Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8001,2,Mod(1,8001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8001, 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("8001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8001 = 3^{2} \cdot 7 \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8001.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: | \(63.8883066572\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.512239 | 0.362207 | 0.181104 | − | 0.983464i | \(-0.442033\pi\) | ||||
0.181104 | + | 0.983464i | \(0.442033\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.73761 | −0.868806 | ||||||||
\(5\) | −1.76990 | −0.791522 | −0.395761 | − | 0.918353i | \(-0.629519\pi\) | ||||
−0.395761 | + | 0.918353i | \(0.629519\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | −1.91455 | −0.676895 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.906610 | −0.286695 | ||||||||
\(11\) | 4.52139 | 1.36325 | 0.681624 | − | 0.731702i | \(-0.261274\pi\) | ||||
0.681624 | + | 0.731702i | \(0.261274\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50554 | 1.24961 | 0.624806 | − | 0.780780i | \(-0.285178\pi\) | ||||
0.624806 | + | 0.780780i | \(0.285178\pi\) | |||||||
\(14\) | −0.512239 | −0.136902 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.49452 | 0.623629 | ||||||||
\(17\) | −5.81738 | −1.41092 | −0.705461 | − | 0.708749i | \(-0.749260\pi\) | ||||
−0.705461 | + | 0.708749i | \(0.749260\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.77727 | 1.55481 | 0.777406 | − | 0.628999i | \(-0.216535\pi\) | ||||
0.777406 | + | 0.628999i | \(0.216535\pi\) | |||||||
\(20\) | 3.07539 | 0.687679 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.31603 | 0.493779 | ||||||||
\(23\) | 0.708155 | 0.147660 | 0.0738302 | − | 0.997271i | \(-0.476478\pi\) | ||||
0.0738302 | + | 0.997271i | \(0.476478\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.86746 | −0.373492 | ||||||||
\(26\) | 2.30791 | 0.452619 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.73761 | 0.328378 | ||||||||
\(29\) | −8.00119 | −1.48578 | −0.742892 | − | 0.669412i | \(-0.766546\pi\) | ||||
−0.742892 | + | 0.669412i | \(0.766546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.44906 | 1.51750 | 0.758748 | − | 0.651384i | \(-0.225811\pi\) | ||||
0.758748 | + | 0.651384i | \(0.225811\pi\) | |||||||
\(32\) | 5.10689 | 0.902778 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.97989 | −0.511046 | ||||||||
\(35\) | 1.76990 | 0.299167 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.40518 | 0.231011 | 0.115505 | − | 0.993307i | \(-0.463151\pi\) | ||||
0.115505 | + | 0.993307i | \(0.463151\pi\) | |||||||
\(38\) | 3.47158 | 0.563165 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.38856 | 0.535778 | ||||||||
\(41\) | 3.06668 | 0.478936 | 0.239468 | − | 0.970904i | \(-0.423027\pi\) | ||||
0.239468 | + | 0.970904i | \(0.423027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.92263 | −0.598196 | −0.299098 | − | 0.954222i | \(-0.596686\pi\) | ||||
−0.299098 | + | 0.954222i | \(0.596686\pi\) | |||||||
\(44\) | −7.85641 | −1.18440 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.362744 | 0.0534837 | ||||||||
\(47\) | −9.77893 | −1.42640 | −0.713201 | − | 0.700959i | \(-0.752756\pi\) | ||||
−0.713201 | + | 0.700959i | \(0.752756\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.956586 | −0.135282 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.82888 | −1.08567 | ||||||||
\(53\) | 10.7565 | 1.47752 | 0.738758 | − | 0.673971i | \(-0.235413\pi\) | ||||
0.738758 | + | 0.673971i | \(0.235413\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.00239 | −1.07904 | ||||||||
\(56\) | 1.91455 | 0.255842 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.09852 | −0.538162 | ||||||||
\(59\) | −10.1623 | −1.32302 | −0.661508 | − | 0.749938i | \(-0.730083\pi\) | ||||
−0.661508 | + | 0.749938i | \(0.730083\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.39913 | −1.20344 | −0.601718 | − | 0.798709i | \(-0.705517\pi\) | ||||
−0.601718 | + | 0.798709i | \(0.705517\pi\) | |||||||
\(62\) | 4.32794 | 0.549649 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.37309 | −0.296636 | ||||||||
\(65\) | −7.97434 | −0.989095 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.67794 | −1.18235 | −0.591174 | − | 0.806544i | \(-0.701335\pi\) | ||||
−0.591174 | + | 0.806544i | \(0.701335\pi\) | |||||||
\(68\) | 10.1083 | 1.22582 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.906610 | 0.108361 | ||||||||
\(71\) | −7.71069 | −0.915091 | −0.457545 | − | 0.889186i | \(-0.651271\pi\) | ||||
−0.457545 | + | 0.889186i | \(0.651271\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.8339 | −1.73617 | −0.868087 | − | 0.496411i | \(-0.834651\pi\) | ||||
−0.868087 | + | 0.496411i | \(0.834651\pi\) | |||||||
\(74\) | 0.719789 | 0.0836738 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −11.7763 | −1.35083 | ||||||||
\(77\) | −4.52139 | −0.515260 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.3576 | 1.50284 | 0.751421 | − | 0.659823i | \(-0.229369\pi\) | ||||
0.751421 | + | 0.659823i | \(0.229369\pi\) | |||||||
\(80\) | −4.41504 | −0.493616 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.57087 | 0.173474 | ||||||||
\(83\) | 15.4133 | 1.69183 | 0.845916 | − | 0.533316i | \(-0.179054\pi\) | ||||
0.845916 | + | 0.533316i | \(0.179054\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 10.2962 | 1.11678 | ||||||||
\(86\) | −2.00932 | −0.216671 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.65641 | −0.922777 | ||||||||
\(89\) | 4.77308 | 0.505946 | 0.252973 | − | 0.967473i | \(-0.418592\pi\) | ||||
0.252973 | + | 0.967473i | \(0.418592\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.50554 | −0.472309 | ||||||||
\(92\) | −1.23050 | −0.128288 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.00914 | −0.516654 | ||||||||
\(95\) | −11.9951 | −1.23067 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.7708 | 1.09360 | 0.546802 | − | 0.837262i | \(-0.315845\pi\) | ||||
0.546802 | + | 0.837262i | \(0.315845\pi\) | |||||||
\(98\) | 0.512239 | 0.0517439 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.24492 | 0.324492 | ||||||||
\(101\) | −5.91868 | −0.588931 | −0.294465 | − | 0.955662i | \(-0.595142\pi\) | ||||
−0.294465 | + | 0.955662i | \(0.595142\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82386 | −0.278243 | −0.139122 | − | 0.990275i | \(-0.544428\pi\) | ||||
−0.139122 | + | 0.990275i | \(0.544428\pi\) | |||||||
\(104\) | −8.62608 | −0.845856 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.50988 | 0.535167 | ||||||||
\(107\) | 7.39664 | 0.715060 | 0.357530 | − | 0.933902i | \(-0.383619\pi\) | ||||
