Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1260,2,Mod(53,1260)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1260, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 9, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1260.53");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1260.ej (of order \(12\), degree \(4\), 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: | \(10.0611506547\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 737.16 | ||
Character | \(\chi\) | \(=\) | 1260.737 |
Dual form | 1260.2.ej.a.53.16 |
$q$-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 \(\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times\).
\(n\) | \(281\) | \(631\) | \(757\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | 2.23607 | + | 0.00183442i | 1.00000 | + | 0.000820380i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.45417 | − | 0.988471i | −0.927587 | − | 0.373607i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72089 | + | 1.57091i | −0.820380 | + | 0.473647i | −0.850548 | − | 0.525898i | \(-0.823729\pi\) |
0.0301675 | + | 0.999545i | \(0.490396\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.380199 | + | 0.380199i | −0.105448 | + | 0.105448i | −0.757863 | − | 0.652414i | \(-0.773756\pi\) |
0.652414 | + | 0.757863i | \(0.273756\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.20115 | + | 0.321846i | 0.291321 | + | 0.0780592i | 0.401520 | − | 0.915850i | \(-0.368482\pi\) |
−0.110199 | + | 0.993910i | \(0.535149\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.59110 | + | 3.22802i | 1.28269 | + | 0.740559i | 0.977339 | − | 0.211682i | \(-0.0678941\pi\) |
0.305347 | + | 0.952241i | \(0.401227\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7.93400 | − | 2.12591i | 1.65435 | − | 0.443283i | 0.693527 | − | 0.720431i | \(-0.256056\pi\) |
0.960827 | + | 0.277148i | \(0.0893893\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.99999 | + | 0.00820379i | 0.999999 | + | 0.00164076i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.09991 | 0.761334 | 0.380667 | − | 0.924712i | \(-0.375694\pi\) | ||||
0.380667 | + | 0.924712i | \(0.375694\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.84794 | + | 4.93277i | 0.511505 | + | 0.885952i | 0.999911 | + | 0.0133360i | \(0.00424510\pi\) |
−0.488406 | + | 0.872616i | \(0.662422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.48586 | − | 2.21479i | −0.927280 | − | 0.374368i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.7991 | − | 2.89360i | 1.77536 | − | 0.475706i | 0.785633 | − | 0.618693i | \(-0.212337\pi\) |
0.989725 | + | 0.142987i | \(0.0456707\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 7.39900i | − | 1.15553i | −0.816203 | − | 0.577765i | \(-0.803925\pi\) | ||
0.816203 | − | 0.577765i | \(-0.196075\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.31257 | + | 8.31257i | −1.26766 | + | 1.26766i | −0.320359 | + | 0.947296i | \(0.603803\pi\) |
−0.947296 | + | 0.320359i | \(0.896197\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.420044 | − | 1.56762i | −0.0612697 | − | 0.228661i | 0.928501 | − | 0.371330i | \(-0.121098\pi\) |
−0.989770 | + | 0.142669i | \(0.954432\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.04585 | + | 4.85174i | 0.720836 | + | 0.693106i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.88301 | − | 10.7595i | 0.396011 | − | 1.47793i | −0.424040 | − | 0.905644i | \(-0.639388\pi\) |
0.820051 | − | 0.572290i | \(-0.193945\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.08698 | + | 3.50766i | −0.820768 | + | 0.472973i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.50159 | − | 9.52904i | −0.716246 | − | 1.24058i | −0.962477 | − | 0.271364i | \(-0.912525\pi\) |
0.246231 | − | 0.969211i | \(-0.420808\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.74059 | + | 6.47889i | −0.478933 | + | 0.829537i | −0.999708 | − | 0.0241574i | \(-0.992310\pi\) |
0.520775 | + | 0.853694i | \(0.325643\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.850848 | + | 0.849453i | −0.105535 | + | 0.105362i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.31033 | − | 4.89021i | 0.160082 | − | 0.597434i | −0.838535 | − | 0.544848i | \(-0.816587\pi\) |
0.998616 | − | 0.0525853i | \(-0.0167462\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.1301i | 1.79561i | 0.440389 | + | 0.897807i | \(0.354841\pi\) | ||||
−0.440389 | + | 0.897807i | \(0.645159\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.39779 | + | 2.51813i | 1.09993 | + | 0.294725i | 0.762735 | − | 0.646711i | \(-0.223856\pi\) |
0.337192 | + | 0.941436i | \(0.390523\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.23032 | − | 1.16575i | 0.937932 | − | 0.132849i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.95167 | − | 2.28150i | −0.444598 | − | 0.256688i | 0.260948 | − | 0.965353i | \(-0.415965\pi\) |
−0.705546 | + | 0.708664i | \(0.749298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.60611 | − | 2.60611i | −0.286057 | − | 0.286057i | 0.549462 | − | 0.835519i | \(-0.314833\pi\) |
−0.835519 | + | 0.549462i | \(0.814833\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.68525 | + | 0.721873i | 0.291257 | + | 0.0782982i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.35104 | − | 7.53622i | 0.461209 | − | 0.798838i | −0.537812 | − | 0.843065i | \(-0.680749\pi\) |
0.999022 | + | 0.0442266i | \(0.0140824\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.30889 | − | 0.557255i | 0.137209 | − | 0.0584162i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.4962 | + | 7.22833i | 1.28208 | + | 0.741611i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.02356 | + | 2.02356i | 0.205461 | + | 0.205461i | 0.802335 | − | 0.596874i | \(-0.203591\pi\) |
−0.596874 | + | 0.802335i | \(0.703591\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2993 | + | 7.10098i | −1.22382 | + | 0.706574i | −0.965731 | − | 0.259547i | \(-0.916427\pi\) |
−0.258091 | + | 0.966121i | \(0.583093\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.925045 | + | 3.45232i | 0.0911474 | + | 0.340167i | 0.996407 | − | 0.0846916i | \(-0.0269905\pi\) |
