Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.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: | \(64.0400224211\) |
Analytic rank: | \(0\) |
Dimension: | \(35\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.64682 | −0.950791 | −0.475395 | − | 0.879772i | \(-0.657695\pi\) | ||||
−0.475395 | + | 0.879772i | \(0.657695\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.19631 | 0.452162 | 0.226081 | − | 0.974108i | \(-0.427409\pi\) | ||||
0.226081 | + | 0.974108i | \(0.427409\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.287991 | −0.0959971 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.54953 | −1.37174 | −0.685868 | − | 0.727726i | \(-0.740577\pi\) | ||||
−0.685868 | + | 0.727726i | \(0.740577\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.333289 | 0.0924378 | 0.0462189 | − | 0.998931i | \(-0.485283\pi\) | ||||
0.0462189 | + | 0.998931i | \(0.485283\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.64682 | 0.425207 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.17504 | 0.770060 | 0.385030 | − | 0.922904i | \(-0.374191\pi\) | ||||
0.385030 | + | 0.922904i | \(0.374191\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.49241 | −1.26005 | −0.630023 | − | 0.776577i | \(-0.716954\pi\) | ||||
−0.630023 | + | 0.776577i | \(0.716954\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.97010 | −0.429911 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.05584 | −1.26273 | −0.631365 | − | 0.775486i | \(-0.717505\pi\) | ||||
−0.631365 | + | 0.775486i | \(0.717505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.41472 | 1.04206 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.32750 | −1.36068 | −0.680341 | − | 0.732896i | \(-0.738168\pi\) | ||||
−0.680341 | + | 0.732896i | \(0.738168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.21716 | −1.65545 | −0.827726 | − | 0.561133i | \(-0.810366\pi\) | ||||
−0.827726 | + | 0.561133i | \(0.810366\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.49225 | 1.30423 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.19631 | −0.202213 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.97265 | −1.63949 | −0.819747 | − | 0.572726i | \(-0.805886\pi\) | ||||
−0.819747 | + | 0.572726i | \(0.805886\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.548867 | −0.0878890 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.20054 | 0.656015 | 0.328007 | − | 0.944675i | \(-0.393623\pi\) | ||||
0.328007 | + | 0.944675i | \(0.393623\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.57956 | 1.15587 | 0.577936 | − | 0.816082i | \(-0.303858\pi\) | ||||
0.577936 | + | 0.816082i | \(0.303858\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.287991 | 0.0429312 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.25633 | 0.620849 | 0.310425 | − | 0.950598i | \(-0.399529\pi\) | ||||
0.310425 | + | 0.950598i | \(0.399529\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.56885 | −0.795549 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.22871 | −0.732166 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.7744 | 1.47997 | 0.739986 | − | 0.672622i | \(-0.234832\pi\) | ||||
0.739986 | + | 0.672622i | \(0.234832\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.54953 | 0.613459 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 9.04500 | 1.19804 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.501509 | 0.0652909 | 0.0326455 | − | 0.999467i | \(-0.489607\pi\) | ||||
0.0326455 | + | 0.999467i | \(0.489607\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6677 | 1.74997 | 0.874984 | − | 0.484152i | \(-0.160872\pi\) | ||||
0.874984 | + | 0.484152i | \(0.160872\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.344527 | −0.0434063 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.333289 | −0.0413394 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.7643 | −1.55941 | −0.779706 | − | 0.626145i | \(-0.784632\pi\) | ||||
−0.779706 | + | 0.626145i | \(0.784632\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.97286 | 1.20059 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −13.3089 | −1.57947 | −0.789736 | − | 0.613447i | \(-0.789783\pi\) | ||||
−0.789736 | + | 0.613447i | \(0.789783\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.58878 | −0.302993 | −0.151497 | − | 0.988458i | \(-0.548409\pi\) | ||||
−0.151497 | + | 0.988458i | \(0.548409\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.64682 | −0.190158 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.44264 | −0.620247 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.02408 | −0.790271 | −0.395135 | − | 0.918623i | \(-0.629302\pi\) | ||||
−0.395135 | + | 0.918623i | \(0.629302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.05309 | −0.894787 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.8318 | −1.29870 | −0.649352 | − | 0.760488i | \(-0.724960\pi\) | ||||
−0.649352 | + | 0.760488i | \(0.724960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.17504 | −0.344381 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 12.0671 | 1.29372 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.84136 | 0.513183 | 0.256592 | − | 0.966520i | \(-0.417400\pi\) | ||||
0.256592 | + | 0.966520i | \(0.417400\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.398717 | 0.0417969 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 15.1790 | 1.57399 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.49241 | 0.563509 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.00650 | 0.711402 | 0.355701 | − | 0.934600i | \(-0.384242\pi\) | ||||
0.355701 | + | 0.934600i | \(0.384242\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.31023 | 0.131683 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.32323 | 0.330674 | 0.165337 | − | 0.986237i | \(-0.447129\pi\) | ||||
0.165337 | + | 0.986237i | \(0.447129\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.3891 | 1.91046 | 0.955232 | − | 0.295858i | \(-0.0956056\pi\) | ||||
0.955232 | + | 0.295858i | \(0.0956056\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.97010 | 0.192262 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.05521 | 0.488706 | 0.244353 | − | 0.969686i | \(-0.421424\pi\) | ||||
0.244353 | + | 0.969686i | \(0.421424\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.1619 | −1.16490 | −0.582451 | − | 0.812866i | \(-0.697906\pi\) | ||||
