Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,8,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(101.212748257\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 3205 x^{14} + 7140274 x^{12} + 8220484645 x^{10} + 6820694102626 x^{8} + \cdots + 57\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{44} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 217.5 | ||
Root | \(19.2574 + 33.3549i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.217 |
Dual form | 324.8.e.m.109.5 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
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 | ||||||||
\(5\) | 6.58929 | + | 11.4130i | 0.0235746 | + | 0.0408323i | 0.877572 | − | 0.479445i | \(-0.159162\pi\) |
−0.853997 | + | 0.520277i | \(0.825829\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 801.604 | − | 1388.42i | 0.883317 | − | 1.52995i | 0.0356875 | − | 0.999363i | \(-0.488638\pi\) |
0.847630 | − | 0.530588i | \(-0.178029\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3472.85 | + | 6015.16i | −0.786705 | + | 1.36261i | 0.141270 | + | 0.989971i | \(0.454881\pi\) |
−0.927975 | + | 0.372642i | \(0.878452\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2098.03 | − | 3633.89i | −0.264856 | − | 0.458743i | 0.702670 | − | 0.711516i | \(-0.251991\pi\) |
−0.967526 | + | 0.252772i | \(0.918658\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 31739.7 | 1.56687 | 0.783433 | − | 0.621476i | \(-0.213467\pi\) | ||||
0.783433 | + | 0.621476i | \(0.213467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −43478.0 | −1.45422 | −0.727112 | − | 0.686518i | \(-0.759138\pi\) | ||||
−0.727112 | + | 0.686518i | \(0.759138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 56384.0 | + | 97659.9i | 0.966292 | + | 1.67367i | 0.706104 | + | 0.708108i | \(0.250451\pi\) |
0.260187 | + | 0.965558i | \(0.416216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 38975.7 | − | 67507.8i | 0.498888 | − | 0.864100i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5963.00 | + | 10328.2i | −0.0454017 | + | 0.0786380i | −0.887833 | − | 0.460165i | \(-0.847790\pi\) |
0.842432 | + | 0.538803i | \(0.181123\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 126979. | + | 219934.i | 0.765535 | + | 1.32595i | 0.939963 | + | 0.341276i | \(0.110859\pi\) |
−0.174428 | + | 0.984670i | \(0.555808\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21128.0 | 0.0832953 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 210306. | 0.682567 | 0.341283 | − | 0.939960i | \(-0.389138\pi\) | ||||
0.341283 | + | 0.939960i | \(0.389138\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −71570.1 | − | 123963.i | −0.162177 | − | 0.280898i | 0.773472 | − | 0.633830i | \(-0.218518\pi\) |
−0.935649 | + | 0.352932i | \(0.885185\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −199683. | + | 345860.i | −0.383002 | + | 0.663378i | −0.991490 | − | 0.130185i | \(-0.958443\pi\) |
0.608488 | + | 0.793563i | \(0.291776\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 169785. | − | 294076.i | 0.238537 | − | 0.413159i | −0.721757 | − | 0.692146i | \(-0.756665\pi\) |
0.960295 | + | 0.278987i | \(0.0899987\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −873367. | − | 1.51272e6i | −1.06050 | − | 1.83684i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −719247. | −0.663610 | −0.331805 | − | 0.943348i | \(-0.607658\pi\) | ||||
−0.331805 | + | 0.943348i | \(0.607658\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −91534.5 | −0.0741849 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.38205e6 | − | 2.39379e6i | −0.876079 | − | 1.51741i | −0.855609 | − | 0.517622i | \(-0.826817\pi\) |
−0.0204695 | − | 0.999790i | \(-0.506516\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −186249. | + | 322592.i | −0.105060 | + | 0.181970i | −0.913763 | − | 0.406248i | \(-0.866837\pi\) |
0.808703 | + | 0.588218i | \(0.200170\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 27649.0 | − | 47889.5i | 0.0124877 | − | 0.0216293i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.18165e6 | + | 2.04668e6i | 0.479986 | + | 0.831360i | 0.999736 | − | 0.0229580i | \(-0.00730840\pi\) |
−0.519750 | + | 0.854318i | \(0.673975\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.76399e6 | 1.24809 | 0.624043 | − | 0.781390i | \(-0.285489\pi\) | ||||
0.624043 | + | 0.781390i | \(0.285489\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.80218e6 | 0.843073 | 0.421537 | − | 0.906811i | \(-0.361491\pi\) | ||||
0.421537 | + | 0.906811i | \(0.361491\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.56771e6 | + | 9.64355e6i | 1.38982 | + | 2.40724i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 137299. | − | 237809.i | 0.0313310 | − | 0.0542668i | −0.849935 | − | 0.526888i | \(-0.823359\pi\) |
0.881266 | + | 0.472621i | \(0.156692\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.28487e6 | − | 3.95751e6i | 0.438620 | − | 0.759712i | −0.558963 | − | 0.829192i | \(-0.688801\pi\) |
0.997583 | + | 0.0694801i | \(0.0221340\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 209142. | + | 362245.i | 0.0369382 | + | 0.0639788i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.11950e6 | 0.769773 | 0.384886 | − | 0.922964i | \(-0.374241\pi\) | ||||
0.384886 | + | 0.922964i | \(0.374241\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.72715e6 | −0.935806 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −286489. | − | 496213.i | −0.0342827 | − | 0.0593794i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.30586e6 | + | 3.99386e6i | −0.256526 | + | 0.444316i | −0.965309 | − | 0.261110i | \(-0.915911\pi\) |
0.708783 | + | 0.705427i | \(0.249245\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.47532e6 | + | 7.75149e6i | −0.432215 | + | 0.748618i | −0.997064 | − | 0.0765763i | \(-0.975601\pi\) |
0.564849 | + | 0.825194i | \(0.308934\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.13855e6 | − | 1.06323e7i | −0.553523 | − | 0.958730i | −0.998017 | − | 0.0629479i | \(-0.979950\pi\) |
