Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [112,10,Mod(65,112)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(112, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("112.65");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 112 = 2^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 112.i (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: | \(57.6840136504\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 430 x^{8} + 61 x^{7} + 146753 x^{6} + 23608 x^{5} + 16136944 x^{4} + 30575648 x^{3} + \cdots + 761760000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{3}\cdot 7^{4} \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 81.5 | ||
Root | \(-5.11725 - 8.86334i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 112.81 |
Dual form | 112.10.i.c.65.5 |
$q$-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 \(\left(\mathbb{Z}/112\mathbb{Z}\right)^\times\).
\(n\) | \(15\) | \(17\) | \(85\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 79.7348 | − | 138.105i | 0.568332 | − | 0.984381i | −0.428399 | − | 0.903590i | \(-0.640922\pi\) |
0.996731 | − | 0.0807907i | \(-0.0257445\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1014.15 | + | 1756.56i | 0.725666 | + | 1.25689i | 0.958699 | + | 0.284421i | \(0.0918014\pi\) |
−0.233034 | + | 0.972469i | \(0.574865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4235.51 | − | 4734.35i | 0.666752 | − | 0.745280i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2873.78 | − | 4977.54i | −0.146003 | − | 0.252885i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4289.29 | − | 7429.26i | 0.0883320 | − | 0.152996i | −0.818474 | − | 0.574543i | \(-0.805180\pi\) |
0.906806 | + | 0.421548i | \(0.138513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −38438.1 | −0.373265 | −0.186633 | − | 0.982430i | \(-0.559757\pi\) | ||||
−0.186633 | + | 0.982430i | \(0.559757\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 323452. | 1.64968 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 150942. | − | 261439.i | 0.438318 | − | 0.759190i | −0.559242 | − | 0.829005i | \(-0.688908\pi\) |
0.997560 | + | 0.0698150i | \(0.0222409\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −458143. | − | 793527.i | −0.806510 | − | 1.39692i | −0.915267 | − | 0.402848i | \(-0.868020\pi\) |
0.108757 | − | 0.994068i | \(-0.465313\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −316119. | − | 962436.i | −0.354702 | − | 1.07990i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 966607. | + | 1.67421e6i | 0.720236 | + | 1.24749i | 0.960905 | + | 0.276878i | \(0.0892999\pi\) |
−0.240669 | + | 0.970607i | \(0.577367\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.08043e6 | + | 1.87136e6i | −0.553182 | + | 0.958139i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.22228e6 | 0.804751 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.52529e6 | 1.18811 | 0.594054 | − | 0.804425i | \(-0.297527\pi\) | ||||
0.594054 | + | 0.804425i | \(0.297527\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 147255. | − | 255054.i | 0.0286380 | − | 0.0496025i | −0.851351 | − | 0.524596i | \(-0.824216\pi\) |
0.879989 | + | 0.474994i | \(0.157550\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −684011. | − | 1.18474e6i | −0.100404 | − | 0.173905i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.26116e7 | + | 2.63858e6i | 1.42057 | + | 0.297210i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.05632e6 | + | 1.39540e7i | 0.706690 | + | 1.22402i | 0.966078 | + | 0.258250i | \(0.0831458\pi\) |
−0.259388 | + | 0.965773i | \(0.583521\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.06486e6 | + | 5.30849e6i | −0.212139 | + | 0.367435i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.28783e7 | 0.711757 | 0.355878 | − | 0.934532i | \(-0.384182\pi\) | ||||
0.355878 | + | 0.934532i | \(0.384182\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.15410e7 | −0.514795 | −0.257398 | − | 0.966306i | \(-0.582865\pi\) | ||||
−0.257398 | + | 0.966306i | \(0.582865\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.82889e6 | − | 1.00959e7i | 0.211899 | − | 0.367020i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.39268e7 | − | 2.41219e7i | −0.416304 | − | 0.721059i | 0.579261 | − | 0.815142i | \(-0.303341\pi\) |
−0.995564 | + | 0.0940834i | \(0.970008\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.47455e6 | − | 4.01048e7i | −0.110884 | − | 0.993833i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.40707e7 | − | 4.16916e7i | −0.498221 | − | 0.862944i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.11827e7 | − | 3.66896e7i | 0.368757 | − | 0.638706i | −0.620614 | − | 0.784116i | \(-0.713117\pi\) |
0.989372 | + | 0.145410i | \(0.0464500\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.73999e7 | 0.256398 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.46120e8 | −1.83346 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.17321e6 | − | 2.03205e6i | 0.0126049 | − | 0.0218324i | −0.859654 | − | 0.510876i | \(-0.829321\pi\) |
0.872259 | + | 0.489044i | \(0.162654\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.34201e6 | + | 7.52057e6i | 0.0401519 | + | 0.0695451i | 0.885403 | − | 0.464824i | \(-0.153882\pi\) |
−0.845251 | + | 0.534369i | \(0.820549\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.57374e7 | − | 7.47691e6i | −0.285818 | − | 0.0597984i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.89820e7 | − | 6.75188e7i | −0.270866 | − | 0.469153i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.26144e8 | − | 2.18488e8i | 0.764771 | − | 1.32462i | −0.175597 | − | 0.984462i | \(-0.556186\pi\) |
0.940368 | − | 0.340159i | \(-0.110481\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.08289e8 | 1.63733 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.50094e8 | 1.16799 | 0.583997 | − | 0.811756i | \(-0.301488\pi\) | ||||
0.583997 | + | 0.811756i | \(0.301488\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.32270e7 | + | 4.02303e7i | −0.0957282 | + | 0.165806i | −0.909912 | − | 0.414801i | \(-0.863851\pi\) |
0.814184 | + | 0.580607i | \(0.197185\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.72296e8 | + | 2.98426e8i | 0.628782 | + | 1.08908i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.70054e7 | − | 5.17737e7i | −0.0551289 | − | 0.167842i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.53584e7 | + | 9.58836e7i | 0.159905 | + | 0.276963i | 0.934834 | − | 0.355084i | \(-0.115548\pi\) |
−0.774929 | + | 0.632048i | \(0.782215\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.33758e8 | − | 4.04880e8i | 0.603369 | − | 1.04507i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.81805e8 | −0.651774 | −0.325887 | − | 0.945409i | \(-0.605663\pi\) | ||||
−0.325887 | + | 0.945409i | \(0.605663\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.12310e8 | 1.27229 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.60823e8 | − | 6.24964e8i | 0.675240 | − | 1.16955i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.45677e8 | + | 2.52321e8i | 0.246115 | + | 0.426283i | 0.962444 | − | 0.271479i | \(-0.0875127\pi\) |
−0.716330 | + | 0.697762i | \(0.754179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.62805e8 | + | 1.81980e8i | −0.248875 | + | 0.278187i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.34827e7 | − | 4.06733e7i | −0.0325518 | − | 0.0563815i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.29250e8 | − | 1.60951e9i | 1.17051 | − | 2.02739i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.01107e8 | 0.115960 | 0.0579798 | − | 0.998318i | \(-0.481534\pi\) | ||||
0.0579798 | + | 0.998318i | \(0.481534\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.93059e7 | −0.0515871 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.29724e8 | − | 9.17509e8i | 0.506528 | − | 0.877332i | −0.493443 | − | 0.869778i | \(-0.664262\pi\) |
0.999971 | − | 0.00755447i | \(-0.00240468\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.52542e8 | − | 4.37415e8i | −0.221088 | − | 0.382936i | 0.734050 | − | 0.679095i | \(-0.237628\pi\) |
