Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [84,12,Mod(25,84)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(84, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 4]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("84.25");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 84 = 2^{2} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 84.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(64.5408271670\) |
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: | \( x^{16} - 581500324 x^{14} - 481772282104 x^{13} + \cdots + 79\!\cdots\!77 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{42}\cdot 3^{15}\cdot 7^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.7 | ||
Root | \(-10168.9 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 84.37 |
Dual form | 84.12.i.b.25.7 |
$q$-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 \(\left(\mathbb{Z}/84\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(43\) | \(73\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −121.500 | − | 210.444i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4949.72 | − | 8573.16i | 0.708346 | − | 1.22689i | −0.257124 | − | 0.966378i | \(-0.582775\pi\) |
0.965470 | − | 0.260513i | \(-0.0838917\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 29163.1 | + | 33568.4i | 0.655835 | + | 0.754904i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −29524.5 | + | 51137.9i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 25007.0 | + | 43313.5i | 0.0468169 | + | 0.0810892i | 0.888484 | − | 0.458907i | \(-0.151759\pi\) |
−0.841667 | + | 0.539996i | \(0.818426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.46252e6 | 1.09248 | 0.546238 | − | 0.837630i | \(-0.316059\pi\) | ||||
0.546238 | + | 0.837630i | \(0.316059\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.40556e6 | −0.817928 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.16934e6 | + | 5.48946e6i | 0.541378 | + | 0.937693i | 0.998825 | + | 0.0484569i | \(0.0154304\pi\) |
−0.457448 | + | 0.889237i | \(0.651236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.02494e7 | + | 1.77525e7i | −0.949632 | + | 1.64481i | −0.203431 | + | 0.979089i | \(0.565209\pi\) |
−0.746201 | + | 0.665721i | \(0.768124\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.52097e6 | − | 1.02158e7i | 0.188129 | − | 0.545840i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.36024e7 | + | 4.08806e7i | −0.764634 | + | 1.32438i | 0.175806 | + | 0.984425i | \(0.443747\pi\) |
−0.940440 | + | 0.339960i | \(0.889586\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.45854e7 | − | 4.25831e7i | −0.503508 | − | 0.872102i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.10208e7 | −0.824046 | −0.412023 | − | 0.911173i | \(-0.635178\pi\) | ||||
−0.412023 | + | 0.911173i | \(0.635178\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.83443e7 | − | 8.37349e7i | −0.303289 | − | 0.525312i | 0.673590 | − | 0.739105i | \(-0.264751\pi\) |
−0.976879 | + | 0.213794i | \(0.931418\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.07671e6 | − | 1.05252e7i | 0.0270297 | − | 0.0468169i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.32137e8 | − | 8.38657e7i | 1.39074 | − | 0.269904i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.14098e7 | + | 1.23685e8i | −0.169297 | + | 0.293230i | −0.938173 | − | 0.346167i | \(-0.887483\pi\) |
0.768876 | + | 0.639398i | \(0.220816\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.77696e8 | − | 3.07778e8i | −0.315371 | − | 0.546238i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.44357e8 | 1.13819 | 0.569095 | − | 0.822272i | \(-0.307294\pi\) | ||||
0.569095 | + | 0.822272i | \(0.307294\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.55607e9 | −1.61418 | −0.807089 | − | 0.590430i | \(-0.798958\pi\) | ||||
−0.807089 | + | 0.590430i | \(0.798958\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.92276e8 | + | 5.06237e8i | 0.236115 | + | 0.408964i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.22680e8 | + | 7.32103e8i | −0.268827 | + | 0.465623i | −0.968559 | − | 0.248783i | \(-0.919969\pi\) |
0.699732 | + | 0.714405i | \(0.253303\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.76354e8 | + | 1.95792e9i | −0.139762 | + | 0.990185i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.70151e8 | − | 1.33394e9i | 0.312564 | − | 0.541378i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.26817e9 | + | 2.19654e9i | 0.416544 | + | 0.721476i | 0.995589 | − | 0.0938196i | \(-0.0299077\pi\) |
−0.579045 | + | 0.815296i | \(0.696574\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.95111e8 | 0.132650 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.98123e9 | 1.09654 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.80141e9 | + | 4.85219e9i | 0.510142 | + | 0.883592i | 0.999931 | + | 0.0117512i | \(0.00374060\pi\) |
−0.489789 | + | 0.871841i | \(0.662926\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.98273e8 | + | 1.03624e9i | −0.0906955 | + | 0.157089i | −0.907804 | − | 0.419395i | \(-0.862242\pi\) |
0.817108 | + | 0.576484i | \(0.195576\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.57765e9 | + | 5.00249e8i | −0.327228 | + | 0.0635058i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.23904e9 | − | 1.25384e10i | 0.773851 | − | 1.34035i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.73114e9 | − | 4.73048e9i | −0.247134 | − | 0.428049i | 0.715595 | − | 0.698515i | \(-0.246156\pi\) |
−0.962730 | + | 0.270466i | \(0.912822\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.14708e10 | 0.882923 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.81232e10 | 1.19210 | 0.596051 | − | 0.802947i | \(-0.296736\pi\) | ||||
0.596051 | + | 0.802947i | \(0.296736\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.87533e9 | + | 1.71046e10i | 0.557540 | + | 0.965687i | 0.997701 | + | 0.0677684i | \(0.0215879\pi\) |
−0.440161 | + | 0.897919i | \(0.645079\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.97425e9 | + | 1.03477e10i | −0.290701 | + | 0.503508i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7.24683e8 | + | 2.10260e9i | −0.0305105 | + | 0.0885234i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.14642e10 | + | 3.71770e10i | −0.784811 | + | 1.35933i | 0.144301 | + | 0.989534i | \(0.453907\pi\) |
−0.929112 | + | 0.369799i | \(0.879427\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.74339e9 | − | 3.01964e9i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.21192e10 | −1.45234 | −0.726170 | − | 0.687515i | \(-0.758701\pi\) | ||||
−0.726170 | + | 0.687515i | \(0.758701\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.27494e10 | 1.53393 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.10590e10 | + | 1.91548e10i | 0.237882 | + | 0.412023i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.39910e10 | + | 2.42332e10i | −0.265586 | + | 0.460008i | −0.967717 | − | 0.252039i | \(-0.918899\pi\) |
0.702131 | + | 0.712048i | \(0.252232\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.26515e10 | + | 4.90944e10i | 0.716484 | + | 0.824715i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.17477e10 | + | 2.03476e10i | −0.175104 | + | 0.303289i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.01464e11 | + | 1.75740e11i | 1.34534 | + | 2.33019i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.42003e10 | 0.640851 | 0.320426 | − | 0.947274i | \(-0.396174\pi\) | ||||
0.320426 | + | 0.947274i | \(0.396174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.95328e9 | −0.0312112 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.07024e10 | + | 1.05140e11i | 0.574696 | + | 0.995403i | 0.996075 | + | 0.0885179i | \(0.0282130\pi\) |
−0.421379 | + | 0.906885i | \(0.638454\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.26479e10 | − | 1.43150e11i | 0.702469 | − | 1.21671i | −0.265128 | − | 0.964213i | \(-0.585414\pi\) |
0.967597 | − | 0.252499i | \(-0.0812525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −7.01537e10 | − | 8.07510e10i | −0.536425 | − | 0.617457i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.05098e11 | − | 1.82035e11i | 0.724410 | − | 1.25472i | −0.234806 | − | 0.972042i | \(-0.575446\pi\) |
