Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [336,6,Mod(239,336)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(336, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("336.239");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 336 = 2^{4} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 336.h (of order \(2\), degree \(1\), 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: | \(53.8889634572\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 239.16 | ||
Character | \(\chi\) | \(=\) | 336.239 |
Dual form | 336.6.h.b.239.15 |
$q$-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 \(\left(\mathbb{Z}/336\mathbb{Z}\right)^\times\).
\(n\) | \(85\) | \(113\) | \(127\) | \(241\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −6.06266 | + | 14.3612i | −0.388920 | + | 0.921272i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 44.6235i | 0.798250i | 0.916897 | + | 0.399125i | \(0.130686\pi\) | ||||
−0.916897 | + | 0.399125i | \(0.869314\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 49.0000i | − | 0.377964i | ||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −169.488 | − | 174.134i | −0.697483 | − | 0.716601i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 190.244 | 0.474055 | 0.237027 | − | 0.971503i | \(-0.423827\pi\) | ||||
0.237027 | + | 0.971503i | \(0.423827\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 542.034 | 0.889546 | 0.444773 | − | 0.895643i | \(-0.353284\pi\) | ||||
0.444773 | + | 0.895643i | \(0.353284\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −640.848 | − | 270.537i | −0.735405 | − | 0.310455i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 377.111i | 0.316481i | 0.987401 | + | 0.158240i | \(0.0505821\pi\) | ||||
−0.987401 | + | 0.158240i | \(0.949418\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 214.658i | 0.136415i | 0.997671 | + | 0.0682075i | \(0.0217280\pi\) | ||||
−0.997671 | + | 0.0682075i | \(0.978272\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 703.699 | + | 297.070i | 0.348208 | + | 0.146998i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4578.90 | 1.80485 | 0.902426 | − | 0.430845i | \(-0.141785\pi\) | ||||
0.902426 | + | 0.430845i | \(0.141785\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1133.74 | 0.362797 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3528.33 | − | 1378.34i | 0.931449 | − | 0.363871i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6957.56i | − | 1.53625i | −0.640300 | − | 0.768125i | \(-0.721190\pi\) | ||
0.640300 | − | 0.768125i | \(-0.278810\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7806.37i | 1.45897i | 0.683999 | + | 0.729483i | \(0.260239\pi\) | ||||
−0.683999 | + | 0.729483i | \(0.739761\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1153.38 | + | 2732.13i | −0.184369 | + | 0.436733i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2186.55 | 0.301710 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5560.43 | 0.667735 | 0.333867 | − | 0.942620i | \(-0.391646\pi\) | ||||
0.333867 | + | 0.942620i | \(0.391646\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3286.17 | + | 7784.27i | −0.345962 | + | 0.819514i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3056.15i | 0.283932i | 0.989872 | + | 0.141966i | \(0.0453424\pi\) | ||||
−0.989872 | + | 0.141966i | \(0.954658\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6656.50i | 0.549003i | 0.961587 | + | 0.274501i | \(0.0885128\pi\) | ||||
−0.961587 | + | 0.274501i | \(0.911487\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7770.48 | − | 7563.17i | 0.572027 | − | 0.556766i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5920.56 | −0.390947 | −0.195474 | − | 0.980709i | \(-0.562624\pi\) | ||||
−0.195474 | + | 0.980709i | \(0.562624\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2401.00 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5415.77 | − | 2286.30i | −0.291565 | − | 0.123086i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 27044.7i | − | 1.32249i | −0.750171 | − | 0.661244i | \(-0.770029\pi\) | ||
0.750171 | − | 0.661244i | \(-0.229971\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8489.34i | 0.378414i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3082.74 | − | 1301.39i | −0.125675 | − | 0.0530545i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3587.75 | 0.134181 | 0.0670906 | − | 0.997747i | \(-0.478628\pi\) | ||||
0.0670906 | + | 0.997747i | \(0.478628\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −47233.3 | −1.62526 | −0.812632 | − | 0.582778i | \(-0.801966\pi\) | ||||
−0.812632 | + | 0.582778i | \(0.801966\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −8532.57 | + | 8304.93i | −0.270850 | + | 0.263624i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 24187.5i | 0.710080i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 31211.8i | 0.849437i | 0.905325 | + | 0.424719i | \(0.139627\pi\) | ||||
−0.905325 | + | 0.424719i | \(0.860373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −27760.3 | + | 65758.5i | −0.701942 | + | 1.66276i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 80798.0 | 1.90219 | 0.951097 | − | 0.308894i | \(-0.0999587\pi\) | ||||
0.951097 | + | 0.308894i | \(0.0999587\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −29201.7 | −0.641359 | −0.320679 | − | 0.947188i | \(-0.603911\pi\) | ||||
−0.320679 | + | 0.947188i | \(0.603911\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −6873.48 | + | 16281.9i | −0.141099 | + | 0.334235i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 9321.94i | − | 0.179176i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 56190.0i | 1.01296i | 0.862252 | + | 0.506479i | \(0.169053\pi\) | ||||
−0.862252 | + | 0.506479i | \(0.830947\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1596.38 | + | 59027.4i | −0.0270348 | + | 0.999634i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −51520.4 | −0.820888 | −0.410444 | − | 0.911886i | \(-0.634626\pi\) | ||||
−0.410444 | + | 0.911886i | \(0.634626\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16828.0 | −0.252631 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 99918.9 | + | 42181.3i | 1.41530 | + | 0.597478i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 77681.5i | 1.03954i | 0.854305 | + | 0.519772i | \(0.173983\pi\) | ||||
−0.854305 | + | 0.519772i | \(0.826017\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 26559.7i | − | 0.336217i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −112109. | − | 47327.4i | −1.34410 | − | 0.567420i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −9578.78 | −0.108893 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 20845.5 | 0.224948 | 0.112474 | − | 0.993655i | \(-0.464122\pi\) | ||||
0.112474 | + | 0.993655i | \(0.464122\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −32244.1 | − | 33127.9i | −0.330645 | − | 0.339708i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 111322.i | 1.08587i | 0.839774 | + | 0.542937i | \(0.182688\pi\) | ||||
−0.839774 | + | 0.542937i | \(0.817312\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 70195.7i | 0.651955i | 0.945378 | + | 0.325977i | \(0.105693\pi\) | ||||
−0.945378 | + | 0.325977i | \(0.894307\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −13256.3 | + | 31401.5i | −0.117341 | + | 0.277957i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 97869.1 | 0.826392 | 0.413196 | − | 0.910642i | \(-0.364412\pi\) | ||||