−0.582451 | + | 0.812866i | \(0.697906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 16.4231 | 1.55881 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.92463 | −0.933631 | −0.466815 | − | 0.884355i | \(-0.654599\pi\) | ||||
−0.466815 | + | 0.884355i | \(0.654599\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.05584 | 0.564710 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.0959845 | −0.00887377 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.79833 | 0.348192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.69824 | 0.881659 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.91753 | −0.623733 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.37688 | −0.299650 | −0.149825 | − | 0.988713i | \(-0.547871\pi\) | ||||
−0.149825 | + | 0.988713i | \(0.547871\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.4822 | −1.09899 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1614 | 1.06255 | 0.531275 | − | 0.847200i | \(-0.321713\pi\) | ||||
0.531275 | + | 0.847200i | \(0.321713\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.57062 | −0.569745 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.41472 | −0.466025 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −18.5676 | −1.58633 | −0.793167 | − | 0.609004i | \(-0.791569\pi\) | ||||
−0.793167 | + | 0.609004i | \(0.791569\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.0714 | −1.78725 | −0.893627 | − | 0.448810i | \(-0.851848\pi\) | ||||
−0.893627 | + | 0.448810i | \(0.851848\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.00940 | −0.590298 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.51631 | −0.126800 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.32750 | 0.608515 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.17087 | 0.756401 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.790632 | 0.0647711 | 0.0323855 | − | 0.999475i | \(-0.489690\pi\) | ||||
0.0323855 | + | 0.999475i | \(0.489690\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.1287 | −0.905637 | −0.452819 | − | 0.891603i | \(-0.649581\pi\) | ||||
−0.452819 | + | 0.891603i | \(0.649581\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.914384 | −0.0739236 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 9.21716 | 0.740340 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.4415 | −0.992941 | −0.496470 | − | 0.868054i | \(-0.665371\pi\) | ||||
−0.496470 | + | 0.868054i | \(0.665371\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.7434 | −1.40714 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.24465 | −0.570958 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.1490 | 0.951582 | 0.475791 | − | 0.879559i | \(-0.342162\pi\) | ||||
0.475791 | + | 0.879559i | \(0.342162\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −7.49225 | −0.583271 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.1773 | 0.864922 | 0.432461 | − | 0.901653i | \(-0.357645\pi\) | ||||
0.432461 | + | 0.901653i | \(0.357645\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.8889 | −0.991455 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.58177 | 0.120961 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.82741 | −0.443050 | −0.221525 | − | 0.975155i | \(-0.571103\pi\) | ||||
−0.221525 | + | 0.975155i | \(0.571103\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.19631 | 0.0904324 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −0.825894 | −0.0620780 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.1873 | −1.80784 | −0.903922 | − | 0.427697i | \(-0.859325\pi\) | ||||
−0.903922 | + | 0.427697i | \(0.859325\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.9710 | 0.815466 | 0.407733 | − | 0.913101i | \(-0.366319\pi\) | ||||
0.407733 | + | 0.913101i | \(0.366319\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −22.5082 | −1.66385 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.97265 | 0.733204 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −14.4449 | −1.05632 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.47768 | 0.471182 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 21.6240 | 1.56466 | 0.782328 | − | 0.622867i | \(-0.214032\pi\) | ||||
0.782328 | + | 0.622867i | \(0.214032\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 23.9764 | 1.72586 | 0.862930 | − | 0.505324i | \(-0.168627\pi\) | ||||
0.862930 | + | 0.505324i | \(0.168627\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0.548867 | 0.0393052 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.45320 | 0.388524 | 0.194262 | − | 0.980950i | \(-0.437769\pi\) | ||||
0.194262 | + | 0.980950i | \(0.437769\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.2752 | 1.36638 | 0.683192 | − | 0.730238i | \(-0.260591\pi\) | ||||
0.683192 | + | 0.730238i | \(0.260591\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.0205 | 1.48268 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.76595 | −0.615249 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.20054 | −0.293379 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.74403 | 0.121218 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.9879 | 1.72845 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.33340 | −0.0917949 | −0.0458975 | − | 0.998946i | \(-0.514615\pi\) | ||||
−0.0458975 | + | 0.998946i | \(0.514615\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.9173 | 1.50175 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.57956 | −0.516922 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.0266 | −0.748532 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.26324 | 0.288083 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.05821 | 0.0711827 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.4274 | −1.30095 | −0.650476 | − | 0.759526i | \(-0.725431\pi\) | ||||
−0.650476 | + | 0.759526i | \(0.725431\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.287991 | −0.0191994 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.15735 | 0.143188 | 0.0715941 | − | 0.997434i | \(-0.477191\pi\) | ||||
0.0715941 | + | 0.997434i | \(0.477191\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 17.8844 | 1.18184 | 0.590918 | − | 0.806731i | \(-0.298766\pi\) | ||||
0.590918 | + | 0.806731i | \(0.298766\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.96304 | 0.589725 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.9828 | 1.24361 | 0.621803 | − | 0.783173i | \(-0.286400\pi\) | ||||
