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: | \( x^{20} + 306 x^{18} + 37827 x^{16} + 2442168 x^{14} + 88368509 x^{12} + 1774000974 x^{10} + \cdots + 2870280625 \) |
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 | 383.15 | ||
Root | \(0.406991i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.383 |
Dual form | 384.6.c.c.383.16 |
$q$-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 | ||||||||
\(3\) | 10.1204 | − | 11.8566i | 0.649222 | − | 0.760599i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 19.3214i | − | 0.345632i | −0.984954 | − | 0.172816i | \(-0.944713\pi\) | ||
0.984954 | − | 0.172816i | \(-0.0552867\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 82.7816i | 0.638541i | 0.947664 | + | 0.319271i | \(0.103438\pi\) | ||||
−0.947664 | + | 0.319271i | \(0.896562\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −38.1561 | − | 239.986i | −0.157021 | − | 0.987595i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 332.396 | 0.828273 | 0.414137 | − | 0.910215i | \(-0.364084\pi\) | ||||
0.414137 | + | 0.910215i | \(0.364084\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1171.14 | −1.92199 | −0.960994 | − | 0.276568i | \(-0.910803\pi\) | ||||
−0.960994 | + | 0.276568i | \(0.910803\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −229.086 | − | 195.540i | −0.262888 | − | 0.224392i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1984.58i | 1.66551i | 0.553644 | + | 0.832754i | \(0.313237\pi\) | ||||
−0.553644 | + | 0.832754i | \(0.686763\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1346.21i | 0.855520i | 0.903892 | + | 0.427760i | \(0.140697\pi\) | ||||
−0.903892 | + | 0.427760i | \(0.859303\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 981.506 | + | 837.781i | 0.485674 | + | 0.414555i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1833.50 | 0.722704 | 0.361352 | − | 0.932429i | \(-0.382315\pi\) | ||||
0.361352 | + | 0.932429i | \(0.382315\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2751.68 | 0.880538 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3231.56 | − | 1976.34i | −0.853105 | − | 0.521739i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1923.64i | − | 0.424747i | −0.977189 | − | 0.212373i | \(-0.931881\pi\) | ||
0.977189 | − | 0.212373i | \(-0.0681193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5801.19i | 1.08421i | 0.840311 | + | 0.542104i | \(0.182372\pi\) | ||||
−0.840311 | + | 0.542104i | \(0.817628\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3363.97 | − | 3941.07i | 0.537733 | − | 0.629984i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1599.46 | 0.220701 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6805.63 | −0.817267 | −0.408634 | − | 0.912698i | \(-0.633995\pi\) | ||||
−0.408634 | + | 0.912698i | \(0.633995\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11852.4 | + | 13885.7i | −1.24780 | + | 1.46186i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4150.50i | 0.385603i | 0.981238 | + | 0.192801i | \(0.0617573\pi\) | ||||
−0.981238 | + | 0.192801i | \(0.938243\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8370.22i | 0.690344i | 0.938539 | + | 0.345172i | \(0.112179\pi\) | ||||
−0.938539 | + | 0.345172i | \(0.887821\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4636.87 | + | 737.231i | −0.341345 | + | 0.0542716i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1805.52 | −0.119222 | −0.0596111 | − | 0.998222i | \(-0.518986\pi\) | ||||
−0.0596111 | + | 0.998222i | \(0.518986\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9954.20 | 0.592265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 23530.3 | + | 20084.7i | 1.26678 | + | 1.08128i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 22703.3i | 1.11019i | 0.831786 | + | 0.555097i | \(0.187319\pi\) | ||||
−0.831786 | + | 0.555097i | \(0.812681\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 6422.36i | − | 0.286278i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 15961.5 | + | 13624.2i | 0.650708 | + | 0.555423i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −18653.9 | −0.697654 | −0.348827 | − | 0.937187i | \(-0.613420\pi\) | ||||
−0.348827 | + | 0.937187i | \(0.613420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 19502.5 | 0.671066 | 0.335533 | − | 0.942028i | \(-0.391084\pi\) | ||||
0.335533 | + | 0.942028i | \(0.391084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19866.4 | − | 3158.63i | 0.630620 | − | 0.100264i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 22628.1i | 0.664302i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 50953.6i | − | 1.38672i | −0.720592 | − | 0.693359i | \(-0.756130\pi\) | ||
0.720592 | − | 0.693359i | \(-0.243870\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 18555.7 | − | 21739.0i | 0.469196 | − | 0.549688i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −69899.0 | −1.64560 | −0.822801 | − | 0.568329i | \(-0.807590\pi\) | ||||
−0.822801 | + | 0.568329i | \(0.807590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 37035.5 | 0.813414 | 0.406707 | − | 0.913559i | \(-0.366677\pi\) | ||||
0.406707 | + | 0.913559i | \(0.366677\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 27848.0 | − | 32625.5i | 0.571665 | − | 0.669736i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27516.3i | 0.528887i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 50543.7i | 0.911170i | 0.890192 | + | 0.455585i | \(0.150570\pi\) | ||||
−0.890192 | + | 0.455585i | \(0.849430\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −56137.2 | + | 18313.8i | −0.950689 | + | 0.310147i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 96377.3 | 1.53560 | 0.767802 | − | 0.640687i | \(-0.221350\pi\) | ||||
0.767802 | + | 0.640687i | \(0.221350\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 38345.0 | 0.575653 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −22807.8 | − | 19468.0i | −0.323062 | − | 0.275755i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17995.1i | 0.240812i | 0.992725 | + | 0.120406i | \(0.0384196\pi\) | ||||
−0.992725 | + | 0.120406i | \(0.961580\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 96949.0i | − | 1.22727i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 68782.2 | + | 58710.2i | 0.824648 | + | 0.703892i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26010.8 | 0.295695 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 48381.9 | 0.522100 | 0.261050 | − | 0.965325i | \(-0.415931\pi\) | ||||
0.261050 | + | 0.965325i | \(0.415931\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12682.9 | − | 79770.2i | −0.130056 | − | 0.817999i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 101239.i | 0.987512i | 0.869600 | + | 0.493756i | \(0.164376\pi\) | ||||
−0.869600 | + | 0.493756i | \(0.835624\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 26652.9i | 0.247544i | 0.992311 | + | 0.123772i | \(0.0394991\pi\) | ||||
−0.992311 | + | 0.123772i | \(0.960501\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16187.1 | − | 18964.1i | 0.143284 | − | 0.167865i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12661.8 | 0.106914 | 0.0534571 | − | 0.998570i | \(-0.482976\pi\) | ||||
0.0534571 | + | 0.998570i | \(0.482976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 198283. | 1.59852 | 0.799262 | − | 0.600983i | \(-0.205224\pi\) | ||||
