Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(143,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 3, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.143");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.p (of order \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 7 x^{14} - 12 x^{13} + 16 x^{12} - 12 x^{11} - 8 x^{10} + 36 x^{9} - 68 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 143.6 | ||
Root | \(-0.533474 - 1.30973i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 864.143 |
Dual form | 864.2.p.b.719.6 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) |
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 | ||||||||
\(5\) | 0.895377 | + | 1.55084i | 0.400425 | + | 0.693556i | 0.993777 | − | 0.111387i | \(-0.0355292\pi\) |
−0.593352 | + | 0.804943i | \(0.702196\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.08793 | − | 1.20546i | −0.789162 | − | 0.455623i | 0.0505056 | − | 0.998724i | \(-0.483917\pi\) |
−0.839667 | + | 0.543101i | \(0.817250\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.36975 | − | 0.790826i | −0.412995 | − | 0.238443i | 0.279081 | − | 0.960268i | \(-0.409970\pi\) |
−0.692076 | + | 0.721825i | \(0.743304\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.35491 | + | 3.09166i | −1.48519 | + | 0.857472i | −0.999858 | − | 0.0168604i | \(-0.994633\pi\) |
−0.485327 | + | 0.874332i | \(0.661300\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.69943i | 0.897244i | 0.893722 | + | 0.448622i | \(0.148085\pi\) | ||||
−0.893722 | + | 0.448622i | \(0.851915\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.12941 | −0.717936 | −0.358968 | − | 0.933350i | \(-0.616871\pi\) | ||||
−0.358968 | + | 0.933350i | \(0.616871\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.36036 | + | 2.35622i | 0.283655 | + | 0.491305i | 0.972282 | − | 0.233811i | \(-0.0751196\pi\) |
−0.688627 | + | 0.725116i | \(0.741786\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.896599 | − | 1.55296i | 0.179320 | − | 0.310591i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.55291 | + | 4.42177i | −0.474064 | + | 0.821102i | −0.999559 | − | 0.0296942i | \(-0.990547\pi\) |
0.525495 | + | 0.850796i | \(0.323880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.95312 | + | 3.43703i | −1.06921 | + | 0.617310i | −0.927966 | − | 0.372665i | \(-0.878444\pi\) |
−0.141246 | + | 0.989975i | \(0.545111\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 4.31738i | − | 0.729771i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 5.24328i | − | 0.861990i | −0.902354 | − | 0.430995i | \(-0.858163\pi\) | ||
0.902354 | − | 0.430995i | \(-0.141837\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.32220 | − | 3.07278i | 0.831189 | − | 0.479887i | −0.0230708 | − | 0.999734i | \(-0.507344\pi\) |
0.854260 | + | 0.519847i | \(0.174011\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.452455 | − | 0.783675i | 0.0689987 | − | 0.119509i | −0.829462 | − | 0.558563i | \(-0.811353\pi\) |
0.898461 | + | 0.439054i | \(0.144686\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.88993 | + | 8.46960i | −0.713269 | + | 1.23542i | 0.250354 | + | 0.968154i | \(0.419453\pi\) |
−0.963623 | + | 0.267264i | \(0.913880\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.593711 | − | 1.02834i | −0.0848159 | − | 0.146905i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.05913 | −0.969646 | −0.484823 | − | 0.874612i | \(-0.661116\pi\) | ||||
−0.484823 | + | 0.874612i | \(0.661116\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.83235i | − | 0.381914i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.10118 | + | 3.52252i | −0.794306 | + | 0.458593i | −0.841476 | − | 0.540294i | \(-0.818313\pi\) |
0.0471702 | + | 0.998887i | \(0.484980\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.05109 | + | 1.76155i | 0.390652 | + | 0.225543i | 0.682443 | − | 0.730939i | \(-0.260918\pi\) |
−0.291790 | + | 0.956482i | \(0.594251\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.58933 | − | 5.53640i | −1.18941 | − | 0.686706i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.03786 | − | 1.79762i | −0.126794 | − | 0.219614i | 0.795639 | − | 0.605772i | \(-0.207135\pi\) |
−0.922433 | + | 0.386158i | \(0.873802\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.31507 | −0.393426 | −0.196713 | − | 0.980461i | \(-0.563027\pi\) | ||||
−0.196713 | + | 0.980461i | \(0.563027\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.631029 | 0.0738563 | 0.0369282 | − | 0.999318i | \(-0.488243\pi\) | ||||
0.0369282 | + | 0.999318i | \(0.488243\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.90662 | + | 3.30237i | 0.217280 | + | 0.376340i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.82515 | + | 4.51785i | 0.880398 | + | 0.508298i | 0.870790 | − | 0.491656i | \(-0.163608\pi\) |
0.00960849 | + | 0.999954i | \(0.496941\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.5542 | + | 7.82551i | 1.48776 | + | 0.858961i | 0.999903 | − | 0.0139604i | \(-0.00444387\pi\) |
0.487861 | + | 0.872921i | \(0.337777\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.73722 | + | 3.31239i | −0.622289 | + | 0.359279i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.16402i | − | 0.123386i | −0.998095 | − | 0.0616929i | \(-0.980350\pi\) | ||
0.998095 | − | 0.0616929i | \(-0.0196499\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.9075 | 1.56274 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.80200 | − | 4.85321i | −0.287479 | − | 0.497929i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.72981 | + | 11.6564i | −0.683309 | + | 1.18353i | 0.290656 | + | 0.956827i | \(0.406126\pi\) |
−0.973965 | + | 0.226698i | \(0.927207\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.28047 | − | 5.68195i | 0.326419 | − | 0.565375i | −0.655379 | − | 0.755300i | \(-0.727491\pi\) |
0.981799 | + | 0.189925i | \(0.0608245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.12167 | + | 2.95700i | −0.504653 | + | 0.291361i | −0.730633 | − | 0.682771i | \(-0.760775\pi\) |