0.413196 | + | 0.910642i | \(0.364412\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1440.79 | 0.0116154 | 0.00580772 | − | 0.999983i | \(-0.498151\pi\) | ||||
0.00580772 | + | 0.999983i | \(0.498151\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −33711.0 | + | 79854.5i | −0.259695 | + | 0.615165i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 212764.i | − | 1.56748i | −0.621089 | − | 0.783740i | \(-0.713309\pi\) | ||
0.621089 | − | 0.783740i | \(-0.286691\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 204327.i | 1.44072i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −91868.5 | − | 94386.7i | −0.620443 | − | 0.637450i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 18478.5 | 0.119619 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −124858. | −0.775272 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −43890.0 | − | 18528.4i | −0.261579 | − | 0.110427i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 190040.i | 1.08785i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 239639.i | 1.31841i | 0.751965 | + | 0.659203i | \(0.229106\pi\) | ||||
−0.751965 | + | 0.659203i | \(0.770894\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −95595.3 | − | 40356.0i | −0.505781 | − | 0.213518i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 157566. | 0.802204 | 0.401102 | − | 0.916033i | \(-0.368627\pi\) | ||||
0.401102 | + | 0.916033i | \(0.368627\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10518.2 | 0.0515600 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 61506.5 | + | 157446.i | 0.290460 | + | 0.743529i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 90882.5i | 0.413694i | 0.978373 | + | 0.206847i | \(0.0663202\pi\) | ||||
−0.978373 | + | 0.206847i | \(0.933680\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 108809.i | 0.477668i | 0.971060 | + | 0.238834i | \(0.0767652\pi\) | ||||
−0.971060 | + | 0.238834i | \(0.923235\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 35894.3 | − | 85026.4i | 0.152047 | − | 0.360169i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 103119. | 0.421693 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 310471. | 1.22631 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 14556.4 | − | 34481.3i | 0.0555599 | − | 0.131610i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 24511.2i | − | 0.0904479i | −0.998977 | − | 0.0452240i | \(-0.985600\pi\) | ||
0.998977 | − | 0.0452240i | \(-0.0144001\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 47092.6i | 0.168078i | 0.996462 | + | 0.0840389i | \(0.0267820\pi\) | ||||
−0.996462 | + | 0.0840389i | \(0.973218\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 65668.0 | − | 63916.0i | 0.226791 | − | 0.220740i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −348348. | −1.16462 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −45035.0 | −0.145815 | −0.0729073 | − | 0.997339i | \(-0.523228\pi\) | ||||
−0.0729073 | + | 0.997339i | \(0.523228\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 388394. | + | 163963.i | 1.21837 | + | 0.514342i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 224366.i | − | 0.682170i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 72731.6i | − | 0.214415i | −0.994237 | − | 0.107207i | \(-0.965809\pi\) | ||
0.994237 | − | 0.107207i | \(-0.0341908\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −121917. | − | 51468.0i | −0.348622 | − | 0.147173i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −172434. | −0.478444 | −0.239222 | − | 0.970965i | \(-0.576892\pi\) | ||||
−0.239222 | + | 0.970965i | \(0.576892\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −77491.8 | −0.208708 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 37379.2 | − | 36382.0i | 0.0977552 | − | 0.0951471i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 230047.i | − | 0.584388i | −0.956359 | − | 0.292194i | \(-0.905615\pi\) | ||
0.956359 | − | 0.292194i | \(-0.0943853\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 55553.3i | − | 0.137124i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −21751.3 | + | 51524.4i | −0.0521857 | + | 0.123617i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 35064.1 | 0.0817956 | 0.0408978 | − | 0.999163i | \(-0.486978\pi\) | ||||
0.0408978 | + | 0.999163i | \(0.486978\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 396840. | 0.900366 | 0.450183 | − | 0.892936i | \(-0.351359\pi\) | ||||
0.450183 | + | 0.892936i | \(0.351359\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 286359. | − | 678327.i | 0.632097 | − | 1.49731i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 248126.i | 0.533019i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 71743.1i | 0.150029i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −67538.8 | − | 172888.i | −0.137530 | − | 0.352055i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 437830. | 0.868404 | 0.434202 | − | 0.900815i | \(-0.357030\pi\) | ||||
0.434202 | + | 0.900815i | \(0.357030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 708524. | 1.36918 | 0.684591 | − | 0.728927i | \(-0.259981\pi\) | ||||
0.684591 | + | 0.728927i | \(0.259981\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −347361. | − | 146640.i | −0.654177 | − | 0.276164i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 530365.i | 0.973664i | 0.873496 | + | 0.486832i | \(0.161848\pi\) | ||||
−0.873496 | + | 0.486832i | \(0.838152\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.00530e6i | 1.79954i | 0.436361 | + | 0.899772i | \(0.356267\pi\) | ||||
−0.436361 | + | 0.899772i | \(0.643733\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −448238. | − | 189226.i | −0.782562 | − | 0.330363i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −340920. | −0.580648 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −136376. | −0.226649 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −776070. | − | 797343.i | −1.25885 | − | 1.29336i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40837.2i | 0.0646682i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 1.00443e6i | − | 1.55316i | −0.630020 | − | 0.776579i | \(-0.716953\pi\) | ||
0.630020 | − | 0.776579i | \(-0.283047\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −489850. | + | 1.16036e6i | −0.739800 | + | 1.75244i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −297036. | −0.438241 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 382512. | 0.551437 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 177040. | − | 419372.i | 0.249437 | − | 0.590866i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 204407.i | 0.281524i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.03170e6i | − | 1.38928i | −0.719358 | − | 0.694639i | \(-0.755564\pi\) | ||
0.719358 | − | 0.694639i | \(-0.244436\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −192156. | − | 197423.i | −0.253045 | − | 0.259981i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 906383. | 1.16747 | 0.583737 | − | 0.811943i | \(-0.301590\pi\) | ||||
0.583737 | + | 0.811943i | \(0.301590\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 132754. | 0.167286 | 0.0836429 | − | 0.996496i | \(-0.473345\pi\) | ||||