0.799262 | + | 0.600983i | \(0.205224\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −68875.5 | + | 80691.4i | −0.530588 | + | 0.621613i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 225671.i | 1.66257i | 0.555849 | + | 0.831284i | \(0.312393\pi\) | ||||
−0.555849 | + | 0.831284i | \(0.687607\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 35425.8i | − | 0.249790i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 44686.2 | + | 281057.i | 0.301793 | + | 1.89815i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −164287. | −1.06350 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −50564.1 | −0.313963 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 49210.6 | + | 42004.6i | 0.293289 | + | 0.250342i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 113546.i | − | 0.649975i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 99291.9i | − | 0.546266i | −0.961976 | − | 0.273133i | \(-0.911940\pi\) | ||
0.961976 | − | 0.273133i | \(-0.0880600\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 99242.0 | + | 84709.7i | 0.525075 | + | 0.448187i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 253584. | 1.29105 | 0.645527 | − | 0.763737i | \(-0.276638\pi\) | ||||
0.645527 | + | 0.763737i | \(0.276638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −111442. | −0.546285 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −38185.8 | + | 62438.4i | −0.180330 | + | 0.294861i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 47885.6i | 0.217973i | 0.994043 | + | 0.108987i | \(0.0347606\pi\) | ||||
−0.994043 | + | 0.108987i | \(0.965239\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 199921.i | − | 0.877652i | −0.898572 | − | 0.438826i | \(-0.855394\pi\) | ||
0.898572 | − | 0.438826i | \(-0.144606\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18272.5 | + | 21407.2i | −0.0774017 | + | 0.0906802i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −389282. | −1.59193 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −37167.6 | −0.146806 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 100740. | − | 118023.i | 0.384512 | − | 0.450476i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 63727.7i | − | 0.235159i | −0.993063 | − | 0.117580i | \(-0.962486\pi\) | ||
0.993063 | − | 0.117580i | \(-0.0375136\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 446578.i | 1.59388i | 0.604060 | + | 0.796939i | \(0.293549\pi\) | ||||
−0.604060 | + | 0.796939i | \(0.706451\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 476271. | − | 75723.9i | 1.64485 | − | 0.261520i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 112087. | 0.374738 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 266348. | 0.862384 | 0.431192 | − | 0.902260i | \(-0.358093\pi\) | ||||
0.431192 | + | 0.902260i | \(0.358093\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 269183. | + | 229766.i | 0.844412 | + | 0.720762i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 151780.i | 0.461476i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 244693.i | 0.721361i | 0.932689 | + | 0.360680i | \(0.117455\pi\) | ||||
−0.932689 | + | 0.360680i | \(0.882545\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −76147.1 | − | 64996.7i | −0.217743 | − | 0.185858i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 199361. | 0.553157 | 0.276579 | − | 0.960991i | \(-0.410799\pi\) | ||||
0.276579 | + | 0.960991i | \(0.410799\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00028e6 | 2.69404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 323072. | − | 51366.3i | 0.844908 | − | 0.134335i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 322299.i | 0.818736i | 0.912369 | + | 0.409368i | \(0.134251\pi\) | ||||
−0.912369 | + | 0.409368i | \(0.865749\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 227789.i | 0.562260i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −188785. | + | 221171.i | −0.452933 | + | 0.530635i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −853012. | −1.98986 | −0.994930 | − | 0.100570i | \(-0.967933\pi\) | ||||
−0.994930 | + | 0.100570i | \(0.967933\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −434775. | −0.986434 | −0.493217 | − | 0.869906i | \(-0.664179\pi\) | ||||
−0.493217 | + | 0.869906i | \(0.664179\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 197372. | − | 231232.i | 0.435671 | − | 0.510412i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 131495.i | 0.282474i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 659666.i | 1.37950i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 163605. | − | 267514.i | 0.333152 | − | 0.544743i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −946078. | −1.87648 | −0.938239 | − | 0.345987i | \(-0.887544\pi\) | ||||
−0.938239 | + | 0.345987i | \(0.887544\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −512156. | −0.989712 | −0.494856 | − | 0.868975i | \(-0.664779\pi\) | ||||
−0.494856 | + | 0.868975i | \(0.664779\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 268292. | + | 229005.i | 0.505267 | + | 0.431279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 589256.i | 1.08178i | 0.841094 | + | 0.540890i | \(0.181912\pi\) | ||||
−0.841094 | + | 0.540890i | \(0.818088\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 2967.84i | − | 0.00531260i | −0.999996 | − | 0.00265630i | \(-0.999154\pi\) | ||
0.999996 | − | 0.00265630i | \(-0.000845528\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −604135. | − | 515670.i | −1.05474 | − | 0.900288i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 159242. | 0.271218 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 80193.6 | 0.133277 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −69959.1 | − | 440013.i | −0.113480 | − | 0.713739i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 447476.i | 0.708604i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 768116.i | − | 1.18774i | −0.804562 | − | 0.593869i | \(-0.797600\pi\) | ||
0.804562 | − | 0.593869i | \(-0.202400\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −707404. | + | 828762.i | −1.06836 | + | 1.25164i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 161725. | 0.238605 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −480232. | −0.692312 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 374813. | − | 439114.i | 0.528086 | − | 0.618682i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.32422e6i | − | 3.20109i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 288136.i | 0.388003i | 0.981001 | + | 0.194001i | \(0.0621466\pi\) | ||||
−0.981001 | + | 0.194001i | \(0.937853\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −104994. | − | 660364.i | −0.138263 | − | 0.869615i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −805116. | −1.03704 | −0.518518 | − | 0.855067i | \(-0.673516\pi\) | ||||
−0.518518 | + | 0.855067i | \(0.673516\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 164519. | 0.207313 | 0.103657 | − | 0.994613i | \(-0.466946\pi\) | ||||
0.103657 | + | 0.994613i | \(0.466946\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 326248. | + | 278475.i | 0.402270 | + | 0.343365i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 470691.i | − | 0.567997i | −0.958825 | − | 0.283998i | \(-0.908339\pi\) | ||
