Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1520,2,Mod(1519,1520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1520.1519");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1520 = 2^{4} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1520.g (of order \(2\), degree \(1\), 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: | \(12.1372611072\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 20x^{14} + 271x^{12} - 2000x^{10} + 10645x^{8} - 29570x^{6} + 58816x^{4} - 56840x^{2} + 38416 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1519.11 | ||
Root | \(1.34352 + 0.775681i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1520.1519 |
Dual form | 1520.2.g.g.1519.5 |
$q$-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 \(\left(\mathbb{Z}/1520\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(401\) | \(1141\) | \(1217\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.55136i | 0.895679i | 0.894114 | + | 0.447840i | \(0.147806\pi\) | ||||
−0.894114 | + | 0.447840i | \(0.852194\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.03407 | − | 0.928731i | −0.909666 | − | 0.415341i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.46240 | −0.552736 | −0.276368 | − | 0.961052i | \(-0.589131\pi\) | ||||
−0.276368 | + | 0.961052i | \(0.589131\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.593276 | 0.197759 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.19396i | 0.661503i | 0.943718 | + | 0.330751i | \(0.107302\pi\) | ||||
−0.943718 | + | 0.330751i | \(0.892698\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35861 | 0.931510 | 0.465755 | − | 0.884914i | \(-0.345783\pi\) | ||||
0.465755 | + | 0.884914i | \(0.345783\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.44080 | − | 3.15559i | 0.372012 | − | 0.814769i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.77822i | 0.916352i | 0.888861 | + | 0.458176i | \(0.151497\pi\) | ||||
−0.888861 | + | 0.458176i | \(0.848503\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.27492 | − | 0.851518i | −0.980733 | − | 0.195352i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 2.26871i | − | 0.495074i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7.11926 | −1.48447 | −0.742234 | − | 0.670141i | \(-0.766234\pi\) | ||||
−0.742234 | + | 0.670141i | \(0.766234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.27492 | + | 3.77822i | 0.654983 | + | 0.755643i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.57447i | 1.07281i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.65663i | − | 1.23610i | −0.786137 | − | 0.618052i | \(-0.787922\pi\) | ||
0.786137 | − | 0.618052i | \(-0.212078\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.93185 | 0.346971 | 0.173485 | − | 0.984836i | \(-0.444497\pi\) | ||||
0.173485 | + | 0.984836i | \(0.444497\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.40362 | −0.592494 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.97463 | + | 1.35818i | 0.502805 | + | 0.229574i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.72463 | −0.776725 | −0.388362 | − | 0.921507i | \(-0.626959\pi\) | ||||
−0.388362 | + | 0.921507i | \(0.626959\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.21042i | 0.834334i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.88349i | − | 1.23119i | −0.788061 | − | 0.615597i | \(-0.788915\pi\) | ||
0.788061 | − | 0.615597i | \(-0.211085\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.50000 | −0.533745 | −0.266872 | − | 0.963732i | \(-0.585990\pi\) | ||||
−0.266872 | + | 0.963732i | \(0.585990\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.20677 | − | 0.550994i | −0.179894 | − | 0.0821374i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.37408 | 0.783889 | 0.391945 | − | 0.919989i | \(-0.371802\pi\) | ||||
0.391945 | + | 0.919989i | \(0.371802\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.86138 | −0.694483 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.86138 | −0.820757 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.9763 | −1.50771 | −0.753854 | − | 0.657042i | \(-0.771807\pi\) | ||||
−0.753854 | + | 0.657042i | \(0.771807\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.03760 | − | 4.46267i | 0.274749 | − | 0.601747i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.32101 | − | 6.63194i | 0.174972 | − | 0.878422i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −13.4615 | −1.75253 | −0.876267 | − | 0.481826i | \(-0.839974\pi\) | ||||
−0.876267 | + | 0.481826i | \(0.839974\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.80004 | −0.486546 | −0.243273 | − | 0.969958i | \(-0.578221\pi\) | ||||
−0.243273 | + | 0.969958i | \(0.578221\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.867609 | −0.109308 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −6.83166 | − | 3.11924i | −0.847363 | − | 0.386895i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0.493890i | 0.0603383i | 0.999545 | + | 0.0301692i | \(0.00960460\pi\) | ||||
−0.999545 | + | 0.0301692i | \(0.990395\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 11.0445i | − | 1.32961i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.93185 | −0.229269 | −0.114634 | − | 0.993408i | \(-0.536570\pi\) | ||||
−0.114634 | + | 0.993408i | \(0.536570\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.0857i | 1.29748i | 0.761011 | + | 0.648739i | \(0.224703\pi\) | ||||
−0.761011 | + | 0.648739i | \(0.775297\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.86138 | + | 5.08058i | −0.676814 | + | 0.586655i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.20845i | − | 0.365636i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.949745 | −0.106855 | −0.0534273 | − | 0.998572i | \(-0.517015\pi\) | ||||
−0.0534273 | + | 0.998572i | \(0.517015\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.86819 | −0.763133 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.79241 | −0.416271 | −0.208136 | − | 0.978100i | \(-0.566740\pi\) | ||||
−0.208136 | + | 0.978100i | \(0.566740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.50895 | − | 7.68517i | 0.380599 | − | 0.833574i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.3268 | 1.10715 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 18.3043i | − | 1.94025i | −0.242596 | − | 0.970127i | \(-0.577999\pi\) | ||
0.242596 | − | 0.970127i | \(-0.422001\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.91164 | −0.514879 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.99700i | 0.310774i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.90467 | + | 5.70230i | 0.811002 | + | 0.585044i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.649442 | −0.0659408 | −0.0329704 | − | 0.999456i | \(-0.510497\pi\) | ||||
−0.0329704 | + | 0.999456i | \(0.510497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.30162i | 0.130818i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.749790 | 0.0746068 | 0.0373034 | − | 0.999304i | \(-0.488123\pi\) | ||||
0.0373034 | + | 0.999304i | \(0.488123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.28806i | 0.225449i | 0.993626 | + | 0.112725i | \(0.0359578\pi\) | ||||
