Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [160,6,Mod(49,160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(160, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("160.49");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 160 = 2^{5} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 160.f (of order \(2\), degree \(1\), 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: | \(25.6614111701\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Character | \(\chi\) | \(=\) | 160.49 |
Dual form | 160.6.f.a.49.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/160\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(97\) | \(101\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | −28.9041 | −1.85420 | −0.927100 | − | 0.374814i | \(-0.877707\pi\) | ||||
−0.927100 | + | 0.374814i | \(0.877707\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −40.5064 | + | 38.5257i | −0.724601 | + | 0.689169i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 128.100i | − | 0.988105i | −0.869432 | − | 0.494053i | \(-0.835515\pi\) | ||
0.869432 | − | 0.494053i | \(-0.164485\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 592.448 | 2.43806 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 433.553i | − | 1.08034i | −0.841556 | − | 0.540170i | \(-0.818360\pi\) | ||
0.841556 | − | 0.540170i | \(-0.181640\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 78.5787 | 0.128957 | 0.0644787 | − | 0.997919i | \(-0.479462\pi\) | ||||
0.0644787 | + | 0.997919i | \(0.479462\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1170.80 | − | 1113.55i | 1.34356 | − | 1.27786i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1487.27i | − | 1.24815i | −0.781363 | − | 0.624077i | \(-0.785475\pi\) | ||
0.781363 | − | 0.624077i | \(-0.214525\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 98.3252i | 0.0624857i | 0.999512 | + | 0.0312429i | \(0.00994653\pi\) | ||||
−0.999512 | + | 0.0312429i | \(0.990053\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3702.61i | 1.83214i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2363.01i | 0.931419i | 0.884938 | + | 0.465710i | \(0.154201\pi\) | ||||
−0.884938 | + | 0.465710i | \(0.845799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 156.542 | − | 3121.08i | 0.0500935 | − | 0.998745i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10100.5 | −2.66645 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1024.44i | − | 0.226199i | −0.993584 | − | 0.113100i | \(-0.963922\pi\) | ||
0.993584 | − | 0.113100i | \(-0.0360779\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4308.96 | −0.805320 | −0.402660 | − | 0.915350i | \(-0.631914\pi\) | ||||
−0.402660 | + | 0.915350i | \(0.631914\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12531.5i | 2.00317i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4935.13 | + | 5188.86i | 0.680971 | + | 0.715982i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6647.54 | 0.798283 | 0.399141 | − | 0.916889i | \(-0.369308\pi\) | ||||
0.399141 | + | 0.916889i | \(0.369308\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2271.25 | −0.239113 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4441.16 | −0.412608 | −0.206304 | − | 0.978488i | \(-0.566144\pi\) | ||||
−0.206304 | + | 0.978488i | \(0.566144\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7066.93 | −0.582854 | −0.291427 | − | 0.956593i | \(-0.594130\pi\) | ||||
−0.291427 | + | 0.956593i | \(0.594130\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −23998.0 | + | 22824.5i | −1.76662 | + | 1.68023i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 15560.5i | 1.02750i | 0.857941 | + | 0.513748i | \(0.171743\pi\) | ||||
−0.857941 | + | 0.513748i | \(0.828257\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 397.456 | 0.0236482 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 42988.3i | 2.31433i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −26793.6 | −1.31021 | −0.655105 | − | 0.755538i | \(-0.727376\pi\) | ||||
−0.655105 | + | 0.755538i | \(0.727376\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 16702.9 | + | 17561.7i | 0.744536 | + | 0.782816i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2842.00i | − | 0.115861i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 32902.0i | − | 1.23053i | −0.788320 | − | 0.615266i | \(-0.789049\pi\) | ||
0.788320 | − | 0.615266i | \(-0.210951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19242.7i | 0.662126i | 0.943609 | + | 0.331063i | \(0.107407\pi\) | ||||
−0.943609 | + | 0.331063i | \(0.892593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 75892.5i | − | 2.40906i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3182.94 | + | 3027.30i | −0.0934427 | + | 0.0888734i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1066.77 | 0.0290326 | 0.0145163 | − | 0.999895i | \(-0.495379\pi\) | ||||
0.0145163 | + | 0.999895i | \(0.495379\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 68300.6i | − | 1.72704i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12397.2 | −0.291862 | −0.145931 | − | 0.989295i | \(-0.546618\pi\) | ||||
−0.145931 | + | 0.989295i | \(0.546618\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 37248.9i | − | 0.818100i | −0.912512 | − | 0.409050i | \(-0.865860\pi\) | ||
0.912512 | − | 0.409050i | \(-0.134140\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4524.72 | + | 90212.0i | −0.0928834 | + | 1.85187i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −55538.0 | −1.06749 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 50784.5 | 0.915510 | 0.457755 | − | 0.889078i | \(-0.348654\pi\) | ||||
0.457755 | + | 0.889078i | \(0.348654\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 147981. | 2.50607 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −38676.4 | −0.616242 | −0.308121 | − | 0.951347i | \(-0.599700\pi\) | ||||
−0.308121 | + | 0.951347i | \(0.599700\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 57298.2 | + | 60244.1i | 0.860188 | + | 0.904413i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 29610.5i | 0.419419i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −132425. | −1.77213 | −0.886067 | − | 0.463558i | \(-0.846573\pi\) | ||||
−0.886067 | + | 0.463558i | \(0.846573\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10065.9i | − | 0.127424i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 124547. | 1.49322 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3788.05 | − | 3982.80i | −0.0430632 | − | 0.0452772i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 95071.6i | 1.02594i | 0.858407 | + | 0.512969i | \(0.171455\pi\) | ||||
−0.858407 | + | 0.512969i | \(0.828545\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 256858.i | − | 2.63393i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 49284.2i | 0.480734i | 0.970682 | + | 0.240367i | \(0.0772677\pi\) | ||||
−0.970682 | + | 0.240367i | \(0.922732\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 143185.i | 1.32986i | 0.746906 | + | 0.664930i | \(0.231539\pi\) | ||||
−0.746906 | + | 0.664930i | \(0.768461\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −142646. | − | 149980.i | −1.26266 | − | 1.32757i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 168772. | 1.42508 | 0.712541 | − | 0.701630i | \(-0.247544\pi\) | ||||
