Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), degree \(2\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} + 148097 x^{10} + 46071824 x^{9} + 21578502553 x^{8} + 3561445462121 x^{7} + \cdots + 45\!\cdots\!96 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{10}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 84) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.4 | ||
Root | \(-28.8366 + 49.9465i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.73 |
Dual form | 252.9.z.d.145.4 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 203.366 | − | 117.413i | 0.325386 | − | 0.187862i | −0.328405 | − | 0.944537i | \(-0.606511\pi\) |
0.653791 | + | 0.756676i | \(0.273178\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1130.34 | + | 2118.29i | 0.470778 | + | 0.882251i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 7474.44 | − | 12946.1i | 0.510514 | − | 0.884237i | −0.489411 | − | 0.872053i | \(-0.662788\pi\) |
0.999926 | − | 0.0121839i | \(-0.00387834\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 39673.5i | − | 1.38908i | −0.719455 | − | 0.694539i | \(-0.755608\pi\) | ||
0.719455 | − | 0.694539i | \(-0.244392\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −84679.4 | − | 48889.7i | −1.01387 | − | 0.585358i | −0.101547 | − | 0.994831i | \(-0.532379\pi\) |
−0.912322 | + | 0.409473i | \(0.865713\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −177843. | + | 102678.i | −1.36465 | + | 0.787882i | −0.990239 | − | 0.139380i | \(-0.955489\pi\) |
−0.374413 | + | 0.927262i | \(0.622156\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 185312. | + | 320970.i | 0.662205 | + | 1.14697i | 0.980035 | + | 0.198825i | \(0.0637124\pi\) |
−0.317830 | + | 0.948148i | \(0.602954\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −167741. | + | 290535.i | −0.429416 | + | 0.743771i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −117048. | −0.165490 | −0.0827448 | − | 0.996571i | \(-0.526369\pi\) | ||||
−0.0827448 | + | 0.996571i | \(0.526369\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 437915. | + | 252830.i | 0.474180 | + | 0.273768i | 0.717988 | − | 0.696056i | \(-0.245063\pi\) |
−0.243808 | + | 0.969823i | \(0.578397\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 478588. | + | 298070.i | 0.318926 | + | 0.198631i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −986447. | − | 1.70858e6i | −0.526341 | − | 0.911649i | −0.999529 | − | 0.0306877i | \(-0.990230\pi\) |
0.473188 | − | 0.880961i | \(-0.343103\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.25966e6i | − | 1.15355i | −0.816903 | − | 0.576776i | \(-0.804311\pi\) | ||
0.816903 | − | 0.576776i | \(-0.195689\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.13332e6 | −1.20900 | −0.604498 | − | 0.796607i | \(-0.706626\pi\) | ||||
−0.604498 | + | 0.796607i | \(0.706626\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.79532e6 | − | 2.76858e6i | 0.982711 | − | 0.567369i | 0.0796238 | − | 0.996825i | \(-0.474628\pi\) |
0.903088 | + | 0.429456i | \(0.141295\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.20947e6 | + | 4.78876e6i | −0.556735 | + | 0.830690i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.39093e6 | − | 5.87326e6i | 0.429749 | − | 0.744347i | −0.567102 | − | 0.823648i | \(-0.691935\pi\) |
0.996851 | + | 0.0793006i | \(0.0252687\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 3.51040e6i | − | 0.383624i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.91904e7 | + | 1.10796e7i | 1.58371 | + | 0.914355i | 0.994312 | + | 0.106511i | \(0.0339680\pi\) |
0.589397 | + | 0.807843i | \(0.299365\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.97144e6 | + | 2.29291e6i | −0.286833 | + | 0.165603i | −0.636513 | − | 0.771266i | \(-0.719624\pi\) |
0.349680 | + | 0.936869i | \(0.386290\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.65820e6 | − | 8.06823e6i | −0.260954 | − | 0.451986i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.86385e7 | + | 3.22828e7i | −0.924934 | + | 1.60203i | −0.133267 | + | 0.991080i | \(0.542547\pi\) |
−0.791667 | + | 0.610952i | \(0.790787\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.19870e7 | −1.65227 | −0.826135 | − | 0.563472i | \(-0.809465\pi\) | ||||
−0.826135 | + | 0.563472i | \(0.809465\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.08607e7 | + | 6.27044e6i | 0.382443 | + | 0.220804i | 0.678881 | − | 0.734249i | \(-0.262465\pi\) |
−0.296438 | + | 0.955052i | \(0.595799\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.58722e7 | + | 1.19951e6i | 1.02046 | + | 0.0341224i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.01064e7 | − | 3.48253e7i | −0.516209 | − | 0.894100i | −0.999823 | − | 0.0188184i | \(-0.994010\pi\) |
0.483614 | − | 0.875281i | \(-0.339324\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 5.31441e6i | − | 0.111981i | −0.998431 | − | 0.0559903i | \(-0.982168\pi\) | ||
0.998431 | − | 0.0559903i | \(-0.0178316\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.29612e7 | −0.439865 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.45415e7 | + | 3.72630e7i | −1.02868 | + | 0.593907i | −0.916605 | − | 0.399793i | \(-0.869082\pi\) |
−0.112072 | + | 0.993700i | \(0.535749\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.40397e7 | − | 4.48445e7i | 1.22552 | − | 0.653948i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.41115e7 | + | 4.17623e7i | −0.296026 | + | 0.512731i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.76415e7i | − | 0.425187i | −0.977141 | − | 0.212593i | \(-0.931809\pi\) | ||
0.977141 | − | 0.212593i | \(-0.0681909\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.57943e8 | − | 9.11884e7i | −1.51780 | − | 0.876303i | −0.999781 | − | 0.0209346i | \(-0.993336\pi\) |
−0.518020 | − | 0.855368i | \(-0.673331\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.37340e7 | + | 5.41173e7i | −0.832814 | + | 0.480826i | −0.854815 | − | 0.518932i | \(-0.826330\pi\) |