−0.993626 | + | 0.112725i | \(0.964042\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.10703 | + | 4.61473i | −0.205625 | + | 0.450352i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.7578i | 1.33001i | 0.746837 | + | 0.665007i | \(0.231572\pi\) | ||||
−0.746837 | + | 0.665007i | \(0.768428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 3.76421i | − | 0.360545i | −0.983617 | − | 0.180273i | \(-0.942302\pi\) | ||
0.983617 | − | 0.180273i | \(-0.0576980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 7.32962i | − | 0.695696i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.32101 | 0.124270 | 0.0621352 | − | 0.998068i | \(-0.480209\pi\) | ||||
0.0621352 | + | 0.998068i | \(0.480209\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.4811 | + | 6.61187i | 1.35037 | + | 0.616560i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.99258 | 0.184214 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 5.52527i | − | 0.506501i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.18655 | 0.562414 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.2302 | 1.10276 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.15248 | − | 10.7267i | −0.281966 | − | 0.959424i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 20.8056i | − | 1.84620i | −0.384557 | − | 0.923101i | \(-0.625646\pi\) | ||
0.384557 | − | 0.923101i | \(-0.374354\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.42976i | − | 0.478064i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 8.00153i | − | 0.699097i | −0.936918 | − | 0.349549i | \(-0.886335\pi\) | ||
0.936918 | − | 0.349549i | \(-0.113665\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.25165 | + | 1.24526i | 0.542087 | + | 0.107978i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.17719 | − | 11.3389i | 0.445581 | − | 0.975896i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 7.61972i | 0.650997i | 0.945543 | + | 0.325498i | \(0.105532\pi\) | ||||
−0.945543 | + | 0.325498i | \(0.894468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.81188i | 0.832232i | 0.909311 | + | 0.416116i | \(0.136609\pi\) | ||||
−0.909311 | + | 0.416116i | \(0.863391\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.33713i | 0.702113i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.36864i | 0.616197i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.18222 | + | 13.5401i | −0.513405 | + | 1.12444i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 7.54176i | − | 0.622034i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −15.3678 | −1.25898 | −0.629488 | − | 0.777010i | \(-0.716736\pi\) | ||||
−0.629488 | + | 0.777010i | \(0.716736\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.7228 | 0.953985 | 0.476992 | − | 0.878907i | \(-0.341727\pi\) | ||||
0.476992 | + | 0.878907i | \(0.341727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.24153i | 0.181217i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.92953 | − | 1.79417i | −0.315627 | − | 0.144111i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.0470i | − | 0.801834i | −0.916114 | − | 0.400917i | \(-0.868692\pi\) | ||
0.916114 | − | 0.400917i | \(-0.131308\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 17.0282i | − | 1.35042i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4112 | 0.820519 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −17.1730 | −1.34509 | −0.672545 | − | 0.740056i | \(-0.734799\pi\) | ||||
−0.672545 | + | 0.740056i | \(0.734799\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.92322 | + | 3.16105i | 0.538972 | + | 0.246087i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.76243i | 0.755439i | 0.925920 | + | 0.377720i | \(0.123292\pi\) | ||||
−0.925920 | + | 0.377720i | \(0.876708\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.71975 | −0.132288 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.53621 | − | 0.505186i | −0.193949 | − | 0.0386325i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.96823 | −0.529785 | −0.264892 | − | 0.964278i | \(-0.585336\pi\) | ||||
−0.264892 | + | 0.964278i | \(0.585336\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.78925 | − | 5.52527i | −0.362033 | − | 0.417671i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 20.8836i | − | 1.56971i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.73639 | −0.279271 | −0.139635 | − | 0.990203i | \(-0.544593\pi\) | ||||
−0.139635 | + | 0.990203i | \(0.544593\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.5703i | 0.785688i | 0.919605 | + | 0.392844i | \(0.128509\pi\) | ||||
−0.919605 | + | 0.392844i | \(0.871491\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 5.89524i | − | 0.435789i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.61026 | + | 4.38791i | 0.706560 | + | 0.322606i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.28924 | −0.606170 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 8.15212i | − | 0.592979i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 23.1684i | 1.67641i | 0.545357 | + | 0.838204i | \(0.316394\pi\) | ||||
−0.545357 | + | 0.838204i | \(0.683606\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 26.6772 | 1.92027 | 0.960133 | − | 0.279543i | \(-0.0901828\pi\) | ||||
0.960133 | + | 0.279543i | \(0.0901828\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.83908 | − | 10.5984i | 0.346533 | − | 0.758965i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 22.9268i | 1.63347i | 0.577016 | + | 0.816733i | \(0.304217\pi\) | ||||
−0.577016 | + | 0.816733i | \(0.695783\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7447i | 1.04523i | 0.852570 | + | 0.522613i | \(0.175043\pi\) | ||||
−0.852570 | + | 0.522613i | \(0.824957\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.766203 | −0.0540438 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.73467i | 0.683240i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.32165 | + | 16.0356i | −0.511366 | + | 1.11998i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.22369 | −0.293567 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.86819 | − | 9.37898i | 0.129226 | − | 0.648758i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.2749 | 1.25810 | 0.629049 | − | 0.777366i | \(-0.283445\pi\) | ||||
0.629049 | + | 0.777366i | \(0.283445\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 2.99700i | − | 0.205351i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.11926 | + | 3.25056i | 0.485529 | + | 0.221686i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.82514 | −0.191783 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −17.1979 | −1.16212 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 12.6895i | 0.853591i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 8.18331i | − | 0.547995i | −0.961730 | − | 0.273997i | \(-0.911654\pi\) | ||
0.961730 | − | 0.273997i | \(-0.0883459\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.94293 | + | 2.24153i | 0.129529 | + | 0.149435i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 19.1869i | − | 1.27348i | −0.771079 | − | 0.636739i | \(-0.780283\pi\) | ||
0.771079 | − | 0.636739i | \(-0.219717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.4180 | 1.21710 | 0.608549 | − | 0.793516i | \(-0.291752\pi\) | ||||
