Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,28,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, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
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: | \(46.1855574838\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 19551870 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-4421.25\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8192.00 | −0.707107 | ||||||||
\(3\) | 186813. | 0.0676503 | 0.0338252 | − | 0.999428i | \(-0.489231\pi\) | ||||
0.0338252 | + | 0.999428i | \(0.489231\pi\) | |||||||
\(4\) | 6.71089e7 | 0.500000 | ||||||||
\(5\) | 1.22070e9 | 0.447214 | ||||||||
\(6\) | −1.53037e9 | −0.0478360 | ||||||||
\(7\) | 1.52169e11 | 0.593610 | 0.296805 | − | 0.954938i | \(-0.404079\pi\) | ||||
0.296805 | + | 0.954938i | \(0.404079\pi\) | |||||||
\(8\) | −5.49756e11 | −0.353553 | ||||||||
\(9\) | −7.59070e12 | −0.995423 | ||||||||
\(10\) | −1.00000e13 | −0.316228 | ||||||||
\(11\) | 5.20477e13 | 0.454570 | 0.227285 | − | 0.973828i | \(-0.427015\pi\) | ||||
0.227285 | + | 0.973828i | \(0.427015\pi\) | |||||||
\(12\) | 1.25368e13 | 0.0338252 | ||||||||
\(13\) | −9.66570e14 | −0.885111 | −0.442556 | − | 0.896741i | \(-0.645928\pi\) | ||||
−0.442556 | + | 0.896741i | \(0.645928\pi\) | |||||||
\(14\) | −1.24656e15 | −0.419746 | ||||||||
\(15\) | 2.28043e14 | 0.0302541 | ||||||||
\(16\) | 4.50360e15 | 0.250000 | ||||||||
\(17\) | −8.84096e15 | −0.216491 | −0.108245 | − | 0.994124i | \(-0.534523\pi\) | ||||
−0.108245 | + | 0.994124i | \(0.534523\pi\) | |||||||
\(18\) | 6.21830e16 | 0.703871 | ||||||||
\(19\) | −4.96067e16 | −0.270624 | −0.135312 | − | 0.990803i | \(-0.543204\pi\) | ||||
−0.135312 | + | 0.990803i | \(0.543204\pi\) | |||||||
\(20\) | 8.19200e16 | 0.223607 | ||||||||
\(21\) | 2.84270e16 | 0.0401579 | ||||||||
\(22\) | −4.26375e17 | −0.321429 | ||||||||
\(23\) | 2.39358e18 | 0.990197 | 0.495098 | − | 0.868837i | \(-0.335132\pi\) | ||||
0.495098 | + | 0.868837i | \(0.335132\pi\) | |||||||
\(24\) | −1.02701e17 | −0.0239180 | ||||||||
\(25\) | 1.49012e18 | 0.200000 | ||||||||
\(26\) | 7.91814e18 | 0.625868 | ||||||||
\(27\) | −2.84260e18 | −0.134991 | ||||||||
\(28\) | 1.02119e19 | 0.296805 | ||||||||
\(29\) | 5.37225e18 | 0.0972261 | 0.0486131 | − | 0.998818i | \(-0.484520\pi\) | ||||
0.0486131 | + | 0.998818i | \(0.484520\pi\) | |||||||
\(30\) | −1.86813e18 | −0.0213929 | ||||||||
\(31\) | 1.60230e20 | 1.17859 | 0.589293 | − | 0.807919i | \(-0.299406\pi\) | ||||
0.589293 | + | 0.807919i | \(0.299406\pi\) | |||||||
\(32\) | −3.68935e19 | −0.176777 | ||||||||
\(33\) | 9.72319e18 | 0.0307518 | ||||||||
\(34\) | 7.24251e19 | 0.153082 | ||||||||
\(35\) | 1.85753e20 | 0.265470 | ||||||||
\(36\) | −5.09403e20 | −0.497712 | ||||||||
\(37\) | −2.24843e21 | −1.51759 | −0.758797 | − | 0.651327i | \(-0.774213\pi\) | ||||
−0.758797 | + | 0.651327i | \(0.774213\pi\) | |||||||
\(38\) | 4.06378e20 | 0.191360 | ||||||||
\(39\) | −1.80568e20 | −0.0598781 | ||||||||
\(40\) | −6.71089e20 | −0.158114 | ||||||||
\(41\) | −4.36695e21 | −0.737218 | −0.368609 | − | 0.929585i | \(-0.620166\pi\) | ||||
−0.368609 | + | 0.929585i | \(0.620166\pi\) | |||||||
\(42\) | −2.32874e20 | −0.0283959 | ||||||||
\(43\) | −5.19463e21 | −0.461031 | −0.230516 | − | 0.973069i | \(-0.574041\pi\) | ||||
−0.230516 | + | 0.973069i | \(0.574041\pi\) | |||||||
\(44\) | 3.49286e21 | 0.227285 | ||||||||
\(45\) | −9.26599e21 | −0.445167 | ||||||||
\(46\) | −1.96082e22 | −0.700175 | ||||||||
\(47\) | 1.42831e21 | 0.0381507 | 0.0190753 | − | 0.999818i | \(-0.493928\pi\) | ||||
0.0190753 | + | 0.999818i | \(0.493928\pi\) | |||||||
\(48\) | 8.41330e20 | 0.0169126 | ||||||||
\(49\) | −4.25571e22 | −0.647627 | ||||||||
\(50\) | −1.22070e22 | −0.141421 | ||||||||
\(51\) | −1.65160e21 | −0.0146457 | ||||||||
\(52\) | −6.48654e22 | −0.442556 | ||||||||
\(53\) | −2.24935e23 | −1.18668 | −0.593338 | − | 0.804953i | \(-0.702190\pi\) | ||||
−0.593338 | + | 0.804953i | \(0.702190\pi\) | |||||||
\(54\) | 2.32866e22 | 0.0954531 | ||||||||
\(55\) | 6.35348e22 | 0.203290 | ||||||||
\(56\) | −8.36555e22 | −0.209873 | ||||||||
\(57\) | −9.26717e21 | −0.0183078 | ||||||||
\(58\) | −4.40094e22 | −0.0687493 | ||||||||
\(59\) | −1.17699e24 | −1.45972 | −0.729859 | − | 0.683598i | \(-0.760414\pi\) | ||||
−0.729859 | + | 0.683598i | \(0.760414\pi\) | |||||||
\(60\) | 1.53037e22 | 0.0151271 | ||||||||
\(61\) | −2.05590e24 | −1.62574 | −0.812868 | − | 0.582448i | \(-0.802095\pi\) | ||||
−0.812868 | + | 0.582448i | \(0.802095\pi\) | |||||||
\(62\) | −1.31261e24 | −0.833386 | ||||||||
\(63\) | −1.15507e24 | −0.590893 | ||||||||
\(64\) | 3.02231e23 | 0.125000 | ||||||||
\(65\) | −1.17989e24 | −0.395834 | ||||||||
\(66\) | −7.96523e22 | −0.0217448 | ||||||||
\(67\) | 3.81110e24 | 0.849260 | 0.424630 | − | 0.905367i | \(-0.360404\pi\) | ||||
0.424630 | + | 0.905367i | \(0.360404\pi\) | |||||||
\(68\) | −5.93307e23 | −0.108245 | ||||||||
\(69\) | 4.47151e23 | 0.0669871 | ||||||||
\(70\) | −1.52169e24 | −0.187716 | ||||||||
\(71\) | −3.12654e24 | −0.318476 | −0.159238 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159238 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(72\) | 4.17303e24 | 0.351935 | ||||||||
\(73\) | 1.49753e25 | 1.04838 | 0.524189 | − | 0.851602i | \(-0.324369\pi\) | ||||
0.524189 | + | 0.851602i | \(0.324369\pi\) | |||||||
\(74\) | 1.84191e25 | 1.07310 | ||||||||
\(75\) | 2.78373e23 | 0.0135301 | ||||||||
\(76\) | −3.32905e24 | −0.135312 | ||||||||
\(77\) | 7.92003e24 | 0.269837 | ||||||||
\(78\) | 1.47921e24 | 0.0423402 | ||||||||
\(79\) | 1.41656e25 | 0.341404 | 0.170702 | − | 0.985323i | \(-0.445397\pi\) | ||||
0.170702 | + | 0.985323i | \(0.445397\pi\) | |||||||
\(80\) | 5.49756e24 | 0.111803 | ||||||||
\(81\) | 5.73526e25 | 0.986291 | ||||||||
\(82\) | 3.57740e25 | 0.521292 | ||||||||
\(83\) | −7.95957e24 | −0.0984771 | −0.0492385 | − | 0.998787i | \(-0.515679\pi\) | ||||
−0.0492385 | + | 0.998787i | \(0.515679\pi\) | |||||||
\(84\) | 1.90771e24 | 0.0200790 | ||||||||
\(85\) | −1.07922e25 | −0.0968175 | ||||||||
\(86\) | 4.25544e25 | 0.325998 | ||||||||
\(87\) | 1.00360e24 | 0.00657738 | ||||||||
\(88\) | −2.86135e25 | −0.160715 | ||||||||
\(89\) | −1.05141e26 | −0.506998 | −0.253499 | − | 0.967336i | \(-0.581581\pi\) | ||||
−0.253499 | + | 0.967336i | \(0.581581\pi\) | |||||||
\(90\) | 7.59070e25 | 0.314781 | ||||||||
\(91\) | −1.47081e26 | −0.525411 | ||||||||
\(92\) | 1.60630e26 | 0.495098 | ||||||||
\(93\) | 2.99330e25 | 0.0797317 | ||||||||
\(94\) | −1.17007e25 | −0.0269766 | ||||||||
\(95\) | −6.05551e25 | −0.121027 | ||||||||
\(96\) | −6.89218e24 | −0.0119590 | ||||||||
\(97\) | −2.67236e26 | −0.403159 | −0.201580 | − | 0.979472i | \(-0.564608\pi\) | ||||
−0.201580 | + | 0.979472i | \(0.564608\pi\) | |||||||
\(98\) | 3.48628e26 | 0.457942 | ||||||||
\(99\) | −3.95079e26 | −0.452489 | ||||||||
\(100\) | 1.00000e26 | 0.100000 | ||||||||
\(101\) | −4.51294e26 | −0.394567 | −0.197283 | − | 0.980346i | \(-0.563212\pi\) | ||||
−0.197283 | + | 0.980346i | \(0.563212\pi\) | |||||||
\(102\) | 1.35299e25 | 0.0103560 | ||||||||
\(103\) | −2.25718e27 | −1.51448 | −0.757240 | − | 0.653137i | \(-0.773453\pi\) | ||||
−0.757240 | + | 0.653137i | \(0.773453\pi\) | |||||||
\(104\) | 5.31377e26 | 0.312934 | ||||||||
\(105\) | 3.47010e25 | 0.0179592 | ||||||||
\(106\) | 1.84267e27 | 0.839107 | ||||||||
\(107\) | −2.71910e27 | −1.09080 | −0.545399 | − | 0.838177i | \(-0.683622\pi\) | ||||
−0.545399 | + | 0.838177i | \(0.683622\pi\) | |||||||
\(108\) | −1.90764e26 | −0.0674955 | ||||||||
\(109\) | −4.53116e27 | −1.41564 | −0.707818 | − | 0.706395i | \(-0.750320\pi\) | ||||
