Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3240,2,Mod(1081,3240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3240, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3240.1081");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3240 = 2^{3} \cdot 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3240.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.8715302549\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1080) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2161.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3240.2161 |
Dual form | 3240.2.q.p.1081.1 |
$q$-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 \(\left(\mathbb{Z}/3240\mathbb{Z}\right)^\times\).
\(n\) | \(1297\) | \(1621\) | \(2431\) | \(3161\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.500000 | + | 0.866025i | 0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.73205i | −0.377964 | + | 0.654654i | −0.990766 | − | 0.135583i | \(-0.956709\pi\) |
0.612801 | + | 0.790237i | \(0.290043\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | − | 3.46410i | 0.603023 | − | 1.04447i | −0.389338 | − | 0.921095i | \(-0.627296\pi\) |
0.992361 | − | 0.123371i | \(-0.0393705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | + | 1.73205i | 0.277350 | + | 0.480384i | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) |
−0.693375 | + | 0.720577i | \(0.743877\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.00000 | −1.21268 | −0.606339 | − | 0.795206i | \(-0.707363\pi\) | ||||
−0.606339 | + | 0.795206i | \(0.707363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.00000 | −1.14708 | −0.573539 | − | 0.819178i | \(-0.694430\pi\) | ||||
−0.573539 | + | 0.819178i | \(0.694430\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | + | 1.73205i | −0.185695 | + | 0.321634i | −0.943811 | − | 0.330487i | \(-0.892787\pi\) |
0.758115 | + | 0.652121i | \(0.226120\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.50000 | − | 6.06218i | −0.628619 | − | 1.08880i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.359211 | − | 0.933257i | \(-0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | −0.338062 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00000 | + | 3.46410i | −0.304997 | + | 0.528271i | −0.977261 | − | 0.212041i | \(-0.931989\pi\) |
0.672264 | + | 0.740312i | \(0.265322\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.00000 | − | 3.46410i | 0.291730 | − | 0.505291i | −0.682489 | − | 0.730896i | \(-0.739102\pi\) |
0.974219 | + | 0.225605i | \(0.0724358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.50000 | + | 2.59808i | 0.214286 | + | 0.371154i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.00000 | −1.23625 | −0.618123 | − | 0.786082i | \(-0.712106\pi\) | ||||
−0.618123 | + | 0.786082i | \(0.712106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.00000 | 0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.00000 | + | 12.1244i | 0.911322 | + | 1.57846i | 0.812198 | + | 0.583382i | \(0.198271\pi\) |
0.0991242 | + | 0.995075i | \(0.468396\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.50000 | − | 9.52628i | 0.704203 | − | 1.21972i | −0.262776 | − | 0.964857i | \(-0.584638\pi\) |
0.966978 | − | 0.254858i | \(-0.0820288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.00000 | + | 1.73205i | −0.124035 | + | 0.214834i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.00000 | − | 12.1244i | −0.855186 | − | 1.48123i | −0.876472 | − | 0.481452i | \(-0.840109\pi\) |
0.0212861 | − | 0.999773i | \(-0.493224\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0000 | −1.40449 | −0.702247 | − | 0.711934i | \(-0.747820\pi\) | ||||
−0.702247 | + | 0.711934i | \(0.747820\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | + | 6.92820i | 0.455842 | + | 0.789542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.50000 | − | 2.59808i | 0.168763 | − | 0.292306i | −0.769222 | − | 0.638982i | \(-0.779356\pi\) |
0.937985 | + | 0.346675i | \(0.112689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.500000 | + | 0.866025i | −0.0548821 | + | 0.0950586i | −0.892161 | − | 0.451717i | \(-0.850812\pi\) |
0.837279 | + | 0.546776i | \(0.184145\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.50000 | − | 4.33013i | −0.271163 | − | 0.469668i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.00000 | −0.419314 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.50000 | − | 4.33013i | −0.256495 | − | 0.444262i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.00000 | + | 13.8564i | −0.812277 | + | 1.40690i | 0.0989899 | + | 0.995088i | \(0.468439\pi\) |
−0.911267 | + | 0.411816i | \(0.864894\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | − | 10.3923i | 0.597022 | − | 1.03407i | −0.396236 | − | 0.918149i | \(-0.629684\pi\) |
0.993258 | − | 0.115924i | \(-0.0369830\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00000 | − | 3.46410i | −0.197066 | − | 0.341328i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.947576 | + | 0.319531i | \(0.896475\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.0000 | −1.81987 | −0.909935 | − | 0.414751i | \(-0.863869\pi\) | ||||
−0.909935 | + | 0.414751i | \(0.863869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.00000 | + | 5.19615i | 0.282216 | + | 0.488813i | 0.971930 | − | 0.235269i | \(-0.0755971\pi\) |
