Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6395796x - 2792983104 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2}\cdot 3\cdot 5\cdot 7 \) |
Twist minimal: | no (minimal twist has level 15) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2272.56\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2540.56 | −1.75434 | −0.877171 | − | 0.480179i | \(-0.840572\pi\) | ||||
−0.877171 | + | 0.480179i | \(0.840572\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | 4.35728e6 | 2.07771 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.50017e8 | 1.01287 | ||||||||
\(7\) | −4.55015e8 | −0.608830 | −0.304415 | − | 0.952539i | \(-0.598461\pi\) | ||||
−0.304415 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(8\) | −5.74199e9 | −1.89068 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.12317e10 | −0.130564 | −0.0652820 | − | 0.997867i | \(-0.520795\pi\) | ||||
−0.0652820 | + | 0.997867i | \(0.520795\pi\) | |||||||
\(12\) | −2.57293e11 | −1.19957 | ||||||||
\(13\) | −8.05046e11 | −1.61963 | −0.809814 | − | 0.586686i | \(-0.800432\pi\) | ||||
−0.809814 | + | 0.586686i | \(0.800432\pi\) | |||||||
\(14\) | 1.15599e12 | 1.06810 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.44998e12 | 1.23918 | ||||||||
\(17\) | 3.31190e11 | 0.0398441 | 0.0199220 | − | 0.999802i | \(-0.493658\pi\) | ||||
0.0199220 | + | 0.999802i | \(0.493658\pi\) | |||||||
\(18\) | −8.85838e12 | −0.584781 | ||||||||
\(19\) | 1.86365e13 | 0.697351 | 0.348675 | − | 0.937244i | \(-0.386632\pi\) | ||||
0.348675 | + | 0.937244i | \(0.386632\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.68682e13 | 0.351508 | ||||||||
\(22\) | 2.85348e13 | 0.229054 | ||||||||
\(23\) | −4.27137e13 | −0.214993 | −0.107497 | − | 0.994205i | \(-0.534284\pi\) | ||||
−0.107497 | + | 0.994205i | \(0.534284\pi\) | |||||||
\(24\) | 3.39059e14 | 1.09158 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.04527e15 | 2.84138 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | −1.98263e15 | −1.26498 | ||||||||
\(29\) | 3.70518e15 | 1.63542 | 0.817712 | − | 0.575627i | \(-0.195242\pi\) | ||||
0.817712 | + | 0.575627i | \(0.195242\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.15562e15 | −1.56801 | −0.784007 | − | 0.620752i | \(-0.786827\pi\) | ||||
−0.784007 | + | 0.620752i | \(0.786827\pi\) | |||||||
\(32\) | −1.80416e15 | −0.283269 | ||||||||
\(33\) | 6.63222e14 | 0.0753811 | ||||||||
\(34\) | −8.41408e14 | −0.0699001 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.51929e16 | 0.692571 | ||||||||
\(37\) | 2.94893e16 | 1.00820 | 0.504100 | − | 0.863645i | \(-0.331824\pi\) | ||||
0.504100 | + | 0.863645i | \(0.331824\pi\) | |||||||
\(38\) | −4.73471e16 | −1.22339 | ||||||||
\(39\) | 4.75372e16 | 0.935093 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −4.25039e16 | −0.494536 | −0.247268 | − | 0.968947i | \(-0.579533\pi\) | ||||
−0.247268 | + | 0.968947i | \(0.579533\pi\) | |||||||
\(42\) | −6.82602e16 | −0.616666 | ||||||||
\(43\) | 1.81773e17 | 1.28266 | 0.641330 | − | 0.767265i | \(-0.278383\pi\) | ||||
0.641330 | + | 0.767265i | \(0.278383\pi\) | |||||||
\(44\) | −4.89398e16 | −0.271275 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.08517e17 | 0.377172 | ||||||||
\(47\) | −3.00481e17 | −0.833276 | −0.416638 | − | 0.909072i | \(-0.636792\pi\) | ||||
−0.416638 | + | 0.909072i | \(0.636792\pi\) | |||||||
\(48\) | −3.21816e17 | −0.715442 | ||||||||
\(49\) | −3.51507e17 | −0.629326 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.95564e16 | −0.0230040 | ||||||||
\(52\) | −3.50781e18 | −3.36512 | ||||||||
\(53\) | −2.29068e18 | −1.79915 | −0.899575 | − | 0.436766i | \(-0.856124\pi\) | ||||
−0.899575 | + | 0.436766i | \(0.856124\pi\) | |||||||
\(54\) | 5.23078e17 | 0.337623 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.61269e18 | 1.15110 | ||||||||
\(57\) | −1.10047e18 | −0.402616 | ||||||||
\(58\) | −9.41323e18 | −2.86909 | ||||||||
\(59\) | −6.29616e18 | −1.60372 | −0.801862 | − | 0.597509i | \(-0.796157\pi\) | ||||
−0.801862 | + | 0.597509i | \(0.796157\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.85242e18 | 1.40942 | 0.704710 | − | 0.709496i | \(-0.251077\pi\) | ||||
0.704710 | + | 0.709496i | \(0.251077\pi\) | |||||||
\(62\) | 1.81793e19 | 2.75083 | ||||||||
\(63\) | −1.58654e18 | −0.202943 | ||||||||
\(64\) | −6.84587e18 | −0.742230 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.68495e18 | −0.132244 | ||||||||
\(67\) | 9.53526e18 | 0.639068 | 0.319534 | − | 0.947575i | \(-0.396474\pi\) | ||||
0.319534 | + | 0.947575i | \(0.396474\pi\) | |||||||
\(68\) | 1.44309e18 | 0.0827846 | ||||||||
\(69\) | 2.52220e18 | 0.124127 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.28098e19 | 0.467015 | 0.233507 | − | 0.972355i | \(-0.424980\pi\) | ||||
0.233507 | + | 0.972355i | \(0.424980\pi\) | |||||||
\(72\) | −2.00211e19 | −0.630226 | ||||||||
\(73\) | −7.89120e18 | −0.214908 | −0.107454 | − | 0.994210i | \(-0.534270\pi\) | ||||
−0.107454 | + | 0.994210i | \(0.534270\pi\) | |||||||
\(74\) | −7.49193e19 | −1.76873 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.12044e19 | 1.44890 | ||||||||
\(77\) | 5.11060e18 | 0.0794913 | ||||||||
\(78\) | −1.20771e20 | −1.64047 | ||||||||
\(79\) | −7.72058e19 | −0.917414 | −0.458707 | − | 0.888587i | \(-0.651687\pi\) | ||||
−0.458707 | + | 0.888587i | \(0.651687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | 1.07984e20 | 0.867586 | ||||||||
\(83\) | 2.36090e20 | 1.67016 | 0.835081 | − | 0.550127i | \(-0.185421\pi\) | ||||
0.835081 | + | 0.550127i | \(0.185421\pi\) | |||||||
\(84\) | 1.17072e20 | 0.730334 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −4.61806e20 | −2.25022 | ||||||||
\(87\) | −2.18787e20 | −0.944213 | ||||||||
\(88\) | 6.44925e19 | 0.246854 | ||||||||
\(89\) | 1.56566e20 | 0.532234 | 0.266117 | − | 0.963941i | \(-0.414259\pi\) | ||||
0.266117 | + | 0.963941i | \(0.414259\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.66308e20 | 0.986079 | ||||||||
\(92\) | −1.86116e20 | −0.446695 | ||||||||
\(93\) | 4.22532e20 | 0.905293 | ||||||||
\(94\) | 7.63389e20 | 1.46185 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.06534e20 | 0.163546 | ||||||||
\(97\) | 1.41907e21 | 1.95389 | 0.976946 | − | 0.213488i | \(-0.0684824\pi\) | ||||
0.976946 | + | 0.213488i | \(0.0684824\pi\) | |||||||
\(98\) | 8.93025e20 | 1.10405 | ||||||||
\(99\) | −3.91626e19 | −0.0435213 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.38972e21 | −1.25185 | −0.625925 | − | 0.779883i | \(-0.715278\pi\) | ||||
−0.625925 | + | 0.779883i | \(0.715278\pi\) | |||||||
\(102\) | 4.96843e19 | 0.0403568 | ||||||||
\(103\) | 1.44366e21 | 1.05846 | 0.529228 | − | 0.848479i | \(-0.322482\pi\) | ||||
0.529228 | + | 0.848479i | \(0.322482\pi\) | |||||||
\(104\) | 4.62257e21 | 3.06220 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.81960e21 | 3.15632 | ||||||||
\(107\) | −7.63760e20 | −0.375342 | −0.187671 | − | 0.982232i | \(-0.560094\pi\) | ||||
−0.187671 | + | 0.982232i | \(0.560094\pi\) | |||||||
\(108\) | −8.97126e20 | −0.399856 | ||||||||
\(109\) | 5.56666e20 | 0.225225 | 0.112612 | − | 0.993639i | \(-0.464078\pi\) | ||||
0.112612 | + | 0.993639i | \(0.464078\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.74131e21 | −0.582084 | ||||||||