−0.707818 | + | 0.706395i | \(0.750320\pi\) | |||||||
\(110\) | −5.20477e26 | −0.143748 | ||||||||
\(111\) | −4.20035e26 | −0.102666 | ||||||||
\(112\) | 6.85306e26 | 0.148403 | ||||||||
\(113\) | −2.52001e27 | −0.483998 | −0.241999 | − | 0.970276i | \(-0.577803\pi\) | ||||
−0.241999 | + | 0.970276i | \(0.577803\pi\) | |||||||
\(114\) | 7.59167e25 | 0.0129456 | ||||||||
\(115\) | 2.92185e27 | 0.442829 | ||||||||
\(116\) | 3.60525e26 | 0.0486131 | ||||||||
\(117\) | 7.33694e27 | 0.881061 | ||||||||
\(118\) | 9.64187e27 | 1.03218 | ||||||||
\(119\) | −1.34532e27 | −0.128511 | ||||||||
\(120\) | −1.25368e26 | −0.0106965 | ||||||||
\(121\) | −1.04010e28 | −0.793366 | ||||||||
\(122\) | 1.68420e28 | 1.14957 | ||||||||
\(123\) | −8.15802e26 | −0.0498730 | ||||||||
\(124\) | 1.07529e28 | 0.589293 | ||||||||
\(125\) | 1.81899e27 | 0.0894427 | ||||||||
\(126\) | 9.46229e27 | 0.417825 | ||||||||
\(127\) | 4.15616e28 | 1.64946 | 0.824730 | − | 0.565526i | \(-0.191327\pi\) | ||||
0.824730 | + | 0.565526i | \(0.191327\pi\) | |||||||
\(128\) | −2.47588e27 | −0.0883883 | ||||||||
\(129\) | −9.70423e26 | −0.0311889 | ||||||||
\(130\) | 9.66570e27 | 0.279897 | ||||||||
\(131\) | −5.42612e27 | −0.141686 | −0.0708430 | − | 0.997487i | \(-0.522569\pi\) | ||||
−0.0708430 | + | 0.997487i | \(0.522569\pi\) | |||||||
\(132\) | 6.52512e26 | 0.0153759 | ||||||||
\(133\) | −7.54858e27 | −0.160645 | ||||||||
\(134\) | −3.12205e28 | −0.600517 | ||||||||
\(135\) | −3.46997e27 | −0.0603698 | ||||||||
\(136\) | 4.86037e27 | 0.0765410 | ||||||||
\(137\) | −2.10760e28 | −0.300650 | −0.150325 | − | 0.988637i | \(-0.548032\pi\) | ||||
−0.150325 | + | 0.988637i | \(0.548032\pi\) | |||||||
\(138\) | −3.66306e27 | −0.0473671 | ||||||||
\(139\) | −7.38363e28 | −0.866104 | −0.433052 | − | 0.901369i | \(-0.642563\pi\) | ||||
−0.433052 | + | 0.901369i | \(0.642563\pi\) | |||||||
\(140\) | 1.24656e28 | 0.132735 | ||||||||
\(141\) | 2.66827e26 | 0.00258091 | ||||||||
\(142\) | 2.56126e28 | 0.225196 | ||||||||
\(143\) | −5.03078e28 | −0.402345 | ||||||||
\(144\) | −3.41855e28 | −0.248856 | ||||||||
\(145\) | 6.55792e27 | 0.0434808 | ||||||||
\(146\) | −1.22678e29 | −0.741315 | ||||||||
\(147\) | −7.95022e27 | −0.0438122 | ||||||||
\(148\) | −1.50889e29 | −0.758797 | ||||||||
\(149\) | −1.91029e29 | −0.877170 | −0.438585 | − | 0.898690i | \(-0.644520\pi\) | ||||
−0.438585 | + | 0.898690i | \(0.644520\pi\) | |||||||
\(150\) | −2.28043e27 | −0.00956720 | ||||||||
\(151\) | −8.87996e27 | −0.0340583 | −0.0170291 | − | 0.999855i | \(-0.505421\pi\) | ||||
−0.0170291 | + | 0.999855i | \(0.505421\pi\) | |||||||
\(152\) | 2.72716e28 | 0.0956802 | ||||||||
\(153\) | 6.71091e28 | 0.215500 | ||||||||
\(154\) | −6.48809e28 | −0.190804 | ||||||||
\(155\) | 1.95593e29 | 0.527080 | ||||||||
\(156\) | −1.21177e28 | −0.0299390 | ||||||||
\(157\) | 6.26636e29 | 1.42027 | 0.710133 | − | 0.704067i | \(-0.248635\pi\) | ||||
0.710133 | + | 0.704067i | \(0.248635\pi\) | |||||||
\(158\) | −1.16044e29 | −0.241409 | ||||||||
\(159\) | −4.20207e28 | −0.0802790 | ||||||||
\(160\) | −4.50360e28 | −0.0790569 | ||||||||
\(161\) | 3.64227e29 | 0.587791 | ||||||||
\(162\) | −4.69832e29 | −0.697413 | ||||||||
\(163\) | 7.21779e28 | 0.0985988 | 0.0492994 | − | 0.998784i | \(-0.484301\pi\) | ||||
0.0492994 | + | 0.998784i | \(0.484301\pi\) | |||||||
\(164\) | −2.93061e29 | −0.368609 | ||||||||
\(165\) | 1.18691e28 | 0.0137526 | ||||||||
\(166\) | 6.52048e28 | 0.0696338 | ||||||||
\(167\) | 6.72685e29 | 0.662429 | 0.331214 | − | 0.943556i | \(-0.392542\pi\) | ||||
0.331214 | + | 0.943556i | \(0.392542\pi\) | |||||||
\(168\) | −1.56279e28 | −0.0141980 | ||||||||
\(169\) | −2.58277e29 | −0.216578 | ||||||||
\(170\) | 8.84096e28 | 0.0684603 | ||||||||
\(171\) | 3.76550e29 | 0.269386 | ||||||||
\(172\) | −3.48605e29 | −0.230516 | ||||||||
\(173\) | 8.69859e29 | 0.531896 | 0.265948 | − | 0.963987i | \(-0.414315\pi\) | ||||
0.265948 | + | 0.963987i | \(0.414315\pi\) | |||||||
\(174\) | −8.22153e27 | −0.00465091 | ||||||||
\(175\) | 2.26749e29 | 0.118722 | ||||||||
\(176\) | 2.34402e29 | 0.113642 | ||||||||
\(177\) | −2.19876e29 | −0.0987504 | ||||||||
\(178\) | 8.61314e29 | 0.358502 | ||||||||
\(179\) | 3.70782e30 | 1.43088 | 0.715439 | − | 0.698675i | \(-0.246227\pi\) | ||||
0.715439 | + | 0.698675i | \(0.246227\pi\) | |||||||
\(180\) | −6.21830e29 | −0.222583 | ||||||||
\(181\) | 1.58156e30 | 0.525321 | 0.262661 | − | 0.964888i | \(-0.415400\pi\) | ||||
0.262661 | + | 0.964888i | \(0.415400\pi\) | |||||||
\(182\) | 1.20489e30 | 0.371522 | ||||||||
\(183\) | −3.84069e29 | −0.109982 | ||||||||
\(184\) | −1.31588e30 | −0.350087 | ||||||||
\(185\) | −2.74466e30 | −0.678689 | ||||||||
\(186\) | −2.45212e29 | −0.0563788 | ||||||||
\(187\) | −4.60152e29 | −0.0984101 | ||||||||
\(188\) | 9.58525e28 | 0.0190753 | ||||||||
\(189\) | −4.32554e29 | −0.0801320 | ||||||||
\(190\) | 4.96067e29 | 0.0855789 | ||||||||
\(191\) | −8.65494e30 | −1.39096 | −0.695478 | − | 0.718547i | \(-0.744807\pi\) | ||||
−0.695478 | + | 0.718547i | \(0.744807\pi\) | |||||||
\(192\) | 5.64607e28 | 0.00845629 | ||||||||
\(193\) | 2.56974e30 | 0.358811 | 0.179405 | − | 0.983775i | \(-0.442583\pi\) | ||||
0.179405 | + | 0.983775i | \(0.442583\pi\) | |||||||
\(194\) | 2.18920e30 | 0.285077 | ||||||||
\(195\) | −2.20419e29 | −0.0267783 | ||||||||
\(196\) | −2.85596e30 | −0.323814 | ||||||||
\(197\) | −1.43330e31 | −1.51720 | −0.758598 | − | 0.651559i | \(-0.774115\pi\) | ||||
−0.758598 | + | 0.651559i | \(0.774115\pi\) | |||||||
\(198\) | 3.23648e30 | 0.319958 | ||||||||
\(199\) | −1.47927e31 | −1.36626 | −0.683128 | − | 0.730299i | \(-0.739381\pi\) | ||||
−0.683128 | + | 0.730299i | \(0.739381\pi\) | |||||||
\(200\) | −8.19200e29 | −0.0707107 | ||||||||
\(201\) | 7.11963e29 | 0.0574527 | ||||||||
\(202\) | 3.69700e30 | 0.279001 | ||||||||
\(203\) | 8.17487e29 | 0.0577144 | ||||||||
\(204\) | −1.10837e29 | −0.00732283 | ||||||||
\(205\) | −5.33074e30 | −0.329694 | ||||||||
\(206\) | 1.84908e31 | 1.07090 | ||||||||
\(207\) | −1.81689e31 | −0.985665 | ||||||||
\(208\) | −4.35304e30 | −0.221278 | ||||||||
\(209\) | −2.58192e30 | −0.123018 | ||||||||
\(210\) | −2.84270e29 | −0.0126990 | ||||||||
\(211\) | 2.00442e31 | 0.839800 | 0.419900 | − | 0.907570i | \(-0.362065\pi\) | ||||
0.419900 | + | 0.907570i | \(0.362065\pi\) | |||||||
\(212\) | −1.50951e31 | −0.593338 | ||||||||
\(213\) | −5.84078e29 | −0.0215450 | ||||||||
\(214\) | 2.22749e31 | 0.771310 | ||||||||
\(215\) | −6.34110e30 | −0.206179 | ||||||||
\(216\) | 1.56274e30 | 0.0477265 | ||||||||
\(217\) | 2.43820e31 | 0.699621 | ||||||||
\(218\) | 3.71192e31 | 1.00101 | ||||||||
\(219\) | 2.79758e30 | 0.0709231 | ||||||||
\(220\) | 4.26375e30 | 0.101645 | ||||||||
\(221\) | 8.54540e30 | 0.191618 | ||||||||
\(222\) | 3.44093e30 | 0.0725956 | ||||||||
\(223\) | 9.30611e31 | 1.84779 | 0.923894 | − | 0.382647i | \(-0.124988\pi\) | ||||
0.923894 | + | 0.382647i | \(0.124988\pi\) | |||||||
\(224\) | −5.61403e30 | −0.104936 | ||||||||
\(225\) | −1.13110e31 | −0.199085 | ||||||||
\(226\) | 2.06439e31 | 0.342238 | ||||||||
\(227\) | 2.62678e31 | 0.410274 | 0.205137 | − | 0.978733i | \(-0.434236\pi\) | ||||
0.205137 | + | 0.978733i | \(0.434236\pi\) | |||||||
\(228\) | −6.21909e29 | −0.00915391 | ||||||||
\(229\) | −1.81385e31 | −0.251665 | −0.125832 | − | 0.992052i | \(-0.540160\pi\) | ||||
−0.125832 | + | 0.992052i | \(0.540160\pi\) | |||||||
\(230\) | −2.39358e31 | −0.313128 | ||||||||
\(231\) | 1.47956e30 | 0.0182546 | ||||||||
\(232\) | −2.95342e30 | −0.0343746 | ||||||||
\(233\) | −1.08135e31 | −0.118757 | −0.0593786 | − | 0.998236i | \(-0.518912\pi\) | ||||
