Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6004,2,Mod(1,6004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6004, 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("6004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6004 = 2^{2} \cdot 19 \cdot 79 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6004.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: | \(47.9421813736\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 6004.1 |
$q$-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 | ||||||||
\(3\) | −0.338800 | −0.195606 | −0.0978032 | − | 0.995206i | \(-0.531182\pi\) | ||||
−0.0978032 | + | 0.995206i | \(0.531182\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.08469 | −1.37952 | −0.689758 | − | 0.724040i | \(-0.742283\pi\) | ||||
−0.689758 | + | 0.724040i | \(0.742283\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.48412 | −1.69484 | −0.847419 | − | 0.530925i | \(-0.821845\pi\) | ||||
−0.847419 | + | 0.530925i | \(0.821845\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.88521 | −0.961738 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.90726 | 1.78111 | 0.890553 | − | 0.454879i | \(-0.150318\pi\) | ||||
0.890553 | + | 0.454879i | \(0.150318\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.46463 | 0.406216 | 0.203108 | − | 0.979156i | \(-0.434896\pi\) | ||||
0.203108 | + | 0.979156i | \(0.434896\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.04509 | 0.269842 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.53371 | −0.614514 | −0.307257 | − | 0.951626i | \(-0.599411\pi\) | ||||
−0.307257 | + | 0.951626i | \(0.599411\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.51922 | 0.331521 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.61368 | 0.544989 | 0.272495 | − | 0.962157i | \(-0.412151\pi\) | ||||
0.272495 | + | 0.962157i | \(0.412151\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.51532 | 0.903065 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.99391 | 0.383729 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.21728 | 0.411739 | 0.205869 | − | 0.978579i | \(-0.433998\pi\) | ||||
0.205869 | + | 0.978579i | \(0.433998\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.75033 | −1.57161 | −0.785803 | − | 0.618477i | \(-0.787750\pi\) | ||||
−0.785803 | + | 0.618477i | \(0.787750\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.00138 | −0.348396 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 13.8321 | 2.33806 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.37694 | −0.226368 | −0.113184 | − | 0.993574i | \(-0.536105\pi\) | ||||
−0.113184 | + | 0.993574i | \(0.536105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.496218 | −0.0794585 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.51019 | 1.48524 | 0.742621 | − | 0.669712i | \(-0.233582\pi\) | ||||
0.742621 | + | 0.669712i | \(0.233582\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4231 | 1.58950 | 0.794752 | − | 0.606934i | \(-0.207601\pi\) | ||||
0.794752 | + | 0.606934i | \(0.207601\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.90000 | 1.32673 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.08096 | 0.595269 | 0.297635 | − | 0.954680i | \(-0.403802\pi\) | ||||
0.297635 | + | 0.954680i | \(0.403802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 13.1073 | 1.87248 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.858421 | 0.120203 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.486802 | −0.0668675 | −0.0334337 | − | 0.999441i | \(-0.510644\pi\) | ||||
−0.0334337 | + | 0.999441i | \(0.510644\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18.2221 | −2.45706 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.338800 | −0.0448752 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −11.1934 | −1.45726 | −0.728628 | − | 0.684909i | \(-0.759842\pi\) | ||||
−0.728628 | + | 0.684909i | \(0.759842\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.62780 | 0.336455 | 0.168228 | − | 0.985748i | \(-0.446196\pi\) | ||||
0.168228 | + | 0.985748i | \(0.446196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 12.9376 | 1.62999 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.51794 | −0.560382 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.4774 | −1.28001 | −0.640006 | − | 0.768370i | \(-0.721068\pi\) | ||||
−0.640006 | + | 0.768370i | \(0.721068\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.885514 | −0.106603 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.34173 | −0.396590 | −0.198295 | − | 0.980142i | \(-0.563540\pi\) | ||||
−0.198295 | + | 0.980142i | \(0.563540\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8433 | 1.26911 | 0.634554 | − | 0.772879i | \(-0.281184\pi\) | ||||
0.634554 | + | 0.772879i | \(0.281184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.52979 | −0.176645 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −26.4889 | −3.01869 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.00000 | −0.112509 | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.98011 | 0.886678 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.71898 | 0.627740 | 0.313870 | − | 0.949466i | \(-0.398374\pi\) | ||||
0.313870 | + | 0.949466i | \(0.398374\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.81571 | 0.847733 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.751216 | −0.0805388 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.0355 | −1.27576 | −0.637878 | − | 0.770137i | \(-0.720188\pi\) | ||||
−0.637878 | + | 0.770137i | \(0.720188\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.56759 | −0.688471 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.96461 | 0.307416 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.08469 | −0.316483 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.8032 | 1.09690 | 0.548449 | − | 0.836184i | \(-0.315219\pi\) | ||||
0.548449 | + | 0.836184i | \(0.315219\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.0437 | −1.71296 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.9850 | 1.39156 | 0.695782 | − | 0.718253i | \(-0.255058\pi\) | ||||
0.695782 | + | 0.718253i | \(0.255058\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 15.0791 | 1.48579 | 0.742894 | − | 0.669410i | \(-0.233453\pi\) | ||||
0.742894 | + | 0.669410i | \(0.233453\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.68633 | −0.457339 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −6.29158 | −0.608230 | −0.304115 | − | 0.952635i | \(-0.598361\pi\) | ||||