0.621803 | + | 0.783173i | \(0.286400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.25633 | −0.277652 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.5674 | 0.751382 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.1282 | 0.719825 | 0.359913 | − | 0.932986i | \(-0.382807\pi\) | ||||
0.359913 | + | 0.932986i | \(0.382807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.7728 | 1.72459 | 0.862293 | − | 0.506410i | \(-0.169028\pi\) | ||||
0.862293 | + | 0.506410i | \(0.169028\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.98220 | −0.191308 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.56885 | 0.355781 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.83056 | −0.116476 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.4848 | 1.23480 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −14.9135 | −0.941330 | −0.470665 | − | 0.882312i | \(-0.655986\pi\) | ||||
−0.470665 | + | 0.882312i | \(0.655986\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 27.5512 | 1.73213 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 5.22871 | 0.327435 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.06625 | 0.378402 | 0.189201 | − | 0.981938i | \(-0.439410\pi\) | ||||
0.189201 | + | 0.981938i | \(0.439410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.9304 | −0.741317 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.11026 | 0.130622 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5058 | 1.26444 | 0.632220 | − | 0.774789i | \(-0.282144\pi\) | ||||
0.632220 | + | 0.774789i | \(0.282144\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7744 | −0.661864 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −7.97284 | −0.487930 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.19171 | 0.438486 | 0.219243 | − | 0.975670i | \(-0.429641\pi\) | ||||
0.219243 | + | 0.975670i | \(0.429641\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.94253 | 0.360983 | 0.180491 | − | 0.983577i | \(-0.442231\pi\) | ||||
0.180491 | + | 0.983577i | \(0.442231\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.656614 | −0.0397401 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.54953 | −0.274347 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.8200 | −1.55137 | −0.775686 | − | 0.631119i | \(-0.782596\pi\) | ||||
−0.775686 | + | 0.631119i | \(0.782596\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.65446 | 0.158919 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.06523 | 0.242511 | 0.121256 | − | 0.992621i | \(-0.461308\pi\) | ||||
0.121256 | + | 0.992621i | \(0.461308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.75585 | −0.401593 | −0.200797 | − | 0.979633i | \(-0.564353\pi\) | ||||
−0.200797 | + | 0.979633i | \(0.564353\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9.04500 | −0.535780 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.02515 | 0.296625 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.91913 | −0.407008 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.5384 | −0.676394 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.99399 | 0.174911 | 0.0874554 | − | 0.996168i | \(-0.472126\pi\) | ||||
0.0874554 | + | 0.996168i | \(0.472126\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.501509 | −0.0291990 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −24.6345 | −1.42944 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.01835 | −0.116724 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.06749 | 0.522642 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.47276 | −0.314402 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.6677 | −0.782610 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.86355 | −0.277578 | −0.138789 | − | 0.990322i | \(-0.544321\pi\) | ||||
−0.138789 | + | 0.990322i | \(0.544321\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −31.9303 | −1.81645 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1236 | 0.630764 | 0.315382 | − | 0.948965i | \(-0.397867\pi\) | ||||
0.315382 | + | 0.948965i | \(0.397867\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.3437 | 0.584659 | 0.292330 | − | 0.956318i | \(-0.405570\pi\) | ||||
0.292330 | + | 0.956318i | \(0.405570\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.344527 | 0.0194119 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.0691 | −1.23952 | −0.619762 | − | 0.784790i | \(-0.712771\pi\) | ||||
−0.619762 | + | 0.784790i | \(0.712771\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 33.3367 | 1.86650 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.32501 | −0.464657 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.4386 | −0.970311 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.333289 | 0.0184876 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.0285 | 1.10758 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5.09188 | 0.280724 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.14828 | −0.228010 | −0.114005 | − | 0.993480i | \(-0.536368\pi\) | ||||
−0.114005 | + | 0.993480i | \(0.536368\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.87204 | 0.157387 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.7643 | 0.697391 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.30726 | 0.0712110 | 0.0356055 | − | 0.999366i | \(-0.488664\pi\) | ||||
0.0356055 | + | 0.999366i | \(0.488664\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.3441 | 0.887687 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 41.9338 | 2.27084 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0362 | −0.811879 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −9.97286 | −0.536921 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12.3661 | 0.663845 | 0.331922 | − | 0.943307i | \(-0.392303\pi\) | ||||
0.331922 | + | 0.943307i | \(0.392303\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.1833 | −1.24097 | −0.620487 | − | 0.784217i | \(-0.713065\pi\) | ||||
−0.620487 | + | 0.784217i | \(0.713065\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.80467 | 0.0963261 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.30510 | −0.122688 | −0.0613440 | − | 0.998117i | \(-0.519539\pi\) | ||||
−0.0613440 | + | 0.998117i | \(0.519539\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.3089 | 0.706361 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.25515 | −0.331058 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1883 | 1.54050 | 0.770250 | − | 0.637742i | \(-0.220131\pi\) | ||||