−0.0593786 | + | 0.998236i | \(0.518912\pi\) | |||||||
\(234\) | −6.01042e31 | −0.623004 | ||||||||
\(235\) | 1.74355e30 | 0.0170615 | ||||||||
\(236\) | −7.89862e31 | −0.729859 | ||||||||
\(237\) | 2.64631e30 | 0.0230961 | ||||||||
\(238\) | 1.10208e31 | 0.0908710 | ||||||||
\(239\) | −2.49336e32 | −1.94273 | −0.971367 | − | 0.237586i | \(-0.923644\pi\) | ||||
−0.971367 | + | 0.237586i | \(0.923644\pi\) | |||||||
\(240\) | 1.02701e30 | 0.00756354 | ||||||||
\(241\) | 1.52145e32 | 1.05932 | 0.529662 | − | 0.848209i | \(-0.322319\pi\) | ||||
0.529662 | + | 0.848209i | \(0.322319\pi\) | |||||||
\(242\) | 8.52052e31 | 0.560995 | ||||||||
\(243\) | 3.23907e31 | 0.201714 | ||||||||
\(244\) | −1.37969e32 | −0.812868 | ||||||||
\(245\) | −5.19496e31 | −0.289628 | ||||||||
\(246\) | 6.68305e30 | 0.0352655 | ||||||||
\(247\) | 4.79483e31 | 0.239533 | ||||||||
\(248\) | −8.80874e31 | −0.416693 | ||||||||
\(249\) | −1.48695e30 | −0.00666201 | ||||||||
\(250\) | −1.49012e31 | −0.0632456 | ||||||||
\(251\) | −1.40439e32 | −0.564799 | −0.282400 | − | 0.959297i | \(-0.591130\pi\) | ||||
−0.282400 | + | 0.959297i | \(0.591130\pi\) | |||||||
\(252\) | −7.75151e31 | −0.295447 | ||||||||
\(253\) | 1.24580e32 | 0.450114 | ||||||||
\(254\) | −3.40473e32 | −1.16634 | ||||||||
\(255\) | −2.01612e30 | −0.00654974 | ||||||||
\(256\) | 2.02824e31 | 0.0625000 | ||||||||
\(257\) | 4.52958e32 | 1.32422 | 0.662111 | − | 0.749406i | \(-0.269661\pi\) | ||||
0.662111 | + | 0.749406i | \(0.269661\pi\) | |||||||
\(258\) | 7.94971e30 | 0.0220539 | ||||||||
\(259\) | −3.42140e32 | −0.900859 | ||||||||
\(260\) | −7.91814e31 | −0.197917 | ||||||||
\(261\) | −4.07791e31 | −0.0967812 | ||||||||
\(262\) | 4.44508e31 | 0.100187 | ||||||||
\(263\) | 7.58089e32 | 1.62300 | 0.811499 | − | 0.584354i | \(-0.198652\pi\) | ||||
0.811499 | + | 0.584354i | \(0.198652\pi\) | |||||||
\(264\) | −5.34538e30 | −0.0108724 | ||||||||
\(265\) | −2.74579e32 | −0.530698 | ||||||||
\(266\) | 6.18380e31 | 0.113593 | ||||||||
\(267\) | −1.96417e31 | −0.0342986 | ||||||||
\(268\) | 2.55759e32 | 0.424630 | ||||||||
\(269\) | −1.08950e33 | −1.72016 | −0.860082 | − | 0.510156i | \(-0.829588\pi\) | ||||
−0.860082 | + | 0.510156i | \(0.829588\pi\) | |||||||
\(270\) | 2.84260e31 | 0.0426879 | ||||||||
\(271\) | 9.86275e32 | 1.40900 | 0.704502 | − | 0.709702i | \(-0.251170\pi\) | ||||
0.704502 | + | 0.709702i | \(0.251170\pi\) | |||||||
\(272\) | −3.98161e31 | −0.0541226 | ||||||||
\(273\) | −2.74767e31 | −0.0355442 | ||||||||
\(274\) | 1.72655e32 | 0.212592 | ||||||||
\(275\) | 7.75572e31 | 0.0909140 | ||||||||
\(276\) | 3.00078e31 | 0.0334936 | ||||||||
\(277\) | 5.21841e32 | 0.554704 | 0.277352 | − | 0.960768i | \(-0.410543\pi\) | ||||
0.277352 | + | 0.960768i | \(0.410543\pi\) | |||||||
\(278\) | 6.04867e32 | 0.612428 | ||||||||
\(279\) | −1.21626e33 | −1.17319 | ||||||||
\(280\) | −1.02119e32 | −0.0938580 | ||||||||
\(281\) | 1.10443e33 | 0.967396 | 0.483698 | − | 0.875235i | \(-0.339293\pi\) | ||||
0.483698 | + | 0.875235i | \(0.339293\pi\) | |||||||
\(282\) | −2.18585e30 | −0.00182498 | ||||||||
\(283\) | 1.51510e33 | 1.20594 | 0.602968 | − | 0.797765i | \(-0.293985\pi\) | ||||
0.602968 | + | 0.797765i | \(0.293985\pi\) | |||||||
\(284\) | −2.09819e32 | −0.159238 | ||||||||
\(285\) | −1.13125e31 | −0.00818751 | ||||||||
\(286\) | 4.12121e32 | 0.284501 | ||||||||
\(287\) | −6.64512e32 | −0.437620 | ||||||||
\(288\) | 2.80047e32 | 0.175968 | ||||||||
\(289\) | −1.58955e33 | −0.953132 | ||||||||
\(290\) | −5.37225e31 | −0.0307456 | ||||||||
\(291\) | −4.99231e31 | −0.0272739 | ||||||||
\(292\) | 1.00498e33 | 0.524189 | ||||||||
\(293\) | 1.40575e33 | 0.700156 | 0.350078 | − | 0.936721i | \(-0.386155\pi\) | ||||
0.350078 | + | 0.936721i | \(0.386155\pi\) | |||||||
\(294\) | 6.51282e31 | 0.0309799 | ||||||||
\(295\) | −1.43675e33 | −0.652806 | ||||||||
\(296\) | 1.23609e33 | 0.536550 | ||||||||
\(297\) | −1.47951e32 | −0.0613628 | ||||||||
\(298\) | 1.56491e33 | 0.620253 | ||||||||
\(299\) | −2.31356e33 | −0.876434 | ||||||||
\(300\) | 1.86813e31 | 0.00676503 | ||||||||
\(301\) | −7.90459e32 | −0.273673 | ||||||||
\(302\) | 7.27447e31 | 0.0240828 | ||||||||
\(303\) | −8.43075e31 | −0.0266926 | ||||||||
\(304\) | −2.23409e32 | −0.0676561 | ||||||||
\(305\) | −2.50965e33 | −0.727051 | ||||||||
\(306\) | −5.49757e32 | −0.152381 | ||||||||
\(307\) | −4.49630e33 | −1.19258 | −0.596290 | − | 0.802769i | \(-0.703359\pi\) | ||||
−0.596290 | + | 0.802769i | \(0.703359\pi\) | |||||||
\(308\) | 5.31504e32 | 0.134919 | ||||||||
\(309\) | −4.21670e32 | −0.102455 | ||||||||
\(310\) | −1.60230e33 | −0.372702 | ||||||||
\(311\) | −2.75632e33 | −0.613853 | −0.306927 | − | 0.951733i | \(-0.599301\pi\) | ||||
−0.306927 | + | 0.951733i | \(0.599301\pi\) | |||||||
\(312\) | 9.92681e31 | 0.0211701 | ||||||||
\(313\) | 3.75694e33 | 0.767335 | 0.383668 | − | 0.923471i | \(-0.374661\pi\) | ||||
0.383668 | + | 0.923471i | \(0.374661\pi\) | |||||||
\(314\) | −5.13340e33 | −1.00428 | ||||||||
\(315\) | −1.40999e33 | −0.264256 | ||||||||
\(316\) | 9.50635e32 | 0.170702 | ||||||||
\(317\) | −1.58056e33 | −0.271964 | −0.135982 | − | 0.990711i | \(-0.543419\pi\) | ||||
−0.135982 | + | 0.990711i | \(0.543419\pi\) | |||||||
\(318\) | 3.44234e32 | 0.0567658 | ||||||||
\(319\) | 2.79613e32 | 0.0441961 | ||||||||
\(320\) | 3.68935e32 | 0.0559017 | ||||||||
\(321\) | −5.07963e32 | −0.0737928 | ||||||||
\(322\) | −2.98375e33 | −0.415631 | ||||||||
\(323\) | 4.38571e32 | 0.0585876 | ||||||||
\(324\) | 3.84887e33 | 0.493146 | ||||||||
\(325\) | −1.44030e33 | −0.177022 | ||||||||
\(326\) | −5.91281e32 | −0.0697199 | ||||||||
\(327\) | −8.46479e32 | −0.0957682 | ||||||||
\(328\) | 2.40075e33 | 0.260646 | ||||||||
\(329\) | 2.17344e32 | 0.0226466 | ||||||||
\(330\) | −9.72319e31 | −0.00972457 | ||||||||
\(331\) | 1.82677e34 | 1.75390 | 0.876952 | − | 0.480578i | \(-0.159573\pi\) | ||||
0.876952 | + | 0.480578i | \(0.159573\pi\) | |||||||
\(332\) | −5.34158e32 | −0.0492385 | ||||||||
\(333\) | 1.70671e34 | 1.51065 | ||||||||
\(334\) | −5.51063e33 | −0.468408 | ||||||||
\(335\) | 4.65222e33 | 0.379801 | ||||||||
\(336\) | 1.28024e32 | 0.0100395 | ||||||||
\(337\) | 1.86275e34 | 1.40330 | 0.701650 | − | 0.712521i | \(-0.252447\pi\) | ||||
0.701650 | + | 0.712521i | \(0.252447\pi\) | |||||||
\(338\) | 2.11580e33 | 0.153144 | ||||||||
\(339\) | −4.70771e32 | −0.0327426 | ||||||||
\(340\) | −7.24251e32 | −0.0484088 | ||||||||
\(341\) | 8.33961e33 | 0.535750 | ||||||||
\(342\) | −3.08469e33 | −0.190485 | ||||||||
\(343\) | −1.64752e34 | −0.978048 | ||||||||
\(344\) | 2.85578e33 | 0.162999 | ||||||||
\(345\) | 5.45838e32 | 0.0299576 | ||||||||
\(346\) | −7.12589e33 | −0.376107 | ||||||||
\(347\) | 9.97856e33 | 0.506547 | 0.253274 | − | 0.967395i | \(-0.418493\pi\) | ||||
0.253274 | + | 0.967395i | \(0.418493\pi\) | |||||||
\(348\) | 6.73508e31 | 0.00328869 | ||||||||
\(349\) | −1.32833e33 | −0.0623969 | −0.0311984 | − | 0.999513i | \(-0.509932\pi\) | ||||
−0.0311984 | + | 0.999513i | \(0.509932\pi\) | |||||||
\(350\) | −1.85753e33 | −0.0839491 | ||||||||
\(351\) | 2.74757e33 | 0.119482 | ||||||||
\(352\) | −1.92022e33 | −0.0803573 | ||||||||
\(353\) | 5.06941e32 | 0.0204173 | 0.0102087 | − | 0.999948i | \(-0.496750\pi\) | ||||
0.0102087 | + | 0.999948i | \(0.496750\pi\) | |||||||
\(354\) | 1.80122e33 | 0.0698271 | ||||||||
\(355\) | −3.81658e33 | −0.142427 | ||||||||
\(356\) | −7.05588e33 | −0.253499 | ||||||||
\(357\) | −2.51322e32 | −0.00869381 | ||||||||
\(358\) | −3.03745e34 | −1.01178 | ||||||||
\(359\) | −1.29578e34 | −0.415677 | −0.207839 | − | 0.978163i | \(-0.566643\pi\) | ||||