−0.304115 | + | 0.952635i | \(0.598361\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.2424 | −1.93887 | −0.969433 | − | 0.245356i | \(-0.921095\pi\) | ||||
−0.969433 | + | 0.245356i | \(0.921095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.466508 | 0.0442790 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0917 | 1.13749 | 0.568747 | − | 0.822512i | \(-0.307428\pi\) | ||||
0.568747 | + | 0.822512i | \(0.307428\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.06238 | −0.751821 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.22578 | −0.390674 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 11.3614 | 1.04150 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.8957 | 2.17234 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.22206 | −0.290523 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.49508 | 0.133724 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.18235 | −0.459859 | −0.229930 | − | 0.973207i | \(-0.573850\pi\) | ||||
−0.229930 | + | 0.973207i | \(0.573850\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.53134 | −0.310917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.8011 | 1.64266 | 0.821328 | − | 0.570456i | \(-0.193233\pi\) | ||||
0.821328 | + | 0.570456i | \(0.193233\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.48412 | −0.388822 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.15060 | −0.529360 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.72878 | −0.147700 | −0.0738500 | − | 0.997269i | \(-0.523529\pi\) | ||||
−0.0738500 | + | 0.997269i | \(0.523529\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17.1941 | −1.45838 | −0.729190 | − | 0.684311i | \(-0.760103\pi\) | ||||
−0.729190 | + | 0.684311i | \(0.760103\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.38263 | −0.116439 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.65197 | 0.723514 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.83963 | −0.568000 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.44077 | −0.366268 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.98047 | −0.162247 | −0.0811233 | − | 0.996704i | \(-0.525851\pi\) | ||||
−0.0811233 | + | 0.996704i | \(0.525851\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.5704 | −1.34848 | −0.674240 | − | 0.738512i | \(-0.735529\pi\) | ||||
−0.674240 | + | 0.738512i | \(0.735529\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.31029 | 0.591002 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.9921 | 2.16806 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −19.2261 | −1.53441 | −0.767206 | − | 0.641401i | \(-0.778354\pi\) | ||||
−0.767206 | + | 0.641401i | \(0.778354\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.164929 | 0.0130797 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7200 | −0.923668 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.35592 | −0.732813 | −0.366406 | − | 0.930455i | \(-0.619412\pi\) | ||||
−0.366406 | + | 0.930455i | \(0.619412\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.17364 | 0.480618 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.03989 | −0.467380 | −0.233690 | − | 0.972311i | \(-0.575080\pi\) | ||||
−0.233690 | + | 0.972311i | \(0.575080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.8548 | −0.834988 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.88521 | −0.220638 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.6995 | −1.26964 | −0.634820 | − | 0.772660i | \(-0.718926\pi\) | ||||
−0.634820 | + | 0.772660i | \(0.718926\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −20.2473 | −1.53055 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.79233 | 0.285049 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.8403 | 1.03447 | 0.517236 | − | 0.855843i | \(-0.326961\pi\) | ||||
0.517236 | + | 0.855843i | \(0.326961\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.7466 | −1.24477 | −0.622384 | − | 0.782712i | \(-0.713836\pi\) | ||||
−0.622384 | + | 0.782712i | \(0.713836\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.890299 | −0.0658128 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.24744 | 0.312278 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.9673 | −1.09452 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −8.94094 | −0.650358 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.352402 | −0.0254989 | −0.0127495 | − | 0.999919i | \(-0.504058\pi\) | ||||
−0.0127495 | + | 0.999919i | \(0.504058\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −21.1203 | −1.52027 | −0.760137 | − | 0.649762i | \(-0.774868\pi\) | ||||
−0.760137 | + | 0.649762i | \(0.774868\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.53068 | 0.109614 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0954 | −0.790512 | −0.395256 | − | 0.918571i | \(-0.629344\pi\) | ||||
−0.395256 | + | 0.918571i | \(0.629344\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2457 | 1.36429 | 0.682144 | − | 0.731218i | \(-0.261048\pi\) | ||||
0.682144 | + | 0.731218i | \(0.261048\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.54973 | 0.250379 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.94256 | −0.697831 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −29.3360 | −2.04892 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.54101 | −0.524137 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 5.90726 | 0.408614 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −28.5102 | −1.96272 | −0.981361 | − | 0.192175i | \(-0.938446\pi\) | ||||
−0.981361 | + | 0.192175i | \(0.938446\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.13218 | 0.0775756 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −32.1520 | −2.19275 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 39.2375 | 2.66362 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.67370 | −0.248246 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.71095 | −0.249626 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.94778 | −0.599188 | −0.299594 | − | 0.954067i | \(-0.596851\pi\) | ||||
−0.299594 | + | 0.954067i | \(0.596851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0277 | −0.868512 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.57611 | −0.104610 | −0.0523052 | − | 0.998631i | \(-0.516657\pi\) | ||||
−0.0523052 | + | 0.998631i | \(0.516657\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5970 | −1.16284 | −0.581422 | − | 0.813602i | \(-0.697504\pi\) | ||||
