Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [126,9,Mod(19,126)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(126, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("126.19");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 126 = 2 \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 126.n (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(51.3297048677\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 8 x^{19} - 26382 x^{18} + 177344 x^{17} + 298653216 x^{16} - 1823810808 x^{15} - 1891249463672 x^{14} + 11806020599312 x^{13} + \cdots + 42\!\cdots\!32 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{18}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 73.8 | ||
Root | \(4.08415 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 126.73 |
Dual form | 126.9.n.d.19.8 |
$q$-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 \(\left(\mathbb{Z}/126\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.65685 | + | 9.79796i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −64.0000 | + | 110.851i | −0.250000 | + | 0.433013i | ||||
\(5\) | 254.021 | − | 146.659i | 0.406434 | − | 0.234655i | −0.282822 | − | 0.959172i | \(-0.591271\pi\) |
0.689256 | + | 0.724517i | \(0.257937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1180.12 | + | 2090.96i | −0.491511 | + | 0.870871i | ||||
\(8\) | −1448.15 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2873.92 | + | 1659.26i | 0.287392 | + | 0.165926i | ||||
\(11\) | −9846.02 | + | 17053.8i | −0.672496 | + | 1.16480i | 0.304698 | + | 0.952449i | \(0.401445\pi\) |
−0.977194 | + | 0.212348i | \(0.931889\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 27364.3i | − | 0.958101i | −0.877787 | − | 0.479050i | \(-0.840981\pi\) | ||
0.877787 | − | 0.479050i | \(-0.159019\pi\) | |||||||
\(14\) | −27162.9 | + | 265.506i | −0.707073 | + | 0.00691135i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8192.00 | − | 14189.0i | −0.125000 | − | 0.216506i | ||||
\(17\) | 41400.9 | + | 23902.8i | 0.495694 | + | 0.286189i | 0.726934 | − | 0.686708i | \(-0.240945\pi\) |
−0.231239 | + | 0.972897i | \(0.574278\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 72270.1 | − | 41725.2i | 0.554555 | − | 0.320172i | −0.196402 | − | 0.980523i | \(-0.562926\pi\) |
0.750957 | + | 0.660351i | \(0.229593\pi\) | |||||||
\(20\) | 37544.8i | 0.234655i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −222790. | −0.951053 | ||||||||
\(23\) | −64660.1 | − | 111995.i | −0.231060 | − | 0.400208i | 0.727060 | − | 0.686574i | \(-0.240886\pi\) |
−0.958120 | + | 0.286366i | \(0.907553\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −152295. | + | 263782.i | −0.389874 | + | 0.675282i | ||||
\(26\) | 268114. | − | 154796.i | 0.586714 | − | 0.338740i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −156258. | − | 264639.i | −0.254220 | − | 0.430548i | ||||
\(29\) | −710274. | −1.00423 | −0.502116 | − | 0.864800i | \(-0.667445\pi\) | ||||
−0.502116 | + | 0.864800i | \(0.667445\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −384515. | − | 222000.i | −0.416358 | − | 0.240384i | 0.277160 | − | 0.960824i | \(-0.410607\pi\) |
−0.693518 | + | 0.720440i | \(0.743940\pi\) | |||||||
\(32\) | 92681.9 | − | 160530.i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 540859.i | 0.404733i | ||||||||
\(35\) | 6883.50 | + | 704224.i | 0.00458709 | + | 0.469287i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 176834. | + | 306285.i | 0.0943537 | + | 0.163425i | 0.909339 | − | 0.416057i | \(-0.136588\pi\) |
−0.814985 | + | 0.579482i | \(0.803255\pi\) | |||||||
\(38\) | 817643. | + | 472066.i | 0.392129 | + | 0.226396i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −367862. | + | 212385.i | −0.143696 | + | 0.0829630i | ||||
\(41\) | − | 3.55628e6i | − | 1.25852i | −0.777195 | − | 0.629260i | \(-0.783358\pi\) | ||
0.777195 | − | 0.629260i | \(-0.216642\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.52843e6 | −1.90957 | −0.954784 | − | 0.297300i | \(-0.903914\pi\) | ||||
−0.954784 | + | 0.297300i | \(0.903914\pi\) | |||||||
\(44\) | −1.26029e6 | − | 2.18289e6i | −0.336248 | − | 0.582399i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 731546. | − | 1.26707e6i | 0.163384 | − | 0.282990i | ||||
\(47\) | −965165. | + | 557238.i | −0.197793 | + | 0.114196i | −0.595625 | − | 0.803262i | \(-0.703096\pi\) |
0.397833 | + | 0.917458i | \(0.369762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.97944e6 | − | 4.93517e6i | −0.516833 | − | 0.856086i | ||||
\(50\) | −3.44603e6 | −0.551365 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.03337e6 | + | 1.75132e6i | 0.414870 | + | 0.239525i | ||||
\(53\) | 5.98041e6 | − | 1.03584e7i | 0.757927 | − | 1.31277i | −0.185978 | − | 0.982554i | \(-0.559545\pi\) |
0.943906 | − | 0.330215i | \(-0.107121\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.77604e6i | 0.631218i | ||||||||
\(56\) | 1.70899e6 | − | 3.02804e6i | 0.173776 | − | 0.307899i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.01792e6 | − | 6.95924e6i | −0.355050 | − | 0.614964i | ||||
\(59\) | −1.01480e7 | − | 5.85894e6i | −0.837474 | − | 0.483516i | 0.0189306 | − | 0.999821i | \(-0.493974\pi\) |
−0.856405 | + | 0.516305i | \(0.827307\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.13956e7 | − | 6.57926e6i | 0.823035 | − | 0.475180i | −0.0284268 | − | 0.999596i | \(-0.509050\pi\) |
0.851462 | + | 0.524416i | \(0.175716\pi\) | |||||||
\(62\) | − | 5.02328e6i | − | 0.339955i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.09715e6 | 0.125000 | ||||||||
\(65\) | −4.01323e6 | − | 6.95112e6i | −0.224823 | − | 0.389405i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.88693e6 | + | 1.36606e7i | −0.391389 | + | 0.677906i | −0.992633 | − | 0.121160i | \(-0.961339\pi\) |
0.601244 | + | 0.799066i | \(0.294672\pi\) | |||||||
\(68\) | −5.29931e6 | + | 3.05956e6i | −0.247847 | + | 0.143095i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −6.86102e6 | + | 4.05114e6i | −0.285757 | + | 0.168727i | ||||
\(71\) | −2.41198e7 | −0.949161 | −0.474580 | − | 0.880212i | \(-0.657400\pi\) | ||||
−0.474580 | + | 0.880212i | \(0.657400\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.51799e7 | + | 8.76413e6i | 0.534537 | + | 0.308615i | 0.742862 | − | 0.669445i | \(-0.233468\pi\) |
−0.208325 | + | 0.978060i | \(0.566801\pi\) | |||||||
\(74\) | −2.00065e6 | + | 3.46522e6i | −0.0667181 | + | 0.115559i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.06816e7i | 0.320172i | ||||||||
\(77\) | −2.40394e7 | − | 4.07132e7i | −0.683849 | − | 1.15817i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.57217e6 | + | 6.18718e6i | 0.0917115 | + | 0.158849i | 0.908231 | − | 0.418468i | \(-0.137433\pi\) |
−0.816520 | + | 0.577317i | \(0.804100\pi\) | |||||||
\(80\) | −4.16188e6 | − | 2.40287e6i | −0.101609 | − | 0.0586637i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.48443e7 | − | 2.01173e7i | 0.770683 | − | 0.444954i | ||||
\(83\) | − | 6.34086e7i | − | 1.33609i | −0.744121 | − | 0.668045i | \(-0.767131\pi\) | ||
0.744121 | − | 0.668045i | \(-0.232869\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.40223e7 | 0.268623 | ||||||||
\(86\) | −3.69304e7 | − | 6.39653e7i | −0.675134 | − | 1.16937i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.42586e7 | − | 2.46965e7i | 0.237763 | − | 0.411818i | ||||
\(89\) | 7.67936e7 | − | 4.43368e7i | 1.22395 | − | 0.706650i | 0.258195 | − | 0.966093i | \(-0.416872\pi\) |
0.965758 | + | 0.259443i | \(0.0835391\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.72177e7 | + | 3.22931e7i | 0.834382 | + | 0.470917i | ||||
\(92\) | 1.65530e7 | 0.231060 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.09196e7 | − | 6.30443e6i | −0.139861 | − | 0.0807485i | ||||
\(95\) | 1.22388e7 | − | 2.11982e7i | 0.150260 | − | 0.260258i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.52152e7i | − | 0.736651i | −0.929697 | − | 0.368325i | \(-0.879931\pi\) | ||
0.929697 | − | 0.368325i | \(-0.120069\pi\) | |||||||
\(98\) | 3.15003e7 | − | 5.71099e7i | 0.341516 | − | 0.619166i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.94937e7 | − | 3.37641e7i | −0.194937 | − | 0.337641i | ||||
\(101\) | −1.53138e8 | − | 8.84145e7i | −1.47163 | − | 0.849646i | −0.472138 | − | 0.881525i | \(-0.656518\pi\) |
−0.999492 | + | 0.0318791i | \(0.989851\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.89388e7 | + | 5.71223e7i | −0.879059 | + | 0.507525i | −0.870348 | − | 0.492437i | \(-0.836106\pi\) |
−0.00871065 | + | 0.999962i | \(0.502773\pi\) | |||||||
\(104\) | 3.96278e7i | 0.338740i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.35321e8 | 1.07187 | ||||||||
\(107\) | −7.14037e6 | − | 1.23675e7i | −0.0544736 | − | 0.0943510i | 0.837503 | − | 0.546433i | \(-0.184015\pi\) |