−0.207839 | + | 0.978163i | \(0.566643\pi\) | |||||||
\(360\) | 5.09403e33 | 0.157390 | ||||||||
\(361\) | −3.11398e34 | −0.926762 | ||||||||
\(362\) | −1.29561e34 | −0.371458 | ||||||||
\(363\) | −1.94305e33 | −0.0536715 | ||||||||
\(364\) | −9.87047e33 | −0.262705 | ||||||||
\(365\) | 1.82804e34 | 0.468849 | ||||||||
\(366\) | 3.14630e33 | 0.0777687 | ||||||||
\(367\) | −2.12850e34 | −0.507087 | −0.253543 | − | 0.967324i | \(-0.581596\pi\) | ||||
−0.253543 | + | 0.967324i | \(0.581596\pi\) | |||||||
\(368\) | 1.07797e34 | 0.247549 | ||||||||
\(369\) | 3.31482e34 | 0.733844 | ||||||||
\(370\) | 2.24843e34 | 0.479905 | ||||||||
\(371\) | −3.42280e34 | −0.704423 | ||||||||
\(372\) | 2.00877e33 | 0.0398659 | ||||||||
\(373\) | −4.23988e34 | −0.811492 | −0.405746 | − | 0.913986i | \(-0.632988\pi\) | ||||
−0.405746 | + | 0.913986i | \(0.632988\pi\) | |||||||
\(374\) | 3.76956e33 | 0.0695864 | ||||||||
\(375\) | 3.39811e32 | 0.00605083 | ||||||||
\(376\) | −7.85224e32 | −0.0134883 | ||||||||
\(377\) | −5.19265e33 | −0.0860559 | ||||||||
\(378\) | 3.54348e33 | 0.0566619 | ||||||||
\(379\) | −2.53814e34 | −0.391639 | −0.195820 | − | 0.980640i | \(-0.562737\pi\) | ||||
−0.195820 | + | 0.980640i | \(0.562737\pi\) | |||||||
\(380\) | −4.06378e33 | −0.0605134 | ||||||||
\(381\) | 7.76424e33 | 0.111587 | ||||||||
\(382\) | 7.09012e34 | 0.983555 | ||||||||
\(383\) | −1.37667e35 | −1.84351 | −0.921755 | − | 0.387772i | \(-0.873245\pi\) | ||||
−0.921755 | + | 0.387772i | \(0.873245\pi\) | |||||||
\(384\) | −4.62526e32 | −0.00597950 | ||||||||
\(385\) | 9.66800e33 | 0.120675 | ||||||||
\(386\) | −2.10513e34 | −0.253717 | ||||||||
\(387\) | 3.94308e34 | 0.458921 | ||||||||
\(388\) | −1.79339e34 | −0.201580 | ||||||||
\(389\) | 1.31877e35 | 1.43169 | 0.715844 | − | 0.698260i | \(-0.246042\pi\) | ||||
0.715844 | + | 0.698260i | \(0.246042\pi\) | |||||||
\(390\) | 1.80568e33 | 0.0189351 | ||||||||
\(391\) | −2.11615e34 | −0.214368 | ||||||||
\(392\) | 2.33960e34 | 0.228971 | ||||||||
\(393\) | −1.01367e33 | −0.00958510 | ||||||||
\(394\) | 1.17416e35 | 1.07282 | ||||||||
\(395\) | 1.72920e34 | 0.152680 | ||||||||
\(396\) | −2.65133e34 | −0.226245 | ||||||||
\(397\) | 6.51145e34 | 0.537039 | 0.268520 | − | 0.963274i | \(-0.413466\pi\) | ||||
0.268520 | + | 0.963274i | \(0.413466\pi\) | |||||||
\(398\) | 1.21182e35 | 0.966089 | ||||||||
\(399\) | −1.41017e33 | −0.0108677 | ||||||||
\(400\) | 6.71089e33 | 0.0500000 | ||||||||
\(401\) | −9.62542e34 | −0.693379 | −0.346690 | − | 0.937980i | \(-0.612694\pi\) | ||||
−0.346690 | + | 0.937980i | \(0.612694\pi\) | |||||||
\(402\) | −5.83240e33 | −0.0406252 | ||||||||
\(403\) | −1.54874e35 | −1.04318 | ||||||||
\(404\) | −3.02858e34 | −0.197283 | ||||||||
\(405\) | 7.00105e34 | 0.441083 | ||||||||
\(406\) | −6.69685e33 | −0.0408102 | ||||||||
\(407\) | −1.17026e35 | −0.689852 | ||||||||
\(408\) | 9.07979e32 | 0.00517802 | ||||||||
\(409\) | 3.10105e35 | 1.71098 | 0.855489 | − | 0.517821i | \(-0.173257\pi\) | ||||
0.855489 | + | 0.517821i | \(0.173257\pi\) | |||||||
\(410\) | 4.36695e34 | 0.233129 | ||||||||
\(411\) | −3.93728e33 | −0.0203391 | ||||||||
\(412\) | −1.51477e35 | −0.757240 | ||||||||
\(413\) | −1.79100e35 | −0.866503 | ||||||||
\(414\) | 1.48840e35 | 0.696970 | ||||||||
\(415\) | −9.71627e33 | −0.0440403 | ||||||||
\(416\) | 3.56601e34 | 0.156467 | ||||||||
\(417\) | −1.37936e34 | −0.0585922 | ||||||||
\(418\) | 2.11511e34 | 0.0869866 | ||||||||
\(419\) | 2.11087e35 | 0.840568 | 0.420284 | − | 0.907393i | \(-0.361931\pi\) | ||||
0.420284 | + | 0.907393i | \(0.361931\pi\) | |||||||
\(420\) | 2.32874e33 | 0.00897958 | ||||||||
\(421\) | 4.74937e35 | 1.77349 | 0.886743 | − | 0.462263i | \(-0.152962\pi\) | ||||
0.886743 | + | 0.462263i | \(0.152962\pi\) | |||||||
\(422\) | −1.64202e35 | −0.593828 | ||||||||
\(423\) | −1.08419e34 | −0.0379761 | ||||||||
\(424\) | 1.23659e35 | 0.419553 | ||||||||
\(425\) | −1.31741e34 | −0.0432981 | ||||||||
\(426\) | 4.78477e33 | 0.0152346 | ||||||||
\(427\) | −3.12844e35 | −0.965054 | ||||||||
\(428\) | −1.82476e35 | −0.545399 | ||||||||
\(429\) | −9.39814e33 | −0.0272188 | ||||||||
\(430\) | 5.19463e34 | 0.145791 | ||||||||
\(431\) | −4.97520e35 | −1.35322 | −0.676608 | − | 0.736343i | \(-0.736551\pi\) | ||||
−0.676608 | + | 0.736343i | \(0.736551\pi\) | |||||||
\(432\) | −1.28019e34 | −0.0337478 | ||||||||
\(433\) | 1.48404e35 | 0.379191 | 0.189595 | − | 0.981862i | \(-0.439282\pi\) | ||||
0.189595 | + | 0.981862i | \(0.439282\pi\) | |||||||
\(434\) | −1.99737e35 | −0.494706 | ||||||||
\(435\) | 1.22510e33 | 0.00294149 | ||||||||
\(436\) | −3.04081e35 | −0.707818 | ||||||||
\(437\) | −1.18737e35 | −0.267971 | ||||||||
\(438\) | −2.29178e34 | −0.0501502 | ||||||||
\(439\) | 3.88897e35 | 0.825209 | 0.412604 | − | 0.910910i | \(-0.364619\pi\) | ||||
0.412604 | + | 0.910910i | \(0.364619\pi\) | |||||||
\(440\) | −3.49286e34 | −0.0718738 | ||||||||
\(441\) | 3.23038e35 | 0.644663 | ||||||||
\(442\) | −7.00039e34 | −0.135495 | ||||||||
\(443\) | −7.59267e35 | −1.42542 | −0.712712 | − | 0.701457i | \(-0.752533\pi\) | ||||
−0.712712 | + | 0.701457i | \(0.752533\pi\) | |||||||
\(444\) | −2.81881e34 | −0.0513329 | ||||||||
\(445\) | −1.28346e35 | −0.226736 | ||||||||
\(446\) | −7.62356e35 | −1.30658 | ||||||||
\(447\) | −3.56866e34 | −0.0593408 | ||||||||
\(448\) | 4.59901e34 | 0.0742013 | ||||||||
\(449\) | 4.69834e33 | 0.00735562 | 0.00367781 | − | 0.999993i | \(-0.498829\pi\) | ||||
0.00367781 | + | 0.999993i | \(0.498829\pi\) | |||||||
\(450\) | 9.26599e34 | 0.140774 | ||||||||
\(451\) | −2.27290e35 | −0.335117 | ||||||||
\(452\) | −1.69115e35 | −0.241999 | ||||||||
\(453\) | −1.65889e33 | −0.00230405 | ||||||||
\(454\) | −2.15186e35 | −0.290108 | ||||||||
\(455\) | −1.79543e35 | −0.234971 | ||||||||
\(456\) | 5.09468e33 | 0.00647279 | ||||||||
\(457\) | 1.07406e36 | 1.32483 | 0.662414 | − | 0.749138i | \(-0.269532\pi\) | ||||
0.662414 | + | 0.749138i | \(0.269532\pi\) | |||||||
\(458\) | 1.48591e35 | 0.177954 | ||||||||
\(459\) | 2.51313e34 | 0.0292243 | ||||||||
\(460\) | 1.96082e35 | 0.221415 | ||||||||
\(461\) | 9.20062e35 | 1.00892 | 0.504458 | − | 0.863436i | \(-0.331692\pi\) | ||||
0.504458 | + | 0.863436i | \(0.331692\pi\) | |||||||
\(462\) | −1.21206e34 | −0.0129079 | ||||||||
\(463\) | 5.38671e35 | 0.557161 | 0.278580 | − | 0.960413i | \(-0.410136\pi\) | ||||
0.278580 | + | 0.960413i | \(0.410136\pi\) | |||||||
\(464\) | 2.41944e34 | 0.0243065 | ||||||||
\(465\) | 3.65394e34 | 0.0356571 | ||||||||
\(466\) | 8.85839e34 | 0.0839740 | ||||||||
\(467\) | −4.52515e35 | −0.416731 | −0.208365 | − | 0.978051i | \(-0.566814\pi\) | ||||
−0.208365 | + | 0.978051i | \(0.566814\pi\) | |||||||
\(468\) | 4.92374e35 | 0.440530 | ||||||||
\(469\) | 5.79929e35 | 0.504129 | ||||||||
\(470\) | −1.42831e34 | −0.0120643 | ||||||||
\(471\) | 1.17064e35 | 0.0960815 | ||||||||
\(472\) | 6.47055e35 | 0.516088 | ||||||||
\(473\) | −2.70369e35 | −0.209571 | ||||||||
\(474\) | −2.16786e34 | −0.0163314 | ||||||||
\(475\) | −7.39198e34 | −0.0541249 | ||||||||
\(476\) | −9.02826e34 | −0.0642555 | ||||||||
\(477\) | 1.70741e36 | 1.18125 | ||||||||
\(478\) | 2.04256e36 | 1.37372 | ||||||||
\(479\) | −2.10559e36 | −1.37672 | −0.688359 | − | 0.725370i | \(-0.741669\pi\) | ||||
−0.688359 | + | 0.725370i | \(0.741669\pi\) | |||||||
\(480\) | −8.41330e33 | −0.00534823 | ||||||||
\(481\) | 2.17326e36 | 1.34324 | ||||||||
\(482\) | −1.24638e36 | −0.749055 | ||||||||
\(483\) | 6.80423e34 | 0.0397642 | ||||||||
\(484\) | −6.98001e35 | −0.396683 | ||||||||
\(485\) | −3.26216e35 | −0.180298 | ||||||||
\(486\) | −2.65345e35 | −0.142633 | ||||||||