0.0836429 | + | 0.996496i | \(0.473345\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 133874. | + | 56515.7i | 0.165070 | + | 0.0696850i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 653204.i | − | 0.788241i | −0.919059 | − | 0.394121i | \(-0.871049\pi\) | ||
0.919059 | − | 0.394121i | \(-0.128951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 264196.i | − | 0.312074i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −806956. | − | 340661.i | −0.933209 | − | 0.393959i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.30676e6 | −1.47979 | −0.739896 | − | 0.672721i | \(-0.765125\pi\) | ||||
−0.739896 | + | 0.672721i | \(0.765125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 503326. | 0.558222 | 0.279111 | − | 0.960259i | \(-0.409960\pi\) | ||||
0.279111 | + | 0.960259i | \(0.409960\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −838027. | − | 380789.i | −0.910421 | − | 0.413684i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 107141.i | − | 0.114036i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 116352.i | 0.121347i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 312351. | − | 739895.i | 0.319260 | − | 0.756261i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −975300. | −0.977134 | −0.488567 | − | 0.872526i | \(-0.662480\pi\) | ||||
−0.488567 | + | 0.872526i | \(0.662480\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 871106. | 0.855598 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 102023. | − | 241671.i | 0.0982531 | − | 0.232742i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 403880.i | 0.381434i | 0.981645 | + | 0.190717i | \(0.0610812\pi\) | ||||
−0.981645 | + | 0.190717i | \(0.938919\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 272461.i | − | 0.252380i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.21155e6 | + | 1.17923e6i | −1.10088 | + | 1.07151i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −894632. | −0.797545 | −0.398772 | − | 0.917050i | \(-0.630564\pi\) | ||||
−0.398772 | + | 0.917050i | \(0.630564\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.20683e6 | 1.05568 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.11560e6 | − | 470956.i | −0.957702 | − | 0.404299i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.52378e6i | − | 1.28393i | −0.766733 | − | 0.641967i | \(-0.778119\pi\) | ||
0.766733 | − | 0.641967i | \(-0.221881\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 384963.i | − | 0.318417i | −0.987245 | − | 0.159209i | \(-0.949106\pi\) | ||
0.987245 | − | 0.159209i | \(-0.0508942\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 381429. | + | 161022.i | 0.309747 | + | 0.130761i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 215687. | 0.171986 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 901496. | 0.705934 | 0.352967 | − | 0.935636i | \(-0.385173\pi\) | ||||
0.352967 | + | 0.935636i | \(0.385173\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.35936e6 | − | 1.32309e6i | 1.04550 | − | 1.01760i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 872264.i | − | 0.658995i | −0.944156 | − | 0.329498i | \(-0.893121\pi\) | ||
0.944156 | − | 0.329498i | \(-0.106879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 377286.i | 0.280030i | 0.990149 | + | 0.140015i | \(0.0447150\pi\) | ||||
−0.990149 | + | 0.140015i | \(0.955285\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 58072.8 | − | 137563.i | 0.0423507 | − | 0.100320i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 149751. | 0.107316 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.27764e6 | 0.899840 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −126379. | + | 299367.i | −0.0874869 | + | 0.207239i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 1.08830e6i | − | 0.740591i | −0.928914 | − | 0.370295i | \(-0.879256\pi\) | ||
0.928914 | − | 0.370295i | \(-0.120744\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 160098.i | 0.107110i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 671241. | − | 262221.i | 0.441558 | − | 0.172495i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.48192e6 | 1.60550 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 326168. | 0.207504 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.59872e6 | − | 674910.i | −1.00038 | − | 0.422317i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 2.10772e6i | − | 1.29737i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 209669.i | 0.126966i | 0.997983 | + | 0.0634832i | \(0.0202209\pi\) | ||||
−0.997983 | + | 0.0634832i | \(0.979779\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.00809e6 | − | 425572.i | −0.600628 | − | 0.253558i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.46997e6 | 0.861803 | 0.430902 | − | 0.902399i | \(-0.358196\pi\) | ||||
0.430902 | + | 0.902399i | \(0.358196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.38412e6 | 1.37552 | 0.687761 | − | 0.725937i | \(-0.258594\pi\) | ||||
0.687761 | + | 0.725937i | \(0.258594\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −370595. | − | 380753.i | −0.210438 | − | 0.216206i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.81250e6i | 1.57197i | 0.618244 | + | 0.785986i | \(0.287844\pi\) | ||||
−0.618244 | + | 0.785986i | \(0.712156\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.32363e6i | − | 0.728266i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −593347. | + | 1.40552e6i | −0.321400 | + | 0.761332i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −80949.8 | −0.0431727 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 614526. | 0.322725 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8735.03 | + | 20691.5i | −0.00451747 | + | 0.0107010i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 290107.i | 0.147764i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 947216.i | 0.475203i | 0.971363 | + | 0.237601i | \(0.0763612\pi\) | ||||
−0.971363 | + | 0.237601i | \(0.923639\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −942428. | − | 968261.i | −0.465734 | − | 0.478500i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.39278e6 | −0.678063 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.63228e6 | 1.74223 | 0.871113 | − | 0.491083i | \(-0.163399\pi\) | ||||
0.871113 | + | 0.491083i | \(0.163399\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3.05555e6 | + | 1.28992e6i | 1.44408 | + | 0.609624i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.48511e6i | 0.691630i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 117649.i | 0.0539949i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.93438e6 | − | 1.23876e6i | −1.32730 | − | 0.560325i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.46255e6 | 1.09790 | 0.548948 | − | 0.835857i | \(-0.315029\pi\) | ||||
0.548948 | + | 0.835857i | \(0.315029\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.32760e6 | −1.02293 | −0.511463 | − | 0.859305i | \(-0.670896\pi\) | ||||
−0.511463 | + | 0.859305i | \(0.670896\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.91247e6 | − | 747109.i | 0.828567 | − | 0.323680i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.40361e6i | 0.599529i | 0.954013 | + | 0.299764i | \(0.0969081\pi\) | ||||
−0.954013 | + | 0.299764i | \(0.903092\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.60549e6i | 1.51843i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −112029. | + | 265373.i | −0.0465220 | + | 0.110201i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.82377e6 | −0.746851 | −0.373425 | − | 0.927660i | \(-0.621817\pi\) | ||||
