Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1248,2,Mod(463,1248)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1248, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 2, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1248.463");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1248 = 2^{5} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1248.bb (of order \(4\), 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: | \(9.96533017226\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 463.1 | ||
Character | \(\chi\) | \(=\) | 1248.463 |
Dual form | 1248.2.bb.f.655.1 |
$q$-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 \(\left(\mathbb{Z}/1248\mathbb{Z}\right)^\times\).
\(n\) | \(703\) | \(769\) | \(833\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −3.08779 | + | 3.08779i | −1.38090 | + | 1.38090i | −0.537875 | + | 0.843024i | \(0.680773\pi\) |
−0.843024 | + | 0.537875i | \(0.819227\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.85816 | + | 2.85816i | 1.08028 | + | 1.08028i | 0.996483 | + | 0.0838010i | \(0.0267060\pi\) |
0.0838010 | + | 0.996483i | \(0.473294\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.57668 | + | 2.57668i | −0.776900 | + | 0.776900i | −0.979302 | − | 0.202403i | \(-0.935125\pi\) |
0.202403 | + | 0.979302i | \(0.435125\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.51077 | + | 0.821294i | 0.973711 | + | 0.227786i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.08779 | + | 3.08779i | −0.797263 | + | 0.797263i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.07196i | − | 0.259989i | −0.991515 | − | 0.129994i | \(-0.958504\pi\) | ||
0.991515 | − | 0.129994i | \(-0.0414959\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.46161 | − | 1.46161i | −0.335317 | − | 0.335317i | 0.519284 | − | 0.854602i | \(-0.326199\pi\) |
−0.854602 | + | 0.519284i | \(0.826199\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.85816 | + | 2.85816i | 0.623702 | + | 0.623702i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.52786 | −1.15264 | −0.576319 | − | 0.817225i | \(-0.695511\pi\) | ||||
−0.576319 | + | 0.817225i | \(0.695511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 14.0688i | − | 2.81377i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.512377i | 0.0951460i | 0.998868 | + | 0.0475730i | \(0.0151487\pi\) | ||||
−0.998868 | + | 0.0475730i | \(0.984851\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.85816 | + | 2.85816i | −0.513341 | + | 0.513341i | −0.915549 | − | 0.402208i | \(-0.868243\pi\) |
0.402208 | + | 0.915549i | \(0.368243\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.57668 | + | 2.57668i | −0.448543 | + | 0.448543i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −17.6508 | −2.98353 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.97885 | − | 1.97885i | −0.325321 | − | 0.325321i | 0.525483 | − | 0.850804i | \(-0.323885\pi\) |
−0.850804 | + | 0.525483i | \(0.823885\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.51077 | + | 0.821294i | 0.562172 | + | 0.131512i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0336607 | − | 0.0336607i | −0.00525692 | − | 0.00525692i | 0.704473 | − | 0.709730i | \(-0.251183\pi\) |
−0.709730 | + | 0.704473i | \(0.751183\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.49466i | 0.532931i | 0.963844 | + | 0.266465i | \(0.0858558\pi\) | ||||
−0.963844 | + | 0.266465i | \(0.914144\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.08779 | + | 3.08779i | −0.460300 | + | 0.460300i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.45565 | + | 6.45565i | 0.941653 | + | 0.941653i | 0.998389 | − | 0.0567363i | \(-0.0180694\pi\) |
−0.0567363 | + | 0.998389i | \(0.518069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.33817i | 1.33402i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 1.07196i | − | 0.150104i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.04121i | − | 1.10455i | −0.833663 | − | 0.552273i | \(-0.813761\pi\) | ||
0.833663 | − | 0.552273i | \(-0.186239\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 15.9125i | − | 2.14564i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.46161 | − | 1.46161i | −0.193596 | − | 0.193596i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.23075 | + | 1.23075i | −0.160231 | + | 0.160231i | −0.782669 | − | 0.622438i | \(-0.786142\pi\) |
0.622438 | + | 0.782669i | \(0.286142\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.66832i | 0.597717i | 0.954297 | + | 0.298859i | \(0.0966059\pi\) | ||||
−0.954297 | + | 0.298859i | \(0.903394\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.85816 | + | 2.85816i | 0.360094 | + | 0.360094i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13.3765 | + | 8.30451i | −1.65915 | + | 1.03005i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.03305 | − | 2.03305i | −0.248376 | − | 0.248376i | 0.571928 | − | 0.820304i | \(-0.306196\pi\) |
−0.820304 | + | 0.571928i | \(0.806196\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.52786 | −0.665476 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.60969 | + | 5.60969i | −0.665747 | + | 0.665747i | −0.956729 | − | 0.290981i | \(-0.906018\pi\) |
0.290981 | + | 0.956729i | \(0.406018\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.73067 | + | 5.73067i | −0.670724 | + | 0.670724i | −0.957883 | − | 0.287159i | \(-0.907289\pi\) |
0.287159 | + | 0.957883i | \(0.407289\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 14.0688i | − | 1.62453i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −14.7292 | −1.67854 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.65963i | 0.749267i | 0.927173 | + | 0.374633i | \(0.122231\pi\) | ||||
−0.927173 | + | 0.374633i | \(0.877769\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.153984 | − | 0.153984i | −0.0169020 | − | 0.0169020i | 0.698605 | − | 0.715507i | \(-0.253804\pi\) |
−0.715507 | + | 0.698605i | \(0.753804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.30998 | + | 3.30998i | 0.359018 | + | 0.359018i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.512377i | 0.0549326i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 11.3765 | − | 11.3765i | 1.20590 | − | 1.20590i | 0.233562 | − | 0.972342i | \(-0.424962\pi\) |
0.972342 | − | 0.233562i | \(-0.0750381\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.68694 | + | 12.3817i | 0.805811 | + | 1.29796i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.85816 | + | 2.85816i | −0.296378 | + | 0.296378i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.02631 | 0.926079 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.80263 | + | 8.80263i | 0.893772 | + | 0.893772i | 0.994876 | − | 0.101104i | \(-0.0322376\pi\) |
−0.101104 | + | 0.994876i | \(0.532238\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.57668 | + | 2.57668i | −0.258967 | + | 0.258967i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.89040 | 0.287605 | 0.143803 | − | 0.989606i | \(-0.454067\pi\) | ||||
0.143803 | + | 0.989606i | \(0.454067\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.15687 | −0.705187 | −0.352594 | − | 0.935777i | \(-0.614700\pi\) | ||||
−0.352594 | + | 0.935777i | \(0.614700\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −17.6508 | −1.72254 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.6510 | 1.02967 | 0.514833 | − | 0.857290i | \(-0.327854\pi\) | ||||
0.514833 | + | 0.857290i | \(0.327854\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.78060 | − | 1.78060i | 0.170551 | − | 0.170551i | −0.616671 | − | 0.787221i | \(-0.711519\pi\) |