0.770250 | + | 0.637742i | \(0.220131\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.1666 | 0.587715 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.9712 | −0.838273 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.58878 | 0.135503 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.0547 | −1.15125 | −0.575624 | − | 0.817715i | \(-0.695241\pi\) | ||||
−0.575624 | + | 0.817715i | \(0.695241\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.20972 | −0.0629756 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.8895 | 0.669187 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −30.8032 | −1.59493 | −0.797463 | − | 0.603367i | \(-0.793825\pi\) | ||||
−0.797463 | + | 0.603367i | \(0.793825\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.64682 | 0.0850413 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.44218 | −0.125778 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10.1672 | −0.522252 | −0.261126 | − | 0.965305i | \(-0.584094\pi\) | ||||
−0.261126 | + | 0.965305i | \(0.584094\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.56111 | 0.284904 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.2823 | 0.831987 | 0.415993 | − | 0.909368i | \(-0.363434\pi\) | ||||
0.415993 | + | 0.909368i | \(0.363434\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.44264 | 0.277383 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.18285 | −0.110960 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 27.5335 | 1.39600 | 0.698001 | − | 0.716096i | \(-0.254073\pi\) | ||||
0.698001 | + | 0.716096i | \(0.254073\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −19.2275 | −0.972377 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −20.0277 | −1.01026 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.02408 | 0.353420 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.5081 | 1.58134 | 0.790672 | − | 0.612240i | \(-0.209731\pi\) | ||||
0.790672 | + | 0.612240i | \(0.209731\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10.8206 | 0.541708 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.07198 | −0.153026 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 8.05309 | 0.400161 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 45.3709 | 2.24895 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.6818 | 0.775415 | 0.387707 | − | 0.921783i | \(-0.373267\pi\) | ||||
0.387707 | + | 0.921783i | \(0.373267\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 30.5774 | 1.50827 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0.599959 | 0.0295221 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 11.8318 | 0.580798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 34.7008 | 1.69930 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.6004 | −1.39722 | −0.698610 | − | 0.715503i | \(-0.746198\pi\) | ||||
−0.698610 | + | 0.715503i | \(0.746198\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.206044 | 0.0100419 | 0.00502097 | − | 0.999987i | \(-0.498402\pi\) | ||||
0.00502097 | + | 0.999987i | \(0.498402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.22579 | −0.0595998 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.17504 | 0.154012 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.3508 | 0.791269 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.49709 | 0.120560 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.2222 | −1.50392 | −0.751960 | − | 0.659208i | \(-0.770892\pi\) | ||||
−0.751960 | + | 0.659208i | \(0.770892\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.7707 | 0.854007 | 0.427004 | − | 0.904250i | \(-0.359569\pi\) | ||||
0.427004 | + | 0.904250i | \(0.359569\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.0671 | −0.578571 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.2611 | 1.59110 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.7496 | 0.703960 | 0.351980 | − | 0.936008i | \(-0.385509\pi\) | ||||
0.351980 | + | 0.936008i | \(0.385509\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.60378 | 0.0763705 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.7852 | 1.13007 | 0.565034 | − | 0.825067i | \(-0.308863\pi\) | ||||
0.565034 | + | 0.825067i | \(0.308863\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.84136 | −0.229503 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.30203 | −0.0615837 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 25.2922 | 1.19361 | 0.596807 | − | 0.802385i | \(-0.296436\pi\) | ||||
0.596807 | + | 0.802385i | \(0.296436\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.1105 | −0.899879 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.3269 | 0.861071 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.398717 | −0.0186921 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −33.7849 | −1.58039 | −0.790196 | − | 0.612854i | \(-0.790021\pi\) | ||||
−0.790196 | + | 0.612854i | \(0.790021\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 17.1920 | 0.802452 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −16.2241 | −0.755630 | −0.377815 | − | 0.925881i | \(-0.623324\pi\) | ||||
−0.377815 | + | 0.925881i | \(0.623324\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.0458 | −0.885131 | −0.442566 | − | 0.896736i | \(-0.645932\pi\) | ||||
−0.442566 | + | 0.896736i | \(0.645932\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −15.1790 | −0.703909 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.6299 | −1.04719 | −0.523593 | − | 0.851969i | \(-0.675409\pi\) | ||||
−0.523593 | + | 0.851969i | \(0.675409\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.2701 | −0.705107 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 20.4889 | 0.944079 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −34.4835 | −1.58555 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.49241 | −0.252009 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.10292 | −0.142073 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 29.5568 | 1.35049 | 0.675243 | − | 0.737595i | \(-0.264039\pi\) | ||||
0.675243 | + | 0.737595i | \(0.264039\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.32378 | −0.151551 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.9306 | 0.542862 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.00650 | −0.318149 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.4466 | 0.699950 | 0.349975 | − | 0.936759i | \(-0.386190\pi\) | ||||