0.712541 | + | 0.701630i | \(0.247544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 169878.i | − | 1.36953i | −0.728763 | − | 0.684766i | \(-0.759905\pi\) | ||
0.728763 | − | 0.684766i | \(-0.240095\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −192141. | −1.48018 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 176203.i | 1.29813i | 0.760733 | + | 0.649064i | \(0.224839\pi\) | ||||
−0.760733 | + | 0.649064i | \(0.775161\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −91036.5 | − | 95717.0i | −0.641905 | − | 0.674908i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 46553.8 | 0.314406 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −190519. | −1.23331 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −26917.2 | −0.167135 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 128368. | 0.765057 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 113901. | + | 132455.i | 0.652005 | + | 0.758214i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 28671.3i | 0.157739i | 0.996885 | + | 0.0788694i | \(0.0251310\pi\) | ||||
−0.996885 | + | 0.0788694i | \(0.974869\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 204263. | 1.08073 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 42028.2i | 0.213975i | 0.994260 | + | 0.106987i | \(0.0341204\pi\) | ||||
−0.994260 | + | 0.106987i | \(0.965880\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12595.4 | 0.0617425 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 409135. | − | 389129.i | 1.93211 | − | 1.83763i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 49062.2i | 0.223329i | 0.993746 | + | 0.111665i | \(0.0356182\pi\) | ||||
−0.993746 | + | 0.111665i | \(0.964382\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 85502.0i | 0.375352i | 0.982231 | + | 0.187676i | \(0.0600956\pi\) | ||||
−0.982231 | + | 0.187676i | \(0.939904\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 449764.i | − | 1.90518i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 34068.0i | − | 0.139318i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 39467.2 | + | 41496.4i | 0.155889 | + | 0.163904i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11488.1 | −0.0438486 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 29442.1i | 0.108643i | 0.998523 | + | 0.0543216i | \(0.0172996\pi\) | ||||
−0.998523 | + | 0.0543216i | \(0.982700\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −131978. | −0.471041 | −0.235520 | − | 0.971869i | \(-0.575679\pi\) | ||||
−0.235520 | + | 0.971869i | \(0.575679\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 881132.i | − | 3.04307i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 174541. | − | 166006.i | 0.583536 | − | 0.555001i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 360997. | 1.16884 | 0.584419 | − | 0.811452i | \(-0.301322\pi\) | ||||
0.584419 | + | 0.811452i | \(0.301322\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 774444. | 2.42939 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 302701. | 0.920340 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 139344. | 0.410788 | 0.205394 | − | 0.978679i | \(-0.434152\pi\) | ||||
0.205394 | + | 0.978679i | \(0.434152\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −482784. | − | 507605.i | −1.38052 | − | 1.45150i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 440004.i | 1.22086i | 0.792071 | + | 0.610429i | \(0.209003\pi\) | ||||
−0.792071 | + | 0.610429i | \(0.790997\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −365118. | −0.983370 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 58252.6i | 0.152344i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −711657. | −1.80782 | −0.903910 | − | 0.427722i | \(-0.859316\pi\) | ||||
−0.903910 | + | 0.427722i | \(0.859316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −399809. | − | 20053.0i | −0.986865 | − | 0.0494977i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 951005.i | 2.28165i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 813579.i | 1.89787i | 0.315468 | + | 0.948936i | \(0.397839\pi\) | ||||
−0.315468 | + | 0.948936i | \(0.602161\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 415019.i | 0.941612i | 0.882237 | + | 0.470806i | \(0.156037\pi\) | ||||
−0.882237 | + | 0.470806i | \(0.843963\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 556192.i | − | 1.22771i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −269268. | + | 256101.i | −0.578437 | + | 0.550151i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −644811. | −1.34843 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.29387e6i | 2.63473i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −598242. | −1.18657 | −0.593285 | − | 0.804992i | \(-0.702169\pi\) | ||||
−0.593285 | + | 0.804992i | \(0.702169\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 150045.i | 0.289954i | 0.989435 | + | 0.144977i | \(0.0463107\pi\) | ||||
−0.989435 | + | 0.144977i | \(0.953689\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 92000.2 | − | 87501.4i | 0.173262 | − | 0.164789i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 120180. | 0.220630 | 0.110315 | − | 0.993897i | \(-0.464814\pi\) | ||||
0.110315 | + | 0.993897i | \(0.464814\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −994244. | −1.77976 | −0.889878 | − | 0.456199i | \(-0.849211\pi\) | ||||
−0.889878 | + | 0.456199i | \(0.849211\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −30834.2 | −0.0538322 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −131230. | −0.223509 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 179896. | − | 171099.i | 0.298976 | − | 0.284356i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.39996e6i | 2.27086i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 42629.2 | 0.0675059 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 854741.i | − | 1.32169i | −0.750524 | − | 0.660843i | \(-0.770199\pi\) | ||
0.750524 | − | 0.660843i | \(-0.229801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 358330. | 0.541171 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 286256. | − | 272258.i | 0.422336 | − | 0.401684i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 551977.i | 0.795741i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.07665e6i | 1.51692i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 116868.i | − | 0.160959i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 135422.i | 0.182359i | 0.995834 | + | 0.0911797i | \(0.0290638\pi\) | ||||
−0.995834 | + | 0.0911797i | \(0.970936\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 92743.2 | − | 1.84908e6i | 0.122131 | − | 2.43500i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −538983. | −0.694241 | −0.347120 | − | 0.937821i | \(-0.612840\pi\) | ||||
−0.347120 | + | 0.937821i | \(0.612840\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.04360e6i | 1.31507i | 0.753426 | + | 0.657533i | \(0.228400\pi\) | ||||
−0.753426 | + | 0.657533i | \(0.771600\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.60528e6 | 1.97934 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 466145.i | 0.562512i | 0.959633 | + | 0.281256i | \(0.0907510\pi\) | ||||