0.357530 | + | 0.933902i | \(0.383619\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.62604 | 0.634660 | 0.317330 | − | 0.948315i | \(-0.397214\pi\) | ||||
0.317330 | + | 0.948315i | \(0.397214\pi\) | |||||||
\(110\) | −4.09913 | −0.390837 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.49452 | −0.235710 | ||||||||
\(113\) | 10.0353 | 0.944043 | 0.472022 | − | 0.881587i | \(-0.343524\pi\) | ||||
0.472022 | + | 0.881587i | \(0.343524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.25336 | −0.116877 | ||||||||
\(116\) | 13.9030 | 1.29086 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.20551 | −0.479206 | ||||||||
\(119\) | 5.81738 | 0.533278 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.44292 | 0.858448 | ||||||||
\(122\) | −4.81460 | −0.435893 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.6812 | −1.31841 | ||||||||
\(125\) | 12.1547 | 1.08715 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.00000 | 0.0887357 | ||||||||
\(128\) | −11.4294 | −1.01022 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −4.08477 | −0.358258 | ||||||||
\(131\) | −8.12188 | −0.709612 | −0.354806 | − | 0.934940i | \(-0.615453\pi\) | ||||
−0.354806 | + | 0.934940i | \(0.615453\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.77727 | −0.587664 | ||||||||
\(134\) | −4.95741 | −0.428255 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 11.1377 | 0.955046 | ||||||||
\(137\) | 14.7897 | 1.26357 | 0.631783 | − | 0.775145i | \(-0.282323\pi\) | ||||
0.631783 | + | 0.775145i | \(0.282323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.6135 | 1.83323 | 0.916615 | − | 0.399772i | \(-0.130911\pi\) | ||||
0.916615 | + | 0.399772i | \(0.130911\pi\) | |||||||
\(140\) | −3.07539 | −0.259918 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.94971 | −0.331453 | ||||||||
\(143\) | 20.3713 | 1.70353 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1613 | 1.17603 | ||||||||
\(146\) | −7.59849 | −0.628855 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.44166 | −0.200703 | ||||||||
\(149\) | −4.37072 | −0.358063 | −0.179032 | − | 0.983843i | \(-0.557296\pi\) | ||||
−0.179032 | + | 0.983843i | \(0.557296\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.2661 | 0.835447 | 0.417723 | − | 0.908574i | \(-0.362828\pi\) | ||||
0.417723 | + | 0.908574i | \(0.362828\pi\) | |||||||
\(152\) | −12.9754 | −1.05245 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.31603 | −0.186631 | ||||||||
\(155\) | −14.9540 | −1.20113 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.6227 | 0.847784 | 0.423892 | − | 0.905713i | \(-0.360664\pi\) | ||||
0.423892 | + | 0.905713i | \(0.360664\pi\) | |||||||
\(158\) | 6.84226 | 0.544341 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.03867 | −0.714569 | ||||||||
\(161\) | −0.708155 | −0.0558104 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.3229 | 0.965201 | 0.482601 | − | 0.875840i | \(-0.339692\pi\) | ||||
0.482601 | + | 0.875840i | \(0.339692\pi\) | |||||||
\(164\) | −5.32870 | −0.416102 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.89530 | 0.612794 | ||||||||
\(167\) | −12.8824 | −0.996867 | −0.498434 | − | 0.866928i | \(-0.666091\pi\) | ||||
−0.498434 | + | 0.866928i | \(0.666091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.29988 | 0.561529 | ||||||||
\(170\) | 5.27409 | 0.404505 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6.81601 | 0.519716 | ||||||||
\(173\) | 24.6030 | 1.87053 | 0.935267 | − | 0.353944i | \(-0.115160\pi\) | ||||
0.935267 | + | 0.353944i | \(0.115160\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.86746 | 0.141167 | ||||||||
\(176\) | 11.2787 | 0.850162 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.44496 | 0.183257 | ||||||||
\(179\) | −18.6149 | −1.39135 | −0.695673 | − | 0.718359i | \(-0.744894\pi\) | ||||
−0.695673 | + | 0.718359i | \(0.744894\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −17.2959 | −1.28559 | −0.642797 | − | 0.766037i | \(-0.722226\pi\) | ||||
−0.642797 | + | 0.766037i | \(0.722226\pi\) | |||||||
\(182\) | −2.30791 | −0.171074 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.35580 | −0.0999507 | ||||||||
\(185\) | −2.48703 | −0.182850 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −26.3026 | −1.92344 | ||||||||
\(188\) | 16.9920 | 1.23927 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.14434 | −0.445757 | ||||||||
\(191\) | −5.42727 | −0.392704 | −0.196352 | − | 0.980534i | \(-0.562909\pi\) | ||||
−0.196352 | + | 0.980534i | \(0.562909\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.7520 | 1.85367 | 0.926836 | − | 0.375466i | \(-0.122517\pi\) | ||||
0.926836 | + | 0.375466i | \(0.122517\pi\) | |||||||
\(194\) | 5.51720 | 0.396112 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.73761 | −0.124115 | ||||||||
\(197\) | 5.11687 | 0.364562 | 0.182281 | − | 0.983247i | \(-0.441652\pi\) | ||||
0.182281 | + | 0.983247i | \(0.441652\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8835 | −1.40950 | −0.704751 | − | 0.709455i | \(-0.748941\pi\) | ||||
−0.704751 | + | 0.709455i | \(0.748941\pi\) | |||||||
\(200\) | 3.57535 | 0.252815 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.03178 | −0.213315 | ||||||||
\(203\) | 8.00119 | 0.561573 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.42772 | −0.379088 | ||||||||
\(206\) | −1.44649 | −0.100782 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.2391 | 0.779294 | ||||||||
\(209\) | 30.6427 | 2.11960 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.94855 | −0.134144 | −0.0670718 | − | 0.997748i | \(-0.521366\pi\) | ||||
−0.0670718 | + | 0.997748i | \(0.521366\pi\) | |||||||
\(212\) | −18.6906 | −1.28367 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.78884 | 0.259000 | ||||||||
\(215\) | 6.94266 | 0.473485 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.44906 | −0.573560 | ||||||||
\(218\) | 3.39412 | 0.229879 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 13.9050 | 0.937478 | ||||||||
\(221\) | −26.2104 | −1.76310 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.65436 | −0.646504 | −0.323252 | − | 0.946313i | \(-0.604776\pi\) | ||||
−0.323252 | + | 0.946313i | \(0.604776\pi\) | |||||||
\(224\) | −5.10689 | −0.341218 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.14048 | 0.341940 | ||||||||
\(227\) | 1.02714 | 0.0681735 | 0.0340867 | − | 0.999419i | \(-0.489148\pi\) | ||||
0.0340867 | + | 0.999419i | \(0.489148\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 27.5983 | 1.82375 | 0.911875 | − | 0.410468i | \(-0.134635\pi\) | ||||
0.911875 | + | 0.410468i | \(0.134635\pi\) | |||||||
\(230\) | −0.642020 | −0.0423335 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 15.3187 | 1.00572 | ||||||||
