Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,22,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.a (trivial) |
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: | yes |
Analytic conductor: | \(27.9477344287\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{1179649}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 294912 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(543.558\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1024.00 | 0.707107 | ||||||||
\(3\) | −114848. | −1.12292 | −0.561462 | − | 0.827503i | \(-0.689761\pi\) | ||||
−0.561462 | + | 0.827503i | \(0.689761\pi\) | |||||||
\(4\) | 1.04858e6 | 0.500000 | ||||||||
\(5\) | −9.76562e6 | −0.447214 | ||||||||
\(6\) | −1.17604e8 | −0.794027 | ||||||||
\(7\) | −2.03949e8 | −0.272892 | −0.136446 | − | 0.990647i | \(-0.543568\pi\) | ||||
−0.136446 | + | 0.990647i | \(0.543568\pi\) | |||||||
\(8\) | 1.07374e9 | 0.353553 | ||||||||
\(9\) | 2.72970e9 | 0.260957 | ||||||||
\(10\) | −1.00000e10 | −0.316228 | ||||||||
\(11\) | −4.40105e10 | −0.511603 | −0.255802 | − | 0.966729i | \(-0.582339\pi\) | ||||
−0.255802 | + | 0.966729i | \(0.582339\pi\) | |||||||
\(12\) | −1.20427e11 | −0.561462 | ||||||||
\(13\) | −1.80893e11 | −0.363929 | −0.181965 | − | 0.983305i | \(-0.558246\pi\) | ||||
−0.181965 | + | 0.983305i | \(0.558246\pi\) | |||||||
\(14\) | −2.08843e11 | −0.192964 | ||||||||
\(15\) | 1.12156e12 | 0.502187 | ||||||||
\(16\) | 1.09951e12 | 0.250000 | ||||||||
\(17\) | 1.29311e13 | 1.55569 | 0.777844 | − | 0.628458i | \(-0.216314\pi\) | ||||
0.777844 | + | 0.628458i | \(0.216314\pi\) | |||||||
\(18\) | 2.79522e12 | 0.184525 | ||||||||
\(19\) | 3.50261e13 | 1.31063 | 0.655313 | − | 0.755357i | \(-0.272537\pi\) | ||||
0.655313 | + | 0.755357i | \(0.272537\pi\) | |||||||
\(20\) | −1.02400e13 | −0.223607 | ||||||||
\(21\) | 2.34231e13 | 0.306437 | ||||||||
\(22\) | −4.50668e13 | −0.361758 | ||||||||
\(23\) | −1.00465e14 | −0.505677 | −0.252838 | − | 0.967509i | \(-0.581364\pi\) | ||||
−0.252838 | + | 0.967509i | \(0.581364\pi\) | |||||||
\(24\) | −1.23317e14 | −0.397013 | ||||||||
\(25\) | 9.53674e13 | 0.200000 | ||||||||
\(26\) | −1.85235e14 | −0.257337 | ||||||||
\(27\) | 8.87849e14 | 0.829889 | ||||||||
\(28\) | −2.13856e14 | −0.136446 | ||||||||
\(29\) | 2.65416e15 | 1.17152 | 0.585758 | − | 0.810486i | \(-0.300797\pi\) | ||||
0.585758 | + | 0.810486i | \(0.300797\pi\) | |||||||
\(30\) | 1.14848e15 | 0.355100 | ||||||||
\(31\) | 1.12512e15 | 0.246548 | 0.123274 | − | 0.992373i | \(-0.460661\pi\) | ||||
0.123274 | + | 0.992373i | \(0.460661\pi\) | |||||||
\(32\) | 1.12590e15 | 0.176777 | ||||||||
\(33\) | 5.05452e15 | 0.574491 | ||||||||
\(34\) | 1.32415e16 | 1.10004 | ||||||||
\(35\) | 1.99169e15 | 0.122041 | ||||||||
\(36\) | 2.86230e15 | 0.130479 | ||||||||
\(37\) | 2.62794e16 | 0.898458 | 0.449229 | − | 0.893417i | \(-0.351699\pi\) | ||||
0.449229 | + | 0.893417i | \(0.351699\pi\) | |||||||
\(38\) | 3.58667e16 | 0.926753 | ||||||||
\(39\) | 2.07752e16 | 0.408665 | ||||||||
\(40\) | −1.04858e16 | −0.158114 | ||||||||
\(41\) | −2.80940e16 | −0.326876 | −0.163438 | − | 0.986554i | \(-0.552258\pi\) | ||||
−0.163438 | + | 0.986554i | \(0.552258\pi\) | |||||||
\(42\) | 2.39852e16 | 0.216684 | ||||||||
\(43\) | 1.48308e17 | 1.04651 | 0.523257 | − | 0.852175i | \(-0.324717\pi\) | ||||
0.523257 | + | 0.852175i | \(0.324717\pi\) | |||||||
\(44\) | −4.61484e16 | −0.255802 | ||||||||
\(45\) | −2.66573e16 | −0.116704 | ||||||||
\(46\) | −1.02876e17 | −0.357567 | ||||||||
\(47\) | −9.51528e16 | −0.263872 | −0.131936 | − | 0.991258i | \(-0.542119\pi\) | ||||
−0.131936 | + | 0.991258i | \(0.542119\pi\) | |||||||
\(48\) | −1.26277e17 | −0.280731 | ||||||||
\(49\) | −5.16951e17 | −0.925530 | ||||||||
\(50\) | 9.76562e16 | 0.141421 | ||||||||
\(51\) | −1.48511e18 | −1.74692 | ||||||||
\(52\) | −1.89680e17 | −0.181965 | ||||||||
\(53\) | 1.03378e18 | 0.811955 | 0.405978 | − | 0.913883i | \(-0.366931\pi\) | ||||
0.405978 | + | 0.913883i | \(0.366931\pi\) | |||||||
\(54\) | 9.09158e17 | 0.586820 | ||||||||
\(55\) | 4.29790e17 | 0.228796 | ||||||||
\(56\) | −2.18988e17 | −0.0964820 | ||||||||
\(57\) | −4.02268e18 | −1.47173 | ||||||||
\(58\) | 2.71786e18 | 0.828387 | ||||||||
\(59\) | −1.03132e18 | −0.262692 | −0.131346 | − | 0.991337i | \(-0.541930\pi\) | ||||
−0.131346 | + | 0.991337i | \(0.541930\pi\) | |||||||
\(60\) | 1.17604e18 | 0.251093 | ||||||||
\(61\) | −8.22371e18 | −1.47606 | −0.738031 | − | 0.674767i | \(-0.764244\pi\) | ||||
−0.738031 | + | 0.674767i | \(0.764244\pi\) | |||||||
\(62\) | 1.15212e18 | 0.174335 | ||||||||
\(63\) | −5.56719e17 | −0.0712132 | ||||||||
\(64\) | 1.15292e18 | 0.125000 | ||||||||
\(65\) | 1.76653e18 | 0.162754 | ||||||||
\(66\) | 5.17583e18 | 0.406227 | ||||||||
\(67\) | −1.74709e19 | −1.17092 | −0.585462 | − | 0.810700i | \(-0.699087\pi\) | ||||
−0.585462 | + | 0.810700i | \(0.699087\pi\) | |||||||
\(68\) | 1.35593e19 | 0.777844 | ||||||||
\(69\) | 1.15382e19 | 0.567836 | ||||||||
\(70\) | 2.03949e18 | 0.0862961 | ||||||||
\(71\) | 2.67322e19 | 0.974591 | 0.487296 | − | 0.873237i | \(-0.337983\pi\) | ||||
0.487296 | + | 0.873237i | \(0.337983\pi\) | |||||||
\(72\) | 2.93100e18 | 0.0922623 | ||||||||
\(73\) | 5.60167e19 | 1.52555 | 0.762777 | − | 0.646662i | \(-0.223836\pi\) | ||||
0.762777 | + | 0.646662i | \(0.223836\pi\) | |||||||
\(74\) | 2.69101e19 | 0.635306 | ||||||||
\(75\) | −1.09528e19 | −0.224585 | ||||||||
\(76\) | 3.67275e19 | 0.655313 | ||||||||
\(77\) | 8.97588e18 | 0.139613 | ||||||||
\(78\) | 2.12738e19 | 0.288970 | ||||||||
\(79\) | −4.33055e19 | −0.514587 | −0.257293 | − | 0.966333i | \(-0.582831\pi\) | ||||
−0.257293 | + | 0.966333i | \(0.582831\pi\) | |||||||
\(80\) | −1.07374e19 | −0.111803 | ||||||||
\(81\) | −1.30521e20 | −1.19286 | ||||||||
\(82\) | −2.87683e19 | −0.231137 | ||||||||
\(83\) | −2.59402e20 | −1.83507 | −0.917535 | − | 0.397655i | \(-0.869824\pi\) | ||||
−0.917535 | + | 0.397655i | \(0.869824\pi\) | |||||||
\(84\) | 2.45609e19 | 0.153219 | ||||||||
\(85\) | −1.26280e20 | −0.695724 | ||||||||
\(86\) | 1.51867e20 | 0.739997 | ||||||||
\(87\) | −3.04825e20 | −1.31552 | ||||||||
\(88\) | −4.72559e19 | −0.180879 | ||||||||
\(89\) | 5.09045e20 | 1.73046 | 0.865230 | − | 0.501376i | \(-0.167173\pi\) | ||||
0.865230 | + | 0.501376i | \(0.167173\pi\) | |||||||
\(90\) | −2.72970e19 | −0.0825219 | ||||||||
\(91\) | 3.68929e19 | 0.0993135 | ||||||||
\(92\) | −1.05345e20 | −0.252838 | ||||||||
\(93\) | −1.29218e20 | −0.276854 | ||||||||
\(94\) | −9.74364e19 | −0.186586 | ||||||||
\(95\) | −3.42052e20 | −0.586130 | ||||||||
\(96\) | −1.29307e20 | −0.198507 | ||||||||
\(97\) | 6.58070e20 | 0.906085 | 0.453042 | − | 0.891489i | \(-0.350339\pi\) | ||||
0.453042 | + | 0.891489i | \(0.350339\pi\) | |||||||
\(98\) | −5.29358e20 | −0.654448 | ||||||||
\(99\) | −1.20136e20 | −0.133507 | ||||||||
\(100\) | 1.00000e20 | 0.100000 | ||||||||
\(101\) | 1.15672e21 | 1.04197 | 0.520984 | − | 0.853566i | \(-0.325565\pi\) | ||||
0.520984 | + | 0.853566i | \(0.325565\pi\) | |||||||
\(102\) | −1.52076e21 | −1.23526 | ||||||||
\(103\) | 2.10354e21 | 1.54226 | 0.771132 | − | 0.636675i | \(-0.219691\pi\) | ||||
0.771132 | + | 0.636675i | \(0.219691\pi\) | |||||||
\(104\) | −1.94233e20 | −0.128668 | ||||||||
\(105\) | −2.28741e20 | −0.137043 | ||||||||
\(106\) | 1.05859e21 | 0.574139 | ||||||||
\(107\) | 9.86090e20 | 0.484604 | 0.242302 | − | 0.970201i | \(-0.422098\pi\) | ||||
0.242302 | + | 0.970201i | \(0.422098\pi\) | |||||||
\(108\) | 9.30978e20 | 0.414944 | ||||||||
\(109\) | 1.78098e21 | 0.720576 | 0.360288 | − | 0.932841i | \(-0.382678\pi\) | ||||
