Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.9059675764\) |
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: | \( x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{40}\cdot 17^{2} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.7 | ||
Root | \(0.500000 + 15.6774i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.10 |
Dual form | 27.10.c.a.19.7 |
$q$-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 \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 12.8270 | + | 22.2170i | 0.566879 | + | 0.981862i | 0.996872 | + | 0.0790305i | \(0.0251825\pi\) |
−0.429994 | + | 0.902832i | \(0.641484\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −73.0637 | + | 126.550i | −0.142703 | + | 0.247168i | ||||
\(5\) | 353.226 | − | 611.805i | 0.252748 | − | 0.437772i | −0.711534 | − | 0.702652i | \(-0.751999\pi\) |
0.964281 | + | 0.264880i | \(0.0853324\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2284.21 | + | 3956.36i | 0.359579 | + | 0.622809i | 0.987891 | − | 0.155153i | \(-0.0495870\pi\) |
−0.628311 | + | 0.777962i | \(0.716254\pi\) | |||||||
\(8\) | 9386.09 | 0.810177 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 18123.3 | 0.573109 | ||||||||
\(11\) | 35716.7 | + | 61863.1i | 0.735537 | + | 1.27399i | 0.954487 | + | 0.298251i | \(0.0964032\pi\) |
−0.218951 | + | 0.975736i | \(0.570263\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 13201.0 | − | 22864.9i | 0.128193 | − | 0.222036i | −0.794784 | − | 0.606893i | \(-0.792416\pi\) |
0.922976 | + | 0.384857i | \(0.125749\pi\) | |||||||
\(14\) | −58599.1 | + | 101497.i | −0.407675 | + | 0.706114i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 157804. | + | 273325.i | 0.601975 | + | 1.04265i | ||||
\(17\) | 314759. | 0.914026 | 0.457013 | − | 0.889460i | \(-0.348919\pi\) | ||||
0.457013 | + | 0.889460i | \(0.348919\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −904019. | −1.59143 | −0.795713 | − | 0.605674i | \(-0.792904\pi\) | ||||
−0.795713 | + | 0.605674i | \(0.792904\pi\) | |||||||
\(20\) | 51616.0 | + | 89401.5i | 0.0721355 | + | 0.124942i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −916276. | + | 1.58704e6i | −0.833920 | + | 1.44439i | ||||
\(23\) | −55921.2 | + | 96858.3i | −0.0416678 | + | 0.0721708i | −0.886107 | − | 0.463480i | \(-0.846600\pi\) |
0.844439 | + | 0.535651i | \(0.179934\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 727026. | + | 1.25925e6i | 0.372237 | + | 0.644734i | ||||
\(26\) | 677318. | 0.290678 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −667571. | −0.205251 | ||||||||
\(29\) | 2.19402e6 | + | 3.80015e6i | 0.576035 | + | 0.997722i | 0.995928 | + | 0.0901485i | \(0.0287342\pi\) |
−0.419893 | + | 0.907573i | \(0.637933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.94392e6 | − | 8.56313e6i | 0.961488 | − | 1.66535i | 0.242721 | − | 0.970096i | \(-0.421960\pi\) |
0.718767 | − | 0.695251i | \(-0.244707\pi\) | |||||||
\(32\) | −1.64546e6 | + | 2.85003e6i | −0.277404 | + | 0.480478i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.03742e6 | + | 6.99301e6i | 0.518142 | + | 0.897448i | ||||
\(35\) | 3.22736e6 | 0.363531 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.32122e6 | −0.554489 | −0.277245 | − | 0.960799i | \(-0.589421\pi\) | ||||
−0.277245 | + | 0.960799i | \(0.589421\pi\) | |||||||
\(38\) | −1.15959e7 | − | 2.00846e7i | −0.902145 | − | 1.56256i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 3.31541e6 | − | 5.74246e6i | 0.204770 | − | 0.354673i | ||||
\(41\) | 2.68019e6 | − | 4.64223e6i | 0.148128 | − | 0.256566i | −0.782407 | − | 0.622767i | \(-0.786008\pi\) |
0.930536 | + | 0.366201i | \(0.119342\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.12275e7 | − | 1.94466e7i | −0.500812 | − | 0.867432i | −1.00000 | 0.000938191i | \(-0.999701\pi\) | |
0.499187 | − | 0.866494i | \(-0.333632\pi\) | |||||||
\(44\) | −1.04384e7 | −0.419852 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.86920e6 | −0.0944824 | ||||||||
\(47\) | −2.23644e7 | − | 3.87363e7i | −0.668524 | − | 1.15792i | −0.978317 | − | 0.207114i | \(-0.933593\pi\) |
0.309793 | − | 0.950804i | \(-0.399740\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 9.74159e6 | − | 1.68729e7i | 0.241406 | − | 0.418127i | ||||
\(50\) | −1.86511e7 | + | 3.23047e7i | −0.422027 | + | 0.730971i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.92903e6 | + | 3.34118e6i | 0.0365868 | + | 0.0633702i | ||||
\(53\) | 4.00972e7 | 0.698027 | 0.349013 | − | 0.937118i | \(-0.386517\pi\) | ||||
0.349013 | + | 0.937118i | \(0.386517\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.04642e7 | 0.743621 | ||||||||
\(56\) | 2.14398e7 | + | 3.71348e7i | 0.291323 | + | 0.504586i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.62853e7 | + | 9.74890e7i | −0.653084 | + | 1.13117i | ||||
\(59\) | −4.79118e7 | + | 8.29857e7i | −0.514764 | + | 0.891598i | 0.485089 | + | 0.874465i | \(0.338787\pi\) |
−0.999853 | + | 0.0171331i | \(0.994546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.01113e7 | − | 1.75132e7i | −0.0935020 | − | 0.161950i | 0.815480 | − | 0.578785i | \(-0.196473\pi\) |
−0.908982 | + | 0.416834i | \(0.863139\pi\) | |||||||
\(62\) | 2.53663e8 | 2.18019 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.71659e7 | 0.574931 | ||||||||
\(65\) | −9.32588e6 | − | 1.61529e7i | −0.0648007 | − | 0.112238i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.12489e7 | + | 1.58048e8i | −0.553211 | + | 0.958190i | 0.444829 | + | 0.895615i | \(0.353264\pi\) |
−0.998040 | + | 0.0625744i | \(0.980069\pi\) | |||||||
\(68\) | −2.29975e7 | + | 3.98328e7i | −0.130434 | + | 0.225918i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.13974e7 | + | 7.17024e7i | 0.206078 | + | 0.356938i | ||||
\(71\) | −1.38543e8 | −0.647025 | −0.323512 | − | 0.946224i | \(-0.604864\pi\) | ||||
−0.323512 | + | 0.946224i | \(0.604864\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.17970e8 | −0.898347 | −0.449173 | − | 0.893445i | \(-0.648281\pi\) | ||||
−0.449173 | + | 0.893445i | \(0.648281\pi\) | |||||||
\(74\) | −8.10823e7 | − | 1.40439e8i | −0.314328 | − | 0.544432i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.60510e7 | − | 1.14404e8i | 0.227101 | − | 0.393350i | ||||
\(77\) | −1.63169e8 | + | 2.82617e8i | −0.528967 | + | 0.916198i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.97294e8 | − | 3.41722e8i | −0.569890 | − | 0.987078i | −0.996576 | − | 0.0826785i | \(-0.973653\pi\) |
0.426686 | − | 0.904400i | \(-0.359681\pi\) | |||||||
\(80\) | 2.22962e8 | 0.608591 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.37515e8 | 0.335883 | ||||||||
\(83\) | −2.36638e8 | − | 4.09870e8i | −0.547310 | − | 0.947969i | −0.998458 | − | 0.0555197i | \(-0.982318\pi\) |
0.451147 | − | 0.892450i | \(-0.351015\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.11181e8 | − | 1.92571e8i | 0.231018 | − | 0.400135i | ||||
\(86\) | 2.88030e8 | − | 4.98883e8i | 0.567799 | − | 0.983458i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.35240e8 | + | 5.80653e8i | 0.595915 | + | 1.03215i | ||||
\(89\) | −2.60507e8 | −0.440113 | −0.220057 | − | 0.975487i | \(-0.570624\pi\) | ||||
−0.220057 | + | 0.975487i | \(0.570624\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.20616e8 | 0.184381 | ||||||||
\(92\) | −8.17161e6 | − | 1.41537e7i | −0.0118922 | − | 0.0205979i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.73736e8 | − | 9.93741e8i | 0.757944 | − | 1.31280i | ||||
\(95\) | −3.19323e8 | + | 5.53083e8i | −0.402229 | + | 0.696682i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.87421e8 | − | 4.97828e8i | −0.329644 | − | 0.570961i | 0.652797 | − | 0.757533i | \(-0.273595\pi\) |
−0.982441 | + | 0.186572i | \(0.940262\pi\) | |||||||
\(98\) | 4.99822e8 | 0.547391 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.12477e8 | −0.212477 | ||||||||
\(101\) | 7.03860e7 | + | 1.21912e8i | 0.0673039 | + | 0.116574i | 0.897714 | − | 0.440579i | \(-0.145227\pi\) |
−0.830410 | + | 0.557153i | \(0.811894\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.70819e7 | − | 2.95867e7i | 0.0149544 | − | 0.0259017i | −0.858451 | − | 0.512895i | \(-0.828573\pi\) |
0.873406 | + | 0.486993i | \(0.161906\pi\) | |||||||
\(104\) | 1.23906e8 | − | 2.14612e8i | 0.103859 | − | 0.179888i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.14326e8 | + | 8.90839e8i | 0.395696 | + | 0.685366i | ||||
\(107\) | −1.61837e9 | −1.19358 | −0.596790 | − | 0.802397i | \(-0.703557\pi\) | ||||
−0.596790 | + | 0.802397i | \(0.703557\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.56262e8 | −0.581015 | −0.290508 | − | 0.956873i | \(-0.593824\pi\) | ||||
−0.290508 | + | 0.956873i | \(0.593824\pi\) | |||||||