0.225980 | + | 0.974132i | \(0.427442\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.01487i | 0.0981111i | 0.998796 | + | 0.0490555i | \(0.0156211\pi\) | ||||
−0.998796 | + | 0.0490555i | \(0.984379\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 4.46314i | − | 0.427491i | −0.976889 | − | 0.213746i | \(-0.931434\pi\) | ||
0.976889 | − | 0.213746i | \(-0.0685664\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.35628 | + | 4.24715i | −0.692021 | + | 0.399538i | −0.804369 | − | 0.594131i | \(-0.797496\pi\) |
0.112348 | + | 0.993669i | \(0.464163\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.43607 | + | 4.21940i | −0.227165 | + | 0.393462i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.45953 | − | 7.72414i | 0.408805 | − | 0.708071i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.24919 | − | 7.35981i | −0.386290 | − | 0.669074i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1650 | 1.08807 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 15.9098i | − | 1.41176i | −0.708329 | − | 0.705882i | \(-0.750551\pi\) | ||
0.708329 | − | 0.705882i | \(-0.249449\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.38769 | − | 0.801182i | 0.121243 | − | 0.0699996i | −0.438152 | − | 0.898901i | \(-0.644367\pi\) |
0.559395 | + | 0.828901i | \(0.311034\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.53397 | + | 3.77239i | 0.566567 | + | 0.327108i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.6153 | + | 6.12877i | 0.906930 | + | 0.523616i | 0.879442 | − | 0.476006i | \(-0.157916\pi\) |
0.0274877 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.618940 | + | 1.07204i | 0.0524978 | + | 0.0909289i | 0.891080 | − | 0.453846i | \(-0.149948\pi\) |
−0.838582 | + | 0.544775i | \(0.816615\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.77985 | 0.817832 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.14327 | −0.759307 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.96982 | − | 5.14387i | −0.243297 | − | 0.421402i | 0.718355 | − | 0.695677i | \(-0.244896\pi\) |
−0.961651 | + | 0.274275i | \(0.911562\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 11.9663 | + | 6.90874i | 0.973803 | + | 0.562226i | 0.900394 | − | 0.435076i | \(-0.143279\pi\) |
0.0734098 | + | 0.997302i | \(0.476612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −10.6606 | − | 6.15488i | −0.856278 | − | 0.494372i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.98995 | − | 2.88095i | 0.398241 | − | 0.229925i | −0.287483 | − | 0.957786i | \(-0.592819\pi\) |
0.685725 | + | 0.727861i | \(0.259485\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.55947i | − | 0.516959i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.2888 | −0.884209 | −0.442104 | − | 0.896964i | \(-0.645768\pi\) | ||||
−0.442104 | + | 0.896964i | \(0.645768\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.378448 | + | 0.655492i | 0.0292852 | + | 0.0507235i | 0.880297 | − | 0.474424i | \(-0.157344\pi\) |
−0.851011 | + | 0.525147i | \(0.824010\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6167 | − | 21.8528i | 0.970517 | − | 1.68098i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.62735 | − | 8.01480i | 0.351811 | − | 0.609354i | −0.634756 | − | 0.772713i | \(-0.718899\pi\) |
0.986567 | + | 0.163359i | \(0.0522327\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.74406 | + | 2.16164i | −0.283025 | + | 0.163404i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 1.56530i | − | 0.116996i | −0.998288 | − | 0.0584980i | \(-0.981369\pi\) | ||
0.998288 | − | 0.0584980i | \(-0.0186311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3.68300i | − | 0.273755i | −0.990588 | − | 0.136878i | \(-0.956293\pi\) | ||
0.990588 | − | 0.136878i | \(-0.0437067\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.13148 | − | 4.69471i | 0.597838 | − | 0.345162i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.92561 | − | 5.06730i | 0.213941 | − | 0.370558i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.8678 | − | 20.5556i | 0.858722 | − | 1.48735i | −0.0144258 | − | 0.999896i | \(-0.504592\pi\) |
0.873148 | − | 0.487455i | \(-0.162075\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.8012 | + | 22.1723i | 0.921451 | + | 1.59600i | 0.797172 | + | 0.603752i | \(0.206328\pi\) |
0.124279 | + | 0.992247i | \(0.460338\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.76656 | 0.410850 | 0.205425 | − | 0.978673i | \(-0.434142\pi\) | ||||
0.205425 | + | 0.978673i | \(0.434142\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.24163i | 0.0880169i | 0.999031 | + | 0.0440085i | \(0.0140129\pi\) | ||||
−0.999031 | + | 0.0440085i | \(0.985987\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.6606 | − | 6.15488i | 0.748226 | − | 0.431988i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 9.53076 | + | 5.50259i | 0.665657 | + | 0.384317i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.28651 | + | 2.47482i | 0.296504 | + | 0.171187i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.62194 | − | 2.80928i | −0.111659 | − | 0.193399i | 0.804780 | − | 0.593573i | \(-0.202283\pi\) |
−0.916439 | + | 0.400174i | \(0.868950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.62047 | 0.110515 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.5729 | 1.12504 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.4374 | − | 19.8101i | −0.769362 | − | 1.33257i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1221 | + | 6.99871i | 0.811758 | + | 0.468669i | 0.847566 | − | 0.530690i | \(-0.178067\pi\) |
−0.0358081 | + | 0.999359i | \(0.511401\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.75366 | − | 5.05393i | −0.581001 | − | 0.335441i | 0.180530 | − | 0.983569i | \(-0.442219\pi\) |
−0.761531 | + | 0.648128i | \(0.775552\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 9.93043 | − | 5.73334i | 0.656221 | − | 0.378869i | −0.134615 | − | 0.990898i | \(-0.542980\pi\) |
0.790836 | + | 0.612029i | \(0.209646\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.74860i | 0.442115i | 0.975261 | + | 0.221058i | \(0.0709509\pi\) | ||||