0.444494 | − | 0.895782i | \(-0.353384\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.91165e7 | 1.50857 | 0.754285 | − | 0.656547i | \(-0.227984\pi\) | ||||
0.754285 | + | 0.656547i | \(0.227984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.78953e7 | 1.32356 | 0.661782 | − | 0.749696i | \(-0.269800\pi\) | ||||
0.661782 | + | 0.749696i | \(0.269800\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −8.26379e6 | − | 1.43133e7i | −0.538772 | − | 0.933180i | −0.998971 | − | 0.0453644i | \(-0.985555\pi\) |
0.460199 | − | 0.887816i | \(-0.347778\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −743060. | + | 1.28702e6i | −0.0455598 | + | 0.0789119i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.54427e7 | − | 4.40680e7i | 1.38404 | − | 2.39723i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.43778e7 | − | 2.49031e7i | −0.737809 | − | 1.27792i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.05686e6 | 0.0941934 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.32673e7 | 1.44113 | 0.720567 | − | 0.693385i | \(-0.243881\pi\) | ||||
0.720567 | + | 0.693385i | \(0.243881\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.69086e6 | + | 1.33210e7i | 0.298900 | + | 0.517709i | 0.975884 | − | 0.218288i | \(-0.0700471\pi\) |
−0.676985 | + | 0.735997i | \(0.736714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.48521e7 | + | 6.03656e7i | −1.28454 | + | 2.22489i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.54717e6 | − | 1.13400e7i | 0.217536 | − | 0.376784i | −0.736518 | − | 0.676418i | \(-0.763531\pi\) |
0.954054 | + | 0.299634i | \(0.0968646\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.43895e6 | + | 1.28846e7i | 0.234942 | + | 0.406931i | 0.959256 | − | 0.282539i | \(-0.0911768\pi\) |
−0.724314 | + | 0.689470i | \(0.757843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.91445e7 | 0.833453 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −157168. | −0.00428130 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.64037e7 | + | 4.57325e7i | 0.653902 | + | 1.13259i | 0.982168 | + | 0.188006i | \(0.0602026\pi\) |
−0.328266 | + | 0.944585i | \(0.606464\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.23026e7 | − | 2.13087e7i | 0.290789 | − | 0.503661i | −0.683208 | − | 0.730224i | \(-0.739416\pi\) |
0.973996 | + | 0.226563i | \(0.0727490\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.67340e6 | + | 2.89841e6i | −0.0360943 | + | 0.0625172i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.27011e7 | − | 2.19989e7i | −0.261934 | − | 0.453682i | 0.704822 | − | 0.709384i | \(-0.251027\pi\) |
−0.966756 | + | 0.255702i | \(0.917693\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.80790e8 | 3.41417 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.65162e7 | 0.660433 | 0.330216 | − | 0.943905i | \(-0.392878\pi\) | ||||
0.330216 | + | 0.943905i | \(0.392878\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.92488e7 | + | 5.06604e7i | 0.485960 | + | 0.841707i | 0.999870 | − | 0.0161373i | \(-0.00513688\pi\) |
−0.513910 | + | 0.857844i | \(0.671804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.25708e7 | − | 3.90938e7i | 0.359703 | − | 0.623024i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.07947e7 | − | 8.79790e7i | 0.745859 | − | 1.29187i | −0.203933 | − | 0.978985i | \(-0.565372\pi\) |
0.949792 | − | 0.312881i | \(-0.101294\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.24861e7 | − | 1.08229e8i | −0.881354 | − | 1.52655i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.18603e8 | 1.54564 | 0.772822 | − | 0.634623i | \(-0.218844\pi\) | ||||
0.772822 | + | 0.634623i | \(0.218844\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.27758e7 | −0.160145 | −0.0800723 | − | 0.996789i | \(-0.525515\pi\) | ||||
−0.0800723 | + | 0.996789i | \(0.525515\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.38577e6 | + | 2.40022e6i | 0.0160912 | + | 0.0278708i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.10227e8 | + | 1.90919e8i | −1.23266 | + | 2.13503i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.16382e6 | + | 1.24081e7i | −0.0743923 | + | 0.128851i | −0.900822 | − | 0.434189i | \(-0.857035\pi\) |
0.826430 | + | 0.563040i | \(0.190368\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.20070e7 | + | 5.54377e7i | 0.320475 | + | 0.555079i | 0.980586 | − | 0.196089i | \(-0.0628242\pi\) |
−0.660111 | + | 0.751168i | \(0.729491\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.78002e7 | −0.538639 | −0.269319 | − | 0.963051i | \(-0.586799\pi\) | ||||
−0.269319 | + | 0.963051i | \(0.586799\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.46950e7 | 0.491997 | 0.245998 | − | 0.969270i | \(-0.420884\pi\) | ||||
0.245998 | + | 0.969270i | \(0.420884\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 9.55993e6 | + | 1.65583e7i | 0.0802082 | + | 0.138925i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 943192. | − | 1.63366e6i | 0.00764648 | − | 0.0132441i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.50993e8 | − | 2.61527e8i | 1.14405 | − | 1.98155i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.78918e7 | − | 8.29510e7i | −0.350972 | − | 0.607901i | 0.635448 | − | 0.772144i | \(-0.280815\pi\) |
−0.986420 | + | 0.164243i | \(0.947482\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.26306e6 | −0.0361164 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.07147e8 | 2.70484 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.65908e7 | − | 1.15339e8i | −0.414993 | − | 0.718789i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.33462e7 | + | 1.09719e8i | −0.382520 | + | 0.662543i | −0.991422 | − | 0.130702i | \(-0.958277\pi\) |
0.608902 | + | 0.793245i | \(0.291610\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.57438e7 | + | 7.92305e7i | −0.259562 | + | 0.449575i | −0.966125 | − | 0.258076i | \(-0.916912\pi\) |