0.349975 | + | 0.936759i | \(0.386190\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.0072 | −0.904755 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.3249 | 1.54906 | 0.774531 | − | 0.632536i | \(-0.217986\pi\) | ||||
0.774531 | + | 0.632536i | \(0.217986\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.2651 | −1.04781 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.31023 | −0.0588903 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −15.9215 | −0.714177 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11.0715 | −0.495629 | −0.247815 | − | 0.968807i | \(-0.579712\pi\) | ||||
−0.247815 | + | 0.968807i | \(0.579712\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.4069 | −0.822360 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.37509 | 0.239663 | 0.119832 | − | 0.992794i | \(-0.461764\pi\) | ||||
0.119832 | + | 0.992794i | \(0.461764\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.32323 | −0.147882 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 21.2257 | 0.942666 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −31.5753 | −1.39955 | −0.699775 | − | 0.714363i | \(-0.746716\pi\) | ||||
−0.699775 | + | 0.714363i | \(0.746716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.09697 | −0.137002 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −29.7399 | −1.31305 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.3891 | −0.854385 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.3643 | −0.851641 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.59668 | 0.421247 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 32.9402 | 1.44314 | 0.721568 | − | 0.692344i | \(-0.243422\pi\) | ||||
0.721568 | + | 0.692344i | \(0.243422\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.0653 | 0.921121 | 0.460560 | − | 0.887628i | \(-0.347648\pi\) | ||||
0.460560 | + | 0.887628i | \(0.347648\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.97010 | −0.0859823 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −29.2649 | −1.27480 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.6732 | 0.594485 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −0.144430 | −0.00626774 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.40000 | 0.0606406 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.05521 | −0.218556 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.8321 | 1.71888 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 25.3356 | 1.09128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 31.9163 | 1.37219 | 0.686095 | − | 0.727512i | \(-0.259324\pi\) | ||||
0.686095 | + | 0.727512i | \(0.259324\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.0672 | −0.775337 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1619 | 0.520960 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.2350 | −0.480373 | −0.240186 | − | 0.970727i | \(-0.577209\pi\) | ||||
−0.240186 | + | 0.970727i | \(0.577209\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.93618 | −0.167992 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 40.2456 | 1.71452 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.40297 | −0.357330 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.4231 | −0.697123 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 33.8271 | 1.43330 | 0.716650 | − | 0.697433i | \(-0.245674\pi\) | ||||
0.716650 | + | 0.697433i | \(0.245674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.52619 | 0.106846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.7882 | 1.00434 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.92063 | −0.249525 | −0.124762 | − | 0.992187i | \(-0.539817\pi\) | ||||
−0.124762 | + | 0.992187i | \(0.539817\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.92463 | 0.417532 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.63397 | −0.404589 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 33.1626 | 1.39025 | 0.695125 | − | 0.718889i | \(-0.255349\pi\) | ||||
0.695125 | + | 0.718889i | \(0.255349\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.383667 | 0.0160559 | 0.00802797 | − | 0.999968i | \(-0.497445\pi\) | ||||
0.00802797 | + | 0.999968i | \(0.497445\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.6107 | −1.48766 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.05584 | −0.252546 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.4167 | 1.34952 | 0.674762 | − | 0.738035i | \(-0.264246\pi\) | ||||
0.674762 | + | 0.738035i | \(0.264246\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −39.4848 | −1.64093 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.1544 | −0.587225 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −49.0183 | −2.03013 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0.0959845 | 0.00396847 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.7747 | 0.857464 | 0.428732 | − | 0.903432i | \(-0.358960\pi\) | ||||
0.428732 | + | 0.903432i | \(0.358960\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 50.6245 | 2.08594 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.98042 | −0.369405 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 36.1912 | 1.48619 | 0.743097 | − | 0.669183i | \(-0.233356\pi\) | ||||
0.743097 | + | 0.669183i | \(0.233356\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.79833 | −0.155716 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −31.7428 | −1.29915 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.6938 | 0.559514 | 0.279757 | − | 0.960071i | \(-0.409746\pi\) | ||||
0.279757 | + | 0.960071i | \(0.409746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 40.4133 | 1.64849 | 0.824246 | − | 0.566231i | \(-0.191599\pi\) | ||||
0.824246 | + | 0.566231i | \(0.191599\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.67602 | 0.149699 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.69824 | −0.394290 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.48952 | −0.303990 | −0.151995 | − | 0.988381i | \(-0.548570\pi\) | ||||
−0.151995 | + | 0.988381i | \(0.548570\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 14.4359 | 0.584973 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.41859 | 0.0573899 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 21.9249 | 0.885536 | 0.442768 | − | 0.896636i | \(-0.353996\pi\) | ||||
