Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(383,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.383");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.c (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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + 18093172325 x^{8} + 74958811500 x^{6} + 79355888475 x^{4} + \cdots + 2870280625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{88}\cdot 3^{14}\cdot 41^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 383.14 | ||
Root | \(-9.62962i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.d.383.13 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 5.16061 | + | 14.7095i | 0.331053 | + | 0.943612i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 48.6693i | 0.870623i | 0.900280 | + | 0.435312i | \(0.143362\pi\) | ||||
−0.900280 | + | 0.435312i | \(0.856638\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 167.754i | 1.29398i | 0.762497 | + | 0.646992i | \(0.223973\pi\) | ||||
−0.762497 | + | 0.646992i | \(0.776027\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −189.736 | + | 151.820i | −0.780807 | + | 0.624772i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 319.315 | 0.795679 | 0.397840 | − | 0.917455i | \(-0.369760\pi\) | ||||
0.397840 | + | 0.917455i | \(0.369760\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −152.547 | −0.250349 | −0.125175 | − | 0.992135i | \(-0.539949\pi\) | ||||
−0.125175 | + | 0.992135i | \(0.539949\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −715.899 | + | 251.163i | −0.821530 | + | 0.288223i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1323.90i | 1.11105i | 0.831501 | + | 0.555523i | \(0.187482\pi\) | ||||
−0.831501 | + | 0.555523i | \(0.812518\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1617.20i | 1.02773i | 0.857870 | + | 0.513867i | \(0.171788\pi\) | ||||
−0.857870 | + | 0.513867i | \(0.828212\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2467.58 | + | 865.716i | −1.22102 | + | 0.428378i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1222.40 | 0.481829 | 0.240914 | − | 0.970546i | \(-0.422553\pi\) | ||||
0.240914 | + | 0.970546i | \(0.422553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 756.298 | 0.242015 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3212.34 | − | 2007.43i | −0.848031 | − | 0.529946i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4549.54i | 1.00455i | 0.864707 | + | 0.502276i | \(0.167504\pi\) | ||||
−0.864707 | + | 0.502276i | \(0.832496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5353.25i | 1.00049i | 0.865884 | + | 0.500245i | \(0.166757\pi\) | ||||
−0.865884 | + | 0.500245i | \(0.833243\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1647.86 | + | 4696.95i | 0.263412 | + | 0.750813i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8164.49 | −1.12657 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3269.34 | −0.392605 | −0.196303 | − | 0.980543i | \(-0.562894\pi\) | ||||
−0.196303 | + | 0.980543i | \(0.562894\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −787.239 | − | 2243.89i | −0.0828791 | − | 0.236233i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 13077.7i | − | 1.21499i | −0.794323 | − | 0.607495i | \(-0.792174\pi\) | ||
0.794323 | − | 0.607495i | \(-0.207826\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 20435.5i | − | 1.68544i | −0.538350 | − | 0.842721i | \(-0.680952\pi\) | ||
0.538350 | − | 0.842721i | \(-0.319048\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7388.96 | − | 9234.33i | −0.543941 | − | 0.679789i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20059.0 | 1.32454 | 0.662269 | − | 0.749266i | \(-0.269594\pi\) | ||||
0.662269 | + | 0.749266i | \(0.269594\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −11334.6 | −0.674395 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −19473.8 | + | 6832.12i | −1.04840 | + | 0.367816i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 33272.4i | 1.62703i | 0.581546 | + | 0.813513i | \(0.302448\pi\) | ||||
−0.581546 | + | 0.813513i | \(0.697552\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 15540.9i | 0.692737i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −23788.2 | + | 8345.77i | −0.969783 | + | 0.340235i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5883.70 | 0.220050 | 0.110025 | − | 0.993929i | \(-0.464907\pi\) | ||||
0.110025 | + | 0.993929i | \(0.464907\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 22967.3 | 0.790289 | 0.395144 | − | 0.918619i | \(-0.370695\pi\) | ||||
0.395144 | + | 0.918619i | \(0.370695\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25468.4 | − | 31829.1i | −0.808445 | − | 1.01035i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 7424.38i | − | 0.217960i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 13938.9i | − | 0.379352i | −0.981847 | − | 0.189676i | \(-0.939256\pi\) | ||
0.981847 | − | 0.189676i | \(-0.0607438\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6308.32 | + | 17980.8i | 0.159511 | + | 0.454659i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −65642.7 | −1.54540 | −0.772700 | − | 0.634772i | \(-0.781094\pi\) | ||||
−0.772700 | + | 0.634772i | \(0.781094\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 55673.0 | 1.22275 | 0.611375 | − | 0.791341i | \(-0.290617\pi\) | ||||
0.611375 | + | 0.791341i | \(0.290617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3902.96 | + | 11124.7i | 0.0801200 | + | 0.228369i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53566.6i | 1.02960i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 82204.2i | − | 1.48192i | −0.671546 | − | 0.740962i | \(-0.734370\pi\) | ||
0.671546 | − | 0.740962i | \(-0.265630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 12950.6 | − | 57611.3i | 0.219320 | − | 0.975653i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −19118.5 | −0.304620 | −0.152310 | − | 0.988333i | \(-0.548671\pi\) | ||||
−0.152310 | + | 0.988333i | \(0.548671\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −64433.2 | −0.967302 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −66921.3 | + | 23478.4i | −0.947908 | + | 0.332561i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 97061.0i | − | 1.29888i | −0.760412 | − | 0.649441i | \(-0.775003\pi\) | ||
0.760412 | − | 0.649441i | \(-0.224997\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 25590.5i | − | 0.323948i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −78743.3 | + | 27626.0i | −0.944075 | + | 0.331216i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −78708.3 | −0.894770 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 159302. | 1.71906 | 0.859532 | − | 0.511082i | \(-0.170755\pi\) | ||||
0.859532 | + | 0.511082i | \(0.170755\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −60585.7 | + | 48478.3i | −0.621272 | + | 0.497118i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 77267.6i | − | 0.753692i | −0.926276 | − | 0.376846i | \(-0.877009\pi\) | ||
0.926276 | − | 0.376846i | \(-0.122991\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 43795.1i | 0.406755i | 0.979100 | + | 0.203377i | \(0.0651918\pi\) | ||||
−0.979100 | + | 0.203377i | \(0.934808\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −42133.8 | − | 120095.i | −0.372956 | − | 1.06305i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −220827. | −1.86463 | −0.932315 | − | 0.361647i | \(-0.882215\pi\) | ||||