0.958825 | − | 0.283998i | \(-0.0916610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34885.2i | 0.0412070i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 599274. | + | 511521.i | 0.693035 | + | 0.591552i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.53286e6 | 1.73584 | 0.867919 | − | 0.496706i | \(-0.165457\pi\) | ||||
0.867919 | + | 0.496706i | \(0.165457\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −924322. | −1.02513 | −0.512567 | − | 0.858647i | \(-0.671305\pi\) | ||||
−0.512567 | + | 0.858647i | \(0.671305\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −350990. | + | 850937.i | −0.381311 | + | 0.924447i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 192329.i | − | 0.204706i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.57661e6i | − | 1.64430i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 975374. | − | 1.14270e6i | 0.996949 | − | 1.16798i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.28007e6 | −1.28248 | −0.641238 | − | 0.767342i | \(-0.721579\pi\) | ||||
−0.641238 | + | 0.767342i | \(0.721579\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 609446. | 0.598596 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 388065. | − | 454639.i | 0.373727 | − | 0.437841i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.72426e6i | 1.62843i | 0.580561 | + | 0.814217i | \(0.302833\pi\) | ||||
−0.580561 | + | 0.814217i | \(0.697167\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 563381.i | − | 0.521859i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −461647. | + | 73398.8i | −0.419478 | + | 0.0666942i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 39731.5 | 0.0354197 | 0.0177099 | − | 0.999843i | \(-0.494362\pi\) | ||||
0.0177099 | + | 0.999843i | \(0.494362\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 438660. | 0.383719 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 213359. | + | 182117.i | 0.183161 | + | 0.156341i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 280025.i | − | 0.235948i | −0.993017 | − | 0.117974i | \(-0.962360\pi\) | ||
0.993017 | − | 0.117974i | \(-0.0376399\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 2.25288e6i | − | 1.86344i | −0.363178 | − | 0.931720i | \(-0.618308\pi\) | ||
0.363178 | − | 0.931720i | \(-0.381692\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.14948e6 | − | 981160.i | −0.933459 | − | 0.796770i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 914647. | 0.729326 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.14847e6 | −0.899334 | −0.449667 | − | 0.893196i | \(-0.648457\pi\) | ||||
−0.449667 | + | 0.893196i | \(0.648457\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.39220e6 | − | 221351.i | 1.07076 | − | 0.170244i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.52077e6i | − | 1.14894i | −0.818524 | − | 0.574472i | \(-0.805207\pi\) | ||
0.818524 | − | 0.574472i | \(-0.194793\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 610831.i | 0.453372i | 0.973968 | + | 0.226686i | \(0.0727891\pi\) | ||||
−0.973968 | + | 0.226686i | \(0.927211\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 263239. | − | 308399.i | 0.191972 | − | 0.224906i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −343585. | −0.246223 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.51871e6 | −1.77392 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 489643. | − | 573643.i | 0.338959 | − | 0.397108i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.29419e6i | − | 1.56121i | −0.625025 | − | 0.780605i | \(-0.714911\pi\) | ||
0.625025 | − | 0.780605i | \(-0.285089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 360421.i | 0.241132i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.07416e6 | − | 656928.i | −0.706604 | − | 0.432142i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.14728e6 | −1.38903 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −692901. | −0.440813 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.20034e6 | + | 1.02457e6i | 0.751101 | + | 0.641115i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 376816.i | − | 0.231942i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.25996e6i | 1.36853i | 0.729233 | + | 0.684265i | \(0.239877\pi\) | ||||
−0.729233 | + | 0.684265i | \(0.760123\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 316012. | + | 269737.i | 0.188281 | + | 0.160711i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.99587e6 | −1.75639 | −0.878196 | − | 0.478301i | \(-0.841253\pi\) | ||||
−0.878196 | + | 0.478301i | \(0.841253\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 686360. | 0.395996 | 0.197998 | − | 0.980202i | \(-0.436556\pi\) | ||||
0.197998 | + | 0.980202i | \(0.436556\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −61029.2 | − | 383848.i | −0.0346546 | − | 0.217963i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 2.99429e6i | − | 1.67358i | −0.547525 | − | 0.836789i | \(-0.684430\pi\) | ||
0.547525 | − | 0.836789i | \(-0.315570\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 639411.i | − | 0.351806i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 128142. | − | 150125.i | 0.0694111 | − | 0.0813188i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.67167e6 | −1.42488 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.22261e6 | −1.69238 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.00670e6 | − | 2.35095e6i | 1.03780 | − | 1.21584i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 149464.i | − | 0.0761282i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.25988e6i | 0.632064i | 0.948749 | + | 0.316032i | \(0.102351\pi\) | ||||
−0.948749 | + | 0.316032i | \(0.897649\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 259677. | + | 1.63325e6i | 0.128328 | + | 0.807129i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −984497. | −0.479295 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.52288e6 | 0.730452 | 0.365226 | − | 0.930919i | \(-0.380992\pi\) | ||||
0.365226 | + | 0.930919i | \(0.380992\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.67568e6 | + | 2.28387e6i | 1.26455 | + | 1.07938i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.92829e6i | 0.898021i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.21534e6i | 1.01673i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −420028. | − | 358522.i | −0.189990 | − | 0.162169i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.32360e6 | −1.03595 | −0.517974 | − | 0.855396i | \(-0.673314\pi\) | ||||
−0.517974 | + | 0.855396i | \(0.673314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 481189. | 0.211472 | 0.105736 | − | 0.994394i | \(-0.466280\pi\) | ||||
0.105736 | + | 0.994394i | \(0.466280\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.78461e6 | + | 2.31458e6i | 1.63966 | + | 1.00278i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 168846.i | − | 0.0721197i | −0.999350 | − | 0.0360598i | \(-0.988519\pi\) | ||
0.999350 | − | 0.0360598i | \(-0.0114807\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35055e6i | 0.568774i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.66264e6 | + | 1.94788e6i | −0.690445 | + | 0.808893i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 272248. | 0.111488 | 0.0557441 | − | 0.998445i | \(-0.482247\pi\) | ||||
0.0557441 | + | 0.998445i | \(0.482247\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 663806. | 0.268085 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −511728. | + | 599517.i | −0.203832 | + | 0.238800i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 715580.i | − | 0.281142i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 118260.i | 0.0458325i | 0.999737 | + | 0.0229163i | \(0.00729511\pi\) | ||||