−0.959633 | + | 0.281256i | \(0.909249\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −599481. | − | 630302.i | −0.708118 | − | 0.744525i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.46788e6 | −1.69754 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.49073e6 | 1.68812 | 0.844061 | − | 0.536248i | \(-0.180159\pi\) | ||||
0.844061 | + | 0.536248i | \(0.180159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −248170. | −0.275237 | −0.137619 | − | 0.990485i | \(-0.543945\pi\) | ||||
−0.137619 | + | 0.990485i | \(0.543945\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.82284e6 | −1.98031 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −16099.5 | + | 15312.3i | −0.0171355 | + | 0.0162976i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7726.27i | 0.00805800i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.11791e6 | 1.14264 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.70931e6i | 1.71252i | 0.516545 | + | 0.856260i | \(0.327218\pi\) | ||||
−0.516545 | + | 0.856260i | \(0.672782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.02449e6 | 1.00625 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.65615e6 | − | 1.74130e6i | −1.59496 | − | 1.67696i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 445935.i | − | 0.421152i | −0.977578 | − | 0.210576i | \(-0.932466\pi\) | ||
0.977578 | − | 0.210576i | \(-0.0675339\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 851549.i | − | 0.788787i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 606928.i | − | 0.551487i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 616116.i | − | 0.549254i | −0.961551 | − | 0.274627i | \(-0.911446\pi\) | ||
0.961551 | − | 0.274627i | \(-0.0885544\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.08531e6 | − | 1.03224e6i | 0.949379 | − | 0.902955i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 3.82764e6 | 3.28589 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 945945.i | − | 0.797049i | −0.917158 | − | 0.398524i | \(-0.869522\pi\) | ||
0.917158 | − | 0.398524i | \(-0.130478\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 859288. | 0.710748 | 0.355374 | − | 0.934724i | \(-0.384354\pi\) | ||||
0.355374 | + | 0.934724i | \(0.384354\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 290946.i | 0.236269i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.35315e6 | − | 67869.4i | −1.07898 | − | 0.0541180i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.32686e6 | 1.03903 | 0.519514 | − | 0.854462i | \(-0.326113\pi\) | ||||
0.519514 | + | 0.854462i | \(0.326113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.55284e6 | −1.96342 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −651484. | −0.492196 | −0.246098 | − | 0.969245i | \(-0.579148\pi\) | ||||
−0.246098 | + | 0.969245i | \(0.579148\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.94978e6 | 1.44717 | 0.723585 | − | 0.690235i | \(-0.242493\pi\) | ||||
0.723585 | + | 0.690235i | \(0.242493\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 109490. | + | 115119.i | 0.0798478 | + | 0.0839531i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 568912.i | 0.407700i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −792120. | −0.557887 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 2.74796e6i | − | 1.90230i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.80561e6 | −1.22872 | −0.614362 | − | 0.789024i | \(-0.710587\pi\) | ||||
−0.614362 | + | 0.789024i | \(0.710587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.26757e6 | + | 1.33274e6i | 0.848044 | + | 0.891645i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.37910e6i | 2.88067i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 185682.i | 0.120113i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 905272.i | 0.575921i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.42452e6i | − | 0.891377i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −741337. | − | 779451.i | −0.456316 | − | 0.479777i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −333416. | −0.201902 | −0.100951 | − | 0.994891i | \(-0.532188\pi\) | ||||
−0.100951 | + | 0.994891i | \(0.532188\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 4.13865e6i | − | 2.46583i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −126148. | −0.0739573 | −0.0369787 | − | 0.999316i | \(-0.511773\pi\) | ||||
−0.0369787 | + | 0.999316i | \(0.511773\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 1.61358e6i | − | 0.930955i | −0.885060 | − | 0.465477i | \(-0.845883\pi\) | ||
0.885060 | − | 0.465477i | \(-0.154117\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.92381e6 | + | 3.07413e6i | 1.66025 | + | 1.74561i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.62558e6 | −0.908571 | −0.454286 | − | 0.890856i | \(-0.650105\pi\) | ||||
−0.454286 | + | 0.890856i | \(0.650105\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −444149. | −0.244372 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.87820e6 | −2.64239 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 146236. | 0.0779918 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12300.9 | − | 245250.i | 0.00645993 | − | 0.128796i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.91019e6i | 2.53939i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.99330e6 | 1.01527 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 325105.i | 0.163100i | 0.996669 | + | 0.0815499i | \(0.0259870\pi\) | ||||
−0.996669 | + | 0.0815499i | \(0.974013\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.93833e6 | 1.94626 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −43211.2 | + | 41098.2i | −0.0210370 | + | 0.0200083i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 805090.i | − | 0.386162i | −0.981183 | − | 0.193081i | \(-0.938152\pi\) | ||
0.981183 | − | 0.193081i | \(-0.0618480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 5.09300e6i | − | 2.40699i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.86816e6i | 0.870020i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.20389e6i | − | 1.01147i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.63133e6 | + | 2.76661e6i | 1.19022 | + | 1.25141i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.17010e6 | −0.967512 | −0.483756 | − | 0.875203i | \(-0.660728\pi\) | ||||
−0.483756 | + | 0.875203i | \(0.660728\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 3.51347e6i | − | 1.54409i | −0.635569 | − | 0.772044i | \(-0.719234\pi\) | ||
0.635569 | − | 0.772044i | \(-0.280766\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −793684. | −0.343859 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 2.21866e6i | − | 0.947665i | −0.880615 | − | 0.473833i | \(-0.842870\pi\) | ||
0.880615 | − | 0.473833i | \(-0.157130\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 502166. | − | 477611.i | 0.211484 | − | 0.201142i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.50679e6 | 2.28680 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.82259e6 | 0.746366 | 0.373183 | − | 0.927758i | \(-0.378266\pi\) | ||||
0.373183 | + | 0.927758i | \(0.378266\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.46643e6 | 0.996096 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 778019. | 0.309901 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.43504e6 | + | 1.50882e6i | 0.563809 | + | 0.592796i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.02561e6i | − | 0.785036i | −0.919744 | − | 0.392518i | \(-0.871604\pi\) | ||