0.959216 | − | 0.282673i | \(-0.0912211\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.57197e10 | − | 7.91888e10i | −0.284615 | − | 0.492967i | 0.687901 | − | 0.725805i | \(-0.258532\pi\) |
−0.972516 | + | 0.232837i | \(0.925199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.47052e10 | 0.195487 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −3.60006e9 | −0.0183814 | −0.00919068 | − | 0.999958i | \(-0.502926\pi\) | ||||
−0.00919068 | + | 0.999958i | \(0.502926\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.33651e11 | + | 4.04695e11i | 1.08325 | + | 1.87625i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.31800e10 | + | 7.47900e10i | −0.182079 | + | 0.315371i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.18449e10 | + | 2.66480e11i | −0.352815 | + | 1.02366i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.41405e11 | − | 2.44921e11i | 0.495616 | − | 0.858433i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.02589e11 | − | 1.77690e11i | −0.328567 | − | 0.569095i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.39174e9 | −0.00994071 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.33083e11 | 1.70036 | 0.850179 | − | 0.526494i | \(-0.176494\pi\) | ||||
0.850179 | + | 0.526494i | \(0.176494\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.89062e11 | + | 3.27465e11i | 0.465973 | + | 0.807089i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.80539e10 | + | 8.32318e10i | −0.108827 | + | 0.188494i | −0.915295 | − | 0.402783i | \(-0.868043\pi\) |
0.806468 | + | 0.591277i | \(0.201376\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.94831e11 | + | 1.73662e11i | −1.86448 | + | 0.361843i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.10231e10 | − | 1.23016e11i | 0.136321 | − | 0.236115i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.83227e10 | − | 3.17359e10i | −0.0324360 | − | 0.0561808i | 0.849352 | − | 0.527827i | \(-0.176993\pi\) |
−0.881788 | + | 0.471647i | \(0.843660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.27117e11 | −1.18856 | −0.594282 | − | 0.804257i | \(-0.702564\pi\) | ||||
−0.594282 | + | 0.804257i | \(0.702564\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.05422e11 | 0.310415 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.65732e10 | + | 6.33466e10i | 0.0511463 | + | 0.0885880i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.50527e11 | + | 7.80336e11i | −0.583710 | + | 1.01102i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.45610e11 | − | 1.79730e11i | 0.535438 | − | 0.215961i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5.76995e11 | − | 9.99385e11i | 0.643647 | − | 1.11483i | −0.340965 | − | 0.940076i | \(-0.610754\pi\) |
0.984612 | − | 0.174754i | \(-0.0559129\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.74264e11 | − | 6.48245e11i | −0.387976 | − | 0.671995i | 0.604201 | − | 0.796832i | \(-0.293492\pi\) |
−0.992177 | + | 0.124837i | \(0.960159\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.74293e11 | −0.360918 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −9.57164e11 | −0.859334 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.07175e12 | − | 1.85633e12i | −0.896697 | − | 1.55312i | −0.831691 | − | 0.555239i | \(-0.812627\pi\) |
−0.0650059 | − | 0.997885i | \(-0.520707\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.08166e11 | − | 5.33759e11i | 0.240492 | − | 0.416544i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.06062e12 | + | 3.99908e11i | −1.50126 | + | 0.291352i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.02063e10 | − | 1.76779e10i | 0.00694765 | − | 0.0120337i | −0.862531 | − | 0.506005i | \(-0.831122\pi\) |
0.869478 | + | 0.493971i | \(0.164455\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.01560e10 | − | 1.04193e11i | −0.0382928 | − | 0.0663251i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.47826e11 | −0.147641 | −0.0738204 | − | 0.997272i | \(-0.523519\pi\) | ||||
−0.0738204 | + | 0.997272i | \(0.523519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.46792e11 | 0.193505 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.05219e11 | − | 1.04827e12i | −0.316544 | − | 0.548270i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.53660e11 | − | 1.65179e12i | 0.467886 | − | 0.810402i | −0.531441 | − | 0.847096i | \(-0.678349\pi\) |
0.999327 | + | 0.0366932i | \(0.0116824\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.12463e11 | − | 2.06715e12i | 0.328136 | − | 0.952056i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.80744e11 | − | 1.17908e12i | 0.294531 | − | 0.510142i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.54501e11 | + | 4.40808e11i | 0.103514 | + | 0.179291i | 0.913130 | − | 0.407669i | \(-0.133658\pi\) |
−0.809616 | + | 0.586959i | \(0.800325\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.05292e12 | −0.402869 | −0.201434 | − | 0.979502i | \(-0.564560\pi\) | ||||
−0.201434 | + | 0.979502i | \(0.564560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.90761e11 | 0.104726 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.06917e11 | + | 1.22442e12i | 0.239841 | + | 0.415417i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.58512e11 | + | 2.74550e11i | −0.0506912 | + | 0.0877997i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.18459e11 | + | 4.81671e11i | 0.126215 | + | 0.145281i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.42442e12 | + | 5.93127e12i | −0.974773 | + | 1.68836i | −0.294092 | + | 0.955777i | \(0.595017\pi\) |
−0.680681 | + | 0.732580i | \(0.738316\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.13876e12 | − | 1.97240e12i | −0.306104 | − | 0.530187i | 0.671403 | − | 0.741093i | \(-0.265692\pi\) |
−0.977506 | + | 0.210906i | \(0.932359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.51817e12 | −0.893567 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.51939e12 | 0.604966 | 0.302483 | − | 0.953155i | \(-0.402184\pi\) | ||||
0.302483 | + | 0.953155i | \(0.402184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.73459e11 | + | 9.93260e11i | 0.130260 | + | 0.225617i | 0.923777 | − | 0.382932i | \(-0.125086\pi\) |
−0.793517 | + | 0.608548i | \(0.791752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.63668e11 | + | 1.14951e12i | −0.142683 | + | 0.247134i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.65445e12 | − | 3.05543e12i | −0.540438 | − | 0.622076i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4.17933e12 | − | 7.23881e12i | 0.806233 | − | 1.39644i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.39370e12 | − | 2.41396e12i | −0.254878 | − | 0.441462i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.02523e12 | −0.177835 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.08695e12 | −0.178919 | −0.0894593 | − | 0.995990i | \(-0.528514\pi\) | ||||
−0.0894593 | + | 0.995990i | \(0.528514\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.20197e12 | − | 3.81392e12i | −0.344130 | − | 0.596051i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.70209e12 | + | 1.33404e13i | −1.14340 | + | 1.98042i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.40098e12 | − | 4.06481e12i | 0.197653 | − | 0.573472i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.39970e12 | − | 4.15641e12i | 0.321896 | − | 0.557540i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.63521e12 | + | 8.02843e12i | 0.591442 | + | 1.02441i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.60167e13 | 1.94489 | 0.972447 | − | 0.233124i | \(-0.0748949\pi\) | ||||
0.972447 | + | 0.233124i | \(0.0748949\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.90348e12 | 0.335672 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.82492e12 | − | 1.00891e13i | −0.641428 | − | 1.11099i | −0.985114 | − | 0.171901i | \(-0.945009\pi\) |
0.343686 | − | 0.939085i | \(-0.388324\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.67803e11 | − | 8.10258e11i | 0.0490871 | − | 0.0850214i | −0.840438 | − | 0.541908i | \(-0.817702\pi\) |