0.608549 | + | 0.793516i | \(0.291752\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.97746 | 0.327493 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.6447i | 1.54902i | 0.632564 | + | 0.774508i | \(0.282002\pi\) | ||||
−0.632564 | + | 0.774508i | \(0.717998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −10.9313 | − | 4.99107i | −0.713077 | − | 0.325582i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 1.47340i | − | 0.0957075i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.28195i | 0.0829222i | 0.999140 | + | 0.0414611i | \(0.0132013\pi\) | ||||
−0.999140 | + | 0.0414611i | \(0.986799\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2057i | 1.04390i | 0.852976 | + | 0.521950i | \(0.174795\pi\) | ||||
−0.852976 | + | 0.521950i | \(0.825205\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.06836i | 0.389286i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.88841 | + | 4.51491i | 0.631747 | + | 0.288447i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.3578 | − | 2.85992i | −0.913563 | − | 0.181972i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 5.88340i | − | 0.372846i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 9.07288i | 0.572675i | 0.958129 | + | 0.286338i | \(0.0924379\pi\) | ||||
−0.958129 | + | 0.286338i | \(0.907562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 15.6193i | − | 0.981980i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 11.9225 | + | 5.44365i | 0.746615 | + | 0.340894i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −22.3731 | −1.39560 | −0.697798 | − | 0.716294i | \(-0.745837\pi\) | ||||
−0.697798 | + | 0.716294i | \(0.745837\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.90931 | 0.429324 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 3.94922i | − | 0.244451i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.5342 | −1.45118 | −0.725591 | − | 0.688126i | \(-0.758434\pi\) | ||||
−0.725591 | + | 0.688126i | \(0.758434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 22.3266 | + | 10.1940i | 1.37151 | + | 0.626213i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 28.3966 | 1.73785 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 11.9163i | − | 0.726551i | −0.931682 | − | 0.363276i | \(-0.881658\pi\) | ||
0.931682 | − | 0.363276i | \(-0.118342\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.28374i | − | 0.381710i | −0.981618 | − | 0.190855i | \(-0.938874\pi\) | ||
0.981618 | − | 0.190855i | \(-0.0611261\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 7.61972i | − | 0.461167i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.28924 | + | 7.18503i | −0.499860 | + | 0.433273i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.6808i | 1.18250i | 0.806487 | + | 0.591252i | \(0.201366\pi\) | ||||
−0.806487 | + | 0.591252i | \(0.798634\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.14612 | 0.0686165 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.4119i | 0.919397i | 0.888075 | + | 0.459699i | \(0.152043\pi\) | ||||
−0.888075 | + | 0.459699i | \(0.847957\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.49163 | −0.504775 | −0.252388 | − | 0.967626i | \(-0.581216\pi\) | ||||
−0.252388 | + | 0.967626i | \(0.581216\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −8.84633 | + | 12.2630i | −0.524011 | + | 0.726397i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 11.5288i | 0.680526i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.72508 | 0.160299 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 1.00752i | − | 0.0590618i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −16.2603 | −0.949939 | −0.474969 | − | 0.880002i | \(-0.657541\pi\) | ||||
−0.474969 | + | 0.880002i | \(0.657541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 27.3816 | + | 12.5021i | 1.59422 | + | 0.727900i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.2302 | −0.709665 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.9108 | −1.38280 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.11840 | 0.295020 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.16319i | 0.0668238i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 7.72957 | + | 3.52922i | 0.442594 | + | 0.202083i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.61145i | 0.434408i | 0.976126 | + | 0.217204i | \(0.0696938\pi\) | ||||
−0.976126 | + | 0.217204i | \(0.930306\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.54961 | −0.201930 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 25.3938i | − | 1.43995i | −0.693998 | − | 0.719976i | \(-0.744153\pi\) | ||
0.693998 | − | 0.719976i | \(-0.255847\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.75926i | − | 0.495103i | −0.968875 | − | 0.247551i | \(-0.920374\pi\) | ||
0.968875 | − | 0.247551i | \(-0.0796259\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.76478 | + | 0.805775i | 0.0994341 | + | 0.0454003i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.5349 | 1.26568 | 0.632842 | − | 0.774281i | \(-0.281888\pi\) | ||||
0.632842 | + | 0.774281i | \(0.281888\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6044 | 0.817687 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −21.3433 | −1.19127 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.21722 | − | 16.1516i | 0.179011 | − | 0.898697i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 10.9992 | + | 12.6895i | 0.610124 | + | 0.703890i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.83964 | 0.322933 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.85906 | −0.433284 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3107 | 0.896517 | 0.448259 | − | 0.893904i | \(-0.352044\pi\) | ||||
0.448259 | + | 0.893904i | \(0.352044\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.80301 | −0.153604 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.458691 | − | 1.00461i | 0.0250610 | − | 0.0548877i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 32.7228 | 1.78253 | 0.891263 | − | 0.453486i | \(-0.149820\pi\) | ||||
0.891263 | + | 0.453486i | \(0.149820\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.04937i | 0.111306i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.23840i | 0.229522i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3461 | 0.936602 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −10.2574 | + | 22.4654i | −0.552240 | + | 1.20950i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −21.7333 | −1.16671 | −0.583353 | − | 0.812219i | \(-0.698259\pi\) | ||||
−0.583353 | + | 0.812219i | \(0.698259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −22.0090 | −1.17811 | −0.589057 | − | 0.808092i | \(-0.700501\pi\) | ||||
−0.589057 | + | 0.808092i | \(0.700501\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.7225i | 0.999331i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.7441i | − | 1.05087i | −0.850833 | − | 0.525435i | \(-0.823902\pi\) | ||
0.850833 | − | 0.525435i | \(-0.176098\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.92953 | + | 1.79417i | 0.208558 | + | 0.0952247i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 8.57169 | 0.453662 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.91631i | − | 0.259473i | −0.991549 | − | 0.129737i | \(-0.958587\pi\) | ||