0.442768 | + | 0.896636i | \(0.353996\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.91753 | 0.278942 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.7412 | 0.955785 | 0.477892 | − | 0.878418i | \(-0.341401\pi\) | ||||
0.477892 | + | 0.878418i | \(0.341401\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6731 | −0.710343 | −0.355171 | − | 0.934801i | \(-0.615577\pi\) | ||||
−0.355171 | + | 0.934801i | \(0.615577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.7907 | −1.31584 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 5.79176 | 0.232042 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −41.1505 | −1.64339 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.6635 | −1.26251 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.7660 | 0.707253 | 0.353627 | − | 0.935387i | \(-0.384948\pi\) | ||||
0.353627 | + | 0.935387i | \(0.384948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.19586 | 0.0872778 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.37688 | 0.134007 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.85604 | −0.0735388 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.83284 | 0.151625 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.3977 | 0.924153 | 0.462077 | − | 0.886840i | \(-0.347104\pi\) | ||||
0.462077 | + | 0.886840i | \(0.347104\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 10.8853 | 0.429274 | 0.214637 | − | 0.976694i | \(-0.431143\pi\) | ||||
0.214637 | + | 0.976694i | \(0.431143\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.4822 | 0.491484 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 36.3724 | 1.42995 | 0.714973 | − | 0.699153i | \(-0.246439\pi\) | ||||
0.714973 | + | 0.699153i | \(0.246439\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.28163 | −0.0895619 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.1588 | 0.711698 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −0.0196962 | −0.000770770 0 | −0.000385385 | − | 1.00000i | \(-0.500123\pi\) | ||||
−0.000385385 | 1.00000i | \(0.500123\pi\) | ||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −12.1614 | −0.475187 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.745545 | 0.0290865 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.1757 | 0.669071 | 0.334535 | − | 0.942383i | \(-0.391421\pi\) | ||||
0.334535 | + | 0.942383i | \(0.391421\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 28.7296 | 1.11745 | 0.558726 | − | 0.829352i | \(-0.311290\pi\) | ||||
0.558726 | + | 0.829352i | \(0.311290\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.74267 | −0.0676798 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.57062 | 0.254798 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 44.3741 | 1.71817 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 31.9933 | 1.23693 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −62.1816 | −2.40049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −23.2239 | −0.895215 | −0.447608 | − | 0.894230i | \(-0.647724\pi\) | ||||
−0.447608 | + | 0.894230i | \(0.647724\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.41472 | 0.208413 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.33551 | −0.166627 | −0.0833136 | − | 0.996523i | \(-0.526550\pi\) | ||||
−0.0833136 | + | 0.996523i | \(0.526550\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.38193 | 0.321669 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.55276 | −0.136142 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.30852 | 0.164861 | 0.0824305 | − | 0.996597i | \(-0.473732\pi\) | ||||
0.0824305 | + | 0.996597i | \(0.473732\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 18.5676 | 0.709430 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −29.4524 | −1.12368 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.59098 | 0.136805 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.30153 | −0.315805 | −0.157903 | − | 0.987455i | \(-0.550473\pi\) | ||||
−0.157903 | + | 0.987455i | \(0.550473\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.56743 | 0.0595419 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 21.0714 | 0.799284 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 13.3369 | 0.505171 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −31.2613 | −1.18241 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.5585 | −0.549865 | −0.274933 | − | 0.961463i | \(-0.588656\pi\) | ||||
−0.274933 | + | 0.961463i | \(0.588656\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 54.7739 | 2.06584 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.00940 | 0.263989 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.97561 | 0.149518 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −19.1840 | −0.720469 | −0.360235 | − | 0.932862i | \(-0.617303\pi\) | ||||
−0.360235 | + | 0.932862i | \(0.617303\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.02288 | 0.0758637 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 55.8176 | 2.09039 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.51631 | 0.0567068 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18.3262 | −0.684403 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −42.4592 | −1.58346 | −0.791730 | − | 0.610871i | \(-0.790819\pi\) | ||||
−0.791730 | + | 0.610871i | \(0.790819\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 23.1953 | 0.863839 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −44.0899 | −1.63972 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.32750 | −0.272136 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.1127 | 0.449236 | 0.224618 | − | 0.974447i | \(-0.427887\pi\) | ||||
0.224618 | + | 0.974447i | \(0.427887\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0704 | 1.07668 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 24.0654 | 0.890091 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.928387 | −0.0342908 | −0.0171454 | − | 0.999853i | \(-0.505458\pi\) | ||||
−0.0171454 | + | 0.999853i | \(0.505458\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.17087 | −0.338273 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.0718 | 2.13910 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 28.7212 | 1.05653 | 0.528263 | − | 0.849081i | \(-0.322843\pi\) | ||||
0.528263 | + | 0.849081i | \(0.322843\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.01460 | 0.110744 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −23.3516 | −0.856686 | −0.428343 | − | 0.903616i | \(-0.640902\pi\) | ||||