−0.891976 | + | 0.452082i | \(0.850681\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.01815e8 | + | 1.76349e8i | −0.721283 | + | 1.24930i | 0.239203 | + | 0.970970i | \(0.423114\pi\) |
−0.960486 | + | 0.278329i | \(0.910220\pi\) | |||||||
\(110\) | −5.65934e7 | + | 3.26742e7i | −0.386540 | + | 0.223169i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.93361e7 | − | 384494.i | 0.249988 | − | 0.00244353i | ||||
\(113\) | −8.03050e7 | −0.492525 | −0.246263 | − | 0.969203i | \(-0.579203\pi\) | ||||
−0.246263 | + | 0.969203i | \(0.579203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.28501e7 | − | 1.89660e7i | −0.187822 | − | 0.108439i | ||||
\(116\) | 4.54576e7 | − | 7.87348e7i | 0.251058 | − | 0.434845i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 1.32573e8i | − | 0.683795i | ||||||
\(119\) | −9.88378e7 | + | 5.83595e7i | −0.492873 | + | 0.291020i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.67086e7 | − | 1.50184e8i | −0.404502 | − | 0.700618i | ||||
\(122\) | 1.28927e8 | + | 7.44358e7i | 0.581974 | + | 0.336003i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.92179e7 | − | 2.84160e7i | 0.208179 | − | 0.120192i | ||||
\(125\) | 2.03919e8i | 0.835253i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.26436e8 | −1.25483 | −0.627413 | − | 0.778687i | \(-0.715886\pi\) | ||||
−0.627413 | + | 0.778687i | \(0.715886\pi\) | |||||||
\(128\) | 1.18633e7 | + | 2.05478e7i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.54045e7 | − | 7.86429e7i | 0.158974 | − | 0.275351i | ||||
\(131\) | 1.32553e8 | − | 7.65293e7i | 0.450094 | − | 0.259862i | −0.257776 | − | 0.966205i | \(-0.582990\pi\) |
0.707870 | + | 0.706343i | \(0.249656\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.95839e6 | + | 2.00355e8i | 0.00625881 | + | 0.640314i | ||||
\(134\) | −1.78461e8 | −0.553508 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.99549e7 | − | 3.46150e7i | −0.175254 | − | 0.101183i | ||||
\(137\) | 6.64691e7 | − | 1.15128e8i | 0.188685 | − | 0.326812i | −0.756127 | − | 0.654425i | \(-0.772911\pi\) |
0.944812 | + | 0.327613i | \(0.106244\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.38269e8i | 1.44192i | 0.692978 | + | 0.720958i | \(0.256298\pi\) | ||||
−0.692978 | + | 0.720958i | \(0.743702\pi\) | |||||||
\(140\) | −7.85047e7 | − | 4.43073e7i | −0.204354 | − | 0.115336i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.36442e8 | − | 2.36325e8i | −0.335579 | − | 0.581240i | ||||
\(143\) | 4.66666e8 | + | 2.69429e8i | 1.11599 | + | 0.644319i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.80425e8 | + | 1.04168e8i | −0.408154 | + | 0.235648i | ||||
\(146\) | 1.98310e8i | 0.436448i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.52695e7 | −0.0943537 | ||||||||
\(149\) | 2.76227e8 | + | 4.78439e8i | 0.560429 | + | 0.970691i | 0.997459 | + | 0.0712445i | \(0.0226971\pi\) |
−0.437030 | + | 0.899447i | \(0.643970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.57729e7 | + | 4.46400e7i | −0.0495742 | + | 0.0858650i | −0.889748 | − | 0.456453i | \(-0.849120\pi\) |
0.840173 | + | 0.542318i | \(0.182453\pi\) | |||||||
\(152\) | −1.04658e8 | + | 6.04245e7i | −0.196065 | + | 0.113198i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 2.62919e8 | − | 4.65845e8i | 0.467454 | − | 0.828245i | ||||
\(155\) | −1.30233e8 | −0.225629 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.43245e8 | − | 8.27027e7i | −0.235766 | − | 0.136120i | 0.377463 | − | 0.926025i | \(-0.376796\pi\) |
−0.613229 | + | 0.789905i | \(0.710130\pi\) | |||||||
\(158\) | −4.04145e7 | + | 6.99999e7i | −0.0648498 | + | 0.112323i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 5.43706e7i | − | 0.0829630i | ||||||
\(161\) | 3.10483e8 | − | 3.03485e6i | 0.462098 | − | 0.00451682i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.57420e7 | + | 1.13868e8i | 0.0931306 | + | 0.161307i | 0.908827 | − | 0.417174i | \(-0.136979\pi\) |
−0.815696 | + | 0.578480i | \(0.803646\pi\) | |||||||
\(164\) | 3.94218e8 | + | 2.27602e8i | 0.544955 | + | 0.314630i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.21275e8 | − | 3.58693e8i | 0.818184 | − | 0.472379i | ||||
\(167\) | 1.02034e9i | 1.31184i | 0.754832 | + | 0.655918i | \(0.227718\pi\) | ||||
−0.754832 | + | 0.655918i | \(0.772282\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.69250e7 | 0.0820430 | ||||||||
\(170\) | 7.93219e7 | + | 1.37390e8i | 0.0949725 | + | 0.164497i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.17820e8 | − | 7.23685e8i | 0.477392 | − | 0.826867i | ||||
\(173\) | 1.16632e8 | − | 6.73374e7i | 0.130206 | − | 0.0751747i | −0.433482 | − | 0.901162i | \(-0.642715\pi\) |
0.563688 | + | 0.825988i | \(0.309382\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.71832e8 | − | 6.29736e8i | −0.396456 | − | 0.671439i | ||||
\(176\) | 3.22634e8 | 0.336248 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.68820e8 | + | 5.01613e8i | 0.865465 | + | 0.499677i | ||||
\(179\) | −6.71392e8 | + | 1.16289e9i | −0.653979 | + | 1.13273i | 0.328169 | + | 0.944619i | \(0.393568\pi\) |
−0.982149 | + | 0.188107i | \(0.939765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.66215e9i | 1.54866i | 0.632784 | + | 0.774328i | \(0.281912\pi\) | ||||
−0.632784 | + | 0.774328i | \(0.718088\pi\) | |||||||
\(182\) | 7.26540e6 | + | 7.43295e8i | 0.00662177 | + | 0.677447i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 9.36379e7 | + | 1.62186e8i | 0.0816921 | + | 0.141495i | ||||
\(185\) | 8.98392e7 | + | 5.18687e7i | 0.0766971 | + | 0.0442811i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.15267e8 | + | 4.70695e8i | −0.666705 | + | 0.384922i | ||||
\(188\) | − | 1.42653e8i | − | 0.114196i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.76932e8 | 0.212500 | ||||||||
\(191\) | 4.00858e8 | + | 6.94306e8i | 0.301201 | + | 0.521696i | 0.976408 | − | 0.215932i | \(-0.0692790\pi\) |
−0.675207 | + | 0.737628i | \(0.735946\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.88128e8 | + | 1.01867e9i | −0.423879 | + | 0.734181i | −0.996315 | − | 0.0857690i | \(-0.972665\pi\) |
0.572436 | + | 0.819950i | \(0.305999\pi\) | |||||||
\(194\) | 6.38976e8 | − | 3.68913e8i | 0.451105 | − | 0.260445i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.37754e8 | − | 1.44239e7i | 0.499904 | − | 0.00977366i | ||||
\(197\) | 3.83159e8 | 0.254398 | 0.127199 | − | 0.991877i | \(-0.459401\pi\) | ||||
0.127199 | + | 0.991877i | \(0.459401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.90479e9 | + | 1.09973e9i | 1.21460 | + | 0.701252i | 0.963759 | − | 0.266775i | \(-0.0859580\pi\) |
0.250846 | + | 0.968027i | \(0.419291\pi\) | |||||||
\(200\) | 2.20546e8 | − | 3.81997e8i | 0.137841 | − | 0.238748i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 2.00059e9i | − | 1.20158i | ||||||
\(203\) | 8.38208e8 | − | 1.48516e9i | 0.493592 | − | 0.874557i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.21561e8 | − | 9.03370e8i | −0.295318 | − | 0.511506i | ||||
\(206\) | −1.11936e9 | − | 6.46266e8i | −0.621588 | − | 0.358874i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.88271e8 | + | 2.24168e8i | −0.207435 | + | 0.119763i | ||||
\(209\) | 1.64331e9i | 0.861258i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.01623e8 | 0.404427 | 0.202213 | − | 0.979341i | \(-0.435187\pi\) | ||||
0.202213 | + | 0.979341i | \(0.435187\pi\) | |||||||
\(212\) | 7.65493e8 | + | 1.32587e9i | 0.378964 | + | 0.656384i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 8.07841e7 | − | 1.39922e8i | 0.0385186 | − | 0.0667162i | ||||
\(215\) | −1.65836e9 | + | 9.57455e8i | −0.776114 | + | 0.448089i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.17967e8 | − | 5.42020e8i | 0.413988 | − | 0.244442i | ||||
\(218\) | −2.30381e9 | −1.02005 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.40281e8 | − | 3.69666e8i | −0.273325 | − | 0.157804i | ||||
\(221\) | 6.54084e8 | − | 1.13291e9i | 0.274198 | − | 0.474925i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 1.04630e9i | − | 0.423095i | −0.977368 | − | 0.211548i | \(-0.932150\pi\) | ||
0.977368 | − | 0.211548i | \(-0.0678503\pi\) | |||||||
\(224\) | 2.26286e8 | + | 3.83239e8i | 0.0898805 | + | 0.152222i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.54273e8 | − | 7.86825e8i | −0.174134 | − | 0.301609i | ||||
\(227\) | −1.84193e9 | − | 1.06344e9i | −0.693697 | − | 0.400506i | 0.111299 | − | 0.993787i | \(-0.464499\pi\) |
−0.804996 | + | 0.593281i | \(0.797832\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.04718e9 | + | 2.33664e9i | −1.47167 | + | 0.849670i | −0.999493 | − | 0.0318328i | \(-0.989866\pi\) |
−0.472179 | + | 0.881503i | \(0.656532\pi\) | |||||||
\(230\) | − | 4.29152e8i | − | 0.153356i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.02859e9 | 0.355050 | ||||||||
\(233\) | −1.30399e9 | − | 2.25857e9i | −0.442435 | − | 0.766320i | 0.555435 | − | 0.831560i | \(-0.312552\pi\) |