0.360288 | + | 0.932841i | \(0.382678\pi\) | |||||||
\(110\) | 4.40105e20 | 0.161783 | ||||||||
\(111\) | −3.01814e21 | −1.00890 | ||||||||
\(112\) | −2.24244e20 | −0.0682231 | ||||||||
\(113\) | 3.61184e21 | 1.00093 | 0.500466 | − | 0.865756i | \(-0.333162\pi\) | ||||
0.500466 | + | 0.865756i | \(0.333162\pi\) | |||||||
\(114\) | −4.11922e21 | −1.04067 | ||||||||
\(115\) | 9.81104e20 | 0.226145 | ||||||||
\(116\) | 2.78309e21 | 0.585758 | ||||||||
\(117\) | −4.93785e20 | −0.0949700 | ||||||||
\(118\) | −1.05607e21 | −0.185751 | ||||||||
\(119\) | −2.63728e21 | −0.424535 | ||||||||
\(120\) | 1.20427e21 | 0.177550 | ||||||||
\(121\) | −5.46332e21 | −0.738262 | ||||||||
\(122\) | −8.42108e21 | −1.04373 | ||||||||
\(123\) | 3.22654e21 | 0.367057 | ||||||||
\(124\) | 1.17977e21 | 0.123274 | ||||||||
\(125\) | −9.31323e20 | −0.0894427 | ||||||||
\(126\) | −5.70081e20 | −0.0503553 | ||||||||
\(127\) | 1.58229e22 | 1.28632 | 0.643158 | − | 0.765734i | \(-0.277624\pi\) | ||||
0.643158 | + | 0.765734i | \(0.277624\pi\) | |||||||
\(128\) | 1.18059e21 | 0.0883883 | ||||||||
\(129\) | −1.70328e22 | −1.17516 | ||||||||
\(130\) | 1.80893e21 | 0.115085 | ||||||||
\(131\) | −1.83709e22 | −1.07840 | −0.539202 | − | 0.842176i | \(-0.681274\pi\) | ||||
−0.539202 | + | 0.842176i | \(0.681274\pi\) | |||||||
\(132\) | 5.30005e21 | 0.287246 | ||||||||
\(133\) | −7.14352e21 | −0.357660 | ||||||||
\(134\) | −1.78902e22 | −0.827968 | ||||||||
\(135\) | −8.67040e21 | −0.371137 | ||||||||
\(136\) | 1.38847e22 | 0.550019 | ||||||||
\(137\) | 7.05876e21 | 0.258918 | 0.129459 | − | 0.991585i | \(-0.458676\pi\) | ||||
0.129459 | + | 0.991585i | \(0.458676\pi\) | |||||||
\(138\) | 1.18151e22 | 0.401521 | ||||||||
\(139\) | −3.37498e22 | −1.06320 | −0.531601 | − | 0.846995i | \(-0.678410\pi\) | ||||
−0.531601 | + | 0.846995i | \(0.678410\pi\) | |||||||
\(140\) | 2.08843e21 | 0.0610206 | ||||||||
\(141\) | 1.09281e22 | 0.296308 | ||||||||
\(142\) | 2.73738e22 | 0.689140 | ||||||||
\(143\) | 7.96120e21 | 0.186187 | ||||||||
\(144\) | 3.00134e21 | 0.0652393 | ||||||||
\(145\) | −2.59195e22 | −0.523918 | ||||||||
\(146\) | 5.73611e22 | 1.07873 | ||||||||
\(147\) | 5.93708e22 | 1.03930 | ||||||||
\(148\) | 2.75560e22 | 0.449229 | ||||||||
\(149\) | −5.68451e22 | −0.863451 | −0.431725 | − | 0.902005i | \(-0.642095\pi\) | ||||
−0.431725 | + | 0.902005i | \(0.642095\pi\) | |||||||
\(150\) | −1.12156e22 | −0.158805 | ||||||||
\(151\) | 1.33443e23 | 1.76213 | 0.881064 | − | 0.472997i | \(-0.156828\pi\) | ||||
0.881064 | + | 0.472997i | \(0.156828\pi\) | |||||||
\(152\) | 3.76090e22 | 0.463376 | ||||||||
\(153\) | 3.52981e22 | 0.405968 | ||||||||
\(154\) | 9.19131e21 | 0.0987210 | ||||||||
\(155\) | −1.09875e22 | −0.110259 | ||||||||
\(156\) | 2.17844e22 | 0.204332 | ||||||||
\(157\) | −1.56723e22 | −0.137463 | −0.0687317 | − | 0.997635i | \(-0.521895\pi\) | ||||
−0.0687317 | + | 0.997635i | \(0.521895\pi\) | |||||||
\(158\) | −4.43448e22 | −0.363868 | ||||||||
\(159\) | −1.18728e23 | −0.911764 | ||||||||
\(160\) | −1.09951e22 | −0.0790569 | ||||||||
\(161\) | 2.04897e22 | 0.137995 | ||||||||
\(162\) | −1.33654e23 | −0.843478 | ||||||||
\(163\) | 1.20617e23 | 0.713575 | 0.356788 | − | 0.934185i | \(-0.383872\pi\) | ||||
0.356788 | + | 0.934185i | \(0.383872\pi\) | |||||||
\(164\) | −2.94587e22 | −0.163438 | ||||||||
\(165\) | −4.93605e22 | −0.256920 | ||||||||
\(166\) | −2.65627e23 | −1.29759 | ||||||||
\(167\) | −3.63531e23 | −1.66732 | −0.833658 | − | 0.552281i | \(-0.813758\pi\) | ||||
−0.833658 | + | 0.552281i | \(0.813758\pi\) | |||||||
\(168\) | 2.51503e22 | 0.108342 | ||||||||
\(169\) | −2.14342e23 | −0.867555 | ||||||||
\(170\) | −1.29311e23 | −0.491952 | ||||||||
\(171\) | 9.56109e22 | 0.342017 | ||||||||
\(172\) | 1.55512e23 | 0.523257 | ||||||||
\(173\) | 5.25008e23 | 1.66219 | 0.831097 | − | 0.556127i | \(-0.187713\pi\) | ||||
0.831097 | + | 0.556127i | \(0.187713\pi\) | |||||||
\(174\) | −3.12141e23 | −0.930215 | ||||||||
\(175\) | −1.94501e22 | −0.0545785 | ||||||||
\(176\) | −4.83901e22 | −0.127901 | ||||||||
\(177\) | 1.18445e23 | 0.294983 | ||||||||
\(178\) | 5.21262e23 | 1.22362 | ||||||||
\(179\) | −4.28059e23 | −0.947428 | −0.473714 | − | 0.880679i | \(-0.657087\pi\) | ||||
−0.473714 | + | 0.880679i | \(0.657087\pi\) | |||||||
\(180\) | −2.79522e22 | −0.0583518 | ||||||||
\(181\) | 4.13461e23 | 0.814346 | 0.407173 | − | 0.913351i | \(-0.366515\pi\) | ||||
0.407173 | + | 0.913351i | \(0.366515\pi\) | |||||||
\(182\) | 3.77783e22 | 0.0702252 | ||||||||
\(183\) | 9.44477e23 | 1.65750 | ||||||||
\(184\) | −1.07874e23 | −0.178784 | ||||||||
\(185\) | −2.56635e23 | −0.401803 | ||||||||
\(186\) | −1.32319e23 | −0.195765 | ||||||||
\(187\) | −5.69105e23 | −0.795895 | ||||||||
\(188\) | −9.97749e22 | −0.131936 | ||||||||
\(189\) | −1.81076e23 | −0.226470 | ||||||||
\(190\) | −3.50261e23 | −0.414456 | ||||||||
\(191\) | 7.69492e22 | 0.0861695 | 0.0430847 | − | 0.999071i | \(-0.486281\pi\) | ||||
0.0430847 | + | 0.999071i | \(0.486281\pi\) | |||||||
\(192\) | −1.32411e23 | −0.140365 | ||||||||
\(193\) | 1.25195e24 | 1.25671 | 0.628355 | − | 0.777926i | \(-0.283728\pi\) | ||||
0.628355 | + | 0.777926i | \(0.283728\pi\) | |||||||
\(194\) | 6.73864e23 | 0.640699 | ||||||||
\(195\) | −2.02883e23 | −0.182760 | ||||||||
\(196\) | −5.42062e23 | −0.462765 | ||||||||
\(197\) | 9.01149e23 | 0.729292 | 0.364646 | − | 0.931146i | \(-0.381190\pi\) | ||||
0.364646 | + | 0.931146i | \(0.381190\pi\) | |||||||
\(198\) | −1.23019e23 | −0.0944034 | ||||||||
\(199\) | −9.25260e23 | −0.673452 | −0.336726 | − | 0.941603i | \(-0.609320\pi\) | ||||
−0.336726 | + | 0.941603i | \(0.609320\pi\) | |||||||
\(200\) | 1.02400e23 | 0.0707107 | ||||||||
\(201\) | 2.00649e24 | 1.31486 | ||||||||
\(202\) | 1.18448e24 | 0.736783 | ||||||||
\(203\) | −5.41312e23 | −0.319698 | ||||||||
\(204\) | −1.55725e24 | −0.873459 | ||||||||
\(205\) | 2.74356e23 | 0.146184 | ||||||||
\(206\) | 2.15402e24 | 1.09055 | ||||||||
\(207\) | −2.74240e23 | −0.131960 | ||||||||
\(208\) | −1.98894e23 | −0.0909823 | ||||||||
\(209\) | −1.54152e24 | −0.670521 | ||||||||
\(210\) | −2.34231e23 | −0.0969040 | ||||||||
\(211\) | −9.91626e23 | −0.390285 | −0.195143 | − | 0.980775i | \(-0.562517\pi\) | ||||
−0.195143 | + | 0.980775i | \(0.562517\pi\) | |||||||
\(212\) | 1.08400e24 | 0.405978 | ||||||||
\(213\) | −3.07014e24 | −1.09439 | ||||||||
\(214\) | 1.00976e24 | 0.342667 | ||||||||
\(215\) | −1.44832e24 | −0.468015 | ||||||||
\(216\) | 9.53321e23 | 0.293410 | ||||||||
\(217\) | −2.29466e23 | −0.0672809 | ||||||||
\(218\) | 1.82372e24 | 0.509524 | ||||||||
\(219\) | −6.43340e24 | −1.71308 | ||||||||
\(220\) | 4.50668e23 | 0.114398 | ||||||||
\(221\) | −2.33915e24 | −0.566160 | ||||||||
\(222\) | −3.09057e24 | −0.713400 | ||||||||
\(223\) | −3.99965e24 | −0.880687 | −0.440343 | − | 0.897829i | \(-0.645143\pi\) | ||||
−0.440343 | + | 0.897829i | \(0.645143\pi\) | |||||||
\(224\) | −2.29626e23 | −0.0482410 | ||||||||
\(225\) | 2.60325e23 | 0.0521914 | ||||||||
\(226\) | 3.69852e24 | 0.707766 | ||||||||
\(227\) | 5.28899e24 | 0.966276 | 0.483138 | − | 0.875544i | \(-0.339497\pi\) | ||||
0.483138 | + | 0.875544i | \(0.339497\pi\) | |||||||
\(228\) | −4.21808e24 | −0.735866 | ||||||||
\(229\) | −1.05761e24 | −0.176219 | −0.0881095 | − | 0.996111i | \(-0.528083\pi\) | ||||
−0.0881095 | + | 0.996111i | \(0.528083\pi\) | |||||||
\(230\) | 1.00465e24 | 0.159909 | ||||||||
\(231\) | −1.03086e24 | −0.156774 | ||||||||
\(232\) | 2.84988e24 | 0.414193 | ||||||||
\(233\) | 1.05916e25 | 1.47138 | 0.735691 | − | 0.677317i | \(-0.236857\pi\) | ||||