0.787221 | + | 0.616671i | \(0.211519\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.97885 | − | 1.97885i | −0.187824 | − | 0.187824i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.99536 | 0.281780 | 0.140890 | − | 0.990025i | \(-0.455004\pi\) | ||||
0.140890 | + | 0.990025i | \(0.455004\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.0688 | − | 17.0688i | 1.59168 | − | 1.59168i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.51077 | + | 0.821294i | 0.324570 | + | 0.0759287i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.06383 | − | 3.06383i | 0.280861 | − | 0.280861i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 2.27861i | − | 0.207146i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0336607 | − | 0.0336607i | −0.00303508 | − | 0.00303508i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 28.0026 | + | 28.0026i | 2.50463 | + | 2.50463i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.1639 | −1.43431 | −0.717156 | − | 0.696913i | \(-0.754557\pi\) | ||||
−0.717156 | + | 0.696913i | \(0.754557\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.49466i | 0.307688i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.118526 | 0.0103557 | 0.00517783 | − | 0.999987i | \(-0.498352\pi\) | ||||
0.00517783 | + | 0.999987i | \(0.498352\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 8.35506i | − | 0.724476i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.08779 | + | 3.08779i | −0.265754 | + | 0.265754i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.38715 | − | 8.38715i | 0.716563 | − | 0.716563i | −0.251337 | − | 0.967900i | \(-0.580870\pi\) |
0.967900 | + | 0.251337i | \(0.0808702\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.73531 | 0.825738 | 0.412869 | − | 0.910790i | \(-0.364527\pi\) | ||||
0.412869 | + | 0.910790i | \(0.364527\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.45565 | + | 6.45565i | 0.543664 | + | 0.543664i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −11.1624 | + | 6.92992i | −0.933443 | + | 0.579509i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.58211 | − | 1.58211i | −0.131387 | − | 0.131387i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9.33817i | 0.770200i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.39777 | + | 6.39777i | −0.524126 | + | 0.524126i | −0.918815 | − | 0.394689i | \(-0.870852\pi\) |
0.394689 | + | 0.918815i | \(0.370852\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.23105 | + | 6.23105i | 0.507076 | + | 0.507076i | 0.913628 | − | 0.406552i | \(-0.133269\pi\) |
−0.406552 | + | 0.913628i | \(0.633269\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.07196i | − | 0.0866628i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 17.6508i | − | 1.41774i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 23.8222i | − | 1.90122i | −0.310393 | − | 0.950608i | \(-0.600461\pi\) | ||
0.310393 | − | 0.950608i | \(-0.399539\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 8.04121i | − | 0.637710i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −15.7995 | − | 15.7995i | −1.24518 | − | 1.24518i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.03428 | + | 4.03428i | −0.315989 | + | 0.315989i | −0.847224 | − | 0.531235i | \(-0.821728\pi\) |
0.531235 | + | 0.847224i | \(0.321728\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 15.9125i | − | 1.23879i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.78853 | + | 4.78853i | 0.370548 | + | 0.370548i | 0.867677 | − | 0.497129i | \(-0.165612\pi\) |
−0.497129 | + | 0.867677i | \(0.665612\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6510 | + | 5.76674i | 0.896227 | + | 0.443596i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.46161 | − | 1.46161i | −0.111772 | − | 0.111772i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.81603 | 0.138070 | 0.0690350 | − | 0.997614i | \(-0.478008\pi\) | ||||
0.0690350 | + | 0.997614i | \(0.478008\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 40.2110 | − | 40.2110i | 3.03967 | − | 3.03967i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.23075 | + | 1.23075i | −0.0925092 | + | 0.0925092i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4962i | 0.784521i | 0.919854 | + | 0.392261i | \(0.128307\pi\) | ||||
−0.919854 | + | 0.392261i | \(0.871693\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0565 | −1.04481 | −0.522407 | − | 0.852696i | \(-0.674966\pi\) | ||||
−0.522407 | + | 0.852696i | \(0.674966\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.66832i | 0.345092i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 12.2205 | 0.898470 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.76210 | + | 2.76210i | 0.201985 | + | 0.201985i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.85816 | + | 2.85816i | 0.207901 | + | 0.207901i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.1540i | 1.09650i | 0.836313 | + | 0.548252i | \(0.184706\pi\) | ||||
−0.836313 | + | 0.548252i | \(0.815294\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16.5694 | + | 16.5694i | −1.19269 | + | 1.19269i | −0.216380 | + | 0.976309i | \(0.569425\pi\) |
−0.976309 | + | 0.216380i | \(0.930575\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.3765 | + | 8.30451i | −0.957909 | + | 0.594698i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6.24885 | − | 6.24885i | 0.445212 | − | 0.445212i | −0.448547 | − | 0.893759i | \(-0.648058\pi\) |
0.893759 | + | 0.448547i | \(0.148058\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.22848 | 0.299749 | 0.149875 | − | 0.988705i | \(-0.452113\pi\) | ||||
0.149875 | + | 0.988705i | \(0.452113\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.03305 | − | 2.03305i | −0.143400 | − | 0.143400i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.46446 | + | 1.46446i | −0.102785 | + | 0.102785i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.207874 | 0.0145186 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.52786 | −0.384213 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.53224 | 0.521016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 24.8295 | 1.70934 | 0.854668 | − | 0.519175i | \(-0.173761\pi\) | ||||
0.854668 | + | 0.519175i | \(0.173761\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.60969 | + | 5.60969i | −0.384369 | + | 0.384369i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7908 | − | 10.7908i | −0.735924 | − | 0.735924i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −16.3382 | −1.10911 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.73067 | + | 5.73067i | −0.387243 | + | 0.387243i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.880394 | − | 3.76340i | 0.0592217 | − | 0.253154i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.83341 | + | 1.83341i | −0.122774 | + | 0.122774i | −0.765824 | − | 0.643050i | \(-0.777669\pi\) |
0.643050 | + | 0.765824i | \(0.277669\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | − | 14.0688i | − | 0.937923i | ||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.42020 | − | 9.42020i | −0.625240 | − | 0.625240i | 0.321626 | − | 0.946867i | \(-0.395771\pi\) |
−0.946867 | + | 0.321626i | \(0.895771\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.97977 | − | 4.97977i | −0.329073 | − | 0.329073i | 0.523161 | − | 0.852234i | \(-0.324753\pi\) |
−0.852234 | + | 0.523161i | \(0.824753\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.7292 | −0.969108 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.38474i | 0.352766i | 0.984322 | + | 0.176383i | \(0.0564397\pi\) | ||||