0.991549 | − | 0.129737i | \(-0.0414132\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.5498 | + | 7.28034i | 0.923675 | + | 0.383176i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.59758i | 0.503742i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.2956 | − | 22.5490i | 0.538896 | − | 1.18027i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.1813 | −0.635860 | −0.317930 | − | 0.948114i | \(-0.602988\pi\) | ||||
−0.317930 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 4.67709i | − | 0.243480i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.0517 | 0.833365 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.99111 | 0.361986 | 0.180993 | − | 0.983484i | \(-0.442069\pi\) | ||||
0.180993 | + | 0.983484i | \(0.442069\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 16.6410 | − | 4.89063i | 0.859336 | − | 0.252551i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 22.3570i | − | 1.15144i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.1744 | −1.03629 | −0.518145 | − | 0.855293i | \(-0.673377\pi\) | ||||
−0.518145 | + | 0.855293i | \(0.673377\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 32.2771 | 1.65361 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 29.1621i | − | 1.49011i | −0.667002 | − | 0.745056i | \(-0.732423\pi\) | ||
0.667002 | − | 0.745056i | \(-0.267577\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.97978 | + | 6.52622i | −0.151864 | + | 0.332607i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.07647 | −0.105553 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6278 | 0.690957 | 0.345479 | − | 0.938427i | \(-0.387717\pi\) | ||||
0.345479 | + | 0.938427i | \(0.387717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 26.8981i | − | 1.36029i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 12.4133 | 0.626167 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.93185 | + | 0.882057i | 0.0972020 | + | 0.0443811i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.3863i | 0.671839i | 0.941891 | + | 0.335920i | \(0.109047\pi\) | ||||
−0.941891 | + | 0.335920i | \(0.890953\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.93185 | + | 9.69857i | −0.0967135 | + | 0.485536i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.3043i | 0.914074i | 0.889448 | + | 0.457037i | \(0.151089\pi\) | ||||
−0.889448 | + | 0.457037i | \(0.848911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.48833 | 0.323207 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.9704 | + | 6.37870i | 0.694196 | + | 0.316960i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 10.3656i | − | 0.513806i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.6505i | 1.16944i | 0.811235 | + | 0.584721i | \(0.198796\pi\) | ||||
−0.811235 | + | 0.584721i | \(0.801204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −11.8209 | −0.583084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 19.6861 | 0.968689 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 7.71405 | + | 3.52213i | 0.378668 | + | 0.172895i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.2218 | −0.745413 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2792i | 1.18612i | 0.805159 | + | 0.593059i | \(0.202080\pi\) | ||||
−0.805159 | + | 0.593059i | \(0.797920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.3249i | 0.893100i | 0.894759 | + | 0.446550i | \(0.147347\pi\) | ||||
−0.894759 | + | 0.446550i | \(0.852653\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3.18831 | 0.155021 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.2749 | + | 12.3733i | −0.692435 | + | 0.600195i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.55719 | 0.268931 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.4314 | −0.551915 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.78109 | −0.230297 | −0.115148 | − | 0.993348i | \(-0.536734\pi\) | ||||
−0.115148 | + | 0.993348i | \(0.536734\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.9008 | −1.43694 | −0.718470 | − | 0.695558i | \(-0.755157\pi\) | ||||
−0.718470 | + | 0.695558i | \(0.755157\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.0056 | − | 9.59086i | −1.00714 | − | 0.459846i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.4342 | + | 6.06217i | 1.45587 | + | 0.289993i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.7551 | 0.561041 | 0.280521 | − | 0.959848i | \(-0.409493\pi\) | ||||
0.280521 | + | 0.959848i | \(0.409493\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.88414 | −0.137340 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 39.8004 | 1.89097 | 0.945486 | − | 0.325662i | \(-0.105587\pi\) | ||||
0.945486 | + | 0.325662i | \(0.105587\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.9998 | + | 37.2324i | −0.805868 | + | 1.76498i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 23.8410i | − | 1.12764i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.72870i | − | 0.175968i | −0.996122 | − | 0.0879842i | \(-0.971957\pi\) | ||
0.996122 | − | 0.0879842i | \(-0.0280425\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.2960 | 0.814439 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.1862i | 0.854464i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 9.99063 | + | 4.56159i | 0.468368 | + | 0.213851i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 22.1456i | − | 1.03593i | −0.855403 | − | 0.517963i | \(-0.826691\pi\) | ||
0.855403 | − | 0.517963i | \(-0.173309\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −21.0616 | −0.983069 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.0413 | −0.467672 | −0.233836 | − | 0.972276i | \(-0.575128\pi\) | ||||
−0.233836 | + | 0.972276i | \(0.575128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.7598 | 1.01126 | 0.505632 | − | 0.862749i | \(-0.331259\pi\) | ||||
0.505632 | + | 0.862749i | \(0.331259\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.78341 | − | 6.09612i | 0.129077 | − | 0.282701i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.84631 | −0.177986 | −0.0889929 | − | 0.996032i | \(-0.528365\pi\) | ||||
−0.0889929 | + | 0.996032i | \(0.528365\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 0.722266i | − | 0.0333512i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15.5865 | 0.718186 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 7.67884i | − | 0.353074i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.7828 | − | 18.9402i | −0.494748 | − | 0.869037i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6.51197 | −0.298163 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 2.72216i | − | 0.124379i | −0.998064 | − | 0.0621893i | \(-0.980192\pi\) | ||
0.998064 | − | 0.0621893i | \(-0.0198082\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.8682 | −0.723527 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 16.1516i | 0.734921i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.32101 | + | 0.603157i | 0.0599841 | + | 0.0273879i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.553011i | 0.0250593i | 0.999922 | + | 0.0125297i | \(0.00398842\pi\) | ||||