0.735691 | + | 0.677317i | \(0.236857\pi\) | |||||||
\(234\) | −5.05636e23 | −0.0671539 | ||||||||
\(235\) | 9.29226e23 | 0.118007 | ||||||||
\(236\) | −1.08142e24 | −0.131346 | ||||||||
\(237\) | 4.97355e24 | 0.577841 | ||||||||
\(238\) | −2.70058e24 | −0.300192 | ||||||||
\(239\) | 1.72062e25 | 1.83023 | 0.915115 | − | 0.403192i | \(-0.132099\pi\) | ||||
0.915115 | + | 0.403192i | \(0.132099\pi\) | |||||||
\(240\) | 1.23317e24 | 0.125547 | ||||||||
\(241\) | −1.73077e25 | −1.68679 | −0.843394 | − | 0.537295i | \(-0.819446\pi\) | ||||
−0.843394 | + | 0.537295i | \(0.819446\pi\) | |||||||
\(242\) | −5.59444e24 | −0.522030 | ||||||||
\(243\) | 5.70290e24 | 0.509600 | ||||||||
\(244\) | −8.62319e24 | −0.738031 | ||||||||
\(245\) | 5.04835e24 | 0.413910 | ||||||||
\(246\) | 3.30398e24 | 0.259549 | ||||||||
\(247\) | −6.33598e24 | −0.476975 | ||||||||
\(248\) | 1.20809e24 | 0.0871677 | ||||||||
\(249\) | 2.97917e25 | 2.06064 | ||||||||
\(250\) | −9.53674e23 | −0.0632456 | ||||||||
\(251\) | −9.29670e24 | −0.591227 | −0.295614 | − | 0.955308i | \(-0.595524\pi\) | ||||
−0.295614 | + | 0.955308i | \(0.595524\pi\) | |||||||
\(252\) | −5.83763e23 | −0.0356066 | ||||||||
\(253\) | 4.42152e24 | 0.258706 | ||||||||
\(254\) | 1.62027e25 | 0.909562 | ||||||||
\(255\) | 1.45031e25 | 0.781245 | ||||||||
\(256\) | 1.20893e24 | 0.0625000 | ||||||||
\(257\) | 9.32271e24 | 0.462641 | 0.231321 | − | 0.972878i | \(-0.425695\pi\) | ||||
0.231321 | + | 0.972878i | \(0.425695\pi\) | |||||||
\(258\) | −1.74416e25 | −0.830960 | ||||||||
\(259\) | −5.35965e24 | −0.245182 | ||||||||
\(260\) | 1.85235e24 | 0.0813771 | ||||||||
\(261\) | 7.24508e24 | 0.305716 | ||||||||
\(262\) | −1.88118e25 | −0.762547 | ||||||||
\(263\) | −2.87230e25 | −1.11865 | −0.559325 | − | 0.828948i | \(-0.688940\pi\) | ||||
−0.559325 | + | 0.828948i | \(0.688940\pi\) | |||||||
\(264\) | 5.42725e24 | 0.203113 | ||||||||
\(265\) | −1.00955e25 | −0.363117 | ||||||||
\(266\) | −7.31497e24 | −0.252904 | ||||||||
\(267\) | −5.84628e25 | −1.94317 | ||||||||
\(268\) | −1.83195e25 | −0.585462 | ||||||||
\(269\) | 2.41759e25 | 0.742991 | 0.371495 | − | 0.928435i | \(-0.378845\pi\) | ||||
0.371495 | + | 0.928435i | \(0.378845\pi\) | |||||||
\(270\) | −8.87849e24 | −0.262434 | ||||||||
\(271\) | −4.48847e25 | −1.27621 | −0.638103 | − | 0.769951i | \(-0.720280\pi\) | ||||
−0.638103 | + | 0.769951i | \(0.720280\pi\) | |||||||
\(272\) | 1.42179e25 | 0.388922 | ||||||||
\(273\) | −4.23708e24 | −0.111521 | ||||||||
\(274\) | 7.22817e24 | 0.183083 | ||||||||
\(275\) | −4.19717e24 | −0.102321 | ||||||||
\(276\) | 1.20987e25 | 0.283918 | ||||||||
\(277\) | −1.57653e25 | −0.356176 | −0.178088 | − | 0.984015i | \(-0.556991\pi\) | ||||
−0.178088 | + | 0.984015i | \(0.556991\pi\) | |||||||
\(278\) | −3.45598e25 | −0.751798 | ||||||||
\(279\) | 3.07124e24 | 0.0643384 | ||||||||
\(280\) | 2.13856e24 | 0.0431481 | ||||||||
\(281\) | 9.40593e25 | 1.82804 | 0.914019 | − | 0.405671i | \(-0.132962\pi\) | ||||
0.914019 | + | 0.405671i | \(0.132962\pi\) | |||||||
\(282\) | 1.11904e25 | 0.209522 | ||||||||
\(283\) | −4.41232e25 | −0.795993 | −0.397997 | − | 0.917387i | \(-0.630294\pi\) | ||||
−0.397997 | + | 0.917387i | \(0.630294\pi\) | |||||||
\(284\) | 2.80308e25 | 0.487296 | ||||||||
\(285\) | 3.92839e25 | 0.658179 | ||||||||
\(286\) | 8.15227e24 | 0.131654 | ||||||||
\(287\) | 5.72974e24 | 0.0892021 | ||||||||
\(288\) | 3.07337e24 | 0.0461312 | ||||||||
\(289\) | 9.81218e25 | 1.42016 | ||||||||
\(290\) | −2.65416e25 | −0.370466 | ||||||||
\(291\) | −7.55780e25 | −1.01746 | ||||||||
\(292\) | 5.87378e25 | 0.762777 | ||||||||
\(293\) | 2.98120e25 | 0.373492 | 0.186746 | − | 0.982408i | \(-0.440206\pi\) | ||||
0.186746 | + | 0.982408i | \(0.440206\pi\) | |||||||
\(294\) | 6.07957e25 | 0.734895 | ||||||||
\(295\) | 1.00715e25 | 0.117479 | ||||||||
\(296\) | 2.82173e25 | 0.317653 | ||||||||
\(297\) | −3.90747e25 | −0.424574 | ||||||||
\(298\) | −5.82094e25 | −0.610552 | ||||||||
\(299\) | 1.81734e25 | 0.184031 | ||||||||
\(300\) | −1.14848e25 | −0.112292 | ||||||||
\(301\) | −3.02472e25 | −0.285586 | ||||||||
\(302\) | 1.36645e26 | 1.24601 | ||||||||
\(303\) | −1.32847e26 | −1.17005 | ||||||||
\(304\) | 3.85116e25 | 0.327657 | ||||||||
\(305\) | 8.03097e25 | 0.660115 | ||||||||
\(306\) | 3.61453e25 | 0.287063 | ||||||||
\(307\) | −4.58514e25 | −0.351884 | −0.175942 | − | 0.984401i | \(-0.556297\pi\) | ||||
−0.175942 | + | 0.984401i | \(0.556297\pi\) | |||||||
\(308\) | 9.41190e24 | 0.0698063 | ||||||||
\(309\) | −2.41587e26 | −1.73185 | ||||||||
\(310\) | −1.12512e25 | −0.0779652 | ||||||||
\(311\) | −1.30419e26 | −0.873691 | −0.436845 | − | 0.899537i | \(-0.643904\pi\) | ||||
−0.436845 | + | 0.899537i | \(0.643904\pi\) | |||||||
\(312\) | 2.23072e25 | 0.144485 | ||||||||
\(313\) | 2.68379e26 | 1.68087 | 0.840434 | − | 0.541914i | \(-0.182300\pi\) | ||||
0.840434 | + | 0.541914i | \(0.182300\pi\) | |||||||
\(314\) | −1.60485e25 | −0.0972013 | ||||||||
\(315\) | 5.43671e24 | 0.0318475 | ||||||||
\(316\) | −4.54091e25 | −0.257293 | ||||||||
\(317\) | 1.49751e26 | 0.820820 | 0.410410 | − | 0.911901i | \(-0.365386\pi\) | ||||
0.410410 | + | 0.911901i | \(0.365386\pi\) | |||||||
\(318\) | −1.21577e26 | −0.644714 | ||||||||
\(319\) | −1.16811e26 | −0.599351 | ||||||||
\(320\) | −1.12590e25 | −0.0559017 | ||||||||
\(321\) | −1.13250e26 | −0.544173 | ||||||||
\(322\) | 2.09815e25 | 0.0975774 | ||||||||
\(323\) | 4.52926e26 | 2.03892 | ||||||||
\(324\) | −1.36862e26 | −0.596429 | ||||||||
\(325\) | −1.72513e25 | −0.0727859 | ||||||||
\(326\) | 1.23512e26 | 0.504574 | ||||||||
\(327\) | −2.04541e26 | −0.809151 | ||||||||
\(328\) | −3.01657e25 | −0.115568 | ||||||||
\(329\) | 1.94063e25 | 0.0720087 | ||||||||
\(330\) | −5.05452e25 | −0.181670 | ||||||||
\(331\) | −2.76489e25 | −0.0962685 | −0.0481343 | − | 0.998841i | \(-0.515328\pi\) | ||||
−0.0481343 | + | 0.998841i | \(0.515328\pi\) | |||||||
\(332\) | −2.72002e26 | −0.917535 | ||||||||
\(333\) | 7.17351e25 | 0.234459 | ||||||||
\(334\) | −3.72255e26 | −1.17897 | ||||||||
\(335\) | 1.70614e26 | 0.523653 | ||||||||
\(336\) | 2.57540e25 | 0.0766093 | ||||||||
\(337\) | 2.02980e25 | 0.0585247 | 0.0292624 | − | 0.999572i | \(-0.490684\pi\) | ||||
0.0292624 | + | 0.999572i | \(0.490684\pi\) | |||||||
\(338\) | −2.19486e26 | −0.613454 | ||||||||
\(339\) | −4.14812e26 | −1.12397 | ||||||||
\(340\) | −1.32415e26 | −0.347862 | ||||||||
\(341\) | −4.95171e25 | −0.126135 | ||||||||
\(342\) | 9.79055e25 | 0.241843 | ||||||||
\(343\) | 2.19346e26 | 0.525462 | ||||||||
\(344\) | 1.59244e26 | 0.369999 | ||||||||
\(345\) | −1.12678e26 | −0.253944 | ||||||||
\(346\) | 5.37608e26 | 1.17535 | ||||||||
\(347\) | 2.67942e26 | 0.568304 | 0.284152 | − | 0.958779i | \(-0.408288\pi\) | ||||
0.284152 | + | 0.958779i | \(0.408288\pi\) | |||||||
\(348\) | −3.19632e26 | −0.657761 | ||||||||
\(349\) | −5.63379e26 | −1.12495 | −0.562475 | − | 0.826814i | \(-0.690151\pi\) | ||||
−0.562475 | + | 0.826814i | \(0.690151\pi\) | |||||||
\(350\) | −1.99169e25 | −0.0385928 | ||||||||
\(351\) | −1.60606e26 | −0.302021 | ||||||||
\(352\) | −4.95514e25 | −0.0904395 | ||||||||
\(353\) | 1.00657e27 | 1.78324 | 0.891622 | − | 0.452781i | \(-0.149568\pi\) | ||||
0.891622 | + | 0.452781i | \(0.149568\pi\) | |||||||
\(354\) | 1.21288e26 | 0.208585 | ||||||||
\(355\) | −2.61057e26 | −0.435850 | ||||||||
\(356\) | 5.33773e26 | 0.865230 | ||||||||
\(357\) | 3.02887e26 | 0.476720 | ||||||||
\(358\) | −4.38332e26 | −0.669933 | ||||||||
\(359\) | 1.04937e27 | 1.55754 | 0.778768 | − | 0.627312i | \(-0.215845\pi\) | ||||
0.778768 | + | 0.627312i | \(0.215845\pi\) | |||||||