−0.689714 | + | 0.724082i | \(0.742264\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.500000 | + | 0.866025i | −0.0466252 | + | 0.0807573i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.00000 | − | 8.66025i | 0.458349 | − | 0.793884i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.50000 | − | 4.33013i | −0.227273 | − | 0.393648i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.00000 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | − | 15.5885i | −0.786334 | − | 1.36197i | −0.928199 | − | 0.372084i | \(-0.878643\pi\) |
0.141865 | − | 0.989886i | \(-0.454690\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.00000 | − | 8.66025i | 0.433555 | − | 0.750939i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.50000 | + | 14.7224i | −0.726204 | + | 1.25782i | 0.232273 | + | 0.972651i | \(0.425384\pi\) |
−0.958477 | + | 0.285171i | \(0.907949\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.00000 | − | 10.3923i | −0.508913 | − | 0.881464i | −0.999947 | − | 0.0103230i | \(-0.996714\pi\) |
0.491033 | − | 0.871141i | \(-0.336619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.00000 | 0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.00000 | − | 13.8564i | −0.655386 | − | 1.13516i | −0.981797 | − | 0.189933i | \(-0.939173\pi\) |
0.326411 | − | 0.945228i | \(-0.394160\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.00000 | + | 6.92820i | −0.325515 | + | 0.563809i | −0.981617 | − | 0.190864i | \(-0.938871\pi\) |
0.656101 | + | 0.754673i | \(0.272204\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.50000 | − | 6.06218i | 0.281127 | − | 0.486926i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −8.00000 | − | 13.8564i | −0.638470 | − | 1.10586i | −0.985769 | − | 0.168107i | \(-0.946235\pi\) |
0.347299 | − | 0.937754i | \(-0.387099\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.00000 | −0.157622 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.0000 | −1.09656 | −0.548282 | − | 0.836293i | \(-0.684718\pi\) | ||||
−0.548282 | + | 0.836293i | \(0.684718\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.50000 | − | 2.59808i | −0.116073 | − | 0.201045i | 0.802135 | − | 0.597143i | \(-0.203697\pi\) |
−0.918208 | + | 0.396098i | \(0.870364\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.50000 | + | 11.2583i | −0.494186 | + | 0.855955i | −0.999978 | − | 0.00670064i | \(-0.997867\pi\) |
0.505792 | + | 0.862656i | \(0.331200\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | − | 1.73205i | −0.0755929 | − | 0.130931i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.00000 | 0.298974 | 0.149487 | − | 0.988764i | \(-0.452238\pi\) | ||||
0.149487 | + | 0.988764i | \(0.452238\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.0000 | −1.41226 | −0.706129 | − | 0.708083i | \(-0.749560\pi\) | ||||
−0.706129 | + | 0.708083i | \(0.749560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.00000 | − | 5.19615i | −0.220564 | − | 0.382029i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.0000 | + | 17.3205i | −0.731272 | + | 1.26660i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.00000 | − | 12.1244i | 0.506502 | − | 0.877288i | −0.493469 | − | 0.869763i | \(-0.664272\pi\) |
0.999972 | − | 0.00752447i | \(-0.00239513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.00000 | − | 8.66025i | −0.359908 | − | 0.623379i | 0.628037 | − | 0.778183i | \(-0.283859\pi\) |
−0.987945 | + | 0.154805i | \(0.950525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.00000 | 0.356235 | 0.178118 | − | 0.984009i | \(-0.442999\pi\) | ||||
0.178118 | + | 0.984009i | \(0.442999\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.00000 | − | 3.46410i | −0.140372 | − | 0.243132i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.0000 | + | 17.3205i | −0.691714 | + | 1.19808i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.50000 | + | 16.4545i | 0.654007 | + | 1.13277i | 0.982142 | + | 0.188142i | \(0.0602466\pi\) |
−0.328135 | + | 0.944631i | \(0.606420\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.00000 | −0.272798 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.0000 | 0.950382 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.00000 | − | 8.66025i | −0.336336 | − | 0.582552i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.00000 | − | 8.66025i | 0.334825 | − | 0.579934i | −0.648626 | − | 0.761107i | \(-0.724656\pi\) |
0.983451 | + | 0.181173i | \(0.0579895\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.50000 | − | 2.59808i | 0.0995585 | − | 0.172440i | −0.811943 | − | 0.583736i | \(-0.801590\pi\) |
0.911502 | + | 0.411296i | \(0.134924\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.5000 | + | 25.1147i | 0.958187 | + | 1.65963i | 0.726900 | + | 0.686743i | \(0.240960\pi\) |
0.231287 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.00000 | −0.393073 | −0.196537 | − | 0.980497i | \(-0.562969\pi\) | ||||
−0.196537 | + | 0.980497i | \(0.562969\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.00000 | 0.260931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3.00000 | − | 5.19615i | −0.194054 | − | 0.336111i | 0.752536 | − | 0.658551i | \(-0.228830\pi\) |