0.889525 | + | 0.456887i | \(0.151035\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.30529e11 | − | 1.02961e11i | 0.0530693 | − | 0.0102993i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.06338e12 | + | 1.05021e13i | −0.578438 | + | 1.00188i | 0.417220 | + | 0.908805i | \(0.363004\pi\) |
−0.995659 | + | 0.0930793i | \(0.970329\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.18429e12 | + | 7.24741e12i | 0.380846 | + | 0.659644i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.04316e13 | 0.906222 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.98561e12 | 0.247654 | 0.123827 | − | 0.992304i | \(-0.460483\pi\) | ||||
0.123827 | + | 0.992304i | \(0.460483\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.35089e12 | − | 7.53596e12i | −0.344734 | − | 0.597097i | 0.640571 | − | 0.767899i | \(-0.278698\pi\) |
−0.985305 | + | 0.170802i | \(0.945364\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.23644e11 | + | 7.33773e11i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.54177e13 | + | 1.20604e13i | 1.11585 | + | 0.872866i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.49900e13 | + | 2.59634e13i | −1.03745 | + | 1.79692i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 6.33248e12 | + | 1.09682e13i | 0.419254 | + | 0.726170i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.10571e13 | 0.700544 | 0.350272 | − | 0.936648i | \(-0.386089\pi\) | ||||
0.350272 | + | 0.936648i | \(0.386089\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.36091e12 | −0.143191 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.62406e12 | − | 1.32053e13i | −0.442808 | − | 0.766965i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.27142e13 | + | 2.20217e13i | −0.707387 | + | 1.22523i | 0.258436 | + | 0.966028i | \(0.416793\pi\) |
−0.965823 | + | 0.259202i | \(0.916540\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.23446e12 | + | 1.20993e12i | −0.332392 | + | 0.0645079i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.68734e12 | − | 4.65461e12i | 0.137341 | − | 0.237882i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.68147e13 | + | 2.91239e13i | 0.824011 | + | 1.42723i | 0.902673 | + | 0.430327i | \(0.141602\pi\) |
−0.0786626 | + | 0.996901i | \(0.525065\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.51084e13 | 1.18023 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.79965e12 | 0.306672 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.46102e12 | + | 1.29229e13i | 0.322969 | + | 0.559398i | 0.981099 | − | 0.193506i | \(-0.0619858\pi\) |
−0.658130 | + | 0.752904i | \(0.728652\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.07841e13 | − | 1.86786e13i | 0.448179 | − | 0.776269i | −0.550089 | − | 0.835106i | \(-0.685406\pi\) |
0.998268 | + | 0.0588375i | \(0.0187394\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.14947e12 | − | 1.49407e13i | 0.205527 | − | 0.596317i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.22961e12 | − | 2.12975e12i | 0.0471454 | − | 0.0816582i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.45333e13 | − | 2.51724e13i | −0.535457 | − | 0.927439i | −0.999141 | − | 0.0414380i | \(-0.986806\pi\) |
0.463684 | − | 0.886001i | \(-0.346527\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.70937e12 | 0.202193 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.02171e13 | 0.688390 | 0.344195 | − | 0.938898i | \(-0.388152\pi\) | ||||
0.344195 | + | 0.938898i | \(0.388152\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.44690e11 | − | 4.23815e11i | −0.00801291 | − | 0.0138788i | 0.861991 | − | 0.506923i | \(-0.169217\pi\) |
−0.870004 | + | 0.493045i | \(0.835884\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.46557e13 | − | 4.27049e13i | 0.776730 | − | 1.34534i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.46241e13 | + | 2.83438e13i | 0.746465 | + | 0.859225i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.95353e12 | + | 5.11566e12i | −0.0861794 | + | 0.149267i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.58534e12 | − | 1.14061e13i | −0.184998 | − | 0.320426i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.82921e13 | −1.84756 | −0.923780 | − | 0.382924i | \(-0.874917\pi\) | ||||
−0.923780 | + | 0.382924i | \(0.874917\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.54649e13 | 1.44543 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.58824e11 | + | 6.21501e11i | 0.00900991 | + | 0.0156056i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.45189e13 | + | 5.97885e13i | −0.835345 | + | 1.44686i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.53797e13 | − | 5.22347e13i | −1.05863 | − | 1.21855i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.47507e13 | − | 2.55489e13i | 0.331801 | − | 0.574696i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.92257e12 | + | 1.02582e13i | 0.128488 | + | 0.222547i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.82225e13 | −0.590655 | −0.295328 | − | 0.955396i | \(-0.595429\pi\) | ||||
−0.295328 | + | 0.955396i | \(0.595429\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.01669e13 | −0.811142 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.53006e13 | + | 6.11425e13i | 0.688019 | + | 1.19168i | 0.972478 | + | 0.232996i | \(0.0748528\pi\) |
−0.284459 | + | 0.958688i | \(0.591814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.75608e13 | − | 3.04162e13i | 0.330408 | − | 0.572283i | −0.652184 | − | 0.758061i | \(-0.726147\pi\) |
0.982592 | + | 0.185778i | \(0.0594804\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.46991e12 | + | 2.45747e13i | −0.153876 | + | 0.446457i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.54610e13 | − | 2.67792e13i | 0.271275 | − | 0.469863i | −0.697913 | − | 0.716182i | \(-0.745888\pi\) |
0.969189 | + | 0.246319i | \(0.0792212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.27616e12 | − | 3.94242e12i | −0.0385793 | − | 0.0668212i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.10777e13 | −0.836477 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.29936e14 | −2.05644 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.59565e13 | − | 6.22785e13i | −0.550071 | − | 0.952751i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.11099e13 | + | 1.92429e13i | −0.164322 | + | 0.284615i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.69022e13 | + | 7.16169e12i | −0.527807 | + | 0.102433i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.86187e13 | + | 3.22486e13i | −0.257571 | + | 0.446125i | −0.965591 | − | 0.260067i | \(-0.916255\pi\) |
0.708020 | + | 0.706192i | \(0.249589\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.21668e12 | − | 7.30350e12i | −0.0564322 | − | 0.0977435i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.40736e13 | −0.700227 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.01286e13 | 1.12953 | 0.564766 | − | 0.825251i | \(-0.308967\pi\) | ||||
0.564766 | + | 0.825251i | \(0.308967\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4.37407e11 | + | 7.57611e11i | 0.00530624 | + | 0.00919068i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.41790e12 | − | 4.18792e12i | 0.0283981 | − | 0.0491869i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.37837e13 | + | 4.78222e13i | −0.839156 | + | 0.543891i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.67771e13 | − | 9.83409e13i | 0.625415 | − | 1.08325i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.20561e13 | − | 7.28433e13i | −0.448763 | − | 0.777280i | 0.549543 | − | 0.835465i | \(-0.314802\pi\) |
−0.998306 | + | 0.0581855i | \(0.981469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.62557e14 | 1.68061 | 0.840305 | − | 0.542114i | \(-0.182376\pi\) | ||||
0.840305 | + | 0.542114i | \(0.182376\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.09855e13 | 0.210247 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −7.77383e13 | − | 1.34647e14i | −0.754873 | − | 1.30748i | −0.945437 | − | 0.325804i | \(-0.894365\pi\) |
0.190564 | − | 0.981675i | \(-0.438968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.97046e13 | − | 1.55373e14i | 0.844421 | − | 1.46258i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.72383e13 | − | 1.30491e13i | 0.613679 | − | 0.119098i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.44669e13 | + | 1.11660e14i | −0.570581 | + | 0.988275i | 0.425925 | + | 0.904758i | \(0.359949\pi\) |