0.706563 | + | 0.707651i | \(0.250245\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.23628e8 | − | 2.14131e8i | −0.680290 | − | 1.17830i | −0.974892 | − | 0.222677i | \(-0.928521\pi\) |
0.294603 | − | 0.955620i | \(-0.404813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.92258e8 | 0.995723 | 0.497862 | − | 0.867256i | \(-0.334119\pi\) | ||||
0.497862 | + | 0.867256i | \(0.334119\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.47504e6 | 0.0224936 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.43028e7 | + | 5.94143e7i | 0.162531 | + | 0.281513i | 0.935776 | − | 0.352595i | \(-0.114701\pi\) |
−0.773244 | + | 0.634108i | \(0.781367\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.31631e7 | + | 4.01196e7i | −0.106595 | + | 0.184628i | −0.914389 | − | 0.404837i | \(-0.867328\pi\) |
0.807794 | + | 0.589465i | \(0.200661\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.15097e7 | − | 1.99354e7i | 0.0500016 | − | 0.0866053i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.12179e7 | + | 1.57994e8i | 0.385160 | + | 0.667116i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.28682e8 | 1.31195 | 0.655977 | − | 0.754781i | \(-0.272257\pi\) | ||||
0.655977 | + | 0.754781i | \(0.272257\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.83253e8 | −3.04075 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3.92934e7 | + | 6.80581e7i | 0.144395 | + | 0.250100i | 0.929147 | − | 0.369710i | \(-0.120543\pi\) |
−0.784752 | + | 0.619810i | \(0.787210\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.68582e8 | − | 2.91993e8i | 0.602923 | − | 1.04429i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.45451e7 | + | 7.71544e7i | −0.150992 | + | 0.261526i | −0.931593 | − | 0.363504i | \(-0.881580\pi\) |
0.780600 | + | 0.625031i | \(0.214914\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.73933e6 | − | 8.20876e6i | −0.0156443 | − | 0.0270967i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.08049e8 | −0.964909 | −0.482454 | − | 0.875921i | \(-0.660255\pi\) | ||||
−0.482454 | + | 0.875921i | \(0.660255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.19656e7 | 0.280694 | 0.140347 | − | 0.990102i | \(-0.455178\pi\) | ||||
0.140347 | + | 0.990102i | \(0.455178\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.70713e8 | + | 4.68889e8i | 0.784956 | + | 1.35958i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.45194e7 | − | 1.46392e8i | 0.238934 | − | 0.413845i | −0.721475 | − | 0.692441i | \(-0.756535\pi\) |
0.960409 | + | 0.278595i | \(0.0898688\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.37236e8 | + | 4.10905e8i | −0.637836 | + | 1.10476i | 0.348071 | + | 0.937468i | \(0.386837\pi\) |
−0.985907 | + | 0.167295i | \(0.946497\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.20372e8 | + | 2.08490e8i | 0.315698 | + | 0.546805i | 0.979586 | − | 0.201027i | \(-0.0644280\pi\) |
−0.663888 | + | 0.747832i | \(0.731095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.29484e8 | −0.573014 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.97071e8 | 1.45507 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.13504e8 | − | 1.96595e8i | −0.263619 | − | 0.456601i | 0.703582 | − | 0.710614i | \(-0.251583\pi\) |
−0.967201 | + | 0.254013i | \(0.918249\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.82135e7 | − | 3.15467e7i | 0.0413063 | − | 0.0715447i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.36590e8 | − | 4.09786e8i | 0.511855 | − | 0.886560i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.20133e8 | + | 5.54486e8i | 0.676624 | + | 1.17195i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.90898e6 | −0.00990699 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.36817e8 | −0.467119 | −0.233560 | − | 0.972342i | \(-0.575037\pi\) | ||||
−0.233560 | + | 0.972342i | \(0.575037\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.72111e8 | − | 6.44516e8i | −0.701474 | − | 1.21499i | −0.967949 | − | 0.251147i | \(-0.919192\pi\) |
0.266475 | − | 0.963842i | \(-0.414141\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.31059e8 | + | 5.73411e8i | −0.610240 | + | 1.05697i | 0.380960 | + | 0.924591i | \(0.375594\pi\) |
−0.991200 | + | 0.132375i | \(0.957740\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.53579e8 | + | 6.12417e8i | −0.623418 | + | 1.07979i | 0.365427 | + | 0.930840i | \(0.380923\pi\) |
−0.988845 | + | 0.148951i | \(0.952410\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.14172e7 | − | 7.17368e7i | −0.0714355 | − | 0.123730i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.37998e9 | −2.27858 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.27088e8 | −0.528534 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.72200e8 | − | 4.71465e8i | −0.421408 | − | 0.729901i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.99065e8 | − | 8.64405e8i | 0.756413 | − | 1.31015i | −0.188256 | − | 0.982120i | \(-0.560284\pi\) |
0.944669 | − | 0.328025i | \(-0.106383\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.55725e7 | + | 2.69724e7i | −0.0226309 | + | 0.0391979i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.58274e8 | − | 6.20549e8i | −0.509930 | − | 0.883225i | −0.999934 | − | 0.0115049i | \(-0.996338\pi\) |
0.490003 | − | 0.871721i | \(-0.336996\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.76391e9 | −2.40900 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.48007e9 | −1.98040 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.19735e8 | − | 9.00207e8i | −0.667772 | − | 1.15662i | −0.978526 | − | 0.206125i | \(-0.933915\pi\) |
0.310753 | − | 0.950491i | \(-0.399419\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.27845e8 | − | 2.21434e8i | 0.160989 | − | 0.278841i | −0.774235 | − | 0.632898i | \(-0.781865\pi\) |
0.935224 | + | 0.354058i | \(0.115198\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.73385e8 | + | 4.73516e8i | −0.330798 | + | 0.572959i | −0.982669 | − | 0.185371i | \(-0.940651\pi\) |