\(233\) | −20.8738 | −1.36749 | −0.683745 | − | 0.729721i | \(-0.739650\pi\) | ||||
−0.683745 | + | 0.729721i | \(0.739650\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 17.3077 | 1.12903 | ||||||||
\(236\) | 17.6581 | 1.14944 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.97989 | 0.193157 | ||||||||
\(239\) | −1.60427 | −0.103772 | −0.0518859 | − | 0.998653i | \(-0.516523\pi\) | ||||
−0.0518859 | + | 0.998653i | \(0.516523\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.27009 | 0.146229 | 0.0731147 | − | 0.997324i | \(-0.476706\pi\) | ||||
0.0731147 | + | 0.997324i | \(0.476706\pi\) | |||||||
\(242\) | 4.83703 | 0.310936 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 16.3320 | 1.04555 | ||||||||
\(245\) | −1.76990 | −0.113075 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.5353 | 1.94291 | ||||||||
\(248\) | −16.1761 | −1.02719 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.22611 | 0.393774 | ||||||||
\(251\) | −1.10118 | −0.0695059 | −0.0347529 | − | 0.999396i | \(-0.511064\pi\) | ||||
−0.0347529 | + | 0.999396i | \(0.511064\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.20184 | 0.201298 | ||||||||
\(254\) | 0.512239 | 0.0321407 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.10838 | −0.0692739 | ||||||||
\(257\) | −12.7463 | −0.795095 | −0.397547 | − | 0.917582i | \(-0.630139\pi\) | ||||
−0.397547 | + | 0.917582i | \(0.630139\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.40518 | −0.0873138 | ||||||||
\(260\) | 13.8563 | 0.859332 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.16034 | −0.257027 | ||||||||
\(263\) | −3.52690 | −0.217478 | −0.108739 | − | 0.994070i | \(-0.534681\pi\) | ||||
−0.108739 | + | 0.994070i | \(0.534681\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −19.0379 | −1.16949 | ||||||||
\(266\) | −3.47158 | −0.212856 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 16.8165 | 1.02723 | ||||||||
\(269\) | 26.5855 | 1.62095 | 0.810474 | − | 0.585775i | \(-0.199210\pi\) | ||||
0.810474 | + | 0.585775i | \(0.199210\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.6486 | 1.67953 | 0.839767 | − | 0.542948i | \(-0.182692\pi\) | ||||
0.839767 | + | 0.542948i | \(0.182692\pi\) | |||||||
\(272\) | −14.5115 | −0.879892 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.57584 | 0.457673 | ||||||||
\(275\) | −8.44352 | −0.509163 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.46296 | −0.388321 | −0.194161 | − | 0.980970i | \(-0.562198\pi\) | ||||
−0.194161 | + | 0.980970i | \(0.562198\pi\) | |||||||
\(278\) | 11.0712 | 0.664009 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −3.38856 | −0.202505 | ||||||||
\(281\) | −10.9292 | −0.651983 | −0.325991 | − | 0.945373i | \(-0.605698\pi\) | ||||
−0.325991 | + | 0.945373i | \(0.605698\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.49884 | 0.326872 | 0.163436 | − | 0.986554i | \(-0.447742\pi\) | ||||
0.163436 | + | 0.986554i | \(0.447742\pi\) | |||||||
\(284\) | 13.3982 | 0.795036 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.4350 | 0.617032 | ||||||||
\(287\) | −3.06668 | −0.181021 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.8419 | 0.990699 | ||||||||
\(290\) | 7.25396 | 0.425967 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 25.7755 | 1.50840 | ||||||||
\(293\) | 15.2212 | 0.889234 | 0.444617 | − | 0.895721i | \(-0.353340\pi\) | ||||
0.444617 | + | 0.895721i | \(0.353340\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9862 | 1.04720 | ||||||||
\(296\) | −2.69029 | −0.156370 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.23885 | −0.129693 | ||||||||
\(299\) | 3.19062 | 0.184518 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.92263 | 0.226097 | ||||||||
\(302\) | 5.25872 | 0.302605 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 16.9060 | 0.969627 | ||||||||
\(305\) | 16.6355 | 0.952546 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −17.3444 | −0.989897 | −0.494948 | − | 0.868922i | \(-0.664813\pi\) | ||||
−0.494948 | + | 0.868922i | \(0.664813\pi\) | |||||||
\(308\) | 7.85641 | 0.447661 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.66001 | −0.435059 | ||||||||
\(311\) | 9.58784 | 0.543676 | 0.271838 | − | 0.962343i | \(-0.412368\pi\) | ||||
0.271838 | + | 0.962343i | \(0.412368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3451 | 1.88478 | 0.942388 | − | 0.334523i | \(-0.108575\pi\) | ||||
0.942388 | + | 0.334523i | \(0.108575\pi\) | |||||||
\(314\) | 5.44136 | 0.307074 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.2102 | −1.30568 | ||||||||
\(317\) | 25.9435 | 1.45713 | 0.728566 | − | 0.684976i | \(-0.240187\pi\) | ||||
0.728566 | + | 0.684976i | \(0.240187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −36.1764 | −2.02549 | ||||||||
\(320\) | 4.20013 | 0.234794 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.362744 | −0.0202149 | ||||||||
\(323\) | −39.4260 | −2.19372 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.41392 | −0.466721 | ||||||||
\(326\) | 6.31225 | 0.349603 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.87132 | −0.324189 | ||||||||
\(329\) | 9.77893 | 0.539130 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.2177 | 1.44105 | 0.720527 | − | 0.693427i | \(-0.243900\pi\) | ||||
0.720527 | + | 0.693427i | \(0.243900\pi\) | |||||||
\(332\) | −26.7824 | −1.46987 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −6.59885 | −0.361073 | ||||||||
\(335\) | 17.1290 | 0.935855 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.2457 | −1.21180 | −0.605901 | − | 0.795540i | \(-0.707187\pi\) | ||||
−0.605901 | + | 0.795540i | \(0.707187\pi\) | |||||||
\(338\) | 3.73928 | 0.203390 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −17.8907 | −0.970261 | ||||||||
\(341\) | 38.2015 | 2.06873 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 7.51007 | 0.404916 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 12.6026 | 0.677521 | ||||||||
\(347\) | −25.4988 | −1.36885 | −0.684423 | − | 0.729085i | \(-0.739946\pi\) | ||||
−0.684423 | + | 0.729085i | \(0.739946\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.4861 | 0.989536 | 0.494768 | − | 0.869025i | \(-0.335253\pi\) | ||||
0.494768 | + | 0.869025i | \(0.335253\pi\) | |||||||
\(350\) | 0.956586 | 0.0511317 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.0902 | 1.23071 | ||||||||
\(353\) | 13.1753 | 0.701251 | 0.350626 | − | 0.936516i | \(-0.385969\pi\) | ||||
0.350626 | + | 0.936516i | \(0.385969\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.6471 | 0.724315 | ||||||||
\(356\) | −8.29377 | −0.439569 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.53529 | −0.503956 | ||||||||