−0.946590 | + | 0.322440i | \(0.895497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.50000 | + | 9.52628i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948609\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.50000 | + | 2.59808i | −0.0958315 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.00000 | − | 8.66025i | −0.318142 | − | 0.551039i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | 0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5000 | + | 23.3827i | 0.842107 | + | 1.45857i | 0.888110 | + | 0.459631i | \(0.152018\pi\) |
−0.0460033 | + | 0.998941i | \(0.514648\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.00000 | − | 10.3923i | 0.372822 | − | 0.645746i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.0000 | + | 20.7846i | −0.739952 | + | 1.28163i | 0.212565 | + | 0.977147i | \(0.431818\pi\) |
−0.952517 | + | 0.304487i | \(0.901515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.50000 | − | 7.79423i | −0.276433 | − | 0.478796i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.0000 | 0.609711 | 0.304855 | − | 0.952399i | \(-0.401392\pi\) | ||||
0.304855 | + | 0.952399i | \(0.401392\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.00000 | −0.546711 | −0.273356 | − | 0.961913i | \(-0.588134\pi\) | ||||
−0.273356 | + | 0.961913i | \(0.588134\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.00000 | + | 3.46410i | 0.120605 | + | 0.208893i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.00000 | − | 3.46410i | 0.120168 | − | 0.208138i | −0.799666 | − | 0.600446i | \(-0.794990\pi\) |
0.919834 | + | 0.392308i | \(0.128323\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.00000 | + | 12.1244i | −0.417585 | + | 0.723278i | −0.995696 | − | 0.0926797i | \(-0.970457\pi\) |
0.578111 | + | 0.815958i | \(0.303790\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.00000 | − | 6.92820i | −0.237775 | − | 0.411839i | 0.722300 | − | 0.691580i | \(-0.243085\pi\) |
−0.960076 | + | 0.279741i | \(0.909752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.00000 | 0.470588 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.50000 | + | 6.06218i | 0.204472 | + | 0.354156i | 0.949964 | − | 0.312358i | \(-0.101119\pi\) |
−0.745492 | + | 0.666514i | \(0.767786\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.00000 | + | 12.1244i | −0.407556 | + | 0.705907i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00000 | + | 1.73205i | −0.0578315 | + | 0.100167i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.00000 | − | 6.92820i | −0.230556 | − | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.0000 | 0.629858 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.0000 | 1.25561 | 0.627803 | − | 0.778372i | \(-0.283954\pi\) | ||||
0.627803 | + | 0.778372i | \(0.283954\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −11.0000 | − | 19.0526i | −0.623753 | − | 1.08037i | −0.988781 | − | 0.149375i | \(-0.952274\pi\) |
0.365028 | − | 0.930997i | \(-0.381059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.00000 | + | 6.92820i | −0.226093 | + | 0.391605i | −0.956647 | − | 0.291250i | \(-0.905929\pi\) |
0.730554 | + | 0.682855i | \(0.239262\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.5000 | + | 23.3827i | −0.758236 | + | 1.31330i | 0.185514 | + | 0.982642i | \(0.440605\pi\) |
−0.943750 | + | 0.330661i | \(0.892728\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 25.0000 | 1.39104 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.00000 | −0.110940 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.00000 | + | 6.92820i | 0.220527 | + | 0.381964i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.00000 | + | 10.3923i | −0.329790 | + | 0.571213i | −0.982470 | − | 0.186421i | \(-0.940311\pi\) |
0.652680 | + | 0.757634i | \(0.273645\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.00000 | − | 12.1244i | 0.382451 | − | 0.662424i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.0000 | − | 19.0526i | −0.599208 | − | 1.03786i | −0.992938 | − | 0.118633i | \(-0.962149\pi\) |
0.393730 | − | 0.919226i | \(-0.371184\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.0000 | −1.51629 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 10.0000 | + | 17.3205i | 0.536828 | + | 0.929814i | 0.999072 | + | 0.0430610i | \(0.0137110\pi\) |
−0.462244 | + | 0.886753i | \(0.652956\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.50000 | − | 2.59808i | 0.0802932 | − | 0.139072i | −0.823083 | − | 0.567922i | \(-0.807748\pi\) |
0.903376 | + | 0.428850i | \(0.141081\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.0000 | − | 22.5167i | 0.691920 | − | 1.19844i | −0.279288 | − | 0.960207i | \(-0.590098\pi\) |
0.971208 | − | 0.238233i | \(-0.0765683\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −18.0000 | −0.950004 | −0.475002 | − | 0.879985i | \(-0.657553\pi\) | ||||
−0.475002 | + | 0.879985i | \(0.657553\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.00000 | 0.315789 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | − | 10.3923i | −0.314054 | − | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.0000 | − | 19.0526i | 0.574195 | − | 0.994535i | −0.421933 | − | 0.906627i | \(-0.638648\pi\) |
0.996129 | − | 0.0879086i | \(-0.0280183\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.00000 | − | 15.5885i | 0.467257 | − | 0.809312i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0000 | + | 27.7128i | 0.828449 | + | 1.43492i | 0.899255 | + | 0.437425i | \(0.144109\pi\) |