−0.905260 | + | 0.424858i | \(0.860324\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.697568 | + | 2.60336i | 0.0674364 | + | 0.251676i | 0.991412 | − | 0.130775i | \(-0.0417466\pi\) |
−0.923976 | + | 0.382451i | \(0.875080\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.95186 | + | 2.85896i | −0.474302 | + | 0.273839i | −0.718039 | − | 0.696003i | \(-0.754960\pi\) |
0.243737 | + | 0.969841i | \(0.421627\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.976035 | − | 0.976035i | −0.0918177 | − | 0.0918177i | 0.659706 | − | 0.751524i | \(-0.270681\pi\) |
−0.751524 | + | 0.659706i | \(0.770681\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 17.7449 | − | 4.73912i | 1.65472 | − | 0.441925i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.62968 | − | 1.97716i | −0.241062 | − | 0.181246i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.564495 | + | 0.977734i | −0.0513177 | + | 0.0888849i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1803 | + | 0.0275163i | 0.999997 | + | 0.00246114i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.69577 | − | 5.69577i | −0.505417 | − | 0.505417i | 0.407699 | − | 0.913116i | \(-0.366331\pi\) |
−0.913116 | + | 0.407699i | \(0.866331\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.1697 | + | 6.44881i | 0.975899 | + | 0.563435i | 0.901029 | − | 0.433758i | \(-0.142813\pi\) |
0.0748691 | + | 0.997193i | \(0.476146\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.5307 | − | 13.4487i | −0.913125 | − | 1.16615i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.47534 | − | 1.19916i | −0.382354 | − | 0.102451i | 0.0625222 | − | 0.998044i | \(-0.480086\pi\) |
−0.444876 | + | 0.895592i | \(0.646752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 7.85056i | − | 0.665876i | −0.942949 | − | 0.332938i | \(-0.891960\pi\) | ||
0.942949 | − | 0.332938i | \(-0.108040\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.437223 | − | 1.63174i | 0.0365624 | − | 0.136453i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.16767 | + | 0.00752097i | 0.761333 | + | 0.000624583i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.03231 | + | 6.98416i | −0.330340 | + | 0.572165i | −0.982578 | − | 0.185849i | \(-0.940497\pi\) |
0.652239 | + | 0.758014i | \(0.273830\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.05240 | + | 5.28692i | 0.248401 | + | 0.430243i | 0.963082 | − | 0.269207i | \(-0.0867616\pi\) |
−0.714681 | + | 0.699450i | \(0.753428\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.35913 | + | 11.0352i | 0.510778 | + | 0.886372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.62219 | + | 13.5182i | −0.289082 | + | 1.07887i | 0.656722 | + | 0.754133i | \(0.271942\pi\) |
−0.945804 | + | 0.324737i | \(0.894724\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −21.5727 | − | 2.62520i | −1.70017 | − | 0.206894i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.02860 | − | 11.3029i | −0.237218 | − | 0.885309i | −0.977137 | − | 0.212613i | \(-0.931803\pi\) |
0.739919 | − | 0.672696i | \(-0.234864\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.72175 | − | 1.72175i | 0.133233 | − | 0.133233i | −0.637345 | − | 0.770578i | \(-0.719968\pi\) |
0.770578 | + | 0.637345i | \(0.219968\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.7109i | 0.977761i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.58199 | − | 2.56749i | 0.728505 | − | 0.195202i | 0.124542 | − | 0.992214i | \(-0.460254\pi\) |
0.603963 | + | 0.797012i | \(0.293587\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.2627 | − | 4.96248i | −0.926973 | − | 0.375128i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.39946 | − | 11.0842i | −0.478318 | − | 0.828471i | 0.521373 | − | 0.853329i | \(-0.325420\pi\) |
−0.999691 | + | 0.0248576i | \(0.992087\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.6067 | 1.53168 | 0.765841 | − | 0.643030i | \(-0.222323\pi\) | ||||
0.765841 | + | 0.643030i | \(0.222323\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 24.1528 | − | 6.45048i | 1.77575 | − | 0.474249i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.77378 | + | 1.01118i | −0.275966 | + | 0.0739450i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.4274 | − | 9.48434i | −1.18864 | − | 0.686262i | −0.230644 | − | 0.973038i | \(-0.574083\pi\) |
−0.957998 | + | 0.286776i | \(0.907417\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.669626 | − | 0.179426i | −0.0482007 | − | 0.0129153i | 0.234638 | − | 0.972083i | \(-0.424609\pi\) |
−0.282839 | + | 0.959167i | \(0.591276\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.03090 | − | 2.03090i | 0.144696 | − | 0.144696i | −0.631048 | − | 0.775744i | \(-0.717375\pi\) |
0.775744 | + | 0.631048i | \(0.217375\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.05795 | + | 3.49756i | −0.429437 | + | 0.247936i | −0.699107 | − | 0.715017i | \(-0.746419\pi\) |
0.269670 | + | 0.962953i | \(0.413085\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.0618 | − | 4.05264i | −0.706203 | − | 0.284439i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0135729 | − | 16.5447i | 0.000947973 | − | 1.15553i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −20.2837 | −1.40305 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.3394 | −1.60675 | −0.803375 | − | 0.595474i | \(-0.796964\pi\) | ||||
−0.803375 | + | 0.595474i | \(0.796964\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.6027 | + | 18.5722i | −1.26869 | + | 1.26661i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.11341 | − | 14.9209i | −0.143468 | − | 1.01290i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.579040 | + | 0.334309i | −0.0389505 | + | 0.0224881i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.20268 | − | 4.20268i | 0.281432 | − | 0.281432i | −0.552248 | − | 0.833680i | \(-0.686230\pi\) |
0.833680 | + | 0.552248i | \(0.186230\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 15.4223 | + | 4.13240i | 1.02362 | + | 0.274277i | 0.731308 | − | 0.682047i | \(-0.238910\pi\) |
0.292308 | + | 0.956324i | \(0.405577\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6115 | − | 10.7453i | −1.22988 | − | 0.710071i | −0.262875 | − | 0.964830i | \(-0.584671\pi\) |
