Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9025,2,Mod(1,9025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("9025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9025 = 5^{2} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9025.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: | \(72.0649878242\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | no (minimal twist has level 1805) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 9025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.717155 | −0.507105 | −0.253553 | − | 0.967322i | \(-0.581599\pi\) | ||||
−0.253553 | + | 0.967322i | \(0.581599\pi\) | |||||||
\(3\) | −1.56975 | −0.906296 | −0.453148 | − | 0.891435i | \(-0.649699\pi\) | ||||
−0.453148 | + | 0.891435i | \(0.649699\pi\) | |||||||
\(4\) | −1.48569 | −0.742844 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.12576 | 0.459588 | ||||||||
\(7\) | −2.51917 | −0.952157 | −0.476078 | − | 0.879403i | \(-0.657942\pi\) | ||||
−0.476078 | + | 0.879403i | \(0.657942\pi\) | |||||||
\(8\) | 2.49978 | 0.883806 | ||||||||
\(9\) | −0.535883 | −0.178628 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.85392 | −1.76502 | −0.882512 | − | 0.470290i | \(-0.844149\pi\) | ||||
−0.882512 | + | 0.470290i | \(0.844149\pi\) | |||||||
\(12\) | 2.33216 | 0.673237 | ||||||||
\(13\) | 0.791698 | 0.219577 | 0.109789 | − | 0.993955i | \(-0.464983\pi\) | ||||
0.109789 | + | 0.993955i | \(0.464983\pi\) | |||||||
\(14\) | 1.80664 | 0.482844 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.17865 | 0.294661 | ||||||||
\(17\) | −0.651447 | −0.157999 | −0.0789996 | − | 0.996875i | \(-0.525173\pi\) | ||||
−0.0789996 | + | 0.996875i | \(0.525173\pi\) | |||||||
\(18\) | 0.384311 | 0.0905831 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.95447 | 0.862936 | ||||||||
\(22\) | 4.19817 | 0.895053 | ||||||||
\(23\) | 4.88134 | 1.01783 | 0.508915 | − | 0.860817i | \(-0.330047\pi\) | ||||
0.508915 | + | 0.860817i | \(0.330047\pi\) | |||||||
\(24\) | −3.92403 | −0.800990 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.567770 | −0.111349 | ||||||||
\(27\) | 5.55045 | 1.06819 | ||||||||
\(28\) | 3.74270 | 0.707304 | ||||||||
\(29\) | 4.83251 | 0.897375 | 0.448687 | − | 0.893689i | \(-0.351892\pi\) | ||||
0.448687 | + | 0.893689i | \(0.351892\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.73907 | 1.21037 | 0.605186 | − | 0.796084i | \(-0.293099\pi\) | ||||
0.605186 | + | 0.796084i | \(0.293099\pi\) | |||||||
\(32\) | −5.84483 | −1.03323 | ||||||||
\(33\) | 9.18920 | 1.59963 | ||||||||
\(34\) | 0.467189 | 0.0801222 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.796155 | 0.132693 | ||||||||
\(37\) | −0.741957 | −0.121977 | −0.0609885 | − | 0.998138i | \(-0.519425\pi\) | ||||
−0.0609885 | + | 0.998138i | \(0.519425\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.24277 | −0.199002 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −8.04494 | −1.25641 | −0.628205 | − | 0.778048i | \(-0.716210\pi\) | ||||
−0.628205 | + | 0.778048i | \(0.716210\pi\) | |||||||
\(42\) | −2.83597 | −0.437600 | ||||||||
\(43\) | 0.761041 | 0.116058 | 0.0580289 | − | 0.998315i | \(-0.481518\pi\) | ||||
0.0580289 | + | 0.998315i | \(0.481518\pi\) | |||||||
\(44\) | 8.69710 | 1.31114 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.50068 | −0.516147 | ||||||||
\(47\) | −11.3005 | −1.64834 | −0.824171 | − | 0.566342i | \(-0.808358\pi\) | ||||
−0.824171 | + | 0.566342i | \(0.808358\pi\) | |||||||
\(48\) | −1.85018 | −0.267050 | ||||||||
\(49\) | −0.653781 | −0.0933973 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.02261 | 0.143194 | ||||||||
\(52\) | −1.17622 | −0.163112 | ||||||||
\(53\) | −12.8983 | −1.77172 | −0.885860 | − | 0.463953i | \(-0.846431\pi\) | ||||
−0.885860 | + | 0.463953i | \(0.846431\pi\) | |||||||
\(54\) | −3.98054 | −0.541683 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.29737 | −0.841522 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.46566 | −0.455064 | ||||||||
\(59\) | 2.14576 | 0.279354 | 0.139677 | − | 0.990197i | \(-0.455394\pi\) | ||||
0.139677 | + | 0.990197i | \(0.455394\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.75915 | −0.865421 | −0.432710 | − | 0.901533i | \(-0.642443\pi\) | ||||
−0.432710 | + | 0.901533i | \(0.642443\pi\) | |||||||
\(62\) | −4.83296 | −0.613787 | ||||||||
\(63\) | 1.34998 | 0.170082 | ||||||||
\(64\) | 1.83436 | 0.229295 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.59008 | −0.811183 | ||||||||
\(67\) | −13.8808 | −1.69581 | −0.847903 | − | 0.530152i | \(-0.822135\pi\) | ||||
−0.847903 | + | 0.530152i | \(0.822135\pi\) | |||||||
\(68\) | 0.967847 | 0.117369 | ||||||||
\(69\) | −7.66249 | −0.922455 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.05037 | 0.718046 | 0.359023 | − | 0.933329i | \(-0.383110\pi\) | ||||
0.359023 | + | 0.933329i | \(0.383110\pi\) | |||||||
\(72\) | −1.33959 | −0.157872 | ||||||||
\(73\) | −11.1309 | −1.30277 | −0.651387 | − | 0.758746i | \(-0.725812\pi\) | ||||
−0.651387 | + | 0.758746i | \(0.725812\pi\) | |||||||
\(74\) | 0.532098 | 0.0618552 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.7470 | 1.68058 | ||||||||
\(78\) | 0.891258 | 0.100915 | ||||||||
\(79\) | −15.7669 | −1.77391 | −0.886955 | − | 0.461856i | \(-0.847184\pi\) | ||||
−0.886955 | + | 0.461856i | \(0.847184\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.10518 | −0.789464 | ||||||||
\(82\) | 5.76948 | 0.637132 | ||||||||
\(83\) | −3.26719 | −0.358621 | −0.179310 | − | 0.983793i | \(-0.557387\pi\) | ||||
−0.179310 | + | 0.983793i | \(0.557387\pi\) | |||||||
\(84\) | −5.87511 | −0.641027 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.545785 | −0.0588535 | ||||||||
\(87\) | −7.58584 | −0.813287 | ||||||||
\(88\) | −14.6335 | −1.55994 | ||||||||
\(89\) | −1.07484 | −0.113932 | −0.0569662 | − | 0.998376i | \(-0.518143\pi\) | ||||
−0.0569662 | + | 0.998376i | \(0.518143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.99442 | −0.209072 | ||||||||
\(92\) | −7.25215 | −0.756089 | ||||||||
\(93\) | −10.5787 | −1.09696 | ||||||||
\(94\) | 8.10419 | 0.835883 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.17493 | 0.936412 | ||||||||
\(97\) | −10.1175 | −1.02728 | −0.513641 | − | 0.858005i | \(-0.671704\pi\) | ||||
−0.513641 | + | 0.858005i | \(0.671704\pi\) | |||||||
\(98\) | 0.468863 | 0.0473623 | ||||||||
\(99\) | 3.13702 | 0.315282 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.63114 | 0.560320 | 0.280160 | − | 0.959953i | \(-0.409613\pi\) | ||||
0.280160 | + | 0.959953i | \(0.409613\pi\) | |||||||
\(102\) | −0.733370 | −0.0726145 | ||||||||
\(103\) | −0.459634 | −0.0452891 | −0.0226446 | − | 0.999744i | \(-0.507209\pi\) | ||||
−0.0226446 | + | 0.999744i | \(0.507209\pi\) | |||||||
\(104\) | 1.97907 | 0.194064 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.25010 | 0.898449 | ||||||||