0.0220010 | + | 0.999758i | \(0.492996\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.48762e6 | + | 1.64330e7i | 0.0723806 | + | 0.125367i | 0.899944 | − | 0.436005i | \(-0.143607\pi\) |
−0.827564 | + | 0.561372i | \(0.810274\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.98197e7 | − | 6.89697e7i | 0.282093 | − | 0.488599i | −0.689807 | − | 0.723993i | \(-0.742305\pi\) |
0.971900 | + | 0.235394i | \(0.0756381\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.14140e8 | −1.31336 | −0.656680 | − | 0.754169i | \(-0.728040\pi\) | ||||
−0.656680 | + | 0.754169i | \(0.728040\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.53723e7 | + | 4.35162e7i | 0.430944 | + | 0.248806i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 7.84586e6 | − | 2.34637e8i | 0.0391249 | − | 1.17006i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.55511e6 | − | 7.88969e6i | −0.0212499 | − | 0.0368060i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.70509e8i | 0.698406i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.22002e8 | 0.853381 | 0.426690 | − | 0.904398i | \(-0.359679\pi\) | ||||
0.426690 | + | 0.904398i | \(0.359679\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.38205e8 | + | 2.52998e8i | −1.48796 | + | 0.859075i | −0.999906 | − | 0.0137373i | \(-0.995627\pi\) |
−0.488056 | + | 0.872812i | \(0.662294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.18523e8 | − | 2.60661e8i | −1.33756 | − | 0.833048i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.73086e8 | + | 2.99795e8i | −0.491339 | + | 0.851023i | −0.999950 | − | 0.00997260i | \(-0.996826\pi\) |
0.508612 | + | 0.860996i | \(0.330159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.04014e8i | − | 0.278632i | −0.990248 | − | 0.139316i | \(-0.955510\pi\) | ||
0.990248 | − | 0.139316i | \(-0.0444904\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.13617e8 | − | 2.96537e8i | −1.22827 | − | 0.709144i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.38035e7 | + | 1.37430e7i | −0.0538480 | + | 0.0310891i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.71762e8 | − | 2.97501e8i | −0.348483 | − | 0.603591i | 0.637497 | − | 0.770453i | \(-0.279970\pi\) |
−0.985980 | + | 0.166862i | \(0.946637\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.21266e8 | + | 7.29654e8i | −0.810305 | + | 1.40349i | 0.102346 | + | 0.994749i | \(0.467365\pi\) |
−0.912651 | + | 0.408740i | \(0.865968\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.18743e8 | 0.205722 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.00370e8 | − | 1.73419e8i | −0.494377 | − | 0.285429i | 0.232011 | − | 0.972713i | \(-0.425469\pi\) |
−0.726388 | + | 0.687284i | \(0.758803\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.70440e8 | + | 7.55349e8i | −0.700166 | + | 1.12420i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.38287e7 | + | 1.10555e8i | 0.0904203 | + | 0.156612i | 0.907688 | − | 0.419646i | \(-0.137846\pi\) |
−0.817268 | + | 0.576258i | \(0.804512\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 4.84232e8i | − | 0.622569i | −0.950317 | − | 0.311284i | \(-0.899241\pi\) | ||
0.950317 | − | 0.311284i | \(-0.100759\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.58252e8 | −0.929537 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.57674e8 | − | 4.37444e8i | 0.845860 | − | 0.488357i | −0.0133921 | − | 0.999910i | \(-0.504263\pi\) |
0.859252 | + | 0.511553i | \(0.170930\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.05041e8 | − | 2.69192e7i | −0.858352 | − | 0.0287019i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.06371e8 | − | 1.05027e9i | 0.590645 | − | 1.02303i | −0.403501 | − | 0.914979i | \(-0.632207\pi\) |
0.994146 | − | 0.108048i | \(-0.0344599\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.75613e8i | 0.256794i | 0.991723 | + | 0.128397i | \(0.0409832\pi\) | ||||
−0.991723 | + | 0.128397i | \(0.959017\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.01220e8 | − | 2.31644e8i | −0.342528 | − | 0.197758i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.26586e9 | + | 7.30846e8i | −1.03519 | + | 0.597667i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.56485e8 | − | 1.65668e9i | −0.718695 | − | 1.24482i | −0.961517 | − | 0.274746i | \(-0.911406\pi\) |
0.242821 | − | 0.970071i | \(-0.421927\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.90016e8 | − | 8.48733e8i | 0.353168 | − | 0.611705i | −0.633635 | − | 0.773632i | \(-0.718438\pi\) |
0.986803 | + | 0.161928i | \(0.0517711\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.49081e9 | −0.989824 | −0.494912 | − | 0.868943i | \(-0.664800\pi\) | ||||
−0.494912 | + | 0.868943i | \(0.664800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.60781e8 | − | 4.96972e8i | −0.548884 | − | 0.316898i | 0.199788 | − | 0.979839i | \(-0.435975\pi\) |
−0.748672 | + | 0.662941i | \(0.769308\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.32304e8 | − | 2.47940e8i | −0.0779090 | − | 0.146004i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.82728e8 | − | 6.62904e8i | −0.216708 | − | 0.375349i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.06983e9i | 1.60890i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.64537e8 | −0.234364 | −0.117182 | − | 0.993110i | \(-0.537386\pi\) | ||||
−0.117182 | + | 0.993110i | \(0.537386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.40576e8 | + | 4.85307e8i | −0.393390 | + | 0.227124i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.05745e7 | + | 1.21341e9i | −0.0182984 | + | 0.547229i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.93962e9 | + | 3.35952e9i | −0.813107 | + | 1.40834i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 6.58116e7i | − | 0.0266123i | −0.999911 | − | 0.0133062i | \(-0.995764\pi\) | ||
0.999911 | − | 0.0133062i | \(-0.00423561\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1.98442e9 | − | 1.14570e9i | −0.747360 | − | 0.431489i | 0.0773791 | − | 0.997002i | \(-0.475345\pi\) |
−0.824739 | + | 0.565513i | \(0.808678\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.77398e9 | − | 1.60156e9i | 1.00870 | − | 0.582373i | 0.0978887 | − | 0.995197i | \(-0.468791\pi\) |