−0.967005 | + | 0.254759i | \(0.918004\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −20.3842 | + | 5.46192i | −1.33541 | + | 0.357823i | −0.854730 | − | 0.519072i | \(-0.826277\pi\) |
−0.480682 | + | 0.876895i | \(0.659611\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.936370 | − | 3.50608i | −0.0610820 | − | 0.228712i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.49125 | 0.225830 | 0.112915 | − | 0.993605i | \(-0.463981\pi\) | ||||
0.112915 | + | 0.993605i | \(0.463981\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.5764 | + | 20.0509i | 0.745700 | + | 1.29159i | 0.949867 | + | 0.312654i | \(0.101218\pi\) |
−0.204167 | + | 0.978936i | \(0.565449\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 11.2740 | + | 10.8581i | 0.720267 | + | 0.693697i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.35302 | + | 0.898439i | −0.213348 | + | 0.0571663i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 20.3285i | 1.28313i | 0.767071 | + | 0.641563i | \(0.221714\pi\) | ||||
−0.767071 | + | 0.641563i | \(0.778286\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −18.2480 | + | 18.2480i | −1.14724 | + | 1.14724i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.0573203 | − | 0.213922i | −0.00357554 | − | 0.0133441i | 0.964115 | − | 0.265485i | \(-0.0855320\pi\) |
−0.967691 | + | 0.252141i | \(0.918865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −29.3630 | − | 3.57319i | −1.82453 | − | 0.222027i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.723773 | + | 2.70116i | −0.0446297 | + | 0.166560i | −0.984644 | − | 0.174575i | \(-0.944145\pi\) |
0.940014 | + | 0.341136i | \(0.110812\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.46633 | − | 24.0537i | 0.397224 | − | 1.47761i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.05513 | − | 8.75575i | −0.308217 | − | 0.533847i | 0.669755 | − | 0.742582i | \(-0.266399\pi\) |
−0.977972 | + | 0.208734i | \(0.933066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.417054 | + | 0.722359i | −0.0253343 | + | 0.0438802i | −0.878415 | − | 0.477899i | \(-0.841398\pi\) |
0.853080 | + | 0.521780i | \(0.174732\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.6173 | + | 7.83221i | −0.821156 | + | 0.472300i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.129352 | − | 0.482749i | 0.00777202 | − | 0.0290056i | −0.961931 | − | 0.273293i | \(-0.911887\pi\) |
0.969703 | + | 0.244287i | \(0.0785539\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.50960i | 0.269020i | 0.990912 | + | 0.134510i | \(0.0429461\pi\) | ||||
−0.990912 | + | 0.134510i | \(0.957054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.7354 | − | 2.87653i | −0.638151 | − | 0.170992i | −0.0747854 | − | 0.997200i | \(-0.523827\pi\) |
−0.563366 | + | 0.826208i | \(0.690494\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −7.31370 | + | 18.1584i | −0.431714 | + | 1.07186i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.3833 | − | 7.72683i | −0.787251 | − | 0.454519i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3240 | − | 15.3240i | −0.895239 | − | 0.895239i | 0.0997714 | − | 0.995010i | \(-0.468189\pi\) |
−0.995010 | + | 0.0997714i | \(0.968189\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.2845 | − | 21.3177i | −0.715228 | − | 1.24116i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.20823 | + | 3.82477i | −0.127705 | + | 0.221192i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 28.6171 | − | 12.1837i | 1.64947 | − | 0.702256i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.37609 | + | 14.4804i | −0.479614 | + | 0.829143i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.4605 | − | 11.4605i | −0.654087 | − | 0.654087i | 0.299888 | − | 0.953974i | \(-0.403051\pi\) |
−0.953974 | + | 0.299888i | \(0.903051\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.38389 | − | 2.53104i | 0.248587 | − | 0.143522i | −0.370530 | − | 0.928821i | \(-0.620824\pi\) |
0.619117 | + | 0.785299i | \(0.287491\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.19662 | − | 8.19791i | −0.124160 | − | 0.463373i | 0.875648 | − | 0.482950i | \(-0.160435\pi\) |
−0.999808 | + | 0.0195769i | \(0.993768\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.17392 | − | 8.11319i | −0.122100 | − | 0.455682i | 0.877620 | − | 0.479357i | \(-0.159130\pi\) |
−0.999720 | + | 0.0236748i | \(0.992463\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.1554 | + | 6.44058i | −0.624583 | + | 0.360603i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 5.67680 | + | 5.67680i | 0.315866 | + | 0.315866i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.90411 | + | 1.89787i | −0.105621 | + | 0.105275i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.518694 | + | 4.26241i | −0.0285965 | + | 0.234994i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.39047 | − | 9.33657i | 0.296287 | − | 0.513185i | −0.678996 | − | 0.734142i | \(-0.737585\pi\) |
0.975284 | + | 0.220957i | \(0.0709181\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.93895 | − | 10.9324i | 0.160572 | − | 0.597302i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.1629 | + | 14.1629i | 0.771501 | + | 0.771501i | 0.978369 | − | 0.206868i | \(-0.0663271\pi\) |
−0.206868 | + | 0.978369i | \(0.566327\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.4979 | − | 8.94770i | −0.839257 | − | 0.484545i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.58755 | − | 16.8946i | −0.409689 | − | 0.912225i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.9409 | + | 7.21878i | 1.44626 | + | 0.387525i | 0.894722 | − | 0.446624i | \(-0.147374\pi\) |
0.551540 | + | 0.834149i | \(0.314041\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.6684i | 1.42753i | 0.700387 | + | 0.713764i | \(0.253011\pi\) | ||||
−0.700387 | + | 0.713764i | \(0.746989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8.32160 | − | 31.0566i | 0.442914 | − | 1.65298i | −0.278472 | − | 0.960444i | \(-0.589828\pi\) |
0.721386 | − | 0.692533i | \(-0.243505\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.0277551 | + | 33.8320i | −0.00147309 | + | 1.79561i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.46072 | − | 4.26209i | 0.129872 | − | 0.224944i | −0.793755 | − | 0.608238i | \(-0.791877\pi\) |