−0.999922 | + | 0.0125297i | \(0.996012\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 26.6415i | − | 1.20477i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 23.5295i | − | 1.06187i | −0.847412 | − | 0.530936i | \(-0.821841\pi\) | ||
0.847412 | − | 0.530936i | \(-0.178159\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.1502 | 1.13271 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.20886 | − | 2.64760i | 0.0543341 | − | 0.119001i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.82514 | 0.126725 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 37.2206i | − | 1.66622i | −0.553106 | − | 0.833111i | \(-0.686558\pi\) | ||
0.553106 | − | 0.833111i | \(-0.313442\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.1451 | −0.676631 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 33.4033 | 1.48938 | 0.744690 | − | 0.667411i | \(-0.232598\pi\) | ||||
0.744690 | + | 0.667411i | \(0.232598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.52513 | − | 0.696353i | −0.0678673 | − | 0.0309873i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 2.66795i | − | 0.118488i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 16.0562i | − | 0.711677i | −0.934547 | − | 0.355839i | \(-0.884195\pi\) | ||
0.934547 | − | 0.355839i | \(-0.115805\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 16.2117i | − | 0.717162i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.74676 | − | 23.8304i | 0.209575 | − | 1.05214i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.12499 | − | 4.65409i | 0.0936384 | − | 0.205084i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.7905i | 0.518545i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10.8102i | − | 0.474517i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 16.3042i | 0.714302i | 0.934047 | + | 0.357151i | \(0.116252\pi\) | ||||
−0.934047 | + | 0.357151i | \(0.883748\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.96826i | 0.348428i | 0.984708 | + | 0.174214i | \(0.0557384\pi\) | ||||
−0.984708 | + | 0.174214i | \(0.944262\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.57169 | − | 7.42985i | 0.374099 | − | 0.324265i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.29895i | 0.317947i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 27.6838 | 1.20364 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.98637 | −0.346579 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 26.4776i | − | 1.14687i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 12.7773 | − | 27.9843i | 0.552410 | − | 1.20987i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 5.79649i | − | 0.250137i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 10.6657i | − | 0.459402i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.79022 | 0.119961 | 0.0599805 | − | 0.998200i | \(-0.480896\pi\) | ||||
0.0599805 | + | 0.998200i | \(0.480896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −16.3984 | −0.703724 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.49593 | + | 7.65667i | −0.149749 | + | 0.327976i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.0858i | 0.645023i | 0.946566 | + | 0.322511i | \(0.104527\pi\) | ||||
−0.946566 | + | 0.322511i | \(0.895473\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.25448 | −0.0962187 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.66824 | + | 28.4565i | −0.241475 | + | 1.21229i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.38891 | 0.0590624 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.80724 | + | 14.9090i | −0.288951 | + | 0.632851i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.40942i | 0.356319i | 0.984002 | + | 0.178159i | \(0.0570143\pi\) | ||||
−0.984002 | + | 0.178159i | \(0.942986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11.7551 | −0.497189 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 12.8596i | − | 0.542933i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 13.7472i | − | 0.579376i | −0.957121 | − | 0.289688i | \(-0.906449\pi\) | ||
0.957121 | − | 0.289688i | \(-0.0935515\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.68704 | − | 1.22687i | −0.113045 | − | 0.0516146i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.0441 | 0.421811 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 34.9636i | − | 1.46575i | −0.680362 | − | 0.732876i | \(-0.738177\pi\) | ||
0.680362 | − | 0.732876i | \(-0.261823\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 39.3338i | 1.64607i | 0.567993 | + | 0.823033i | \(0.307720\pi\) | ||||
−0.567993 | + | 0.823033i | \(0.692280\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −35.9426 | −1.50152 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3150 | − | 26.8981i | −0.972302 | − | 1.12173i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 21.3816i | − | 0.890128i | −0.895499 | − | 0.445064i | \(-0.853181\pi\) | ||
0.895499 | − | 0.445064i | \(-0.146819\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.3860i | 1.71994i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.54603 | 0.230088 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.0815i | − | 0.997353i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.05306 | − | 1.85057i | −0.167574 | − | 0.0765118i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −0.143920 | −0.00594020 | −0.00297010 | − | 0.999996i | \(-0.500945\pi\) | ||||
−0.00297010 | + | 0.999996i | \(0.500945\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.25850 | − | 1.64501i | −0.340286 | − | 0.0677813i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.5677 | −1.46306 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 6.83002i | 0.280475i | 0.990118 | + | 0.140238i | \(0.0447867\pi\) | ||||
−0.990118 | + | 0.140238i | \(0.955213\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.13149 | + | 11.2388i | −0.210371 | + | 0.460746i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.8744 | −0.936187 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.79091 | 0.400046 | 0.200023 | − | 0.979791i | \(-0.435898\pi\) | ||||
0.200023 | + | 0.979791i | \(0.435898\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 0.892334i | − | 0.0363991i | −0.999834 | − | 0.0181995i | \(-0.994207\pi\) | ||
0.999834 | − | 0.0181995i | \(-0.00579341\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.293014i | 0.0119324i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −12.5839 | − | 5.74564i | −0.511609 | − | 0.233594i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.0511i | 0.773261i | 0.922235 | + | 0.386630i | \(0.126361\pi\) | ||||
−0.922235 | + | 0.386630i | \(0.873639\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.1020 | −0.611964 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 18.0494 | 0.730201 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.40119i | − | 0.0565935i | −0.999600 | − | 0.0282968i | \(-0.990992\pi\) | ||
0.999600 | − | 0.0282968i | \(-0.00900834\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −24.8770 | − | 11.3585i | −1.00314 | − | 0.458020i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17.6034i | 0.708686i | 0.935116 | + | 0.354343i | \(0.115295\pi\) | ||||