−0.997870 | + | 0.0652405i | \(0.979219\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.63448e8 | + | 2.83101e8i | −0.0535931 | + | 0.0928260i | ||||
\(236\) | 1.29894e9 | − | 7.49944e8i | 0.418737 | − | 0.241758i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.13091e9 | − | 6.38278e8i | −0.352470 | − | 0.198931i | ||||
\(239\) | 2.50883e9 | 0.768917 | 0.384459 | − | 0.923142i | \(-0.374388\pi\) | ||||
0.384459 | + | 0.923142i | \(0.374388\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.39883e9 | − | 8.07613e8i | −0.414664 | − | 0.239406i | 0.278128 | − | 0.960544i | \(-0.410286\pi\) |
−0.692792 | + | 0.721138i | \(0.743619\pi\) | |||||||
\(242\) | 9.80996e8 | − | 1.69914e9i | 0.286026 | − | 0.495412i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.68429e9i | 0.475180i | ||||||||
\(245\) | −1.48063e9 | − | 8.16675e8i | −0.410943 | − | 0.226665i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.14178e9 | − | 1.97762e9i | −0.306757 | − | 0.531319i | ||||
\(248\) | 5.56837e8 | + | 3.21490e8i | 0.147205 | + | 0.0849887i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.99799e9 | + | 1.15354e9i | −0.511486 | + | 0.295307i | ||||
\(251\) | − | 7.67075e9i | − | 1.93260i | −0.257411 | − | 0.966302i | \(-0.582869\pi\) | ||
0.257411 | − | 0.966302i | \(-0.417131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.54658e9 | 0.621549 | ||||||||
\(254\) | −1.84660e9 | − | 3.19841e9i | −0.443648 | − | 0.768421i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.34218e8 | + | 2.32472e8i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 9.62997e7 | − | 5.55987e7i | 0.0220746 | − | 0.0127448i | −0.488922 | − | 0.872327i | \(-0.662610\pi\) |
0.510997 | + | 0.859583i | \(0.329276\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −8.49116e8 | + | 8.29976e6i | −0.188698 | + | 0.00184445i | ||||
\(260\) | 1.02739e9 | 0.224823 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.49966e9 | + | 8.65830e8i | 0.318264 | + | 0.183750i | ||||
\(263\) | 1.92395e9 | − | 3.33238e9i | 0.402135 | − | 0.696518i | −0.591849 | − | 0.806049i | \(-0.701602\pi\) |
0.993983 | + | 0.109532i | \(0.0349351\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 3.50833e9i | − | 0.711405i | ||||||
\(266\) | −1.95199e9 | + | 1.15257e9i | −0.389898 | + | 0.230218i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.00953e9 | − | 1.74855e9i | −0.195695 | − | 0.338953i | ||||
\(269\) | −3.56338e9 | − | 2.05732e9i | −0.680539 | − | 0.392909i | 0.119519 | − | 0.992832i | \(-0.461865\pi\) |
−0.800058 | + | 0.599922i | \(0.795198\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.46088e9 | + | 3.15284e9i | −1.01248 | + | 0.584554i | −0.911916 | − | 0.410377i | \(-0.865397\pi\) |
−0.100561 | + | 0.994931i | \(0.532064\pi\) | |||||||
\(272\) | − | 7.83247e8i | − | 0.143095i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.50402e9 | 0.266841 | ||||||||
\(275\) | −2.99899e9 | − | 5.19440e9i | −0.524378 | − | 0.908249i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.46807e7 | − | 1.46671e8i | 0.0143835 | − | 0.0249130i | −0.858744 | − | 0.512405i | \(-0.828755\pi\) |
0.873128 | + | 0.487492i | \(0.162088\pi\) | |||||||
\(278\) | −5.27394e9 | + | 3.04491e9i | −0.882990 | + | 0.509795i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −9.96838e6 | − | 1.01983e9i | −0.00162178 | − | 0.165918i | ||||
\(281\) | −4.27204e9 | −0.685188 | −0.342594 | − | 0.939484i | \(-0.611306\pi\) | ||||
−0.342594 | + | 0.939484i | \(0.611306\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.97705e9 | + | 4.60555e9i | 1.24364 | + | 0.718019i | 0.969834 | − | 0.243765i | \(-0.0783825\pi\) |
0.273811 | + | 0.961784i | \(0.411716\pi\) | |||||||
\(284\) | 1.54367e9 | − | 2.67371e9i | 0.237290 | − | 0.410999i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.09649e9i | 0.911205i | ||||||||
\(287\) | 7.43604e9 | + | 4.19683e9i | 1.09601 | + | 0.618577i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.34519e9 | − | 4.06199e9i | −0.336191 | − | 0.582301i | ||||
\(290\) | −2.04127e9 | − | 1.17853e9i | −0.288609 | − | 0.166628i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.94303e9 | + | 1.12181e9i | −0.267269 | + | 0.154308i | ||||
\(293\) | 6.22459e9i | 0.844578i | 0.906461 | + | 0.422289i | \(0.138773\pi\) | ||||
−0.906461 | + | 0.422289i | \(0.861227\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.43707e9 | −0.453837 | ||||||||
\(296\) | −2.56083e8 | − | 4.43549e8i | −0.0333591 | − | 0.0577796i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.12515e9 | + | 5.41292e9i | −0.396283 | + | 0.686383i | ||||
\(299\) | −3.06466e9 | + | 1.76938e9i | −0.383440 | + | 0.221379i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 7.70433e9 | − | 1.36507e10i | 0.938575 | − | 1.66299i | ||||
\(302\) | −5.83174e8 | −0.0701085 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.18407e9 | − | 6.83625e8i | −0.138639 | − | 0.0800431i | ||||
\(305\) | 1.92982e9 | − | 3.34254e9i | 0.223006 | − | 0.386258i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9.75323e9i | 1.09798i | 0.835829 | + | 0.548991i | \(0.184988\pi\) | ||||
−0.835829 | + | 0.548991i | \(0.815012\pi\) | |||||||
\(308\) | 6.05162e9 | − | 5.91522e7i | 0.672464 | − | 0.00657306i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.36711e8 | − | 1.27602e9i | −0.0797720 | − | 0.138169i | ||||
\(311\) | −1.41768e10 | − | 8.18496e9i | −1.51543 | − | 0.874933i | −0.999836 | − | 0.0180989i | \(-0.994239\pi\) |
−0.515592 | − | 0.856834i | \(-0.672428\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.41041e10 | − | 8.14301e9i | 1.46950 | − | 0.848414i | 0.470081 | − | 0.882623i | \(-0.344225\pi\) |
0.999415 | + | 0.0342090i | \(0.0108912\pi\) | |||||||
\(314\) | − | 1.87135e9i | − | 0.192502i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.14475e8 | −0.0917115 | ||||||||
\(317\) | 5.18198e9 | + | 8.97545e9i | 0.513167 | + | 0.888831i | 0.999883 | + | 0.0152710i | \(0.00486110\pi\) |
−0.486717 | + | 0.873560i | \(0.661806\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.99337e9 | − | 1.21129e10i | 0.675342 | − | 1.16973i | ||||
\(320\) | 5.32721e8 | − | 3.07567e8i | 0.0508043 | − | 0.0293319i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.78609e9 | + | 3.02493e9i | 0.166142 | + | 0.281379i | ||||
\(323\) | 3.98939e9 | 0.366519 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.21821e9 | + | 4.16744e9i | 0.646988 | + | 0.373539i | ||||
\(326\) | −7.43785e8 | + | 1.28827e9i | −0.0658533 | + | 0.114061i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.15004e9i | 0.444954i | ||||||||
\(329\) | −2.61542e7 | − | 2.67573e9i | −0.00223233 | − | 0.228380i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.08132e9 | − | 1.87289e9i | −0.0900825 | − | 0.156027i | 0.817463 | − | 0.575981i | \(-0.195380\pi\) |
−0.907546 | + | 0.419953i | \(0.862046\pi\) | |||||||
\(332\) | 7.02892e9 | + | 4.05815e9i | 0.578544 | + | 0.334022i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −9.99726e9 | + | 5.77192e9i | −0.803332 | + | 0.463804i | ||||
\(335\) | 4.62677e9i | 0.367365i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.73513e9 | 0.134528 | 0.0672640 | − | 0.997735i | \(-0.478573\pi\) | ||||
0.0672640 | + | 0.997735i | \(0.478573\pi\) | |||||||
\(338\) | 3.78585e8 | + | 6.55729e8i | 0.0290066 | + | 0.0502409i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −8.97425e8 | + | 1.55439e9i | −0.0671557 | + | 0.116317i | ||||
\(341\) | 7.57188e9 | − | 4.37163e9i | 0.559998 | − | 0.323315i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.38353e10 | − | 4.05808e8i | 0.999570 | − | 0.0293186i | ||||
\(344\) | 9.45418e9 | 0.675134 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.31954e9 | + | 7.61836e8i | 0.0920699 | + | 0.0531566i | ||||
\(347\) | −4.70131e8 | + | 8.14291e8i | −0.0324266 | + | 0.0561645i | −0.881783 | − | 0.471655i | \(-0.843657\pi\) |
0.849357 | + | 0.527819i | \(0.176990\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.33733e9i | − | 0.0901437i | −0.998984 | − | 0.0450719i | \(-0.985648\pi\) | ||
0.998984 | − | 0.0450719i | \(-0.0143517\pi\) | |||||||
\(350\) | 4.06673e9 | − | 7.20552e9i | 0.271002 | − | 0.480168i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.82509e9 | + | 3.16116e9i | 0.118882 | + | 0.205909i | ||||
\(353\) | −1.04605e9 | − | 6.03937e8i | −0.0673679 | − | 0.0388949i | 0.465938 | − | 0.884818i | \(-0.345717\pi\) |
−0.533306 | + | 0.845923i | \(0.679050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.12694e9 | + | 3.53739e9i | −0.385771 | + | 0.222725i | ||||
\(356\) | 1.13502e10i | 0.706650i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.51919e10 | −0.924866 | ||||||||
\(359\) | 1.58025e10 | + | 2.73707e10i | 0.951366 | + | 1.64781i | 0.742473 | + | 0.669876i | \(0.233653\pi\) |
0.208893 | + | 0.977939i | \(0.433014\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00980e9 | + | 8.67723e9i | −0.294979 | + | 0.510919i | ||||