0.923627 | + | 0.383293i | \(0.125210\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.3403 | + | 19.6419i | 0.596856 | + | 1.03378i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 21.0095 | + | 5.64795i | 1.09969 | + | 0.295627i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.34435 | − | 19.9454i | 0.278973 | − | 1.04114i | −0.674160 | − | 0.738586i | \(-0.735494\pi\) |
0.953132 | − | 0.302554i | \(-0.0978393\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −17.7108 | + | 23.5559i | −0.919501 | + | 1.22296i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.40708 | − | 27.6436i | −0.383524 | − | 1.43133i | −0.840480 | − | 0.541842i | \(-0.817727\pi\) |
0.456956 | − | 0.889489i | \(-0.348940\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.55878 | + | 1.55878i | −0.0802813 | + | 0.0802813i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.2503i | − | 0.526522i | −0.964725 | − | 0.263261i | \(-0.915202\pi\) | ||
0.964725 | − | 0.263261i | \(-0.0847980\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.2850 | − | 7.31099i | 1.39420 | − | 0.373574i | 0.517939 | − | 0.855417i | \(-0.326699\pi\) |
0.876257 | + | 0.481843i | \(0.160033\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 18.4057 | − | 2.59159i | 0.938040 | − | 0.132080i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.54833 | + | 2.68179i | 0.0785036 | + | 0.135972i | 0.902605 | − | 0.430471i | \(-0.141652\pi\) |
−0.824101 | + | 0.566443i | \(0.808319\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2141 | 0.516550 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.83201 | − | 5.10883i | −0.444387 | − | 0.257053i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.0435 | + | 6.71038i | −1.25690 | + | 0.336785i | −0.824997 | − | 0.565137i | \(-0.808823\pi\) |
−0.431900 | + | 0.901922i | \(0.642157\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.1316 | − | 8.73625i | −0.755638 | − | 0.436268i | 0.0720896 | − | 0.997398i | \(-0.477033\pi\) |
−0.827727 | + | 0.561131i | \(0.810367\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.95822 | − | 0.792652i | −0.147359 | − | 0.0394848i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.8375 | + | 24.8375i | −1.23115 | + | 1.23115i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.1742 | − | 15.6890i | 1.34368 | − | 0.775772i | 0.356332 | − | 0.934360i | \(-0.384027\pi\) |
0.987345 | + | 0.158588i | \(0.0506940\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.08264 | + | 28.8240i | 0.200894 | + | 1.41834i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.82265 | − | 5.83221i | −0.285823 | − | 0.286292i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.1134 | 1.17802 | 0.589008 | − | 0.808127i | \(-0.299519\pi\) | ||||
0.589008 | + | 0.808127i | \(0.299519\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.7464 | −1.35228 | −0.676139 | − | 0.736774i | \(-0.736348\pi\) | ||||
−0.676139 | + | 0.736774i | \(0.736348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6.00309 | + | 1.61908i | 0.291192 | + | 0.0785371i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.5842 | − | 12.2028i | 0.754173 | − | 0.590535i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −20.5060 | + | 11.8391i | −0.987739 | + | 0.570271i | −0.904598 | − | 0.426266i | \(-0.859829\pi\) |
−0.0831413 | + | 0.996538i | \(0.526495\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.7820 | − | 12.7820i | 0.614264 | − | 0.614264i | −0.329790 | − | 0.944054i | \(-0.606978\pi\) |
0.944054 | + | 0.329790i | \(0.106978\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 51.2223 | + | 13.7250i | 2.45029 | + | 0.656554i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.1416 | + | 12.2061i | 1.00903 | + | 0.582565i | 0.910908 | − | 0.412609i | \(-0.135382\pi\) |
0.0981240 | + | 0.995174i | \(0.468716\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −10.8575 | + | 2.90926i | −0.515855 | + | 0.138223i | −0.507349 | − | 0.861741i | \(-0.669374\pi\) |
−0.00850631 | + | 0.999964i | \(0.502708\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.74304 | − | 16.8435i | 0.461865 | − | 0.798459i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −7.29747 | −0.344389 | −0.172194 | − | 0.985063i | \(-0.555086\pi\) | ||||
−0.172194 | + | 0.985063i | \(0.555086\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 11.6232 | + | 20.1319i | 0.547313 | + | 0.947974i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.92778 | − | 1.24366i | 0.137256 | − | 0.0583037i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.66995 | − | 1.78721i | 0.312007 | − | 0.0836020i | −0.0994176 | − | 0.995046i | \(-0.531698\pi\) |
0.411425 | + | 0.911444i | \(0.365031\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.23973i | 0.104315i | 0.998639 | + | 0.0521574i | \(0.0166097\pi\) | ||||
−0.998639 | + | 0.0521574i | \(0.983390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.7669 | + | 24.7669i | −1.15101 | + | 1.15101i | −0.164665 | + | 0.986349i | \(0.552654\pi\) |
−0.986349 | + | 0.164665i | \(0.947346\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.33559 | − | 23.6447i | −0.293176 | − | 1.09415i | −0.942655 | − | 0.333769i | \(-0.891680\pi\) |
0.649479 | − | 0.760380i | \(-0.274987\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.04958 | + | 10.7062i | −0.371695 | + | 0.494364i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.55933 | − | 35.6759i | 0.439538 | − | 1.64038i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.9290 | + | 16.1860i | 1.28147 | + | 0.742663i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.9499 | − | 24.1620i | −0.637388 | − | 1.10399i | −0.986004 | − | 0.166722i | \(-0.946682\pi\) |
0.348616 | − | 0.937266i | \(-0.386652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.00565 | + | 5.20594i | −0.137046 | + | 0.237371i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.52110 | + | 4.52852i | 0.205292 | + | 0.205629i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.32679 | + | 23.6119i | −0.286694 | + | 1.06996i | 0.660898 | + | 0.750476i | \(0.270176\pi\) |