−0.932315 | + | 0.361647i | \(0.882215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 152973. | 1.23325 | 0.616623 | − | 0.787259i | \(-0.288500\pi\) | ||||
0.616623 | + | 0.787259i | \(0.288500\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −16871.8 | − | 48090.3i | −0.129973 | − | 0.370467i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 142603.i | − | 1.05059i | −0.850922 | − | 0.525293i | \(-0.823956\pi\) | ||
0.850922 | − | 0.525293i | \(-0.176044\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 59493.2i | 0.419491i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28943.8 | − | 23159.7i | 0.195475 | − | 0.156411i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −222090. | −1.43768 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59088.7 | −0.366894 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 192366. | − | 67489.1i | 1.14648 | − | 0.402227i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 188900.i | 1.08133i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 49483.5i | 0.272240i | 0.990692 | + | 0.136120i | \(0.0434632\pi\) | ||||
−0.990692 | + | 0.136120i | \(0.956537\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 300595. | − | 105460.i | 1.59040 | − | 0.557972i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −260380. | −1.32565 | −0.662826 | − | 0.748773i | \(-0.730643\pi\) | ||||
−0.662826 | + | 0.748773i | \(0.730643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −271293. | −1.32987 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 97700.4 | − | 156342.i | 0.461383 | − | 0.738316i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 107894.i | 0.491132i | 0.969380 | + | 0.245566i | \(0.0789737\pi\) | ||||
−0.969380 | + | 0.245566i | \(0.921026\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 91076.8i | − | 0.399826i | −0.979814 | − | 0.199913i | \(-0.935934\pi\) | ||
0.979814 | − | 0.199913i | \(-0.0640659\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 103517. | + | 295057.i | 0.438493 | + | 1.24985i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −48710.8 | −0.199198 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −221423. | −0.874587 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −58493.2 | − | 166725.i | −0.223261 | − | 0.636367i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 396732.i | 1.46397i | 0.681322 | + | 0.731984i | \(0.261405\pi\) | ||||
−0.681322 | + | 0.731984i | \(0.738595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 396191.i | − | 1.41404i | −0.707192 | − | 0.707022i | \(-0.750038\pi\) | ||
0.707192 | − | 0.707022i | \(-0.249962\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −200994. | − | 251191.i | −0.694150 | − | 0.867513i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −260539. | −0.871050 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −92070.4 | −0.298106 | −0.149053 | − | 0.988829i | \(-0.547623\pi\) | ||||
−0.149053 | + | 0.988829i | \(0.547623\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −489419. | + | 171706.i | −1.53528 | + | 0.538633i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 205062.i | 0.623478i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 299401.i | − | 0.882640i | −0.897350 | − | 0.441320i | \(-0.854510\pi\) | ||
0.897350 | − | 0.441320i | \(-0.145490\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −228598. | + | 80200.4i | −0.653675 | + | 0.229333i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 61166.1 | 0.169715 | 0.0848574 | − | 0.996393i | \(-0.472957\pi\) | ||||
0.0848574 | + | 0.996393i | \(0.472957\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −348022. | −0.937325 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −245523. | − | 306842.i | −0.642100 | − | 0.802463i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 349424.i | 0.887641i | 0.896116 | + | 0.443821i | \(0.146377\pi\) | ||||
−0.896116 | + | 0.443821i | \(0.853623\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 126872.i | 0.313164i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30363.5 | + | 86546.0i | 0.0728482 | + | 0.207641i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 172914. | 0.403365 | 0.201682 | − | 0.979451i | \(-0.435359\pi\) | ||||
0.201682 | + | 0.979451i | \(0.435359\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −370619. | −0.840874 | −0.420437 | − | 0.907322i | \(-0.638123\pi\) | ||||
−0.420437 | + | 0.907322i | \(0.638123\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 118525. | + | 337837.i | 0.261628 | + | 0.745726i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 159117.i | − | 0.341811i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 422741.i | 0.884036i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 336756. | − | 538884.i | 0.685742 | − | 1.09734i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 636934. | 1.26331 | 0.631656 | − | 0.775249i | \(-0.282375\pi\) | ||||
0.631656 | + | 0.775249i | \(0.282375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 791811. | 1.53013 | 0.765064 | − | 0.643954i | \(-0.222707\pi\) | ||||
0.765064 | + | 0.643954i | \(0.222707\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 109209. | − | 38314.4i | 0.205670 | − | 0.0721564i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 229538.i | 0.421395i | 0.977551 | + | 0.210698i | \(0.0675735\pi\) | ||||
−0.977551 | + | 0.210698i | \(0.932426\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 42046.2i | 0.0752651i | 0.999292 | + | 0.0376325i | \(0.0119816\pi\) | ||||
−0.999292 | + | 0.0376325i | \(0.988018\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 205034. | − | 71933.4i | 0.357961 | − | 0.125586i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −763206. | −1.29987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 636484. | 1.05780 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −231933. | + | 185584.i | −0.376215 | + | 0.301033i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 516398.i | 0.817747i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 80176.3i | − | 0.123977i | −0.998077 | − | 0.0619883i | \(-0.980256\pi\) | ||
0.998077 | − | 0.0619883i | \(-0.0197442\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −338757. | − | 965569.i | −0.511610 | − | 1.45826i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 994581. | 1.46739 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −898031. | −1.29462 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 287307. | + | 818919.i | 0.404795 | + | 1.15380i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 201957.i | − | 0.278150i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 73558.4i | 0.0990536i | 0.998773 | + | 0.0495268i | \(0.0157713\pi\) | ||||
−0.998773 | + | 0.0495268i | \(0.984229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −143497. | + | 114821.i | −0.188967 | + | 0.151204i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 359120. | 0.462568 | 0.231284 | − | 0.972886i | \(-0.425707\pi\) | ||||
0.231284 | + | 0.972886i | \(0.425707\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −867580. | −1.09325 | −0.546627 | − | 0.837376i | \(-0.684088\pi\) | ||||
−0.546627 | + | 0.837376i | \(0.684088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −787935. | + | 276436.i | −0.971539 | + | 0.340851i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 520013.i | − | 0.627515i | −0.949503 | − | 0.313758i | \(-0.898412\pi\) | ||