−0.955139 | + | 0.296159i | \(0.904294\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.36998e9 | − | 1.53133e9i | 1.09993 | − | 1.22947i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −943656. | − | 1.63446e6i | −0.000695964 | − | 0.00120544i | 0.865677 | − | 0.500603i | \(-0.166888\pi\) |
−0.866373 | + | 0.499397i | \(0.833555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.32240e7 | − | 9.21867e7i | 0.0361151 | − | 0.0625531i | −0.847403 | − | 0.530950i | \(-0.821835\pi\) |
0.883518 | + | 0.468397i | \(0.155168\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.56948e9 | 1.60654 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.40785e9 | −1.38924 | −0.694620 | − | 0.719377i | \(-0.744427\pi\) | ||||
−0.694620 | + | 0.719377i | \(0.744427\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.96057e9 | + | 3.39580e9i | −1.04530 | + | 1.81051i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.10463e8 | + | 1.91327e8i | 0.0544980 | + | 0.0943932i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.98429e8 | − | 1.82194e9i | −0.273559 | − | 0.832861i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.14218e9 | + | 1.97831e9i | 0.484395 | + | 0.838997i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.02685e9 | − | 1.77856e9i | 0.404515 | − | 0.700640i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −4.21360e8 | −0.154368 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.51077e9 | −0.515326 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.20218e8 | + | 1.59386e9i | −0.292575 | + | 0.506755i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.02677e8 | − | 1.77843e8i | −0.0304617 | − | 0.0527612i | 0.850393 | − | 0.526149i | \(-0.176364\pi\) |
−0.880854 | + | 0.473387i | \(0.843031\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.69730e9 | − | 1.19198e9i | −1.57884 | − | 0.330321i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.25372e9 | + | 3.90356e9i | 0.583980 | + | 1.01148i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.94515e9 | − | 5.10114e9i | 0.714273 | − | 1.23716i | −0.248966 | − | 0.968512i | \(-0.580091\pi\) |
0.963239 | − | 0.268645i | \(-0.0865759\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.53632e9 | −0.349073 | −0.174537 | − | 0.984651i | \(-0.555843\pi\) | ||||
−0.174537 | + | 0.984651i | \(0.555843\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.44179e9 | −0.946395 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.64872e8 | + | 2.85567e8i | −0.0329712 | + | 0.0571079i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.58932e9 | + | 7.94893e9i | 0.862169 | + | 1.49332i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.89544e9 | − | 2.57979e9i | −1.04133 | − | 0.455676i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.06047e8 | + | 5.30089e8i | 0.0508686 | + | 0.0881070i | 0.890338 | − | 0.455299i | \(-0.150468\pi\) |
−0.839470 | + | 0.543406i | \(0.817134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.27233e8 | − | 9.13194e8i | 0.0825289 | − | 0.142944i | −0.821807 | − | 0.569766i | \(-0.807034\pi\) |
0.904336 | + | 0.426822i | \(0.140367\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.73510e9 | −0.255984 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.97355e8 | 0.0831266 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.84813e9 | − | 3.20105e9i | 0.242764 | − | 0.420479i | −0.718737 | − | 0.695282i | \(-0.755279\pi\) |
0.961500 | + | 0.274803i | \(0.0886128\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.37800e9 | − | 5.85087e9i | −0.419153 | − | 0.725995i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.20204e10 | + | 2.51488e9i | 1.40994 | + | 0.294986i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.57764e9 | + | 1.13928e10i | 0.729837 | + | 1.26412i | 0.956952 | + | 0.290247i | \(0.0937375\pi\) |
−0.227114 | + | 0.973868i | \(0.572929\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.38738e9 | − | 2.40301e9i | 0.145719 | − | 0.252393i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.15786e9 | −0.612641 | −0.306320 | − | 0.951928i | \(-0.599098\pi\) | ||||
−0.306320 | + | 0.951928i | \(0.599098\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.12701e9 | −0.860673 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.63321e9 | + | 4.56085e9i | −0.235506 | + | 0.407909i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.73798e9 | + | 1.34026e10i | 0.656780 | + | 1.13758i | 0.981444 | + | 0.191747i | \(0.0614155\pi\) |
−0.324664 | + | 0.945829i | \(0.605251\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.28351e9 | + | 1.30413e10i | 0.345246 | + | 1.05112i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.87091e8 | − | 3.24051e8i | −0.0143276 | − | 0.0248161i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.98868e9 | + | 3.44450e9i | −0.144786 | + | 0.250777i | −0.929293 | − | 0.369343i | \(-0.879583\pi\) |
0.784507 | + | 0.620120i | \(0.212916\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −2.68948e10 | −1.86258 | −0.931288 | − | 0.364283i | \(-0.881314\pi\) | ||||
−0.931288 | + | 0.364283i | \(0.881314\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.38484e9 | 0.0912785 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.63406e10 | + | 2.83028e10i | −1.02564 | + | 1.77646i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.29487e9 | − | 2.24277e9i | −0.0774351 | − | 0.134121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.41248e9 | − | 1.05210e10i | 0.536569 | − | 0.599765i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.68177e8 | + | 1.50373e9i | 0.0472018 | + | 0.0817559i | 0.888661 | − | 0.458565i | \(-0.151636\pi\) |
−0.841459 | + | 0.540321i | \(0.818303\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.30896e9 | + | 1.26595e10i | −0.379182 | + | 0.656763i | −0.990943 | − | 0.134280i | \(-0.957128\pi\) |
0.611761 | + | 0.791042i | \(0.290461\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.24329e10 | −0.615767 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.40160e9 | −0.208215 | −0.104108 | − | 0.994566i | \(-0.533199\pi\) | ||||
−0.104108 | + | 0.994566i | \(0.533199\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.76429e10 | + | 3.05585e10i | −0.797502 | + | 1.38131i | 0.123736 | + | 0.992315i | \(0.460512\pi\) |
−0.921238 | + | 0.388999i | \(0.872821\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.01162e10 | − | 3.48423e10i | −0.869288 | − | 1.50565i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.91669e10 | − | 2.14243e10i | 0.792173 | − | 0.885472i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.30605e10 | + | 2.26215e10i | 0.516498 | + | 0.894600i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.55564e9 | − | 9.62266e9i | 0.210314 | − | 0.364274i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.86042e9 | −0.284962 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.08123e10 | −0.375533 | −0.187766 | − | 0.982214i | \(-0.560125\pi\) | ||||
−0.187766 | + | 0.982214i | \(0.560125\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.99412e10 | − | 3.45391e10i | 0.663808 | − | 1.14975i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.17043e10 | − | 2.02724e10i | −0.373569 | − | 0.647041i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.83812e8 | − | 1.77744e9i | −0.0178733 | − | 0.0544159i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.70400e9 | + | 6.41551e9i | 0.108811 | + | 0.188466i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.80193e9 | + | 1.00492e10i | −0.163609 | + | 0.283379i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.21844e10 | −0.871512 | −0.435756 | − | 0.900065i | \(-0.643519\pi\) | ||||
−0.435756 | + | 0.900065i | \(0.643519\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.24197e10 | 0.323065 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.50385e9 | + | 7.80090e9i | −0.112582 | + | 0.194997i | −0.916810 | − | 0.399323i | \(-0.869245\pi\) |
0.804229 | + | 0.594320i | \(0.202579\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.31909e10 | − | 4.01679e10i | −0.557261 | − | 0.965204i | −0.997724 | − | 0.0674334i | \(-0.978519\pi\) |
0.440463 | − | 0.897771i | \(-0.354814\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.50612e9 | − | 1.77964e9i | −0.196552 | − | 0.0411223i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.17672e10 | + | 3.77018e10i | 0.483838 | + | 0.838032i | 0.999828 | − | 0.0185626i | \(-0.00590900\pi\) |