\(112\) | −2.47982e21 | −0.754451 | ||||||||
\(113\) | 2.01218e21 | 0.557625 | 0.278812 | − | 0.960346i | \(-0.410059\pi\) | ||||
0.278812 | + | 0.960346i | \(0.410059\pi\) | |||||||
\(114\) | 2.79580e21 | 0.706325 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 1.61445e22 | 3.39794 | ||||||||
\(117\) | −2.80702e21 | −0.539876 | ||||||||
\(118\) | 1.59958e22 | 2.81348 | ||||||||
\(119\) | −1.50696e20 | −0.0242583 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.27410e21 | −0.982953 | ||||||||
\(122\) | −1.99495e22 | −2.47260 | ||||||||
\(123\) | 2.50981e21 | 0.285521 | ||||||||
\(124\) | −3.11791e22 | −3.25788 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.03069e21 | 0.356032 | ||||||||
\(127\) | 1.13891e22 | 0.925875 | 0.462937 | − | 0.886391i | \(-0.346796\pi\) | ||||
0.462937 | + | 0.886391i | \(0.346796\pi\) | |||||||
\(128\) | 2.11759e22 | 1.58540 | ||||||||
\(129\) | −1.07335e22 | −0.740544 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.80367e22 | 1.05879 | 0.529394 | − | 0.848376i | \(-0.322419\pi\) | ||||
0.529394 | + | 0.848376i | \(0.322419\pi\) | |||||||
\(132\) | 2.88985e21 | 0.156620 | ||||||||
\(133\) | −8.47988e21 | −0.424568 | ||||||||
\(134\) | −2.42249e22 | −1.12114 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.90169e21 | −0.0753323 | ||||||||
\(137\) | −1.76881e22 | −0.648805 | −0.324403 | − | 0.945919i | \(-0.605163\pi\) | ||||
−0.324403 | + | 0.945919i | \(0.605163\pi\) | |||||||
\(138\) | −6.40780e21 | −0.217760 | ||||||||
\(139\) | 4.69444e22 | 1.47887 | 0.739433 | − | 0.673230i | \(-0.235094\pi\) | ||||
0.739433 | + | 0.673230i | \(0.235094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.77431e22 | 0.481092 | ||||||||
\(142\) | −3.25441e22 | −0.819304 | ||||||||
\(143\) | 9.04205e21 | 0.211465 | ||||||||
\(144\) | 1.90029e22 | 0.413061 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.00480e22 | 0.377022 | ||||||||
\(147\) | 2.07562e22 | 0.363341 | ||||||||
\(148\) | 1.28493e23 | 2.09475 | ||||||||
\(149\) | −1.89144e22 | −0.287300 | −0.143650 | − | 0.989629i | \(-0.545884\pi\) | ||||
−0.143650 | + | 0.989629i | \(0.545884\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.07037e23 | 1.41344 | 0.706721 | − | 0.707493i | \(-0.250174\pi\) | ||||
0.706721 | + | 0.707493i | \(0.250174\pi\) | |||||||
\(152\) | −1.07011e23 | −1.31847 | ||||||||
\(153\) | 1.15479e21 | 0.0132814 | ||||||||
\(154\) | −1.29838e22 | −0.139455 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.07133e23 | 1.94286 | ||||||||
\(157\) | −9.13669e22 | −0.801387 | −0.400694 | − | 0.916212i | \(-0.631231\pi\) | ||||
−0.400694 | + | 0.916212i | \(0.631231\pi\) | |||||||
\(158\) | 1.96146e23 | 1.60946 | ||||||||
\(159\) | 1.35262e23 | 1.03874 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.94354e22 | 0.130895 | ||||||||
\(162\) | −3.08873e22 | −0.194927 | ||||||||
\(163\) | 1.52600e23 | 0.902786 | 0.451393 | − | 0.892325i | \(-0.350927\pi\) | ||||
0.451393 | + | 0.892325i | \(0.350927\pi\) | |||||||
\(164\) | −1.85201e23 | −1.02751 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.99802e23 | −2.93003 | ||||||||
\(167\) | −1.39482e23 | −0.639726 | −0.319863 | − | 0.947464i | \(-0.603637\pi\) | ||||
−0.319863 | + | 0.947464i | \(0.603637\pi\) | |||||||
\(168\) | −1.54277e23 | −0.664589 | ||||||||
\(169\) | 4.01034e23 | 1.62320 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.49814e22 | 0.232450 | ||||||||
\(172\) | 7.92038e23 | 2.66500 | ||||||||
\(173\) | 1.32428e23 | 0.419272 | 0.209636 | − | 0.977779i | \(-0.432772\pi\) | ||||
0.209636 | + | 0.977779i | \(0.432772\pi\) | |||||||
\(174\) | 5.55842e23 | 1.65647 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.12127e22 | −0.161792 | ||||||||
\(177\) | 3.71782e23 | 0.925910 | ||||||||
\(178\) | −3.97765e23 | −0.933721 | ||||||||
\(179\) | 4.79594e23 | 1.06149 | 0.530746 | − | 0.847531i | \(-0.321912\pi\) | ||||
0.530746 | + | 0.847531i | \(0.321912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.92105e22 | 0.0575326 | 0.0287663 | − | 0.999586i | \(-0.490842\pi\) | ||||
0.0287663 | + | 0.999586i | \(0.490842\pi\) | |||||||
\(182\) | −9.30626e23 | −1.72992 | ||||||||
\(183\) | −4.63677e23 | −0.813728 | ||||||||
\(184\) | 2.45262e23 | 0.406483 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1.07347e24 | −1.58819 | ||||||||
\(187\) | −3.71984e21 | −0.00520220 | ||||||||
\(188\) | −1.30928e24 | −1.73131 | ||||||||
\(189\) | 9.36835e22 | 0.117169 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.53666e23 | −0.955956 | −0.477978 | − | 0.878372i | \(-0.658630\pi\) | ||||
−0.477978 | + | 0.878372i | \(0.658630\pi\) | |||||||
\(192\) | 4.04242e23 | 0.428527 | ||||||||
\(193\) | −4.47860e23 | −0.449563 | −0.224781 | − | 0.974409i | \(-0.572167\pi\) | ||||
−0.224781 | + | 0.974409i | \(0.572167\pi\) | |||||||
\(194\) | −3.60523e24 | −3.42779 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.53162e24 | −1.30756 | ||||||||
\(197\) | −9.31605e23 | −0.753940 | −0.376970 | − | 0.926226i | \(-0.623034\pi\) | ||||
−0.376970 | + | 0.926226i | \(0.623034\pi\) | |||||||
\(198\) | 9.94948e22 | 0.0763512 | ||||||||
\(199\) | −1.91931e24 | −1.39698 | −0.698488 | − | 0.715622i | \(-0.746143\pi\) | ||||
−0.698488 | + | 0.715622i | \(0.746143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.63048e23 | −0.368966 | ||||||||
\(202\) | 3.53066e24 | 2.19617 | ||||||||
\(203\) | −1.68591e24 | −0.995696 | ||||||||
\(204\) | −8.52130e22 | −0.0477957 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.66769e24 | −1.85689 | ||||||||
\(207\) | −1.48934e23 | −0.0716645 | ||||||||
\(208\) | −4.38748e24 | −2.00701 | ||||||||
\(209\) | −2.09320e23 | −0.0910488 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.64026e24 | 0.645575 | 0.322788 | − | 0.946471i | \(-0.395380\pi\) | ||||
0.322788 | + | 0.946471i | \(0.395380\pi\) | |||||||
\(212\) | −9.98113e24 | −3.73812 | ||||||||
\(213\) | −7.56408e23 | −0.269631 | ||||||||
\(214\) | 1.94038e24 | 0.658478 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.18223e24 | 0.363861 | ||||||||
\(217\) | 3.25592e24 | 0.954654 | ||||||||
\(218\) | −1.41424e24 | −0.395121 | ||||||||
\(219\) | 4.65967e23 | 0.124077 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.66623e23 | −0.0645326 | ||||||||
\(222\) | 4.42391e24 | 1.02117 | ||||||||
\(223\) | −6.69527e23 | −0.147424 | −0.0737119 | − | 0.997280i | \(-0.523485\pi\) | ||||
−0.0737119 | + | 0.997280i | \(0.523485\pi\) | |||||||
\(224\) | 8.20919e23 | 0.172463 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.11205e24 | −0.978265 | ||||||||
\(227\) | −4.72465e24 | −0.863174 | −0.431587 | − | 0.902071i | \(-0.642046\pi\) | ||||
−0.431587 | + | 0.902071i | \(0.642046\pi\) | |||||||
\(228\) | −4.79504e24 | −0.836520 | ||||||||
\(229\) | 9.75963e24 | 1.62615 | 0.813076 | − | 0.582158i | \(-0.197792\pi\) | ||||
0.813076 | + | 0.582158i | \(0.197792\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.01776e23 | −0.0458943 | ||||||||
\(232\) | −2.12751e25 | −3.09206 | ||||||||
\(233\) | 9.76904e24 | 1.35711 | 0.678555 | − | 0.734550i | \(-0.262607\pi\) | ||||
0.678555 | + | 0.734550i | \(0.262607\pi\) | |||||||