\(110\) | 6.47305e8 | + | 1.12116e9i | 0.421543 | + | 0.730133i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −7.20914e8 | + | 1.24866e9i | −0.432915 | + | 0.749831i | ||||
\(113\) | 9.66311e8 | − | 1.67370e9i | 0.557524 | − | 0.965661i | −0.440178 | − | 0.897911i | \(-0.645085\pi\) |
0.997702 | − | 0.0677501i | \(-0.0215821\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.95056e7 | + | 6.84257e7i | 0.0210629 | + | 0.0364820i | ||||
\(116\) | −6.41212e8 | −0.328807 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.45826e9 | −1.16724 | ||||||||
\(119\) | 7.18976e8 | + | 1.24530e9i | 0.328665 | + | 0.569264i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.37239e9 | + | 2.37705e9i | −0.582028 | + | 1.00810i | ||||
\(122\) | 2.59394e8 | − | 4.49284e8i | 0.106009 | − | 0.183612i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.22443e8 | + | 1.25131e9i | 0.274414 | + | 0.475298i | ||||
\(125\) | 2.40700e9 | 0.881824 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.98705e9 | 1.70109 | 0.850545 | − | 0.525903i | \(-0.176272\pi\) | ||||
0.850545 | + | 0.525903i | \(0.176272\pi\) | |||||||
\(128\) | 1.83228e9 | + | 3.17361e9i | 0.603320 | + | 1.04498i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.39246e8 | − | 4.14387e8i | 0.0734683 | − | 0.127251i | ||||
\(131\) | −9.58360e7 | + | 1.65993e8i | −0.0284320 | + | 0.0492457i | −0.879891 | − | 0.475175i | \(-0.842385\pi\) |
0.851459 | + | 0.524421i | \(0.175718\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.06497e9 | − | 3.57663e9i | −0.572243 | − | 0.991155i | ||||
\(134\) | −4.68180e9 | −1.25441 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.95436e9 | 0.740523 | ||||||||
\(137\) | 5.00385e8 | + | 8.66692e8i | 0.121356 | + | 0.210195i | 0.920303 | − | 0.391207i | \(-0.127942\pi\) |
−0.798947 | + | 0.601402i | \(0.794609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.75119e8 | − | 1.16934e9i | 0.153396 | − | 0.265689i | −0.779078 | − | 0.626927i | \(-0.784312\pi\) |
0.932474 | + | 0.361238i | \(0.117646\pi\) | |||||||
\(140\) | −2.35803e8 | + | 4.08423e8i | −0.0518768 | + | 0.0898533i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.77709e9 | − | 3.07800e9i | −0.366785 | − | 0.635290i | ||||
\(143\) | 1.88599e9 | 0.377161 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.09993e9 | 0.582366 | ||||||||
\(146\) | −2.79590e9 | − | 4.84264e9i | −0.509253 | − | 0.882053i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.61852e8 | − | 7.99951e8i | 0.0791270 | − | 0.137052i | ||||
\(149\) | 1.76496e9 | − | 3.05700e9i | 0.293357 | − | 0.508110i | −0.681244 | − | 0.732056i | \(-0.738561\pi\) |
0.974601 | + | 0.223947i | \(0.0718941\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.86323e8 | − | 4.95926e8i | −0.0448188 | − | 0.0776284i | 0.842746 | − | 0.538312i | \(-0.180938\pi\) |
−0.887565 | + | 0.460683i | \(0.847604\pi\) | |||||||
\(152\) | −8.48521e9 | −1.28934 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.37186e9 | −1.19944 | ||||||||
\(155\) | −3.49264e9 | − | 6.04943e9i | −0.486028 | − | 0.841825i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.20086e8 | + | 7.27610e8i | −0.0551810 | + | 0.0955763i | −0.892296 | − | 0.451450i | \(-0.850907\pi\) |
0.837115 | + | 0.547026i | \(0.184240\pi\) | |||||||
\(158\) | 5.06137e9 | − | 8.76654e9i | 0.646117 | − | 1.11911i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.16244e9 | + | 2.01340e9i | 0.140227 | + | 0.242880i | ||||
\(161\) | −5.10942e8 | −0.0599315 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.00425e9 | −0.777173 | −0.388586 | − | 0.921412i | \(-0.627037\pi\) | ||||
−0.388586 | + | 0.921412i | \(0.627037\pi\) | |||||||
\(164\) | 3.91650e8 | + | 6.78357e8i | 0.0422766 | + | 0.0732253i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 6.07072e9 | − | 1.05148e10i | 0.620517 | − | 1.07477i | ||||
\(167\) | −4.63508e9 | + | 8.02820e9i | −0.461141 | + | 0.798719i | −0.999018 | − | 0.0443040i | \(-0.985893\pi\) |
0.537877 | + | 0.843023i | \(0.319226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.95372e9 | + | 8.58009e9i | 0.467133 | + | 0.809099i | ||||
\(170\) | 5.70448e9 | 0.523836 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.28129e9 | 0.285869 | ||||||||
\(173\) | 4.13667e9 | + | 7.16492e9i | 0.351110 | + | 0.608141i | 0.986444 | − | 0.164097i | \(-0.0524709\pi\) |
−0.635334 | + | 0.772237i | \(0.719138\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.32136e9 | + | 5.75276e9i | −0.267697 | + | 0.463665i | ||||
\(176\) | −1.12725e10 | + | 1.95245e10i | −0.885549 | + | 1.53382i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.34152e9 | − | 5.78769e9i | −0.249491 | − | 0.432131i | ||||
\(179\) | 2.36310e10 | 1.72046 | 0.860229 | − | 0.509907i | \(-0.170320\pi\) | ||||
0.860229 | + | 0.509907i | \(0.170320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.40618e10 | 0.973841 | 0.486921 | − | 0.873446i | \(-0.338120\pi\) | ||||
0.486921 | + | 0.873446i | \(0.338120\pi\) | |||||||
\(182\) | 1.54714e9 | + | 2.67972e9i | 0.104522 | + | 0.181037i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.24881e8 | + | 9.09121e8i | −0.0337583 | + | 0.0584711i | ||||
\(185\) | −2.23282e9 | + | 3.86735e9i | −0.140146 | + | 0.242740i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.12422e10 | + | 1.94720e10i | 0.672299 | + | 1.16446i | ||||
\(188\) | 6.53611e9 | 0.381600 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.63838e10 | −0.912061 | ||||||||
\(191\) | −4.87596e9 | − | 8.44541e9i | −0.265100 | − | 0.459167i | 0.702490 | − | 0.711694i | \(-0.252072\pi\) |
−0.967590 | + | 0.252527i | \(0.918738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.97588e9 | + | 8.61847e9i | −0.258144 | + | 0.447118i | −0.965745 | − | 0.259494i | \(-0.916444\pi\) |
0.707601 | + | 0.706612i | \(0.249778\pi\) | |||||||
\(194\) | 7.37349e9 | − | 1.27713e10i | 0.373737 | − | 0.647331i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.42351e9 | + | 2.46560e9i | 0.0688984 | + | 0.119336i | ||||
\(197\) | 3.23117e9 | 0.152849 | 0.0764244 | − | 0.997075i | \(-0.475650\pi\) | ||||
0.0764244 | + | 0.997075i | \(0.475650\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.90155e10 | −1.31157 | −0.655785 | − | 0.754947i | \(-0.727662\pi\) | ||||
−0.655785 | + | 0.754947i | \(0.727662\pi\) | |||||||
\(200\) | 6.82393e9 | + | 1.18194e10i | 0.301578 | + | 0.522348i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.80568e9 | + | 3.12754e9i | −0.0763063 | + | 0.132166i | ||||
\(203\) | −1.00232e10 | + | 1.73607e10i | −0.414260 | + | 0.717520i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.89343e9 | − | 3.27951e9i | −0.0748783 | − | 0.129693i | ||||
\(206\) | 8.76437e8 | 0.0339092 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 8.33270e9 | 0.308675 | ||||||||
\(209\) | −3.22886e10 | − | 5.59255e10i | −1.17055 | − | 2.02746i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.12768e9 | − | 3.68525e9i | 0.0738985 | − | 0.127996i | −0.826708 | − | 0.562631i | \(-0.809789\pi\) |
0.900607 | + | 0.434635i | \(0.143123\pi\) | |||||||
\(212\) | −2.92965e9 | + | 5.07430e9i | −0.0996102 | + | 0.172530i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.07589e10 | − | 3.59554e10i | −0.676615 | − | 1.17193i | ||||
\(215\) | −1.58634e10 | −0.506317 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.51718e10 | 1.38292 | ||||||||
\(218\) | −1.09833e10 | − | 1.90236e10i | −0.329365 | − | 0.570477i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −3.68710e9 | + | 6.38625e9i | −0.106117 | + | 0.183799i | ||||
\(221\) | 4.15515e9 | − | 7.19692e9i | 0.117171 | − | 0.202947i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.11759e10 | − | 3.66777e10i | −0.573416 | − | 0.993185i | −0.996212 | − | 0.0869601i | \(-0.972285\pi\) |
0.422796 | − | 0.906225i | \(-0.361049\pi\) | |||||||
\(224\) | −1.50343e10 | −0.398995 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.95795e10 | 1.26419 | ||||||||
\(227\) | 2.96301e10 | + | 5.13208e10i | 0.740656 | + | 1.28285i | 0.952197 | + | 0.305485i | \(0.0988186\pi\) |
−0.211541 | + | 0.977369i | \(0.567848\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.07523e10 | − | 5.32645e10i | 0.738954 | − | 1.27991i | −0.214013 | − | 0.976831i | \(-0.568653\pi\) |
0.952967 | − | 0.303075i | \(-0.0980133\pi\) | |||||||
\(230\) | −1.01348e9 | + | 1.75539e9i | −0.0238802 | + | 0.0413617i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.05932e10 | + | 3.56685e10i | 0.466690 | + | 0.808331i | ||||
\(233\) | 4.69389e10 | 1.04335 | 0.521677 | − | 0.853143i | \(-0.325307\pi\) | ||||
0.521677 | + | 0.853143i | \(0.325307\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.15987e10 | −0.675872 | ||||||||