−0.581422 | + | 0.813602i | \(0.697504\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.97443 | 0.590474 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −26.6286 | −1.74450 | −0.872248 | − | 0.489063i | \(-0.837339\pi\) | ||||
−0.872248 | + | 0.489063i | \(0.837339\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.5885 | −0.821184 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.338800 | 0.0220074 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −22.4660 | −1.45320 | −0.726601 | − | 0.687059i | \(-0.758901\pi\) | ||||
−0.726601 | + | 0.687059i | \(0.758901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.2590 | 0.982921 | 0.491461 | − | 0.870900i | \(-0.336463\pi\) | ||||
0.491461 | + | 0.870900i | \(0.336463\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.68540 | −0.557169 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −40.4321 | −2.58311 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.46463 | 0.0931924 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.93759 | −0.122790 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.6697 | 0.673463 | 0.336732 | − | 0.941601i | \(-0.390679\pi\) | ||||
0.336732 | + | 0.941601i | \(0.390679\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 15.4397 | 0.970683 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.64796 | −0.165822 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.7725 | 0.671969 | 0.335984 | − | 0.941868i | \(-0.390931\pi\) | ||||
0.335984 | + | 0.941868i | \(0.390931\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.17437 | 0.383656 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.39733 | −0.395985 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.7910 | 0.973714 | 0.486857 | − | 0.873482i | \(-0.338143\pi\) | ||||
0.486857 | + | 0.873482i | \(0.338143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.50164 | 0.0922447 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.07762 | 0.249546 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −22.9870 | −1.40154 | −0.700770 | − | 0.713387i | \(-0.747160\pi\) | ||||
−0.700770 | + | 0.713387i | \(0.747160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.72036 | 0.529724 | 0.264862 | − | 0.964286i | \(-0.414674\pi\) | ||||
0.264862 | + | 0.964286i | \(0.414674\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.22510 | 0.134669 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.6732 | 1.60845 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4.41417 | 0.265222 | 0.132611 | − | 0.991168i | \(-0.457664\pi\) | ||||
0.132611 | + | 0.991168i | \(0.457664\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.2466 | 1.51147 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6091 | −0.811848 | −0.405924 | − | 0.913907i | \(-0.633050\pi\) | ||||
−0.405924 | + | 0.913907i | \(0.633050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.7878 | −0.700714 | −0.350357 | − | 0.936616i | \(-0.613940\pi\) | ||||
−0.350357 | + | 0.936616i | \(0.613940\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.04509 | 0.0619060 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −42.6448 | −2.51725 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5803 | −0.622372 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.66012 | −0.214560 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.8709 | 1.10245 | 0.551224 | − | 0.834357i | \(-0.314161\pi\) | ||||
0.551224 | + | 0.834357i | \(0.314161\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 34.5282 | 2.01031 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.7786 | 0.683461 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.82808 | 0.221383 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.7383 | −2.69395 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.73814 | −0.272199 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.10595 | −0.464145 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.4752 | 1.22566 | 0.612828 | − | 0.790216i | \(-0.290032\pi\) | ||||
0.612828 | + | 0.790216i | \(0.290032\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.10880 | −0.290629 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.784787 | 0.0445012 | 0.0222506 | − | 0.999752i | \(-0.492917\pi\) | ||||
0.0222506 | + | 0.999752i | \(0.492917\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3559 | 1.77234 | 0.886169 | − | 0.463362i | \(-0.153357\pi\) | ||||
0.886169 | + | 0.463362i | \(0.153357\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −39.9087 | −2.24860 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.62243 | 0.428118 | 0.214059 | − | 0.976821i | \(-0.431331\pi\) | ||||
0.214059 | + | 0.976821i | \(0.431331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.0981 | 0.733351 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.13159 | 0.118974 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.53371 | −0.140979 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.61330 | 0.366840 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.85812 | 0.379255 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.2995 | −1.00889 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.5149 | 0.852774 | 0.426387 | − | 0.904541i | \(-0.359786\pi\) | ||||
0.426387 | + | 0.904541i | \(0.359786\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.97277 | 0.217706 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 32.3194 | 1.76580 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 19.7990 | 1.07852 | 0.539259 | − | 0.842140i | \(-0.318704\pi\) | ||||
0.539259 | + | 0.842140i | \(0.318704\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.09668 | −0.222501 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −51.6905 | −2.79920 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −27.3860 | −1.47870 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.73154 | 0.147061 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.86787 | −0.476052 | −0.238026 | − | 0.971259i | \(-0.576500\pi\) | ||||
−0.238026 | + | 0.971259i | \(0.576500\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.19957 | 0.0642115 | 0.0321058 | − | 0.999484i | \(-0.489779\pi\) | ||||
0.0321058 | + | 0.999484i | \(0.489779\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.92035 | 0.155877 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −36.8592 | −1.96182 | −0.980909 | − | 0.194466i | \(-0.937703\pi\) | ||||