\(487\) | 1.39900e36 | 0.731437 | 0.365718 | − | 0.930726i | \(-0.380823\pi\) | ||||
0.365718 | + | 0.930726i | \(0.380823\pi\) | |||||||
\(488\) | 1.13025e36 | 0.574785 | ||||||||
\(489\) | 1.34838e34 | 0.00667024 | ||||||||
\(490\) | 4.25571e35 | 0.204798 | ||||||||
\(491\) | −1.78697e36 | −0.836597 | −0.418298 | − | 0.908310i | \(-0.637373\pi\) | ||||
−0.418298 | + | 0.908310i | \(0.637373\pi\) | |||||||
\(492\) | −5.47475e34 | −0.0249365 | ||||||||
\(493\) | −4.74958e34 | −0.0210485 | ||||||||
\(494\) | −3.92793e35 | −0.169375 | ||||||||
\(495\) | −4.82274e35 | −0.202359 | ||||||||
\(496\) | 7.21612e35 | 0.294647 | ||||||||
\(497\) | −4.75761e35 | −0.189050 | ||||||||
\(498\) | 1.21811e34 | 0.00471075 | ||||||||
\(499\) | −5.03865e36 | −1.89652 | −0.948259 | − | 0.317499i | \(-0.897157\pi\) | ||||
−0.948259 | + | 0.317499i | \(0.897157\pi\) | |||||||
\(500\) | 1.22070e35 | 0.0447214 | ||||||||
\(501\) | 1.25666e35 | 0.0448135 | ||||||||
\(502\) | 1.15048e36 | 0.399373 | ||||||||
\(503\) | −5.02862e36 | −1.69934 | −0.849671 | − | 0.527313i | \(-0.823199\pi\) | ||||
−0.849671 | + | 0.527313i | \(0.823199\pi\) | |||||||
\(504\) | 6.35004e35 | 0.208912 | ||||||||
\(505\) | −5.50896e35 | −0.176456 | ||||||||
\(506\) | −1.02056e36 | −0.318278 | ||||||||
\(507\) | −4.82494e34 | −0.0146516 | ||||||||
\(508\) | 2.78915e36 | 0.824730 | ||||||||
\(509\) | −5.99564e36 | −1.72642 | −0.863209 | − | 0.504847i | \(-0.831549\pi\) | ||||
−0.863209 | + | 0.504847i | \(0.831549\pi\) | |||||||
\(510\) | 1.65160e34 | 0.00463136 | ||||||||
\(511\) | 2.27877e36 | 0.622327 | ||||||||
\(512\) | −1.66153e35 | −0.0441942 | ||||||||
\(513\) | 1.41012e35 | 0.0365319 | ||||||||
\(514\) | −3.71063e36 | −0.936366 | ||||||||
\(515\) | −2.75535e36 | −0.677296 | ||||||||
\(516\) | −6.51240e34 | −0.0155944 | ||||||||
\(517\) | 7.43405e34 | 0.0173422 | ||||||||
\(518\) | 2.80281e36 | 0.637004 | ||||||||
\(519\) | 1.62501e35 | 0.0359829 | ||||||||
\(520\) | 6.48654e35 | 0.139948 | ||||||||
\(521\) | 5.03095e36 | 1.05765 | 0.528824 | − | 0.848732i | \(-0.322633\pi\) | ||||
0.528824 | + | 0.848732i | \(0.322633\pi\) | |||||||
\(522\) | 3.34062e35 | 0.0684346 | ||||||||
\(523\) | 3.80823e36 | 0.760239 | 0.380119 | − | 0.924937i | \(-0.375883\pi\) | ||||
0.380119 | + | 0.924937i | \(0.375883\pi\) | |||||||
\(524\) | −3.64141e35 | −0.0708430 | ||||||||
\(525\) | 4.23596e34 | 0.00803158 | ||||||||
\(526\) | −6.21027e36 | −1.14763 | ||||||||
\(527\) | −1.41659e36 | −0.255153 | ||||||||
\(528\) | 4.37893e34 | 0.00768795 | ||||||||
\(529\) | −1.14003e35 | −0.0195103 | ||||||||
\(530\) | 2.24935e36 | 0.375260 | ||||||||
\(531\) | 8.93414e36 | 1.45304 | ||||||||
\(532\) | −5.06577e35 | −0.0803227 | ||||||||
\(533\) | 4.22096e36 | 0.652520 | ||||||||
\(534\) | 1.60904e35 | 0.0242528 | ||||||||
\(535\) | −3.31921e36 | −0.487820 | ||||||||
\(536\) | −2.09517e36 | −0.300259 | ||||||||
\(537\) | 6.92669e35 | 0.0967994 | ||||||||
\(538\) | 8.92515e36 | 1.21634 | ||||||||
\(539\) | −2.21500e36 | −0.294392 | ||||||||
\(540\) | −2.32866e35 | −0.0301849 | ||||||||
\(541\) | 8.39039e35 | 0.106076 | 0.0530382 | − | 0.998592i | \(-0.483109\pi\) | ||||
0.0530382 | + | 0.998592i | \(0.483109\pi\) | |||||||
\(542\) | −8.07956e36 | −0.996317 | ||||||||
\(543\) | 2.95456e35 | 0.0355381 | ||||||||
\(544\) | 3.26174e35 | 0.0382705 | ||||||||
\(545\) | −5.53120e36 | −0.633092 | ||||||||
\(546\) | 2.25089e35 | 0.0251336 | ||||||||
\(547\) | 5.66797e36 | 0.617445 | 0.308722 | − | 0.951152i | \(-0.400099\pi\) | ||||
0.308722 | + | 0.951152i | \(0.400099\pi\) | |||||||
\(548\) | −1.41439e36 | −0.150325 | ||||||||
\(549\) | 1.56058e37 | 1.61830 | ||||||||
\(550\) | −6.35348e35 | −0.0642859 | ||||||||
\(551\) | −2.66500e35 | −0.0263118 | ||||||||
\(552\) | −2.45824e35 | −0.0236835 | ||||||||
\(553\) | 2.15555e36 | 0.202661 | ||||||||
\(554\) | −4.27492e36 | −0.392235 | ||||||||
\(555\) | −5.12738e35 | −0.0459135 | ||||||||
\(556\) | −4.95507e36 | −0.433052 | ||||||||
\(557\) | 9.07435e36 | 0.774053 | 0.387026 | − | 0.922069i | \(-0.373502\pi\) | ||||
0.387026 | + | 0.922069i | \(0.373502\pi\) | |||||||
\(558\) | 9.96359e36 | 0.829572 | ||||||||
\(559\) | 5.02097e36 | 0.408064 | ||||||||
\(560\) | 8.36555e35 | 0.0663676 | ||||||||
\(561\) | −8.59623e34 | −0.00665747 | ||||||||
\(562\) | −9.04752e36 | −0.684052 | ||||||||
\(563\) | −1.68489e37 | −1.24368 | −0.621840 | − | 0.783145i | \(-0.713614\pi\) | ||||
−0.621840 | + | 0.783145i | \(0.713614\pi\) | |||||||
\(564\) | 1.79065e34 | 0.00129045 | ||||||||
\(565\) | −3.07619e36 | −0.216451 | ||||||||
\(566\) | −1.24117e37 | −0.852726 | ||||||||
\(567\) | 8.72726e36 | 0.585472 | ||||||||
\(568\) | 1.71883e36 | 0.112598 | ||||||||
\(569\) | −3.14141e36 | −0.200960 | −0.100480 | − | 0.994939i | \(-0.532038\pi\) | ||||
−0.100480 | + | 0.994939i | \(0.532038\pi\) | |||||||
\(570\) | 9.26717e34 | 0.00578944 | ||||||||
\(571\) | 2.78070e37 | 1.69655 | 0.848274 | − | 0.529557i | \(-0.177642\pi\) | ||||
0.848274 | + | 0.529557i | \(0.177642\pi\) | |||||||
\(572\) | −3.37610e36 | −0.201172 | ||||||||
\(573\) | −1.61685e36 | −0.0940986 | ||||||||
\(574\) | 5.44368e36 | 0.309444 | ||||||||
\(575\) | 3.56671e36 | 0.198039 | ||||||||
\(576\) | −2.29415e36 | −0.124428 | ||||||||
\(577\) | −1.74113e37 | −0.922482 | −0.461241 | − | 0.887275i | \(-0.652596\pi\) | ||||
−0.461241 | + | 0.887275i | \(0.652596\pi\) | |||||||
\(578\) | 1.30216e37 | 0.673966 | ||||||||
\(579\) | 4.80060e35 | 0.0242737 | ||||||||
\(580\) | 4.40094e35 | 0.0217404 | ||||||||
\(581\) | −1.21120e36 | −0.0584570 | ||||||||
\(582\) | 4.08970e35 | 0.0192855 | ||||||||
\(583\) | −1.17073e37 | −0.539427 | ||||||||
\(584\) | −8.23277e36 | −0.370657 | ||||||||
\(585\) | 8.95622e36 | 0.394022 | ||||||||
\(586\) | −1.15159e37 | −0.495085 | ||||||||
\(587\) | −2.14558e37 | −0.901426 | −0.450713 | − | 0.892669i | \(-0.648830\pi\) | ||||
−0.450713 | + | 0.892669i | \(0.648830\pi\) | |||||||
\(588\) | −5.33530e35 | −0.0219061 | ||||||||
\(589\) | −7.94849e36 | −0.318954 | ||||||||
\(590\) | 1.17699e37 | 0.461603 | ||||||||
\(591\) | −2.67758e36 | −0.102639 | ||||||||
\(592\) | −1.01260e37 | −0.379398 | ||||||||
\(593\) | −4.77291e37 | −1.74801 | −0.874007 | − | 0.485913i | \(-0.838487\pi\) | ||||
−0.874007 | + | 0.485913i | \(0.838487\pi\) | |||||||
\(594\) | 1.21201e36 | 0.0433901 | ||||||||
\(595\) | −1.64223e36 | −0.0574719 | ||||||||
\(596\) | −1.28197e37 | −0.438585 | ||||||||
\(597\) | −2.76347e36 | −0.0924276 | ||||||||
\(598\) | 1.89527e37 | 0.619733 | ||||||||
\(599\) | 3.32612e37 | 1.06335 | 0.531674 | − | 0.846949i | \(-0.321563\pi\) | ||||
0.531674 | + | 0.846949i | \(0.321563\pi\) | |||||||
\(600\) | −1.53037e35 | −0.00478360 | ||||||||
\(601\) | −1.18443e37 | −0.361996 | −0.180998 | − | 0.983483i | \(-0.557933\pi\) | ||||
−0.180998 | + | 0.983483i | \(0.557933\pi\) | |||||||
\(602\) | 6.47544e36 | 0.193516 | ||||||||
\(603\) | −2.89289e37 | −0.845373 | ||||||||
\(604\) | −5.95924e35 | −0.0170291 | ||||||||
\(605\) | −1.26966e37 | −0.354804 | ||||||||
\(606\) | 6.90647e35 | 0.0188745 | ||||||||
\(607\) | 1.62584e37 | 0.434540 | 0.217270 | − | 0.976112i | \(-0.430285\pi\) | ||||
0.217270 | + | 0.976112i | \(0.430285\pi\) | |||||||
\(608\) | 1.83016e36 | 0.0478401 | ||||||||
\(609\) | 1.52717e35 | 0.00390440 | ||||||||
\(610\) | 2.05590e37 | 0.514103 | ||||||||
\(611\) | −1.38056e36 | −0.0337676 | ||||||||
\(612\) | 4.50361e36 | 0.107750 | ||||||||
\(613\) | −6.57104e37 | −1.53786 | −0.768932 | − | 0.639331i | \(-0.779212\pi\) | ||||
−0.768932 | + | 0.639331i | \(0.779212\pi\) | |||||||
\(614\) | 3.68337e37 | 0.843281 | ||||||||