\(107\) | 5.11103 | 0.494102 | 0.247051 | − | 0.969002i | \(-0.420538\pi\) | ||||
0.247051 | + | 0.969002i | \(0.420538\pi\) | |||||||
\(108\) | −8.24624 | −0.793495 | ||||||||
\(109\) | 10.1536 | 0.972537 | 0.486269 | − | 0.873809i | \(-0.338358\pi\) | ||||
0.486269 | + | 0.873809i | \(0.338358\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.16469 | 0.110547 | ||||||||
\(112\) | −2.96921 | −0.280564 | ||||||||
\(113\) | −5.61000 | −0.527745 | −0.263872 | − | 0.964558i | \(-0.585000\pi\) | ||||
−0.263872 | + | 0.964558i | \(0.585000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.17960 | −0.666609 | ||||||||
\(117\) | −0.424257 | −0.0392226 | ||||||||
\(118\) | −1.53884 | −0.141662 | ||||||||
\(119\) | 1.64111 | 0.150440 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.2684 | 2.11531 | ||||||||
\(122\) | 4.84736 | 0.438860 | ||||||||
\(123\) | 12.6286 | 1.13868 | ||||||||
\(124\) | −10.0122 | −0.899118 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.968146 | −0.0862493 | ||||||||
\(127\) | −10.8609 | −0.963747 | −0.481873 | − | 0.876241i | \(-0.660044\pi\) | ||||
−0.481873 | + | 0.876241i | \(0.660044\pi\) | |||||||
\(128\) | 10.3741 | 0.916953 | ||||||||
\(129\) | −1.19465 | −0.105183 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16.3484 | 1.42837 | 0.714184 | − | 0.699958i | \(-0.246798\pi\) | ||||
0.714184 | + | 0.699958i | \(0.246798\pi\) | |||||||
\(132\) | −13.6523 | −1.18828 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.95467 | 0.859952 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.62847 | −0.139641 | ||||||||
\(137\) | −18.3333 | −1.56632 | −0.783162 | − | 0.621818i | \(-0.786394\pi\) | ||||
−0.783162 | + | 0.621818i | \(0.786394\pi\) | |||||||
\(138\) | 5.49519 | 0.467782 | ||||||||
\(139\) | −9.37358 | −0.795057 | −0.397529 | − | 0.917590i | \(-0.630132\pi\) | ||||
−0.397529 | + | 0.917590i | \(0.630132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.7389 | 1.49389 | ||||||||
\(142\) | −4.33905 | −0.364125 | ||||||||
\(143\) | −4.63454 | −0.387559 | ||||||||
\(144\) | −0.631616 | −0.0526347 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 7.98258 | 0.660643 | ||||||||
\(147\) | 1.02627 | 0.0846456 | ||||||||
\(148\) | 1.10232 | 0.0906099 | ||||||||
\(149\) | −7.69847 | −0.630683 | −0.315342 | − | 0.948978i | \(-0.602119\pi\) | ||||
−0.315342 | + | 0.948978i | \(0.602119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.167275 | 0.0136126 | 0.00680631 | − | 0.999977i | \(-0.497833\pi\) | ||||
0.00680631 | + | 0.999977i | \(0.497833\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.349100 | 0.0282230 | ||||||||
\(154\) | −10.5759 | −0.852231 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 1.84637 | 0.147828 | ||||||||
\(157\) | 14.8860 | 1.18803 | 0.594016 | − | 0.804453i | \(-0.297542\pi\) | ||||
0.594016 | + | 0.804453i | \(0.297542\pi\) | |||||||
\(158\) | 11.3073 | 0.899559 | ||||||||
\(159\) | 20.2471 | 1.60570 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.2969 | −0.969133 | ||||||||
\(162\) | 5.09552 | 0.400342 | ||||||||
\(163\) | 18.7516 | 1.46874 | 0.734369 | − | 0.678751i | \(-0.237478\pi\) | ||||
0.734369 | + | 0.678751i | \(0.237478\pi\) | |||||||
\(164\) | 11.9523 | 0.933316 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.34308 | 0.181859 | ||||||||
\(167\) | −11.1787 | −0.865036 | −0.432518 | − | 0.901625i | \(-0.642375\pi\) | ||||
−0.432518 | + | 0.901625i | \(0.642375\pi\) | |||||||
\(168\) | 9.88530 | 0.762668 | ||||||||
\(169\) | −12.3732 | −0.951786 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.13067 | −0.0862128 | ||||||||
\(173\) | −5.09894 | −0.387665 | −0.193833 | − | 0.981035i | \(-0.562092\pi\) | ||||
−0.193833 | + | 0.981035i | \(0.562092\pi\) | |||||||
\(174\) | 5.44022 | 0.412422 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.89970 | −0.520084 | ||||||||
\(177\) | −3.36831 | −0.253178 | ||||||||
\(178\) | 0.770825 | 0.0577757 | ||||||||
\(179\) | −0.474937 | −0.0354984 | −0.0177492 | − | 0.999842i | \(-0.505650\pi\) | ||||
−0.0177492 | + | 0.999842i | \(0.505650\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.41389 | 0.105093 | 0.0525466 | − | 0.998618i | \(-0.483266\pi\) | ||||
0.0525466 | + | 0.998618i | \(0.483266\pi\) | |||||||
\(182\) | 1.43031 | 0.106022 | ||||||||
\(183\) | 10.6102 | 0.784327 | ||||||||
\(184\) | 12.2023 | 0.899564 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.58654 | 0.556272 | ||||||||
\(187\) | 3.81352 | 0.278872 | ||||||||
\(188\) | 16.7890 | 1.22446 | ||||||||
\(189\) | −13.9825 | −1.01708 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.6109 | 0.912496 | 0.456248 | − | 0.889853i | \(-0.349193\pi\) | ||||
0.456248 | + | 0.889853i | \(0.349193\pi\) | |||||||
\(192\) | −2.87949 | −0.207809 | ||||||||
\(193\) | −12.6096 | −0.907660 | −0.453830 | − | 0.891088i | \(-0.649943\pi\) | ||||
−0.453830 | + | 0.891088i | \(0.649943\pi\) | |||||||
\(194\) | 7.25585 | 0.520940 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.971315 | 0.0693796 | ||||||||
\(197\) | 1.50078 | 0.106926 | 0.0534631 | − | 0.998570i | \(-0.482974\pi\) | ||||
0.0534631 | + | 0.998570i | \(0.482974\pi\) | |||||||
\(198\) | −2.24973 | −0.159881 | ||||||||
\(199\) | −15.6650 | −1.11046 | −0.555231 | − | 0.831696i | \(-0.687370\pi\) | ||||
−0.555231 | + | 0.831696i | \(0.687370\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.7893 | 1.53690 | ||||||||
\(202\) | −4.03841 | −0.284141 | ||||||||
\(203\) | −12.1739 | −0.854441 | ||||||||
\(204\) | −1.51928 | −0.106371 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0.329629 | 0.0229664 | ||||||||
\(207\) | −2.61583 | −0.181813 | ||||||||
\(208\) | 0.933131 | 0.0647010 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.8162 | −1.22652 | −0.613259 | − | 0.789882i | \(-0.710142\pi\) | ||||
−0.613259 | + | 0.789882i | \(0.710142\pi\) | |||||||
\(212\) | 19.1629 | 1.31611 | ||||||||
\(213\) | −9.49757 | −0.650763 | ||||||||
\(214\) | −3.66540 | −0.250562 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 13.8749 | 0.944068 | ||||||||
\(217\) | −16.9769 | −1.15246 | ||||||||
\(218\) | −7.28170 | −0.493179 | ||||||||
\(219\) | 17.4727 | 1.18070 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.515749 | −0.0346930 | ||||||||
\(222\) | −0.835262 | −0.0560591 | ||||||||
\(223\) | −18.4288 | −1.23408 | −0.617041 | − | 0.786931i | \(-0.711669\pi\) | ||||
−0.617041 | + | 0.786931i | \(0.711669\pi\) | |||||||
\(224\) | 14.7241 | 0.983797 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.02325 | 0.267622 | ||||||||
\(227\) | 4.13839 | 0.274674 | 0.137337 | − | 0.990524i | \(-0.456146\pi\) | ||||
0.137337 | + | 0.990524i | \(0.456146\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.37089 | −0.0905907 | −0.0452953 | − | 0.998974i | \(-0.514423\pi\) | ||||
−0.0452953 | + | 0.998974i | \(0.514423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −23.1492 | −1.52310 | ||||||||