−0.984322 | + | 0.176383i | \(0.943560\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −39.8673 | −2.60066 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.65963i | 0.432589i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.48045 | + | 6.48045i | −0.419186 | + | 0.419186i | −0.884923 | − | 0.465737i | \(-0.845789\pi\) |
0.465737 | + | 0.884923i | \(0.345789\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.2281 | − | 16.2281i | 1.04534 | − | 1.04534i | 0.0464205 | − | 0.998922i | \(-0.485219\pi\) |
0.998922 | − | 0.0464205i | \(-0.0147814\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.8343 | − | 28.8343i | −1.84215 | − | 1.84215i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.93097 | − | 6.33180i | −0.250122 | − | 0.402883i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.153984 | − | 0.153984i | −0.00975835 | − | 0.00975835i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 0.990551i | − | 0.0625230i | −0.999511 | − | 0.0312615i | \(-0.990048\pi\) | ||
0.999511 | − | 0.0312615i | \(-0.00995247\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.2435 | − | 14.2435i | 0.895484 | − | 0.895484i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.30998 | + | 3.30998i | 0.207279 | + | 0.207279i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 16.9182i | 1.05533i | 0.849453 | + | 0.527665i | \(0.176932\pi\) | ||||
−0.849453 | + | 0.527665i | \(0.823068\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 11.3117i | − | 0.702877i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.512377i | 0.0317153i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 28.7035i | − | 1.76993i | −0.465655 | − | 0.884966i | \(-0.654181\pi\) | ||
0.465655 | − | 0.884966i | \(-0.345819\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.8295 | + | 24.8295i | 1.52527 | + | 1.52527i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.3765 | − | 11.3765i | 0.696229 | − | 0.696229i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 25.8818i | 1.57804i | 0.614366 | + | 0.789021i | \(0.289412\pi\) | ||||
−0.614366 | + | 0.789021i | \(0.710588\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.06113 | − | 6.06113i | −0.368187 | − | 0.368187i | 0.498628 | − | 0.866816i | \(-0.333837\pi\) |
−0.866816 | + | 0.498628i | \(0.833837\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7.68694 | + | 12.3817i | 0.465235 | + | 0.749376i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 36.2510 | + | 36.2510i | 2.18602 | + | 2.18602i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.49785 | 0.150081 | 0.0750407 | − | 0.997180i | \(-0.476091\pi\) | ||||
0.0750407 | + | 0.997180i | \(0.476091\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.85816 | + | 2.85816i | −0.171114 | + | 0.171114i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.26380 | + | 6.26380i | −0.373667 | + | 0.373667i | −0.868811 | − | 0.495144i | \(-0.835115\pi\) |
0.495144 | + | 0.868811i | \(0.335115\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.9847i | 0.712416i | 0.934407 | + | 0.356208i | \(0.115931\pi\) | ||||
−0.934407 | + | 0.356208i | \(0.884069\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 9.02631 | 0.534672 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.192415i | − | 0.0113579i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8509 | 0.932406 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.80263 | + | 8.80263i | 0.516019 | + | 0.516019i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.26151 | + | 3.26151i | 0.190539 | + | 0.190539i | 0.795929 | − | 0.605390i | \(-0.206983\pi\) |
−0.605390 | + | 0.795929i | \(0.706983\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.60061i | − | 0.442525i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.57668 | + | 2.57668i | −0.149514 | + | 0.149514i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.4070 | − | 4.54000i | −1.12234 | − | 0.262555i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.98830 | + | 9.98830i | −0.575716 | + | 0.575716i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.89040 | 0.166049 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −14.4148 | − | 14.4148i | −0.825387 | − | 0.825387i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.00180 | − | 7.00180i | 0.399614 | − | 0.399614i | −0.478483 | − | 0.878097i | \(-0.658813\pi\) |
0.878097 | + | 0.478483i | \(0.158813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.15687 | −0.407140 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 29.2550 | 1.65890 | 0.829450 | − | 0.558582i | \(-0.188654\pi\) | ||||
0.829450 | + | 0.558582i | \(0.188654\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.65852 | 0.150269 | 0.0751343 | − | 0.997173i | \(-0.476061\pi\) | ||||
0.0751343 | + | 0.997173i | \(0.476061\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.6508 | −0.994509 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.19502 | + | 5.19502i | −0.291781 | + | 0.291781i | −0.837784 | − | 0.546002i | \(-0.816149\pi\) |
0.546002 | + | 0.837784i | \(0.316149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.32023 | − | 1.32023i | −0.0739189 | − | 0.0739189i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.6510 | 0.594478 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.56679 | + | 1.56679i | −0.0871787 | + | 0.0871787i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.5547 | − | 49.3924i | 0.640937 | − | 2.73980i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.78060 | − | 1.78060i | 0.0984675 | − | 0.0984675i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 36.9026i | 2.03450i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.6385 | + | 14.6385i | 0.804603 | + | 0.804603i | 0.983811 | − | 0.179208i | \(-0.0573535\pi\) |
−0.179208 | + | 0.983811i | \(0.557353\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.97885 | − | 1.97885i | −0.108440 | − | 0.108440i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.5552 | 0.685965 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 19.9550i | − | 1.08702i | −0.839404 | − | 0.543508i | \(-0.817096\pi\) | ||
0.839404 | − | 0.543508i | \(-0.182904\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.99536 | 0.162686 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 14.7292i | − | 0.797629i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.68288 | + | 6.68288i | −0.360841 | + | 0.360841i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17.0688 | − | 17.0688i | 0.918956 | − | 0.918956i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.2961 | 0.713770 | 0.356885 | − | 0.934148i | \(-0.383839\pi\) | ||||
0.356885 | + | 0.934148i | \(0.383839\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.5685 | + | 20.5685i | 1.10101 | + | 1.10101i | 0.994290 | + | 0.106716i | \(0.0340334\pi\) |
0.106716 | + | 0.994290i | \(0.465967\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.51077 | + | 0.821294i | 0.187391 | + | 0.0438374i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.37647 | + | 3.37647i | 0.179712 | + | 0.179712i | 0.791230 | − | 0.611519i | \(-0.209441\pi\) |
−0.611519 | + | 0.791230i | \(0.709441\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 34.6430i | − | 1.83866i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.06383 | − | 3.06383i | 0.162155 | − | 0.162155i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.1733 | − | 10.1733i | −0.536927 | − | 0.536927i | 0.385698 | − | 0.922625i | \(-0.373961\pi\) |
−0.922625 | + | 0.385698i | \(0.873961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 14.7274i | − | 0.775124i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.27861i | − | 0.119596i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 35.3902i | − | 1.85241i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.7553i | 0.665820i | 0.942959 | + | 0.332910i | \(0.108030\pi\) | ||||