−0.428343 | + | 0.903616i | \(0.640902\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.790632 | −0.0289665 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.40745 | 0.124672 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.04759 | 0.220974 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.95874 | −0.0714755 | −0.0357377 | − | 0.999361i | \(-0.511378\pi\) | ||||
−0.0357377 | + | 0.999361i | \(0.511378\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.5598 | 0.895007 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 11.1287 | 0.405013 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −42.9548 | −1.56122 | −0.780610 | − | 0.625018i | \(-0.785092\pi\) | ||||
−0.780610 | + | 0.625018i | \(0.785092\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −45.3718 | −1.64689 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.6348 | 1.18301 | 0.591504 | − | 0.806302i | \(-0.298534\pi\) | ||||
0.591504 | + | 0.806302i | \(0.298534\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.5494 | −0.526725 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.914384 | 0.0330596 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.167148 | 0.00603535 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.1553 | −1.05137 | −0.525683 | − | 0.850680i | \(-0.676190\pi\) | ||||
−0.525683 | + | 0.850680i | \(0.676190\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.99001 | −0.359781 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 24.8016 | 0.892051 | 0.446026 | − | 0.895020i | \(-0.352839\pi\) | ||||
0.446026 | + | 0.895020i | \(0.352839\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.21716 | −0.331090 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.6471 | 0.704837 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.0711 | −0.826609 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 60.5491 | 2.16662 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −39.6764 | −1.41792 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12.4415 | 0.444057 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −35.1673 | −1.25358 | −0.626790 | − | 0.779189i | \(-0.715631\pi\) | ||||
−0.626790 | + | 0.779189i | \(0.715631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −33.7693 | −1.20222 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.8729 | −0.422152 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.55529 | 0.161763 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.7434 | 0.629294 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −3.45504 | −0.122384 | −0.0611919 | − | 0.998126i | \(-0.519490\pi\) | ||||
−0.0611919 | + | 0.998126i | \(0.519490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.5140 | 0.478091 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.39427 | −0.0492641 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.7777 | 0.415627 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.24465 | 0.255340 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.8434 | −0.416908 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 34.6555 | 1.21842 | 0.609211 | − | 0.793008i | \(-0.291486\pi\) | ||||
0.609211 | + | 0.793008i | \(0.291486\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −27.6538 | −0.971057 | −0.485528 | − | 0.874221i | \(-0.661373\pi\) | ||||
−0.485528 | + | 0.874221i | \(0.661373\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.78626 | −0.343219 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −12.1490 | −0.425560 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −41.6301 | −1.45645 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.114827 | −0.00401238 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.1004 | −1.22501 | −0.612505 | − | 0.790466i | \(-0.709838\pi\) | ||||
−0.612505 | + | 0.790466i | \(0.709838\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.1490 | −0.493204 | −0.246602 | − | 0.969117i | \(-0.579314\pi\) | ||||
−0.246602 | + | 0.969117i | \(0.579314\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7.49225 | 0.260847 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −54.1327 | −1.88238 | −0.941189 | − | 0.337880i | \(-0.890290\pi\) | ||||
−0.941189 | + | 0.337880i | \(0.890290\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.39897 | −0.291708 | −0.145854 | − | 0.989306i | \(-0.546593\pi\) | ||||
−0.145854 | + | 0.989306i | \(0.546593\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.5208 | 1.47503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.6813 | −0.612621 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.1773 | −0.386805 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −49.9084 | −1.72509 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.3732 | −0.703361 | −0.351681 | − | 0.936120i | \(-0.614390\pi\) | ||||
−0.351681 | + | 0.936120i | \(0.614390\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.6922 | 0.851456 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.69469 | −0.230577 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.8889 | 0.443392 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.6021 | 0.398653 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.1256 | 0.381831 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.3927 | 2.07024 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.6038 | −1.39025 | −0.695123 | − | 0.718891i | \(-0.744650\pi\) | ||||
−0.695123 | + | 0.718891i | \(0.744650\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.58177 | −0.0540953 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.5582 | 1.52208 | 0.761039 | − | 0.648706i | \(-0.224690\pi\) | ||||
0.761039 | + | 0.648706i | \(0.224690\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.1624 | 0.653812 | 0.326906 | − | 0.945057i | \(-0.393994\pi\) | ||||
0.326906 | + | 0.945057i | \(0.393994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.27550 | −0.282028 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −9.56387 | −0.325558 | −0.162779 | − | 0.986663i | \(-0.552046\pi\) | ||||
−0.162779 | + | 0.986663i | \(0.552046\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.82741 | 0.198138 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.3945 | 0.386979 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 31.9563 | 1.08404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.25422 | −0.144149 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.01781 | −0.0682926 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.19631 | −0.0404426 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.6092 | 1.06737 | 0.533684 | − | 0.845684i | \(-0.320807\pi\) | ||||