−0.373425 | + | 0.927660i | \(0.621817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.43002e6 | 0.981391 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 756973. | − | 1.79312e6i | 0.301519 | − | 0.714236i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 1.30308e6i | − | 0.511965i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.60865e6i | 1.01100i | 0.862827 | + | 0.505499i | \(0.168692\pi\) | ||||
−0.862827 | + | 0.505499i | \(0.831308\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 532180. | − | 517982.i | 0.203466 | − | 0.198038i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.32519e6 | −0.499854 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.80916e6 | −1.78977 | −0.894884 | − | 0.446299i | \(-0.852742\pi\) | ||||
−0.894884 | + | 0.446299i | \(0.852742\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.72920e6 | − | 1.15215e6i | −1.00221 | − | 0.423087i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 3.77124e6i | − | 1.36657i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 121899.i | 0.0435914i | 0.999762 | + | 0.0217957i | \(0.00693834\pi\) | ||||
−0.999762 | + | 0.0217957i | \(0.993062\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.44151e6 | − | 1.45285e6i | −1.21461 | − | 0.512754i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.67894e6 | −1.28152 | −0.640760 | − | 0.767741i | \(-0.721381\pi\) | ||||
−0.640760 | + | 0.767741i | \(0.721381\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 415978. | 0.143027 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.15912e6 | − | 1.12820e6i | 0.393416 | − | 0.382920i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.10472e6i | 0.705212i | 0.935772 | + | 0.352606i | \(0.114704\pi\) | ||||
−0.935772 | + | 0.352606i | \(0.885296\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.72676e6i | 0.571201i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −955270. | + | 2.26284e6i | −0.311993 | + | 0.739048i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.50740e6 | −0.808593 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 671819. | 0.213932 | 0.106966 | − | 0.994263i | \(-0.465886\pi\) | ||||
0.106966 | + | 0.994263i | \(0.465886\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −63768.4 | + | 151054.i | −0.0200527 | + | 0.0475008i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.47259e6i | 1.69954i | 0.527151 | + | 0.849771i | \(0.323260\pi\) | ||||
−0.527151 | + | 0.849771i | \(0.676740\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.23132e6i | 1.29782i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.63401e6 | − | 71236.1i | −0.797958 | − | 0.0215805i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.05784e6 | 0.316543 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.97372e6 | 1.47019 | 0.735094 | − | 0.677965i | \(-0.237138\pi\) | ||||
0.735094 | + | 0.677965i | \(0.237138\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.30518e6 | − | 550990.i | −0.381124 | − | 0.160894i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 175800.i | − | 0.0507158i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 2.29902e6i | − | 0.655274i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.56262e6 | − | 659670.i | −0.440062 | − | 0.185775i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −147486. | −0.0410408 | −0.0205204 | − | 0.999789i | \(-0.506532\pi\) | ||||
−0.0205204 | + | 0.999789i | \(0.506532\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.87541e6 | −1.06565 | −0.532823 | − | 0.846227i | \(-0.678869\pi\) | ||||
−0.532823 | + | 0.846227i | \(0.678869\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.00347e6 | + | 1.03097e6i | 0.272679 | + | 0.280153i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 427547.i | 0.114818i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.31443e6i | 0.614292i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −625173. | + | 1.48091e6i | −0.164005 | + | 0.388494i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.53594e6 | 1.95409 | 0.977045 | − | 0.213035i | \(-0.0683348\pi\) | ||||
0.977045 | + | 0.213035i | \(0.0683348\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.26964e6 | −1.09439 | −0.547194 | − | 0.837006i | \(-0.684304\pi\) | ||||
−0.547194 | + | 0.837006i | \(0.684304\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.88228e6 | + | 4.45874e6i | −0.476937 | + | 1.12977i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 982895.i | 0.246209i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.60539e6i | 1.38818i | 0.719890 | + | 0.694088i | \(0.244192\pi\) | ||||
−0.719890 | + | 0.694088i | \(0.755808\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 406942. | + | 418096.i | 0.0996404 | + | 0.102372i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 209607. | 0.0507454 | 0.0253727 | − | 0.999678i | \(-0.491923\pi\) | ||||
0.0253727 | + | 0.999678i | \(0.491923\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.46642e6 | −0.829815 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 352010. | + | 148603.i | 0.0833271 | + | 0.0351770i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.52872e6i | 0.591951i | 0.955196 | + | 0.295975i | \(0.0956447\pi\) | ||||
−0.955196 | + | 0.295975i | \(0.904355\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 581413.i | 0.134599i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −676307. | − | 285506.i | −0.154845 | − | 0.0653688i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.18519e6 | 0.268385 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.30478e6 | −0.740206 | −0.370103 | − | 0.928991i | \(-0.620678\pi\) | ||||
−0.370103 | + | 0.928991i | \(0.620678\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 519789. | + | 1.33057e6i | 0.115158 | + | 0.294786i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 6.34695e6i | 1.39095i | 0.718549 | + | 0.695476i | \(0.244807\pi\) | ||||
−0.718549 | + | 0.695476i | \(0.755193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 383220.i | − | 0.0830799i | −0.999137 | − | 0.0415399i | \(-0.986774\pi\) | ||
0.999137 | − | 0.0415399i | \(-0.0132264\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 2.11191e6 | − | 5.00270e6i | 0.452943 | − | 1.07293i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.95851e6 | 1.90083 | 0.950415 | − | 0.310983i | \(-0.100658\pi\) | ||||
0.950415 | + | 0.310983i | \(0.100658\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.52938e6 | 0.321057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 273032. | − | 646757.i | 0.0567101 | − | 0.134335i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.26636e6i | 0.260257i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 243366.i | 0.0494909i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.70940e6 | + | 4.58376e6i | −0.947697 | + | 0.922413i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5.76160e6 | −1.14737 | −0.573686 | − | 0.819075i | \(-0.694487\pi\) | ||||
−0.573686 | + | 0.819075i | \(0.694487\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.01394e6 | 0.593981 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.22217e6 | + | 1.36025e6i | 0.628464 | + | 0.265309i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 930200.i | 0.179565i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.10617e6i | 1.16667i | 0.812233 | + | 0.583333i | \(0.198252\pi\) | ||||