\(359\) | 22.4620 | 1.18550 | 0.592750 | − | 0.805387i | \(-0.298042\pi\) | ||||
0.592750 | + | 0.805387i | \(0.298042\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 26.9314 | 1.41744 | ||||||||
\(362\) | −8.85962 | −0.465651 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 7.82888 | 0.410345 | ||||||||
\(365\) | 26.2545 | 1.37422 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.0265 | 1.04537 | 0.522687 | − | 0.852524i | \(-0.324929\pi\) | ||||
0.522687 | + | 0.852524i | \(0.324929\pi\) | |||||||
\(368\) | 1.76650 | 0.0920854 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.27395 | −0.0662297 | ||||||||
\(371\) | −10.7565 | −0.558448 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.24279 | −0.323239 | −0.161620 | − | 0.986853i | \(-0.551672\pi\) | ||||
−0.161620 | + | 0.986853i | \(0.551672\pi\) | |||||||
\(374\) | −13.4732 | −0.696683 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.7222 | 0.965526 | ||||||||
\(377\) | −36.0497 | −1.85665 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.99359 | 0.205137 | 0.102568 | − | 0.994726i | \(-0.467294\pi\) | ||||
0.102568 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(380\) | 20.8428 | 1.06921 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.78006 | −0.142240 | ||||||||
\(383\) | −20.9510 | −1.07055 | −0.535274 | − | 0.844679i | \(-0.679792\pi\) | ||||
−0.535274 | + | 0.844679i | \(0.679792\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.00239 | 0.407840 | ||||||||
\(386\) | 13.1912 | 0.671414 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.7154 | −0.950130 | ||||||||
\(389\) | 26.6789 | 1.35267 | 0.676337 | − | 0.736592i | \(-0.263566\pi\) | ||||
0.676337 | + | 0.736592i | \(0.263566\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.11960 | −0.208337 | ||||||||
\(392\) | −1.91455 | −0.0966993 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.62106 | 0.132047 | ||||||||
\(395\) | −23.6415 | −1.18953 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.2639 | −1.26796 | −0.633980 | − | 0.773350i | \(-0.718580\pi\) | ||||
−0.633980 | + | 0.773350i | \(0.718580\pi\) | |||||||
\(398\) | −10.1851 | −0.510532 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.65842 | −0.232921 | ||||||||
\(401\) | 4.62871 | 0.231147 | 0.115573 | − | 0.993299i | \(-0.463129\pi\) | ||||
0.115573 | + | 0.993299i | \(0.463129\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 38.0676 | 1.89628 | ||||||||
\(404\) | 10.2844 | 0.511666 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.09852 | 0.203406 | ||||||||
\(407\) | 6.35337 | 0.314925 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.67492 | −0.428947 | −0.214474 | − | 0.976730i | \(-0.568804\pi\) | ||||
−0.214474 | + | 0.976730i | \(0.568804\pi\) | |||||||
\(410\) | −2.78029 | −0.137309 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.90678 | 0.241740 | ||||||||
\(413\) | 10.1623 | 0.500053 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.2800 | −1.33912 | ||||||||
\(416\) | 23.0093 | 1.12812 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 15.6964 | 0.767734 | ||||||||
\(419\) | 6.05288 | 0.295703 | 0.147851 | − | 0.989010i | \(-0.452764\pi\) | ||||
0.147851 | + | 0.989010i | \(0.452764\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.79082 | −0.330964 | −0.165482 | − | 0.986213i | \(-0.552918\pi\) | ||||
−0.165482 | + | 0.986213i | \(0.552918\pi\) | |||||||
\(422\) | −0.998121 | −0.0485878 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −20.5938 | −1.00012 | ||||||||
\(425\) | 10.8637 | 0.526969 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.39913 | 0.454856 | ||||||||
\(428\) | −12.8525 | −0.621248 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.55630 | 0.171500 | ||||||||
\(431\) | −0.560045 | −0.0269764 | −0.0134882 | − | 0.999909i | \(-0.504294\pi\) | ||||
−0.0134882 | + | 0.999909i | \(0.504294\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6991 | 1.23502 | 0.617509 | − | 0.786564i | \(-0.288142\pi\) | ||||
0.617509 | + | 0.786564i | \(0.288142\pi\) | |||||||
\(434\) | −4.32794 | −0.207748 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −11.5135 | −0.551396 | ||||||||
\(437\) | 4.79936 | 0.229584 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.51782 | −0.167896 | −0.0839482 | − | 0.996470i | \(-0.526753\pi\) | ||||
−0.0839482 | + | 0.996470i | \(0.526753\pi\) | |||||||
\(440\) | 15.3210 | 0.730398 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.4260 | −0.638609 | ||||||||
\(443\) | 14.9106 | 0.708426 | 0.354213 | − | 0.935165i | \(-0.384749\pi\) | ||||
0.354213 | + | 0.935165i | \(0.384749\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.44787 | −0.400468 | ||||||||
\(446\) | −4.94533 | −0.234168 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.37309 | 0.112118 | ||||||||
\(449\) | −33.5903 | −1.58522 | −0.792612 | − | 0.609727i | \(-0.791279\pi\) | ||||
−0.792612 | + | 0.609727i | \(0.791279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.8657 | 0.652908 | ||||||||
\(452\) | −17.4375 | −0.820190 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.526139 | 0.0246929 | ||||||||
\(455\) | 7.97434 | 0.373843 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.2864 | −0.621511 | −0.310756 | − | 0.950490i | \(-0.600582\pi\) | ||||
−0.310756 | + | 0.950490i | \(0.600582\pi\) | |||||||
\(458\) | 14.1369 | 0.660576 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.17785 | 0.101543 | ||||||||
\(461\) | 20.5088 | 0.955191 | 0.477595 | − | 0.878580i | \(-0.341509\pi\) | ||||
0.477595 | + | 0.878580i | \(0.341509\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.6108 | −0.911392 | −0.455696 | − | 0.890135i | \(-0.650610\pi\) | ||||
−0.455696 | + | 0.890135i | \(0.650610\pi\) | |||||||
\(464\) | −19.9591 | −0.926578 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.6924 | −0.495315 | ||||||||
\(467\) | 19.6880 | 0.911053 | 0.455526 | − | 0.890222i | \(-0.349451\pi\) | ||||
0.455526 | + | 0.890222i | \(0.349451\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 9.67794 | 0.446886 | ||||||||
\(470\) | 8.86567 | 0.408943 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 19.4562 | 0.895543 | ||||||||
\(473\) | −17.7357 | −0.815490 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.6563 | −0.580711 | ||||||||
\(476\) | −10.1083 | −0.463315 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −0.821770 | −0.0375869 | ||||||||
\(479\) | 20.8553 | 0.952904 | 0.476452 | − | 0.879200i | \(-0.341923\pi\) | ||||
0.476452 | + | 0.879200i | \(0.341923\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.33111 | 0.288674 | ||||||||
\(482\) | 1.16283 | 0.0529654 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −16.4081 | −0.745824 | ||||||||
