Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(1079,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("1764.1079");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.e (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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | 12.0.653473922154496.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4x^{10} + 13x^{8} - 28x^{6} + 52x^{4} - 64x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{9} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1079.7 | ||
Root | \(0.892524 + 1.09700i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1079 |
Dual form | 1764.2.e.g.1079.8 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.892524 | − | 1.09700i | 0.631109 | − | 0.775694i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.406803 | − | 1.95819i | −0.203402 | − | 0.979095i | ||||
\(5\) | 2.56483i | 1.14703i | 0.819197 | + | 0.573513i | \(0.194420\pi\) | ||||
−0.819197 | + | 0.573513i | \(0.805580\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −2.51121 | − | 1.30147i | −0.887847 | − | 0.460139i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.81361 | + | 2.28917i | 0.889740 | + | 0.723899i | ||||
\(11\) | 1.15061 | 0.346923 | 0.173461 | − | 0.984841i | \(-0.444505\pi\) | ||||
0.173461 | + | 0.984841i | \(0.444505\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.578337 | 0.160402 | 0.0802009 | − | 0.996779i | \(-0.474444\pi\) | ||||
0.0802009 | + | 0.996779i | \(0.474444\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.66902 | + | 1.59320i | −0.917256 | + | 0.398299i | ||||
\(17\) | 5.39325i | 1.30806i | 0.756470 | + | 0.654028i | \(0.226922\pi\) | ||||
−0.756470 | + | 0.654028i | \(0.773078\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.20555i | − | 1.42365i | −0.702356 | − | 0.711825i | \(-0.747869\pi\) | ||
0.702356 | − | 0.711825i | \(-0.252131\pi\) | |||||||
\(20\) | 5.02242 | − | 1.04338i | 1.12305 | − | 0.233307i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.02695 | − | 1.26222i | 0.218946 | − | 0.269106i | ||||
\(23\) | 7.62536 | 1.59000 | 0.794999 | − | 0.606611i | \(-0.207471\pi\) | ||||
0.794999 | + | 0.606611i | \(0.207471\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.57834 | −0.315667 | ||||||||
\(26\) | 0.516180 | − | 0.634434i | 0.101231 | − | 0.124423i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.41421i | 0.262613i | 0.991342 | + | 0.131306i | \(0.0419172\pi\) | ||||
−0.991342 | + | 0.131306i | \(0.958083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.04888i | 0.906805i | 0.891306 | + | 0.453402i | \(0.149790\pi\) | ||||
−0.891306 | + | 0.453402i | \(0.850210\pi\) | |||||||
\(32\) | −1.52696 | + | 5.44687i | −0.269930 | + | 0.962880i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.91638 | + | 4.81361i | 1.01465 | + | 0.825527i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.83276 | 1.61650 | 0.808248 | − | 0.588842i | \(-0.200416\pi\) | ||||
0.808248 | + | 0.588842i | \(0.200416\pi\) | |||||||
\(38\) | −6.80747 | − | 5.53860i | −1.10432 | − | 0.898480i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.33804 | − | 6.44082i | 0.527791 | − | 1.01838i | ||||
\(41\) | − | 6.21115i | − | 0.970018i | −0.874509 | − | 0.485009i | \(-0.838816\pi\) | ||
0.874509 | − | 0.485009i | \(-0.161184\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2544i | 1.71628i | 0.513413 | + | 0.858142i | \(0.328381\pi\) | ||||
−0.513413 | + | 0.858142i | \(0.671619\pi\) | |||||||
\(44\) | −0.468073 | − | 2.25312i | −0.0705647 | − | 0.339671i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.80581 | − | 8.36499i | 1.00346 | − | 1.23335i | ||||
\(47\) | 11.0772 | 1.61578 | 0.807888 | − | 0.589336i | \(-0.200611\pi\) | ||||
0.807888 | + | 0.589336i | \(0.200611\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.40870 | + | 1.73143i | −0.199221 | + | 0.244861i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.235269 | − | 1.13249i | −0.0326260 | − | 0.157049i | ||||
\(53\) | 4.53333i | 0.622701i | 0.950295 | + | 0.311351i | \(0.100781\pi\) | ||||
−0.950295 | + | 0.311351i | \(0.899219\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.95112i | 0.397929i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.55139 | + | 1.26222i | 0.203707 | + | 0.165737i | ||||
\(59\) | 4.83896 | 0.629979 | 0.314990 | − | 0.949095i | \(-0.397999\pi\) | ||||
0.314990 | + | 0.949095i | \(0.397999\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.951124 | −0.121779 | −0.0608895 | − | 0.998145i | \(-0.519394\pi\) | ||||
−0.0608895 | + | 0.998145i | \(0.519394\pi\) | |||||||
\(62\) | 5.53860 | + | 4.50624i | 0.703403 | + | 0.572293i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.61235 | + | 6.53653i | 0.576544 | + | 0.817066i | ||||
\(65\) | 1.48333i | 0.183985i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.78389i | − | 0.340106i | −0.985435 | − | 0.170053i | \(-0.945606\pi\) | ||
0.985435 | − | 0.170053i | \(-0.0543939\pi\) | |||||||
\(68\) | 10.5610 | − | 2.19399i | 1.28071 | − | 0.266061i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68835 | 0.437726 | 0.218863 | − | 0.975756i | \(-0.429765\pi\) | ||||
0.218863 | + | 0.975756i | \(0.429765\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −14.0383 | −1.64306 | −0.821530 | − | 0.570165i | \(-0.806879\pi\) | ||||
−0.821530 | + | 0.570165i | \(0.806879\pi\) | |||||||
\(74\) | 8.77597 | − | 10.7865i | 1.02019 | − | 1.25391i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −12.1517 | + | 2.52444i | −1.39389 | + | 0.289573i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.8816i | − | 1.44930i | −0.689118 | − | 0.724649i | \(-0.742002\pi\) | ||
0.689118 | − | 0.724649i | \(-0.257998\pi\) | |||||||
\(80\) | −4.08627 | − | 9.41041i | −0.456859 | − | 1.05212i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.81361 | − | 5.54359i | −0.752437 | − | 0.612188i | ||||
\(83\) | 8.77597 | 0.963288 | 0.481644 | − | 0.876367i | \(-0.340040\pi\) | ||||
0.481644 | + | 0.876367i | \(0.340040\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −13.8328 | −1.50037 | ||||||||
\(86\) | 12.3461 | + | 10.0448i | 1.33131 | + | 1.08316i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.88943 | − | 1.49749i | −0.308014 | − | 0.159633i | ||||
\(89\) | 5.68395i | 0.602497i | 0.953546 | + | 0.301249i | \(0.0974034\pi\) | ||||
−0.953546 | + | 0.301249i | \(0.902597\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.10202 | − | 14.9319i | −0.323408 | − | 1.55676i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.88666 | − | 12.1517i | 1.01973 | − | 1.25335i | ||||
\(95\) | 15.9162 | 1.63296 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.8816 | 1.30793 | 0.653966 | − | 0.756524i | \(-0.273104\pi\) | ||||
0.653966 | + | 0.756524i | \(0.273104\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.642073 | + | 3.09069i | 0.0642073 | + | 0.309069i | ||||
\(101\) | − | 3.75747i | − | 0.373882i | −0.982371 | − | 0.186941i | \(-0.940143\pi\) | ||
0.982371 | − | 0.186941i | \(-0.0598574\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.79445i | 0.176812i | 0.996085 | + | 0.0884062i | \(0.0281774\pi\) | ||||
−0.996085 | + | 0.0884062i | \(0.971823\pi\) | |||||||
\(104\) | −1.45233 | − | 0.752688i | −0.142412 | − | 0.0738071i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.97305 | + | 4.04611i | 0.483025 | + | 0.392993i | ||||
\(107\) | −10.1631 | −0.982503 | −0.491252 | − | 0.871018i | \(-0.663460\pi\) | ||||
−0.491252 | + | 0.871018i | \(0.663460\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.2544 | −1.46111 | −0.730555 | − | 0.682854i | \(-0.760738\pi\) | ||||
−0.730555 | + | 0.682854i | \(0.760738\pi\) | |||||||
\(110\) | 3.23737 | + | 2.63395i | 0.308671 | + | 0.251137i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.06053i | 0.476055i | 0.971258 | + | 0.238027i | \(0.0765008\pi\) | ||||
−0.971258 | + | 0.238027i | \(0.923499\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 19.5577i | 1.82377i | ||||||||
\(116\) | 2.76930 | − | 0.575307i | 0.257123 | − | 0.0534159i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.31889 | − | 5.30833i | 0.397586 | − | 0.488671i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.67609 | −0.879644 | ||||||||
\(122\) | −0.848901 | + | 1.04338i | −0.0768559 | + | 0.0944632i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.88666 | − | 2.05390i | 0.887848 | − | 0.184446i | ||||
\(125\) | 8.77597i | 0.784947i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.470539i | 0.0417536i | 0.999782 | + | 0.0208768i | \(0.00664577\pi\) | ||||
−0.999782 | + | 0.0208768i | \(0.993354\pi\) | |||||||
\(128\) | 11.2872 | + | 0.774269i | 0.997655 | + | 0.0684364i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.62721 | + | 1.32391i | 0.142716 | + | 0.116115i | ||||
\(131\) | 15.9162 | 1.39060 | 0.695301 | − | 0.718719i | \(-0.255271\pi\) | ||||
0.695301 | + | 0.718719i | \(0.255271\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −3.05391 | − | 2.48469i | −0.263818 | − | 0.214644i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.01916 | − | 13.5436i | 0.601888 | − | 1.16135i | ||||
\(137\) | 8.55440i | 0.730852i | 0.930840 | + | 0.365426i | \(0.119077\pi\) | ||||
−0.930840 | + | 0.365426i | \(0.880923\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 16.0000i | − | 1.35710i | −0.734553 | − | 0.678551i | \(-0.762608\pi\) | ||
0.734553 | − | 0.678551i | \(-0.237392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.29194 | − | 4.04611i | 0.276253 | − | 0.339542i | ||||
\(143\) | 0.665442 | 0.0556471 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.62721 | −0.301224 | ||||||||
\(146\) | −12.5295 | + | 15.4000i | −1.03695 | + | 1.27451i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.00000 | − | 19.2544i | −0.328798 | − | 1.58270i | ||||
\(149\) | − | 16.8032i | − | 1.37657i | −0.725441 | − | 0.688285i | \(-0.758364\pi\) | ||
0.725441 | − | 0.688285i | \(-0.241636\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.09775i | 0.170713i | 0.996350 | + | 0.0853563i | \(0.0272029\pi\) | ||||
−0.996350 | + | 0.0853563i | \(0.972797\pi\) | |||||||
\(152\) | −8.07634 | + | 15.5834i | −0.655077 | + | 1.26398i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.9495 | −1.04013 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3622 | −1.38566 | −0.692828 | − | 0.721103i | \(-0.743636\pi\) | ||||
−0.692828 | + | 0.721103i | \(0.743636\pi\) | |||||||
\(158\) | −14.1311 | − | 11.4972i | −1.12421 | − | 0.914665i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −13.9703 | − | 3.91638i | −1.10445 | − | 0.309617i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 0.470539i | − | 0.0368554i | −0.999830 | − | 0.0184277i | \(-0.994134\pi\) | ||
0.999830 | − | 0.0184277i | \(-0.00586606\pi\) | |||||||
\(164\) | −12.1626 | + | 2.52671i | −0.949740 | + | 0.197303i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.83276 | − | 9.62721i | 0.607940 | − | 0.747217i | ||||
\(167\) | −20.7551 | −1.60608 | −0.803040 | − | 0.595925i | \(-0.796785\pi\) | ||||
−0.803040 | + | 0.595925i | \(0.796785\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6655 | −0.974271 | ||||||||
\(170\) | −12.3461 | + | 15.1745i | −0.946900 | + | 1.16383i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 22.0383 | − | 4.57834i | 1.68041 | − | 0.349095i | ||||
\(173\) | − | 14.1692i | − | 1.07727i | −0.842540 | − | 0.538633i | \(-0.818941\pi\) | ||
0.842540 | − | 0.538633i | \(-0.181059\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −4.22163 | + | 1.83315i | −0.318217 | + | 0.138179i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.23527 | + | 5.07306i | 0.467353 | + | 0.380242i | ||||
\(179\) | 1.15061 | 0.0860009 | 0.0430004 | − | 0.999075i | \(-0.486308\pi\) | ||||
0.0430004 | + | 0.999075i | \(0.486308\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.83276 | −0.284887 | −0.142444 | − | 0.989803i | \(-0.545496\pi\) | ||||
−0.142444 | + | 0.989803i | \(0.545496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −19.1489 | − | 9.92417i | −1.41167 | − | 0.731620i | ||||
\(185\) | 25.2193i | 1.85416i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.20555i | 0.453795i | ||||||||
\(188\) | −4.50624 | − | 21.6913i | −0.328651 | − | 1.58200i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 14.2056 | − | 17.4600i | 1.03058 | − | 1.26668i | ||||
\(191\) | −9.92659 | −0.718263 | −0.359131 | − | 0.933287i | \(-0.616927\pi\) | ||||
−0.359131 | + | 0.933287i | \(0.616927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6761 | 0.912445 | 0.456222 | − | 0.889866i | \(-0.349202\pi\) | ||||
0.456222 | + | 0.889866i | \(0.349202\pi\) | |||||||
\(194\) | 11.4972 | − | 14.1311i | 0.825448 | − | 1.01455i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.70491i | 0.121469i | 0.998154 | + | 0.0607347i | \(0.0193444\pi\) | ||||
−0.998154 | + | 0.0607347i | \(0.980656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8433i | 1.05222i | 0.850418 | + | 0.526108i | \(0.176349\pi\) | ||||
−0.850418 | + | 0.526108i | \(0.823651\pi\) | |||||||
\(200\) | 3.96354 | + | 2.05416i | 0.280264 | + | 0.145251i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.12193 | − | 3.35363i | −0.290018 | − | 0.235961i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.9305 | 1.11264 | ||||||||
\(206\) | 1.96851 | + | 1.60159i | 0.137152 | + | 0.111588i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12193 | + | 0.921405i | −0.147129 | + | 0.0638879i | ||||
\(209\) | − | 7.14019i | − | 0.493897i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.15667i | − | 0.0796287i | −0.999207 | − | 0.0398144i | \(-0.987323\pi\) | ||
0.999207 | − | 0.0398144i | \(-0.0126767\pi\) | |||||||
\(212\) | 8.87713 | − | 1.84417i | 0.609684 | − | 0.126658i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −9.07080 | + | 11.1489i | −0.620067 | + | 0.762122i | ||||
\(215\) | −28.8657 | −1.96862 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −13.6149 | + | 16.7341i | −0.922120 | + | 1.13337i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.77886 | − | 1.20053i | 0.389611 | − | 0.0809395i | ||||
\(221\) | 3.11912i | 0.209815i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.6655i | − | 1.58476i | −0.610027 | − | 0.792380i | \(-0.708842\pi\) | ||
0.610027 | − | 0.792380i | \(-0.291158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.55139 | + | 4.51664i | 0.369273 | + | 0.300443i | ||||
\(227\) | 9.44142 | 0.626649 | 0.313324 | − | 0.949646i | \(-0.398557\pi\) | ||||
0.313324 | + | 0.949646i | \(0.398557\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.578337 | 0.0382176 | 0.0191088 | − | 0.999817i | \(-0.493917\pi\) | ||||
0.0191088 | + | 0.999817i | \(0.493917\pi\) | |||||||
\(230\) | 21.4548 | + | 17.4557i | 1.41469 | + | 1.15100i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.84056 | − | 3.55139i | 0.120838 | − | 0.233160i | ||||
\(233\) | − | 0.305630i | − | 0.0200225i | −0.999950 | − | 0.0100112i | \(-0.996813\pi\) | ||
0.999950 | − | 0.0100112i | \(-0.00318673\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 28.4111i | 1.85334i | ||||||||
\(236\) | −1.96851 | − | 9.47561i | −0.128139 | − | 0.616810i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.92659 | 0.642098 | 0.321049 | − | 0.947063i | \(-0.395965\pi\) | ||||
0.321049 | + | 0.947063i | \(0.395965\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.29274 | −0.598598 | −0.299299 | − | 0.954159i | \(-0.596753\pi\) | ||||
−0.299299 | + | 0.954159i | \(0.596753\pi\) | |||||||
\(242\) | −8.63614 | + | 10.6146i | −0.555152 | + | 0.682335i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.386920 | + | 1.86248i | 0.0247700 | + | 0.119233i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.58890i | − | 0.228356i | ||||||
\(248\) | 6.57096 | − | 12.6788i | 0.417256 | − | 0.805104i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.62721 | + | 7.83276i | 0.608878 | + | 0.495387i | ||||
\(251\) | −3.93701 | −0.248502 | −0.124251 | − | 0.992251i | \(-0.539653\pi\) | ||||
−0.124251 | + | 0.992251i | \(0.539653\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.77384 | 0.551607 | ||||||||
\(254\) | 0.516180 | + | 0.419967i | 0.0323880 | + | 0.0263511i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.9234 | − | 11.6909i | 0.682716 | − | 0.730684i | ||||
\(257\) | 15.8891i | 0.991133i | 0.868570 | + | 0.495566i | \(0.165040\pi\) | ||||
−0.868570 | + | 0.495566i | \(0.834960\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.90465 | − | 0.603425i | 0.180139 | − | 0.0374228i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.2056 | − | 17.4600i | 0.877622 | − | 1.07868i | ||||
\(263\) | 1.38712 | 0.0855336 | 0.0427668 | − | 0.999085i | \(-0.486383\pi\) | ||||
0.0427668 | + | 0.999085i | \(0.486383\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.6272 | −0.714254 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.45138 | + | 1.13249i | −0.332996 | + | 0.0691781i | ||||
\(269\) | − | 1.60869i | − | 0.0980837i | −0.998797 | − | 0.0490419i | \(-0.984383\pi\) | ||
0.998797 | − | 0.0490419i | \(-0.0156168\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.30330i | 0.504390i | 0.967676 | + | 0.252195i | \(0.0811524\pi\) | ||||
−0.967676 | + | 0.252195i | \(0.918848\pi\) | |||||||
\(272\) | −8.59251 | − | 19.7880i | −0.520998 | − | 1.19982i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.38415 | + | 7.63501i | 0.566917 | + | 0.461248i | ||||
\(275\) | −1.81606 | −0.109512 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.83276 | −0.230288 | −0.115144 | − | 0.993349i | \(-0.536733\pi\) | ||||
−0.115144 | + | 0.993349i | \(0.536733\pi\) | |||||||
\(278\) | −17.5519 | − | 14.2804i | −1.05270 | − | 0.856480i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 28.9348i | 1.72610i | 0.505115 | + | 0.863052i | \(0.331450\pi\) | ||||
−0.505115 | + | 0.863052i | \(0.668550\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 31.0278i | − | 1.84441i | −0.386703 | − | 0.922204i | \(-0.626386\pi\) | ||
0.386703 | − | 0.922204i | \(-0.373614\pi\) | |||||||
\(284\) | −1.50043 | − | 7.22249i | −0.0890343 | − | 0.428576i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.593923 | − | 0.729988i | 0.0351194 | − | 0.0431651i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0872 | −0.711011 | ||||||||
\(290\) | −3.23737 | + | 3.97904i | −0.190105 | + | 0.233657i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.71083 | + | 27.4897i | 0.334201 | + | 1.60871i | ||||
\(293\) | − | 5.01850i | − | 0.293184i | −0.989197 | − | 0.146592i | \(-0.953170\pi\) | ||
0.989197 | − | 0.146592i | \(-0.0468305\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.4111i | 0.722602i | ||||||||
\(296\) | −24.6921 | − | 12.7970i | −1.43520 | − | 0.743813i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −18.4330 | − | 14.9972i | −1.06780 | − | 0.868766i | ||||
\(299\) | 4.41003 | 0.255039 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.30123 | + | 1.87229i | 0.132421 | + | 0.107738i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 9.88666 | + | 22.7683i | 0.567039 | + | 1.30585i | ||||
\(305\) | − | 2.43947i | − | 0.139684i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.3622i | 0.876768i | 0.898788 | + | 0.438384i | \(0.144449\pi\) | ||||
−0.898788 | + | 0.438384i | \(0.855551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −11.5577 | + | 14.2056i | −0.656435 | + | 0.806821i | ||||
\(311\) | −4.83896 | −0.274392 | −0.137196 | − | 0.990544i | \(-0.543809\pi\) | ||||
−0.137196 | + | 0.990544i | \(0.543809\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −19.7633 | −1.11709 | −0.558543 | − | 0.829475i | \(-0.688640\pi\) | ||||
−0.558543 | + | 0.829475i | \(0.688640\pi\) | |||||||
\(314\) | −15.4962 | + | 19.0463i | −0.874501 | + | 1.07484i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −25.2247 | + | 5.24029i | −1.41900 | + | 0.294789i | ||||
\(317\) | 5.96248i | 0.334886i | 0.985882 | + | 0.167443i | \(0.0535511\pi\) | ||||
−0.985882 | + | 0.167443i | \(0.946449\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.62721i | 0.0911064i | ||||||||
\(320\) | −16.7651 | + | 11.8299i | −0.937195 | + | 0.661311i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.4681 | 1.86222 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.912811 | −0.0506336 | ||||||||
\(326\) | −0.516180 | − | 0.419967i | −0.0285885 | − | 0.0232598i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −8.08362 | + | 15.5975i | −0.446343 | + | 0.861228i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.15667i | − | 0.0635766i | −0.999495 | − | 0.0317883i | \(-0.989880\pi\) | ||
0.999495 | − | 0.0317883i | \(-0.0101202\pi\) | |||||||
\(332\) | −3.57009 | − | 17.1850i | −0.195934 | − | 0.943151i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.5244 | + | 22.7683i | −1.01361 | + | 1.24583i | ||||
\(335\) | 7.14019 | 0.390110 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.25443 | 0.177280 | 0.0886399 | − | 0.996064i | \(-0.471748\pi\) | ||||
0.0886399 | + | 0.996064i | \(0.471748\pi\) | |||||||
\(338\) | −11.3043 | + | 13.8940i | −0.614872 | + | 0.755736i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 5.62721 | + | 27.0872i | 0.305178 | + | 1.46901i | ||||
\(341\) | 5.80930i | 0.314591i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 14.6473 | − | 28.2622i | 0.789729 | − | 1.52380i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.5436 | − | 12.6464i | −0.835629 | − | 0.679873i | ||||
\(347\) | −16.4013 | −0.880470 | −0.440235 | − | 0.897883i | \(-0.645105\pi\) | ||||
−0.440235 | + | 0.897883i | \(0.645105\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.20555 | 0.439233 | 0.219617 | − | 0.975586i | \(-0.429519\pi\) | ||||
0.219617 | + | 0.975586i | \(0.429519\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.75694 | + | 6.26724i | −0.0936451 | + | 0.334045i | ||||
\(353\) | 24.9557i | 1.32826i | 0.747617 | + | 0.664130i | \(0.231198\pi\) | ||||
−0.747617 | + | 0.664130i | \(0.768802\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.45998i | 0.502083i | ||||||||
\(356\) | 11.1303 | − | 2.31225i | 0.589902 | − | 0.122549i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.02695 | − | 1.26222i | 0.0542760 | − | 0.0667103i | ||||
\(359\) | 1.38712 | 0.0732095 | 0.0366048 | − | 0.999330i | \(-0.488346\pi\) | ||||
0.0366048 | + | 0.999330i | \(0.488346\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.5089 | −1.02678 | ||||||||
\(362\) | −3.42083 | + | 4.20453i | −0.179795 | + | 0.220985i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 36.0058i | − | 1.88463i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.9200i | 0.570017i | 0.958525 | + | 0.285008i | \(0.0919964\pi\) | ||||
−0.958525 | + | 0.285008i | \(0.908004\pi\) | |||||||
\(368\) | −27.9776 | + | 12.1487i | −1.45843 | + | 0.633295i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 27.6655 | + | 22.5089i | 1.43826 | + | 1.17018i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.6655 | 1.53602 | 0.768011 | − | 0.640436i | \(-0.221246\pi\) | ||||
0.768011 | + | 0.640436i | \(0.221246\pi\) | |||||||
\(374\) | 6.80747 | + | 5.53860i | 0.352006 | + | 0.286394i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −27.8172 | − | 14.4166i | −1.43456 | − | 0.743481i | ||||
\(377\) | 0.817892i | 0.0421236i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.66553i | − | 0.393752i | −0.980428 | − | 0.196876i | \(-0.936920\pi\) | ||
0.980428 | − | 0.196876i | \(-0.0630796\pi\) | |||||||
\(380\) | −6.47475 | − | 31.1669i | −0.332147 | − | 1.59883i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.85971 | + | 10.8894i | −0.453302 | + | 0.557152i | ||||
\(383\) | −10.8407 | −0.553933 | −0.276967 | − | 0.960880i | \(-0.589329\pi\) | ||||
−0.276967 | + | 0.960880i | \(0.589329\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.3137 | − | 13.9056i | 0.575853 | − | 0.707778i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.24029 | − | 25.2247i | −0.266036 | − | 1.28059i | ||||
\(389\) | − | 22.6125i | − | 1.14650i | −0.819381 | − | 0.573249i | \(-0.805683\pi\) | ||
0.819381 | − | 0.573249i | \(-0.194317\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.1255i | 2.07981i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.87028 | + | 1.52167i | 0.0942231 | + | 0.0766605i | ||||
\(395\) | 33.0392 | 1.66238 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.5577 | 1.08195 | 0.540976 | − | 0.841038i | \(-0.318055\pi\) | ||||
0.540976 | + | 0.841038i | \(0.318055\pi\) | |||||||
\(398\) | 16.2831 | + | 13.2480i | 0.816197 | + | 0.664063i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.79095 | − | 2.51460i | 0.289548 | − | 0.125730i | ||||
\(401\) | 1.26176i | 0.0630095i | 0.999504 | + | 0.0315047i | \(0.0100299\pi\) | ||||
−0.999504 | + | 0.0315047i | \(0.989970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.91995i | 0.145453i | ||||||||
\(404\) | −7.35784 | + | 1.52855i | −0.366066 | + | 0.0760482i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3137 | 0.560800 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.4494 | 1.70341 | 0.851707 | − | 0.524018i | \(-0.175568\pi\) | ||||
0.851707 | + | 0.524018i | \(0.175568\pi\) | |||||||
\(410\) | 14.2184 | − | 17.4757i | 0.702195 | − | 0.863064i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.51388 | − | 0.729988i | 0.173116 | − | 0.0359639i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 22.5089i | 1.10492i | ||||||||
\(416\) | −0.883096 | + | 3.15013i | −0.0432974 | + | 0.154448i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.83276 | − | 6.37279i | −0.383113 | − | 0.311703i | ||||
\(419\) | −16.5816 | −0.810064 | −0.405032 | − | 0.914302i | \(-0.632740\pi\) | ||||
−0.405032 | + | 0.914302i | \(0.632740\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.36274 | −0.407575 | −0.203788 | − | 0.979015i | \(-0.565325\pi\) | ||||
−0.203788 | + | 0.979015i | \(0.565325\pi\) | |||||||
\(422\) | −1.26887 | − | 1.03236i | −0.0617675 | − | 0.0502545i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.89999 | − | 11.3842i | 0.286529 | − | 0.552863i | ||||
\(425\) | − | 8.51237i | − | 0.412911i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 4.13438 | + | 19.9013i | 0.199843 | + | 0.961965i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −25.7633 | + | 31.6655i | −1.24242 | + | 1.52705i | ||||
\(431\) | −37.1565 | −1.78976 | −0.894882 | − | 0.446303i | \(-0.852740\pi\) | ||||
−0.894882 | + | 0.446303i | \(0.852740\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.56777 | 0.363684 | 0.181842 | − | 0.983328i | \(-0.441794\pi\) | ||||
0.181842 | + | 0.983328i | \(0.441794\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.20555 | + | 29.8711i | 0.297192 | + | 1.43057i | ||||
\(437\) | − | 47.3196i | − | 2.26360i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.8222i | 0.802880i | 0.915885 | + | 0.401440i | \(0.131490\pi\) | ||||
−0.915885 | + | 0.401440i | \(0.868510\pi\) | |||||||
\(440\) | 3.84080 | − | 7.41089i | 0.183103 | − | 0.353300i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.42166 | + | 2.78389i | 0.162752 | + | 0.132416i | ||||
\(443\) | 12.4643 | 0.592198 | 0.296099 | − | 0.955157i | \(-0.404314\pi\) | ||||
0.296099 | + | 0.955157i | \(0.404314\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.5783 | −0.691079 | ||||||||
\(446\) | −25.9610 | − | 21.1220i | −1.22929 | − | 1.00016i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.44582i | 0.351390i | 0.984445 | + | 0.175695i | \(0.0562172\pi\) | ||||
−0.984445 | + | 0.175695i | \(0.943783\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 7.14663i | − | 0.336522i | ||||||
\(452\) | 9.90949 | − | 2.05864i | 0.466103 | − | 0.0968303i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.42669 | − | 10.3572i | 0.395484 | − | 0.486088i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.68665 | −0.266010 | −0.133005 | − | 0.991115i | \(-0.542463\pi\) | ||||
−0.133005 | + | 0.991115i | \(0.542463\pi\) | |||||||
\(458\) | 0.516180 | − | 0.634434i | 0.0241195 | − | 0.0296451i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 38.2978 | − | 7.95615i | 1.78564 | − | 0.370957i | ||||
\(461\) | 0.790801i | 0.0368313i | 0.999830 | + | 0.0184156i | \(0.00586221\pi\) | ||||
−0.999830 | + | 0.0184156i | \(0.994138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 25.2927i | − | 1.17545i | −0.809060 | − | 0.587727i | \(-0.800023\pi\) | ||
0.809060 | − | 0.587727i | \(-0.199977\pi\) | |||||||
\(464\) | −2.25312 | − | 5.18878i | −0.104598 | − | 0.240883i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.335275 | − | 0.272782i | −0.0155313 | − | 0.0126364i | ||||
\(467\) | −40.8448 | −1.89007 | −0.945036 | − | 0.326966i | \(-0.893974\pi\) | ||||
−0.945036 | + | 0.326966i | \(0.893974\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 31.1669 | + | 25.3576i | 1.43762 | + | 1.16966i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.1517 | − | 6.29776i | −0.559325 | − | 0.289878i | ||||
\(473\) | 12.9495i | 0.595418i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 9.79445i | 0.449400i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.85971 | − | 10.8894i | 0.405234 | − | 0.498071i | ||||
\(479\) | 15.2507 | 0.696823 | 0.348412 | − | 0.937342i | \(-0.386721\pi\) | ||||
0.348412 | + | 0.937342i | \(0.386721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.68665 | 0.259289 | ||||||||
\(482\) | −8.29399 | + | 10.1941i | −0.377781 | + | 0.464329i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.93626 | + | 18.9476i | 0.178921 | + | 0.861256i | ||||
\(485\) | 33.0392i | 1.50023i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 24.6066i | − | 1.11503i | −0.830166 | − | 0.557516i | \(-0.811755\pi\) | ||
0.830166 | − | 0.557516i | \(-0.188245\pi\) | |||||||
\(488\) | 2.38847 | + | 1.23786i | 0.108121 | + | 0.0560353i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.3472 | −1.41468 | −0.707339 | − | 0.706875i | \(-0.750104\pi\) | ||||
−0.707339 | + | 0.706875i | \(0.750104\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.62721 | −0.343512 | ||||||||
\(494\) | −3.93701 | − | 3.20318i | −0.177135 | − | 0.144118i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.04385 | − | 18.5244i | −0.361180 | − | 0.831772i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.2544i | 0.503817i | 0.967751 | + | 0.251909i | \(0.0810583\pi\) | ||||
−0.967751 | + | 0.251909i | \(0.918942\pi\) | |||||||
\(500\) | 17.1850 | − | 3.57009i | 0.768538 | − | 0.159659i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −3.51388 | + | 4.31889i | −0.156832 | + | 0.192761i | ||||
\(503\) | 27.6588 | 1.23325 | 0.616623 | − | 0.787259i | \(-0.288500\pi\) | ||||
0.616623 | + | 0.787259i | \(0.288500\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.63726 | 0.428852 | ||||||||
\(506\) | 7.83086 | − | 9.62487i | 0.348124 | − | 0.427878i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.921405 | − | 0.191417i | 0.0408807 | − | 0.00849274i | ||||
\(509\) | − | 29.7947i | − | 1.32063i | −0.750990 | − | 0.660313i | \(-0.770423\pi\) | ||
0.750990 | − | 0.660313i | \(-0.229577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.07550 | − | 22.4174i | −0.135919 | − | 0.990720i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.4303 | + | 14.1814i | 0.768816 | + | 0.625513i | ||||
\(515\) | −4.60245 | −0.202808 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.7456 | 0.560550 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.93051 | − | 3.72496i | 0.0846587 | − | 0.163351i | ||||
\(521\) | 1.84520i | 0.0808397i | 0.999183 | + | 0.0404199i | \(0.0128696\pi\) | ||||
−0.999183 | + | 0.0404199i | \(0.987130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0000i | − | 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | −6.47475 | − | 31.1669i | −0.282851 | − | 1.36153i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.23804 | − | 1.52167i | 0.0539811 | − | 0.0663479i | ||||
\(527\) | −27.2299 | −1.18615 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 35.1461 | 1.52809 | ||||||||
\(530\) | −10.3776 | + | 12.7550i | −0.450772 | + | 0.554042i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 3.59214i | − | 0.155593i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 26.0666i | − | 1.12696i | ||||||
\(536\) | −3.62314 | + | 6.99093i | −0.156496 | + | 0.301962i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.76473 | − | 1.43580i | −0.0760829 | − | 0.0619016i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.3416 | −1.13251 | −0.566257 | − | 0.824229i | \(-0.691609\pi\) | ||||
−0.566257 | + | 0.824229i | \(0.691609\pi\) | |||||||
\(542\) | 9.10869 | + | 7.41089i | 0.391252 | + | 0.318325i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −29.3764 | − | 8.23527i | −1.25950 | − | 0.353084i | ||||
\(545\) | − | 39.1250i | − | 1.67593i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 0.805013i | − | 0.0344199i | −0.999852 | − | 0.0172099i | \(-0.994522\pi\) | ||
0.999852 | − | 0.0172099i | \(-0.00547836\pi\) | |||||||
\(548\) | 16.7512 | − | 3.47996i | 0.715574 | − | 0.148656i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.62087 | + | 1.99221i | −0.0691142 | + | 0.0849480i | ||||
\(551\) | 8.77597 | 0.373869 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −3.42083 | + | 4.20453i | −0.145337 | + | 0.178633i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −31.3311 | + | 6.50885i | −1.32873 | + | 0.276037i | ||||
\(557\) | − | 14.8909i | − | 0.630948i | −0.948934 | − | 0.315474i | \(-0.897836\pi\) | ||
0.948934 | − | 0.315474i | \(-0.102164\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.50885i | 0.275295i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 31.7414 | + | 25.8250i | 1.33893 | + | 1.08936i | ||||
\(563\) | −43.3825 | −1.82836 | −0.914178 | − | 0.405313i | \(-0.867163\pi\) | ||||
−0.914178 | + | 0.405313i | \(0.867163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.9794 | −0.546047 | ||||||||
\(566\) | −34.0373 | − | 27.6930i | −1.43070 | − | 1.16402i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.26222 | − | 4.80027i | −0.388634 | − | 0.201415i | ||||
\(569\) | − | 21.8786i | − | 0.917201i | −0.888643 | − | 0.458600i | \(-0.848351\pi\) | ||
0.888643 | − | 0.458600i | \(-0.151649\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 37.7038i | − | 1.57786i | −0.614485 | − | 0.788928i | \(-0.710636\pi\) | ||
0.614485 | − | 0.788928i | \(-0.289364\pi\) | |||||||
\(572\) | −0.270704 | − | 1.30306i | −0.0113187 | − | 0.0544838i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −12.0354 | −0.501910 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.4111 | 1.09951 | 0.549754 | − | 0.835326i | \(-0.314721\pi\) | ||||
0.549754 | + | 0.835326i | \(0.314721\pi\) | |||||||
\(578\) | −10.7881 | + | 13.2596i | −0.448726 | + | 0.551527i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.47556 | + | 7.10278i | 0.0612694 | + | 0.294927i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5.21611i | 0.216029i | ||||||||
\(584\) | 35.2532 | + | 18.2704i | 1.45879 | + | 0.756036i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.50528 | − | 4.47913i | −0.227421 | − | 0.185031i | ||||
\(587\) | 16.1527 | 0.666692 | 0.333346 | − | 0.942805i | \(-0.391822\pi\) | ||||
0.333346 | + | 0.942805i | \(0.391822\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.3311 | 1.29097 | ||||||||
\(590\) | 13.6149 | + | 11.0772i | 0.560518 | + | 0.456041i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −36.0766 | + | 15.6655i | −1.48274 | + | 0.643849i | ||||
\(593\) | 6.44765i | 0.264773i | 0.991198 | + | 0.132387i | \(0.0422641\pi\) | ||||
−0.991198 | + | 0.132387i | \(0.957736\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −32.9038 | + | 6.83559i | −1.34779 | + | 0.279997i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.93605 | − | 4.83779i | 0.160957 | − | 0.197832i | ||||
\(599\) | 18.9391 | 0.773829 | 0.386915 | − | 0.922116i | \(-0.373541\pi\) | ||||
0.386915 | + | 0.922116i | \(0.373541\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.4111 | −0.751004 | −0.375502 | − | 0.926821i | \(-0.622530\pi\) | ||||
−0.375502 | + | 0.926821i | \(0.622530\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.10780 | − | 0.853372i | 0.167144 | − | 0.0347232i | ||||
\(605\) | − | 24.8175i | − | 1.00897i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 24.6066i | − | 0.998751i | −0.866386 | − | 0.499376i | \(-0.833563\pi\) | ||
0.866386 | − | 0.499376i | \(-0.166437\pi\) | |||||||
\(608\) | 33.8008 | + | 9.47561i | 1.37080 | + | 0.384287i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.67609 | − | 2.17728i | −0.108352 | − | 0.0881556i | ||||
\(611\) | 6.40636 | 0.259173 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.09775 | 0.327065 | 0.163533 | − | 0.986538i | \(-0.447711\pi\) | ||||
0.163533 | + | 0.986538i | \(0.447711\pi\) | |||||||
\(614\) | 16.8523 | + | 13.7111i | 0.680104 | + | 0.553337i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.14459i | 0.207113i | 0.994624 | + | 0.103557i | \(0.0330223\pi\) | ||||
−0.994624 | + | 0.103557i | \(0.966978\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.2922i | 1.45871i | 0.684137 | + | 0.729354i | \(0.260179\pi\) | ||||
−0.684137 | + | 0.729354i | \(0.739821\pi\) | |||||||
\(620\) | 5.26790 | + | 25.3576i | 0.211564 | + | 1.01838i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.31889 | + | 5.30833i | −0.173172 | + | 0.212844i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.4005 | −1.21602 | ||||||||
\(626\) | −17.6392 | + | 21.6802i | −0.705004 | + | 0.866517i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7.06301 | + | 33.9985i | 0.281845 | + | 1.35669i | ||||
\(629\) | 53.0306i | 2.11447i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 19.7250i | − | 0.785238i | −0.919701 | − | 0.392619i | \(-0.871569\pi\) | ||
0.919701 | − | 0.392619i | \(-0.128431\pi\) | |||||||
\(632\) | −16.7651 | + | 32.3485i | −0.666878 | + | 1.28675i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 6.54082 | + | 5.32166i | 0.259769 | + | 0.211350i | ||||
\(635\) | −1.20685 | −0.0478924 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.78505 | + | 1.45233i | 0.0706707 | + | 0.0574981i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.98587 | + | 28.9497i | −0.0784983 | + | 1.14434i | ||||
\(641\) | 20.6860i | 0.817048i | 0.912748 | + | 0.408524i | \(0.133956\pi\) | ||||
−0.912748 | + | 0.408524i | \(0.866044\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.0278i | − | 0.592637i | −0.955089 | − | 0.296318i | \(-0.904241\pi\) | ||
0.955089 | − | 0.296318i | \(-0.0957589\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 29.8711 | − | 36.7144i | 1.17526 | − | 1.44451i | ||||
\(647\) | −22.3909 | −0.880277 | −0.440139 | − | 0.897930i | \(-0.645071\pi\) | ||||
−0.440139 | + | 0.897930i | \(0.645071\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.56777 | 0.218554 | ||||||||
\(650\) | −0.814705 | + | 1.00135i | −0.0319554 | + | 0.0392762i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −0.921405 | + | 0.191417i | −0.0360850 | + | 0.00749646i | ||||
\(653\) | − | 31.0978i | − | 1.21695i | −0.793573 | − | 0.608475i | \(-0.791782\pi\) | ||
0.793573 | − | 0.608475i | \(-0.208218\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 40.8222i | 1.59506i | ||||||||
\(656\) | 9.89558 | + | 22.7888i | 0.386357 | + | 0.889754i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.1631 | 0.395898 | 0.197949 | − | 0.980212i | \(-0.436572\pi\) | ||||
0.197949 | + | 0.980212i | \(0.436572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.1255 | 0.588314 | 0.294157 | − | 0.955757i | \(-0.404961\pi\) | ||||
0.294157 | + | 0.955757i | \(0.404961\pi\) | |||||||
\(662\) | −1.26887 | − | 1.03236i | −0.0493159 | − | 0.0401238i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −22.0383 | − | 11.4217i | −0.855252 | − | 0.443246i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 10.7839i | 0.417554i | ||||||||
\(668\) | 8.44325 | + | 40.6425i | 0.326679 | + | 1.57251i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.37279 | − | 7.83276i | 0.246202 | − | 0.302606i | ||||
\(671\) | −1.09438 | −0.0422479 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 36.8716 | 1.42130 | 0.710648 | − | 0.703548i | \(-0.248402\pi\) | ||||
0.710648 | + | 0.703548i | \(0.248402\pi\) | |||||||
\(674\) | 2.90465 | − | 3.57009i | 0.111883 | − | 0.137515i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.15238 | + | 24.8015i | 0.198168 | + | 0.953904i | ||||
\(677\) | 10.3705i | 0.398569i | 0.979942 | + | 0.199285i | \(0.0638618\pi\) | ||||
−0.979942 | + | 0.199285i | \(0.936138\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 34.7370 | + | 18.0029i | 1.33210 | + | 0.690381i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.37279 | + | 5.18494i | 0.244027 | + | 0.198542i | ||||
\(683\) | −9.19275 | −0.351751 | −0.175875 | − | 0.984412i | \(-0.556276\pi\) | ||||
−0.175875 | + | 0.984412i | \(0.556276\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.9406 | −0.838306 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −17.9305 | − | 41.2927i | −0.683594 | − | 1.57427i | ||||
\(689\) | 2.62179i | 0.0998824i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.8433i | 0.869001i | 0.900672 | + | 0.434501i | \(0.143075\pi\) | ||||
−0.900672 | + | 0.434501i | \(0.856925\pi\) | |||||||
\(692\) | −27.7460 | + | 5.76409i | −1.05475 | + | 0.219118i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.6386 | + | 17.9922i | −0.555673 | + | 0.682975i | ||||
\(695\) | 41.0372 | 1.55663 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 33.4983 | 1.26884 | ||||||||
\(698\) | 7.32365 | − | 9.00146i | 0.277204 | − | 0.340710i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.1044i | − | 0.721563i | −0.932650 | − | 0.360782i | \(-0.882510\pi\) | ||
0.932650 | − | 0.360782i | \(-0.117490\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 61.0177i | − | 2.30133i | ||||||
\(704\) | 5.30704 | + | 7.52102i | 0.200016 | + | 0.283459i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 27.3764 | + | 22.2736i | 1.03032 | + | 0.838277i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.56777 | −0.359325 | −0.179663 | − | 0.983728i | \(-0.557501\pi\) | ||||
−0.179663 | + | 0.983728i | \(0.557501\pi\) | |||||||
\(710\) | 10.3776 | + | 8.44325i | 0.389463 | + | 0.316870i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.39748 | − | 14.2736i | 0.277232 | − | 0.534925i | ||||
\(713\) | 38.4995i | 1.44182i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.70674i | 0.0638286i | ||||||||
\(716\) | −0.468073 | − | 2.25312i | −0.0174927 | − | 0.0842031i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.23804 | − | 1.52167i | 0.0462032 | − | 0.0567882i | ||||
\(719\) | 30.5014 | 1.13751 | 0.568756 | − | 0.822506i | \(-0.307425\pi\) | ||||
0.568756 | + | 0.822506i | \(0.307425\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.4121 | + | 21.4011i | −0.648012 | + | 0.796468i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.55918 | + | 7.50528i | 0.0579465 | + | 0.278932i | ||||
\(725\) | − | 2.23211i | − | 0.0828983i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 32.5189i | − | 1.20606i | −0.797719 | − | 0.603030i | \(-0.793960\pi\) | ||
0.797719 | − | 0.603030i | \(-0.206040\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −39.4983 | − | 32.1361i | −1.46190 | − | 1.18941i | ||||
\(731\) | −60.6980 | −2.24500 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −19.0106 | −0.702171 | −0.351086 | − | 0.936343i | \(-0.614187\pi\) | ||||
−0.351086 | + | 0.936343i | \(0.614187\pi\) | |||||||
\(734\) | 11.9792 | + | 9.74632i | 0.442159 | + | 0.359743i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.6436 | + | 41.5343i | −0.429189 | + | 1.53098i | ||||
\(737\) | − | 3.20318i | − | 0.117991i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 19.7250i | − | 0.725595i | −0.931868 | − | 0.362797i | \(-0.881822\pi\) | ||
0.931868 | − | 0.362797i | \(-0.118178\pi\) | |||||||
\(740\) | 49.3843 | − | 10.2593i | 1.81540 | − | 0.377140i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.8849 | −1.24312 | −0.621558 | − | 0.783368i | \(-0.713500\pi\) | ||||
−0.621558 | + | 0.783368i | \(0.713500\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 43.0972 | 1.57896 | ||||||||
\(746\) | 26.4772 | − | 32.5430i | 0.969399 | − | 1.19148i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 12.1517 | − | 2.52444i | 0.444308 | − | 0.0923026i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30.5089i | 1.11328i | 0.830753 | + | 0.556642i | \(0.187910\pi\) | ||||
−0.830753 | + | 0.556642i | \(0.812090\pi\) | |||||||
\(752\) | −40.6425 | + | 17.6482i | −1.48208 | + | 0.643562i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.897225 | + | 0.729988i | 0.0326750 | + | 0.0265846i | ||||
\(755\) | −5.38037 | −0.195812 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −48.0766 | −1.74737 | −0.873687 | − | 0.486488i | \(-0.838278\pi\) | ||||
−0.873687 | + | 0.486488i | \(0.838278\pi\) | |||||||
\(758\) | −8.40906 | − | 6.84166i | −0.305431 | − | 0.248500i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −39.9688 | − | 20.7144i | −1.44982 | − | 0.751390i | ||||
\(761\) | 13.4055i | 0.485950i | 0.970033 | + | 0.242975i | \(0.0781232\pi\) | ||||
−0.970033 | + | 0.242975i | \(0.921877\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4.03817 | + | 19.4382i | 0.146096 | + | 0.703248i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.67557 | + | 11.8922i | −0.349593 | + | 0.429683i | ||||
\(767\) | 2.79855 | 0.101050 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.4700 | −0.485741 | −0.242871 | − | 0.970059i | \(-0.578089\pi\) | ||||
−0.242871 | + | 0.970059i | \(0.578089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.15667 | − | 24.8222i | −0.185593 | − | 0.893371i | ||||
\(773\) | − | 28.5479i | − | 1.02680i | −0.858151 | − | 0.513398i | \(-0.828387\pi\) | ||
0.858151 | − | 0.513398i | \(-0.171613\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.96883i | − | 0.286249i | ||||||
\(776\) | −32.3485 | − | 16.7651i | −1.16124 | − | 0.601831i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.8058 | − | 20.1822i | −0.889332 | − | 0.723566i | ||||
\(779\) | −38.5436 | −1.38097 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.24386 | 0.151857 | ||||||||
\(782\) | 45.1145 | + | 36.7055i | 1.61329 | + | 1.31259i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 44.5311i | − | 1.58938i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 25.7633i | − | 0.918362i | −0.888343 | − | 0.459181i | \(-0.848143\pi\) | ||
0.888343 | − | 0.459181i | \(-0.151857\pi\) | |||||||
\(788\) | 3.33853 | − | 0.693561i | 0.118930 | − | 0.0247071i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 29.4882 | − | 36.2439i | 1.04914 | − | 1.28950i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.550070 | −0.0195336 | ||||||||
\(794\) | 19.2408 | − | 23.6488i | 0.682830 | − | 0.839263i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 29.0661 | − | 6.03831i | 1.03022 | − | 0.214022i | ||||
\(797\) | − | 23.3741i | − | 0.827954i | −0.910287 | − | 0.413977i | \(-0.864139\pi\) | ||
0.910287 | − | 0.413977i | \(-0.135861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 59.7422i | 2.11353i | ||||||||
\(800\) | 2.41005 | − | 8.59700i | 0.0852083 | − | 0.303950i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.38415 | + | 1.12615i | 0.0488761 | + | 0.0397659i | ||||
\(803\) | −16.1527 | −0.570015 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.20318 | + | 2.60613i | 0.112827 | + | 0.0917969i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.89023 | + | 9.43580i | −0.172038 | + | 0.331950i | ||||
\(809\) | − | 20.6019i | − | 0.724326i | −0.932115 | − | 0.362163i | \(-0.882038\pi\) | ||
0.932115 | − | 0.362163i | \(-0.117962\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.64782i | − | 0.0929776i | −0.998919 | − | 0.0464888i | \(-0.985197\pi\) | ||
0.998919 | − | 0.0464888i | \(-0.0148032\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 10.0978 | − | 12.4111i | 0.353926 | − | 0.435009i | ||||
\(815\) | 1.20685 | 0.0422741 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 69.8399 | 2.44339 | ||||||||
\(818\) | 30.7469 | − | 37.7909i | 1.07504 | − | 1.32133i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.48059 | − | 31.1950i | −0.226312 | − | 1.08938i | ||||
\(821\) | 43.5201i | 1.51886i | 0.650589 | + | 0.759430i | \(0.274522\pi\) | ||||
−0.650589 | + | 0.759430i | \(0.725478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 10.5683i | − | 0.368387i | −0.982890 | − | 0.184194i | \(-0.941033\pi\) | ||
0.982890 | − | 0.184194i | \(-0.0589674\pi\) | |||||||
\(824\) | 2.33542 | − | 4.50624i | 0.0813583 | − | 0.156982i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.92486 | 0.136481 | 0.0682403 | − | 0.997669i | \(-0.478262\pi\) | ||||
0.0682403 | + | 0.997669i | \(0.478262\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −15.2061 | −0.528129 | −0.264064 | − | 0.964505i | \(-0.585063\pi\) | ||||
−0.264064 | + | 0.964505i | \(0.585063\pi\) | |||||||
\(830\) | 24.6921 | + | 20.0897i | 0.857077 | + | 0.697323i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.66750 | + | 3.78032i | 0.0924788 | + | 0.131059i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 53.2333i | − | 1.84221i | ||||||
\(836\) | −13.9819 | + | 2.90465i | −0.483572 | + | 0.100459i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −14.7995 | + | 18.1900i | −0.511239 | + | 0.628362i | ||||
\(839\) | −12.2841 | −0.424093 | −0.212046 | − | 0.977260i | \(-0.568013\pi\) | ||||
−0.212046 | + | 0.977260i | \(0.568013\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000 | 0.931034 | ||||||||
\(842\) | −7.46394 | + | 9.17390i | −0.257224 | + | 0.316153i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.26499 | + | 0.470539i | −0.0779641 | + | 0.0161966i | ||||
\(845\) | − | 32.4849i | − | 1.11751i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −7.22249 | − | 16.6329i | −0.248021 | − | 0.571176i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.33804 | − | 7.59749i | −0.320292 | − | 0.260592i | ||||
\(851\) | 74.9784 | 2.57022 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2056 | −0.554867 | −0.277434 | − | 0.960745i | \(-0.589484\pi\) | ||||
−0.277434 | + | 0.960745i | \(0.589484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 25.5217 | + | 13.2270i | 0.872313 | + | 0.452088i | ||||
\(857\) | 15.9873i | 0.546117i | 0.961997 | + | 0.273059i | \(0.0880353\pi\) | ||||
−0.961997 | + | 0.273059i | \(0.911965\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 31.9688i | − | 1.09076i | −0.838188 | − | 0.545381i | \(-0.816385\pi\) | ||
0.838188 | − | 0.545381i | \(-0.183615\pi\) | |||||||
\(860\) | 11.7426 | + | 56.5245i | 0.400421 | + | 1.92747i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −33.1630 | + | 40.7605i | −1.12954 | + | 1.38831i | ||||
\(863\) | 38.9847 | 1.32705 | 0.663527 | − | 0.748153i | \(-0.269059\pi\) | ||||
0.663527 | + | 0.748153i | \(0.269059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 36.3416 | 1.23565 | ||||||||
\(866\) | 6.75442 | − | 8.30182i | 0.229524 | − | 0.282107i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 14.8218i | − | 0.502795i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.61003i | − | 0.0545536i | ||||||
\(872\) | 38.3071 | + | 19.8532i | 1.29724 | + | 0.672313i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −51.9094 | − | 42.2338i | −1.75586 | − | 1.42858i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.07663 | −0.205193 | −0.102597 | − | 0.994723i | \(-0.532715\pi\) | ||||
−0.102597 | + | 0.994723i | \(0.532715\pi\) | |||||||
\(878\) | 18.4539 | + | 15.0142i | 0.622789 | + | 0.506705i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.70172 | − | 10.8277i | −0.158495 | − | 0.365003i | ||||
\(881\) | 15.9575i | 0.537621i | 0.963193 | + | 0.268810i | \(0.0866305\pi\) | ||||
−0.963193 | + | 0.268810i | \(0.913370\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 43.2544i | − | 1.45563i | −0.685775 | − | 0.727814i | \(-0.740537\pi\) | ||
0.685775 | − | 0.727814i | \(-0.259463\pi\) | |||||||
\(884\) | 6.10783 | − | 1.26887i | 0.205429 | − | 0.0426766i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 11.1247 | − | 13.6733i | 0.373742 | − | 0.459364i | ||||
\(887\) | 46.1811 | 1.55061 | 0.775305 | − | 0.631587i | \(-0.217596\pi\) | ||||
0.775305 | + | 0.631587i | \(0.217596\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −13.0115 | + | 15.9924i | −0.436147 | + | 0.536066i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −46.3416 | + | 9.62721i | −1.55163 | + | 0.322343i | ||||
\(893\) | − | 68.7401i | − | 2.30030i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.95112i | 0.0986452i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.16804 | + | 6.64557i | 0.272571 | + | 0.221765i | ||||
\(899\) | −7.14019 | −0.238139 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −24.4494 | −0.814528 | ||||||||
\(902\) | −7.83983 | − | 6.37853i | −0.261038 | − | 0.212382i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.58613 | − | 12.7081i | 0.219051 | − | 0.422664i | ||||
\(905\) | − | 9.83037i | − | 0.326773i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 8.94108i | − | 0.296884i | −0.988921 | − | 0.148442i | \(-0.952574\pi\) | ||
0.988921 | − | 0.148442i | \(-0.0474258\pi\) | |||||||
\(908\) | −3.84080 | − | 18.4881i | −0.127461 | − | 0.613549i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −37.8219 | −1.25310 | −0.626548 | − | 0.779383i | \(-0.715533\pi\) | ||||
−0.626548 | + | 0.779383i | \(0.715533\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.0978 | 0.334187 | ||||||||
\(914\) | −5.07547 | + | 6.23824i | −0.167882 | + | 0.206343i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −0.235269 | − | 1.13249i | −0.00777352 | − | 0.0374187i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38.7244i | − | 1.27740i | −0.769455 | − | 0.638701i | \(-0.779472\pi\) | ||
0.769455 | − | 0.638701i | \(-0.220528\pi\) | |||||||
\(920\) | 25.4538 | − | 49.1136i | 0.839187 | − | 1.61923i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.867506 | + | 0.705808i | 0.0285698 | + | 0.0232446i | ||||
\(923\) | 2.13311 | 0.0702121 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −15.5194 | −0.510275 | ||||||||
\(926\) | −27.7460 | − | 22.5744i | −0.911792 | − | 0.741840i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −7.70304 | − | 2.15944i | −0.252865 | − | 0.0708872i | ||||
\(929\) | − | 11.9222i | − | 0.391154i | −0.980688 | − | 0.195577i | \(-0.937342\pi\) | ||
0.980688 | − | 0.195577i | \(-0.0626580\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.598481 | + | 0.124331i | −0.0196039 | + | 0.00407260i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −36.4550 | + | 44.8066i | −1.19284 | + | 1.46612i | ||||
\(935\) | −15.9162 | −0.520514 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.1744 | −0.920417 | −0.460208 | − | 0.887811i | \(-0.652225\pi\) | ||||
−0.460208 | + | 0.887811i | \(0.652225\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 55.6344 | − | 11.5577i | 1.81459 | − | 0.376972i | ||||
\(941\) | − | 53.9054i | − | 1.75727i | −0.477496 | − | 0.878634i | \(-0.658456\pi\) | ||
0.477496 | − | 0.878634i | \(-0.341544\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 47.3622i | − | 1.54233i | ||||||
\(944\) | −17.7543 | + | 7.70942i | −0.577852 | + | 0.250920i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 14.2056 | + | 11.5577i | 0.461862 | + | 0.375774i | ||||
\(947\) | 36.7275 | 1.19348 | 0.596742 | − | 0.802433i | \(-0.296462\pi\) | ||||
0.596742 | + | 0.802433i | \(0.296462\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.11888 | −0.263550 | ||||||||
\(950\) | 10.7445 | + | 8.74178i | 0.348597 | + | 0.283621i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 58.9090i | 1.90825i | 0.299408 | + | 0.954125i | \(0.403211\pi\) | ||||
−0.299408 | + | 0.954125i | \(0.596789\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 25.4600i | − | 0.823865i | ||||||
\(956\) | −4.03817 | − | 19.4382i | −0.130604 | − | 0.628675i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 13.6116 | − | 16.7300i | 0.439772 | − | 0.540521i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.50885 | 0.177705 | ||||||||
\(962\) | 5.07547 | − | 6.23824i | 0.163640 | − | 0.201129i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.78032 | + | 18.1970i | 0.121756 | + | 0.586084i | ||||
\(965\) | 32.5120i | 1.04660i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 43.6061i | − | 1.40228i | −0.713025 | − | 0.701139i | \(-0.752675\pi\) | ||
0.713025 | − | 0.701139i | \(-0.247325\pi\) | |||||||
\(968\) | 24.2987 | + | 12.5931i | 0.780990 | + | 0.404759i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 36.2439 | + | 29.4882i | 1.16372 | + | 0.946810i | ||||
\(971\) | 59.7960 | 1.91895 | 0.959473 | − | 0.281801i | \(-0.0909317\pi\) | ||||
0.959473 | + | 0.281801i | \(0.0909317\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −26.9934 | − | 21.9620i | −0.864923 | − | 0.703707i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.48970 | − | 1.51533i | 0.111702 | − | 0.0485045i | ||||
\(977\) | 41.5794i | 1.33024i | 0.746736 | + | 0.665121i | \(0.231620\pi\) | ||||
−0.746736 | + | 0.665121i | \(0.768380\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.54002i | 0.209020i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.9781 | + | 34.3877i | −0.892816 | + | 1.09736i | ||||
\(983\) | −0.428934 | −0.0136809 | −0.00684043 | − | 0.999977i | \(-0.502177\pi\) | ||||
−0.00684043 | + | 0.999977i | \(0.502177\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.37279 | −0.139329 | ||||||||
\(986\) | −6.80747 | + | 8.36703i | −0.216794 | + | 0.266460i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.02775 | + | 1.45998i | −0.223583 | + | 0.0464480i | ||||
\(989\) | 85.8190i | 2.72889i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 31.5466i | − | 1.00211i | −0.865415 | − | 0.501056i | \(-0.832945\pi\) | ||
0.865415 | − | 0.501056i | \(-0.167055\pi\) | |||||||
\(992\) | −27.5006 | − | 7.70942i | −0.873144 | − | 0.244774i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −38.0706 | −1.20692 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −34.7144 | −1.09942 | −0.549708 | − | 0.835357i | \(-0.685261\pi\) | ||||
−0.549708 | + | 0.835357i | \(0.685261\pi\) | |||||||
\(998\) | 12.3461 | + | 10.0448i | 0.390808 | + | 0.317964i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1764.2.e.g.1079.7 | 12 | ||
3.2 | odd | 2 | inner | 1764.2.e.g.1079.6 | 12 | ||
4.3 | odd | 2 | inner | 1764.2.e.g.1079.5 | 12 | ||
7.6 | odd | 2 | 252.2.e.a.71.7 | yes | 12 | ||
12.11 | even | 2 | inner | 1764.2.e.g.1079.8 | 12 | ||
21.20 | even | 2 | 252.2.e.a.71.6 | yes | 12 | ||
28.27 | even | 2 | 252.2.e.a.71.5 | ✓ | 12 | ||
56.13 | odd | 2 | 4032.2.h.h.575.10 | 12 | |||
56.27 | even | 2 | 4032.2.h.h.575.9 | 12 | |||
84.83 | odd | 2 | 252.2.e.a.71.8 | yes | 12 | ||
168.83 | odd | 2 | 4032.2.h.h.575.3 | 12 | |||
168.125 | even | 2 | 4032.2.h.h.575.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.e.a.71.5 | ✓ | 12 | 28.27 | even | 2 | ||
252.2.e.a.71.6 | yes | 12 | 21.20 | even | 2 | ||
252.2.e.a.71.7 | yes | 12 | 7.6 | odd | 2 | ||
252.2.e.a.71.8 | yes | 12 | 84.83 | odd | 2 | ||
1764.2.e.g.1079.5 | 12 | 4.3 | odd | 2 | inner | ||
1764.2.e.g.1079.6 | 12 | 3.2 | odd | 2 | inner | ||
1764.2.e.g.1079.7 | 12 | 1.1 | even | 1 | trivial | ||
1764.2.e.g.1079.8 | 12 | 12.11 | even | 2 | inner | ||
4032.2.h.h.575.3 | 12 | 168.83 | odd | 2 | |||
4032.2.h.h.575.4 | 12 | 168.125 | even | 2 | |||
4032.2.h.h.575.9 | 12 | 56.27 | even | 2 | |||
4032.2.h.h.575.10 | 12 | 56.13 | odd | 2 |