\(362\) | −1.62857e10 | + | 9.40253e9i | −0.948355 | + | 0.547533i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.24167e9 | + | 4.27590e9i | −0.412509 | + | 0.243569i | ||||
\(365\) | 5.14136e9 | 0.289672 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.60965e8 | + | 1.50668e8i | 0.0143853 | + | 0.00830533i | 0.507175 | − | 0.861843i | \(-0.330690\pi\) |
−0.492790 | + | 0.870148i | \(0.664023\pi\) | |||||||
\(368\) | −1.05939e9 | + | 1.83492e9i | −0.0577651 | + | 0.100052i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.17365e9i | 0.0626229i | ||||||||
\(371\) | 1.46014e10 | + | 2.47289e10i | 0.770722 | + | 1.30530i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.65408e10 | − | 2.86496e10i | −0.854520 | − | 1.48007i | −0.877090 | − | 0.480327i | \(-0.840518\pi\) |
0.0225698 | − | 0.999745i | \(-0.492815\pi\) | |||||||
\(374\) | −9.22370e9 | − | 5.32530e9i | −0.471432 | − | 0.272181i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.39771e9 | − | 8.06967e8i | 0.0699303 | − | 0.0403743i | ||||
\(377\) | 1.94362e10i | 0.962156i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.26256e10 | 1.09659 | 0.548294 | − | 0.836285i | \(-0.315277\pi\) | ||||
0.548294 | + | 0.836285i | \(0.315277\pi\) | |||||||
\(380\) | 1.56656e9 | + | 2.71336e9i | 0.0751300 | + | 0.130129i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.53519e9 | + | 7.85518e9i | −0.212981 | + | 0.368895i | ||||
\(383\) | −2.09715e10 | + | 1.21079e10i | −0.974616 | + | 0.562695i | −0.900640 | − | 0.434565i | \(-0.856902\pi\) |
−0.0739756 | + | 0.997260i | \(0.523569\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.20775e10 | − | 6.81641e9i | −0.549709 | − | 0.310251i | ||||
\(386\) | −1.33078e10 | −0.599456 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.22918e9 | + | 4.17377e9i | 0.318979 | + | 0.184163i | ||||
\(389\) | 5.38937e9 | − | 9.33466e9i | 0.235364 | − | 0.407662i | −0.724015 | − | 0.689785i | \(-0.757705\pi\) |
0.959378 | + | 0.282123i | \(0.0910385\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.18224e9i | − | 0.264508i | ||||||
\(392\) | 4.31469e9 | + | 7.14689e9i | 0.182728 | + | 0.302672i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.16747e9 | + | 3.75417e9i | 0.0899433 | + | 0.155786i | ||||
\(395\) | 1.81481e9 | + | 1.04778e9i | 0.0745493 | + | 0.0430411i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.11612e10 | + | 6.44391e9i | −0.449312 | + | 0.259410i | −0.707540 | − | 0.706674i | \(-0.750195\pi\) |
0.258228 | + | 0.966084i | \(0.416862\pi\) | |||||||
\(398\) | 2.48841e10i | 0.991721i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.99039e9 | 0.194937 | ||||||||
\(401\) | 3.32886e9 | + | 5.76576e9i | 0.128742 | + | 0.222987i | 0.923189 | − | 0.384346i | \(-0.125573\pi\) |
−0.794448 | + | 0.607333i | \(0.792240\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.07487e9 | + | 1.05220e10i | −0.230312 | + | 0.398913i | ||||
\(404\) | 1.96017e10 | − | 1.13171e10i | 0.735815 | − | 0.424823i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.92931e10 | − | 1.88582e8i | 0.710065 | − | 0.00694060i | ||||
\(407\) | −6.96444e9 | −0.253810 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.21707e10 | − | 1.85737e10i | −1.14965 | − | 0.663752i | −0.200850 | − | 0.979622i | \(-0.564370\pi\) |
−0.948803 | + | 0.315870i | \(0.897704\pi\) | |||||||
\(410\) | 5.90079e9 | − | 1.02205e10i | 0.208821 | − | 0.361689i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 1.46233e10i | − | 0.507525i | ||||||
\(413\) | 2.42266e10 | − | 1.43048e10i | 0.832708 | − | 0.491679i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.29945e9 | − | 1.61071e10i | −0.313520 | − | 0.543032i | ||||
\(416\) | −4.39279e9 | − | 2.53618e9i | −0.146679 | − | 0.0846849i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.61011e10 | + | 9.29595e9i | −0.527411 | + | 0.304501i | ||||
\(419\) | 3.13974e10i | 1.01868i | 0.860566 | + | 0.509339i | \(0.170110\pi\) | ||||
−0.860566 | + | 0.509339i | \(0.829890\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.64445e8 | 0.0307008 | 0.0153504 | − | 0.999882i | \(-0.495114\pi\) | ||||
0.0153504 | + | 0.999882i | \(0.495114\pi\) | |||||||
\(422\) | 4.53466e9 | + | 7.85426e9i | 0.142987 | + | 0.247660i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.66056e9 | + | 1.50005e10i | −0.267968 | + | 0.464134i | ||||
\(425\) | −1.26103e10 | + | 7.28054e9i | −0.386517 | + | 0.223156i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.08800e8 | + | 3.15921e10i | 0.00928893 | + | 0.950314i | ||||
\(428\) | 1.82794e9 | 0.0544736 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.87622e10 | − | 1.08324e10i | −0.548795 | − | 0.316847i | ||||
\(431\) | 3.21242e10 | − | 5.56407e10i | 0.930943 | − | 1.61244i | 0.149230 | − | 0.988803i | \(-0.452321\pi\) |
0.781713 | − | 0.623638i | \(-0.214346\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.85656e9i | 0.138158i | 0.997611 | + | 0.0690792i | \(0.0220061\pi\) | ||||
−0.997611 | + | 0.0690792i | \(0.977994\pi\) | |||||||
\(434\) | 1.05035e10 | + | 5.92807e9i | 0.296057 | + | 0.167092i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.30323e10 | − | 2.25726e10i | −0.360641 | − | 0.624649i | ||||
\(437\) | −9.34599e9 | − | 5.39591e9i | −0.256271 | − | 0.147958i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.97737e10 | − | 1.14163e10i | 0.532389 | − | 0.307375i | −0.209600 | − | 0.977787i | \(-0.567216\pi\) |
0.741989 | + | 0.670412i | \(0.233883\pi\) | |||||||
\(440\) | − | 8.36460e9i | − | 0.223169i | ||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.48002e10 | 0.387775 | ||||||||
\(443\) | −1.83252e10 | − | 3.17402e10i | −0.475811 | − | 0.824129i | 0.523805 | − | 0.851838i | \(-0.324512\pi\) |
−0.999616 | + | 0.0277093i | \(0.991179\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.30048e10 | − | 2.25250e10i | 0.331637 | − | 0.574413i | ||||
\(446\) | 1.02516e10 | − | 5.91878e9i | 0.259092 | − | 0.149587i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.47489e9 | + | 4.38506e9i | −0.0614389 | + | 0.108859i | ||||
\(449\) | −7.21152e10 | −1.77436 | −0.887179 | − | 0.461425i | \(-0.847338\pi\) | ||||
−0.887179 | + | 0.461425i | \(0.847338\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.06480e10 | + | 3.50152e10i | 1.46592 | + | 0.846350i | ||||
\(452\) | 5.13952e9 | − | 8.90190e9i | 0.123131 | − | 0.213270i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 2.40629e10i | − | 0.566401i | ||||||
\(455\) | 1.92706e10 | − | 1.88362e8i | 0.449624 | − | 0.00439490i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00998e10 | + | 5.21344e10i | 0.690080 | + | 1.19525i | 0.971811 | + | 0.235760i | \(0.0757578\pi\) |
−0.281732 | + | 0.959493i | \(0.590909\pi\) | |||||||
\(458\) | −4.57887e10 | − | 2.64361e10i | −1.04063 | − | 0.600808i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.20481e9 | − | 2.42765e9i | 0.0939108 | − | 0.0542194i | ||||
\(461\) | 8.97724e10i | 1.98765i | 0.110972 | + | 0.993824i | \(0.464604\pi\) | ||||
−0.110972 | + | 0.993824i | \(0.535396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.64822e10 | −0.793883 | −0.396942 | − | 0.917844i | \(-0.629928\pi\) | ||||
−0.396942 | + | 0.917844i | \(0.629928\pi\) | |||||||
\(464\) | 5.81857e9 | + | 1.00781e10i | 0.125529 | + | 0.217423i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.47529e10 | − | 2.55528e10i | 0.312849 | − | 0.541870i | ||||
\(467\) | −7.40477e9 | + | 4.27515e9i | −0.155684 | + | 0.0898842i | −0.575818 | − | 0.817578i | \(-0.695316\pi\) |
0.420134 | + | 0.907462i | \(0.361983\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.92562e10 | − | 3.26124e10i | −0.397996 | − | 0.674048i | ||||
\(470\) | −3.69841e9 | −0.0757921 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.46958e10 | + | 8.48465e9i | 0.296092 | + | 0.170949i | ||||
\(473\) | 6.42791e10 | − | 1.11335e11i | 1.28418 | − | 2.22426i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.54181e10i | 0.499308i | ||||||||
\(476\) | −1.43602e8 | − | 1.46913e10i | −0.00279725 | − | 0.286176i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.41921e10 | + | 2.45814e10i | 0.271853 | + | 0.470864i | ||||
\(479\) | −7.84934e10 | − | 4.53182e10i | −1.49105 | − | 0.860856i | −0.491098 | − | 0.871104i | \(-0.663404\pi\) |
−0.999947 | + | 0.0102484i | \(0.996738\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.38129e9 | − | 4.83894e9i | 0.156578 | − | 0.0904003i | ||||
\(482\) | − | 1.82742e10i | − | 0.338571i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.21974e10 | 0.404502 | ||||||||
\(485\) | −9.56441e9 | − | 1.65660e10i | −0.172859 | − | 0.299400i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00698e10 | + | 3.47619e10i | −0.356802 | + | 0.617999i | −0.987425 | − | 0.158090i | \(-0.949466\pi\) |
0.630623 | + | 0.776090i | \(0.282800\pi\) | |||||||