−0.975261 | + | 0.221058i | \(0.929049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.5133 | −1.14244 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.0677896 | + | 0.117415i | 0.00438494 | + | 0.00759495i | 0.868210 | − | 0.496198i | \(-0.165271\pi\) |
−0.863825 | + | 0.503793i | \(0.831938\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.71742 | + | 16.8311i | −0.625954 | + | 1.08418i | 0.362401 | + | 0.932022i | \(0.381957\pi\) |
−0.988355 | + | 0.152163i | \(0.951376\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.06319 | − | 1.84150i | 0.0679248 | − | 0.117649i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.7577 | − | 9.67507i | 1.06627 | − | 0.615610i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.7837i | 1.18561i | 0.805344 | + | 0.592807i | \(0.201980\pi\) | ||||
−0.805344 | + | 0.592807i | \(0.798020\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 4.30324i | − | 0.270542i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.6937 | + | 10.7928i | −1.16608 | + | 0.673238i | −0.952754 | − | 0.303742i | \(-0.901764\pi\) |
−0.213329 | + | 0.976981i | \(0.568430\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.32058 | + | 10.9476i | −0.392742 | + | 0.680249i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.56995 | + | 14.8436i | −0.528446 | + | 0.915295i | 0.471004 | + | 0.882131i | \(0.343892\pi\) |
−0.999450 | + | 0.0331642i | \(0.989442\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.32058 | − | 10.9476i | −0.388270 | − | 0.672504i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −20.1271 | −1.22717 | −0.613585 | − | 0.789629i | \(-0.710273\pi\) | ||||
−0.613585 | + | 0.789629i | \(0.710273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.20336i | − | 0.376827i | −0.982090 | − | 0.188414i | \(-0.939665\pi\) | ||
0.982090 | − | 0.188414i | \(-0.0603345\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.45623 | + | 1.41811i | −0.148116 | + | 0.0855151i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6060 | + | 6.12340i | 0.637256 | + | 0.367920i | 0.783557 | − | 0.621320i | \(-0.213403\pi\) |
−0.146301 | + | 0.989240i | \(0.546737\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1623 | + | 8.75399i | 0.904510 | + | 0.522219i | 0.878661 | − | 0.477447i | \(-0.158438\pi\) |
0.0258492 | + | 0.999666i | \(0.491771\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.79698 | + | 6.57656i | 0.225707 | + | 0.390936i | 0.956531 | − | 0.291630i | \(-0.0941975\pi\) |
−0.730824 | + | 0.682565i | \(0.760864\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.8165 | −0.874590 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.31420 | 0.194953 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.6164 | + | 21.8523i | 0.737061 | + | 1.27663i | 0.953813 | + | 0.300400i | \(0.0971202\pi\) |
−0.216753 | + | 0.976227i | \(0.569546\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.9257 | − | 6.30797i | −0.636120 | − | 0.367264i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.5692 | − | 8.41155i | −0.842561 | − | 0.486453i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.88938 | + | 1.09084i | −0.108902 | + | 0.0628748i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.30900i | 0.361253i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.5997 | 1.68934 | 0.844671 | − | 0.535286i | \(-0.179796\pi\) | ||||
0.844671 | + | 0.535286i | \(0.179796\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.3607 | − | 17.9453i | −0.587502 | − | 1.01758i | −0.994558 | − | 0.104180i | \(-0.966778\pi\) |
0.407057 | − | 0.913403i | \(-0.366555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.73680 | − | 3.00823i | 0.0981700 | − | 0.170035i | −0.812757 | − | 0.582603i | \(-0.802034\pi\) |
0.910927 | + | 0.412567i | \(0.135368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.64385 | + | 13.2395i | −0.429321 | + | 0.743606i | −0.996813 | − | 0.0797728i | \(-0.974581\pi\) |
0.567492 | + | 0.823379i | \(0.307914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.99370 | − | 4.03781i | 0.391572 | − | 0.226074i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 11.5770i | − | 0.644164i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.0879i | 0.615047i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.4196 | − | 11.7893i | 1.12577 | − | 0.649963i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.09986 | + | 5.36912i | −0.170384 | + | 0.295114i | −0.938554 | − | 0.345132i | \(-0.887834\pi\) |
0.768170 | + | 0.640246i | \(0.221167\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.85854 | − | 3.21909i | 0.101543 | − | 0.175878i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.63097 | − | 16.6813i | −0.524632 | − | 0.908690i | −0.999589 | − | 0.0286803i | \(-0.990870\pi\) |
0.474956 | − | 0.880009i | \(-0.342464\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.8724 | 0.588772 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.7393i | 1.06582i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 22.9191 | − | 13.2323i | 1.23036 | − | 0.710349i | 0.263255 | − | 0.964726i | \(-0.415204\pi\) |
0.967105 | + | 0.254378i | \(0.0818706\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.8362 | − | 8.56568i | −0.794164 | − | 0.458511i | 0.0472627 | − | 0.998882i | \(-0.484950\pi\) |
−0.841426 | + | 0.540372i | \(0.818284\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −26.8134 | − | 15.4807i | −1.42713 | − | 0.823955i | −0.430239 | − | 0.902715i | \(-0.641571\pi\) |
−0.996894 | + | 0.0787597i | \(0.974904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.96823 | − | 5.14113i | −0.157538 | − | 0.272863i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.43781 | 0.339775 | 0.169887 | − | 0.985463i | \(-0.445660\pi\) | ||||
0.169887 | + | 0.985463i | \(0.445660\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.20680 | −0.484569 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.565009 | + | 0.978624i | 0.0295739 | + | 0.0512235i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.8725 | − | 13.7828i | −1.24614 | − | 0.719457i | −0.275800 | − | 0.961215i | \(-0.588943\pi\) |