−0.812233 | + | 0.583333i | \(0.801748\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.04451e6 | + | 440947.i | 0.197534 | + | 0.0833900i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.14096e6 | −0.775171 | −0.387585 | − | 0.921834i | \(-0.626691\pi\) | ||||
−0.387585 | + | 0.921834i | \(0.626691\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.62378e6 | 0.486194 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.47828e6 | − | 1.43884e6i | 0.271172 | − | 0.263937i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.95910e6i | − | 0.718961i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 5.59199e6i | − | 1.00535i | −0.864477 | − | 0.502673i | \(-0.832350\pi\) | ||
0.864477 | − | 0.502673i | \(-0.167650\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.04541e6 | − | 2.47636e6i | 0.186076 | − | 0.440777i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.65132e6 | 1.34839 | 0.674197 | − | 0.738552i | \(-0.264490\pi\) | ||||
0.674197 | + | 0.738552i | \(0.264490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.96760e6 | −0.866798 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 469806. | − | 1.11288e6i | 0.0811706 | − | 0.192277i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 7.91287e6i | − | 1.35375i | −0.736097 | − | 0.676877i | \(-0.763333\pi\) | ||
0.736097 | − | 0.676877i | \(-0.236667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.43088e6i | 0.242411i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 295871. | + | 757382.i | 0.0496375 | + | 0.127064i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.13238e6 | −0.520423 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.12635e6 | −0.185330 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.30375e6 | + | 1.39470e6i | 0.538380 | + | 0.227280i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.06748e7i | − | 1.72292i | −0.507826 | − | 0.861460i | \(-0.669551\pi\) | ||
0.507826 | − | 0.861460i | \(-0.330449\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 3.59838e6i | − | 0.575244i | −0.957744 | − | 0.287622i | \(-0.907135\pi\) | ||
0.957744 | − | 0.287622i | \(-0.0928647\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 797812. | + | 336801.i | 0.126329 | + | 0.0533304i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.94387e6 | −0.461735 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.45300e7 | 2.25749 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −608082. | − | 624749.i | −0.0935892 | − | 0.0961545i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.65654e6i | 0.252571i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 4.36727e6i | 0.659668i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −212582. | + | 503563.i | −0.0318119 | + | 0.0753560i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −456775. | −0.0677221 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.15956e7 | −1.70333 | −0.851666 | − | 0.524086i | \(-0.824407\pi\) | ||||
−0.851666 | + | 0.524086i | \(0.824407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.40590e6 | + | 5.69910e6i | −0.350170 | + | 0.829482i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 64293.3i | 0.00927202i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 550260.i | − | 0.0786321i | −0.999227 | − | 0.0393160i | \(-0.987482\pi\) | ||
0.999227 | − | 0.0393160i | \(-0.0125179\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 8.00550e6 | + | 8.22493e6i | 1.13359 | + | 1.16467i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.49349e6 | 0.209568 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.75331e6 | 0.382862 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.56339e6 | − | 1.50430e6i | −0.491056 | − | 0.207302i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.20802e6i | 0.711270i | 0.934625 | + | 0.355635i | \(0.115735\pi\) | ||||
−0.934625 | + | 0.355635i | \(0.884265\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.60805e6i | 0.488363i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.03032e6 | − | 434954.i | −0.138218 | − | 0.0583493i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.38957e6 | 0.450685 | 0.225343 | − | 0.974280i | \(-0.427650\pi\) | ||||
0.225343 | + | 0.974280i | \(0.427650\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.49428e6 | 1.25124 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.89234e6 | + | 78222.6i | 0.377826 | + | 0.0102182i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.22684e7i | − | 1.58857i | −0.607547 | − | 0.794284i | \(-0.707846\pi\) | ||
0.607547 | − | 0.794284i | \(-0.292154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.40136e6i | − | 0.179871i | −0.995948 | − | 0.0899354i | \(-0.971334\pi\) | ||
0.995948 | − | 0.0899354i | \(-0.0286661\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.65441e6 | + | 6.28777e6i | −0.337740 | + | 0.800036i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.19128e6 | 0.654795 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.11633e7 | 1.39590 | 0.697950 | − | 0.716146i | \(-0.254096\pi\) | ||||
0.697950 | + | 0.716146i | \(0.254096\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.29554e6 | + | 1.01753e7i | −0.532502 | + | 1.26139i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.52450e6i | 0.310267i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 5.14508e6i | − | 0.626932i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.21187e6 | − | 4.09950e6i | 0.508844 | − | 0.495269i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.39598e7 | −1.67218 | −0.836091 | − | 0.548591i | \(-0.815164\pi\) | ||||
−0.836091 | + | 0.548591i | \(0.815164\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.67570e6 | −0.199025 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.61667e6 | − | 3.21542e6i | −0.897009 | − | 0.378677i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7.08900e6i | − | 0.827843i | −0.910313 | − | 0.413922i | \(-0.864159\pi\) | ||
0.910313 | − | 0.413922i | \(-0.135841\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 824574.i | 0.0954855i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.44373e7 | − | 6.09478e6i | −1.65787 | − | 0.699878i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.17685e7 | 1.34016 | 0.670079 | − | 0.742290i | \(-0.266260\pi\) | ||||
0.670079 | + | 0.742290i | \(0.266260\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00504e7 | −1.13501 | −0.567504 | − | 0.823371i | \(-0.692091\pi\) | ||||
−0.567504 | + | 0.823371i | \(0.692091\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.43503e6 | − | 5.29003e6i | 0.608708 | − | 0.592468i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 5.57162e6i | − | 0.618861i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 3.19698e6i | − | 0.352183i | −0.984374 | − | 0.176091i | \(-0.943655\pi\) | ||
0.984374 | − | 0.176091i | \(-0.0563454\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.06688e6 | − | 4.89603e6i | 0.225825 | − | 0.534935i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.20915e6 | −0.347766 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.41787e7 | −1.52400 | −0.761999 | − | 0.647578i | \(-0.775782\pi\) | ||||
−0.761999 | + | 0.647578i | \(0.775782\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 826802. | − | 1.95853e6i | 0.0881482 | − | 0.208805i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.12714e6i | 0.753707i | 0.926273 | + | 0.376853i | \(0.122994\pi\) | ||||