\(232\) | 12.0802 | 0.793105 | ||||||||
\(233\) | −1.01441 | −0.0664564 | −0.0332282 | − | 0.999448i | \(-0.510579\pi\) | ||||
−0.0332282 | + | 0.999448i | \(0.510579\pi\) | |||||||
\(234\) | 0.304258 | 0.0198900 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.18793 | −0.207517 | ||||||||
\(237\) | 24.7500 | 1.60769 | ||||||||
\(238\) | −1.17693 | −0.0762889 | ||||||||
\(239\) | 5.54538 | 0.358701 | 0.179351 | − | 0.983785i | \(-0.442600\pi\) | ||||
0.179351 | + | 0.983785i | \(0.442600\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.0078 | 1.61089 | 0.805445 | − | 0.592670i | \(-0.201926\pi\) | ||||
0.805445 | + | 0.592670i | \(0.201926\pi\) | |||||||
\(242\) | −16.6871 | −1.07268 | ||||||||
\(243\) | −5.49800 | −0.352697 | ||||||||
\(244\) | 10.0420 | 0.642873 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −9.05664 | −0.577430 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 16.8462 | 1.06973 | ||||||||
\(249\) | 5.12867 | 0.325016 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.9588 | 0.691713 | 0.345857 | − | 0.938287i | \(-0.387588\pi\) | ||||
0.345857 | + | 0.938287i | \(0.387588\pi\) | |||||||
\(252\) | −2.00565 | −0.126344 | ||||||||
\(253\) | −28.5750 | −1.79649 | ||||||||
\(254\) | 7.78894 | 0.488721 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −11.1086 | −0.694287 | ||||||||
\(257\) | −15.0295 | −0.937514 | −0.468757 | − | 0.883327i | \(-0.655298\pi\) | ||||
−0.468757 | + | 0.883327i | \(0.655298\pi\) | |||||||
\(258\) | 0.856746 | 0.0533387 | ||||||||
\(259\) | 1.86912 | 0.116141 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.58966 | −0.160296 | ||||||||
\(262\) | −11.7244 | −0.724334 | ||||||||
\(263\) | −14.8709 | −0.916980 | −0.458490 | − | 0.888700i | \(-0.651610\pi\) | ||||
−0.458490 | + | 0.888700i | \(0.651610\pi\) | |||||||
\(264\) | 22.9710 | 1.41377 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.68722 | 0.103256 | ||||||||
\(268\) | 20.6225 | 1.25972 | ||||||||
\(269\) | −3.34506 | −0.203952 | −0.101976 | − | 0.994787i | \(-0.532516\pi\) | ||||
−0.101976 | + | 0.994787i | \(0.532516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.34209 | 0.567492 | 0.283746 | − | 0.958900i | \(-0.408423\pi\) | ||||
0.283746 | + | 0.958900i | \(0.408423\pi\) | |||||||
\(272\) | −0.767825 | −0.0465562 | ||||||||
\(273\) | 3.13074 | 0.189481 | ||||||||
\(274\) | 13.1479 | 0.794291 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.3841 | 0.685240 | ||||||||
\(277\) | 2.79175 | 0.167740 | 0.0838700 | − | 0.996477i | \(-0.473272\pi\) | ||||
0.0838700 | + | 0.996477i | \(0.473272\pi\) | |||||||
\(278\) | 6.72232 | 0.403178 | ||||||||
\(279\) | −3.61135 | −0.216206 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.7534 | −1.65563 | −0.827816 | − | 0.561000i | \(-0.810417\pi\) | ||||
−0.827816 | + | 0.561000i | \(0.810417\pi\) | |||||||
\(282\) | −12.7215 | −0.757557 | ||||||||
\(283\) | −1.13648 | −0.0675569 | −0.0337784 | − | 0.999429i | \(-0.510754\pi\) | ||||
−0.0337784 | + | 0.999429i | \(0.510754\pi\) | |||||||
\(284\) | −8.98896 | −0.533396 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.32368 | 0.196533 | ||||||||
\(287\) | 20.2666 | 1.19630 | ||||||||
\(288\) | 3.13215 | 0.184563 | ||||||||
\(289\) | −16.5756 | −0.975036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.8820 | 0.931021 | ||||||||
\(292\) | 16.5370 | 0.967757 | ||||||||
\(293\) | −25.0362 | −1.46263 | −0.731314 | − | 0.682041i | \(-0.761092\pi\) | ||||
−0.731314 | + | 0.682041i | \(0.761092\pi\) | |||||||
\(294\) | −0.735997 | −0.0429242 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.85473 | −0.107804 | ||||||||
\(297\) | −32.4919 | −1.88537 | ||||||||
\(298\) | 5.52100 | 0.319823 | ||||||||
\(299\) | 3.86454 | 0.223492 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.91719 | −0.110505 | ||||||||
\(302\) | −0.119962 | −0.00690304 | ||||||||
\(303\) | −8.83949 | −0.507816 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.250359 | −0.0143120 | ||||||||
\(307\) | −18.8926 | −1.07826 | −0.539130 | − | 0.842223i | \(-0.681247\pi\) | ||||
−0.539130 | + | 0.842223i | \(0.681247\pi\) | |||||||
\(308\) | −21.9095 | −1.24841 | ||||||||
\(309\) | 0.721512 | 0.0410454 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.9570 | 0.791430 | 0.395715 | − | 0.918373i | \(-0.370497\pi\) | ||||
0.395715 | + | 0.918373i | \(0.370497\pi\) | |||||||
\(312\) | −3.10665 | −0.175879 | ||||||||
\(313\) | −0.212626 | −0.0120183 | −0.00600917 | − | 0.999982i | \(-0.501913\pi\) | ||||
−0.00600917 | + | 0.999982i | \(0.501913\pi\) | |||||||
\(314\) | −10.6756 | −0.602457 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 23.4246 | 1.31774 | ||||||||
\(317\) | 7.50284 | 0.421402 | 0.210701 | − | 0.977551i | \(-0.432425\pi\) | ||||
0.210701 | + | 0.977551i | \(0.432425\pi\) | |||||||
\(318\) | −14.5203 | −0.814261 | ||||||||
\(319\) | −28.2891 | −1.58389 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.02305 | −0.447803 | ||||||||
\(322\) | 8.81881 | 0.491453 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 10.5561 | 0.586449 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −13.4478 | −0.744805 | ||||||||
\(327\) | −15.9386 | −0.881406 | ||||||||
\(328\) | −20.1106 | −1.11042 | ||||||||
\(329\) | 28.4678 | 1.56948 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.22616 | −0.177326 | −0.0886629 | − | 0.996062i | \(-0.528259\pi\) | ||||
−0.0886629 | + | 0.996062i | \(0.528259\pi\) | |||||||
\(332\) | 4.85403 | 0.266399 | ||||||||
\(333\) | 0.397602 | 0.0217885 | ||||||||
\(334\) | 8.01688 | 0.438664 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 4.66092 | 0.254274 | ||||||||
\(337\) | 34.5994 | 1.88475 | 0.942375 | − | 0.334560i | \(-0.108588\pi\) | ||||
0.942375 | + | 0.334560i | \(0.108588\pi\) | |||||||
\(338\) | 8.87352 | 0.482656 | ||||||||
\(339\) | 8.80631 | 0.478293 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −39.4500 | −2.13634 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.2812 | 1.04109 | ||||||||
\(344\) | 1.90244 | 0.102572 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.65673 | 0.196587 | ||||||||
\(347\) | −0.0848311 | −0.00455397 | −0.00227698 | − | 0.999997i | \(-0.500725\pi\) | ||||
−0.00227698 | + | 0.999997i | \(0.500725\pi\) | |||||||
\(348\) | 11.2702 | 0.604145 | ||||||||
\(349\) | −17.8090 | −0.953295 | −0.476648 | − | 0.879094i | \(-0.658148\pi\) | ||||
−0.476648 | + | 0.879094i | \(0.658148\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.39428 | 0.234549 | ||||||||
\(352\) | 34.2152 | 1.82368 | ||||||||
\(353\) | −15.1330 | −0.805451 | −0.402725 | − | 0.915321i | \(-0.631937\pi\) | ||||
−0.402725 | + | 0.915321i | \(0.631937\pi\) | |||||||
\(354\) | 2.41560 | 0.128388 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.59687 | 0.0846340 | ||||||||
\(357\) | −2.57613 | −0.136343 | ||||||||
\(358\) | 0.340603 | 0.0180015 | ||||||||