−0.970337 | + | 0.241758i | \(0.922276\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 14.7389 | + | 8.50953i | 0.765208 | + | 0.441793i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −23.2547 | + | 13.4261i | −1.20408 | + | 0.695178i | −0.961461 | − | 0.274942i | \(-0.911341\pi\) |
−0.242623 | + | 0.970121i | \(0.578008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 31.5709i | − | 1.62599i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.63966 | −0.238323 | −0.119162 | − | 0.992875i | \(-0.538021\pi\) | ||||
−0.119162 | + | 0.992875i | \(0.538021\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.7531 | + | 30.7493i | 0.907141 | + | 1.57122i | 0.818017 | + | 0.575195i | \(0.195074\pi\) |
0.0891248 | + | 0.996020i | \(0.471593\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.41430 | + | 5.91373i | −0.174009 | + | 0.301392i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.19920 | + | 5.54117i | −0.162206 | + | 0.280949i | −0.935659 | − | 0.352904i | \(-0.885194\pi\) |
0.773454 | + | 0.633853i | \(0.218527\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.71666 | + | 5.03257i | −0.440821 | + | 0.254508i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.1807i | 0.814141i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3.01894i | − | 0.151516i | −0.997126 | − | 0.0757581i | \(-0.975862\pi\) | ||
0.997126 | − | 0.0757581i | \(-0.0241377\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −25.1191 | + | 14.5025i | −1.25439 | + | 0.724222i | −0.971978 | − | 0.235072i | \(-0.924467\pi\) |
−0.282411 | + | 0.959294i | \(0.591134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.2523 | − | 36.8100i | 1.05865 | − | 1.83364i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.14652 | + | 7.18198i | −0.205535 | + | 0.355998i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −0.662169 | − | 1.14691i | −0.0327422 | − | 0.0567111i | 0.849190 | − | 0.528087i | \(-0.177091\pi\) |
−0.881932 | + | 0.471376i | \(0.843757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 16.9851 | 0.835781 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.0271i | 1.37580i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.2974 | + | 15.7602i | −1.33357 | + | 0.769935i | −0.985844 | − | 0.167663i | \(-0.946378\pi\) |
−0.347722 | + | 0.937598i | \(0.613045\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −30.9851 | − | 17.8893i | −1.51012 | − | 0.871869i | −0.999930 | − | 0.0118087i | \(-0.996241\pi\) |
−0.510192 | − | 0.860061i | \(-0.670426\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.74505 | + | 3.31691i | 0.278676 | + | 0.160894i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.24697 | − | 7.35597i | −0.205525 | − | 0.355980i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.1129 | −0.824301 | −0.412150 | − | 0.911116i | \(-0.635222\pi\) | ||||
−0.412150 | + | 0.911116i | \(0.635222\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.1099 | −0.918363 | −0.459182 | − | 0.888342i | \(-0.651857\pi\) | ||||
−0.459182 | + | 0.888342i | \(0.651857\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.25713 | − | 7.37356i | −0.203646 | − | 0.352725i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.4886 | − | 17.0253i | −1.40742 | − | 0.812572i | −0.412277 | − | 0.911058i | \(-0.635266\pi\) |
−0.995138 | + | 0.0984868i | \(0.968600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 17.1586 | + | 9.90651i | 0.815229 | + | 0.470673i | 0.848768 | − | 0.528765i | \(-0.177345\pi\) |
−0.0335394 | + | 0.999437i | \(0.510678\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.80521 | − | 1.04224i | 0.0855749 | − | 0.0494067i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8.73916i | − | 0.412426i | −0.978507 | − | 0.206213i | \(-0.933886\pi\) | ||
0.978507 | − | 0.206213i | \(-0.0661140\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.72012 | −0.457703 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 13.3479 | + | 23.1192i | 0.625758 | + | 1.08384i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.25081 | + | 2.16647i | −0.0585104 | + | 0.101343i | −0.893797 | − | 0.448472i | \(-0.851968\pi\) |
0.835287 | + | 0.549815i | \(0.185302\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.63419 | − | 4.56255i | 0.122686 | − | 0.212499i | −0.798140 | − | 0.602472i | \(-0.794182\pi\) |
0.920826 | + | 0.389973i | \(0.127516\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.2227 | + | 8.78883i | −0.707459 | + | 0.408451i | −0.810119 | − | 0.586265i | \(-0.800598\pi\) |
0.102661 | + | 0.994716i | \(0.467264\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.29842i | 0.106358i | 0.998585 | + | 0.0531791i | \(0.0169354\pi\) | ||||
−0.998585 | + | 0.0531791i | \(0.983065\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00439i | 0.231081i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.23950 | + | 0.715626i | −0.0569923 | + | 0.0329045i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.80582 | + | 4.85983i | −0.128740 | + | 0.222984i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0219 | + | 31.2149i | −0.823442 | + | 1.42624i | 0.0796622 | + | 0.996822i | \(0.474616\pi\) |
−0.903104 | + | 0.429422i | \(0.858717\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.2104 | + | 28.0773i | 0.739132 | + | 1.28021i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −24.1029 | −1.09446 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.72292i | 0.123387i | 0.998095 | + | 0.0616937i | \(0.0196502\pi\) | ||||
−0.998095 | + | 0.0616937i | \(0.980350\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.1715 | − | 7.60457i | 0.594421 | − | 0.343189i | −0.172422 | − | 0.985023i | \(-0.555159\pi\) |
0.766844 | + | 0.641834i | \(0.221826\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.3580 | − | 9.44432i | −0.736729 | − | 0.425351i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.92161 | + | 3.99619i | 0.310477 | + | 0.179254i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.7305 | + | 34.1743i | 0.883260 | + | 1.52985i | 0.847695 | + | 0.530483i | \(0.177990\pi\) |