−0.999737 | + | 0.0229163i | \(0.992705\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 996059. | − | 158367.i | 0.380820 | − | 0.0605478i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.87941e6 | −0.708904 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −525577. | −0.195598 | −0.0977989 | − | 0.995206i | \(-0.531180\pi\) | ||||
−0.0977989 | + | 0.995206i | \(0.531180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.34626e6 | − | 1.14913e6i | −0.494370 | − | 0.421978i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.25286e6i | 0.816358i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 806611.i | − | 0.288447i | −0.989545 | − | 0.144224i | \(-0.953932\pi\) | ||
0.989545 | − | 0.144224i | \(-0.0460684\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.17726e6 | − | 1.00487e6i | −0.415490 | − | 0.354648i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.37292e6 | 0.478241 | 0.239121 | − | 0.970990i | \(-0.423141\pi\) | ||||
0.239121 | + | 0.970990i | \(0.423141\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 531654. | 0.182800 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.00873e6 | − | 319375.i | 0.681781 | − | 0.108399i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 5.48298e6i | − | 1.83714i | −0.395258 | − | 0.918570i | \(-0.629345\pi\) | ||
0.395258 | − | 0.918570i | \(-0.370655\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.63872e6i | 1.20367i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.56637e6 | − | 3.00664e6i | 0.838181 | − | 0.981974i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 976577. | 0.314930 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −65596.8 | −0.0208885 | −0.0104442 | − | 0.999945i | \(-0.503325\pi\) | ||||
−0.0104442 | + | 0.999945i | \(0.503325\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.12783e6 | + | 1.32132e6i | −0.354660 | + | 0.415504i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.35838e6i | 0.732409i | 0.930534 | + | 0.366205i | \(0.119343\pi\) | ||||
−0.930534 | + | 0.366205i | \(0.880657\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 6.79401e6i | − | 2.08384i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 353850. | + | 1.08465e6i | 0.107197 | + | 0.328589i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.26216e6 | −0.676921 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −40774.2 | −0.0120525 | −0.00602625 | − | 0.999982i | \(-0.501918\pi\) | ||||
−0.00602625 | + | 0.999982i | \(0.501918\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 567758. | + | 484620.i | 0.165790 | + | 0.141513i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.54420e6i | − | 0.445481i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.86215e6i | − | 0.530755i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.37038e6 | − | 2.02328e6i | −0.667541 | − | 0.569791i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.09087e6 | 0.581824 | 0.290912 | − | 0.956750i | \(-0.406041\pi\) | ||||
0.290912 | + | 0.956750i | \(0.406041\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.59228e6 | 1.53774 | 0.768871 | − | 0.639403i | \(-0.220819\pi\) | ||||
0.768871 | + | 0.639403i | \(0.220819\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 68891.5 | + | 433298.i | 0.0187204 | + | 0.117743i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.46094e6i | 1.46654i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.61445e6i | 0.428503i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.93968e6 | + | 4.61555e6i | −1.03352 | + | 1.21082i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.47562e6 | −0.901236 | −0.450618 | − | 0.892717i | \(-0.648796\pi\) | ||||
−0.450618 | + | 0.892717i | \(0.648796\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 262773. | 0.0673537 | 0.0336768 | − | 0.999433i | \(-0.489278\pi\) | ||||
0.0336768 | + | 0.999433i | \(0.489278\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −376150. | + | 440680.i | −0.0953098 | + | 0.111661i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.46828e6i | 0.618288i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.40059e6i | − | 1.33746i | −0.743506 | − | 0.668729i | \(-0.766839\pi\) | ||
0.743506 | − | 0.668729i | \(-0.233161\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −379814. | − | 2.38887e6i | −0.0929981 | − | 0.584918i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.14902e6 | 1.00447 | 0.502234 | − | 0.864732i | \(-0.332512\pi\) | ||||
0.502234 | + | 0.864732i | \(0.332512\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 347690. | 0.0832324 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −755591. | − | 644948.i | −0.178862 | − | 0.152671i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.27971e6i | 1.23593i | 0.786205 | + | 0.617966i | \(0.212043\pi\) | ||||
−0.786205 | + | 0.617966i | \(0.787957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.37961e6i | 0.319385i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.29488e6 | + | 4.51954e6i | 1.21230 | + | 1.03478i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.87319e6 | −0.424184 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.04997e6 | −1.35507 | −0.677537 | − | 0.735489i | \(-0.736953\pi\) | ||||
−0.677537 | + | 0.735489i | \(0.736953\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.92221e6 | − | 6.41329e6i | 0.868960 | − | 1.42085i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.14860e6i | 1.12833i | 0.825661 | + | 0.564166i | \(0.190802\pi\) | ||||
−0.825661 | + | 0.564166i | \(0.809198\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 311898.i | 0.0676176i | 0.999428 | + | 0.0338088i | \(0.0107637\pi\) | ||||
−0.999428 | + | 0.0338088i | \(0.989236\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.13437e6 | − | 1.32897e6i | 0.243288 | − | 0.285025i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.10534e6 | −0.658895 | −0.329448 | − | 0.944174i | \(-0.606863\pi\) | ||||
−0.329448 | + | 0.944174i | \(0.606863\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.21803e6 | 0.885477 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.69554e6 | − | 3.15797e6i | 0.559879 | − | 0.655928i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.78222e6i | 0.571794i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.70435e6i | 0.753318i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.44846e6 | − | 866269.i | 1.09642 | − | 0.174324i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.51933e6 | −0.700845 | −0.350422 | − | 0.936592i | \(-0.613962\pi\) | ||||
−0.350422 | + | 0.936592i | \(0.613962\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.97036e6 | 1.57078 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.79959e6 | + | 1.53607e6i | 0.350998 | + | 0.299601i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 934807.i | − | 0.180455i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.00090e7i | 1.91235i | 0.292791 | + | 0.956177i | \(0.405416\pi\) | ||||
−0.292791 | + | 0.956177i | \(0.594584\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.90122e6 | + | 2.47638e6i | 0.548666 | + | 0.468323i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.74286e6 | −0.887844 | −0.443922 | − | 0.896066i | \(-0.646413\pi\) | ||||