0.910811 | + | 0.412825i | \(0.135458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.43830e8 | − | 1.28835e9i | −0.252377 | − | 0.437130i | 0.711803 | − | 0.702380i | \(-0.247879\pi\) |
−0.964180 | + | 0.265249i | \(0.914546\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.50137e8 | − | 1.12607e9i | 0.213173 | − | 0.369227i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −9.50233e8 | −0.291232 | −0.145616 | − | 0.989341i | \(-0.546516\pi\) | ||||
−0.145616 | + | 0.989341i | \(0.546516\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.55088e9 | − | 2.05010e9i | −1.05261 | − | 0.607725i | −0.129232 | − | 0.991614i | \(-0.541251\pi\) |
−0.923379 | + | 0.383889i | \(0.874584\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −9.04318e7 | + | 1.35071e9i | −0.0250990 | + | 0.374884i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 4.07358e9 | + | 7.05564e9i | 1.09443 | + | 1.89561i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4.77515e9i | − | 1.20307i | −0.798845 | − | 0.601537i | \(-0.794555\pi\) | ||
0.798845 | − | 0.601537i | \(-0.205445\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.54042e9 | 1.35226 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.28158e9 | − | 2.47197e9i | 0.981457 | − | 0.566645i | 0.0787473 | − | 0.996895i | \(-0.474908\pi\) |
0.902710 | + | 0.430250i | \(0.141575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.50423e9 | − | 4.02085e9i | 0.556514 | − | 0.893550i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3.41497e9 | + | 5.91490e9i | −0.713779 | + | 1.23630i | 0.249650 | + | 0.968336i | \(0.419685\pi\) |
−0.963429 | + | 0.267965i | \(0.913649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.59256e9i | − | 0.322933i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.01169e9 | + | 1.73880e9i | 0.575176 | + | 0.332078i | 0.759214 | − | 0.650841i | \(-0.225584\pi\) |
−0.184038 | + | 0.982919i | \(0.558917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.59984e9 | + | 3.23307e9i | −1.03824 | + | 0.599429i | −0.919335 | − | 0.393477i | \(-0.871272\pi\) |
−0.118907 | + | 0.992905i | \(0.537939\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.50754e9 | + | 4.34318e9i | 0.438446 | + | 0.759411i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.15914e9 | − | 3.73973e9i | 0.366742 | − | 0.635216i | −0.622312 | − | 0.782769i | \(-0.713806\pi\) |
0.989054 | + | 0.147553i | \(0.0471397\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.64214e9 | −0.904938 | −0.452469 | − | 0.891780i | \(-0.649457\pi\) | ||||
−0.452469 | + | 0.891780i | \(0.649457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.51708e9 | + | 2.03059e9i | 0.548323 | + | 0.316574i | 0.748445 | − | 0.663197i | \(-0.230801\pi\) |
−0.200122 | + | 0.979771i | \(0.564134\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.90489e9 | − | 3.68452e9i | 1.01772 | − | 0.543067i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.29252e9 | + | 2.23871e9i | 0.185287 | + | 0.320927i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 8.43223e7i | − | 0.0114412i | −0.999984 | − | 0.00572061i | \(-0.998179\pi\) | ||
0.999984 | − | 0.00572061i | \(-0.00182094\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.20356e9 | 0.687088 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.27340e10 | − | 7.35197e9i | 1.59323 | − | 0.919854i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.67205e9 | − | 8.75554e9i | −0.569169 | − | 1.06664i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −5.38438e8 | + | 9.32601e8i | −0.0622209 | + | 0.107770i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 6.10423e9i | − | 0.687191i | −0.939118 | − | 0.343596i | \(-0.888355\pi\) | ||
0.939118 | − | 0.343596i | \(-0.111645\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.74096e9 | + | 1.00514e9i | 0.186100 | + | 0.107445i | 0.590156 | − | 0.807289i | \(-0.299066\pi\) |
−0.404055 | + | 0.914735i | \(0.632400\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.10102e10 | + | 6.35672e9i | −1.14714 | + | 0.662302i | −0.948189 | − | 0.317708i | \(-0.897087\pi\) |
−0.198951 | + | 0.980009i | \(0.563754\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.98773e9 | − | 5.17489e9i | −0.295872 | − | 0.512465i | 0.679315 | − | 0.733846i | \(-0.262277\pi\) |
−0.975187 | + | 0.221381i | \(0.928943\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.74866e8 | + | 1.51531e9i | −0.0844849 | + | 0.146332i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00795e10 | 1.84477 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.15265e10 | + | 6.65485e9i | 1.03316 | + | 0.596492i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.12850e10 | + | 7.02842e9i | 0.963201 | + | 0.599894i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.42439e9 | + | 1.11274e10i | 0.535205 | + | 0.927002i | 0.999153 | + | 0.0411400i | \(0.0130990\pi\) |
−0.463948 | + | 0.885862i | \(0.653568\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.75362e9i | 0.695038i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.70137e9 | −0.752166 | −0.376083 | − | 0.926586i | \(-0.622729\pi\) | ||||
−0.376083 | + | 0.926586i | \(0.622729\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.54634e9 | − | 3.77953e9i | 0.484151 | − | 0.279525i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.37718e10 | − | 1.38565e9i | −0.994976 | − | 0.100110i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.48892e8 | − | 1.12391e9i | 0.0447563 | − | 0.0775203i | −0.842779 | − | 0.538259i | \(-0.819082\pi\) |
0.887536 | + | 0.460739i | \(0.152416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.01643e10i | 1.35919i | 0.733587 | + | 0.679596i | \(0.237845\pi\) | ||||
−0.733587 | + | 0.679596i | \(0.762155\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.27487e10 | + | 1.31340e10i | 1.46507 | + | 0.845857i | 0.999238 | − | 0.0390186i | \(-0.0124232\pi\) |
