Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,32,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, 32, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 32);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 32 \) |
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: | \(60.8771328190\) |
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: | \( x^{2} - x - 17573188320 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-132563.\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32768.0 | −0.707107 | ||||||||
\(3\) | 2.09091e7 | 0.841311 | 0.420655 | − | 0.907221i | \(-0.361800\pi\) | ||||
0.420655 | + | 0.907221i | \(0.361800\pi\) | |||||||
\(4\) | 1.07374e9 | 0.500000 | ||||||||
\(5\) | 3.05176e10 | 0.447214 | ||||||||
\(6\) | −6.85150e11 | −0.594896 | ||||||||
\(7\) | 1.72878e13 | 1.37632 | 0.688162 | − | 0.725557i | \(-0.258418\pi\) | ||||
0.688162 | + | 0.725557i | \(0.258418\pi\) | |||||||
\(8\) | −3.51844e13 | −0.353553 | ||||||||
\(9\) | −1.80482e14 | −0.292196 | ||||||||
\(10\) | −1.00000e15 | −0.316228 | ||||||||
\(11\) | −1.40404e16 | −1.01342 | −0.506712 | − | 0.862115i | \(-0.669139\pi\) | ||||
−0.506712 | + | 0.862115i | \(0.669139\pi\) | |||||||
\(12\) | 2.24510e16 | 0.420655 | ||||||||
\(13\) | 1.12100e17 | 0.607410 | 0.303705 | − | 0.952766i | \(-0.401776\pi\) | ||||
0.303705 | + | 0.952766i | \(0.401776\pi\) | |||||||
\(14\) | −5.66487e17 | −0.973208 | ||||||||
\(15\) | 6.38096e17 | 0.376246 | ||||||||
\(16\) | 1.15292e18 | 0.250000 | ||||||||
\(17\) | −1.87926e19 | −1.59232 | −0.796158 | − | 0.605088i | \(-0.793138\pi\) | ||||
−0.796158 | + | 0.605088i | \(0.793138\pi\) | |||||||
\(18\) | 5.91403e18 | 0.206614 | ||||||||
\(19\) | −1.17369e20 | −1.77367 | −0.886837 | − | 0.462083i | \(-0.847102\pi\) | ||||
−0.886837 | + | 0.462083i | \(0.847102\pi\) | |||||||
\(20\) | 3.27680e19 | 0.223607 | ||||||||
\(21\) | 3.61473e20 | 1.15792 | ||||||||
\(22\) | 4.60074e20 | 0.716600 | ||||||||
\(23\) | −2.47133e21 | −1.93263 | −0.966315 | − | 0.257363i | \(-0.917146\pi\) | ||||
−0.966315 | + | 0.257363i | \(0.917146\pi\) | |||||||
\(24\) | −7.35674e20 | −0.297448 | ||||||||
\(25\) | 9.31323e20 | 0.200000 | ||||||||
\(26\) | −3.67328e21 | −0.429504 | ||||||||
\(27\) | −1.66887e22 | −1.08714 | ||||||||
\(28\) | 1.85627e22 | 0.688162 | ||||||||
\(29\) | 6.20136e22 | 1.33450 | 0.667249 | − | 0.744835i | \(-0.267472\pi\) | ||||
0.667249 | + | 0.744835i | \(0.267472\pi\) | |||||||
\(30\) | −2.09091e22 | −0.266046 | ||||||||
\(31\) | 1.42328e23 | 1.08939 | 0.544696 | − | 0.838634i | \(-0.316645\pi\) | ||||
0.544696 | + | 0.838634i | \(0.316645\pi\) | |||||||
\(32\) | −3.77789e22 | −0.176777 | ||||||||
\(33\) | −2.93572e23 | −0.852605 | ||||||||
\(34\) | 6.15797e23 | 1.12594 | ||||||||
\(35\) | 5.27582e23 | 0.615511 | ||||||||
\(36\) | −1.93791e23 | −0.146098 | ||||||||
\(37\) | 1.53344e24 | 0.756030 | 0.378015 | − | 0.925799i | \(-0.376607\pi\) | ||||
0.378015 | + | 0.925799i | \(0.376607\pi\) | |||||||
\(38\) | 3.84596e24 | 1.25418 | ||||||||
\(39\) | 2.34391e24 | 0.511021 | ||||||||
\(40\) | −1.07374e24 | −0.158114 | ||||||||
\(41\) | −6.64565e24 | −0.667403 | −0.333701 | − | 0.942679i | \(-0.608298\pi\) | ||||
−0.333701 | + | 0.942679i | \(0.608298\pi\) | |||||||
\(42\) | −1.18448e25 | −0.818770 | ||||||||
\(43\) | 1.23317e24 | 0.0591920 | 0.0295960 | − | 0.999562i | \(-0.490578\pi\) | ||||
0.0295960 | + | 0.999562i | \(0.490578\pi\) | |||||||
\(44\) | −1.50757e25 | −0.506712 | ||||||||
\(45\) | −5.50787e24 | −0.130674 | ||||||||
\(46\) | 8.09804e25 | 1.36658 | ||||||||
\(47\) | −1.65205e26 | −1.99760 | −0.998798 | − | 0.0490256i | \(-0.984388\pi\) | ||||
−0.998798 | + | 0.0490256i | \(0.984388\pi\) | |||||||
\(48\) | 2.41066e25 | 0.210328 | ||||||||
\(49\) | 1.41093e26 | 0.894267 | ||||||||
\(50\) | −3.05176e25 | −0.141421 | ||||||||
\(51\) | −3.92938e26 | −1.33963 | ||||||||
\(52\) | 1.20366e26 | 0.303705 | ||||||||
\(53\) | 2.10693e25 | 0.0395708 | 0.0197854 | − | 0.999804i | \(-0.493702\pi\) | ||||
0.0197854 | + | 0.999804i | \(0.493702\pi\) | |||||||
\(54\) | 5.46856e26 | 0.768723 | ||||||||
\(55\) | −4.28478e26 | −0.453217 | ||||||||
\(56\) | −6.08261e26 | −0.486604 | ||||||||
\(57\) | −2.45409e27 | −1.49221 | ||||||||
\(58\) | −2.03206e27 | −0.943633 | ||||||||
\(59\) | 2.11570e27 | 0.753786 | 0.376893 | − | 0.926257i | \(-0.376992\pi\) | ||||
0.376893 | + | 0.926257i | \(0.376992\pi\) | |||||||
\(60\) | 6.85150e26 | 0.188123 | ||||||||
\(61\) | −2.54907e27 | −0.541712 | −0.270856 | − | 0.962620i | \(-0.587307\pi\) | ||||
−0.270856 | + | 0.962620i | \(0.587307\pi\) | |||||||
\(62\) | −4.66380e27 | −0.770316 | ||||||||
\(63\) | −3.12014e27 | −0.402157 | ||||||||
\(64\) | 1.23794e27 | 0.125000 | ||||||||
\(65\) | 3.42101e27 | 0.271642 | ||||||||
\(66\) | 9.61975e27 | 0.602883 | ||||||||
\(67\) | 2.58183e28 | 1.28165 | 0.640823 | − | 0.767688i | \(-0.278593\pi\) | ||||
0.640823 | + | 0.767688i | \(0.278593\pi\) | |||||||
\(68\) | −2.01784e28 | −0.796158 | ||||||||
\(69\) | −5.16733e28 | −1.62594 | ||||||||
\(70\) | −1.72878e28 | −0.435232 | ||||||||
\(71\) | −6.76939e28 | −1.36787 | −0.683936 | − | 0.729542i | \(-0.739733\pi\) | ||||
−0.683936 | + | 0.729542i | \(0.739733\pi\) | |||||||
\(72\) | 6.35014e27 | 0.103307 | ||||||||
\(73\) | −5.88515e28 | −0.773131 | −0.386566 | − | 0.922262i | \(-0.626339\pi\) | ||||
−0.386566 | + | 0.922262i | \(0.626339\pi\) | |||||||
\(74\) | −5.02476e28 | −0.534594 | ||||||||
\(75\) | 1.94731e28 | 0.168262 | ||||||||
\(76\) | −1.26024e29 | −0.886837 | ||||||||
\(77\) | −2.42727e29 | −1.39480 | ||||||||
\(78\) | −7.68051e28 | −0.361346 | ||||||||
\(79\) | −2.13368e29 | −0.823965 | −0.411982 | − | 0.911192i | \(-0.635163\pi\) | ||||
−0.411982 | + | 0.911192i | \(0.635163\pi\) | |||||||
\(80\) | 3.51844e28 | 0.111803 | ||||||||
\(81\) | −2.37468e29 | −0.622425 | ||||||||
\(82\) | 2.17765e29 | 0.471925 | ||||||||
\(83\) | −1.06637e29 | −0.191513 | −0.0957564 | − | 0.995405i | \(-0.530527\pi\) | ||||
−0.0957564 | + | 0.995405i | \(0.530527\pi\) | |||||||
\(84\) | 3.88129e29 | 0.578958 | ||||||||
\(85\) | −5.73506e29 | −0.712106 | ||||||||
\(86\) | −4.04086e28 | −0.0418550 | ||||||||
\(87\) | 1.29665e30 | 1.12273 | ||||||||
\(88\) | 4.94001e29 | 0.358300 | ||||||||
\(89\) | −5.07280e29 | −0.308818 | −0.154409 | − | 0.988007i | \(-0.549347\pi\) | ||||
−0.154409 | + | 0.988007i | \(0.549347\pi\) | |||||||
\(90\) | 1.80482e29 | 0.0924006 | ||||||||
\(91\) | 1.93796e30 | 0.835993 | ||||||||
\(92\) | −2.65357e30 | −0.966315 | ||||||||
\(93\) | 2.97595e30 | 0.916517 | ||||||||
\(94\) | 5.41345e30 | 1.41251 | ||||||||
\(95\) | −3.58183e30 | −0.793211 | ||||||||
\(96\) | −7.89924e29 | −0.148724 | ||||||||
\(97\) | 2.99146e30 | 0.479646 | 0.239823 | − | 0.970817i | \(-0.422911\pi\) | ||||
0.239823 | + | 0.970817i | \(0.422911\pi\) | |||||||
\(98\) | −4.62334e30 | −0.632342 | ||||||||
\(99\) | 2.53403e30 | 0.296119 | ||||||||
\(100\) | 1.00000e30 | 0.100000 | ||||||||
\(101\) | 5.56134e30 | 0.476648 | 0.238324 | − | 0.971186i | \(-0.423402\pi\) | ||||
0.238324 | + | 0.971186i | \(0.423402\pi\) | |||||||
\(102\) | 1.28758e31 | 0.947264 | ||||||||
\(103\) | −9.44476e30 | −0.597330 | −0.298665 | − | 0.954358i | \(-0.596541\pi\) | ||||
−0.298665 | + | 0.954358i | \(0.596541\pi\) | |||||||
\(104\) | −3.94416e30 | −0.214752 | ||||||||
\(105\) | 1.10313e31 | 0.517836 | ||||||||
\(106\) | −6.90400e29 | −0.0279808 | ||||||||
\(107\) | 3.40170e31 | 1.19192 | 0.595961 | − | 0.803014i | \(-0.296771\pi\) | ||||
0.595961 | + | 0.803014i | \(0.296771\pi\) | |||||||