\(615\) | −9.95852e35 | −0.0223039 | ||||||||
\(616\) | −4.35408e36 | −0.0954019 | ||||||||
\(617\) | 4.95910e37 | 1.06305 | 0.531524 | − | 0.847043i | \(-0.321619\pi\) | ||||
0.531524 | + | 0.847043i | \(0.321619\pi\) | |||||||
\(618\) | 3.45432e36 | 0.0724466 | ||||||||
\(619\) | 4.50080e37 | 0.923561 | 0.461781 | − | 0.886994i | \(-0.347211\pi\) | ||||
0.461781 | + | 0.886994i | \(0.347211\pi\) | |||||||
\(620\) | 1.31261e37 | 0.263540 | ||||||||
\(621\) | −6.80398e36 | −0.133668 | ||||||||
\(622\) | 2.25798e37 | 0.434060 | ||||||||
\(623\) | −1.59991e37 | −0.300959 | ||||||||
\(624\) | −8.13204e35 | −0.0149695 | ||||||||
\(625\) | 2.22045e36 | 0.0400000 | ||||||||
\(626\) | −3.07768e37 | −0.542588 | ||||||||
\(627\) | −4.82335e35 | −0.00832218 | ||||||||
\(628\) | 4.20528e37 | 0.710133 | ||||||||
\(629\) | 1.98783e37 | 0.328545 | ||||||||
\(630\) | 1.15507e37 | 0.186857 | ||||||||
\(631\) | 3.74258e37 | 0.592617 | 0.296309 | − | 0.955092i | \(-0.404244\pi\) | ||||
0.296309 | + | 0.955092i | \(0.404244\pi\) | |||||||
\(632\) | −7.78760e36 | −0.120704 | ||||||||
\(633\) | 3.74452e36 | 0.0568127 | ||||||||
\(634\) | 1.29480e37 | 0.192308 | ||||||||
\(635\) | 5.07344e37 | 0.737661 | ||||||||
\(636\) | −2.81996e36 | −0.0401395 | ||||||||
\(637\) | 4.11344e37 | 0.573222 | ||||||||
\(638\) | −2.29059e36 | −0.0312513 | ||||||||
\(639\) | 2.37326e37 | 0.317018 | ||||||||
\(640\) | −3.02231e36 | −0.0395285 | ||||||||
\(641\) | −1.44495e37 | −0.185042 | −0.0925211 | − | 0.995711i | \(-0.529493\pi\) | ||||
−0.0925211 | + | 0.995711i | \(0.529493\pi\) | |||||||
\(642\) | 4.16123e36 | 0.0521794 | ||||||||
\(643\) | −2.85263e37 | −0.350265 | −0.175133 | − | 0.984545i | \(-0.556035\pi\) | ||||
−0.175133 | + | 0.984545i | \(0.556035\pi\) | |||||||
\(644\) | 2.44429e37 | 0.293895 | ||||||||
\(645\) | −1.18460e36 | −0.0139481 | ||||||||
\(646\) | −3.59277e36 | −0.0414277 | ||||||||
\(647\) | 1.04680e38 | 1.18210 | 0.591050 | − | 0.806635i | \(-0.298713\pi\) | ||||
0.591050 | + | 0.806635i | \(0.298713\pi\) | |||||||
\(648\) | −3.15299e37 | −0.348707 | ||||||||
\(649\) | −6.12594e37 | −0.663544 | ||||||||
\(650\) | 1.17989e37 | 0.125174 | ||||||||
\(651\) | 4.55487e36 | 0.0473296 | ||||||||
\(652\) | 4.84378e36 | 0.0492994 | ||||||||
\(653\) | −1.52185e38 | −1.51720 | −0.758600 | − | 0.651556i | \(-0.774116\pi\) | ||||
−0.758600 | + | 0.651556i | \(0.774116\pi\) | |||||||
\(654\) | 6.93435e36 | 0.0677183 | ||||||||
\(655\) | −6.62368e36 | −0.0633639 | ||||||||
\(656\) | −1.96670e37 | −0.184304 | ||||||||
\(657\) | −1.13673e38 | −1.04358 | ||||||||
\(658\) | −1.78048e36 | −0.0160136 | ||||||||
\(659\) | 1.20125e38 | 1.05847 | 0.529237 | − | 0.848474i | \(-0.322478\pi\) | ||||
0.529237 | + | 0.848474i | \(0.322478\pi\) | |||||||
\(660\) | 7.96523e35 | 0.00687631 | ||||||||
\(661\) | 1.16495e36 | 0.00985346 | 0.00492673 | − | 0.999988i | \(-0.498432\pi\) | ||||
0.00492673 | + | 0.999988i | \(0.498432\pi\) | |||||||
\(662\) | −1.49649e38 | −1.24020 | ||||||||
\(663\) | 1.59639e36 | 0.0129630 | ||||||||
\(664\) | 4.37582e36 | 0.0348169 | ||||||||
\(665\) | −9.21458e36 | −0.0718428 | ||||||||
\(666\) | −1.39814e38 | −1.06819 | ||||||||
\(667\) | 1.28589e37 | 0.0962730 | ||||||||
\(668\) | 4.51431e37 | 0.331214 | ||||||||
\(669\) | 1.73850e37 | 0.125004 | ||||||||
\(670\) | −3.81110e37 | −0.268560 | ||||||||
\(671\) | −1.07005e38 | −0.739011 | ||||||||
\(672\) | −1.04877e36 | −0.00709898 | ||||||||
\(673\) | −7.30965e37 | −0.484946 | −0.242473 | − | 0.970158i | \(-0.577959\pi\) | ||||
−0.242473 | + | 0.970158i | \(0.577959\pi\) | |||||||
\(674\) | −1.52596e38 | −0.992283 | ||||||||
\(675\) | −4.23580e36 | −0.0269982 | ||||||||
\(676\) | −1.73326e37 | −0.108289 | ||||||||
\(677\) | −1.69952e38 | −1.04083 | −0.520415 | − | 0.853913i | \(-0.674223\pi\) | ||||
−0.520415 | + | 0.853913i | \(0.674223\pi\) | |||||||
\(678\) | 3.85655e36 | 0.0231525 | ||||||||
\(679\) | −4.06649e37 | −0.239319 | ||||||||
\(680\) | 5.93307e36 | 0.0342302 | ||||||||
\(681\) | 4.90716e36 | 0.0277552 | ||||||||
\(682\) | −6.83181e37 | −0.378832 | ||||||||
\(683\) | 3.18220e38 | 1.73001 | 0.865004 | − | 0.501765i | \(-0.167316\pi\) | ||||
0.865004 | + | 0.501765i | \(0.167316\pi\) | |||||||
\(684\) | 2.52698e37 | 0.134693 | ||||||||
\(685\) | −2.57276e37 | −0.134455 | ||||||||
\(686\) | 1.34965e38 | 0.691584 | ||||||||
\(687\) | −3.38850e36 | −0.0170252 | ||||||||
\(688\) | −2.33945e37 | −0.115258 | ||||||||
\(689\) | 2.17415e38 | 1.05034 | ||||||||
\(690\) | −4.47151e36 | −0.0211832 | ||||||||
\(691\) | 2.86475e38 | 1.33086 | 0.665432 | − | 0.746459i | \(-0.268248\pi\) | ||||
0.665432 | + | 0.746459i | \(0.268248\pi\) | |||||||
\(692\) | 5.83753e37 | 0.265948 | ||||||||
\(693\) | −6.01185e37 | −0.268602 | ||||||||
\(694\) | −8.17443e37 | −0.358183 | ||||||||
\(695\) | −9.01322e37 | −0.387334 | ||||||||
\(696\) | −5.51738e35 | −0.00232545 | ||||||||
\(697\) | 3.86080e37 | 0.159601 | ||||||||
\(698\) | 1.08817e37 | 0.0441213 | ||||||||
\(699\) | −2.02009e36 | −0.00803396 | ||||||||
\(700\) | 1.52169e37 | 0.0593610 | ||||||||
\(701\) | 3.03977e38 | 1.16318 | 0.581590 | − | 0.813482i | \(-0.302431\pi\) | ||||
0.581590 | + | 0.813482i | \(0.302431\pi\) | |||||||
\(702\) | −2.25081e37 | −0.0844866 | ||||||||
\(703\) | 1.11537e38 | 0.410698 | ||||||||
\(704\) | 1.57305e37 | 0.0568212 | ||||||||
\(705\) | 3.25717e35 | 0.00115422 | ||||||||
\(706\) | −4.15286e36 | −0.0144372 | ||||||||
\(707\) | −6.86727e37 | −0.234219 | ||||||||
\(708\) | −1.47556e37 | −0.0493752 | ||||||||
\(709\) | −2.29087e38 | −0.752103 | −0.376051 | − | 0.926599i | \(-0.622718\pi\) | ||||
−0.376051 | + | 0.926599i | \(0.622718\pi\) | |||||||
\(710\) | 3.12654e37 | 0.100711 | ||||||||
\(711\) | −1.07527e38 | −0.339841 | ||||||||
\(712\) | 5.78018e37 | 0.179251 | ||||||||
\(713\) | 3.83523e38 | 1.16703 | ||||||||
\(714\) | 2.05883e36 | 0.00614745 | ||||||||
\(715\) | −6.14108e37 | −0.179934 | ||||||||
\(716\) | 2.48828e38 | 0.715439 | ||||||||
\(717\) | −4.65792e37 | −0.131427 | ||||||||
\(718\) | 1.06150e38 | 0.293928 | ||||||||
\(719\) | −8.47935e37 | −0.230421 | −0.115211 | − | 0.993341i | \(-0.536754\pi\) | ||||
−0.115211 | + | 0.993341i | \(0.536754\pi\) | |||||||
\(720\) | −4.17303e37 | −0.111292 | ||||||||
\(721\) | −3.43472e38 | −0.899010 | ||||||||
\(722\) | 2.55097e38 | 0.655320 | ||||||||
\(723\) | 2.84227e37 | 0.0716636 | ||||||||
\(724\) | 1.06137e38 | 0.262661 | ||||||||
\(725\) | 8.00527e36 | 0.0194452 | ||||||||
\(726\) | 1.59174e37 | 0.0379515 | ||||||||
\(727\) | 6.68474e37 | 0.156448 | 0.0782240 | − | 0.996936i | \(-0.475075\pi\) | ||||
0.0782240 | + | 0.996936i | \(0.475075\pi\) | |||||||
\(728\) | 8.08589e37 | 0.185761 | ||||||||
\(729\) | −4.31297e38 | −0.972645 | ||||||||
\(730\) | −1.49753e38 | −0.331526 | ||||||||
\(731\) | 4.59255e37 | 0.0998089 | ||||||||
\(732\) | −2.57745e37 | −0.0549908 | ||||||||
\(733\) | 6.44770e38 | 1.35052 | 0.675260 | − | 0.737580i | \(-0.264031\pi\) | ||||
0.675260 | + | 0.737580i | \(0.264031\pi\) | |||||||
\(734\) | 1.74367e38 | 0.358564 | ||||||||
\(735\) | −9.70485e36 | −0.0195934 | ||||||||
\(736\) | −8.83074e37 | −0.175044 | ||||||||
\(737\) | 1.98359e38 | 0.386048 | ||||||||
\(738\) | −2.71550e38 | −0.518906 | ||||||||
\(739\) | −9.08269e38 | −1.70418 | −0.852088 | − | 0.523398i | \(-0.824664\pi\) | ||||
−0.852088 | + | 0.523398i | \(0.824664\pi\) | |||||||
\(740\) | −1.84191e38 | −0.339344 | ||||||||
\(741\) | 8.95737e36 | 0.0162045 | ||||||||
\(742\) | 2.80396e38 | 0.498102 | ||||||||
\(743\) | 2.09598e38 | 0.365627 | 0.182813 | − | 0.983148i | \(-0.441480\pi\) | ||||
0.182813 | + | 0.983148i | \(0.441480\pi\) | |||||||