−0.942959 | + | 0.332910i | \(0.891970\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0336607 | − | 0.0336607i | −0.00175231 | − | 0.00175231i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 22.9831 | − | 22.9831i | 1.19322 | − | 1.19322i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 13.6959i | − | 0.709147i | −0.935028 | − | 0.354573i | \(-0.884626\pi\) | ||
0.935028 | − | 0.354573i | \(-0.115374\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 28.0026 | + | 28.0026i | 1.44605 | + | 1.44605i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.420812 | + | 1.79884i | −0.0216729 | + | 0.0926447i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 16.8734 | + | 16.8734i | 0.866730 | + | 0.866730i | 0.992109 | − | 0.125379i | \(-0.0400145\pi\) |
−0.125379 | + | 0.992109i | \(0.540015\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −16.1639 | −0.828100 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.81081 | − | 2.81081i | 0.143625 | − | 0.143625i | −0.631638 | − | 0.775263i | \(-0.717617\pi\) |
0.775263 | + | 0.631638i | \(0.217617\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.4805 | − | 45.4805i | 2.31790 | − | 2.31790i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.49466i | 0.177644i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 34.2597 | 1.73703 | 0.868517 | − | 0.495660i | \(-0.165074\pi\) | ||||
0.868517 | + | 0.495660i | \(0.165074\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.92564i | 0.299673i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.118526 | 0.00597884 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −20.5635 | − | 20.5635i | −1.03466 | − | 1.03466i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.1956 | + | 16.1956i | 0.812836 | + | 0.812836i | 0.985058 | − | 0.172223i | \(-0.0550948\pi\) |
−0.172223 | + | 0.985058i | \(0.555095\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 8.35506i | − | 0.418276i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 18.5045 | − | 18.5045i | 0.924069 | − | 0.924069i | −0.0732452 | − | 0.997314i | \(-0.523336\pi\) |
0.997314 | + | 0.0732452i | \(0.0233356\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.3817 | + | 7.68694i | −0.616778 | + | 0.382914i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.08779 | + | 3.08779i | −0.153433 | + | 0.153433i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.1977 | 0.505483 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −19.3758 | − | 19.3758i | −0.958070 | − | 0.958070i | 0.0410856 | − | 0.999156i | \(-0.486918\pi\) |
−0.999156 | + | 0.0410856i | \(0.986918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.38715 | − | 8.38715i | 0.413708 | − | 0.413708i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.03539 | −0.346189 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.950941 | 0.0466798 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 9.73531 | 0.476740 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −36.1631 | −1.76668 | −0.883341 | − | 0.468731i | \(-0.844711\pi\) | ||||
−0.883341 | + | 0.468731i | \(0.844711\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.701961 | + | 0.701961i | −0.0342115 | + | 0.0342115i | −0.724006 | − | 0.689794i | \(-0.757701\pi\) |
0.689794 | + | 0.724006i | \(0.257701\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.45565 | + | 6.45565i | 0.313884 | + | 0.313884i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.0812 | −0.731547 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.3428 | + | 13.3428i | −0.645704 | + | 0.645704i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.1624 | + | 6.92992i | −0.538923 | + | 0.334580i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.65259 | − | 2.65259i | 0.127771 | − | 0.127771i | −0.640330 | − | 0.768100i | \(-0.721202\pi\) |
0.768100 | + | 0.640330i | \(0.221202\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.2434i | 1.30923i | 0.755961 | + | 0.654617i | \(0.227170\pi\) | ||||
−0.755961 | + | 0.654617i | \(0.772830\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.58211 | − | 1.58211i | −0.0758564 | − | 0.0758564i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.07960 | + | 8.07960i | 0.386500 | + | 0.386500i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.4482 | 1.35776 | 0.678878 | − | 0.734251i | \(-0.262466\pi\) | ||||
0.678878 | + | 0.734251i | \(0.262466\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 9.33817i | 0.444675i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2562 | 1.24747 | 0.623735 | − | 0.781636i | \(-0.285614\pi\) | ||||
0.623735 | + | 0.781636i | \(0.285614\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 70.2562i | 3.33046i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.39777 | + | 6.39777i | −0.302604 | + | 0.302604i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.3557 | + | 10.3557i | −0.488717 | + | 0.488717i | −0.907901 | − | 0.419185i | \(-0.862316\pi\) |
0.419185 | + | 0.907901i | \(0.362316\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.173466 | 0.00816820 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.23105 | + | 6.23105i | 0.292760 | + | 0.292760i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −61.9678 | − | 14.4965i | −2.90509 | − | 0.679605i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.3069 | + | 20.3069i | 0.949918 | + | 0.949918i | 0.998804 | − | 0.0488865i | \(-0.0155673\pi\) |
−0.0488865 | + | 0.998804i | \(0.515567\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 1.07196i | − | 0.0500348i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13.3085 | + | 13.3085i | −0.619838 | + | 0.619838i | −0.945490 | − | 0.325652i | \(-0.894416\pi\) |
0.325652 | + | 0.945490i | \(0.394416\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.24915 | − | 3.24915i | −0.151001 | − | 0.151001i | 0.627564 | − | 0.778565i | \(-0.284052\pi\) |
−0.778565 | + | 0.627564i | \(0.784052\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 17.6508i | − | 0.818535i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 40.2993i | 1.86483i | 0.361392 | + | 0.932414i | \(0.382302\pi\) | ||||
−0.361392 | + | 0.932414i | \(0.617698\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 11.6215i | − | 0.536633i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 23.8222i | − | 1.09767i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −9.00464 | − | 9.00464i | −0.414034 | − | 0.414034i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −20.5632 | + | 20.5632i | −0.943506 | + | 0.943506i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 8.04121i | − | 0.368182i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −19.0201 | − | 19.0201i | −0.869049 | − | 0.869049i | 0.123318 | − | 0.992367i | \(-0.460646\pi\) |
−0.992367 | + | 0.123318i | \(0.960646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.32206 | − | 8.57249i | −0.242665 | − | 0.390872i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −15.7995 | − | 15.7995i | −0.718903 | − | 0.718903i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −54.3613 | −2.46842 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 8.43408 | − | 8.43408i | 0.382184 | − | 0.382184i | −0.489704 | − | 0.871889i | \(-0.662895\pi\) |
0.871889 | + | 0.489704i | \(0.162895\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.03428 | + | 4.03428i | −0.182436 | + | 0.182436i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.3787i | 1.05507i | 0.849534 | + | 0.527533i | \(0.176883\pi\) | ||||