−0.926273 | + | 0.376853i | \(0.877006\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.78191e7i | − | 1.86922i | −0.355678 | − | 0.934609i | \(-0.615750\pi\) | ||
0.355678 | − | 0.934609i | \(-0.384250\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.61558e7 | − | 6.31129e6i | 1.68113 | − | 0.656733i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.80639e6 | 0.392910 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.93732e6 | −0.505581 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −586472. | − | 247582.i | −0.0595769 | − | 0.0251507i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.09690e6i | 0.211325i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 5.00865e6i | − | 0.500780i | −0.968145 | − | 0.250390i | \(-0.919441\pi\) | ||
0.968145 | − | 0.250390i | \(-0.0805589\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.44249e7 | + | 6.08954e6i | 1.43088 | + | 0.604054i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.06936e7 | −1.05242 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.30142e6 | −0.127078 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.36943e7 | − | 1.40697e7i | −1.32675 | − | 1.36311i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.66542e6i | 0.544611i | 0.962211 | + | 0.272306i | \(0.0877862\pi\) | ||||
−0.962211 | + | 0.272306i | \(0.912214\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.14723e7i | − | 1.09427i | −0.837046 | − | 0.547133i | \(-0.815719\pi\) | ||
0.837046 | − | 0.547133i | \(-0.184281\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.80083e6 | − | 4.26580e6i | 0.170441 | − | 0.403739i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.08061e7 | −1.01486 | −0.507432 | − | 0.861692i | \(-0.669405\pi\) | ||||
−0.507432 | + | 0.861692i | \(0.669405\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 682546. | 0.0636093 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.31904e6 | + | 5.49334e6i | −0.214465 | + | 0.508024i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.87285e7i | 1.71878i | 0.511318 | + | 0.859392i | \(0.329157\pi\) | ||||
−0.511318 | + | 0.859392i | \(0.670843\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.03116e6i | 0.640360i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.94935e6 | + | 5.08501e6i | 0.447337 | + | 0.459599i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.06692e6 | 0.544195 | 0.272098 | − | 0.962270i | \(-0.412283\pi\) | ||||
0.272098 | + | 0.962270i | \(0.412283\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 8.66576e6 | 0.771442 | 0.385721 | − | 0.922616i | \(-0.373953\pi\) | ||||
0.385721 | + | 0.922616i | \(0.373953\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.93554e6 | − | 1.23925e6i | −0.259360 | − | 0.109490i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 469360.i | 0.0411578i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.18580e7i | − | 2.77270i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.48164e7 | + | 6.25482e6i | 1.27990 | + | 0.540318i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.98583e6 | −0.770464 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.47083e7 | −1.25177 | −0.625886 | − | 0.779915i | \(-0.715262\pi\) | ||||
−0.625886 | + | 0.779915i | \(0.715262\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.00021e6 | − | 1.56268e6i | 0.337927 | − | 0.132011i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 8.29853e6i | − | 0.695872i | −0.937518 | − | 0.347936i | \(-0.886883\pi\) | ||
0.937518 | − | 0.347936i | \(-0.113117\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.02143e6i | − | 0.0850225i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.49509e6 | + | 1.30167e7i | −0.454053 | + | 1.07556i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1.26991e7 | −1.04165 | −0.520826 | − | 0.853663i | \(-0.674376\pi\) | ||||
−0.520826 | + | 0.853663i | \(0.674376\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.05550e6 | −0.330231 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −804842. | + | 1.90651e6i | −0.0650607 | + | 0.154116i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.46591e7i | − | 1.17641i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 9.85072e6i | − | 0.784825i | −0.919789 | − | 0.392413i | \(-0.871641\pi\) | ||
0.919789 | − | 0.392413i | \(-0.128359\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.62327e6 | + | 1.57996e6i | −0.128398 | + | 0.124972i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.85543e6 | −0.381299 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.15251e6 | −0.0898591 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.38080e6 | + | 3.96015e6i | 0.726184 | + | 0.306563i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.12185e7i | − | 0.862262i | −0.902289 | − | 0.431131i | \(-0.858115\pi\) | ||
0.902289 | − | 0.431131i | \(-0.141885\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.19359e6i | 0.0910891i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.79418e6 | + | 1.60173e6i | 0.287505 | + | 0.121372i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.45480e6 | 0.410422 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.40771e7 | −1.79882 | −0.899412 | − | 0.437101i | \(-0.856005\pi\) | ||||
−0.899412 | + | 0.437101i | \(0.856005\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 9.78460e6 | − | 9.52355e6i | 0.725887 | − | 0.706521i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.57446e7i | 2.63322i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.60151e6i | 0.336617i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.92243e6 | − | 1.87666e7i | 0.575520 | − | 1.36329i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.64759e7 | 1.18858 | 0.594289 | − | 0.804252i | \(-0.297434\pi\) | ||||
0.594289 | + | 0.804252i | \(0.297434\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.43959e6 | 0.246416 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.05149e6 | + | 7.22837e6i | −0.217103 | + | 0.514274i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 7.88807e6i | − | 0.557347i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 9.00670e6i | − | 0.632018i | −0.948756 | − | 0.316009i | \(-0.897657\pi\) | ||
0.948756 | − | 0.316009i | \(-0.102343\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.05493e7 | − | 9.72648e6i | 0.735196 | − | 0.677855i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.51024e6 | −0.173749 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.72333e7 | 1.18470 | 0.592348 | − | 0.805682i | \(-0.298201\pi\) | ||||
0.592348 | + | 0.805682i | \(0.298201\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.53868e6 | + | 649560.i | 0.105058 | + | 0.0443507i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.93784e6i | 0.402680i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.11962e6i | − | 0.0754154i | −0.999289 | − | 0.0377077i | \(-0.987994\pi\) | ||
0.999289 | − | 0.0377077i | \(-0.0120056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.67095e6 | − | 705401.i | −0.111794 | − | 0.0471944i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.11818e6 | −0.140764 | −0.0703818 | − | 0.997520i | \(-0.522422\pi\) | ||||