−0.996506 | + | 0.0835170i | \(0.973385\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.51857e14 | − | 2.63024e14i | −1.30360 | − | 2.25790i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.87229e13 | −0.572288 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.95520e14 | 1.57972 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.09211e13 | + | 1.40159e14i | 0.634452 | + | 1.09890i | 0.986631 | + | 0.162970i | \(0.0521074\pi\) |
−0.352179 | + | 0.935933i | \(0.614559\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.49292e13 | + | 4.31787e13i | −0.189698 | + | 0.328567i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.67506e13 | + | 1.06629e14i | −0.271461 | + | 0.787620i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.49137e12 | − | 1.29754e13i | 0.0537233 | − | 0.0930515i | −0.837913 | − | 0.545804i | \(-0.816224\pi\) |
0.891636 | + | 0.452752i | \(0.149558\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.12096e11 | + | 7.13772e11i | 0.00286964 | + | 0.00497035i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −1.33119e14 | −0.900251 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46414e14 | −0.961758 | −0.480879 | − | 0.876787i | \(-0.659682\pi\) | ||||
−0.480879 | + | 0.876787i | \(0.659682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.69196e13 | − | 1.33229e14i | −0.490851 | − | 0.850179i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.03039e14 | − | 1.78468e14i | 0.638861 | − | 1.10654i | −0.346822 | − | 0.937931i | \(-0.612739\pi\) |
0.985683 | − | 0.168609i | \(-0.0539275\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.44390e13 | + | 1.66201e13i | 0.0869966 | + | 0.100138i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.59420e13 | − | 7.95740e13i | 0.269030 | − | 0.465973i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.28674e13 | + | 7.42485e13i | 0.244008 | + | 0.422634i | 0.961852 | − | 0.273569i | \(-0.0882043\pi\) |
−0.717844 | + | 0.696204i | \(0.754871\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.99217e14 | −1.65582 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.33542e13 | 0.125663 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.12483e14 | + | 3.68032e14i | 1.11184 | + | 1.92576i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.18685e13 | + | 8.98388e13i | −0.263971 | + | 0.457210i | −0.967293 | − | 0.253660i | \(-0.918366\pi\) |
0.703323 | + | 0.710871i | \(0.251699\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.45268e14 | + | 1.67212e14i | 0.719149 | + | 0.827783i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.92898e13 | − | 1.54655e14i | 0.430039 | − | 0.744850i | −0.566837 | − | 0.823830i | \(-0.691833\pi\) |
0.996876 | + | 0.0789803i | \(0.0251664\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.07044e13 | − | 1.22464e14i | −0.331336 | − | 0.573891i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.45172e13 | −0.157410 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.14299e12 | −0.0317038 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.39715e14 | + | 2.41994e14i | 0.603622 | + | 1.04550i | 0.992268 | + | 0.124117i | \(0.0396099\pi\) |
−0.388645 | + | 0.921388i | \(0.627057\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.45243e12 | + | 7.71183e12i | −0.0187269 | + | 0.0324360i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.11826e13 | + | 2.35544e14i | −0.332459 | + | 0.964599i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.57975e14 | + | 4.46827e14i | −1.02876 | + | 1.78186i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.83447e13 | + | 1.53017e14i | 0.343109 | + | 0.594282i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.47340e14 | 0.557370 | 0.278685 | − | 0.960383i | \(-0.410102\pi\) | ||||
0.278685 | + | 0.960383i | \(0.410102\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.13118e14 | 0.416852 | 0.208426 | − | 0.978038i | \(-0.433166\pi\) | ||||
0.208426 | + | 0.978038i | \(0.433166\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.49588e13 | − | 4.32300e13i | −0.0896091 | − | 0.155208i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.55839e14 | − | 2.69921e14i | 0.545176 | − | 0.944273i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.22325e13 | + | 1.01369e13i | −0.178069 | + | 0.0345581i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 8.88728e12 | − | 1.53932e13i | 0.0295293 | − | 0.0511463i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.21901e14 | + | 3.84344e14i | 0.718678 | + | 1.24479i | 0.961524 | + | 0.274722i | \(0.0885859\pi\) |
−0.242845 | + | 0.970065i | \(0.578081\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.99750e14 | 1.26213 | 0.631067 | − | 0.775729i | \(-0.282617\pi\) | ||||
0.631067 | + | 0.775729i | \(0.282617\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.18956e14 | 0.674010 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.83823e14 | − | 8.38006e14i | −1.45224 | − | 2.51536i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.14931e14 | − | 3.72271e14i | 0.629134 | − | 1.08969i | −0.358591 | − | 0.933495i | \(-0.616743\pi\) |
0.987726 | − | 0.156198i | \(-0.0499239\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.19647e13 | − | 7.19388e13i | −0.262548 | − | 0.205377i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.77263e13 | + | 1.17305e14i | −0.188598 | + | 0.326661i | −0.944783 | − | 0.327697i | \(-0.893728\pi\) |
0.756185 | + | 0.654358i | \(0.227061\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.38503e14 | + | 2.39895e14i | 0.376254 | + | 0.651690i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.80420e14 | −0.743220 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.79795e13 | 0.253385 | 0.126692 | − | 0.991942i | \(-0.459564\pi\) | ||||
0.126692 | + | 0.991942i | \(0.459564\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.11149e13 | + | 3.65720e13i | 0.0532865 | + | 0.0922949i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.09462e13 | + | 1.57523e14i | −0.223998 | + | 0.387976i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.32007e14 | − | 1.22655e14i | 1.51935 | − | 0.294864i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.69842e14 | + | 6.40586e14i | −0.867916 | + | 1.50327i | −0.00379321 | + | 0.999993i | \(0.501207\pi\) |
−0.864123 | + | 0.503281i | \(0.832126\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.54766e13 | + | 7.87678e13i | 0.104188 | + | 0.180459i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.05197e14 | 0.459003 | 0.229501 | − | 0.973308i | \(-0.426290\pi\) | ||||
0.229501 | + | 0.973308i | \(0.426290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.01270e14 | 0.658052 | 0.329026 | − | 0.944321i | \(-0.393280\pi\) | ||||
0.329026 | + | 0.944321i | \(0.393280\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.16295e14 | + | 2.01430e14i | 0.248068 | + | 0.429667i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.92054e14 | + | 3.32648e14i | −0.400111 | + | 0.693013i | −0.993739 | − | 0.111727i | \(-0.964362\pi\) |
0.593628 | + | 0.804740i | \(0.297695\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.91463e13 | − | 2.29636e14i | 0.161057 | − | 0.467293i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.60435e14 | + | 4.51087e14i | −0.517708 | + | 0.896697i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.89126e13 | − | 6.73986e13i | −0.0755707 | − | 0.130892i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.00794e15 | 1.91259 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.49769e14 | −0.277696 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.73993e14 | − | 6.47776e14i | −0.677671 | − | 1.17376i | −0.975681 | − | 0.219197i | \(-0.929656\pi\) |
0.298010 | − | 0.954563i | \(-0.403677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.04438e14 | + | 1.80892e14i | −0.184953 | + | 0.320347i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.34523e14 | + | 3.85056e14i | 0.579052 | + | 0.666523i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.68276e14 | − | 4.64668e14i | 0.453945 | − | 0.786255i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.99482e13 | + | 1.21154e14i | 0.115709 | + | 0.200414i | 0.918063 | − | 0.396435i | \(-0.129753\pi\) |