−0.0708063 | + | 0.997490i | \(0.522557\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.5000 | − | 23.3827i | −0.689818 | − | 1.19480i | −0.971897 | − | 0.235408i | \(-0.924357\pi\) |
0.282079 | − | 0.959391i | \(-0.408976\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.00000 | + | 6.92820i | −0.203859 | + | 0.353094i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.0000 | + | 31.1769i | −0.912636 | + | 1.58073i | −0.102311 | + | 0.994753i | \(0.532624\pi\) |
−0.810326 | + | 0.585980i | \(0.800710\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.50000 | − | 4.33013i | −0.126430 | − | 0.218984i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.00000 | 0.150946 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0000 | − | 25.9808i | −0.749064 | − | 1.29742i | −0.948272 | − | 0.317460i | \(-0.897170\pi\) |
0.199207 | − | 0.979957i | \(-0.436163\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.00000 | − | 12.1244i | 0.348695 | − | 0.603957i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | + | 20.7846i | −0.594818 | + | 1.03025i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.5000 | − | 21.6506i | −0.618085 | − | 1.07056i | −0.989835 | − | 0.142222i | \(-0.954575\pi\) |
0.371750 | − | 0.928333i | \(-0.378758\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −28.0000 | −1.37779 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.00000 | −0.0490881 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 18.0000 | + | 31.1769i | 0.879358 | + | 1.52309i | 0.852047 | + | 0.523465i | \(0.175361\pi\) |
0.0273103 | + | 0.999627i | \(0.491306\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.50000 | + | 2.59808i | −0.0731055 | + | 0.126622i | −0.900261 | − | 0.435351i | \(-0.856624\pi\) |
0.827155 | + | 0.561973i | \(0.189958\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.50000 | − | 4.33013i | 0.121268 | − | 0.210042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.0000 | + | 19.0526i | 0.532327 | + | 0.922018i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14.0000 | −0.674356 | −0.337178 | − | 0.941441i | \(-0.609472\pi\) | ||||
−0.337178 | + | 0.941441i | \(0.609472\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.0000 | 1.24948 | 0.624740 | − | 0.780833i | \(-0.285205\pi\) | ||||
0.624740 | + | 0.780833i | \(0.285205\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.50000 | − | 4.33013i | −0.119591 | − | 0.207138i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.50000 | − | 14.7224i | 0.405683 | − | 0.702663i | −0.588718 | − | 0.808339i | \(-0.700367\pi\) |
0.994401 | + | 0.105675i | \(0.0337004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.5000 | − | 33.7750i | 0.926473 | − | 1.60470i | 0.137298 | − | 0.990530i | \(-0.456158\pi\) |
0.789175 | − | 0.614168i | \(-0.210508\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.00000 | − | 3.46410i | −0.0937614 | − | 0.162400i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.0000 | + | 24.2487i | −0.654892 | + | 1.13431i | 0.327028 | + | 0.945015i | \(0.393953\pi\) |
−0.981921 | + | 0.189292i | \(0.939381\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0000 | − | 36.3731i | 0.978068 | − | 1.69406i | 0.308651 | − | 0.951175i | \(-0.400123\pi\) |
0.669417 | − | 0.742887i | \(-0.266544\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.00000 | + | 15.5885i | 0.418265 | + | 0.724457i | 0.995765 | − | 0.0919339i | \(-0.0293048\pi\) |
−0.577500 | + | 0.816391i | \(0.695972\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 13.0000 | 0.601568 | 0.300784 | − | 0.953692i | \(-0.402752\pi\) | ||||
0.300784 | + | 0.953692i | \(0.402752\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 28.0000 | 1.29292 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.00000 | + | 13.8564i | 0.367840 | + | 0.637118i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.50000 | − | 4.33013i | 0.114708 | − | 0.198680i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.0000 | − | 24.2487i | 0.639676 | − | 1.10795i | −0.345827 | − | 0.938298i | \(-0.612402\pi\) |
0.985504 | − | 0.169654i | \(-0.0542649\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.00000 | − | 10.3923i | −0.273576 | − | 0.473848i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.0000 | −0.726523 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 40.0000 | 1.81257 | 0.906287 | − | 0.422664i | \(-0.138905\pi\) | ||||
0.906287 | + | 0.422664i | \(0.138905\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.00000 | − | 5.19615i | −0.135388 | − | 0.234499i | 0.790358 | − | 0.612646i | \(-0.209895\pi\) |
−0.925746 | + | 0.378147i | \(0.876561\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.00000 | − | 8.66025i | 0.225189 | − | 0.390038i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.5000 | + | 21.6506i | 0.559577 | + | 0.969216i | 0.997532 | + | 0.0702185i | \(0.0223697\pi\) |
−0.437955 | + | 0.898997i | \(0.644297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 15.0000 | 0.668817 | 0.334408 | − | 0.942428i | \(-0.391463\pi\) | ||||
0.334408 | + | 0.942428i | \(0.391463\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.0000 | 0.533993 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.0000 | + | 24.2487i | 0.620539 | + | 1.07481i | 0.989385 | + | 0.145315i | \(0.0464195\pi\) |