\(234\) | 7.13140e24 | 0.947127 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2.74341e25 | −3.33208 | ||||||||
\(237\) | 4.55893e24 | 0.529669 | ||||||||
\(238\) | 3.82853e23 | 0.0425573 | ||||||||
\(239\) | −7.90678e23 | −0.0841050 | −0.0420525 | − | 0.999115i | \(-0.513390\pi\) | ||||
−0.0420525 | + | 0.999115i | \(0.513390\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.04969e24 | −0.297219 | −0.148610 | − | 0.988896i | \(-0.547480\pi\) | ||||
−0.148610 | + | 0.988896i | \(0.547480\pi\) | |||||||
\(242\) | 1.84803e25 | 1.72444 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | 3.42152e25 | 2.92837 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.37632e24 | −0.500901 | ||||||||
\(247\) | −1.50032e25 | −1.12945 | ||||||||
\(248\) | 4.10875e25 | 2.96461 | ||||||||
\(249\) | −1.39409e25 | −0.964268 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.91006e25 | 1.21471 | 0.607357 | − | 0.794429i | \(-0.292230\pi\) | ||||
0.607357 | + | 0.794429i | \(0.292230\pi\) | |||||||
\(252\) | −6.91300e24 | −0.421658 | ||||||||
\(253\) | 4.79749e23 | 0.0280704 | ||||||||
\(254\) | −2.89348e25 | −1.62430 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3.94418e25 | −2.03909 | ||||||||
\(257\) | −2.69227e25 | −1.33605 | −0.668023 | − | 0.744141i | \(-0.732859\pi\) | ||||
−0.668023 | + | 0.744141i | \(0.732859\pi\) | |||||||
\(258\) | 2.72692e25 | 1.29917 | ||||||||
\(259\) | −1.34181e25 | −0.613822 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.29192e25 | 0.545141 | ||||||||
\(262\) | −4.58234e25 | −1.85748 | ||||||||
\(263\) | −1.23729e25 | −0.481879 | −0.240939 | − | 0.970540i | \(-0.577455\pi\) | ||||
−0.240939 | + | 0.970540i | \(0.577455\pi\) | |||||||
\(264\) | −3.80822e24 | −0.142521 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.15436e25 | 0.744838 | ||||||||
\(267\) | −9.24508e24 | −0.307286 | ||||||||
\(268\) | 4.15478e25 | 1.32780 | ||||||||
\(269\) | 4.72661e25 | 1.45262 | 0.726308 | − | 0.687369i | \(-0.241235\pi\) | ||||
0.726308 | + | 0.687369i | \(0.241235\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.40314e25 | 1.25194 | 0.625972 | − | 0.779846i | \(-0.284703\pi\) | ||||
0.625972 | + | 0.779846i | \(0.284703\pi\) | |||||||
\(272\) | 1.80498e24 | 0.0493740 | ||||||||
\(273\) | −2.16301e25 | −0.569313 | ||||||||
\(274\) | 4.49376e25 | 1.13823 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.09900e25 | 0.257899 | ||||||||
\(277\) | 3.46903e25 | 0.783738 | 0.391869 | − | 0.920021i | \(-0.371829\pi\) | ||||
0.391869 | + | 0.920021i | \(0.371829\pi\) | |||||||
\(278\) | −1.19265e26 | −2.59444 | ||||||||
\(279\) | −2.49501e25 | −0.522671 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.44630e25 | 0.669788 | 0.334894 | − | 0.942256i | \(-0.391300\pi\) | ||||
0.334894 | + | 0.942256i | \(0.391300\pi\) | |||||||
\(282\) | −4.50773e25 | −0.844000 | ||||||||
\(283\) | 5.31368e25 | 0.958601 | 0.479301 | − | 0.877651i | \(-0.340890\pi\) | ||||
0.479301 | + | 0.877651i | \(0.340890\pi\) | |||||||
\(284\) | 5.58160e25 | 0.970323 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.29719e25 | −0.370982 | ||||||||
\(287\) | 1.93399e25 | 0.301089 | ||||||||
\(288\) | −6.29071e24 | −0.0944232 | ||||||||
\(289\) | −6.89822e25 | −0.998412 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.37946e25 | −1.12808 | ||||||||
\(292\) | −3.43842e25 | −0.446518 | ||||||||
\(293\) | −8.33915e25 | −1.04475 | −0.522374 | − | 0.852716i | \(-0.674954\pi\) | ||||
−0.522374 | + | 0.852716i | \(0.674954\pi\) | |||||||
\(294\) | −5.27322e25 | −0.637425 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.69327e26 | −1.90618 | ||||||||
\(297\) | 2.31251e24 | 0.0251270 | ||||||||
\(298\) | 4.80530e25 | 0.504022 | ||||||||
\(299\) | 3.43865e25 | 0.348209 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.27096e25 | −0.780922 | ||||||||
\(302\) | −2.71935e26 | −2.47966 | ||||||||
\(303\) | 8.20615e25 | 0.722756 | ||||||||
\(304\) | 1.01568e26 | 0.864144 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.93381e24 | −0.0233000 | ||||||||
\(307\) | −1.20325e26 | −0.923429 | −0.461715 | − | 0.887029i | \(-0.652766\pi\) | ||||
−0.461715 | + | 0.887029i | \(0.652766\pi\) | |||||||
\(308\) | 2.22683e25 | 0.165160 | ||||||||
\(309\) | −8.52465e25 | −0.611100 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.17519e25 | 0.346691 | 0.173345 | − | 0.984861i | \(-0.444542\pi\) | ||||
0.173345 | + | 0.984861i | \(0.444542\pi\) | |||||||
\(312\) | −2.72958e26 | −1.76796 | ||||||||
\(313\) | 1.55997e26 | 0.977017 | 0.488508 | − | 0.872559i | \(-0.337541\pi\) | ||||
0.488508 | + | 0.872559i | \(0.337541\pi\) | |||||||
\(314\) | 2.32123e26 | 1.40591 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.36408e26 | −1.90612 | ||||||||
\(317\) | 3.05641e26 | 1.67529 | 0.837643 | − | 0.546219i | \(-0.183933\pi\) | ||||
0.837643 | + | 0.546219i | \(0.183933\pi\) | |||||||
\(318\) | −3.43642e26 | −1.82230 | ||||||||
\(319\) | −4.16156e25 | −0.213527 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.50993e25 | 0.216704 | ||||||||
\(322\) | −4.93767e25 | −0.229634 | ||||||||
\(323\) | 6.17222e24 | 0.0277853 | ||||||||
\(324\) | 5.29744e25 | 0.230857 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.87689e26 | −1.58379 | ||||||||
\(327\) | −3.28706e25 | −0.130034 | ||||||||
\(328\) | 2.44057e26 | 0.935009 | ||||||||
\(329\) | 1.36723e26 | 0.507324 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.13740e26 | −1.44057 | −0.720283 | − | 0.693680i | \(-0.755988\pi\) | ||||
−0.720283 | + | 0.693680i | \(0.755988\pi\) | |||||||
\(332\) | 1.02871e27 | 3.47012 | ||||||||
\(333\) | 1.02823e26 | 0.336067 | ||||||||
\(334\) | 3.54361e26 | 1.12230 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.46431e26 | 0.435583 | ||||||||
\(337\) | 5.50567e26 | 1.58743 | 0.793717 | − | 0.608287i | \(-0.208143\pi\) | ||||
0.793717 | + | 0.608287i | \(0.208143\pi\) | |||||||
\(338\) | −1.01885e27 | −2.84764 | ||||||||
\(339\) | −1.18817e26 | −0.321945 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.03700e25 | 0.204726 | ||||||||
\(342\) | −1.65089e26 | −0.407797 | ||||||||
\(343\) | 4.14088e26 | 0.991983 | ||||||||
\(344\) | −1.04374e27 | −2.42510 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.36441e26 | −0.735547 | ||||||||
\(347\) | −5.09948e26 | −1.08160 | −0.540800 | − | 0.841151i | \(-0.681878\pi\) | ||||
−0.540800 | + | 0.841151i | \(0.681878\pi\) | |||||||
\(348\) | −9.53318e26 | −1.96180 | ||||||||
\(349\) | 1.73631e26 | 0.346706 | 0.173353 | − | 0.984860i | \(-0.444540\pi\) | ||||
0.173353 | + | 0.984860i | \(0.444540\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.65752e26 | 0.311698 | ||||||||
\(352\) | 2.02638e25 | 0.0369848 | ||||||||
\(353\) | 2.48553e26 | 0.440337 | 0.220168 | − | 0.975462i | \(-0.429339\pi\) | ||||
0.220168 | + | 0.975462i | \(0.429339\pi\) | |||||||
\(354\) | −9.44533e26 | −1.62436 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.82203e26 | 1.10583 | ||||||||
\(357\) | 8.89847e24 | 0.0140055 | ||||||||
\(358\) | −1.21844e27 | −1.86222 | ||||||||
\(359\) | −9.77934e26 | −1.45150 | −0.725751 | − | 0.687957i | \(-0.758508\pi\) | ||||
−0.725751 | + | 0.687957i | \(0.758508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.66891e26 | −0.513702 | ||||||||
\(362\) | −7.42110e25 | −0.100932 | ||||||||
\(363\) | 4.29528e26 | 0.567508 | ||||||||
\(364\) | 1.59611e27 | 2.04879 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.17800e27 | 1.42756 | ||||||||
\(367\) | −1.01737e27 | −1.19808 | −0.599040 | − | 0.800719i | \(-0.704451\pi\) | ||||
−0.599040 | + | 0.800719i | \(0.704451\pi\) | |||||||
\(368\) | −2.32789e26 | −0.266416 | ||||||||
\(369\) | −1.48202e26 | −0.164845 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.04229e27 | 1.09538 | ||||||||
\(372\) | 1.84109e27 | 1.88094 | ||||||||
\(373\) | −2.95914e26 | −0.293916 | −0.146958 | − | 0.989143i | \(-0.546948\pi\) | ||||
−0.146958 | + | 0.989143i | \(0.546948\pi\) | |||||||
\(374\) | 9.45046e24 | 0.00912643 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.72536e27 | 1.57546 | ||||||||
\(377\) | −2.98284e27 | −2.64878 | ||||||||
\(378\) | −2.38008e26 | −0.205555 | ||||||||
\(379\) | 1.34431e27 | 1.12924 | 0.564621 | − | 0.825350i | \(-0.309022\pi\) | ||||
0.564621 | + | 0.825350i | \(0.309022\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.72518e26 | −0.534554 | ||||||||
\(382\) | 2.16879e27 | 1.67707 | ||||||||
\(383\) | −1.85260e27 | −1.39378 | −0.696890 | − | 0.717178i | \(-0.745434\pi\) | ||||
−0.696890 | + | 0.717178i | \(0.745434\pi\) | |||||||
\(384\) | −1.25042e27 | −0.915328 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.13781e27 | 0.788686 | ||||||||
\(387\) | 6.33805e26 | 0.427553 | ||||||||
\(388\) | 6.18329e27 | 4.05963 | ||||||||
\(389\) | −7.11190e26 | −0.454480 | −0.227240 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227240 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.41464e25 | −0.00856621 | ||||||||
\(392\) | 2.01835e27 | 1.18985 | ||||||||
\(393\) | −1.06505e27 | −0.611292 | ||||||||
\(394\) | 2.36680e27 | 1.32267 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −1.70642e26 | −0.0904248 | ||||||||
\(397\) | 1.18258e27 | 0.610279 | 0.305140 | − | 0.952308i | \(-0.401297\pi\) | ||||
0.305140 | + | 0.952308i | \(0.401297\pi\) | |||||||
\(398\) | 4.87613e27 | 2.45077 | ||||||||
\(399\) | 5.00728e26 | 0.245125 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.57138e27 | 1.19440 | 0.597200 | − | 0.802092i | \(-0.296280\pi\) | ||||
0.597200 | + | 0.802092i | \(0.296280\pi\) | |||||||
\(402\) | 1.43046e27 | 0.647293 | ||||||||
\(403\) | 5.76061e27 | 2.53960 | ||||||||
\(404\) | −6.05539e27 | −2.60099 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.28316e27 | 1.74679 | ||||||||
\(407\) | −3.31216e26 | −0.131634 | ||||||||
\(408\) | 1.12293e26 | 0.0434931 | ||||||||
\(409\) | 3.03164e27 | 1.14441 | 0.572206 | − | 0.820110i | \(-0.306088\pi\) | ||||
0.572206 | + | 0.820110i | \(0.306088\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.04446e27 | 0.374588 | ||||||||
\(412\) | 6.29042e27 | 2.19917 | ||||||||
\(413\) | 2.86485e27 | 0.976396 | ||||||||
\(414\) | 3.78374e26 | 0.125724 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.45243e27 | 0.458791 | ||||||||
\(417\) | −2.77202e27 | −0.853823 | ||||||||
\(418\) | 5.31789e26 | 0.159731 | ||||||||
\(419\) | −3.03379e27 | −0.888666 | −0.444333 | − | 0.895862i | \(-0.646559\pi\) | ||||
−0.444333 | + | 0.895862i | \(0.646559\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.04419e27 | 0.569586 | 0.284793 | − | 0.958589i | \(-0.408075\pi\) | ||||
0.284793 | + | 0.958589i | \(0.408075\pi\) | |||||||
\(422\) | −4.16717e27 | −1.13256 | ||||||||
\(423\) | −1.04771e27 | −0.277759 | ||||||||
\(424\) | 1.31531e28 | 3.40162 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.92170e27 | 0.473025 | ||||||||
\(427\) | −3.57297e27 | −0.858097 | ||||||||
\(428\) | −3.32792e27 | −0.779854 | ||||||||
\(429\) | −5.33924e26 | −0.122089 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.51063e27 | −0.546729 | −0.273365 | − | 0.961910i | \(-0.588137\pi\) | ||||
−0.273365 | + | 0.961910i | \(0.588137\pi\) | |||||||
\(432\) | −1.12210e27 | −0.238481 | ||||||||
\(433\) | −1.97726e27 | −0.410149 | −0.205075 | − | 0.978746i | \(-0.565744\pi\) | ||||
−0.205075 | + | 0.978746i | \(0.565744\pi\) | |||||||
\(434\) | −8.27184e27 | −1.67479 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.42555e27 | 0.467953 | ||||||||
\(437\) | −7.96034e26 | −0.149926 | ||||||||
\(438\) | −1.18382e27 | −0.217674 | ||||||||
\(439\) | −9.05989e27 | −1.62647 | −0.813234 | − | 0.581937i | \(-0.802295\pi\) | ||||
−0.813234 | + | 0.581937i | \(0.802295\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.22563e27 | −0.209775 | ||||||||
\(442\) | 6.77372e26 | 0.113212 | ||||||||
\(443\) | 1.58685e27 | 0.258998 | 0.129499 | − | 0.991580i | \(-0.458663\pi\) | ||||
0.129499 | + | 0.991580i | \(0.458663\pi\) | |||||||
\(444\) | −7.58740e27 | −1.20940 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.70097e27 | 0.258632 | ||||||||
\(447\) | 1.11687e27 | 0.165873 | ||||||||
\(448\) | 3.11497e27 | 0.451892 | ||||||||
\(449\) | −1.13467e28 | −1.60799 | −0.803994 | − | 0.594638i | \(-0.797296\pi\) | ||||
−0.803994 | + | 0.594638i | \(0.797296\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.77392e26 | 0.0645686 | ||||||||
\(452\) | 8.76762e27 | 1.15859 | ||||||||
\(453\) | −6.32045e27 | −0.816051 | ||||||||
\(454\) | 1.20033e28 | 1.51430 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.31887e27 | 0.761217 | ||||||||
\(457\) | −1.26834e28 | −1.49319 | −0.746594 | − | 0.665280i | \(-0.768312\pi\) | ||||
−0.746594 | + | 0.665280i | \(0.768312\pi\) | |||||||
\(458\) | −2.47949e28 | −2.85282 | ||||||||
\(459\) | −6.81891e25 | −0.00766799 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.19162e27 | 0.342888 | 0.171444 | − | 0.985194i | \(-0.445157\pi\) | ||||
0.171444 | + | 0.985194i | \(0.445157\pi\) | |||||||
\(462\) | 7.66679e26 | 0.0805143 | ||||||||
\(463\) | −7.25637e26 | −0.0744936 | −0.0372468 | − | 0.999306i | \(-0.511859\pi\) | ||||
−0.0372468 | + | 0.999306i | \(0.511859\pi\) | |||||||
\(464\) | 2.01932e28 | 2.02659 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.48188e28 | −2.38083 | ||||||||
\(467\) | 8.56374e27 | 0.803223 | 0.401611 | − | 0.915810i | \(-0.368450\pi\) | ||||
0.401611 | + | 0.915810i | \(0.368450\pi\) | |||||||
\(468\) | −1.22310e28 | −1.12171 | ||||||||
\(469\) | −4.33869e27 | −0.389084 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.39512e27 | 0.462681 | ||||||||
\(472\) | 3.61525e28 | 3.03213 | ||||||||
\(473\) | −2.04163e27 | −0.167469 | ||||||||
\(474\) | −1.15822e28 | −0.929221 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.56627e26 | −0.0504018 | ||||||||
\(477\) | −7.98710e27 | −0.599717 | ||||||||
\(478\) | 2.00876e27 | 0.147549 | ||||||||
\(479\) | 1.42126e28 | 1.02130 | 0.510648 | − | 0.859790i | \(-0.329406\pi\) | ||||
0.510648 | + | 0.859790i | \(0.329406\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.37402e28 | −1.63291 | ||||||||
\(482\) | 7.74791e27 | 0.521424 | ||||||||
\(483\) | −1.14764e27 | −0.0755720 | ||||||||
\(484\) | −3.16953e28 | −2.04230 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.82386e27 | 0.112541 | ||||||||
\(487\) | −1.18992e28 | −0.718561 | −0.359281 | − | 0.933230i | \(-0.616978\pi\) | ||||
−0.359281 | + | 0.933230i | \(0.616978\pi\) | |||||||
\(488\) | −4.50885e28 | −2.66476 | ||||||||
\(489\) | −9.01088e27 | −0.521224 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.56760e28 | −0.868718 | −0.434359 | − | 0.900740i | \(-0.643025\pi\) | ||||
−0.434359 | + | 0.900740i | \(0.643025\pi\) | |||||||
\(492\) | 1.09360e28 | 0.593230 | ||||||||
\(493\) | 1.22712e27 | 0.0651620 | ||||||||
\(494\) | 3.81166e28 | 1.98144 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.89980e28 | −1.94305 | ||||||||
\(497\) | −5.82866e27 | −0.284333 | ||||||||
\(498\) | 3.54177e28 | 1.69166 | ||||||||
\(499\) | 4.89071e27 | 0.228726 | 0.114363 | − | 0.993439i | \(-0.463517\pi\) | ||||
0.114363 | + | 0.993439i | \(0.463517\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.23625e27 | 0.369346 | ||||||||
\(502\) | −4.85263e28 | −2.13102 | ||||||||
\(503\) | −1.30763e27 | −0.0562367 | −0.0281183 | − | 0.999605i | \(-0.508952\pi\) | ||||
−0.0281183 | + | 0.999605i | \(0.508952\pi\) | |||||||
\(504\) | 9.10989e27 | 0.383701 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.21883e27 | −0.0492450 | ||||||||
\(507\) | −2.36807e28 | −0.937153 | ||||||||
\(508\) | 4.96257e28 | 1.92370 | ||||||||
\(509\) | −3.01844e28 | −1.14616 | −0.573080 | − | 0.819499i | \(-0.694252\pi\) | ||||
−0.573080 | + | 0.819499i | \(0.694252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.59061e27 | 0.130843 | ||||||||
\(512\) | 5.57951e28 | 1.99187 | ||||||||
\(513\) | −3.83709e27 | −0.134205 | ||||||||
\(514\) | 6.83988e28 | 2.34388 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −4.67690e28 | −1.53864 | ||||||||
\(517\) | 3.37492e27 | 0.108796 | ||||||||
\(518\) | 3.40894e28 | 1.07685 | ||||||||
\(519\) | −7.81975e27 | −0.242067 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.89002e28 | −0.859221 | −0.429610 | − | 0.903014i | \(-0.641349\pi\) | ||||
−0.429610 | + | 0.903014i | \(0.641349\pi\) | |||||||
\(522\) | −3.28219e28 | −0.956364 | ||||||||
\(523\) | 2.23003e28 | 0.636859 | 0.318429 | − | 0.947947i | \(-0.396845\pi\) | ||||
0.318429 | + | 0.947947i | \(0.396845\pi\) | |||||||
\(524\) | 7.85912e28 | 2.19986 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.14342e28 | 0.845380 | ||||||||
\(527\) | −2.36987e27 | −0.0624760 | ||||||||
\(528\) | 3.61455e27 | 0.0934109 | ||||||||
\(529\) | −3.76471e28 | −0.953778 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.19534e28 | −0.534575 | ||||||||
\(532\) | −3.69492e28 | −0.882131 | ||||||||
\(533\) | 3.42176e28 | 0.800965 | ||||||||
\(534\) | 2.34877e28 | 0.539084 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.47514e28 | −1.20827 | ||||||||
\(537\) | −2.83195e28 | −0.612852 | ||||||||
\(538\) | −1.20082e29 | −2.54838 | ||||||||
\(539\) | 3.94803e27 | 0.0821672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.31280e28 | 0.863352 | 0.431676 | − | 0.902029i | \(-0.357922\pi\) | ||||
0.431676 | + | 0.902029i | \(0.357922\pi\) | |||||||
\(542\) | −1.11864e29 | −2.19634 | ||||||||
\(543\) | −1.72485e27 | −0.0332165 | ||||||||
\(544\) | −5.97519e26 | −0.0112866 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 5.49526e28 | 0.998769 | ||||||||
\(547\) | −1.23562e28 | −0.220301 | −0.110150 | − | 0.993915i | \(-0.535133\pi\) | ||||
−0.110150 | + | 0.993915i | \(0.535133\pi\) | |||||||
\(548\) | −7.70719e28 | −1.34803 | ||||||||
\(549\) | 2.73797e28 | 0.469806 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.90516e28 | 1.14046 | ||||||||
\(552\) | −1.44825e28 | −0.234683 | ||||||||
\(553\) | 3.51298e28 | 0.558550 | ||||||||
\(554\) | −8.81328e28 | −1.37494 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.04550e29 | 3.07266 | ||||||||
\(557\) | −6.98412e28 | −1.02951 | −0.514757 | − | 0.857336i | \(-0.672118\pi\) | ||||
−0.514757 | + | 0.857336i | \(0.672118\pi\) | |||||||
\(558\) | 6.33872e28 | 0.916944 | ||||||||
\(559\) | −1.46336e29 | −2.07743 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.19653e26 | 0.00300349 | ||||||||
\(562\) | −8.75553e28 | −1.17504 | ||||||||
\(563\) | 1.18199e29 | 1.55695 | 0.778474 | − | 0.627676i | \(-0.215994\pi\) | ||||
0.778474 | + | 0.627676i | \(0.215994\pi\) | |||||||
\(564\) | 7.73116e28 | 0.999572 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.34997e29 | −1.68171 | ||||||||
\(567\) | −5.53192e27 | −0.0676478 | ||||||||
\(568\) | −7.35539e28 | −0.882975 | ||||||||
\(569\) | −8.18956e28 | −0.965121 | −0.482560 | − | 0.875863i | \(-0.660293\pi\) | ||||
−0.482560 | + | 0.875863i | \(0.660293\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.32446e29 | −1.50439 | −0.752193 | − | 0.658943i | \(-0.771004\pi\) | ||||
−0.752193 | + | 0.658943i | \(0.771004\pi\) | |||||||
\(572\) | 3.93988e28 | 0.439364 | ||||||||
\(573\) | 5.04081e28 | 0.551921 | ||||||||
\(574\) | −4.91341e28 | −0.528212 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.38701e28 | −0.247410 | ||||||||
\(577\) | −6.37145e28 | −0.648474 | −0.324237 | − | 0.945976i | \(-0.605107\pi\) | ||||
−0.324237 | + | 0.945976i | \(0.605107\pi\) | |||||||
\(578\) | 1.75253e29 | 1.75156 | ||||||||
\(579\) | 2.64457e28 | 0.259555 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.07425e29 | −1.01685 | ||||||||
\(582\) | 2.12885e29 | 1.97904 | ||||||||
\(583\) | 2.57283e28 | 0.234904 | ||||||||
\(584\) | 4.53112e28 | 0.406322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.11861e29 | 1.83285 | ||||||||
\(587\) | −8.14731e28 | −0.692332 | −0.346166 | − | 0.938173i | \(-0.612517\pi\) | ||||
−0.346166 | + | 0.938173i | \(0.612517\pi\) | |||||||
\(588\) | 9.04404e28 | 0.754919 | ||||||||
\(589\) | −1.33356e29 | −1.09346 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.50104e28 | 0.435287 | ||||||||
\(592\) | 1.60716e29 | 1.24934 | ||||||||
\(593\) | −1.55191e29 | −1.18520 | −0.592601 | − | 0.805496i | \(-0.701899\pi\) | ||||
−0.592601 | + | 0.805496i | \(0.701899\pi\) | |||||||
\(594\) | −5.87507e27 | −0.0440814 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8.24152e28 | −0.596927 | ||||||||
\(597\) | 1.13334e29 | 0.806544 | ||||||||
\(598\) | −8.73609e28 | −0.610878 | ||||||||
\(599\) | 2.80190e27 | 0.0192518 | 0.00962590 | − | 0.999954i | \(-0.496936\pi\) | ||||
0.00962590 | + | 0.999954i | \(0.496936\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.09945e28 | −0.603716 | −0.301858 | − | 0.953353i | \(-0.597607\pi\) | ||||
−0.301858 | + | 0.953353i | \(0.597607\pi\) | |||||||
\(602\) | 2.10129e29 | 1.37000 | ||||||||
\(603\) | 3.32474e28 | 0.213023 | ||||||||
\(604\) | 4.66392e29 | 2.93673 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −2.08482e29 | −1.26796 | ||||||||
\(607\) | 2.38304e28 | 0.142446 | 0.0712231 | − | 0.997460i | \(-0.477310\pi\) | ||||
0.0712231 | + | 0.997460i | \(0.477310\pi\) | |||||||
\(608\) | −3.36232e28 | −0.197538 | ||||||||
\(609\) | 9.95515e28 | 0.574865 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.41901e29 | 1.34960 | ||||||||
\(612\) | 5.03174e27 | 0.0275949 | ||||||||
\(613\) | −2.31419e29 | −1.24757 | −0.623784 | − | 0.781597i | \(-0.714405\pi\) | ||||
−0.623784 | + | 0.781597i | \(0.714405\pi\) | |||||||
\(614\) | 3.05693e29 | 1.62001 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.93450e28 | −0.150292 | ||||||||
\(617\) | −3.03072e29 | −1.52599 | −0.762995 | − | 0.646404i | \(-0.776272\pi\) | ||||
−0.762995 | + | 0.646404i | \(0.776272\pi\) | |||||||
\(618\) | 2.16574e29 | 1.07208 | ||||||||
\(619\) | −5.21875e28 | −0.253989 | −0.126994 | − | 0.991903i | \(-0.540533\pi\) | ||||
−0.126994 | + | 0.991903i | \(0.540533\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 8.79438e27 | 0.0413755 | ||||||||
\(622\) | −1.31479e29 | −0.608214 | ||||||||
\(623\) | −7.12400e28 | −0.324040 | ||||||||
\(624\) | 2.59076e29 | 1.15875 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.96321e29 | −1.71402 | ||||||||
\(627\) | 1.23601e28 | 0.0525671 | ||||||||
\(628\) | −3.98111e29 | −1.66505 | ||||||||
\(629\) | 9.76657e27 | 0.0401708 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.18444e29 | −0.869025 | −0.434513 | − | 0.900666i | \(-0.643079\pi\) | ||||
−0.434513 | + | 0.900666i | \(0.643079\pi\) | |||||||
\(632\) | 4.43315e29 | 1.73454 | ||||||||
\(633\) | −9.68557e28 | −0.372723 | ||||||||
\(634\) | −7.76498e29 | −2.93902 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.89376e29 | 2.15820 | ||||||||
\(637\) | 2.82979e29 | 1.01927 | ||||||||
\(638\) | 1.05727e29 | 0.374600 | ||||||||
\(639\) | 4.46651e28 | 0.155672 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.14377e29 | 0.723050 | 0.361525 | − | 0.932362i | \(-0.382256\pi\) | ||||
0.361525 | + | 0.932362i | \(0.382256\pi\) | |||||||
\(642\) | −1.14577e29 | −0.380173 | ||||||||
\(643\) | 1.80517e29 | 0.589255 | 0.294627 | − | 0.955612i | \(-0.404804\pi\) | ||||
0.294627 | + | 0.955612i | \(0.404804\pi\) | |||||||
\(644\) | 8.46855e28 | 0.271961 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.56809e28 | −0.0487449 | ||||||||
\(647\) | −4.97248e29 | −1.52082 | −0.760411 | − | 0.649442i | \(-0.775003\pi\) | ||||
−0.760411 | + | 0.649442i | \(0.775003\pi\) | |||||||
\(648\) | −6.98092e28 | −0.210075 | ||||||||
\(649\) | 7.07167e28 | 0.209388 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.92259e29 | −0.551170 | ||||||||
\(652\) | 6.64921e29 | 1.87573 | ||||||||
\(653\) | −4.69947e29 | −1.30455 | −0.652275 | − | 0.757983i | \(-0.726185\pi\) | ||||
−0.652275 | + | 0.757983i | \(0.726185\pi\) | |||||||
\(654\) | 8.35096e28 | 0.228123 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.31645e29 | −0.612820 | ||||||||
\(657\) | −2.75149e28 | −0.0716360 | ||||||||
\(658\) | −3.47353e29 | −0.890019 | ||||||||
\(659\) | −4.34544e29 | −1.09581 | −0.547907 | − | 0.836539i | \(-0.684575\pi\) | ||||
−0.547907 | + | 0.836539i | \(0.684575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.23242e29 | 1.03389 | 0.516944 | − | 0.856019i | \(-0.327070\pi\) | ||||
0.516944 | + | 0.856019i | \(0.327070\pi\) | |||||||
\(662\) | 1.05113e30 | 2.52725 | ||||||||
\(663\) | 1.57438e28 | 0.0372579 | ||||||||
\(664\) | −1.35563e30 | −3.15774 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −2.61227e29 | −0.589575 | ||||||||
\(667\) | −1.58262e29 | −0.351606 | ||||||||
\(668\) | −6.07761e29 | −1.32917 | ||||||||
\(669\) | 3.95349e28 | 0.0851151 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.81962e28 | −0.184019 | ||||||||
\(672\) | −4.84744e28 | −0.0995716 | ||||||||
\(673\) | −4.15920e28 | −0.0841108 | −0.0420554 | − | 0.999115i | \(-0.513391\pi\) | ||||
−0.0420554 | + | 0.999115i | \(0.513391\pi\) | |||||||
\(674\) | −1.39875e30 | −2.78490 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.74742e30 | 3.37254 | ||||||||
\(677\) | 1.60090e29 | 0.304218 | 0.152109 | − | 0.988364i | \(-0.451394\pi\) | ||||
0.152109 | + | 0.988364i | \(0.451394\pi\) | |||||||
\(678\) | 3.01861e29 | 0.564801 | ||||||||
\(679\) | −6.45698e29 | −1.18959 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.78986e29 | 0.498354 | ||||||||
\(682\) | −2.04185e29 | −0.359159 | ||||||||
\(683\) | −1.83629e29 | −0.318071 | −0.159035 | − | 0.987273i | \(-0.550838\pi\) | ||||
−0.159035 | + | 0.987273i | \(0.550838\pi\) | |||||||
\(684\) | 2.83142e29 | 0.482965 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.05201e30 | −1.74028 | ||||||||
\(687\) | −5.76297e29 | −0.938859 | ||||||||
\(688\) | 9.90661e29 | 1.58945 | ||||||||
\(689\) | 1.84410e30 | 2.91396 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.13171e29 | 1.39969 | 0.699846 | − | 0.714293i | \(-0.253252\pi\) | ||||
0.699846 | + | 0.714293i | \(0.253252\pi\) | |||||||
\(692\) | 5.77027e29 | 0.871128 | ||||||||
\(693\) | 1.78196e28 | 0.0264971 | ||||||||
\(694\) | 1.29555e30 | 1.89750 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 1.25627e30 | 1.78520 | ||||||||
\(697\) | −1.40769e28 | −0.0197043 | ||||||||
\(698\) | −4.41121e29 | −0.608241 | ||||||||
\(699\) | −5.76852e29 | −0.783527 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.77685e29 | −0.366027 | −0.183014 | − | 0.983110i | \(-0.558585\pi\) | ||||
−0.183014 | + | 0.983110i | \(0.558585\pi\) | |||||||
\(702\) | −4.21102e29 | −0.546824 | ||||||||
\(703\) | 5.49577e29 | 0.703069 | ||||||||
\(704\) | 7.68909e28 | 0.0969085 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.31463e29 | −0.772501 | ||||||||
\(707\) | 6.32343e29 | 0.762164 | ||||||||
\(708\) | 1.61996e30 | 1.92378 | ||||||||
\(709\) | −6.85586e29 | −0.802189 | −0.401094 | − | 0.916037i | \(-0.631370\pi\) | ||||
−0.401094 | + | 0.916037i | \(0.631370\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.69200e29 | −0.305805 | ||||||||
\(712\) | −8.99002e29 | −1.00628 | ||||||||
\(713\) | 3.05643e29 | 0.337113 | ||||||||
\(714\) | −2.26071e28 | −0.0245705 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.08972e30 | 2.20548 | ||||||||
\(717\) | 4.66888e28 | 0.0485581 | ||||||||
\(718\) | 2.48450e30 | 2.54643 | ||||||||
\(719\) | 1.48014e28 | 0.0149503 | 0.00747517 | − | 0.999972i | \(-0.497621\pi\) | ||||
0.00747517 | + | 0.999972i | \(0.497621\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.56885e29 | −0.644420 | ||||||||
\(722\) | 9.32107e29 | 0.901209 | ||||||||
\(723\) | 1.80081e29 | 0.171600 | ||||||||
\(724\) | 1.27278e29 | 0.119536 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −1.09124e30 | −0.995603 | ||||||||
\(727\) | 9.70389e29 | 0.872639 | 0.436320 | − | 0.899792i | \(-0.356282\pi\) | ||||
0.436320 | + | 0.899792i | \(0.356282\pi\) | |||||||
\(728\) | −2.10334e30 | −1.86436 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.02015e28 | 0.0511064 | ||||||||
\(732\) | −2.02037e30 | −1.69070 | ||||||||
\(733\) | 2.15653e30 | 1.77895 | 0.889473 | − | 0.456988i | \(-0.151072\pi\) | ||||
0.889473 | + | 0.456988i | \(0.151072\pi\) | |||||||
\(734\) | 2.58469e30 | 2.10184 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7.70623e28 | 0.0609011 | ||||||||
\(737\) | −1.07097e29 | −0.0834393 | ||||||||
\(738\) | 3.76516e29 | 0.289195 | ||||||||
\(739\) | 6.89652e29 | 0.522232 | 0.261116 | − | 0.965307i | \(-0.415910\pi\) | ||||
0.261116 | + | 0.965307i | \(0.415910\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.85925e29 | 0.652088 | ||||||||
\(742\) | −2.64801e30 | −1.92167 | ||||||||
\(743\) | 1.50941e30 | 1.08000 | 0.540002 | − | 0.841664i | \(-0.318424\pi\) | ||||
0.540002 | + | 0.841664i | \(0.318424\pi\) | |||||||
\(744\) | −2.42618e30 | −1.71162 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.51787e29 | 0.515629 | ||||||||