0.651871 | + | 0.758330i | \(0.273985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.48020e7 | + | 4.29584e7i | 0.0294231 | + | 0.0509622i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.23140e8 | 0.710813 | 0.355407 | − | 0.934712i | \(-0.384342\pi\) | ||||
0.355407 | + | 0.934712i | \(0.384342\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.96461e8 | 1.11477 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.84643e7 | + | 3.19812e7i | 0.0198751 | + | 0.0344246i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.99355e8 | − | 8.64908e8i | 0.527325 | − | 0.913353i | −0.472168 | − | 0.881508i | \(-0.656529\pi\) |
0.999493 | − | 0.0318446i | \(-0.0101382\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.76552e8 | + | 9.98617e8i | −0.586178 | + | 1.01529i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.64259e8 | + | 9.77324e8i | 0.562986 | + | 0.975120i | 0.997234 | + | 0.0743264i | \(0.0236807\pi\) |
−0.434248 | + | 0.900793i | \(0.642986\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.00421e7 | 0.0480996 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.94136e8 | −0.938012 | −0.469006 | − | 0.883195i | \(-0.655388\pi\) | ||||
−0.469006 | + | 0.883195i | \(0.655388\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.26334e8 | + | 1.25805e9i | 0.660603 | + | 1.14420i | 0.980457 | + | 0.196731i | \(0.0630326\pi\) |
−0.319855 | + | 0.947467i | \(0.603634\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.33744e7 | + | 1.27088e8i | −0.0655288 | + | 0.113499i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.48948e8 | + | 6.04396e8i | −0.300564 | + | 0.520592i | −0.976264 | − | 0.216585i | \(-0.930508\pi\) |
0.675700 | + | 0.737177i | \(0.263842\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.78961e9 | + | 3.09970e9i | 1.51405 | + | 2.62241i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.61882e6 | 0.00295445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −6.85058e8 | −0.549491 | −0.274746 | − | 0.961517i | \(-0.588594\pi\) | ||||
−0.274746 | + | 0.961517i | \(0.588594\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.70211e8 | + | 8.14429e8i | 0.364156 | + | 0.630736i | 0.988640 | − | 0.150301i | \(-0.0480243\pi\) |
−0.624485 | + | 0.781037i | \(0.714691\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.32810e8 | − | 9.22853e8i | 0.405513 | − | 0.702369i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.30361e8 | + | 1.26502e9i | −0.536979 | + | 0.930074i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.68117e8 | − | 1.50362e9i | −0.627403 | − | 1.08669i | −0.988071 | − | 0.153999i | \(-0.950785\pi\) |
0.360668 | − | 0.932694i | \(-0.382549\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.43144e9 | −3.09542 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.02227e7 | 0.0413611 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.15321e8 | + | 1.06577e9i | 0.408651 | + | 0.707804i | 0.994739 | − | 0.102443i | \(-0.0326660\pi\) |
−0.586088 | + | 0.810248i | \(0.699333\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.82570e8 | − | 1.18225e9i | 0.445820 | − | 0.772184i | −0.552289 | − | 0.833653i | \(-0.686245\pi\) |
0.998109 | + | 0.0614695i | \(0.0195787\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.23708e9 | − | 2.14268e9i | 0.781691 | − | 1.35393i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.98595e8 | + | 5.17182e8i | 0.185603 | + | 0.321474i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.26767e8 | 0.437245 | 0.218623 | − | 0.975809i | \(-0.429844\pi\) | ||||
0.218623 | + | 0.975809i | \(0.429844\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.44713e9 | −1.44860 | −0.724301 | − | 0.689484i | \(-0.757837\pi\) | ||||
−0.724301 | + | 0.689484i | \(0.757837\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.45146e9 | − | 4.24605e9i | −1.40521 | − | 2.43389i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.82198e8 | + | 1.70122e9i | −0.554081 | + | 0.959696i | 0.443894 | + | 0.896079i | \(0.353597\pi\) |
−0.997974 | + | 0.0636165i | \(0.979737\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.61317e8 | + | 7.99025e8i | −0.252108 | + | 0.436664i | −0.964106 | − | 0.265518i | \(-0.914457\pi\) |
0.711998 | + | 0.702181i | \(0.247790\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.37339e7 | + | 5.84288e7i | 0.0181470 | + | 0.0314316i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.60127e9 | 1.35620 | 0.678099 | − | 0.734970i | \(-0.262804\pi\) | ||||
0.678099 | + | 0.734970i | \(0.262804\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.94210e8 | 0.510341 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.43271e7 | − | 7.67768e7i | −0.0220612 | − | 0.0382111i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.96931e8 | − | 1.03391e9i | 0.292562 | − | 0.506732i | −0.681853 | − | 0.731489i | \(-0.738826\pi\) |
0.974415 | + | 0.224758i | \(0.0721590\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.16305e8 | + | 1.24068e9i | −0.340522 | + | 0.589801i | −0.984530 | − | 0.175218i | \(-0.943937\pi\) |
0.644008 | + | 0.765019i | \(0.277270\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.95620e9 | − | 3.38824e9i | −0.915968 | − | 1.58650i | −0.805478 | − | 0.592626i | \(-0.798091\pi\) |
−0.110491 | − | 0.993877i | \(-0.535242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −7.73537e8 | −0.351457 | −0.175728 | − | 0.984439i | \(-0.556228\pi\) | ||||
−0.175728 | + | 0.984439i | \(0.556228\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.78888e9 | 1.69592 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.38694e9 | − | 2.40224e9i | −0.602618 | − | 1.04377i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.69458e9 | + | 2.93510e9i | −0.725496 | + | 1.25660i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.97145e8 | + | 5.14669e8i | −0.123536 | + | 0.213971i | −0.921160 | − | 0.389185i | \(-0.872757\pi\) |
0.797624 | + | 0.603155i | \(0.206090\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.41227e8 | − | 7.64227e8i | −0.180782 | − | 0.313123i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −6.07759e7 | −0.0241900 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.53444e8 | 0.0994331 | 0.0497165 | − | 0.998763i | \(-0.484168\pi\) | ||||