−0.980909 | + | 0.194466i | \(0.937703\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 10.3082 | 0.547103 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3.84926 | −0.203725 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 32.8930 | 1.73602 | 0.868012 | − | 0.496542i | \(-0.165397\pi\) | ||||
0.868012 | + | 0.496542i | \(0.165397\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.09588 | −0.424923 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −33.4481 | −1.75075 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 17.9928 | 0.939219 | 0.469609 | − | 0.882874i | \(-0.344395\pi\) | ||||
0.469609 | + | 0.882874i | \(0.344395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −27.4389 | −1.42841 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.18288 | 0.113330 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.2887 | 0.843396 | 0.421698 | − | 0.906736i | \(-0.361434\pi\) | ||||
0.421698 | + | 0.906736i | \(0.361434\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.506533 | −0.0261572 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.24751 | 0.167255 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.1494 | −0.726805 | −0.363402 | − | 0.931632i | \(-0.618385\pi\) | ||||
−0.363402 | + | 0.931632i | \(0.618385\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.75578 | 0.0899514 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31.8077 | −1.62530 | −0.812650 | − | 0.582752i | \(-0.801976\pi\) | ||||
−0.812650 | + | 0.582752i | \(0.801976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 81.7100 | 4.16433 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0728 | −1.52869 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.14502 | −0.463671 | −0.231835 | − | 0.972755i | \(-0.574473\pi\) | ||||
−0.231835 | + | 0.972755i | \(0.574473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.62229 | −0.334904 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −6.36981 | −0.321314 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.08469 | 0.155208 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.0203 | 1.85799 | 0.928997 | − | 0.370087i | \(-0.120672\pi\) | ||||
0.928997 | + | 0.370087i | \(0.120672\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.51922 | 0.0760562 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.64571 | −0.331871 | −0.165935 | − | 0.986137i | \(-0.553064\pi\) | ||||
−0.165935 | + | 0.986137i | \(0.553064\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.8160 | −0.638412 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −24.6162 | −1.22319 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.13395 | −0.403185 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −30.4596 | −1.50613 | −0.753065 | − | 0.657946i | \(-0.771425\pi\) | ||||
−0.753065 | + | 0.657946i | \(0.771425\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.585713 | 0.0288911 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 50.1926 | 2.46981 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.6413 | −0.865977 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.82535 | 0.285269 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.79385 | 0.478461 | 0.239230 | − | 0.970963i | \(-0.423105\pi\) | ||||
0.239230 | + | 0.970963i | \(0.423105\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.3652 | −1.23622 | −0.618111 | − | 0.786091i | \(-0.712102\pi\) | ||||
−0.618111 | + | 0.786091i | \(0.712102\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.7744 | −0.572493 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.4405 | −0.554946 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11.7834 | −0.570237 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.93129 | −0.141524 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −28.6505 | −1.38005 | −0.690023 | − | 0.723787i | \(-0.742400\pi\) | ||||
−0.690023 | + | 0.723787i | \(0.742400\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.24308 | −0.396137 | −0.198069 | − | 0.980188i | \(-0.563467\pi\) | ||||
−0.198069 | + | 0.980188i | \(0.563467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.31727 | 0.111105 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.61368 | 0.125029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.5811 | 1.22092 | 0.610461 | − | 0.792047i | \(-0.290984\pi\) | ||||
0.610461 | + | 0.792047i | \(0.290984\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.8174 | −1.80083 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.5111 | 1.40211 | 0.701056 | − | 0.713106i | \(-0.252712\pi\) | ||||
0.701056 | + | 0.713106i | \(0.252712\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 37.1257 | 1.75993 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.670985 | 0.0317365 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.3951 | −0.868121 | −0.434060 | − | 0.900884i | \(-0.642920\pi\) | ||||
−0.434060 | + | 0.900884i | \(0.642920\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 56.1792 | 2.64537 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.61405 | 0.263771 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 20.2590 | 0.949757 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −27.1112 | −1.26821 | −0.634104 | − | 0.773247i | \(-0.718631\pi\) | ||||
−0.634104 | + | 0.773247i | \(0.718631\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −5.05199 | −0.235807 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.5785 | 1.75021 | 0.875103 | − | 0.483937i | \(-0.160793\pi\) | ||||
0.875103 | + | 0.483937i | \(0.160793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.58950 | 0.352714 | 0.176357 | − | 0.984326i | \(-0.443569\pi\) | ||||
0.176357 | + | 0.984326i | \(0.443569\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −9.14492 | −0.424086 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.3208 | 1.21798 | 0.608991 | − | 0.793177i | \(-0.291574\pi\) | ||||
0.608991 | + | 0.793177i | \(0.291574\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 46.9817 | 2.16941 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.51381 | 0.300141 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 61.5718 | 2.83108 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.51532 | 0.207177 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.40453 | 0.0643090 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.2534 | −0.879709 | −0.439855 | − | 0.898069i | \(-0.644970\pi\) | ||||