\(236\) | −7.00123e9 | − | 1.21265e10i | −0.146916 | − | 0.254467i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.84446e10 | + | 3.19470e10i | −0.372626 | + | 0.645407i | ||||
\(239\) | 5.22440e9 | − | 9.04892e9i | 0.103573 | − | 0.179393i | −0.809581 | − | 0.587008i | \(-0.800306\pi\) |
0.913154 | + | 0.407614i | \(0.133639\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.49700e10 | − | 2.59288e10i | −0.285854 | − | 0.495114i | 0.686962 | − | 0.726693i | \(-0.258944\pi\) |
−0.972816 | + | 0.231580i | \(0.925611\pi\) | |||||||
\(242\) | −7.04147e10 | −1.31976 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.95507e9 | 0.0533719 | ||||||||
\(245\) | −6.88196e9 | − | 1.19199e10i | −0.122030 | − | 0.211361i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.19340e10 | + | 2.06703e10i | −0.204009 | + | 0.353354i | ||||
\(248\) | 4.64041e10 | − | 8.03743e10i | 0.778976 | − | 1.34923i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.08746e10 | + | 5.34764e10i | 0.499887 | + | 0.865830i | ||||
\(251\) | 1.50652e9 | 0.0239576 | 0.0119788 | − | 0.999928i | \(-0.496187\pi\) | ||||
0.0119788 | + | 0.999928i | \(0.496187\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.98928e9 | −0.122593 | ||||||||
\(254\) | 6.39689e10 | + | 1.10797e11i | 0.964311 | + | 1.67024i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.72509e10 | + | 4.72000e10i | −0.396553 | + | 0.686850i | ||||
\(257\) | −4.35790e10 | + | 7.54811e10i | −0.623130 | + | 1.07929i | 0.365770 | + | 0.930705i | \(0.380806\pi\) |
−0.988899 | + | 0.148587i | \(0.952528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.44390e10 | − | 2.50090e10i | −0.199383 | − | 0.345341i | ||||
\(260\) | 2.72553e9 | 0.0369889 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.91715e9 | −0.0644700 | ||||||||
\(263\) | −2.10643e10 | − | 3.64844e10i | −0.271485 | − | 0.470226i | 0.697757 | − | 0.716334i | \(-0.254181\pi\) |
−0.969242 | + | 0.246108i | \(0.920848\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.41633e10 | − | 2.45316e10i | 0.176425 | − | 0.305577i | ||||
\(266\) | 5.29747e10 | − | 9.17548e10i | 0.648785 | − | 1.12373i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.33340e10 | − | 2.30951e10i | −0.157889 | − | 0.273472i | ||||
\(269\) | −6.32241e10 | −0.736202 | −0.368101 | − | 0.929786i | \(-0.619992\pi\) | ||||
−0.368101 | + | 0.929786i | \(0.619992\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.63811e11 | −1.84493 | −0.922467 | − | 0.386075i | \(-0.873831\pi\) | ||||
−0.922467 | + | 0.386075i | \(0.873831\pi\) | |||||||
\(272\) | 4.96703e10 | + | 8.60314e10i | 0.550220 | + | 0.953009i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.28369e10 | + | 2.22341e10i | −0.137588 | + | 0.238310i | ||||
\(275\) | −5.19339e10 | + | 8.99522e10i | −0.547588 | + | 0.948451i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.63022e10 | + | 1.49480e11i | 0.880771 | + | 1.52554i | 0.850485 | + | 0.525999i | \(0.176308\pi\) |
0.0302857 | + | 0.999541i | \(0.490358\pi\) | |||||||
\(278\) | 3.46390e10 | 0.347827 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.02923e10 | 0.294525 | ||||||||
\(281\) | −1.27714e10 | − | 2.21208e10i | −0.122197 | − | 0.211652i | 0.798437 | − | 0.602079i | \(-0.205661\pi\) |
−0.920634 | + | 0.390427i | \(0.872327\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.69467e10 | − | 6.39936e10i | 0.342402 | − | 0.593058i | −0.642476 | − | 0.766306i | \(-0.722093\pi\) |
0.984878 | + | 0.173248i | \(0.0554261\pi\) | |||||||
\(284\) | 1.01224e10 | − | 1.75326e10i | 0.0923321 | − | 0.159924i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.41916e10 | + | 4.19010e10i | 0.213805 | + | 0.370320i | ||||
\(287\) | 2.44885e10 | 0.213056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.95145e10 | −0.164557 | ||||||||
\(290\) | 3.97628e10 | + | 6.88712e10i | 0.330131 | + | 0.571803i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.59257e10 | − | 2.75841e10i | 0.128196 | − | 0.222043i | ||||
\(293\) | 1.01768e11 | − | 1.76267e11i | 0.806687 | − | 1.39722i | −0.108459 | − | 0.994101i | \(-0.534592\pi\) |
0.915146 | − | 0.403122i | \(-0.132075\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.38474e10 | + | 5.86253e10i | 0.260211 | + | 0.450699i | ||||
\(296\) | −5.93316e10 | −0.449234 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.05566e10 | 0.665192 | ||||||||
\(299\) | 1.47643e9 | + | 2.55726e9i | 0.0106830 | + | 0.0185035i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 5.12919e10 | − | 8.88401e10i | 0.360163 | − | 0.623821i | ||||
\(302\) | 7.34533e9 | − | 1.27225e10i | 0.0508136 | − | 0.0880118i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.42658e11 | − | 2.47091e11i | −0.957998 | − | 1.65930i | ||||
\(305\) | −1.42862e10 | −0.0945297 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.22523e10 | 0.528476 | 0.264238 | − | 0.964457i | \(-0.414880\pi\) | ||||
0.264238 | + | 0.964457i | \(0.414880\pi\) | |||||||
\(308\) | −2.38434e10 | − | 4.12980e10i | −0.150970 | − | 0.261488i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.96002e10 | − | 1.55192e11i | 0.551038 | − | 0.954425i | ||||
\(311\) | −1.16047e11 | + | 2.00999e11i | −0.703415 | + | 1.21835i | 0.263846 | + | 0.964565i | \(0.415009\pi\) |
−0.967261 | + | 0.253785i | \(0.918324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.15040e10 | − | 5.45665e10i | −0.185531 | − | 0.321349i | 0.758224 | − | 0.651994i | \(-0.226067\pi\) |
−0.943755 | + | 0.330645i | \(0.892734\pi\) | |||||||
\(314\) | −2.15537e10 | −0.125124 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.76600e10 | 0.325299 | ||||||||
\(317\) | −1.15735e11 | − | 2.00459e11i | −0.643722 | − | 1.11496i | −0.984595 | − | 0.174850i | \(-0.944056\pi\) |
0.340873 | − | 0.940109i | \(-0.389277\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.56726e11 | + | 2.71458e11i | −0.847390 | + | 1.46772i | ||||
\(320\) | 2.72570e10 | − | 4.72105e10i | 0.145312 | − | 0.251689i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.55385e9 | − | 1.13516e10i | −0.0339739 | − | 0.0588445i | ||||
\(323\) | −2.84548e11 | −1.45460 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.83899e10 | 0.190872 | ||||||||
\(326\) | −8.98436e10 | − | 1.55614e11i | −0.440563 | − | 0.763077i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.51565e10 | − | 4.35724e10i | 0.120010 | − | 0.207864i | ||||
\(329\) | 1.02170e11 | − | 1.76963e11i | 0.480775 | − | 0.832726i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.72274e10 | − | 1.33762e11i | −0.353627 | − | 0.612500i | 0.633255 | − | 0.773943i | \(-0.281718\pi\) |
−0.986882 | + | 0.161443i | \(0.948385\pi\) | |||||||
\(332\) | 6.91587e10 | 0.312410 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.37817e11 | −1.04564 | ||||||||
\(335\) | 6.44629e10 | + | 1.11653e11i | 0.279646 | + | 0.484361i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.76249e10 | + | 1.17130e11i | −0.285609 | + | 0.494690i | −0.972757 | − | 0.231828i | \(-0.925529\pi\) |
0.687148 | + | 0.726518i | \(0.258863\pi\) | |||||||
\(338\) | −1.27083e11 | + | 2.20113e11i | −0.529616 | + | 0.917321i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.62466e10 | + | 2.81399e10i | 0.0659337 | + | 0.114201i | ||||
\(341\) | 7.06323e11 | 2.82884 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.73359e11 | 1.06638 | ||||||||
\(344\) | −1.05382e11 | − | 1.82528e11i | −0.405747 | − | 0.702774i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.06122e11 | + | 1.83809e11i | −0.398074 | + | 0.689484i | ||||
\(347\) | −1.41753e11 | + | 2.45523e11i | −0.524867 | + | 0.909096i | 0.474714 | + | 0.880140i | \(0.342551\pi\) |
−0.999581 | + | 0.0289556i | \(0.990782\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.86799e10 | − | 8.43160e10i | −0.175645 | − | 0.304225i | 0.764740 | − | 0.644340i | \(-0.222868\pi\) |
−0.940384 | + | 0.340114i | \(0.889534\pi\) | |||||||
\(350\) | −1.70412e11 | −0.607008 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.35082e11 | −0.816164 | ||||||||
\(353\) | 1.91861e10 | + | 3.32314e10i | 0.0657660 | + | 0.113910i | 0.897034 | − | 0.441962i | \(-0.145718\pi\) |
−0.831268 | + | 0.555873i | \(0.812384\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.89368e10 | + | 8.47611e10i | −0.163534 | + | 0.283249i | ||||
\(356\) | 1.90336e10 | − | 3.29672e10i | 0.0628053 | − | 0.108782i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.03115e11 | + | 5.25011e11i | 0.975291 | + | 1.68925i | ||||
\(359\) | 4.48036e11 | 1.42360 | 0.711800 | − | 0.702383i | \(-0.247880\pi\) | ||||
0.711800 | + | 0.702383i | \(0.247880\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.94563e11 | 1.53264 | ||||||||
\(362\) | 1.80371e11 | + | 3.12412e11i | 0.552050 | + | 0.956178i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −8.81262e9 | + | 1.52639e10i | −0.0263117 | + | 0.0455732i | ||||
