Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1900,2,Mod(1749,1900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1900.1749");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1900 = 2^{2} \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1900.c (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(15.1715763840\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.4227136.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 9x^{4} + 22x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1749.5 | ||
Root | \(2.19869i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1900.1749 |
Dual form | 1900.2.c.g.1749.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1900\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) | \(951\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.19869i | 0.692065i | 0.938223 | + | 0.346032i | \(0.112471\pi\) | ||||
−0.938223 | + | 0.346032i | \(0.887529\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.19869i | − 0.453063i | −0.974004 | − | 0.226531i | \(-0.927261\pi\) | ||||
0.974004 | − | 0.226531i | \(-0.0727386\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.56314 | 0.521046 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.86718 | −1.76902 | −0.884510 | − | 0.466521i | \(-0.845507\pi\) | ||||
−0.884510 | + | 0.466521i | \(0.845507\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 0.364448i | − 0.101080i | −0.998722 | − | 0.0505399i | \(-0.983906\pi\) | ||||
0.998722 | − | 0.0505399i | \(-0.0160942\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 1.19869i | − 0.290725i | −0.989378 | − | 0.145363i | \(-0.953565\pi\) | ||||
0.989378 | − | 0.145363i | \(-0.0464349\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.43686 | 0.313549 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 8.23163i | − 1.71641i | −0.513305 | − | 0.858206i | \(-0.671579\pi\) | ||||
0.513305 | − | 0.858206i | \(-0.328421\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.46980i | 1.05266i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.86718 | 1.46090 | 0.730449 | − | 0.682967i | \(-0.239311\pi\) | ||||
0.730449 | + | 0.682967i | \(0.239311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.30404 | 1.31184 | 0.655922 | − | 0.754829i | \(-0.272280\pi\) | ||||
0.655922 | + | 0.754829i | \(0.272280\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 7.03293i | − 1.22428i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 7.13828i | − 1.17353i | −0.809759 | − | 0.586763i | \(-0.800402\pi\) | ||||
0.809759 | − | 0.586763i | \(-0.199598\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.436861 | 0.0699537 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.43686 | 0.380574 | 0.190287 | − | 0.981729i | \(-0.439058\pi\) | ||||
0.190287 | + | 0.981729i | \(0.439058\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 7.39738i | − 1.12809i | −0.825744 | − | 0.564045i | \(-0.809244\pi\) | ||||
0.825744 | − | 0.564045i | \(-0.190756\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 13.7014i | 1.99856i | 0.0379717 | + | 0.999279i | \(0.487910\pi\) | ||||
−0.0379717 | + | 0.999279i | \(0.512090\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.56314 | 0.794734 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.43686 | 0.201201 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 7.39738i | − 1.01611i | −0.861325 | − | 0.508054i | \(-0.830365\pi\) | ||||
0.861325 | − | 0.508054i | \(-0.169635\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.19869i | 0.158771i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8606 | −1.67431 | −0.837156 | − | 0.546964i | \(-0.815783\pi\) | ||||
−0.837156 | + | 0.546964i | \(0.815783\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30404 | −0.166965 | −0.0834825 | − | 0.996509i | \(-0.526604\pi\) | ||||
−0.0834825 | + | 0.996509i | \(0.526604\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.87372i | − 0.236067i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.9330i | − 1.45785i | −0.684592 | − | 0.728927i | \(-0.740019\pi\) | ||||
0.684592 | − | 0.728927i | \(-0.259981\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.86718 | 1.18787 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.12628 | 0.252343 | 0.126171 | − | 0.992008i | \(-0.459731\pi\) | ||||
0.126171 | + | 0.992008i | \(0.459731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.50273i | 0.292922i | 0.989216 | + | 0.146461i | \(0.0467883\pi\) | ||||
−0.989216 | + | 0.146461i | \(0.953212\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.03293i | 0.801477i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.74090 | 0.870919 | 0.435460 | − | 0.900208i | \(-0.356586\pi\) | ||||
0.435460 | + | 0.900208i | \(0.356586\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.86718 | −0.207464 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.02093i | − 0.331590i | −0.986160 | − | 0.165795i | \(-0.946981\pi\) | ||||
0.986160 | − | 0.165795i | \(-0.0530191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.43032i | 1.01104i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.68942 | 0.603077 | 0.301539 | − | 0.953454i | \(-0.402500\pi\) | ||||
0.301539 | + | 0.953454i | \(0.402500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.436861 | −0.0457954 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 8.75529i | 0.907881i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 1.09334i | − 0.111012i | −0.998458 | − | 0.0555061i | \(-0.982323\pi\) | ||||
0.998458 | − | 0.0555061i | \(-0.0176772\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.17122 | −0.921742 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.8672 | 1.08132 | 0.540662 | − | 0.841240i | \(-0.318174\pi\) | ||||