0.949503 | − | 0.313758i | \(-0.101588\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 976257.i | 1.15317i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.20918e6 | − | 424224.i | 1.39836 | − | 0.490596i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −206539. | −0.233888 | −0.116944 | − | 0.993139i | \(-0.537310\pi\) | ||||
−0.116944 | + | 0.993139i | \(0.537310\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.65009e6 | 1.83006 | 0.915030 | − | 0.403385i | \(-0.132166\pi\) | ||||
0.915030 | + | 0.403385i | \(0.132166\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 914264. | − | 106813.i | 0.993244 | − | 0.116041i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 551645.i | − | 0.587144i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 246701.i | − | 0.257293i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −98663.3 | − | 281223.i | −0.100846 | − | 0.287443i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.56162e6 | 1.56455 | 0.782277 | − | 0.622931i | \(-0.214058\pi\) | ||||
0.782277 | + | 0.622931i | \(0.214058\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 390330. | 0.383381 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −332515. | − | 947777.i | −0.320229 | − | 0.912758i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.51207e6i | 1.42804i | 0.700127 | + | 0.714019i | \(0.253127\pi\) | ||||
−0.700127 | + | 0.714019i | \(0.746873\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 548447.i | − | 0.508025i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −690710. | − | 863213.i | −0.627616 | − | 0.784362i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 387053. | 0.345049 | 0.172524 | − | 0.985005i | \(-0.444808\pi\) | ||||
0.172524 | + | 0.985005i | \(0.444808\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.61935e6 | −1.41653 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.42771e6 | − | 500894.i | 1.22564 | − | 0.429999i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.62869e6i | 1.37233i | 0.727446 | + | 0.686165i | \(0.240707\pi\) | ||||
−0.727446 | + | 0.686165i | \(0.759293\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 549923.i | 0.454861i | 0.973794 | + | 0.227431i | \(0.0730325\pi\) | ||||
−0.973794 | + | 0.227431i | \(0.926968\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 376423. | − | 132063.i | 0.305681 | − | 0.107244i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 241498. | 0.192567 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.37805e6 | 1.07911 | 0.539553 | − | 0.841951i | \(-0.318593\pi\) | ||||
0.539553 | + | 0.841951i | \(0.318593\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −812728. | − | 1.01570e6i | −0.625078 | − | 0.781190i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.03707e6i | 1.53900i | 0.638645 | + | 0.769502i | \(0.279495\pi\) | ||||
−0.638645 | + | 0.769502i | \(0.720505\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 1.15726e6i | − | 0.858947i | −0.903079 | − | 0.429473i | \(-0.858699\pi\) | ||
0.903079 | − | 0.429473i | \(-0.141301\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −406183. | − | 1.15776e6i | −0.296217 | − | 0.844315i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.19385e6 | 1.57218 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −332847. | −0.234423 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 822096. | + | 2.34325e6i | 0.569102 | + | 1.62213i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.48372e6i | − | 1.69018i | −0.534621 | − | 0.845092i | \(-0.679546\pi\) | ||
0.534621 | − | 0.845092i | \(-0.320454\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 286356.i | 0.191580i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.02575e6 | − | 641004.i | −0.674761 | − | 0.421667i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −186474. | −0.120626 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.42814e6 | 2.18094 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.13656e6 | − | 398748.i | 0.711193 | − | 0.249512i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.11780e6i | 0.688044i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.54604e6i | 1.54177i | 0.636976 | + | 0.770884i | \(0.280185\pi\) | ||||
−0.636976 | + | 0.770884i | \(0.719815\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −644202. | + | 226010.i | −0.383819 | + | 0.134658i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.66268e6 | 1.56106 | 0.780528 | − | 0.625121i | \(-0.214950\pi\) | ||||
0.780528 | + | 0.625121i | \(0.214950\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −400195. | −0.230893 | −0.115446 | − | 0.993314i | \(-0.536830\pi\) | ||||
−0.115446 | + | 0.993314i | \(0.536830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.54910e6 | − | 1.23953e6i | 0.879636 | − | 0.703851i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.54428e6i | − | 0.863136i | −0.902080 | − | 0.431568i | \(-0.857961\pi\) | ||
0.902080 | − | 0.431568i | \(-0.142039\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.45274e6i | 0.799302i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.13960e6 | − | 3.24824e6i | −0.617292 | − | 1.75949i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.14101e6 | −1.14186 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −115371. | −0.0605884 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 789436. | + | 2.25015e6i | 0.408270 | + | 1.16371i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.36498e6i | 1.71393i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 337952.i | − | 0.169545i | −0.996400 | − | 0.0847725i | \(-0.972984\pi\) | ||
0.996400 | − | 0.0847725i | \(-0.0270163\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 620313. | − | 496351.i | 0.306549 | − | 0.245289i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 678398. | 0.330273 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.92048e6 | 0.921158 | 0.460579 | − | 0.887619i | \(-0.347642\pi\) | ||||
0.460579 | + | 0.887619i | \(0.347642\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.09761e6 | − | 735917.i | 0.991345 | − | 0.347800i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70937e6i | 0.796070i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 918027.i | 0.421328i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −875113. | + | 307021.i | −0.395837 | + | 0.138874i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.67762e6 | −0.747946 | −0.373973 | − | 0.927440i | \(-0.622005\pi\) | ||||
−0.373973 | + | 0.927440i | \(0.622005\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.93176e6 | −1.72792 | −0.863960 | − | 0.503560i | \(-0.832023\pi\) | ||||
−0.863960 | + | 0.503560i | \(0.832023\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 490034. | + | 306229.i | 0.212304 | + | 0.132672i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.20933e6i | 1.37081i | 0.728161 | + | 0.685406i | \(0.240375\pi\) | ||||
−0.728161 | + | 0.685406i | \(0.759625\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.19479e6i | − | 1.34546i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.14612e6 | − | 3.26682e6i | −0.475948 | − | 1.35661i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 913329. | 0.374017 | 0.187008 | − | 0.982358i | \(-0.440121\pi\) | ||||
