Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(793,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.793");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(22\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{3})\) |
Twist minimal: | no (minimal twist has level 504) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1369.6 | ||
Character | \(\chi\) | \(=\) | 1512.1369 |
Dual form | 1512.2.q.d.793.6 |
$q$-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 \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0309846 | + | 0.0536670i | −0.0138567 | + | 0.0240006i | −0.872871 | − | 0.487952i | \(-0.837744\pi\) |
0.859014 | + | 0.511952i | \(0.171078\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.981674 | + | 2.45689i | −0.371038 | + | 0.928618i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.59027 | − | 2.75442i | −0.479483 | − | 0.830490i | 0.520240 | − | 0.854020i | \(-0.325843\pi\) |
−0.999723 | + | 0.0235306i | \(0.992509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.252417 | − | 0.437198i | −0.0700078 | − | 0.121257i | 0.828897 | − | 0.559402i | \(-0.188969\pi\) |
−0.898904 | + | 0.438145i | \(0.855636\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.554700 | − | 0.960769i | 0.134535 | − | 0.233021i | −0.790885 | − | 0.611965i | \(-0.790379\pi\) |
0.925420 | + | 0.378944i | \(0.123713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.933573 | + | 1.61700i | 0.214176 | + | 0.370964i | 0.953017 | − | 0.302915i | \(-0.0979599\pi\) |
−0.738841 | + | 0.673880i | \(0.764627\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.10248 | + | 5.37365i | −0.646912 | + | 1.12048i | 0.336945 | + | 0.941525i | \(0.390607\pi\) |
−0.983856 | + | 0.178960i | \(0.942727\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49808 | + | 4.32680i | 0.499616 | + | 0.865360i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.39645 | + | 4.15077i | −0.445010 | + | 0.770779i | −0.998053 | − | 0.0623731i | \(-0.980133\pi\) |
0.553043 | + | 0.833153i | \(0.313466\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.53716 | −0.455687 | −0.227843 | − | 0.973698i | \(-0.573167\pi\) | ||||
−0.227843 | + | 0.973698i | \(0.573167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.101437 | − | 0.128809i | −0.0171460 | − | 0.0217728i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.26085 | − | 7.38001i | −0.700479 | − | 1.21327i | −0.968298 | − | 0.249797i | \(-0.919636\pi\) |
0.267819 | − | 0.963469i | \(-0.413697\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.94516 | + | 8.56527i | 0.772305 | + | 1.33767i | 0.936297 | + | 0.351210i | \(0.114230\pi\) |
−0.163992 | + | 0.986462i | \(0.552437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.95574 | + | 6.85154i | −0.603244 | + | 1.04485i | 0.389082 | + | 0.921203i | \(0.372792\pi\) |
−0.992326 | + | 0.123646i | \(0.960541\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.58336 | −0.960282 | −0.480141 | − | 0.877191i | \(-0.659414\pi\) | ||||
−0.480141 | + | 0.877191i | \(0.659414\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.07263 | − | 4.82373i | −0.724662 | − | 0.689105i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.58258 | − | 2.74112i | 0.217385 | − | 0.376521i | −0.736623 | − | 0.676304i | \(-0.763581\pi\) |
0.954008 | + | 0.299782i | \(0.0969140\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.197095 | 0.0265763 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.01304 | −1.17340 | −0.586699 | − | 0.809805i | \(-0.699573\pi\) | ||||
−0.586699 | + | 0.809805i | \(0.699573\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8819 | −1.77739 | −0.888697 | − | 0.458496i | \(-0.848388\pi\) | ||||
−0.888697 | + | 0.458496i | \(0.848388\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0312842 | 0.00388032 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.33283 | 0.407170 | 0.203585 | − | 0.979057i | \(-0.434741\pi\) | ||||
0.203585 | + | 0.979057i | \(0.434741\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.25651 | −0.267798 | −0.133899 | − | 0.990995i | \(-0.542750\pi\) | ||||
−0.133899 | + | 0.990995i | \(0.542750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.07503 | − | 3.59406i | 0.242864 | − | 0.420652i | −0.718665 | − | 0.695356i | \(-0.755247\pi\) |
0.961529 | + | 0.274704i | \(0.0885799\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.32844 | − | 1.20317i | 0.949114 | − | 0.137114i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.97850 | −0.335107 | −0.167554 | − | 0.985863i | \(-0.553587\pi\) | ||||
−0.167554 | + | 0.985863i | \(0.553587\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.17289 | + | 3.76355i | −0.238506 | + | 0.413104i | −0.960286 | − | 0.279019i | \(-0.909991\pi\) |
0.721780 | + | 0.692122i | \(0.243324\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0343744 | + | 0.0595381i | 0.00372842 | + | 0.00645782i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.30077 | + | 7.44915i | 0.455880 | + | 0.789608i | 0.998738 | − | 0.0502166i | \(-0.0159912\pi\) |
−0.542858 | + | 0.839824i | \(0.682658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.32194 | − | 0.190974i | 0.138577 | − | 0.0200195i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.115706 | −0.0118712 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.27671 | + | 5.67542i | −0.332699 | + | 0.576252i | −0.983040 | − | 0.183391i | \(-0.941293\pi\) |
0.650341 | + | 0.759642i | \(0.274626\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.25827 | + | 5.64349i | 0.324210 | + | 0.561548i | 0.981352 | − | 0.192219i | \(-0.0615683\pi\) |
−0.657142 | + | 0.753767i | \(0.728235\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.50978 | + | 14.7394i | −0.838494 | + | 1.45231i | 0.0526599 | + | 0.998613i | \(0.483230\pi\) |
−0.891154 | + | 0.453701i | \(0.850103\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.86075 | + | 15.3473i | 0.856601 | + | 1.48368i | 0.875152 | + | 0.483848i | \(0.160761\pi\) |