−0.0703818 | + | 0.997520i | \(0.522422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.09378e6 | 0.0722001 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.73211e6 | + | 8.97146e6i | 0.572556 | + | 0.588250i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 4.79559e6i | − | 0.312347i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.63493e7i | − | 1.70479i | −0.522902 | − | 0.852393i | \(-0.675150\pi\) | ||
0.522902 | − | 0.852393i | \(-0.324850\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.91291e6 | − | 1.40065e7i | 0.380026 | − | 0.900206i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.10144e6 | −0.134168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.02559e6 | 0.255323 | 0.127662 | − | 0.991818i | \(-0.459253\pi\) | ||||
0.127662 | + | 0.991818i | \(0.459253\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.28122e6 | + | 1.25101e7i | −0.332759 | + | 0.788238i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.11368e7i | 1.32305i | 0.749922 | + | 0.661527i | \(0.230091\pi\) | ||||
−0.749922 | + | 0.661527i | \(0.769909\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 70598.9i | − | 0.00439022i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.85216e6 | + | 2.93034e6i | 0.176206 | + | 0.181036i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.94468e6 | 0.119360 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.28275e7 | −0.782217 | −0.391108 | − | 0.920345i | \(-0.627908\pi\) | ||||
−0.391108 | + | 0.920345i | \(0.627908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.80020e6 | − | 2.44858e6i | −0.351404 | − | 0.148347i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.82599e6i | − | 0.109913i | −0.998489 | − | 0.0549566i | \(-0.982498\pi\) | ||
0.998489 | − | 0.0549566i | \(-0.0175021\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.85040e6i | 0.529308i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 3.91287e6 | + | 1.65184e6i | 0.232511 | + | 0.0981556i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −656025. | −0.0387326 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.53713e7 | 0.901743 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.58990e6 | − | 2.45485e7i | −0.558997 | − | 1.43094i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2.00962e6i | − | 0.116396i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.74454e7i | 1.57955i | 0.613398 | + | 0.789774i | \(0.289802\pi\) | ||||
−0.613398 | + | 0.789774i | \(0.710198\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 5.42385e6 | − | 1.28480e7i | 0.310181 | − | 0.734755i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.04254e7 | −0.592452 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.56021e7 | −1.44575 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −7.31659e6 | + | 1.73315e7i | −0.410573 | + | 0.972565i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.81269e7i | − | 1.56847i | −0.620465 | − | 0.784234i | \(-0.713056\pi\) | ||
0.620465 | − | 0.784234i | \(-0.286944\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.23271e6i | − | 0.123727i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.35270e7 | − | 1.31661e7i | 0.744938 | − | 0.725064i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.55544e6 | −0.304039 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00120e7 | 0.544542 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.18834e7 | + | 9.23817e6i | 1.18285 | + | 0.499347i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.60102e7i | − | 1.39724i | −0.715491 | − | 0.698622i | \(-0.753797\pi\) | ||
0.715491 | − | 0.698622i | \(-0.246203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.50958e6i | 0.133983i | 0.997754 | + | 0.0669913i | \(0.0213400\pi\) | ||||
−0.997754 | + | 0.0669913i | \(0.978660\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.52854e6 | + | 2.33390e6i | 0.293349 | + | 0.123839i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.24554e6 | 0.171156 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.42887e6 | −0.0748922 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.62495e6 | + | 4.50156e6i | −0.240933 | + | 0.234506i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.92935e6i | 0.307007i | 0.988148 | + | 0.153504i | \(0.0490557\pi\) | ||||
−0.988148 | + | 0.153504i | \(0.950944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.73575e6i | 0.449574i | 0.974408 | + | 0.224787i | \(0.0721686\pi\) | ||||
−0.974408 | + | 0.224787i | \(0.927831\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.30764e6 | + | 3.09752e6i | −0.0668886 | + | 0.158445i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −6.46971e6 | −0.328943 | −0.164472 | − | 0.986382i | \(-0.552592\pi\) | ||||
−0.164472 | + | 0.986382i | \(0.552592\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.72888e7 | 0.873731 | 0.436865 | − | 0.899527i | \(-0.356089\pi\) | ||||
0.436865 | + | 0.899527i | \(0.356089\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.46546e6 | + | 1.29466e7i | −0.274552 | + | 0.650357i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 905445.i | − | 0.0452115i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 7.69461e6i | − | 0.381918i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.07599e7 | + | 2.75434e7i | 0.530875 | + | 1.35895i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.19248e6 | 0.205621 | 0.102810 | − | 0.994701i | \(-0.467217\pi\) | ||||
0.102810 | + | 0.994701i | \(0.467217\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.78965e7 | −1.36006 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.25268e7 | + | 5.28824e6i | 0.607113 | + | 0.256296i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 3.45796e6i | − | 0.166601i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.11806e6i | 0.293025i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.41827e6 | − | 2.28735e6i | −0.257983 | − | 0.108909i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.54606e7 | 1.20516 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.78255e7 | −1.77997 | −0.889985 | − | 0.455990i | \(-0.849285\pi\) | ||||
−0.889985 | + | 0.455990i | \(0.849285\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.62349e6 | + | 1.66799e6i | 0.0759512 | + | 0.0780331i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.24919e7i | 0.580998i | 0.956875 | + | 0.290499i | \(0.0938213\pi\) | ||||
−0.956875 | + | 0.290499i | \(0.906179\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.06556e6i | 0.234231i | 0.993118 | + | 0.117116i | \(0.0373648\pi\) | ||||
−0.993118 | + | 0.117116i | \(0.962635\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −907891. | + | 2.15061e6i | −0.0417374 | + | 0.0988675i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.86177e7 | −1.30800 | −0.653999 | − | 0.756495i | \(-0.726910\pi\) | ||||
−0.653999 | + | 0.756495i | \(0.726910\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.02655e7 | 0.466488 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −7.74592e6 | + | 1.83485e7i | −0.349965 | + | 0.828997i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.06898e7i | 0.480197i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.69178e7i | 0.755613i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.53307e6 | − | 3.62991e6i | −0.156898 | − | 0.161198i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.31196e6 | 0.411170 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.65453e7 | −1.16544 | −0.582719 | − | 0.812674i | \(-0.698011\pi\) | ||||