−0.802354 | + | 0.596848i | \(0.796419\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.96028e12 | −0.00802245 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.86402e13 | 0.0452926 | 0.0226463 | − | 0.999744i | \(-0.492791\pi\) | ||||
0.0226463 | + | 0.999744i | \(0.492791\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.88476e14 | − | 4.99655e14i | −0.446120 | − | 0.772703i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.46179e13 | + | 2.53190e13i | −0.0221084 | + | 0.0382928i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.28528e14 | + | 6.08367e14i | 0.781822 | + | 0.899923i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.75867e14 | + | 9.97430e14i | −0.833238 | + | 1.44321i | 0.0622193 | + | 0.998063i | \(0.480182\pi\) |
−0.895457 | + | 0.445148i | \(0.853151\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.01109e13 | + | 5.21536e13i | 0.0426202 | + | 0.0738204i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.85521e14 | −1.36472 | −0.682358 | − | 0.731019i | \(-0.739045\pi\) | ||||
−0.682358 | + | 0.731019i | \(0.739045\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.20184e15 | 1.62833 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.21352e13 | − | 7.29803e13i | −0.0558601 | − | 0.0967525i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.82938e14 | − | 6.63268e14i | 0.496799 | − | 0.860481i | −0.503194 | − | 0.864173i | \(-0.667842\pi\) |
0.999993 | + | 0.00369203i | \(0.00117521\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.86179e14 | + | 8.30322e14i | −0.363348 | + | 1.05422i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.47068e14 | + | 2.54730e14i | −0.182757 | + | 0.316544i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −8.18168e14 | − | 1.41711e15i | −0.995183 | − | 1.72371i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.22799e13 | −0.0503426 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.63479e14 | −0.540268 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.90199e14 | − | 6.75845e14i | −0.445327 | − | 0.771329i | 0.552748 | − | 0.833349i | \(-0.313579\pi\) |
−0.998075 | + | 0.0620194i | \(0.980246\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.32813e14 | + | 2.30039e14i | −0.148416 | + | 0.257064i | −0.930642 | − | 0.365930i | \(-0.880751\pi\) |
0.782226 | + | 0.622995i | \(0.214084\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.21584e14 | + | 1.01225e14i | −0.570752 | + | 0.110767i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.06440e14 | − | 5.30769e14i | 0.328388 | − | 0.568784i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.37744e14 | − | 1.10461e15i | −0.669330 | − | 1.15931i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.30841e14 | −0.340095 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.23489e15 | 1.24345 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.04041e15 | − | 1.80205e15i | −1.02627 | − | 1.77755i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.18436e13 | − | 1.07116e14i | 0.0597636 | − | 0.103514i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −9.17151e13 | + | 3.69919e13i | −0.0868365 | + | 0.0350242i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.32642e14 | + | 4.02947e14i | −0.215825 | + | 0.373820i | −0.953528 | − | 0.301306i | \(-0.902577\pi\) |
0.737702 | + | 0.675126i | \(0.235911\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.27930e14 | + | 2.21581e14i | 0.116298 | + | 0.201434i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −9.05198e14 | −0.806423 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −4.31654e14 | −0.376882 | −0.188441 | − | 0.982084i | \(-0.560343\pi\) | ||||
−0.188441 | + | 0.982084i | \(0.560343\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.53274e13 | − | 6.11889e13i | −0.0302318 | − | 0.0523631i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.32912e14 | − | 1.61585e15i | 0.782540 | − | 1.35540i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.87394e15 | + | 3.63679e14i | −1.54087 | + | 0.299040i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.71781e14 | − | 2.97533e14i | 0.138472 | − | 0.239841i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.93906e13 | + | 3.35855e13i | 0.0153246 | + | 0.0265429i | 0.873586 | − | 0.486670i | \(-0.161789\pi\) |
−0.858261 | + | 0.513213i | \(0.828455\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.27577e15 | −1.76345 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.70367e13 | 0.0585332 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −2.67759e14 | − | 4.63772e14i | −0.199502 | − | 0.345548i | 0.748865 | − | 0.662723i | \(-0.230599\pi\) |
−0.948367 | + | 0.317175i | \(0.897266\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.78193e13 | + | 3.08639e13i | −0.0130204 | + | 0.0225519i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.05220e13 | − | 1.46585e14i | 0.0362055 | − | 0.105047i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.33929e14 | + | 7.51587e14i | −0.305001 | + | 0.528277i | −0.977262 | − | 0.212038i | \(-0.931990\pi\) |
0.672261 | + | 0.740314i | \(0.265323\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.01450e14 | + | 8.68538e14i | 0.345724 | + | 0.598811i | 0.985485 | − | 0.169762i | \(-0.0543000\pi\) |
−0.639761 | + | 0.768574i | \(0.720967\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.66427e15 | 1.12557 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.32110e15 | 1.54000 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.70850e14 | − | 2.95920e14i | −0.111211 | − | 0.192623i | 0.805048 | − | 0.593210i | \(-0.202140\pi\) |
−0.916259 | + | 0.400587i | \(0.868806\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −2.76720e14 | + | 4.79292e14i | −0.176729 | + | 0.306104i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.51996e15 | − | 1.74956e15i | −0.952495 | − | 1.09638i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.34265e13 | + | 1.09858e14i | −0.0390026 | + | 0.0675545i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.27458e14 | + | 7.40379e14i | 0.257950 | + | 0.446783i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.31315e15 | 0.777689 | 0.388845 | − | 0.921303i | \(-0.372874\pi\) | ||||
0.388845 | + | 0.921303i | \(0.372874\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.98201e15 | 1.15205 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.06106e14 | − | 5.30191e14i | −0.174639 | − | 0.302483i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.42951e15 | + | 2.47598e15i | −0.800543 | + | 1.38658i | 0.118715 | + | 0.992928i | \(0.462122\pi\) |
−0.919259 | + | 0.393654i | \(0.871211\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.82997e15 | + | 2.10640e15i | 1.00601 | + | 1.15797i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.39351e14 | − | 2.41362e14i | 0.0752055 | − | 0.130260i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.07552e15 | − | 1.86285e15i | −0.569862 | − | 0.987030i | −0.996579 | − | 0.0826451i | \(-0.973663\pi\) |
0.426717 | − | 0.904385i | \(-0.359670\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.46561e15 | −1.80289 | −0.901447 | − | 0.432889i | \(-0.857494\pi\) | ||||
−0.901447 | + | 0.432889i | \(0.857494\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.22543e14 | 0.164756 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.39983e15 | − | 2.42458e15i | −0.702136 | − | 1.21613i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.39119e14 | − | 1.45340e15i | 0.413319 | − | 0.715890i | −0.581931 | − | 0.813238i | \(-0.697703\pi\) |
0.995250 | + | 0.0973481i | \(0.0310360\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.20481e14 | + | 9.29847e14i | −0.155027 | + | 0.449797i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.18176e14 | + | 1.07071e15i | −0.293688 | + | 0.508682i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.51033e14 | + | 4.34802e14i | 0.117138 | + | 0.202889i | 0.918632 | − | 0.395113i | \(-0.129295\pi\) |