−0.443922 | + | 0.896066i | \(0.646413\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.81763e6 | 0.707419 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.54127e6 | + | 245052.i | −0.282727 | + | 0.0449517i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 5.78635e6i | − | 1.05079i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.00050e7i | − | 1.79872i | −0.437209 | − | 0.899360i | \(-0.644033\pi\) | ||
0.437209 | − | 0.899360i | \(-0.355967\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.01761e6 | − | 2.36373e6i | 0.359122 | − | 0.420731i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 118388. | 0.0208635 | 0.0104317 | − | 0.999946i | \(-0.496679\pi\) | ||||
0.0104317 | + | 0.999946i | \(0.496679\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.95607e6 | 0.341316 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.01232e7 | − | 1.18599e7i | 1.74903 | − | 2.04908i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.60168e6i | 1.12943i | 0.825285 | + | 0.564716i | \(0.191014\pi\) | ||||
−0.825285 | + | 0.564716i | \(0.808986\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.06586e6i | 0.519398i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.66058e6 | − | 4.35037e6i | 0.446358 | − | 0.729849i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 514973. | 0.0855591 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −600146. | −0.0987485 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.82136e6 | + | 3.26179e6i | 0.622729 | + | 0.531541i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.04770e6i | 0.976103i | 0.872815 | + | 0.488052i | \(0.162292\pi\) | ||||
−0.872815 | + | 0.488052i | \(0.837708\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.86066e6i | − | 0.297449i | −0.988879 | − | 0.148724i | \(-0.952483\pi\) | ||
0.988879 | − | 0.148724i | \(-0.0475167\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.70079e6 | + | 2.30531e6i | 0.427654 | + | 0.365032i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.15129e7 | −1.80576 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.07463e6 | −0.477699 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 711762. | + | 4.47668e6i | 0.109546 | + | 0.689000i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 4.86082e6i | − | 0.741125i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 244644.i | − | 0.0369530i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.63280e6 | + | 1.01138e7i | −1.29186 | + | 1.51349i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.30873e6 | 0.490557 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.48260e6 | −0.511577 | −0.255788 | − | 0.966733i | \(-0.582335\pi\) | ||||
−0.255788 | + | 0.966733i | \(0.582335\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.40009e6 | + | 5.15494e6i | −0.640415 | + | 0.750281i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 3.83111e6i | − | 0.552502i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.39011e6i | − | 1.05605i | −0.849230 | − | 0.528023i | \(-0.822934\pi\) | ||
0.849230 | − | 0.528023i | \(-0.177066\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −744139. | − | 4.68032e6i | −0.105372 | − | 0.662742i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.58964e6 | 0.363379 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.18409e6 | −0.581819 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.55907e6 | + | 1.33077e6i | 0.214849 | + | 0.183388i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.55684e6i | 0.212620i | 0.994333 | + | 0.106310i | \(0.0339037\pi\) | ||||
−0.994333 | + | 0.106310i | \(0.966096\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.80271e6i | − | 1.32683i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.82137e6 | + | 6.67607e6i | 1.04924 | + | 0.895599i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.43554e6 | 0.190873 | 0.0954364 | − | 0.995436i | \(-0.469575\pi\) | ||||
0.0954364 | + | 0.995436i | \(0.469575\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.36028e6 | 0.574637 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.51605e6 | − | 4.64713e6i | −0.198041 | − | 0.607054i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.69381e6i | 0.607778i | 0.952707 | + | 0.303889i | \(0.0982852\pi\) | ||||
−0.952707 | + | 0.303889i | \(0.901715\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.38793e6i | 0.819917i | 0.912104 | + | 0.409959i | \(0.134457\pi\) | ||||
−0.912104 | + | 0.409959i | \(0.865543\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.57466e6 | + | 1.12172e7i | −1.21825 | + | 1.42725i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.04520e6 | 0.636369 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.73246e6 | 1.21698 | 0.608490 | − | 0.793562i | \(-0.291776\pi\) | ||||
0.608490 | + | 0.793562i | \(0.291776\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.18321e6 | + | 6.07241e6i | −0.642543 | + | 0.752774i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.97827e6i | 0.980547i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.54647e6i | 0.919544i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.43043e6 | − | 863402.i | 0.656061 | − | 0.104309i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.95499e6 | 0.713323 | 0.356661 | − | 0.934234i | \(-0.383915\pi\) | ||||
0.356661 | + | 0.934234i | \(0.383915\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.80964e6 | −0.927562 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.98655e6 | + | 5.96349e6i | 0.822800 | + | 0.702315i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.08446e7i | 1.26642i | 0.773979 | + | 0.633211i | \(0.218264\pi\) | ||||
−0.773979 | + | 0.633211i | \(0.781736\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.17426e6i | 0.367578i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −35188.4 | − | 30035.6i | −0.00404076 | − | 0.00344906i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.05961e7 | −1.20664 | −0.603321 | − | 0.797499i | \(-0.706156\pi\) | ||||
−0.603321 | + | 0.797499i | \(0.706156\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.04222e6 | 0.795286 | 0.397643 | − | 0.917540i | \(-0.369828\pi\) | ||||
0.397643 | + | 0.917540i | \(0.369828\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.22281e7 | + | 1.94419e6i | −1.36952 | + | 0.217744i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 976972.i | 0.108516i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 638984.i | − | 0.0703911i | −0.999380 | − | 0.0351956i | \(-0.988795\pi\) | ||
0.999380 | − | 0.0351956i | \(-0.0112054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.61159e6 | − | 1.88807e6i | 0.176081 | − | 0.206288i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.11451e6 | 0.229144 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.19943e7 | 1.28921 | 0.644603 | − | 0.764518i | \(-0.277023\pi\) | ||||
0.644603 | + | 0.764518i | \(0.277023\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 811589. | − | 950820.i | 0.0865263 | − | 0.101370i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.01397e7i | − | 1.07229i | −0.844126 | − | 0.536144i | \(-0.819880\pi\) | ||
0.844126 | − | 0.536144i | \(-0.180120\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.43700e6i | 0.675239i | 0.941283 | + | 0.337619i | \(0.109622\pi\) | ||||