−0.947592 | + | 0.319482i | \(0.896491\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 7.50191i | − | 0.338556i | −0.985568 | − | 0.169278i | \(-0.945856\pi\) | ||
0.985568 | − | 0.169278i | \(-0.0541436\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.92459 | + | 1.31954i | 0.221792 | + | 0.0594291i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 14.9557 | − | 37.1318i | 0.670854 | − | 1.66559i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.2317 | − | 9.37137i | −0.726630 | − | 0.419520i | 0.0905579 | − | 0.995891i | \(-0.471135\pi\) |
−0.817188 | + | 0.576371i | \(0.804468\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −16.1780 | − | 16.1780i | −0.721342 | − | 0.721342i | 0.247537 | − | 0.968879i | \(-0.420379\pi\) |
−0.968879 | + | 0.247537i | \(0.920379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.5150 | + | 15.8557i | −1.22440 | + | 0.705569i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.7815 | + | 35.9945i | −0.921122 | + | 1.59543i | −0.123439 | + | 0.992352i | \(0.539392\pi\) |
−0.797683 | + | 0.603078i | \(0.793941\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.5746 | − | 15.4693i | −0.910168 | − | 0.684323i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.06213 | + | 7.72131i | 0.0908683 | + | 0.340242i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.60549 | + | 3.60549i | 0.158569 | + | 0.158569i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −0.376731 | + | 0.217506i | −0.0165049 | + | 0.00952910i | −0.508230 | − | 0.861222i | \(-0.669700\pi\) |
0.491725 | + | 0.870751i | \(0.336367\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.80535 | + | 6.73764i | 0.0789422 | + | 0.294616i | 0.994098 | − | 0.108483i | \(-0.0345994\pi\) |
−0.915156 | + | 0.403100i | \(0.867933\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.83320 | + | 6.84158i | 0.0798553 | + | 0.298024i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.5103 | − | 22.2339i | 1.67436 | − | 0.966693i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.81309 | + | 2.81309i | 0.121849 | + | 0.121849i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.55503 | + | 5.82256i | 0.0672299 | + | 0.251731i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −21.3509 | − | 5.27449i | −0.919647 | − | 0.227189i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.69165 | + | 16.7864i | −0.416677 | + | 0.721705i | −0.995603 | − | 0.0936748i | \(-0.970139\pi\) |
0.578926 | + | 0.815380i | \(0.303472\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −11.0779 | + | 6.38374i | −0.474527 | + | 0.273449i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.02367 | − | 6.02367i | −0.257554 | − | 0.257554i | 0.566505 | − | 0.824058i | \(-0.308295\pi\) |
−0.824058 | + | 0.566505i | \(0.808295\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 22.9230 | + | 13.2346i | 0.976552 | + | 0.563813i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.44286 | + | 9.50528i | 0.316502 | + | 0.404206i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −36.2868 | − | 9.72301i | −1.53752 | − | 0.411977i | −0.612056 | − | 0.790814i | \(-0.709657\pi\) |
−0.925463 | + | 0.378837i | \(0.876324\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.32086i | − | 0.267344i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.65324 | − | 36.0264i | 0.406835 | − | 1.51833i | −0.393810 | − | 0.919192i | \(-0.628843\pi\) |
0.800645 | − | 0.599139i | \(-0.204490\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.18069 | − | 2.18427i | −0.0917423 | − | 0.0918930i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.66323 | − | 15.0052i | 0.363182 | − | 0.629049i | −0.625301 | − | 0.780384i | \(-0.715024\pi\) |
0.988483 | + | 0.151335i | \(0.0483571\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0308 | + | 19.1059i | 0.461625 | + | 0.799558i | 0.999042 | − | 0.0437587i | \(-0.0139333\pi\) |
−0.537417 | + | 0.843317i | \(0.680600\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 39.6874 | − | 10.5644i | 1.65508 | − | 0.440568i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 6.46928 | − | 24.1437i | 0.269320 | − | 1.00512i | −0.690233 | − | 0.723587i | \(-0.742492\pi\) |
0.959553 | − | 0.281528i | \(-0.0908413\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.81976 | + | 8.97187i | 0.158470 | + | 0.372216i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.05787 | + | 33.8044i | 0.375139 | + | 1.40004i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −11.5063 | + | 11.5063i | −0.474915 | + | 0.474915i | −0.903501 | − | 0.428586i | \(-0.859012\pi\) |
0.428586 | + | 0.903501i | \(0.359012\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.7728i | 1.51520i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.4299 | − | 12.1729i | 1.86558 | − | 0.499881i | 0.865581 | − | 0.500768i | \(-0.166949\pi\) |
1.00000 | 0.000887582i | \(0.000282526\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.87651 | − | 4.42589i | −0.240913 | − | 0.181444i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.48145 | − | 6.03005i | −0.142248 | − | 0.246381i | 0.786095 | − | 0.618106i | \(-0.212100\pi\) |
−0.928343 | + | 0.371725i | \(0.878766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.5177 | −1.12247 | −0.561235 | − | 0.827657i | \(-0.689674\pi\) | ||||
−0.561235 | + | 0.827657i | \(0.689674\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.26404 | + | 2.18524i | −0.0513906 | + | 0.0888428i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.6839 | − | 7.95377i | 1.20483 | − | 0.322834i | 0.400099 | − | 0.916472i | \(-0.368976\pi\) |
0.804732 | + | 0.593638i | \(0.202309\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.755709 | + | 0.436309i | 0.0305727 | + | 0.0176512i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.8859 | − | 7.47201i | −1.12630 | − | 0.301792i | −0.352871 | − | 0.935672i | \(-0.614795\pi\) |
−0.773431 | + | 0.633880i | \(0.781461\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −0.259882 | + | 0.259882i | −0.0104625 | + | 0.0104625i | −0.712319 | − | 0.701856i | \(-0.752355\pi\) |
0.701856 | + | 0.712319i | \(0.252355\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −16.3858 | + | 9.46036i | −0.658602 | + | 0.380244i | −0.791744 | − | 0.610853i | \(-0.790827\pi\) |