0.187008 | + | 0.982358i | \(0.440121\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −139253. | −0.0562389 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −304934. | − | 869163.i | −0.121462 | − | 0.346206i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.70957e6i | 1.06455i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 205159.i | − | 0.0795106i | −0.999209 | − | 0.0397553i | \(-0.987342\pi\) | ||
0.999209 | − | 0.0397553i | \(-0.0126578\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.98546e6 | + | 2.48132e6i | 0.759092 | + | 0.948673i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.58160e6 | −2.10535 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.30940e6 | −0.859465 | −0.429732 | − | 0.902956i | \(-0.641392\pi\) | ||||
−0.429732 | + | 0.902956i | \(0.641392\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.77862e6 | + | 974840.i | −1.02035 | + | 0.357977i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 694021.i | − | 0.251489i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.30015e6i | 0.464939i | 0.972604 | + | 0.232470i | \(0.0746806\pi\) | ||||
−0.972604 | + | 0.232470i | \(0.925319\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −727876. | + | 255365.i | −0.256889 | + | 0.0901259i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 421140. | 0.146700 | 0.0733499 | − | 0.997306i | \(-0.476631\pi\) | ||||
0.0733499 | + | 0.997306i | \(0.476631\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.60705e6 | −0.896390 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.10251e6 | + | 3.87735e6i | 1.05302 | + | 1.31601i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.99605e6i | 1.33893i | 0.742844 | + | 0.669464i | \(0.233476\pi\) | ||||
−0.742844 | + | 0.669464i | \(0.766524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.61833e6i | 0.535334i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.34372e6 | − | 3.83005e6i | −0.438862 | − | 1.25090i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00082e6 | 1.29020 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.38885e6 | 0.442262 | 0.221131 | − | 0.975244i | \(-0.429025\pi\) | ||||
0.221131 | + | 0.975244i | \(0.429025\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.40004e6 | − | 3.99058e6i | −0.440259 | − | 1.25488i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.31621e6i | 0.408758i | 0.978892 | + | 0.204379i | \(0.0655174\pi\) | ||||
−0.978892 | + | 0.204379i | \(0.934483\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 816624.i | − | 0.250472i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.80390e6 | + | 630297.i | 0.849426 | + | 0.190945i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.04395e6 | −0.312388 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.83849e6 | 0.839033 | 0.419516 | − | 0.907748i | \(-0.362200\pi\) | ||||
0.419516 | + | 0.907748i | \(0.362200\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.58707e6 | + | 556802.i | −0.463438 | + | 0.162591i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 987017.i | 0.284741i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 930485.i | − | 0.265210i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.33969e6 | − | 470012.i | 0.377280 | − | 0.132364i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 983535. | 0.273687 | 0.136844 | − | 0.990593i | \(-0.456304\pi\) | ||||
0.136844 | + | 0.990593i | \(0.456304\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.50363e6 | −0.963414 | −0.481707 | − | 0.876332i | \(-0.659983\pi\) | ||||
−0.481707 | + | 0.876332i | \(0.659983\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.80591e6 | + | 3.04535e6i | −1.03421 | + | 0.827534i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.00126e6i | 0.268890i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.85287e6i | 1.02262i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −251377. | − | 716509.i | −0.0659452 | − | 0.187966i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.96042e6 | 1.28625 | 0.643125 | − | 0.765762i | \(-0.277638\pi\) | ||||
0.643125 | + | 0.765762i | \(0.277638\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.86224e6 | −0.989964 | −0.494982 | − | 0.868903i | \(-0.664825\pi\) | ||||
−0.494982 | + | 0.868903i | \(0.664825\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.14268e6 | − | 3.25701e6i | −0.289535 | − | 0.825270i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.97687e6i | 0.495192i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 7.78526e6i | − | 1.92802i | −0.265862 | − | 0.964011i | \(-0.585657\pi\) | ||
0.265862 | − | 0.964011i | \(-0.414343\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.15057e6 | − | 1.72081e6i | 0.526572 | − | 0.421343i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.74367e6 | −1.63263 | −0.816314 | − | 0.577609i | \(-0.803986\pi\) | ||||
−0.816314 | + | 0.577609i | \(0.803986\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.72389e6 | 1.13084 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.83571e6 | + | 2.04738e6i | −1.38142 | + | 0.484651i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 3.85833e6i | − | 0.903200i | −0.892221 | − | 0.451600i | \(-0.850853\pi\) | ||
0.892221 | − | 0.451600i | \(-0.149147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 4.17592e6i | − | 0.966743i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.82776e6 | − | 2.04459e6i | 1.33431 | − | 0.468124i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.24547e6 | 0.282037 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.64250e6 | 0.367888 | 0.183944 | − | 0.982937i | \(-0.441114\pi\) | ||||
0.183944 | + | 0.982937i | \(0.441114\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.65764e6 | − | 4.25281e6i | 0.588794 | − | 0.942202i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 77799.5i | − | 0.0170500i | −0.999964 | − | 0.00852500i | \(-0.997286\pi\) | ||
0.999964 | − | 0.00852500i | \(-0.00271363\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 213758.i | − | 0.0463414i | −0.999732 | − | 0.0231707i | \(-0.992624\pi\) | ||
0.999732 | − | 0.0231707i | \(-0.00737613\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.34454e6 | − | 3.83238e6i | −0.288364 | − | 0.821933i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.85122e6 | 0.604977 | 0.302489 | − | 0.953153i | \(-0.402183\pi\) | ||||
0.302489 | + | 0.953153i | \(0.402183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.33832e6 | 0.490875 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −475140. | − | 1.35431e6i | −0.0986891 | − | 0.281297i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 6.52537e6i | − | 1.34107i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.22309e6i | 0.248728i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −5.05141e6 | − | 6.31298e6i | −1.01652 | − | 1.27039i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.52181e6 | −1.69704 | −0.848522 | − | 0.529161i | \(-0.822507\pi\) | ||||
−0.848522 | + | 0.529161i | \(0.822507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 498730. | 0.0982886 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.01636e6 | + | 1.05825e6i | −0.588322 | + | 0.206405i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.75312e6i | 1.49666i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.25067e6i | − | 1.19427i | −0.802139 | − | 0.597137i | \(-0.796305\pi\) | ||
0.802139 | − | 0.597137i | \(-0.203695\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.40402e6 | − | 1.54509e6i | 0.832870 | − | 0.292201i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.91380e6 | −1.10704 | −0.553519 | − | 0.832837i | \(-0.686715\pi\) | ||||