\(365\) | −7.69926e10 | + | 1.33355e11i | −0.227055 | + | 0.393271i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.74037e10 | + | 6.47850e10i | 0.107626 | + | 0.186414i | 0.914808 | − | 0.403889i | \(-0.132342\pi\) |
−0.807182 | + | 0.590302i | \(0.799008\pi\) | |||||||
\(368\) | −3.52983e10 | −0.100332 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.14561e11 | −0.317783 | ||||||||
\(371\) | 9.15902e10 | + | 1.58639e11i | 0.250996 | + | 0.434738i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.39696e11 | − | 2.41961e11i | 0.373675 | − | 0.647225i | −0.616452 | − | 0.787392i | \(-0.711431\pi\) |
0.990128 | + | 0.140167i | \(0.0447641\pi\) | |||||||
\(374\) | −2.88406e11 | + | 4.99535e11i | −0.762224 | + | 1.32021i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.09914e11 | − | 3.63582e11i | −0.541623 | − | 0.938118i | ||||
\(377\) | 1.15853e11 | 0.295374 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.40616e11 | −1.59485 | −0.797427 | − | 0.603415i | \(-0.793806\pi\) | ||||
−0.797427 | + | 0.603415i | \(0.793806\pi\) | |||||||
\(380\) | −4.66618e10 | − | 8.08206e10i | −0.114798 | − | 0.198836i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.25088e11 | − | 2.16659e11i | 0.300559 | − | 0.520584i | ||||
\(383\) | 1.66528e11 | − | 2.88435e11i | 0.395451 | − | 0.684942i | −0.597707 | − | 0.801714i | \(-0.703921\pi\) |
0.993159 | + | 0.116772i | \(0.0372548\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.15271e11 | + | 1.99655e11i | 0.267390 | + | 0.463134i | ||||
\(386\) | −2.55302e11 | −0.585345 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.40002e10 | 0.188164 | ||||||||
\(389\) | −8.15796e10 | − | 1.41300e11i | −0.180638 | − | 0.312873i | 0.761460 | − | 0.648212i | \(-0.224483\pi\) |
−0.942098 | + | 0.335338i | \(0.891149\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.76017e10 | + | 3.04870e10i | −0.0380855 | + | 0.0659660i | ||||
\(392\) | 9.14355e10 | − | 1.58371e11i | 0.195581 | − | 0.338757i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4.14462e10 | + | 7.17870e10i | 0.0866467 | + | 0.150076i | ||||
\(395\) | −2.78757e11 | −0.576153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.79119e11 | 0.563939 | 0.281969 | − | 0.959423i | \(-0.409012\pi\) | ||||
0.281969 | + | 0.959423i | \(0.409012\pi\) | |||||||
\(398\) | −3.72182e11 | − | 6.44638e11i | −0.743501 | − | 1.28778i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.29455e11 | + | 3.97428e11i | −0.448155 | + | 0.776227i | ||||
\(401\) | 3.79966e11 | − | 6.58121e11i | 0.733830 | − | 1.27103i | −0.221405 | − | 0.975182i | \(-0.571064\pi\) |
0.955235 | − | 0.295848i | \(-0.0956024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.30530e11 | − | 2.26084e11i | −0.246511 | − | 0.426970i | ||||
\(404\) | −2.05707e10 | −0.0384178 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.14269e11 | −0.939341 | ||||||||
\(407\) | −2.25773e11 | − | 3.91051e11i | −0.407847 | − | 0.706412i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.89971e10 | − | 3.29039e10i | 0.0335685 | − | 0.0581423i | −0.848753 | − | 0.528789i | \(-0.822646\pi\) |
0.882322 | + | 0.470647i | \(0.155979\pi\) | |||||||
\(410\) | 4.85739e10 | − | 8.41325e10i | 0.0848938 | − | 0.147040i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.49613e9 | + | 4.32342e9i | 0.00426805 | + | 0.00739248i | ||||
\(413\) | −4.37762e11 | −0.740394 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.34347e11 | −0.553326 | ||||||||
\(416\) | 4.34436e10 | + | 7.52465e10i | 0.0711223 | + | 0.123187i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 8.28331e11 | − | 1.43471e12i | 1.32712 | − | 2.29864i | ||||
\(419\) | −3.66823e11 | + | 6.35355e11i | −0.581424 | + | 1.00706i | 0.413887 | + | 0.910328i | \(0.364171\pi\) |
−0.995311 | + | 0.0967277i | \(0.969162\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.60716e11 | + | 2.78368e11i | 0.249339 | + | 0.431867i | 0.963342 | − | 0.268275i | \(-0.0864535\pi\) |
−0.714004 | + | 0.700142i | \(0.753120\pi\) | |||||||
\(422\) | 1.09167e11 | 0.167566 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.76356e11 | 0.565525 | ||||||||
\(425\) | 2.28838e11 | + | 3.96359e11i | 0.340234 | + | 0.589303i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.61924e10 | − | 8.00077e10i | 0.0672428 | − | 0.116468i | ||||
\(428\) | 1.18244e11 | − | 2.04805e11i | 0.170327 | − | 0.295015i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.03479e11 | − | 3.52437e11i | −0.287020 | − | 0.497133i | ||||
\(431\) | −3.86098e11 | −0.538952 | −0.269476 | − | 0.963007i | \(-0.586850\pi\) | ||||
−0.269476 | + | 0.963007i | \(0.586850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.48808e11 | 0.750282 | 0.375141 | − | 0.926968i | \(-0.377594\pi\) | ||||
0.375141 | + | 0.926968i | \(0.377594\pi\) | |||||||
\(434\) | 5.79418e11 | + | 1.00358e12i | 0.783950 | + | 1.35784i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.25617e10 | − | 1.08360e11i | 0.0829123 | − | 0.143608i | ||||
\(437\) | 5.05538e10 | − | 8.75617e10i | 0.0663113 | − | 0.114854i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.50050e11 | + | 2.59895e11i | 0.192817 | + | 0.333969i | 0.946183 | − | 0.323633i | \(-0.104904\pi\) |
−0.753365 | + | 0.657602i | \(0.771571\pi\) | |||||||
\(440\) | 4.73662e11 | 0.602465 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.13192e11 | 0.265687 | ||||||||
\(443\) | 2.11330e11 | + | 3.66034e11i | 0.260702 | + | 0.451549i | 0.966429 | − | 0.256935i | \(-0.0827127\pi\) |
−0.705727 | + | 0.708484i | \(0.749379\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.20178e10 | + | 1.59379e11i | −0.111238 | + | 0.192669i | ||||
\(446\) | 5.43246e11 | − | 9.40929e11i | 0.650114 | − | 1.12603i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.76263e11 | + | 3.05296e11i | 0.206733 | + | 0.358072i | ||||
\(449\) | −1.63406e12 | −1.89741 | −0.948704 | − | 0.316165i | \(-0.897605\pi\) | ||||
−0.948704 | + | 0.316165i | \(0.897605\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.82911e11 | 0.435816 | ||||||||
\(452\) | 1.41205e11 | + | 2.44573e11i | 0.159120 | + | 0.275605i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.60130e11 | + | 1.31658e12i | −0.839724 | + | 1.45445i | ||||
\(455\) | 4.26045e10 | − | 7.37932e10i | 0.0466020 | − | 0.0807170i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.23184e11 | − | 1.07939e12i | −0.668334 | − | 1.15759i | −0.978370 | − | 0.206863i | \(-0.933675\pi\) |
0.310036 | − | 0.950725i | \(-0.399659\pi\) | |||||||
\(458\) | 1.57784e12 | 1.67559 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.15457e10 | −0.0120229 | ||||||||
\(461\) | 1.44026e11 | + | 2.49459e11i | 0.148520 | + | 0.257244i | 0.930681 | − | 0.365833i | \(-0.119216\pi\) |
−0.782161 | + | 0.623077i | \(0.785882\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.86329e11 | + | 1.36196e12i | −0.795225 | + | 1.37737i | 0.127472 | + | 0.991842i | \(0.459314\pi\) |
−0.922696 | + | 0.385527i | \(0.874020\pi\) | |||||||
\(464\) | −6.92449e11 | + | 1.19936e12i | −0.693517 | + | 1.20121i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 6.02085e11 | + | 1.04284e12i | 0.591454 | + | 1.02443i | ||||
\(467\) | −2.12882e11 | −0.207116 | −0.103558 | − | 0.994623i | \(-0.533023\pi\) | ||||
−0.103558 | + | 0.994623i | \(0.533023\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.33726e11 | −0.795693 | ||||||||
\(470\) | −4.05317e11 | − | 7.02029e11i | −0.383137 | − | 0.663613i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.49705e11 | + | 7.78911e11i | −0.417050 | + | 0.722352i | ||||
\(473\) | 8.02019e11 | − | 1.38914e12i | 0.736732 | − | 1.27606i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.57245e11 | − | 1.13838e12i | −0.592388 | − | 1.02605i | ||||
\(476\) | −2.10124e11 | −0.187605 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.68053e11 | 0.234853 | ||||||||
\(479\) | 7.62418e11 | + | 1.32055e12i | 0.661733 | + | 1.14616i | 0.980160 | + | 0.198208i | \(0.0635123\pi\) |
−0.318426 | + | 0.947948i | \(0.603154\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.34466e10 | + | 1.44534e11i | −0.0710814 | + | 0.123117i | ||||
\(482\) | 3.84040e11 | − | 6.65176e11i | 0.324089 | − | 0.561339i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.00544e11 | − | 3.47353e11i | −0.166114 | − | 0.287718i | ||||
\(485\) | −4.06098e11 | −0.333267 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.81008e12 | −1.45820 | −0.729101 | − | 0.684406i | \(-0.760062\pi\) | ||||
−0.729101 | + | 0.684406i | \(0.760062\pi\) | |||||||
\(488\) | −9.49052e10 | − | 1.64381e11i | −0.0757532 | − | 0.131208i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.76550e11 | − | 3.05793e11i | 0.138352 | − | 0.239632i | ||||