−0.0185508 | + | 0.999828i | \(0.505905\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.62928 | − | 11.4822i | 0.634970 | − | 1.09980i | −0.351552 | − | 0.936168i | \(-0.614346\pi\) |
0.986522 | − | 0.163631i | \(-0.0523208\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.10094 | − | 1.90689i | −0.103568 | − | 0.179385i | 0.809584 | − | 0.587004i | \(-0.199693\pi\) |
−0.913152 | + | 0.407619i | \(0.866359\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.192258 | − | 0.333001i | −0.0179282 | − | 0.0310525i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.81597 | + | 2.30600i | 0.166470 | + | 0.211391i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.442104 | − | 0.765746i | 0.0401912 | − | 0.0696133i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.619455 | −0.0554057 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.61290 | −0.409329 | −0.204664 | − | 0.978832i | \(-0.565610\pi\) | ||||
−0.204664 | + | 0.978832i | \(0.565610\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −0.0760695 | + | 0.131756i | −0.00664623 | + | 0.0115116i | −0.869329 | − | 0.494233i | \(-0.835449\pi\) |
0.862683 | + | 0.505745i | \(0.168782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.88925 | + | 0.706325i | −0.423952 | + | 0.0612461i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.77770 | − | 3.07907i | −0.151879 | − | 0.263063i | 0.780039 | − | 0.625731i | \(-0.215199\pi\) |
−0.931918 | + | 0.362668i | \(0.881866\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.60945 | − | 13.1800i | −0.645425 | − | 1.11791i | −0.984203 | − | 0.177043i | \(-0.943347\pi\) |
0.338778 | − | 0.940866i | \(-0.389987\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.802820 | + | 1.39052i | −0.0671352 | + | 0.116281i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.148506 | − | 0.257220i | −0.0123328 | − | 0.0213610i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.183457 | − | 0.317757i | 0.0150294 | − | 0.0260317i | −0.858413 | − | 0.512959i | \(-0.828549\pi\) |
0.873442 | + | 0.486928i | \(0.161882\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.29162 | + | 10.8974i | 0.512005 | + | 0.886818i | 0.999903 | + | 0.0139176i | \(0.00443024\pi\) |
−0.487899 | + | 0.872900i | \(0.662236\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0786128 | − | 0.136161i | 0.00631434 | − | 0.0109368i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.45468 | −0.435331 | −0.217666 | − | 0.976023i | \(-0.569844\pi\) | ||||
−0.217666 | + | 0.976023i | \(0.569844\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10.1569 | − | 12.8976i | −0.800473 | − | 1.01648i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.83559 | + | 6.64343i | 0.300426 | + | 0.520354i | 0.976233 | − | 0.216726i | \(-0.0695377\pi\) |
−0.675806 | + | 0.737079i | \(0.736204\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.47493 | + | 16.4111i | 0.733192 | + | 1.26993i | 0.955512 | + | 0.294952i | \(0.0953037\pi\) |
−0.222320 | + | 0.974974i | \(0.571363\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.37257 | − | 11.0376i | 0.490198 | − | 0.849048i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.9919 | 1.82407 | 0.912034 | − | 0.410115i | \(-0.134512\pi\) | ||||
0.912034 | + | 0.410115i | \(0.134512\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −13.0828 | + | 1.89000i | −0.988965 | + | 0.142871i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.27901 | − | 7.41146i | 0.319828 | − | 0.553959i | −0.660624 | − | 0.750717i | \(-0.729708\pi\) |
0.980452 | + | 0.196758i | \(0.0630415\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.632669 | 0.0470259 | 0.0235130 | − | 0.999724i | \(-0.492515\pi\) | ||||
0.0235130 | + | 0.999724i | \(0.492515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.528083 | 0.0388255 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.52849 | −0.258028 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −23.5831 | −1.70641 | −0.853205 | − | 0.521575i | \(-0.825345\pi\) | ||||
−0.853205 | + | 0.521575i | \(0.825345\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 25.6059 | 1.84315 | 0.921577 | − | 0.388196i | \(-0.126902\pi\) | ||||
0.921577 | + | 0.388196i | \(0.126902\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −9.45810 | −0.673862 | −0.336931 | − | 0.941529i | \(-0.609389\pi\) | ||||
−0.336931 | + | 0.941529i | \(0.609389\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.15133 | − | 7.19032i | 0.294280 | − | 0.509708i | −0.680537 | − | 0.732714i | \(-0.738253\pi\) |
0.974817 | + | 0.223005i | \(0.0715868\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.84547 | − | 9.96253i | −0.550644 | − | 0.699232i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.612896 | −0.0428065 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.96926 | − | 5.14291i | 0.205388 | − | 0.355742i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1164 | − | 17.5222i | −0.696444 | − | 1.20628i | −0.969691 | − | 0.244333i | \(-0.921431\pi\) |
0.273247 | − | 0.961944i | \(-0.411902\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.245134 | − | 0.424585i | −0.0167180 | − | 0.0289564i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.49066 | − | 6.23352i | 0.169077 | − | 0.423159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.560062 | −0.0376739 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.41918 | + | 4.19014i | −0.162000 | + | 0.280593i | −0.935586 | − | 0.353099i | \(-0.885128\pi\) |
0.773586 | + | 0.633692i | \(0.218461\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.336106 | + | 0.582153i | 0.0223082 | + | 0.0386389i | 0.876964 | − | 0.480556i | \(-0.159565\pi\) |
−0.854656 | + | 0.519195i | \(0.826232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.06776 | − | 5.31352i | 0.202724 | − | 0.351128i | −0.746681 | − | 0.665182i | \(-0.768354\pi\) |
0.949405 | + | 0.314054i | \(0.101687\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.1492 | − | 21.0431i | −0.795922 | − | 1.37858i | −0.922252 | − | 0.386589i | \(-0.873653\pi\) |