0.919744 | − | 0.392518i | \(-0.128396\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.63116e6 | −1.00596 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.43225e6i | 1.29462i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.39891e6 | −1.26493 | −0.632466 | − | 0.774588i | \(-0.717957\pi\) | ||||
−0.632466 | + | 0.774588i | \(0.717957\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.29220e6 | − | 3.82848e6i | −1.20895 | − | 1.40588i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 80499.2i | − | 0.0291701i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 3.13155e6i | − | 1.11986i | −0.828542 | − | 0.559928i | \(-0.810829\pi\) | ||
0.828542 | − | 0.559928i | \(-0.189171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 828719.i | − | 0.292479i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.68971e6i | 0.588592i | 0.955714 | + | 0.294296i | \(0.0950852\pi\) | ||||
−0.955714 | + | 0.294296i | \(0.904915\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.24965e6 | − | 2.13964e6i | 0.773504 | − | 0.735680i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −4.18679e6 | −1.42103 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.88788e6i | 1.30268i | 0.758784 | + | 0.651342i | \(0.225794\pi\) | ||||
−0.758784 | + | 0.651342i | \(0.774206\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.51443e6 | 1.16255 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 1.21479e6i | − | 0.396752i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.05710e6 | + | 1.95651e6i | −0.663380 | + | 0.630941i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 213582. | 0.0680123 | 0.0340061 | − | 0.999422i | \(-0.489173\pi\) | ||||
0.0340061 | + | 0.999422i | \(0.489173\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −364060. | −0.114483 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.71761e6 | 1.15452 | 0.577261 | − | 0.816560i | \(-0.304121\pi\) | ||||
0.577261 | + | 0.816560i | \(0.304121\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −338593. | −0.103852 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.99419e6 | + | 5.70107e6i | −1.81590 | + | 1.72711i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 2.88206e6i | − | 0.862417i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.38621e6 | −0.409752 | −0.204876 | − | 0.978788i | \(-0.565679\pi\) | ||||
−0.204876 | + | 0.978788i | \(0.565679\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 1.41810e6i | − | 0.414097i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.21474e6 | −1.21589 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.56664e6 | − | 1.49004e6i | 0.446530 | − | 0.424695i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 2.47136e6i | − | 0.695979i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 721117.i | − | 0.200665i | −0.994954 | − | 0.100332i | \(-0.968009\pi\) | ||
0.994954 | − | 0.100332i | \(-0.0319906\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 1.36768e6i | − | 0.376079i | −0.982161 | − | 0.188040i | \(-0.939787\pi\) | ||
0.982161 | − | 0.188040i | \(-0.0602133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.21882e6i | 2.50510i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.64189e6 | − | 232821.i | −1.24659 | − | 0.0625244i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.46498e6 | 0.654250 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 984707.i | 0.258323i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.51906e6 | 0.653198 | 0.326599 | − | 0.945163i | \(-0.394097\pi\) | ||||
0.326599 | + | 0.945163i | \(0.394097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.29790e6i | 1.10163i | 0.834626 | + | 0.550817i | \(0.185684\pi\) | ||||
−0.834626 | + | 0.550817i | \(0.814316\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.14077e6 | − | 1.19942e6i | −0.289050 | − | 0.303911i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −232343. | −0.0582004 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 386299. | 0.0956670 | 0.0478335 | − | 0.998855i | \(-0.484768\pi\) | ||||
0.0478335 | + | 0.998855i | \(0.484768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 235472. | 0.0576558 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.13129e6 | 0.273884 | 0.136942 | − | 0.990579i | \(-0.456273\pi\) | ||||
0.136942 | + | 0.990579i | \(0.456273\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.36408e6 | − | 5.10178e6i | 1.28409 | − | 1.22130i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 850998.i | − | 0.201446i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.41752e6 | 1.03410 | 0.517051 | − | 0.855955i | \(-0.327030\pi\) | ||||
0.517051 | + | 0.855955i | \(0.327030\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.92548e6i | 0.445757i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.81470e6 | 0.873404 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 387796. | + | 407734.i | 0.0878163 | + | 0.0923312i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.26658e6i | 0.507668i | 0.967248 | + | 0.253834i | \(0.0816917\pi\) | ||||
−0.967248 | + | 0.253834i | \(0.918308\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.50222e7i | 3.32814i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.97491e6i | 1.96688i | 0.181233 | + | 0.983440i | \(0.441991\pi\) | ||||
−0.181233 | + | 0.983440i | \(0.558009\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.13135e6i | 0.462063i | 0.972946 | + | 0.231032i | \(0.0742101\pi\) | ||||
−0.972946 | + | 0.231032i | \(0.925790\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.04495e6 | + | 4.79825e6i | −1.08199 | + | 1.02908i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.21641e6 | −0.258099 | −0.129050 | − | 0.991638i | \(-0.541193\pi\) | ||||
−0.129050 | + | 0.991638i | \(0.541193\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 136653.i | − | 0.0286872i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.04343e7 | −2.16726 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.06389e6i | 0.629680i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 306881. | + | 15392.1i | 0.0624073 | + | 0.00313013i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.58738e7 | −3.19437 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.14993e6 | −1.82213 | −0.911065 | − | 0.412264i | \(-0.864738\pi\) | ||||
−0.911065 | + | 0.412264i | \(0.864738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 522355. | 0.102945 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.74929e6 | −1.70650 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.66270e6 | − | 3.85101e6i | −0.707045 | − | 0.743396i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 5.29419e6i | − | 1.01153i | −0.862672 | − | 0.505763i | \(-0.831211\pi\) | ||
0.862672 | − | 0.505763i | \(-0.168789\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.02760e6 | −0.761684 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.58951e6i | 1.04633i | 0.852231 | + | 0.523166i | \(0.175249\pi\) | ||||