\(108\) | −1.79194e31 | −0.543569 | ||||||||
\(109\) | 1.12629e31 | 0.296169 | 0.148085 | − | 0.988975i | \(-0.452689\pi\) | ||||
0.148085 | + | 0.988975i | \(0.452689\pi\) | |||||||
\(110\) | 1.40404e31 | 0.320473 | ||||||||
\(111\) | 3.20628e31 | 0.636056 | ||||||||
\(112\) | 1.99315e31 | 0.344081 | ||||||||
\(113\) | −1.71220e31 | −0.257537 | −0.128769 | − | 0.991675i | \(-0.541102\pi\) | ||||
−0.128769 | + | 0.991675i | \(0.541102\pi\) | |||||||
\(114\) | 8.04156e31 | 1.05515 | ||||||||
\(115\) | −7.54189e31 | −0.864298 | ||||||||
\(116\) | 6.65866e31 | 0.667249 | ||||||||
\(117\) | −2.02320e31 | −0.177483 | ||||||||
\(118\) | −6.93273e31 | −0.533007 | ||||||||
\(119\) | −3.24884e32 | −2.19154 | ||||||||
\(120\) | −2.24510e31 | −0.133023 | ||||||||
\(121\) | 5.18822e30 | 0.0270299 | ||||||||
\(122\) | 8.35278e31 | 0.383048 | ||||||||
\(123\) | −1.38955e32 | −0.561493 | ||||||||
\(124\) | 1.52824e32 | 0.544696 | ||||||||
\(125\) | 2.84217e31 | 0.0894427 | ||||||||
\(126\) | 1.02241e32 | 0.284368 | ||||||||
\(127\) | −7.80052e32 | −1.91940 | −0.959701 | − | 0.281022i | \(-0.909327\pi\) | ||||
−0.959701 | + | 0.281022i | \(0.909327\pi\) | |||||||
\(128\) | −4.05648e31 | −0.0883883 | ||||||||
\(129\) | 2.57846e31 | 0.0497988 | ||||||||
\(130\) | −1.12100e32 | −0.192080 | ||||||||
\(131\) | 7.18592e32 | 1.09340 | 0.546698 | − | 0.837330i | \(-0.315885\pi\) | ||||
0.546698 | + | 0.837330i | \(0.315885\pi\) | |||||||
\(132\) | −3.15220e32 | −0.426303 | ||||||||
\(133\) | −2.02906e33 | −2.44115 | ||||||||
\(134\) | −8.46014e32 | −0.906261 | ||||||||
\(135\) | −5.09300e32 | −0.486183 | ||||||||
\(136\) | 6.61207e32 | 0.562969 | ||||||||
\(137\) | 1.47730e33 | 1.12279 | 0.561395 | − | 0.827548i | \(-0.310265\pi\) | ||||
0.561395 | + | 0.827548i | \(0.310265\pi\) | |||||||
\(138\) | 1.69323e33 | 1.14971 | ||||||||
\(139\) | 5.43580e32 | 0.330016 | 0.165008 | − | 0.986292i | \(-0.447235\pi\) | ||||
0.165008 | + | 0.986292i | \(0.447235\pi\) | |||||||
\(140\) | 5.66487e32 | 0.307755 | ||||||||
\(141\) | −3.45430e33 | −1.68060 | ||||||||
\(142\) | 2.21819e33 | 0.967231 | ||||||||
\(143\) | −1.57392e33 | −0.615565 | ||||||||
\(144\) | −2.08081e32 | −0.0730491 | ||||||||
\(145\) | 1.89251e33 | 0.596806 | ||||||||
\(146\) | 1.92845e33 | 0.546686 | ||||||||
\(147\) | 2.95014e33 | 0.752356 | ||||||||
\(148\) | 1.64651e33 | 0.378015 | ||||||||
\(149\) | −3.63270e33 | −0.751350 | −0.375675 | − | 0.926752i | \(-0.622589\pi\) | ||||
−0.375675 | + | 0.926752i | \(0.622589\pi\) | |||||||
\(150\) | −6.38096e32 | −0.118979 | ||||||||
\(151\) | 6.05619e33 | 1.01872 | 0.509362 | − | 0.860552i | \(-0.329881\pi\) | ||||
0.509362 | + | 0.860552i | \(0.329881\pi\) | |||||||
\(152\) | 4.12957e33 | 0.627088 | ||||||||
\(153\) | 3.39173e33 | 0.465269 | ||||||||
\(154\) | 7.95368e33 | 0.986273 | ||||||||
\(155\) | 4.34351e33 | 0.487191 | ||||||||
\(156\) | 2.51675e33 | 0.255510 | ||||||||
\(157\) | 2.21456e33 | 0.203631 | 0.101815 | − | 0.994803i | \(-0.467535\pi\) | ||||
0.101815 | + | 0.994803i | \(0.467535\pi\) | |||||||
\(158\) | 6.99163e33 | 0.582631 | ||||||||
\(159\) | 4.40541e32 | 0.0332913 | ||||||||
\(160\) | −1.15292e33 | −0.0790569 | ||||||||
\(161\) | −4.27238e34 | −2.65992 | ||||||||
\(162\) | 7.78135e33 | 0.440121 | ||||||||
\(163\) | −1.25964e34 | −0.647649 | −0.323824 | − | 0.946117i | \(-0.604969\pi\) | ||||
−0.323824 | + | 0.946117i | \(0.604969\pi\) | |||||||
\(164\) | −7.13572e33 | −0.333701 | ||||||||
\(165\) | −8.95909e33 | −0.381297 | ||||||||
\(166\) | 3.49429e33 | 0.135420 | ||||||||
\(167\) | −1.61993e34 | −0.571992 | −0.285996 | − | 0.958231i | \(-0.592324\pi\) | ||||
−0.285996 | + | 0.958231i | \(0.592324\pi\) | |||||||
\(168\) | −1.27182e34 | −0.409385 | ||||||||
\(169\) | −2.14936e34 | −0.631052 | ||||||||
\(170\) | 1.87926e34 | 0.503535 | ||||||||
\(171\) | 2.11830e34 | 0.518261 | ||||||||
\(172\) | 1.32411e33 | 0.0295960 | ||||||||
\(173\) | 8.33177e34 | 1.70225 | 0.851124 | − | 0.524965i | \(-0.175922\pi\) | ||||
0.851124 | + | 0.524965i | \(0.175922\pi\) | |||||||
\(174\) | −4.24886e34 | −0.793888 | ||||||||
\(175\) | 1.61005e34 | 0.275265 | ||||||||
\(176\) | −1.61874e34 | −0.253356 | ||||||||
\(177\) | 4.42375e34 | 0.634168 | ||||||||
\(178\) | 1.66226e34 | 0.218367 | ||||||||
\(179\) | −1.19965e35 | −1.44488 | −0.722442 | − | 0.691432i | \(-0.756980\pi\) | ||||
−0.722442 | + | 0.691432i | \(0.756980\pi\) | |||||||
\(180\) | −5.91403e33 | −0.0653371 | ||||||||
\(181\) | −9.22700e34 | −0.935497 | −0.467749 | − | 0.883861i | \(-0.654935\pi\) | ||||
−0.467749 | + | 0.883861i | \(0.654935\pi\) | |||||||
\(182\) | −6.35030e34 | −0.591137 | ||||||||
\(183\) | −5.32987e34 | −0.455748 | ||||||||
\(184\) | 8.69521e34 | 0.683288 | ||||||||
\(185\) | 4.67968e34 | 0.338107 | ||||||||
\(186\) | −9.75160e34 | −0.648075 | ||||||||
\(187\) | 2.63855e35 | 1.61369 | ||||||||
\(188\) | −1.77388e35 | −0.998798 | ||||||||
\(189\) | −2.88512e35 | −1.49625 | ||||||||
\(190\) | 1.17369e35 | 0.560885 | ||||||||
\(191\) | 9.20859e34 | 0.405673 | 0.202837 | − | 0.979213i | \(-0.434984\pi\) | ||||
0.202837 | + | 0.979213i | \(0.434984\pi\) | |||||||
\(192\) | 2.58842e34 | 0.105164 | ||||||||
\(193\) | −4.07145e35 | −1.52620 | −0.763098 | − | 0.646283i | \(-0.776323\pi\) | ||||
−0.763098 | + | 0.646283i | \(0.776323\pi\) | |||||||
\(194\) | −9.80241e34 | −0.339161 | ||||||||
\(195\) | 7.15303e34 | 0.228536 | ||||||||
\(196\) | 1.51498e35 | 0.447133 | ||||||||
\(197\) | 1.97536e35 | 0.538791 | 0.269395 | − | 0.963030i | \(-0.413176\pi\) | ||||
0.269395 | + | 0.963030i | \(0.413176\pi\) | |||||||
\(198\) | −8.30351e34 | −0.209388 | ||||||||
\(199\) | 4.46274e35 | 1.04083 | 0.520413 | − | 0.853914i | \(-0.325778\pi\) | ||||
0.520413 | + | 0.853914i | \(0.325778\pi\) | |||||||
\(200\) | −3.27680e34 | −0.0707107 | ||||||||
\(201\) | 5.39838e35 | 1.07826 | ||||||||
\(202\) | −1.82234e35 | −0.337041 | ||||||||
\(203\) | 1.07208e36 | 1.83670 | ||||||||
\(204\) | −4.21914e35 | −0.669816 | ||||||||
\(205\) | −2.02809e35 | −0.298472 | ||||||||
\(206\) | 3.09486e35 | 0.422376 | ||||||||
\(207\) | 4.46030e35 | 0.564707 | ||||||||
\(208\) | 1.29242e35 | 0.151853 | ||||||||
\(209\) | 1.64791e36 | 1.79748 | ||||||||
\(210\) | −3.61473e35 | −0.366165 | ||||||||
\(211\) | 3.17406e35 | 0.298701 | 0.149351 | − | 0.988784i | \(-0.452282\pi\) | ||||
0.149351 | + | 0.988784i | \(0.452282\pi\) | |||||||
\(212\) | 2.26230e34 | 0.0197854 | ||||||||
\(213\) | −1.41542e36 | −1.15080 | ||||||||
\(214\) | −1.11467e36 | −0.842815 | ||||||||
\(215\) | 3.76334e34 | 0.0264714 | ||||||||
\(216\) | 5.87182e35 | 0.384362 | ||||||||
\(217\) | 2.46054e36 | 1.49936 | ||||||||
\(218\) | −3.69063e35 | −0.209423 | ||||||||
\(219\) | −1.23053e36 | −0.650444 | ||||||||
\(220\) | −4.60074e35 | −0.226609 | ||||||||
\(221\) | −2.10665e36 | −0.967190 | ||||||||
\(222\) | −1.05063e36 | −0.449760 | ||||||||
\(223\) | 1.18359e36 | 0.472582 | 0.236291 | − | 0.971682i | \(-0.424068\pi\) | ||||
0.236291 | + | 0.971682i | \(0.424068\pi\) | |||||||
\(224\) | −6.53115e35 | −0.243302 | ||||||||
\(225\) | −1.68087e35 | −0.0584393 | ||||||||
\(226\) | 5.61055e35 | 0.182106 | ||||||||
\(227\) | 1.73010e34 | 0.00524408 | 0.00262204 | − | 0.999997i | \(-0.499165\pi\) | ||||
0.00262204 | + | 0.999997i | \(0.499165\pi\) | |||||||
\(228\) | −2.63506e36 | −0.746105 | ||||||||
\(229\) | −1.57133e36 | −0.415737 | −0.207868 | − | 0.978157i | \(-0.566653\pi\) | ||||
−0.207868 | + | 0.978157i | \(0.566653\pi\) | |||||||
\(230\) | 2.47133e36 | 0.611151 | ||||||||
\(231\) | −5.07521e36 | −1.17346 | ||||||||