−0.801494 | + | 0.598002i | \(0.795961\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.03115e15 | −0.930957 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3.06387e15 | 1.37944 | 0.689719 | − | 0.724077i | \(-0.257734\pi\) | ||||
0.689719 | + | 0.724077i | \(0.257734\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.07837e14 | + | 1.05280e15i | 0.268837 | + | 0.465639i | 0.968562 | − | 0.248773i | \(-0.0800275\pi\) |
−0.699725 | + | 0.714412i | \(0.746694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −3.38669e14 | + | 5.86592e14i | −0.147154 | + | 0.254878i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.22149e15 | + | 2.37058e14i | −0.521443 | + | 0.101197i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.18367e15 | − | 2.05018e15i | 0.496467 | − | 0.859906i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.24566e14 | + | 2.15754e14i | 0.0513366 | + | 0.0889176i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −9.05289e14 | −0.366614 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.29369e15 | 0.912794 | 0.456397 | − | 0.889776i | \(-0.349140\pi\) | ||||
0.456397 | + | 0.889776i | \(0.349140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.32064e14 | + | 2.28742e14i | 0.0516494 | + | 0.0894593i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.13358e15 | − | 5.42753e15i | 1.20444 | − | 2.08615i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.04173e14 | + | 2.86349e15i | −0.152686 | + | 1.08175i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.35078e14 | + | 9.26782e14i | −0.198684 | + | 0.344130i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.49382e13 | + | 1.64438e14i | 0.0346515 | + | 0.0600181i | 0.882831 | − | 0.469691i | \(-0.155635\pi\) |
−0.848180 | + | 0.529709i | \(0.822301\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.75159e15 | 0.628452 | 0.314226 | − | 0.949348i | \(-0.398255\pi\) | ||||
0.314226 | + | 0.949348i | \(0.398255\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.74321e15 | 1.32028 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.59994e15 | + | 2.77118e15i | 0.554793 | + | 0.960930i | 0.997920 | + | 0.0644710i | \(0.0205360\pi\) |
−0.443126 | + | 0.896459i | \(0.646131\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.40110e14 | + | 2.42678e14i | −0.0477665 | + | 0.0827341i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.02563e15 | + | 1.99047e14i | −0.343793 | + | 0.0667206i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.12815e15 | + | 1.95401e15i | −0.371829 | + | 0.644026i | −0.989847 | − | 0.142138i | \(-0.954602\pi\) |
0.618018 | + | 0.786164i | \(0.287936\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.75706e14 | + | 8.23948e14i | 0.154174 | + | 0.267038i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.16626e15 | −0.371693 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.01218e15 | 0.944084 | 0.472042 | − | 0.881576i | \(-0.343517\pi\) | ||||
0.472042 | + | 0.881576i | \(0.343517\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.47975e15 | − | 2.56300e15i | −0.456121 | − | 0.790024i | 0.542631 | − | 0.839971i | \(-0.317428\pi\) |
−0.998752 | + | 0.0499469i | \(0.984095\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.12636e15 | − | 1.95091e15i | 0.341469 | − | 0.591442i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.94033e15 | + | 8.53111e15i | −0.876753 | + | 2.54382i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.14831e15 | − | 3.72098e15i | 0.630094 | − | 1.09135i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.94603e15 | − | 3.37062e15i | −0.561443 | − | 0.972447i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.98442e13 | −0.0169843 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 4.01157e15 | 1.12004 | 0.560018 | − | 0.828481i | \(-0.310794\pi\) | ||||
0.560018 | + | 0.828481i | \(0.310794\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3.52773e14 | − | 6.11021e14i | −0.0969002 | − | 0.167836i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.58231e15 | + | 6.20474e15i | −0.968111 | + | 1.67682i | −0.267096 | + | 0.963670i | \(0.586064\pi\) |
−0.701015 | + | 0.713147i | \(0.747269\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.58065e15 | + | 1.81942e15i | 0.420293 | + | 0.483782i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.41546e15 | + | 2.45164e15i | −0.370329 | + | 0.641428i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.37708e13 | + | 1.27775e14i | 0.0189920 | + | 0.0328951i | 0.875365 | − | 0.483462i | \(-0.160621\pi\) |
−0.856373 | + | 0.516357i | \(0.827288\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.62770e14 | −0.0919037 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.27352e14 | −0.0566809 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.85472e15 | + | 3.21248e15i | 0.455065 | + | 0.788196i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.43011e15 | − | 2.47703e15i | 0.345335 | − | 0.598138i | −0.640079 | − | 0.768309i | \(-0.721099\pi\) |
0.985415 | + | 0.170171i | \(0.0544319\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.61268e13 | − | 9.91370e13i | −0.0204694 | − | 0.0235615i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.59902e15 | + | 6.23369e15i | −0.841915 | + | 1.45824i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.67606e15 | + | 4.63507e15i | 0.616191 | + | 1.06727i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2.94680e15 | 0.667923 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.67571e14 | 0.0820147 | 0.0410073 | − | 0.999159i | \(-0.486943\pi\) | ||||
0.0410073 | + | 0.999159i | \(0.486943\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.46382e15 | − | 2.53541e15i | −0.321539 | − | 0.556922i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 1.01678e15 | − | 1.76112e15i | 0.219881 | − | 0.380846i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.75910e15 | + | 5.10388e15i | −0.374528 | + | 1.08666i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.52656e15 | + | 6.10818e15i | −0.739259 | + | 1.28043i | 0.213570 | + | 0.976928i | \(0.431491\pi\) |
−0.952829 | + | 0.303507i | \(0.901842\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.26744e15 | − | 2.19527e15i | −0.261604 | − | 0.453111i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.56418e15 | 0.927620 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7.24108e14 | 0.144917 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.62752e14 | − | 6.28304e14i | −0.0714914 | − | 0.123827i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.63237e15 | − | 6.29146e15i | 0.704988 | − | 1.22108i | −0.261708 | − | 0.965147i | \(-0.584286\pi\) |
0.966696 | − | 0.255928i | \(-0.0823810\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.21561e15 | − | 1.40035e15i | 1.37921 | − | 0.267665i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.05727e15 | + | 1.83124e15i | −0.199032 | + | 0.344734i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.23778e15 | + | 3.87595e15i | 0.414914 | + | 0.718652i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.82541e15 | −1.61174 | −0.805871 | − | 0.592091i | \(-0.798302\pi\) | ||||
−0.805871 | + | 0.592091i | \(0.798302\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.93171e15 | − | 8.54196e15i | −0.873880 | − | 1.51360i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.25078e15 | + | 5.63051e15i | −0.567434 | + | 0.982825i | 0.429384 | + | 0.903122i | \(0.358731\pi\) |
−0.996819 | + | 0.0797030i | \(0.974603\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.64788e14 | − | 4.70990e15i | 0.114315 | − | 0.809900i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.36596e14 | − | 2.36591e14i | 0.0231401 | − | 0.0400799i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.66487e15 | − | 8.07979e15i | −0.778565 | − | 1.34851i | −0.932769 | − | 0.360475i | \(-0.882615\pi\) |
0.154204 | − | 0.988039i | \(-0.450719\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.28512e15 | 1.19794 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.14846e15 | 1.15817 | 0.579087 | − | 0.815266i | \(-0.303409\pi\) | ||||