−0.852231 | + | 0.523166i | \(0.824751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.52362e6 | −0.282332 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 9.89562e6 | + | 1.04044e7i | 1.81522 | + | 1.90855i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.58808e6i | 0.288390i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.40479e6i | 0.612123i | 0.952012 | + | 0.306062i | \(0.0990114\pi\) | ||||
−0.952012 | + | 0.306062i | \(0.900989\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − | 1.27179e7i | − | 2.26372i | ||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 1.05370e7i | − | 1.85693i | −0.371421 | − | 0.928465i | \(-0.621129\pi\) | ||
0.371421 | − | 0.928465i | \(-0.378871\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.89871e6 | − | 1.99633e6i | −0.331307 | − | 0.348340i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.05534e7 | 1.82336 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.81588e6i | 1.33716i | 0.743640 | + | 0.668580i | \(0.233098\pi\) | ||||
−0.743640 | + | 0.668580i | \(0.766902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.77158e6 | −0.808369 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 993134.i | − | 0.166615i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.51632e6 | − | 5.79993e6i | −0.916498 | − | 0.963618i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.74632e6 | 1.11005 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.05698e7 | 3.35206 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −977378. | −0.157750 | −0.0788748 | − | 0.996885i | \(-0.525133\pi\) | ||||
−0.0788748 | + | 0.996885i | \(0.525133\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.82809e6 | 1.09155 | 0.545777 | − | 0.837931i | \(-0.316235\pi\) | ||||
0.545777 | + | 0.837931i | \(0.316235\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.15561e7 | + | 579615.i | 1.82984 | + | 0.0917786i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.40860e6i | 1.00516i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 852544. | 0.132458 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1.94928e7i | − | 3.00011i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −348981. | −0.0532088 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.83634e6 | + | 6.50204e6i | −1.03262 | + | 0.982122i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 2.35158e7i | − | 3.51904i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 172318.i | − | 0.0255481i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 4.14464e6i | − | 0.608827i | −0.952540 | − | 0.304414i | \(-0.901540\pi\) | ||
0.952540 | − | 0.304414i | \(-0.0984605\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.19958e7i | − | 1.74594i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 6.54468e6 | + | 6.88117e6i | 0.943838 | + | 0.992364i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.25850e6 | −0.322739 | −0.161369 | − | 0.986894i | \(-0.551591\pi\) | ||||
−0.161369 | + | 0.986894i | \(0.551591\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.14003e7i | 1.61430i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 100728. | 0.0141342 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 6.50548e6i | − | 0.904620i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.78296e6 | − | 7.40238e6i | 1.07254 | − | 1.02009i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.08783e7 | −1.48567 | −0.742835 | − | 0.669474i | \(-0.766519\pi\) | ||||
−0.742835 | + | 0.669474i | \(0.766519\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −555310. | −0.0751633 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.86377e7 | 2.50026 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.08080e6 | −0.409630 | −0.204815 | − | 0.978801i | \(-0.565659\pi\) | ||||
−0.204815 | + | 0.978801i | \(0.565659\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.78835e6 | − | 7.13737e6i | −0.894630 | − | 0.940626i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 1.89563e7i | − | 2.47626i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −828106. | −0.107227 | −0.0536136 | − | 0.998562i | \(-0.517074\pi\) | ||||
−0.0536136 | + | 0.998562i | \(0.517074\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.09946e7i | 1.41120i | 0.708609 | + | 0.705601i | \(0.249323\pi\) | ||||
−0.708609 | + | 0.705601i | \(0.750677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.72917e7 | 2.20014 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 7.37512e6 | + | 369910.i | 0.930250 | + | 0.0466581i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.05176e7i | 1.31516i | 0.753384 | + | 0.657580i | \(0.228420\pi\) | ||||
−0.753384 | + | 0.657580i | \(0.771580\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 4.33692e6i | − | 0.537632i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.95444e6i | 0.608912i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.16164e7i | 1.41547i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.88573e6 | + | 1.79352e6i | −0.227819 | + | 0.216679i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.07272e7 | −1.28497 | −0.642484 | − | 0.766299i | \(-0.722096\pi\) | ||||
−0.642484 | + | 0.766299i | \(0.722096\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 423680.i | − | 0.0503210i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.47368e6 | −0.409093 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.76839e6i | 1.02396i | 0.858997 | + | 0.511980i | \(0.171088\pi\) | ||||
−0.858997 | + | 0.511980i | \(0.828912\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.71725e6 | − | 7.33988e6i | 0.893655 | − | 0.849956i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.87378e7 | 3.30002 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −6.28188e6 | −0.715356 | −0.357678 | − | 0.933845i | \(-0.616432\pi\) | ||||
−0.357678 | + | 0.933845i | \(0.616432\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.18519e7 | −1.33844 | −0.669222 | − | 0.743063i | \(-0.733372\pi\) | ||||
−0.669222 | + | 0.743063i | \(0.733372\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 632008. | 0.0707831 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.09032e6 | − | 1.03700e6i | 0.121106 | − | 0.115184i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 7.80939e6i | − | 0.860291i | −0.902760 | − | 0.430145i | \(-0.858462\pi\) | ||
0.902760 | − | 0.430145i | \(-0.141538\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.79310e6 | 0.414430 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.22273e6i | 0.132503i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −9.77560e6 | −1.05073 | −0.525366 | − | 0.850876i | \(-0.676072\pi\) | ||||
−0.525366 | + | 0.850876i | \(0.676072\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.19973e6 | + | 4.94547e6i | −0.554361 | + | 0.527253i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.46302e7i | − | 1.54717i | −0.633691 | − | 0.773586i | \(-0.718461\pi\) | ||
0.633691 | − | 0.773586i | \(-0.281539\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 7.48407e6i | − | 0.785076i | −0.919736 | − | 0.392538i | \(-0.871597\pi\) | ||
0.919736 | − | 0.392538i | \(-0.128403\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2.38675e7i | − | 2.48358i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.69637e7i | 1.75105i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.71661e6 | − | 977161.i | −0.994981 | − | 0.100061i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.23216e6 | −0.125169 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 9.88670e6i | − | 0.996380i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.89503e6 | −0.989335 | −0.494668 | − | 0.869082i | \(-0.664710\pi\) | ||||