0.0355642 | + | 0.999367i | \(0.488677\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 18.4749 | 0.823756 | 0.411878 | − | 0.911239i | \(-0.364873\pi\) | ||||
0.411878 | + | 0.911239i | \(0.364873\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.7490 | 0.522826 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.0068 | + | 29.4566i | 0.753813 | + | 1.30564i | 0.945962 | + | 0.324277i | \(0.105121\pi\) |
−0.192149 | + | 0.981366i | \(0.561546\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.31754 | − | 0.760683i | −0.0582846 | − | 0.0336506i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.17165 | − | 5.29525i | −0.404151 | − | 0.233337i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.3960 | − | 7.73416i | 0.589153 | − | 0.340148i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12.0788i | 0.529182i | 0.964361 | + | 0.264591i | \(0.0852369\pi\) | ||||
−0.964361 | + | 0.264591i | \(0.914763\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.27483 | −0.230652 | −0.115326 | − | 0.993328i | \(-0.536791\pi\) | ||||
−0.115326 | + | 0.993328i | \(0.536791\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.7151 | − | 22.0232i | −0.553877 | − | 0.959344i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.79883 | − | 13.5080i | 0.339080 | − | 0.587303i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −19.0000 | + | 32.9089i | −0.822980 | + | 1.42544i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.57390 | + | 0.908690i | −0.0680455 | + | 0.0392861i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.87809i | 0.0808950i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 23.6734i | 1.01780i | 0.860826 | + | 0.508900i | \(0.169948\pi\) | ||||
−0.860826 | + | 0.508900i | \(0.830052\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.92161 | − | 3.99619i | 0.296489 | − | 0.171178i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5319 | + | 18.2418i | −0.450312 | + | 0.779964i | −0.998405 | − | 0.0564536i | \(-0.982021\pi\) |
0.548093 | + | 0.836417i | \(0.315354\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.98910 | − | 13.8375i | 0.340347 | − | 0.589498i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −10.8922 | − | 18.8659i | −0.463184 | − | 0.802259i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.64427 | −0.408641 | −0.204321 | − | 0.978904i | \(-0.565498\pi\) | ||||
−0.204321 | + | 0.978904i | \(0.565498\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.59535i | 0.236658i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −36.8534 | + | 21.2773i | −1.55319 | + | 0.896733i | −0.555307 | + | 0.831645i | \(0.687399\pi\) |
−0.997880 | + | 0.0650873i | \(0.979267\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −13.1733 | − | 7.60561i | −0.554205 | − | 0.319970i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8.25996 | + | 4.76889i | 0.346275 | + | 0.199922i | 0.663044 | − | 0.748581i | \(-0.269264\pi\) |
−0.316768 | + | 0.948503i | \(0.602598\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −13.4455 | − | 23.2882i | −0.562675 | − | 0.974582i | −0.997262 | − | 0.0739518i | \(-0.976439\pi\) |
0.434587 | − | 0.900630i | \(-0.356894\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.87880 | 0.203460 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.52363 | −0.354843 | −0.177422 | − | 0.984135i | \(-0.556776\pi\) | ||||
−0.177422 | + | 0.984135i | \(0.556776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −18.8667 | − | 32.6781i | −0.782724 | − | 1.35572i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.66924 | + | 5.58254i | 0.400459 | + | 0.231205i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.4568 | − | 11.2334i | −0.803067 | − | 0.463651i | 0.0414756 | − | 0.999140i | \(-0.486794\pi\) |
−0.844542 | + | 0.535489i | \(0.820127\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 18.6297 | − | 10.7559i | 0.767625 | − | 0.443189i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 28.8424i | 1.18442i | 0.805785 | + | 0.592208i | \(0.201743\pi\) | ||||
−0.805785 | + | 0.592208i | \(0.798257\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 15.9719 | 0.654783 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.40225 | − | 14.5531i | −0.343307 | − | 0.594625i | 0.641738 | − | 0.766924i | \(-0.278214\pi\) |
−0.985045 | + | 0.172299i | \(0.944880\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.8802 | − | 25.7732i | 0.606974 | − | 1.05131i | −0.384762 | − | 0.923016i | \(-0.625716\pi\) |
0.991736 | − | 0.128294i | \(-0.0409502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.60926 | − | 13.1796i | 0.309360 | − | 0.535828i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.9599 | − | 12.1012i | 0.850737 | − | 0.491173i | −0.0101625 | − | 0.999948i | \(-0.503235\pi\) |
0.860899 | + | 0.508775i | \(0.169902\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 60.4720i | − | 2.44643i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.3189i | 1.54769i | 0.633377 | + | 0.773843i | \(0.281668\pi\) | ||||
−0.633377 | + | 0.773843i | \(0.718332\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.31357 | − | 4.22249i | 0.294433 | − | 0.169991i | −0.345506 | − | 0.938417i | \(-0.612293\pi\) |
0.639939 | + | 0.768425i | \(0.278959\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.12431 | + | 7.14352i | −0.165770 | + | 0.287122i | −0.936929 | − | 0.349521i | \(-0.886344\pi\) |
0.771158 | + | 0.636643i | \(0.219678\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.40318 | + | 2.43038i | −0.0562173 | + | 0.0973713i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.40923 | + | 11.1011i | 0.256369 | + | 0.444044i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.3972 | 0.773415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 34.0954i | − | 1.35732i | −0.734454 | − | 0.678659i | \(-0.762561\pi\) | ||
0.734454 | − | 0.678659i | \(-0.237439\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 24.6735 | − | 14.2452i | 0.979138 | − | 0.565305i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.35854 | + | 3.67111i | 0.251935 | + | 0.145455i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −20.9715 | − | 12.1079i | −0.828324 | − | 0.478233i | 0.0249544 | − | 0.999689i | \(-0.492056\pi\) |