\(359\) | 9.00023 | 0.475014 | 0.237507 | − | 0.971386i | \(-0.423670\pi\) | ||||
0.237507 | + | 0.971386i | \(0.423670\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −1.01398 | −0.0532934 | ||||||||
\(363\) | −36.5256 | −1.91710 | ||||||||
\(364\) | 2.96309 | 0.155308 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −7.60915 | −0.397737 | ||||||||
\(367\) | 5.86064 | 0.305923 | 0.152962 | − | 0.988232i | \(-0.451119\pi\) | ||||
0.152962 | + | 0.988232i | \(0.451119\pi\) | |||||||
\(368\) | 5.75337 | 0.299915 | ||||||||
\(369\) | 4.31115 | 0.224429 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 32.4931 | 1.68696 | ||||||||
\(372\) | 15.7166 | 0.814867 | ||||||||
\(373\) | 24.6228 | 1.27492 | 0.637460 | − | 0.770484i | \(-0.279985\pi\) | ||||
0.637460 | + | 0.770484i | \(0.279985\pi\) | |||||||
\(374\) | −2.73489 | −0.141418 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −28.2487 | −1.45681 | ||||||||
\(377\) | 3.82589 | 0.197043 | ||||||||
\(378\) | 10.0277 | 0.515767 | ||||||||
\(379\) | −2.67753 | −0.137536 | −0.0687679 | − | 0.997633i | \(-0.521907\pi\) | ||||
−0.0687679 | + | 0.997633i | \(0.521907\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 17.0489 | 0.873440 | ||||||||
\(382\) | −9.04401 | −0.462732 | ||||||||
\(383\) | 27.8484 | 1.42299 | 0.711494 | − | 0.702692i | \(-0.248019\pi\) | ||||
0.711494 | + | 0.702692i | \(0.248019\pi\) | |||||||
\(384\) | −16.2848 | −0.831031 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.04306 | 0.460280 | ||||||||
\(387\) | −0.407829 | −0.0207311 | ||||||||
\(388\) | 15.0315 | 0.763110 | ||||||||
\(389\) | 14.8564 | 0.753249 | 0.376624 | − | 0.926366i | \(-0.377085\pi\) | ||||
0.376624 | + | 0.926366i | \(0.377085\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.17994 | −0.160816 | ||||||||
\(392\) | −1.63431 | −0.0825451 | ||||||||
\(393\) | −25.6630 | −1.29452 | ||||||||
\(394\) | −1.07629 | −0.0542229 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.66063 | −0.234205 | ||||||||
\(397\) | 11.1189 | 0.558043 | 0.279022 | − | 0.960285i | \(-0.409990\pi\) | ||||
0.279022 | + | 0.960285i | \(0.409990\pi\) | |||||||
\(398\) | 11.2342 | 0.563121 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.4510 | 1.42078 | 0.710388 | − | 0.703810i | \(-0.248519\pi\) | ||||
0.710388 | + | 0.703810i | \(0.248519\pi\) | |||||||
\(402\) | −15.6263 | −0.779371 | ||||||||
\(403\) | 5.33531 | 0.265771 | ||||||||
\(404\) | −8.36612 | −0.416230 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.73059 | 0.433292 | ||||||||
\(407\) | 4.34336 | 0.215292 | ||||||||
\(408\) | 2.55630 | 0.126556 | ||||||||
\(409\) | 15.8493 | 0.783695 | 0.391847 | − | 0.920030i | \(-0.371836\pi\) | ||||
0.391847 | + | 0.920030i | \(0.371836\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.7788 | 1.41955 | ||||||||
\(412\) | 0.682873 | 0.0336428 | ||||||||
\(413\) | −5.40554 | −0.265989 | ||||||||
\(414\) | 1.87595 | 0.0921981 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.62734 | −0.226874 | ||||||||
\(417\) | 14.7142 | 0.720557 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.2300 | −0.499769 | −0.249885 | − | 0.968276i | \(-0.580393\pi\) | ||||
−0.249885 | + | 0.968276i | \(0.580393\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1606 | −1.51868 | −0.759338 | − | 0.650696i | \(-0.774477\pi\) | ||||
−0.759338 | + | 0.650696i | \(0.774477\pi\) | |||||||
\(422\) | 12.7770 | 0.621974 | ||||||||
\(423\) | 6.05572 | 0.294439 | ||||||||
\(424\) | −32.2430 | −1.56586 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 6.81123 | 0.330005 | ||||||||
\(427\) | 17.0275 | 0.824016 | ||||||||
\(428\) | −7.59340 | −0.367041 | ||||||||
\(429\) | 7.27506 | 0.351243 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 9.60728 | 0.462767 | 0.231383 | − | 0.972863i | \(-0.425675\pi\) | ||||
0.231383 | + | 0.972863i | \(0.425675\pi\) | |||||||
\(432\) | 6.54202 | 0.314753 | ||||||||
\(433\) | 20.8460 | 1.00179 | 0.500897 | − | 0.865507i | \(-0.333004\pi\) | ||||
0.500897 | + | 0.865507i | \(0.333004\pi\) | |||||||
\(434\) | 12.1751 | 0.584421 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −15.0851 | −0.722443 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −12.5307 | −0.598738 | ||||||||
\(439\) | −1.11124 | −0.0530364 | −0.0265182 | − | 0.999648i | \(-0.508442\pi\) | ||||
−0.0265182 | + | 0.999648i | \(0.508442\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.350350 | 0.0166833 | ||||||||
\(442\) | 0.369872 | 0.0175930 | ||||||||
\(443\) | −28.7487 | −1.36589 | −0.682947 | − | 0.730468i | \(-0.739302\pi\) | ||||
−0.682947 | + | 0.730468i | \(0.739302\pi\) | |||||||
\(444\) | −1.73036 | −0.0821194 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.2163 | 0.625810 | ||||||||
\(447\) | 12.0847 | 0.571586 | ||||||||
\(448\) | −4.62107 | −0.218325 | ||||||||
\(449\) | 31.9695 | 1.50873 | 0.754367 | − | 0.656452i | \(-0.227944\pi\) | ||||
0.754367 | + | 0.656452i | \(0.227944\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.0945 | 2.21759 | ||||||||
\(452\) | 8.33472 | 0.392032 | ||||||||
\(453\) | −0.262580 | −0.0123371 | ||||||||
\(454\) | −2.96787 | −0.139289 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12.0035 | −0.561498 | −0.280749 | − | 0.959781i | \(-0.590583\pi\) | ||||
−0.280749 | + | 0.959781i | \(0.590583\pi\) | |||||||
\(458\) | 0.983138 | 0.0459390 | ||||||||
\(459\) | −3.61583 | −0.168772 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.9752 | −1.58238 | −0.791191 | − | 0.611569i | \(-0.790539\pi\) | ||||
−0.791191 | + | 0.611569i | \(0.790539\pi\) | |||||||
\(462\) | 16.6015 | 0.772374 | ||||||||
\(463\) | −24.1005 | −1.12004 | −0.560022 | − | 0.828478i | \(-0.689207\pi\) | ||||
−0.560022 | + | 0.828478i | \(0.689207\pi\) | |||||||
\(464\) | 5.69582 | 0.264422 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.727492 | 0.0337004 | ||||||||
\(467\) | 0.621098 | 0.0287410 | 0.0143705 | − | 0.999897i | \(-0.495426\pi\) | ||||
0.0143705 | + | 0.999897i | \(0.495426\pi\) | |||||||
\(468\) | 0.630314 | 0.0291363 | ||||||||
\(469\) | 34.9680 | 1.61467 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.3673 | −1.07671 | ||||||||
\(472\) | 5.36393 | 0.246895 | ||||||||
\(473\) | −4.45508 | −0.204845 | ||||||||
\(474\) | −17.7496 | −0.815267 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.43817 | −0.111753 | ||||||||
\(477\) | 6.91199 | 0.316478 | ||||||||
\(478\) | −3.97690 | −0.181899 | ||||||||
\(479\) | 31.0733 | 1.41978 | 0.709888 | − | 0.704314i | \(-0.248745\pi\) | ||||
0.709888 | + | 0.704314i | \(0.248745\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.587405 | −0.0267834 | ||||||||
\(482\) | −17.9344 | −0.816892 | ||||||||
\(483\) | 19.3031 | 0.878322 | ||||||||
\(484\) | −34.5696 | −1.57134 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 3.94292 | 0.178855 | ||||||||
\(487\) | 37.2206 | 1.68663 | 0.843313 | − | 0.537423i | \(-0.180602\pi\) | ||||