−0.439855 | + | 0.898069i | \(0.644970\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.01671 | −0.0919542 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.97075 | 0.180675 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −33.3245 | −1.51319 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.52108 | −0.340813 | −0.170406 | − | 0.985374i | \(-0.554508\pi\) | ||||
−0.170406 | + | 0.985374i | \(0.554508\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.16979 | 0.143343 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.14655 | −0.0517431 | −0.0258715 | − | 0.999665i | \(-0.508236\pi\) | ||||
−0.0258715 | + | 0.999665i | \(0.508236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.61794 | −0.253020 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 52.5746 | 2.36305 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.9847 | 0.672156 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.6929 | −1.06064 | −0.530320 | − | 0.847797i | \(-0.677928\pi\) | ||||
−0.530320 | + | 0.847797i | \(0.677928\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.04632 | 0.0914226 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0.419221 | 0.0186921 | 0.00934606 | − | 0.999956i | \(-0.497025\pi\) | ||||
0.00934606 | + | 0.999956i | \(0.497025\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −43.1396 | −1.91968 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.67762 | 0.163329 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.1532 | 0.760302 | 0.380151 | − | 0.924924i | \(-0.375872\pi\) | ||||
0.380151 | + | 0.924924i | \(0.375872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −48.6225 | −2.15093 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.99391 | 0.0880334 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −46.5144 | −2.04967 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 24.1073 | 1.06024 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.65780 | 0.248350 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −35.7570 | −1.56654 | −0.783271 | − | 0.621680i | \(-0.786450\pi\) | ||||
−0.783271 | + | 0.621680i | \(0.786450\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 37.9493 | 1.65941 | 0.829703 | − | 0.558205i | \(-0.188510\pi\) | ||||
0.829703 | + | 0.558205i | \(0.188510\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.85977 | 0.299385 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.1708 | 0.965775 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1687 | −0.702987 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 32.2954 | 1.40150 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 13.9289 | 0.603330 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.4076 | 0.839063 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.68909 | −0.202349 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 77.4284 | 3.33508 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 39.4666 | 1.69680 | 0.848401 | − | 0.529354i | \(-0.177566\pi\) | ||||
0.848401 | + | 0.529354i | \(0.177566\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.67377 | 0.243485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 62.4414 | 2.67470 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 31.0747 | 1.32866 | 0.664330 | − | 0.747440i | \(-0.268717\pi\) | ||||
0.664330 | + | 0.747440i | \(0.268717\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.58176 | −0.323582 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.21728 | 0.0944594 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.48412 | 0.190684 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1.43903 | −0.0610835 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.3467 | 0.607891 | 0.303945 | − | 0.952689i | \(-0.401696\pi\) | ||||
0.303945 | + | 0.952689i | \(0.401696\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.2660 | 0.645682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.07092 | 0.214094 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 34.7398 | 1.46411 | 0.732053 | − | 0.681248i | \(-0.238562\pi\) | ||||
0.732053 | + | 0.681248i | \(0.238562\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.2993 | −1.56919 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.7837 | −1.50278 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.144869 | 0.00607321 | 0.00303660 | − | 0.999995i | \(-0.499033\pi\) | ||||
0.00303660 | + | 0.999995i | \(0.499033\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.76371 | −0.241204 | −0.120602 | − | 0.992701i | \(-0.538482\pi\) | ||||
−0.120602 | + | 0.992701i | \(0.538482\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.119394 | 0.00498775 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.8016 | 0.492160 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.07164 | −0.0862434 | −0.0431217 | − | 0.999070i | \(-0.513730\pi\) | ||||
−0.0431217 | + | 0.999070i | \(0.513730\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.15557 | 0.297375 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −25.6446 | −1.06392 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.87567 | −0.119098 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 13.0352 | 0.538941 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.8255 | −0.529367 | −0.264683 | − | 0.964335i | \(-0.585267\pi\) | ||||
−0.264683 | + | 0.964335i | \(0.585267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.75033 | −0.360551 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.75911 | 0.154629 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 20.5701 | 0.844714 | 0.422357 | − | 0.906430i | \(-0.361203\pi\) | ||||
0.422357 | + | 0.906430i | \(0.361203\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −35.0466 | −1.43677 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6.52043 | −0.266864 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.65119 | 0.230901 | 0.115451 | − | 0.993313i | \(-0.463169\pi\) | ||||
0.115451 | + | 0.993313i | \(0.463169\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.9956 | 1.10117 | 0.550586 | − | 0.834779i | \(-0.314404\pi\) | ||||
0.550586 | + | 0.834779i | \(0.314404\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 30.2294 | 1.23104 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −73.7109 | −2.99678 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.9708 | 0.932356 | 0.466178 | − | 0.884691i | \(-0.345631\pi\) | ||||
0.466178 | + | 0.884691i | \(0.345631\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.36854 | 0.136500 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.97711 | 0.241808 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.0176 | −0.485388 | −0.242694 | − | 0.970103i | \(-0.578031\pi\) | ||||