−0.553519 | + | 0.832837i | \(0.686715\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.02313e6 | −1.11610 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.35941e6 | − | 2.94866e6i | −0.432803 | − | 0.540894i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.10119e7i | − | 1.99972i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 916915.i | 0.164846i | 0.996597 | + | 0.0824228i | \(0.0262658\pi\) | ||||
−0.996597 | + | 0.0824228i | \(0.973734\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 315655. | + | 899720.i | 0.0561847 | + | 0.160145i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 4.30667e6 | 0.758964 | 0.379482 | − | 0.925199i | \(-0.376102\pi\) | ||||
0.379482 | + | 0.925199i | \(0.376102\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.76056e6 | 0.656181 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.79601e6 | − | 5.11922e6i | −0.310305 | − | 0.884471i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.12915e6i | 0.535342i | 0.963510 | + | 0.267671i | \(0.0862540\pi\) | ||||
−0.963510 | + | 0.267671i | \(0.913746\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.33939e6i | 1.58222i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.24643e6 | − | 5.19501e6i | 0.544644 | − | 0.871551i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.13148e6 | −0.354130 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 6.40514e6 | 1.05391 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.13984e6 | + | 1.80324e6i | −0.837589 | + | 0.293857i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 181277.i | − | 0.0292583i | −0.999893 | − | 0.0146292i | \(-0.995343\pi\) | ||
0.999893 | − | 0.0146292i | \(-0.00465677\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.82852e6i | 1.25148i | 0.780030 | + | 0.625742i | \(0.215204\pi\) | ||||
−0.780030 | + | 0.625742i | \(0.784796\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.86622e6 | + | 654739.i | −0.295505 | + | 0.103674i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.08715e6 | −1.11159 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.94209e6 | −0.767841 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.11635e6 | + | 893261.i | −0.171816 | + | 0.137481i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.99498e6i | 0.304172i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 1.07475e7i | − | 1.62339i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 892343. | + | 2.54347e6i | 0.133535 | + | 0.380620i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.61930e6 | −0.536602 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.25741e7 | −1.84706 | −0.923532 | − | 0.383520i | \(-0.874712\pi\) | ||||
−0.923532 | + | 0.383520i | \(0.874712\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.91262e6 | − | 5.45160e6i | −0.278374 | − | 0.793459i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.44511e6i | 1.07369i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.40198e6i | − | 0.486143i | −0.970008 | − | 0.243071i | \(-0.921845\pi\) | ||
0.970008 | − | 0.243071i | \(-0.0781549\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.35773e6 | + | 3.48689e6i | −0.617063 | + | 0.493750i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.35754e6 | −1.03241 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.37901e7 | 1.91759 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.34052e6 | − | 821140.i | 0.322537 | − | 0.113158i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.75680e6i | 1.05936i | 0.848197 | + | 0.529681i | \(0.177689\pi\) | ||||
−0.848197 | + | 0.529681i | \(0.822311\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.11738e6i | 0.421950i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.21829e6 | + | 2.18160e6i | −0.834187 | + | 0.292663i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −3.17845e6 | −0.422614 | −0.211307 | − | 0.977420i | \(-0.567772\pi\) | ||||
−0.211307 | + | 0.977420i | \(0.567772\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.94037e6 | 0.914664 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.66456e6 | + | 2.17252e6i | 1.26248 | + | 0.283796i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.26620e7i | 1.63954i | 0.572691 | + | 0.819771i | \(0.305900\pi\) | ||||
−0.572691 | + | 0.819771i | \(0.694100\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 3.92129e6i | − | 0.503314i | −0.967816 | − | 0.251657i | \(-0.919025\pi\) | ||
0.967816 | − | 0.251657i | \(-0.0809755\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.28697e6 | + | 9.36895e6i | 0.418224 | + | 1.19208i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 924496. | 0.116610 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.12254e6 | −0.140366 | −0.0701828 | − | 0.997534i | \(-0.522358\pi\) | ||||
−0.0701828 | + | 0.997534i | \(0.522358\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.08623e6 | + | 1.16471e7i | 0.506554 | + | 1.44385i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 3.20722e6i | − | 0.394174i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.06244e7i | 1.29459i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.12717e6 | + | 1.40867e6i | 0.136175 | + | 0.170185i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.81465e6 | −0.456940 | −0.228470 | − | 0.973551i | \(-0.573372\pi\) | ||||
−0.228470 | + | 0.973551i | \(0.573372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8.65730e6 | −1.02824 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.37638e6 | + | 1.18456e6i | −0.397633 | + | 0.139504i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 6.15809e6i | − | 0.719133i | −0.933119 | − | 0.359567i | \(-0.882925\pi\) | ||
0.933119 | − | 0.359567i | \(-0.117075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.08090e7i | − | 1.25167i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −618476. | + | 216984.i | −0.0710210 | + | 0.0249168i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −8.31895e6 | −0.947331 | −0.473665 | − | 0.880705i | \(-0.657069\pi\) | ||||
−0.473665 | + | 0.880705i | \(0.657069\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.13436e7 | −1.28104 | −0.640521 | − | 0.767941i | \(-0.721282\pi\) | ||||
−0.640521 | + | 0.767941i | \(0.721282\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.11620e6 | + | 2.64472e6i | 0.237009 | + | 0.296201i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.87581e6i | − | 0.319427i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.37972e7i | 1.51991i | 0.649974 | + | 0.759956i | \(0.274780\pi\) | ||||
−0.649974 | + | 0.759956i | \(0.725220\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.93861e6 | − | 1.12263e7i | −0.430328 | − | 1.22658i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −3.05995e6 | −0.331597 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.47858e6 | −0.158926 | −0.0794629 | − | 0.996838i | \(-0.525321\pi\) | ||||
−0.0794629 | + | 0.996838i | \(0.525321\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.28465e6 | + | 9.36234e6i | 0.350188 | + | 0.998152i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.64855e6i | 0.174337i | 0.996194 | + | 0.0871684i | \(0.0277818\pi\) | ||||
−0.996194 | + | 0.0871684i | \(0.972218\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.87090e6i | 0.406056i | 0.979173 | + | 0.203028i | \(0.0650782\pi\) | ||||