−0.494668 | + | 0.869082i | \(0.664710\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.47055e7i | 2.45067i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.10458e6 | − | 1.16137e6i | −0.108709 | − | 0.114298i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 31231.6 | 0.00304962 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.34470e6 | −0.711577 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.34899e7 | −1.29677 | −0.648386 | − | 0.761312i | \(-0.724556\pi\) | ||||
−0.648386 | + | 0.761312i | \(0.724556\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.56805e7 | 1.49566 | 0.747828 | − | 0.663893i | \(-0.231097\pi\) | ||||
0.747828 | + | 0.663893i | \(0.231097\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.27398e6 | + | 7.86939e6i | −0.783096 | + | 0.744803i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.70592e7i | 1.60213i | 0.598579 | + | 0.801064i | \(0.295732\pi\) | ||||
−0.598579 | + | 0.801064i | \(0.704268\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.42648e7 | −1.32939 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 1.59544e7i | − | 1.47546i | ||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 8.71978e6 | 0.800245 | 0.400122 | − | 0.916462i | \(-0.368968\pi\) | ||||
0.400122 | + | 0.916462i | \(0.368968\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.61917e6 | − | 1.70241e6i | −0.147465 | − | 0.155046i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 2.20681e7i | − | 1.99458i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.58270e6i | 0.859556i | 0.902935 | + | 0.429778i | \(0.141408\pi\) | ||||
−0.902935 | + | 0.429778i | \(0.858592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.66657e7i | 1.48361i | 0.670616 | + | 0.741804i | \(0.266030\pi\) | ||||
−0.670616 | + | 0.741804i | \(0.733970\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.37796e6i | 0.298450i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −510196. | + | 485248.i | −0.0447387 | + | 0.0425510i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.42076e6 | 0.210686 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 3.91427e6i | − | 0.338131i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.34271e6 | 0.715321 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.89257e6i | 0.416389i | 0.978087 | + | 0.208194i | \(0.0667587\pi\) | ||||
−0.978087 | + | 0.208194i | \(0.933241\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.58115e6 | + | 3.15244e7i | −0.133572 | + | 2.66310i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.32965e7 | 1.11498 | 0.557490 | − | 0.830184i | \(-0.311765\pi\) | ||||
0.557490 | + | 0.830184i | \(0.311765\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.21786e7 | 1.01374 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.55788e7 | 1.28726 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4.92824e6 | −0.404241 | −0.202120 | − | 0.979361i | \(-0.564783\pi\) | ||||
−0.202120 | + | 0.979361i | \(0.564783\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.89015e6 | − | 1.98733e6i | −0.153911 | − | 0.161824i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 3.01645e7i | − | 2.43839i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.10540e6 | −0.168961 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.24185e7i | 0.989403i | 0.869063 | + | 0.494702i | \(0.164723\pi\) | ||||
−0.869063 | + | 0.494702i | \(0.835277\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.29034e7 | −2.60260 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.29402e6 | − | 3.46338e6i | −0.258681 | − | 0.271981i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.60522e6i | 0.514998i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 1.34735e7i | − | 1.04301i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.45892e7i | 1.88994i | 0.327153 | + | 0.944971i | \(0.393911\pi\) | ||||
−0.327153 | + | 0.944971i | \(0.606089\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 653621.i | 0.0498813i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.73275e7 | + | 1.82183e7i | 1.31299 | + | 1.38050i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.31330e6 | 0.475015 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.05841e7i | − | 1.53786i | −0.639334 | − | 0.768930i | \(-0.720790\pi\) | ||
0.639334 | − | 0.768930i | \(-0.279210\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00872e7 | 2.23207 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 1.01821e7i | − | 0.750091i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.31249e6 | + | 1.37997e6i | 0.0960135 | + | 0.100950i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.30882e7 | −3.13011 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.88556e6 | −0.424586 | −0.212293 | − | 0.977206i | \(-0.568093\pi\) | ||||
−0.212293 | + | 0.977206i | \(0.568093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.83420e7 | 1.31404 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.17315e6 | 0.510345 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −3.19735e6 | − | 160368.i | −0.225915 | − | 0.0113311i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.65798e6i | − | 0.537376i | −0.963227 | − | 0.268688i | \(-0.913410\pi\) | ||
0.963227 | − | 0.268688i | \(-0.0865900\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.67283e7 | 1.16582 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.05104e7i | 0.727491i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.64697e7 | 1.13220 | 0.566102 | − | 0.824335i | \(-0.308451\pi\) | ||||
0.566102 | + | 0.824335i | \(0.308451\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 465343. | − | 442588.i | 0.0317727 | − | 0.0302191i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 462503.i | − | 0.0313650i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1.03197e7i | − | 0.695116i | −0.937658 | − | 0.347558i | \(-0.887011\pi\) | ||
0.937658 | − | 0.347558i | \(-0.112989\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 223321.i | − | 0.0149412i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 1.43842e7i | − | 0.955903i | −0.878386 | − | 0.477952i | \(-0.841379\pi\) | ||
0.878386 | − | 0.477952i | \(-0.158621\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.13428e6 | − | 1.19259e6i | −0.0748735 | − | 0.0787230i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.29138e7 | −1.50243 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 2.16196e7i | − | 1.40813i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.39860e6 | 0.219887 | 0.109944 | − | 0.993938i | \(-0.464933\pi\) | ||||
0.109944 | + | 0.993938i | \(0.464933\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 4.94060e7i | − | 3.17536i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.34595e6 | − | 5.08454e6i | 0.341317 | − | 0.324627i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.89557e6 | −0.564201 | −0.282101 | − | 0.959385i | \(-0.591031\pi\) | ||||