0.579087 | + | 0.815266i | \(0.303409\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.71193e15 | − | 9.89335e15i | −0.911850 | − | 1.57937i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.53879e15 | − | 2.66527e15i | 0.242057 | − | 0.419254i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 9.17564e15 | − | 1.78073e15i | 1.42228 | − | 0.276025i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.33373e15 | − | 4.04213e15i | 0.356476 | − | 0.617434i | −0.630893 | − | 0.775869i | \(-0.717312\pi\) |
0.987369 | + | 0.158435i | \(0.0506448\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.34344e15 | − | 2.32690e15i | −0.202230 | − | 0.350272i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.41001e15 | −1.09929 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.72097e15 | 0.690246 | 0.345123 | − | 0.938557i | \(-0.387837\pi\) | ||||
0.345123 | + | 0.938557i | \(0.387837\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.86850e14 | + | 4.96839e14i | 0.0413357 | + | 0.0715955i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.09532e14 | − | 1.05574e15i | 0.0865727 | − | 0.149948i | −0.819488 | − | 0.573097i | \(-0.805742\pi\) |
0.906060 | + | 0.423149i | \(0.139075\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.32492e15 | − | 3.84413e15i | 0.185483 | − | 0.538162i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.85265e15 | + | 3.20888e15i | −0.255655 | + | 0.442808i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.09711e15 | + | 7.09641e15i | 0.557318 | + | 0.965304i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 4.52570e15 | 0.606864 | 0.303432 | − | 0.952853i | \(-0.401867\pi\) | ||||
0.303432 | + | 0.952853i | \(0.401867\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.17911e15 | 0.816820 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −2.34216e15 | − | 4.05675e15i | −0.305232 | − | 0.528677i | 0.672081 | − | 0.740478i | \(-0.265401\pi\) |
−0.977313 | + | 0.211800i | \(0.932067\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.37713e15 | + | 4.11731e15i | −0.305417 | + | 0.528998i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.01211e15 | + | 1.16500e15i | 0.128207 | + | 0.147574i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.65418e15 | + | 1.49895e16i | −1.08086 | + | 1.87211i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.53207e14 | + | 7.84977e14i | 0.0558105 | + | 0.0966666i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.30605e15 | −0.158588 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.12195e16 | −2.54069 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.54085e15 | − | 1.13291e16i | −0.772277 | − | 1.33762i | −0.936312 | − | 0.351169i | \(-0.885784\pi\) |
0.164035 | − | 0.986455i | \(-0.447549\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.08597e15 | − | 7.07712e15i | 0.475743 | − | 0.824011i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.04989e14 | − | 1.20848e14i | −0.0120551 | − | 0.0138762i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.74984e14 | + | 1.51552e15i | −0.0990827 | + | 0.171616i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.05067e15 | − | 5.28392e15i | −0.340703 | − | 0.590115i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1.03303e16 | −1.13787 | −0.568933 | − | 0.822384i | \(-0.692644\pi\) | ||||
−0.568933 | + | 0.822384i | \(0.692644\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.35847e15 | −0.582148 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −8.26157e14 | − | 1.43095e15i | −0.0885286 | − | 0.153336i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −4.93905e14 | + | 8.55469e14i | −0.0522045 | + | 0.0904209i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.77100e15 | + | 1.96455e16i | −0.705953 | + | 2.04826i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.81303e15 | − | 3.14026e15i | 0.186466 | − | 0.322969i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.46347e15 | − | 9.46301e15i | −0.554309 | − | 0.960091i | −0.997957 | − | 0.0638900i | \(-0.979649\pi\) |
0.443648 | − | 0.896201i | \(-0.353684\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.55193e16 | −1.55330 | −0.776652 | − | 0.629930i | \(-0.783084\pi\) | ||||
−0.776652 | + | 0.629930i | \(0.783084\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.24106e15 | −0.517513 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1.01037e14 | − | 1.75001e14i | −0.00984268 | − | 0.0170480i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.59488e16 | − | 2.76241e16i | 1.53287 | − | 2.65502i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.76985e15 | + | 7.31622e14i | −0.357489 | + | 0.0693786i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.25247e15 | + | 1.25617e16i | −0.678577 | + | 1.17533i | 0.296833 | + | 0.954929i | \(0.404069\pi\) |
−0.975410 | + | 0.220400i | \(0.929264\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.41636e15 | + | 2.45320e15i | 0.130760 | + | 0.226482i | 0.923970 | − | 0.382466i | \(-0.124925\pi\) |
−0.793210 | + | 0.608948i | \(0.791592\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.97593e14 | −0.0544388 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.88975e16 | 1.69873 | 0.849363 | − | 0.527809i | \(-0.176986\pi\) | ||||
0.849363 | + | 0.527809i | \(0.176986\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.55663e14 | + | 2.69617e14i | 0.0138082 | + | 0.0239165i | 0.872847 | − | 0.487994i | \(-0.162271\pi\) |
−0.859039 | + | 0.511911i | \(0.828938\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.53158e15 | + | 6.11688e15i | −0.309146 | + | 0.535457i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.16238e16 | + | 4.68828e15i | −1.00415 | + | 0.405011i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.22667e15 | + | 2.12465e15i | −0.104581 | + | 0.181139i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −6.93689e14 | − | 1.20150e15i | −0.0583680 | − | 0.101096i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.14467e16 | 0.950583 | 0.475292 | − | 0.879828i | \(-0.342343\pi\) | ||||
0.475292 | + | 0.879828i | \(0.342343\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.91573e15 | −0.320948 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.45638e15 | − | 4.25457e15i | −0.198721 | − | 0.344195i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.71652e15 | − | 2.97310e15i | 0.137068 | − | 0.237410i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.23454e16 | − | 2.39590e15i | 0.973077 | − | 0.188847i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.94596e13 | + | 1.02987e14i | −0.00462626 | + | 0.00801291i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.37089e15 | − | 5.83855e15i | −0.258900 | − | 0.448428i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.10747e15 | 0.538884 | 0.269442 | − | 0.963017i | \(-0.413161\pi\) | ||||
0.269442 | + | 0.963017i | \(0.413161\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.19827e16 | −0.896891 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.28558e15 | + | 1.26190e16i | 0.538356 | + | 0.932460i | 0.998993 | + | 0.0448714i | \(0.0142878\pi\) |
−0.460637 | + | 0.887589i | \(0.652379\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.82398e15 | − | 1.18195e16i | 0.497824 | − | 0.862256i | −0.502173 | − | 0.864767i | \(-0.667466\pi\) |
0.999997 | + | 0.00251138i | \(0.000799397\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.97295e15 | − | 8.62576e15i | 0.214127 | − | 0.621269i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.49537e15 | − | 1.64465e16i | 0.675231 | − | 1.16954i | −0.301170 | − | 0.953571i | \(-0.597377\pi\) |
0.976401 | − | 0.215965i | \(-0.0692896\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −9.44070e15 | − | 1.63518e16i | −0.662851 | − | 1.14809i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.43542e15 | 0.0995114 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.14702e15 | −0.146970 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.99434e15 | − | 6.91840e15i | −0.269989 | − | 0.467634i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.60024e15 | + | 2.77169e15i | −0.106809 | + | 0.184998i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.89136e13 | − | 1.13855e14i | −0.00651946 | − | 0.00750429i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.97907e15 | − | 1.03561e16i | 0.389167 | − | 0.674057i | −0.603171 | − | 0.797612i | \(-0.706096\pi\) |