0.465828 | + | 0.884875i | \(0.345756\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.53872e9 | + | 4.92983e9i | −0.537625 | + | 0.310398i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −1.13441e10 | − | 1.96486e10i | −0.682958 | − | 1.18292i | −0.974074 | − | 0.226230i | \(-0.927360\pi\) |
0.291116 | − | 0.956688i | \(-0.405973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.25936e10 | − | 2.18128e10i | 0.741517 | − | 1.28435i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.94493e9 | 0.165922 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.38693e8 | + | 5.41955e8i | 0.0517439 | + | 0.0298744i | 0.525649 | − | 0.850702i | \(-0.323823\pi\) |
−0.473905 | + | 0.880576i | \(0.657156\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.62741e10 | + | 5.44179e8i | 0.859018 | + | 0.0287241i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.91674e9 | + | 3.31989e9i | 0.0990211 | + | 0.171510i | 0.911280 | − | 0.411788i | \(-0.135096\pi\) |
−0.812259 | + | 0.583297i | \(0.801762\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.64369e9i | 0.229878i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.26734e10 | 1.58357 | 0.791785 | − | 0.610800i | \(-0.209152\pi\) | ||||
0.791785 | + | 0.610800i | \(0.209152\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.54251e10 | − | 8.90569e9i | 0.716858 | − | 0.413878i | −0.0967371 | − | 0.995310i | \(-0.530841\pi\) |
0.813595 | + | 0.581432i | \(0.197507\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.43603e9 | − | 3.96794e9i | 0.338453 | − | 0.180602i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.92749e9 | − | 1.19988e10i | 0.302536 | − | 0.524008i | −0.674173 | − | 0.738573i | \(-0.735500\pi\) |
0.976710 | + | 0.214565i | \(0.0688333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 3.62394e10i | − | 1.55051i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.17791e9 | − | 4.72152e9i | −0.335934 | − | 0.193951i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.66863e10 | + | 9.63385e9i | −0.671735 | + | 0.387827i | −0.796734 | − | 0.604330i | \(-0.793441\pi\) |
0.124998 | + | 0.992157i | \(0.460107\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.58138e9 | − | 1.65954e10i | −0.370553 | − | 0.641817i | 0.619097 | − | 0.785314i | \(-0.287499\pi\) |
−0.989651 | + | 0.143497i | \(0.954165\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.00306e10 | − | 1.73736e10i | 0.380285 | − | 0.658672i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.94926e10 | −1.07482 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.45544e10 | + | 1.99500e10i | 1.23484 | + | 0.712935i | 0.968035 | − | 0.250815i | \(-0.0806987\pi\) |
0.266805 | + | 0.963751i | \(0.414032\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.77806e9 | + | 5.31744e10i | −0.0611148 | + | 1.82769i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.23984e8 | − | 1.08077e9i | −0.0210369 | − | 0.0364369i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.17883e10i | 1.68026i | 0.542387 | + | 0.840129i | \(0.317521\pi\) | ||||
−0.542387 | + | 0.840129i | \(0.682479\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.78196e9 | 0.184055 | 0.0920273 | − | 0.995756i | \(-0.470665\pi\) | ||||
0.0920273 | + | 0.995756i | \(0.470665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.84083e10 | − | 1.64016e10i | 0.870743 | − | 0.502724i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.34612e9 | − | 5.82088e9i | −0.281138 | − | 0.175096i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.29999e10 | + | 2.25165e10i | −0.376730 | + | 0.652516i | −0.990584 | − | 0.136903i | \(-0.956285\pi\) |
0.613854 | + | 0.789420i | \(0.289618\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.85244e10i | 1.09593i | 0.836500 | + | 0.547967i | \(0.184598\pi\) | ||||
−0.836500 | + | 0.547967i | \(0.815402\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −6.59128e10 | − | 3.80548e10i | −1.80736 | − | 1.04348i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.36255e10 | − | 3.09607e10i | 1.44382 | − | 0.833591i | 0.445720 | − | 0.895172i | \(-0.352948\pi\) |
0.998102 | + | 0.0615814i | \(0.0196144\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.82777e9 | − | 1.18260e10i | −0.177282 | − | 0.307061i | 0.763667 | − | 0.645611i | \(-0.223397\pi\) |
−0.940949 | + | 0.338550i | \(0.890064\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.75037e9 | + | 1.51561e10i | −0.223144 | + | 0.386498i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.45335e10 | −1.58782 | −0.793908 | − | 0.608038i | \(-0.791957\pi\) | ||||
−0.793908 | + | 0.608038i | \(0.791957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.21999e10 | − | 2.43641e10i | −1.02001 | − | 0.588904i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.18255e10 | − | 1.89872e10i | 0.275914 | − | 0.443013i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.13781e10 | + | 3.70279e10i | 0.490122 | + | 0.848916i | 0.999935 | − | 0.0113692i | \(-0.00361901\pi\) |
−0.509814 | + | 0.860285i | \(0.670286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.19885e10i | 0.708256i | 0.935197 | + | 0.354128i | \(0.115222\pi\) | ||||
−0.935197 | + | 0.354128i | \(0.884778\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.84419e9 | −0.148935 | −0.0744677 | − | 0.997223i | \(-0.523726\pi\) | ||||
−0.0744677 | + | 0.997223i | \(0.523726\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.83350e10 | − | 1.05857e10i | 0.385490 | − | 0.222563i | −0.294714 | − | 0.955585i | \(-0.595224\pi\) |
0.680204 | + | 0.733023i | \(0.261891\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.94519e10 | − | 2.99112e9i | −1.84883 | − | 0.0618219i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.08942e10 | + | 5.35104e10i | −0.617210 | + | 1.06904i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.88928e10i | − | 1.35332i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.99972e9 | − | 5.77334e9i | −0.189953 | − | 0.109669i | 0.402008 | − | 0.915636i | \(-0.368313\pi\) |