0.540662 | + | 0.841240i | \(0.318174\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 9.74090i | − 0.959799i | −0.877323 | − | 0.479900i | \(-0.840673\pi\) | ||||
0.877323 | − | 0.479900i | \(-0.159327\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 16.3634i | − 1.58191i | −0.611877 | − | 0.790953i | \(-0.709585\pi\) | ||||
0.611877 | − | 0.790953i | \(-0.290415\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.29749 | −0.890538 | −0.445269 | − | 0.895397i | \(-0.646892\pi\) | ||||
−0.445269 | + | 0.895397i | \(0.646892\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.55660 | 0.812156 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.96707i | − 0.279118i | −0.990214 | − | 0.139559i | \(-0.955432\pi\) | ||||
0.990214 | − | 0.139559i | \(-0.0445685\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 0.569683i | − 0.0526672i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.43686 | −0.131717 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 23.4238 | 2.12943 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92104i | 0.263382i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.3579i | 1.00785i | 0.863747 | + | 0.503926i | \(0.168111\pi\) | ||||
−0.863747 | + | 0.503926i | \(0.831889\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 8.86718 | 0.780711 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.56314 | −0.136572 | −0.0682861 | − | 0.997666i | \(-0.521753\pi\) | ||||
−0.0682861 | + | 0.997666i | \(0.521753\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 1.19869i | − 0.103940i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.8397i | 1.35328i | 0.736315 | + | 0.676639i | \(0.236564\pi\) | ||||
−0.736315 | + | 0.676639i | \(0.763436\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 19.8606 | 1.68456 | 0.842278 | − | 0.539043i | \(-0.181214\pi\) | ||||
0.842278 | + | 0.539043i | \(0.181214\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.4238 | −1.38313 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.13828i | 0.178812i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.66849i | 0.550007i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.68942 | −0.220326 | −0.110163 | − | 0.993914i | \(-0.535137\pi\) | ||||
−0.110163 | + | 0.993914i | \(0.535137\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.1647 | 1.39684 | 0.698421 | − | 0.715688i | \(-0.253887\pi\) | ||||
0.698421 | + | 0.715688i | \(0.253887\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 1.87372i | − 0.151481i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.3634i | 1.30594i | 0.757384 | + | 0.652969i | \(0.226477\pi\) | ||||
−0.757384 | + | 0.652969i | \(0.773523\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.86718 | 0.703213 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.86718 | −0.777643 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 8.28549i | − 0.648970i | −0.945891 | − | 0.324485i | \(-0.894809\pi\) | ||||
0.945891 | − | 0.324485i | \(-0.105191\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 7.49727i | 0.580156i | 0.957003 | + | 0.290078i | \(0.0936813\pi\) | ||||
−0.957003 | + | 0.290078i | \(0.906319\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.8672 | 0.989783 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.56314 | 0.119536 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 14.7464i | − 1.12114i | −0.828105 | − | 0.560572i | \(-0.810581\pi\) | ||||
0.828105 | − | 0.560572i | \(-0.189419\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 15.4159i | − 1.15873i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.2526 | −0.990543 | −0.495271 | − | 0.868738i | \(-0.664931\pi\) | ||||
−0.495271 | + | 0.868738i | \(0.664931\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.7344 | 1.24385 | 0.621927 | − | 0.783075i | \(-0.286350\pi\) | ||||
0.621927 | + | 0.783075i | \(0.286350\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 1.56314i | − 0.115551i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.03293i | 0.514299i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.55660 | 0.476922 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.13282 | −0.299041 | −0.149520 | − | 0.988759i | \(-0.547773\pi\) | ||||
−0.149520 | + | 0.988759i | \(0.547773\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.08680i | 0.510119i | 0.966925 | + | 0.255060i | \(0.0820951\pi\) | ||||
−0.966925 | + | 0.255060i | \(0.917905\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 20.4753i | − 1.45880i | −0.684087 | − | 0.729401i | \(-0.739799\pi\) | ||||
0.684087 | − | 0.729401i | \(-0.260201\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.74090 | −0.619626 | −0.309813 | − | 0.950798i | \(-0.600266\pi\) | ||||
−0.309813 | + | 0.950798i | \(0.600266\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14.3040 | 1.00893 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 9.43032i | − 0.661878i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 12.8672i | − 0.894331i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −5.86718 | −0.405841 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.7344 | −1.28973 | −0.644863 | − | 0.764298i | \(-0.723086\pi\) | ||||
−0.644863 | + | 0.764298i | \(0.723086\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.54875i | 0.174638i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 8.75529i | − 0.594348i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.00000 | −0.202721 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.436861 | −0.0293864 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.27110i | 0.286014i | 0.989722 | + | 0.143007i | \(0.0456772\pi\) | ||||