0.843313 | + | 0.537423i | \(0.180602\pi\) | |||||||
\(488\) | −16.8964 | −0.764864 | ||||||||
\(489\) | −29.4353 | −1.33111 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.5493 | 1.73971 | 0.869853 | − | 0.493310i | \(-0.164213\pi\) | ||||
0.869853 | + | 0.493310i | \(0.164213\pi\) | |||||||
\(492\) | −18.7621 | −0.845861 | ||||||||
\(493\) | −3.14813 | −0.141784 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.94298 | 0.356650 | ||||||||
\(497\) | −15.2419 | −0.683693 | ||||||||
\(498\) | −3.67806 | −0.164818 | ||||||||
\(499\) | −5.38788 | −0.241194 | −0.120597 | − | 0.992702i | \(-0.538481\pi\) | ||||
−0.120597 | + | 0.992702i | \(0.538481\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.5478 | 0.783978 | ||||||||
\(502\) | −7.85916 | −0.350771 | ||||||||
\(503\) | −26.5719 | −1.18478 | −0.592392 | − | 0.805650i | \(-0.701816\pi\) | ||||
−0.592392 | + | 0.805650i | \(0.701816\pi\) | |||||||
\(504\) | 3.37465 | 0.150319 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 20.4927 | 0.911012 | ||||||||
\(507\) | 19.4229 | 0.862600 | ||||||||
\(508\) | 16.1359 | 0.715914 | ||||||||
\(509\) | −28.1487 | −1.24767 | −0.623836 | − | 0.781556i | \(-0.714427\pi\) | ||||
−0.623836 | + | 0.781556i | \(0.714427\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 28.0406 | 1.24044 | ||||||||
\(512\) | −12.7817 | −0.564876 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.7785 | 0.475418 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.77487 | 0.0781343 | ||||||||
\(517\) | 66.1520 | 2.90936 | ||||||||
\(518\) | −1.34045 | −0.0588958 | ||||||||
\(519\) | 8.00406 | 0.351339 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.50660 | −0.416492 | −0.208246 | − | 0.978077i | \(-0.566775\pi\) | ||||
−0.208246 | + | 0.978077i | \(0.566775\pi\) | |||||||
\(522\) | 1.85719 | 0.0812869 | ||||||||
\(523\) | −17.3457 | −0.758473 | −0.379237 | − | 0.925300i | \(-0.623813\pi\) | ||||
−0.379237 | + | 0.925300i | \(0.623813\pi\) | |||||||
\(524\) | −24.2887 | −1.06106 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10.6648 | 0.465006 | ||||||||
\(527\) | −4.39015 | −0.191238 | ||||||||
\(528\) | 10.8308 | 0.471350 | ||||||||
\(529\) | 0.827475 | 0.0359772 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.14988 | −0.0499004 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.36916 | −0.275879 | ||||||||
\(534\) | −1.21000 | −0.0523619 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −34.6989 | −1.49876 | ||||||||
\(537\) | 0.745532 | 0.0321721 | ||||||||
\(538\) | 2.39893 | 0.103425 | ||||||||
\(539\) | 3.82718 | 0.164848 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5619 | −0.798039 | −0.399020 | − | 0.916942i | \(-0.630649\pi\) | ||||
−0.399020 | + | 0.916942i | \(0.630649\pi\) | |||||||
\(542\) | −6.69973 | −0.287778 | ||||||||
\(543\) | −2.21945 | −0.0952456 | ||||||||
\(544\) | 3.80760 | 0.163249 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.24523 | −0.0960870 | ||||||||
\(547\) | 5.56689 | 0.238023 | 0.119011 | − | 0.992893i | \(-0.462027\pi\) | ||||
0.119011 | + | 0.992893i | \(0.462027\pi\) | |||||||
\(548\) | 27.2376 | 1.16353 | ||||||||
\(549\) | 3.62211 | 0.154588 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −19.1545 | −0.815271 | ||||||||
\(553\) | 39.7194 | 1.68904 | ||||||||
\(554\) | −2.00212 | −0.0850618 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.9262 | 0.590603 | ||||||||
\(557\) | −25.5819 | −1.08394 | −0.541970 | − | 0.840398i | \(-0.682321\pi\) | ||||
−0.541970 | + | 0.840398i | \(0.682321\pi\) | |||||||
\(558\) | 2.58990 | 0.109639 | ||||||||
\(559\) | 0.602515 | 0.0254837 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.98628 | −0.252741 | ||||||||
\(562\) | 19.9035 | 0.839580 | ||||||||
\(563\) | 12.8773 | 0.542712 | 0.271356 | − | 0.962479i | \(-0.412528\pi\) | ||||
0.271356 | + | 0.962479i | \(0.412528\pi\) | |||||||
\(564\) | −26.3545 | −1.10972 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.815034 | 0.0342585 | ||||||||
\(567\) | 17.8992 | 0.751694 | ||||||||
\(568\) | 15.1246 | 0.634614 | ||||||||
\(569\) | −11.4205 | −0.478773 | −0.239387 | − | 0.970924i | \(-0.576946\pi\) | ||||
−0.239387 | + | 0.970924i | \(0.576946\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.1881 | 0.468208 | 0.234104 | − | 0.972212i | \(-0.424784\pi\) | ||||
0.234104 | + | 0.972212i | \(0.424784\pi\) | |||||||
\(572\) | 6.88547 | 0.287896 | ||||||||
\(573\) | −19.7960 | −0.826991 | ||||||||
\(574\) | −14.5343 | −0.606650 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.983004 | −0.0409585 | ||||||||
\(577\) | −0.256987 | −0.0106985 | −0.00534924 | − | 0.999986i | \(-0.501703\pi\) | ||||
−0.00534924 | + | 0.999986i | \(0.501703\pi\) | |||||||
\(578\) | 11.8873 | 0.494446 | ||||||||
\(579\) | 19.7940 | 0.822609 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.23061 | 0.341463 | ||||||||
\(582\) | −11.3899 | −0.472126 | ||||||||
\(583\) | 75.5057 | 3.12713 | ||||||||
\(584\) | −27.8248 | −1.15140 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 17.9548 | 0.741706 | ||||||||
\(587\) | −2.50510 | −0.103397 | −0.0516983 | − | 0.998663i | \(-0.516463\pi\) | ||||
−0.0516983 | + | 0.998663i | \(0.516463\pi\) | |||||||
\(588\) | −1.52472 | −0.0628785 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.35585 | −0.0969068 | ||||||||
\(592\) | −0.874504 | −0.0359419 | ||||||||
\(593\) | 27.9054 | 1.14594 | 0.572969 | − | 0.819577i | \(-0.305791\pi\) | ||||
0.572969 | + | 0.819577i | \(0.305791\pi\) | |||||||
\(594\) | 23.3018 | 0.956083 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11.4375 | 0.468499 | ||||||||
\(597\) | 24.5901 | 1.00641 | ||||||||
\(598\) | −2.77148 | −0.113334 | ||||||||
\(599\) | −33.3364 | −1.36209 | −0.681045 | − | 0.732242i | \(-0.738474\pi\) | ||||
−0.681045 | + | 0.732242i | \(0.738474\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.2223 | −1.35516 | −0.677582 | − | 0.735447i | \(-0.736972\pi\) | ||||
−0.677582 | + | 0.735447i | \(0.736972\pi\) | |||||||
\(602\) | 1.37493 | 0.0560378 | ||||||||
\(603\) | 7.43847 | 0.302918 | ||||||||
\(604\) | −0.248518 | −0.0101121 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6.33929 | 0.257516 | ||||||||
\(607\) | 20.6372 | 0.837640 | 0.418820 | − | 0.908069i | \(-0.362444\pi\) | ||||
0.418820 | + | 0.908069i | \(0.362444\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 19.1100 | 0.774377 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.94655 | −0.361938 | ||||||||
\(612\) | −0.518653 | −0.0209653 | ||||||||
\(613\) | −27.6480 | −1.11669 | −0.558346 | − | 0.829608i | \(-0.688564\pi\) | ||||
−0.558346 | + | 0.829608i | \(0.688564\pi\) | |||||||
\(614\) | 13.5490 | 0.546791 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.8643 | 1.48531 | ||||||||
\(617\) | −19.4964 | −0.784896 | −0.392448 | − | 0.919774i | \(-0.628372\pi\) | ||||
−0.392448 | + | 0.919774i | \(0.628372\pi\) | |||||||
\(618\) | −0.517436 | −0.0208143 | ||||||||