−0.242694 | + | 0.970103i | \(0.578031\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.93905 | 0.400781 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.8926 | −0.519038 | −0.259519 | − | 0.965738i | \(-0.583564\pi\) | ||||
−0.259519 | + | 0.965738i | \(0.583564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10.1606 | −0.408390 | −0.204195 | − | 0.978930i | \(-0.565458\pi\) | ||||
−0.204195 | + | 0.978930i | \(0.565458\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.21144 | 0.209128 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 53.9685 | 2.16220 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −27.1885 | −1.08754 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.00138 | −0.0799275 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 3.48877 | 0.139106 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.3400 | 1.12820 | 0.564098 | − | 0.825708i | \(-0.309224\pi\) | ||||
0.564098 | + | 0.825708i | \(0.309224\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.65925 | 0.383921 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 15.9860 | 0.634383 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.1974 | 0.760630 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 9.64161 | 0.381416 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.40962 | 0.0556767 | 0.0278384 | − | 0.999612i | \(-0.491138\pi\) | ||||
0.0278384 | + | 0.999612i | \(0.491138\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.9832 | −0.472573 | −0.236287 | − | 0.971683i | \(-0.575930\pi\) | ||||
−0.236287 | + | 0.971683i | \(0.575930\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.8931 | 0.428915 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.6259 | −1.75443 | −0.877213 | − | 0.480101i | \(-0.840600\pi\) | ||||
−0.877213 | + | 0.480101i | \(0.840600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −66.1223 | −2.59553 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −13.2937 | −0.521021 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.2720 | −1.53683 | −0.768416 | − | 0.639951i | \(-0.778955\pi\) | ||||
−0.768416 | + | 0.639951i | \(0.778955\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −57.9955 | −2.26607 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −31.2851 | −1.22055 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.7789 | −0.419884 | −0.209942 | − | 0.977714i | \(-0.567328\pi\) | ||||
−0.209942 | + | 0.977714i | \(0.567328\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −23.6337 | −0.919243 | −0.459621 | − | 0.888115i | \(-0.652015\pi\) | ||||
−0.459621 | + | 0.888115i | \(0.652015\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.25727 | 0.0488284 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.8321 | 0.536387 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.79526 | 0.224393 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.03151 | 0.117205 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.5231 | 0.599262 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.51520 | 0.366784 | 0.183392 | − | 0.983040i | \(-0.441292\pi\) | ||||
0.183392 | + | 0.983040i | \(0.441292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.00316 | 0.346532 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −49.8809 | −1.91708 | −0.958539 | − | 0.284962i | \(-0.908019\pi\) | ||||
−0.958539 | + | 0.284962i | \(0.908019\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −48.4428 | −1.85906 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.533988 | 0.0204625 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −41.1571 | −1.57483 | −0.787417 | − | 0.616421i | \(-0.788582\pi\) | ||||
−0.787417 | + | 0.616421i | \(0.788582\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.33277 | 0.203755 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.96188 | 0.227460 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.712987 | −0.0271627 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.6379 | 0.632934 | 0.316467 | − | 0.948604i | \(-0.397503\pi\) | ||||
0.316467 | + | 0.948604i | \(0.397503\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 76.4260 | 2.90319 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.0383 | 2.01186 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.0961 | −0.912703 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.02177 | 0.341235 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.7052 | −0.895332 | −0.447666 | − | 0.894201i | \(-0.647745\pi\) | ||||
−0.447666 | + | 0.894201i | \(0.647745\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.37694 | −0.0519323 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.26499 | 0.160629 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −62.7106 | −2.35848 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.5771 | 1.14835 | 0.574173 | − | 0.818734i | \(-0.305324\pi\) | ||||
0.574173 | + | 0.818734i | \(0.305324\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.88521 | 0.108204 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −22.8705 | −0.856508 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −26.6887 | −0.998100 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.61148 | 0.284256 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.6191 | −0.768963 | −0.384482 | − | 0.923133i | \(-0.625620\pi\) | ||||
−0.384482 | + | 0.923133i | \(0.625620\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −67.6164 | −2.51817 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.16977 | −0.192266 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 10.0117 | 0.371827 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.908317 | −0.0336876 | −0.0168438 | − | 0.999858i | \(-0.505362\pi\) | ||||
−0.0168438 | + | 0.999858i | \(0.505362\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.9977 | −0.777693 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −26.4090 | −0.976773 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 51.9088 | 1.91730 | 0.958648 | − | 0.284595i | \(-0.0918591\pi\) | ||||
0.958648 | + | 0.284595i | \(0.0918591\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 13.6984 | 0.505273 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −61.8925 | −2.27984 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.64811 | −0.0974123 | −0.0487062 | − | 0.998813i | \(-0.515510\pi\) | ||||