\(232\) | −2.18191e36 | −0.471816 | ||||||||
\(233\) | −6.37806e36 | −1.29024 | −0.645122 | − | 0.764080i | \(-0.723193\pi\) | ||||
−0.645122 | + | 0.764080i | \(0.723193\pi\) | |||||||
\(234\) | 6.62961e35 | 0.125500 | ||||||||
\(235\) | −5.04167e36 | −0.893352 | ||||||||
\(236\) | 2.27172e36 | 0.376893 | ||||||||
\(237\) | −4.46133e36 | −0.693210 | ||||||||
\(238\) | 1.06458e37 | 1.54965 | ||||||||
\(239\) | 3.04721e36 | 0.415656 | 0.207828 | − | 0.978165i | \(-0.433361\pi\) | ||||
0.207828 | + | 0.978165i | \(0.433361\pi\) | |||||||
\(240\) | 7.35674e35 | 0.0940614 | ||||||||
\(241\) | 1.21299e36 | 0.145409 | 0.0727047 | − | 0.997354i | \(-0.476837\pi\) | ||||
0.0727047 | + | 0.997354i | \(0.476837\pi\) | |||||||
\(242\) | −1.70007e35 | −0.0191130 | ||||||||
\(243\) | 5.34294e36 | 0.563486 | ||||||||
\(244\) | −2.73704e36 | −0.270856 | ||||||||
\(245\) | 4.30583e36 | 0.399928 | ||||||||
\(246\) | 4.55327e36 | 0.397036 | ||||||||
\(247\) | −1.31571e37 | −1.07735 | ||||||||
\(248\) | −5.00772e36 | −0.385158 | ||||||||
\(249\) | −2.22969e36 | −0.161122 | ||||||||
\(250\) | −9.31323e35 | −0.0632456 | ||||||||
\(251\) | −5.23269e36 | −0.334027 | −0.167014 | − | 0.985955i | \(-0.553412\pi\) | ||||
−0.167014 | + | 0.985955i | \(0.553412\pi\) | |||||||
\(252\) | −3.35022e36 | −0.201078 | ||||||||
\(253\) | 3.46983e37 | 1.95858 | ||||||||
\(254\) | 2.55608e37 | 1.35722 | ||||||||
\(255\) | −1.19915e37 | −0.599102 | ||||||||
\(256\) | 1.32923e36 | 0.0625000 | ||||||||
\(257\) | −2.76137e36 | −0.122225 | −0.0611126 | − | 0.998131i | \(-0.519465\pi\) | ||||
−0.0611126 | + | 0.998131i | \(0.519465\pi\) | |||||||
\(258\) | −8.44908e35 | −0.0352131 | ||||||||
\(259\) | 2.65098e37 | 1.04054 | ||||||||
\(260\) | 3.67328e36 | 0.135821 | ||||||||
\(261\) | −1.11923e37 | −0.389936 | ||||||||
\(262\) | −2.35468e37 | −0.773147 | ||||||||
\(263\) | 2.48833e37 | 0.770183 | 0.385091 | − | 0.922878i | \(-0.374170\pi\) | ||||
0.385091 | + | 0.922878i | \(0.374170\pi\) | |||||||
\(264\) | 1.03291e37 | 0.301441 | ||||||||
\(265\) | 6.42985e35 | 0.0176966 | ||||||||
\(266\) | 6.64882e37 | 1.72615 | ||||||||
\(267\) | −1.06068e37 | −0.259812 | ||||||||
\(268\) | 2.77222e37 | 0.640823 | ||||||||
\(269\) | −8.65600e37 | −1.88867 | −0.944336 | − | 0.328982i | \(-0.893295\pi\) | ||||
−0.944336 | + | 0.328982i | \(0.893295\pi\) | |||||||
\(270\) | 1.66887e37 | 0.343783 | ||||||||
\(271\) | −7.04664e36 | −0.137075 | −0.0685375 | − | 0.997649i | \(-0.521833\pi\) | ||||
−0.0685375 | + | 0.997649i | \(0.521833\pi\) | |||||||
\(272\) | −2.16664e37 | −0.398079 | ||||||||
\(273\) | 4.05210e37 | 0.703330 | ||||||||
\(274\) | −4.84080e37 | −0.793933 | ||||||||
\(275\) | −1.30761e37 | −0.202685 | ||||||||
\(276\) | −5.54838e37 | −0.812971 | ||||||||
\(277\) | 8.82814e37 | 1.22302 | 0.611509 | − | 0.791238i | \(-0.290563\pi\) | ||||
0.611509 | + | 0.791238i | \(0.290563\pi\) | |||||||
\(278\) | −1.78120e37 | −0.233356 | ||||||||
\(279\) | −2.56876e37 | −0.318316 | ||||||||
\(280\) | −1.85627e37 | −0.217616 | ||||||||
\(281\) | −2.56349e36 | −0.0284370 | −0.0142185 | − | 0.999899i | \(-0.504526\pi\) | ||||
−0.0142185 | + | 0.999899i | \(0.504526\pi\) | |||||||
\(282\) | 1.13191e38 | 1.18836 | ||||||||
\(283\) | −1.16177e38 | −1.15460 | −0.577298 | − | 0.816533i | \(-0.695893\pi\) | ||||
−0.577298 | + | 0.816533i | \(0.695893\pi\) | |||||||
\(284\) | −7.26858e37 | −0.683936 | ||||||||
\(285\) | −7.48929e37 | −0.667337 | ||||||||
\(286\) | 5.15742e37 | 0.435270 | ||||||||
\(287\) | −1.14889e38 | −0.918562 | ||||||||
\(288\) | 6.81841e36 | 0.0516535 | ||||||||
\(289\) | 2.13874e38 | 1.53547 | ||||||||
\(290\) | −6.20136e37 | −0.422005 | ||||||||
\(291\) | 6.25488e37 | 0.403532 | ||||||||
\(292\) | −6.31913e37 | −0.386566 | ||||||||
\(293\) | −1.14934e38 | −0.666805 | −0.333402 | − | 0.942785i | \(-0.608197\pi\) | ||||
−0.333402 | + | 0.942785i | \(0.608197\pi\) | |||||||
\(294\) | −9.66701e37 | −0.531996 | ||||||||
\(295\) | 6.45661e37 | 0.337103 | ||||||||
\(296\) | −5.39530e37 | −0.267297 | ||||||||
\(297\) | 2.34316e38 | 1.10173 | ||||||||
\(298\) | 1.19036e38 | 0.531285 | ||||||||
\(299\) | −2.77035e38 | −1.17390 | ||||||||
\(300\) | 2.09091e37 | 0.0841311 | ||||||||
\(301\) | 2.13189e37 | 0.0814673 | ||||||||
\(302\) | −1.98449e38 | −0.720347 | ||||||||
\(303\) | 1.16283e38 | 0.401009 | ||||||||
\(304\) | −1.35318e38 | −0.443418 | ||||||||
\(305\) | −7.77913e37 | −0.242261 | ||||||||
\(306\) | −1.11140e38 | −0.328995 | ||||||||
\(307\) | 1.02249e38 | 0.287749 | 0.143874 | − | 0.989596i | \(-0.454044\pi\) | ||||
0.143874 | + | 0.989596i | \(0.454044\pi\) | |||||||
\(308\) | −2.60626e38 | −0.697400 | ||||||||
\(309\) | −1.97482e38 | −0.502540 | ||||||||
\(310\) | −1.42328e38 | −0.344496 | ||||||||
\(311\) | 5.49215e38 | 1.26461 | 0.632305 | − | 0.774720i | \(-0.282109\pi\) | ||||
0.632305 | + | 0.774720i | \(0.282109\pi\) | |||||||
\(312\) | −8.24688e37 | −0.180673 | ||||||||
\(313\) | 3.18159e38 | 0.663294 | 0.331647 | − | 0.943403i | \(-0.392396\pi\) | ||||
0.331647 | + | 0.943403i | \(0.392396\pi\) | |||||||
\(314\) | −7.25667e37 | −0.143989 | ||||||||
\(315\) | −9.52191e37 | −0.179850 | ||||||||
\(316\) | −2.29102e38 | −0.411982 | ||||||||
\(317\) | 4.84708e38 | 0.829968 | 0.414984 | − | 0.909829i | \(-0.363787\pi\) | ||||
0.414984 | + | 0.909829i | \(0.363787\pi\) | |||||||
\(318\) | −1.44357e37 | −0.0235405 | ||||||||
\(319\) | −8.70693e38 | −1.35241 | ||||||||
\(320\) | 3.77789e37 | 0.0559017 | ||||||||
\(321\) | 7.11266e38 | 1.00278 | ||||||||
\(322\) | 1.39997e39 | 1.88085 | ||||||||
\(323\) | 2.20568e39 | 2.82425 | ||||||||
\(324\) | −2.54979e38 | −0.311212 | ||||||||
\(325\) | 1.04401e38 | 0.121482 | ||||||||
\(326\) | 4.12760e38 | 0.457957 | ||||||||
\(327\) | 2.35497e38 | 0.249170 | ||||||||
\(328\) | 2.33823e38 | 0.235962 | ||||||||
\(329\) | −2.85604e39 | −2.74934 | ||||||||
\(330\) | 2.93572e38 | 0.269617 | ||||||||
\(331\) | 1.17621e39 | 1.03074 | 0.515371 | − | 0.856967i | \(-0.327654\pi\) | ||||
0.515371 | + | 0.856967i | \(0.327654\pi\) | |||||||
\(332\) | −1.14501e38 | −0.0957564 | ||||||||
\(333\) | −2.76758e38 | −0.220909 | ||||||||
\(334\) | 5.30817e38 | 0.404459 | ||||||||
\(335\) | 7.87912e38 | 0.573170 | ||||||||
\(336\) | 4.16750e38 | 0.289479 | ||||||||
\(337\) | 3.32696e38 | 0.220690 | 0.110345 | − | 0.993893i | \(-0.464804\pi\) | ||||
0.110345 | + | 0.993893i | \(0.464804\pi\) | |||||||
\(338\) | 7.04303e38 | 0.446221 | ||||||||
\(339\) | −3.58007e38 | −0.216669 | ||||||||
\(340\) | −6.15797e38 | −0.356053 | ||||||||
\(341\) | −1.99834e39 | −1.10402 | ||||||||
\(342\) | −6.94126e38 | −0.366466 | ||||||||
\(343\) | −2.88397e38 | −0.145523 | ||||||||
\(344\) | −4.33884e37 | −0.0209275 | ||||||||
\(345\) | −1.57694e39 | −0.727143 | ||||||||
\(346\) | −2.73015e39 | −1.20367 | ||||||||
\(347\) | −2.52708e39 | −1.06540 | −0.532700 | − | 0.846304i | \(-0.678823\pi\) | ||||
−0.532700 | + | 0.846304i | \(0.678823\pi\) | |||||||
\(348\) | 1.39227e39 | 0.561364 | ||||||||
\(349\) | −2.89784e39 | −1.11758 | −0.558792 | − | 0.829308i | \(-0.688735\pi\) | ||||
−0.558792 | + | 0.829308i | \(0.688735\pi\) | |||||||
\(350\) | −5.27582e38 | −0.194642 | ||||||||
\(351\) | −1.87080e39 | −0.660339 | ||||||||
\(352\) | 5.30430e38 | 0.179150 | ||||||||
\(353\) | 4.87022e39 | 1.57413 | 0.787065 | − | 0.616871i | \(-0.211600\pi\) | ||||
0.787065 | + | 0.616871i | \(0.211600\pi\) | |||||||
\(354\) | −1.44957e39 | −0.448425 | ||||||||
\(355\) | −2.06585e39 | −0.611731 | ||||||||
\(356\) | −5.44688e38 | −0.154409 | ||||||||
\(357\) | −6.79303e39 | −1.84377 | ||||||||