0.0497165 | + | 0.998763i | \(0.484168\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.01104e9 | + | 1.75117e9i | 0.385462 | + | 0.667640i | 0.991833 | − | 0.127542i | \(-0.0407086\pi\) |
−0.606371 | + | 0.795182i | \(0.707375\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.89264e8 | + | 3.27815e8i | −0.0711384 | + | 0.123215i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.01723e9 | − | 5.22600e9i | 1.10246 | − | 1.90951i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.63510e8 | + | 9.76029e8i | 0.203025 | + | 0.351650i | 0.949502 | − | 0.313762i | \(-0.101589\pi\) |
−0.746477 | + | 0.665412i | \(0.768256\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.33239e9 | −0.817171 | −0.408585 | − | 0.912720i | \(-0.633978\pi\) | ||||
−0.408585 | + | 0.912720i | \(0.633978\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.17957e8 | −0.0407571 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.79595e8 | + | 1.35030e9i | 0.262033 | + | 0.453855i | 0.966782 | − | 0.255602i | \(-0.0822736\pi\) |
−0.704749 | + | 0.709457i | \(0.748940\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.24624e9 | − | 3.89059e9i | 0.744701 | − | 1.28986i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.08974e7 | − | 1.40118e8i | 0.0260981 | − | 0.0452033i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.17928e9 | + | 2.04256e9i | 0.375317 | + | 0.650068i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.32561e9 | 0.410661 | 0.205330 | − | 0.978693i | \(-0.434173\pi\) | ||||
0.205330 | + | 0.978693i | \(0.434173\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.51546e9 | −0.463221 | −0.231611 | − | 0.972809i | \(-0.574400\pi\) | ||||
−0.231611 | + | 0.972809i | \(0.574400\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.03027e9 | + | 6.98064e9i | 1.19949 | + | 2.07758i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.65589e9 | + | 8.06424e9i | −1.36744 | + | 2.36847i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −3.00312e8 | + | 5.20156e8i | −0.0859068 | + | 0.148795i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.25964e8 | + | 2.18176e8i | 0.0355639 | + | 0.0615984i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.21323e10 | 3.33720 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.01912e9 | 0.548242 | 0.274121 | − | 0.961695i | \(-0.411613\pi\) | ||||
0.274121 | + | 0.961695i | \(0.411613\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.17917e8 | + | 2.04238e8i | 0.0312025 | + | 0.0540442i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.72818e9 | − | 2.99330e9i | 0.451475 | − | 0.781977i | −0.547003 | − | 0.837130i | \(-0.684231\pi\) |
0.998478 | + | 0.0551535i | \(0.0175648\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.59259e8 | − | 4.49050e8i | 0.0660243 | − | 0.114357i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.20119e8 | − | 3.81258e8i | −0.0553504 | − | 0.0958697i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.42067e9 | 1.32911 | 0.664553 | − | 0.747241i | \(-0.268622\pi\) | ||||
0.664553 | + | 0.747241i | \(0.268622\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.67576e9 | 0.405760 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.69379e9 | + | 2.93373e9i | 0.400018 | + | 0.692852i | 0.993728 | − | 0.111828i | \(-0.0356705\pi\) |
−0.593709 | + | 0.804680i | \(0.702337\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.08905e8 | − | 1.88629e8i | 0.0254026 | − | 0.0439986i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.93587e9 | − | 5.08508e9i | 0.668104 | − | 1.15719i | −0.310330 | − | 0.950629i | \(-0.600439\pi\) |
0.978434 | − | 0.206561i | \(-0.0662272\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.15789e9 | − | 3.73757e9i | −0.485068 | − | 0.840163i | 0.514785 | − | 0.857320i | \(-0.327872\pi\) |
−0.999853 | + | 0.0171568i | \(0.994539\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.79041e9 | 1.92829 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.82938e9 | 0.396450 | 0.198225 | − | 0.980157i | \(-0.436482\pi\) | ||||
0.198225 | + | 0.980157i | \(0.436482\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.66313e9 | − | 6.34472e9i | −0.774882 | − | 1.34213i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.49784e9 | − | 4.32639e9i | 0.522065 | − | 0.904243i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.23343e8 | + | 1.07966e9i | −0.127202 | + | 0.220320i | −0.922592 | − | 0.385778i | \(-0.873933\pi\) |
0.795390 | + | 0.606099i | \(0.207266\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.52078e9 | − | 9.56227e9i | −1.11326 | − | 1.92822i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.56586e9 | −1.68686 | −0.843431 | − | 0.537238i | \(-0.819468\pi\) | ||||
−0.843431 | + | 0.537238i | \(0.819468\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.70597e8 | 0.130513 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.74716e9 | + | 3.02617e9i | 0.332154 | + | 0.575307i | 0.982934 | − | 0.183959i | \(-0.0588914\pi\) |
−0.650780 | + | 0.759266i | \(0.725558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.78615e9 | + | 6.55781e9i | −0.711439 | + | 1.23225i | 0.252878 | + | 0.967498i | \(0.418623\pi\) |
−0.964317 | + | 0.264750i | \(0.914710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.89479e8 | − | 3.28188e8i | 0.0347870 | − | 0.0602529i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.62910e8 | + | 1.49460e9i | 0.156605 | + | 0.271248i | 0.933642 | − | 0.358207i | \(-0.116612\pi\) |
−0.777037 | + | 0.629454i | \(0.783278\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.42485e9 | −0.252712 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.54370e9 | 0.796706 | 0.398353 | − | 0.917232i | \(-0.369582\pi\) | ||||
0.398353 | + | 0.917232i | \(0.369582\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.02615e9 | − | 1.77735e9i | −0.175879 | − | 0.304631i | 0.764586 | − | 0.644521i | \(-0.222943\pi\) |