\(747\) | 8.23197e29 | 0.556721 | ||||||||
\(748\) | −1.62084e28 | −0.0108087 | ||||||||
\(749\) | 3.47522e29 | 0.228520 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.21031e30 | −1.41330 | −0.706649 | − | 0.707565i | \(-0.749794\pi\) | ||||
−0.706649 | + | 0.707565i | \(0.749794\pi\) | |||||||
\(752\) | −1.63761e30 | −1.03258 | ||||||||
\(753\) | −1.12787e30 | −0.701315 | ||||||||
\(754\) | 7.57808e30 | 4.64686 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.08206e29 | 0.243445 | ||||||||
\(757\) | −1.21005e30 | −0.711700 | −0.355850 | − | 0.934543i | \(-0.615809\pi\) | ||||
−0.355850 | + | 0.934543i | \(0.615809\pi\) | |||||||
\(758\) | −3.41529e30 | −1.98108 | ||||||||
\(759\) | −2.83287e28 | −0.0162064 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.67440e29 | 0.538375 | 0.269188 | − | 0.963088i | \(-0.413245\pi\) | ||||
0.269188 | + | 0.963088i | \(0.413245\pi\) | |||||||
\(762\) | 1.70857e30 | 0.937790 | ||||||||
\(763\) | −2.53291e29 | −0.137124 | ||||||||
\(764\) | −3.71966e30 | −1.98620 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.70664e30 | 2.44517 | ||||||||
\(767\) | 5.06870e30 | 2.59744 | ||||||||
\(768\) | 2.32900e30 | 1.17727 | ||||||||
\(769\) | 9.63350e29 | 0.480350 | 0.240175 | − | 0.970730i | \(-0.422795\pi\) | ||||
0.240175 | + | 0.970730i | \(0.422795\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.58976e30 | 0.771366 | ||||||||
\(772\) | −1.95145e30 | −0.934063 | ||||||||
\(773\) | −1.68443e30 | −0.795368 | −0.397684 | − | 0.917522i | \(-0.630186\pi\) | ||||
−0.397684 | + | 0.917522i | \(0.630186\pi\) | |||||||
\(774\) | −1.61022e30 | −0.750074 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.14828e30 | −3.69418 | ||||||||
\(777\) | 7.92324e29 | 0.354391 | ||||||||
\(778\) | 1.80682e30 | 0.797313 | ||||||||
\(779\) | −7.92123e29 | −0.344865 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.43876e29 | −0.0609753 | ||||||||
\(782\) | 3.59397e28 | 0.0150281 | ||||||||
\(783\) | −7.62864e29 | −0.314738 | ||||||||
\(784\) | −1.91571e30 | −0.779849 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.70582e30 | 1.07242 | ||||||||
\(787\) | 2.94830e30 | 1.15302 | 0.576510 | − | 0.817090i | \(-0.304414\pi\) | ||||
0.576510 | + | 0.817090i | \(0.304414\pi\) | |||||||
\(788\) | −4.05927e30 | −1.56647 | ||||||||
\(789\) | 7.30610e29 | 0.278213 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.15570e29 | −0.339499 | ||||||||
\(792\) | 2.24871e29 | 0.0822848 | ||||||||
\(793\) | −6.32156e30 | −2.28274 | ||||||||
\(794\) | −3.00440e30 | −1.07064 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.36299e30 | −2.90252 | ||||||||
\(797\) | −2.94698e30 | −1.00940 | −0.504702 | − | 0.863294i | \(-0.668398\pi\) | ||||
−0.504702 | + | 0.863294i | \(0.668398\pi\) | |||||||
\(798\) | −1.27213e30 | −0.430032 | ||||||||
\(799\) | −9.95162e28 | −0.0332011 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.45913e29 | 0.177411 | ||||||||
\(802\) | −6.53274e30 | −2.09539 | ||||||||
\(803\) | 8.86317e28 | 0.0280593 | ||||||||
\(804\) | −2.45336e30 | −0.766606 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.46352e31 | −4.45532 | ||||||||
\(807\) | −2.79102e30 | −0.838668 | ||||||||
\(808\) | 7.97975e30 | 2.36685 | ||||||||
\(809\) | −6.41034e30 | −1.87682 | −0.938408 | − | 0.345529i | \(-0.887699\pi\) | ||||
−0.938408 | + | 0.345529i | \(0.887699\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.93724e29 | 0.254967 | 0.127484 | − | 0.991841i | \(-0.459310\pi\) | ||||
0.127484 | + | 0.991841i | \(0.459310\pi\) | |||||||
\(812\) | −7.34600e30 | −2.06877 | ||||||||
\(813\) | −2.60001e30 | −0.722810 | ||||||||
\(814\) | 8.41473e29 | 0.230932 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.06582e29 | −0.0285061 | ||||||||
\(817\) | 3.38762e30 | 0.894464 | ||||||||
\(818\) | −7.70204e30 | −2.00769 | ||||||||
\(819\) | 1.27724e30 | 0.328693 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.68313e29 | −0.0673036 | −0.0336518 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336518 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(822\) | −2.65352e30 | −0.657155 | ||||||||
\(823\) | −1.38875e30 | −0.339568 | −0.169784 | − | 0.985481i | \(-0.554307\pi\) | ||||
−0.169784 | + | 0.985481i | \(0.554307\pi\) | |||||||
\(824\) | −8.28946e30 | −2.00120 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.27831e30 | −1.71293 | ||||||||
\(827\) | 2.46558e30 | 0.572943 | 0.286471 | − | 0.958089i | \(-0.407518\pi\) | ||||
0.286471 | + | 0.958089i | \(0.407518\pi\) | |||||||
\(828\) | −6.48946e29 | −0.148898 | ||||||||
\(829\) | 8.57512e30 | 1.94275 | 0.971376 | − | 0.237547i | \(-0.0763434\pi\) | ||||
0.971376 | + | 0.237547i | \(0.0763434\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.04843e30 | −0.452491 | ||||||||
\(832\) | 5.51124e30 | 1.20214 | ||||||||
\(833\) | −1.16416e29 | −0.0250749 | ||||||||
\(834\) | 7.04248e30 | 1.49790 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.12066e29 | −0.189173 | ||||||||
\(837\) | 1.47328e30 | 0.301764 | ||||||||
\(838\) | 7.70753e30 | 1.55902 | ||||||||
\(839\) | 3.24689e30 | 0.648585 | 0.324293 | − | 0.945957i | \(-0.394874\pi\) | ||||
0.324293 | + | 0.945957i | \(0.394874\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.59553e30 | 1.67461 | ||||||||
\(842\) | −5.19339e30 | −0.999249 | ||||||||
\(843\) | −2.03501e30 | −0.386702 | ||||||||
\(844\) | 7.14708e30 | 1.34132 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.66177e30 | 0.487284 | ||||||||
\(847\) | 3.30982e30 | 0.598452 | ||||||||
\(848\) | −1.24841e31 | −2.22947 | ||||||||
\(849\) | −3.13768e30 | −0.553449 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.25960e30 | −0.216756 | ||||||||
\(852\) | −3.29588e30 | −0.560216 | ||||||||
\(853\) | −2.10639e30 | −0.353650 | −0.176825 | − | 0.984242i | \(-0.556583\pi\) | ||||
−0.176825 | + | 0.984242i | \(0.556583\pi\) | |||||||
\(854\) | 9.07733e30 | 1.50540 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.38551e30 | 0.709651 | ||||||||
\(857\) | −6.52123e30 | −1.04239 | −0.521196 | − | 0.853437i | \(-0.674514\pi\) | ||||
−0.521196 | + | 0.853437i | \(0.674514\pi\) | |||||||
\(858\) | 1.35647e30 | 0.214187 | ||||||||
\(859\) | 5.13120e30 | 0.800369 | 0.400185 | − | 0.916435i | \(-0.368946\pi\) | ||||
0.400185 | + | 0.916435i | \(0.368946\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.14200e30 | −0.173834 | ||||||||
\(862\) | 6.37841e30 | 0.959150 | ||||||||
\(863\) | −8.76491e30 | −1.30207 | −0.651035 | − | 0.759048i | \(-0.725665\pi\) | ||||
−0.651035 | + | 0.759048i | \(0.725665\pi\) | |||||||
\(864\) | 3.71460e29 | 0.0545152 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.02335e30 | 0.719542 | ||||||||
\(867\) | 4.07333e30 | 0.576434 | ||||||||
\(868\) | 1.41869e31 | 1.98350 | ||||||||
\(869\) | 8.67154e29 | 0.119781 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.67632e30 | −1.03505 | ||||||||
\(872\) | −3.19637e30 | −0.425828 | ||||||||
\(873\) | 4.94799e30 | 0.651297 | ||||||||
\(874\) | 2.02237e30 | 0.263021 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.03035e30 | 0.257797 | ||||||||
\(877\) | 2.89130e30 | 0.362741 | 0.181371 | − | 0.983415i | \(-0.441947\pi\) | ||||
0.181371 | + | 0.983415i | \(0.441947\pi\) | |||||||