\(491\) | −5.76915e11 | + | 9.99245e11i | −0.447966 | + | 0.775899i | −0.998254 | − | 0.0590757i | \(-0.981185\pi\) |
0.550288 | + | 0.834975i | \(0.314518\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.90587e11 | + | 1.19613e12i | 0.526511 | + | 0.911944i | ||||
\(494\) | −6.12309e11 | −0.462593 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.12068e12 | 2.31517 | ||||||||
\(497\) | −3.16460e11 | − | 5.48125e11i | −0.232657 | − | 0.402973i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.00972e12 | − | 1.74888e12i | 0.729032 | − | 1.26272i | −0.228260 | − | 0.973600i | \(-0.573304\pi\) |
0.957293 | − | 0.289121i | \(-0.0933629\pi\) | |||||||
\(500\) | −1.75865e11 | + | 3.04607e11i | −0.125839 | + | 0.217959i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.93241e10 | + | 3.34703e10i | 0.0135810 | + | 0.0235230i | ||||
\(503\) | 7.16624e11 | 0.499155 | 0.249578 | − | 0.968355i | \(-0.419708\pi\) | ||||
0.249578 | + | 0.968355i | \(0.419708\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.94486e10 | 0.0680437 | ||||||||
\(506\) | −1.02478e11 | − | 1.77498e11i | −0.0694953 | − | 0.120369i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3.64372e11 | + | 6.31112e11i | −0.242750 | + | 0.420455i | ||||
\(509\) | −7.90670e11 | + | 1.36948e12i | −0.522114 | + | 0.904327i | 0.477555 | + | 0.878602i | \(0.341523\pi\) |
−0.999669 | + | 0.0257257i | \(0.991810\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.97889e11 | − | 8.62369e11i | −0.323027 | − | 0.559499i | ||||
\(512\) | 4.78068e11 | 0.307450 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.23595e12 | −1.41296 | ||||||||
\(515\) | −1.20675e10 | − | 2.09015e10i | −0.00755936 | − | 0.0130932i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.59757e12 | − | 2.76707e12i | 0.983448 | − | 1.70338i | ||||
\(518\) | 3.70417e11 | − | 6.41582e11i | 0.226052 | − | 0.391533i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.75336e10 | − | 1.51613e11i | −0.0525001 | − | 0.0909328i | ||||
\(521\) | −1.03065e12 | −0.612834 | −0.306417 | − | 0.951897i | \(-0.599130\pi\) | ||||
−0.306417 | + | 0.951897i | \(0.599130\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.03811e12 | 1.19116 | 0.595579 | − | 0.803297i | \(-0.296923\pi\) | ||||
0.595579 | + | 0.803297i | \(0.296923\pi\) | |||||||
\(524\) | −1.40043e10 | − | 2.42561e10i | −0.00811465 | − | 0.0140550i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.40383e11 | − | 9.35971e11i | 0.307798 | − | 0.533122i | ||||
\(527\) | 1.55615e12 | − | 2.69532e12i | 0.878825 | − | 1.52217i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.94322e11 | + | 1.54901e12i | 0.496528 | + | 0.860011i | ||||
\(530\) | 7.26693e11 | 0.400046 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.03497e11 | 0.326642 | ||||||||
\(533\) | −7.07626e10 | − | 1.22564e11i | −0.0379779 | − | 0.0657797i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.71651e11 | + | 9.90128e11i | −0.301675 | + | 0.522516i | ||||
\(536\) | −8.56471e11 | + | 1.48345e12i | −0.448199 | + | 0.776303i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −8.10975e11 | − | 1.40465e12i | −0.417337 | − | 0.722849i | ||||
\(539\) | 1.39175e12 | 0.710251 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.53998e12 | −0.772905 | −0.386453 | − | 0.922309i | \(-0.626300\pi\) | ||||
−0.386453 | + | 0.922309i | \(0.626300\pi\) | |||||||
\(542\) | −2.10120e12 | − | 3.63939e12i | −1.04585 | − | 1.81147i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.17925e11 | + | 8.97072e11i | −0.253555 | + | 0.439170i | ||||
\(545\) | −3.02454e11 | + | 5.23865e11i | −0.146850 | + | 0.254352i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.59604e11 | + | 1.66208e12i | 0.458299 | + | 0.793797i | 0.998871 | − | 0.0475005i | \(-0.0151256\pi\) |
−0.540572 | + | 0.841298i | \(0.681792\pi\) | |||||||
\(548\) | −1.46240e11 | −0.0692713 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.66463e12 | −1.24166 | ||||||||
\(551\) | −1.98343e12 | − | 3.43541e12i | −0.916717 | − | 1.58780i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.01319e11 | − | 1.56113e12i | 0.409841 | − | 0.709865i | ||||
\(554\) | −2.21400e12 | + | 3.83475e12i | −0.998580 | + | 1.72959i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 9.86533e10 | + | 1.70873e11i | 0.0437799 | + | 0.0758291i | ||||
\(557\) | 2.71058e11 | 0.119320 | 0.0596601 | − | 0.998219i | \(-0.480998\pi\) | ||||
0.0596601 | + | 0.998219i | \(0.480998\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.92858e11 | −0.256802 | ||||||||
\(560\) | 5.09291e11 | + | 8.82118e11i | 0.218836 | + | 0.379036i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.27638e11 | − | 5.67486e11i | 0.138542 | − | 0.239962i | ||||
\(563\) | 1.54117e11 | − | 2.66939e11i | 0.0646492 | − | 0.111976i | −0.831889 | − | 0.554942i | \(-0.812740\pi\) |
0.896538 | + | 0.442966i | \(0.146074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.82652e11 | − | 1.18239e12i | −0.281826 | − | 0.488137i | ||||
\(566\) | 1.89566e12 | 0.776402 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.30037e12 | −0.524205 | ||||||||
\(569\) | 1.79082e12 | + | 3.10180e12i | 0.716222 | + | 1.24053i | 0.962486 | + | 0.271330i | \(0.0874636\pi\) |
−0.246264 | + | 0.969203i | \(0.579203\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.45411e10 | − | 7.71475e10i | 0.0175347 | − | 0.0303710i | −0.857125 | − | 0.515109i | \(-0.827752\pi\) |
0.874660 | + | 0.484738i | \(0.161085\pi\) | |||||||
\(572\) | −1.37797e11 | + | 2.38672e11i | −0.0538219 | + | 0.0932222i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.14113e11 | + | 5.44060e11i | 0.120777 | + | 0.209191i | ||||
\(575\) | −1.62624e11 | −0.0620413 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.29975e11 | −0.161492 | −0.0807462 | − | 0.996735i | \(-0.525730\pi\) | ||||
−0.0807462 | + | 0.996735i | \(0.525730\pi\) | |||||||
\(578\) | −2.50312e11 | − | 4.33553e11i | −0.0932838 | − | 0.161572i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −2.26493e11 | + | 3.92297e11i | −0.0831051 | + | 0.143942i | ||||
\(581\) | 1.08106e12 | − | 1.87245e12i | 0.393603 | − | 0.681740i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.43214e12 | + | 2.48054e12i | 0.513424 | + | 0.889277i | ||||
\(584\) | −2.04589e12 | −0.727820 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.22149e12 | 1.82917 | ||||||||
\(587\) | 1.13503e12 | + | 1.96594e12i | 0.394582 | + | 0.683436i | 0.993048 | − | 0.117712i | \(-0.0375561\pi\) |
−0.598466 | + | 0.801148i | \(0.704223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.46940e12 | + | 7.74123e12i | −1.53014 | + | 2.65028i | ||||
\(590\) | −8.68320e11 | + | 1.50397e12i | −0.295016 | + | 0.510983i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.97514e11 | − | 1.72774e12i | −0.333788 | − | 0.578138i | ||||
\(593\) | 4.09944e12 | 1.36138 | 0.680688 | − | 0.732573i | \(-0.261681\pi\) | ||||
0.680688 | + | 0.732573i | \(0.261681\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.01584e12 | 0.332277 | ||||||||
\(596\) | 2.57909e11 | + | 4.46712e11i | 0.0837256 | + | 0.145017i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.78764e10 | + | 6.56039e10i | −0.0121119 | + | 0.0209785i | ||||
\(599\) | −8.09154e11 | + | 1.40150e12i | −0.256809 | + | 0.444806i | −0.965385 | − | 0.260828i | \(-0.916005\pi\) |
0.708576 | + | 0.705634i | \(0.249338\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.60804e11 | − | 1.49096e12i | −0.269134 | − | 0.466155i | 0.699504 | − | 0.714629i | \(-0.253404\pi\) |
−0.968639 | + | 0.248474i | \(0.920071\pi\) | |||||||
\(602\) | 2.63168e12 | 0.816675 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.36793e10 | 0.0255830 | ||||||||
\(605\) | 9.69528e11 | + | 1.67927e12i | 0.294213 | + | 0.509591i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.07028e12 | − | 3.58583e12i | 0.618985 | − | 1.07211i | −0.370686 | − | 0.928758i | \(-0.620877\pi\) |
0.989671 | − | 0.143356i | \(-0.0457894\pi\) | |||||||
\(608\) | 1.48753e12 | − | 2.57648e12i | 0.441468 | − | 0.764646i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.83249e11 | − | 3.17397e11i | −0.0535869 | − | 0.0928152i | ||||
\(611\) | −1.18093e12 | −0.342799 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.88290e12 | 0.538585 | 0.269292 | − | 0.963058i | \(-0.413210\pi\) | ||||
0.269292 | + | 0.963058i | \(0.413210\pi\) | |||||||
\(614\) | 1.05505e12 | + | 1.82740e12i | 0.299582 | + | 0.518891i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.53152e12 | + | 2.65267e12i | −0.428557 | + | 0.742283i | ||||
\(617\) | −1.45653e12 | + | 2.52278e12i | −0.404609 | + | 0.700803i | −0.994276 | − | 0.106844i | \(-0.965926\pi\) |