−0.0487062 | + | 0.998813i | \(0.515510\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.496218 | −0.0182290 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.3942 | −1.22511 | −0.612557 | − | 0.790427i | \(-0.709859\pi\) | ||||
−0.612557 | + | 0.790427i | \(0.709859\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.10915 | 0.223822 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.5005 | −0.603721 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 28.2122 | 1.03085 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.63282 | −0.169054 | −0.0845270 | − | 0.996421i | \(-0.526938\pi\) | ||||
−0.0845270 | + | 0.996421i | \(0.526938\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.61488 | −0.131734 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 51.1146 | 1.86025 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33.5146 | −1.21811 | −0.609055 | − | 0.793128i | \(-0.708451\pi\) | ||||
−0.609055 | + | 0.793128i | \(0.708451\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.23096 | −0.189872 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.94894 | 0.251899 | 0.125949 | − | 0.992037i | \(-0.459802\pi\) | ||||
0.125949 | + | 0.992037i | \(0.459802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 90.7692 | 3.28606 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −22.5500 | −0.815297 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.3942 | −0.591962 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.0036 | 1.37045 | 0.685223 | − | 0.728334i | \(-0.259705\pi\) | ||||
0.685223 | + | 0.728334i | \(0.259705\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −3.64972 | −0.131441 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −32.8033 | −1.17985 | −0.589926 | − | 0.807457i | \(-0.700843\pi\) | ||||
−0.589926 | + | 0.807457i | \(0.700843\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −39.5106 | −1.41926 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.09188 | −0.0750457 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.51019 | 0.340738 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.7405 | −0.706369 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.42106 | 0.157996 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 59.3067 | 2.11675 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.8568 | 1.09993 | 0.549963 | − | 0.835189i | \(-0.314642\pi\) | ||||
0.549963 | + | 0.835189i | \(0.314642\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −5.34999 | −0.190465 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −54.2208 | −1.92787 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.84876 | 0.136674 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.508754 | −0.0180437 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.6793 | −0.838765 | −0.419382 | − | 0.907810i | \(-0.637753\pi\) | ||||
−0.419382 | + | 0.907810i | \(0.637753\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.3400 | −0.365802 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 34.7249 | 1.22694 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 64.0539 | 2.26041 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36.1527 | 1.27421 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.78799 | 0.274150 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.7466 | −0.870044 | −0.435022 | − | 0.900420i | \(-0.643259\pi\) | ||||
−0.435022 | + | 0.900420i | \(0.643259\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.6336 | 1.60241 | 0.801206 | − | 0.598389i | \(-0.204192\pi\) | ||||
0.801206 | + | 0.598389i | \(0.204192\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.95446 | −0.103617 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 28.8601 | 1.01093 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4231 | 0.364657 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 18.9489 | 0.662129 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −47.3053 | −1.65097 | −0.825484 | − | 0.564426i | \(-0.809098\pi\) | ||||
−0.825484 | + | 0.564426i | \(0.809098\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.4445 | 0.503505 | 0.251753 | − | 0.967792i | \(-0.418993\pi\) | ||||
0.251753 | + | 0.967792i | \(0.418993\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −9.03688 | −0.314624 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 10.2502 | 0.356435 | 0.178218 | − | 0.983991i | \(-0.442967\pi\) | ||||
0.178218 | + | 0.983991i | \(0.442967\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.0441 | −1.59918 | −0.799590 | − | 0.600547i | \(-0.794950\pi\) | ||||
−0.799590 | + | 0.600547i | \(0.794950\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.49552 | −0.0518791 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.2101 | −1.15066 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 18.6312 | 0.644759 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −17.4474 | −0.603070 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.67240 | 0.0922614 | 0.0461307 | − | 0.998935i | \(-0.485311\pi\) | ||||
0.0461307 | + | 0.998935i | \(0.485311\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0837 | −0.830471 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.61075 | 0.158803 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 33.4839 | 1.15188 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −107.151 | −3.68176 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.99372 | 0.137064 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.59888 | −0.123368 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.0188 | 0.959345 | 0.479672 | − | 0.877448i | \(-0.340755\pi\) | ||||
0.479672 | + | 0.877448i | \(0.340755\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8.90000 | 0.304373 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.52577 | 0.188757 | 0.0943783 | − | 0.995536i | \(-0.469914\pi\) | ||||
0.0943783 | + | 0.995536i | \(0.469914\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.3461 | −1.51307 | −0.756534 | − | 0.653954i | \(-0.773109\pi\) | ||||
−0.756534 | + | 0.653954i | \(0.773109\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.4481 | 0.492389 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0.737216 | 0.0250951 | 0.0125476 | − | 0.999921i | \(-0.496006\pi\) | ||||
0.0125476 | + | 0.999921i | \(0.496006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.5128 | 1.75149 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.58462 | 0.121740 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.90726 | −0.200390 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.3455 | −0.519962 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.1695 | −1.05493 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −6.70411 | −0.226640 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.07642 | 0.272721 | 0.136361 | − | 0.990659i | \(-0.456459\pi\) | ||||