−0.941283 | + | 0.337619i | \(0.890378\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.92505e6 | − | 3.62362e6i | −0.616543 | − | 0.377063i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.48966e6 | −0.153768 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.40513e6 | 0.655886 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 5.30552e6 | + | 4.52862e6i | 0.538964 | + | 0.460042i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.35063e7i | − | 1.36116i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.35312e7i | 1.35289i | 0.736493 | + | 0.676445i | \(0.236480\pi\) | ||||
−0.736493 | + | 0.676445i | \(0.763520\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.10721e6 | − | 7.77362e6i | −0.903392 | − | 0.771106i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.91846e6 | −0.188807 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.16578e7 | −1.13833 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.66707e6 | + | 1.67748e7i | 0.258394 | + | 1.62519i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.36979e6i | − | 0.323935i | −0.986796 | − | 0.161967i | \(-0.948216\pi\) | ||
0.986796 | − | 0.161967i | \(-0.0517839\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 5.93188e6i | − | 0.565802i | −0.959149 | − | 0.282901i | \(-0.908703\pi\) | ||
0.959149 | − | 0.282901i | \(-0.0912968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.63671e6 | − | 1.91750e6i | 0.154908 | − | 0.181483i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.62942e7 | 1.53029 | 0.765143 | − | 0.643860i | \(-0.222668\pi\) | ||||
0.765143 | + | 0.643860i | \(0.222668\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.20048e6 | −0.577848 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.86013e6 | + | 5.69390e6i | −0.449464 | + | 0.526572i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 8.96912e6i | − | 0.823127i | −0.911381 | − | 0.411564i | \(-0.864983\pi\) | ||
0.911381 | − | 0.411564i | \(-0.135017\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 4.89962e6i | − | 0.446230i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.41313e6 | − | 8.88800e6i | −0.127723 | − | 0.803324i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.28105e6 | 0.742800 | 0.371400 | − | 0.928473i | \(-0.378878\pi\) | ||||
0.371400 | + | 0.928473i | \(0.378878\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.16993e6 | −0.638280 | −0.319140 | − | 0.947708i | \(-0.603394\pi\) | ||||
−0.319140 | + | 0.947708i | \(0.603394\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.75573e7 | − | 2.35220e7i | −2.43474 | − | 2.07822i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.15322e6i | 0.188814i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 3.52700e6i | − | 0.306966i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.41630e6 | + | 2.91604e6i | 0.295114 | + | 0.251900i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.48254e6 | 0.555826 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 781505. | 0.0665111 | 0.0332555 | − | 0.999447i | \(-0.489412\pi\) | ||||
0.0332555 | + | 0.999447i | \(0.489412\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.89222e6 | − | 5.43827e6i | −0.751192 | − | 0.459411i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 976634.i | − | 0.0818956i | −0.999161 | − | 0.0409478i | \(-0.986962\pi\) | ||
0.999161 | − | 0.0409478i | \(-0.0130377\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.00513e6i | 0.333382i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −8.14808e6 | + | 9.54591e6i | −0.673267 | + | 0.788769i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.17475e6 | 0.0963590 | 0.0481795 | − | 0.998839i | \(-0.484658\pi\) | ||||
0.0481795 | + | 0.998839i | \(0.484658\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 925218. | 0.0753386 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.66499e6 | − | 1.95063e6i | 0.134592 | − | 0.157682i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 2.65887e7i | − | 2.13378i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.25020e7i | 0.996058i | 0.867161 | + | 0.498029i | \(0.165943\pi\) | ||||
−0.867161 | + | 0.498029i | \(0.834057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.60351e6 | − | 1.04991e6i | 0.522326 | − | 0.0830464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.86277e6 | −0.303345 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.23700e6 | −0.642225 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.58077e6 | − | 4.76356e6i | −0.432017 | − | 0.368756i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.36812e7i | 1.05155i | 0.850624 | + | 0.525774i | \(0.176224\pi\) | ||||
−0.850624 | + | 0.525774i | \(0.823776\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 9.16184e6i | − | 0.699189i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 413618. | + | 353051.i | 0.0313420 | + | 0.0267525i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −8.38069e6 | −0.630567 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.64829e6 | −0.347278 | −0.173639 | − | 0.984809i | \(-0.555553\pi\) | ||||
−0.173639 | + | 0.984809i | \(0.555553\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.21298e7 | − | 1.92855e6i | 0.899867 | − | 0.143073i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.06365e7i | 0.783562i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.52149e6i | 0.550223i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.55132e7 | − | 1.81745e7i | 1.12694 | − | 1.32028i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.82672e7 | 1.31780 | 0.658899 | − | 0.752231i | \(-0.271022\pi\) | ||||
0.658899 | + | 0.752231i | \(0.271022\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.20637e6 | −0.158067 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.35449e6 | + | 1.09593e7i | −0.665540 | + | 0.779716i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 5.29326e6i | − | 0.374006i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 2.11523e7i | − | 1.48430i | −0.670235 | − | 0.742149i | \(-0.733807\pi\) | ||
0.670235 | − | 0.742149i | \(-0.266193\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 6.53704e6 | + | 1.27733e7i | 0.455577 | + | 0.890196i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.66114e7 | −1.14977 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.38899e6 | −0.164231 | −0.0821153 | − | 0.996623i | \(-0.526168\pi\) | ||||
−0.0821153 | + | 0.996623i | \(0.526168\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.28037e6 | − | 1.94645e6i | −0.155699 | − | 0.132900i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.69368e7i | − | 1.14858i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 6.98369e6i | − | 0.470407i | −0.971946 | − | 0.235203i | \(-0.924424\pi\) | ||
0.971946 | − | 0.235203i | \(-0.0755756\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.86931e7 | − | 1.59558e7i | −1.25065 | − | 1.06752i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.91909e7 | 1.27533 | 0.637665 | − | 0.770314i | \(-0.279901\pi\) | ||||
0.637665 | + | 0.770314i | \(0.279901\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.23131e6 | −0.0812787 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.67738e6 | − | 2.31292e7i | −0.241122 | − | 1.51656i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.04816e6i | 0.0682691i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 3.04159e7i | − | 1.96789i | −0.178465 | − | 0.983946i | \(-0.557113\pi\) | ||