−0.591960 | + | 0.805967i | \(0.701646\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.77852e10 | + | 3.91358e10i | −1.26635 | + | 0.731128i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.41961e9 | − | 7.65500e9i | −0.0798762 | − | 0.138350i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.40949e10 | − | 5.90541e10i | 0.606141 | − | 1.04987i | −0.385729 | − | 0.922612i | \(-0.626050\pi\) |
0.991870 | − | 0.127255i | \(-0.0406165\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.71885e10 | 0.639857 | 0.319929 | − | 0.947442i | \(-0.396341\pi\) | ||||
0.319929 | + | 0.947442i | \(0.396341\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.91152e9 | + | 5.72242e9i | 0.167785 | + | 0.0968706i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.74595e10 | − | 8.89404e10i | −0.777853 | − | 1.45772i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.66255e10 | + | 4.61166e10i | 0.429432 | + | 0.743799i | 0.996823 | − | 0.0796501i | \(-0.0253803\pi\) |
−0.567390 | + | 0.823449i | \(0.692047\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9.10881e10i | − | 1.42295i | −0.702711 | − | 0.711475i | \(-0.748027\pi\) | ||
0.702711 | − | 0.711475i | \(-0.251973\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.28270e10 | −0.658494 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.02031e9 | + | 2.89848e9i | −0.0747927 | + | 0.0431816i | −0.536930 | − | 0.843627i | \(-0.680416\pi\) |
0.462137 | + | 0.886808i | \(0.347083\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.00629e9 | + | 3.00938e10i | −0.0147584 | + | 0.441361i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.27082e10 | + | 2.20113e10i | −0.180657 | + | 0.312907i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.27743e10i | − | 1.15860i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.38767e10 | + | 3.68792e10i | 0.866945 | + | 0.500531i | 0.866332 | − | 0.499469i | \(-0.166471\pi\) |
0.000613137 | 1.00000i | \(0.499805\pi\) | ||||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8.49467e10 | + | 4.90440e10i | −1.13538 | + | 0.655510i | −0.945281 | − | 0.326256i | \(-0.894213\pi\) |
−0.190095 | + | 0.981766i | \(0.560880\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.47216e10 | − | 4.28190e10i | −0.320504 | − | 0.555129i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.95256e10 | + | 5.11398e10i | −0.377030 | + | 0.653035i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.29322e11 | −1.60237 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.85892e9 | + | 2.22795e9i | 0.0471032 | + | 0.0271950i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.80069e10 | + | 7.73435e10i | 0.450305 | + | 0.916365i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.61177e10 | + | 2.79168e10i | 0.188155 | + | 0.325894i | 0.944635 | − | 0.328123i | \(-0.106416\pi\) |
−0.756480 | + | 0.654017i | \(0.773083\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 1.87015e10i | − | 0.211978i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.97958e10 | −1.11471 | −0.557356 | − | 0.830273i | \(-0.688184\pi\) | ||||
−0.557356 | + | 0.830273i | \(0.688184\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.08161e10 | − | 1.20182e10i | 0.225836 | − | 0.130386i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.10428e10 | − | 8.19554e10i | 0.545801 | − | 0.876349i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.01561e10 | − | 5.22319e10i | 0.313295 | − | 0.542644i | −0.665778 | − | 0.746150i | \(-0.731900\pi\) |
0.979074 | + | 0.203506i | \(0.0652337\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.63983e11i | 1.67939i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.10263e8 | + | 6.36604e7i | 0.00109748 | + | 0.000633630i | 0.500549 | − | 0.865708i | \(-0.333132\pi\) |
−0.499451 | + | 0.866342i | \(0.666465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.35488e10 | + | 2.51429e10i | −0.427349 | + | 0.246730i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.12713e10 | + | 8.88046e10i | 0.489132 | + | 0.847201i | 0.999922 | − | 0.0125047i | \(-0.00398046\pi\) |
−0.510790 | + | 0.859705i | \(0.670647\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.04428e10 | − | 5.27285e10i | 0.286378 | − | 0.496022i | −0.686564 | − | 0.727069i | \(-0.740882\pi\) |
0.972943 | + | 0.231047i | \(0.0742152\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.24337e11 | −1.13745 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.41312e10 | − | 1.39322e10i | −0.217709 | − | 0.125694i | 0.387180 | − | 0.922004i | \(-0.373449\pi\) |
−0.604889 | + | 0.796310i | \(0.706783\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.12574e10 | − | 6.00709e9i | 0.0987951 | − | 0.0527181i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.06906e10 | − | 8.77986e10i | −0.438786 | − | 0.760000i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 4.01355e9i | − | 0.0338047i | −0.999857 | − | 0.0169023i | \(-0.994620\pi\) | ||
0.999857 | − | 0.0169023i | \(-0.00538043\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.03840e11 | −0.862787 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.32222e11 | + | 7.63384e10i | −1.06926 | + | 0.617340i | −0.927980 | − | 0.372630i | \(-0.878456\pi\) |
−0.141283 | + | 0.989969i | \(0.545123\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.59540e10 | − | 4.86384e10i | −0.207079 | − | 0.388071i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.45784e10 | − | 9.45325e10i | 0.423949 | − | 0.734301i | −0.572373 | − | 0.819993i | \(-0.693977\pi\) |
0.996322 | + | 0.0856928i | \(0.0273104\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.79228e11i | 1.37375i | 0.726776 | + | 0.686875i | \(0.241018\pi\) | ||||
−0.726776 | + | 0.686875i | \(0.758982\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.85271e9 | − | 1.06966e9i | −0.0138289 | − | 0.00798409i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.96127e10 | − | 2.28704e10i | 0.291796 | − | 0.168469i | −0.346955 | − | 0.937882i | \(-0.612784\pi\) |
0.638752 | + | 0.769413i | \(0.279451\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.09839e11 | − | 1.90247e11i | −0.788119 | − | 1.36506i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.70156e10 | − | 1.16074e11i | 0.474607 | − | 0.822044i | −0.524970 | − | 0.851121i | \(-0.675924\pi\) |