0.992338 | + | 0.123555i | \(0.0394296\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 8.29749e15 | + | 1.43717e16i | 0.533345 | + | 0.923780i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.04006e16 | −0.660221 | −0.330111 | − | 0.943942i | \(-0.607086\pi\) | ||||
−0.330111 | + | 0.943942i | \(0.607086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.40425e16 | 0.880360 | 0.440180 | − | 0.897910i | \(-0.354915\pi\) | ||||
0.440180 | + | 0.897910i | \(0.354915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.73898e15 | − | 1.16723e16i | −0.417259 | − | 0.722715i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.17716e16 | + | 2.03890e16i | −0.719873 | + | 1.24686i | 0.241177 | + | 0.970481i | \(0.422467\pi\) |
−0.961050 | + | 0.276375i | \(0.910867\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.84627e16 | + | 2.12516e16i | 1.11515 | + | 1.28361i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 8.71941e13 | − | 1.51025e14i | 0.00520187 | − | 0.00900991i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.66446e15 | − | 1.50073e16i | −0.510574 | − | 0.884340i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.03882e15 | 0.293294 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.67762e16 | 0.964573 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.40034e15 | + | 7.62161e15i | 0.249924 | + | 0.432881i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.03855e15 | + | 1.39232e16i | −0.451016 | + | 0.781182i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.47886e15 | + | 1.58964e16i | −0.303674 | + | 0.881082i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.21166e15 | + | 9.02686e15i | −0.285370 | + | 0.494276i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.25037e16 | + | 2.16570e16i | 0.676392 | + | 1.17154i | 0.976060 | + | 0.217501i | \(0.0697906\pi\) |
−0.299668 | + | 0.954043i | \(0.596876\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.16883e15 | −0.383131 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.16094e16 | 1.14102 | 0.570508 | − | 0.821292i | \(-0.306746\pi\) | ||||
0.570508 | + | 0.821292i | \(0.306746\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.30335e15 | − | 2.25746e15i | −0.0679940 | − | 0.117769i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.43918e15 | − | 2.49274e15i | 0.0741823 | − | 0.128488i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −4.19536e15 | + | 8.14202e14i | −0.213667 | + | 0.0414668i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.18711e16 | + | 2.05614e16i | −0.597388 | + | 1.03471i | 0.395817 | + | 0.918329i | \(0.370461\pi\) |
−0.993205 | + | 0.116377i | \(0.962872\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.42903e15 | + | 5.93925e15i | 0.170507 | + | 0.295328i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.65054e16 | 1.30234 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 7.02255e15 | 0.340969 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.88028e15 | + | 8.45289e15i | 0.234156 | + | 0.405571i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.80122e15 | − | 1.35121e16i | 0.369893 | − | 0.640674i | −0.619655 | − | 0.784874i | \(-0.712728\pi\) |
0.989549 | + | 0.144200i | \(0.0460609\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.19256e16 | − | 2.49736e16i | −1.49594 | − | 1.17019i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.57806e15 | − | 1.48576e16i | 0.397228 | − | 0.688019i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.56918e15 | + | 2.71789e15i | 0.0718138 | + | 0.124385i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.89670e14 | 0.0402403 | 0.0201201 | − | 0.999798i | \(-0.493595\pi\) | ||||
0.0201201 | + | 0.999798i | \(0.493595\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −8.53455e15 | −0.381522 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.33102e16 | + | 2.30539e16i | 0.588086 | + | 1.01860i | 0.994483 | + | 0.104899i | \(0.0334518\pi\) |
−0.406397 | + | 0.913697i | \(0.633215\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.99289e16 | + | 3.45178e16i | −0.870299 | + | 1.50740i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.20069e15 | − | 1.20338e15i | 0.267649 | − | 0.0519431i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.01137e16 | − | 1.75174e16i | 0.431503 | − | 0.747385i | −0.565500 | − | 0.824748i | \(-0.691317\pi\) |
0.997003 | + | 0.0773632i | \(0.0246501\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.44428e16 | + | 2.50157e16i | 0.609099 | + | 1.05499i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −7.51403e15 | −0.313242 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1.14065e16 | 0.470046 | 0.235023 | − | 0.971990i | \(-0.424484\pi\) | ||||
0.235023 | + | 0.971990i | \(0.424484\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.38998e16 | + | 5.87162e16i | 1.38095 | + | 2.39188i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −5.53107e14 | + | 9.58009e14i | −0.0222737 | + | 0.0385793i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.30978e14 | − | 1.54058e15i | 0.0211385 | − | 0.0613314i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 8.02989e15 | − | 1.39082e16i | 0.316032 | − | 0.547383i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.20594e15 | + | 1.07490e16i | 0.241470 | + | 0.418238i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.25462e16 | −0.867309 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.90477e16 | −0.724429 | −0.362215 | − | 0.932095i | \(-0.617979\pi\) | ||||
−0.362215 | + | 0.932095i | \(0.617979\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.57872e16 | + | 2.73443e16i | 0.593642 | + | 1.02822i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.73660e16 | − | 3.00788e16i | 0.645646 | − | 1.11829i | −0.338506 | − | 0.940964i | \(-0.609921\pi\) |
0.984152 | − | 0.177328i | \(-0.0567453\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.12050e16 | − | 2.44082e16i | −0.779502 | − | 0.897253i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.73743e15 | + | 1.51337e16i | −0.317584 | + | 0.550071i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8.05853e15 | − | 1.39578e16i | −0.289625 | − | 0.501645i | 0.684095 | − | 0.729393i | \(-0.260197\pi\) |
−0.973720 | + | 0.227748i | \(0.926864\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.39950e15 | −0.0497356 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 5.39940e15 | 0.189743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7.46353e15 | − | 1.29272e16i | −0.259358 | − | 0.449222i | 0.706712 | − | 0.707501i | \(-0.250178\pi\) |
−0.966070 | + | 0.258280i | \(0.916844\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.24703e16 | − | 2.15991e16i | 0.428525 | − | 0.742227i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.99075e15 | + | 6.89571e15i | 0.203581 | + | 0.234334i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.67269e16 | − | 6.36129e16i | 1.23426 | − | 2.13779i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.12354e16 | − | 1.94603e16i | −0.373408 | − | 0.646762i | 0.616679 | − | 0.787215i | \(-0.288478\pi\) |
−0.990087 | + | 0.140452i | \(0.955144\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.04871e15 | 0.297417 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.13538e16 | 0.369076 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.44345e16 | + | 2.50012e16i | 0.464064 | + | 0.803782i | 0.999159 | − | 0.0410101i | \(-0.0130576\pi\) |
−0.535095 | + | 0.844792i | \(0.679724\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1.02465e15 | + | 1.77475e15i | −0.0325812 | + | 0.0564322i |
(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 | 84.12.i.b.37.7 | yes | 16 | |
3.2 | odd | 2 | 252.12.k.d.37.2 | 16 | |||
7.4 | even | 3 | inner | 84.12.i.b.25.7 | ✓ | 16 | |
21.11 | odd | 6 | 252.12.k.d.109.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
84.12.i.b.25.7 | ✓ | 16 | 7.4 | even | 3 | inner | |
84.12.i.b.37.7 | yes | 16 | 1.1 | even | 1 | trivial | |
252.12.k.d.37.2 | 16 | 3.2 | odd | 2 | |||
252.12.k.d.109.2 | 16 | 21.11 | odd | 6 |