0.589667 | + | 0.807646i | \(0.299259\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.23748e12 | + | 2.14337e12i | 0.338789 | + | 0.586799i | 0.984205 | − | 0.177032i | \(-0.0566495\pi\) |
−0.645417 | + | 0.763831i | \(0.723316\pi\) | |||||||
\(620\) | 1.02074e12 | 0.277430 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −5.95413e12 | −1.59500 | ||||||||
\(623\) | −5.95052e11 | − | 1.03066e12i | −0.158255 | − | 0.274107i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.69756e11 | + | 9.86847e11i | −0.149358 | + | 0.258696i | ||||
\(626\) | 8.08203e11 | − | 1.39985e12i | 0.210347 | − | 0.364331i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.13860e10 | − | 1.06324e11i | −0.0157489 | − | 0.0272780i | ||||
\(629\) | −1.98966e12 | −0.506817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.10645e12 | 1.28229 | 0.641146 | − | 0.767419i | \(-0.278459\pi\) | ||||
0.641146 | + | 0.767419i | \(0.278459\pi\) | |||||||
\(632\) | −1.85182e12 | − | 3.20744e12i | −0.461712 | − | 0.799708i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.96907e12 | − | 5.14257e12i | 0.729824 | − | 1.26409i | ||||
\(635\) | 1.76155e12 | − | 3.05110e12i | 0.429946 | − | 0.744689i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.57198e11 | − | 4.45480e11i | −0.0618928 | − | 0.107202i | ||||
\(638\) | −8.04130e12 | −1.92147 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.58884e12 | 0.609951 | ||||||||
\(641\) | −3.03247e11 | − | 5.25239e11i | −0.0709472 | − | 0.122884i | 0.828370 | − | 0.560182i | \(-0.189269\pi\) |
−0.899317 | + | 0.437298i | \(0.855936\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.25492e12 | − | 2.17359e12i | 0.289512 | − | 0.501450i | −0.684181 | − | 0.729312i | \(-0.739840\pi\) |
0.973693 | + | 0.227862i | \(0.0731736\pi\) | |||||||
\(644\) | 3.73313e10 | − | 6.46598e10i | 0.00855238 | − | 0.0148132i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.64990e12 | − | 6.32182e12i | −0.824584 | − | 1.42822i | ||||
\(647\) | −2.81592e12 | −0.631758 | −0.315879 | − | 0.948799i | \(-0.602299\pi\) | ||||
−0.315879 | + | 0.948799i | \(0.602299\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.84501e12 | −1.51451 | ||||||||
\(650\) | 4.92428e11 | + | 8.52910e11i | 0.108201 | + | 0.187410i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5.11757e11 | − | 8.86389e11i | 0.110905 | − | 0.192092i | ||||
\(653\) | 5.41859e10 | − | 9.38527e10i | 0.0116621 | − | 0.0201994i | −0.860135 | − | 0.510066i | \(-0.829621\pi\) |
0.871798 | + | 0.489866i | \(0.162954\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.77035e10 | + | 1.17266e11i | 0.0143723 | + | 0.0248935i | ||||
\(656\) | 1.69178e12 | 0.356678 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.24213e12 | 1.09016 | ||||||||
\(659\) | −3.26356e12 | − | 5.65265e12i | −0.674073 | − | 1.16753i | −0.976739 | − | 0.214432i | \(-0.931210\pi\) |
0.302666 | − | 0.953097i | \(-0.402123\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.14242e12 | + | 3.71079e12i | −0.436515 | + | 0.756066i | −0.997418 | − | 0.0718158i | \(-0.977121\pi\) |
0.560903 | + | 0.827881i | \(0.310454\pi\) | |||||||
\(662\) | 1.98119e12 | − | 3.43153e12i | 0.400927 | − | 0.694426i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.22111e12 | − | 3.84707e12i | −0.443418 | − | 0.768023i | ||||
\(665\) | −2.91760e12 | −0.578533 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.90768e11 | −0.0960085 | ||||||||
\(668\) | −6.77313e11 | − | 1.17314e12i | −0.131612 | − | 0.227959i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.65373e12 | + | 2.86435e12i | −0.317050 | + | 0.549147i | ||||
\(671\) | 7.22282e11 | − | 1.25103e12i | 0.137548 | − | 0.238241i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.48556e12 | − | 4.30512e12i | −0.467043 | − | 0.808942i | 0.532248 | − | 0.846588i | \(-0.321347\pi\) |
−0.999291 | + | 0.0376463i | \(0.988014\pi\) | |||||||
\(674\) | −3.46970e12 | −0.647623 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.44775e12 | −0.266644 | ||||||||
\(677\) | 3.82144e12 | + | 6.61893e12i | 0.699163 | + | 1.21099i | 0.968757 | + | 0.248011i | \(0.0797770\pi\) |
−0.269595 | + | 0.962974i | \(0.586890\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.31306e12 | − | 2.27428e12i | 0.237066 | − | 0.410611i | ||||
\(680\) | 1.04356e12 | − | 1.80749e12i | 0.187165 | − | 0.324180i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.06000e12 | + | 1.56924e13i | 1.60361 | + | 2.77753i | ||||
\(683\) | 4.20646e12 | 0.739646 | 0.369823 | − | 0.929102i | \(-0.379418\pi\) | ||||
0.369823 | + | 0.929102i | \(0.379418\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.06995e11 | 0.122690 | ||||||||
\(686\) | 3.50638e12 | + | 6.07323e12i | 0.604506 | + | 1.04703i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.54349e12 | − | 6.13750e12i | 0.602952 | − | 1.04434i | ||||
\(689\) | 5.29324e11 | − | 9.16816e11i | 0.0894818 | − | 0.154987i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.16845e12 | + | 2.02381e12i | 0.194966 | + | 0.337690i | 0.946889 | − | 0.321560i | \(-0.104207\pi\) |
−0.751924 | + | 0.659250i | \(0.770874\pi\) | |||||||
\(692\) | −1.20896e12 | −0.200417 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.27305e12 | −1.19014 | ||||||||
\(695\) | −4.76938e11 | − | 8.26082e11i | −0.0775409 | − | 0.134305i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.43615e11 | − | 1.46118e12i | 0.135393 | − | 0.234508i | ||||
\(698\) | 1.24883e12 | − | 2.16304e12i | 0.199138 | − | 0.344918i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.85341e11 | − | 8.40635e11i | −0.0764022 | − | 0.132333i | ||||
\(701\) | −1.10126e12 | −0.172250 | −0.0861251 | − | 0.996284i | \(-0.527448\pi\) | ||||
−0.0861251 | + | 0.996284i | \(0.527448\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.71450e12 | 0.882429 | ||||||||
\(704\) | 2.75611e12 | + | 4.77373e12i | 0.422883 | + | 0.732454i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.92201e11 | + | 8.52518e11i | −0.0745627 | + | 0.129146i | ||||
\(707\) | −3.21553e11 | + | 5.56946e11i | −0.0484022 | + | 0.0838350i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.57748e11 | − | 1.13925e12i | −0.0977578 | − | 0.169322i | 0.812998 | − | 0.582266i | \(-0.197834\pi\) |
−0.910756 | + | 0.412944i | \(0.864500\pi\) | |||||||
\(710\) | −2.51085e12 | −0.370816 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −2.44514e12 | −0.356570 | ||||||||
\(713\) | 5.52940e11 | + | 9.57720e11i | 0.0801263 | + | 0.138783i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.66180e11 | − | 1.15386e12i | 0.0953266 | − | 0.165111i | ||||
\(716\) | −1.72657e12 | + | 2.99051e12i | −0.245514 | + | 0.425243i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.74695e12 | + | 9.95402e12i | 0.807008 | + | 1.39778i | ||||
\(719\) | 1.32450e13 | 1.84830 | 0.924151 | − | 0.382027i | \(-0.124774\pi\) | ||||
0.924151 | + | 0.382027i | \(0.124774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.56074e11 | 0.0215091 | ||||||||
\(722\) | 6.34376e12 | + | 1.09877e13i | 0.868819 | + | 1.50484i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.02741e12 | + | 1.77952e12i | −0.138970 | + | 0.240702i | ||||
\(725\) | −3.19021e12 | + | 5.52561e12i | −0.428843 | + | 0.742778i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.35848e12 | − | 4.08501e12i | −0.313132 | − | 0.542360i | 0.665907 | − | 0.746035i | \(-0.268045\pi\) |
−0.979039 | + | 0.203675i | \(0.934712\pi\) | |||||||
\(728\) | 1.13211e12 | 0.149382 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.95034e12 | −0.514851 | ||||||||
\(731\) | −3.53396e12 | − | 6.12100e12i | −0.457755 | − | 0.792855i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.29559e11 | + | 1.43684e12i | −0.106140 | + | 0.183840i | −0.914203 | − | 0.405256i | \(-0.867183\pi\) |
0.808063 | + | 0.589096i | \(0.200516\pi\) | |||||||
\(734\) | −9.59553e11 | + | 1.66199e12i | −0.122022 | + | 0.211348i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.84032e11 | − | 3.18753e11i | −0.0231177 | − | 0.0400410i | ||||
\(737\) | −1.30364e13 | −1.62763 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.72028e12 | −0.705533 | −0.352767 | − | 0.935711i | \(-0.614759\pi\) | ||||
−0.352767 | + | 0.935711i | \(0.614759\pi\) | |||||||
\(740\) | −3.26276e11 | − | 5.65126e11i | −0.0399984 | − | 0.0692792i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.34966e12 | + | 4.06972e12i | −0.284568 | + | 0.492887i | ||||
\(743\) | −3.35872e12 | + | 5.81747e12i | −0.404318 | + | 0.700300i | −0.994242 | − | 0.107159i | \(-0.965825\pi\) |
0.589923 | + | 0.807459i | \(0.299158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.24686e12 | − | 2.15962e12i | −0.148291 | − | 0.256847i | ||||
\(746\) | 7.16752e12 | 0.847314 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −3.28558e12 | −0.383755 | ||||||||
\(749\) | −3.69670e12 | − | 6.40287e12i | −0.429186 | − | 0.743373i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.55508e12 | + | 7.88962e12i | −0.522536 | + | 0.905058i | 0.477121 | + | 0.878838i | \(0.341680\pi\) |
−0.999656 | + | 0.0262203i | \(0.991653\pi\) | |||||||
\(752\) | 7.05839e12 | − | 1.22255e13i | 0.804869 | − | 1.39407i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.48605e12 | + | 2.57391e12i | 0.167441 | + | 0.290016i | ||||
\(755\) | −4.04547e11 | −0.0453114 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.86606e12 | −0.538575 | −0.269288 | − | 0.963060i | \(-0.586788\pi\) | ||||
−0.269288 | + | 0.963060i | \(0.586788\pi\) | |||||||
\(758\) | −8.21717e12 | − | 1.42326e13i | −0.904089 | − | 1.56593i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.99719e12 | + | 5.19129e12i | −0.325877 | + | 0.564435i | ||||
\(761\) | 1.85589e12 | − | 3.21450e12i | 0.200596 | − | 0.347442i | −0.748125 | − | 0.663558i | \(-0.769046\pi\) |
0.948720 | + | 0.316116i | \(0.102379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.95588e12 | − | 3.38768e12i | −0.208921 | − | 0.361862i | ||||
\(764\) | 1.42502e12 | 0.151322 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 8.54423e12 | 0.896692 | ||||||||
\(767\) | 1.26497e12 | + | 2.19099e12i | 0.131978 | + | 0.228592i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.31651e12 | − | 5.74436e12i | 0.341989 | − | 0.592343i | −0.642813 | − | 0.766023i | \(-0.722233\pi\) |
0.984802 | + | 0.173681i | \(0.0555660\pi\) | |||||||
\(770\) | −2.95716e12 | + | 5.12194e12i | −0.303156 | + | 0.525081i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.27112e11 | − | 1.25940e12i | −0.0736756 | − | 0.127610i | ||||
\(773\) | 7.34772e12 | 0.740193 | 0.370096 | − | 0.928993i | \(-0.379325\pi\) | ||||
0.370096 | + | 0.928993i | \(0.379325\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.43774e13 | 1.43161 | ||||||||
\(776\) | −2.69776e12 | − | 4.67266e12i | −0.267070 | − | 0.462579i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.09284e12 | − | 3.62491e12i | 0.204799 | − | 0.354723i | ||||
\(779\) | −2.42295e12 | + | 4.19666e12i | −0.235736 | + | 0.408306i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.94829e12 | − | 8.57069e12i | −0.475911 | − | 0.824301i | ||||
\(782\) | −9.03108e11 | −0.0863593 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.14905e12 | 0.581281 | ||||||||
\(785\) | 2.96770e11 | + | 5.14021e11i | 0.0278937 | + | 0.0483134i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.90682e12 | − | 3.30271e12i | 0.177184 | − | 0.306891i | −0.763731 | − | 0.645535i | \(-0.776635\pi\) |
0.940915 | + | 0.338643i | \(0.109968\pi\) | |||||||
\(788\) | −2.36081e11 | + | 4.08905e11i | −0.0218119 | + | 0.0377793i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.57561e12 | − | 6.19314e12i | −0.326609 | − | 0.565703i | ||||
\(791\) | 8.82902e12 | 0.801897 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.33916e11 | −0.0479451 | ||||||||
\(794\) | 3.58026e12 | + | 6.20119e12i | 0.319685 | + | 0.553710i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.11998e12 | − | 3.67192e12i | 0.187164 | − | 0.324178i | ||||
\(797\) | −8.93658e12 | + | 1.54786e13i | −0.784529 | + | 1.35884i | 0.144751 | + | 0.989468i | \(0.453762\pi\) |
−0.929280 | + | 0.369376i | \(0.879572\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.03941e12 | − | 1.21926e13i | −0.611048 | − | 1.05837i | ||||
\(800\) | −4.78518e12 | −0.413041 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.94953e13 | 1.66397 | ||||||||
\(803\) | −7.78517e12 | − | 1.34843e13i | −0.660767 | − | 1.14448i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.80478e11 | + | 3.12597e11i | −0.0151476 | + | 0.0262363i | ||||
\(806\) | 3.34861e12 | − | 5.79996e12i | 0.279484 | − | 0.484080i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.60650e11 | + | 1.14428e12i | 0.0545281 | + | 0.0944454i | ||||
\(809\) | −1.16949e13 | −0.959908 | −0.479954 | − | 0.877294i | \(-0.659347\pi\) | ||||
−0.479954 | + | 0.877294i | \(0.659347\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.78089e12 | −0.306902 | −0.153451 | − | 0.988156i | \(-0.549039\pi\) | ||||
−0.153451 | + | 0.988156i | \(0.549039\pi\) | |||||||
\(812\) | −1.46466e12 | − | 2.53687e12i | −0.118232 | − | 0.204784i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.79198e12 | − | 1.00320e13i | 0.462400 | − | 0.800900i | ||||
\(815\) | −2.47408e12 | + | 4.28524e12i | −0.196429 | + | 0.340224i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01499e13 | + | 1.75801e13i | 0.797006 | + | 1.38045i | ||||
\(818\) | 9.74701e11 | 0.0761170 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5.53363e11 | 0.0427413 | ||||||||
\(821\) | 3.66299e12 | + | 6.34448e12i | 0.281379 | + | 0.487362i | 0.971725 | − | 0.236117i | \(-0.0758750\pi\) |
−0.690346 | + | 0.723480i | \(0.742542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.23057e12 | + | 5.59552e12i | −0.245460 | + | 0.425149i | −0.962261 | − | 0.272129i | \(-0.912272\pi\) |
0.716801 | + | 0.697278i | \(0.245606\pi\) | |||||||
\(824\) | 1.60332e11 | − | 2.77703e11i | 0.0121157 | − | 0.0209850i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.61517e12 | − | 9.72576e12i | −0.419713 | − | 0.726965i | ||||
\(827\) | 1.17187e13 | 0.871176 | 0.435588 | − | 0.900146i | \(-0.356540\pi\) | ||||
0.435588 | + | 0.900146i | \(0.356540\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.81041e12 | −0.206669 | −0.103334 | − | 0.994647i | \(-0.532951\pi\) | ||||
−0.103334 | + | 0.994647i | \(0.532951\pi\) | |||||||
\(830\) | −4.28867e12 | − | 7.42819e12i | −0.313668 | − | 0.543290i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.01867e12 | − | 1.76439e12i | 0.0737018 | − | 0.127655i | ||||
\(833\) | 3.06626e12 | − | 5.31091e12i | 0.220651 | − | 0.382179i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.27446e12 | + | 5.67153e12i | 0.233105 | + | 0.403749i | ||||
\(836\) | 9.43650e12 | 0.668163 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.88209e13 | −1.31839 | ||||||||
\(839\) | −8.01390e12 | − | 1.38805e13i | −0.558361 | − | 0.967109i | −0.997634 | − | 0.0687556i | \(-0.978097\pi\) |
0.439273 | − | 0.898354i | \(-0.355236\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.37384e12 | + | 4.11162e12i | −0.163633 | + | 0.283420i | ||||
\(842\) | −4.12300e12 | + | 7.14125e12i | −0.282689 | + | 0.489632i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.10913e11 | + | 5.38517e11i | 0.0210910 | + | 0.0365307i | ||||
\(845\) | 6.99912e12 | 0.472268 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.25393e13 | −0.837141 | ||||||||
\(848\) | 6.32749e12 | + | 1.09595e13i | 0.420194 | + | 0.727798i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −5.87061e12 | + | 1.01682e13i | −0.385743 | + | 0.668127i | ||||
\(851\) | 3.53490e11 | − | 6.12263e11i | 0.0231044 | − | 0.0400179i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.96613e12 | + | 1.55298e13i | 0.579875 | + | 1.00437i | 0.995493 | + | 0.0948337i | \(0.0302319\pi\) |
−0.415618 | + | 0.909539i | \(0.636435\pi\) | |||||||
\(854\) | 2.37004e12 | 0.152474 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.51902e13 | −0.967011 | ||||||||
\(857\) | −2.18082e12 | − | 3.77729e12i | −0.138104 | − | 0.239203i | 0.788675 | − | 0.614810i | \(-0.210767\pi\) |
−0.926779 | + | 0.375607i | \(0.877434\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.67580e12 | + | 6.36667e12i | −0.230347 | + | 0.398973i | −0.957910 | − | 0.287068i | \(-0.907319\pi\) |
0.727563 | + | 0.686041i | \(0.240653\pi\) | |||||||
\(860\) | 1.15904e12 | − | 2.00751e12i | 0.0722527 | − | 0.125145i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −4.95248e12 | − | 8.57795e12i | −0.305520 | − | 0.529177i | ||||
\(863\) | −1.41639e13 | −0.869231 | −0.434615 | − | 0.900616i | \(-0.643116\pi\) | ||||
−0.434615 | + | 0.900616i | \(0.643116\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.84471e12 | 0.354969 | ||||||||
\(866\) | 7.03956e12 | + | 1.21929e13i | 0.425319 | + | 0.736674i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.30042e12 | + | 5.71649e12i | −0.197347 | + | 0.341815i | ||||
\(869\) | 1.40933e13 | − | 2.44104e13i | 0.838350 | − | 1.45206i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.40916e12 | + | 4.17278e12i | 0.141835 | + | 0.245666i | ||||
\(872\) | −8.03695e12 | −0.470725 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.59381e12 | 0.150362 | ||||||||
\(875\) | 5.49810e12 | + | 9.52299e12i | 0.317085 | + | 0.549208i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.34330e12 | − | 4.05872e12i | 0.133761 | − | 0.231681i | −0.791362 | − | 0.611347i | \(-0.790628\pi\) |
0.925124 | + | 0.379666i | \(0.123961\pi\) | |||||||
\(878\) | −3.84939e12 | + | 6.66733e12i | −0.218608 | + | 0.378640i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 7.96346e12 | + | 1.37931e13i | 0.447641 | + | 0.775337i | ||||
\(881\) | −1.22598e13 | −0.685635 | −0.342817 | − | 0.939402i | \(-0.611381\pi\) | ||||
−0.342817 | + | 0.939402i | \(0.611381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.77194e12 | −0.374878 | −0.187439 | − | 0.982276i | \(-0.560019\pi\) | ||||
−0.187439 | + | 0.982276i | \(0.560019\pi\) | |||||||
\(884\) | 6.07181e11 | + | 1.05167e12i | 0.0334413 | + | 0.0579220i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.42145e12 | + | 9.39023e12i | −0.295573 | + | 0.511947i | ||||
\(887\) | −1.08701e13 | + | 1.88276e13i | −0.589627 | + | 1.02126i | 0.404654 | + | 0.914470i | \(0.367392\pi\) |
−0.994281 | + | 0.106795i | \(0.965941\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13915e13 | + | 1.97306e13i | 0.611676 | + | 1.05945i | ||||
\(890\) | −4.72125e12 | −0.252233 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 6.18875e12 | 0.327311 | ||||||||
\(893\) | 2.02179e13 | + | 3.50183e13i | 1.06391 | + | 1.84274i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.34709e12 | − | 1.44576e13i | 0.434842 | − | 0.753169i | ||||
\(896\) | −8.37063e12 | + | 1.44984e13i | −0.433883 | + | 0.751507i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.09601e13 | − | 3.63040e13i | −1.07560 | − | 1.86299i | ||||
\(899\) | 4.33882e13 | 2.21540 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.26210e13 | 0.638015 | ||||||||
\(902\) | 4.91159e12 | + | 8.50713e12i | 0.247055 | + | 0.427911i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 9.06989e12 | − | 1.57095e13i | 0.451694 | − | 0.782356i | ||||
\(905\) | 4.96700e12 | − | 8.60309e12i | 0.246136 | − | 0.426320i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.13948e13 | + | 1.97364e13i | 0.559079 | + | 0.968354i | 0.997574 | + | 0.0696198i | \(0.0221786\pi\) |
−0.438494 | + | 0.898734i | \(0.644488\pi\) | |||||||
\(908\) | −8.65954e12 | −0.422774 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.18595e12 | 0.105671 | ||||||||
\(911\) | −5.63882e12 | − | 9.76672e12i | −0.271241 | − | 0.469803i | 0.697939 | − | 0.716157i | \(-0.254101\pi\) |
−0.969180 | + | 0.246354i | \(0.920767\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.69039e13 | − | 2.92784e13i | 0.805134 | − | 1.39453i | ||||
\(914\) | 1.59872e13 | − | 2.76906e13i | 0.757728 | − | 1.31242i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.49375e12 | + | 7.78340e12i | 0.210901 | + | 0.365292i | ||||
\(917\) | −8.75637e11 | −0.0408942 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.27954e12 | −0.105421 | −0.0527105 | − | 0.998610i | \(-0.516786\pi\) | ||||
−0.0527105 | + | 0.998610i | \(0.516786\pi\) | |||||||
\(920\) | 3.70803e11 | + | 6.42250e11i | 0.0170647 | + | 0.0295569i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.69483e12 | + | 6.39963e12i | −0.168386 | + | 0.291653i | ||||
\(923\) | −1.82891e12 | + | 3.16776e12i | −0.0829438 | + | 0.143663i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.59569e12 | − | 7.95997e12i | −0.206402 | − | 0.357498i | ||||
\(926\) | −4.03450e13 | −1.80318 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.44407e13 | −0.639179 | ||||||||
\(929\) | −9.43673e12 | − | 1.63449e13i | −0.415672 | − | 0.719965i | 0.579827 | − | 0.814740i | \(-0.303120\pi\) |
−0.995499 | + | 0.0947745i | \(0.969787\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8.80659e12 | + | 1.52535e13i | −0.384179 | + | 0.665418i | ||||
\(932\) | −3.42953e12 | + | 5.94012e12i | −0.148889 | + | 0.257884i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.73064e12 | − | 4.72961e12i | −0.117410 | − | 0.203359i | ||||
\(935\) | 1.58841e13 | 0.679689 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.08798e13 | −0.461096 | −0.230548 | − | 0.973061i | \(-0.574052\pi\) | ||||
−0.230548 | + | 0.973061i | \(0.574052\pi\) | |||||||
\(938\) | −1.06942e13 | − | 1.85229e13i | −0.451061 | − | 0.781261i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.30872e12 | − | 3.99882e12i | 0.0964486 | − | 0.167054i | ||||
\(941\) | 1.41900e13 | − | 2.45778e13i | 0.589970 | − | 1.02186i | −0.404266 | − | 0.914641i | \(-0.632473\pi\) |
0.994236 | − | 0.107216i | \(-0.0341936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.99759e11 | + | 5.19198e11i | 0.0123444 | + | 0.0213811i | ||||
\(944\) | −3.02427e13 | −1.23950 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.11500e13 | 1.67055 | ||||||||
\(947\) | 1.79187e12 | + | 3.10361e12i | 0.0723988 | + | 0.125398i | 0.899952 | − | 0.435989i | \(-0.143601\pi\) |
−0.827553 | + | 0.561387i | \(0.810268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.87743e12 | + | 4.98385e12i | −0.115161 | + | 0.199465i | ||||
\(950\) | 1.68610e13 | − | 2.92040e13i | 0.671624 | − | 1.16329i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 6.74837e12 | + | 1.16885e13i | 0.266276 | + | 0.461204i | ||||
\(953\) | −2.91182e12 | −0.114353 | −0.0571763 | − | 0.998364i | \(-0.518210\pi\) | ||||
−0.0571763 | + | 0.998364i | \(0.518210\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.88926e12 | −0.268014 | ||||||||
\(956\) | 7.63428e11 | + | 1.32230e12i | 0.0295602 | + | 0.0511998i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.95591e13 | + | 3.38773e13i | −0.750245 | + | 1.29946i | ||||
\(959\) | −2.28597e12 | + | 3.95941e12i | −0.0872743 | + | 0.151163i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.56649e13 | − | 6.17735e13i | −1.34892 | − | 2.33640i | ||||
\(962\) | −4.28148e12 | −0.161178 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.37505e12 | 0.163168 | ||||||||
\(965\) | 3.51522e12 | + | 6.08853e12i | 0.130491 | + | 0.226016i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.34163e13 | − | 2.32377e13i | 0.493417 | − | 0.854623i | −0.506555 | − | 0.862208i | \(-0.669081\pi\) |
0.999971 | + | 0.00758529i | \(0.00241450\pi\) | |||||||
\(968\) | −1.28814e13 | + | 2.23112e13i | −0.471546 | + | 0.816742i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5.20902e12 | − | 9.02228e12i | −0.188922 | − | 0.327223i | ||||
\(971\) | −5.18797e13 | −1.87288 | −0.936442 | − | 0.350824i | \(-0.885902\pi\) | ||||
−0.936442 | + | 0.350824i | \(0.885902\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.16844e12 | 0.220632 | ||||||||
\(974\) | −2.32179e13 | − | 4.02146e13i | −0.826624 | − | 1.43175i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3.19120e12 | − | 5.52731e12i | 0.112572 | − | 0.194980i | ||||
\(977\) | 2.77975e13 | − | 4.81466e13i | 0.976067 | − | 1.69060i | 0.299700 | − | 0.954034i | \(-0.403113\pi\) |
0.676367 | − | 0.736565i | \(-0.263553\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.30445e12 | − | 1.61158e13i | −0.323719 | − | 0.560698i | ||||
\(980\) | 2.01129e12 | 0.0696557 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.96003e13 | −1.01577 | ||||||||
\(983\) | 2.01121e13 | + | 3.48351e13i | 0.687015 | + | 1.18994i | 0.972799 | + | 0.231650i | \(0.0744125\pi\) |
−0.285785 | + | 0.958294i | \(0.592254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.14133e12 | − | 1.97685e12i | 0.0386322 | − | 0.0669129i | ||||
\(986\) | −1.77163e13 | + | 3.06856e13i | −0.596935 | + | 1.03392i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.74388e12 | − | 3.02049e12i | −0.0582252 | − | 0.100849i | ||||
\(989\) | 2.51142e12 | 0.0834710 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.34682e13 | 0.443588 | 0.221794 | − | 0.975094i | \(-0.428809\pi\) | ||||
0.221794 | + | 0.975094i | \(0.428809\pi\) | |||||||
\(992\) | 1.62701e13 | + | 2.81806e13i | 0.533442 | + | 0.923949i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.11847e12 | − | 1.40616e13i | 0.263776 | − | 0.456874i | ||||
\(995\) | −1.02490e13 | + | 1.77518e13i | −0.331496 | + | 0.574169i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.87292e13 | + | 3.24399e13i | 0.600331 | + | 1.03980i | 0.992771 | + | 0.120026i | \(0.0382977\pi\) |
−0.392440 | + | 0.919778i | \(0.628369\pi\) | |||||||
\(998\) | 5.18065e13 | 1.65309 | ||||||||
\(999\) | 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 | 27.10.c.a.10.7 | 16 | ||
3.2 | odd | 2 | 9.10.c.a.4.2 | ✓ | 16 | ||
9.2 | odd | 6 | 9.10.c.a.7.2 | yes | 16 | ||
9.4 | even | 3 | 81.10.a.d.1.2 | 8 | |||
9.5 | odd | 6 | 81.10.a.c.1.7 | 8 | |||
9.7 | even | 3 | inner | 27.10.c.a.19.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.10.c.a.4.2 | ✓ | 16 | 3.2 | odd | 2 | ||
9.10.c.a.7.2 | yes | 16 | 9.2 | odd | 6 | ||
27.10.c.a.10.7 | 16 | 1.1 | even | 1 | trivial | ||
27.10.c.a.19.7 | 16 | 9.7 | even | 3 | inner | ||
81.10.a.c.1.7 | 8 | 9.5 | odd | 6 | |||
81.10.a.d.1.2 | 8 | 9.4 | even | 3 |