0.133142 | + | 0.991097i | \(0.457493\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.1275 | + | 14.1943i | −0.726263 | + | 0.568681i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9999 | + | 0.0820378i | 0.999995 | + | 0.00328151i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13.9026 | 0.554332 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.77349 | −0.110411 | −0.0552055 | − | 0.998475i | \(-0.517581\pi\) | ||||
−0.0552055 | + | 0.998475i | \(0.517581\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.7257 | − | 12.7466i | −0.505003 | − | 0.505832i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.76305 | + | 0.0738011i | −0.149098 | + | 0.00292411i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.12501 | − | 2.38158i | 0.162928 | − | 0.0940667i | −0.416319 | − | 0.909219i | \(-0.636680\pi\) |
0.579247 | + | 0.815152i | \(0.303347\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −12.2522 | + | 12.2522i | −0.483178 | + | 0.483178i | −0.906145 | − | 0.422967i | \(-0.860989\pi\) |
0.422967 | + | 0.906145i | \(0.360989\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.54590 | − | 0.414222i | −0.0607755 | − | 0.0162848i | 0.228303 | − | 0.973590i | \(-0.426682\pi\) |
−0.289079 | + | 0.957305i | \(0.593349\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 29.9385 | + | 17.2850i | 1.17519 | + | 0.678495i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.78720 | + | 1.01478i | −0.148205 | + | 0.0397113i | −0.332159 | − | 0.943224i | \(-0.607777\pi\) |
0.183954 | + | 0.982935i | \(0.441110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 24.9643 | + | 14.4405i | 0.975436 | + | 0.564236i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 25.1996 | 0.981635 | 0.490818 | − | 0.871262i | \(-0.336698\pi\) | ||||
0.490818 | + | 0.871262i | \(0.336698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.7559 | + | 30.7542i | 0.690626 | + | 1.19620i | 0.971633 | + | 0.236494i | \(0.0759984\pi\) |
−0.281007 | + | 0.959706i | \(0.590668\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −23.5226 | − | 30.0916i | −0.912168 | − | 1.16690i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 32.5287 | − | 8.71603i | 1.25952 | − | 0.337486i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 23.5045i | − | 0.907380i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.74176 | − | 9.74176i | 0.375517 | − | 0.375517i | −0.493965 | − | 0.869482i | \(-0.664453\pi\) |
0.869482 | + | 0.493965i | \(0.164453\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.59716 | − | 24.6209i | −0.253549 | − | 0.946259i | −0.968892 | − | 0.247485i | \(-0.920396\pi\) |
0.715342 | − | 0.698774i | \(-0.246271\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.96592 | − | 6.96637i | −0.113821 | − | 0.267345i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.419816 | + | 1.56677i | −0.0160638 | + | 0.0599510i | −0.973493 | − | 0.228719i | \(-0.926546\pi\) |
0.957429 | + | 0.288670i | \(0.0932130\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10.0050 | − | 2.68962i | −0.382270 | − | 0.102765i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.99464 | + | 5.18687i | 0.114087 | + | 0.197604i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.68922 | − | 11.5861i | 0.254470 | − | 0.440755i | −0.710281 | − | 0.703918i | \(-0.751432\pi\) |
0.964751 | + | 0.263163i | \(0.0847657\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0144013 | − | 17.5544i | 0.000546271 | − | 0.665875i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.38134 | − | 8.88729i | 0.0901998 | − | 0.336630i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.6890i | 0.856950i | 0.903554 | + | 0.428475i | \(0.140949\pi\) | ||||
−0.903554 | + | 0.428475i | \(0.859051\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 69.7193 | + | 18.6812i | 2.62951 | + | 0.704576i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 37.2035 | − | 5.26952i | 1.39918 | − | 0.198181i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 32.7244 | + | 18.8934i | 1.22899 | + | 0.709558i | 0.966819 | − | 0.255463i | \(-0.0822279\pi\) |
0.262172 | + | 0.965021i | \(0.415561\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 33.0822 | + | 33.0822i | 1.23894 | + | 1.23894i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.980653 | − | 3.64787i | 0.0366743 | − | 0.136423i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.5922 | − | 42.5949i | 0.917133 | − | 1.58852i | 0.113385 | − | 0.993551i | \(-0.463831\pi\) |
0.803748 | − | 0.594970i | \(-0.202836\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.14230 | − | 9.38693i | 0.0425414 | − | 0.349588i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 20.4995 | + | 0.0336348i | 0.761333 | + | 0.00124916i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.0541 | + | 20.0541i | 0.743766 | + | 0.743766i | 0.973301 | − | 0.229534i | \(-0.0737203\pi\) |
−0.229534 | + | 0.973301i | \(0.573720\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −12.6600 | + | 7.30925i | −0.468247 | + | 0.270342i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.72817 | + | 25.1099i | 0.248510 | + | 0.927454i | 0.971586 | + | 0.236685i | \(0.0760610\pi\) |
−0.723076 | + | 0.690769i | \(0.757272\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.11681 | + | 15.3641i | 0.151645 | + | 0.565945i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.88907 | + | 3.97740i | −0.253418 | + | 0.146311i | −0.621328 | − | 0.783550i | \(-0.713407\pi\) |
0.367910 | + | 0.929861i | \(0.380073\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.0815 | + | 11.0815i | 0.406541 | + | 0.406541i | 0.880531 | − | 0.473989i | \(-0.157186\pi\) |
−0.473989 | + | 0.880531i | \(0.657186\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.02933 | + | 15.6097i | −0.330809 | + | 0.571894i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.861397 | − | 7.07859i | 0.0314747 | − | 0.258646i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 19.8106 | − | 34.3130i | 0.722899 | − | 1.25210i | −0.236934 | − | 0.971526i | \(-0.576142\pi\) |