−0.979173 | + | 0.203028i | \(0.934922\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.92675e6 | − | 2.45388e6i | −0.408606 | − | 0.255343i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.62824e7 | 1.68073 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.83021e6 | −0.699413 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.59594e6 | + | 2.66493e6i | −0.771636 | + | 0.270718i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.32828e6i | − | 0.436203i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.47448e7i | − | 1.47423i | −0.675765 | − | 0.737117i | \(-0.736187\pi\) | ||
0.675765 | − | 0.737117i | \(-0.263813\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.17935e6 | − | 413759.i | 0.116986 | − | 0.0410429i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.40833e6 | −0.237018 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.72906e6 | 0.168834 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.24548e7 | − | 9.96585e6i | 1.20666 | − | 0.965522i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.09176e7i | 1.04950i | 0.851256 | + | 0.524750i | \(0.175841\pi\) | ||||
−0.851256 | + | 0.524750i | \(0.824159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.82933e7i | − | 1.74487i | −0.488726 | − | 0.872437i | \(-0.662538\pi\) | ||
0.488726 | − | 0.872437i | \(-0.337462\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 5.13265e6 | + | 1.46298e7i | 0.485783 | + | 1.38464i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 381744. | 0.0358518 | 0.0179259 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179259 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.87876e6 | 0.175089 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.63439e6 | − | 1.32095e7i | −0.428588 | − | 1.22162i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1.41687e7i | − | 1.30031i | −0.759800 | − | 0.650157i | \(-0.774703\pi\) | ||
0.759800 | − | 0.650157i | \(-0.225297\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.26725e7i | − | 1.15414i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.05632e7 | + | 8.45225e6i | −0.954731 | + | 0.763939i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.91811e6 | 0.261751 | 0.130876 | − | 0.991399i | \(-0.458221\pi\) | ||||
0.130876 | + | 0.991399i | \(0.458221\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.08812e7 | 0.968662 | 0.484331 | − | 0.874885i | \(-0.339063\pi\) | ||||
0.484331 | + | 0.874885i | \(0.339063\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.97068e6 | − | 1.04222e6i | 0.262465 | − | 0.0920824i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.32037e7i | − | 1.15782i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.56134e6i | 0.484022i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.08200e6 | + | 379607.i | −0.0934682 | + | 0.0327920i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.33382e6 | 0.628816 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.31612e7 | 1.12010 | 0.560049 | − | 0.828459i | \(-0.310782\pi\) | ||||
0.560049 | + | 0.828459i | \(0.310782\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.42949e6 | − | 1.51822e6i | −0.205237 | − | 0.128255i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.27738e6i | − | 0.442534i | −0.975213 | − | 0.221267i | \(-0.928981\pi\) | ||
0.975213 | − | 0.221267i | \(-0.0710193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.67236e7i | 2.22444i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.85328e6 | + | 5.28246e6i | 0.153135 | + | 0.436484i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.46685e6 | 0.612471 | 0.306236 | − | 0.951956i | \(-0.400930\pi\) | ||||
0.306236 | + | 0.951956i | \(0.400930\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.25115e6 | −0.427591 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4.47724e6 | − | 1.27616e7i | −0.361925 | − | 1.03161i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.07562e6i | − | 0.407325i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.56640e6i | 0.363814i | 0.983316 | + | 0.181907i | \(0.0582269\pi\) | ||||
−0.983316 | + | 0.181907i | \(0.941773\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.13246e6 | − | 1.01635e7i | −0.643263 | − | 0.803916i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.43264e6 | 0.348097 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.73136e7 | 1.34991 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 7.64911e6 | − | 2.68359e6i | 0.592131 | − | 0.207741i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 967522.i | 0.0743645i | 0.999309 | + | 0.0371822i | \(0.0118382\pi\) | ||||
−0.999309 | + | 0.0371822i | \(0.988162\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 5.28720e6i | − | 0.403494i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.43602e7 | + | 5.03808e6i | −1.08815 | + | 0.381762i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.29620e7 | 0.975265 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.59701e7 | 1.94025 | 0.970125 | − | 0.242606i | \(-0.0780023\pi\) | ||||
0.970125 | + | 0.242606i | \(0.0780023\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.24802e7 | + | 1.55971e7i | 0.925865 | + | 1.15710i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.54379e6i | 0.482065i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.37072e6i | − | 0.173426i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.06587e6 | − | 3.03808e6i | −0.0774295 | − | 0.220700i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.05306e7 | −0.759677 | −0.379838 | − | 0.925053i | \(-0.624020\pi\) | ||||
−0.379838 | + | 0.925053i | \(0.624020\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.34683e6 | −0.526334 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.51549e6 | + | 2.42720e7i | 0.605848 | + | 1.72687i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.44081e6i | 0.243117i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.45606e7i | − | 1.72347i | −0.507358 | − | 0.861735i | \(-0.669378\pi\) | ||
0.507358 | − | 0.861735i | \(-0.330622\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.28933e6 | + | 1.28971e7i | 0.438314 | + | 0.898822i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.70545e7 | 1.87260 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.82797e7 | 1.25664 | 0.628318 | − | 0.777957i | \(-0.283744\pi\) | ||||
0.628318 | + | 0.777957i | \(0.283744\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 8.11440e6 | − | 2.84683e6i | 0.554036 | − | 0.194376i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.45091e6i | − | 0.301843i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.01860e7i | 1.35969i | 0.733356 | + | 0.679844i | \(0.237953\pi\) | ||||
−0.733356 | + | 0.679844i | \(0.762047\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.62883e6 | − | 1.27313e6i | 0.242785 | − | 0.0851777i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.29183e7 | −1.52304 | −0.761518 | − | 0.648143i | \(-0.775546\pi\) | ||||
−0.761518 | + | 0.648143i | \(0.775546\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.93087e7 | −1.27456 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.62747e6 | − | 2.90257e6i | 0.237850 | − | 0.190318i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.70447e7i | − | 2.41280i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.29724e7i | 1.48630i | 0.669126 | + | 0.743149i | \(0.266669\pi\) | ||||