−0.515990 | + | 0.856595i | \(0.672576\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.82476e10 | − | 4.89263e10i | 0.604194 | − | 1.04650i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.76560e10 | 0.363517 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.74289e10 | 0.543773 | 0.271887 | − | 0.962329i | \(-0.412352\pi\) | ||||
0.271887 | + | 0.962329i | \(0.412352\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.75409e9 | − | 9.96638e9i | 0.109875 | − | 0.190310i | −0.805844 | − | 0.592128i | \(-0.798288\pi\) |
0.915720 | + | 0.401818i | \(0.131622\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.54067e10 | − | 2.66852e10i | −0.283453 | − | 0.490955i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.59084e10 | − | 4.85320e10i | 1.16867 | − | 0.860559i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.76102e10 | + | 3.05017e10i | 0.301042 | + | 0.521420i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.24697e10 | + | 3.89186e10i | −0.370424 | + | 0.641594i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.69146e10 | 0.428012 | 0.214006 | − | 0.976832i | \(-0.431349\pi\) | ||||
0.214006 | + | 0.976832i | \(0.431349\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.65842e10 | 0.254480 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.88224e10 | − | 8.45630e10i | 0.723084 | − | 1.25242i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.78979e10 | + | 3.10001e10i | 0.255919 | + | 0.443265i | 0.965145 | − | 0.261716i | \(-0.0842885\pi\) |
−0.709225 | + | 0.704982i | \(0.750955\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.00186e11 | + | 2.09606e10i | 1.38343 | + | 0.289438i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.30047e10 | − | 2.25248e10i | −0.173468 | − | 0.300455i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.63817e10 | + | 1.14976e11i | −0.855554 | + | 1.48186i | 0.0205759 | + | 0.999788i | \(0.493450\pi\) |
−0.876130 | + | 0.482075i | \(0.839883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.59298e10 | 1.07038 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.64623e10 | 0.559499 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.64397e10 | + | 6.31154e10i | −0.424316 | + | 0.734937i | −0.996356 | − | 0.0852884i | \(-0.972819\pi\) |
0.572040 | + | 0.820226i | \(0.306152\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.06838e10 | + | 3.58253e10i | 0.232953 | + | 0.403486i | 0.958676 | − | 0.284501i | \(-0.0918279\pi\) |
−0.725723 | + | 0.687987i | \(0.758495\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.21510e10 | + | 3.69943e10i | 0.132398 | + | 0.403091i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.26857e9 | + | 1.60536e10i | 0.0977273 | + | 0.169269i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.09314e10 | − | 1.40177e11i | 0.825958 | − | 1.43060i | −0.0752266 | − | 0.997166i | \(-0.523968\pi\) |
0.901185 | − | 0.433435i | \(-0.142699\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.69272e9 | −0.0167250 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.39939e11 | 1.33894 | 0.669471 | − | 0.742838i | \(-0.266521\pi\) | ||||
0.669471 | + | 0.742838i | \(0.266521\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.86550e10 | − | 1.53555e11i | 0.821607 | − | 1.42306i | −0.0828783 | − | 0.996560i | \(-0.526411\pi\) |
0.904485 | − | 0.426505i | \(-0.140255\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.48187e11 | − | 2.56668e11i | −1.33048 | − | 2.30446i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.45462e10 | − | 6.09705e10i | 0.474565 | − | 0.530458i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.37270e10 | + | 2.37759e10i | 0.115754 | + | 0.200492i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.06172e9 | − | 1.39633e10i | 0.0659036 | − | 0.114148i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1.65710e11 | −1.31355 | −0.656773 | − | 0.754088i | \(-0.728079\pi\) | ||||
−0.656773 | + | 0.754088i | \(0.728079\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.75922e9 | 0.0365879 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.53199e9 | − | 1.65099e10i | 0.0710853 | − | 0.123123i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.71546e10 | − | 6.43536e10i | −0.268839 | − | 0.465643i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.88819e10 | + | 5.46391e10i | −0.343241 | + | 0.383667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.44749e10 | − | 1.46315e11i | −0.575753 | − | 0.997233i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.80688e9 | + | 1.52540e10i | −0.0582737 | + | 0.100933i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.12825e11 | −1.36741 | −0.683706 | − | 0.729757i | \(-0.739633\pi\) | ||||
−0.683706 | + | 0.729757i | \(0.739633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.05455e10 | −0.502606 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.94338e10 | + | 1.37583e11i | −0.481486 | + | 0.833959i | −0.999774 | − | 0.0212476i | \(-0.993236\pi\) |
0.518288 | + | 0.855206i | \(0.326570\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.48658e11 | + | 2.57484e11i | 0.875468 | + | 1.51635i | 0.856264 | + | 0.516539i | \(0.172780\pi\) |
0.0192038 | + | 0.999816i | \(0.493887\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.31094e10 | − | 7.03574e10i | −0.132249 | − | 0.402636i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.66580e10 | − | 1.32776e11i | −0.426374 | − | 0.738502i | 0.570174 | − | 0.821524i | \(-0.306876\pi\) |
−0.996548 | + | 0.0830226i | \(0.973543\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.94103e10 | − | 3.36196e10i | 0.104948 | − | 0.181775i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.00969e8 | −0.00158216 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.76612e11 | −1.41403 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.15298e10 | − | 7.19318e10i | 0.206483 | − | 0.357640i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −8.48762e9 | − | 1.47010e10i | −0.0410507 | − | 0.0711019i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.73188e11 | − | 3.62342e10i | −0.814962 | − | 0.170505i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.22438e11 | + | 2.12070e11i | 0.560650 | + | 0.971074i | 0.997440 | + | 0.0715104i | \(0.0227819\pi\) |
−0.436790 | + | 0.899563i | \(0.643885\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.63043e10 | − | 8.02013e10i | 0.206358 | − | 0.357423i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.11716e11 | 2.21987 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.96265e10 | −0.209594 | −0.104797 | − | 0.994494i | \(-0.533419\pi\) | ||||
−0.104797 | + | 0.994494i | \(0.533419\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.91990e11 | + | 3.32536e11i | −0.789550 | + | 1.36754i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.26324e9 | − | 2.18800e9i | −0.00505931 | − | 0.00876298i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.08822e11 | − | 1.48680e11i | −0.814616 | − | 0.580001i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.12651e11 | + | 5.41527e11i | 1.18816 | + | 2.05795i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.52077e11 | + | 2.63405e11i | −0.563094 | + | 0.975308i | 0.434130 | + | 0.900850i | \(0.357056\pi\) |
−0.997224 | + | 0.0744576i | \(0.976277\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.96999e11 | 1.79325 | 0.896626 | − | 0.442788i | \(-0.146011\pi\) | ||||
0.896626 | + | 0.442788i | \(0.146011\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.54203e10 | −0.300385 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.82246e10 | + | 1.52809e11i | −0.302415 | + | 0.523798i | −0.976682 | − | 0.214689i | \(-0.931126\pi\) |
0.674267 | + | 0.738487i | \(0.264460\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53632e11 | + | 4.39304e11i | 0.847573 | + | 1.46804i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.99334e11 | − | 6.26262e10i | −0.975325 | − | 0.204056i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.72570e10 | − | 1.51134e11i | −0.277253 | − | 0.480215i | 0.693448 | − | 0.720506i | \(-0.256091\pi\) |