−0.940465 | + | 0.339890i | \(0.889610\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.55637e9 | + | 9.62392e9i | −0.941617 | + | 1.63093i | −0.179229 | + | 0.983807i | \(0.557360\pi\) |
−0.762387 | + | 0.647121i | \(0.775973\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.10381e9 | − | 7.10801e9i | 0.679954 | − | 1.17771i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −3.03142e9 | − | 5.25057e9i | −0.496668 | − | 0.860254i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 6.67505e9 | 1.06949 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.39194e9 | −0.695910 | −0.347955 | − | 0.937511i | \(-0.613124\pi\) | ||||
−0.347955 | + | 0.937511i | \(0.613124\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.19208e8 | + | 3.79679e8i | 0.0339741 | + | 0.0588449i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.66469e9 | + | 6.34743e9i | −0.561758 | + | 0.972994i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.20464e9 | − | 2.08649e9i | 0.180656 | − | 0.312906i | −0.761448 | − | 0.648226i | \(-0.775511\pi\) |
0.942104 | + | 0.335320i | \(0.108845\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.53259e9 | + | 9.58272e9i | 0.820710 | + | 1.42151i | 0.905154 | + | 0.425084i | \(0.139755\pi\) |
−0.0844440 | + | 0.996428i | \(0.526911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.76306e9 | 0.255919 | 0.127960 | − | 0.991779i | \(-0.459157\pi\) | ||||
0.127960 | + | 0.991779i | \(0.459157\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.91987e10 | 2.75686 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.64242e8 | − | 6.30886e8i | −0.0511911 | − | 0.0886655i | 0.839294 | − | 0.543677i | \(-0.182968\pi\) |
−0.890485 | + | 0.455012i | \(0.849635\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.01355e8 | + | 1.75551e8i | −0.0140929 | + | 0.0244095i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.92192e9 | − | 6.79296e9i | 0.533826 | − | 0.924614i | −0.465393 | − | 0.885104i | \(-0.654087\pi\) |
0.999219 | − | 0.0395098i | \(-0.0125796\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.39234e9 | − | 7.60776e9i | −0.591550 | − | 1.02459i | −0.994024 | − | 0.109163i | \(-0.965183\pi\) |
0.402474 | − | 0.915431i | \(-0.368150\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −9.18602e8 | −0.121130 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.34487e9 | −0.175485 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.29363e9 | − | 2.24063e9i | −0.165303 | − | 0.286313i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.17483e9 | − | 5.49897e9i | 0.401484 | − | 0.695390i | −0.592422 | − | 0.805628i | \(-0.701828\pi\) |
0.993905 | + | 0.110238i | \(0.0351613\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.97708e8 | − | 1.20847e9i | 0.0864199 | − | 0.149684i | −0.819575 | − | 0.572971i | \(-0.805791\pi\) |
0.905995 | + | 0.423288i | \(0.139124\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.69677e9 | + | 6.40300e9i | 0.453188 | + | 0.784945i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.46689e9 | 1.13693 | 0.568466 | − | 0.822707i | \(-0.307537\pi\) | ||||
0.568466 | + | 0.822707i | \(0.307537\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.72565e8 | 0.0205133 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.50900e9 | + | 2.61366e9i | 0.175761 | + | 0.304427i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.39119e9 | − | 1.10699e10i | 0.736900 | − | 1.27635i | −0.216984 | − | 0.976175i | \(-0.569622\pi\) |
0.953885 | − | 0.300174i | \(-0.0970447\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.80348e7 | + | 1.69801e8i | −0.0110773 | + | 0.0191864i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.27162e9 | − | 3.93455e9i | −0.254109 | − | 0.440130i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.73834e9 | −0.958111 | −0.479056 | − | 0.877785i | \(-0.659021\pi\) | ||||
−0.479056 | + | 0.877785i | \(0.659021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.14366e9 | −0.992605 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.17488e9 | + | 1.24272e10i | 0.763566 | + | 1.32253i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.81745e9 | − | 4.87997e9i | 0.296889 | − | 0.514227i | −0.678533 | − | 0.734570i | \(-0.737384\pi\) |
0.975423 | + | 0.220342i | \(0.0707175\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.43191e10 | + | 2.48015e10i | −1.47946 | + | 2.56250i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.92042e8 | + | 3.32626e8i | 0.0196483 | + | 0.0340318i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.93370e10 | 1.94017 | 0.970083 | − | 0.242775i | \(-0.0780575\pi\) | ||||
0.970083 | + | 0.242775i | \(0.0780575\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.96828e10 | −1.95575 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.64824e8 | + | 8.05099e8i | 0.0453008 | + | 0.0784632i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.45328e9 | + | 1.11774e10i | −0.622888 | + | 1.07887i | 0.366057 | + | 0.930592i | \(0.380707\pi\) |
−0.988945 | + | 0.148281i | \(0.952626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.33787e9 | + | 1.09775e10i | −0.600112 | + | 1.03942i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.31110e9 | + | 7.46704e9i | 0.404319 | + | 0.700301i | 0.994242 | − | 0.107159i | \(-0.0341752\pi\) |
−0.589923 | + | 0.807460i | \(0.700842\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.64148e10 | −1.51043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.86134e10 | −1.69656 | −0.848281 | − | 0.529546i | \(-0.822362\pi\) | ||||
−0.848281 | + | 0.529546i | \(0.822362\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.18865e8 | + | 5.52290e8i | 0.0285197 | + | 0.0493976i | 0.879933 | − | 0.475098i | \(-0.157587\pi\) |