\(619\) | 26.9685 | 1.08396 | 0.541978 | − | 0.840392i | \(-0.317675\pi\) | ||||
0.541978 | + | 0.840392i | \(0.317675\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 27.0937 | 1.08723 | ||||||||
\(622\) | −10.0094 | −0.401338 | ||||||||
\(623\) | 2.70770 | 0.108482 | ||||||||
\(624\) | −1.46478 | −0.0586382 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0.152486 | 0.00609456 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −22.1159 | −0.882522 | ||||||||
\(629\) | 0.483346 | 0.0192723 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.601618 | −0.0239500 | −0.0119750 | − | 0.999928i | \(-0.503812\pi\) | ||||
−0.0119750 | + | 0.999928i | \(0.503812\pi\) | |||||||
\(632\) | −39.4137 | −1.56779 | ||||||||
\(633\) | 27.9670 | 1.11159 | ||||||||
\(634\) | −5.38070 | −0.213695 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −30.0809 | −1.19279 | ||||||||
\(637\) | −0.517597 | −0.0205079 | ||||||||
\(638\) | 20.2877 | 0.803198 | ||||||||
\(639\) | −3.24229 | −0.128263 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.42208 | −0.293154 | −0.146577 | − | 0.989199i | \(-0.546826\pi\) | ||||
−0.146577 | + | 0.989199i | \(0.546826\pi\) | |||||||
\(642\) | 5.75377 | 0.227083 | ||||||||
\(643\) | −6.20548 | −0.244720 | −0.122360 | − | 0.992486i | \(-0.539046\pi\) | ||||
−0.122360 | + | 0.992486i | \(0.539046\pi\) | |||||||
\(644\) | 18.2694 | 0.719915 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −24.3051 | −0.955530 | −0.477765 | − | 0.878488i | \(-0.658553\pi\) | ||||
−0.477765 | + | 0.878488i | \(0.658553\pi\) | |||||||
\(648\) | −17.7614 | −0.697733 | ||||||||
\(649\) | −12.5611 | −0.493067 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.6494 | 1.04447 | ||||||||
\(652\) | −27.8590 | −1.09104 | ||||||||
\(653\) | 1.38625 | 0.0542483 | 0.0271242 | − | 0.999632i | \(-0.491365\pi\) | ||||
0.0271242 | + | 0.999632i | \(0.491365\pi\) | |||||||
\(654\) | 11.4305 | 0.446966 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.48214 | −0.370215 | ||||||||
\(657\) | 5.96486 | 0.232711 | ||||||||
\(658\) | −20.4158 | −0.795892 | ||||||||
\(659\) | 30.4152 | 1.18481 | 0.592405 | − | 0.805641i | \(-0.298179\pi\) | ||||
0.592405 | + | 0.805641i | \(0.298179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 18.4422 | 0.717317 | 0.358659 | − | 0.933469i | \(-0.383234\pi\) | ||||
0.358659 | + | 0.933469i | \(0.383234\pi\) | |||||||
\(662\) | 2.31366 | 0.0899228 | ||||||||
\(663\) | 0.809598 | 0.0314422 | ||||||||
\(664\) | −8.16726 | −0.316951 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −0.285143 | −0.0110490 | ||||||||
\(667\) | 23.5891 | 0.913374 | ||||||||
\(668\) | 16.6081 | 0.642587 | ||||||||
\(669\) | 28.9286 | 1.11844 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.5675 | 1.52749 | ||||||||
\(672\) | −23.1132 | −0.891611 | ||||||||
\(673\) | −28.6496 | −1.10436 | −0.552181 | − | 0.833724i | \(-0.686204\pi\) | ||||
−0.552181 | + | 0.833724i | \(0.686204\pi\) | |||||||
\(674\) | −24.8131 | −0.955767 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 18.3827 | 0.707028 | ||||||||
\(677\) | 5.02624 | 0.193174 | 0.0965870 | − | 0.995325i | \(-0.469207\pi\) | ||||
0.0965870 | + | 0.995325i | \(0.469207\pi\) | |||||||
\(678\) | −6.31549 | −0.242545 | ||||||||
\(679\) | 25.4878 | 0.978133 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.49624 | −0.248936 | ||||||||
\(682\) | 28.2918 | 1.08335 | ||||||||
\(683\) | −12.9236 | −0.494509 | −0.247254 | − | 0.968951i | \(-0.579528\pi\) | ||||
−0.247254 | + | 0.968951i | \(0.579528\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −13.8276 | −0.527940 | ||||||||
\(687\) | 2.15195 | 0.0821020 | ||||||||
\(688\) | 0.896998 | 0.0341977 | ||||||||
\(689\) | −10.2116 | −0.389030 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.0901 | 0.916432 | 0.458216 | − | 0.888841i | \(-0.348489\pi\) | ||||
0.458216 | + | 0.888841i | \(0.348489\pi\) | |||||||
\(692\) | 7.57544 | 0.287975 | ||||||||
\(693\) | −7.90268 | −0.300198 | ||||||||
\(694\) | 0.0608371 | 0.00230934 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −18.9629 | −0.718788 | ||||||||
\(697\) | 5.24086 | 0.198512 | ||||||||
\(698\) | 12.7718 | 0.483421 | ||||||||
\(699\) | 1.59238 | 0.0602292 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.98543 | −0.263836 | −0.131918 | − | 0.991261i | \(-0.542114\pi\) | ||||
−0.131918 | + | 0.991261i | \(0.542114\pi\) | |||||||
\(702\) | −3.15138 | −0.118941 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −10.7382 | −0.404712 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.8527 | 0.408448 | ||||||||
\(707\) | −14.1858 | −0.533512 | ||||||||
\(708\) | 5.00426 | 0.188072 | ||||||||
\(709\) | −0.256274 | −0.00962456 | −0.00481228 | − | 0.999988i | \(-0.501532\pi\) | ||||
−0.00481228 | + | 0.999988i | \(0.501532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.44919 | 0.316869 | ||||||||
\(712\) | −2.68685 | −0.100694 | ||||||||
\(713\) | 32.8957 | 1.23195 | ||||||||
\(714\) | 1.84748 | 0.0691404 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.705608 | 0.0263698 | ||||||||
\(717\) | −8.70487 | −0.325089 | ||||||||
\(718\) | −6.45456 | −0.240882 | ||||||||
\(719\) | 18.5286 | 0.690999 | 0.345500 | − | 0.938419i | \(-0.387709\pi\) | ||||
0.345500 | + | 0.938419i | \(0.387709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.15790 | 0.0431224 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −39.2559 | −1.45994 | ||||||||
\(724\) | −2.10059 | −0.0780679 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 26.1945 | 0.972170 | ||||||||
\(727\) | 35.1390 | 1.30323 | 0.651617 | − | 0.758548i | \(-0.274091\pi\) | ||||
0.651617 | + | 0.758548i | \(0.274091\pi\) | |||||||
\(728\) | −4.98561 | −0.184779 | ||||||||
\(729\) | 29.9460 | 1.10911 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.495778 | −0.0183370 | ||||||||
\(732\) | −15.7634 | −0.582633 | ||||||||
\(733\) | −34.9872 | −1.29228 | −0.646142 | − | 0.763217i | \(-0.723618\pi\) | ||||
−0.646142 | + | 0.763217i | \(0.723618\pi\) | |||||||
\(734\) | −4.20299 | −0.155135 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −28.5306 | −1.05165 | ||||||||
\(737\) | 81.2569 | 2.99314 | ||||||||
\(738\) | −3.09176 | −0.113809 | ||||||||
\(739\) | −4.73129 | −0.174043 | −0.0870216 | − | 0.996206i | \(-0.527735\pi\) | ||||
−0.0870216 | + | 0.996206i | \(0.527735\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −23.3026 | −0.855464 | ||||||||
\(743\) | −6.77084 | −0.248398 | −0.124199 | − | 0.992257i | \(-0.539636\pi\) | ||||
−0.124199 | + | 0.992257i | \(0.539636\pi\) | |||||||
\(744\) | −26.4443 | −0.969496 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −17.6584 | −0.646519 | ||||||||
\(747\) | 1.75083 | 0.0640596 | ||||||||
\(748\) | −5.66570 | −0.207159 | ||||||||
\(749\) | −12.8756 | −0.470463 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.77014 | −0.101084 | −0.0505419 | − | 0.998722i | \(-0.516095\pi\) | ||||