\(878\) | 2.30172e31 | 2.85338 | ||||||||
\(879\) | 4.92418e30 | 0.603186 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.24707e30 | 0.747187 | 0.373594 | − | 0.927593i | \(-0.378125\pi\) | ||||
0.373594 | + | 0.927593i | \(0.378125\pi\) | |||||||
\(882\) | 3.11378e30 | 0.368017 | ||||||||
\(883\) | −4.71833e30 | −0.551063 | −0.275531 | − | 0.961292i | \(-0.588854\pi\) | ||||
−0.275531 | + | 0.961292i | \(0.588854\pi\) | |||||||
\(884\) | −1.16175e30 | −0.134080 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.03148e30 | −0.454370 | ||||||||
\(887\) | 1.75208e31 | 1.95145 | 0.975724 | − | 0.219005i | \(-0.0702813\pi\) | ||||
0.975724 | + | 0.219005i | \(0.0702813\pi\) | |||||||
\(888\) | 9.99861e30 | 1.10053 | ||||||||
\(889\) | −5.18223e30 | −0.563700 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.36552e29 | −0.0145071 | ||||||||
\(892\) | −2.91732e30 | −0.306304 | ||||||||
\(893\) | −5.59990e30 | −0.581086 | ||||||||
\(894\) | −2.83748e30 | −0.290997 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −9.63536e30 | −0.965237 | ||||||||
\(897\) | −2.03049e30 | −0.201039 | ||||||||
\(898\) | 2.88269e31 | 2.82096 | ||||||||
\(899\) | −2.65129e31 | −2.56437 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.58650e29 | −0.0716855 | ||||||||
\(902\) | −1.21284e30 | −0.113275 | ||||||||
\(903\) | 4.88392e30 | 0.450866 | ||||||||
\(904\) | −1.15539e31 | −1.05429 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.60575e31 | 1.43163 | ||||||||
\(907\) | −1.53542e31 | −1.35316 | −0.676582 | − | 0.736367i | \(-0.736540\pi\) | ||||
−0.676582 | + | 0.736367i | \(0.736540\pi\) | |||||||
\(908\) | −2.05866e31 | −1.79343 | ||||||||
\(909\) | −4.84565e30 | −0.417283 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.68310e31 | 1.41634 | 0.708168 | − | 0.706044i | \(-0.249522\pi\) | ||||
0.708168 | + | 0.706044i | \(0.249522\pi\) | |||||||
\(912\) | −5.99752e30 | −0.498914 | ||||||||
\(913\) | −2.65170e30 | −0.218063 | ||||||||
\(914\) | 3.22228e31 | 2.61956 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.25255e31 | 3.37868 | ||||||||
\(917\) | −8.20699e30 | −0.644623 | ||||||||
\(918\) | 1.73238e29 | 0.0134523 | ||||||||
\(919\) | −2.16596e31 | −1.66279 | −0.831394 | − | 0.555683i | \(-0.812457\pi\) | ||||
−0.831394 | + | 0.555683i | \(0.812457\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 7.10508e30 | 0.533142 | ||||||||
\(922\) | −8.10850e30 | −0.601542 | ||||||||
\(923\) | −1.03125e31 | −0.756391 | ||||||||
\(924\) | −1.31492e30 | −0.0953553 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.84352e30 | 0.130687 | ||||||||
\(927\) | 5.03372e30 | 0.352819 | ||||||||
\(928\) | −6.68473e30 | −0.463266 | ||||||||
\(929\) | 2.21057e31 | 1.51474 | 0.757372 | − | 0.652983i | \(-0.226483\pi\) | ||||
0.757372 | + | 0.652983i | \(0.226483\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.55086e30 | −0.438861 | ||||||||
\(932\) | 4.25665e31 | 2.81969 | ||||||||
\(933\) | −3.05590e30 | −0.200162 | ||||||||
\(934\) | −2.17567e31 | −1.40913 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.61179e31 | 1.02073 | ||||||||
\(937\) | −8.91926e30 | −0.558551 | −0.279276 | − | 0.960211i | \(-0.590094\pi\) | ||||
−0.279276 | + | 0.960211i | \(0.590094\pi\) | |||||||
\(938\) | 1.10227e31 | 0.682586 | ||||||||
\(939\) | −9.21149e30 | −0.564081 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.27960e31 | −0.766270 | −0.383135 | − | 0.923692i | \(-0.625156\pi\) | ||||
−0.383135 | + | 0.923692i | \(0.625156\pi\) | |||||||
\(942\) | −1.37066e31 | −0.811701 | ||||||||
\(943\) | 1.81550e30 | 0.106322 | ||||||||
\(944\) | −3.43139e31 | −1.98731 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.18687e30 | 0.293798 | ||||||||
\(947\) | 1.21493e31 | 0.680578 | 0.340289 | − | 0.940321i | \(-0.389475\pi\) | ||||
0.340289 | + | 0.940321i | \(0.389475\pi\) | |||||||
\(948\) | 1.98645e31 | 1.10050 | ||||||||
\(949\) | 6.35278e30 | 0.348071 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.80478e31 | −0.967226 | ||||||||
\(952\) | 8.65298e29 | 0.0458646 | ||||||||
\(953\) | −3.78850e30 | −0.198606 | −0.0993030 | − | 0.995057i | \(-0.531661\pi\) | ||||
−0.0993030 | + | 0.995057i | \(0.531661\pi\) | |||||||
\(954\) | 2.02917e31 | 1.05211 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −3.44521e30 | −0.174746 | ||||||||
\(957\) | 2.45736e30 | 0.123280 | ||||||||
\(958\) | −3.61080e31 | −1.79170 | ||||||||
\(959\) | 8.04834e30 | 0.395012 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3.03775e31 | 1.45867 | ||||||||
\(962\) | 6.03135e31 | 2.86468 | ||||||||
\(963\) | −2.66307e30 | −0.125114 | ||||||||
\(964\) | −1.32884e31 | −0.617536 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.91565e30 | 0.132579 | ||||||||
\(967\) | −2.64473e31 | −1.18961 | −0.594804 | − | 0.803871i | \(-0.702770\pi\) | ||||
−0.594804 | + | 0.803871i | \(0.702770\pi\) | |||||||
\(968\) | 4.17678e31 | 1.85845 | ||||||||
\(969\) | −3.64463e29 | −0.0160418 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.46560e31 | 0.631269 | 0.315634 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315634 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(972\) | −3.12808e30 | −0.133285 | ||||||||
\(973\) | −2.13604e31 | −0.900378 | ||||||||
\(974\) | 3.02306e31 | 1.26060 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.27955e31 | 1.74653 | ||||||||
\(977\) | 2.70997e30 | 0.109414 | 0.0547068 | − | 0.998502i | \(-0.482578\pi\) | ||||
0.0547068 | + | 0.998502i | \(0.482578\pi\) | |||||||
\(978\) | 2.28927e31 | 0.914404 | ||||||||
\(979\) | −1.75851e30 | −0.0694906 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.94097e30 | 0.0750749 | ||||||||
\(982\) | 3.98257e31 | 1.52403 | ||||||||
\(983\) | 4.42442e31 | 1.67511 | 0.837556 | − | 0.546351i | \(-0.183983\pi\) | ||||
0.837556 | + | 0.546351i | \(0.183983\pi\) | |||||||
\(984\) | −1.44113e31 | −0.539828 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.11757e30 | −0.114316 | ||||||||
\(987\) | −8.07337e30 | −0.292904 | ||||||||
\(988\) | −6.53733e31 | −2.34667 | ||||||||
\(989\) | −7.76422e30 | −0.275763 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.26640e31 | −0.440349 | −0.220175 | − | 0.975460i | \(-0.570663\pi\) | ||||
−0.220175 | + | 0.975460i | \(0.570663\pi\) | |||||||
\(992\) | 1.29099e31 | 0.444170 | ||||||||
\(993\) | 2.44309e31 | 0.831712 | ||||||||
\(994\) | 1.48081e31 | 0.498817 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.07445e31 | −2.00347 | ||||||||
\(997\) | −3.47593e31 | −1.13441 | −0.567207 | − | 0.823575i | \(-0.691976\pi\) | ||||
−0.567207 | + | 0.823575i | \(0.691976\pi\) | |||||||
\(998\) | −1.24251e31 | −0.401264 | ||||||||
\(999\) | −6.07159e30 | −0.194028 |
(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 | 75.22.a.e.1.1 | 3 | ||
5.2 | odd | 4 | 75.22.b.e.49.1 | 6 | |||
5.3 | odd | 4 | 75.22.b.e.49.6 | 6 | |||
5.4 | even | 2 | 15.22.a.d.1.3 | ✓ | 3 | ||
15.14 | odd | 2 | 45.22.a.b.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.22.a.d.1.3 | ✓ | 3 | 5.4 | even | 2 | ||
45.22.a.b.1.1 | 3 | 15.14 | odd | 2 | |||
75.22.a.e.1.1 | 3 | 1.1 | even | 1 | trivial | ||
75.22.b.e.49.1 | 6 | 5.2 | odd | 4 | |||
75.22.b.e.49.6 | 6 | 5.3 | odd | 4 |