\(360\) | −2.86230e25 | −0.0412610 | ||||||||
\(361\) | 5.12617e26 | 0.717741 | ||||||||
\(362\) | 4.23384e26 | 0.575830 | ||||||||
\(363\) | 6.27452e26 | 0.829012 | ||||||||
\(364\) | 3.86850e25 | 0.0496568 | ||||||||
\(365\) | −5.47038e26 | −0.682248 | ||||||||
\(366\) | 9.67144e26 | 1.17203 | ||||||||
\(367\) | −5.00538e26 | −0.589445 | −0.294723 | − | 0.955583i | \(-0.595227\pi\) | ||||
−0.294723 | + | 0.955583i | \(0.595227\pi\) | |||||||
\(368\) | −1.10463e26 | −0.126419 | ||||||||
\(369\) | −7.66884e25 | −0.0853008 | ||||||||
\(370\) | −2.62794e26 | −0.284117 | ||||||||
\(371\) | −2.10838e26 | −0.221576 | ||||||||
\(372\) | −1.35495e26 | −0.138427 | ||||||||
\(373\) | 5.47776e26 | 0.544077 | 0.272039 | − | 0.962286i | \(-0.412302\pi\) | ||||
0.272039 | + | 0.962286i | \(0.412302\pi\) | |||||||
\(374\) | −5.82764e26 | −0.562783 | ||||||||
\(375\) | 1.06961e26 | 0.100437 | ||||||||
\(376\) | −1.02169e26 | −0.0932930 | ||||||||
\(377\) | −4.80120e26 | −0.426349 | ||||||||
\(378\) | −1.85421e26 | −0.160139 | ||||||||
\(379\) | −1.26713e27 | −1.06441 | −0.532205 | − | 0.846615i | \(-0.678637\pi\) | ||||
−0.532205 | + | 0.846615i | \(0.678637\pi\) | |||||||
\(380\) | −3.58667e26 | −0.293065 | ||||||||
\(381\) | −1.81723e27 | −1.44443 | ||||||||
\(382\) | 7.87959e25 | 0.0609310 | ||||||||
\(383\) | −5.06606e26 | −0.381139 | −0.190570 | − | 0.981674i | \(-0.561033\pi\) | ||||
−0.190570 | + | 0.981674i | \(0.561033\pi\) | |||||||
\(384\) | −1.35589e26 | −0.0992534 | ||||||||
\(385\) | −8.76551e25 | −0.0624367 | ||||||||
\(386\) | 1.28200e27 | 0.888629 | ||||||||
\(387\) | 4.04836e26 | 0.273095 | ||||||||
\(388\) | 6.90036e26 | 0.453042 | ||||||||
\(389\) | −1.46115e27 | −0.933738 | −0.466869 | − | 0.884327i | \(-0.654618\pi\) | ||||
−0.466869 | + | 0.884327i | \(0.654618\pi\) | |||||||
\(390\) | −2.07752e26 | −0.129231 | ||||||||
\(391\) | −1.29913e27 | −0.786675 | ||||||||
\(392\) | −5.55072e26 | −0.327224 | ||||||||
\(393\) | 2.10986e27 | 1.21097 | ||||||||
\(394\) | 9.22777e26 | 0.515687 | ||||||||
\(395\) | 4.22905e26 | 0.230130 | ||||||||
\(396\) | −1.25971e26 | −0.0667533 | ||||||||
\(397\) | −3.60855e27 | −1.86223 | −0.931113 | − | 0.364730i | \(-0.881161\pi\) | ||||
−0.931113 | + | 0.364730i | \(0.881161\pi\) | |||||||
\(398\) | −9.47466e26 | −0.476202 | ||||||||
\(399\) | 8.20419e26 | 0.401625 | ||||||||
\(400\) | 1.04858e26 | 0.0500000 | ||||||||
\(401\) | −3.67006e25 | −0.0170474 | −0.00852369 | − | 0.999964i | \(-0.502713\pi\) | ||||
−0.00852369 | + | 0.999964i | \(0.502713\pi\) | |||||||
\(402\) | 2.05465e27 | 0.929745 | ||||||||
\(403\) | −2.03526e26 | −0.0897259 | ||||||||
\(404\) | 1.21291e27 | 0.520984 | ||||||||
\(405\) | 1.27462e27 | 0.533463 | ||||||||
\(406\) | −5.54304e26 | −0.226060 | ||||||||
\(407\) | −1.15657e27 | −0.459654 | ||||||||
\(408\) | −1.59463e27 | −0.617629 | ||||||||
\(409\) | −2.39045e27 | −0.902371 | −0.451185 | − | 0.892430i | \(-0.648999\pi\) | ||||
−0.451185 | + | 0.892430i | \(0.648999\pi\) | |||||||
\(410\) | 2.80940e26 | 0.103367 | ||||||||
\(411\) | −8.10684e26 | −0.290745 | ||||||||
\(412\) | 2.20572e27 | 0.771132 | ||||||||
\(413\) | 2.10336e26 | 0.0716866 | ||||||||
\(414\) | −2.80822e26 | −0.0933098 | ||||||||
\(415\) | 2.53322e27 | 0.820668 | ||||||||
\(416\) | −2.03668e26 | −0.0643342 | ||||||||
\(417\) | 3.87610e27 | 1.19390 | ||||||||
\(418\) | −1.57851e27 | −0.474130 | ||||||||
\(419\) | 6.65037e27 | 1.94804 | 0.974021 | − | 0.226458i | \(-0.0727145\pi\) | ||||
0.974021 | + | 0.226458i | \(0.0727145\pi\) | |||||||
\(420\) | −2.39852e26 | −0.0685214 | ||||||||
\(421\) | 5.66789e26 | 0.157928 | 0.0789641 | − | 0.996877i | \(-0.474839\pi\) | ||||
0.0789641 | + | 0.996877i | \(0.474839\pi\) | |||||||
\(422\) | −1.01543e27 | −0.275973 | ||||||||
\(423\) | −2.59739e26 | −0.0688594 | ||||||||
\(424\) | 1.11001e27 | 0.287069 | ||||||||
\(425\) | 1.23321e27 | 0.311137 | ||||||||
\(426\) | −3.14383e27 | −0.773851 | ||||||||
\(427\) | 1.67721e27 | 0.402806 | ||||||||
\(428\) | 1.03399e27 | 0.242302 | ||||||||
\(429\) | −9.14328e26 | −0.209074 | ||||||||
\(430\) | −1.48308e27 | −0.330937 | ||||||||
\(431\) | 3.51896e27 | 0.766307 | 0.383153 | − | 0.923685i | \(-0.374838\pi\) | ||||
0.383153 | + | 0.923685i | \(0.374838\pi\) | |||||||
\(432\) | 9.76201e26 | 0.207472 | ||||||||
\(433\) | 1.55391e27 | 0.322332 | 0.161166 | − | 0.986927i | \(-0.448474\pi\) | ||||
0.161166 | + | 0.986927i | \(0.448474\pi\) | |||||||
\(434\) | −2.34974e26 | −0.0475748 | ||||||||
\(435\) | 2.97681e27 | 0.588320 | ||||||||
\(436\) | 1.86749e27 | 0.360288 | ||||||||
\(437\) | −3.51890e27 | −0.662753 | ||||||||
\(438\) | −6.58781e27 | −1.21133 | ||||||||
\(439\) | 5.58352e27 | 1.00238 | 0.501188 | − | 0.865338i | \(-0.332897\pi\) | ||||
0.501188 | + | 0.865338i | \(0.332897\pi\) | |||||||
\(440\) | 4.61484e26 | 0.0808916 | ||||||||
\(441\) | −1.41112e27 | −0.241524 | ||||||||
\(442\) | −2.39529e27 | −0.400336 | ||||||||
\(443\) | −6.81633e27 | −1.11253 | −0.556265 | − | 0.831005i | \(-0.687766\pi\) | ||||
−0.556265 | + | 0.831005i | \(0.687766\pi\) | |||||||
\(444\) | −3.16475e27 | −0.504450 | ||||||||
\(445\) | −4.97115e27 | −0.773885 | ||||||||
\(446\) | −4.09565e27 | −0.622739 | ||||||||
\(447\) | 6.52855e27 | 0.969589 | ||||||||
\(448\) | −2.35137e26 | −0.0341115 | ||||||||
\(449\) | −3.94071e27 | −0.558455 | −0.279227 | − | 0.960225i | \(-0.590078\pi\) | ||||
−0.279227 | + | 0.960225i | \(0.590078\pi\) | |||||||
\(450\) | 2.66573e26 | 0.0369049 | ||||||||
\(451\) | 1.23643e27 | 0.167231 | ||||||||
\(452\) | 3.78729e27 | 0.500466 | ||||||||
\(453\) | −1.53256e28 | −1.97873 | ||||||||
\(454\) | 5.41593e27 | 0.683261 | ||||||||
\(455\) | −3.60282e26 | −0.0444143 | ||||||||
\(456\) | −4.31931e27 | −0.520336 | ||||||||
\(457\) | −2.47274e26 | −0.0291111 | −0.0145555 | − | 0.999894i | \(-0.504633\pi\) | ||||
−0.0145555 | + | 0.999894i | \(0.504633\pi\) | |||||||
\(458\) | −1.08299e27 | −0.124606 | ||||||||
\(459\) | 1.14809e28 | 1.29105 | ||||||||
\(460\) | 1.02876e27 | 0.113073 | ||||||||
\(461\) | −6.40047e27 | −0.687625 | −0.343813 | − | 0.939038i | \(-0.611719\pi\) | ||||
−0.343813 | + | 0.939038i | \(0.611719\pi\) | |||||||
\(462\) | −1.05560e27 | −0.110856 | ||||||||
\(463\) | −8.60733e26 | −0.0883625 | −0.0441812 | − | 0.999024i | \(-0.514068\pi\) | ||||
−0.0441812 | + | 0.999024i | \(0.514068\pi\) | |||||||
\(464\) | 2.91828e27 | 0.292879 | ||||||||
\(465\) | 1.26189e27 | 0.123813 | ||||||||
\(466\) | 1.08458e28 | 1.04042 | ||||||||
\(467\) | −1.25054e28 | −1.17292 | −0.586461 | − | 0.809977i | \(-0.699479\pi\) | ||||
−0.586461 | + | 0.809977i | \(0.699479\pi\) | |||||||
\(468\) | −5.17771e26 | −0.0474850 | ||||||||
\(469\) | 3.56316e27 | 0.319536 | ||||||||
\(470\) | 9.51528e26 | 0.0834438 | ||||||||
\(471\) | 1.79993e27 | 0.154361 | ||||||||
\(472\) | −1.10737e27 | −0.0928756 | ||||||||
\(473\) | −6.52710e27 | −0.535400 | ||||||||
\(474\) | 5.09291e27 | 0.408596 | ||||||||
\(475\) | 3.34035e27 | 0.262125 | ||||||||
\(476\) | −2.76539e27 | −0.212268 | ||||||||
\(477\) | 2.82192e27 | 0.211886 | ||||||||
\(478\) | 1.76191e28 | 1.29417 | ||||||||
\(479\) | 9.68180e27 | 0.695718 | 0.347859 | − | 0.937547i | \(-0.386909\pi\) | ||||
0.347859 | + | 0.937547i | \(0.386909\pi\) | |||||||
\(480\) | 1.26277e27 | 0.0887749 | ||||||||
\(481\) | −4.75377e27 | −0.326975 | ||||||||
\(482\) | −1.77231e28 | −1.19274 | ||||||||
\(483\) | −2.35320e27 | −0.154958 | ||||||||
\(484\) | −5.72871e27 | −0.369131 | ||||||||
\(485\) | −6.42646e27 | −0.405213 | ||||||||
\(486\) | 5.83977e27 | 0.360342 | ||||||||
\(487\) | −4.62318e27 | −0.279182 | −0.139591 | − | 0.990209i | \(-0.544579\pi\) | ||||