−0.368846 | + | 0.929490i | \(0.620247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 12.0000 | − | 20.7846i | 0.530849 | − | 0.919457i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.00000 | − | 3.46410i | 0.0881305 | − | 0.152647i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −8.00000 | − | 13.8564i | −0.351840 | − | 0.609404i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −40.0000 | −1.75243 | −0.876216 | − | 0.481919i | \(-0.839940\pi\) | ||||
−0.876216 | + | 0.481919i | \(0.839940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.0000 | 0.437269 | 0.218635 | − | 0.975807i | \(-0.429840\pi\) | ||||
0.218635 | + | 0.975807i | \(0.429840\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 17.5000 | + | 30.3109i | 0.762312 | + | 1.32036i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.00000 | + | 10.3923i | 0.259403 | + | 0.449299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | 0.516877 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.0000 | 0.945854 | 0.472927 | − | 0.881102i | \(-0.343197\pi\) | ||||
0.472927 | + | 0.881102i | \(0.343197\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.50000 | − | 16.4545i | −0.406935 | − | 0.704833i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.0000 | − | 24.2487i | 0.598597 | − | 1.03680i | −0.394432 | − | 0.918925i | \(-0.629059\pi\) |
0.993028 | − | 0.117875i | \(-0.0376081\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.00000 | − | 8.66025i | 0.213007 | − | 0.368939i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.00000 | + | 5.19615i | 0.127573 | + | 0.220963i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.0000 | 0.423714 | 0.211857 | − | 0.977301i | \(-0.432049\pi\) | ||||
0.211857 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.00000 | −0.338364 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.00000 | + | 3.46410i | 0.0842900 | + | 0.145994i | 0.905088 | − | 0.425223i | \(-0.139804\pi\) |
−0.820798 | + | 0.571218i | \(0.806471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.00000 | + | 5.19615i | −0.126211 | + | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −5.00000 | + | 8.66025i | −0.209611 | + | 0.363057i | −0.951592 | − | 0.307364i | \(-0.900553\pi\) |
0.741981 | + | 0.670421i | \(0.233886\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.50000 | + | 4.33013i | 0.104622 | + | 0.181210i | 0.913584 | − | 0.406651i | \(-0.133303\pi\) |
−0.808962 | + | 0.587861i | \(0.799970\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.0000 | −0.666089 | −0.333044 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333044 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00000 | − | 1.73205i | −0.0414870 | − | 0.0718576i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −18.0000 | + | 31.1769i | −0.745484 | + | 1.29122i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −7.50000 | + | 12.9904i | −0.309558 | + | 0.536170i | −0.978266 | − | 0.207355i | \(-0.933514\pi\) |
0.668708 | + | 0.743525i | \(0.266848\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.5000 | + | 30.3109i | 0.721075 | + | 1.24894i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.00000 | 0.369586 | 0.184793 | − | 0.982777i | \(-0.440839\pi\) | ||||
0.184793 | + | 0.982777i | \(0.440839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | 0.409960 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.00000 | + | 15.5885i | 0.367730 | + | 0.636927i | 0.989210 | − | 0.146503i | \(-0.0468017\pi\) |
−0.621480 | + | 0.783430i | \(0.713468\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.50000 | − | 9.52628i | 0.224350 | − | 0.388585i | −0.731774 | − | 0.681547i | \(-0.761308\pi\) |
0.956124 | + | 0.292962i | \(0.0946409\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.50000 | − | 4.33013i | 0.101639 | − | 0.176045i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.0000 | + | 31.1769i | 0.730597 | + | 1.26543i | 0.956628 | + | 0.291312i | \(0.0940917\pi\) |
−0.226031 | + | 0.974120i | \(0.572575\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.00000 | 0.323645 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.5000 | + | 28.5788i | 0.664265 | + | 1.15054i | 0.979484 | + | 0.201522i | \(0.0645887\pi\) |
−0.315219 | + | 0.949019i | \(0.602078\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.0000 | + | 27.7128i | −0.643094 | + | 1.11387i | 0.341644 | + | 0.939829i | \(0.389016\pi\) |
−0.984738 | + | 0.174042i | \(0.944317\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | − | 0.866025i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 30.0000 | 1.19618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0000 | 0.517522 | 0.258761 | − | 0.965941i | \(-0.416686\pi\) | ||||
0.258761 | + | 0.965941i | \(0.416686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.00000 | + | 5.19615i | 0.119051 | + | 0.206203i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.00000 | + | 5.19615i | −0.118864 | + | 0.205879i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.00000 | − | 5.19615i | −0.118308 | − | 0.204916i | 0.800789 | − | 0.598947i | \(-0.204414\pi\) |