\(358\) | 3.93101e39 | 1.02169 | ||||||||
\(359\) | −4.94989e39 | −1.23206 | −0.616030 | − | 0.787723i | \(-0.711260\pi\) | ||||
−0.616030 | + | 0.787723i | \(0.711260\pi\) | |||||||
\(360\) | 1.93791e38 | 0.0462003 | ||||||||
\(361\) | 9.39669e39 | 2.14592 | ||||||||
\(362\) | 3.02350e39 | 0.661497 | ||||||||
\(363\) | 1.08481e38 | 0.0227406 | ||||||||
\(364\) | 2.08087e39 | 0.417997 | ||||||||
\(365\) | −1.79601e39 | −0.345755 | ||||||||
\(366\) | 1.74649e39 | 0.322263 | ||||||||
\(367\) | 2.60673e39 | 0.461076 | 0.230538 | − | 0.973063i | \(-0.425951\pi\) | ||||
0.230538 | + | 0.973063i | \(0.425951\pi\) | |||||||
\(368\) | −2.84925e39 | −0.483157 | ||||||||
\(369\) | 1.19942e39 | 0.195013 | ||||||||
\(370\) | −1.53344e39 | −0.239078 | ||||||||
\(371\) | 3.64243e38 | 0.0544622 | ||||||||
\(372\) | 3.19541e39 | 0.458258 | ||||||||
\(373\) | 5.14959e39 | 0.708412 | 0.354206 | − | 0.935167i | \(-0.384751\pi\) | ||||
0.354206 | + | 0.935167i | \(0.384751\pi\) | |||||||
\(374\) | −8.64601e39 | −1.14105 | ||||||||
\(375\) | 5.94273e38 | 0.0752491 | ||||||||
\(376\) | 5.81265e39 | 0.706257 | ||||||||
\(377\) | 6.95170e39 | 0.810588 | ||||||||
\(378\) | 9.45395e39 | 1.05801 | ||||||||
\(379\) | −1.10887e40 | −1.19117 | −0.595584 | − | 0.803293i | \(-0.703079\pi\) | ||||
−0.595584 | + | 0.803293i | \(0.703079\pi\) | |||||||
\(380\) | −3.84596e39 | −0.396605 | ||||||||
\(381\) | −1.63102e40 | −1.61481 | ||||||||
\(382\) | −3.01747e39 | −0.286854 | ||||||||
\(383\) | 1.77078e39 | 0.161653 | 0.0808266 | − | 0.996728i | \(-0.474244\pi\) | ||||
0.0808266 | + | 0.996728i | \(0.474244\pi\) | |||||||
\(384\) | −8.48175e38 | −0.0743621 | ||||||||
\(385\) | −7.40744e39 | −0.623774 | ||||||||
\(386\) | 1.33413e40 | 1.07918 | ||||||||
\(387\) | −2.22565e38 | −0.0172957 | ||||||||
\(388\) | 3.21205e39 | 0.239823 | ||||||||
\(389\) | 1.78976e40 | 1.28403 | 0.642015 | − | 0.766692i | \(-0.278099\pi\) | ||||
0.642015 | + | 0.766692i | \(0.278099\pi\) | |||||||
\(390\) | −2.34391e39 | −0.161599 | ||||||||
\(391\) | 4.64427e40 | 3.07736 | ||||||||
\(392\) | −4.96428e39 | −0.316171 | ||||||||
\(393\) | 1.50251e40 | 0.919885 | ||||||||
\(394\) | −6.47287e39 | −0.380983 | ||||||||
\(395\) | −6.51146e39 | −0.368488 | ||||||||
\(396\) | 2.72089e39 | 0.148060 | ||||||||
\(397\) | 1.42952e40 | 0.748063 | 0.374032 | − | 0.927416i | \(-0.377975\pi\) | ||||
0.374032 | + | 0.927416i | \(0.377975\pi\) | |||||||
\(398\) | −1.46235e40 | −0.735976 | ||||||||
\(399\) | −4.24258e40 | −2.05376 | ||||||||
\(400\) | 1.07374e39 | 0.0500000 | ||||||||
\(401\) | 1.59146e38 | 0.00712948 | 0.00356474 | − | 0.999994i | \(-0.498865\pi\) | ||||
0.00356474 | + | 0.999994i | \(0.498865\pi\) | |||||||
\(402\) | −1.76894e40 | −0.762447 | ||||||||
\(403\) | 1.59549e40 | 0.661708 | ||||||||
\(404\) | 5.97144e39 | 0.238324 | ||||||||
\(405\) | −7.24694e39 | −0.278357 | ||||||||
\(406\) | −3.51299e40 | −1.29874 | ||||||||
\(407\) | −2.15300e40 | −0.766180 | ||||||||
\(408\) | 1.38253e40 | 0.473632 | ||||||||
\(409\) | 6.33912e39 | 0.209083 | 0.104541 | − | 0.994521i | \(-0.466663\pi\) | ||||
0.104541 | + | 0.994521i | \(0.466663\pi\) | |||||||
\(410\) | 6.64565e39 | 0.211051 | ||||||||
\(411\) | 3.08890e40 | 0.944616 | ||||||||
\(412\) | −1.01412e40 | −0.298665 | ||||||||
\(413\) | 3.65759e40 | 1.03745 | ||||||||
\(414\) | −1.46155e40 | −0.399308 | ||||||||
\(415\) | −3.25431e39 | −0.0856472 | ||||||||
\(416\) | −4.23501e39 | −0.107376 | ||||||||
\(417\) | 1.13658e40 | 0.277646 | ||||||||
\(418\) | −5.39986e40 | −1.27101 | ||||||||
\(419\) | −9.89389e39 | −0.224414 | −0.112207 | − | 0.993685i | \(-0.535792\pi\) | ||||
−0.112207 | + | 0.993685i | \(0.535792\pi\) | |||||||
\(420\) | 1.18448e40 | 0.258918 | ||||||||
\(421\) | −4.00753e40 | −0.844315 | −0.422157 | − | 0.906523i | \(-0.638727\pi\) | ||||
−0.422157 | + | 0.906523i | \(0.638727\pi\) | |||||||
\(422\) | −1.04008e40 | −0.211214 | ||||||||
\(423\) | 2.98166e40 | 0.583690 | ||||||||
\(424\) | −7.41311e38 | −0.0139904 | ||||||||
\(425\) | −1.75020e40 | −0.318463 | ||||||||
\(426\) | 4.63805e40 | 0.813742 | ||||||||
\(427\) | −4.40678e40 | −0.745571 | ||||||||
\(428\) | 3.65255e40 | 0.595961 | ||||||||
\(429\) | −3.29093e40 | −0.517881 | ||||||||
\(430\) | −1.23317e39 | −0.0187181 | ||||||||
\(431\) | −1.32321e41 | −1.93745 | −0.968725 | − | 0.248136i | \(-0.920182\pi\) | ||||
−0.968725 | + | 0.248136i | \(0.920182\pi\) | |||||||
\(432\) | −1.92408e40 | −0.271785 | ||||||||
\(433\) | −7.69902e40 | −1.04924 | −0.524618 | − | 0.851338i | \(-0.675792\pi\) | ||||
−0.524618 | + | 0.851338i | \(0.675792\pi\) | |||||||
\(434\) | −8.06270e40 | −1.06020 | ||||||||
\(435\) | 3.95706e40 | 0.502099 | ||||||||
\(436\) | 1.20934e40 | 0.148085 | ||||||||
\(437\) | 2.90058e41 | 3.42785 | ||||||||
\(438\) | 4.03221e40 | 0.459933 | ||||||||
\(439\) | −6.36959e40 | −0.701313 | −0.350656 | − | 0.936504i | \(-0.614041\pi\) | ||||
−0.350656 | + | 0.936504i | \(0.614041\pi\) | |||||||
\(440\) | 1.50757e40 | 0.160237 | ||||||||
\(441\) | −2.54648e40 | −0.261301 | ||||||||
\(442\) | 6.90306e40 | 0.683906 | ||||||||
\(443\) | 6.37157e39 | 0.0609521 | 0.0304761 | − | 0.999535i | \(-0.490298\pi\) | ||||
0.0304761 | + | 0.999535i | \(0.490298\pi\) | |||||||
\(444\) | 3.44272e40 | 0.318028 | ||||||||
\(445\) | −1.54810e40 | −0.138108 | ||||||||
\(446\) | −3.87840e40 | −0.334166 | ||||||||
\(447\) | −7.59565e40 | −0.632119 | ||||||||
\(448\) | 2.14013e40 | 0.172040 | ||||||||
\(449\) | −1.42862e41 | −1.10943 | −0.554715 | − | 0.832040i | \(-0.687173\pi\) | ||||
−0.554715 | + | 0.832040i | \(0.687173\pi\) | |||||||
\(450\) | 5.50787e39 | 0.0413228 | ||||||||
\(451\) | 9.33074e40 | 0.676362 | ||||||||
\(452\) | −1.83847e40 | −0.128769 | ||||||||
\(453\) | 1.26630e41 | 0.857064 | ||||||||
\(454\) | −5.66918e38 | −0.00370812 | ||||||||
\(455\) | 5.91418e40 | 0.373868 | ||||||||
\(456\) | 8.63456e40 | 0.527576 | ||||||||
\(457\) | −5.32708e40 | −0.314621 | −0.157311 | − | 0.987549i | \(-0.550282\pi\) | ||||
−0.157311 | + | 0.987549i | \(0.550282\pi\) | |||||||
\(458\) | 5.14895e40 | 0.293970 | ||||||||
\(459\) | 3.13625e41 | 1.73107 | ||||||||
\(460\) | −8.09804e40 | −0.432149 | ||||||||
\(461\) | −1.55667e41 | −0.803214 | −0.401607 | − | 0.915812i | \(-0.631548\pi\) | ||||
−0.401607 | + | 0.915812i | \(0.631548\pi\) | |||||||
\(462\) | 1.66305e41 | 0.829762 | ||||||||
\(463\) | −2.90324e41 | −1.40080 | −0.700401 | − | 0.713749i | \(-0.746996\pi\) | ||||
−0.700401 | + | 0.713749i | \(0.746996\pi\) | |||||||
\(464\) | 7.14968e40 | 0.333625 | ||||||||
\(465\) | 9.08189e40 | 0.409879 | ||||||||
\(466\) | 2.08996e41 | 0.912340 | ||||||||
\(467\) | −1.49482e41 | −0.631216 | −0.315608 | − | 0.948890i | \(-0.602209\pi\) | ||||
−0.315608 | + | 0.948890i | \(0.602209\pi\) | |||||||
\(468\) | −2.17239e40 | −0.0887416 | ||||||||
\(469\) | 4.46342e41 | 1.76396 | ||||||||
\(470\) | 1.65205e41 | 0.631695 | ||||||||
\(471\) | 4.63045e40 | 0.171317 | ||||||||
\(472\) | −7.44396e40 | −0.266504 | ||||||||
\(473\) | −1.73142e40 | −0.0599866 | ||||||||
\(474\) | 1.46189e41 | 0.490174 | ||||||||
\(475\) | −1.09309e41 | −0.354735 | ||||||||
\(476\) | −3.48841e41 | −1.09577 | ||||||||
\(477\) | −3.80263e39 | −0.0115624 | ||||||||
\(478\) | −9.98509e40 | −0.293913 | ||||||||
\(479\) | 9.00830e40 | 0.256710 | 0.128355 | − | 0.991728i | \(-0.459030\pi\) | ||||
0.128355 | + | 0.991728i | \(0.459030\pi\) | |||||||
\(480\) | −2.41066e40 | −0.0665114 | ||||||||
\(481\) | 1.71898e41 | 0.459221 | ||||||||
\(482\) | −3.97472e40 | −0.102820 | ||||||||