−0.970701 | + | 0.240291i | \(0.922757\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.58446e11 | + | 4.47641e11i | −0.800916 | + | 1.38723i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.64285e11 | 1.10119 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −9.42224e10 | −0.277867 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.94008e11 | − | 3.36032e11i | 0.558243 | − | 0.966905i | −0.439401 | − | 0.898291i | \(-0.644809\pi\) |
0.997643 | − | 0.0686134i | \(-0.0218575\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.70095e10 | − | 6.41023e10i | −0.103919 | − | 0.179993i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.39817e10 | − | 2.55685e11i | −0.230145 | − | 0.700686i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.02948e11 | − | 5.24721e11i | −0.810360 | − | 1.40359i | −0.912612 | − | 0.408827i | \(-0.865938\pi\) |
0.102251 | − | 0.994759i | \(-0.467395\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −3.35970e10 | + | 5.81918e10i | −0.0877324 | + | 0.151957i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.73944e11 | −0.443479 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.34706e11 | −1.33119 | −0.665593 | − | 0.746315i | \(-0.731821\pi\) | ||||
−0.665593 | + | 0.746315i | \(0.731821\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.20461e11 | + | 2.08645e11i | −0.292876 | + | 0.507277i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.26206e11 | + | 2.18595e11i | 0.299699 | + | 0.519094i | 0.976067 | − | 0.217470i | \(-0.0697804\pi\) |
−0.676368 | + | 0.736564i | \(0.736447\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.36974e10 | − | 8.23772e10i | 0.170954 | − | 0.191088i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.31663e10 | + | 5.74457e10i | 0.0751619 | + | 0.130184i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.16836e10 | + | 7.21981e10i | −0.0922979 | + | 0.159865i | −0.908478 | − | 0.417933i | \(-0.862755\pi\) |
0.816180 | + | 0.577798i | \(0.196088\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.83606e11 | 1.26277 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.27479e10 | −0.0692495 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.12283e11 | + | 1.94480e11i | −0.232075 | + | 0.401966i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.67001e10 | − | 9.82075e10i | −0.114558 | − | 0.198421i | 0.803045 | − | 0.595919i | \(-0.203212\pi\) |
−0.917603 | + | 0.397498i | \(0.869879\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.18891e11 | + | 6.91782e11i | −1.22246 | + | 1.36644i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.56734e11 | − | 4.44676e11i | −0.495831 | − | 0.858805i | 0.504157 | − | 0.863612i | \(-0.331803\pi\) |
−0.999988 | + | 0.00480724i | \(0.998470\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.66022e9 | + | 9.80379e9i | −0.0106896 | + | 0.0185149i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.48260e11 | 1.75138 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.38223e11 | 0.249693 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.87550e11 | + | 6.71256e11i | −0.684814 | + | 1.18613i | 0.288681 | + | 0.957425i | \(0.406783\pi\) |
−0.973495 | + | 0.228708i | \(0.926550\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.69662e11 | − | 8.13478e11i | −0.811889 | − | 1.40623i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4.65133e9 | − | 1.41611e10i | −0.00786686 | − | 0.0239510i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.85792e11 | − | 4.95007e11i | −0.472970 | − | 0.819209i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.22499e11 | + | 2.12174e11i | −0.198390 | + | 0.343621i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.73463e11 | −1.54297 | −0.771483 | − | 0.636250i | \(-0.780485\pi\) | ||||
−0.771483 | + | 0.636250i | \(0.780485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.24555e11 | −1.27924 | −0.639618 | − | 0.768693i | \(-0.720907\pi\) | ||||
−0.639618 | + | 0.768693i | \(0.720907\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −8.00451e10 | + | 1.38642e11i | −0.121563 | + | 0.210554i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.26165e11 | + | 5.64935e11i | 0.484939 | + | 0.839940i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.39956e10 | + | 1.12969e10i | 0.0786019 | + | 0.0164450i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.62921e10 | + | 4.55393e10i | 0.0374773 | + | 0.0649125i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.22097e11 | + | 3.84683e11i | −0.310024 | + | 0.536977i | −0.978367 | − | 0.206876i | \(-0.933670\pi\) |
0.668343 | + | 0.743853i | \(0.267004\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.57077e11 | 1.03501 | 0.517505 | − | 0.855680i | \(-0.326861\pi\) | ||||
0.517505 | + | 0.855680i | \(0.326861\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.46371e12 | 1.95999 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.85688e11 | − | 1.53406e12i | 1.16175 | − | 2.01222i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.04945e10 | + | 8.74591e10i | 0.0648865 | + | 0.112387i | 0.896644 | − | 0.442753i | \(-0.145998\pi\) |
−0.831757 | + | 0.555140i | \(0.812665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.86764e11 | + | 1.37525e11i | −0.235136 | + | 0.173144i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.63399e11 | + | 6.29425e11i | 0.448298 | + | 0.776475i | 0.998275 | − | 0.0587046i | \(-0.0186970\pi\) |
−0.549977 | + | 0.835180i | \(0.685364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.95477e11 | + | 5.11781e11i | −0.357194 | + | 0.618678i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.76103e10 | 0.115641 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.85410e11 | −0.215291 | −0.107645 | − | 0.994189i | \(-0.534331\pi\) | ||||
−0.107645 | + | 0.994189i | \(0.534331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.52388e10 | − | 9.56764e10i | 0.0628709 | − | 0.108896i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.40776e10 | − | 1.45627e11i | −0.0938077 | − | 0.162480i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −4.84766e11 | − | 1.01422e11i | −0.530250 | − | 0.110938i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.49165e11 | + | 7.77977e11i | 0.481707 | + | 0.834341i | 0.999780 | − | 0.0209954i | \(-0.00668354\pi\) |
−0.518072 | + | 0.855337i | \(0.673350\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.35435e11 | − | 5.80990e11i | 0.352737 | − | 0.610959i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.56915e11 | −0.677416 | −0.338708 | − | 0.940892i | \(-0.609990\pi\) | ||||
−0.338708 | + | 0.940892i | \(0.609990\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.36860e11 | −0.745196 | −0.372598 | − | 0.927993i | \(-0.621533\pi\) | ||||
−0.372598 | + | 0.927993i | \(0.621533\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.76300e10 | − | 8.24976e10i | 0.0472435 | − | 0.0818282i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.97280e11 | − | 6.88109e11i | −0.386519 | − | 0.669470i | 0.605460 | − | 0.795876i | \(-0.292989\pi\) |
−0.991979 | + | 0.126406i | \(0.959656\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.00115e11 | − | 1.52262e12i | −0.477301 | − | 1.45316i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.94720e11 | − | 5.10470e11i | −0.275941 | − | 0.477943i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.95026e10 | + | 8.57410e10i | −0.0454729 | + | 0.0787614i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.97997e12 | 1.78459 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.43498e11 | −0.215359 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.76669e11 | − | 9.98820e11i | 0.500515 | − | 0.866917i | −0.499485 | − | 0.866322i | \(-0.666478\pi\) |
1.00000 | 0.000594242i | \(-0.000189153\pi\) | ||||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.09670e11 | − | 5.36364e11i | −0.263783 | − | 0.456885i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.30576e12 | − | 1.45955e12i | 1.09170 | − | 1.22027i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.02537e11 | + | 1.77599e11i | 0.0841479 | + | 0.145748i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.72094e11 | + | 1.68372e12i | −0.783120 | + | 1.35640i | 0.146996 | + | 0.989137i | \(0.453039\pi\) |