−0.849534 | + | 0.527533i | \(0.823117\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.549248 | 0.0247369 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 15.9125i | − | 0.715214i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −32.0668 | −1.43839 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.6272 | + | 18.6272i | 0.833867 | + | 0.833867i | 0.988043 | − | 0.154176i | \(-0.0492723\pi\) |
−0.154176 | + | 0.988043i | \(0.549272\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.78853 | + | 4.78853i | 0.213936 | + | 0.213936i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2441i | 0.545939i | 0.962023 | + | 0.272969i | \(0.0880058\pi\) | ||||
−0.962023 | + | 0.272969i | \(0.911994\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.92492 | + | 8.92492i | −0.397154 | + | 0.397154i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.6510 | + | 5.76674i | 0.517437 | + | 0.256110i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 25.7075 | − | 25.7075i | 1.13947 | − | 1.13947i | 0.150920 | − | 0.988546i | \(-0.451776\pi\) |
0.988546 | − | 0.150920i | \(-0.0482237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.7584 | −1.44914 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.46161 | − | 1.46161i | −0.0645319 | − | 0.0645319i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 22.0989 | − | 22.0989i | 0.973793 | − | 0.973793i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −33.2683 | −1.46314 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.81603 | 0.0797148 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −41.6747 | −1.82580 | −0.912902 | − | 0.408179i | \(-0.866164\pi\) | ||||
−0.912902 | + | 0.408179i | \(0.866164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.6394 | −0.727591 | −0.363796 | − | 0.931479i | \(-0.618519\pi\) | ||||
−0.363796 | + | 0.931479i | \(0.618519\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 40.2110 | − | 40.2110i | 1.75495 | − | 1.75495i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.06383 | + | 3.06383i | 0.133463 | + | 0.133463i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.55722 | 0.328575 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.23075 | + | 1.23075i | −0.0534102 | + | 0.0534102i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0905295 | − | 0.145820i | −0.00392127 | − | 0.00631617i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −32.8879 | + | 32.8879i | −1.42187 | + | 1.42187i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10.4962i | 0.452944i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −24.0615 | − | 24.0615i | −1.03640 | − | 1.03640i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.7679 | − | 23.7679i | −1.02186 | − | 1.02186i | −0.999756 | − | 0.0221074i | \(-0.992962\pi\) |
−0.0221074 | − | 0.999756i | \(-0.507038\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.0565 | −0.603223 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.9962i | 0.471027i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.4838 | −0.875824 | −0.437912 | − | 0.899018i | \(-0.644282\pi\) | ||||
−0.437912 | + | 0.899018i | \(0.644282\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.66832i | 0.199239i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.748898 | − | 0.748898i | 0.0319041 | − | 0.0319041i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −19.0343 | + | 19.0343i | −0.809420 | + | 0.809420i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 12.2205 | 0.518732 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 30.8045 | + | 30.8045i | 1.30523 | + | 1.30523i | 0.924819 | + | 0.380408i | \(0.124217\pi\) |
0.380408 | + | 0.924819i | \(0.375783\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.87014 | + | 12.2689i | −0.121394 | + | 0.518921i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.76210 | + | 2.76210i | 0.116616 | + | 0.116616i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 33.7226i | − | 1.42124i | −0.703578 | − | 0.710618i | \(-0.748415\pi\) | ||
0.703578 | − | 0.710618i | \(-0.251585\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.24903 | + | 9.24903i | −0.389110 | + | 0.389110i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.85816 | + | 2.85816i | 0.120031 | + | 0.120031i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.5317i | 1.57341i | 0.617329 | + | 0.786705i | \(0.288215\pi\) | ||||
−0.617329 | + | 0.786705i | \(0.711785\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.4261i | − | 0.436318i | −0.975913 | − | 0.218159i | \(-0.929995\pi\) | ||
0.975913 | − | 0.218159i | \(-0.0700051\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.1540i | 0.633066i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 77.7706i | 3.24326i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.95723 | − | 5.95723i | −0.248003 | − | 0.248003i | 0.572148 | − | 0.820150i | \(-0.306110\pi\) |
−0.820150 | + | 0.572148i | \(0.806110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −16.5694 | + | 16.5694i | −0.688600 | + | 0.688600i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 0.880223i | − | 0.0365178i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 20.7197 | + | 20.7197i | 0.858121 | + | 0.858121i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3765 | + | 8.30451i | −0.553049 | + | 0.343349i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.72078 | − | 1.72078i | −0.0710241 | − | 0.0710241i | 0.670702 | − | 0.741727i | \(-0.265993\pi\) |
−0.741727 | + | 0.670702i | \(0.765993\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.35506 | 0.344264 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.24885 | − | 6.24885i | 0.257044 | − | 0.257044i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 13.4905 | − | 13.4905i | 0.553990 | − | 0.553990i | −0.373600 | − | 0.927590i | \(-0.621877\pi\) |
0.927590 | + | 0.373600i | \(0.121877\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 18.9209i | 0.775683i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.22848 | 0.173060 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 37.0916i | − | 1.51552i | −0.652533 | − | 0.757760i | \(-0.726294\pi\) | ||
0.652533 | − | 0.757760i | \(-0.273706\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −17.3441 | −0.707483 | −0.353741 | − | 0.935343i | \(-0.615091\pi\) | ||||
−0.353741 | + | 0.935343i | \(0.615091\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.03305 | − | 2.03305i | −0.0827920 | − | 0.0827920i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.03585 | + | 7.03585i | 0.286048 | + | 0.286048i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.0268909i | 0.00109147i | 1.00000 | 0.000545735i | \(0.000173713\pi\) | |||||
−1.00000 | 0.000545735i | \(0.999826\pi\) | ||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.46446 | + | 1.46446i | −0.0593427 | + | 0.0593427i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.3623 | + | 27.9662i | 0.702403 | + | 1.13139i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.4415 | + | 21.4415i | −0.866013 | + | 0.866013i | −0.992028 | − | 0.126015i | \(-0.959781\pi\) |
0.126015 | + | 0.992028i | \(0.459781\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.207874 | 0.00838229 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.1510 | − | 10.1510i | −0.408663 | − | 0.408663i | 0.472609 | − | 0.881272i | \(-0.343312\pi\) |
−0.881272 | + | 0.472609i | \(0.843312\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.4442 | − | 10.4442i | 0.419789 | − | 0.419789i | −0.465342 | − | 0.885131i | \(-0.654069\pi\) |