−0.669126 | + | 0.743149i | \(0.733331\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.05891e6 | + | 2.29706e7i | 0.517951 | + | 1.47633i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.92824e7 | 1.23110 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.71489e7 | −1.08767 | −0.543835 | − | 0.839192i | \(-0.683028\pi\) | ||||
−0.543835 | + | 0.839192i | \(0.683028\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.01434e6 | + | 5.74154e6i | 0.126920 | + | 0.361763i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.55577e6i | 0.410357i | 0.978725 | + | 0.205178i | \(0.0657775\pi\) | ||||
−0.978725 | + | 0.205178i | \(0.934223\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.56620e7i | 1.59580i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.22253e7 | − | 9.78222e6i | 0.755277 | − | 0.604343i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −897544. | −0.0550893 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.14557e7 | −1.30836 | −0.654180 | − | 0.756339i | \(-0.726986\pi\) | ||||
−0.654180 | + | 0.756339i | \(0.726986\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2.22417e7 | + | 7.80322e6i | −1.34751 | + | 0.472757i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.13075e7i | − | 0.680640i | −0.940310 | − | 0.340320i | \(-0.889465\pi\) | ||
0.940310 | − | 0.340320i | \(-0.110535\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.04865e6i | 0.242134i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.06736e6 | − | 2.83032e6i | 0.479379 | − | 0.168184i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.11494e7 | 1.24869 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.09607e7 | −1.22964 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.13290e6 | − | 1.46147e7i | 0.532359 | − | 0.851892i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 4.48100e6i | − | 0.259538i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 619355.i | 0.0356454i | 0.999841 | + | 0.0178227i | \(0.00567344\pi\) | ||||
−0.999841 | + | 0.0178227i | \(0.994327\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.99743e6 | + | 5.69333e6i | 0.114230 | + | 0.325592i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.39222e7 | 1.35944 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.50361e6 | −0.197848 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.35682e6 | − | 2.38197e7i | −0.468946 | − | 1.33665i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.08343e6i | − | 0.116180i | −0.998311 | − | 0.0580901i | \(-0.981499\pi\) | ||
0.998311 | − | 0.0580901i | \(-0.0185011\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.65560e7i | 1.47162i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47358e7 | + | 1.84160e7i | 0.811505 | + | 1.01418i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.77772e7 | 0.972916 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.98025e6 | −0.542815 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.39572e7 | + | 8.40506e6i | −1.29495 | + | 0.454315i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 343117.i | 0.0184320i | 0.999958 | + | 0.00921598i | \(0.00293358\pi\) | ||||
−0.999958 | + | 0.00921598i | \(0.997066\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 3.02023e6i | − | 0.161246i | −0.996745 | − | 0.0806228i | \(-0.974309\pi\) | ||
0.996745 | − | 0.0806228i | \(-0.0256909\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.08907e6 | + | 2.83794e6i | −0.429212 | + | 0.150583i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.45716e7 | 0.768447 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.30484e7 | 1.73219 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.88514e6 | + | 4.85545e6i | 0.202394 | + | 0.252941i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 4.37269e6i | − | 0.226407i | −0.993572 | − | 0.113204i | \(-0.963889\pi\) | ||
0.993572 | − | 0.113204i | \(-0.0361113\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.95780e7i | − | 1.52219i | −0.648641 | − | 0.761095i | \(-0.724662\pi\) | ||
0.648641 | − | 0.761095i | \(-0.275338\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.24628e6 | + | 3.55230e6i | 0.0637499 | + | 0.181708i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.90787e7 | 1.47846 | 0.739232 | − | 0.673451i | \(-0.235189\pi\) | ||||
0.739232 | + | 0.673451i | \(0.235189\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.57279e7 | 1.30023 | 0.650113 | − | 0.759838i | \(-0.274722\pi\) | ||||
0.650113 | + | 0.759838i | \(0.274722\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.11157e6 | + | 2.02703e7i | 0.357242 | + | 1.01826i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1.50058e7i | − | 0.749284i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.97691e6i | 0.147758i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.07463e7 | − | 1.71964e7i | 0.530206 | − | 0.848447i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.13952e7 | 0.558877 | 0.279439 | − | 0.960164i | \(-0.409852\pi\) | ||||
0.279439 | + | 0.960164i | \(0.409852\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −187181. | −0.00912581 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.99642e7 | + | 1.05125e7i | −1.45222 | + | 0.509492i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.69380e7i | − | 0.816057i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 9.91239e6i | − | 0.474756i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.70227e7 | − | 5.97219e6i | 0.810513 | − | 0.284357i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.99644e6 | −0.189169 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.53215e6 | −0.166213 | −0.0831067 | − | 0.996541i | \(-0.526484\pi\) | ||||
−0.0831067 | + | 0.996541i | \(0.526484\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.49338e7 | − | 1.19495e7i | 0.698643 | − | 0.559027i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.78472e7i | − | 1.29518i | −0.761990 | − | 0.647589i | \(-0.775777\pi\) | ||
0.761990 | − | 0.647589i | \(-0.224223\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.12202e6i | 0.421801i | 0.977508 | + | 0.210901i | \(0.0676397\pi\) | ||||
−0.977508 | + | 0.210901i | \(0.932360\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.13216e7 | + | 3.22703e7i | 0.520475 | + | 1.48353i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.82202e7 | −1.74689 | −0.873445 | − | 0.486923i | \(-0.838119\pi\) | ||||
−0.873445 | + | 0.486923i | \(0.838119\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.70062e7 | −0.772801 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.71770e6 | − | 4.89600e6i | −0.0776066 | − | 0.221204i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 2.62491e7i | − | 1.17914i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.12635e6i | 0.0949706i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.02254e7 | + | 2.41852e7i | −1.34226 | + | 1.07402i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.16888e7 | −1.39922 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.52280e7 | 0.668566 | 0.334283 | − | 0.942473i | \(-0.391506\pi\) | ||||
0.334283 | + | 0.942473i | \(0.391506\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.65342e7 | − | 1.28175e7i | 1.59488 | − | 0.559541i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.39351e7i | 1.03895i | 0.854485 | + | 0.519477i | \(0.173873\pi\) | ||||
−0.854485 | + | 0.519477i | \(0.826127\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 4.20111e7i | − | 1.81327i | −0.421919 | − | 0.906634i | \(-0.638643\pi\) | ||