−0.935116 | + | 0.354343i | \(0.884705\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 24.7967i | − | 0.996663i | −0.866987 | − | 0.498332i | \(-0.833946\pi\) | ||
0.866987 | − | 0.498332i | \(-0.166054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 39.6861i | − | 1.59255i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 26.7683i | 1.07245i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.54983 | + | 24.7467i | −0.141993 | + | 0.989868i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 14.5502 | + | 2.89824i | 0.581079 | + | 0.115745i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 17.8507i | − | 0.711753i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.4713i | 1.69076i | 0.534168 | + | 0.845378i | \(0.320625\pi\) | ||||
−0.534168 | + | 0.845378i | \(0.679375\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 28.3510i | 1.12685i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −19.3229 | + | 42.3202i | −0.766804 | + | 1.67943i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.3275 | −0.646918 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.14612 | −0.0453399 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 12.4209i | − | 0.490597i | −0.969448 | − | 0.245298i | \(-0.921114\pi\) | ||
0.969448 | − | 0.245298i | \(-0.0788860\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.5374 | 1.44089 | 0.720447 | − | 0.693510i | \(-0.243937\pi\) | ||||
0.720447 | + | 0.693510i | \(0.243937\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −5.04279 | + | 11.0445i | −0.198560 | + | 0.434878i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.56726 | −0.179557 | −0.0897787 | − | 0.995962i | \(-0.528616\pi\) | ||||
−0.0897787 | + | 0.995962i | \(0.528616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 29.5339i | − | 1.15931i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 4.38282i | − | 0.171776i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 11.3938i | 0.445873i | 0.974833 | + | 0.222936i | \(0.0715642\pi\) | ||||
−0.974833 | + | 0.222936i | \(0.928436\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.43127 | + | 16.2757i | −0.290364 | + | 0.635945i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.57686i | 0.256588i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.73407 | −0.223367 | −0.111684 | − | 0.993744i | \(-0.535624\pi\) | ||||
−0.111684 | + | 0.993744i | \(0.535624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.21794i | 0.241850i | 0.992662 | + | 0.120925i | \(0.0385860\pi\) | ||||
−0.992662 | + | 0.120925i | \(0.961414\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −19.6861 | −0.764544 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.5598 | − | 8.33905i | −0.448270 | − | 0.323375i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 47.3902i | 1.83496i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 12.6953 | 0.490827 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 8.33713i | − | 0.321852i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.6412 | −0.525829 | −0.262915 | − | 0.964819i | \(-0.584684\pi\) | ||||
−0.262915 | + | 0.964819i | \(0.584684\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −21.0616 | + | 18.2559i | −0.810660 | + | 0.702671i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −27.1885 | −1.04494 | −0.522470 | − | 0.852658i | \(-0.674989\pi\) | ||||
−0.522470 | + | 0.852658i | \(0.674989\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.949745 | 0.0364479 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29.7658 | 1.14063 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 7.54176i | − | 0.288577i | −0.989536 | − | 0.144289i | \(-0.953911\pi\) | ||
0.989536 | − | 0.144289i | \(-0.0460894\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.07667 | − | 15.4991i | 0.270386 | − | 0.592190i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 28.5730i | 1.09013i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −36.8650 | −1.40445 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.05081i | − | 0.306267i | −0.988205 | − | 0.153134i | \(-0.951064\pi\) | ||
0.988205 | − | 0.153134i | \(-0.0489365\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 1.90350i | − | 0.0723078i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.11259 | − | 19.9581i | 0.345660 | − | 0.757053i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 29.7855 | 1.12821 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −36.6815 | −1.38742 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −24.0914 | −0.909919 | −0.454959 | − | 0.890512i | \(-0.650346\pi\) | ||||
−0.454959 | + | 0.890512i | \(0.650346\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.1974 | + | 4.02311i | 0.761760 | + | 0.151734i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.74296 | − | 16.9584i | 0.291617 | − | 0.638689i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.09649 | −0.0412379 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.8492 | 0.783009 | 0.391505 | − | 0.920176i | \(-0.371955\pi\) | ||||
0.391505 | + | 0.920176i | \(0.371955\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.563461 | −0.0211314 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.7533 | −0.515067 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.84349 | − | 14.9884i | 0.255932 | − | 0.560533i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.98876 | −0.0742717 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.5723i | 1.17745i | 0.808334 | + | 0.588725i | \(0.200370\pi\) | ||||
−0.808334 | + | 0.588725i | \(0.799630\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 3.34606i | − | 0.124614i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.1409 | −0.934999 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.1502 | − | 21.7999i | 0.934054 | − | 0.809628i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −23.4978 | −0.871484 | −0.435742 | − | 0.900072i | \(-0.643514\pi\) | ||||
−0.435742 | + | 0.900072i | \(0.643514\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −30.0188 | −1.11181 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 13.2237i | − | 0.489098i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.5959i | 0.723792i | 0.932219 | + | 0.361896i | \(0.117870\pi\) | ||||
−0.932219 | + | 0.361896i | \(0.882130\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.00427 | + | 15.3405i | −0.258356 | + | 0.565843i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.08357 | −0.0399140 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 24.9089i | − | 0.916290i | −0.888878 | − | 0.458145i | \(-0.848514\pi\) | ||
0.888878 | − | 0.458145i | \(-0.151486\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.43676 | − | 22.2741i | 0.162989 | − | 0.818260i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 32.3345i | − | 1.18624i | −0.805115 | − | 0.593119i | \(-0.797897\pi\) | ||
0.805115 | − | 0.593119i | \(-0.202103\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.2592 | + | 14.2725i | 1.14525 | + | 0.522905i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.24995 | −0.0823213 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 20.1194i | − | 0.735147i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.0405 | −1.57057 | −0.785285 | − | 0.619134i | \(-0.787484\pi\) | ||||
−0.785285 | + | 0.619134i | \(0.787484\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.0753 | −0.512933 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −23.8450 | − | 10.8873i | −0.867807 | − | 0.396229i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 18.6163i | 0.676622i | 0.941034 | + | 0.338311i | \(0.109856\pi\) | ||||
−0.941034 | + | 0.338311i | \(0.890144\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 24.2313 | 0.879539 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.35647 | 0.339172 | 0.169586 | − | 0.985515i | \(-0.445757\pi\) | ||||
0.169586 | + | 0.985515i | \(0.445757\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.50478i | 0.199286i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.08178 | − | 4.55943i | 0.0752668 | − | 0.164847i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −45.2118 | −1.63250 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.57965 | −0.129085 | −0.0645427 | − | 0.997915i | \(-0.520559\pi\) | ||||
−0.0645427 | + | 0.997915i | \(0.520559\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 34.7088i | − | 1.25001i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.31435 | −0.119209 | −0.0596044 | − | 0.998222i | \(-0.518984\pi\) | ||||
−0.0596044 | + | 0.998222i | \(0.518984\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.32665 | + | 7.29895i | 0.227260 | + | 0.262186i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 10.7188i | 0.384536i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.71294 | + | 33.7013i | −0.240516 | + | 1.20747i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.23840i | − | 0.151662i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.1072 | 1.32610 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −9.33092 | + | 20.4363i | −0.333035 | + | 0.729401i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 46.4213i | − | 1.65474i | −0.561657 | − | 0.827370i | \(-0.689836\pi\) | ||
0.561657 | − | 0.827370i | \(-0.310164\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 36.5101i | − | 1.29979i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.93185 | −0.0686887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −12.7629 | −0.453223 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −15.8146 | + | 34.6366i | −0.560886 | + | 1.22843i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −32.4726 | −1.15024 | −0.575119 | − | 0.818070i | \(-0.695044\pi\) | ||||
−0.575119 | + | 0.818070i | \(0.695044\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 20.3044i | 0.718319i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 10.8595i | − | 0.383703i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.3214 | −0.858285 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −21.1772 | − | 9.66922i | −0.746398 | − | 0.340795i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 18.4865 | 0.650757 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.69828 | 0.340973 | 0.170487 | − | 0.985360i | \(-0.445466\pi\) | ||||
0.170487 | + | 0.985360i | \(0.445466\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.1242 | 0.741769 | 0.370885 | − | 0.928679i | \(-0.379055\pi\) | ||||
0.370885 | + | 0.928679i | \(0.379055\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.74836 | 0.341890 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 34.9311 | + | 15.9491i | 1.22358 | + | 0.558671i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.9622 | + | 2.98031i | 0.523461 | + | 0.104268i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.91396 | −0.101822 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16.1721 | 0.564410 | 0.282205 | − | 0.959354i | \(-0.408934\pi\) | ||||
0.282205 | + | 0.959354i | \(0.408934\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.5211 | −1.34276 | −0.671380 | − | 0.741113i | \(-0.734298\pi\) | ||||
−0.671380 | + | 0.741113i | \(0.734298\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.1466 | − | 12.8596i | −0.388074 | − | 0.447714i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 17.4324i | 0.606182i | 0.952962 | + | 0.303091i | \(0.0980187\pi\) | ||||
−0.952962 | + | 0.303091i | \(0.901981\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.9228i | 0.518289i | 0.965839 | + | 0.259144i | \(0.0834406\pi\) | ||||
−0.965839 | + | 0.259144i | \(0.916559\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −30.5320 | −1.05914 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 18.3673i | − | 0.636391i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.06667 | − | 19.8575i | 0.313765 | − | 0.687197i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.7691i | 0.372233i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.4357 | −0.636471 | −0.318235 | − | 0.948012i | \(-0.603090\pi\) | ||||
−0.318235 | + | 0.948012i | \(0.603090\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.3107 | −0.527955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −23.9094 | −0.823485 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.49810 | + | 1.59718i | 0.120338 | + | 0.0549448i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.04723 | −0.310866 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.1736i | − | 0.452117i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 33.6359 | 1.15302 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 52.1480i | − | 1.78551i | −0.450538 | − | 0.892757i | \(-0.648768\pi\) | ||
0.450538 | − | 0.892757i | \(-0.351232\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.68965 | + | 3.38304i | 0.160383 | + | 0.115698i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −40.1131 | −1.37024 | −0.685119 | − | 0.728431i | \(-0.740250\pi\) | ||||
−0.685119 | + | 0.728431i | \(0.740250\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.6430i | 1.65968i | 0.558003 | + | 0.829839i | \(0.311568\pi\) | ||||
−0.558003 | + | 0.829839i | \(0.688432\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −17.8854 | −0.609533 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.3735i | 0.625442i | 0.949845 | + | 0.312721i | \(0.101241\pi\) | ||||
−0.949845 | + | 0.312721i | \(0.898759\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 14.1739 | + | 6.47161i | 0.481927 | + | 0.220041i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.22759i | 0.143576i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.08370i | − | 0.0706846i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.65878i | 0.0562058i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.385298 | −0.0130404 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.61019 | + | 15.6867i | 0.155853 | + | 0.530308i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.1870 | 0.918041 | 0.459020 | − | 0.888426i | \(-0.348201\pi\) | ||||
0.459020 | + | 0.888426i | \(0.348201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 25.2257i | − | 0.850840i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.3814 | 0.652976 | 0.326488 | − | 0.945201i | \(-0.394135\pi\) | ||||
0.326488 | + | 0.945201i | \(0.394135\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.74348 | 0.159631 | 0.0798154 | − | 0.996810i | \(-0.474567\pi\) | ||||
0.0798154 | + | 0.996810i | \(0.474567\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.3953 | + | 42.4788i | −0.651964 | + | 1.42791i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 29.1621i | − | 0.979166i | −0.871957 | − | 0.489583i | \(-0.837149\pi\) | ||
0.871957 | − | 0.489583i | \(-0.162851\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.4262i | 1.02046i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 15.0685i | − | 0.504814i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.9737 | − | 4.57612i | −0.768786 | − | 0.153134i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.60009 | + | 3.47010i | 0.254043 | + | 0.115993i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 37.0943i | − | 1.23854i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 12.8596i | − | 0.428892i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 41.4708i | − | 1.38159i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.94050i | 0.264243i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.81701 | − | 21.5009i | 0.326329 | − | 0.714713i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 34.2149i | − | 1.13609i | −0.822999 | − | 0.568043i | \(-0.807701\pi\) | ||
0.822999 | − | 0.568043i | \(-0.192299\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.444832 | 0.0147542 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −38.6457 | −1.28039 | −0.640195 | − | 0.768213i | \(-0.721146\pi\) | ||||
−0.640195 | + | 0.768213i | \(0.721146\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.32039i | − | 0.275365i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.47510 | + | 11.9914i | −0.181001 | + | 0.396422i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.7015i | 0.386416i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 34.4725i | − | 1.13714i | −0.822634 | − | 0.568572i | \(-0.807496\pi\) | ||
0.822634 | − | 0.568572i | \(-0.192504\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −11.8081 | −0.389091 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.48833 | −0.213566 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.4728 | − | 17.8507i | −0.508742 | − | 0.586927i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.35745i | 0.0445846i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.59777 | 0.118039 | 0.0590195 | − | 0.998257i | \(-0.481203\pi\) | ||||
0.0590195 | + | 0.998257i | \(0.481203\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.7820 | + | 4.13955i | 0.681102 | + | 0.135668i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 39.3950 | 1.28974 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.8609 | + | 7.69848i | 0.551412 | + | 0.251767i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.2584i | 1.21718i | 0.793485 | + | 0.608590i | \(0.208265\pi\) | ||||
−0.793485 | + | 0.608590i | \(0.791735\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.5888 | 0.443453 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.4378i | 1.15524i | 0.816306 | + | 0.577620i | \(0.196019\pi\) | ||||
−0.816306 | + | 0.577620i | \(0.803981\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 56.1246i | 1.82767i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.57113 | + | 16.5820i | −0.246289 | + | 0.539413i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.40034 | 0.110496 | 0.0552481 | − | 0.998473i | \(-0.482405\pi\) | ||||
0.0552481 | + | 0.998473i | \(0.482405\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 37.2324i | 1.20861i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 34.9597i | 1.13365i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28.6783 | 0.928982 | 0.464491 | − | 0.885578i | \(-0.346237\pi\) | ||||
0.464491 | + | 0.885578i | \(0.346237\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 21.5172 | − | 47.1263i | 0.696281 | − | 1.52497i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.6566i | 0.732385i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 11.1431i | − | 0.359829i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −27.2680 | −0.879611 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.16217i | 0.263022i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −54.2634 | − | 24.7759i | −1.74680 | − | 0.797566i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.4948 | −0.466121 | −0.233061 | − | 0.972462i | \(-0.574874\pi\) | ||||
−0.233061 | + | 0.972462i | \(0.574874\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 25.0569 | + | 4.99107i | 0.804944 | + | 0.160336i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.7760 | 0.538367 | 0.269183 | − | 0.963089i | \(-0.413246\pi\) | ||||
0.269183 | + | 0.963089i | \(0.413246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 14.3489i | − | 0.460005i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.6861 | + | 17.0637i | −0.630459 | + | 0.546475i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 50.1439 | 1.60425 | 0.802124 | − | 0.597158i | \(-0.203704\pi\) | ||||
0.802124 | + | 0.597158i | \(0.203704\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 40.1589 | 1.28348 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 2.23321i | − | 0.0713010i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 27.2922i | 0.870487i | 0.900313 | + | 0.435243i | \(0.143338\pi\) | ||||
−0.900313 | + | 0.435243i | \(0.856662\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 21.2928 | − | 46.6348i | 0.678445 | − | 1.48591i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 12.1922i | − | 0.388083i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 24.9174 | 0.792327 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.5622 | −1.86029 | −0.930145 | − | 0.367191i | \(-0.880319\pi\) | ||||
−0.930145 | + | 0.367191i | \(0.880319\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25.3038i | 0.802992i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.6939 | − | 29.9919i | 0.434125 | − | 0.950806i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 48.1715i | − | 1.52561i | −0.646631 | − | 0.762803i | \(-0.723823\pi\) | ||
0.646631 | − | 0.762803i | \(-0.276177\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 26.3373i | − | 0.833276i |
(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 | 1520.2.g.g.1519.11 | yes | 16 | |
4.3 | odd | 2 | 1520.2.g.e.1519.6 | yes | 16 | ||
5.4 | even | 2 | inner | 1520.2.g.g.1519.6 | yes | 16 | |
19.18 | odd | 2 | 1520.2.g.e.1519.5 | ✓ | 16 | ||
20.19 | odd | 2 | 1520.2.g.e.1519.11 | yes | 16 | ||
76.75 | even | 2 | inner | 1520.2.g.g.1519.12 | yes | 16 | |
95.94 | odd | 2 | 1520.2.g.e.1519.12 | yes | 16 | ||
380.379 | even | 2 | inner | 1520.2.g.g.1519.5 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1520.2.g.e.1519.5 | ✓ | 16 | 19.18 | odd | 2 | ||
1520.2.g.e.1519.6 | yes | 16 | 4.3 | odd | 2 | ||
1520.2.g.e.1519.11 | yes | 16 | 20.19 | odd | 2 | ||
1520.2.g.e.1519.12 | yes | 16 | 95.94 | odd | 2 | ||
1520.2.g.g.1519.5 | yes | 16 | 380.379 | even | 2 | inner | |
1520.2.g.g.1519.6 | yes | 16 | 5.4 | even | 2 | inner | |
1520.2.g.g.1519.11 | yes | 16 | 1.1 | even | 1 | trivial | |
1520.2.g.g.1519.12 | yes | 16 | 76.75 | even | 2 | inner |