0.533684 | + | 0.845684i | \(0.320807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.93055 | −0.166303 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20.6076 | −0.694286 | −0.347143 | − | 0.937812i | \(-0.612848\pi\) | ||||
−0.347143 | + | 0.937812i | \(0.612848\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.9465 | 1.04143 | 0.520716 | − | 0.853730i | \(-0.325665\pi\) | ||||
0.520716 | + | 0.853730i | \(0.325665\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.825894 | 0.0277621 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −38.6004 | −1.29608 | −0.648038 | − | 0.761608i | \(-0.724410\pi\) | ||||
−0.648038 | + | 0.761608i | \(0.724410\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.03979 | −0.135490 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.6378 | 1.22741 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −23.3775 | −0.782298 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.1873 | 0.808493 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.32385 | 0.110980 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.5387 | 2.25254 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.2090 | 1.13967 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.9325 | −0.496923 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −10.9710 | −0.364687 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −29.6058 | −0.983044 | −0.491522 | − | 0.870865i | \(-0.663559\pi\) | ||||
−0.491522 | + | 0.870865i | \(0.663559\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.957062 | −0.0317437 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.60413 | −0.318199 | −0.159100 | − | 0.987263i | \(-0.550859\pi\) | ||||
−0.159100 | + | 0.987263i | \(0.550859\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 53.8290 | 1.78148 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 22.5082 | 0.744098 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.5488 | 0.480445 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.7499 | 0.387595 | 0.193797 | − | 0.981042i | \(-0.437920\pi\) | ||||
0.193797 | + | 0.981042i | \(0.437920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.00938 | 0.263918 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.43570 | −0.146003 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.97265 | −0.327899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −5.58389 | −0.183399 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15.0897 | −0.495078 | −0.247539 | − | 0.968878i | \(-0.579622\pi\) | ||||
−0.247539 | + | 0.968878i | \(0.579622\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.5864 | 1.00243 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −18.3186 | −0.599724 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 14.4449 | 0.472400 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.4595 | 0.897064 | 0.448532 | − | 0.893767i | \(-0.351947\pi\) | ||||
0.448532 | + | 0.893767i | \(0.351947\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0341 | −0.555888 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.0253 | 0.620208 | 0.310104 | − | 0.950703i | \(-0.399636\pi\) | ||||
0.310104 | + | 0.950703i | \(0.399636\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.4378 | −0.828369 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.47768 | −0.210719 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 12.7366 | 0.413884 | 0.206942 | − | 0.978353i | \(-0.433649\pi\) | ||||
0.206942 | + | 0.978353i | \(0.433649\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.862811 | −0.0280080 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.3438 | 1.17853 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −60.2907 | −1.95301 | −0.976504 | − | 0.215499i | \(-0.930862\pi\) | ||||
−0.976504 | + | 0.215499i | \(0.930862\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.6240 | −0.699735 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −54.8994 | −1.77465 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.2125 | −0.717280 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 53.9561 | 1.74052 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.45586 | −0.0469144 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.9764 | −0.771828 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.26848 | −0.0729496 | −0.0364748 | − | 0.999335i | \(-0.511613\pi\) | ||||
−0.0364748 | + | 0.999335i | \(0.511613\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 28.7182 | 0.922562 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 17.0183 | 0.546144 | 0.273072 | − | 0.961994i | \(-0.411960\pi\) | ||||
0.273072 | + | 0.961994i | \(0.411960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −25.2079 | −0.808128 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.548867 | −0.0175778 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 17.3760 | 0.555908 | 0.277954 | − | 0.960594i | \(-0.410344\pi\) | ||||
0.277954 | + | 0.960594i | \(0.410344\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −22.0259 | −0.703952 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.50253 | 0.111827 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −28.1829 | −0.898896 | −0.449448 | − | 0.893306i | \(-0.648379\pi\) | ||||
−0.449448 | + | 0.893306i | \(0.648379\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −5.45320 | −0.173753 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −8.38540 | −0.266910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −45.9006 | −1.45955 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.7891 | 0.723919 | 0.361959 | − | 0.932194i | \(-0.382108\pi\) | ||||
0.361959 | + | 0.932194i | \(0.382108\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.83146 | 0.216790 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.2752 | −0.611066 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.3945 | 0.424208 | 0.212104 | − | 0.977247i | \(-0.431968\pi\) | ||||
0.212104 | + | 0.977247i | \(0.431968\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −53.9991 | −1.70846 |
(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 | 8020.2.a.e.1.9 | ✓ | 35 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.e.1.9 | ✓ | 35 | 1.1 | even | 1 | trivial |