0.178465 | − | 0.983946i | \(-0.442887\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.29548e7 | + | 1.51772e7i | −0.832612 | + | 0.975450i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.62853e6 | 0.550896 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.16178e6 | 0.390811 | 0.195405 | − | 0.980723i | \(-0.437398\pi\) | ||||
0.195405 | + | 0.980723i | \(0.437398\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.16782e6 | − | 7.22594e6i | 0.388622 | − | 0.455292i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.27781e7i | − | 1.42579i | −0.701269 | − | 0.712897i | \(-0.747383\pi\) | ||
0.701269 | − | 0.712897i | \(-0.252617\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.64142e7i | 1.02072i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.46310e6 | − | 9.20224e6i | −0.0903897 | − | 0.568513i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.18464e7 | 1.34088 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.17621e7 | −1.93684 | −0.968419 | − | 0.249326i | \(-0.919791\pi\) | ||||
−0.968419 | + | 0.249326i | \(0.919791\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.04438e7 | + | 1.74502e7i | 1.23858 | + | 1.05721i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.28739e7i | 0.774930i | 0.921884 | + | 0.387465i | \(0.126649\pi\) | ||||
−0.921884 | + | 0.387465i | \(0.873351\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.59630e7i | 0.954687i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.67977e6 | − | 5.70163e6i | −0.396925 | − | 0.338802i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.58746e6 | −0.329891 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.32341e7 | −1.36301 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.80178e6 | + | 6.21637e6i | −0.221607 | + | 0.362354i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 5.14623e6i | − | 0.298068i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 2.15917e7i | − | 1.24265i | −0.783552 | − | 0.621327i | \(-0.786594\pi\) | ||
0.783552 | − | 0.621327i | \(-0.213406\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 402097. | − | 471079.i | 0.0229953 | − | 0.0269402i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.86814e7 | −1.06162 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.28402e7 | −1.28978 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.43940e6 | − | 5.20100e6i | 0.249119 | − | 0.291856i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1.94436e7i | 1.08425i | 0.840297 | + | 0.542126i | \(0.182380\pi\) | ||||
−0.840297 | + | 0.542126i | \(0.817620\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 3.58319e6i | − | 0.198565i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.31855e6 | − | 686622.i | 0.237825 | − | 0.0378126i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.23105e7 | 0.673729 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.93261e6 | 0.159501 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −3.32013e6 | − | 2.83396e6i | −0.179462 | − | 0.153183i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 2.43124e7i | − | 1.30604i | −0.757341 | − | 0.653020i | \(-0.773502\pi\) | ||
0.757341 | − | 0.653020i | \(-0.226498\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.09629e7i | 0.585293i | 0.956221 | + | 0.292647i | \(0.0945360\pi\) | ||||
−0.956221 | + | 0.292647i | \(0.905464\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2.67114e7 | − | 2.28000e7i | −1.41733 | − | 1.20979i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.72782e6 | 0.249326 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.12681e7 | −0.590603 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.32664e7 | + | 3.69920e6i | −1.21204 | + | 0.192707i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 2.05702e6i | − | 0.106507i | −0.998581 | − | 0.0532537i | \(-0.983041\pi\) | ||
0.998581 | − | 0.0532537i | \(-0.0169592\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 2.72914e7i | − | 1.40451i | −0.711924 | − | 0.702256i | \(-0.752176\pi\) | ||
0.711924 | − | 0.702256i | \(-0.247824\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 9.25657e6 | − | 1.08446e7i | 0.473495 | − | 0.554725i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.02167e7 | −0.519456 | −0.259728 | − | 0.965682i | \(-0.583633\pi\) | ||||
−0.259728 | + | 0.965682i | \(0.583633\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.19066e7 | 1.10710 | 0.553551 | − | 0.832815i | \(-0.313272\pi\) | ||||
0.553551 | + | 0.832815i | \(0.313272\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.16230e7 | + | 1.36169e7i | −0.583868 | + | 0.684032i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.97549e7i | 0.986422i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 3.85194e6i | − | 0.191189i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.14651e7 | − | 1.87469e7i | 0.565674 | − | 0.924944i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.65586e7 | 0.812116 | 0.406058 | − | 0.913847i | \(-0.366903\pi\) | ||||
0.406058 | + | 0.913847i | \(0.366903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.68107e7 | 0.819590 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.80312e7 | − | 1.53908e7i | −0.873886 | − | 0.745920i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.93268e7i | − | 0.931148i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 4.18578e6i | − | 0.200479i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7.24235e6 | + | 6.18183e6i | 0.344834 | + | 0.294339i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.24781e7 | −0.590643 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.67539e6 | −0.361183 | −0.180592 | − | 0.983558i | \(-0.557801\pi\) | ||||
−0.180592 | + | 0.983558i | \(0.557801\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −992471. | − | 6.24222e6i | −0.0464304 | − | 0.292027i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 3.53759e6i | − | 0.164534i | −0.996610 | − | 0.0822670i | \(-0.973784\pi\) | ||
0.996610 | − | 0.0822670i | \(-0.0262160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.36445e7i | 0.630921i | 0.948939 | + | 0.315461i | \(0.102159\pi\) | ||||
−0.948939 | + | 0.315461i | \(0.897841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.47721e6 | + | 4.07374e6i | −0.159854 | + | 0.187277i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 2.32847e7 | 1.06425 | 0.532126 | − | 0.846665i | \(-0.321393\pi\) | ||||
0.532126 | + | 0.846665i | \(0.321393\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.22728e6 | 0.282982 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.54902e7 | + | 2.98632e7i | −1.15167 | + | 1.34924i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.68005e7i | 0.754697i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.96739e7i | 2.66526i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.84606e6 | − | 1.16110e7i | −0.0819806 | − | 0.515623i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9.39952e6 | 0.415036 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.33930e7 | 1.90511 | 0.952556 | − | 0.304364i | \(-0.0984439\pi\) | ||||
0.952556 | + | 0.304364i | \(0.0984439\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.72013e7 | − | 2.32181e7i | −1.18745 | − | 1.01357i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.09569e7i | − | 0.909678i | −0.890574 | − | 0.454839i | \(-0.849697\pi\) | ||