−0.853279 | + | 0.521455i | \(0.825389\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3299 | − | 19.6240i | −0.446808 | − | 0.773895i | 0.551368 | − | 0.834262i | \(-0.314106\pi\) |
−0.998176 | + | 0.0603676i | \(0.980773\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −38.6020 | −1.51760 | −0.758800 | − | 0.651323i | \(-0.774214\pi\) | ||||
−0.758800 | + | 0.651323i | \(0.774214\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 11.1428 | 0.437393 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1416 | + | 22.7619i | 0.514271 | + | 0.890743i | 0.999863 | + | 0.0165576i | \(0.00527069\pi\) |
−0.485592 | + | 0.874185i | \(0.661396\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.48501 | + | 1.43472i | 0.0970973 | + | 0.0560592i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 33.1862 | + | 19.1601i | 1.29275 | + | 0.746370i | 0.979141 | − | 0.203182i | \(-0.0651283\pi\) |
0.313610 | + | 0.949552i | \(0.398462\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 38.7145 | − | 22.3518i | 1.50582 | − | 0.869385i | 0.505842 | − | 0.862626i | \(-0.331182\pi\) |
0.999977 | − | 0.00675901i | \(-0.00215148\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.5109i | 0.523928i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −13.8915 | −0.537882 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.78616 | − | 4.82576i | −0.107558 | − | 0.186297i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.8138 | + | 22.1942i | −0.493937 | + | 0.855524i | −0.999976 | − | 0.00698696i | \(-0.997776\pi\) |
0.506039 | + | 0.862511i | \(0.331109\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.1613 | − | 19.3320i | 0.428964 | − | 0.742988i | −0.567817 | − | 0.823155i | \(-0.692212\pi\) |
0.996781 | + | 0.0801666i | \(0.0255452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.1027 | − | 16.2251i | 1.07848 | − | 0.622662i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.5229i | − | 0.785288i | −0.919691 | − | 0.392644i | \(-0.871560\pi\) | ||
0.919691 | − | 0.392644i | \(-0.128440\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 21.9502i | 0.838676i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 37.8010 | − | 21.8244i | 1.44010 | − | 0.831444i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.97960 | − | 10.3570i | 0.227475 | − | 0.393998i | −0.729584 | − | 0.683891i | \(-0.760286\pi\) |
0.957059 | + | 0.289893i | \(0.0936198\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.10837 | + | 1.91975i | −0.0420429 | + | 0.0728204i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.3675 | + | 19.6891i | 0.430576 | + | 0.745779i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −41.9171 | −1.58319 | −0.791593 | − | 0.611049i | \(-0.790748\pi\) | ||||
−0.791593 | + | 0.611049i | \(0.790748\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.4084i | 0.618853i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −13.6988 | + | 7.90899i | −0.515195 | + | 0.297448i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.41486 | + | 2.54892i | 0.165803 | + | 0.0957266i | 0.580606 | − | 0.814185i | \(-0.302816\pi\) |
−0.414802 | + | 0.909912i | \(0.636149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −16.1968 | − | 9.35122i | −0.606575 | − | 0.350206i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.75666 | + | 15.1670i | 0.327480 | + | 0.567213i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35.1676 | 1.31153 | 0.655765 | − | 0.754965i | \(-0.272346\pi\) | ||||
0.655765 | + | 0.754965i | \(0.272346\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.2582 | 0.531003 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.57787 | + | 7.92911i | 0.170018 | + | 0.294480i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.9209 | + | 11.5013i | 0.738826 | + | 0.426561i | 0.821642 | − | 0.570003i | \(-0.193058\pi\) |
−0.0828164 | + | 0.996565i | \(0.526391\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.89915 | + | 1.67383i | 0.107229 | + | 0.0619087i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.38177 | + | 4.26187i | −0.272652 | + | 0.157416i | −0.630092 | − | 0.776520i | \(-0.716983\pi\) |
0.357440 | + | 0.933936i | \(0.383650\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.28305i | 0.120933i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −32.3956 | −1.19169 | −0.595846 | − | 0.803099i | \(-0.703183\pi\) | ||||
−0.595846 | + | 0.803099i | \(0.703183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.22350 | − | 3.85122i | −0.0815725 | − | 0.141288i | 0.822353 | − | 0.568978i | \(-0.192661\pi\) |
−0.903926 | + | 0.427690i | \(0.859328\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5.31821 | − | 9.21141i | 0.194844 | − | 0.337480i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.22339 | − | 2.11897i | 0.0447016 | − | 0.0774255i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.3801 | − | 18.6946i | 1.18157 | − | 0.682177i | 0.225189 | − | 0.974315i | \(-0.427700\pi\) |
0.956376 | + | 0.292138i | \(0.0943666\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.7437i | 0.900517i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 46.7837i | − | 1.70038i | −0.526474 | − | 0.850191i | \(-0.676486\pi\) | ||
0.526474 | − | 0.850191i | \(-0.323514\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.83226 | + | 3.36726i | −0.211419 | + | 0.122063i | −0.601971 | − | 0.798518i | \(-0.705618\pi\) |
0.390552 | + | 0.920581i | \(0.372284\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.38016 | + | 9.31870i | −0.194775 | + | 0.337360i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 21.7809 | − | 37.7255i | 0.786461 | − | 1.36219i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.91160 | − | 15.4353i | −0.321361 | − | 0.556613i | 0.659408 | − | 0.751785i | \(-0.270807\pi\) |
−0.980769 | + | 0.195172i | \(0.937473\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.9682 | 0.682237 | 0.341119 | − | 0.940020i | \(-0.389194\pi\) | ||||