−0.0505419 | + | 0.998722i | \(0.516095\pi\) | |||||||
\(752\) | −13.3192 | −0.485702 | ||||||||
\(753\) | −17.2026 | −0.626897 | ||||||||
\(754\) | −2.74376 | −0.0999217 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 20.7737 | 0.755532 | ||||||||
\(757\) | −1.03606 | −0.0376561 | −0.0188280 | − | 0.999823i | \(-0.505994\pi\) | ||||
−0.0188280 | + | 0.999823i | \(0.505994\pi\) | |||||||
\(758\) | 1.92021 | 0.0697451 | ||||||||
\(759\) | 44.8556 | 1.62815 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.4025 | 1.17459 | 0.587296 | − | 0.809373i | \(-0.300193\pi\) | ||||
0.587296 | + | 0.809373i | \(0.300193\pi\) | |||||||
\(762\) | −12.2267 | −0.442926 | ||||||||
\(763\) | −25.5786 | −0.926008 | ||||||||
\(764\) | −18.7359 | −0.677842 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −19.9717 | −0.721605 | ||||||||
\(767\) | 1.69879 | 0.0613399 | ||||||||
\(768\) | 17.4377 | 0.629230 | ||||||||
\(769\) | 48.0188 | 1.73160 | 0.865801 | − | 0.500388i | \(-0.166809\pi\) | ||||
0.865801 | + | 0.500388i | \(0.166809\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 23.5925 | 0.849665 | ||||||||
\(772\) | 18.7340 | 0.674250 | ||||||||
\(773\) | 10.6208 | 0.382004 | 0.191002 | − | 0.981590i | \(-0.438826\pi\) | ||||
0.191002 | + | 0.981590i | \(0.438826\pi\) | |||||||
\(774\) | 0.292477 | 0.0105129 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −25.2916 | −0.907917 | ||||||||
\(777\) | −2.93405 | −0.105258 | ||||||||
\(778\) | −10.6543 | −0.381976 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −35.4184 | −1.26737 | ||||||||
\(782\) | 2.28051 | 0.0815508 | ||||||||
\(783\) | 26.8226 | 0.958562 | ||||||||
\(784\) | −0.770576 | −0.0275206 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 18.4043 | 0.656461 | ||||||||
\(787\) | −26.1251 | −0.931259 | −0.465629 | − | 0.884980i | \(-0.654172\pi\) | ||||
−0.465629 | + | 0.884980i | \(0.654172\pi\) | |||||||
\(788\) | −2.22969 | −0.0794295 | ||||||||
\(789\) | 23.3436 | 0.831055 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 14.1326 | 0.502496 | ||||||||
\(792\) | 7.84185 | 0.278648 | ||||||||
\(793\) | −5.35120 | −0.190027 | ||||||||
\(794\) | −7.97400 | −0.282987 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 23.2733 | 0.824899 | ||||||||
\(797\) | −23.4923 | −0.832139 | −0.416069 | − | 0.909333i | \(-0.636593\pi\) | ||||
−0.416069 | + | 0.909333i | \(0.636593\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.36165 | 0.260437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.575987 | 0.0203515 | ||||||||
\(802\) | −20.4038 | −0.720483 | ||||||||
\(803\) | 65.1594 | 2.29943 | ||||||||
\(804\) | −32.3722 | −1.14168 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.82624 | −0.134774 | ||||||||
\(807\) | 5.25091 | 0.184841 | ||||||||
\(808\) | 14.0766 | 0.495214 | ||||||||
\(809\) | 18.6786 | 0.656706 | 0.328353 | − | 0.944555i | \(-0.393506\pi\) | ||||
0.328353 | + | 0.944555i | \(0.393506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16.1813 | −0.568202 | −0.284101 | − | 0.958794i | \(-0.591695\pi\) | ||||
−0.284101 | + | 0.958794i | \(0.591695\pi\) | |||||||
\(812\) | 18.0866 | 0.634717 | ||||||||
\(813\) | −14.6648 | −0.514315 | ||||||||
\(814\) | −3.11486 | −0.109176 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.20529 | 0.0421937 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −11.3664 | −0.397416 | ||||||||
\(819\) | 1.06878 | 0.0373461 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.3762 | 1.09504 | 0.547519 | − | 0.836793i | \(-0.315572\pi\) | ||||
0.547519 | + | 0.836793i | \(0.315572\pi\) | |||||||
\(822\) | −20.6389 | −0.719863 | ||||||||
\(823\) | 12.2385 | 0.426608 | 0.213304 | − | 0.976986i | \(-0.431578\pi\) | ||||
0.213304 | + | 0.976986i | \(0.431578\pi\) | |||||||
\(824\) | −1.14899 | −0.0400268 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.87661 | 0.134885 | ||||||||
\(827\) | −6.21619 | −0.216158 | −0.108079 | − | 0.994142i | \(-0.534470\pi\) | ||||
−0.108079 | + | 0.994142i | \(0.534470\pi\) | |||||||
\(828\) | 3.88630 | 0.135058 | ||||||||
\(829\) | −52.2819 | −1.81583 | −0.907913 | − | 0.419158i | \(-0.862325\pi\) | ||||
−0.907913 | + | 0.419158i | \(0.862325\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −4.38235 | −0.152022 | ||||||||
\(832\) | 1.45226 | 0.0503481 | ||||||||
\(833\) | 0.425904 | 0.0147567 | ||||||||
\(834\) | −10.5524 | −0.365398 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 37.4049 | 1.29290 | ||||||||
\(838\) | 7.33651 | 0.253436 | ||||||||
\(839\) | 44.5398 | 1.53768 | 0.768842 | − | 0.639439i | \(-0.220833\pi\) | ||||
0.768842 | + | 0.639439i | \(0.220833\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.64685 | −0.194719 | ||||||||
\(842\) | 22.3470 | 0.770129 | ||||||||
\(843\) | 43.5660 | 1.50049 | ||||||||
\(844\) | 26.4693 | 0.911112 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4.34290 | −0.149312 | ||||||||
\(847\) | −58.6171 | −2.01411 | ||||||||
\(848\) | −15.2025 | −0.522057 | ||||||||
\(849\) | 1.78399 | 0.0612265 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.62174 | −0.124152 | ||||||||
\(852\) | 14.1104 | 0.483415 | ||||||||
\(853\) | −40.0057 | −1.36977 | −0.684885 | − | 0.728651i | \(-0.740148\pi\) | ||||
−0.684885 | + | 0.728651i | \(0.740148\pi\) | |||||||
\(854\) | −12.2113 | −0.417863 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.7765 | 0.436690 | ||||||||
\(857\) | −27.8347 | −0.950817 | −0.475408 | − | 0.879765i | \(-0.657700\pi\) | ||||
−0.475408 | + | 0.879765i | \(0.657700\pi\) | |||||||
\(858\) | −5.21735 | −0.178117 | ||||||||
\(859\) | −1.48811 | −0.0507737 | −0.0253869 | − | 0.999678i | \(-0.508082\pi\) | ||||
−0.0253869 | + | 0.999678i | \(0.508082\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −31.8135 | −1.08420 | ||||||||
\(862\) | −6.88991 | −0.234671 | ||||||||
\(863\) | 13.3429 | 0.454196 | 0.227098 | − | 0.973872i | \(-0.427076\pi\) | ||||
0.227098 | + | 0.973872i | \(0.427076\pi\) | |||||||
\(864\) | −32.4415 | −1.10368 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −14.9498 | −0.508015 | ||||||||
\(867\) | 26.0196 | 0.883671 | ||||||||
\(868\) | 25.2223 | 0.856102 | ||||||||
\(869\) | 92.2979 | 3.13099 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.9894 | −0.372361 | ||||||||
\(872\) | 25.3817 | 0.859534 | ||||||||
\(873\) | 5.42182 | 0.183501 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −25.9590 | −0.877074 | ||||||||
\(877\) | −0.167258 | −0.00564790 | −0.00282395 | − | 0.999996i | \(-0.500899\pi\) | ||||
−0.00282395 | + | 0.999996i | \(0.500899\pi\) | |||||||
\(878\) | 0.796928 | 0.0268950 | ||||||||
\(879\) | 39.3005 | 1.32557 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.5156 | −0.960715 | −0.480357 | − | 0.877073i | \(-0.659493\pi\) | ||||
−0.480357 | + | 0.877073i | \(0.659493\pi\) | |||||||
\(882\) | −0.251255 | −0.00846021 | ||||||||
\(883\) | 34.8335 | 1.17224 | 0.586121 | − | 0.810224i | \(-0.300654\pi\) | ||||
0.586121 | + | 0.810224i | \(0.300654\pi\) | |||||||
\(884\) | 0.766242 | 0.0257715 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20.6173 | 0.692652 | ||||||||
\(887\) | 25.7718 | 0.865332 | 0.432666 | − | 0.901554i | \(-0.357573\pi\) | ||||
0.432666 | + | 0.901554i | \(0.357573\pi\) | |||||||
\(888\) | 2.91146 | 0.0977023 | ||||||||
\(889\) | 27.3604 | 0.917638 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 41.5932 | 1.39342 | ||||||||
\(892\) | 27.3794 | 0.916731 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −8.66659 | −0.289854 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −26.1342 | −0.873083 | ||||||||
\(897\) | −6.06637 | −0.202550 | ||||||||
\(898\) | −22.9271 | −0.765088 | ||||||||
\(899\) | 32.5666 | 1.08616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.40257 | 0.279930 | ||||||||
\(902\) | −33.7741 | −1.12455 | ||||||||
\(903\) | 3.00951 | 0.100150 | ||||||||
\(904\) | −14.0238 | −0.466424 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.188310 | 0.00625619 | ||||||||
\(907\) | −23.4162 | −0.777521 | −0.388761 | − | 0.921339i | \(-0.627097\pi\) | ||||
−0.388761 | + | 0.921339i | \(0.627097\pi\) | |||||||
\(908\) | −6.14835 | −0.204040 | ||||||||
\(909\) | −3.01763 | −0.100089 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.45626 | 0.247037 | 0.123518 | − | 0.992342i | \(-0.460582\pi\) | ||||
0.123518 | + | 0.992342i | \(0.460582\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.1259 | 0.632974 | ||||||||
\(914\) | 8.60834 | 0.284739 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.03671 | 0.0672948 | ||||||||
\(917\) | −41.1845 | −1.36003 | ||||||||
\(918\) | 2.59311 | 0.0855854 | ||||||||
\(919\) | 40.0009 | 1.31951 | 0.659754 | − | 0.751481i | \(-0.270660\pi\) | ||||
0.659754 | + | 0.751481i | \(0.270660\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 29.6567 | 0.977223 | ||||||||
\(922\) | 24.3655 | 0.802434 | ||||||||
\(923\) | 4.79006 | 0.157667 | ||||||||
\(924\) | 34.3924 | 1.13143 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 17.2838 | 0.567981 | ||||||||
\(927\) | 0.246310 | 0.00808989 | ||||||||
\(928\) | −28.2452 | −0.927194 | ||||||||
\(929\) | −20.1755 | −0.661936 | −0.330968 | − | 0.943642i | \(-0.607375\pi\) | ||||
−0.330968 | + | 0.943642i | \(0.607375\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 1.50710 | 0.0493667 | ||||||||
\(933\) | −21.9090 | −0.717270 | ||||||||
\(934\) | −0.445424 | −0.0145747 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1.06055 | −0.0346652 | ||||||||
\(937\) | −34.1398 | −1.11530 | −0.557649 | − | 0.830077i | \(-0.688297\pi\) | ||||
−0.557649 | + | 0.830077i | \(0.688297\pi\) | |||||||
\(938\) | −25.0775 | −0.818810 | ||||||||
\(939\) | 0.333770 | 0.0108922 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.7549 | −0.872184 | −0.436092 | − | 0.899902i | \(-0.643638\pi\) | ||||
−0.436092 | + | 0.899902i | \(0.643638\pi\) | |||||||
\(942\) | 16.7580 | 0.546005 | ||||||||
\(943\) | −39.2701 | −1.27881 | ||||||||
\(944\) | 2.52909 | 0.0823149 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.19498 | 0.103878 | ||||||||
\(947\) | −15.6563 | −0.508763 | −0.254381 | − | 0.967104i | \(-0.581872\pi\) | ||||
−0.254381 | + | 0.967104i | \(0.581872\pi\) | |||||||
\(948\) | −36.7708 | −1.19426 | ||||||||
\(949\) | −8.81230 | −0.286060 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −11.7776 | −0.381915 | ||||||||
\(952\) | 4.10241 | 0.132960 | ||||||||
\(953\) | −13.5072 | −0.437541 | −0.218771 | − | 0.975776i | \(-0.570205\pi\) | ||||
−0.218771 | + | 0.975776i | \(0.570205\pi\) | |||||||
\(954\) | −4.95697 | −0.160488 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.23871 | −0.266459 | ||||||||
\(957\) | 44.4069 | 1.43547 | ||||||||
\(958\) | −22.2844 | −0.719977 | ||||||||
\(959\) | 46.1848 | 1.49139 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.4151 | 0.465003 | ||||||||
\(962\) | 0.421261 | 0.0135820 | ||||||||
\(963\) | −2.73892 | −0.0882603 | ||||||||
\(964\) | −37.1537 | −1.19664 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.8433 | −0.445402 | ||||||||
\(967\) | 21.9060 | 0.704450 | 0.352225 | − | 0.935915i | \(-0.385425\pi\) | ||||
0.352225 | + | 0.935915i | \(0.385425\pi\) | |||||||
\(968\) | 58.1659 | 1.86952 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.9663 | 0.993756 | 0.496878 | − | 0.867821i | \(-0.334480\pi\) | ||||
0.496878 | + | 0.867821i | \(0.334480\pi\) | |||||||
\(972\) | 8.16832 | 0.261999 | ||||||||
\(973\) | 23.6137 | 0.757019 | ||||||||
\(974\) | −26.6929 | −0.855297 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.96664 | −0.255006 | ||||||||
\(977\) | 9.89768 | 0.316655 | 0.158327 | − | 0.987387i | \(-0.449390\pi\) | ||||
0.158327 | + | 0.987387i | \(0.449390\pi\) | |||||||
\(978\) | 21.1097 | 0.675014 | ||||||||
\(979\) | 6.29201 | 0.201093 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.44113 | −0.173722 | ||||||||
\(982\) | −27.6459 | −0.882215 | ||||||||
\(983\) | −10.3096 | −0.328827 | −0.164413 | − | 0.986392i | \(-0.552573\pi\) | ||||
−0.164413 | + | 0.986392i | \(0.552573\pi\) | |||||||
\(984\) | 31.5686 | 1.00637 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.25770 | 0.0718997 | ||||||||
\(987\) | −44.6873 | −1.42241 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.71490 | 0.118127 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −20.4090 | −0.648314 | −0.324157 | − | 0.946003i | \(-0.605081\pi\) | ||||
−0.324157 | + | 0.946003i | \(0.605081\pi\) | |||||||
\(992\) | −39.3887 | −1.25059 | ||||||||
\(993\) | 5.06426 | 0.160710 | ||||||||
\(994\) | 10.9308 | 0.346704 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −7.61961 | −0.241437 | ||||||||
\(997\) | −47.0764 | −1.49092 | −0.745462 | − | 0.666549i | \(-0.767771\pi\) | ||||
−0.745462 | + | 0.666549i | \(0.767771\pi\) | |||||||
\(998\) | 3.86394 | 0.122311 | ||||||||
\(999\) | −4.11820 | −0.130294 |
(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 | 9025.2.a.cv.1.17 | 40 | ||
5.2 | odd | 4 | 1805.2.b.m.1084.17 | ✓ | 40 | ||
5.3 | odd | 4 | 1805.2.b.m.1084.24 | yes | 40 | ||
5.4 | even | 2 | inner | 9025.2.a.cv.1.24 | 40 | ||
19.18 | odd | 2 | inner | 9025.2.a.cv.1.23 | 40 | ||
95.18 | even | 4 | 1805.2.b.m.1084.18 | yes | 40 | ||
95.37 | even | 4 | 1805.2.b.m.1084.23 | yes | 40 | ||
95.94 | odd | 2 | inner | 9025.2.a.cv.1.18 | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.b.m.1084.17 | ✓ | 40 | 5.2 | odd | 4 | ||
1805.2.b.m.1084.18 | yes | 40 | 95.18 | even | 4 | ||
1805.2.b.m.1084.23 | yes | 40 | 95.37 | even | 4 | ||
1805.2.b.m.1084.24 | yes | 40 | 5.3 | odd | 4 | ||
9025.2.a.cv.1.17 | 40 | 1.1 | even | 1 | trivial | ||
9025.2.a.cv.1.18 | 40 | 95.94 | odd | 2 | inner | ||
9025.2.a.cv.1.23 | 40 | 19.18 | odd | 2 | inner | ||
9025.2.a.cv.1.24 | 40 | 5.4 | even | 2 | inner |