−0.930116 | + | 0.367266i | \(0.880294\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.09787e12 | 1.65916 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.04431e9 | 0.00546980 | 0.00273490 | − | 0.999996i | \(-0.499129\pi\) | ||||
0.00273490 | + | 0.999996i | \(0.499129\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.83056e11 | − | 1.18309e12i | 0.520769 | − | 0.901999i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.00036e10 | − | 8.66087e10i | −0.0374350 | − | 0.0648393i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.05927e12 | − | 1.18403e12i | 0.778762 | − | 0.870481i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.49974e10 | + | 6.06172e10i | 0.0252687 | + | 0.0437667i | 0.878383 | − | 0.477957i | \(-0.158623\pi\) |
−0.853115 | + | 0.521724i | \(0.825289\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.90996e11 | + | 8.50430e11i | −0.348184 | + | 0.603072i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.76650e12 | 1.92697 | 0.963484 | − | 0.267766i | \(-0.0862855\pi\) | ||||
0.963484 | + | 0.267766i | \(0.0862855\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.14888e12 | 1.47028 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −7.27740e11 | + | 1.26048e12i | −0.489148 | + | 0.847230i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.88478e11 | − | 8.46068e11i | −0.322563 | − | 0.558696i | 0.658453 | − | 0.752622i | \(-0.271211\pi\) |
−0.981016 | + | 0.193926i | \(0.937878\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.20863e10 | + | 2.80360e11i | 0.0597449 | + | 0.181896i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01812e12 | − | 1.76344e12i | −0.649040 | − | 1.12417i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.12230e11 | − | 8.87208e11i | 0.320872 | − | 0.555767i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.38944e11 | −0.147092 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.46795e12 | 1.49308 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.65660e11 | + | 9.79751e11i | −0.336345 | + | 0.582567i | −0.983742 | − | 0.179586i | \(-0.942524\pi\) |
0.647397 | + | 0.762153i | \(0.275858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.54001e12 | − | 2.66738e12i | −0.900050 | − | 1.55893i | −0.827428 | − | 0.561572i | \(-0.810197\pi\) |
−0.0726222 | − | 0.997360i | \(-0.523137\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.14261e12 | + | 4.48274e11i | 1.23091 | + | 0.257529i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.44540e10 | − | 7.69966e10i | −0.0251052 | − | 0.0434834i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.68084e11 | + | 1.67677e12i | −0.537480 | + | 0.930943i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.34862e10 | −0.00736145 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −4.95019e11 | −0.265674 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.91401e9 | − | 3.31517e9i | 0.00101007 | − | 0.00174950i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.17135e11 | + | 5.49294e11i | 0.164573 | + | 0.285049i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.17141e11 | − | 1.38778e11i | −0.161847 | − | 0.0708226i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.39651e12 | + | 2.41883e12i | 0.700901 | + | 1.21400i | 0.968151 | + | 0.250369i | \(0.0805518\pi\) |
−0.267250 | + | 0.963627i | \(0.586115\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.14445e12 | + | 3.71429e12i | −1.05856 | + | 1.83348i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.15908e11 | 0.104830 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.47553e12 | −0.704700 | −0.352350 | − | 0.935868i | \(-0.614617\pi\) | ||||
−0.352350 | + | 0.935868i | \(0.614617\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.49560e10 | − | 4.32250e10i | 0.0117246 | − | 0.0203076i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.07323e12 | − | 3.59094e12i | −0.958220 | − | 1.65969i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.88418e11 | + | 1.44030e11i | 0.313032 | + | 0.0654920i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.60583e12 | + | 4.51343e12i | 1.16581 | + | 2.01924i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −1.10846e12 | + | 1.91990e12i | −0.487944 | + | 0.845144i | −0.999904 | − | 0.0138652i | \(-0.995586\pi\) |
0.511960 | + | 0.859010i | \(0.328920\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.43614e11 | 0.192155 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.12984e11 | −0.176035 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.26827e11 | − | 5.66082e11i | 0.137098 | − | 0.237460i | −0.789299 | − | 0.614009i | \(-0.789556\pi\) |
0.926397 | + | 0.376549i | \(0.122889\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.44192e12 | − | 4.22953e12i | −1.00812 | − | 1.74612i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −9.26762e11 | − | 2.82156e12i | −0.376569 | − | 1.14648i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.29888e12 | − | 2.24973e12i | −0.519474 | − | 0.899756i | −0.999744 | − | 0.0226349i | \(-0.992794\pi\) |
0.480269 | − | 0.877121i | \(-0.340539\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.19555e11 | + | 8.99896e11i | −0.204536 | + | 0.354266i | −0.949985 | − | 0.312296i | \(-0.898902\pi\) |
0.745449 | + | 0.666563i | \(0.232235\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.76896e11 | 0.107305 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.17742e12 | −1.59369 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.33010e11 | + | 4.03585e11i | −0.0875152 | + | 0.151581i | −0.906460 | − | 0.422291i | \(-0.861226\pi\) |
0.818945 | + | 0.573872i | \(0.194559\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.16556e12 | + | 2.01881e12i | 0.431003 | + | 0.746519i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.19359e12 | + | 1.33416e12i | −0.434572 | + | 0.485754i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.81718e11 | − | 3.14744e11i | −0.0651461 | − | 0.112836i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.24052e11 | + | 3.88069e11i | −0.0790946 | + | 0.136996i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.17776e12 | −1.79999 | −0.899996 | − | 0.435897i | \(-0.856431\pi\) | ||||
−0.899996 | + | 0.435897i | \(0.856431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.69856e11 | −0.0923874 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.50961e11 | + | 6.07882e11i | −0.118335 | + | 0.204963i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.94396e12 | − | 3.36705e12i | −0.645568 | − | 1.11816i | −0.984170 | − | 0.177227i | \(-0.943287\pi\) |
0.338601 | − | 0.940930i | \(-0.390046\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.59344e12 | − | 2.89889e12i | 0.848302 | − | 0.948212i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.81351e12 | + | 4.87315e12i | 0.906493 | + | 1.57009i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.53757e11 | − | 6.12726e11i | 0.112275 | − | 0.194467i | −0.804412 | − | 0.594072i | \(-0.797519\pi\) |
0.916687 | + | 0.399605i | \(0.130853\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.16274e12 | −0.988845 | −0.494422 | − | 0.869222i | \(-0.664620\pi\) | ||||
−0.494422 | + | 0.869222i | \(0.664620\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.45005e12 | −0.446636 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.31668e12 | + | 4.01260e12i | −0.703018 | + | 1.21766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.94652e12 | + | 3.37148e12i | 0.581983 | + | 1.00802i | 0.995244 | + | 0.0974119i | \(0.0310564\pi\) |
−0.413261 | + | 0.910613i | \(0.635610\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.43053e12 | − | 4.35531e12i | −0.421424 | − | 1.28304i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.35319e11 | + | 9.27200e11i | 0.155392 | + | 0.269146i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.04157e12 | − | 5.26815e12i | 0.870012 | − | 1.50691i | 0.00802931 | − | 0.999968i | \(-0.497444\pi\) |
0.861983 | − | 0.506937i | \(-0.169223\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.16552e12 | 1.17417 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.40996e12 | −1.50283 | −0.751416 | − | 0.659829i | \(-0.770629\pi\) | ||||
−0.751416 | + | 0.659829i | \(0.770629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.49701e11 | + | 1.12531e12i | −0.177871 | + | 0.308082i | −0.941151 | − | 0.337986i | \(-0.890254\pi\) |