0.341119 | + | 0.940020i | \(0.389194\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.3266i | 0.442783i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −16.6554 | + | 9.61597i | −0.596740 | + | 0.344528i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.54081 | + | 2.62164i | 0.162483 | + | 0.0938096i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 8.93578 | + | 5.15907i | 0.318932 | + | 0.184135i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.03810 | + | 1.79804i | 0.0370041 | + | 0.0640931i | 0.883934 | − | 0.467611i | \(-0.154885\pi\) |
−0.846930 | + | 0.531704i | \(0.821552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.4792 | 0.728155 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −21.7844 | −0.773588 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.7593 | − | 30.7601i | −0.629068 | − | 1.08958i | −0.987739 | − | 0.156113i | \(-0.950103\pi\) |
0.358671 | − | 0.933464i | \(-0.383230\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.3327 | − | 18.0900i | −1.10847 | − | 0.639977i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.864352 | − | 0.499034i | −0.0305023 | − | 0.0176105i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10.1727 | − | 5.87320i | 0.358540 | − | 0.207003i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 41.7225i | 1.46688i | 0.679752 | + | 0.733442i | \(0.262087\pi\) | ||||
−0.679752 | + | 0.733442i | \(0.737913\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.03064 | 0.106420 | 0.0532102 | − | 0.998583i | \(-0.483055\pi\) | ||||
0.0532102 | + | 0.998583i | \(0.483055\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1078 | − | 17.5071i | −0.354059 | − | 0.613248i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.41592 | + | 2.45244i | −0.0495366 | + | 0.0858000i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.9259 | − | 44.9049i | 0.904819 | − | 1.56719i | 0.0836589 | − | 0.996494i | \(-0.473339\pi\) |
0.821160 | − | 0.570698i | \(-0.193327\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −28.3812 | + | 16.3859i | −0.989307 | + | 0.571177i | −0.905067 | − | 0.425269i | \(-0.860180\pi\) |
−0.0842401 | + | 0.996445i | \(0.526846\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 52.8295i | 1.83706i | 0.395350 | + | 0.918531i | \(0.370623\pi\) | ||||
−0.395350 | + | 0.918531i | \(0.629377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 0.0144624i | − | 0.000502300i | −1.00000 | 0.000251150i | \(-0.999920\pi\) | |||
1.00000 | 0.000251150i | \(-7.99435e-5\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.80427 | − | 2.19639i | 0.131810 | − | 0.0761006i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.677708 | + | 1.17382i | −0.0234531 | + | 0.0406219i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.6802 | − | 28.8909i | 0.575864 | − | 0.997425i | −0.420083 | − | 0.907486i | \(-0.637999\pi\) |
0.995947 | − | 0.0899399i | \(-0.0286675\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.46530 | + | 2.53797i | 0.0505275 | + | 0.0875162i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 45.1869 | 1.55448 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 20.4890i | 0.704010i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.3543 | − | 7.13276i | 0.423500 | − | 0.244508i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 32.7219 | + | 18.8920i | 1.12038 | + | 0.646850i | 0.941497 | − | 0.337021i | \(-0.109419\pi\) |
0.178880 | + | 0.983871i | \(0.442753\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.00665 | − | 5.19999i | −0.307661 | − | 0.177628i | 0.338218 | − | 0.941068i | \(-0.390176\pi\) |
−0.645879 | + | 0.763439i | \(0.723509\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.3547 | + | 17.9348i | 0.353297 | + | 0.611929i | 0.986825 | − | 0.161791i | \(-0.0517271\pi\) |
−0.633528 | + | 0.773720i | \(0.718394\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.67705 | 0.159209 | 0.0796043 | − | 0.996827i | \(-0.474634\pi\) | ||||
0.0796043 | + | 0.996827i | \(0.474634\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.5729 | 0.563495 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −7.14567 | − | 12.3767i | −0.242400 | − | 0.419849i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1152 | + | 6.41739i | 0.376626 | + | 0.217445i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −25.3995 | − | 14.6644i | −0.858660 | − | 0.495748i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.04467 | + | 5.22194i | −0.305417 | + | 0.176333i | −0.644874 | − | 0.764289i | \(-0.723090\pi\) |
0.339457 | + | 0.940622i | \(0.389757\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 29.7734i | − | 1.00309i | −0.865131 | − | 0.501546i | \(-0.832765\pi\) | ||
0.865131 | − | 0.501546i | \(-0.167235\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 52.9294 | 1.78122 | 0.890608 | − | 0.454772i | \(-0.150279\pi\) | ||||
0.890608 | + | 0.454772i | \(0.150279\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 22.4416 | + | 38.8700i | 0.753515 | + | 1.30513i | 0.946109 | + | 0.323848i | \(0.104977\pi\) |
−0.192594 | + | 0.981278i | \(0.561690\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −19.1787 | + | 33.2184i | −0.643232 | + | 1.11411i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.3026 | − | 26.5048i | 0.512081 | − | 0.886951i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.42753 | − | 1.40153i | 0.0811434 | − | 0.0468481i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 35.0978i | − | 1.17058i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 26.1148i | − | 0.870009i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.71174 | − | 3.29768i | 0.189865 | − | 0.109618i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.19627 | − | 14.1964i | 0.272153 | − | 0.471382i | −0.697260 | − | 0.716818i | \(-0.745598\pi\) |
0.969413 | + | 0.245436i | \(0.0789311\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.4518 | + | 23.2991i | −0.445677 | + | 0.771935i | −0.998099 | − | 0.0616295i | \(-0.980370\pi\) |
0.552422 | + | 0.833564i | \(0.313704\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.3772 | − | 21.4380i | −0.409626 | − | 0.709493i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.86319 | −0.127574 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 22.2518i | 0.734020i | 0.930217 | + | 0.367010i | \(0.119619\pi\) | ||||
−0.930217 | + | 0.367010i | \(0.880381\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.7519 | − | 10.2491i | 0.584310 | − | 0.337352i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −8.14257 | − | 4.70112i | −0.267726 | − | 0.154572i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8.55489 | + | 4.93917i | 0.280677 | + | 0.162049i | 0.633730 | − | 0.773555i | \(-0.281523\pi\) |
−0.353053 | + | 0.935603i | \(0.614856\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.85796 | + | 3.21809i | 0.0608923 | + | 0.105469i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.4781 | 0.342670 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.11802 | −0.0691926 | −0.0345963 | − | 0.999401i | \(-0.511015\pi\) | ||||
−0.0345963 | + | 0.999401i | \(0.511015\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.56180 | − | 6.16922i | −0.116111 | − | 0.201111i | 0.802112 | − | 0.597173i | \(-0.203710\pi\) |
−0.918223 | + | 0.396063i | \(0.870376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.4803 | + | 8.36018i | 0.471542 | + | 0.272245i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.5581 | + | 25.7256i | 1.44794 | + | 0.835970i | 0.998359 | − | 0.0572679i | \(-0.0182389\pi\) |
0.449584 | + | 0.893238i | \(0.351572\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.37910 | + | 1.95093i | −0.109690 | + | 0.0633297i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 45.3652i | − | 1.46952i | −0.678326 | − | 0.734761i | \(-0.737294\pi\) | ||
0.678326 | − | 0.734761i | \(-0.262706\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 42.5046 | 1.37542 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −14.7760 | − | 25.5928i | −0.477143 | − | 0.826436i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.12641 | − | 14.0754i | 0.262142 | − | 0.454044i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.9238 | + | 39.7052i | −0.737944 | + | 1.27816i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.55341 | − | 1.47421i | 0.0821121 | − | 0.0474075i | −0.458382 | − | 0.888755i | \(-0.651571\pi\) |
0.540494 | + | 0.841348i | \(0.318237\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.8052i | 0.699763i | 0.936794 | + | 0.349882i | \(0.113778\pi\) | ||||
−0.936794 | + | 0.349882i | \(0.886222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 2.98444i | − | 0.0956768i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −26.7110 | + | 15.4216i | −0.854560 | + | 0.493381i | −0.862187 | − | 0.506590i | \(-0.830906\pi\) |
0.00762657 | + | 0.999971i | \(0.497572\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.920536 | + | 1.59441i | −0.0294204 | + | 0.0509577i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.49316 | + | 11.2465i | −0.207100 | + | 0.358707i | −0.950800 | − | 0.309806i | \(-0.899736\pi\) |
0.743700 | + | 0.668513i | \(0.233069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5.16324 | + | 8.94300i | 0.164515 | + | 0.284948i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.46201 | 0.0782873 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 47.5865i | − | 1.51163i | −0.654783 | − | 0.755817i | \(-0.727240\pi\) | ||
0.654783 | − | 0.755817i | \(-0.272760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.92557 | + | 1.11173i | −0.0610447 | + | 0.0352442i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.41748 | − | 4.28248i | −0.234914 | − | 0.135628i | 0.377923 | − | 0.925837i | \(-0.376638\pi\) |
−0.612837 | + | 0.790209i | \(0.709972\pi\) | |||||||
\(998\) | 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 | 864.2.p.b.143.6 | 16 | ||
3.2 | odd | 2 | 288.2.p.b.47.1 | 16 | |||
4.3 | odd | 2 | 216.2.l.b.35.2 | 16 | |||
8.3 | odd | 2 | inner | 864.2.p.b.143.3 | 16 | ||
8.5 | even | 2 | 216.2.l.b.35.6 | 16 | |||
9.2 | odd | 6 | 2592.2.f.b.1295.12 | 16 | |||
9.4 | even | 3 | 288.2.p.b.239.2 | 16 | |||
9.5 | odd | 6 | inner | 864.2.p.b.719.3 | 16 | ||
9.7 | even | 3 | 2592.2.f.b.1295.6 | 16 | |||
12.11 | even | 2 | 72.2.l.b.11.7 | yes | 16 | ||
24.5 | odd | 2 | 72.2.l.b.11.3 | ✓ | 16 | ||
24.11 | even | 2 | 288.2.p.b.47.2 | 16 | |||
36.7 | odd | 6 | 648.2.f.b.323.15 | 16 | |||
36.11 | even | 6 | 648.2.f.b.323.2 | 16 | |||
36.23 | even | 6 | 216.2.l.b.179.6 | 16 | |||
36.31 | odd | 6 | 72.2.l.b.59.3 | yes | 16 | ||
72.5 | odd | 6 | 216.2.l.b.179.2 | 16 | |||
72.11 | even | 6 | 2592.2.f.b.1295.5 | 16 | |||
72.13 | even | 6 | 72.2.l.b.59.7 | yes | 16 | ||
72.29 | odd | 6 | 648.2.f.b.323.16 | 16 | |||
72.43 | odd | 6 | 2592.2.f.b.1295.11 | 16 | |||
72.59 | even | 6 | inner | 864.2.p.b.719.6 | 16 | ||
72.61 | even | 6 | 648.2.f.b.323.1 | 16 | |||
72.67 | odd | 6 | 288.2.p.b.239.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.2.l.b.11.3 | ✓ | 16 | 24.5 | odd | 2 | ||
72.2.l.b.11.7 | yes | 16 | 12.11 | even | 2 | ||
72.2.l.b.59.3 | yes | 16 | 36.31 | odd | 6 | ||
72.2.l.b.59.7 | yes | 16 | 72.13 | even | 6 | ||
216.2.l.b.35.2 | 16 | 4.3 | odd | 2 | |||
216.2.l.b.35.6 | 16 | 8.5 | even | 2 | |||
216.2.l.b.179.2 | 16 | 72.5 | odd | 6 | |||
216.2.l.b.179.6 | 16 | 36.23 | even | 6 | |||
288.2.p.b.47.1 | 16 | 3.2 | odd | 2 | |||
288.2.p.b.47.2 | 16 | 24.11 | even | 2 | |||
288.2.p.b.239.1 | 16 | 72.67 | odd | 6 | |||
288.2.p.b.239.2 | 16 | 9.4 | even | 3 | |||
648.2.f.b.323.1 | 16 | 72.61 | even | 6 | |||
648.2.f.b.323.2 | 16 | 36.11 | even | 6 | |||
648.2.f.b.323.15 | 16 | 36.7 | odd | 6 | |||
648.2.f.b.323.16 | 16 | 72.29 | odd | 6 | |||
864.2.p.b.143.3 | 16 | 8.3 | odd | 2 | inner | ||
864.2.p.b.143.6 | 16 | 1.1 | even | 1 | trivial | ||
864.2.p.b.719.3 | 16 | 9.5 | odd | 6 | inner | ||
864.2.p.b.719.6 | 16 | 72.59 | even | 6 | inner | ||
2592.2.f.b.1295.5 | 16 | 72.11 | even | 6 | |||
2592.2.f.b.1295.6 | 16 | 9.7 | even | 3 | |||
2592.2.f.b.1295.11 | 16 | 72.43 | odd | 6 | |||
2592.2.f.b.1295.12 | 16 | 9.2 | odd | 6 |