\(744\) | −1.64559e37 | −0.0281894 | ||||||||
\(745\) | −2.33189e38 | −0.392282 | ||||||||
\(746\) | 3.47331e38 | 0.573812 | ||||||||
\(747\) | 6.04187e37 | 0.0980264 | ||||||||
\(748\) | −3.08803e37 | −0.0492050 | ||||||||
\(749\) | −4.13761e38 | −0.647509 | ||||||||
\(750\) | −2.78373e36 | −0.00427858 | ||||||||
\(751\) | −5.96152e38 | −0.899949 | −0.449975 | − | 0.893041i | \(-0.648567\pi\) | ||||
−0.449975 | + | 0.893041i | \(0.648567\pi\) | |||||||
\(752\) | 6.43255e36 | 0.00953767 | ||||||||
\(753\) | −2.62359e37 | −0.0382088 | ||||||||
\(754\) | 4.25382e37 | 0.0608507 | ||||||||
\(755\) | −1.08398e37 | −0.0152313 | ||||||||
\(756\) | −2.90282e37 | −0.0400660 | ||||||||
\(757\) | −7.52761e38 | −1.02062 | −0.510309 | − | 0.859991i | \(-0.670469\pi\) | ||||
−0.510309 | + | 0.859991i | \(0.670469\pi\) | |||||||
\(758\) | 2.07924e38 | 0.276931 | ||||||||
\(759\) | 2.32732e37 | 0.0304503 | ||||||||
\(760\) | 3.32905e37 | 0.0427895 | ||||||||
\(761\) | −4.68849e37 | −0.0592025 | −0.0296013 | − | 0.999562i | \(-0.509424\pi\) | ||||
−0.0296013 | + | 0.999562i | \(0.509424\pi\) | |||||||
\(762\) | −6.36047e37 | −0.0789036 | ||||||||
\(763\) | −6.89500e38 | −0.840336 | ||||||||
\(764\) | −5.80823e38 | −0.695478 | ||||||||
\(765\) | 8.19202e37 | 0.0963744 | ||||||||
\(766\) | 1.12777e39 | 1.30356 | ||||||||
\(767\) | 1.13764e39 | 1.29201 | ||||||||
\(768\) | 3.78902e36 | 0.00422814 | ||||||||
\(769\) | −1.28141e39 | −1.40502 | −0.702510 | − | 0.711674i | \(-0.747937\pi\) | ||||
−0.702510 | + | 0.711674i | \(0.747937\pi\) | |||||||
\(770\) | −7.92003e37 | −0.0853300 | ||||||||
\(771\) | 8.46184e37 | 0.0895840 | ||||||||
\(772\) | 1.72452e38 | 0.179405 | ||||||||
\(773\) | 1.05565e39 | 1.07918 | 0.539591 | − | 0.841927i | \(-0.318579\pi\) | ||||
0.539591 | + | 0.841927i | \(0.318579\pi\) | |||||||
\(774\) | −3.23017e38 | −0.324506 | ||||||||
\(775\) | 2.38761e38 | 0.235717 | ||||||||
\(776\) | 1.46915e38 | 0.142538 | ||||||||
\(777\) | −6.39161e37 | −0.0609434 | ||||||||
\(778\) | −1.08033e39 | −1.01236 | ||||||||
\(779\) | 2.16630e38 | 0.199509 | ||||||||
\(780\) | −1.47921e37 | −0.0133891 | ||||||||
\(781\) | −1.62729e38 | −0.144769 | ||||||||
\(782\) | 1.73355e38 | 0.151581 | ||||||||
\(783\) | −1.52711e37 | −0.0131247 | ||||||||
\(784\) | −1.91660e38 | −0.161907 | ||||||||
\(785\) | 7.64936e38 | 0.635162 | ||||||||
\(786\) | 8.30398e36 | 0.00677769 | ||||||||
\(787\) | −2.14383e39 | −1.72001 | −0.860006 | − | 0.510283i | \(-0.829540\pi\) | ||||
−0.860006 | + | 0.510283i | \(0.829540\pi\) | |||||||
\(788\) | −9.61868e38 | −0.758598 | ||||||||
\(789\) | 1.41621e38 | 0.109796 | ||||||||
\(790\) | −1.41656e38 | −0.107961 | ||||||||
\(791\) | −3.83466e38 | −0.287306 | ||||||||
\(792\) | 2.17197e38 | 0.159979 | ||||||||
\(793\) | 1.98717e39 | 1.43896 | ||||||||
\(794\) | −5.33418e38 | −0.379744 | ||||||||
\(795\) | −5.12948e37 | −0.0359019 | ||||||||
\(796\) | −9.92724e38 | −0.683128 | ||||||||
\(797\) | 2.60844e39 | 1.76479 | 0.882395 | − | 0.470510i | \(-0.155930\pi\) | ||||
0.882395 | + | 0.470510i | \(0.155930\pi\) | |||||||
\(798\) | 1.15521e37 | 0.00768463 | ||||||||
\(799\) | −1.26277e37 | −0.00825927 | ||||||||
\(800\) | −5.49756e37 | −0.0353553 | ||||||||
\(801\) | 7.98092e38 | 0.504678 | ||||||||
\(802\) | 7.88514e38 | 0.490293 | ||||||||
\(803\) | 7.79432e38 | 0.476561 | ||||||||
\(804\) | 4.77790e37 | 0.0287263 | ||||||||
\(805\) | 4.44613e38 | 0.262868 | ||||||||
\(806\) | 1.26872e39 | 0.737639 | ||||||||
\(807\) | −2.03532e38 | −0.116370 | ||||||||
\(808\) | 2.48101e38 | 0.139500 | ||||||||
\(809\) | 3.01667e39 | 1.66810 | 0.834051 | − | 0.551688i | \(-0.186016\pi\) | ||||
0.834051 | + | 0.551688i | \(0.186016\pi\) | |||||||
\(810\) | −5.73526e38 | −0.311893 | ||||||||
\(811\) | −6.69658e38 | −0.358155 | −0.179078 | − | 0.983835i | \(-0.557311\pi\) | ||||
−0.179078 | + | 0.983835i | \(0.557311\pi\) | |||||||
\(812\) | 5.48606e37 | 0.0288572 | ||||||||
\(813\) | 1.84249e38 | 0.0953196 | ||||||||
\(814\) | 9.58673e38 | 0.487799 | ||||||||
\(815\) | 8.81078e37 | 0.0440947 | ||||||||
\(816\) | −7.43817e36 | −0.00366141 | ||||||||
\(817\) | 2.57688e38 | 0.124766 | ||||||||
\(818\) | −2.54038e39 | −1.20984 | ||||||||
\(819\) | 1.11645e39 | 0.523006 | ||||||||
\(820\) | −3.57740e38 | −0.164847 | ||||||||
\(821\) | −1.05326e39 | −0.477422 | −0.238711 | − | 0.971091i | \(-0.576725\pi\) | ||||
−0.238711 | + | 0.971091i | \(0.576725\pi\) | |||||||
\(822\) | 3.22542e37 | 0.0143819 | ||||||||
\(823\) | 2.68231e38 | 0.117655 | 0.0588276 | − | 0.998268i | \(-0.481264\pi\) | ||||
0.0588276 | + | 0.998268i | \(0.481264\pi\) | |||||||
\(824\) | 1.24090e39 | 0.535449 | ||||||||
\(825\) | 1.44887e37 | 0.00615036 | ||||||||
\(826\) | 1.46719e39 | 0.612710 | ||||||||
\(827\) | −2.78651e39 | −1.14482 | −0.572409 | − | 0.819968i | \(-0.693991\pi\) | ||||
−0.572409 | + | 0.819968i | \(0.693991\pi\) | |||||||
\(828\) | −1.21930e39 | −0.492833 | ||||||||
\(829\) | 3.50578e39 | 1.39412 | 0.697058 | − | 0.717015i | \(-0.254492\pi\) | ||||
0.697058 | + | 0.717015i | \(0.254492\pi\) | |||||||
\(830\) | 7.95957e37 | 0.0311412 | ||||||||
\(831\) | 9.74867e37 | 0.0375259 | ||||||||
\(832\) | −2.92128e38 | −0.110639 | ||||||||
\(833\) | 3.76246e38 | 0.140205 | ||||||||
\(834\) | 1.12997e38 | 0.0414310 | ||||||||
\(835\) | 8.21148e38 | 0.296247 | ||||||||
\(836\) | −1.73270e38 | −0.0615088 | ||||||||
\(837\) | −4.55470e38 | −0.159099 | ||||||||
\(838\) | −1.72923e39 | −0.594371 | ||||||||
\(839\) | −3.34496e39 | −1.13137 | −0.565685 | − | 0.824621i | \(-0.691388\pi\) | ||||
−0.565685 | + | 0.824621i | \(0.691388\pi\) | |||||||
\(840\) | −1.90771e37 | −0.00634952 | ||||||||
\(841\) | −3.02427e39 | −0.990547 | ||||||||
\(842\) | −3.89068e39 | −1.25404 | ||||||||
\(843\) | 2.06322e38 | 0.0654446 | ||||||||
\(844\) | 1.34514e39 | 0.419900 | ||||||||
\(845\) | −3.15279e38 | −0.0968566 | ||||||||
\(846\) | 8.88168e37 | 0.0268532 | ||||||||
\(847\) | −1.58271e39 | −0.470950 | ||||||||
\(848\) | −1.01302e39 | −0.296669 | ||||||||
\(849\) | 2.83040e38 | 0.0815820 | ||||||||
\(850\) | 1.07922e38 | 0.0306164 | ||||||||
\(851\) | −5.38178e39 | −1.50272 | ||||||||
\(852\) | −3.91968e37 | −0.0107725 | ||||||||
\(853\) | −5.83249e39 | −1.57776 | −0.788882 | − | 0.614545i | \(-0.789340\pi\) | ||||
−0.788882 | + | 0.614545i | \(0.789340\pi\) | |||||||
\(854\) | 2.56282e39 | 0.682396 | ||||||||
\(855\) | 4.59655e38 | 0.120473 | ||||||||
\(856\) | 1.49484e39 | 0.385655 | ||||||||
\(857\) | −3.39841e39 | −0.863048 | −0.431524 | − | 0.902102i | \(-0.642024\pi\) | ||||
−0.431524 | + | 0.902102i | \(0.642024\pi\) | |||||||
\(858\) | 7.69895e37 | 0.0192466 | ||||||||
\(859\) | 4.28955e39 | 1.05561 | 0.527805 | − | 0.849365i | \(-0.323015\pi\) | ||||
0.527805 | + | 0.849365i | \(0.323015\pi\) | |||||||
\(860\) | −4.25544e38 | −0.103090 | ||||||||
\(861\) | −1.24139e38 | −0.0296051 | ||||||||
\(862\) | 4.07568e39 | 0.956869 | ||||||||
\(863\) | −1.58857e39 | −0.367165 | −0.183583 | − | 0.983004i | \(-0.558770\pi\) | ||||
−0.183583 | + | 0.983004i | \(0.558770\pi\) | |||||||
\(864\) | 1.04873e38 | 0.0238633 | ||||||||
\(865\) | 1.06184e39 | 0.237871 | ||||||||
\(866\) | −1.21572e39 | −0.268128 | ||||||||
\(867\) | −2.96948e38 | −0.0644797 | ||||||||
\(868\) | 1.63625e39 | 0.349810 | ||||||||
\(869\) | 7.37286e38 | 0.155192 | ||||||||
\(870\) | −1.00360e37 | −0.00207995 | ||||||||
\(871\) | −3.68369e39 | −0.751689 | ||||||||
\(872\) | 2.49103e39 | 0.500503 | ||||||||
\(873\) | 2.02851e39 | 0.401314 | ||||||||
\(874\) | 9.72697e38 | 0.189484 | ||||||||
\(875\) | 2.76793e38 | 0.0530941 | ||||||||
\(876\) | 1.87743e38 | 0.0354615 | ||||||||