\(485\) | −19.0631 | −0.865612 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.76655 | −0.397250 | −0.198625 | − | 0.980076i | \(-0.563648\pi\) | ||||
−0.198625 | + | 0.980076i | \(0.563648\pi\) | |||||||
\(488\) | 17.9951 | 0.814600 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.906610 | −0.0409565 | ||||||||
\(491\) | −14.8972 | −0.672299 | −0.336150 | − | 0.941809i | \(-0.609125\pi\) | ||||
−0.336150 | + | 0.941809i | \(0.609125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.5459 | 2.09632 | ||||||||
\(494\) | 15.6413 | 0.703737 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 21.0763 | 0.946355 | ||||||||
\(497\) | 7.71069 | 0.345872 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.1802 | 1.30629 | 0.653143 | − | 0.757235i | \(-0.273450\pi\) | ||||
0.653143 | + | 0.757235i | \(0.273450\pi\) | |||||||
\(500\) | −21.1202 | −0.944522 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.564067 | −0.0251756 | ||||||||
\(503\) | −23.4436 | −1.04530 | −0.522650 | − | 0.852547i | \(-0.675057\pi\) | ||||
−0.522650 | + | 0.852547i | \(0.675057\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4755 | 0.466152 | ||||||||
\(506\) | 1.64011 | 0.0729116 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.73761 | −0.0770940 | ||||||||
\(509\) | 7.08841 | 0.314188 | 0.157094 | − | 0.987584i | \(-0.449787\pi\) | ||||
0.157094 | + | 0.987584i | \(0.449787\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.8339 | 0.656212 | ||||||||
\(512\) | 22.2910 | 0.985131 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.52917 | −0.287989 | ||||||||
\(515\) | 4.99795 | 0.220236 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −44.2143 | −1.94454 | ||||||||
\(518\) | −0.719789 | −0.0316257 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 15.2673 | 0.669514 | ||||||||
\(521\) | −9.75971 | −0.427581 | −0.213790 | − | 0.976880i | \(-0.568581\pi\) | ||||
−0.213790 | + | 0.976880i | \(0.568581\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 32.8898 | 1.43817 | 0.719086 | − | 0.694921i | \(-0.244561\pi\) | ||||
0.719086 | + | 0.694921i | \(0.244561\pi\) | |||||||
\(524\) | 14.1127 | 0.616515 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.80662 | −0.0787722 | ||||||||
\(527\) | −49.1514 | −2.14107 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.4985 | −0.978196 | ||||||||
\(530\) | −9.75193 | −0.423597 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 11.7763 | 0.510566 | ||||||||
\(533\) | 13.8171 | 0.598483 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.0913 | −0.565986 | ||||||||
\(536\) | 18.5289 | 0.800326 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 13.6181 | 0.587119 | ||||||||
\(539\) | 4.52139 | 0.194750 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.9664 | −0.901414 | −0.450707 | − | 0.892672i | \(-0.648828\pi\) | ||||
−0.450707 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(542\) | 14.1627 | 0.608339 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −29.7087 | −1.27375 | ||||||||
\(545\) | −11.7274 | −0.502347 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.7390 | 1.22879 | 0.614395 | − | 0.788998i | \(-0.289400\pi\) | ||||
0.614395 | + | 0.788998i | \(0.289400\pi\) | |||||||
\(548\) | −25.6987 | −1.09779 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.32510 | −0.184423 | ||||||||
\(551\) | −54.2262 | −2.31011 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.3576 | −0.568021 | ||||||||
\(554\) | −3.31058 | −0.140653 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −37.5558 | −1.59272 | ||||||||
\(557\) | 31.6142 | 1.33954 | 0.669769 | − | 0.742570i | \(-0.266393\pi\) | ||||
0.669769 | + | 0.742570i | \(0.266393\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.6736 | −0.747512 | ||||||||
\(560\) | 4.41504 | 0.186569 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.59837 | −0.236153 | ||||||||
\(563\) | 8.46335 | 0.356688 | 0.178344 | − | 0.983968i | \(-0.442926\pi\) | ||||
0.178344 | + | 0.983968i | \(0.442926\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −17.7615 | −0.747231 | ||||||||
\(566\) | 2.81672 | 0.118396 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 14.7625 | 0.619421 | ||||||||
\(569\) | −21.5578 | −0.903751 | −0.451875 | − | 0.892081i | \(-0.649245\pi\) | ||||
−0.451875 | + | 0.892081i | \(0.649245\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.14040 | 0.256968 | 0.128484 | − | 0.991712i | \(-0.458989\pi\) | ||||
0.128484 | + | 0.991712i | \(0.458989\pi\) | |||||||
\(572\) | −35.3974 | −1.48004 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.57087 | −0.0655670 | ||||||||
\(575\) | −1.32245 | −0.0551501 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.78498 | −0.115940 | −0.0579701 | − | 0.998318i | \(-0.518463\pi\) | ||||
−0.0579701 | + | 0.998318i | \(0.518463\pi\) | |||||||
\(578\) | 8.62707 | 0.358839 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −24.6068 | −1.02174 | ||||||||
\(581\) | −15.4133 | −0.639452 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 48.6342 | 2.01422 | ||||||||
\(584\) | 28.4002 | 1.17521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.79690 | 0.322087 | ||||||||
\(587\) | −8.46781 | −0.349504 | −0.174752 | − | 0.984612i | \(-0.555912\pi\) | ||||
−0.174752 | + | 0.984612i | \(0.555912\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 57.2616 | 2.35942 | ||||||||
\(590\) | 9.21322 | 0.379302 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.50525 | 0.144065 | ||||||||
\(593\) | −12.5095 | −0.513704 | −0.256852 | − | 0.966451i | \(-0.582685\pi\) | ||||
−0.256852 | + | 0.966451i | \(0.582685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −10.2962 | −0.422102 | ||||||||
\(596\) | 7.59461 | 0.311087 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.63436 | 0.0668339 | ||||||||
\(599\) | −46.3136 | −1.89232 | −0.946161 | − | 0.323695i | \(-0.895075\pi\) | ||||
−0.946161 | + | 0.323695i | \(0.895075\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.5205 | 1.00021 | 0.500106 | − | 0.865964i | \(-0.333294\pi\) | ||||
0.500106 | + | 0.865964i | \(0.333294\pi\) | |||||||
\(602\) | 2.00932 | 0.0818939 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.8386 | −0.725841 | ||||||||
\(605\) | −16.7130 | −0.679480 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7627 | 0.477434 | 0.238717 | − | 0.971089i | \(-0.423273\pi\) | ||||
0.238717 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(608\) | 34.6108 | 1.40365 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.52135 | 0.345019 | ||||||||
\(611\) | −44.0593 | −1.78245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 30.9049 | 1.24824 | 0.624119 | − | 0.781329i | \(-0.285458\pi\) | ||||