0.890574 | − | 0.454839i | \(-0.150303\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.32913e7i | − | 0.573674i | −0.957979 | − | 0.286837i | \(-0.907396\pi\) | ||
0.957979 | − | 0.286837i | \(-0.0926037\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.27335e6 | + | 3.64759e6i | 0.183405 | + | 0.156548i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.96276e7 | 1.26441 | 0.632205 | − | 0.774801i | \(-0.282150\pi\) | ||||
0.632205 | + | 0.774801i | \(0.282150\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.21955e6 | 0.348814 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.86598e7 | + | 6.08744e6i | −0.787430 | + | 0.256886i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 2.43061e6i | − | 0.101997i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.64814e7i | 0.687760i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.17313e7 | + | 2.54594e7i | −0.901789 | + | 1.05649i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.11594e7 | 0.460514 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.50565e7 | −1.84904 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.01241e6 | + | 8.21542e6i | −0.286186 | + | 0.335282i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.40048e6i | 0.340944i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.59307e7i | 1.04664i | 0.852137 | + | 0.523318i | \(0.175306\pi\) | ||||
−0.852137 | + | 0.523318i | \(0.824694\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.42958e7 | − | 3.86287e6i | 0.975262 | − | 0.155060i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.62650e7 | −1.04853 | −0.524265 | − | 0.851555i | \(-0.675660\pi\) | ||||
−0.524265 | + | 0.851555i | \(0.675660\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.20354e7 | 1.27190 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.46774e6 | − | 3.81352e6i | −0.176415 | − | 0.150582i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.09921e7i | 0.824391i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.40150e7i | − | 0.937982i | −0.883203 | − | 0.468991i | \(-0.844618\pi\) | ||
0.883203 | − | 0.468991i | \(-0.155382\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.67953e7 | + | 2.28716e7i | 1.04090 | + | 0.888480i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.18616e7 | 3.16283 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.87269e7 | −0.719635 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.39632e6 | − | 1.01697e6i | 0.244473 | − | 0.0388696i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 199297.i | − | 0.00757638i | −0.999993 | − | 0.00378819i | \(-0.998794\pi\) | ||
0.999993 | − | 0.00378819i | \(-0.00120582\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.34005e7i | 0.506695i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.03193e7 | + | 3.55207e7i | −1.14029 | + | 1.33591i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.27457e7 | 0.476798 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.11339e7 | 0.786375 | 0.393188 | − | 0.919458i | \(-0.371372\pi\) | ||||
0.393188 | + | 0.919458i | \(0.371372\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.94622e6 | − | 8.13787e6i | 0.257089 | − | 0.301194i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 2.91277e7i | − | 1.07234i | −0.844110 | − | 0.536169i | \(-0.819871\pi\) | ||
0.844110 | − | 0.536169i | \(-0.180129\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.60992e6i | 0.278677i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.16875e6 | − | 3.16108e6i | −0.188281 | − | 0.115148i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.30882e7 | −0.474248 | −0.237124 | − | 0.971479i | \(-0.576205\pi\) | ||||
−0.237124 | + | 0.971479i | \(0.576205\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.33738e7 | −1.56337 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.55020e7 | − | 3.03034e7i | −1.27292 | − | 1.08652i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.88256e7i | − | 1.38480i | −0.721515 | − | 0.692398i | \(-0.756554\pi\) | ||
0.721515 | − | 0.692398i | \(-0.243446\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.82796e7i | 0.648572i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −7.58122e6 | − | 6.47108e6i | −0.267583 | − | 0.228400i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.96405e6 | −0.139185 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.02465e6 | −0.175508 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −483125. | − | 3.03865e6i | −0.0167878 | − | 0.105588i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 9.89559e6i | 0.342076i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.38341e7i | 1.16356i | 0.813346 | + | 0.581780i | \(0.197644\pi\) | ||||
−0.813346 | + | 0.581780i | \(0.802356\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.70383e7 | + | 3.16768e7i | −0.925061 | + | 1.08376i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.86651e7 | 1.31604 | 0.658022 | − | 0.752998i | \(-0.271393\pi\) | ||||
0.658022 | + | 0.752998i | \(0.271393\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.65498e7 | 0.560417 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.26140e7 | + | 3.82090e7i | −1.09873 | + | 1.28723i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.73321e7i | 1.58643i | 0.608944 | + | 0.793213i | \(0.291593\pi\) | ||||
−0.608944 | + | 0.793213i | \(0.708407\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.98148e6i | 0.199458i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −7.56571e6 | − | 4.75851e7i | −0.251002 | − | 1.57869i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.15996e7 | −0.712954 | −0.356477 | − | 0.934304i | \(-0.616022\pi\) | ||||
−0.356477 | + | 0.934304i | \(0.616022\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.13853e7 | 0.373898 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.77212e6 | − | 1.51263e6i | −0.0579031 | − | 0.0494241i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.53468e7i | 0.498915i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.42907e7i | 0.785699i | 0.919603 | + | 0.392849i | \(0.128511\pi\) | ||||
−0.919603 | + | 0.392849i | \(0.871489\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.49379e7 | + | 1.27505e7i | 0.480747 | + | 0.410350i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −57342.9 | −0.00183621 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.08871e7 | 1.62132 | 0.810662 | − | 0.585514i | \(-0.199107\pi\) | ||||
0.810662 | + | 0.585514i | \(0.199107\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.19928e7 | + | 1.34503e7i | 0.697215 | + | 0.426400i |
(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.c.383.15 | yes | 20 | |
3.2 | odd | 2 | 384.6.c.b.383.5 | yes | 20 | ||
4.3 | odd | 2 | 384.6.c.b.383.6 | yes | 20 | ||
8.3 | odd | 2 | 384.6.c.d.383.15 | yes | 20 | ||
8.5 | even | 2 | 384.6.c.a.383.6 | yes | 20 | ||
12.11 | even | 2 | inner | 384.6.c.c.383.16 | yes | 20 | |
24.5 | odd | 2 | 384.6.c.d.383.16 | yes | 20 | ||
24.11 | even | 2 | 384.6.c.a.383.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.c.a.383.5 | ✓ | 20 | 24.11 | even | 2 | ||
384.6.c.a.383.6 | yes | 20 | 8.5 | even | 2 | ||
384.6.c.b.383.5 | yes | 20 | 3.2 | odd | 2 | ||
384.6.c.b.383.6 | yes | 20 | 4.3 | odd | 2 | ||
384.6.c.c.383.15 | yes | 20 | 1.1 | even | 1 | trivial | |
384.6.c.c.383.16 | yes | 20 | 12.11 | even | 2 | inner | |
384.6.c.d.383.15 | yes | 20 | 8.3 | odd | 2 | ||
384.6.c.d.383.16 | yes | 20 | 24.5 | odd | 2 |