−0.139591 | + | 0.990209i | \(0.544579\pi\) | |||||||
\(488\) | −8.83014e27 | −0.521867 | ||||||||
\(489\) | −1.38527e28 | −0.801291 | ||||||||
\(490\) | 5.16951e27 | 0.292678 | ||||||||
\(491\) | −2.14634e28 | −1.18944 | −0.594719 | − | 0.803934i | \(-0.702737\pi\) | ||||
−0.594719 | + | 0.803934i | \(0.702737\pi\) | |||||||
\(492\) | 3.38328e27 | 0.183529 | ||||||||
\(493\) | 3.43213e28 | 1.82251 | ||||||||
\(494\) | −6.48804e27 | −0.337272 | ||||||||
\(495\) | 1.17320e27 | 0.0597060 | ||||||||
\(496\) | 1.23708e27 | 0.0616369 | ||||||||
\(497\) | −5.45200e27 | −0.265958 | ||||||||
\(498\) | 3.05067e28 | 1.45709 | ||||||||
\(499\) | 2.68376e28 | 1.25513 | 0.627564 | − | 0.778565i | \(-0.284052\pi\) | ||||
0.627564 | + | 0.778565i | \(0.284052\pi\) | |||||||
\(500\) | −9.76563e26 | −0.0447214 | ||||||||
\(501\) | 4.17508e28 | 1.87227 | ||||||||
\(502\) | −9.51982e27 | −0.418061 | ||||||||
\(503\) | −1.25016e27 | −0.0537651 | −0.0268826 | − | 0.999639i | \(-0.508558\pi\) | ||||
−0.0268826 | + | 0.999639i | \(0.508558\pi\) | |||||||
\(504\) | −5.97773e26 | −0.0251777 | ||||||||
\(505\) | −1.12961e28 | −0.465983 | ||||||||
\(506\) | 4.52764e27 | 0.182933 | ||||||||
\(507\) | 2.46168e28 | 0.974198 | ||||||||
\(508\) | 1.65915e28 | 0.643158 | ||||||||
\(509\) | −2.39131e28 | −0.908029 | −0.454014 | − | 0.890994i | \(-0.650009\pi\) | ||||
−0.454014 | + | 0.890994i | \(0.650009\pi\) | |||||||
\(510\) | 1.48511e28 | 0.552424 | ||||||||
\(511\) | −1.14245e28 | −0.416312 | ||||||||
\(512\) | 1.23794e27 | 0.0441942 | ||||||||
\(513\) | 3.10979e28 | 1.08767 | ||||||||
\(514\) | 9.54645e27 | 0.327137 | ||||||||
\(515\) | −2.05423e28 | −0.689722 | ||||||||
\(516\) | −1.78602e28 | −0.587578 | ||||||||
\(517\) | 4.18772e27 | 0.134998 | ||||||||
\(518\) | −5.48828e27 | −0.173370 | ||||||||
\(519\) | −6.02961e28 | −1.86652 | ||||||||
\(520\) | 1.89680e27 | 0.0575423 | ||||||||
\(521\) | 1.24898e28 | 0.371328 | 0.185664 | − | 0.982613i | \(-0.440556\pi\) | ||||
0.185664 | + | 0.982613i | \(0.440556\pi\) | |||||||
\(522\) | 7.41896e27 | 0.216174 | ||||||||
\(523\) | −6.85611e28 | −1.95799 | −0.978995 | − | 0.203886i | \(-0.934643\pi\) | ||||
−0.978995 | + | 0.203886i | \(0.934643\pi\) | |||||||
\(524\) | −1.92633e28 | −0.539202 | ||||||||
\(525\) | 2.23380e27 | 0.0612874 | ||||||||
\(526\) | −2.94123e28 | −0.791005 | ||||||||
\(527\) | 1.45490e28 | 0.383551 | ||||||||
\(528\) | 5.55750e27 | 0.143623 | ||||||||
\(529\) | −2.93783e28 | −0.744291 | ||||||||
\(530\) | −1.03378e28 | −0.256763 | ||||||||
\(531\) | −2.81520e27 | −0.0685514 | ||||||||
\(532\) | −7.49052e27 | −0.178830 | ||||||||
\(533\) | 5.08202e27 | 0.118960 | ||||||||
\(534\) | −5.98659e28 | −1.37403 | ||||||||
\(535\) | −9.62978e27 | −0.216721 | ||||||||
\(536\) | −1.87592e28 | −0.413984 | ||||||||
\(537\) | 4.91617e28 | 1.06389 | ||||||||
\(538\) | 2.47561e28 | 0.525374 | ||||||||
\(539\) | 2.27513e28 | 0.473504 | ||||||||
\(540\) | −9.09158e27 | −0.185569 | ||||||||
\(541\) | 6.77012e28 | 1.35527 | 0.677634 | − | 0.735399i | \(-0.263005\pi\) | ||||
0.677634 | + | 0.735399i | \(0.263005\pi\) | |||||||
\(542\) | −4.59619e28 | −0.902413 | ||||||||
\(543\) | −4.74851e28 | −0.914449 | ||||||||
\(544\) | 1.45591e28 | 0.275009 | ||||||||
\(545\) | −1.73923e28 | −0.322251 | ||||||||
\(546\) | −4.33877e27 | −0.0788576 | ||||||||
\(547\) | −1.66829e28 | −0.297443 | −0.148721 | − | 0.988879i | \(-0.547516\pi\) | ||||
−0.148721 | + | 0.988879i | \(0.547516\pi\) | |||||||
\(548\) | 7.40164e27 | 0.129459 | ||||||||
\(549\) | −2.24483e28 | −0.385189 | ||||||||
\(550\) | −4.29790e27 | −0.0723516 | ||||||||
\(551\) | 9.29649e28 | 1.53542 | ||||||||
\(552\) | 1.23891e28 | 0.200760 | ||||||||
\(553\) | 8.83209e27 | 0.140427 | ||||||||
\(554\) | −1.61437e28 | −0.251854 | ||||||||
\(555\) | 2.94740e28 | 0.451194 | ||||||||
\(556\) | −3.53893e28 | −0.531601 | ||||||||
\(557\) | 9.39997e28 | 1.38563 | 0.692815 | − | 0.721116i | \(-0.256370\pi\) | ||||
0.692815 | + | 0.721116i | \(0.256370\pi\) | |||||||
\(558\) | 3.14495e27 | 0.0454941 | ||||||||
\(559\) | −2.68279e28 | −0.380857 | ||||||||
\(560\) | 2.18988e27 | 0.0305103 | ||||||||
\(561\) | 6.53606e28 | 0.893729 | ||||||||
\(562\) | 9.63167e28 | 1.29262 | ||||||||
\(563\) | 5.21769e28 | 0.687290 | 0.343645 | − | 0.939100i | \(-0.388338\pi\) | ||||
0.343645 | + | 0.939100i | \(0.388338\pi\) | |||||||
\(564\) | 1.14589e28 | 0.148154 | ||||||||
\(565\) | −3.52718e28 | −0.447630 | ||||||||
\(566\) | −4.51821e28 | −0.562852 | ||||||||
\(567\) | 2.66197e28 | 0.325522 | ||||||||
\(568\) | 2.87035e28 | 0.344570 | ||||||||
\(569\) | 9.80844e27 | 0.115590 | 0.0577951 | − | 0.998328i | \(-0.481593\pi\) | ||||
0.0577951 | + | 0.998328i | \(0.481593\pi\) | |||||||
\(570\) | 4.02268e28 | 0.465403 | ||||||||
\(571\) | 4.43638e28 | 0.503906 | 0.251953 | − | 0.967740i | \(-0.418927\pi\) | ||||
0.251953 | + | 0.967740i | \(0.418927\pi\) | |||||||
\(572\) | 8.34793e27 | 0.0930937 | ||||||||
\(573\) | −8.83745e27 | −0.0967617 | ||||||||
\(574\) | 5.86725e27 | 0.0630754 | ||||||||
\(575\) | −9.58110e27 | −0.101135 | ||||||||
\(576\) | 3.14714e27 | 0.0326197 | ||||||||
\(577\) | −1.56720e29 | −1.59507 | −0.797533 | − | 0.603276i | \(-0.793862\pi\) | ||||
−0.797533 | + | 0.603276i | \(0.793862\pi\) | |||||||
\(578\) | 1.00477e29 | 1.00421 | ||||||||
\(579\) | −1.43784e29 | −1.41119 | ||||||||
\(580\) | −2.71786e28 | −0.261959 | ||||||||
\(581\) | 5.29046e28 | 0.500776 | ||||||||
\(582\) | −7.73919e28 | −0.719456 | ||||||||
\(583\) | −4.54973e28 | −0.415399 | ||||||||
\(584\) | 6.01475e28 | 0.539365 | ||||||||
\(585\) | 4.82212e27 | 0.0424719 | ||||||||
\(586\) | 3.05275e28 | 0.264099 | ||||||||
\(587\) | −1.20878e29 | −1.02718 | −0.513592 | − | 0.858035i | \(-0.671685\pi\) | ||||
−0.513592 | + | 0.858035i | \(0.671685\pi\) | |||||||
\(588\) | 6.22548e28 | 0.519650 | ||||||||
\(589\) | 3.94085e28 | 0.323132 | ||||||||
\(590\) | 1.03132e28 | 0.0830705 | ||||||||
\(591\) | −1.03495e29 | −0.818939 | ||||||||
\(592\) | 2.88945e28 | 0.224614 | ||||||||
\(593\) | −3.14301e28 | −0.240033 | −0.120017 | − | 0.992772i | \(-0.538295\pi\) | ||||
−0.120017 | + | 0.992772i | \(0.538295\pi\) | |||||||
\(594\) | −4.00125e28 | −0.300219 | ||||||||
\(595\) | 2.57547e28 | 0.189858 | ||||||||
\(596\) | −5.96064e28 | −0.431725 | ||||||||
\(597\) | 1.06264e29 | 0.756235 | ||||||||
\(598\) | 1.86096e28 | 0.130129 | ||||||||
\(599\) | 1.87438e29 | 1.28788 | 0.643942 | − | 0.765075i | \(-0.277298\pi\) | ||||
0.643942 | + | 0.765075i | \(0.277298\pi\) | |||||||
\(600\) | −1.17604e28 | −0.0794027 | ||||||||
\(601\) | −2.65601e29 | −1.76217 | −0.881085 | − | 0.472958i | \(-0.843186\pi\) | ||||
−0.881085 | + | 0.472958i | \(0.843186\pi\) | |||||||
\(602\) | −3.09731e28 | −0.201940 | ||||||||
\(603\) | −4.76903e28 | −0.305561 | ||||||||
\(604\) | 1.39925e29 | 0.881064 | ||||||||
\(605\) | 5.33528e28 | 0.330161 | ||||||||
\(606\) | −1.36036e29 | −0.827351 | ||||||||
\(607\) | −2.33120e29 | −1.39347 | −0.696737 | − | 0.717326i | \(-0.745366\pi\) | ||||
−0.696737 | + | 0.717326i | \(0.745366\pi\) | |||||||
\(608\) | 3.94359e28 | 0.231688 | ||||||||
\(609\) | 6.21686e28 | 0.358996 | ||||||||
\(610\) | 8.22371e28 | 0.466772 | ||||||||
\(611\) | 1.72125e28 | 0.0960309 | ||||||||
\(612\) | 3.70128e28 | 0.202984 | ||||||||
\(613\) | −5.29871e28 | −0.285651 | −0.142825 | − | 0.989748i | \(-0.545619\pi\) | ||||
−0.142825 | + | 0.989748i | \(0.545619\pi\) | |||||||
\(614\) | −4.69519e28 | −0.248820 | ||||||||
\(615\) | −3.15092e28 | −0.164153 | ||||||||
\(616\) | 9.63778e27 | 0.0493605 | ||||||||