0.959833 | − | 0.280572i | \(-0.0905243\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.81568 | + | 11.8275i | 0.248048 | + | 0.430447i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.30716 | + | 9.30716i | 0.338274 | + | 0.338274i | 0.855718 | − | 0.517443i | \(-0.173116\pi\) |
−0.517443 | + | 0.855718i | \(0.673116\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.5097 | + | 19.9242i | 1.25098 | + | 0.722252i | 0.971303 | − | 0.237844i | \(-0.0764407\pi\) |
0.279673 | + | 0.960095i | \(0.409774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.9787 | − | 2.12159i | 0.542265 | − | 0.0768066i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.71463 | + | 1.53123i | 0.206343 | + | 0.0552895i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 52.6681i | − | 1.89926i | −0.313373 | − | 0.949630i | \(-0.601459\pi\) | ||
0.313373 | − | 0.949630i | \(-0.398541\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.1005 | + | 41.4276i | −0.399257 | + | 1.49005i | 0.415151 | + | 0.909753i | \(0.363729\pi\) |
−0.814407 | + | 0.580294i | \(0.802938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14.1992 | + | 24.6872i | 0.510051 | + | 0.886790i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.8841 | − | 41.3686i | 0.855738 | − | 1.48218i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −23.7680 | − | 41.1674i | −0.850487 | − | 1.47309i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.12426 | + | 30.2210i | −0.289967 | + | 1.07863i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.301878 | − | 1.12663i | 0.0107608 | − | 0.0401599i | −0.960337 | − | 0.278843i | \(-0.910049\pi\) |
0.971097 | + | 0.238683i | \(0.0767157\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.43057 | + | 3.36013i | 0.0508652 | + | 0.119473i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.04110 | − | 3.88543i | −0.0369705 | − | 0.137976i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.61236 | − | 1.61236i | 0.0571127 | − | 0.0571127i | −0.677974 | − | 0.735086i | \(-0.737142\pi\) |
0.735086 | + | 0.677974i | \(0.237142\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.01814i | − | 0.0713965i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −29.5261 | + | 7.91150i | −1.04195 | + | 0.279191i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.2333 | − | 5.90969i | −1.70000 | − | 0.208289i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.67507 | − | 4.63335i | −0.0940503 | − | 0.162900i | 0.815162 | − | 0.579234i | \(-0.196648\pi\) |
−0.909212 | + | 0.416334i | \(0.863315\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.7244 | 0.692618 | 0.346309 | − | 0.938120i | \(-0.387435\pi\) | ||||
0.346309 | + | 0.938120i | \(0.387435\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.75141 | − | 25.2795i | −0.236492 | − | 0.885503i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −73.3096 | + | 19.6432i | −2.56478 | + | 0.687230i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −24.7054 | − | 14.2636i | −0.862223 | − | 0.497805i | 0.00253295 | − | 0.999997i | \(-0.499194\pi\) |
−0.864756 | + | 0.502192i | \(0.832527\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.24340 | + | 0.333167i | 0.0433421 | + | 0.0116135i | 0.280425 | − | 0.959876i | \(-0.409525\pi\) |
−0.237083 | + | 0.971489i | \(0.576191\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −33.6915 | + | 33.6915i | −1.17157 | + | 1.17157i | −0.189733 | + | 0.981836i | \(0.560762\pi\) |
−0.981836 | + | 0.189733i | \(0.939238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.0337 | + | 11.5665i | −0.695799 | + | 0.401720i | −0.805781 | − | 0.592214i | \(-0.798254\pi\) |
0.109982 | + | 0.993934i | \(0.464921\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.49929 | + | 7.45164i | 0.155891 | + | 0.258184i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.85311 | − | 3.84679i | 0.133342 | − | 0.133124i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −22.8467 | −0.788756 | −0.394378 | − | 0.918948i | \(-0.629040\pi\) | ||||
−0.394378 | + | 0.918948i | \(0.629040\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.1908 | −0.420371 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.0233172 | + | 28.4224i | −0.000802136 | + | 0.977761i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.35183 | − | 1.84153i | 0.0808097 | − | 0.0632759i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 79.5284 | − | 45.9157i | 2.72620 | − | 1.57397i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −14.3579 | + | 14.3579i | −0.491604 | + | 0.491604i | −0.908811 | − | 0.417207i | \(-0.863009\pi\) |
0.417207 | + | 0.908811i | \(0.363009\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −44.9798 | − | 12.0523i | −1.53648 | − | 0.411699i | −0.611355 | − | 0.791357i | \(-0.709375\pi\) |
−0.925127 | + | 0.379658i | \(0.876042\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.7100 | + | 8.49281i | 0.501898 | + | 0.289771i | 0.729497 | − | 0.683984i | \(-0.239754\pi\) |
−0.227599 | + | 0.973755i | \(0.573088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −29.8155 | + | 7.98905i | −1.01493 | + | 0.271950i | −0.727689 | − | 0.685907i | \(-0.759406\pi\) |
−0.287243 | + | 0.957858i | \(0.592739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 21.4307 | − | 5.72349i | 0.728665 | − | 0.194605i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.3361 | 0.486319 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.36107 | + | 2.35744i | 0.0461180 | + | 0.0798787i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.4111 | − | 11.1189i | −0.926665 | − | 0.375889i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −51.0998 | + | 13.6921i | −1.72552 | + | 0.462351i | −0.979142 | − | 0.203175i | \(-0.934874\pi\) |
−0.746375 | + | 0.665526i | \(0.768207\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 40.0911i | − | 1.35070i | −0.737496 | − | 0.675351i | \(-0.763992\pi\) | ||
0.737496 | − | 0.675351i | \(-0.236008\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9.29675 | + | 9.29675i | −0.312860 | + | 0.312860i | −0.846017 | − | 0.533156i | \(-0.821006\pi\) |