0.885131 | + | 0.465342i | \(0.154069\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.52786 | −0.221825 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 65.0316 | 2.60544 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −102.588 | −4.10352 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.53224 | 0.300809 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.12125 | + | 2.12125i | −0.0845796 | + | 0.0845796i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.3320 | − | 21.3320i | −0.849215 | − | 0.849215i | 0.140820 | − | 0.990035i | \(-0.455026\pi\) |
−0.990035 | + | 0.140820i | \(0.955026\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 24.8295 | 0.986886 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 49.9106 | − | 49.9106i | 1.98064 | − | 1.98064i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.66939 | + | 32.7841i | −0.303872 | + | 1.29895i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.60969 | + | 5.60969i | −0.221916 | + | 0.221916i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 28.5426i | − | 1.12736i | −0.825992 | − | 0.563682i | \(-0.809384\pi\) | ||
0.825992 | − | 0.563682i | \(-0.190616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −18.1283 | − | 18.1283i | −0.714912 | − | 0.714912i | 0.252647 | − | 0.967559i | \(-0.418699\pi\) |
−0.967559 | + | 0.252647i | \(0.918699\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −10.7908 | − | 10.7908i | −0.424886 | − | 0.424886i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.0407 | 0.905824 | 0.452912 | − | 0.891555i | \(-0.350385\pi\) | ||||
0.452912 | + | 0.891555i | \(0.350385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.34253i | − | 0.248966i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16.3382 | −0.640343 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.8261i | 0.580191i | 0.956998 | + | 0.290095i | \(0.0936870\pi\) | ||||
−0.956998 | + | 0.290095i | \(0.906313\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.365983 | + | 0.365983i | −0.0143001 | + | 0.0143001i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.73067 | + | 5.73067i | −0.223575 | + | 0.223575i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.8920 | −0.580112 | −0.290056 | − | 0.957010i | \(-0.593674\pi\) | ||||
−0.290056 | + | 0.957010i | \(0.593674\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.6359 | − | 21.6359i | −0.841538 | − | 0.841538i | 0.147521 | − | 0.989059i | \(-0.452871\pi\) |
−0.989059 | + | 0.147521i | \(0.952871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.880394 | − | 3.76340i | 0.0341917 | − | 0.146158i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 25.7986 | + | 25.7986i | 1.00043 | + | 1.00043i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 2.83235i | − | 0.109669i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.83341 | + | 1.83341i | −0.0708836 | + | 0.0708836i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.0288 | − | 12.0288i | −0.464366 | − | 0.464366i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.0331i | 1.35043i | 0.737623 | + | 0.675213i | \(0.235948\pi\) | ||||
−0.737623 | + | 0.675213i | \(0.764052\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 14.0688i | − | 0.541510i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.24823i | 0.278572i | 0.990252 | + | 0.139286i | \(0.0444807\pi\) | ||||
−0.990252 | + | 0.139286i | \(0.955519\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 50.3187i | 1.93105i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.42020 | − | 9.42020i | −0.360983 | − | 0.360983i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.11346 | − | 7.11346i | 0.272189 | − | 0.272189i | −0.557792 | − | 0.829981i | \(-0.688351\pi\) |
0.829981 | + | 0.557792i | \(0.188351\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 51.7955i | 1.97900i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.97977 | − | 4.97977i | −0.189990 | − | 0.189990i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.60420 | − | 28.2308i | 0.251600 | − | 1.07551i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −32.6940 | − | 32.6940i | −1.24374 | − | 1.24374i | −0.958439 | − | 0.285298i | \(-0.907908\pi\) |
−0.285298 | − | 0.958439i | \(-0.592092\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −14.7292 | −0.559515 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −30.0605 | + | 30.0605i | −1.14026 | + | 1.14026i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0360829 | + | 0.0360829i | −0.00136674 | + | 0.00136674i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.38474i | 0.203670i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29.6221 | −1.11881 | −0.559406 | − | 0.828894i | \(-0.688971\pi\) | ||||
−0.559406 | + | 0.828894i | \(0.688971\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.78463i | 0.218171i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −39.8673 | −1.50149 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.26122 | + | 8.26122i | 0.310695 | + | 0.310695i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.8554 | + | 25.8554i | 0.971021 | + | 0.971021i | 0.999592 | − | 0.0285709i | \(-0.00909562\pi\) |
−0.0285709 | + | 0.999592i | \(0.509096\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.65963i | 0.249756i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.7995 | − | 15.7995i | 0.591696 | − | 0.591696i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.0688 | − | 55.8651i | 0.488747 | − | 2.08923i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.48045 | + | 6.48045i | −0.242017 | + | 0.242017i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 31.2277 | 1.16460 | 0.582299 | − | 0.812975i | \(-0.302153\pi\) | ||||
0.582299 | + | 0.812975i | \(0.302153\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.4555 | − | 20.4555i | −0.761802 | − | 0.761802i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 16.2281 | − | 16.2281i | 0.603529 | − | 0.603529i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.20855 | 0.267719 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.2172 | 0.786902 | 0.393451 | − | 0.919346i | \(-0.371281\pi\) | ||||
0.393451 | + | 0.919346i | \(0.371281\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.74614 | 0.138556 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.8649 | − | 23.8649i | 0.881469 | − | 0.881469i | −0.112215 | − | 0.993684i | \(-0.535794\pi\) |
0.993684 | + | 0.112215i | \(0.0357944\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −28.8343 | − | 28.8343i | −1.06357 | − | 1.06357i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4770 | 0.385927 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.5318 | + | 28.5318i | −1.04956 | + | 1.04956i | −0.0508533 | + | 0.998706i | \(0.516194\pi\) |
−0.998706 | + | 0.0508533i | \(0.983806\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.93097 | − | 6.33180i | −0.144408 | − | 0.232605i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −14.7470 | + | 14.7470i | −0.541013 | + | 0.541013i | −0.923826 | − | 0.382813i | \(-0.874956\pi\) |
0.382813 | + | 0.923826i | \(0.374956\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 39.5099i | − | 1.44753i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.153984 | − | 0.153984i | −0.00563399 | − | 0.00563399i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 30.4421 | + | 30.4421i | 1.11233 | + | 1.11233i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.2644 | −1.61523 | −0.807615 | − | 0.589710i | \(-0.799242\pi\) | ||||
−0.807615 | + | 0.589710i | \(0.799242\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 0.990551i | − | 0.0360977i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −38.4803 | −1.40044 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.4803i | 0.562641i | 0.959614 | + | 0.281320i | \(0.0907724\pi\) | ||||