\(617\) | −9.06542e28 | −0.456450 | −0.228225 | − | 0.973608i | \(-0.573292\pi\) | ||||
−0.228225 | + | 0.973608i | \(0.573292\pi\) | |||||||
\(618\) | −2.47385e29 | −1.22460 | ||||||||
\(619\) | 1.52550e29 | 0.742441 | 0.371220 | − | 0.928545i | \(-0.378939\pi\) | ||||
0.371220 | + | 0.928545i | \(0.378939\pi\) | |||||||
\(620\) | −1.15212e28 | −0.0551297 | ||||||||
\(621\) | −8.91979e28 | −0.419655 | ||||||||
\(622\) | −1.33549e29 | −0.617793 | ||||||||
\(623\) | −1.03819e29 | −0.472229 | ||||||||
\(624\) | 2.28426e28 | 0.102166 | ||||||||
\(625\) | 9.09495e27 | 0.0400000 | ||||||||
\(626\) | 2.74820e29 | 1.18855 | ||||||||
\(627\) | 1.77040e29 | 0.752943 | ||||||||
\(628\) | −1.64336e28 | −0.0687317 | ||||||||
\(629\) | 3.39822e29 | 1.39772 | ||||||||
\(630\) | 5.56719e27 | 0.0225196 | ||||||||
\(631\) | −3.07474e29 | −1.22321 | −0.611604 | − | 0.791164i | \(-0.709475\pi\) | ||||
−0.611604 | + | 0.791164i | \(0.709475\pi\) | |||||||
\(632\) | −4.64989e28 | −0.181934 | ||||||||
\(633\) | 1.13886e29 | 0.438260 | ||||||||
\(634\) | 1.53345e29 | 0.580407 | ||||||||
\(635\) | −1.54521e29 | −0.575258 | ||||||||
\(636\) | −1.24495e29 | −0.455882 | ||||||||
\(637\) | 9.35129e28 | 0.336827 | ||||||||
\(638\) | −1.19614e29 | −0.423806 | ||||||||
\(639\) | 7.29711e28 | 0.254327 | ||||||||
\(640\) | −1.15292e28 | −0.0395285 | ||||||||
\(641\) | 4.26974e29 | 1.44010 | 0.720049 | − | 0.693923i | \(-0.244119\pi\) | ||||
0.720049 | + | 0.693923i | \(0.244119\pi\) | |||||||
\(642\) | −1.15968e29 | −0.384788 | ||||||||
\(643\) | −1.96406e29 | −0.641120 | −0.320560 | − | 0.947228i | \(-0.603871\pi\) | ||||
−0.320560 | + | 0.947228i | \(0.603871\pi\) | |||||||
\(644\) | 2.14850e28 | 0.0689976 | ||||||||
\(645\) | 1.66336e29 | 0.525545 | ||||||||
\(646\) | 4.63797e29 | 1.44174 | ||||||||
\(647\) | 4.70139e29 | 1.43791 | 0.718955 | − | 0.695057i | \(-0.244621\pi\) | ||||
0.718955 | + | 0.695057i | \(0.244621\pi\) | |||||||
\(648\) | −1.40146e29 | −0.421739 | ||||||||
\(649\) | 4.53889e28 | 0.134394 | ||||||||
\(650\) | −1.76653e28 | −0.0514674 | ||||||||
\(651\) | 2.63538e28 | 0.0755513 | ||||||||
\(652\) | 1.26476e29 | 0.356788 | ||||||||
\(653\) | −3.28351e29 | −0.911485 | −0.455742 | − | 0.890112i | \(-0.650626\pi\) | ||||
−0.455742 | + | 0.890112i | \(0.650626\pi\) | |||||||
\(654\) | −2.09450e29 | −0.572156 | ||||||||
\(655\) | 1.79403e29 | 0.482277 | ||||||||
\(656\) | −3.08897e28 | −0.0817191 | ||||||||
\(657\) | 1.52909e29 | 0.398104 | ||||||||
\(658\) | 1.98720e28 | 0.0509179 | ||||||||
\(659\) | −5.89725e28 | −0.148714 | −0.0743571 | − | 0.997232i | \(-0.523690\pi\) | ||||
−0.0743571 | + | 0.997232i | \(0.523690\pi\) | |||||||
\(660\) | −5.17583e28 | −0.128460 | ||||||||
\(661\) | −2.99109e29 | −0.730657 | −0.365328 | − | 0.930879i | \(-0.619043\pi\) | ||||
−0.365328 | + | 0.930879i | \(0.619043\pi\) | |||||||
\(662\) | −2.83125e28 | −0.0680721 | ||||||||
\(663\) | 2.68647e29 | 0.635755 | ||||||||
\(664\) | −2.78530e29 | −0.648795 | ||||||||
\(665\) | 6.97609e28 | 0.159950 | ||||||||
\(666\) | 7.34567e28 | 0.165788 | ||||||||
\(667\) | −2.66651e29 | −0.592408 | ||||||||
\(668\) | −3.81190e29 | −0.833658 | ||||||||
\(669\) | 4.59352e29 | 0.988944 | ||||||||
\(670\) | 1.74709e29 | 0.370279 | ||||||||
\(671\) | 3.61930e29 | 0.755158 | ||||||||
\(672\) | 2.63720e28 | 0.0541710 | ||||||||
\(673\) | −4.08136e29 | −0.825366 | −0.412683 | − | 0.910875i | \(-0.635408\pi\) | ||||
−0.412683 | + | 0.910875i | \(0.635408\pi\) | |||||||
\(674\) | 2.07852e28 | 0.0413832 | ||||||||
\(675\) | 8.46719e28 | 0.165978 | ||||||||
\(676\) | −2.24754e29 | −0.433778 | ||||||||
\(677\) | −6.17392e28 | −0.117322 | −0.0586611 | − | 0.998278i | \(-0.518683\pi\) | ||||
−0.0586611 | + | 0.998278i | \(0.518683\pi\) | |||||||
\(678\) | −4.24768e29 | −0.794767 | ||||||||
\(679\) | −1.34212e29 | −0.247264 | ||||||||
\(680\) | −1.35593e29 | −0.245976 | ||||||||
\(681\) | −6.07430e29 | −1.08505 | ||||||||
\(682\) | −5.07055e28 | −0.0891906 | ||||||||
\(683\) | 8.86519e29 | 1.53557 | 0.767787 | − | 0.640706i | \(-0.221358\pi\) | ||||
0.767787 | + | 0.640706i | \(0.221358\pi\) | |||||||
\(684\) | 1.00255e29 | 0.171009 | ||||||||
\(685\) | −6.89332e28 | −0.115792 | ||||||||
\(686\) | 2.24610e29 | 0.371558 | ||||||||
\(687\) | 1.21464e29 | 0.197880 | ||||||||
\(688\) | 1.63066e29 | 0.261629 | ||||||||
\(689\) | −1.87004e29 | −0.295494 | ||||||||
\(690\) | −1.15382e29 | −0.179566 | ||||||||
\(691\) | −3.58171e29 | −0.548998 | −0.274499 | − | 0.961587i | \(-0.588512\pi\) | ||||
−0.274499 | + | 0.961587i | \(0.588512\pi\) | |||||||
\(692\) | 5.50511e29 | 0.831097 | ||||||||
\(693\) | 2.45015e28 | 0.0364329 | ||||||||
\(694\) | 2.74372e29 | 0.401851 | ||||||||
\(695\) | 3.29588e29 | 0.475479 | ||||||||
\(696\) | −3.27303e29 | −0.465108 | ||||||||
\(697\) | −3.63287e29 | −0.508518 | ||||||||
\(698\) | −5.76900e29 | −0.795460 | ||||||||
\(699\) | −1.21643e30 | −1.65225 | ||||||||
\(700\) | −2.03949e28 | −0.0272892 | ||||||||
\(701\) | −9.30503e29 | −1.22653 | −0.613265 | − | 0.789877i | \(-0.710144\pi\) | ||||
−0.613265 | + | 0.789877i | \(0.710144\pi\) | |||||||
\(702\) | −1.64460e29 | −0.213561 | ||||||||
\(703\) | 9.20465e29 | 1.17754 | ||||||||
\(704\) | −5.07407e28 | −0.0639504 | ||||||||
\(705\) | −1.06720e29 | −0.132513 | ||||||||
\(706\) | 1.03073e30 | 1.26094 | ||||||||
\(707\) | −2.35912e29 | −0.284345 | ||||||||
\(708\) | 1.24198e29 | 0.147492 | ||||||||
\(709\) | −1.29300e30 | −1.51290 | −0.756452 | − | 0.654049i | \(-0.773069\pi\) | ||||
−0.756452 | + | 0.654049i | \(0.773069\pi\) | |||||||
\(710\) | −2.67322e29 | −0.308193 | ||||||||
\(711\) | −1.18211e29 | −0.134285 | ||||||||
\(712\) | 5.46583e29 | 0.611810 | ||||||||
\(713\) | −1.13035e29 | −0.124673 | ||||||||
\(714\) | 3.10156e29 | 0.337092 | ||||||||
\(715\) | −7.77461e28 | −0.0832655 | ||||||||
\(716\) | −4.48852e29 | −0.473714 | ||||||||
\(717\) | −1.97609e30 | −2.05521 | ||||||||
\(718\) | 1.07456e30 | 1.10134 | ||||||||
\(719\) | −3.29773e29 | −0.333090 | −0.166545 | − | 0.986034i | \(-0.553261\pi\) | ||||
−0.166545 | + | 0.986034i | \(0.553261\pi\) | |||||||
\(720\) | −2.93100e28 | −0.0291759 | ||||||||
\(721\) | −4.29013e29 | −0.420872 | ||||||||
\(722\) | 5.24920e29 | 0.507519 | ||||||||
\(723\) | 1.98776e30 | 1.89413 | ||||||||
\(724\) | 4.33545e29 | 0.407173 | ||||||||
\(725\) | 2.53121e29 | 0.234303 | ||||||||
\(726\) | 6.42511e29 | 0.586200 | ||||||||
\(727\) | 1.06829e30 | 0.960677 | 0.480338 | − | 0.877083i | \(-0.340514\pi\) | ||||
0.480338 | + | 0.877083i | \(0.340514\pi\) | |||||||
\(728\) | 3.96135e28 | 0.0351126 | ||||||||
\(729\) | 7.10333e29 | 0.620616 | ||||||||
\(730\) | −5.60167e29 | −0.482422 | ||||||||
\(731\) | 1.91778e30 | 1.62805 | ||||||||
\(732\) | 9.90356e29 | 0.828752 | ||||||||
\(733\) | 1.28132e30 | 1.05698 | 0.528490 | − | 0.848939i | \(-0.322758\pi\) | ||||
0.528490 | + | 0.848939i | \(0.322758\pi\) | |||||||
\(734\) | −5.12551e29 | −0.416801 | ||||||||
\(735\) | −5.79793e29 | −0.464789 | ||||||||
\(736\) | −1.13114e29 | −0.0893919 | ||||||||
\(737\) | 7.68901e29 | 0.599049 | ||||||||
\(738\) | −7.85289e28 | −0.0603168 | ||||||||
\(739\) | −1.68393e29 | −0.127514 | −0.0637569 | − | 0.997965i | \(-0.520308\pi\) | ||||
−0.0637569 | + | 0.997965i | \(0.520308\pi\) | |||||||
\(740\) | −2.69101e29 | −0.200901 | ||||||||
\(741\) | 7.27674e29 | 0.535607 | ||||||||
\(742\) | −2.15898e29 | −0.156678 | ||||||||
\(743\) | 5.78502e28 | 0.0413925 | 0.0206963 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206963 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(744\) | −1.38746e29 | −0.0978827 | ||||||||
\(745\) | 5.55128e29 | 0.386147 | ||||||||