0.624119 | + | 0.781329i | \(0.285458\pi\) | |||||||
\(614\) | −8.88447 | −0.358548 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.65641 | 0.348777 | ||||||||
\(617\) | 13.1853 | 0.530819 | 0.265409 | − | 0.964136i | \(-0.414493\pi\) | ||||
0.265409 | + | 0.964136i | \(0.414493\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.45213 | 0.379913 | 0.189957 | − | 0.981792i | \(-0.439165\pi\) | ||||
0.189957 | + | 0.981792i | \(0.439165\pi\) | |||||||
\(620\) | 25.9842 | 1.04355 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4.91126 | 0.196924 | ||||||||
\(623\) | −4.77308 | −0.191230 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.1753 | −0.487011 | ||||||||
\(626\) | 17.0806 | 0.682680 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.4581 | −0.736559 | ||||||||
\(629\) | −8.17448 | −0.325938 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.85549 | −0.193294 | −0.0966471 | − | 0.995319i | \(-0.530812\pi\) | ||||
−0.0966471 | + | 0.995319i | \(0.530812\pi\) | |||||||
\(632\) | −25.5737 | −1.01727 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.2893 | 0.527784 | ||||||||
\(635\) | −1.76990 | −0.0702362 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.50554 | 0.178516 | ||||||||
\(638\) | −18.5310 | −0.733648 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 20.2288 | 0.799613 | ||||||||
\(641\) | −15.7405 | −0.621714 | −0.310857 | − | 0.950457i | \(-0.600616\pi\) | ||||
−0.310857 | + | 0.950457i | \(0.600616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −15.8560 | −0.625301 | −0.312650 | − | 0.949868i | \(-0.601217\pi\) | ||||
−0.312650 | + | 0.949868i | \(0.601217\pi\) | |||||||
\(644\) | 1.23050 | 0.0484884 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −20.1955 | −0.794581 | ||||||||
\(647\) | 15.1236 | 0.594568 | 0.297284 | − | 0.954789i | \(-0.403919\pi\) | ||||
0.297284 | + | 0.954789i | \(0.403919\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.9476 | −1.80360 | ||||||||
\(650\) | −4.30994 | −0.169050 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.4124 | −0.838573 | ||||||||
\(653\) | −20.8010 | −0.814005 | −0.407002 | − | 0.913427i | \(-0.633426\pi\) | ||||
−0.407002 | + | 0.913427i | \(0.633426\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.3749 | 0.561674 | ||||||||
\(656\) | 7.64989 | 0.298678 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.00914 | 0.195277 | ||||||||
\(659\) | 31.6785 | 1.23402 | 0.617009 | − | 0.786956i | \(-0.288344\pi\) | ||||
0.617009 | + | 0.786956i | \(0.288344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.8992 | 1.70748 | 0.853741 | − | 0.520699i | \(-0.174328\pi\) | ||||
0.853741 | + | 0.520699i | \(0.174328\pi\) | |||||||
\(662\) | 13.4297 | 0.521961 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −29.5096 | −1.14519 | ||||||||
\(665\) | 11.9951 | 0.465149 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.66608 | −0.219391 | ||||||||
\(668\) | 22.3845 | 0.866084 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.77411 | 0.338974 | ||||||||
\(671\) | −42.4971 | −1.64058 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7216 | −0.683119 | −0.341559 | − | 0.939860i | \(-0.610955\pi\) | ||||
−0.341559 | + | 0.939860i | \(0.610955\pi\) | |||||||
\(674\) | −11.3951 | −0.438923 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.6844 | −0.487860 | ||||||||
\(677\) | −12.4005 | −0.476588 | −0.238294 | − | 0.971193i | \(-0.576588\pi\) | ||||
−0.238294 | + | 0.971193i | \(0.576588\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7708 | −0.413344 | ||||||||
\(680\) | −19.7125 | −0.755940 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 19.5683 | 0.749308 | ||||||||
\(683\) | −1.68638 | −0.0645277 | −0.0322638 | − | 0.999479i | \(-0.510272\pi\) | ||||
−0.0322638 | + | 0.999479i | \(0.510272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.1762 | −1.00014 | ||||||||
\(686\) | −0.512239 | −0.0195574 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −9.78507 | −0.373052 | ||||||||
\(689\) | 48.4637 | 1.84632 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 25.0625 | 0.953421 | 0.476711 | − | 0.879060i | \(-0.341829\pi\) | ||||
0.476711 | + | 0.879060i | \(0.341829\pi\) | |||||||
\(692\) | −42.7505 | −1.62513 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.0615 | −0.495807 | ||||||||
\(695\) | −38.2536 | −1.45104 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.8401 | −0.675740 | ||||||||
\(698\) | 9.46927 | 0.358417 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.24492 | −0.122647 | ||||||||
\(701\) | −10.7055 | −0.404341 | −0.202170 | − | 0.979350i | \(-0.564799\pi\) | ||||
−0.202170 | + | 0.979350i | \(0.564799\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 9.52331 | 0.359178 | ||||||||
\(704\) | −10.7297 | −0.404389 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.74891 | 0.253998 | ||||||||
\(707\) | 5.91868 | 0.222595 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 36.9834 | 1.38894 | 0.694471 | − | 0.719521i | \(-0.255639\pi\) | ||||
0.694471 | + | 0.719521i | \(0.255639\pi\) | |||||||
\(710\) | 6.99059 | 0.262352 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.13831 | −0.342472 | ||||||||
\(713\) | 5.98324 | 0.224074 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −36.0551 | −1.34838 | ||||||||
\(716\) | 32.3455 | 1.20881 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.5059 | 0.429397 | ||||||||
\(719\) | 19.8493 | 0.740253 | 0.370127 | − | 0.928981i | \(-0.379314\pi\) | ||||
0.370127 | + | 0.928981i | \(0.379314\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.82386 | 0.105166 | ||||||||
\(722\) | 13.7953 | 0.513408 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 30.0535 | 1.11693 | ||||||||
\(725\) | 14.9419 | 0.554929 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.7556 | 0.918133 | 0.459066 | − | 0.888402i | \(-0.348184\pi\) | ||||
0.459066 | + | 0.888402i | \(0.348184\pi\) | |||||||
\(728\) | 8.62608 | 0.319704 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 13.4485 | 0.497753 | ||||||||
\(731\) | 22.8194 | 0.844007 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.8614 | 1.69393 | 0.846964 | − | 0.531650i | \(-0.178428\pi\) | ||||
0.846964 | + | 0.531650i | \(0.178428\pi\) | |||||||
\(734\) | 10.2583 | 0.378643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.61647 | 0.133305 | ||||||||
\(737\) | −43.7577 | −1.61183 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.00988 | 0.257863 | 0.128931 | − | 0.991654i | \(-0.458845\pi\) | ||||
0.128931 | + | 0.991654i | \(0.458845\pi\) | |||||||
\(740\) | 4.32149 | 0.158861 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.50988 | −0.202274 | ||||||||