−0.282101 | + | 0.959385i | \(0.591031\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.96119e7 | −1.86579 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.68168e7 | −1.05264 | −0.526321 | − | 0.850286i | \(-0.676429\pi\) | ||||
−0.526321 | + | 0.850286i | \(0.676429\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.17614e7 | −1.35324 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.39462e7 | + | 3.56915e7i | 2.09719 | + | 2.20501i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 2.58540e6i | − | 0.158686i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.14740e7 | 0.699681 | 0.349840 | − | 0.936809i | \(-0.386236\pi\) | ||||
0.349840 | + | 0.936809i | \(0.386236\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.28894e7i | 0.780900i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.97879e6 | 0.359886 | 0.179943 | − | 0.983677i | \(-0.442409\pi\) | ||||
0.179943 | + | 0.983677i | \(0.442409\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −674535. | + | 1.34486e7i | −0.0403413 | + | 0.804309i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.46133e7i | 1.46257i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 436679.i | − | 0.0257821i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.37484e6i | 0.315310i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.03474e7i | 0.603149i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.46227e7 | + | 1.39077e7i | −0.846942 | + | 0.805527i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.28293e6 | −0.0738356 | −0.0369178 | − | 0.999318i | \(-0.511754\pi\) | ||||
−0.0369178 | + | 0.999318i | \(0.511754\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.78083e7i | 1.01843i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.25716e7 | 1.28269 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.51206e6i | 0.0853860i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.13700e7 | + | 2.98360e7i | −1.76034 | + | 1.67426i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.38090e7 | −0.770047 | −0.385024 | − | 0.922907i | \(-0.625807\pi\) | ||||
−0.385024 | + | 0.922907i | \(0.625807\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.31428e7 | 1.28247 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.84552e7 | −4.32057 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.61494e7 | −0.883826 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.22613e7 | + | 1.16617e7i | −0.666880 | + | 0.634270i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.73417e7i | 1.47789i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.36073e7 | 1.26816 | 0.634082 | − | 0.773266i | \(-0.281378\pi\) | ||||
0.634082 | + | 0.773266i | \(0.281378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.59317e6i | 0.0850569i | 0.999095 | + | 0.0425284i | \(0.0135413\pi\) | ||||
−0.999095 | + | 0.0425284i | \(0.986459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.48370e7 | −1.31787 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.64431e6 | + | 5.36831e6i | −0.297658 | + | 0.283102i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 694857.i | − | 0.0364200i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 5.96353e6i | − | 0.310666i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.05321e6i | 0.468754i | 0.972146 | + | 0.234377i | \(0.0753050\pi\) | ||||
−0.972146 | + | 0.234377i | \(0.924695\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.59075e7i | 0.818657i | 0.912387 | + | 0.409329i | \(0.134237\pi\) | ||||
−0.912387 | + | 0.409329i | \(0.865763\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.91117e7 | + | 1.96170e6i | 2.00065 | + | 0.100346i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.64781e7 | 1.34624 | 0.673122 | − | 0.739532i | \(-0.264953\pi\) | ||||
0.673122 | + | 0.739532i | \(0.264953\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.54704e7i | 0.781835i | 0.920426 | + | 0.390918i | \(0.127842\pi\) | ||||
−0.920426 | + | 0.390918i | \(0.872158\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.83518e7 | −1.92657 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 591125.i | − | 0.0295166i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.69514e7 | − | 1.78230e7i | −0.841377 | − | 0.884635i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.35227e7 | 2.14735 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −3.82791e7 | −1.87740 | −0.938701 | − | 0.344733i | \(-0.887970\pi\) | ||||
−0.938701 | + | 0.344733i | \(0.887970\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.94617e7 | 0.948834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.88306e7 | 0.912630 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.47896e7 | − | 1.40664e7i | 0.712551 | − | 0.677708i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.44809e6i | 0.165147i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.63567e7 | −2.68334 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.57082e7i | 0.743536i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.94396e7 | 1.38535 | 0.692676 | − | 0.721249i | \(-0.256432\pi\) | ||||
0.692676 | + | 0.721249i | \(0.256432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.24422e6 | − | 2.35961e6i | −0.104991 | − | 0.110389i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.36598e7i | 0.635320i | 0.948205 | + | 0.317660i | \(0.102897\pi\) | ||||
−0.948205 | + | 0.317660i | \(0.897103\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.49700e7i | − | 0.692212i | −0.938195 | − | 0.346106i | \(-0.887504\pi\) | ||
0.938195 | − | 0.346106i | \(-0.112496\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 1.64439e7i | − | 0.755957i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 2.36162e6i | − | 0.107940i | −0.998543 | − | 0.0539701i | \(-0.982812\pi\) | ||
0.998543 | − | 0.0539701i | \(-0.0171876\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.88267e7 | − | 2.74171e7i | 1.30995 | − | 1.24589i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.28955e7 | 1.03443 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.20178e7i | − | 0.989063i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 83825.7 | 0.00374397 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.63250e7i | 2.50130i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.69674e7 | − | 1.45906e7i | 0.749195 | − | 0.644250i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.52212e7 | −0.668268 | −0.334134 | − | 0.942526i | \(-0.608444\pi\) | ||||
−0.334134 | + | 0.942526i | \(0.608444\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5.21895e7 | 2.27830 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.72576e7 | 1.18317 | 0.591586 | − | 0.806242i | \(-0.298502\pi\) | ||||
0.591586 | + | 0.806242i | \(0.298502\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.90157e7 | −0.820748 | −0.410374 | − | 0.911917i | \(-0.634602\pi\) | ||||
−0.410374 | + | 0.911917i | \(0.634602\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.66381e7 | − | 3.85218e7i | −1.57244 | − | 1.65329i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 2.99966e7i | − | 1.28016i | −0.768310 | − | 0.640078i | \(-0.778902\pi\) | ||