\(746\) | 5.60923e29 | 0.384721 | ||||||||
\(747\) | −7.08090e29 | −0.478875 | ||||||||
\(748\) | −5.96750e29 | −0.397947 | ||||||||
\(749\) | −2.01112e29 | −0.132245 | ||||||||
\(750\) | 1.09528e29 | 0.0710199 | ||||||||
\(751\) | 1.16126e30 | 0.742526 | 0.371263 | − | 0.928528i | \(-0.378925\pi\) | ||||
0.371263 | + | 0.928528i | \(0.378925\pi\) | |||||||
\(752\) | −1.04622e29 | −0.0659681 | ||||||||
\(753\) | 1.06771e30 | 0.663903 | ||||||||
\(754\) | −4.91642e29 | −0.301474 | ||||||||
\(755\) | −1.30315e30 | −0.788048 | ||||||||
\(756\) | −1.89872e29 | −0.113235 | ||||||||
\(757\) | −2.47468e30 | −1.45550 | −0.727749 | − | 0.685843i | \(-0.759434\pi\) | ||||
−0.727749 | + | 0.685843i | \(0.759434\pi\) | |||||||
\(758\) | −1.29754e30 | −0.752652 | ||||||||
\(759\) | −5.07803e29 | −0.290507 | ||||||||
\(760\) | −3.67275e29 | −0.207228 | ||||||||
\(761\) | 8.23029e29 | 0.458011 | 0.229006 | − | 0.973425i | \(-0.426453\pi\) | ||||
0.229006 | + | 0.973425i | \(0.426453\pi\) | |||||||
\(762\) | −1.86084e30 | −1.02137 | ||||||||
\(763\) | −3.63227e29 | −0.196640 | ||||||||
\(764\) | 8.06870e28 | 0.0430847 | ||||||||
\(765\) | −3.44708e29 | −0.181554 | ||||||||
\(766\) | −5.18765e29 | −0.269506 | ||||||||
\(767\) | 1.86559e29 | 0.0956013 | ||||||||
\(768\) | −1.38843e29 | −0.0701827 | ||||||||
\(769\) | −8.22507e29 | −0.410122 | −0.205061 | − | 0.978749i | \(-0.565739\pi\) | ||||
−0.205061 | + | 0.978749i | \(0.565739\pi\) | |||||||
\(770\) | −8.97588e28 | −0.0441494 | ||||||||
\(771\) | −1.07069e30 | −0.519511 | ||||||||
\(772\) | 1.31276e30 | 0.628355 | ||||||||
\(773\) | −4.08869e30 | −1.93063 | −0.965316 | − | 0.261083i | \(-0.915920\pi\) | ||||
−0.965316 | + | 0.261083i | \(0.915920\pi\) | |||||||
\(774\) | 4.14552e29 | 0.193108 | ||||||||
\(775\) | 1.07300e29 | 0.0493095 | ||||||||
\(776\) | 7.06597e29 | 0.320349 | ||||||||
\(777\) | 6.15545e29 | 0.275321 | ||||||||
\(778\) | −1.49622e30 | −0.660252 | ||||||||
\(779\) | −9.84024e29 | −0.428413 | ||||||||
\(780\) | −2.12738e29 | −0.0913802 | ||||||||
\(781\) | −1.17650e30 | −0.498604 | ||||||||
\(782\) | −1.33030e30 | −0.556263 | ||||||||
\(783\) | 2.35649e30 | 0.972228 | ||||||||
\(784\) | −5.68393e29 | −0.231382 | ||||||||
\(785\) | 1.53050e29 | 0.0614755 | ||||||||
\(786\) | 2.16050e30 | 0.856282 | ||||||||
\(787\) | 2.27937e30 | 0.891414 | 0.445707 | − | 0.895179i | \(-0.352952\pi\) | ||||
0.445707 | + | 0.895179i | \(0.352952\pi\) | |||||||
\(788\) | 9.44924e29 | 0.364646 | ||||||||
\(789\) | 3.29878e30 | 1.25616 | ||||||||
\(790\) | 4.33055e29 | 0.162727 | ||||||||
\(791\) | −7.36629e29 | −0.273147 | ||||||||
\(792\) | −1.28995e29 | −0.0472017 | ||||||||
\(793\) | 1.48761e30 | 0.537182 | ||||||||
\(794\) | −3.69516e30 | −1.31679 | ||||||||
\(795\) | 1.15945e30 | 0.407753 | ||||||||
\(796\) | −9.70205e29 | −0.336726 | ||||||||
\(797\) | 3.26331e30 | 1.11775 | 0.558877 | − | 0.829250i | \(-0.311232\pi\) | ||||
0.558877 | + | 0.829250i | \(0.311232\pi\) | |||||||
\(798\) | 8.40109e29 | 0.283991 | ||||||||
\(799\) | −1.23043e30 | −0.410503 | ||||||||
\(800\) | 1.07374e29 | 0.0353553 | ||||||||
\(801\) | 1.38954e30 | 0.451576 | ||||||||
\(802\) | −3.75814e28 | −0.0120543 | ||||||||
\(803\) | −2.46532e30 | −0.780478 | ||||||||
\(804\) | 2.10396e30 | 0.657429 | ||||||||
\(805\) | −2.00095e29 | −0.0617134 | ||||||||
\(806\) | −2.08411e29 | −0.0634458 | ||||||||
\(807\) | −2.77655e30 | −0.834322 | ||||||||
\(808\) | 1.24202e30 | 0.368392 | ||||||||
\(809\) | 1.06157e30 | 0.310805 | 0.155403 | − | 0.987851i | \(-0.450333\pi\) | ||||
0.155403 | + | 0.987851i | \(0.450333\pi\) | |||||||
\(810\) | 1.30521e30 | 0.377215 | ||||||||
\(811\) | −5.07809e30 | −1.44871 | −0.724355 | − | 0.689428i | \(-0.757862\pi\) | ||||
−0.724355 | + | 0.689428i | \(0.757862\pi\) | |||||||
\(812\) | −5.67607e29 | −0.159849 | ||||||||
\(813\) | 5.15491e30 | 1.43308 | ||||||||
\(814\) | −1.18433e30 | −0.325025 | ||||||||
\(815\) | −1.17790e30 | −0.319121 | ||||||||
\(816\) | −1.63290e30 | −0.436729 | ||||||||
\(817\) | 5.19464e30 | 1.37159 | ||||||||
\(818\) | −2.44782e30 | −0.638073 | ||||||||
\(819\) | 1.00707e29 | 0.0259166 | ||||||||
\(820\) | 2.87683e29 | 0.0730918 | ||||||||
\(821\) | −3.24366e30 | −0.813640 | −0.406820 | − | 0.913508i | \(-0.633362\pi\) | ||||
−0.406820 | + | 0.913508i | \(0.633362\pi\) | |||||||
\(822\) | −8.30141e29 | −0.205588 | ||||||||
\(823\) | 1.47953e30 | 0.361764 | 0.180882 | − | 0.983505i | \(-0.442105\pi\) | ||||
0.180882 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(824\) | 2.25865e30 | 0.545273 | ||||||||
\(825\) | 4.82037e29 | 0.114898 | ||||||||
\(826\) | 2.15384e29 | 0.0506901 | ||||||||
\(827\) | 1.06680e30 | 0.247898 | 0.123949 | − | 0.992289i | \(-0.460444\pi\) | ||||
0.123949 | + | 0.992289i | \(0.460444\pi\) | |||||||
\(828\) | −2.87562e29 | −0.0659800 | ||||||||
\(829\) | 1.37112e30 | 0.310637 | 0.155319 | − | 0.987864i | \(-0.450360\pi\) | ||||
0.155319 | + | 0.987864i | \(0.450360\pi\) | |||||||
\(830\) | 2.59402e30 | 0.580300 | ||||||||
\(831\) | 1.81061e30 | 0.399958 | ||||||||
\(832\) | −2.08556e29 | −0.0454912 | ||||||||
\(833\) | −6.68475e30 | −1.43983 | ||||||||
\(834\) | 3.96913e30 | 0.844212 | ||||||||
\(835\) | 3.55010e30 | 0.745647 | ||||||||
\(836\) | −1.61640e30 | −0.335260 | ||||||||
\(837\) | 9.98936e29 | 0.204607 | ||||||||
\(838\) | 6.80997e30 | 1.37747 | ||||||||
\(839\) | 7.78595e29 | 0.155529 | 0.0777645 | − | 0.996972i | \(-0.475222\pi\) | ||||
0.0777645 | + | 0.996972i | \(0.475222\pi\) | |||||||
\(840\) | −2.45609e29 | −0.0484520 | ||||||||
\(841\) | 1.91173e30 | 0.372450 | ||||||||
\(842\) | 5.80392e29 | 0.111672 | ||||||||
\(843\) | −1.08025e31 | −2.05275 | ||||||||
\(844\) | −1.03980e30 | −0.195143 | ||||||||
\(845\) | 2.09319e30 | 0.387983 | ||||||||
\(846\) | −2.65973e29 | −0.0486909 | ||||||||
\(847\) | 1.11424e30 | 0.201466 | ||||||||
\(848\) | 1.13665e30 | 0.202989 | ||||||||
\(849\) | 5.06746e30 | 0.893839 | ||||||||
\(850\) | 1.26280e30 | 0.220007 | ||||||||
\(851\) | −2.64016e30 | −0.454329 | ||||||||
\(852\) | −3.21928e30 | −0.547196 | ||||||||
\(853\) | −5.07514e30 | −0.852086 | −0.426043 | − | 0.904703i | \(-0.640093\pi\) | ||||
−0.426043 | + | 0.904703i | \(0.640093\pi\) | |||||||
\(854\) | 1.71747e30 | 0.284827 | ||||||||
\(855\) | −9.33700e29 | −0.152955 | ||||||||
\(856\) | 1.05881e30 | 0.171333 | ||||||||
\(857\) | −7.65635e30 | −1.22384 | −0.611918 | − | 0.790921i | \(-0.709602\pi\) | ||||
−0.611918 | + | 0.790921i | \(0.709602\pi\) | |||||||
\(858\) | −9.36272e29 | −0.147838 | ||||||||
\(859\) | 6.42591e30 | 1.00232 | 0.501160 | − | 0.865355i | \(-0.332907\pi\) | ||||
0.501160 | + | 0.865355i | \(0.332907\pi\) | |||||||
\(860\) | −1.51867e30 | −0.234008 | ||||||||
\(861\) | −6.58049e29 | −0.100167 | ||||||||
\(862\) | 3.60341e30 | 0.541861 | ||||||||
\(863\) | −1.00027e31 | −1.48594 | −0.742972 | − | 0.669322i | \(-0.766585\pi\) | ||||
−0.742972 | + | 0.669322i | \(0.766585\pi\) | |||||||
\(864\) | 9.99629e29 | 0.146705 | ||||||||
\(865\) | −5.12703e30 | −0.743356 | ||||||||
\(866\) | 1.59121e30 | 0.227923 | ||||||||
\(867\) | −1.12691e31 | −1.59473 | ||||||||
\(868\) | −2.40613e29 | −0.0336405 | ||||||||
\(869\) | 1.90590e30 | 0.263264 | ||||||||
\(870\) | 3.04825e30 | 0.416005 | ||||||||
\(871\) | 3.16036e30 | 0.426134 | ||||||||
\(872\) | 1.91231e30 | 0.254762 | ||||||||
\(873\) | 1.79634e30 | 0.236449 | ||||||||
\(874\) | −3.60335e30 | −0.468637 | ||||||||
\(875\) | 1.89942e29 | 0.0244082 | ||||||||
\(876\) | −6.74591e30 | −0.856540 | ||||||||
\(877\) | 1.69135e30 | 0.212197 | 0.106098 | − | 0.994356i | \(-0.466164\pi\) | ||||