\(743\) | −39.8673 | −1.46259 | −0.731295 | − | 0.682062i | \(-0.761084\pi\) | ||||
−0.731295 | + | 0.682062i | \(0.761084\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.73573 | 0.283415 | ||||||||
\(746\) | −3.19780 | −0.117080 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 45.7037 | 1.67109 | ||||||||
\(749\) | −7.39664 | −0.270267 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38.8090 | 1.41616 | 0.708081 | − | 0.706131i | \(-0.249561\pi\) | ||||
0.708081 | + | 0.706131i | \(0.249561\pi\) | |||||||
\(752\) | −24.3937 | −0.889547 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −18.4660 | −0.672493 | ||||||||
\(755\) | −18.1700 | −0.661275 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −21.5550 | −0.783431 | −0.391715 | − | 0.920086i | \(-0.628118\pi\) | ||||
−0.391715 | + | 0.920086i | \(0.628118\pi\) | |||||||
\(758\) | 2.04567 | 0.0743021 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 22.9652 | 0.833034 | ||||||||
\(761\) | 52.8809 | 1.91693 | 0.958466 | − | 0.285208i | \(-0.0920628\pi\) | ||||
0.958466 | + | 0.285208i | \(0.0920628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.62604 | −0.239879 | ||||||||
\(764\) | 9.43049 | 0.341183 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.7319 | −0.387760 | ||||||||
\(767\) | −45.7865 | −1.65326 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.78240 | 0.280641 | 0.140320 | − | 0.990106i | \(-0.455187\pi\) | ||||
0.140320 | + | 0.990106i | \(0.455187\pi\) | |||||||
\(770\) | 4.09913 | 0.147723 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −44.7470 | −1.61048 | ||||||||
\(773\) | −1.15634 | −0.0415908 | −0.0207954 | − | 0.999784i | \(-0.506620\pi\) | ||||
−0.0207954 | + | 0.999784i | \(0.506620\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −15.7783 | −0.566774 | ||||||||
\(776\) | −20.6211 | −0.740256 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.6660 | 0.489949 | ||||||||
\(779\) | 20.7837 | 0.744655 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.8630 | −1.24750 | ||||||||
\(782\) | −2.11022 | −0.0754613 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.49452 | 0.0890899 | ||||||||
\(785\) | −18.8011 | −0.671040 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.3058 | −0.474301 | −0.237150 | − | 0.971473i | \(-0.576213\pi\) | ||||
−0.237150 | + | 0.971473i | \(0.576213\pi\) | |||||||
\(788\) | −8.89113 | −0.316733 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12.1101 | −0.430858 | ||||||||
\(791\) | −10.0353 | −0.356815 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −42.3482 | −1.50383 | ||||||||
\(794\) | −12.9412 | −0.459264 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 34.5498 | 1.22458 | ||||||||
\(797\) | −30.0527 | −1.06452 | −0.532260 | − | 0.846581i | \(-0.678657\pi\) | ||||
−0.532260 | + | 0.846581i | \(0.678657\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 56.8877 | 2.01254 | ||||||||
\(800\) | −9.53692 | −0.337181 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.37100 | 0.0837230 | ||||||||
\(803\) | −67.0697 | −2.36684 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.25336 | 0.0441752 | ||||||||
\(806\) | 19.4997 | 0.686847 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 11.3316 | 0.398644 | ||||||||
\(809\) | −2.96928 | −0.104394 | −0.0521972 | − | 0.998637i | \(-0.516622\pi\) | ||||
−0.0521972 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.1036 | −1.47846 | −0.739229 | − | 0.673454i | \(-0.764810\pi\) | ||||
−0.739229 | + | 0.673454i | \(0.764810\pi\) | |||||||
\(812\) | −13.9030 | −0.487898 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.25444 | 0.114068 | ||||||||
\(815\) | −21.8102 | −0.763978 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −26.5847 | −0.930082 | ||||||||
\(818\) | −4.44363 | −0.155368 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.43126 | 0.329354 | ||||||||
\(821\) | 33.9197 | 1.18381 | 0.591903 | − | 0.806009i | \(-0.298377\pi\) | ||||
0.591903 | + | 0.806009i | \(0.298377\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.8587 | −0.692230 | −0.346115 | − | 0.938192i | \(-0.612499\pi\) | ||||
−0.346115 | + | 0.938192i | \(0.612499\pi\) | |||||||
\(824\) | 5.40642 | 0.188342 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.20551 | 0.181123 | ||||||||
\(827\) | −28.0532 | −0.975507 | −0.487753 | − | 0.872981i | \(-0.662183\pi\) | ||||
−0.487753 | + | 0.872981i | \(0.662183\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.5414 | 1.02602 | 0.513008 | − | 0.858384i | \(-0.328531\pi\) | ||||
0.513008 | + | 0.858384i | \(0.328531\pi\) | |||||||
\(830\) | −13.9739 | −0.485040 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −10.6920 | −0.370680 | ||||||||
\(833\) | −5.81738 | −0.201560 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 22.8005 | 0.789043 | ||||||||
\(836\) | −53.2450 | −1.84152 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 3.10052 | 0.107106 | ||||||||
\(839\) | −3.38509 | −0.116866 | −0.0584331 | − | 0.998291i | \(-0.518610\pi\) | ||||
−0.0584331 | + | 0.998291i | \(0.518610\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0190 | 1.20755 | ||||||||
\(842\) | −3.47852 | −0.119878 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.38582 | 0.116545 | ||||||||
\(845\) | −12.9200 | −0.444463 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.44292 | −0.324463 | ||||||||
\(848\) | 26.8322 | 0.921422 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 5.56483 | 0.190872 | ||||||||
\(851\) | 0.995087 | 0.0341111 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44.5454 | −1.52520 | −0.762602 | − | 0.646868i | \(-0.776079\pi\) | ||||
−0.762602 | + | 0.646868i | \(0.776079\pi\) | |||||||
\(854\) | 4.81460 | 0.164752 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −14.1612 | −0.484021 | ||||||||
\(857\) | −3.18608 | −0.108834 | −0.0544172 | − | 0.998518i | \(-0.517330\pi\) | ||||
−0.0544172 | + | 0.998518i | \(0.517330\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.23145 | −0.0761361 | −0.0380681 | − | 0.999275i | \(-0.512120\pi\) | ||||
−0.0380681 | + | 0.999275i | \(0.512120\pi\) | |||||||
\(860\) | −12.0636 | −0.411367 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −0.286877 | −0.00977105 | ||||||||
\(863\) | −31.3862 | −1.06840 | −0.534199 | − | 0.845359i | \(-0.679387\pi\) | ||||
−0.534199 | + | 0.845359i | \(0.679387\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43.5448 | −1.48057 | ||||||||
\(866\) | 13.1640 | 0.447333 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.6812 | 0.498312 | ||||||||
\(869\) | 60.3947 | 2.04875 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.6043 | −1.47748 | ||||||||