0.126330 | − | 0.991988i | \(-0.459680\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.203983 | − | 0.353309i | 0.0133064 | − | 0.0230473i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5978 | − | 23.5521i | −0.879569 | − | 1.52346i | −0.851815 | − | 0.523843i | \(-0.824498\pi\) |
−0.0277545 | − | 0.999615i | \(-0.508836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.9027 | + | 22.3481i | 0.831135 | + | 1.43957i | 0.897139 | + | 0.441749i | \(0.145642\pi\) |
−0.0660031 | + | 0.997819i | \(0.521025\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.416049 | − | 0.122771i | 0.0265804 | − | 0.00784356i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.471299 | − | 0.816313i | 0.0299880 | − | 0.0519408i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 27.0741 | 1.70890 | 0.854450 | − | 0.519533i | \(-0.173894\pi\) | ||||
0.854450 | + | 0.519533i | \(0.173894\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.7351 | 1.24073 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.76073 | + | 11.7099i | −0.421723 | + | 0.730445i | −0.996108 | − | 0.0881399i | \(-0.971908\pi\) |
0.574385 | + | 0.818585i | \(0.305241\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.3146 | − | 3.22368i | 1.38656 | − | 0.200310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.68727 | − | 11.5827i | −0.412355 | − | 0.714220i | 0.582792 | − | 0.812621i | \(-0.301960\pi\) |
−0.995147 | + | 0.0984018i | \(0.968627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.0980716 | + | 0.169865i | 0.00602449 | + | 0.0104347i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.91594 | + | 6.78261i | −0.238759 | + | 0.413543i | −0.960359 | − | 0.278768i | \(-0.910074\pi\) |
0.721599 | + | 0.692311i | \(0.243407\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.1737 | + | 26.2816i | 0.921735 | + | 1.59649i | 0.796730 | + | 0.604335i | \(0.206561\pi\) |
0.125005 | + | 0.992156i | \(0.460105\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.94523 | − | 13.7615i | 0.479115 | − | 0.829852i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3462 | + | 19.6522i | 0.681728 | + | 1.18079i | 0.974453 | + | 0.224591i | \(0.0721046\pi\) |
−0.292725 | + | 0.956197i | \(0.594562\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.0826 | − | 17.4635i | 0.601475 | − | 1.04179i | −0.391122 | − | 0.920339i | \(-0.627913\pi\) |
0.992598 | − | 0.121447i | \(-0.0387536\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.9059 | −1.00495 | −0.502477 | − | 0.864591i | \(-0.667578\pi\) | ||||
−0.502477 | + | 0.864591i | \(0.667578\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −25.8985 | + | 3.74142i | −1.52874 | + | 0.220849i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.88462 | + | 13.6566i | 0.463801 | + | 0.803327i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.40597 | − | 4.16727i | −0.140558 | − | 0.243454i | 0.787149 | − | 0.616763i | \(-0.211556\pi\) |
−0.927707 | + | 0.373309i | \(0.878223\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.279266 | − | 0.483703i | 0.0162595 | − | 0.0281623i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.13247 | 0.181155 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.9502 | − | 16.4448i | −0.746439 | − | 0.947862i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.430125 | − | 0.744999i | 0.0246289 | − | 0.0426585i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 15.9188 | 0.908534 | 0.454267 | − | 0.890866i | \(-0.349901\pi\) | ||||
0.454267 | + | 0.890866i | \(0.349901\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.262869 | 0.0149059 | 0.00745297 | − | 0.999972i | \(-0.497628\pi\) | ||||
0.00745297 | + | 0.999972i | \(0.497628\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.25068 | −0.353309 | −0.176655 | − | 0.984273i | \(-0.556528\pi\) | ||||
−0.176655 | + | 0.984273i | \(0.556528\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 19.6792 | 1.10530 | 0.552648 | − | 0.833415i | \(-0.313618\pi\) | ||||
0.552648 | + | 0.833415i | \(0.313618\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.2440 | 0.853499 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.07141 | 0.115256 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.26111 | − | 2.18431i | 0.0699540 | − | 0.121164i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 6.46271 | − | 16.1746i | 0.356301 | − | 0.891734i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.5338 | 1.34850 | 0.674249 | − | 0.738504i | \(-0.264467\pi\) | ||||
0.674249 | + | 0.738504i | \(0.264467\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.103267 | + | 0.178863i | −0.00564206 | + | 0.00977233i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.89471 | − | 11.9420i | −0.375579 | − | 0.650521i | 0.614835 | − | 0.788656i | \(-0.289223\pi\) |
−0.990413 | + | 0.138135i | \(0.955889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.03475 | + | 6.98840i | 0.218494 | + | 0.378443i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.8311 | − | 7.72757i | 0.908792 | − | 0.417250i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 19.6957 | 1.05732 | 0.528661 | − | 0.848833i | \(-0.322694\pi\) | ||||
0.528661 | + | 0.848833i | \(0.322694\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5.34712 | − | 9.26149i | 0.286225 | − | 0.495756i | −0.686681 | − | 0.726959i | \(-0.740933\pi\) |
0.972905 | + | 0.231203i | \(0.0742662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.83073 | − | 10.0991i | −0.310338 | − | 0.537522i | 0.668097 | − | 0.744074i | \(-0.267109\pi\) |
−0.978436 | + | 0.206552i | \(0.933776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.0699170 | − | 0.121100i | 0.00371081 | − | 0.00642731i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.82159 | + | 15.2794i | 0.465586 | + | 0.806418i | 0.999228 | − | 0.0392925i | \(-0.0125104\pi\) |
−0.533642 | + | 0.845710i | \(0.679177\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.75688 | − | 13.4353i | 0.408257 | − | 0.707122i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.128588 | + | 0.222721i | 0.00673061 | + | 0.0116578i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.69146 | − | 2.92969i | −0.0882934 | − | 0.152929i | 0.818496 | − | 0.574512i | \(-0.194808\pi\) |
−0.906790 | + | 0.421583i | \(0.861475\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.18104 | + | 6.57912i | 0.268986 | + | 0.341571i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.69511 | + | 11.5963i | −0.346660 | + | 0.600433i | −0.985654 | − | 0.168779i | \(-0.946018\pi\) |
0.638994 | + | 0.769212i | \(0.279351\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.41962 | 0.124617 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −27.6131 | −1.41839 | −0.709194 | − | 0.705013i | \(-0.750941\pi\) | ||||
−0.709194 | + | 0.705013i | \(0.750941\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.5020 | − | 21.6541i | 0.638822 | − | 1.10647i | −0.346869 | − | 0.937913i | \(-0.612755\pi\) |
0.985692 | − | 0.168559i | \(-0.0539114\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.193483 | + | 0.484242i | −0.00986083 | + | 0.0246792i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.0683229 | − | 0.118339i | −0.00346411 | − | 0.00600001i | 0.864288 | − | 0.502997i | \(-0.167769\pi\) |
−0.867752 | + | 0.496997i | \(0.834436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.44189 | + | 5.96153i | 0.174064 | + | 0.301488i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0922877 | − | 0.159847i | 0.00464350 | − | 0.00804277i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.91030 | + | 13.7010i | 0.397006 | + | 0.687635i | 0.993355 | − | 0.115090i | \(-0.0367157\pi\) |
−0.596349 | + | 0.802726i | \(0.703382\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.52745 | + | 9.57383i | −0.276028 | + | 0.478094i | −0.970394 | − | 0.241528i | \(-0.922352\pi\) |
0.694366 | + | 0.719622i | \(0.255685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.640420 | + | 1.10924i | 0.0319016 | + | 0.0552552i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.5518 | + | 23.4724i | −0.671737 | + | 1.16348i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.0128 | −1.78072 | −0.890358 | − | 0.455260i | \(-0.849546\pi\) | ||||
−0.890358 | + | 0.455260i | \(0.849546\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.84787 | − | 22.1441i | 0.435375 | − | 1.08964i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.134652 | − | 0.233225i | −0.00660982 | − | 0.0114485i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.4877 | − | 28.5576i | −0.805477 | − | 1.39513i | −0.915968 | − | 0.401251i | \(-0.868576\pi\) |
0.110491 | − | 0.993877i | \(-0.464758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.9800 | − | 25.9461i | 0.730080 | − | 1.26454i | −0.226769 | − | 0.973949i | \(-0.572816\pi\) |
0.956849 | − | 0.290587i | \(-0.0938505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.54274 | 0.268862 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 13.6275 | − | 34.1063i | 0.659480 | − | 1.65052i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.4021 | − | 21.4811i | 0.597389 | − | 1.03471i | −0.395816 | − | 0.918330i | \(-0.629538\pi\) |
0.993205 | − | 0.116379i | \(-0.0371286\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.00906 | −0.240720 | −0.120360 | − | 0.992730i | \(-0.538405\pi\) | ||||
−0.120360 | + | 0.992730i | \(0.538405\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.5856 | −0.554213 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −40.5836 | −1.93695 | −0.968475 | − | 0.249110i | \(-0.919862\pi\) | ||||
−0.968475 | + | 0.249110i | \(0.919862\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 28.2665 | 1.34298 | 0.671490 | − | 0.741014i | \(-0.265655\pi\) | ||||
0.671490 | + | 0.741014i | \(0.265655\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.533031 | −0.0252681 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −36.6443 | −1.72935 | −0.864676 | − | 0.502329i | \(-0.832477\pi\) | ||||
−0.864676 | + | 0.502329i | \(0.832477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.7283 | − | 27.2421i | 0.740615 | − | 1.28278i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0307108 | + | 0.0768618i | −0.00143975 | + | 0.00360334i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.38308 | −0.298588 | −0.149294 | − | 0.988793i | \(-0.547700\pi\) | ||||
−0.149294 | + | 0.988793i | \(0.547700\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.24366 | + | 12.5464i | −0.337371 | + | 0.584343i | −0.983937 | − | 0.178514i | \(-0.942871\pi\) |
0.646567 | + | 0.762858i | \(0.276204\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.2527 | + | 22.9544i | 0.615907 | + | 1.06678i | 0.990225 | + | 0.139482i | \(0.0445438\pi\) |
−0.374317 | + | 0.927301i | \(0.622123\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 11.6879 | + | 20.2440i | 0.540851 | + | 0.936782i | 0.998855 | + | 0.0478318i | \(0.0152311\pi\) |
−0.458004 | + | 0.888950i | \(0.651436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.27176 | + | 8.18841i | −0.151076 | + | 0.378106i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.1627 | 1.15698 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.66428 | + | 8.07877i | −0.214012 | + | 0.370679i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.64803 | + | 8.05063i | 0.212374 | + | 0.367842i | 0.952457 | − | 0.304673i | \(-0.0985472\pi\) |
−0.740083 | + | 0.672515i | \(0.765214\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.15102 | + | 3.72567i | −0.0980780 | + | 0.169876i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.203055 | − | 0.351702i | −0.00922026 | − | 0.0159700i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.04947 | − | 3.54979i | 0.0928704 | − | 0.160856i | −0.815847 | − | 0.578267i | \(-0.803729\pi\) |
0.908718 | + | 0.417411i | \(0.137062\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.98703 | − | 8.63778i | −0.225061 | − | 0.389818i | 0.731277 | − | 0.682081i | \(-0.238925\pi\) |
−0.956338 | + | 0.292264i | \(0.905592\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.65862 | + | 4.60487i | 0.119738 | + | 0.207393i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.21515 | − | 5.54399i | 0.0993632 | − | 0.248682i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.60415 | − | 9.70667i | 0.250876 | − | 0.434530i | −0.712891 | − | 0.701275i | \(-0.752615\pi\) |
0.963767 | + | 0.266744i | \(0.0859480\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.69350 | 0.0755094 | 0.0377547 | − | 0.999287i | \(-0.487979\pi\) | ||||
0.0377547 | + | 0.999287i | \(0.487979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.403825 | −0.0179700 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.4777 | + | 35.4685i | −0.907659 | + | 1.57211i | −0.0903524 | + | 0.995910i | \(0.528799\pi\) |
−0.817307 | + | 0.576202i | \(0.804534\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.79320 | + | 8.62631i | 0.300514 | + | 0.381606i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.527345 | − | 0.913388i | −0.0232376 | − | 0.0402487i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.4693 | + | 18.1334i | 0.460439 | + | 0.797504i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5075 | + | 26.8598i | −0.679396 | + | 1.17675i | 0.295767 | + | 0.955260i | \(0.404425\pi\) |
−0.975163 | + | 0.221488i | \(0.928909\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.67840 | − | 6.37117i | −0.160845 | − | 0.278592i | 0.774327 | − | 0.632786i | \(-0.218089\pi\) |
−0.935172 | + | 0.354194i | \(0.884755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.40736 | + | 2.43762i | −0.0613056 | + | 0.106184i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.75077 | − | 13.4247i | −0.336990 | − | 0.583684i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.49648 | − | 4.32404i | 0.108135 | − | 0.187295i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.09819 | −0.0474788 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −5.21976 | + | 21.6432i | −0.224831 | + | 0.932238i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.4735 | − | 25.0688i | −0.622262 | − | 1.07779i | −0.989063 | − | 0.147491i | \(-0.952880\pi\) |
0.366801 | − | 0.930299i | \(-0.380453\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.410812 | + | 0.711546i | 0.0175972 | + | 0.0304793i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.34891 | − | 16.1928i | 0.399731 | − | 0.692354i | −0.593962 | − | 0.804493i | \(-0.702437\pi\) |
0.993692 | + | 0.112140i | \(0.0357704\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.94905 | −0.381242 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.92392 | − | 7.31785i | 0.124338 | − | 0.311187i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 17.1787 | − | 29.7544i | 0.727886 | − | 1.26074i | −0.229889 | − | 0.973217i | \(-0.573836\pi\) |
0.957775 | − | 0.287519i | \(-0.0928303\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.99397 | 0.168927 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.7471 | 0.621516 | 0.310758 | − | 0.950489i | \(-0.399417\pi\) | ||||
0.310758 | + | 0.950489i | \(0.399417\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.136449 | 0.00574047 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −3.33642 | −0.139870 | −0.0699349 | − | 0.997552i | \(-0.522279\pi\) | ||||
−0.0699349 | + | 0.997552i | \(0.522279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.8072 | 0.787057 | 0.393528 | − | 0.919313i | \(-0.371254\pi\) | ||||
0.393528 | + | 0.919313i | \(0.371254\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −31.0010 | −1.29283 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.6961 | + | 30.6505i | −0.736697 | + | 1.27600i | 0.217277 | + | 0.976110i | \(0.430282\pi\) |
−0.953975 | + | 0.299887i | \(0.903051\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.11357 | − | 9.03313i | −0.295121 | − | 0.374758i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −10.0669 | −0.416930 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.2921 | − | 29.9508i | 0.713722 | − | 1.23620i | −0.249728 | − | 0.968316i | \(-0.580341\pi\) |
0.963450 | − | 0.267887i | \(-0.0863256\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.36862 | − | 4.10257i | −0.0975973 | − | 0.169043i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 15.9787 | + | 27.6759i | 0.656166 | + | 1.13651i | 0.981600 | + | 0.190949i | \(0.0611564\pi\) |
−0.325434 | + | 0.945565i | \(0.605510\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.180023 | + | 0.0260070i | −0.00738023 | + | 0.00106618i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.84952 | 0.402440 | 0.201220 | − | 0.979546i | \(-0.435509\pi\) | ||||
0.201220 | + | 0.979546i | \(0.435509\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.77340 | + | 6.53572i | −0.153920 | + | 0.266598i | −0.932665 | − | 0.360743i | \(-0.882523\pi\) |
0.778745 | + | 0.627340i | \(0.215857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.0273968 | + | 0.0474527i | 0.00111384 | + | 0.00192923i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.42922 | + | 9.40368i | −0.220365 | + | 0.381683i | −0.954919 | − | 0.296867i | \(-0.904058\pi\) |
0.734554 | + | 0.678550i | \(0.237392\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.66175 | + | 2.87823i | 0.0672272 | + | 0.116441i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.8823 | + | 41.3653i | −0.964596 | + | 1.67073i | −0.253899 | + | 0.967231i | \(0.581713\pi\) |
−0.710697 | + | 0.703499i | \(0.751620\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.7769 | + | 32.5225i | 0.755929 | + | 1.30931i | 0.944911 | + | 0.327327i | \(0.106148\pi\) |
−0.188982 | + | 0.981980i | \(0.560519\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.9829 | − | 31.1472i | −0.722792 | − | 1.25191i | −0.959876 | − | 0.280424i | \(-0.909525\pi\) |
0.237084 | − | 0.971489i | \(-0.423808\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.5237 | + | 3.25388i | −0.902393 | + | 0.130364i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4712 | + | 21.6008i | −0.498848 | + | 0.864030i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.45398 | −0.376955 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.8848 | −1.26931 | −0.634656 | − | 0.772794i | \(-0.718858\pi\) | ||||
−0.634656 | + | 0.772794i | \(0.718858\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.142929 | − | 0.247560i | 0.00567196 | − | 0.00982413i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.828512 | + | 3.43534i | −0.0328268 | + | 0.136113i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.33939 | + | 14.4442i | 0.329386 | + | 0.570513i | 0.982390 | − | 0.186841i | \(-0.0598249\pi\) |
−0.653004 | + | 0.757354i | \(0.726492\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 23.5295 | + | 40.7544i | 0.927915 | + | 1.60720i | 0.786805 | + | 0.617201i | \(0.211734\pi\) |
0.141109 | + | 0.989994i | \(0.454933\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.2324 | − | 21.1872i | 0.480906 | − | 0.832954i | −0.518854 | − | 0.854863i | \(-0.673641\pi\) |
0.999760 | + | 0.0219091i | \(0.00697444\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.3331 | + | 24.8257i | 0.562625 | + | 0.974495i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.91306 | + | 10.2417i | −0.231396 | + | 0.400789i | −0.958219 | − | 0.286035i | \(-0.907663\pi\) |
0.726823 | + | 0.686824i | \(0.240996\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.00471397 | − | 0.00816484i | −0.000184190 | − | 0.000319027i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.51539 | + | 6.08883i | −0.136940 | + | 0.237187i | −0.926337 | − | 0.376696i | \(-0.877060\pi\) |
0.789397 | + | 0.613883i | \(0.210393\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8605 | 0.578006 | 0.289003 | − | 0.957328i | \(-0.406676\pi\) | ||||
0.289003 | + | 0.957328i | \(0.406676\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.113585 | − | 0.284276i | 0.00440465 | − | 0.0110238i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.8699 | − | 25.7554i | −0.575764 | − | 0.997253i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.0759 | + | 38.2366i | 0.852231 | + | 1.47611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.81679 | − | 13.5391i | 0.301315 | − | 0.521893i | −0.675119 | − | 0.737709i | \(-0.735908\pi\) |
0.976434 | + | 0.215816i | \(0.0692411\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.7122 | −0.949767 | −0.474883 | − | 0.880049i | \(-0.657510\pi\) | ||||
−0.474883 | + | 0.880049i | \(0.657510\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.7272 | − | 13.6219i | −0.411674 | − | 0.522762i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 16.7467 | − | 29.0061i | 0.640794 | − | 1.10989i | −0.344462 | − | 0.938800i | \(-0.611939\pi\) |
0.985256 | − | 0.171087i | \(-0.0547279\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.220326 | 0.00841821 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.59788 | −0.0608745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.67672 | −0.101827 | −0.0509137 | − | 0.998703i | \(-0.516213\pi\) | ||||
−0.0509137 | + | 0.998703i | \(0.516213\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.943104 | 0.0357740 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 10.9723 | 0.415607 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.3715 | 1.37373 | 0.686866 | − | 0.726784i | \(-0.258986\pi\) | ||||
0.686866 | + | 0.726784i | \(0.258986\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.95563 | − | 13.7796i | 0.300052 | − | 0.519706i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.0640 | + | 2.46515i | −0.641758 | + | 0.0927114i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.9074 | −0.447191 | −0.223596 | − | 0.974682i | \(-0.571779\pi\) | ||||
−0.223596 | + | 0.974682i | \(0.571779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.87148 | − | 13.6338i | 0.294789 | − | 0.510590i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.0497501 | − | 0.0861698i | −0.00186055 | − | 0.00322257i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −8.44050 | − | 14.6194i | −0.314778 | − | 0.545211i | 0.664613 | − | 0.747188i | \(-0.268597\pi\) |
−0.979390 | + | 0.201977i | \(0.935263\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.8592 | − | 35.3769i | −1.03753 | − | 1.31750i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −23.9461 | −0.889336 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.24570 | − | 2.15762i | 0.0462006 | − | 0.0800218i | −0.842000 | − | 0.539477i | \(-0.818622\pi\) |
0.888201 | + | 0.459455i | \(0.151955\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.38850 | + | 7.60110i | 0.162314 | + | 0.281137i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.25653 | − | 10.8366i | 0.231090 | − | 0.400260i | −0.727039 | − | 0.686596i | \(-0.759104\pi\) |
0.958129 | + | 0.286336i | \(0.0924374\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.30009 | − | 9.18003i | −0.195231 | − | 0.338151i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.0051 | + | 17.3294i | −0.368044 | + | 0.637472i | −0.989260 | − | 0.146168i | \(-0.953306\pi\) |
0.621215 | + | 0.783640i | \(0.286639\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.49879 | − | 9.52419i | −0.201731 | − | 0.349408i | 0.747355 | − | 0.664425i | \(-0.231323\pi\) |
−0.949086 | + | 0.315016i | \(0.897990\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.0113687 | + | 0.0196912i | 0.000416517 | + | 0.000721428i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46.4049 | + | 6.70388i | −1.69560 | + | 0.244955i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −14.4335 | + | 24.9996i | −0.526686 | + | 0.912247i | 0.472830 | + | 0.881154i | \(0.343232\pi\) |
−0.999516 | + | 0.0310938i | \(0.990101\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.779774 | −0.0283789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.3626 | −0.631053 | −0.315527 | − | 0.948917i | \(-0.602181\pi\) | ||||
−0.315527 | + | 0.948917i | \(0.602181\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −26.0020 | + | 45.0367i | −0.942571 | + | 1.63258i | −0.182027 | + | 0.983293i | \(0.558266\pi\) |
−0.760543 | + | 0.649287i | \(0.775067\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.7028 | + | 27.5592i | 0.785696 | + | 0.997712i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.27504 | + | 3.94049i | 0.0821470 | + | 0.142283i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.5839 | + | 23.5280i | 0.489849 | + | 0.848443i | 0.999932 | − | 0.0116822i | \(-0.00371865\pi\) |
−0.510083 | + | 0.860125i | \(0.670385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.2452 | + | 21.2093i | −0.440428 | + | 0.762845i | −0.997721 | − | 0.0674716i | \(-0.978507\pi\) |
0.557293 | + | 0.830316i | \(0.311840\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.33802 | − | 10.9778i | −0.227668 | − | 0.394333i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.23334 | + | 15.9926i | −0.330819 | + | 0.572995i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.58845 | + | 6.21537i | 0.128405 | + | 0.222403i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.169011 | − | 0.292736i | 0.00603227 | − | 0.0104482i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.87862 | 0.0669657 | 0.0334828 | − | 0.999439i | \(-0.489340\pi\) | ||||
0.0334828 | + | 0.999439i | \(0.489340\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.76579 | − | 0.832955i | 0.205008 | − | 0.0296165i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.50402 | + | 6.06914i | 0.124431 | + | 0.215521i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.6067 | − | 30.4957i | −0.623662 | − | 1.08021i | −0.988798 | − | 0.149259i | \(-0.952311\pi\) |
0.365137 | − | 0.930954i | \(-0.381022\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.65179 | + | 6.32509i | −0.129191 | + | 0.223765i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −13.1994 | −0.465797 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00688 | − | 0.145459i | 0.0354880 | − | 0.00512677i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.53614 | + | 2.66067i | −0.0540077 | + | 0.0935441i | −0.891765 | − | 0.452498i | \(-0.850533\pi\) |
0.837758 | + | 0.546042i | \(0.183866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.8034 | −0.519818 | −0.259909 | − | 0.965633i | \(-0.583693\pi\) | ||||
−0.259909 | + | 0.965633i | \(0.583693\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.475377 | −0.0166517 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −14.7719 | −0.516802 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.0122 | −0.872933 | −0.436467 | − | 0.899720i | \(-0.643770\pi\) | ||||
−0.436467 | + | 0.899720i | \(0.643770\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.4961 | 1.37675 | 0.688374 | − | 0.725356i | \(-0.258325\pi\) | ||||
0.688374 | + | 0.725356i | \(0.258325\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4528 | −0.433026 | −0.216513 | − | 0.976280i | \(-0.569468\pi\) | ||||
−0.216513 | + | 0.976280i | \(0.569468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.2995 | + | 24.7675i | −0.496643 | + | 0.860211i | −0.999993 | − | 0.00387209i | \(-0.998767\pi\) |
0.503350 | + | 0.864083i | \(0.332101\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −7.44828 | + | 2.19790i | −0.258068 | + | 0.0761528i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.17431 | −0.0406386 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −21.0794 | + | 36.5107i | −0.727743 | + | 1.26049i | 0.230092 | + | 0.973169i | \(0.426097\pi\) |
−0.957835 | + | 0.287319i | \(0.907236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.01405 | + | 5.22048i | 0.103933 | + | 0.180017i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.394904 | + | 0.683993i | 0.0135851 | + | 0.0235301i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.44735 | + | 1.83791i | 0.0497316 | + | 0.0631514i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 52.8768 | 1.81259 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −25.6206 | + | 44.3761i | −0.877232 | + | 1.51941i | −0.0228654 | + | 0.999739i | \(0.507279\pi\) |
−0.854366 | + | 0.519671i | \(0.826054\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −18.9029 | − | 32.7408i | −0.645710 | − | 1.11840i | −0.984137 | − | 0.177410i | \(-0.943228\pi\) |
0.338427 | − | 0.940993i | \(-0.390105\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.3112 | − | 38.6442i | 0.761249 | − | 1.31852i | −0.180958 | − | 0.983491i | \(-0.557920\pi\) |
0.942207 | − | 0.335031i | \(-0.108747\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 15.4848 | + | 26.8205i | 0.527109 | + | 0.912980i | 0.999501 | + | 0.0315912i | \(0.0100575\pi\) |
−0.472392 | + | 0.881389i | \(0.656609\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.743379 | + | 1.28757i | −0.0252756 | + | 0.0437787i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.73661 | + | 8.20405i | 0.160678 | + | 0.278303i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.841263 | − | 1.45711i | −0.0285051 | − | 0.0493723i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.608103 | − | 1.52193i | 0.0205576 | − | 0.0514507i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.5843 | + | 20.0646i | −0.391174 | + | 0.677533i | −0.992605 | − | 0.121392i | \(-0.961264\pi\) |
0.601431 | + | 0.798925i | \(0.294597\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0143 | −0.472155 | −0.236077 | − | 0.971734i | \(-0.575862\pi\) | ||||
−0.236077 | + | 0.971734i | \(0.575862\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.9269 | −1.34365 | −0.671824 | − | 0.740711i | \(-0.734489\pi\) | ||||
−0.671824 | + | 0.740711i | \(0.734489\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.4221 | + | 23.2477i | −0.450669 | + | 0.780581i | −0.998428 | − | 0.0560549i | \(-0.982148\pi\) |
0.547759 | + | 0.836636i | \(0.315481\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.52836 | − | 11.3334i | 0.151876 | − | 0.380110i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6.14605 | − | 10.6453i | −0.205670 | − | 0.356230i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.265167 | + | 0.459283i | 0.00886356 | + | 0.0153521i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.08017 | − | 10.5312i | 0.202785 | − | 0.351234i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.75572 | − | 3.04100i | −0.0584915 | − | 0.101310i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0196030 | + | 0.0339534i | −0.000651626 | + | 0.00112865i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.8808 | − | 32.7026i | −0.626928 | − | 1.08587i | −0.988165 | − | 0.153397i | \(-0.950979\pi\) |
0.361237 | − | 0.932474i | \(-0.382355\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.93650 | + | 13.7464i | −0.262948 | + | 0.455439i | −0.967024 | − | 0.254685i | \(-0.918028\pi\) |
0.704076 | + | 0.710125i | \(0.251361\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 13.8219 | 0.457438 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −0.249035 | − | 0.316236i | −0.00822388 | − | 0.0104430i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.22203 | + | 9.04482i | 0.172259 | + | 0.298361i | 0.939209 | − | 0.343345i | \(-0.111560\pi\) |
−0.766950 | + | 0.641706i | \(0.778227\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.569580 | + | 0.986541i | 0.0187479 | + | 0.0324724i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.2879 | − | 36.8717i | 0.699941 | − | 1.21233i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 19.1634 | 0.628730 | 0.314365 | − | 0.949302i | \(-0.398208\pi\) | ||||
0.314365 | + | 0.949302i | \(0.398208\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.06428 | − | 12.7057i | 0.100428 | − | 0.416414i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0.109329 | − | 0.189363i | 0.00357543 | − | 0.00619283i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.09451 | 0.101093 | 0.0505467 | − | 0.998722i | \(-0.483904\pi\) | ||||
0.0505467 | + | 0.998722i | \(0.483904\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −15.3113 | −0.499133 | −0.249567 | − | 0.968358i | \(-0.580288\pi\) | ||||
−0.249567 | + | 0.968358i | \(0.580288\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −61.3691 | −1.99845 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.01549 | −0.0329991 | −0.0164995 | − | 0.999864i | \(-0.505252\pi\) | ||||
−0.0164995 | + | 0.999864i | \(0.505252\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.09509 | −0.0680094 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 35.4930 | 1.14973 | 0.574865 | − | 0.818248i | \(-0.305055\pi\) | ||||
0.574865 | + | 0.818248i | \(0.305055\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.730713 | − | 1.26563i | 0.0236453 | − | 0.0409549i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.31006 | − | 1.34498i | 0.300638 | − | 0.0434316i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.5628 | −0.792350 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.793390 | + | 1.37419i | −0.0255401 | + | 0.0442368i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.87762 | + | 11.9124i | 0.221169 | + | 0.383077i | 0.955163 | − | 0.296079i | \(-0.0956793\pi\) |
−0.733994 | + | 0.679156i | \(0.762346\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.6567 | + | 37.5104i | 0.694995 | + | 1.20377i | 0.970182 | + | 0.242376i | \(0.0779269\pi\) |
−0.275187 | + | 0.961391i | \(0.588740\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.8517 | − | 5.75718i | 1.27759 | − | 0.184567i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 9.56840 | 0.306120 | 0.153060 | − | 0.988217i | \(-0.451087\pi\) | ||||
0.153060 | + | 0.988217i | \(0.451087\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.6787 | − | 23.6923i | 0.437174 | − | 0.757208i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.56644 | + | 14.8375i | 0.273227 | + | 0.473243i | 0.969686 | − | 0.244353i | \(-0.0785757\pi\) |
−0.696459 | + | 0.717596i | \(0.745242\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.293056 | − | 0.507587i | 0.00933753 | − | 0.0161731i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −24.5452 | − | 42.5135i | −0.780492 | − | 1.35185i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.32891 | − | 10.9620i | 0.201044 | − | 0.348219i | −0.747821 | − | 0.663901i | \(-0.768900\pi\) |
0.948865 | + | 0.315682i | \(0.102233\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.257255 | + | 0.445579i | 0.00815553 | + | 0.0141258i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.8352 | + | 22.2312i | 0.406495 | + | 0.704069i | 0.994494 | − | 0.104792i | \(-0.0334177\pi\) |
−0.588000 | + | 0.808861i | \(0.700084\pi\) | |||||||
\(998\) | 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 | 1512.2.q.d.1369.6 | 22 | ||
3.2 | odd | 2 | 504.2.q.c.25.11 | ✓ | 22 | ||
4.3 | odd | 2 | 3024.2.q.l.2881.6 | 22 | |||
7.2 | even | 3 | 1512.2.t.c.289.6 | 22 | |||
9.4 | even | 3 | 1512.2.t.c.361.6 | 22 | |||
9.5 | odd | 6 | 504.2.t.c.193.4 | yes | 22 | ||
12.11 | even | 2 | 1008.2.q.l.529.1 | 22 | |||
21.2 | odd | 6 | 504.2.t.c.457.4 | yes | 22 | ||
28.23 | odd | 6 | 3024.2.t.k.289.6 | 22 | |||
36.23 | even | 6 | 1008.2.t.l.193.8 | 22 | |||
36.31 | odd | 6 | 3024.2.t.k.1873.6 | 22 | |||
63.23 | odd | 6 | 504.2.q.c.121.11 | yes | 22 | ||
63.58 | even | 3 | inner | 1512.2.q.d.793.6 | 22 | ||
84.23 | even | 6 | 1008.2.t.l.961.8 | 22 | |||
252.23 | even | 6 | 1008.2.q.l.625.1 | 22 | |||
252.247 | odd | 6 | 3024.2.q.l.2305.6 | 22 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.q.c.25.11 | ✓ | 22 | 3.2 | odd | 2 | ||
504.2.q.c.121.11 | yes | 22 | 63.23 | odd | 6 | ||
504.2.t.c.193.4 | yes | 22 | 9.5 | odd | 6 | ||
504.2.t.c.457.4 | yes | 22 | 21.2 | odd | 6 | ||
1008.2.q.l.529.1 | 22 | 12.11 | even | 2 | |||
1008.2.q.l.625.1 | 22 | 252.23 | even | 6 | |||
1008.2.t.l.193.8 | 22 | 36.23 | even | 6 | |||
1008.2.t.l.961.8 | 22 | 84.23 | even | 6 | |||
1512.2.q.d.793.6 | 22 | 63.58 | even | 3 | inner | ||
1512.2.q.d.1369.6 | 22 | 1.1 | even | 1 | trivial | ||
1512.2.t.c.289.6 | 22 | 7.2 | even | 3 | |||
1512.2.t.c.361.6 | 22 | 9.4 | even | 3 | |||
3024.2.q.l.2305.6 | 22 | 252.247 | odd | 6 | |||
3024.2.q.l.2881.6 | 22 | 4.3 | odd | 2 | |||
3024.2.t.k.289.6 | 22 | 28.23 | odd | 6 | |||
3024.2.t.k.1873.6 | 22 | 36.31 | odd | 6 |