\(483\) | −8.93318e41 | −2.23782 | ||||||||
\(484\) | 5.57081e39 | 0.0135150 | ||||||||
\(485\) | 9.12921e40 | 0.214504 | ||||||||
\(486\) | −1.75077e41 | −0.398445 | ||||||||
\(487\) | 2.08879e41 | 0.460463 | 0.230232 | − | 0.973136i | \(-0.426052\pi\) | ||||
0.230232 | + | 0.973136i | \(0.426052\pi\) | |||||||
\(488\) | 8.96873e40 | 0.191524 | ||||||||
\(489\) | −2.63380e41 | −0.544874 | ||||||||
\(490\) | −1.41093e41 | −0.282792 | ||||||||
\(491\) | 5.18801e41 | 1.00748 | 0.503742 | − | 0.863854i | \(-0.331956\pi\) | ||||
0.503742 | + | 0.863854i | \(0.331956\pi\) | |||||||
\(492\) | −1.49202e41 | −0.280747 | ||||||||
\(493\) | −1.16540e42 | −2.12494 | ||||||||
\(494\) | 4.31130e41 | 0.761800 | ||||||||
\(495\) | 7.73325e40 | 0.132428 | ||||||||
\(496\) | 1.64093e41 | 0.272348 | ||||||||
\(497\) | −1.17028e42 | −1.88263 | ||||||||
\(498\) | 7.30624e40 | 0.113930 | ||||||||
\(499\) | −3.17894e41 | −0.480534 | −0.240267 | − | 0.970707i | \(-0.577235\pi\) | ||||
−0.240267 | + | 0.970707i | \(0.577235\pi\) | |||||||
\(500\) | 3.05176e40 | 0.0447214 | ||||||||
\(501\) | −3.38712e41 | −0.481223 | ||||||||
\(502\) | 1.71465e41 | 0.236193 | ||||||||
\(503\) | −2.67214e39 | −0.00356908 | −0.00178454 | − | 0.999998i | \(-0.500568\pi\) | ||||
−0.00178454 | + | 0.999998i | \(0.500568\pi\) | |||||||
\(504\) | 1.09780e41 | 0.142184 | ||||||||
\(505\) | 1.69719e41 | 0.213164 | ||||||||
\(506\) | −1.13699e42 | −1.38492 | ||||||||
\(507\) | −4.49413e41 | −0.530911 | ||||||||
\(508\) | −8.37575e41 | −0.959701 | ||||||||
\(509\) | 1.25901e42 | 1.39928 | 0.699638 | − | 0.714498i | \(-0.253345\pi\) | ||||
0.699638 | + | 0.714498i | \(0.253345\pi\) | |||||||
\(510\) | 3.92938e41 | 0.423629 | ||||||||
\(511\) | −1.01741e42 | −1.06408 | ||||||||
\(512\) | −4.35561e40 | −0.0441942 | ||||||||
\(513\) | 1.95874e42 | 1.92823 | ||||||||
\(514\) | 9.04845e40 | 0.0864263 | ||||||||
\(515\) | −2.88231e41 | −0.267134 | ||||||||
\(516\) | 2.76860e40 | 0.0248994 | ||||||||
\(517\) | 2.31954e42 | 2.02441 | ||||||||
\(518\) | −8.68672e41 | −0.735774 | ||||||||
\(519\) | 1.74210e42 | 1.43212 | ||||||||
\(520\) | −1.20366e41 | −0.0960400 | ||||||||
\(521\) | 1.93165e42 | 1.49604 | 0.748020 | − | 0.663676i | \(-0.231005\pi\) | ||||
0.748020 | + | 0.663676i | \(0.231005\pi\) | |||||||
\(522\) | 3.66750e41 | 0.275726 | ||||||||
\(523\) | 5.98151e41 | 0.436551 | 0.218275 | − | 0.975887i | \(-0.429957\pi\) | ||||
0.218275 | + | 0.975887i | \(0.429957\pi\) | |||||||
\(524\) | 7.71582e41 | 0.546698 | ||||||||
\(525\) | 3.36648e41 | 0.231583 | ||||||||
\(526\) | −8.15376e41 | −0.544602 | ||||||||
\(527\) | −2.67472e42 | −1.73466 | ||||||||
\(528\) | −3.38465e41 | −0.213151 | ||||||||
\(529\) | 4.47228e42 | 2.73506 | ||||||||
\(530\) | −2.10693e40 | −0.0125134 | ||||||||
\(531\) | −3.81846e41 | −0.220254 | ||||||||
\(532\) | −2.17869e42 | −1.22057 | ||||||||
\(533\) | −7.44976e41 | −0.405387 | ||||||||
\(534\) | 3.47563e41 | 0.183715 | ||||||||
\(535\) | 1.03812e42 | 0.533043 | ||||||||
\(536\) | −9.08401e41 | −0.453131 | ||||||||
\(537\) | −2.50836e42 | −1.21560 | ||||||||
\(538\) | 2.83640e42 | 1.33549 | ||||||||
\(539\) | −1.98100e42 | −0.906272 | ||||||||
\(540\) | −5.46856e41 | −0.243092 | ||||||||
\(541\) | 9.64612e41 | 0.416673 | 0.208336 | − | 0.978057i | \(-0.433195\pi\) | ||||
0.208336 | + | 0.978057i | \(0.433195\pi\) | |||||||
\(542\) | 2.30904e41 | 0.0969266 | ||||||||
\(543\) | −1.92928e42 | −0.787044 | ||||||||
\(544\) | 7.09966e41 | 0.281484 | ||||||||
\(545\) | 3.43717e41 | 0.132451 | ||||||||
\(546\) | −1.32779e42 | −0.497330 | ||||||||
\(547\) | 4.34799e42 | 1.58302 | 0.791508 | − | 0.611159i | \(-0.209297\pi\) | ||||
0.791508 | + | 0.611159i | \(0.209297\pi\) | |||||||
\(548\) | 1.58623e42 | 0.561395 | ||||||||
\(549\) | 4.60060e41 | 0.158286 | ||||||||
\(550\) | 4.28478e41 | 0.143320 | ||||||||
\(551\) | −7.27849e42 | −2.36696 | ||||||||
\(552\) | 1.81809e42 | 0.574857 | ||||||||
\(553\) | −3.68866e42 | −1.13404 | ||||||||
\(554\) | −2.89280e42 | −0.864804 | ||||||||
\(555\) | 9.78479e41 | 0.284453 | ||||||||
\(556\) | 5.83665e41 | 0.165008 | ||||||||
\(557\) | 4.75748e42 | 1.30804 | 0.654021 | − | 0.756476i | \(-0.273081\pi\) | ||||
0.654021 | + | 0.756476i | \(0.273081\pi\) | |||||||
\(558\) | 8.41732e41 | 0.225084 | ||||||||
\(559\) | 1.38238e41 | 0.0359538 | ||||||||
\(560\) | 6.08261e41 | 0.153878 | ||||||||
\(561\) | 5.51698e42 | 1.35762 | ||||||||
\(562\) | 8.40004e40 | 0.0201080 | ||||||||
\(563\) | −7.57947e42 | −1.76506 | −0.882529 | − | 0.470259i | \(-0.844161\pi\) | ||||
−0.882529 | + | 0.470259i | \(0.844161\pi\) | |||||||
\(564\) | −3.70903e42 | −0.840299 | ||||||||
\(565\) | −5.22523e41 | −0.115174 | ||||||||
\(566\) | 3.80689e42 | 0.816423 | ||||||||
\(567\) | −4.10530e42 | −0.856658 | ||||||||
\(568\) | 2.38177e42 | 0.483615 | ||||||||
\(569\) | −1.13132e41 | −0.0223536 | −0.0111768 | − | 0.999938i | \(-0.503558\pi\) | ||||
−0.0111768 | + | 0.999938i | \(0.503558\pi\) | |||||||
\(570\) | 2.45409e42 | 0.471878 | ||||||||
\(571\) | −3.31794e41 | −0.0620882 | −0.0310441 | − | 0.999518i | \(-0.509883\pi\) | ||||
−0.0310441 | + | 0.999518i | \(0.509883\pi\) | |||||||
\(572\) | −1.68998e42 | −0.307782 | ||||||||
\(573\) | 1.92544e42 | 0.341297 | ||||||||
\(574\) | 3.76468e42 | 0.649522 | ||||||||
\(575\) | −2.30160e42 | −0.386526 | ||||||||
\(576\) | −2.23426e41 | −0.0365245 | ||||||||
\(577\) | −1.34557e40 | −0.00214131 | −0.00107066 | − | 0.999999i | \(-0.500341\pi\) | ||||
−0.00107066 | + | 0.999999i | \(0.500341\pi\) | |||||||
\(578\) | −7.00823e42 | −1.08574 | ||||||||
\(579\) | −8.51304e42 | −1.28401 | ||||||||
\(580\) | 2.03206e42 | 0.298403 | ||||||||
\(581\) | −1.84352e42 | −0.263584 | ||||||||
\(582\) | −2.04960e42 | −0.285340 | ||||||||
\(583\) | −2.95821e41 | −0.0401020 | ||||||||
\(584\) | 2.07065e42 | 0.273343 | ||||||||
\(585\) | −6.17430e41 | −0.0793729 | ||||||||
\(586\) | 3.76614e42 | 0.471502 | ||||||||
\(587\) | 1.52213e42 | 0.185593 | 0.0927965 | − | 0.995685i | \(-0.470419\pi\) | ||||
0.0927965 | + | 0.995685i | \(0.470419\pi\) | |||||||
\(588\) | 3.16769e42 | 0.376178 | ||||||||
\(589\) | −1.67049e43 | −1.93223 | ||||||||
\(590\) | −2.11570e42 | −0.238368 | ||||||||
\(591\) | 4.13031e42 | 0.453290 | ||||||||
\(592\) | 1.76793e42 | 0.189008 | ||||||||
\(593\) | 1.84601e42 | 0.192259 | 0.0961296 | − | 0.995369i | \(-0.469354\pi\) | ||||
0.0961296 | + | 0.995369i | \(0.469354\pi\) | |||||||
\(594\) | −7.67806e42 | −0.779043 | ||||||||
\(595\) | −9.91466e42 | −0.980088 | ||||||||
\(596\) | −3.90058e42 | −0.375675 | ||||||||
\(597\) | 9.33119e42 | 0.875659 | ||||||||
\(598\) | 9.07788e42 | 0.830072 | ||||||||
\(599\) | −9.39650e41 | −0.0837241 | −0.0418620 | − | 0.999123i | \(-0.513329\pi\) | ||||
−0.0418620 | + | 0.999123i | \(0.513329\pi\) | |||||||
\(600\) | −6.85150e41 | −0.0594896 | ||||||||
\(601\) | 1.58484e43 | 1.34101 | 0.670505 | − | 0.741905i | \(-0.266077\pi\) | ||||
0.670505 | + | 0.741905i | \(0.266077\pi\) | |||||||
\(602\) | −6.98576e41 | −0.0576061 | ||||||||
\(603\) | −4.65974e42 | −0.374492 | ||||||||
\(604\) | 6.50278e42 | 0.509362 | ||||||||
\(605\) | 1.58332e41 | 0.0120882 | ||||||||
\(606\) | −3.81035e42 | −0.283556 | ||||||||
\(607\) | 1.95801e43 | 1.42033 | 0.710167 | − | 0.704034i | \(-0.248620\pi\) | ||||
0.710167 | + | 0.704034i | \(0.248620\pi\) | |||||||
\(608\) | 4.43409e42 | 0.313544 | ||||||||
\(609\) | 2.24163e43 | 1.54524 | ||||||||
\(610\) | 2.54907e42 | 0.171304 | ||||||||
\(611\) | −1.85195e43 | −1.21336 | ||||||||
\(612\) | 3.64184e42 | 0.232635 | ||||||||