−0.959614 | + | 0.281320i | \(0.909228\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 14.2435 | − | 14.2435i | 0.517008 | − | 0.517008i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 15.3450 | − | 15.3450i | 0.556257 | − | 0.556257i | −0.371983 | − | 0.928240i | \(-0.621322\pi\) |
0.928240 | + | 0.371983i | \(0.121322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.1785 | 0.368486 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.30998 | + | 3.30998i | 0.119673 | + | 0.119673i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.33170 | + | 3.31008i | −0.192517 | + | 0.119520i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.693724 | + | 0.693724i | 0.0250163 | + | 0.0250163i | 0.719504 | − | 0.694488i | \(-0.244369\pi\) |
−0.694488 | + | 0.719504i | \(0.744369\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.9182i | 0.609295i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.77394 | − | 2.77394i | 0.0997716 | − | 0.0997716i | −0.655459 | − | 0.755231i | \(-0.727525\pi\) |
0.755231 | + | 0.655459i | \(0.227525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 40.2110 | + | 40.2110i | 1.44442 | + | 1.44442i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 11.3117i | − | 0.405806i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0983980i | 0.00352547i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 28.9088i | − | 1.03444i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.512377i | 0.0183109i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 73.5578 | + | 73.5578i | 2.62539 | + | 2.62539i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.16585 | + | 9.16585i | −0.326727 | + | 0.326727i | −0.851341 | − | 0.524613i | \(-0.824210\pi\) |
0.524613 | + | 0.851341i | \(0.324210\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 28.7035i | − | 1.02187i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.56123 | + | 8.56123i | 0.304402 | + | 0.304402i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.83406 | + | 16.3894i | −0.136152 | + | 0.582004i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.8295 | + | 24.8295i | 0.880613 | + | 0.880613i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.6299 | 0.766172 | 0.383086 | − | 0.923713i | \(-0.374861\pi\) | ||||
0.383086 | + | 0.923713i | \(0.374861\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.92020 | − | 6.92020i | 0.244819 | − | 0.244819i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.3765 | − | 11.3765i | 0.401968 | − | 0.401968i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 29.5323i | − | 1.04217i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 97.5710 | 3.43893 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 25.8818i | 0.911084i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.8260 | −0.450937 | −0.225468 | − | 0.974250i | \(-0.572391\pi\) | ||||
−0.225468 | + | 0.974250i | \(0.572391\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.35046 | − | 5.35046i | −0.187880 | − | 0.187880i | 0.606899 | − | 0.794779i | \(-0.292413\pi\) |
−0.794779 | + | 0.606899i | \(0.792413\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −6.06113 | − | 6.06113i | −0.212573 | − | 0.212573i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 24.9140i | − | 0.872698i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.10785 | − | 5.10785i | 0.178701 | − | 0.178701i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.68694 | + | 12.3817i | 0.268604 | + | 0.432653i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −11.7654 | + | 11.7654i | −0.410614 | + | 0.410614i | −0.881953 | − | 0.471338i | \(-0.843771\pi\) |
0.471338 | + | 0.881953i | \(0.343771\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.95031 | −0.346846 | −0.173423 | − | 0.984847i | \(-0.555483\pi\) | ||||
−0.173423 | + | 0.984847i | \(0.555483\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.2510 | + | 36.2510i | 1.26210 | + | 1.26210i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0.583398 | − | 0.583398i | 0.0202867 | − | 0.0202867i | −0.696891 | − | 0.717177i | \(-0.745434\pi\) |
0.717177 | + | 0.696891i | \(0.245434\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −43.6976 | −1.51768 | −0.758840 | − | 0.651277i | \(-0.774234\pi\) | ||||
−0.758840 | + | 0.651277i | \(0.774234\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.49785 | 0.0866496 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.0101 | 0.346831 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.5719 | −1.02338 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.85816 | + | 2.85816i | −0.0987925 | + | 0.0987925i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 25.4022 | + | 25.4022i | 0.876982 | + | 0.876982i | 0.993221 | − | 0.116239i | \(-0.0370838\pi\) |
−0.116239 | + | 0.993221i | \(0.537084\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7375 | 0.990947 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −6.26380 | + | 6.26380i | −0.215737 | + | 0.215737i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −53.7821 | + | 18.1692i | −1.85016 | + | 0.625039i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.51263 | − | 6.51263i | 0.223777 | − | 0.223777i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 11.9847i | 0.411314i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 10.9388 | + | 10.9388i | 0.374977 | + | 0.374977i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −15.3474 | − | 15.3474i | −0.525486 | − | 0.525486i | 0.393737 | − | 0.919223i | \(-0.371182\pi\) |
−0.919223 | + | 0.393737i | \(0.871182\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.02631 | 0.308693 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 45.0479i | − | 1.53881i | −0.638762 | − | 0.769404i | \(-0.720553\pi\) | ||
0.638762 | − | 0.769404i | \(-0.279447\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.0655 | 0.821106 | 0.410553 | − | 0.911837i | \(-0.365336\pi\) | ||||
0.410553 | + | 0.911837i | \(0.365336\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 0.192415i | − | 0.00655750i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.38306 | + | 7.38306i | −0.251322 | + | 0.251322i | −0.821513 | − | 0.570190i | \(-0.806869\pi\) |
0.570190 | + | 0.821513i | \(0.306869\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.60750 | + | 5.60750i | −0.190661 | + | 0.190661i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.8509 | 0.538325 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.1598 | − | 17.1598i | −0.582105 | − | 0.582105i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.46782 | − | 8.80728i | −0.185270 | − | 0.298423i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.80263 | + | 8.80263i | 0.297924 | + | 0.297924i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 160.072i | 5.41143i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.141964 | − | 0.141964i | 0.00479380 | − | 0.00479380i | −0.704706 | − | 0.709500i | \(-0.748921\pi\) |
0.709500 | + | 0.704706i | \(0.248921\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.26151 | + | 3.26151i | 0.110008 | + | 0.110008i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 15.3692i | − | 0.517802i | −0.965904 | − | 0.258901i | \(-0.916640\pi\) | ||
0.965904 | − | 0.258901i | \(-0.0833604\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 47.6748i | − | 1.60438i | −0.597066 | − | 0.802192i | \(-0.703667\pi\) | ||
0.597066 | − | 0.802192i | \(-0.296333\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 7.60061i | − | 0.255492i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 50.4271i | − | 1.69317i | −0.532250 | − | 0.846587i | \(-0.678653\pi\) | ||