−0.919097 | + | 0.394030i | \(0.871080\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −33.0000 | −1.29736 | −0.648682 | − | 0.761060i | \(-0.724679\pi\) | ||||
−0.648682 | + | 0.761060i | \(0.724679\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 56.0000 | 2.19819 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.5000 | + | 35.5070i | 0.802227 | + | 1.38950i | 0.918147 | + | 0.396239i | \(0.129685\pi\) |
−0.115920 | + | 0.993259i | \(0.536982\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.00000 | − | 15.5885i | 0.351659 | − | 0.609091i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.00000 | − | 15.5885i | 0.350590 | − | 0.607240i | −0.635763 | − | 0.771885i | \(-0.719314\pi\) |
0.986353 | + | 0.164644i | \(0.0526477\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.0000 | + | 36.3731i | 0.816805 | + | 1.41475i | 0.908024 | + | 0.418917i | \(0.137590\pi\) |
−0.0912190 | + | 0.995831i | \(0.529076\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 10.0000 | 0.387783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.00000 | −0.0774403 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.0000 | − | 38.1051i | −0.849301 | − | 1.47103i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.0000 | + | 25.9808i | −0.578208 | + | 1.00148i | 0.417477 | + | 0.908687i | \(0.362914\pi\) |
−0.995685 | + | 0.0927975i | \(0.970419\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.00000 | + | 1.73205i | −0.0384331 | + | 0.0665681i | −0.884602 | − | 0.466347i | \(-0.845570\pi\) |
0.846169 | + | 0.532915i | \(0.178903\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.0000 | − | 27.7128i | −0.614024 | − | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.00000 | 0.344375 | 0.172188 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172188 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −17.0000 | −0.649537 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.00000 | − | 15.5885i | −0.342873 | − | 0.593873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.50000 | − | 16.4545i | 0.361397 | − | 0.625958i | −0.626794 | − | 0.779185i | \(-0.715633\pi\) |
0.988191 | + | 0.153227i | \(0.0489666\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.00000 | − | 10.3923i | 0.227593 | − | 0.394203i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.0000 | 0.377695 | 0.188847 | − | 0.982006i | \(-0.439525\pi\) | ||||
0.188847 | + | 0.982006i | \(0.439525\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0000 | 1.13147 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.0000 | + | 20.7846i | 0.451306 | + | 0.781686i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −13.0000 | + | 22.5167i | −0.488225 | + | 0.845631i | −0.999908 | − | 0.0135434i | \(-0.995689\pi\) |
0.511683 | + | 0.859174i | \(0.329022\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.50000 | − | 6.06218i | 0.131076 | − | 0.227030i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.00000 | + | 6.92820i | 0.149592 | + | 0.259100i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.0000 | −1.71551 | −0.857755 | − | 0.514058i | \(-0.828142\pi\) | ||||
−0.857755 | + | 0.514058i | \(0.828142\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.00000 | 0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.00000 | − | 1.73205i | −0.0371391 | − | 0.0643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.0000 | + | 27.7128i | −0.593407 | + | 1.02781i | 0.400362 | + | 0.916357i | \(0.368884\pi\) |
−0.993770 | + | 0.111454i | \(0.964449\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.0000 | − | 17.3205i | 0.369863 | − | 0.640622i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −56.0000 | −2.06279 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0000 | −0.551784 | −0.275892 | − | 0.961189i | \(-0.588973\pi\) | ||||
−0.275892 | + | 0.961189i | \(0.588973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.00000 | − | 13.8564i | 0.293097 | − | 0.507659i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −12.0000 | + | 20.7846i | −0.438470 | + | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50000 | + | 2.59808i | 0.0547358 | + | 0.0948051i | 0.892095 | − | 0.451848i | \(-0.149235\pi\) |
−0.837359 | + | 0.546653i | \(0.815902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.00000 | 0.0726912 | 0.0363456 | − | 0.999339i | \(-0.488428\pi\) | ||||
0.0363456 | + | 0.999339i | \(0.488428\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −15.0000 | − | 25.9808i | −0.543750 | − | 0.941802i | −0.998684 | − | 0.0512772i | \(-0.983671\pi\) |
0.454935 | − | 0.890525i | \(-0.349663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.0000 | − | 32.9090i | 0.687846 | − | 1.19138i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −14.0000 | + | 24.2487i | −0.505511 | + | 0.875570i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.5000 | + | 30.3109i | 0.631066 | + | 1.09304i | 0.987334 | + | 0.158655i | \(0.0507157\pi\) |
−0.356268 | + | 0.934384i | \(0.615951\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0000 | 0.539513 | 0.269756 | − | 0.962929i | \(-0.413057\pi\) | ||||
0.269756 | + | 0.962929i | \(0.413057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.00000 | 0.251447 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.00000 | − | 13.8564i | 0.285532 | − | 0.494556i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 20.0000 | + | 34.6410i | 0.712923 | + | 1.23482i | 0.963755 | + | 0.266788i | \(0.0859624\pi\) |