0.763280 | + | 0.646068i | \(0.223588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.14807e12 | + | 3.72057e12i | 0.579611 | + | 1.00392i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.81159e12 | + | 3.79018e11i | 0.481797 | + | 0.100801i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.68290e12 | + | 2.91487e12i | 0.441162 | + | 0.764115i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −6.26750e11 | + | 1.08556e12i | −0.161953 | + | 0.280512i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.86415e12 | 1.23902 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.33319e12 | 0.837004 | 0.418502 | − | 0.908216i | \(-0.362555\pi\) | ||||
0.418502 | + | 0.908216i | \(0.362555\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.62118e11 | + | 1.49323e12i | −0.213427 | + | 0.369667i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.53215e12 | − | 2.65376e12i | −0.373954 | − | 0.647708i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.71993e11 | + | 1.54155e12i | 0.0413890 | + | 0.370963i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −7.18715e11 | − | 1.24485e12i | −0.170531 | − | 0.295368i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.73337e11 | + | 1.68587e12i | −0.227721 | + | 0.394424i | −0.957132 | − | 0.289651i | \(-0.906461\pi\) |
0.729412 | + | 0.684075i | \(0.239794\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.31531e12 | 0.303443 | 0.151722 | − | 0.988423i | \(-0.451518\pi\) | ||||
0.151722 | + | 0.988423i | \(0.451518\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.73295e12 | −0.849246 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.35402e12 | + | 5.80933e12i | −0.752483 | + | 1.30334i | 0.194134 | + | 0.980975i | \(0.437810\pi\) |
−0.946616 | + | 0.322363i | \(0.895523\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.00644e10 | − | 1.74321e10i | −0.00222684 | − | 0.00385699i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.92023e11 | − | 6.10966e10i | −0.0637240 | − | 0.0133322i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.93686e12 | + | 6.81883e12i | 0.847306 | + | 1.46758i | 0.883604 | + | 0.468236i | \(0.155110\pi\) |
−0.0362978 | + | 0.999341i | \(0.511556\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.08261e11 | − | 3.60718e11i | 0.0442101 | − | 0.0765741i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.66997e11 | 0.0559065 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.22995e12 | −1.69986 | −0.849929 | − | 0.526897i | \(-0.823356\pi\) | ||||
−0.849929 | + | 0.526897i | \(0.823356\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.84912e12 | + | 4.93481e12i | −0.580502 | + | 1.00546i | 0.414918 | + | 0.909859i | \(0.363810\pi\) |
−0.995420 | + | 0.0955999i | \(0.969523\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 9.25231e11 | + | 1.60255e12i | 0.185969 | + | 0.322107i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.68413e12 | − | 1.12165e13i | −0.730529 | − | 2.22412i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.37418e12 | + | 7.57630e12i | 0.855718 | + | 1.48215i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.56622e12 | + | 4.44482e12i | −0.495308 | + | 0.857899i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7.44964e10 | 0.0141868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.28143e12 | 1.74400 | 0.872002 | − | 0.489503i | \(-0.162822\pi\) | ||||
0.872002 | + | 0.489503i | \(0.162822\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.40102e12 | + | 4.15869e12i | −0.445173 | + | 0.771063i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −6.45102e11 | − | 1.11735e12i | −0.118026 | − | 0.204428i | 0.800959 | − | 0.598719i | \(-0.204323\pi\) |
−0.918986 | + | 0.394291i | \(0.870990\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.28238e11 | − | 4.78674e11i | 0.0773163 | − | 0.0864223i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.18228e11 | + | 1.24401e12i | 0.127968 | + | 0.221646i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.27194e11 | − | 2.20307e11i | 0.0223653 | − | 0.0387379i | −0.854626 | − | 0.519244i | \(-0.826214\pi\) |
0.876991 | + | 0.480506i | \(0.159547\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.19473e13 | 2.07329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.39650e12 | −1.26684 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.14225e11 | + | 1.41028e12i | −0.137644 | + | 0.238407i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.84952e11 | − | 1.35958e12i | −0.130976 | − | 0.226857i | 0.793077 | − | 0.609121i | \(-0.208478\pi\) |
−0.924053 | + | 0.382264i | \(0.875144\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.08836e11 | + | 2.33432e11i | −0.0343958 | + | 0.0384468i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.55806e12 | − | 2.69864e12i | −0.253310 | − | 0.438746i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.94388e12 | − | 3.36689e12i | 0.311976 | − | 0.540359i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 6.94240e12 | 1.09992 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −8.33084e12 | −1.30304 | −0.651520 | − | 0.758632i | \(-0.725868\pi\) | ||||
−0.651520 | + | 0.758632i | \(0.725868\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.38189e12 | − | 1.27858e13i | 1.13990 | − | 1.97437i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.50464e12 | − | 7.80227e12i | −0.686767 | − | 1.18951i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.10016e12 | − | 6.39402e12i | −0.316129 | − | 0.962468i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.16510e12 | − | 2.01801e12i | −0.173163 | − | 0.299926i | 0.766361 | − | 0.642410i | \(-0.222065\pi\) |
−0.939524 | + | 0.342483i | \(0.888732\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.18176e11 | − | 5.51098e11i | 0.0466933 | − | 0.0808752i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.69352e11 | 0.0825046 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.68820e11 | −0.0957044 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.18704e12 | − | 3.78806e12i | 0.309044 | − | 0.535280i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.83347e11 | − | 1.35680e12i | −0.109314 | − | 0.189337i | 0.806179 | − | 0.591672i | \(-0.201532\pi\) |
−0.915492 | + | 0.402335i | \(0.868199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.14052e12 | − | 6.57054e11i | −0.432806 | − | 0.0905508i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.17603e11 | − | 1.58934e12i | −0.124891 | − | 0.216318i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −4.88927e12 | + | 8.46847e12i | −0.657239 | + | 1.13837i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.09663e11 | −0.0278367 | −0.0139183 | − | 0.999903i | \(-0.504430\pi\) | ||||
−0.0139183 | + | 0.999903i | \(0.504430\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.28830e12 | 0.562356 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.74202e12 | + | 3.01726e12i | −0.225644 | + | 0.390827i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.07588e12 | − | 7.05962e12i | −0.521498 | − | 0.903262i | −0.999687 | − | 0.0250047i | \(-0.992040\pi\) |
0.478189 | − | 0.878257i | \(-0.341293\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.44730e12 | − | 1.29720e13i | −0.182922 | − | 1.63950i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.08214e12 | − | 1.87432e12i | −0.135107 | − | 0.234013i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.82789e12 | + | 6.63011e12i | −0.472128 | + | 0.817750i | −0.999491 | − | 0.0318898i | \(-0.989847\pi\) |
0.527363 | + | 0.849640i | \(0.323181\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.61657e12 | 0.684367 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.82269e12 | 0.941686 | 0.470843 | − | 0.882217i | \(-0.343950\pi\) | ||||
0.470843 | + | 0.882217i | \(0.343950\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.20754e11 | + | 1.07518e12i | −0.0738272 | + | 0.127872i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 8.09847e11 | + | 1.40270e12i | 0.0951613 | + | 0.164824i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.17350e10 | − | 2.45517e9i | −0.00136243 | − | 0.000285045i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.68288e12 | + | 9.84304e12i | 0.651912 | + | 1.12914i | 0.982658 | + | 0.185425i | \(0.0593660\pi\) |