0.421919 | − | 0.906634i | \(-0.361357\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.21214e6 | + | 1.47777e6i | −0.180777 | + | 0.0634233i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.42404e7 | 0.607735 | 0.303867 | − | 0.952714i | \(-0.401722\pi\) | ||||
0.303867 | + | 0.952714i | \(0.401722\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.30108e6 | −0.352274 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.13533e6 | − | 1.83962e7i | 0.174508 | − | 0.776307i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.24395e7i | 1.36127i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.41562e6i | 0.351179i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −962318. | − | 2.74292e6i | −0.0399335 | − | 0.113824i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.43548e7 | −1.00505 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.40493e7 | −1.80770 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.76913e7 | + | 5.04261e7i | 0.722006 | + | 2.05796i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 1.80378e7i | − | 0.732084i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9.67370e6i | 0.390458i | 0.980758 | + | 0.195229i | \(0.0625450\pi\) | ||||
−0.980758 | + | 0.195229i | \(0.937455\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.17307e7 | + | 1.46604e7i | 0.470886 | + | 0.588488i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 915385. | 0.0365433 | 0.0182716 | − | 0.999833i | \(-0.494184\pi\) | ||||
0.0182716 | + | 0.999833i | \(0.494184\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.10484e6 | −0.242380 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1.64423e7 | + | 5.76855e6i | −0.649246 | + | 0.227779i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 4.36799e7i | − | 1.71537i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.37044e7i | − | 0.925849i | −0.886398 | − | 0.462925i | \(-0.846800\pi\) | ||
0.886398 | − | 0.462925i | \(-0.153200\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.74508e7 | + | 1.31391e7i | −1.45483 | + | 0.510408i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.00136e7 | 0.386890 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.47260e6 | −0.0950166 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.64896e6 | − | 8.30952e6i | −0.254129 | − | 0.317597i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 726976.i | − | 0.0276364i | −0.999905 | − | 0.0138182i | \(-0.995601\pi\) | ||
0.999905 | − | 0.0138182i | \(-0.00439860\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.83303e7i | − | 0.693099i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.37411e7 | + | 3.91666e7i | 0.516793 | + | 1.47303i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.05745e7 | −0.769662 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.31585e7 | −0.489617 | −0.244808 | − | 0.969571i | \(-0.578725\pi\) | ||||
−0.244808 | + | 0.969571i | \(0.578725\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.06525e6 | − | 5.88665e6i | −0.0764379 | − | 0.217873i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.83098e7i | 1.04223i | 0.853488 | + | 0.521113i | \(0.174483\pi\) | ||||
−0.853488 | + | 0.521113i | \(0.825517\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.59862e7i | − | 0.585417i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.62271e7 | + | 1.63897e7i | 0.955369 | + | 0.597023i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.47806e7 | 1.26026 | 0.630132 | − | 0.776488i | \(-0.283001\pi\) | ||||
0.630132 | + | 0.776488i | \(0.283001\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.49277e6 | −0.306115 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.27156e7 | − | 7.96946e6i | 0.814465 | − | 0.285744i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.91370e7i | 1.03923i | 0.854399 | + | 0.519617i | \(0.173925\pi\) | ||||
−0.854399 | + | 0.519617i | \(0.826075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.09991e7i | 1.09987i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.13690e7 | + | 7.49702e6i | −0.754231 | + | 0.264612i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.80998e7 | −0.635516 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28086.4 | −0.000981042 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.18989e7 | − | 3.35259e7i | 1.45592 | − | 1.16497i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.85369e7i | 1.33217i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.15601e7i | 0.397554i | 0.980045 | + | 0.198777i | \(0.0636969\pi\) | ||||
−0.980045 | + | 0.198777i | \(0.936303\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.10489e7 | − | 3.14931e7i | −0.378017 | − | 1.07747i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.20504e7 | −0.410161 | −0.205080 | − | 0.978745i | \(-0.565746\pi\) | ||||
−0.205080 | + | 0.978745i | \(0.565746\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.52785e7 | 0.517368 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −595387. | − | 1.69705e6i | −0.0200580 | − | 0.0571720i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 2.16156e7i | − | 0.724487i | −0.932084 | − | 0.362243i | \(-0.882011\pi\) | ||
0.932084 | − | 0.362243i | \(-0.117989\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 3.09931e7i | − | 1.03349i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.90246e7 | + | 2.32244e7i | −0.962927 | + | 0.770497i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.88290e7 | −1.28166 | −0.640829 | − | 0.767684i | \(-0.721409\pi\) | ||||
−0.640829 | + | 0.767684i | \(0.721409\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.11715e7 | −0.366876 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.94971e7 | + | 1.73654e7i | −1.61729 | + | 0.567403i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.49803e7i | − | 0.812094i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.70519e7i | 1.52192i | 0.648797 | + | 0.760962i | \(0.275272\pi\) | ||||
−0.648797 | + | 0.760962i | \(0.724728\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.97109e6 | − | 1.74404e6i | 0.159985 | − | 0.0561285i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.04636e6 | −0.0655275 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −5.60514e6 | −0.178586 | −0.0892932 | − | 0.996005i | \(-0.528461\pi\) | ||||
−0.0892932 | + | 0.996005i | \(0.528461\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.05022e7 | + | 6.56299e6i | 0.332942 | + | 0.208060i |
(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 | 384.6.c.d.383.14 | yes | 20 | |
3.2 | odd | 2 | 384.6.c.a.383.8 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.a.383.7 | ✓ | 20 | ||
8.3 | odd | 2 | 384.6.c.c.383.14 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.b.383.7 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.d.383.13 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.c.383.13 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.b.383.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.7 | ✓ | 20 | 4.3 | odd | 2 | ||
384.6.c.a.383.8 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.b.383.7 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.b.383.8 | yes | 20 | 24.11 | even | 2 | ||
384.6.c.c.383.13 | yes | 20 | 24.5 | odd | 2 | ||
384.6.c.c.383.14 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.d.383.13 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.d.383.14 | yes | 20 | 1.1 | even | 1 | trivial |