-0.789519\pi\) | ||||
−0.789228 | + | 0.614101i | \(0.789519\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.5606 | 0.646983 | 0.323492 | − | 0.946231i | \(-0.395143\pi\) | ||||
0.323492 | + | 0.946231i | \(0.395143\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.33975 | −0.220455 | −0.110227 | − | 0.993906i | \(-0.535158\pi\) | ||||
−0.110227 | + | 0.993906i | \(0.535158\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2886 | 1.08670 | 0.543348 | − | 0.839507i | \(-0.317156\pi\) | ||||
0.543348 | + | 0.839507i | \(0.317156\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.5359 | 0.711527 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −57.9615 | −2.00584 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.06678 | −0.140401 | −0.0702003 | − | 0.997533i | \(-0.522364\pi\) | ||||
−0.0702003 | + | 0.997533i | \(0.522364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.0000 | −0.793103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 36.3906 | 1.25188 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.72363 | −0.334108 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.53590 | −0.0869295 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.2591 | 1.65236 | 0.826181 | − | 0.563406i | \(-0.190509\pi\) | ||||
0.826181 | + | 0.563406i | \(0.190509\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.85641 | −0.0634136 | −0.0317068 | − | 0.999497i | \(-0.510094\pi\) | ||||
−0.0317068 | + | 0.999497i | \(0.510094\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −38.4449 | −1.31172 | −0.655861 | − | 0.754882i | \(-0.727694\pi\) | ||||
−0.655861 | + | 0.754882i | \(0.727694\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.5665 | −1.24474 | −0.622369 | − | 0.782724i | \(-0.713830\pi\) | ||||
−0.622369 | + | 0.782724i | \(0.713830\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.7846 | 0.502692 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 19.5959 | 0.664746 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.1469 | 0.750421 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.1436 | −0.342916 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.4896 | 0.387975 | 0.193988 | − | 0.981004i | \(-0.437858\pi\) | ||||
0.193988 | + | 0.981004i | \(0.437858\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.14359 | 0.139601 | 0.0698006 | − | 0.997561i | \(-0.477764\pi\) | ||||
0.0698006 | + | 0.997561i | \(0.477764\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.8756 | 1.10635 | 0.553177 | − | 0.833064i | \(-0.313415\pi\) | ||||
0.553177 | + | 0.833064i | \(0.313415\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −10.2784 | −0.345116 | −0.172558 | − | 0.984999i | \(-0.555203\pi\) | ||||
−0.172558 | + | 0.984999i | \(0.555203\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.85641 | −0.196418 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.4233 | −0.415730 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.0764 | 0.671080 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.8564 | −0.462137 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 20.9086 | 0.696566 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −28.1436 | −0.935525 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −35.9090 | −1.19234 | −0.596169 | − | 0.802859i | \(-0.703311\pi\) | ||||
−0.596169 | + | 0.802859i | \(0.703311\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.7391 | 1.44914 | 0.724570 | − | 0.689201i | \(-0.242038\pi\) | ||||
0.724570 | + | 0.689201i | \(0.242038\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.3923 | 0.343935 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 18.2832 | 0.603766 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 55.1271 | 1.81848 | 0.909238 | − | 0.416277i | \(-0.136665\pi\) | ||||
0.909238 | + | 0.416277i | \(0.136665\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.3205 | −1.16259 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.378937 | −0.0124594 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.46410 | 0.113653 | 0.0568267 | − | 0.998384i | \(-0.481902\pi\) | ||||
0.0568267 | + | 0.998384i | \(0.481902\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.51666 | 0.246349 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −10.7589 | −0.351854 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.1769 | −1.73721 | −0.868607 | − | 0.495502i | \(-0.834984\pi\) | ||||
−0.868607 | + | 0.495502i | \(0.834984\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.2896 | −1.34600 | −0.673001 | − | 0.739641i | \(-0.734995\pi\) | ||||