0.999577 | + | 0.0290771i | \(0.00925685\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.21594e11 | −0.839015 | −0.419508 | − | 0.907752i | \(-0.637797\pi\) | ||||
−0.419508 | + | 0.907752i | \(0.637797\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.51231e10 | − | 2.02783e10i | −0.239238 | − | 0.138124i | 0.375589 | − | 0.926787i | \(-0.377441\pi\) |
−0.614826 | + | 0.788662i | \(0.710774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.51888e11 | − | 9.45974e10i | −1.00825 | − | 0.627953i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.55036e10 | − | 7.88146e10i | −0.298212 | − | 0.516519i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.92908e11i | 1.23239i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.35096e11 | 1.48296 | 0.741478 | − | 0.670978i | \(-0.234125\pi\) | ||||
0.741478 | + | 0.670978i | \(0.234125\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.51478e10 | − | 2.60661e10i | 0.277678 | − | 0.160317i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.89987e11 | + | 1.27331e11i | 1.15389 | + | 0.773349i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.51414e11 | + | 2.62257e11i | −0.896881 | + | 1.55344i | −0.0654207 | + | 0.997858i | \(0.520839\pi\) |
−0.831460 | + | 0.555585i | \(0.812494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.17949e11i | − | 0.690001i | −0.938603 | − | 0.345000i | \(-0.887879\pi\) | ||
0.938603 | − | 0.345000i | \(-0.112121\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.55386e11 | + | 8.97120e10i | 0.886735 | + | 0.511957i | 0.872873 | − | 0.487947i | \(-0.162254\pi\) |
0.0138619 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.86875e11 | − | 1.65627e11i | 1.61701 | − | 0.933582i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.14200e11 | + | 1.97801e11i | 0.628079 | + | 1.08786i | 0.987937 | + | 0.154858i | \(0.0494918\pi\) |
−0.359858 | + | 0.933007i | \(0.617175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.94106e10 | + | 1.02902e11i | −0.322774 | + | 0.559061i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.80179e11 | 1.48557 | 0.742785 | − | 0.669530i | \(-0.233504\pi\) | ||||
0.742785 | + | 0.669530i | \(0.233504\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.31508e9 | − | 4.80071e9i | −0.0435573 | − | 0.0251478i | 0.478063 | − | 0.878325i | \(-0.341339\pi\) |
−0.521621 | + | 0.853178i | \(0.674672\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.15719e11 | − | 3.86943e9i | −0.591720 | − | 0.0197861i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.16903e10 | − | 3.75688e10i | −0.109588 | − | 0.189812i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.85530e10i | 0.338171i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.19348e11 | −0.581776 | −0.290888 | − | 0.956757i | \(-0.593951\pi\) | ||||
−0.290888 | + | 0.956757i | \(0.593951\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.44704e10 | − | 4.87690e10i | 0.402115 | − | 0.232161i | −0.285281 | − | 0.958444i | \(-0.592087\pi\) |
0.687396 | + | 0.726283i | \(0.258754\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.97354e10 | − | 4.25476e10i | 0.375121 | − | 0.200169i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.69347e11 | − | 2.93317e11i | 0.778204 | − | 1.34789i | −0.154772 | − | 0.987950i | \(-0.549464\pi\) |
0.932976 | − | 0.359939i | \(-0.117203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.12907e10i | 0.369214i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.33012e11 | − | 1.34530e11i | −1.03396 | − | 0.596955i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.57158e11 | − | 1.48470e11i | 1.12794 | − | 0.651219i | 0.184527 | − | 0.982827i | \(-0.440925\pi\) |
0.943417 | + | 0.331608i | \(0.107591\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.22126e10 | − | 2.11529e10i | −0.0523443 | − | 0.0906630i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.59364e11 | + | 2.76026e11i | −0.675240 | + | 1.16955i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.94718e11 | 0.806370 | 0.403185 | − | 0.915118i | \(-0.367903\pi\) | ||||
0.403185 | + | 0.915118i | \(0.367903\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.50865e11 | + | 2.02572e11i | 1.43654 | + | 0.829389i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.46340e10 | − | 4.37642e11i | 0.0585714 | − | 1.75163i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.00882e11 | − | 3.47938e11i | −0.794979 | − | 1.37694i | −0.922852 | − | 0.385154i | \(-0.874148\pi\) |
0.127873 | − | 0.991791i | \(-0.459185\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.87410e11i | 0.725161i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.39270e11 | −0.532884 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.54791e11 | − | 8.93684e10i | 0.579201 | − | 0.334402i | −0.181615 | − | 0.983370i | \(-0.558132\pi\) |
0.760816 | + | 0.648968i | \(0.224799\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.20587e11 | − | 1.37384e11i | −0.816280 | − | 0.508389i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.96337e10 | − | 3.40065e10i | 0.0710639 | − | 0.123086i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.97437e11i | 0.706790i | 0.935474 | + | 0.353395i | \(0.114973\pi\) | ||||
−0.935474 | + | 0.353395i | \(0.885027\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.50006e11 | + | 2.02076e11i | 1.22576 | + | 0.707695i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.01144e11 | − | 5.83958e10i | 0.350370 | − | 0.202286i | −0.314478 | − | 0.949265i | \(-0.601830\pi\) |
0.664848 | + | 0.746979i | \(0.268496\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.78624e11 | + | 4.82591e11i | 0.944384 | + | 1.63572i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.45542e10 | + | 1.46452e11i | −0.283503 | + | 0.491042i | −0.972245 | − | 0.233965i | \(-0.924830\pi\) |
0.688742 | + | 0.725006i | \(0.258163\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.84466e11 | 0.605287 | 0.302644 | − | 0.953104i | \(-0.402131\pi\) | ||||