−0.851413 | + | 0.524495i | \(0.824254\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.47963e8 | + | 6.02690e8i | −0.0308309 | + | 0.0534007i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.53239e10 | − | 2.65417e10i | 1.33255 | − | 2.30804i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.06054e9 | − | 3.56896e9i | −0.177518 | − | 0.307470i | 0.763512 | − | 0.645794i | \(-0.223473\pi\) |
−0.941030 | + | 0.338324i | \(0.890140\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3.24261e8 | 0.0274209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.66290e10 | 1.39325 | 0.696626 | − | 0.717434i | \(-0.254684\pi\) | ||||
0.696626 | + | 0.717434i | \(0.254684\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.93790e9 | − | 1.20168e10i | −0.570665 | − | 0.988422i | −0.996498 | − | 0.0836194i | \(-0.973352\pi\) |
0.425832 | − | 0.904802i | \(-0.359981\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.43449e10 | − | 2.48461e10i | 1.16913 | − | 2.02499i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.79917e9 | + | 1.00445e10i | −0.464069 | + | 0.803791i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.45402e9 | + | 2.51843e9i | 0.115299 | + | 0.199705i | 0.917899 | − | 0.396813i | \(-0.129884\pi\) |
−0.802600 | + | 0.596518i | \(0.796551\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.15930e10 | −0.902747 | −0.451373 | − | 0.892335i | \(-0.649066\pi\) | ||||
−0.451373 | + | 0.892335i | \(0.649066\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.97963e10 | 1.52767 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 3.11172e9 | + | 5.38966e9i | 0.235841 | + | 0.408489i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30718e10 | + | 2.26410e10i | −0.981875 | + | 1.70066i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.67382e8 | − | 2.89914e8i | 0.0123499 | − | 0.0213907i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.67357e9 | + | 6.36281e9i | 0.268644 | + | 0.465304i | 0.968512 | − | 0.248968i | \(-0.0800913\pi\) |
−0.699868 | + | 0.714272i | \(0.746758\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.64972e10 | −1.90363 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.56302e9 | 0.111303 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.00220e10 | − | 1.73586e10i | −0.701215 | − | 1.21454i | −0.968040 | − | 0.250795i | \(-0.919308\pi\) |
0.266825 | − | 0.963745i | \(-0.414025\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.38892e9 | − | 9.33389e9i | 0.373756 | − | 0.647364i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.73154e9 | + | 1.68555e10i | −0.663250 | + | 1.14878i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19128e9 | + | 2.06336e9i | 0.0804875 | + | 0.139408i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.67527e10 | −1.11241 | −0.556207 | − | 0.831044i | \(-0.687744\pi\) | ||||
−0.556207 | + | 0.831044i | \(0.687744\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.39682e9 | 0.223615 | 0.111807 | − | 0.993730i | \(-0.464336\pi\) | ||||
0.111807 | + | 0.993730i | \(0.464336\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.40616e8 | + | 4.16758e8i | 0.0155694 | + | 0.0269670i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.68179e9 | − | 1.50373e10i | 0.556970 | − | 0.964701i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.51881e9 | − | 1.64871e10i | 0.600318 | − | 1.03978i | −0.392454 | − | 0.919771i | \(-0.628374\pi\) |
0.992773 | − | 0.120010i | \(-0.0382927\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.15285e10 | + | 1.99680e10i | 0.720898 | + | 1.24863i | 0.960640 | + | 0.277796i | \(0.0896039\pi\) |
−0.239742 | + | 0.970837i | \(0.577063\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.00057e10 | −1.84474 | −0.922369 | − | 0.386309i | \(-0.873750\pi\) | ||||
−0.922369 | + | 0.386309i | \(0.873750\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.43064e10 | −0.872144 | −0.436072 | − | 0.899912i | \(-0.643631\pi\) | ||||
−0.436072 | + | 0.899912i | \(0.643631\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.77204e10 | − | 4.80132e10i | −1.66166 | − | 2.87808i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.85457e8 | + | 6.67632e8i | −0.0229126 | + | 0.0396857i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −8.72280e9 | + | 1.51083e10i | −0.509905 | + | 0.883181i | 0.490030 | + | 0.871706i | \(0.336986\pi\) |
−0.999934 | + | 0.0114748i | \(0.996347\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.55382e9 | + | 1.48157e10i | 0.495877 | + | 0.858885i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.94903e8 | 0.0339194 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.61013e10 | −2.60688 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.18579e10 | + | 2.05384e10i | 0.659558 | + | 1.14239i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.23762e10 | + | 2.14362e10i | −0.682756 | + | 1.18257i | 0.291380 | + | 0.956607i | \(0.405886\pi\) |
−0.974136 | + | 0.225961i | \(0.927448\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.33437e10 | + | 2.31120e10i | −0.724175 | + | 1.25431i | 0.235138 | + | 0.971962i | \(0.424446\pi\) |
−0.959313 | + | 0.282345i | \(0.908888\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.61886e10 | − | 2.80395e10i | −0.871432 | − | 1.50936i | −0.860515 | − | 0.509424i | \(-0.829858\pi\) |
−0.0109167 | − | 0.999940i | \(-0.503475\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.52760e9 | 0.0809042 | 0.0404521 | − | 0.999181i | \(-0.487120\pi\) | ||||
0.0404521 | + | 0.999181i | \(0.487120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.33880e9 | 0.0703332 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.53641e8 | + | 1.65175e9i | 0.0492964 | + | 0.0853839i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.95828e9 | − | 8.58800e9i | 0.254254 | − | 0.440381i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.64879e9 | − | 2.85579e9i | 0.0832027 | − | 0.144111i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.07656e9 | − | 1.57211e10i | −0.454384 | − | 0.787015i | 0.544269 | − | 0.838911i | \(-0.316807\pi\) |
−0.998653 | + | 0.0518954i | \(0.983474\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.17484e9 | −0.452046 | −0.226023 | − | 0.974122i | \(-0.572572\pi\) | ||||