\(488\) | −1.65026e10 | + | 9.52779e9i | −0.290987 | + | 0.168001i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.73952e8 | − | 1.91270e10i | −0.00648682 | − | 0.331789i | ||||
\(491\) | 3.33248e10 | 0.573379 | 0.286689 | − | 0.958024i | \(-0.407445\pi\) | ||||
0.286689 | + | 0.958024i | \(0.407445\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.94060e10 | − | 1.69775e10i | −0.497792 | − | 0.287400i | ||||
\(494\) | 1.29178e10 | − | 2.23742e10i | 0.216910 | − | 0.375699i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.27449e9i | 0.120192i | ||||||||
\(497\) | 2.84642e10 | − | 5.04335e10i | 0.466523 | − | 0.826597i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.21701e10 | + | 9.03612e10i | 0.841432 | + | 1.45740i | 0.888684 | + | 0.458520i | \(0.151620\pi\) |
−0.0472517 | + | 0.998883i | \(0.515046\pi\) | |||||||
\(500\) | −2.26047e10 | − | 1.30508e10i | −0.361675 | − | 0.208813i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 7.51577e10 | − | 4.33923e10i | 1.18347 | − | 0.683279i | ||||
\(503\) | − | 5.93676e10i | − | 0.927423i | −0.885986 | − | 0.463711i | \(-0.846517\pi\) | ||
0.885986 | − | 0.463711i | \(-0.153483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.18672e10 | −0.797494 | ||||||||
\(506\) | 1.44056e10 | + | 2.49513e10i | 0.219751 | + | 0.380619i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.08919e10 | − | 3.61859e10i | 0.313707 | − | 0.543356i | ||||
\(509\) | −2.93270e10 | + | 1.69319e10i | −0.436914 | + | 0.252253i | −0.702288 | − | 0.711893i | \(-0.747838\pi\) |
0.265374 | + | 0.964146i | \(0.414505\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.62396e10 | + | 2.13979e10i | −0.531495 | + | 0.313825i | ||||
\(512\) | −3.03700e9 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.08951e9 | + | 6.29027e8i | 0.0156091 | + | 0.00901191i | ||||
\(515\) | −1.67550e10 | + | 2.90206e10i | −0.238186 | + | 0.412551i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 2.19463e10i | − | 0.307184i | ||||||
\(518\) | −4.88465e9 | − | 8.27265e9i | −0.0678444 | − | 0.114902i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.81178e9 | + | 1.00663e10i | 0.0794869 | + | 0.137675i | ||||
\(521\) | −7.52763e10 | − | 4.34608e10i | −1.02166 | − | 0.589857i | −0.107077 | − | 0.994251i | \(-0.534149\pi\) |
−0.914585 | + | 0.404394i | \(0.867483\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.16722e9 | + | 6.73896e8i | −0.0156008 | + | 0.00900712i | −0.507780 | − | 0.861487i | \(-0.669534\pi\) |
0.492179 | + | 0.870494i | \(0.336200\pi\) | |||||||
\(524\) | 1.95915e10i | 0.259862i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.35341e10 | 0.568704 | ||||||||
\(527\) | −1.06128e10 | − | 1.83820e10i | −0.137591 | − | 0.238314i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.07936e10 | − | 5.33361e10i | 0.393222 | − | 0.681081i | ||||
\(530\) | 3.43745e10 | − | 1.98461e10i | 0.435645 | − | 0.251520i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.23349e10 | − | 1.26056e10i | −0.278829 | − | 0.157368i | ||||
\(533\) | −9.73151e10 | −1.20579 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.62761e9 | − | 2.09440e9i | −0.0442798 | − | 0.0255650i | ||||
\(536\) | 1.14215e10 | − | 1.97826e10i | 0.138377 | − | 0.239676i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 4.65518e10i | − | 0.555658i | ||||||
\(539\) | 1.13499e11 | − | 2.21902e9i | 1.34474 | − | 0.0262910i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.82020e10 | − | 4.88474e10i | −0.329224 | − | 0.570233i | 0.653134 | − | 0.757242i | \(-0.273454\pi\) |
−0.982358 | + | 0.187010i | \(0.940120\pi\) | |||||||
\(542\) | −6.17828e10 | − | 3.56703e10i | −0.715929 | − | 0.413342i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 7.67422e9 | − | 4.43072e9i | 0.0876272 | − | 0.0505916i | ||||
\(545\) | 5.97284e10i | 0.677010i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.05773e10 | −1.01174 | −0.505872 | − | 0.862609i | \(-0.668829\pi\) | ||||
−0.505872 | + | 0.862609i | \(0.668829\pi\) | |||||||
\(548\) | 8.50805e9 | + | 1.47364e10i | 0.0943426 | + | 0.163406i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.39297e10 | − | 5.87680e10i | 0.370791 | − | 0.642229i | ||||
\(551\) | −5.13316e10 | + | 2.96363e10i | −0.556902 | + | 0.321527i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.71527e10 | + | 1.67661e8i | −0.183414 | + | 0.00179280i | ||||
\(554\) | 1.91611e9 | 0.0203414 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.96678e10 | − | 3.44492e10i | −0.624368 | − | 0.360479i | ||||
\(557\) | 8.50601e10 | − | 1.47328e11i | 0.883701 | − | 1.53061i | 0.0365050 | − | 0.999333i | \(-0.488378\pi\) |
0.847196 | − | 0.531281i | \(-0.178289\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.78646e11i | 1.82956i | ||||||||
\(560\) | 9.93582e9 | − | 5.86667e9i | 0.101030 | − | 0.0596540i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.41663e10 | − | 4.18573e10i | −0.242251 | − | 0.419590i | ||||
\(563\) | −1.07954e11 | − | 6.23275e10i | −1.07450 | − | 0.620364i | −0.145094 | − | 0.989418i | \(-0.546348\pi\) |
−0.929408 | + | 0.369054i | \(0.879682\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.03992e10 | + | 1.17775e10i | −0.200179 | + | 0.115573i | ||||
\(566\) | 1.04212e11i | 1.01543i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.49292e10 | 0.335579 | ||||||||
\(569\) | 6.46031e10 | + | 1.11896e11i | 0.616317 | + | 1.06749i | 0.990152 | + | 0.139997i | \(0.0447093\pi\) |
−0.373835 | + | 0.927495i | \(0.621957\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.09591e10 | + | 8.82638e10i | −0.479377 | + | 0.830306i | −0.999720 | − | 0.0236516i | \(-0.992471\pi\) |
0.520343 | + | 0.853957i | \(0.325804\pi\) | |||||||
\(572\) | −5.97332e10 | + | 3.44870e10i | −0.557997 | + | 0.322160i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 9.44215e8 | + | 9.65989e10i | 0.00869808 | + | 0.889866i | ||||
\(575\) | 3.93896e10 | 0.360338 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.37255e11 | − | 7.92444e10i | −1.23830 | − | 0.714933i | −0.269553 | − | 0.962985i | \(-0.586876\pi\) |
−0.968747 | + | 0.248053i | \(0.920209\pi\) | |||||||
\(578\) | 2.65328e10 | − | 4.59562e10i | 0.237723 | − | 0.411749i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 2.66671e10i | − | 0.235648i | ||||||
\(581\) | 1.32585e11 | + | 7.48297e10i | 1.16356 | + | 0.656703i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.17766e11 | + | 2.03977e11i | 1.01941 | + | 1.76566i | ||||
\(584\) | −2.19829e10 | − | 1.26918e10i | −0.188987 | − | 0.109112i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.09882e10 | + | 3.52116e10i | −0.517196 | + | 0.298604i | ||||
\(587\) | 1.98747e11i | 1.67397i | 0.547227 | + | 0.836984i | \(0.315683\pi\) | ||||
−0.547227 | + | 0.836984i | \(0.684317\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.70519e10 | −0.307857 | ||||||||
\(590\) | −1.94430e10 | − | 3.36763e10i | −0.160456 | − | 0.277918i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.89725e9 | − | 5.01818e9i | 0.0235884 | − | 0.0408563i | ||||
\(593\) | 7.00747e9 | − | 4.04576e9i | 0.0566686 | − | 0.0327176i | −0.471398 | − | 0.881921i | \(-0.656250\pi\) |
0.528067 | + | 0.849203i | \(0.322917\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.65480e10 | + | 2.93200e10i | −0.132031 | + | 0.233936i | ||||
\(596\) | −7.07140e10 | −0.560429 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.46726e10 | − | 2.00183e10i | −0.271133 | − | 0.156539i | ||||
\(599\) | 9.11259e10 | − | 1.57835e11i | 0.707839 | − | 1.22601i | −0.257818 | − | 0.966193i | \(-0.583004\pi\) |
0.965657 | − | 0.259820i | \(-0.0836631\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 2.47060e11i | − | 1.89367i | −0.321713 | − | 0.946837i | \(-0.604259\pi\) | ||
0.321713 | − | 0.946837i | \(-0.395741\pi\) | |||||||
\(602\) | 1.77331e11 | − | 1.73334e9i | 1.35020 | − | 0.0131977i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.29893e9 | − | 5.71392e9i | −0.0247871 | − | 0.0429325i | ||||
\(605\) | −4.40517e10 | − | 2.54332e10i | −0.328807 | − | 0.189837i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.95009e10 | − | 2.28059e10i | 0.290973 | − | 0.167993i | −0.347408 | − | 0.937714i | \(-0.612938\pi\) |
0.638380 | + | 0.769721i | \(0.279605\pi\) | |||||||
\(608\) | − | 1.54687e10i | − | 0.113198i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.36668e10 | 0.315379 | ||||||||
\(611\) | 1.52484e10 | + | 2.64111e10i | 0.109411 | + | 0.189505i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.26313e10 | − | 3.91986e10i | 0.160276 | − | 0.277606i | −0.774692 | − | 0.632339i | \(-0.782095\pi\) |
0.934968 | + | 0.354733i | \(0.115428\pi\) | |||||||
\(614\) | −9.55617e10 | + | 5.51726e10i | −0.672373 | + | 0.388195i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.48127e10 | + | 5.89589e10i | 0.241777 | + | 0.409475i | ||||
\(617\) | 3.39761e10 | 0.234440 | 0.117220 | − | 0.993106i | \(-0.462602\pi\) | ||||