0.302644 | + | 0.953104i | \(0.402131\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.98611e10 | − | 4.03343e10i | −0.226783 | − | 0.130933i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.40856e10 | + | 3.86724e10i | −0.0765298 | + | 0.122878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.50650e11 | + | 2.60933e11i | 0.473596 | + | 0.820293i | 0.999543 | − | 0.0302244i | \(-0.00962218\pi\) |
−0.525947 | + | 0.850518i | \(0.676289\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.97849e11i | 0.608900i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.94329e11 | 1.50533 | 0.752666 | − | 0.658403i | \(-0.228768\pi\) | ||||
0.752666 | + | 0.658403i | \(0.228768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.78956e10 | − | 3.34260e10i | 0.172626 | − | 0.0996658i | −0.411197 | − | 0.911546i | \(-0.634889\pi\) |
0.583824 | + | 0.811881i | \(0.301556\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.91107e11 | + | 6.39031e9i | 0.563870 | + | 0.0188549i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.39565e11 | − | 7.61348e11i | 1.27011 | − | 2.19989i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.20153e11i | 0.343581i | 0.985134 | + | 0.171790i | \(0.0549552\pi\) | ||||
−0.985134 | + | 0.171790i | \(0.945045\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.05856e11 | + | 1.76586e11i | 0.856640 | + | 0.494582i | 0.862886 | − | 0.505399i | \(-0.168655\pi\) |
−0.00624545 | + | 0.999980i | \(0.501988\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.46912e11 | + | 8.48198e10i | −0.407241 | + | 0.235120i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.34694e11 | + | 5.79707e11i | 0.908862 | + | 1.57420i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.13829e11 | + | 5.43568e11i | −0.843508 | + | 1.46100i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.14468e10 | −0.214484 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.79863e11 | − | 2.77049e11i | −1.25089 | − | 0.722201i | −0.279602 | − | 0.960116i | \(-0.590203\pi\) |
−0.971286 | + | 0.237915i | \(0.923536\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.42051e11 | − | 4.53610e11i | −0.618302 | − | 1.15871i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.09678e10 | + | 1.57561e11i | 0.230036 | + | 0.398433i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.84023e11i | 1.19959i | 0.800154 | + | 0.599795i | \(0.204751\pi\) | ||||
−0.800154 | + | 0.599795i | \(0.795249\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.41419e11 | −1.32845 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.62356e11 | − | 9.37360e10i | 0.390486 | − | 0.225447i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.98353e9 | + | 2.08848e11i | −0.0166300 | + | 0.497333i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.05691e11 | − | 1.83062e11i | 0.246743 | − | 0.427371i | −0.715877 | − | 0.698226i | \(-0.753973\pi\) |
0.962620 | + | 0.270855i | \(0.0873064\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.05159e11i | − | 0.243089i | −0.992586 | − | 0.121544i | \(-0.961215\pi\) | ||
0.992586 | − | 0.121544i | \(-0.0387847\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.59612e10 | + | 1.49887e10i | 0.0588429 | + | 0.0339730i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.35080e11 | − | 4.24399e11i | 1.64986 | − | 0.952546i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.78260e10 | − | 1.00158e11i | −0.127277 | − | 0.220450i | 0.795344 | − | 0.606159i | \(-0.207290\pi\) |
−0.922621 | + | 0.385708i | \(0.873957\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.35537e11 | − | 7.54373e11i | 0.949349 | − | 1.64432i | 0.202550 | − | 0.979272i | \(-0.435077\pi\) |
0.746799 | − | 0.665049i | \(-0.231590\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −5.49297e11 | −1.17432 | −0.587159 | − | 0.809472i | \(-0.699754\pi\) | ||||
−0.587159 | + | 0.809472i | \(0.699754\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.02301e11 | − | 1.74533e11i | −0.640060 | − | 0.369539i | 0.144577 | − | 0.989493i | \(-0.453818\pi\) |
−0.784638 | + | 0.619954i | \(0.787151\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.05897e11 | − | 2.48600e11i | 1.05071 | − | 0.516322i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.68553e10 | − | 9.84763e10i | −0.116957 | − | 0.202575i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 7.74760e11i | − | 1.56358i | −0.623543 | − | 0.781789i | \(-0.714307\pi\) | ||
0.623543 | − | 0.781789i | \(-0.285693\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.86546e11 | −0.972613 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.54203e11 | + | 8.90290e10i | −0.302458 | + | 0.174624i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.15638e10 | − | 1.85671e10i | 0.0224681 | − | 0.0360752i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.65601e11 | − | 6.33240e11i | 0.697091 | − | 1.20740i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.31150e11i | 0.814390i | 0.913341 | + | 0.407195i | \(0.133493\pi\) | ||||
−0.913341 | + | 0.407195i | \(0.866507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.55977e11 | + | 1.47788e11i | 0.474545 | + | 0.273979i | 0.718140 | − | 0.695898i | \(-0.244994\pi\) |
−0.243596 | + | 0.969877i | \(0.578327\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.08069e11 | − | 4.66539e11i | 1.48414 | − | 0.856870i | 0.484305 | − | 0.874899i | \(-0.339072\pi\) |
0.999837 | + | 0.0180286i | \(0.00573900\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 3.21149e11 | + | 5.56246e11i | 0.578980 | + | 1.00282i | 0.995597 | + | 0.0937400i | \(0.0298822\pi\) |
−0.416617 | + | 0.909082i | \(0.636784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.02724e11 | − | 1.77922e11i | 0.183487 | − | 0.317809i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.01136e11 | −1.05413 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.28077e12 | + | 7.39452e11i | 2.22535 | + | 1.28481i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.61187e11 | + | 1.92733e11i | −0.616170 | + | 0.328795i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.91337e11 | − | 5.04610e11i | −0.492490 | − | 0.853017i | 0.507473 | − | 0.861668i | \(-0.330580\pi\) |