−0.226023 | + | 0.974122i | \(0.572572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.23071e10 | 0.601578 | 0.300789 | − | 0.953691i | \(-0.402750\pi\) | ||||
0.300789 | + | 0.953691i | \(0.402750\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.55099e10 | + | 2.68639e10i | 0.746234 | + | 1.29252i | 0.949616 | + | 0.313416i | \(0.101474\pi\) |
−0.203381 | + | 0.979100i | \(0.565193\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.66672e10 | − | 4.61890e10i | 1.27298 | − | 2.20487i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.38190e9 | + | 1.27858e10i | −0.346887 | + | 0.600826i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7.81508e8 | + | 1.35361e9i | 0.0364379 | + | 0.0631122i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.02870e9 | −0.139026 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.28287e10 | −1.03979 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.41833e7 | − | 1.45810e8i | −0.00377534 | − | 0.00653908i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.65417e7 | + | 1.15254e8i | −0.00296120 | + | 0.00512896i | −0.867502 | − | 0.497433i | \(-0.834276\pi\) |
0.864541 | + | 0.502562i | \(0.167609\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.33539e10 | + | 2.31297e10i | −0.585187 | + | 1.01357i | 0.409665 | + | 0.912236i | \(0.365646\pi\) |
−0.994852 | + | 0.101338i | \(0.967688\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.58700e10 | + | 2.74877e10i | 0.690129 | + | 1.19534i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.46601e10 | 1.05609 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.37032e9 | 0.355744 | 0.177872 | − | 0.984054i | \(-0.443079\pi\) | ||||
0.177872 | + | 0.984054i | \(0.443079\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.89695e9 | − | 1.36779e10i | −0.330562 | − | 0.572551i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.19681e9 | − | 1.41973e10i | 0.340525 | − | 0.589806i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.66443e8 | − | 1.67393e9i | 0.0395477 | − | 0.0684986i | −0.845574 | − | 0.533858i | \(-0.820742\pi\) |
0.885122 | + | 0.465360i | \(0.154075\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.79722e10 | + | 6.57698e10i | 1.54220 | + | 2.67118i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.90528e9 | −0.116238 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.14070e10 | −0.850093 | −0.425047 | − | 0.905171i | \(-0.639742\pi\) | ||||
−0.425047 | + | 0.905171i | \(0.639742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.88033e10 | + | 3.25683e10i | 0.735650 | + | 1.27418i | 0.954437 | + | 0.298411i | \(0.0964566\pi\) |
−0.218787 | + | 0.975773i | \(0.570210\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.07081e9 | − | 1.39791e10i | 0.313420 | − | 0.542859i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −8.87399e8 | + | 1.53702e9i | −0.0339543 | + | 0.0588105i | −0.882503 | − | 0.470306i | \(-0.844143\pi\) |
0.848549 | + | 0.529117i | \(0.177477\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.87904e9 | − | 1.01828e10i | −0.223293 | − | 0.386754i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.18953e10 | −1.19372 | −0.596859 | − | 0.802346i | \(-0.703585\pi\) | ||||
−0.596859 | + | 0.802346i | \(0.703585\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.88818e8 | −0.00701506 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.04965e10 | − | 1.81804e10i | −0.384307 | − | 0.665639i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.84909e10 | + | 3.20272e10i | −0.672089 | + | 1.16409i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.21806e8 | + | 7.30590e8i | −0.0151101 | + | 0.0261715i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.43527e9 | + | 4.21802e9i | 0.0866074 | + | 0.150008i | 0.906075 | − | 0.423117i | \(-0.139064\pi\) |
−0.819468 | + | 0.573125i | \(0.805731\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.51483e9 | −0.0531003 | −0.0265501 | − | 0.999647i | \(-0.508452\pi\) | ||||
−0.0265501 | + | 0.999647i | \(0.508452\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.38524e10 | 0.830112 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.54996e9 | − | 1.65410e10i | −0.327620 | − | 0.567454i | 0.654419 | − | 0.756132i | \(-0.272913\pi\) |
−0.982039 | + | 0.188678i | \(0.939580\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.77793e10 | + | 3.07946e10i | −0.605584 | + | 1.04890i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.88595e10 | − | 3.26656e10i | 0.633275 | − | 1.09686i | −0.353602 | − | 0.935396i | \(-0.615043\pi\) |
0.986878 | − | 0.161469i | \(-0.0516232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.80862e8 | − | 6.59673e8i | −0.0126982 | − | 0.0219939i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.50356e10 | −1.48036 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.03952e10 | −0.339292 | −0.169646 | − | 0.985505i | \(-0.554262\pi\) | ||||
−0.169646 | + | 0.985505i | \(0.554262\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.60401e8 | + | 6.24234e8i | 0.0115986 | + | 0.0200894i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.60232e9 | − | 4.50734e9i | 0.0831624 | − | 0.144042i | −0.821444 | − | 0.570289i | \(-0.806831\pi\) |
0.904607 | + | 0.426247i | \(0.140165\pi\) | |||||||
\(998\) | 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 | 324.8.e.m.217.5 | 16 | ||
3.2 | odd | 2 | inner | 324.8.e.m.217.4 | 16 | ||
9.2 | odd | 6 | 324.8.a.e.1.5 | yes | 8 | ||
9.4 | even | 3 | inner | 324.8.e.m.109.5 | 16 | ||
9.5 | odd | 6 | inner | 324.8.e.m.109.4 | 16 | ||
9.7 | even | 3 | 324.8.a.e.1.4 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.8.a.e.1.4 | ✓ | 8 | 9.7 | even | 3 | ||
324.8.a.e.1.5 | yes | 8 | 9.2 | odd | 6 | ||
324.8.e.m.109.4 | 16 | 9.5 | odd | 6 | inner | ||
324.8.e.m.109.5 | 16 | 9.4 | even | 3 | inner | ||
324.8.e.m.217.4 | 16 | 3.2 | odd | 2 | inner | ||
324.8.e.m.217.5 | 16 | 1.1 | even | 1 | trivial |