0.768310 | − | 0.640078i | \(-0.221098\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.67279e6 | 0.155862 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 6.41576e7i | − | 2.70741i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.52999e6 | −0.0642038 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.13437e7 | − | 3.29552e7i | −1.30795 | − | 1.37520i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 5.36698e6i | − | 0.222714i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.41427e6i | 0.182163i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.98493e7i | 1.63534i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 2.61661e7i | − | 1.06787i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.59889e7 | − | 1.68110e7i | −0.648929 | − | 0.682293i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.81689e7 | −0.733348 | −0.366674 | − | 0.930349i | \(-0.619504\pi\) | ||||
−0.366674 | + | 0.930349i | \(0.619504\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.91984e7i | 1.17206i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.14560e6 | 0.0856550 | 0.0428275 | − | 0.999082i | \(-0.486363\pi\) | ||||
0.0428275 | + | 0.999082i | \(0.486363\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.67683e7i | 0.665751i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.14277e7 | + | 2.25294e7i | 0.846101 | + | 0.889603i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.38380e6 | 0.211430 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.88257e6 | 0.190704 | 0.0953519 | − | 0.995444i | \(-0.469602\pi\) | ||||
0.0953519 | + | 0.995444i | \(0.469602\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.63709e6 | 0.374366 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −974156. | −0.0376378 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.04062e6 | − | 2.07475e7i | 0.0399888 | − | 0.797281i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.48300e7i | 3.24228i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.34515e7 | 1.27168 | 0.635838 | − | 0.771823i | \(-0.280655\pi\) | ||||
0.635838 | + | 0.771823i | \(0.280655\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 39080.0i | 0.00147768i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.64621e6 | 0.137132 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.61190e7 | − | 2.48418e7i | 0.977074 | − | 0.929296i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 3.63111e7i | − | 1.35111i | −0.737310 | − | 0.675554i | \(-0.763904\pi\) | ||
0.737310 | − | 0.675554i | \(-0.236096\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.66390e7i | 1.72618i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.70043e7i | − | 1.36232i | −0.732136 | − | 0.681158i | \(-0.761477\pi\) | ||
0.732136 | − | 0.681158i | \(-0.238523\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.04945e7i | − | 0.384311i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.98473e7 | − | 5.24101e7i | −1.81577 | − | 1.90913i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.25663e7 | 0.455335 | 0.227668 | − | 0.973739i | \(-0.426890\pi\) | ||||
0.227668 | + | 0.973739i | \(0.426890\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.92697e6i | − | 0.105500i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.69858e7 | 1.68467 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.08701e7i | − | 1.10105i | −0.834819 | − | 0.550524i | \(-0.814428\pi\) | ||
0.834819 | − | 0.550524i | \(-0.185572\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.42327e7 | − | 2.30477e7i | 0.859791 | − | 0.817747i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.28377e7 | 0.453115 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.28485e6 | 0.220673 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.00620e7 | −0.351460 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.99885e7 | 3.47443 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.78059e6 | − | 6.07779e6i | −0.199827 | − | 0.210101i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.55508e7i | − | 0.878696i | −0.898317 | − | 0.439348i | \(-0.855209\pi\) | ||
0.898317 | − | 0.439348i | \(-0.144791\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −4.22683e6 | −0.144612 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 2.78585e7i | − | 0.948221i | −0.880465 | − | 0.474110i | \(-0.842770\pi\) | ||
0.880465 | − | 0.474110i | \(-0.157230\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.09528e7 | 0.370888 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −355546. | + | 7.08874e6i | −0.0119780 | + | 0.238813i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.73322e7i | 0.580920i | 0.956887 | + | 0.290460i | \(0.0938084\pi\) | ||||
−0.956887 | + | 0.290460i | \(0.906192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.74135e7i | 1.91451i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 1.00644e8i | − | 3.33900i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1.02000e7i | − | 0.336681i | −0.985729 | − | 0.168340i | \(-0.946159\pi\) | ||
0.985729 | − | 0.168340i | \(-0.0538408\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.86805e6 | + | 4.63000e6i | −0.159869 | + | 0.152051i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.76146e7 | −1.88252 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.66992e7i | − | 0.542881i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.05292e7 | −0.340573 | −0.170286 | − | 0.985395i | \(-0.554469\pi\) | ||||
−0.170286 | + | 0.985395i | \(0.554469\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 9.39687e6i | − | 0.302420i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.02733e7 | − | 3.83040e7i | 1.28961 | − | 1.22655i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.69241e7 | 1.49506 | 0.747529 | − | 0.664229i | \(-0.231240\pi\) | ||||
0.747529 | + | 0.664229i | \(0.231240\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6.71435e7 | −2.12858 |
(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 | 160.6.f.a.49.2 | 28 | ||
4.3 | odd | 2 | 40.6.f.a.29.14 | yes | 28 | ||
5.2 | odd | 4 | 800.6.d.e.401.6 | 28 | |||
5.3 | odd | 4 | 800.6.d.e.401.23 | 28 | |||
5.4 | even | 2 | inner | 160.6.f.a.49.27 | 28 | ||
8.3 | odd | 2 | 40.6.f.a.29.16 | yes | 28 | ||
8.5 | even | 2 | inner | 160.6.f.a.49.28 | 28 | ||
20.3 | even | 4 | 200.6.d.e.101.28 | 28 | |||
20.7 | even | 4 | 200.6.d.e.101.1 | 28 | |||
20.19 | odd | 2 | 40.6.f.a.29.15 | yes | 28 | ||
40.3 | even | 4 | 200.6.d.e.101.27 | 28 | |||
40.13 | odd | 4 | 800.6.d.e.401.24 | 28 | |||
40.19 | odd | 2 | 40.6.f.a.29.13 | ✓ | 28 | ||
40.27 | even | 4 | 200.6.d.e.101.2 | 28 | |||
40.29 | even | 2 | inner | 160.6.f.a.49.1 | 28 | ||
40.37 | odd | 4 | 800.6.d.e.401.5 | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.6.f.a.29.13 | ✓ | 28 | 40.19 | odd | 2 | ||
40.6.f.a.29.14 | yes | 28 | 4.3 | odd | 2 | ||
40.6.f.a.29.15 | yes | 28 | 20.19 | odd | 2 | ||
40.6.f.a.29.16 | yes | 28 | 8.3 | odd | 2 | ||
160.6.f.a.49.1 | 28 | 40.29 | even | 2 | inner | ||
160.6.f.a.49.2 | 28 | 1.1 | even | 1 | trivial | ||
160.6.f.a.49.27 | 28 | 5.4 | even | 2 | inner | ||
160.6.f.a.49.28 | 28 | 8.5 | even | 2 | inner | ||
200.6.d.e.101.1 | 28 | 20.7 | even | 4 | |||
200.6.d.e.101.2 | 28 | 40.27 | even | 4 | |||
200.6.d.e.101.27 | 28 | 40.3 | even | 4 | |||
200.6.d.e.101.28 | 28 | 20.3 | even | 4 | |||
800.6.d.e.401.5 | 28 | 40.37 | odd | 4 | |||
800.6.d.e.401.6 | 28 | 5.2 | odd | 4 | |||
800.6.d.e.401.23 | 28 | 5.3 | odd | 4 | |||
800.6.d.e.401.24 | 28 | 40.13 | odd | 4 |