0.533156 | + | 0.846017i | \(0.321006\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.958383 | − | 3.57674i | −0.0321794 | − | 0.120095i | 0.947968 | − | 0.318366i | \(-0.103134\pi\) |
−0.980147 | + | 0.198271i | \(0.936467\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.34825 | + | 19.6084i | 0.279991 | + | 0.657646i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.71182 | − | 10.1207i | 0.0907476 | − | 0.338675i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −14.2893 | − | 24.7967i | −0.477638 | − | 0.828864i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.6763 | + | 20.2239i | 0.389426 | + | 0.674505i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.92582 | − | 11.9959i | 0.230733 | − | 0.399641i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 46.0779 | + | 0.0378014i | 1.53168 | + | 0.00125656i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.94768 | + | 11.0009i | −0.0978763 | + | 0.365279i | −0.997440 | − | 0.0715107i | \(-0.977218\pi\) |
0.899564 | + | 0.436790i | \(0.143885\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32.6632i | − | 1.08218i | −0.840965 | − | 0.541090i | \(-0.818012\pi\) | ||
0.840965 | − | 0.541090i | \(-0.181988\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.1849 | + | 2.99698i | 0.370166 | + | 0.0991856i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −21.0378 | − | 26.8673i | −0.694728 | − | 0.887238i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −15.2690 | − | 8.81555i | −0.503677 | − | 0.290798i | 0.226554 | − | 0.973999i | \(-0.427254\pi\) |
−0.730231 | + | 0.683201i | \(0.760587\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.75245 | − | 5.75245i | −0.189344 | − | 0.189344i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 54.0191 | − | 14.3794i | 1.77614 | − | 0.472792i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −10.0115 | + | 17.3405i | −0.328468 | + | 0.568923i | −0.982208 | − | 0.187796i | \(-0.939866\pi\) |
0.653740 | + | 0.756719i | \(0.273199\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5503 | + | 43.4147i | 0.411320 | + | 1.42286i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.44029 | + | 2.25415i | −0.276027 | + | 0.0737185i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.61057 | + | 5.61057i | 0.183289 | + | 0.183289i | 0.792788 | − | 0.609498i | \(-0.208629\pi\) |
−0.609498 | + | 0.792788i | \(0.708629\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −10.4386 | + | 6.02672i | −0.340288 | + | 0.196466i | −0.660400 | − | 0.750914i | \(-0.729613\pi\) |
0.320111 | + | 0.947380i | \(0.396280\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.7296 | − | 58.7037i | −0.512227 | − | 1.91166i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.92765 | + | 33.3184i | 0.290110 | + | 1.08270i | 0.945024 | + | 0.327001i | \(0.106038\pi\) |
−0.654915 | + | 0.755703i | \(0.727295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.53042 | + | 2.61564i | −0.147064 | + | 0.0849072i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.1921 | − | 10.1921i | −0.330156 | − | 0.330156i | 0.522490 | − | 0.852646i | \(-0.325003\pi\) |
−0.852646 | + | 0.522490i | \(0.825003\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −36.7153 | − | 21.2377i | −1.18808 | − | 0.687237i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.79788 | + | 7.36668i | 0.316390 | + | 0.237883i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.721506 | + | 1.24969i | −0.0232744 | + | 0.0403124i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.49700 | − | 0.402436i | −0.0481901 | − | 0.0129549i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.82630 | + | 6.82630i | 0.219519 | + | 0.219519i | 0.808296 | − | 0.588777i | \(-0.200390\pi\) |
−0.588777 | + | 0.808296i | \(0.700390\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.92560 | + | 3.42115i | 0.190162 | + | 0.109790i | 0.592058 | − | 0.805895i | \(-0.298316\pi\) |
−0.401897 | + | 0.915685i | \(0.631649\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.76005 | + | 19.2666i | −0.248776 | + | 0.617658i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.1269 | − | 11.5558i | −1.37975 | − | 0.369704i | −0.508721 | − | 0.860931i | \(-0.669882\pi\) |
−0.871031 | + | 0.491228i | \(0.836548\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.3403i | 0.873801i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −13.0325 | + | 48.6380i | −0.415673 | + | 1.55131i | 0.367812 | + | 0.929900i | \(0.380107\pi\) |
−0.783485 | + | 0.621411i | \(0.786560\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.54496 | − | 4.53750i | 0.144814 | − | 0.144577i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −48.2802 | + | 83.6237i | −1.53522 | + | 2.65908i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.3110 | − | 38.6437i | −0.708731 | − | 1.22756i | −0.965328 | − | 0.261040i | \(-0.915935\pi\) |
0.256597 | − | 0.966518i | \(-0.417399\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.5524 | + | 7.80967i | −0.429640 | + | 0.247583i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.85753 | − | 18.1286i | 0.153840 | − | 0.574137i | −0.845362 | − | 0.534193i | \(-0.820615\pi\) |
0.999202 | − | 0.0399439i | \(-0.0127179\pi\) | |||||||
\(998\) | 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 | 1260.2.ej.a.737.16 | yes | 64 | |
3.2 | odd | 2 | inner | 1260.2.ej.a.737.1 | yes | 64 | |
5.3 | odd | 4 | inner | 1260.2.ej.a.233.11 | yes | 64 | |
7.4 | even | 3 | inner | 1260.2.ej.a.557.6 | yes | 64 | |
15.8 | even | 4 | inner | 1260.2.ej.a.233.6 | yes | 64 | |
21.11 | odd | 6 | inner | 1260.2.ej.a.557.11 | yes | 64 | |
35.18 | odd | 12 | inner | 1260.2.ej.a.53.1 | ✓ | 64 | |
105.53 | even | 12 | inner | 1260.2.ej.a.53.16 | yes | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1260.2.ej.a.53.1 | ✓ | 64 | 35.18 | odd | 12 | inner | |
1260.2.ej.a.53.16 | yes | 64 | 105.53 | even | 12 | inner | |
1260.2.ej.a.233.6 | yes | 64 | 15.8 | even | 4 | inner | |
1260.2.ej.a.233.11 | yes | 64 | 5.3 | odd | 4 | inner | |
1260.2.ej.a.557.6 | yes | 64 | 7.4 | even | 3 | inner | |
1260.2.ej.a.557.11 | yes | 64 | 21.11 | odd | 6 | inner | |
1260.2.ej.a.737.1 | yes | 64 | 3.2 | odd | 2 | inner | |
1260.2.ej.a.737.16 | yes | 64 | 1.1 | even | 1 | trivial |