−0.330747 | + | 0.943720i | \(0.607301\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.14603e12 | − | 3.71703e12i | 0.243253 | − | 0.421326i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.13877e12 | 0.239554 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.15682e13 | −1.28037 | −0.640184 | − | 0.768222i | \(-0.721142\pi\) | ||||
−0.640184 | + | 0.768222i | \(0.721142\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.32234e12 | − | 2.29036e12i | 0.144629 | − | 0.250505i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.05812e12 | − | 1.83272e12i | −0.114368 | − | 0.198091i | 0.803159 | − | 0.595765i | \(-0.203151\pi\) |
−0.917527 | + | 0.397674i | \(0.869818\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.11013e11 | − | 6.42439e11i | −0.0225398 | − | 0.0686233i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.75965e12 | − | 3.04780e12i | −0.185759 | − | 0.321744i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.50959e10 | + | 7.81083e10i | −0.00470498 | + | 0.00814926i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.61186e12 | 0.269328 | 0.134664 | − | 0.990891i | \(-0.457005\pi\) | ||||
0.134664 | + | 0.990891i | \(0.457005\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.70835e12 | 0.581789 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.15174e12 | − | 7.19102e12i | 0.418237 | − | 0.724407i | −0.577525 | − | 0.816373i | \(-0.695982\pi\) |
0.995762 | + | 0.0919653i | \(0.0293149\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.18199e11 | + | 5.51137e11i | 0.0316841 | + | 0.0548784i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.08830e13 | − | 1.21648e13i | 1.07116 | − | 1.19732i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.90011e12 | − | 1.02193e13i | −0.574039 | − | 0.994265i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.07272e12 | − | 1.85801e12i | 0.103171 | − | 0.178698i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00565e13 | 0.956130 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.49710e12 | 0.704661 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.23933e12 | − | 7.34274e12i | 0.393923 | − | 0.682295i | −0.599040 | − | 0.800719i | \(-0.704451\pi\) |
0.992963 | + | 0.118424i | \(0.0377843\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.05859e13 | + | 1.83353e13i | 0.972478 | + | 1.68438i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.01985e13 | + | 1.13996e13i | −0.926278 | + | 1.03537i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.66899e11 | − | 2.89077e11i | −0.0149873 | − | 0.0259588i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.85159e12 | − | 1.18673e13i | 0.608331 | − | 1.05366i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.15126e12 | −0.715587 | −0.357794 | − | 0.933801i | \(-0.616471\pi\) | ||||
−0.357794 | + | 0.933801i | \(0.616471\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.40853e12 | −0.729894 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.37291e11 | − | 1.45023e12i | 0.0718671 | − | 0.124477i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.99254e11 | + | 3.45119e11i | 0.0169117 | + | 0.0292920i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.77292e12 | + | 2.36650e13i | 0.652383 | + | 1.98621i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.81103e12 | + | 1.00650e13i | 0.482305 | + | 0.835377i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.95100e12 | − | 3.37922e12i | 0.160136 | − | 0.277363i | −0.774782 | − | 0.632229i | \(-0.782140\pi\) |
0.934917 | + | 0.354866i | \(0.115474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.54921e13 | 1.25752 | 0.628761 | − | 0.777598i | \(-0.283562\pi\) | ||||
0.628761 | + | 0.777598i | \(0.283562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.59687e12 | 0.529579 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.33414e13 | + | 2.31080e13i | −1.05924 | + | 1.83465i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.28742e12 | + | 9.15808e12i | 0.415188 | + | 0.719126i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.37368e12 | + | 2.87398e11i | 0.106686 | + | 0.0223207i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.37626e12 | + | 5.84785e12i | 0.259353 | + | 0.449213i | 0.966069 | − | 0.258285i | \(-0.0831573\pi\) |
−0.706716 | + | 0.707498i | \(0.749824\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.11164e11 | − | 1.57818e12i | 0.0692305 | − | 0.119911i | −0.829332 | − | 0.558756i | \(-0.811279\pi\) |
0.898563 | + | 0.438845i | \(0.144612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.95611e12 | 0.222166 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.37120e13 | 1.76276 | 0.881382 | − | 0.472404i | \(-0.156614\pi\) | ||||
0.881382 | + | 0.472404i | \(0.156614\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.38126e12 | − | 1.62488e13i | 0.689868 | − | 1.19489i | −0.282013 | − | 0.959411i | \(-0.591002\pi\) |
0.971880 | − | 0.235475i | \(-0.0756646\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.29061e13 | − | 2.23540e13i | −0.938838 | − | 1.62611i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.11603e13 | − | 4.88367e12i | −0.803110 | − | 0.351434i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.24499e12 | − | 1.08166e13i | −0.444573 | − | 0.770022i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.27242e11 | − | 5.66800e11i | 0.0230465 | − | 0.0399177i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.63044e12 | 0.392296 | 0.196148 | − | 0.980574i | \(-0.437157\pi\) | ||||
0.196148 | + | 0.980574i | \(0.437157\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.97112e12 | 0.411599 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 1.11580e13 | − | 1.93263e13i | 0.760964 | − | 1.31803i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.25614e12 | − | 1.60321e13i | −0.624561 | − | 1.08177i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.42037e13 | + | 2.97168e12i | 0.948258 | + | 0.198393i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.41378e13 | − | 2.44873e13i | −0.933892 | − | 1.61755i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.55746e13 | + | 2.69760e13i | −1.01797 | + | 1.76317i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.09580e13 | 1.35544 | 0.677719 | − | 0.735321i | \(-0.262968\pi\) | ||||
0.677719 | + | 0.735321i | \(0.262968\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.06819e13 | −0.683595 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −5.40299e12 | + | 9.35825e12i | −0.342153 | + | 0.592626i | −0.984832 | − | 0.173509i | \(-0.944489\pi\) |
0.642679 | + | 0.766135i | \(0.277823\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.86016e12 | − | 8.41804e12i | −0.304566 | − | 0.527524i | 0.672599 | − | 0.740007i | \(-0.265178\pi\) |
−0.977165 | + | 0.212484i | \(0.931845\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.07108e12 | − | 1.23946e13i | −0.252462 | − | 0.768629i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −8.16020e12 | − | 1.41339e13i | −0.500786 | − | 0.867387i | −1.00000 | 0.000907842i | \(-0.999711\pi\) | |
0.499214 | − | 0.866479i | \(-0.333622\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.56949e13 | + | 2.71844e13i | −0.953206 | + | 1.65100i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.37809e12 | 0.263147 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.49793e11 | 0.0564989 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.84875e12 | + | 8.39829e12i | −0.285462 | + | 0.494435i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.90559e11 | − | 5.03262e11i | −0.0169305 | − | 0.0293245i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.78467e12 | + | 1.99486e12i | −0.102925 | + | 0.115047i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.01234e13 | + | 1.75342e13i | 0.577867 | + | 1.00089i | 0.995724 | + | 0.0923817i | \(0.0294480\pi\) |
−0.417857 | + | 0.908513i | \(0.637219\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.32129e13 | + | 2.28854e13i | −0.746531 | + | 1.29303i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.15345e13 | −0.645072 | −0.322536 | − | 0.946557i | \(-0.604535\pi\) | ||||