\(613\) | 1.98433e43 | 1.23588 | 0.617939 | − | 0.786226i | \(-0.287968\pi\) | ||||
0.617939 | + | 0.786226i | \(0.287968\pi\) | |||||||
\(614\) | −3.35049e42 | −0.203469 | ||||||||
\(615\) | −4.24056e42 | −0.251107 | ||||||||
\(616\) | 8.54020e42 | 0.493136 | ||||||||
\(617\) | −2.01865e43 | −1.13669 | −0.568344 | − | 0.822791i | \(-0.692416\pi\) | ||||
−0.568344 | + | 0.822791i | \(0.692416\pi\) | |||||||
\(618\) | 6.47108e42 | 0.355349 | ||||||||
\(619\) | −1.28098e43 | −0.686020 | −0.343010 | − | 0.939332i | \(-0.611447\pi\) | ||||
−0.343010 | + | 0.939332i | \(0.611447\pi\) | |||||||
\(620\) | 4.66380e42 | 0.243595 | ||||||||
\(621\) | 4.12433e43 | 2.10104 | ||||||||
\(622\) | −1.79967e43 | −0.894214 | ||||||||
\(623\) | −8.76977e42 | −0.425034 | ||||||||
\(624\) | 2.70234e42 | 0.127755 | ||||||||
\(625\) | 8.67362e41 | 0.0400000 | ||||||||
\(626\) | −1.04254e43 | −0.469020 | ||||||||
\(627\) | 3.44563e43 | 1.51224 | ||||||||
\(628\) | 2.37787e42 | 0.101815 | ||||||||
\(629\) | −2.88173e43 | −1.20384 | ||||||||
\(630\) | 3.12014e42 | 0.127173 | ||||||||
\(631\) | −9.11677e42 | −0.362565 | −0.181283 | − | 0.983431i | \(-0.558025\pi\) | ||||
−0.181283 | + | 0.983431i | \(0.558025\pi\) | |||||||
\(632\) | 7.50720e42 | 0.291315 | ||||||||
\(633\) | 6.63668e42 | 0.251300 | ||||||||
\(634\) | −1.58829e43 | −0.586876 | ||||||||
\(635\) | −2.38053e43 | −0.858383 | ||||||||
\(636\) | 4.73028e41 | 0.0166457 | ||||||||
\(637\) | 1.58165e43 | 0.543187 | ||||||||
\(638\) | 2.85309e43 | 0.956301 | ||||||||
\(639\) | 1.22175e43 | 0.399687 | ||||||||
\(640\) | −1.23794e42 | −0.0395285 | ||||||||
\(641\) | −7.56603e42 | −0.235813 | −0.117907 | − | 0.993025i | \(-0.537618\pi\) | ||||
−0.117907 | + | 0.993025i | \(0.537618\pi\) | |||||||
\(642\) | −2.33068e43 | −0.709070 | ||||||||
\(643\) | 5.52599e43 | 1.64112 | 0.820559 | − | 0.571561i | \(-0.193662\pi\) | ||||
0.820559 | + | 0.571561i | \(0.193662\pi\) | |||||||
\(644\) | −4.58744e43 | −1.32996 | ||||||||
\(645\) | 7.86882e41 | 0.0222707 | ||||||||
\(646\) | −7.22757e43 | −1.99705 | ||||||||
\(647\) | −5.65084e43 | −1.52439 | −0.762197 | − | 0.647346i | \(-0.775879\pi\) | ||||
−0.762197 | + | 0.647346i | \(0.775879\pi\) | |||||||
\(648\) | 8.35516e42 | 0.220060 | ||||||||
\(649\) | −2.97052e43 | −0.763905 | ||||||||
\(650\) | −3.42101e42 | −0.0859008 | ||||||||
\(651\) | 5.14477e43 | 1.26142 | ||||||||
\(652\) | −1.35253e43 | −0.323824 | ||||||||
\(653\) | −9.93457e42 | −0.232271 | −0.116135 | − | 0.993233i | \(-0.537051\pi\) | ||||
−0.116135 | + | 0.993233i | \(0.537051\pi\) | |||||||
\(654\) | −7.71678e42 | −0.176190 | ||||||||
\(655\) | 2.19297e43 | 0.488981 | ||||||||
\(656\) | −7.66192e42 | −0.166851 | ||||||||
\(657\) | 1.06216e43 | 0.225906 | ||||||||
\(658\) | 9.35868e43 | 1.94408 | ||||||||
\(659\) | −2.37067e43 | −0.481003 | −0.240501 | − | 0.970649i | \(-0.577312\pi\) | ||||
−0.240501 | + | 0.970649i | \(0.577312\pi\) | |||||||
\(660\) | −9.61975e42 | −0.190648 | ||||||||
\(661\) | 3.30974e43 | 0.640725 | 0.320363 | − | 0.947295i | \(-0.396195\pi\) | ||||
0.320363 | + | 0.947295i | \(0.396195\pi\) | |||||||
\(662\) | −3.85420e43 | −0.728845 | ||||||||
\(663\) | −4.40482e43 | −0.813707 | ||||||||
\(664\) | 3.75196e42 | 0.0677100 | ||||||||
\(665\) | −6.19220e43 | −1.09171 | ||||||||
\(666\) | 9.06879e42 | 0.156206 | ||||||||
\(667\) | −1.53256e44 | −2.57909 | ||||||||
\(668\) | −1.73938e43 | −0.285996 | ||||||||
\(669\) | 2.47479e43 | 0.397588 | ||||||||
\(670\) | −2.58183e43 | −0.405292 | ||||||||
\(671\) | 3.57898e43 | 0.548985 | ||||||||
\(672\) | −1.36561e43 | −0.204693 | ||||||||
\(673\) | 3.83414e43 | 0.561609 | 0.280805 | − | 0.959765i | \(-0.409399\pi\) | ||||
0.280805 | + | 0.959765i | \(0.409399\pi\) | |||||||
\(674\) | −1.09018e43 | −0.156052 | ||||||||
\(675\) | −1.55426e43 | −0.217428 | ||||||||
\(676\) | −2.30786e43 | −0.315526 | ||||||||
\(677\) | 1.18717e44 | 1.58631 | 0.793153 | − | 0.609022i | \(-0.208438\pi\) | ||||
0.793153 | + | 0.609022i | \(0.208438\pi\) | |||||||
\(678\) | 1.17312e43 | 0.153208 | ||||||||
\(679\) | 5.17158e43 | 0.660149 | ||||||||
\(680\) | 2.01784e43 | 0.251767 | ||||||||
\(681\) | 3.61748e41 | 0.00441190 | ||||||||
\(682\) | 6.54815e43 | 0.780658 | ||||||||
\(683\) | −1.22953e44 | −1.43291 | −0.716453 | − | 0.697635i | \(-0.754236\pi\) | ||||
−0.716453 | + | 0.697635i | \(0.754236\pi\) | |||||||
\(684\) | 2.27451e43 | 0.259130 | ||||||||
\(685\) | 4.50835e43 | 0.502127 | ||||||||
\(686\) | 9.45020e42 | 0.102900 | ||||||||
\(687\) | −3.28552e43 | −0.349764 | ||||||||
\(688\) | 1.42175e42 | 0.0147980 | ||||||||
\(689\) | 2.36187e42 | 0.0240357 | ||||||||
\(690\) | 5.16733e43 | 0.514168 | ||||||||
\(691\) | 1.32263e44 | 1.28686 | 0.643428 | − | 0.765507i | \(-0.277512\pi\) | ||||
0.643428 | + | 0.765507i | \(0.277512\pi\) | |||||||
\(692\) | 8.94617e43 | 0.851124 | ||||||||
\(693\) | 4.38079e43 | 0.407556 | ||||||||
\(694\) | 8.28075e43 | 0.753352 | ||||||||
\(695\) | 1.65888e43 | 0.147587 | ||||||||
\(696\) | −4.56218e43 | −0.396944 | ||||||||
\(697\) | 1.24889e44 | 1.06272 | ||||||||
\(698\) | 9.49564e43 | 0.790252 | ||||||||
\(699\) | −1.33360e44 | −1.08550 | ||||||||
\(700\) | 1.72878e43 | 0.137632 | ||||||||
\(701\) | 1.62662e44 | 1.26665 | 0.633325 | − | 0.773886i | \(-0.281690\pi\) | ||||
0.633325 | + | 0.773886i | \(0.281690\pi\) | |||||||
\(702\) | 6.13024e43 | 0.466930 | ||||||||
\(703\) | −1.79978e44 | −1.34095 | ||||||||
\(704\) | −1.73811e43 | −0.126678 | ||||||||
\(705\) | −1.05417e44 | −0.751586 | ||||||||
\(706\) | −1.59587e44 | −1.11308 | ||||||||
\(707\) | 9.61434e43 | 0.656022 | ||||||||
\(708\) | 4.74996e43 | 0.317084 | ||||||||
\(709\) | −2.46555e43 | −0.161027 | −0.0805133 | − | 0.996754i | \(-0.525656\pi\) | ||||
−0.0805133 | + | 0.996754i | \(0.525656\pi\) | |||||||
\(710\) | 6.76939e43 | 0.432559 | ||||||||
\(711\) | 3.85090e43 | 0.240759 | ||||||||
\(712\) | 1.78483e43 | 0.109184 | ||||||||
\(713\) | −3.51739e44 | −2.10539 | ||||||||
\(714\) | 2.22594e44 | 1.30374 | ||||||||
\(715\) | −4.80322e43 | −0.275289 | ||||||||
\(716\) | −1.28811e44 | −0.722442 | ||||||||
\(717\) | 6.37144e43 | 0.349696 | ||||||||
\(718\) | 1.62198e44 | 0.871198 | ||||||||
\(719\) | −1.33187e44 | −0.700108 | −0.350054 | − | 0.936729i | \(-0.613837\pi\) | ||||
−0.350054 | + | 0.936729i | \(0.613837\pi\) | |||||||
\(720\) | −6.35014e42 | −0.0326685 | ||||||||
\(721\) | −1.63279e44 | −0.822119 | ||||||||
\(722\) | −3.07911e44 | −1.51739 | ||||||||
\(723\) | 2.53625e43 | 0.122335 | ||||||||
\(724\) | −9.90742e43 | −0.467749 | ||||||||
\(725\) | 5.77547e43 | 0.266900 | ||||||||
\(726\) | −3.55471e42 | −0.0160800 | ||||||||
\(727\) | 3.69856e44 | 1.63775 | 0.818877 | − | 0.573969i | \(-0.194597\pi\) | ||||
0.818877 | + | 0.573969i | \(0.194597\pi\) | |||||||
\(728\) | −6.81858e43 | −0.295568 | ||||||||
\(729\) | 2.58394e44 | 1.09649 | ||||||||
\(730\) | 5.88515e43 | 0.244486 | ||||||||
\(731\) | −2.31746e43 | −0.0942523 | ||||||||
\(732\) | −5.72291e43 | −0.227874 | ||||||||
\(733\) | −2.48074e44 | −0.967095 | −0.483547 | − | 0.875318i | \(-0.660652\pi\) | ||||
−0.483547 | + | 0.875318i | \(0.660652\pi\) | |||||||
\(734\) | −8.54174e43 | −0.326030 | ||||||||
\(735\) | 9.00310e43 | 0.336464 | ||||||||
\(736\) | 9.33641e43 | 0.341644 | ||||||||
\(737\) | −3.62498e44 | −1.29885 | ||||||||
\(738\) | −3.93026e43 | −0.137895 | ||||||||
\(739\) | 7.67405e43 | 0.263655 | 0.131827 | − | 0.991273i | \(-0.457916\pi\) | ||||
0.131827 | + | 0.991273i | \(0.457916\pi\) | |||||||
\(740\) | 5.02476e43 | 0.169053 | ||||||||
\(741\) | −2.75103e44 | −0.906384 | ||||||||