0.136361 | + | 0.990659i | \(0.456459\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −6.39346 | −0.215646 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.8201 | 1.51003 | 0.755014 | − | 0.655708i | \(-0.227630\pi\) | ||||
0.755014 | + | 0.655708i | \(0.227630\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −38.9580 | −1.31104 | −0.655521 | − | 0.755177i | \(-0.727551\pi\) | ||||
−0.655521 | + | 0.755177i | \(0.727551\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11.6982 | −0.393229 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 37.9365 | 1.27378 | 0.636892 | − | 0.770953i | \(-0.280220\pi\) | ||||
0.636892 | + | 0.770953i | \(0.280220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23.2383 | 0.779387 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 47.1406 | 1.57927 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.08096 | 0.136564 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −42.6930 | −1.42707 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.29695 | −0.0433040 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.4020 | −0.647091 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.23342 | 0.0410910 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.8350 | 0.526954 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 51.6582 | 1.71718 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.9918 | −0.364975 | −0.182488 | − | 0.983208i | \(-0.558415\pi\) | ||||
−0.182488 | + | 0.983208i | \(0.558415\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −40.3499 | −1.33832 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.02940 | −0.133500 | −0.0667500 | − | 0.997770i | \(-0.521263\pi\) | ||||
−0.0667500 | + | 0.997770i | \(0.521263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.7835 | 1.11807 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.74630 | 0.0907898 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −84.3062 | −2.78404 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.78258 | 0.190750 | 0.0953748 | − | 0.995441i | \(-0.469595\pi\) | ||||
0.0953748 | + | 0.995441i | \(0.469595\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.27581 | −0.239746 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.89441 | −0.161101 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.21733 | −0.204425 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −43.5064 | −1.42894 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 16.5042 | 0.541484 | 0.270742 | − | 0.962652i | \(-0.412731\pi\) | ||||
0.270742 | + | 0.962652i | \(0.412731\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.1073 | 0.429575 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −0.265886 | −0.00870472 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 46.1694 | 1.50990 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.59864 | −0.0848938 | −0.0424469 | − | 0.999099i | \(-0.513515\pi\) | ||||
−0.0424469 | + | 0.999099i | \(0.513515\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −10.6234 | −0.346681 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.2239 | −0.757079 | −0.378540 | − | 0.925585i | \(-0.623574\pi\) | ||||
−0.378540 | + | 0.925585i | \(0.623574\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.8566 | 0.809441 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 27.5800 | 0.897179 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.4744 | −0.827808 | −0.413904 | − | 0.910320i | \(-0.635835\pi\) | ||||
−0.413904 | + | 0.910320i | \(0.635835\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.8814 | 0.515532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.58248 | −0.0837427 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.82084 | −0.0589827 | −0.0294914 | − | 0.999565i | \(-0.509389\pi\) | ||||
−0.0294914 | + | 0.999565i | \(0.509389\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.08705 | 0.0351762 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4.43763 | −0.143448 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.75208 | 0.250328 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.5683 | 1.46995 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.1526 | 0.584958 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 65.1497 | 2.09724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.9154 | 0.543962 | 0.271981 | − | 0.962303i | \(-0.412321\pi\) | ||||
0.271981 | + | 0.962303i | \(0.412321\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.858421 | 0.0275765 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −23.9082 | −0.767251 | −0.383625 | − | 0.923489i | \(-0.625325\pi\) | ||||
−0.383625 | + | 0.923489i | \(0.625325\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 77.1002 | 2.47172 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.24059 | −0.0717562 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.22674 | 0.167218 | 0.0836092 | − | 0.996499i | \(-0.473355\pi\) | ||||
0.0836092 | + | 0.996499i | \(0.473355\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −71.0966 | −2.27226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 58.4035 | 1.86468 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.0200 | −0.893699 | −0.446849 | − | 0.894609i | \(-0.647454\pi\) | ||||
−0.446849 | + | 0.894609i | \(0.647454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.2258 | 1.09052 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.19988 | 0.197344 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.2425 | 0.866262 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.85812 | −0.186089 | −0.0930446 | − | 0.995662i | \(-0.529660\pi\) | ||||
−0.0930446 | + | 0.995662i | \(0.529660\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −5.25644 | −0.166808 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −59.3669 | −1.88206 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.23537 | 0.165806 | 0.0829029 | − | 0.996558i | \(-0.473581\pi\) | ||||
0.0829029 | + | 0.996558i | \(0.473581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.74550 | −0.0868637 |
(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 | 6004.2.a.g.1.13 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6004.2.a.g.1.13 | ✓ | 27 | 1.1 | even | 1 | trivial |