−0.322536 | + | 0.946557i | \(0.604535\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.65115e13 | −0.914035 | −0.457017 | − | 0.889458i | \(-0.651082\pi\) | ||||
−0.457017 | + | 0.889458i | \(0.651082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.79476e11 | − | 6.57271e11i | 0.0207941 | − | 0.0360164i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.41136e12 | − | 1.63010e13i | −0.510500 | − | 0.884213i | −0.999926 | − | 0.0121677i | \(-0.996127\pi\) |
0.489425 | − | 0.872045i | \(-0.337207\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.39888e12 | + | 7.15252e12i | −0.343595 | + | 0.384062i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.00531e12 | − | 3.47329e12i | −0.106594 | − | 0.184626i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.27609e13 | + | 2.21025e13i | −0.671506 | + | 1.16308i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.06729e12 | −0.420266 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.18501e13 | −0.611160 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.66373e11 | − | 1.15419e12i | 0.0340251 | − | 0.0589331i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.39472e12 | − | 1.10760e13i | −0.323266 | − | 0.559913i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.64832e12 | + | 1.11075e13i | 0.182599 | + | 0.555930i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.72753e13 | − | 4.72422e13i | −1.35161 | − | 2.34105i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.05352e13 | + | 1.82476e13i | −0.516906 | + | 0.895308i | 0.482901 | + | 0.875675i | \(0.339583\pi\) |
−0.999807 | + | 0.0196327i | \(0.993750\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.08925e12 | −0.295819 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.97328e13 | 0.949198 | 0.474599 | − | 0.880202i | \(-0.342593\pi\) | ||||
0.474599 | + | 0.880202i | \(0.342593\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.20874e12 | + | 2.09360e12i | −0.0575725 | + | 0.0997186i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.40443e12 | + | 2.43254e12i | 0.0662377 | + | 0.114727i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1.27686e12 | − | 2.67143e11i | −0.0596323 | − | 0.0124762i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.24173e13 | + | 2.15074e13i | 0.574259 | + | 0.994645i | 0.996122 | + | 0.0879858i | \(0.0280430\pi\) |
−0.421863 | + | 0.906660i | \(0.638624\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.69695e13 | + | 2.93921e13i | −0.777145 | + | 1.34605i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.61314e12 | −0.435971 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.48172e13 | −1.56371 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.45150e12 | + | 2.51407e12i | −0.0645593 | + | 0.111820i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.81790e13 | + | 3.14869e13i | 0.800754 | + | 1.38695i | 0.919121 | + | 0.393976i | \(0.128901\pi\) |
−0.118367 | + | 0.992970i | \(0.537766\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.97742e13 | + | 2.19244e13i | −1.29887 | + | 0.956431i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.26673e13 | + | 2.19404e13i | 0.547288 | + | 0.947931i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.62637e12 | − | 4.54901e12i | 0.112384 | − | 0.194655i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.42112e12 | 0.399277 | 0.199639 | − | 0.979870i | \(-0.436023\pi\) | ||||
0.199639 | + | 0.979870i | \(0.436023\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.74130e13 | 1.99023 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.16425e13 | − | 2.01654e13i | 0.484054 | − | 0.838406i | −0.515778 | − | 0.856722i | \(-0.672497\pi\) |
0.999832 | + | 0.0183158i | \(0.00583043\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.24483e13 | + | 2.15610e13i | 0.512633 | + | 0.887906i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.80265e13 | + | 5.86365e12i | 1.14321 | + | 0.239180i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.01843e13 | − | 1.76397e13i | −0.411488 | − | 0.712717i | 0.583565 | − | 0.812066i | \(-0.301657\pi\) |
−0.995053 | + | 0.0993491i | \(0.968324\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.92802e11 | − | 1.54638e12i | 0.0357320 | − | 0.0618896i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.44493e13 | −0.969289 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.26713e13 | 0.890344 | 0.445172 | − | 0.895445i | \(-0.353143\pi\) | ||||
0.445172 | + | 0.895445i | \(0.353143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.76092e12 | + | 3.05001e12i | −0.0685054 | + | 0.118655i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.09535e12 | − | 5.36130e12i | −0.119291 | − | 0.206617i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.16764e13 | − | 3.55493e13i | −0.445785 | − | 1.35721i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.31764e13 | + | 2.28223e13i | 0.498360 | + | 0.863184i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.42373e9 | + | 9.39417e9i | −0.000203226 | + | 0.000351998i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.96495e13 | −1.10064 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.32858e12 | −0.159194 | −0.0795969 | − | 0.996827i | \(-0.525363\pi\) | ||||
−0.0795969 | + | 0.996827i | \(0.525363\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.20556e13 | + | 3.82014e13i | −0.803640 | + | 1.39195i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.63561e13 | + | 2.83297e13i | 0.590465 | + | 1.02272i | 0.994170 | + | 0.107826i | \(0.0343890\pi\) |
−0.403705 | + | 0.914889i | \(0.632278\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.50712e12 | + | 7.27350e12i | −0.232745 | + | 0.260157i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.62275e12 | − | 1.14709e13i | −0.234702 | − | 0.406516i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.14481e12 | − | 5.44698e12i | 0.110426 | − | 0.191263i | −0.805516 | − | 0.592573i | \(-0.798112\pi\) |
0.915942 | + | 0.401311i | \(0.131445\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.49941e12 | 0.0869591 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.11817e11 | −0.0210917 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 5.33975e12 | − | 9.24871e12i | 0.182402 | − | 0.315930i | −0.760296 | − | 0.649577i | \(-0.774946\pi\) |
0.942698 | + | 0.333647i | \(0.108279\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.46388e12 | − | 7.73166e12i | −0.151095 | − | 0.261704i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.88133e13 | + | 2.10290e13i | −0.631011 | + | 0.705329i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.11556e13 | − | 1.93221e13i | −0.370774 | − | 0.642200i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.84247e13 | − | 4.92330e13i | 0.936191 | − | 1.62153i | 0.163695 | − | 0.986511i | \(-0.447659\pi\) |
0.772496 | − | 0.635019i | \(-0.219008\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.90504e13 | 1.27454 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.15702e13 | −2.31488 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.88145e12 | − | 1.53831e13i | 0.284679 | − | 0.493079i | −0.687852 | − | 0.725851i | \(-0.741446\pi\) |
0.972531 | + | 0.232772i | \(0.0747796\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.79034e13 | + | 3.10096e13i | 0.568709 | + | 0.985034i |
(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 | 112.10.i.c.81.5 | 10 | ||
4.3 | odd | 2 | 7.10.c.a.4.2 | yes | 10 | ||
7.2 | even | 3 | inner | 112.10.i.c.65.5 | 10 | ||
12.11 | even | 2 | 63.10.e.b.46.4 | 10 | |||
28.3 | even | 6 | 49.10.a.f.1.4 | 5 | |||
28.11 | odd | 6 | 49.10.a.e.1.4 | 5 | |||
28.19 | even | 6 | 49.10.c.g.30.2 | 10 | |||
28.23 | odd | 6 | 7.10.c.a.2.2 | ✓ | 10 | ||
28.27 | even | 2 | 49.10.c.g.18.2 | 10 | |||
84.23 | even | 6 | 63.10.e.b.37.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.10.c.a.2.2 | ✓ | 10 | 28.23 | odd | 6 | ||
7.10.c.a.4.2 | yes | 10 | 4.3 | odd | 2 | ||
49.10.a.e.1.4 | 5 | 28.11 | odd | 6 | |||
49.10.a.f.1.4 | 5 | 28.3 | even | 6 | |||
49.10.c.g.18.2 | 10 | 28.27 | even | 2 | |||
49.10.c.g.30.2 | 10 | 28.19 | even | 6 | |||
63.10.e.b.37.4 | 10 | 84.23 | even | 6 | |||
63.10.e.b.46.4 | 10 | 12.11 | even | 2 | |||
112.10.i.c.65.5 | 10 | 7.2 | even | 3 | inner | ||
112.10.i.c.81.5 | 10 | 1.1 | even | 1 | trivial |