\(742\) | −1.19355e43 | −0.0385106 | ||||||||
\(743\) | −5.47245e44 | −1.72924 | −0.864620 | − | 0.502427i | \(-0.832441\pi\) | ||||
−0.864620 | + | 0.502427i | \(0.832441\pi\) | |||||||
\(744\) | −1.04707e44 | −0.324038 | ||||||||
\(745\) | −1.10861e44 | −0.336014 | ||||||||
\(746\) | −1.68742e44 | −0.500923 | ||||||||
\(747\) | 1.92461e43 | 0.0559594 | ||||||||
\(748\) | 2.83313e44 | 0.806847 | ||||||||
\(749\) | 5.88080e44 | 1.64047 | ||||||||
\(750\) | −1.94731e43 | −0.0532092 | ||||||||
\(751\) | 4.53013e44 | 1.21253 | 0.606263 | − | 0.795264i | \(-0.292668\pi\) | ||||
0.606263 | + | 0.795264i | \(0.292668\pi\) | |||||||
\(752\) | −1.90469e44 | −0.499399 | ||||||||
\(753\) | −1.09411e44 | −0.281021 | ||||||||
\(754\) | −2.27793e44 | −0.573173 | ||||||||
\(755\) | 1.84820e44 | 0.455587 | ||||||||
\(756\) | −3.09787e44 | −0.748127 | ||||||||
\(757\) | −3.88934e44 | −0.920215 | −0.460108 | − | 0.887863i | \(-0.652189\pi\) | ||||
−0.460108 | + | 0.887863i | \(0.652189\pi\) | |||||||
\(758\) | 3.63354e44 | 0.842282 | ||||||||
\(759\) | 7.25511e44 | 1.64777 | ||||||||
\(760\) | 1.26024e44 | 0.280442 | ||||||||
\(761\) | −5.46740e44 | −1.19212 | −0.596058 | − | 0.802941i | \(-0.703267\pi\) | ||||
−0.596058 | + | 0.802941i | \(0.703267\pi\) | |||||||
\(762\) | 5.34453e44 | 1.14185 | ||||||||
\(763\) | 1.94711e44 | 0.407624 | ||||||||
\(764\) | 9.88765e43 | 0.202837 | ||||||||
\(765\) | 1.03507e44 | 0.208075 | ||||||||
\(766\) | −5.80250e43 | −0.114306 | ||||||||
\(767\) | 2.37169e44 | 0.457858 | ||||||||
\(768\) | 2.77930e43 | 0.0525819 | ||||||||
\(769\) | −8.57160e44 | −1.58929 | −0.794646 | − | 0.607073i | \(-0.792343\pi\) | ||||
−0.794646 | + | 0.607073i | \(0.792343\pi\) | |||||||
\(770\) | 2.42727e44 | 0.441075 | ||||||||
\(771\) | −5.77378e43 | −0.102829 | ||||||||
\(772\) | −4.37168e44 | −0.763098 | ||||||||
\(773\) | −2.48088e44 | −0.424447 | −0.212224 | − | 0.977221i | \(-0.568071\pi\) | ||||
−0.212224 | + | 0.977221i | \(0.568071\pi\) | |||||||
\(774\) | 7.29302e42 | 0.0122299 | ||||||||
\(775\) | 1.32553e44 | 0.217878 | ||||||||
\(776\) | −1.05253e44 | −0.169581 | ||||||||
\(777\) | 5.54296e44 | 0.875419 | ||||||||
\(778\) | −5.86467e44 | −0.907946 | ||||||||
\(779\) | 7.79996e44 | 1.18375 | ||||||||
\(780\) | 7.68051e43 | 0.114268 | ||||||||
\(781\) | 9.50447e44 | 1.38623 | ||||||||
\(782\) | −1.52184e45 | −2.17602 | ||||||||
\(783\) | −1.03493e45 | −1.45078 | ||||||||
\(784\) | 1.62669e44 | 0.223567 | ||||||||
\(785\) | 6.75830e43 | 0.0910664 | ||||||||
\(786\) | −4.92343e44 | −0.650457 | ||||||||
\(787\) | 7.42427e44 | 0.961713 | 0.480857 | − | 0.876799i | \(-0.340326\pi\) | ||||
0.480857 | + | 0.876799i | \(0.340326\pi\) | |||||||
\(788\) | 2.12103e44 | 0.269395 | ||||||||
\(789\) | 5.20288e44 | 0.647963 | ||||||||
\(790\) | 2.13368e44 | 0.260560 | ||||||||
\(791\) | −2.96003e44 | −0.354454 | ||||||||
\(792\) | −8.91583e43 | −0.104694 | ||||||||
\(793\) | −2.85749e44 | −0.329042 | ||||||||
\(794\) | −4.68426e44 | −0.528961 | ||||||||
\(795\) | 1.34443e43 | 0.0148883 | ||||||||
\(796\) | 4.79183e44 | 0.520413 | ||||||||
\(797\) | 6.95745e44 | 0.741047 | 0.370524 | − | 0.928823i | \(-0.379178\pi\) | ||||
0.370524 | + | 0.928823i | \(0.379178\pi\) | |||||||
\(798\) | 1.39021e45 | 1.45223 | ||||||||
\(799\) | 3.10465e45 | 3.18080 | ||||||||
\(800\) | −3.51844e43 | −0.0353553 | ||||||||
\(801\) | 9.15549e43 | 0.0902355 | ||||||||
\(802\) | −5.21489e42 | −0.00504130 | ||||||||
\(803\) | 8.26296e44 | 0.783510 | ||||||||
\(804\) | 5.79647e44 | 0.539132 | ||||||||
\(805\) | −1.30383e45 | −1.18955 | ||||||||
\(806\) | −5.22811e44 | −0.467898 | ||||||||
\(807\) | −1.80989e45 | −1.58896 | ||||||||
\(808\) | −1.95672e44 | −0.168521 | ||||||||
\(809\) | −5.39805e44 | −0.456073 | −0.228037 | − | 0.973653i | \(-0.573231\pi\) | ||||
−0.228037 | + | 0.973653i | \(0.573231\pi\) | |||||||
\(810\) | 2.37468e44 | 0.196828 | ||||||||
\(811\) | 6.12229e44 | 0.497841 | 0.248920 | − | 0.968524i | \(-0.419924\pi\) | ||||
0.248920 | + | 0.968524i | \(0.419924\pi\) | |||||||
\(812\) | 1.15114e45 | 0.918351 | ||||||||
\(813\) | −1.47339e44 | −0.115323 | ||||||||
\(814\) | 7.05495e44 | 0.541771 | ||||||||
\(815\) | −3.84412e44 | −0.289637 | ||||||||
\(816\) | −4.53026e44 | −0.334908 | ||||||||
\(817\) | −1.44737e44 | −0.104987 | ||||||||
\(818\) | −2.07720e44 | −0.147844 | ||||||||
\(819\) | −3.49766e44 | −0.244274 | ||||||||
\(820\) | −2.17765e44 | −0.149236 | ||||||||
\(821\) | 2.89962e44 | 0.194995 | 0.0974973 | − | 0.995236i | \(-0.468916\pi\) | ||||
0.0974973 | + | 0.995236i | \(0.468916\pi\) | |||||||
\(822\) | −1.01217e45 | −0.667944 | ||||||||
\(823\) | −9.30283e44 | −0.602445 | −0.301223 | − | 0.953554i | \(-0.597395\pi\) | ||||
−0.301223 | + | 0.953554i | \(0.597395\pi\) | |||||||
\(824\) | 3.32308e44 | 0.211188 | ||||||||
\(825\) | −2.73410e44 | −0.170521 | ||||||||
\(826\) | −1.19852e45 | −0.733590 | ||||||||
\(827\) | 4.60750e44 | 0.276777 | 0.138389 | − | 0.990378i | \(-0.455808\pi\) | ||||
0.138389 | + | 0.990378i | \(0.455808\pi\) | |||||||
\(828\) | 4.78921e44 | 0.282354 | ||||||||
\(829\) | −3.33913e45 | −1.93214 | −0.966069 | − | 0.258284i | \(-0.916843\pi\) | ||||
−0.966069 | + | 0.258284i | \(0.916843\pi\) | |||||||
\(830\) | 1.06637e44 | 0.0605617 | ||||||||
\(831\) | 1.84589e45 | 1.02894 | ||||||||
\(832\) | 1.38773e44 | 0.0759263 | ||||||||
\(833\) | −2.65151e45 | −1.42396 | ||||||||
\(834\) | −3.72434e44 | −0.196325 | ||||||||
\(835\) | −4.94362e44 | −0.255803 | ||||||||
\(836\) | 1.76943e45 | 0.898742 | ||||||||
\(837\) | −2.37527e45 | −1.18432 | ||||||||
\(838\) | 3.24203e44 | 0.158684 | ||||||||
\(839\) | −3.12484e45 | −1.50147 | −0.750737 | − | 0.660601i | \(-0.770302\pi\) | ||||
−0.750737 | + | 0.660601i | \(0.770302\pi\) | |||||||
\(840\) | −3.88129e44 | −0.183083 | ||||||||
\(841\) | 1.68626e45 | 0.780886 | ||||||||
\(842\) | 1.31319e45 | 0.597021 | ||||||||
\(843\) | −5.36003e43 | −0.0239243 | ||||||||
\(844\) | 3.40812e44 | 0.149351 | ||||||||
\(845\) | −6.55933e44 | −0.282215 | ||||||||
\(846\) | −9.77030e44 | −0.412731 | ||||||||
\(847\) | 8.96929e43 | 0.0372019 | ||||||||
\(848\) | 2.42913e43 | 0.00989270 | ||||||||
\(849\) | −2.42916e45 | −0.971375 | ||||||||
\(850\) | 5.73506e44 | 0.225188 | ||||||||
\(851\) | −3.78962e45 | −1.46113 | ||||||||
\(852\) | −1.51980e45 | −0.575402 | ||||||||
\(853\) | −1.87985e44 | −0.0698896 | −0.0349448 | − | 0.999389i | \(-0.511126\pi\) | ||||
−0.0349448 | + | 0.999389i | \(0.511126\pi\) | |||||||
\(854\) | 1.44401e45 | 0.527198 | ||||||||
\(855\) | 6.46455e44 | 0.231773 | ||||||||
\(856\) | −1.19687e45 | −0.421408 | ||||||||
\(857\) | 1.66635e45 | 0.576186 | 0.288093 | − | 0.957602i | \(-0.406979\pi\) | ||||
0.288093 | + | 0.957602i | \(0.406979\pi\) | |||||||
\(858\) | 1.07837e45 | 0.366197 | ||||||||
\(859\) | 1.58190e45 | 0.527576 | 0.263788 | − | 0.964581i | \(-0.415028\pi\) | ||||
0.263788 | + | 0.964581i | \(0.415028\pi\) | |||||||
\(860\) | 4.04086e43 | 0.0132357 | ||||||||
\(861\) | −2.40223e45 | −0.772796 | ||||||||
\(862\) | 4.33589e45 | 1.36998 | ||||||||
\(863\) | 4.50883e45 | 1.39925 | 0.699627 | − | 0.714508i | \(-0.253350\pi\) | ||||
0.699627 | + | 0.714508i | \(0.253350\pi\) | |||||||
\(864\) | 6.30482e44 | 0.192181 | ||||||||
\(865\) | 2.54265e45 | 0.761268 | ||||||||
\(866\) | 2.52281e45 | 0.741922 | ||||||||
\(867\) | 4.47192e45 | 1.29181 | ||||||||
\(868\) | 2.64198e45 | 0.749678 | ||||||||
\(869\) | 2.99576e45 | 0.835026 | ||||||||
\(870\) | −1.29665e45 | −0.355038 | ||||||||
\(871\) | 2.89422e45 | 0.778486 | ||||||||