−0.582719 | + | 0.812674i | \(0.698011\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1.56292e7 | + | 6.59797e6i | 0.682285 | + | 0.288030i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.02490e7i | − | 0.878951i | −0.898255 | − | 0.439476i | \(-0.855164\pi\) | ||
0.898255 | − | 0.439476i | \(-0.144836\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 3.11513e7i | − | 1.34454i | −0.740306 | − | 0.672271i | \(-0.765319\pi\) | ||
0.740306 | − | 0.672271i | \(-0.234681\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −2.29920e6 | − | 970619.i | −0.0986776 | − | 0.0416573i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.00955e7 | −0.857608 | −0.428804 | − | 0.903398i | \(-0.641065\pi\) | ||||
−0.428804 | + | 0.903398i | \(0.641065\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.17423e7 | 0.498310 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −303701. | + | 1.12296e7i | −0.0128160 | + | 0.473881i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.27089e6i | − | 0.0533311i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.56468e6i | 0.0652934i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.50470e7 | + | 3.56434e7i | −0.624410 | + | 1.47910i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 5.43133e7 | 2.24134 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.01989e7 | 0.418542 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1.97745e6 | + | 4.68417e6i | −0.0807022 | + | 0.191167i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.77084e7i | 0.718717i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.84073e6i | − | 0.114660i | −0.998355 | − | 0.0573299i | \(-0.981741\pi\) | ||
0.998355 | − | 0.0573299i | \(-0.0182587\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.93850e7 | − | 1.88679e7i | 0.778138 | − | 0.757378i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.98893e6 | 0.279007 | 0.139503 | − | 0.990222i | \(-0.455449\pi\) | ||||
0.139503 | + | 0.990222i | \(0.455449\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.80143e6 | −0.389146 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3.02694e7 | + | 1.27784e7i | 1.19523 | + | 0.504571i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 7.72075e6i | − | 0.303205i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.42936e7i | 0.558281i | 0.960250 | + | 0.279141i | \(0.0900496\pi\) | ||||
−0.960250 | + | 0.279141i | \(0.909950\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.01110e6 | − | 1.27115e6i | −0.116971 | − | 0.0493797i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.37953e7 | 1.69209 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.30408e6 | 0.242252 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.22235e7 | − | 1.18974e7i | 0.467192 | − | 0.454727i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.82939e6i | 0.107561i | 0.998553 | + | 0.0537804i | \(0.0171271\pi\) | ||||
−0.998553 | + | 0.0537804i | \(0.982873\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 515393.i | − | 0.0194879i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −8.91194e6 | + | 2.11106e7i | −0.335172 | + | 0.793955i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.20143e6 | −0.119761 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.90222e7 | −1.82408 | −0.912041 | − | 0.410100i | \(-0.865494\pi\) | ||||
−0.912041 | + | 0.410100i | \(0.865494\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.44541e7 | + | 3.42388e7i | −0.534967 | + | 1.26723i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.87482e7i | 1.05837i | 0.848507 | + | 0.529184i | \(0.177502\pi\) | ||||
−0.848507 | + | 0.529184i | \(0.822498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.39938e7i | 0.512456i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.71487e6 | − | 3.01382e6i | 0.281028 | − | 0.109784i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.26394e6 | 0.118268 | 0.0591339 | − | 0.998250i | \(-0.481166\pi\) | ||||
0.0591339 | + | 0.998250i | \(0.481166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.58283e7 | −0.570518 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.03909e7 | − | 1.70512e7i | −1.44821 | − | 0.611371i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.40785e7i | 1.21548i | 0.794135 | + | 0.607741i | \(0.207924\pi\) | ||||
−0.794135 | + | 0.607741i | \(0.792076\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.95375e7i | 0.693204i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.90089e7 | + | 8.02472e6i | 0.670931 | + | 0.283237i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.45324e6 | 0.156362 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.23103e7 | −1.12858 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.65877e7 | − | 1.70424e7i | −0.576395 | − | 0.592194i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.16168e7i | 1.09295i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 213581.i | − | 0.00734506i | −0.999993 | − | 0.00367253i | \(-0.998831\pi\) | ||
0.999993 | − | 0.00367253i | \(-0.00116901\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 490771. | − | 1.16254e6i | 0.0167907 | − | 0.0397738i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.63347e6 | 0.259821 | 0.129910 | − | 0.991526i | \(-0.458531\pi\) | ||||
0.129910 | + | 0.991526i | \(0.458531\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.33162e6 | 0.180542 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.72566e6 | + | 8.82534e6i | −0.125514 | + | 0.297317i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.42456e7i | − | 0.812638i | −0.913731 | − | 0.406319i | \(-0.866812\pi\) | ||
0.913731 | − | 0.406319i | \(-0.133188\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.47784e7i | 0.492800i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −244198. | − | 250891.i | −0.00810157 | − | 0.00832363i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.16068e7 | 0.713192 | 0.356596 | − | 0.934259i | \(-0.383937\pi\) | ||||
0.356596 | + | 0.934259i | \(0.383937\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.36667e7 | −0.777227 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.16629e6 | − | 1.75882e6i | −0.136131 | − | 0.0574684i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.04794e7i | 0.990868i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.65466e7i | 0.535211i | 0.963529 | + | 0.267606i | \(0.0862324\pi\) | ||||
−0.963529 | + | 0.267606i | \(0.913768\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.36032e7 | − | 5.74265e6i | −0.437791 | − | 0.184816i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.48600e7 | −1.43649 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.55649e7 | −0.495915 | −0.247957 | − | 0.968771i | \(-0.579759\pi\) | ||||
−0.247957 | + | 0.968771i | \(0.579759\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.96190e7 | − | 7.66417e6i | 0.621961 | − | 0.242969i |
(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 | 336.6.h.b.239.16 | yes | 40 | |
3.2 | odd | 2 | inner | 336.6.h.b.239.26 | yes | 40 | |
4.3 | odd | 2 | inner | 336.6.h.b.239.25 | yes | 40 | |
12.11 | even | 2 | inner | 336.6.h.b.239.15 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
336.6.h.b.239.15 | ✓ | 40 | 12.11 | even | 2 | inner | |
336.6.h.b.239.16 | yes | 40 | 1.1 | even | 1 | trivial | |
336.6.h.b.239.25 | yes | 40 | 4.3 | odd | 2 | inner | |
336.6.h.b.239.26 | yes | 40 | 3.2 | odd | 2 | inner |