\(877\) | 2.78657e39 | 0.518293 | 0.259147 | − | 0.965838i | \(-0.416559\pi\) | ||||
0.259147 | + | 0.965838i | \(0.416559\pi\) | |||||||
\(878\) | −3.18585e39 | −0.583511 | ||||||||
\(879\) | 2.62612e38 | 0.0473657 | ||||||||
\(880\) | 2.86135e38 | 0.0508224 | ||||||||
\(881\) | 1.86266e39 | 0.325806 | 0.162903 | − | 0.986642i | \(-0.447914\pi\) | ||||
0.162903 | + | 0.986642i | \(0.447914\pi\) | |||||||
\(882\) | −2.64633e39 | −0.455846 | ||||||||
\(883\) | −1.12897e39 | −0.191520 | −0.0957601 | − | 0.995404i | \(-0.530528\pi\) | ||||
−0.0957601 | + | 0.995404i | \(0.530528\pi\) | |||||||
\(884\) | 5.73472e38 | 0.0958091 | ||||||||
\(885\) | −2.68403e38 | −0.0441625 | ||||||||
\(886\) | 6.21991e39 | 1.00793 | ||||||||
\(887\) | −3.48784e39 | −0.556656 | −0.278328 | − | 0.960486i | \(-0.589780\pi\) | ||||
−0.278328 | + | 0.960486i | \(0.589780\pi\) | |||||||
\(888\) | 2.30917e38 | 0.0362978 | ||||||||
\(889\) | 6.32437e39 | 0.979136 | ||||||||
\(890\) | 1.05141e39 | 0.160327 | ||||||||
\(891\) | 2.98507e39 | 0.448338 | ||||||||
\(892\) | 6.24522e39 | 0.923894 | ||||||||
\(893\) | −7.08540e37 | −0.0103245 | ||||||||
\(894\) | 2.92345e38 | 0.0419603 | ||||||||
\(895\) | 4.52615e39 | 0.639908 | ||||||||
\(896\) | −3.76751e38 | −0.0524682 | ||||||||
\(897\) | −4.32202e38 | −0.0592911 | ||||||||
\(898\) | −3.84888e37 | −0.00520121 | ||||||||
\(899\) | 8.60796e38 | 0.114589 | ||||||||
\(900\) | −7.59070e38 | −0.0995423 | ||||||||
\(901\) | 1.98864e39 | 0.256904 | ||||||||
\(902\) | 1.86196e39 | 0.236963 | ||||||||
\(903\) | −1.47668e38 | −0.0185140 | ||||||||
\(904\) | 1.38539e39 | 0.171119 | ||||||||
\(905\) | 1.93062e39 | 0.234931 | ||||||||
\(906\) | 1.35896e37 | 0.00162921 | ||||||||
\(907\) | −3.51472e39 | −0.415138 | −0.207569 | − | 0.978220i | \(-0.566555\pi\) | ||||
−0.207569 | + | 0.978220i | \(0.566555\pi\) | |||||||
\(908\) | 1.76280e39 | 0.205137 | ||||||||
\(909\) | 3.42563e39 | 0.392761 | ||||||||
\(910\) | 1.47081e39 | 0.166150 | ||||||||
\(911\) | 9.61927e38 | 0.107064 | 0.0535321 | − | 0.998566i | \(-0.482952\pi\) | ||||
0.0535321 | + | 0.998566i | \(0.482952\pi\) | |||||||
\(912\) | −4.17356e37 | −0.00457696 | ||||||||
\(913\) | −4.14277e38 | −0.0447647 | ||||||||
\(914\) | −8.79869e39 | −0.936795 | ||||||||
\(915\) | −4.68835e38 | −0.0491853 | ||||||||
\(916\) | −1.21725e39 | −0.125832 | ||||||||
\(917\) | −8.25684e38 | −0.0841062 | ||||||||
\(918\) | −2.05876e38 | −0.0206647 | ||||||||
\(919\) | −4.28853e39 | −0.424179 | −0.212089 | − | 0.977250i | \(-0.568027\pi\) | ||||
−0.212089 | + | 0.977250i | \(0.568027\pi\) | |||||||
\(920\) | −1.60630e39 | −0.156564 | ||||||||
\(921\) | −8.39967e38 | −0.0806784 | ||||||||
\(922\) | −7.53715e39 | −0.713411 | ||||||||
\(923\) | 3.02202e39 | 0.281886 | ||||||||
\(924\) | 9.92918e37 | 0.00912729 | ||||||||
\(925\) | −3.35042e39 | −0.303519 | ||||||||
\(926\) | −4.41279e39 | −0.393972 | ||||||||
\(927\) | 1.71336e40 | 1.50755 | ||||||||
\(928\) | −1.98201e38 | −0.0171873 | ||||||||
\(929\) | −2.10447e40 | −1.79858 | −0.899290 | − | 0.437353i | \(-0.855916\pi\) | ||||
−0.899290 | + | 0.437353i | \(0.855916\pi\) | |||||||
\(930\) | −2.99330e38 | −0.0252134 | ||||||||
\(931\) | 2.11112e39 | 0.175264 | ||||||||
\(932\) | −7.25679e38 | −0.0593786 | ||||||||
\(933\) | −5.14916e38 | −0.0415274 | ||||||||
\(934\) | 3.70700e39 | 0.294673 | ||||||||
\(935\) | −5.61709e38 | −0.0440103 | ||||||||
\(936\) | −4.03352e39 | −0.311502 | ||||||||
\(937\) | 1.07956e40 | 0.821795 | 0.410897 | − | 0.911682i | \(-0.365215\pi\) | ||||
0.410897 | + | 0.911682i | \(0.365215\pi\) | |||||||
\(938\) | −4.75078e39 | −0.356473 | ||||||||
\(939\) | 7.01844e38 | 0.0519105 | ||||||||
\(940\) | 1.17007e38 | 0.00853076 | ||||||||
\(941\) | −6.73545e39 | −0.484069 | −0.242034 | − | 0.970268i | \(-0.577815\pi\) | ||||
−0.242034 | + | 0.970268i | \(0.577815\pi\) | |||||||
\(942\) | −9.58985e38 | −0.0679399 | ||||||||
\(943\) | −1.04526e40 | −0.729991 | ||||||||
\(944\) | −5.30067e39 | −0.364930 | ||||||||
\(945\) | −5.28020e38 | −0.0358361 | ||||||||
\(946\) | 2.21486e39 | 0.148189 | ||||||||
\(947\) | 1.10409e40 | 0.728249 | 0.364124 | − | 0.931350i | \(-0.381368\pi\) | ||||
0.364124 | + | 0.931350i | \(0.381368\pi\) | |||||||
\(948\) | 1.77591e38 | 0.0115480 | ||||||||
\(949\) | −1.44747e40 | −0.927930 | ||||||||
\(950\) | 6.05551e38 | 0.0382721 | ||||||||
\(951\) | −2.95270e38 | −0.0183985 | ||||||||
\(952\) | 7.39595e38 | 0.0454355 | ||||||||
\(953\) | 1.05932e40 | 0.641612 | 0.320806 | − | 0.947145i | \(-0.396046\pi\) | ||||
0.320806 | + | 0.947145i | \(0.396046\pi\) | |||||||
\(954\) | −1.39871e40 | −0.835267 | ||||||||
\(955\) | −1.05651e40 | −0.622055 | ||||||||
\(956\) | −1.67326e40 | −0.971367 | ||||||||
\(957\) | 5.22354e37 | 0.00298988 | ||||||||
\(958\) | 1.72490e40 | 0.973487 | ||||||||
\(959\) | −3.20711e39 | −0.178469 | ||||||||
\(960\) | 6.89218e37 | 0.00378177 | ||||||||
\(961\) | 7.19098e39 | 0.389065 | ||||||||
\(962\) | −1.78034e40 | −0.949814 | ||||||||
\(963\) | 2.06399e40 | 1.08581 | ||||||||
\(964\) | 1.02103e40 | 0.529662 | ||||||||
\(965\) | 3.13689e39 | 0.160465 | ||||||||
\(966\) | −5.57402e38 | −0.0281176 | ||||||||
\(967\) | 9.48098e39 | 0.471624 | 0.235812 | − | 0.971799i | \(-0.424225\pi\) | ||||
0.235812 | + | 0.971799i | \(0.424225\pi\) | |||||||
\(968\) | 5.71803e39 | 0.280497 | ||||||||
\(969\) | 8.19307e37 | 0.00396347 | ||||||||
\(970\) | 2.67236e39 | 0.127490 | ||||||||
\(971\) | 1.33762e40 | 0.629324 | 0.314662 | − | 0.949204i | \(-0.398109\pi\) | ||||
0.314662 | + | 0.949204i | \(0.398109\pi\) | |||||||
\(972\) | 2.17370e39 | 0.100857 | ||||||||
\(973\) | −1.12356e40 | −0.514128 | ||||||||
\(974\) | −1.14606e40 | −0.517204 | ||||||||
\(975\) | −2.69067e38 | −0.0119756 | ||||||||
\(976\) | −9.25897e39 | −0.406434 | ||||||||
\(977\) | −2.56073e40 | −1.10863 | −0.554317 | − | 0.832306i | \(-0.687020\pi\) | ||||
−0.554317 | + | 0.832306i | \(0.687020\pi\) | |||||||
\(978\) | −1.10459e38 | −0.00471657 | ||||||||
\(979\) | −5.47234e39 | −0.230466 | ||||||||
\(980\) | −3.48628e39 | −0.144814 | ||||||||
\(981\) | 3.43947e40 | 1.40916 | ||||||||
\(982\) | 1.46388e40 | 0.591563 | ||||||||
\(983\) | 1.03636e39 | 0.0413085 | 0.0206543 | − | 0.999787i | \(-0.493425\pi\) | ||||
0.0206543 | + | 0.999787i | \(0.493425\pi\) | |||||||
\(984\) | 4.48492e38 | 0.0176328 | ||||||||
\(985\) | −1.74963e40 | −0.678511 | ||||||||
\(986\) | 3.89086e38 | 0.0148836 | ||||||||
\(987\) | 4.06027e37 | 0.00153205 | ||||||||
\(988\) | 3.21776e39 | 0.119766 | ||||||||
\(989\) | −1.24337e40 | −0.456511 | ||||||||
\(990\) | 3.95079e39 | 0.143090 | ||||||||
\(991\) | 4.36938e40 | 1.56108 | 0.780541 | − | 0.625104i | \(-0.214944\pi\) | ||||
0.780541 | + | 0.625104i | \(0.214944\pi\) | |||||||
\(992\) | −5.91145e39 | −0.208347 | ||||||||
\(993\) | 3.41264e39 | 0.118652 | ||||||||
\(994\) | 3.89743e39 | 0.133679 | ||||||||
\(995\) | −1.80575e40 | −0.611008 | ||||||||
\(996\) | −9.97875e37 | −0.00333100 | ||||||||
\(997\) | −3.43978e40 | −1.13278 | −0.566391 | − | 0.824137i | \(-0.691661\pi\) | ||||
−0.566391 | + | 0.824137i | \(0.691661\pi\) | |||||||
\(998\) | 4.12766e40 | 1.34104 | ||||||||
\(999\) | 6.39138e39 | 0.204862 |
(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 | 10.28.a.a.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 50.28.b.e.49.1 | 4 | |||
5.3 | odd | 4 | 50.28.b.e.49.4 | 4 | |||
5.4 | even | 2 | 50.28.a.e.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.28.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.28.a.e.1.1 | 2 | 5.4 | even | 2 | |||
50.28.b.e.49.1 | 4 | 5.2 | odd | 4 | |||
50.28.b.e.49.4 | 4 | 5.3 | odd | 4 |