−0.989722 | + | 0.143007i | \(0.954323\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 21.5631i | 1.43120i | 0.698512 | + | 0.715598i | \(0.253846\pi\) | ||||
−0.698512 | + | 0.715598i | \(0.746154\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −27.4172 | −1.81178 | −0.905891 | − | 0.423511i | \(-0.860797\pi\) | ||||
−0.905891 | + | 0.423511i | \(0.860797\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.43032 | −0.554674 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.86718i | 0.515396i | 0.966226 | + | 0.257698i | \(0.0829640\pi\) | ||||
−0.966226 | + | 0.257698i | \(0.917036\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 9.27895i | 0.602732i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.30404 | −0.601828 | −0.300914 | − | 0.953651i | \(-0.597292\pi\) | ||||
−0.300914 | + | 0.953651i | \(0.597292\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.9056 | −1.41106 | −0.705531 | − | 0.708679i | \(-0.749291\pi\) | ||||
−0.705531 | + | 0.708679i | \(0.749291\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.1712i | 0.909084i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.364448i | − 0.0231893i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.62116 | 0.229482 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.43032 | −0.468997 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.2964i | 3.03637i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 5.05387i | − 0.315251i | −0.987499 | − | 0.157626i | \(-0.949616\pi\) | ||||
0.987499 | − | 0.157626i | \(-0.0503840\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.55660 | −0.531681 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.2975 | 0.761196 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 17.7673i | − 1.09558i | −0.836617 | − | 0.547789i | \(-0.815470\pi\) | ||||
0.836617 | − | 0.547789i | \(-0.184530\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.81986i | 0.417368i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.17776 | −0.559578 | −0.279789 | − | 0.960062i | \(-0.590264\pi\) | ||||
−0.279789 | + | 0.960062i | \(0.590264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.7278 | −1.25912 | −0.629562 | − | 0.776950i | \(-0.716766\pi\) | ||||
−0.629562 | + | 0.776950i | \(0.716766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 0.523661i | − 0.0316934i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 24.5895i | − 1.47744i | −0.674012 | − | 0.738721i | \(-0.735430\pi\) | ||||
0.674012 | − | 0.738721i | \(-0.264570\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 11.4172 | 0.683532 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.73436 | 0.222773 | 0.111386 | − | 0.993777i | \(-0.464471\pi\) | ||||
0.111386 | + | 0.993777i | \(0.464471\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 13.0318i | − 0.774663i | −0.921941 | − | 0.387332i | \(-0.873397\pi\) | ||||
0.921941 | − | 0.387332i | \(-0.126603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.92104i | − 0.172424i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.5631 | 0.915479 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.31058 | 0.0768277 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 19.9001i | 1.16258i | 0.813698 | + | 0.581288i | \(0.197451\pi\) | ||||
−0.813698 | + | 0.581288i | \(0.802549\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 32.0923i | − 1.86218i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.86718 | −0.511096 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.0264i | 0.748347i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 8.02093i | − 0.457779i | −0.973452 | − | 0.228889i | \(-0.926491\pi\) | ||||
0.973452 | − | 0.228889i | \(-0.0735094\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 11.6763 | 0.664243 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.1778 | −0.917357 | −0.458678 | − | 0.888602i | \(-0.651677\pi\) | ||||
−0.458678 | + | 0.888602i | \(0.651677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 7.13828i | − 0.403480i | −0.979439 | − | 0.201740i | \(-0.935340\pi\) | ||||
0.979439 | − | 0.201740i | \(-0.0646595\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 3.96052i | − 0.222445i | −0.993796 | − | 0.111223i | \(-0.964523\pi\) | ||||
0.993796 | − | 0.111223i | \(-0.0354766\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −46.1581 | −2.58436 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 19.6146 | 1.09478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 1.19869i | − 0.0666970i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 11.1448i | − 0.616310i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 16.4238 | 0.905472 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.94852 | −0.326960 | −0.163480 | − | 0.986547i | \(-0.552272\pi\) | ||||
−0.163480 | + | 0.986547i | \(0.552272\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 11.1581i | − 0.611462i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 8.90666i | − 0.485176i | −0.970129 | − | 0.242588i | \(-0.922004\pi\) | ||||
0.970129 | − | 0.242588i | \(-0.0779964\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.55660 | 0.193168 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −42.8541 | −2.32068 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 15.0593i | − 0.813127i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.5961i | 0.998290i | 0.866519 | + | 0.499145i | \(0.166352\pi\) | ||||
−0.866519 | + | 0.499145i | \(0.833648\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.3040 | 0.765678 | 0.382839 | − | 0.923815i | \(-0.374946\pi\) | ||||
0.382839 | + | 0.923815i | \(0.374946\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.99346 | 0.106403 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 12.7673i | − 0.679534i | −0.940510 | − | 0.339767i | \(-0.889652\pi\) | ||||
0.940510 | − | 0.339767i | \(-0.110348\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 1.72235i | − 0.0911566i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.69596 | −0.142287 | −0.0711437 | − | 0.997466i | \(-0.522665\pi\) | ||||
−0.0711437 | + | 0.997466i | \(0.522665\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.0779i | 1.47371i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.43140i | − 0.179118i | −0.995982 | − | 0.0895589i | \(-0.971454\pi\) | ||||
0.995982 | − | 0.0895589i | \(-0.0285457\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.80915 | 0.198297 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.86718 | −0.460361 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 15.5697i | 0.806168i | 0.915163 | + | 0.403084i | \(0.132062\pi\) | ||||
−0.915163 | + | 0.403084i | \(0.867938\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.86718i | − 0.147667i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.164672 | 0.00845864 | 0.00422932 | − | 0.999991i | \(-0.498654\pi\) | ||||
0.00422932 | + | 0.999991i | \(0.498654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.6146 | −0.697498 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.3514i | 1.14210i | 0.820915 | + | 0.571051i | \(0.193464\pi\) | ||||
−0.820915 | + | 0.571051i | \(0.806536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 11.5631i | − 0.587787i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.34243 | 0.473680 | 0.236840 | − | 0.971549i | \(-0.423888\pi\) | ||||
0.236840 | + | 0.971549i | \(0.423888\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.86718 | −0.499005 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 1.87372i | − 0.0945167i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 4.83533i | − 0.242678i | −0.992611 | − | 0.121339i | \(-0.961281\pi\) | ||||
0.992611 | − | 0.121339i | \(-0.0387188\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.43686 | 0.0719330 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 37.4622 | 1.87077 | 0.935386 | − | 0.353629i | \(-0.115053\pi\) | ||||
0.935386 | + | 0.353629i | \(0.115053\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 2.66194i | − 0.132601i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 41.8816i | 2.07599i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.42377 | −0.465976 | −0.232988 | − | 0.972480i | \(-0.574850\pi\) | ||||
−0.232988 | + | 0.972480i | \(0.574850\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −18.9869 | −0.936555 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4159i | 0.758568i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.8068i | 1.16582i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.4303 | −1.34006 | −0.670029 | − | 0.742335i | \(-0.733718\pi\) | ||||
−0.670029 | + | 0.742335i | \(0.733718\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.4303 | 0.898239 | 0.449119 | − | 0.893472i | \(-0.351738\pi\) | ||||
0.449119 | + | 0.893472i | \(0.351738\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 21.4172i | 1.04134i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.56314i | 0.0756456i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.56314 | −0.123750 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −15.5117 | −0.747170 | −0.373585 | − | 0.927596i | \(-0.621872\pi\) | ||||
−0.373585 | + | 0.927596i | \(0.621872\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 31.8870i | − 1.53239i | −0.642607 | − | 0.766196i | \(-0.722147\pi\) | ||||
0.642607 | − | 0.766196i | \(-0.277853\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.23163i | − 0.393772i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.7278 | −0.702920 | −0.351460 | − | 0.936203i | \(-0.614315\pi\) | ||||
−0.351460 | + | 0.936203i | \(0.614315\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.69596 | 0.414093 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 6.46087i | − 0.306965i | −0.988151 | − | 0.153483i | \(-0.950951\pi\) | ||||
0.988151 | − | 0.153483i | \(-0.0490489\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 3.22378i | − 0.152480i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −21.2910 | −1.00478 | −0.502391 | − | 0.864641i | \(-0.667546\pi\) | ||||
−0.502391 | + | 0.864641i | \(0.667546\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.2975 | −0.673243 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 20.5751i | 0.966705i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 19.6465i | − 0.919023i | −0.888172 | − | 0.459512i | \(-0.848024\pi\) | ||||
0.888172 | − | 0.459512i | \(-0.151976\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.55660 | 0.306036 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.16467 | 0.0542442 | 0.0271221 | − | 0.999632i | \(-0.491366\pi\) | ||||
0.0271221 | + | 0.999632i | \(0.491366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.15375i | 0.239515i | 0.992803 | + | 0.119758i | \(0.0382117\pi\) | ||||
−0.992803 | + | 0.119758i | \(0.961788\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 4.17122i | − 0.193021i | −0.995332 | − | 0.0965104i | \(-0.969232\pi\) | ||||
0.995332 | − | 0.0965104i | \(-0.0307681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.3040 | −0.660499 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.6146 | −0.903794 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 43.4018i | 1.99561i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 11.5631i | − 0.529440i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.35552 | 0.107626 | 0.0538132 | − | 0.998551i | \(-0.482862\pi\) | ||||
0.0538132 | + | 0.998551i | \(0.482862\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.60153 | −0.118620 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 11.8277i | − 0.538179i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9056i | 0.902008i | 0.892522 | + | 0.451004i | \(0.148934\pi\) | ||||
−0.892522 | + | 0.451004i | \(0.851066\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.93175 | 0.449129 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.90557 | 0.356773 | 0.178387 | − | 0.983960i | \(-0.442912\pi\) | ||||
0.178387 | + | 0.983960i | \(0.442912\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 9.43032i | − 0.424720i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.54875i | − 0.114327i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 35.7147 | 1.59881 | 0.799405 | − | 0.600792i | \(-0.205148\pi\) | ||||
0.799405 | + | 0.600792i | \(0.205148\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.98691 | −0.401506 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 30.7991i | 1.37327i | 0.727004 | + | 0.686633i | \(0.240912\pi\) | ||||
−0.727004 | + | 0.686633i | \(0.759088\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 15.4238i | 0.684994i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.5631 | −0.778472 | −0.389236 | − | 0.921138i | \(-0.627261\pi\) | ||||
−0.389236 | + | 0.921138i | \(0.627261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.00000 | 0.132712 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.46980i | 0.241497i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 80.3887i | − 3.53549i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.6763 | 0.775905 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.6081 | −1.07810 | −0.539050 | − | 0.842274i | \(-0.681217\pi\) | ||||
−0.539050 | + | 0.842274i | \(0.681217\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 43.7147i | 1.91151i | 0.294162 | + | 0.955756i | \(0.404960\pi\) | ||||
−0.294162 | + | 0.955756i | \(0.595040\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 8.75529i | − 0.381386i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −44.7597 | −1.94607 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −20.1030 | −0.872394 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 0.888109i | − 0.0384683i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 15.8857i | − 0.685520i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −32.6399 | −1.40590 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.38538 | −0.360516 | −0.180258 | − | 0.983619i | \(-0.557693\pi\) | ||||
−0.180258 | + | 0.983619i | \(0.557693\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.0593i | 0.860828i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 26.3040i | 1.12468i | 0.826906 | + | 0.562340i | \(0.190099\pi\) | ||||
−0.826906 | + | 0.562340i | \(0.809901\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.03839 | −0.0869965 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.86718 | 0.335153 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 9.27895i | − 0.394581i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 2.66740i | 0.113021i | 0.998402 | + | 0.0565107i | \(0.0179975\pi\) | ||||
−0.998402 | + | 0.0565107i | \(0.982002\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.69596 | −0.114027 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.43032 | −0.355928 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 37.7751i | − 1.59203i | −0.605276 | − | 0.796016i | \(-0.706937\pi\) | ||||
0.605276 | − | 0.796016i | \(-0.293063\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.23817i | 0.0939943i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −38.8606 | −1.62912 | −0.814561 | − | 0.580078i | \(-0.803022\pi\) | ||||
−0.814561 | + | 0.580078i | \(0.803022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.17122 | 0.174560 | 0.0872800 | − | 0.996184i | \(-0.472183\pi\) | ||||
0.0872800 | + | 0.996184i | \(0.472183\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 4.95398i | − 0.206955i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 39.3413i | 1.63780i | 0.573935 | + | 0.818901i | \(0.305416\pi\) | ||||
−0.573935 | + | 0.818901i | \(0.694584\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.49489 | −0.353035 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.62116 | −0.150231 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 43.4018i | 1.79752i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 17.8672i | − 0.737457i | −0.929537 | − | 0.368729i | \(-0.879793\pi\) | ||||
0.929537 | − | 0.368729i | \(-0.120207\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.30404 | 0.300958 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 24.5435 | 1.00959 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.0803i | 0.537142i | 0.963260 | + | 0.268571i | \(0.0865514\pi\) | ||||
−0.963260 | + | 0.268571i | \(0.913449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 10.4776i | − 0.428821i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.7278 | −0.438326 | −0.219163 | − | 0.975688i | \(-0.570333\pi\) | ||||
−0.219163 | + | 0.975688i | \(0.570333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8026 | 1.62358 | 0.811791 | − | 0.583948i | \(-0.198493\pi\) | ||||
0.811791 | + | 0.583948i | \(0.198493\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 18.6530i | − 0.759609i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.0318i | 1.74661i | 0.487175 | + | 0.873304i | \(0.338027\pi\) | ||||
−0.487175 | + | 0.873304i | \(0.661973\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 11.3040 | 0.458063 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.99346 | 0.202014 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.4722i | 0.624915i | 0.949932 | + | 0.312458i | \(0.101152\pi\) | ||||
−0.949932 | + | 0.312458i | \(0.898848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.5237i | 1.43013i | 0.699059 | + | 0.715064i | \(0.253603\pi\) | ||||
−0.699059 | + | 0.715064i | \(0.746397\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.0449 | 0.604707 | 0.302354 | − | 0.953196i | \(-0.402228\pi\) | ||||
0.302354 | + | 0.953196i | \(0.402228\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 45.0253 | 1.80680 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 6.81986i | − 0.273232i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 7.03293i | − 0.280868i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.55660 | −0.341174 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.6399 | 1.41880 | 0.709402 | − | 0.704805i | \(-0.248965\pi\) | ||||
0.709402 | + | 0.704805i | \(0.248965\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 22.4567i | − 0.892574i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.02748i | − 0.0803315i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.32367 | 0.131482 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.98691 | 0.275966 | 0.137983 | − | 0.990435i | \(-0.455938\pi\) | ||||
0.137983 | + | 0.990435i | \(0.455938\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 3.74744i | − 0.147785i | −0.997266 | − | 0.0738924i | \(-0.976458\pi\) | ||||
0.997266 | − | 0.0738924i | \(-0.0235421\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 34.1658i | 1.34319i | 0.740916 | + | 0.671597i | \(0.234391\pi\) | ||||
−0.740916 | + | 0.671597i | \(0.765609\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 75.4556 | 2.96189 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.4949 | 0.411327 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5446i | 0.530041i | 0.964243 | + | 0.265020i | \(0.0853787\pi\) | ||||
−0.964243 | + | 0.265020i | \(0.914621\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.91211i | 0.152626i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.6334 | 0.881671 | 0.440836 | − | 0.897588i | \(-0.354682\pi\) | ||||
0.440836 | + | 0.897588i | \(0.354682\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.96161 | −0.154089 | −0.0770443 | − | 0.997028i | \(-0.524548\pi\) | ||||
−0.0770443 | + | 0.997028i | \(0.524548\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 0.523661i | − 0.0203373i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 64.7597i | − 2.50750i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5.11973 | −0.197940 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.65102 | 0.295365 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 28.9605i | − 1.11635i | −0.829725 | − | 0.558173i | \(-0.811503\pi\) | ||||
0.829725 | − | 0.558173i | \(-0.188497\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 24.7518i | 0.951290i | 0.879637 | + | 0.475645i | \(0.157785\pi\) | ||||
−0.879637 | + | 0.475645i | \(0.842215\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.31058 | −0.0502955 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −25.8475 | −0.990480 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 40.0593i | − 1.53283i | −0.642347 | − | 0.766414i | \(-0.722039\pi\) | ||||
0.642347 | − | 0.766414i | \(-0.277961\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 32.8648i | − 1.25387i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.69596 | −0.102708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.2162 | 1.33969 | 0.669843 | − | 0.742503i | \(-0.266361\pi\) | ||||
0.669843 | + | 0.742503i | \(0.266361\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.9935i | 0.417607i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 2.92104i | − 0.110642i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −9.43032 | −0.356687 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −38.1283 | −1.44008 | −0.720042 | − | 0.693930i | \(-0.755878\pi\) | ||||
−0.720042 | + | 0.693930i | \(0.755878\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 7.13828i | − 0.269225i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 13.0264i | − 0.489908i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.08789 | 0.228635 | 0.114318 | − | 0.993444i | \(-0.463532\pi\) | ||||
0.114318 | + | 0.993444i | \(0.463532\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.1001 | 0.453789 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 60.1241i | − 2.25167i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 11.1527i | − 0.416504i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.1647 | 0.453666 | 0.226833 | − | 0.973934i | \(-0.427163\pi\) | ||||
0.226833 | + | 0.973934i | \(0.427163\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.6763 | −0.434849 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 26.2580i | − 0.976546i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 25.6859i | − 0.952639i | −0.879272 | − | 0.476320i | \(-0.841971\pi\) | ||||
0.879272 | − | 0.476320i | \(-0.158029\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.5884 | −0.836609 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.86718 | −0.327964 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 43.4502i | 1.60487i | 0.596741 | + | 0.802434i | \(0.296462\pi\) | ||||
−0.596741 | + | 0.802434i | \(0.703538\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 70.0133i | 2.57897i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.4172 | 1.59713 | 0.798564 | − | 0.601910i | \(-0.205593\pi\) | ||||
0.798564 | + | 0.601910i | \(0.205593\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.436861 | 0.0160485 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 26.6709i | − 0.978459i | −0.872155 | − | 0.489230i | \(-0.837278\pi\) | ||||
0.872155 | − | 0.489230i | \(-0.162722\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 4.72214i | − 0.172774i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −19.6146 | −0.716703 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.52674 | −0.0557114 | −0.0278557 | − | 0.999612i | \(-0.508868\pi\) | ||||
−0.0278557 | + | 0.999612i | \(0.508868\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 8.90666i | − 0.324577i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 9.38191i | − 0.340991i | −0.985358 | − | 0.170496i | \(-0.945463\pi\) | ||||
0.985358 | − | 0.170496i | \(-0.0545369\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −57.8925 | −2.10136 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.70251 | −0.242966 | −0.121483 | − | 0.992594i | \(-0.538765\pi\) | ||||
−0.121483 | + | 0.992594i | \(0.538765\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.1448i | 0.403470i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.68703i | 0.169239i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.0637 | 1.30049 | 0.650245 | − | 0.759724i | \(-0.274666\pi\) | ||||
0.650245 | + | 0.759724i | \(0.274666\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.05802 | 0.218174 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 11.6763i | 0.419968i | 0.977705 | + | 0.209984i | \(0.0673413\pi\) | ||||
−0.977705 | + | 0.209984i | \(0.932659\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 10.2567i | − 0.367958i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.43686 | 0.0873096 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.4753 | −0.446400 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.0318i | 1.53783i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.1880i | 1.53949i | 0.638354 | + | 0.769743i | \(0.279616\pi\) | ||||
−0.638354 | + | 0.769743i | \(0.720384\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21.2975 | 0.758211 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.55660 | −0.126458 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.475254i | 0.0168768i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 29.1658i | 1.03310i | 0.856256 | + | 0.516552i | \(0.172785\pi\) | ||||
−0.856256 | + | 0.516552i | \(0.827215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16.4238 | 0.581031 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.89335 | 0.314231 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 14.6840i | − 0.518186i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 11.0013i | − 0.387264i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.43032 | −0.0854454 | −0.0427227 | − | 0.999087i | \(-0.513603\pi\) | ||||
−0.0427227 | + | 0.999087i | \(0.513603\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −42.2779 | −1.48458 | −0.742288 | − | 0.670081i | \(-0.766259\pi\) | ||||
−0.742288 | + | 0.670081i | \(0.766259\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 24.8462i | − 0.871396i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 7.39738i | − 0.258802i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.682874 | −0.0238616 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 52.5136 | 1.83274 | 0.916369 | − | 0.400334i | \(-0.131106\pi\) | ||||
0.916369 | + | 0.400334i | \(0.131106\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36.3150i | 1.26586i | 0.774209 | + | 0.632930i | \(0.218148\pi\) | ||||
−0.774209 | + | 0.632930i | \(0.781852\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 46.3150i | 1.61053i | 0.592916 | + | 0.805264i | \(0.297977\pi\) | ||||
−0.592916 | + | 0.805264i | \(0.702023\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0899 | −0.697750 | −0.348875 | − | 0.937169i | \(-0.613436\pi\) | ||||
−0.348875 | + | 0.937169i | \(0.613436\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 29.4753 | 1.02249 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 6.66849i | − 0.231049i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 39.9516i | 1.38093i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.5930 | 0.365711 | 0.182855 | − | 0.983140i | \(-0.441466\pi\) | ||||
0.182855 | + | 0.983140i | \(0.441466\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 32.8925 | 1.13422 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.47634i | 0.154173i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 28.0779i | − 0.964767i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.6212 | 0.536117 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −58.7597 | −2.01426 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 40.0648i | − 1.37179i | −0.727700 | − | 0.685896i | \(-0.759410\pi\) | ||||
0.727700 | − | 0.685896i | \(-0.240590\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 38.3019i | − 1.30837i | −0.756336 | − | 0.654183i | \(-0.773012\pi\) | ||||
0.756336 | − | 0.654183i | \(-0.226988\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 39.9056 | 1.36156 | 0.680780 | − | 0.732488i | \(-0.261641\pi\) | ||||
0.680780 | + | 0.732488i | \(0.261641\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.50143 | 0.119328 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 23.3315i | − 0.794214i | −0.917772 | − | 0.397107i | \(-0.870014\pi\) | ||||
0.917772 | − | 0.397107i | \(-0.129986\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 18.6554i | 0.633571i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −45.4172 | −1.54067 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.34898 | −0.147359 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1.70905i | − 0.0578426i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 10.4105i | − 0.351537i | −0.984432 | − | 0.175768i | \(-0.943759\pi\) | ||||
0.984432 | − | 0.175768i | \(-0.0562410\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.8541 | −0.804578 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.7662 | −0.800704 | −0.400352 | − | 0.916361i | \(-0.631112\pi\) | ||||
−0.400352 | + | 0.916361i | \(0.631112\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 28.3908i | − 0.955428i | −0.878515 | − | 0.477714i | \(-0.841466\pi\) | ||||
0.878515 | − | 0.477714i | \(-0.158534\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 32.5644i | 1.09341i | 0.837326 | + | 0.546703i | \(0.184117\pi\) | ||||
−0.837326 | + | 0.546703i | \(0.815883\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.6146 | 0.456620 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9551 | 0.367008 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 13.7014i | 0.458501i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 3.59607i | − 0.120069i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 57.4622 | 1.91647 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.86718 | −0.295409 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 10.6290i | − 0.353711i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 57.2109i | − 1.89966i | −0.312771 | − | 0.949829i | \(-0.601257\pi\) | ||||
0.312771 | − | 0.949829i | \(-0.398743\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.9869 | 0.563420 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.0617 | −1.39357 | −0.696783 | − | 0.717282i | \(-0.745386\pi\) | ||||
−0.696783 | + | 0.717282i | \(0.745386\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.7243i | 0.586590i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.87372i | 0.0618757i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.68287 | −0.187461 | −0.0937304 | − | 0.995598i | \(-0.529879\pi\) | ||||
−0.0937304 | + | 0.995598i | \(0.529879\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.61462 | 0.316813 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 0.774918i | − 0.0255067i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 15.2264i | − 0.500100i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 30.9289 | 1.01474 | 0.507372 | − | 0.861727i | \(-0.330617\pi\) | ||||
0.507372 | + | 0.861727i | \(0.330617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.56314 | 0.182325 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 19.3921i | − 0.634870i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 44.5357i | − 1.45492i | −0.686152 | − | 0.727458i | \(-0.740701\pi\) | ||||
0.686152 | − | 0.727458i | \(-0.259299\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.55660 | 0.279234 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.08134 | −0.0678498 | −0.0339249 | − | 0.999424i | \(-0.510801\pi\) | ||||
−0.0339249 | + | 0.999424i | \(0.510801\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 20.0593i | − 0.653221i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.7189i | 1.71313i | 0.516036 | + | 0.856567i | \(0.327407\pi\) | ||||
−0.516036 | + | 0.856567i | \(0.672593\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.912115 | 0.0296085 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.74744 | 0.153946 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.22071i | − 0.104329i | −0.998639 | − | 0.0521645i | \(-0.983388\pi\) | ||||
0.998639 | − | 0.0521645i | \(-0.0166120\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 55.3293i | − 1.78854i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.9869 | 0.613119 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 22.3490 | 0.720935 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 25.5782i | − 0.824247i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.65956i | 0.0855256i | 0.999085 | + | 0.0427628i | \(0.0136160\pi\) | ||||
−0.999085 | + | 0.0427628i | \(0.986384\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.43686 | 0.0461586 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.1263 | 1.12726 | 0.563628 | − | 0.826029i | \(-0.309405\pi\) | ||||
0.563628 | + | 0.826029i | \(0.309405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 23.8068i | − 0.763210i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18.1668i | 0.581209i | 0.956843 | + | 0.290604i | \(0.0938563\pi\) | ||||
−0.956843 | + | 0.290604i | \(0.906144\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −33.3808 | −1.06686 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.5333 | −0.464012 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 48.4556i | − 1.54549i | −0.634714 | − | 0.772747i | \(-0.718882\pi\) | ||||
0.634714 | − | 0.772747i | \(-0.281118\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.6870i | 0.626645i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −60.8925 | −1.93627 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 29.8157 | 0.947127 | 0.473563 | − | 0.880760i | \(-0.342967\pi\) | ||||
0.473563 | + | 0.880760i | \(0.342967\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 7.13044i | − 0.226278i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.6894i | 0.940273i | 0.882594 | + | 0.470137i | \(0.155795\pi\) | ||||
−0.882594 | + | 0.470137i | \(0.844205\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 39.0449 | 1.23533 |
(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 | 1900.2.c.g.1749.5 | 6 | ||
5.2 | odd | 4 | 1900.2.a.f.1.3 | ✓ | 3 | ||
5.3 | odd | 4 | 1900.2.a.h.1.1 | yes | 3 | ||
5.4 | even | 2 | inner | 1900.2.c.g.1749.2 | 6 | ||
20.3 | even | 4 | 7600.2.a.bj.1.3 | 3 | |||
20.7 | even | 4 | 7600.2.a.by.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1900.2.a.f.1.3 | ✓ | 3 | 5.2 | odd | 4 | ||
1900.2.a.h.1.1 | yes | 3 | 5.3 | odd | 4 | ||
1900.2.c.g.1749.2 | 6 | 5.4 | even | 2 | inner | ||
1900.2.c.g.1749.5 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.bj.1.3 | 3 | 20.3 | even | 4 | |||
7600.2.a.by.1.1 | 3 | 20.7 | even | 4 |