−0.250832 | + | 0.968031i | \(0.580704\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | −0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.0000 | 0.781243 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.50000 | + | 2.59808i | 0.0531327 | + | 0.0920286i | 0.891368 | − | 0.453279i | \(-0.149746\pi\) |
−0.838236 | + | 0.545308i | \(0.816413\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.0000 | + | 17.3205i | −0.353775 | + | 0.612756i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −24.0000 | + | 41.5692i | −0.846942 | + | 1.46695i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.00000 | − | 1.73205i | −0.0352454 | − | 0.0610468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.0000 | 0.843795 | 0.421898 | − | 0.906644i | \(-0.361364\pi\) | ||||
0.421898 | + | 0.906644i | \(0.361364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0000 | 1.54505 | 0.772524 | − | 0.634985i | \(-0.218994\pi\) | ||||
0.772524 | + | 0.634985i | \(0.218994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.00000 | − | 12.1244i | −0.245199 | − | 0.424698i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0000 | − | 17.3205i | 0.349856 | − | 0.605968i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23.0000 | − | 39.8372i | 0.802706 | − | 1.39033i | −0.115124 | − | 0.993351i | \(-0.536726\pi\) |
0.917829 | − | 0.396976i | \(-0.129940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10.0000 | + | 17.3205i | 0.348578 | + | 0.603755i | 0.985997 | − | 0.166762i | \(-0.0533313\pi\) |
−0.637419 | + | 0.770517i | \(0.719998\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 39.0000 | 1.35616 | 0.678081 | − | 0.734987i | \(-0.262812\pi\) | ||||
0.678081 | + | 0.734987i | \(0.262812\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.00000 | −0.0694629 | −0.0347314 | − | 0.999397i | \(-0.511058\pi\) | ||||
−0.0347314 | + | 0.999397i | \(0.511058\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.50000 | − | 12.9904i | −0.259860 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.50000 | − | 2.59808i | 0.0519096 | − | 0.0899101i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.00000 | + | 13.8564i | −0.276191 | + | 0.478376i | −0.970435 | − | 0.241363i | \(-0.922405\pi\) |
0.694244 | + | 0.719740i | \(0.255739\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.5000 | + | 21.6506i | 0.431034 | + | 0.746574i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 9.00000 | 0.309609 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.0000 | 0.343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.00000 | − | 5.19615i | −0.102839 | − | 0.178122i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0000 | − | 24.2487i | 0.479351 | − | 0.830260i | −0.520369 | − | 0.853942i | \(-0.674205\pi\) |
0.999720 | + | 0.0236816i | \(0.00753881\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5000 | − | 18.1865i | 0.358673 | − | 0.621240i | −0.629066 | − | 0.777352i | \(-0.716563\pi\) |
0.987739 | + | 0.156112i | \(0.0498959\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.5000 | − | 35.5070i | −0.699451 | − | 1.21148i | −0.968657 | − | 0.248402i | \(-0.920095\pi\) |
0.269206 | − | 0.963083i | \(-0.413239\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −33.0000 | −1.12333 | −0.561667 | − | 0.827364i | \(-0.689840\pi\) | ||||
−0.561667 | + | 0.827364i | \(0.689840\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0000 | −0.442013 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.00000 | − | 10.3923i | −0.203536 | − | 0.352535i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.0000 | − | 24.2487i | 0.474372 | − | 0.821636i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.00000 | − | 1.73205i | 0.0338062 | − | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0000 | + | 27.7128i | 0.540282 | + | 0.935795i | 0.998888 | + | 0.0471555i | \(0.0150156\pi\) |
−0.458606 | + | 0.888640i | \(0.651651\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 54.0000 | 1.81931 | 0.909653 | − | 0.415369i | \(-0.136347\pi\) | ||||
0.909653 | + | 0.415369i | \(0.136347\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.0000 | −0.740359 | −0.370179 | − | 0.928960i | \(-0.620704\pi\) | ||||
−0.370179 | + | 0.928960i | \(0.620704\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −11.5000 | − | 19.9186i | −0.386132 | − | 0.668801i | 0.605793 | − | 0.795622i | \(-0.292856\pi\) |
−0.991926 | + | 0.126821i | \(0.959522\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.00000 | + | 10.3923i | −0.201234 | + | 0.348547i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −10.0000 | + | 17.3205i | −0.334637 | + | 0.579609i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.00000 | + | 3.46410i | 0.0668526 | + | 0.115792i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14.0000 | 0.466926 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 45.0000 | 1.49917 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9.50000 | − | 16.4545i | −0.315791 | − | 0.546966i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.00000 | + | 10.3923i | −0.199227 | + | 0.345071i | −0.948278 | − | 0.317441i | \(-0.897176\pi\) |
0.749051 | + | 0.662512i | \(0.230510\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.00000 | + | 1.73205i | −0.0331315 | + | 0.0573854i | −0.882116 | − | 0.471033i | \(-0.843881\pi\) |
0.848984 | + | 0.528418i | \(0.177215\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000 | + | 3.46410i | 0.0661903 | + | 0.114645i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 36.0000 | 1.18882 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 32.0000 | 1.05558 | 0.527791 | − | 0.849374i | \(-0.323020\pi\) | ||||
0.527791 | + | 0.849374i | \(0.323020\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.00000 | − | 5.19615i | 0.0986394 | − | 0.170848i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.00000 | + | 6.92820i | −0.131236 | + | 0.227307i | −0.924153 | − | 0.382022i | \(-0.875228\pi\) |
0.792917 | + | 0.609329i | \(0.208561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.50000 | − | 12.9904i | −0.245803 | − | 0.425743i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.0000 | −0.654070 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.0000 | −1.82944 | −0.914720 | − | 0.404088i | \(-0.867589\pi\) | ||||
−0.914720 | + | 0.404088i | \(0.867589\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.0000 | + | 29.4449i | 0.554184 | + | 0.959875i | 0.997967 | + | 0.0637405i | \(0.0203030\pi\) |
−0.443782 | + | 0.896135i | \(0.646364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.5000 | + | 45.8993i | −0.861134 | + | 1.49153i | 0.00970072 | + | 0.999953i | \(0.496912\pi\) |
−0.870835 | + | 0.491575i | \(0.836421\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | − | 20.7846i | −0.389536 | − | 0.674697i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.00000 | −0.194359 | −0.0971795 | − | 0.995267i | \(-0.530982\pi\) | ||||
−0.0971795 | + | 0.995267i | \(0.530982\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 14.0000 | 0.453029 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −17.0000 | − | 29.4449i | −0.548959 | − | 0.950824i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | + | 15.5885i | −0.290323 | + | 0.502853i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.00000 | − | 8.66025i | 0.160956 | − | 0.278783i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.0000 | + | 25.9808i | 0.482367 | + | 0.835485i | 0.999795 | − | 0.0202420i | \(-0.00644366\pi\) |
−0.517428 | + | 0.855727i | \(0.673110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −14.0000 | −0.449281 | −0.224641 | − | 0.974442i | \(-0.572121\pi\) | ||||
−0.224641 | + | 0.974442i | \(0.572121\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0000 | 0.769405 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.00000 | + | 1.73205i | 0.0319928 | + | 0.0554132i | 0.881579 | − | 0.472037i | \(-0.156481\pi\) |
−0.849586 | + | 0.527451i | \(0.823148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.50000 | + | 2.59808i | −0.0478426 | + | 0.0828658i | −0.888955 | − | 0.457995i | \(-0.848568\pi\) |
0.841112 | + | 0.540860i | \(0.181901\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.50000 | + | 4.33013i | 0.0796566 | + | 0.137969i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.00000 | −0.127193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.0000 | −1.74713 | −0.873566 | − | 0.486705i | \(-0.838199\pi\) | ||||
−0.873566 | + | 0.486705i | \(0.838199\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.00000 | − | 13.8564i | −0.253617 | − | 0.439278i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 24.0000 | − | 41.5692i | 0.760088 | − | 1.31651i | −0.182717 | − | 0.983165i | \(-0.558489\pi\) |
0.942805 | − | 0.333345i | \(-0.108177\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 3240.2.q.p.2161.1 | 2 | ||
3.2 | odd | 2 | 3240.2.q.b.2161.1 | 2 | |||
9.2 | odd | 6 | 1080.2.a.l.1.1 | yes | 1 | ||
9.4 | even | 3 | inner | 3240.2.q.p.1081.1 | 2 | ||
9.5 | odd | 6 | 3240.2.q.b.1081.1 | 2 | |||
9.7 | even | 3 | 1080.2.a.e.1.1 | ✓ | 1 | ||
36.7 | odd | 6 | 2160.2.a.e.1.1 | 1 | |||
36.11 | even | 6 | 2160.2.a.m.1.1 | 1 | |||
45.2 | even | 12 | 5400.2.f.x.649.2 | 2 | |||
45.7 | odd | 12 | 5400.2.f.f.649.2 | 2 | |||
45.29 | odd | 6 | 5400.2.a.q.1.1 | 1 | |||
45.34 | even | 6 | 5400.2.a.j.1.1 | 1 | |||
45.38 | even | 12 | 5400.2.f.x.649.1 | 2 | |||
45.43 | odd | 12 | 5400.2.f.f.649.1 | 2 | |||
72.11 | even | 6 | 8640.2.a.k.1.1 | 1 | |||
72.29 | odd | 6 | 8640.2.a.t.1.1 | 1 | |||
72.43 | odd | 6 | 8640.2.a.bi.1.1 | 1 | |||
72.61 | even | 6 | 8640.2.a.cd.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1080.2.a.e.1.1 | ✓ | 1 | 9.7 | even | 3 | ||
1080.2.a.l.1.1 | yes | 1 | 9.2 | odd | 6 | ||
2160.2.a.e.1.1 | 1 | 36.7 | odd | 6 | |||
2160.2.a.m.1.1 | 1 | 36.11 | even | 6 | |||
3240.2.q.b.1081.1 | 2 | 9.5 | odd | 6 | |||
3240.2.q.b.2161.1 | 2 | 3.2 | odd | 2 | |||
3240.2.q.p.1081.1 | 2 | 9.4 | even | 3 | inner | ||
3240.2.q.p.2161.1 | 2 | 1.1 | even | 1 | trivial | ||
5400.2.a.j.1.1 | 1 | 45.34 | even | 6 | |||
5400.2.a.q.1.1 | 1 | 45.29 | odd | 6 | |||
5400.2.f.f.649.1 | 2 | 45.43 | odd | 12 | |||
5400.2.f.f.649.2 | 2 | 45.7 | odd | 12 | |||
5400.2.f.x.649.1 | 2 | 45.38 | even | 12 | |||
5400.2.f.x.649.2 | 2 | 45.2 | even | 12 | |||
8640.2.a.k.1.1 | 1 | 72.11 | even | 6 | |||
8640.2.a.t.1.1 | 1 | 72.29 | odd | 6 | |||
8640.2.a.bi.1.1 | 1 | 72.43 | odd | 6 | |||
8640.2.a.cd.1.1 | 1 | 72.61 | even | 6 |