0.532250 | − | 0.846587i | \(-0.321347\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −46.1990 | − | 46.1990i | −1.54946 | − | 1.54946i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.57668 | + | 2.57668i | −0.0863222 | + | 0.0863222i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 18.8713i | − | 0.631505i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.4100 | − | 32.4100i | −1.08335 | − | 1.08335i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.4070 | − | 4.54000i | −0.647981 | − | 0.151586i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.46446 | − | 1.46446i | −0.0488423 | − | 0.0488423i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.61986 | −0.287169 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −9.98830 | + | 9.98830i | −0.332390 | + | 0.332390i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 43.4036 | − | 43.4036i | 1.44278 | − | 1.44278i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.3735i | 1.04174i | 0.853636 | + | 0.520870i | \(0.174392\pi\) | ||||
−0.853636 | + | 0.520870i | \(0.825608\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.89040 | 0.0958684 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37.5437i | − | 1.24388i | −0.783066 | − | 0.621939i | \(-0.786345\pi\) | ||
0.783066 | − | 0.621939i | \(-0.213655\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.793538 | 0.0262623 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −14.4148 | − | 14.4148i | −0.476538 | − | 0.476538i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.338766 | + | 0.338766i | 0.0111870 | + | 0.0111870i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 30.2192i | 0.996841i | 0.866935 | + | 0.498420i | \(0.166086\pi\) | ||||
−0.866935 | + | 0.498420i | \(0.833914\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.00180 | − | 7.00180i | 0.230717 | − | 0.230717i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −24.3015 | + | 15.0871i | −0.799894 | + | 0.496598i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −27.8401 | + | 27.8401i | −0.915377 | + | 0.915377i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.15687 | −0.235062 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 21.2995 | + | 21.2995i | 0.698815 | + | 0.698815i | 0.964155 | − | 0.265340i | \(-0.0854842\pi\) |
−0.265340 | + | 0.964155i | \(0.585484\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6488 | − | 13.6488i | 0.447322 | − | 0.447322i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 29.2550 | 0.957766 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −17.0576 | −0.557842 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.9894 | 1.17572 | 0.587861 | − | 0.808962i | \(-0.299970\pi\) | ||||
0.587861 | + | 0.808962i | \(0.299970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.65852 | 0.0867576 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.4948 | − | 11.4948i | 0.374720 | − | 0.374720i | −0.494473 | − | 0.869193i | \(-0.664639\pi\) |
0.869193 | + | 0.494473i | \(0.164639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.186072 | + | 0.186072i | 0.00605932 | + | 0.00605932i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −17.6508 | −0.574180 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −5.55235 | + | 5.55235i | −0.180427 | + | 0.180427i | −0.791542 | − | 0.611115i | \(-0.790721\pi\) |
0.611115 | + | 0.791542i | \(0.290721\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.8256 | + | 15.4125i | −0.805873 | + | 0.500310i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.19502 | + | 5.19502i | −0.168460 | + | 0.168460i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 10.6622i | − | 0.345384i | −0.984976 | − | 0.172692i | \(-0.944753\pi\) | ||
0.984976 | − | 0.172692i | \(-0.0552465\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −46.7922 | − | 46.7922i | −1.51416 | − | 1.51416i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.32023 | − | 1.32023i | −0.0426771 | − | 0.0426771i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 47.9437 | 1.54818 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.6618i | 0.472962i | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.6510 | 0.343222 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 102.325i | − | 3.29397i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.807895 | − | 0.807895i | 0.0259801 | − | 0.0259801i | −0.693997 | − | 0.719978i | \(-0.744152\pi\) |
0.719978 | + | 0.693997i | \(0.244152\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.56679 | + | 1.56679i | −0.0503326 | + | 0.0503326i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.7850 | −0.410290 | −0.205145 | − | 0.978732i | \(-0.565767\pi\) | ||||
−0.205145 | + | 0.978732i | \(0.565767\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 27.8251 | + | 27.8251i | 0.892031 | + | 0.892031i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.5547 | − | 49.3924i | 0.370045 | − | 1.58182i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 10.2997 | + | 10.2997i | 0.329517 | + | 0.329517i | 0.852403 | − | 0.522886i | \(-0.175145\pi\) |
−0.522886 | + | 0.852403i | \(0.675145\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 58.6272i | 1.87373i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.78060 | − | 1.78060i | 0.0568502 | − | 0.0568502i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −36.2990 | − | 36.2990i | −1.15776 | − | 1.15776i | −0.984957 | − | 0.172800i | \(-0.944718\pi\) |
−0.172800 | − | 0.984957i | \(-0.555282\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.5902i | 1.22959i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 36.9026i | 1.17462i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 19.3180i | − | 0.614276i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 22.9756i | − | 0.729843i | −0.931038 | − | 0.364922i | \(-0.881096\pi\) | ||
0.931038 | − | 0.364922i | \(-0.118904\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.6385 | + | 14.6385i | 0.464538 | + | 0.464538i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.0566 | + | 13.0566i | −0.413923 | + | 0.413923i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 38.3954i | − | 1.21599i | −0.793940 | − | 0.607997i | \(-0.791973\pi\) | ||
0.793940 | − | 0.607997i | \(-0.208027\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.97885 | − | 1.97885i | −0.0626080 | − | 0.0626080i |
(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 | 1248.2.bb.f.463.1 | 24 | ||
4.3 | odd | 2 | 312.2.t.e.307.1 | yes | 24 | ||
8.3 | odd | 2 | inner | 1248.2.bb.f.463.12 | 24 | ||
8.5 | even | 2 | 312.2.t.e.307.6 | yes | 24 | ||
12.11 | even | 2 | 936.2.w.j.307.12 | 24 | |||
13.5 | odd | 4 | inner | 1248.2.bb.f.655.12 | 24 | ||
24.5 | odd | 2 | 936.2.w.j.307.7 | 24 | |||
52.31 | even | 4 | 312.2.t.e.187.6 | yes | 24 | ||
104.5 | odd | 4 | 312.2.t.e.187.1 | ✓ | 24 | ||
104.83 | even | 4 | inner | 1248.2.bb.f.655.1 | 24 | ||
156.83 | odd | 4 | 936.2.w.j.811.7 | 24 | |||
312.5 | even | 4 | 936.2.w.j.811.12 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.t.e.187.1 | ✓ | 24 | 104.5 | odd | 4 | ||
312.2.t.e.187.6 | yes | 24 | 52.31 | even | 4 | ||
312.2.t.e.307.1 | yes | 24 | 4.3 | odd | 2 | ||
312.2.t.e.307.6 | yes | 24 | 8.5 | even | 2 | ||
936.2.w.j.307.7 | 24 | 24.5 | odd | 2 | |||
936.2.w.j.307.12 | 24 | 12.11 | even | 2 | |||
936.2.w.j.811.7 | 24 | 156.83 | odd | 4 | |||
936.2.w.j.811.12 | 24 | 312.5 | even | 4 | |||
1248.2.bb.f.463.1 | 24 | 1.1 | even | 1 | trivial | ||
1248.2.bb.f.463.12 | 24 | 8.3 | odd | 2 | inner | ||
1248.2.bb.f.655.1 | 24 | 104.83 | even | 4 | inner | ||
1248.2.bb.f.655.12 | 24 | 13.5 | odd | 4 | inner |