−0.673001 | + | 0.739641i | \(0.734995\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 46.3644 | 1.50983 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.7321 | −0.738692 | −0.369346 | − | 0.929292i | \(-0.620418\pi\) | ||||
−0.369346 | + | 0.929292i | \(0.620418\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −49.9507 | −1.62147 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.5692 | −0.957841 | −0.478920 | − | 0.877858i | \(-0.658972\pi\) | ||||
−0.478920 | + | 0.877858i | \(0.658972\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 41.5692 | 1.34515 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −12.4233 | −0.401170 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.85993 | 0.188638 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −7.24693 | −0.233046 | −0.116523 | − | 0.993188i | \(-0.537175\pi\) | ||||
−0.116523 | + | 0.993188i | \(0.537175\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.3731 | −1.07099 | −0.535496 | − | 0.844538i | \(-0.679875\pi\) | ||||
−0.535496 | + | 0.844538i | \(0.679875\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −0.203072 | −0.00651019 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −51.4641 | −1.64648 | −0.823241 | − | 0.567692i | \(-0.807837\pi\) | ||||
−0.823241 | + | 0.567692i | \(0.807837\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.0000 | 0.383522 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 57.6038 | 1.83728 | 0.918638 | − | 0.395100i | \(-0.129290\pi\) | ||||
0.918638 | + | 0.395100i | \(0.129290\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.00000 | 0.191176 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −54.8497 | −1.74412 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.5644 | 0.526186 | 0.263093 | − | 0.964770i | \(-0.415257\pi\) | ||||
0.263093 | + | 0.964770i | \(0.415257\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −45.4641 | −1.44131 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.79367 | 0.215158 | 0.107579 | − | 0.994197i | \(-0.465690\pi\) | ||||
0.107579 | + | 0.994197i | \(0.465690\pi\) | |||||||
\(998\) | 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 | 9216.2.a.bk.1.3 | 4 | ||
3.2 | odd | 2 | 1024.2.a.g.1.1 | 4 | |||
4.3 | odd | 2 | 9216.2.a.bb.1.4 | 4 | |||
8.3 | odd | 2 | inner | 9216.2.a.bk.1.2 | 4 | ||
8.5 | even | 2 | 9216.2.a.bb.1.1 | 4 | |||
12.11 | even | 2 | 1024.2.a.j.1.3 | 4 | |||
24.5 | odd | 2 | 1024.2.a.j.1.4 | 4 | |||
24.11 | even | 2 | 1024.2.a.g.1.2 | 4 | |||
32.3 | odd | 8 | 2304.2.k.f.577.2 | 8 | |||
32.5 | even | 8 | 2304.2.k.k.1729.4 | 8 | |||
32.11 | odd | 8 | 2304.2.k.f.1729.1 | 8 | |||
32.13 | even | 8 | 2304.2.k.k.577.3 | 8 | |||
32.19 | odd | 8 | 2304.2.k.k.577.4 | 8 | |||
32.21 | even | 8 | 2304.2.k.f.1729.2 | 8 | |||
32.27 | odd | 8 | 2304.2.k.k.1729.3 | 8 | |||
32.29 | even | 8 | 2304.2.k.f.577.1 | 8 | |||
48.5 | odd | 4 | 1024.2.b.h.513.7 | 8 | |||
48.11 | even | 4 | 1024.2.b.h.513.1 | 8 | |||
48.29 | odd | 4 | 1024.2.b.h.513.2 | 8 | |||
48.35 | even | 4 | 1024.2.b.h.513.8 | 8 | |||
96.5 | odd | 8 | 256.2.e.b.193.4 | yes | 8 | ||
96.11 | even | 8 | 256.2.e.a.193.4 | yes | 8 | ||
96.29 | odd | 8 | 256.2.e.a.65.1 | ✓ | 8 | ||
96.35 | even | 8 | 256.2.e.a.65.4 | yes | 8 | ||
96.53 | odd | 8 | 256.2.e.a.193.1 | yes | 8 | ||
96.59 | even | 8 | 256.2.e.b.193.1 | yes | 8 | ||
96.77 | odd | 8 | 256.2.e.b.65.4 | yes | 8 | ||
96.83 | even | 8 | 256.2.e.b.65.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
256.2.e.a.65.1 | ✓ | 8 | 96.29 | odd | 8 | ||
256.2.e.a.65.4 | yes | 8 | 96.35 | even | 8 | ||
256.2.e.a.193.1 | yes | 8 | 96.53 | odd | 8 | ||
256.2.e.a.193.4 | yes | 8 | 96.11 | even | 8 | ||
256.2.e.b.65.1 | yes | 8 | 96.83 | even | 8 | ||
256.2.e.b.65.4 | yes | 8 | 96.77 | odd | 8 | ||
256.2.e.b.193.1 | yes | 8 | 96.59 | even | 8 | ||
256.2.e.b.193.4 | yes | 8 | 96.5 | odd | 8 | ||
1024.2.a.g.1.1 | 4 | 3.2 | odd | 2 | |||
1024.2.a.g.1.2 | 4 | 24.11 | even | 2 | |||
1024.2.a.j.1.3 | 4 | 12.11 | even | 2 | |||
1024.2.a.j.1.4 | 4 | 24.5 | odd | 2 | |||
1024.2.b.h.513.1 | 8 | 48.11 | even | 4 | |||
1024.2.b.h.513.2 | 8 | 48.29 | odd | 4 | |||
1024.2.b.h.513.7 | 8 | 48.5 | odd | 4 | |||
1024.2.b.h.513.8 | 8 | 48.35 | even | 4 | |||
2304.2.k.f.577.1 | 8 | 32.29 | even | 8 | |||
2304.2.k.f.577.2 | 8 | 32.3 | odd | 8 | |||
2304.2.k.f.1729.1 | 8 | 32.11 | odd | 8 | |||
2304.2.k.f.1729.2 | 8 | 32.21 | even | 8 | |||
2304.2.k.k.577.3 | 8 | 32.13 | even | 8 | |||
2304.2.k.k.577.4 | 8 | 32.19 | odd | 8 | |||
2304.2.k.k.1729.3 | 8 | 32.27 | odd | 8 | |||
2304.2.k.k.1729.4 | 8 | 32.5 | even | 8 | |||
9216.2.a.bb.1.1 | 4 | 8.5 | even | 2 | |||
9216.2.a.bb.1.4 | 4 | 4.3 | odd | 2 | |||
9216.2.a.bk.1.2 | 4 | 8.3 | odd | 2 | inner | ||
9216.2.a.bk.1.3 | 4 | 1.1 | even | 1 | trivial |