0.106098 | + | 0.994356i | \(0.466164\pi\) | |||||||
\(878\) | 5.71752e30 | 0.708787 | ||||||||
\(879\) | −3.42385e30 | −0.419403 | ||||||||
\(880\) | 4.72559e29 | 0.0571990 | ||||||||
\(881\) | 7.04503e30 | 0.842628 | 0.421314 | − | 0.906915i | \(-0.361569\pi\) | ||||
0.421314 | + | 0.906915i | \(0.361569\pi\) | |||||||
\(882\) | −1.44499e30 | −0.170783 | ||||||||
\(883\) | −7.12748e30 | −0.832431 | −0.416216 | − | 0.909266i | \(-0.636644\pi\) | ||||
−0.416216 | + | 0.909266i | \(0.636644\pi\) | |||||||
\(884\) | −2.45278e30 | −0.283080 | ||||||||
\(885\) | −1.15669e30 | −0.131920 | ||||||||
\(886\) | −6.97992e30 | −0.786677 | ||||||||
\(887\) | 7.82765e30 | 0.871834 | 0.435917 | − | 0.899987i | \(-0.356424\pi\) | ||||
0.435917 | + | 0.899987i | \(0.356424\pi\) | |||||||
\(888\) | −3.24070e30 | −0.356700 | ||||||||
\(889\) | −3.22706e30 | −0.351026 | ||||||||
\(890\) | −5.09045e30 | −0.547219 | ||||||||
\(891\) | 5.74431e30 | 0.610270 | ||||||||
\(892\) | −4.19394e30 | −0.440343 | ||||||||
\(893\) | −3.33283e30 | −0.345838 | ||||||||
\(894\) | 6.68523e30 | 0.685603 | ||||||||
\(895\) | 4.18026e30 | 0.423703 | ||||||||
\(896\) | −2.40780e29 | −0.0241205 | ||||||||
\(897\) | −2.08718e30 | −0.206652 | ||||||||
\(898\) | −4.03529e30 | −0.394887 | ||||||||
\(899\) | 2.98625e30 | 0.288834 | ||||||||
\(900\) | 2.72970e29 | 0.0260957 | ||||||||
\(901\) | 1.33679e31 | 1.26315 | ||||||||
\(902\) | 1.26611e30 | 0.118250 | ||||||||
\(903\) | 3.47383e30 | 0.320691 | ||||||||
\(904\) | 3.87818e30 | 0.353883 | ||||||||
\(905\) | −4.03770e30 | −0.364187 | ||||||||
\(906\) | −1.56935e31 | −1.39918 | ||||||||
\(907\) | 4.42371e30 | 0.389862 | 0.194931 | − | 0.980817i | \(-0.437552\pi\) | ||||
0.194931 | + | 0.980817i | \(0.437552\pi\) | |||||||
\(908\) | 5.54591e30 | 0.483138 | ||||||||
\(909\) | 3.15751e30 | 0.271909 | ||||||||
\(910\) | −3.68929e29 | −0.0314057 | ||||||||
\(911\) | 1.34581e31 | 1.13251 | 0.566253 | − | 0.824231i | \(-0.308392\pi\) | ||||
0.566253 | + | 0.824231i | \(0.308392\pi\) | |||||||
\(912\) | −4.42298e30 | −0.367933 | ||||||||
\(913\) | 1.14164e31 | 0.938828 | ||||||||
\(914\) | −2.53208e29 | −0.0205846 | ||||||||
\(915\) | −9.22341e30 | −0.741259 | ||||||||
\(916\) | −1.10898e30 | −0.0881095 | ||||||||
\(917\) | 3.74672e30 | 0.294288 | ||||||||
\(918\) | 1.17564e31 | 0.912908 | ||||||||
\(919\) | 2.07587e31 | 1.59363 | 0.796815 | − | 0.604223i | \(-0.206517\pi\) | ||||
0.796815 | + | 0.604223i | \(0.206517\pi\) | |||||||
\(920\) | 1.05345e30 | 0.0799545 | ||||||||
\(921\) | 5.26594e30 | 0.395139 | ||||||||
\(922\) | −6.55408e30 | −0.486224 | ||||||||
\(923\) | −4.83568e30 | −0.354682 | ||||||||
\(924\) | −1.08094e30 | −0.0783871 | ||||||||
\(925\) | 2.50620e30 | 0.179692 | ||||||||
\(926\) | −8.81390e29 | −0.0624817 | ||||||||
\(927\) | 5.74203e30 | 0.402465 | ||||||||
\(928\) | 2.98832e30 | 0.207097 | ||||||||
\(929\) | −2.58824e30 | −0.177353 | −0.0886767 | − | 0.996060i | \(-0.528264\pi\) | ||||
−0.0886767 | + | 0.996060i | \(0.528264\pi\) | |||||||
\(930\) | 1.29218e30 | 0.0875489 | ||||||||
\(931\) | −1.81068e31 | −1.21302 | ||||||||
\(932\) | 1.11061e31 | 0.735691 | ||||||||
\(933\) | 1.49784e31 | 0.981088 | ||||||||
\(934\) | −1.28055e31 | −0.829381 | ||||||||
\(935\) | 5.55767e30 | 0.355935 | ||||||||
\(936\) | −5.30198e29 | −0.0335770 | ||||||||
\(937\) | −1.82163e31 | −1.14076 | −0.570381 | − | 0.821380i | \(-0.693205\pi\) | ||||
−0.570381 | + | 0.821380i | \(0.693205\pi\) | |||||||
\(938\) | 3.64867e30 | 0.225946 | ||||||||
\(939\) | −3.08228e31 | −1.88749 | ||||||||
\(940\) | 9.74364e29 | 0.0590037 | ||||||||
\(941\) | 1.59208e31 | 0.953394 | 0.476697 | − | 0.879068i | \(-0.341834\pi\) | ||||
0.476697 | + | 0.879068i | \(0.341834\pi\) | |||||||
\(942\) | 1.84313e30 | 0.109150 | ||||||||
\(943\) | 2.82247e30 | 0.165294 | ||||||||
\(944\) | −1.13395e30 | −0.0656730 | ||||||||
\(945\) | 1.76832e30 | 0.101281 | ||||||||
\(946\) | −6.68375e30 | −0.378585 | ||||||||
\(947\) | 6.90254e30 | 0.386664 | 0.193332 | − | 0.981133i | \(-0.438071\pi\) | ||||
0.193332 | + | 0.981133i | \(0.438071\pi\) | |||||||
\(948\) | 5.21514e30 | 0.288921 | ||||||||
\(949\) | −1.01330e31 | −0.555194 | ||||||||
\(950\) | 3.42052e30 | 0.185351 | ||||||||
\(951\) | −1.71986e31 | −0.921718 | ||||||||
\(952\) | −2.83176e30 | −0.150096 | ||||||||
\(953\) | 8.59868e30 | 0.450771 | 0.225386 | − | 0.974270i | \(-0.427636\pi\) | ||||
0.225386 | + | 0.974270i | \(0.427636\pi\) | |||||||
\(954\) | 2.88964e30 | 0.149826 | ||||||||
\(955\) | −7.51457e29 | −0.0385362 | ||||||||
\(956\) | 1.80420e31 | 0.915115 | ||||||||
\(957\) | 1.34155e31 | 0.673026 | ||||||||
\(958\) | 9.91416e30 | 0.491947 | ||||||||
\(959\) | −1.43962e30 | −0.0706567 | ||||||||
\(960\) | 1.29307e30 | 0.0627733 | ||||||||
\(961\) | −1.95596e31 | −0.939214 | ||||||||
\(962\) | −4.86786e30 | −0.231206 | ||||||||
\(963\) | 2.69173e30 | 0.126461 | ||||||||
\(964\) | −1.81484e31 | −0.843394 | ||||||||
\(965\) | −1.22261e31 | −0.562018 | ||||||||
\(966\) | −2.40968e30 | −0.109572 | ||||||||
\(967\) | −2.71571e30 | −0.122153 | −0.0610766 | − | 0.998133i | \(-0.519453\pi\) | ||||
−0.0610766 | + | 0.998133i | \(0.519453\pi\) | |||||||
\(968\) | −5.86620e30 | −0.261015 | ||||||||
\(969\) | −5.20177e31 | −2.28956 | ||||||||
\(970\) | −6.58070e30 | −0.286529 | ||||||||
\(971\) | −2.52216e30 | −0.108635 | −0.0543175 | − | 0.998524i | \(-0.517298\pi\) | ||||
−0.0543175 | + | 0.998524i | \(0.517298\pi\) | |||||||
\(972\) | 5.97992e30 | 0.254800 | ||||||||
\(973\) | 6.88323e30 | 0.290140 | ||||||||
\(974\) | −4.73414e30 | −0.197411 | ||||||||
\(975\) | 1.98128e30 | 0.0817329 | ||||||||
\(976\) | −9.04207e30 | −0.369016 | ||||||||
\(977\) | −3.27075e30 | −0.132055 | −0.0660274 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660274 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(978\) | −1.41851e31 | −0.566598 | ||||||||
\(979\) | −2.24034e31 | −0.885309 | ||||||||
\(980\) | 5.29358e30 | 0.206955 | ||||||||
\(981\) | 4.86154e30 | 0.188039 | ||||||||
\(982\) | −2.19785e31 | −0.841060 | ||||||||
\(983\) | −1.41284e29 | −0.00534910 | −0.00267455 | − | 0.999996i | \(-0.500851\pi\) | ||||
−0.00267455 | + | 0.999996i | \(0.500851\pi\) | |||||||
\(984\) | 3.46447e30 | 0.129774 | ||||||||
\(985\) | −8.80029e30 | −0.326149 | ||||||||
\(986\) | 3.51450e31 | 1.28871 | ||||||||
\(987\) | −2.22877e30 | −0.0808603 | ||||||||
\(988\) | −6.64376e30 | −0.238488 | ||||||||
\(989\) | −1.48998e31 | −0.529198 | ||||||||
\(990\) | 1.20136e30 | 0.0422185 | ||||||||
\(991\) | 2.73270e31 | 0.950209 | 0.475105 | − | 0.879929i | \(-0.342410\pi\) | ||||
0.475105 | + | 0.879929i | \(0.342410\pi\) | |||||||
\(992\) | 1.26677e30 | 0.0435839 | ||||||||
\(993\) | 3.17542e30 | 0.108102 | ||||||||
\(994\) | −5.58285e30 | −0.188061 | ||||||||
\(995\) | 9.03574e30 | 0.301177 | ||||||||
\(996\) | 3.12389e31 | 1.03032 | ||||||||
\(997\) | 2.01068e31 | 0.656213 | 0.328106 | − | 0.944641i | \(-0.393590\pi\) | ||||
0.328106 | + | 0.944641i | \(0.393590\pi\) | |||||||
\(998\) | 2.74817e31 | 0.887509 | ||||||||
\(999\) | 2.33322e31 | 0.745620 |
(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 | 10.22.a.d.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 80.22.a.c.1.2 | 2 | |||
5.2 | odd | 4 | 50.22.b.e.49.4 | 4 | |||
5.3 | odd | 4 | 50.22.b.e.49.1 | 4 | |||
5.4 | even | 2 | 50.22.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.22.a.d.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.22.a.d.1.2 | 2 | 5.4 | even | 2 | |||
50.22.b.e.49.1 | 4 | 5.3 | odd | 4 | |||
50.22.b.e.49.4 | 4 | 5.2 | odd | 4 | |||
80.22.a.c.1.2 | 2 | 4.3 | odd | 2 |