\(872\) | −12.6859 | −0.429598 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.45842 | 0.0831572 | ||||||||
\(875\) | −12.1547 | −0.410904 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.7012 | −0.665262 | −0.332631 | − | 0.943057i | \(-0.607936\pi\) | ||||
−0.332631 | + | 0.943057i | \(0.607936\pi\) | |||||||
\(878\) | −1.80196 | −0.0608133 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −19.9621 | −0.672922 | ||||||||
\(881\) | −31.4991 | −1.06123 | −0.530615 | − | 0.847613i | \(-0.678039\pi\) | ||||
−0.530615 | + | 0.847613i | \(0.678039\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.4081 | 1.19158 | 0.595789 | − | 0.803141i | \(-0.296839\pi\) | ||||
0.595789 | + | 0.803141i | \(0.296839\pi\) | |||||||
\(884\) | 45.5435 | 1.53179 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.63781 | 0.256597 | ||||||||
\(887\) | 2.81610 | 0.0945554 | 0.0472777 | − | 0.998882i | \(-0.484945\pi\) | ||||
0.0472777 | + | 0.998882i | \(0.484945\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.00000 | −0.0335389 | ||||||||
\(890\) | −4.32733 | −0.145052 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.7755 | 0.561686 | ||||||||
\(893\) | −66.2744 | −2.21779 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 32.9465 | 1.10128 | ||||||||
\(896\) | 11.4294 | 0.381828 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −17.2062 | −0.574180 | ||||||||
\(899\) | −67.6025 | −2.25467 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −62.5745 | −2.08466 | ||||||||
\(902\) | 7.10253 | 0.236488 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.2131 | −0.639019 | ||||||||
\(905\) | 30.6120 | 1.01758 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.9748 | 0.696456 | 0.348228 | − | 0.937410i | \(-0.386783\pi\) | ||||
0.348228 | + | 0.937410i | \(0.386783\pi\) | |||||||
\(908\) | −1.78477 | −0.0592295 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4.08477 | 0.135409 | ||||||||
\(911\) | 23.5213 | 0.779296 | 0.389648 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389648 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.6896 | 2.30639 | ||||||||
\(914\) | −6.80581 | −0.225116 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −47.9552 | −1.58448 | ||||||||
\(917\) | 8.12188 | 0.268208 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 53.3169 | 1.75876 | 0.879381 | − | 0.476119i | \(-0.157957\pi\) | ||||
0.879381 | + | 0.476119i | \(0.157957\pi\) | |||||||
\(920\) | 2.39962 | 0.0791132 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.5054 | 0.345977 | ||||||||
\(923\) | −34.7408 | −1.14351 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.62413 | −0.0862808 | ||||||||
\(926\) | −10.0454 | −0.330113 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −40.8612 | −1.34133 | ||||||||
\(929\) | 24.8127 | 0.814078 | 0.407039 | − | 0.913411i | \(-0.366561\pi\) | ||||
0.407039 | + | 0.913411i | \(0.366561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.77727 | 0.222116 | ||||||||
\(932\) | 36.2706 | 1.18808 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 10.0850 | 0.329990 | ||||||||
\(935\) | 46.5529 | 1.52244 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.9476 | −0.782335 | −0.391168 | − | 0.920319i | \(-0.627929\pi\) | ||||
−0.391168 | + | 0.920319i | \(0.627929\pi\) | |||||||
\(938\) | 4.95741 | 0.161865 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.0741 | −0.980908 | ||||||||
\(941\) | −19.1449 | −0.624108 | −0.312054 | − | 0.950064i | \(-0.601017\pi\) | ||||
−0.312054 | + | 0.950064i | \(0.601017\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.17169 | 0.0707198 | ||||||||
\(944\) | −25.3500 | −0.825071 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −9.08493 | −0.295376 | ||||||||
\(947\) | 7.26965 | 0.236232 | 0.118116 | − | 0.993000i | \(-0.462315\pi\) | ||||
0.118116 | + | 0.993000i | \(0.462315\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −66.8346 | −2.16954 | ||||||||
\(950\) | −6.48305 | −0.210338 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −11.1377 | −0.360974 | ||||||||
\(953\) | 32.7433 | 1.06066 | 0.530330 | − | 0.847791i | \(-0.322068\pi\) | ||||
0.530330 | + | 0.847791i | \(0.322068\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.60571 | 0.310834 | ||||||||
\(956\) | 2.78760 | 0.0901575 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 10.6829 | 0.345149 | ||||||||
\(959\) | −14.7897 | −0.477583 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.3867 | 1.30280 | ||||||||
\(962\) | 3.24304 | 0.104560 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.94454 | −0.127045 | ||||||||
\(965\) | −45.5785 | −1.46722 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −48.1172 | −1.54735 | −0.773673 | − | 0.633585i | \(-0.781583\pi\) | ||||
−0.773673 | + | 0.633585i | \(0.781583\pi\) | |||||||
\(968\) | −18.0789 | −0.581079 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −9.76487 | −0.313531 | ||||||||
\(971\) | 30.7999 | 0.988415 | 0.494207 | − | 0.869344i | \(-0.335458\pi\) | ||||
0.494207 | + | 0.869344i | \(0.335458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −21.6135 | −0.692896 | ||||||||
\(974\) | −4.49057 | −0.143887 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −23.4463 | −0.750498 | ||||||||
\(977\) | 27.6351 | 0.884124 | 0.442062 | − | 0.896985i | \(-0.354247\pi\) | ||||
0.442062 | + | 0.896985i | \(0.354247\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.5810 | 0.689730 | ||||||||
\(980\) | 3.07539 | 0.0982399 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −7.63090 | −0.243512 | ||||||||
\(983\) | 9.55349 | 0.304709 | 0.152354 | − | 0.988326i | \(-0.451314\pi\) | ||||
0.152354 | + | 0.988326i | \(0.451314\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.05633 | −0.288559 | ||||||||
\(986\) | 23.8426 | 0.759304 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −53.0584 | −1.68801 | ||||||||
\(989\) | −2.77783 | −0.0883298 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.7123 | −0.499118 | −0.249559 | − | 0.968360i | \(-0.580286\pi\) | ||||
−0.249559 | + | 0.968360i | \(0.580286\pi\) | |||||||
\(992\) | 43.1484 | 1.36996 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.94971 | 0.125277 | ||||||||
\(995\) | 35.1917 | 1.11565 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 38.0575 | 1.20529 | 0.602647 | − | 0.798008i | \(-0.294113\pi\) | ||||
0.602647 | + | 0.798008i | \(0.294113\pi\) | |||||||
\(998\) | 14.9472 | 0.473146 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 8001.2.a.y.1.17 | yes | 28 | |
3.2 | odd | 2 | inner | 8001.2.a.y.1.12 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8001.2.a.y.1.12 | ✓ | 28 | 3.2 | odd | 2 | inner | |
8001.2.a.y.1.17 | yes | 28 | 1.1 | even | 1 | trivial |