−0.999963 | + | 0.00865063i | \(0.997246\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.79255e11i | − | 0.297554i | −0.988871 | − | 0.148777i | \(-0.952466\pi\) | ||
0.988871 | − | 0.148777i | \(-0.0475337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.09789e12 | −1.80599 | −0.902993 | − | 0.429655i | \(-0.858635\pi\) | ||||
−0.902993 | + | 0.429655i | \(0.858635\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.05091e11 | + | 2.91615e11i | −0.815972 | + | 0.471102i | −0.849026 | − | 0.528352i | \(-0.822810\pi\) |
0.0330533 | + | 0.999454i | \(0.489477\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.50938e11 | + | 4.70265e11i | 0.401753 | + | 0.752896i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.68542e11 | + | 9.84744e11i | −0.894040 | + | 1.54852i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 2.84784e11i | − | 0.443838i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.12569e10 | − | 2.95932e10i | −0.0784718 | − | 0.0453057i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.74283e11 | + | 3.31562e11i | −0.871419 | + | 0.503114i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.23607e10 | + | 5.60503e10i | 0.0482418 | + | 0.0835572i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.66059e11 | + | 8.07237e11i | −0.688671 | + | 1.19281i | 0.283598 | + | 0.958943i | \(0.408472\pi\) |
−0.972268 | + | 0.233869i | \(0.924861\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.47091e11 | −1.08468 | −0.542338 | − | 0.840160i | \(-0.682461\pi\) | ||||
−0.542338 | + | 0.840160i | \(0.682461\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.88010e10 | − | 3.97223e10i | −0.0990174 | − | 0.0571677i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.03124e12 | − | 6.42270e11i | −1.45842 | − | 0.908322i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.60674e11 | + | 6.24705e11i | 0.505653 | + | 0.875817i | 0.999979 | + | 0.00653993i | \(0.00208174\pi\) |
−0.494326 | + | 0.869277i | \(0.664585\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.66577e12i | 2.29513i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.61869e11 | 0.904077 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.66284e10 | + | 3.26944e10i | −0.0760276 | + | 0.0438945i | −0.537532 | − | 0.843243i | \(-0.680643\pi\) |
0.461504 | + | 0.887138i | \(0.347310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.90822e10 | − | 1.18119e12i | 0.105264 | − | 1.57224i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.71622e11 | + | 2.97258e11i | −0.224557 | + | 0.388945i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.46812e11i | 0.190460i | 0.995455 | + | 0.0952301i | \(0.0303587\pi\) | ||||
−0.995455 | + | 0.0952301i | \(0.969641\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.76414e11 | − | 1.59588e11i | −0.352535 | − | 0.203536i | 0.313266 | − | 0.949665i | \(-0.398577\pi\) |
−0.665801 | + | 0.746129i | \(0.731910\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.04625e12 | − | 6.04054e11i | 1.32309 | − | 0.763887i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.63248e11 | + | 2.82754e11i | 0.202977 | + | 0.351567i | 0.949486 | − | 0.313808i | \(-0.101605\pi\) |
−0.746509 | + | 0.665375i | \(0.768272\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.48770e11 | − | 4.30882e11i | 0.306714 | − | 0.531243i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.37626e12 | −1.66851 | −0.834254 | − | 0.551380i | \(-0.814102\pi\) | ||||
−0.834254 | + | 0.551380i | \(0.814102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.89033e11 | − | 2.24608e11i | −0.467706 | − | 0.270030i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −8.30697e11 | − | 2.77771e10i | −0.982128 | − | 0.0328407i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.98599e11 | − | 5.17189e11i | −0.350103 | − | 0.606395i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.30138e11i | − | 0.265387i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.03059e11 | −0.460959 | −0.230480 | − | 0.973077i | \(-0.574029\pi\) | ||||
−0.230480 | + | 0.973077i | \(0.574029\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.41001e12 | − | 8.14067e11i | 1.58615 | − | 0.915764i | 0.592216 | − | 0.805779i | \(-0.298253\pi\) |
0.993933 | − | 0.109985i | \(-0.0350802\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.20331e11 | − | 1.17571e11i | 0.245824 | − | 0.131174i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 5.36831e11 | − | 9.29819e11i | 0.589196 | − | 1.02052i | −0.405143 | − | 0.914254i | \(-0.632778\pi\) |
0.994338 | − | 0.106263i | \(-0.0338886\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.11408e12i | 1.21279i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.63659e9 | − | 3.83164e9i | −0.00710773 | − | 0.00410365i | 0.496442 | − | 0.868070i | \(-0.334640\pi\) |
−0.503550 | + | 0.863966i | \(0.667973\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.03180e11 | + | 1.75041e11i | −0.322074 | + | 0.185950i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −7.65953e11 | − | 1.32667e12i | −0.800602 | − | 1.38668i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26964e11 | + | 2.19908e11i | −0.131639 | + | 0.228006i | −0.924309 | − | 0.381646i | \(-0.875357\pi\) |
0.792669 | + | 0.609652i | \(0.208691\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.33405e11 | −0.238132 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.46237e11 | − | 1.99900e11i | −0.350423 | − | 0.202317i | 0.314449 | − | 0.949275i | \(-0.398180\pi\) |
−0.664872 | + | 0.746958i | \(0.731514\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.z.d.73.4 | 12 | ||
3.2 | odd | 2 | 84.9.m.b.73.3 | yes | 12 | ||
7.5 | odd | 6 | inner | 252.9.z.d.145.4 | 12 | ||
21.5 | even | 6 | 84.9.m.b.61.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.9.m.b.61.3 | ✓ | 12 | 21.5 | even | 6 | ||
84.9.m.b.73.3 | yes | 12 | 3.2 | odd | 2 | ||
252.9.z.d.73.4 | 12 | 1.1 | even | 1 | trivial | ||
252.9.z.d.145.4 | 12 | 7.5 | odd | 6 | inner |