0.117220 | + | 0.993106i | \(0.462602\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.85975e10 | − | 2.22843e10i | −0.262904 | − | 0.151787i | 0.362755 | − | 0.931885i | \(-0.381836\pi\) |
−0.625658 | + | 0.780097i | \(0.715170\pi\) | |||||||
\(620\) | 8.33493e9 | − | 1.44365e10i | 0.0564073 | − | 0.0977003i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 1.85204e11i | − | 1.23734i | ||||||
\(623\) | 2.08096e9 | + | 2.12895e11i | 0.0138138 | + | 1.41323i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.95834e10 | − | 5.12400e10i | −0.193878 | − | 0.335807i | ||||
\(626\) | 1.59570e11 | + | 9.21277e10i | 1.03909 | + | 0.599919i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.83354e10 | − | 1.05859e10i | 0.117883 | − | 0.0680598i | ||||
\(629\) | 1.69073e10i | 0.108012i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.19363e11 | 0.752924 | 0.376462 | − | 0.926432i | \(-0.377141\pi\) | ||||
0.376462 | + | 0.926432i | \(0.377141\pi\) | |||||||
\(632\) | −5.17305e9 | − | 8.95999e9i | −0.0324249 | − | 0.0561616i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −5.86274e10 | + | 1.01546e11i | −0.362864 | + | 0.628498i | ||||
\(635\) | −8.29218e10 | + | 4.78749e10i | −0.510004 | + | 0.294451i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.35047e11 | + | 8.15303e10i | −0.820217 | + | 0.495178i | ||||
\(638\) | 1.58242e11 | 0.955078 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.02705e9 | + | 3.47972e9i | 0.0359240 | + | 0.0207408i | ||||
\(641\) | −8.05963e10 | + | 1.39597e11i | −0.477401 | + | 0.826882i | −0.999664 | − | 0.0259018i | \(-0.991754\pi\) |
0.522264 | + | 0.852784i | \(0.325088\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.72715e10i | 0.335039i | 0.985869 | + | 0.167519i | \(0.0535756\pi\) | ||||
−0.985869 | + | 0.167519i | \(0.946424\pi\) | |||||||
\(644\) | −1.95345e10 | + | 3.46117e10i | −0.113569 | + | 0.201224i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.25674e10 | + | 3.90879e10i | 0.129584 | + | 0.224446i | ||||
\(647\) | −4.30146e10 | − | 2.48345e10i | −0.245470 | − | 0.141722i | 0.372218 | − | 0.928145i | \(-0.378597\pi\) |
−0.617688 | + | 0.786423i | \(0.711931\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.99834e11 | − | 1.15374e11i | 1.12640 | − | 0.650325i | ||||
\(650\) | 9.42984e10i | 0.528264i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.68299e10 | −0.0931306 | ||||||||
\(653\) | 1.75732e11 | + | 3.04377e11i | 0.966492 | + | 1.67401i | 0.705553 | + | 0.708657i | \(0.250699\pi\) |
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.24475e10 | − | 3.88801e10i | 0.121956 | − | 0.211233i | ||||
\(656\) | −5.04599e10 | + | 2.91330e10i | −0.272478 | + | 0.157315i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.60687e10 | − | 1.53925e10i | 0.139065 | − | 0.0821117i | ||||
\(659\) | −7.49500e10 | −0.397402 | −0.198701 | − | 0.980060i | \(-0.563672\pi\) | ||||
−0.198701 | + | 0.980060i | \(0.563672\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.13344e10 | + | 5.27319e10i | 0.478441 | + | 0.276228i | 0.719767 | − | 0.694216i | \(-0.244249\pi\) |
−0.241326 | + | 0.970444i | \(0.577582\pi\) | |||||||
\(662\) | 1.22337e10 | − | 2.11894e10i | 0.0636979 | − | 0.110328i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.18254e10i | 0.472379i | ||||||||
\(665\) | 2.98813e10 | + | 5.06071e10i | 0.152797 | + | 0.258777i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.59264e10 | + | 7.95469e10i | 0.232038 | + | 0.401902i | ||||
\(668\) | −1.13106e11 | − | 6.53019e10i | −0.568042 | − | 0.327959i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.53329e10 | + | 2.61729e10i | −0.224964 | + | 0.129883i | ||||
\(671\) | 2.59118e11i | 1.27823i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.87077e11 | −0.911929 | −0.455965 | − | 0.889998i | \(-0.650706\pi\) | ||||
−0.455965 | + | 0.889998i | \(0.650706\pi\) | |||||||
\(674\) | 9.81538e9 | + | 1.70007e10i | 0.0475628 | + | 0.0823812i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4.28320e9 | + | 7.41872e9i | −0.0205108 | + | 0.0355257i | ||||
\(677\) | −2.65310e11 | + | 1.53177e11i | −1.26299 | + | 0.729185i | −0.973651 | − | 0.228043i | \(-0.926767\pi\) |
−0.289334 | + | 0.957228i | \(0.593434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.36362e11 | + | 7.69617e10i | 0.641528 | + | 0.362072i | ||||
\(680\) | −2.03064e10 | −0.0949725 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.56661e10 | + | 4.94593e10i | 0.395978 | + | 0.228618i | ||||
\(683\) | 1.68227e11 | − | 2.91377e11i | 0.773057 | − | 1.33897i | −0.162823 | − | 0.986655i | \(-0.552060\pi\) |
0.935880 | − | 0.352319i | \(-0.114607\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 3.89932e10i | − | 0.177104i | ||||||
\(686\) | 8.22406e10 | + | 1.33262e11i | 0.371355 | + | 0.601743i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.34809e10 | + | 9.26317e10i | 0.238696 | + | 0.413434i | ||||
\(689\) | −2.83450e11 | − | 1.63650e11i | −1.25776 | − | 0.726171i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.51262e11 | − | 1.45066e11i | 1.10208 | − | 0.636289i | 0.165317 | − | 0.986240i | \(-0.447135\pi\) |
0.936768 | + | 0.349952i | \(0.113802\pi\) | |||||||
\(692\) | 1.72384e10i | 0.0751747i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.06379e10 | −0.0458581 | ||||||||
\(695\) | 7.89421e10 | + | 1.36732e11i | 0.338353 | + | 0.586044i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.50050e10 | − | 1.47233e11i | 0.360175 | − | 0.623841i | ||||
\(698\) | 1.31031e10 | − | 7.56506e9i | 0.0552015 | − | 0.0318706i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 9.36043e10 | − | 9.14944e8i | 0.389856 | − | 0.00381068i | ||||
\(701\) | 3.91859e11 | 1.62277 | 0.811386 | − | 0.584510i | \(-0.198713\pi\) | ||||
0.811386 | + | 0.584510i | \(0.198713\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.55596e10 | + | 1.47569e10i | 0.104649 | + | 0.0604188i | ||||
\(704\) | −2.06486e10 | + | 3.57644e10i | −0.0840620 | + | 0.145600i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.36655e10i | − | 0.0550057i | ||||||
\(707\) | 3.65593e11 | − | 2.15867e11i | 1.46325 | − | 0.863989i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.48776e11 | − | 2.57687e11i | −0.588772 | − | 1.01978i | −0.994394 | − | 0.105742i | \(-0.966278\pi\) |
0.405621 | − | 0.914041i | \(-0.367055\pi\) | |||||||
\(710\) | −6.93184e10 | − | 4.00210e10i | −0.272782 | − | 0.157490i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.11209e11 | + | 6.42065e10i | −0.432733 | + | 0.249838i | ||||
\(713\) | 5.74182e10i | 0.222173i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.58057e11 | 0.604770 | ||||||||
\(716\) | −8.59382e10 | − | 1.48849e11i | −0.326990 | − | 0.566363i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.78785e11 | + | 3.09664e11i | −0.672717 | + | 1.16518i | ||||
\(719\) | 2.77663e11 | − | 1.60309e11i | 1.03897 | − | 0.599849i | 0.119428 | − | 0.992843i | \(-0.461894\pi\) |
0.919541 | + | 0.392994i | \(0.128561\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.68106e9 | − | 2.74288e11i | −0.00992122 | − | 1.01500i | ||||
\(722\) | −1.13359e11 | −0.417164 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.84251e11 | − | 1.06377e11i | −0.670588 | − | 0.387164i | ||||
\(725\) | 1.08171e11 | − | 1.87358e11i | 0.391524 | − | 0.678140i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.99101e11i | 1.78670i | 0.449364 | + | 0.893349i | \(0.351651\pi\) | ||||
−0.449364 | + | 0.893349i | \(0.648349\pi\) | |||||||
\(728\) | −8.28601e10 | − | 4.67655e10i | −0.294999 | − | 0.166494i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.90839e10 | + | 5.03749e10i | 0.102415 | + | 0.177387i | ||||
\(731\) | −2.70283e11 | − | 1.56048e11i | −0.946562 | − | 0.546498i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.43929e11 | − | 1.98568e11i | 1.19139 | − | 0.687848i | 0.232766 | − | 0.972533i | \(-0.425222\pi\) |
0.958621 | + | 0.284685i | \(0.0918890\pi\) | |||||||
\(734\) | 3.40923e9i | 0.0117455i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.39713e10 | −0.0816921 | ||||||||
\(737\) | −1.55310e11 | − | 2.69004e11i | −0.526415 | − | 0.911778i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.33494e10 | + | 2.31219e10i | −0.0447595 | + | 0.0775257i | −0.887537 | − | 0.460736i | \(-0.847585\pi\) |
0.842778 | + | 0.538262i | \(0.180919\pi\) | |||||||
\(740\) | −1.14994e10 | + | 6.63919e9i | −0.0383485 | + | 0.0221405i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.59695e11 | + | 2.82952e11i | −0.526837 | + | 0.933462i | ||||
\(743\) | −2.98139e11 | −0.978281 | −0.489141 | − | 0.872205i | \(-0.662690\pi\) | ||||
−0.489141 | + | 0.872205i | \(0.662690\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.40335e11 | + | 8.10224e10i | 0.455555 | + | 0.263015i | ||||
\(746\) | 1.87138e11 | − | 3.24133e11i | 0.604237 | − | 1.04657i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 1.20498e11i | − | 0.384922i | ||||||
\(749\) | 3.42864e10 | − | 3.35136e8i | 0.108942 | − | 0.00106486i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.87148e10 | + | 6.70559e10i | 0.121707 | + | 0.210803i | 0.920441 | − | 0.390881i | \(-0.127830\pi\) |
−0.798734 | + | 0.601685i | \(0.794496\pi\) | |||||||
\(752\) | 1.58133e10 | + | 9.12979e9i | 0.0494482 | + | 0.0285489i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.90435e11 | + | 1.09948e11i | −0.589198 | + | 0.340173i | ||||
\(755\) | 1.51193e10i | 0.0465313i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.03553e11 | −1.53342 | −0.766711 | − | 0.641992i | \(-0.778108\pi\) | ||||
−0.766711 | + | 0.641992i | \(0.778108\pi\) | |||||||
\(758\) | 1.27990e11 | + | 2.21685e11i | 0.387703 | + | 0.671521i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.77236e10 | + | 3.06982e10i | −0.0531249 | + | 0.0920150i | ||||
\(761\) | −8.89472e10 | + | 5.13537e10i | −0.265212 | + | 0.153120i | −0.626710 | − | 0.779253i | \(-0.715599\pi\) |
0.361498 | + | 0.932373i | \(0.382266\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.48584e11 | − | 4.21003e11i | −0.733459 | − | 1.24219i | ||||
\(764\) | −1.02620e11 | −0.301201 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.37265e11 | − | 1.36985e11i | −0.689158 | − | 0.397885i | ||||
\(767\) | −1.60326e11 | + | 2.77693e11i | −0.463257 | + | 0.802385i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.28224e10i | 0.151047i | 0.997144 | + | 0.0755236i | \(0.0240628\pi\) | ||||
−0.997144 | + | 0.0755236i | \(0.975937\pi\) | |||||||
\(770\) | −1.53358e9 | − | 1.56894e11i | −0.00436257 | − | 0.446317i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.52803e10 | − | 1.30389e11i | −0.211940 | − | 0.367090i | ||||
\(773\) | −3.29208e11 | − | 1.90068e11i | −0.922046 | − | 0.532344i | −0.0377590 | − | 0.999287i | \(-0.512022\pi\) |
−0.884287 | + | 0.466943i | \(0.845355\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.17119e11 | − | 6.76188e10i | 0.324654 | − | 0.187439i | ||||
\(776\) | 9.44417e10i | 0.260445i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21947e11 | 0.332855 | ||||||||
\(779\) | −1.48386e11 | − | 2.57013e11i | −0.402943 | − | 0.697918i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.37484e11 | − | 4.11334e11i | 0.638307 | − | 1.10558i | ||||
\(782\) | 6.05733e10 | − | 3.49720e10i | 0.161977 | − | 0.0935176i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.56173e10 | + | 8.27040e10i | −0.120744 | + | 0.218908i | ||||
\(785\) | −4.85164e10 | −0.127765 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.12322e11 | + | 2.38054e11i | 1.07482 | + | 0.620550i | 0.929495 | − | 0.368834i | \(-0.120243\pi\) |
0.145328 | + | 0.989384i | \(0.453576\pi\) | |||||||
\(788\) | −2.45222e10 | + | 4.24736e10i | −0.0635995 | + | 0.110158i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.37086e10i | 0.0608693i | ||||||||
\(791\) | 9.47694e10 | − | 1.67915e11i | 0.242082 | − | 0.428926i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.80037e11 | − | 3.11833e11i | −0.455270 | − | 0.788551i | ||||
\(794\) | −1.26274e11 | − | 7.29045e10i | −0.317711 | − | 0.183431i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.43813e11 | + | 1.40766e11i | −0.607302 | + | 0.350626i | ||||
\(797\) | − | 2.92025e11i | − | 0.723746i | −0.932227 | − | 0.361873i | \(-0.882137\pi\) | ||
0.932227 | − | 0.361873i | \(-0.117863\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.32782e10 | −0.130726 | ||||||||
\(800\) | 2.82299e10 | + | 4.88956e10i | 0.0689207 | + | 0.119374i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.76618e10 | + | 6.52322e10i | −0.0910340 | + | 0.157676i | ||||
\(803\) | −2.98923e11 | + | 1.72583e11i | −0.718948 | + | 0.415085i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 7.84242e10 | − | 4.63061e10i | 0.186753 | − | 0.110269i | ||||
\(806\) | −1.37459e11 | −0.325711 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.21768e11 | + | 1.28038e11i | 0.520300 | + | 0.300395i | ||||
\(809\) | 2.54870e11 | − | 4.41447e11i | 0.595009 | − | 1.03059i | −0.398536 | − | 0.917153i | \(-0.630482\pi\) |
0.993546 | − | 0.113434i | \(-0.0361850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 2.98657e11i | − | 0.690381i | −0.938533 | − | 0.345191i | \(-0.887814\pi\) | ||
0.938533 | − | 0.345191i | \(-0.112186\pi\) | |||||||
\(812\) | 1.10986e11 | + | 1.87966e11i | 0.255296 | + | 0.432371i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3.93968e10 | − | 6.82373e10i | −0.0897353 | − | 0.155426i | ||||
\(815\) | 3.33997e10 | + | 1.92833e10i | 0.0757029 | + | 0.0437071i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.71811e11 | + | 2.72400e11i | −1.05896 | + | 0.611391i | ||||
\(818\) | − | 4.20276e11i | − | 0.938688i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.33520e11 | 0.295318 | ||||||||
\(821\) | −2.07864e11 | − | 3.60031e11i | −0.457516 | − | 0.792441i | 0.541313 | − | 0.840821i | \(-0.317927\pi\) |
−0.998829 | + | 0.0483802i | \(0.984594\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.28735e11 | + | 2.22976e11i | −0.280606 | + | 0.486025i | −0.971534 | − | 0.236899i | \(-0.923869\pi\) |
0.690928 | + | 0.722924i | \(0.257202\pi\) | |||||||
\(824\) | 1.43279e11 | − | 8.27220e10i | 0.310794 | − | 0.179437i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.77204e11 | + | 1.56452e11i | 0.595497 | + | 0.336093i | ||||
\(827\) | −2.54192e11 | −0.543426 | −0.271713 | − | 0.962378i | \(-0.587590\pi\) | ||||
−0.271713 | + | 0.962378i | \(0.587590\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −6.50967e11 | − | 3.75836e11i | −1.37829 | − | 0.795757i | −0.386337 | − | 0.922358i | \(-0.626260\pi\) |
−0.991954 | + | 0.126601i | \(0.959593\pi\) | |||||||
\(830\) | 1.05211e11 | − | 1.82231e11i | 0.221692 | − | 0.383982i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 5.73871e10i | − | 0.119763i | ||||||
\(833\) | −5.38704e9 | − | 2.75537e11i | −0.0111885 | − | 0.572269i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.49643e11 | + | 2.59188e11i | 0.307829 | + | 0.533175i | ||||
\(836\) | −1.82163e11 | − | 1.05172e11i | −0.372936 | − | 0.215315i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.07630e11 | + | 1.77610e11i | −0.623811 | + | 0.360157i | ||||
\(839\) | 2.44756e11i | 0.493954i | 0.969021 | + | 0.246977i | \(0.0794372\pi\) | ||||
−0.969021 | + | 0.246977i | \(0.920563\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.24316e9 | 0.00848214 | ||||||||
\(842\) | 5.45572e9 | + | 9.44959e9i | 0.0108544 | + | 0.0188003i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.13038e10 | + | 8.88609e10i | −0.101107 | + | 0.175122i | ||||
\(845\) | 1.70004e10 | − | 9.81517e9i | 0.0333451 | − | 0.0192518i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.16355e11 | − | 4.06970e9i | 0.808966 | − | 0.00790731i | ||||
\(848\) | −1.95966e11 | −0.378964 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.42669e11 | − | 8.23699e10i | −0.273309 | − | 0.157795i | ||||
\(851\) | 2.28682e10 | − | 3.96089e10i | 0.0436028 | − | 0.0755222i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.02397e11i | 0.193416i | 0.995313 | + | 0.0967078i | \(0.0308312\pi\) | ||||
−0.995313 | + | 0.0967078i | \(0.969169\pi\) | |||||||
\(854\) | −3.07791e11 | + | 1.81738e11i | −0.578662 | + | 0.341675i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.03404e10 | + | 1.79100e10i | 0.0192593 | + | 0.0333581i | ||||
\(857\) | 7.52580e11 | + | 4.34502e11i | 1.39518 | + | 0.805506i | 0.993883 | − | 0.110442i | \(-0.0352267\pi\) |
0.401295 | + | 0.915949i | \(0.368560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.47218e11 | + | 3.15936e11i | −1.00505 | + | 0.580266i | −0.909738 | − | 0.415182i | \(-0.863718\pi\) |
−0.0953112 | + | 0.995448i | \(0.530385\pi\) | |||||||
\(860\) | − | 2.45109e11i | − | 0.448089i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.26887e11 | 1.31655 | ||||||||
\(863\) | 1.45694e10 | + | 2.52350e10i | 0.0262663 | + | 0.0454946i | 0.878860 | − | 0.477080i | \(-0.158305\pi\) |
−0.852593 | + | 0.522575i | \(0.824972\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.97513e10 | − | 3.42103e10i | 0.0352802 | − | 0.0611071i | ||||
\(866\) | −4.75844e10 | + | 2.74729e10i | −0.0846044 | + | 0.0488464i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1.33371e9 | + | 1.36447e11i | 0.00234955 | + | 0.240373i | ||||
\(869\) | −1.40687e11 | −0.246702 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.73812e11 | + | 2.15820e11i | 0.649502 | + | 0.374990i | ||||
\(872\) | 1.47444e11 | − | 2.55380e11i | 0.255012 | − | 0.441694i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 1.22096e11i | − | 0.209244i | ||||||
\(875\) | −4.26387e11 | − | 2.40649e11i | −0.727398 | − | 0.410536i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.09627e10 | + | 1.89879e10i | 0.0185318 | + | 0.0320980i | 0.875143 | − | 0.483865i | \(-0.160767\pi\) |
−0.856611 | + | 0.515963i | \(0.827434\pi\) | |||||||
\(878\) | 2.23713e11 | + | 1.29161e11i | 0.376456 | + | 0.217347i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.19560e10 | − | 4.73173e10i | 0.136663 | − | 0.0789022i | ||||
\(881\) | − | 1.09148e11i | − | 0.181181i | −0.995888 | − | 0.0905907i | \(-0.971124\pi\) | ||
0.995888 | − | 0.0905907i | \(-0.0288755\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.59857e11 | 0.427457 | 0.213728 | − | 0.976893i | \(-0.431439\pi\) | ||||
0.213728 | + | 0.976893i | \(0.431439\pi\) | |||||||
\(884\) | 8.37227e10 | + | 1.45012e11i | 0.137099 | + | 0.237462i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.07326e11 | − | 3.59100e11i | 0.336449 | − | 0.582747i | ||||
\(887\) | 5.97593e11 | − | 3.45020e11i | 0.965408 | − | 0.557379i | 0.0675747 | − | 0.997714i | \(-0.478474\pi\) |
0.897833 | + | 0.440336i | \(0.145141\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.85234e11 | − | 6.82566e11i | 0.616761 | − | 1.09279i | ||||
\(890\) | 2.94265e11 | 0.469006 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.15984e11 | + | 6.69634e10i | 0.183206 | + | 0.105774i | ||||
\(893\) | −4.65017e10 | + | 8.05433e10i | −0.0731245 | + | 0.126655i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.93863e11i | 0.613838i | ||||||||
\(896\) | −5.69648e10 | + | 5.56807e8i | −0.0883841 | + | 0.000863919i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.07945e11 | − | 7.06582e11i | −0.627331 | − | 1.08657i | ||||
\(899\) | 2.73111e11 | + | 1.57681e11i | 0.418120 | + | 0.241402i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.95189e11 | − | 2.85897e11i | 0.751400 | − | 0.433821i | ||||
\(902\) | 7.92303e11i | 1.19692i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.16294e11 | 0.174134 | ||||||||
\(905\) | 2.43769e11 | + | 4.22221e11i | 0.363400 | + | 0.629427i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.10593e11 | + | 1.91553e11i | −0.163417 | + | 0.283047i | −0.936092 | − | 0.351755i | \(-0.885585\pi\) |
0.772675 | + | 0.634802i | \(0.218918\pi\) | |||||||
\(908\) | 2.35767e11 | − | 1.36120e11i | 0.346849 | − | 0.200253i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.10857e11 | + | 1.87747e11i | 0.161658 | + | 0.273784i | ||||
\(911\) | −5.57854e11 | −0.809929 | −0.404964 | − | 0.914332i | \(-0.632716\pi\) | ||||
−0.404964 | + | 0.914332i | \(0.632716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.08136e12 | + | 6.24322e11i | 1.55627 | + | 0.898515i | ||||
\(914\) | −3.40541e11 | + | 5.89834e11i | −0.487960 | + | 0.845171i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 5.98180e11i | − | 0.849670i | ||||||
\(917\) | 3.59193e9 | + | 3.67476e11i | 0.00507985 | + | 0.519699i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.76298e11 | + | 3.05357e11i | 0.247164 | + | 0.428100i | 0.962738 | − | 0.270437i | \(-0.0871681\pi\) |
−0.715574 | + | 0.698537i | \(0.753835\pi\) | |||||||
\(920\) | 4.75720e10 | + | 2.74657e10i | 0.0664049 | + | 0.0383389i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −8.79587e11 | + | 5.07830e11i | −1.21718 | + | 0.702739i | ||||
\(923\) | 6.60021e11i | 0.909392i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.07723e11 | −0.147144 | ||||||||
\(926\) | −2.06374e11 | − | 3.57451e11i | −0.280680 | − | 0.486152i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.58296e10 | + | 1.14020e11i | −0.0887624 | + | 0.153741i | ||||
\(929\) | −4.96997e11 | + | 2.86941e11i | −0.667253 | + | 0.385239i | −0.795035 | − | 0.606563i | \(-0.792548\pi\) |
0.127782 | + | 0.991802i | \(0.459214\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.21245e11 | − | 2.32347e11i | −0.560707 | − | 0.309271i | ||||
\(932\) | 3.33821e11 | 0.442435 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.37754e10 | − | 4.83678e10i | −0.110085 | − | 0.0635578i | ||||
\(935\) | −1.38064e11 | + | 2.39133e11i | −0.180648 | + | 0.312891i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.48860e11i | 1.10123i | 0.834760 | + | 0.550615i | \(0.185607\pi\) | ||||
−0.834760 | + | 0.550615i | \(0.814393\pi\) | |||||||
\(938\) | 2.10605e11 | − | 3.73155e11i | 0.272055 | − | 0.482034i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.09214e10 | − | 3.62369e10i | −0.0267966 | − | 0.0464130i | ||||
\(941\) | −3.68293e11 | − | 2.12634e11i | −0.469715 | − | 0.271190i | 0.246405 | − | 0.969167i | \(-0.420751\pi\) |
−0.716121 | + | 0.697977i | \(0.754084\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −3.98284e11 | + | 2.29949e11i | −0.503670 | + | 0.290794i | ||||
\(944\) | 1.91986e11i | 0.241758i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.45447e12 | 1.81610 | ||||||||
\(947\) | 3.53892e11 | + | 6.12958e11i | 0.440018 | + | 0.762133i | 0.997690 | − | 0.0679279i | \(-0.0216388\pi\) |
−0.557672 | + | 0.830061i | \(0.688305\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.39824e11 | − | 4.15388e11i | 0.295684 | − | 0.512140i | ||||
\(950\) | −2.49045e11 | + | 1.43786e11i | −0.305762 | + | 0.176532i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.43132e11 | − | 8.45136e10i | 0.174257 | − | 0.102891i | ||||
\(953\) | 1.11824e12 | 1.35570 | 0.677851 | − | 0.735199i | \(-0.262911\pi\) | ||||
0.677851 | + | 0.735199i | \(0.262911\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.03653e11 | + | 1.17579e11i | 0.244837 | + | 0.141357i | ||||
\(956\) | −1.60565e11 | + | 2.78107e11i | −0.192229 | + | 0.332951i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.02543e12i | − | 1.21743i | ||||||
\(959\) | 1.62287e11 | + | 2.74849e11i | 0.191870 | + | 0.324952i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.27878e11 | − | 5.67901e11i | −0.384431 | − | 0.665854i | ||||
\(962\) | 9.48235e10 | + | 5.47463e10i | 0.110717 | + | 0.0639227i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.79050e11 | − | 1.03374e11i | 0.207332 | − | 0.119703i | ||||
\(965\) | 3.45017e11i | 0.397861i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.31325e12 | −1.50190 | −0.750952 | − | 0.660356i | \(-0.770405\pi\) | ||||
−0.750952 | + | 0.660356i | \(0.770405\pi\) | |||||||
\(968\) | 1.25568e11 | + | 2.17489e11i | 0.143013 | + | 0.247706i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.08209e11 | − | 1.87423e11i | 0.122230 | − | 0.211708i | ||||
\(971\) | 1.44855e12 | − | 8.36318e11i | 1.62950 | − | 0.940794i | 0.645262 | − | 0.763961i | \(-0.276748\pi\) |
0.984241 | − | 0.176833i | \(-0.0565851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.12550e12 | − | 6.35221e11i | −1.25572 | − | 0.708719i | ||||
\(974\) | −4.54128e11 | −0.504594 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.86706e11 | − | 1.07795e11i | −0.205759 | − | 0.118795i | ||||
\(977\) | −4.87813e11 | + | 8.44917e11i | −0.535396 | + | 0.927333i | 0.463748 | + | 0.885967i | \(0.346504\pi\) |
−0.999144 | + | 0.0413657i | \(0.986829\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.74616e12i | 1.90088i | ||||||||
\(980\) | 1.85290e11 | − | 1.11862e11i | 0.200885 | − | 0.121277i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.88513e11 | + | 3.26515e11i | 0.202720 | + | 0.351121i | ||||
\(983\) | 8.75801e11 | + | 5.05644e11i | 0.937975 | + | 0.541540i | 0.889325 | − | 0.457276i | \(-0.151175\pi\) |
0.0486500 | + | 0.998816i | \(0.484508\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.73305e10 | − | 5.61938e10i | 0.103396 | − | 0.0596957i | ||||
\(986\) | − | 3.84158e11i | − | 0.406446i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.92296e11 | 0.306757 | ||||||||
\(989\) | 4.22129e11 | + | 7.31150e11i | 0.441225 | + | 0.764225i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.10221e11 | + | 1.90909e11i | −0.114280 | + | 0.197939i | −0.917492 | − | 0.397755i | \(-0.869790\pi\) |
0.803211 | + | 0.595694i | \(0.203123\pi\) | |||||||
\(992\) | −7.12752e10 | + | 4.11507e10i | −0.0736023 | + | 0.0424943i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.55163e11 | − | 6.40396e9i | 0.671126 | − | 0.00655998i | ||||
\(995\) | 6.45143e11 | 0.658209 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.24638e11 | + | 2.45165e11i | 0.429772 | + | 0.248129i | 0.699250 | − | 0.714878i | \(-0.253518\pi\) |
−0.269477 | + | 0.963007i | \(0.586851\pi\) | |||||||
\(998\) | −5.90237e11 | + | 1.02232e12i | −0.594982 | + | 1.03054i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 126.9.n.d.73.8 | yes | 20 | |
3.2 | odd | 2 | inner | 126.9.n.d.73.3 | yes | 20 | |
7.5 | odd | 6 | inner | 126.9.n.d.19.8 | yes | 20 | |
21.5 | even | 6 | inner | 126.9.n.d.19.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.9.n.d.19.3 | ✓ | 20 | 21.5 | even | 6 | inner | |
126.9.n.d.19.8 | yes | 20 | 7.5 | odd | 6 | inner | |
126.9.n.d.73.3 | yes | 20 | 3.2 | odd | 2 | inner | |
126.9.n.d.73.8 | yes | 20 | 1.1 | even | 1 | trivial |