\(872\) | −3.96278e44 | −0.104712 | ||||||||
\(873\) | −5.39904e44 | −0.140151 | ||||||||
\(874\) | −9.50462e45 | −2.42386 | ||||||||
\(875\) | 4.91349e44 | 0.123102 | ||||||||
\(876\) | −1.32128e45 | −0.325222 | ||||||||
\(877\) | −3.33310e45 | −0.806036 | −0.403018 | − | 0.915192i | \(-0.632039\pi\) | ||||
−0.403018 | + | 0.915192i | \(0.632039\pi\) | |||||||
\(878\) | 2.08719e45 | 0.495903 | ||||||||
\(879\) | −2.40316e45 | −0.560990 | ||||||||
\(880\) | −4.94001e44 | −0.113304 | ||||||||
\(881\) | 8.52925e45 | 1.92214 | 0.961068 | − | 0.276311i | \(-0.0891121\pi\) | ||||
0.961068 | + | 0.276311i | \(0.0891121\pi\) | |||||||
\(882\) | 8.34430e44 | 0.184768 | ||||||||
\(883\) | −3.84364e45 | −0.836280 | −0.418140 | − | 0.908383i | \(-0.637318\pi\) | ||||
−0.418140 | + | 0.908383i | \(0.637318\pi\) | |||||||
\(884\) | −2.26200e45 | −0.483595 | ||||||||
\(885\) | 1.35002e45 | 0.283609 | ||||||||
\(886\) | −2.08784e44 | −0.0430997 | ||||||||
\(887\) | 2.95824e45 | 0.600092 | 0.300046 | − | 0.953925i | \(-0.402998\pi\) | ||||
0.300046 | + | 0.953925i | \(0.402998\pi\) | |||||||
\(888\) | −1.12811e45 | −0.224880 | ||||||||
\(889\) | −1.34854e46 | −2.64172 | ||||||||
\(890\) | 5.07280e44 | 0.0976569 | ||||||||
\(891\) | 3.33413e45 | 0.630781 | ||||||||
\(892\) | 1.27087e45 | 0.236291 | ||||||||
\(893\) | 1.93900e46 | 3.54308 | ||||||||
\(894\) | 2.48894e45 | 0.446975 | ||||||||
\(895\) | −3.66104e45 | −0.646171 | ||||||||
\(896\) | −7.01277e44 | −0.121651 | ||||||||
\(897\) | −5.79256e45 | −0.987614 | ||||||||
\(898\) | 4.68132e45 | 0.784485 | ||||||||
\(899\) | 8.82627e45 | 1.45379 | ||||||||
\(900\) | −1.80482e44 | −0.0292196 | ||||||||
\(901\) | −3.95948e44 | −0.0630092 | ||||||||
\(902\) | −3.05750e45 | −0.478261 | ||||||||
\(903\) | 4.45759e44 | 0.0685393 | ||||||||
\(904\) | 6.02428e44 | 0.0910531 | ||||||||
\(905\) | −2.81586e45 | −0.418367 | ||||||||
\(906\) | −4.14940e45 | −0.606036 | ||||||||
\(907\) | −8.06932e44 | −0.115858 | −0.0579288 | − | 0.998321i | \(-0.518450\pi\) | ||||
−0.0579288 | + | 0.998321i | \(0.518450\pi\) | |||||||
\(908\) | 1.85768e43 | 0.00262204 | ||||||||
\(909\) | −1.00372e45 | −0.139275 | ||||||||
\(910\) | −1.93796e45 | −0.264364 | ||||||||
\(911\) | −5.29138e45 | −0.709634 | −0.354817 | − | 0.934936i | \(-0.615457\pi\) | ||||
−0.354817 | + | 0.934936i | \(0.615457\pi\) | |||||||
\(912\) | −2.82937e45 | −0.373053 | ||||||||
\(913\) | 1.49722e45 | 0.194084 | ||||||||
\(914\) | 1.74558e45 | 0.222471 | ||||||||
\(915\) | −1.62655e45 | −0.203817 | ||||||||
\(916\) | −1.68721e45 | −0.207868 | ||||||||
\(917\) | 1.24229e46 | 1.50487 | ||||||||
\(918\) | −1.02769e46 | −1.22405 | ||||||||
\(919\) | −1.26770e46 | −1.48465 | −0.742326 | − | 0.670039i | \(-0.766278\pi\) | ||||
−0.742326 | + | 0.670039i | \(0.766278\pi\) | |||||||
\(920\) | 2.65357e45 | 0.305576 | ||||||||
\(921\) | 2.13793e45 | 0.242086 | ||||||||
\(922\) | 5.10089e45 | 0.567958 | ||||||||
\(923\) | −7.58846e45 | −0.830859 | ||||||||
\(924\) | −5.44947e45 | −0.586730 | ||||||||
\(925\) | 1.42812e45 | 0.151206 | ||||||||
\(926\) | 9.51332e45 | 0.990517 | ||||||||
\(927\) | 1.70461e45 | 0.174538 | ||||||||
\(928\) | −2.34281e45 | −0.235908 | ||||||||
\(929\) | −1.42045e46 | −1.40664 | −0.703320 | − | 0.710873i | \(-0.748300\pi\) | ||||
−0.703320 | + | 0.710873i | \(0.748300\pi\) | |||||||
\(930\) | −2.97595e45 | −0.289828 | ||||||||
\(931\) | −1.65600e46 | −1.58614 | ||||||||
\(932\) | −6.84839e45 | −0.645122 | ||||||||
\(933\) | 1.14836e46 | 1.06393 | ||||||||
\(934\) | 4.89824e45 | 0.446337 | ||||||||
\(935\) | 8.05223e45 | 0.721666 | ||||||||
\(936\) | 7.11849e44 | 0.0627498 | ||||||||
\(937\) | −5.11233e45 | −0.443256 | −0.221628 | − | 0.975131i | \(-0.571137\pi\) | ||||
−0.221628 | + | 0.975131i | \(0.571137\pi\) | |||||||
\(938\) | −1.46257e46 | −1.24731 | ||||||||
\(939\) | 6.65242e45 | 0.558037 | ||||||||
\(940\) | −5.41345e45 | −0.446676 | ||||||||
\(941\) | −3.09574e45 | −0.251262 | −0.125631 | − | 0.992077i | \(-0.540095\pi\) | ||||
−0.125631 | + | 0.992077i | \(0.540095\pi\) | |||||||
\(942\) | −1.51731e45 | −0.121139 | ||||||||
\(943\) | 1.64236e46 | 1.28984 | ||||||||
\(944\) | 2.43924e45 | 0.188447 | ||||||||
\(945\) | −8.80468e45 | −0.669145 | ||||||||
\(946\) | 5.67351e44 | 0.0424169 | ||||||||
\(947\) | 9.70650e45 | 0.713901 | 0.356951 | − | 0.934123i | \(-0.383816\pi\) | ||||
0.356951 | + | 0.934123i | \(0.383816\pi\) | |||||||
\(948\) | −4.79032e45 | −0.346605 | ||||||||
\(949\) | −6.59723e45 | −0.469608 | ||||||||
\(950\) | 3.58183e45 | 0.250835 | ||||||||
\(951\) | 1.01348e46 | 0.698261 | ||||||||
\(952\) | 1.14308e46 | 0.774827 | ||||||||
\(953\) | −1.66762e46 | −1.11213 | −0.556067 | − | 0.831137i | \(-0.687690\pi\) | ||||
−0.556067 | + | 0.831137i | \(0.687690\pi\) | |||||||
\(954\) | 1.24605e44 | 0.00817588 | ||||||||
\(955\) | 2.81024e45 | 0.181422 | ||||||||
\(956\) | 3.27191e45 | 0.207828 | ||||||||
\(957\) | −1.82054e46 | −1.13780 | ||||||||
\(958\) | −2.95184e45 | −0.181521 | ||||||||
\(959\) | 2.55392e46 | 1.54532 | ||||||||
\(960\) | 7.89924e44 | 0.0470307 | ||||||||
\(961\) | 3.18808e45 | 0.186774 | ||||||||
\(962\) | −5.63274e45 | −0.324718 | ||||||||
\(963\) | −6.13945e45 | −0.348275 | ||||||||
\(964\) | 1.30244e45 | 0.0727047 | ||||||||
\(965\) | −1.24251e46 | −0.682536 | ||||||||
\(966\) | 2.92722e46 | 1.58238 | ||||||||
\(967\) | −1.87173e46 | −0.995712 | −0.497856 | − | 0.867260i | \(-0.665879\pi\) | ||||
−0.497856 | + | 0.867260i | \(0.665879\pi\) | |||||||
\(968\) | −1.82544e44 | −0.00955652 | ||||||||
\(969\) | 4.61188e46 | 2.37607 | ||||||||
\(970\) | −2.99146e45 | −0.151677 | ||||||||
\(971\) | −7.35947e45 | −0.367239 | −0.183619 | − | 0.982997i | \(-0.558781\pi\) | ||||
−0.183619 | + | 0.982997i | \(0.558781\pi\) | |||||||
\(972\) | 5.73694e45 | 0.281743 | ||||||||
\(973\) | 9.39732e45 | 0.454208 | ||||||||
\(974\) | −6.84454e45 | −0.325597 | ||||||||
\(975\) | 2.18293e45 | 0.102204 | ||||||||
\(976\) | −2.93887e45 | −0.135428 | ||||||||
\(977\) | 2.82554e46 | 1.28155 | 0.640775 | − | 0.767728i | \(-0.278613\pi\) | ||||
0.640775 | + | 0.767728i | \(0.278613\pi\) | |||||||
\(978\) | 8.63044e45 | 0.385284 | ||||||||
\(979\) | 7.12240e45 | 0.312964 | ||||||||
\(980\) | 4.62334e45 | 0.199964 | ||||||||
\(981\) | −2.03275e45 | −0.0865395 | ||||||||
\(982\) | −1.70001e46 | −0.712399 | ||||||||
\(983\) | −7.33102e45 | −0.302402 | −0.151201 | − | 0.988503i | \(-0.548314\pi\) | ||||
−0.151201 | + | 0.988503i | \(0.548314\pi\) | |||||||
\(984\) | 4.88904e45 | 0.198518 | ||||||||
\(985\) | 6.02833e45 | 0.240955 | ||||||||
\(986\) | 3.81878e46 | 1.50256 | ||||||||
\(987\) | −5.97173e46 | −2.31305 | ||||||||
\(988\) | −1.41273e46 | −0.538674 | ||||||||
\(989\) | −3.04757e45 | −0.114396 | ||||||||
\(990\) | −2.53403e45 | −0.0936411 | ||||||||
\(991\) | −4.55867e46 | −1.65843 | −0.829213 | − | 0.558933i | \(-0.811211\pi\) | ||||
−0.829213 | + | 0.558933i | \(0.811211\pi\) | |||||||
\(992\) | −5.37700e45 | −0.192579 | ||||||||
\(993\) | 2.45935e46 | 0.867174 | ||||||||
\(994\) | 3.83477e46 | 1.33122 | ||||||||
\(995\) | 1.36192e46 | 0.465472 | ||||||||
\(996\) | −2.39411e45 | −0.0805609 | ||||||||
\(997\) | 9.50456e45 | 0.314889 | 0.157444 | − | 0.987528i | \(-0.449674\pi\) | ||||
0.157444 | + | 0.987528i | \(0.449674\pi\) | |||||||
\(998\) | 1.04168e46 | 0.339789 | ||||||||
\(999\) | −2.55911e46 | −0.821909 |
(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 | 10.32.a.a.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.32.a.a.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |