Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,20,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(13.7290017934\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −512.000 | −0.707107 | ||||||||
\(3\) | −19683.0 | −0.577350 | ||||||||
\(4\) | 262144. | 0.500000 | ||||||||
\(5\) | −3.73247e6 | −0.854637 | −0.427319 | − | 0.904101i | \(-0.640542\pi\) | ||||
−0.427319 | + | 0.904101i | \(0.640542\pi\) | |||||||
\(6\) | 1.00777e7 | 0.408248 | ||||||||
\(7\) | −1.49673e8 | −1.40188 | −0.700940 | − | 0.713220i | \(-0.747236\pi\) | ||||
−0.700940 | + | 0.713220i | \(0.747236\pi\) | |||||||
\(8\) | −1.34218e8 | −0.353553 | ||||||||
\(9\) | 3.87420e8 | 0.333333 | ||||||||
\(10\) | 1.91103e9 | 0.604320 | ||||||||
\(11\) | −7.45967e9 | −0.953870 | −0.476935 | − | 0.878939i | \(-0.658252\pi\) | ||||
−0.476935 | + | 0.878939i | \(0.658252\pi\) | |||||||
\(12\) | −5.15978e9 | −0.288675 | ||||||||
\(13\) | 5.92385e10 | 1.54932 | 0.774661 | − | 0.632376i | \(-0.217920\pi\) | ||||
0.774661 | + | 0.632376i | \(0.217920\pi\) | |||||||
\(14\) | 7.66324e10 | 0.991279 | ||||||||
\(15\) | 7.34663e10 | 0.493425 | ||||||||
\(16\) | 6.87195e10 | 0.250000 | ||||||||
\(17\) | 5.23110e11 | 1.06986 | 0.534932 | − | 0.844895i | \(-0.320337\pi\) | ||||
0.534932 | + | 0.844895i | \(0.320337\pi\) | |||||||
\(18\) | −1.98359e11 | −0.235702 | ||||||||
\(19\) | 9.69502e11 | 0.689270 | 0.344635 | − | 0.938737i | \(-0.388003\pi\) | ||||
0.344635 | + | 0.938737i | \(0.388003\pi\) | |||||||
\(20\) | −9.78446e11 | −0.427319 | ||||||||
\(21\) | 2.94601e12 | 0.809376 | ||||||||
\(22\) | 3.81935e12 | 0.674488 | ||||||||
\(23\) | −1.36837e12 | −0.158413 | −0.0792064 | − | 0.996858i | \(-0.525239\pi\) | ||||
−0.0792064 | + | 0.996858i | \(0.525239\pi\) | |||||||
\(24\) | 2.64181e12 | 0.204124 | ||||||||
\(25\) | −5.14212e12 | −0.269595 | ||||||||
\(26\) | −3.03301e13 | −1.09554 | ||||||||
\(27\) | −7.62560e12 | −0.192450 | ||||||||
\(28\) | −3.92358e13 | −0.700940 | ||||||||
\(29\) | −9.86429e13 | −1.26266 | −0.631328 | − | 0.775516i | \(-0.717490\pi\) | ||||
−0.631328 | + | 0.775516i | \(0.717490\pi\) | |||||||
\(30\) | −3.76147e13 | −0.348904 | ||||||||
\(31\) | 1.94952e14 | 1.32432 | 0.662158 | − | 0.749364i | \(-0.269641\pi\) | ||||
0.662158 | + | 0.749364i | \(0.269641\pi\) | |||||||
\(32\) | −3.51844e13 | −0.176777 | ||||||||
\(33\) | 1.46829e14 | 0.550717 | ||||||||
\(34\) | −2.67833e14 | −0.756508 | ||||||||
\(35\) | 5.58649e14 | 1.19810 | ||||||||
\(36\) | 1.01560e14 | 0.166667 | ||||||||
\(37\) | 1.18732e15 | 1.50193 | 0.750967 | − | 0.660340i | \(-0.229588\pi\) | ||||
0.750967 | + | 0.660340i | \(0.229588\pi\) | |||||||
\(38\) | −4.96385e14 | −0.487388 | ||||||||
\(39\) | −1.16599e15 | −0.894502 | ||||||||
\(40\) | 5.00964e14 | 0.302160 | ||||||||
\(41\) | 1.87020e15 | 0.892157 | 0.446078 | − | 0.894994i | \(-0.352820\pi\) | ||||
0.446078 | + | 0.894994i | \(0.352820\pi\) | |||||||
\(42\) | −1.50836e15 | −0.572315 | ||||||||
\(43\) | −1.48369e14 | −0.0450186 | −0.0225093 | − | 0.999747i | \(-0.507166\pi\) | ||||
−0.0225093 | + | 0.999747i | \(0.507166\pi\) | |||||||
\(44\) | −1.95551e15 | −0.476935 | ||||||||
\(45\) | −1.44604e15 | −0.284879 | ||||||||
\(46\) | 7.00608e14 | 0.112015 | ||||||||
\(47\) | −1.05723e16 | −1.37797 | −0.688985 | − | 0.724775i | \(-0.741944\pi\) | ||||
−0.688985 | + | 0.724775i | \(0.741944\pi\) | |||||||
\(48\) | −1.35261e15 | −0.144338 | ||||||||
\(49\) | 1.10030e16 | 0.965270 | ||||||||
\(50\) | 2.63277e15 | 0.190633 | ||||||||
\(51\) | −1.02964e16 | −0.617686 | ||||||||
\(52\) | 1.55290e16 | 0.774661 | ||||||||
\(53\) | −3.63439e16 | −1.51290 | −0.756451 | − | 0.654051i | \(-0.773068\pi\) | ||||
−0.756451 | + | 0.654051i | \(0.773068\pi\) | |||||||
\(54\) | 3.90431e15 | 0.136083 | ||||||||
\(55\) | 2.78430e16 | 0.815213 | ||||||||
\(56\) | 2.00887e16 | 0.495640 | ||||||||
\(57\) | −1.90827e16 | −0.397950 | ||||||||
\(58\) | 5.05052e16 | 0.892832 | ||||||||
\(59\) | 4.14701e16 | 0.623220 | 0.311610 | − | 0.950210i | \(-0.399132\pi\) | ||||
0.311610 | + | 0.950210i | \(0.399132\pi\) | |||||||
\(60\) | 1.92587e16 | 0.246712 | ||||||||
\(61\) | 1.47498e17 | 1.61492 | 0.807461 | − | 0.589921i | \(-0.200841\pi\) | ||||
0.807461 | + | 0.589921i | \(0.200841\pi\) | |||||||
\(62\) | −9.98154e16 | −0.936433 | ||||||||
\(63\) | −5.79863e16 | −0.467294 | ||||||||
\(64\) | 1.80144e16 | 0.125000 | ||||||||
\(65\) | −2.21106e17 | −1.32411 | ||||||||
\(66\) | −7.51763e16 | −0.389416 | ||||||||
\(67\) | −3.73864e17 | −1.67881 | −0.839407 | − | 0.543504i | \(-0.817097\pi\) | ||||
−0.839407 | + | 0.543504i | \(0.817097\pi\) | |||||||
\(68\) | 1.37130e17 | 0.534932 | ||||||||
\(69\) | 2.69337e16 | 0.0914597 | ||||||||
\(70\) | −2.86028e17 | −0.847184 | ||||||||
\(71\) | 6.82838e17 | 1.76752 | 0.883758 | − | 0.467944i | \(-0.155005\pi\) | ||||
0.883758 | + | 0.467944i | \(0.155005\pi\) | |||||||
\(72\) | −5.19987e16 | −0.117851 | ||||||||
\(73\) | −6.94764e16 | −0.138124 | −0.0690622 | − | 0.997612i | \(-0.522001\pi\) | ||||
−0.0690622 | + | 0.997612i | \(0.522001\pi\) | |||||||
\(74\) | −6.07907e17 | −1.06203 | ||||||||
\(75\) | 1.01212e17 | 0.155651 | ||||||||
\(76\) | 2.54149e17 | 0.344635 | ||||||||
\(77\) | 1.11651e18 | 1.33721 | ||||||||
\(78\) | 5.96987e17 | 0.632508 | ||||||||
\(79\) | 4.08505e17 | 0.383477 | 0.191739 | − | 0.981446i | \(-0.438587\pi\) | ||||
0.191739 | + | 0.981446i | \(0.438587\pi\) | |||||||
\(80\) | −2.56494e17 | −0.213659 | ||||||||
\(81\) | 1.50095e17 | 0.111111 | ||||||||
\(82\) | −9.57542e17 | −0.630850 | ||||||||
\(83\) | −1.99775e17 | −0.117301 | −0.0586503 | − | 0.998279i | \(-0.518680\pi\) | ||||
−0.0586503 | + | 0.998279i | \(0.518680\pi\) | |||||||
\(84\) | 7.72278e17 | 0.404688 | ||||||||
\(85\) | −1.95250e18 | −0.914346 | ||||||||
\(86\) | 7.59648e16 | 0.0318330 | ||||||||
\(87\) | 1.94159e18 | 0.728995 | ||||||||
\(88\) | 1.00122e18 | 0.337244 | ||||||||
\(89\) | 1.27068e18 | 0.384443 | 0.192221 | − | 0.981352i | \(-0.438431\pi\) | ||||
0.192221 | + | 0.981352i | \(0.438431\pi\) | |||||||
\(90\) | 7.40371e17 | 0.201440 | ||||||||
\(91\) | −8.86638e18 | −2.17197 | ||||||||
\(92\) | −3.58711e17 | −0.0792064 | ||||||||
\(93\) | −3.83724e18 | −0.764594 | ||||||||
\(94\) | 5.41302e18 | 0.974372 | ||||||||
\(95\) | −3.61864e18 | −0.589076 | ||||||||
\(96\) | 6.92534e17 | 0.102062 | ||||||||
\(97\) | 2.51426e18 | 0.335798 | 0.167899 | − | 0.985804i | \(-0.446302\pi\) | ||||
0.167899 | + | 0.985804i | \(0.446302\pi\) | |||||||
\(98\) | −5.63354e18 | −0.682549 | ||||||||
\(99\) | −2.89003e18 | −0.317957 | ||||||||
\(100\) | −1.34798e18 | −0.134798 | ||||||||
\(101\) | 1.60915e19 | 1.46401 | 0.732004 | − | 0.681300i | \(-0.238585\pi\) | ||||
0.732004 | + | 0.681300i | \(0.238585\pi\) | |||||||
\(102\) | 5.27175e18 | 0.436770 | ||||||||
\(103\) | 1.50360e17 | 0.0113548 | 0.00567739 | − | 0.999984i | \(-0.498193\pi\) | ||||
0.00567739 | + | 0.999984i | \(0.498193\pi\) | |||||||
\(104\) | −7.95085e18 | −0.547768 | ||||||||
\(105\) | −1.09959e19 | −0.691723 | ||||||||
\(106\) | 1.86081e19 | 1.06978 | ||||||||
\(107\) | 2.03779e19 | 1.07155 | 0.535776 | − | 0.844360i | \(-0.320019\pi\) | ||||
0.535776 | + | 0.844360i | \(0.320019\pi\) | |||||||
\(108\) | −1.99900e18 | −0.0962250 | ||||||||
\(109\) | 3.58279e19 | 1.58005 | 0.790023 | − | 0.613077i | \(-0.210069\pi\) | ||||
0.790023 | + | 0.613077i | \(0.210069\pi\) | |||||||
\(110\) | −1.42556e19 | −0.576443 | ||||||||
\(111\) | −2.33700e19 | −0.867142 | ||||||||
\(112\) | −1.02854e19 | −0.350470 | ||||||||
\(113\) | −1.67259e18 | −0.0523776 | −0.0261888 | − | 0.999657i | \(-0.508337\pi\) | ||||
−0.0261888 | + | 0.999657i | \(0.508337\pi\) | |||||||
\(114\) | 9.77035e18 | 0.281393 | ||||||||
\(115\) | 5.10742e18 | 0.135385 | ||||||||
\(116\) | −2.58586e19 | −0.631328 | ||||||||
\(117\) | 2.29502e19 | 0.516441 | ||||||||
\(118\) | −2.12327e19 | −0.440683 | ||||||||
\(119\) | −7.82953e19 | −1.49982 | ||||||||
\(120\) | −9.86048e18 | −0.174452 | ||||||||
\(121\) | −5.51238e18 | −0.0901318 | ||||||||
\(122\) | −7.55188e19 | −1.14192 | ||||||||
\(123\) | −3.68111e19 | −0.515087 | ||||||||
\(124\) | 5.11055e19 | 0.662158 | ||||||||
\(125\) | 9.03841e19 | 1.08504 | ||||||||
\(126\) | 2.96890e19 | 0.330426 | ||||||||
\(127\) | −3.02978e19 | −0.312806 | −0.156403 | − | 0.987693i | \(-0.549990\pi\) | ||||
−0.156403 | + | 0.987693i | \(0.549990\pi\) | |||||||
\(128\) | −9.22337e18 | −0.0883883 | ||||||||
\(129\) | 2.92034e18 | 0.0259915 | ||||||||
\(130\) | 1.13206e20 | 0.936286 | ||||||||
\(131\) | 1.61202e20 | 1.23964 | 0.619818 | − | 0.784746i | \(-0.287206\pi\) | ||||
0.619818 | + | 0.784746i | \(0.287206\pi\) | |||||||
\(132\) | 3.84903e19 | 0.275359 | ||||||||
\(133\) | −1.45108e20 | −0.966275 | ||||||||
\(134\) | 1.91418e20 | 1.18710 | ||||||||
\(135\) | 2.84623e19 | 0.164475 | ||||||||
\(136\) | −7.02107e19 | −0.378254 | ||||||||
\(137\) | 5.03120e19 | 0.252829 | 0.126414 | − | 0.991978i | \(-0.459653\pi\) | ||||
0.126414 | + | 0.991978i | \(0.459653\pi\) | |||||||
\(138\) | −1.37901e19 | −0.0646718 | ||||||||
\(139\) | −3.17871e20 | −1.39191 | −0.695955 | − | 0.718086i | \(-0.745019\pi\) | ||||
−0.695955 | + | 0.718086i | \(0.745019\pi\) | |||||||
\(140\) | 1.46447e20 | 0.599050 | ||||||||
\(141\) | 2.08095e20 | 0.795572 | ||||||||
\(142\) | −3.49613e20 | −1.24982 | ||||||||
\(143\) | −4.41899e20 | −1.47785 | ||||||||
\(144\) | 2.66233e19 | 0.0833333 | ||||||||
\(145\) | 3.68182e20 | 1.07911 | ||||||||
\(146\) | 3.55719e19 | 0.0976687 | ||||||||
\(147\) | −2.16572e20 | −0.557299 | ||||||||
\(148\) | 3.11248e20 | 0.750967 | ||||||||
\(149\) | 4.24814e20 | 0.961455 | 0.480728 | − | 0.876870i | \(-0.340373\pi\) | ||||
0.480728 | + | 0.876870i | \(0.340373\pi\) | |||||||
\(150\) | −5.18208e19 | −0.110062 | ||||||||
\(151\) | −5.76835e20 | −1.15019 | −0.575097 | − | 0.818086i | \(-0.695036\pi\) | ||||
−0.575097 | + | 0.818086i | \(0.695036\pi\) | |||||||
\(152\) | −1.30124e20 | −0.243694 | ||||||||
\(153\) | 2.02664e20 | 0.356621 | ||||||||
\(154\) | −5.71653e20 | −0.945552 | ||||||||
\(155\) | −7.27653e20 | −1.13181 | ||||||||
\(156\) | −3.05657e20 | −0.447251 | ||||||||
\(157\) | 5.56405e20 | 0.766204 | 0.383102 | − | 0.923706i | \(-0.374856\pi\) | ||||
0.383102 | + | 0.923706i | \(0.374856\pi\) | |||||||
\(158\) | −2.09154e20 | −0.271159 | ||||||||
\(159\) | 7.15357e20 | 0.873474 | ||||||||
\(160\) | 1.31325e20 | 0.151080 | ||||||||
\(161\) | 2.04808e20 | 0.222076 | ||||||||
\(162\) | −7.68485e19 | −0.0785674 | ||||||||
\(163\) | 1.49613e21 | 1.44273 | 0.721367 | − | 0.692553i | \(-0.243514\pi\) | ||||
0.721367 | + | 0.692553i | \(0.243514\pi\) | |||||||
\(164\) | 4.90261e20 | 0.446078 | ||||||||
\(165\) | −5.48034e20 | −0.470663 | ||||||||
\(166\) | 1.02285e20 | 0.0829440 | ||||||||
\(167\) | −9.59191e20 | −0.734681 | −0.367340 | − | 0.930087i | \(-0.619732\pi\) | ||||
−0.367340 | + | 0.930087i | \(0.619732\pi\) | |||||||
\(168\) | −3.95406e20 | −0.286158 | ||||||||
\(169\) | 2.04727e21 | 1.40040 | ||||||||
\(170\) | 9.99678e20 | 0.646540 | ||||||||
\(171\) | 3.75605e20 | 0.229757 | ||||||||
\(172\) | −3.88940e19 | −0.0225093 | ||||||||
\(173\) | −5.51701e20 | −0.302180 | −0.151090 | − | 0.988520i | \(-0.548278\pi\) | ||||
−0.151090 | + | 0.988520i | \(0.548278\pi\) | |||||||
\(174\) | −9.94093e20 | −0.515477 | ||||||||
\(175\) | 7.69635e20 | 0.377941 | ||||||||
\(176\) | −5.12625e20 | −0.238468 | ||||||||
\(177\) | −8.16257e20 | −0.359816 | ||||||||
\(178\) | −6.50589e20 | −0.271842 | ||||||||
\(179\) | −1.32712e21 | −0.525782 | −0.262891 | − | 0.964826i | \(-0.584676\pi\) | ||||
−0.262891 | + | 0.964826i | \(0.584676\pi\) | |||||||
\(180\) | −3.79070e20 | −0.142440 | ||||||||
\(181\) | −2.95073e21 | −1.05192 | −0.525961 | − | 0.850509i | \(-0.676294\pi\) | ||||
−0.525961 | + | 0.850509i | \(0.676294\pi\) | |||||||
\(182\) | 4.53959e21 | 1.53581 | ||||||||
\(183\) | −2.90319e21 | −0.932375 | ||||||||
\(184\) | 1.83660e20 | 0.0560074 | ||||||||
\(185\) | −4.43163e21 | −1.28361 | ||||||||
\(186\) | 1.96467e21 | 0.540650 | ||||||||
\(187\) | −3.90223e21 | −1.02051 | ||||||||
\(188\) | −2.77147e21 | −0.688985 | ||||||||
\(189\) | 1.14134e21 | 0.269792 | ||||||||
\(190\) | 1.85274e21 | 0.416540 | ||||||||
\(191\) | 4.41459e21 | 0.944220 | 0.472110 | − | 0.881540i | \(-0.343493\pi\) | ||||
0.472110 | + | 0.881540i | \(0.343493\pi\) | |||||||
\(192\) | −3.54577e20 | −0.0721688 | ||||||||
\(193\) | 5.13561e21 | 0.994941 | 0.497470 | − | 0.867481i | \(-0.334262\pi\) | ||||
0.497470 | + | 0.867481i | \(0.334262\pi\) | |||||||
\(194\) | −1.28730e21 | −0.237445 | ||||||||
\(195\) | 4.35203e21 | 0.764475 | ||||||||
\(196\) | 2.88437e21 | 0.482635 | ||||||||
\(197\) | 8.08427e20 | 0.128888 | 0.0644439 | − | 0.997921i | \(-0.479473\pi\) | ||||
0.0644439 | + | 0.997921i | \(0.479473\pi\) | |||||||
\(198\) | 1.47970e21 | 0.224829 | ||||||||
\(199\) | −4.98582e21 | −0.722159 | −0.361079 | − | 0.932535i | \(-0.617592\pi\) | ||||
−0.361079 | + | 0.932535i | \(0.617592\pi\) | |||||||
\(200\) | 6.90164e20 | 0.0953164 | ||||||||
\(201\) | 7.35876e21 | 0.969264 | ||||||||
\(202\) | −8.23885e21 | −1.03521 | ||||||||
\(203\) | 1.47641e22 | 1.77009 | ||||||||
\(204\) | −2.69913e21 | −0.308843 | ||||||||
\(205\) | −6.98047e21 | −0.762470 | ||||||||
\(206\) | −7.69844e19 | −0.00802905 | ||||||||
\(207\) | −5.30136e20 | −0.0528043 | ||||||||
\(208\) | 4.07084e21 | 0.387331 | ||||||||
\(209\) | −7.23217e21 | −0.657474 | ||||||||
\(210\) | 5.62990e21 | 0.489122 | ||||||||
\(211\) | 1.35801e22 | 1.12777 | 0.563883 | − | 0.825854i | \(-0.309307\pi\) | ||||
0.563883 | + | 0.825854i | \(0.309307\pi\) | |||||||
\(212\) | −9.52733e21 | −0.756451 | ||||||||
\(213\) | −1.34403e22 | −1.02048 | ||||||||
\(214\) | −1.04335e22 | −0.757701 | ||||||||
\(215\) | 5.53782e20 | 0.0384746 | ||||||||
\(216\) | 1.02349e21 | 0.0680414 | ||||||||
\(217\) | −2.91790e22 | −1.85653 | ||||||||
\(218\) | −1.83439e22 | −1.11726 | ||||||||
\(219\) | 1.36750e21 | 0.0797462 | ||||||||
\(220\) | 7.29888e21 | 0.407606 | ||||||||
\(221\) | 3.09883e22 | 1.65756 | ||||||||
\(222\) | 1.19654e22 | 0.613162 | ||||||||
\(223\) | 2.50315e21 | 0.122911 | 0.0614554 | − | 0.998110i | \(-0.480426\pi\) | ||||
0.0614554 | + | 0.998110i | \(0.480426\pi\) | |||||||
\(224\) | 5.26614e21 | 0.247820 | ||||||||
\(225\) | −1.99216e21 | −0.0898651 | ||||||||
\(226\) | 8.56368e20 | 0.0370365 | ||||||||
\(227\) | 8.31116e19 | 0.00344680 | 0.00172340 | − | 0.999999i | \(-0.499451\pi\) | ||||
0.00172340 | + | 0.999999i | \(0.499451\pi\) | |||||||
\(228\) | −5.00242e21 | −0.198975 | ||||||||
\(229\) | 3.24628e20 | 0.0123865 | 0.00619325 | − | 0.999981i | \(-0.498029\pi\) | ||||
0.00619325 | + | 0.999981i | \(0.498029\pi\) | |||||||
\(230\) | −2.61500e21 | −0.0957320 | ||||||||
\(231\) | −2.19762e22 | −0.772040 | ||||||||
\(232\) | 1.32396e22 | 0.446416 | ||||||||
\(233\) | −1.38992e22 | −0.449892 | −0.224946 | − | 0.974371i | \(-0.572221\pi\) | ||||
−0.224946 | + | 0.974371i | \(0.572221\pi\) | |||||||
\(234\) | −1.17505e22 | −0.365179 | ||||||||
\(235\) | 3.94608e22 | 1.17766 | ||||||||
\(236\) | 1.08711e22 | 0.311610 | ||||||||
\(237\) | −8.04060e21 | −0.221401 | ||||||||
\(238\) | 4.00872e22 | 1.06053 | ||||||||
\(239\) | −6.81749e21 | −0.173318 | −0.0866592 | − | 0.996238i | \(-0.527619\pi\) | ||||
−0.0866592 | + | 0.996238i | \(0.527619\pi\) | |||||||
\(240\) | 5.04856e21 | 0.123356 | ||||||||
\(241\) | −1.10203e22 | −0.258841 | −0.129420 | − | 0.991590i | \(-0.541312\pi\) | ||||
−0.129420 | + | 0.991590i | \(0.541312\pi\) | |||||||
\(242\) | 2.82234e21 | 0.0637328 | ||||||||
\(243\) | −2.95431e21 | −0.0641500 | ||||||||
\(244\) | 3.86656e22 | 0.807461 | ||||||||
\(245\) | −4.10684e22 | −0.824955 | ||||||||
\(246\) | 1.88473e22 | 0.364221 | ||||||||
\(247\) | 5.74318e22 | 1.06790 | ||||||||
\(248\) | −2.61660e22 | −0.468216 | ||||||||
\(249\) | 3.93218e21 | 0.0677235 | ||||||||
\(250\) | −4.62767e22 | −0.767242 | ||||||||
\(251\) | 1.28693e22 | 0.205426 | 0.102713 | − | 0.994711i | \(-0.467248\pi\) | ||||
0.102713 | + | 0.994711i | \(0.467248\pi\) | |||||||
\(252\) | −1.52007e22 | −0.233647 | ||||||||
\(253\) | 1.02076e22 | 0.151105 | ||||||||
\(254\) | 1.55125e22 | 0.221187 | ||||||||
\(255\) | 3.84310e22 | 0.527898 | ||||||||
\(256\) | 4.72237e21 | 0.0625000 | ||||||||
\(257\) | −1.11082e23 | −1.41671 | −0.708354 | − | 0.705857i | \(-0.750562\pi\) | ||||
−0.708354 | + | 0.705857i | \(0.750562\pi\) | |||||||
\(258\) | −1.49521e21 | −0.0183788 | ||||||||
\(259\) | −1.77709e23 | −2.10553 | ||||||||
\(260\) | −5.79616e22 | −0.662054 | ||||||||
\(261\) | −3.82163e22 | −0.420885 | ||||||||
\(262\) | −8.25356e22 | −0.876555 | ||||||||
\(263\) | 8.23499e22 | 0.843497 | 0.421748 | − | 0.906713i | \(-0.361417\pi\) | ||||
0.421748 | + | 0.906713i | \(0.361417\pi\) | |||||||
\(264\) | −1.97070e22 | −0.194708 | ||||||||
\(265\) | 1.35653e23 | 1.29298 | ||||||||
\(266\) | 7.42953e22 | 0.683259 | ||||||||
\(267\) | −2.50108e22 | −0.221958 | ||||||||
\(268\) | −9.80061e22 | −0.839407 | ||||||||
\(269\) | 1.28354e23 | 1.06111 | 0.530556 | − | 0.847650i | \(-0.321983\pi\) | ||||
0.530556 | + | 0.847650i | \(0.321983\pi\) | |||||||
\(270\) | −1.45727e22 | −0.116301 | ||||||||
\(271\) | 2.82596e22 | 0.217750 | 0.108875 | − | 0.994055i | \(-0.465275\pi\) | ||||
0.108875 | + | 0.994055i | \(0.465275\pi\) | |||||||
\(272\) | 3.59479e22 | 0.267466 | ||||||||
\(273\) | 1.74517e23 | 1.25399 | ||||||||
\(274\) | −2.57597e22 | −0.178777 | ||||||||
\(275\) | 3.83586e22 | 0.257159 | ||||||||
\(276\) | 7.06051e21 | 0.0457298 | ||||||||
\(277\) | 4.69743e22 | 0.293969 | 0.146985 | − | 0.989139i | \(-0.453043\pi\) | ||||
0.146985 | + | 0.989139i | \(0.453043\pi\) | |||||||
\(278\) | 1.62750e23 | 0.984228 | ||||||||
\(279\) | 7.55284e22 | 0.441439 | ||||||||
\(280\) | −7.49806e22 | −0.423592 | ||||||||
\(281\) | 1.44399e22 | 0.0788593 | 0.0394296 | − | 0.999222i | \(-0.487446\pi\) | ||||
0.0394296 | + | 0.999222i | \(0.487446\pi\) | |||||||
\(282\) | −1.06544e23 | −0.562554 | ||||||||
\(283\) | −2.54603e23 | −1.29985 | −0.649924 | − | 0.759999i | \(-0.725199\pi\) | ||||
−0.649924 | + | 0.759999i | \(0.725199\pi\) | |||||||
\(284\) | 1.79002e23 | 0.883758 | ||||||||
\(285\) | 7.12257e22 | 0.340103 | ||||||||
\(286\) | 2.26253e23 | 1.04500 | ||||||||
\(287\) | −2.79918e23 | −1.25070 | ||||||||
\(288\) | −1.36311e22 | −0.0589256 | ||||||||
\(289\) | 3.45721e22 | 0.144609 | ||||||||
\(290\) | −1.88509e23 | −0.763048 | ||||||||
\(291\) | −4.94882e22 | −0.193873 | ||||||||
\(292\) | −1.82128e22 | −0.0690622 | ||||||||
\(293\) | 1.20485e21 | 0.00442274 | 0.00221137 | − | 0.999998i | \(-0.499296\pi\) | ||||
0.00221137 | + | 0.999998i | \(0.499296\pi\) | |||||||
\(294\) | 1.10885e23 | 0.394070 | ||||||||
\(295\) | −1.54786e23 | −0.532627 | ||||||||
\(296\) | −1.59359e23 | −0.531014 | ||||||||
\(297\) | 5.68845e22 | 0.183572 | ||||||||
\(298\) | −2.17505e23 | −0.679852 | ||||||||
\(299\) | −8.10604e22 | −0.245433 | ||||||||
\(300\) | 2.65322e22 | 0.0778255 | ||||||||
\(301\) | 2.22067e22 | 0.0631107 | ||||||||
\(302\) | 2.95340e23 | 0.813309 | ||||||||
\(303\) | −3.16729e23 | −0.845245 | ||||||||
\(304\) | 6.66237e22 | 0.172318 | ||||||||
\(305\) | −5.50531e23 | −1.38017 | ||||||||
\(306\) | −1.03764e23 | −0.252169 | ||||||||
\(307\) | 4.80032e22 | 0.113098 | 0.0565490 | − | 0.998400i | \(-0.481990\pi\) | ||||
0.0565490 | + | 0.998400i | \(0.481990\pi\) | |||||||
\(308\) | 2.92686e23 | 0.668606 | ||||||||
\(309\) | −2.95954e21 | −0.00655569 | ||||||||
\(310\) | 3.72558e23 | 0.800310 | ||||||||
\(311\) | −2.92996e23 | −0.610434 | −0.305217 | − | 0.952283i | \(-0.598729\pi\) | ||||
−0.305217 | + | 0.952283i | \(0.598729\pi\) | |||||||
\(312\) | 1.56497e23 | 0.316254 | ||||||||
\(313\) | 9.11835e23 | 1.78750 | 0.893748 | − | 0.448569i | \(-0.148066\pi\) | ||||
0.893748 | + | 0.448569i | \(0.148066\pi\) | |||||||
\(314\) | −2.84880e23 | −0.541788 | ||||||||
\(315\) | 2.16432e23 | 0.399366 | ||||||||
\(316\) | 1.07087e23 | 0.191739 | ||||||||
\(317\) | 1.82852e23 | 0.317714 | 0.158857 | − | 0.987302i | \(-0.449219\pi\) | ||||
0.158857 | + | 0.987302i | \(0.449219\pi\) | |||||||
\(318\) | −3.66263e23 | −0.617639 | ||||||||
\(319\) | 7.35844e23 | 1.20441 | ||||||||
\(320\) | −6.72383e22 | −0.106830 | ||||||||
\(321\) | −4.01098e23 | −0.618661 | ||||||||
\(322\) | −1.04862e23 | −0.157031 | ||||||||
\(323\) | 5.07157e23 | 0.737425 | ||||||||
\(324\) | 3.93464e22 | 0.0555556 | ||||||||
\(325\) | −3.04612e23 | −0.417690 | ||||||||
\(326\) | −7.66017e23 | −1.02017 | ||||||||
\(327\) | −7.05201e23 | −0.912240 | ||||||||
\(328\) | −2.51014e23 | −0.315425 | ||||||||
\(329\) | 1.58238e24 | 1.93175 | ||||||||
\(330\) | 2.80594e23 | 0.332809 | ||||||||
\(331\) | −3.98958e23 | −0.459792 | −0.229896 | − | 0.973215i | \(-0.573839\pi\) | ||||
−0.229896 | + | 0.973215i | \(0.573839\pi\) | |||||||
\(332\) | −5.23699e22 | −0.0586503 | ||||||||
\(333\) | 4.59991e23 | 0.500644 | ||||||||
\(334\) | 4.91106e23 | 0.519498 | ||||||||
\(335\) | 1.39544e24 | 1.43478 | ||||||||
\(336\) | 2.02448e23 | 0.202344 | ||||||||
\(337\) | −1.41916e24 | −1.37895 | −0.689474 | − | 0.724311i | \(-0.742158\pi\) | ||||
−0.689474 | + | 0.724311i | \(0.742158\pi\) | |||||||
\(338\) | −1.04820e24 | −0.990233 | ||||||||
\(339\) | 3.29217e22 | 0.0302402 | ||||||||
\(340\) | −5.11835e23 | −0.457173 | ||||||||
\(341\) | −1.45428e24 | −1.26323 | ||||||||
\(342\) | −1.92310e23 | −0.162463 | ||||||||
\(343\) | 5.92534e22 | 0.0486877 | ||||||||
\(344\) | 1.99137e22 | 0.0159165 | ||||||||
\(345\) | −1.00529e23 | −0.0781649 | ||||||||
\(346\) | 2.82471e23 | 0.213674 | ||||||||
\(347\) | −1.47004e23 | −0.108193 | −0.0540964 | − | 0.998536i | \(-0.517228\pi\) | ||||
−0.0540964 | + | 0.998536i | \(0.517228\pi\) | |||||||
\(348\) | 5.08976e23 | 0.364497 | ||||||||
\(349\) | 7.67378e23 | 0.534771 | 0.267385 | − | 0.963590i | \(-0.413840\pi\) | ||||
0.267385 | + | 0.963590i | \(0.413840\pi\) | |||||||
\(350\) | −3.94053e23 | −0.267244 | ||||||||
\(351\) | −4.51729e23 | −0.298167 | ||||||||
\(352\) | 2.62464e23 | 0.168622 | ||||||||
\(353\) | −1.87042e24 | −1.16971 | −0.584857 | − | 0.811137i | \(-0.698849\pi\) | ||||
−0.584857 | + | 0.811137i | \(0.698849\pi\) | |||||||
\(354\) | 4.17923e23 | 0.254429 | ||||||||
\(355\) | −2.54868e24 | −1.51059 | ||||||||
\(356\) | 3.33102e23 | 0.192221 | ||||||||
\(357\) | 1.54109e24 | 0.865923 | ||||||||
\(358\) | 6.79484e23 | 0.371784 | ||||||||
\(359\) | 1.62492e24 | 0.865835 | 0.432918 | − | 0.901434i | \(-0.357484\pi\) | ||||
0.432918 | + | 0.901434i | \(0.357484\pi\) | |||||||
\(360\) | 1.94084e23 | 0.100720 | ||||||||
\(361\) | −1.03849e24 | −0.524907 | ||||||||
\(362\) | 1.51077e24 | 0.743821 | ||||||||
\(363\) | 1.08500e23 | 0.0520376 | ||||||||
\(364\) | −2.32427e24 | −1.08598 | ||||||||
\(365\) | 2.59319e23 | 0.118046 | ||||||||
\(366\) | 1.48644e24 | 0.659289 | ||||||||
\(367\) | −3.00365e23 | −0.129814 | −0.0649071 | − | 0.997891i | \(-0.520675\pi\) | ||||
−0.0649071 | + | 0.997891i | \(0.520675\pi\) | |||||||
\(368\) | −9.40340e22 | −0.0396032 | ||||||||
\(369\) | 7.24553e23 | 0.297386 | ||||||||
\(370\) | 2.26900e24 | 0.907648 | ||||||||
\(371\) | 5.43969e24 | 2.12091 | ||||||||
\(372\) | −1.00591e24 | −0.382297 | ||||||||
\(373\) | 2.68937e24 | 0.996359 | 0.498180 | − | 0.867074i | \(-0.334002\pi\) | ||||
0.498180 | + | 0.867074i | \(0.334002\pi\) | |||||||
\(374\) | 1.99794e24 | 0.721611 | ||||||||
\(375\) | −1.77903e24 | −0.626450 | ||||||||
\(376\) | 1.41899e24 | 0.487186 | ||||||||
\(377\) | −5.84345e24 | −1.95626 | ||||||||
\(378\) | −5.84368e23 | −0.190772 | ||||||||
\(379\) | −2.46626e22 | −0.00785176 | −0.00392588 | − | 0.999992i | \(-0.501250\pi\) | ||||
−0.00392588 | + | 0.999992i | \(0.501250\pi\) | |||||||
\(380\) | −9.48605e23 | −0.294538 | ||||||||
\(381\) | 5.96351e23 | 0.180599 | ||||||||
\(382\) | −2.26027e24 | −0.667664 | ||||||||
\(383\) | 4.45159e24 | 1.28271 | 0.641353 | − | 0.767246i | \(-0.278373\pi\) | ||||
0.641353 | + | 0.767246i | \(0.278373\pi\) | |||||||
\(384\) | 1.81544e23 | 0.0510310 | ||||||||
\(385\) | −4.16734e24 | −1.14283 | ||||||||
\(386\) | −2.62943e24 | −0.703529 | ||||||||
\(387\) | −5.74811e22 | −0.0150062 | ||||||||
\(388\) | 6.59098e23 | 0.167899 | ||||||||
\(389\) | −7.02195e24 | −1.74557 | −0.872784 | − | 0.488107i | \(-0.837688\pi\) | ||||
−0.872784 | + | 0.488107i | \(0.837688\pi\) | |||||||
\(390\) | −2.22824e24 | −0.540565 | ||||||||
\(391\) | −7.15811e23 | −0.169480 | ||||||||
\(392\) | −1.47680e24 | −0.341274 | ||||||||
\(393\) | −3.17295e24 | −0.715704 | ||||||||
\(394\) | −4.13915e23 | −0.0911374 | ||||||||
\(395\) | −1.52473e24 | −0.327734 | ||||||||
\(396\) | −7.57604e23 | −0.158978 | ||||||||
\(397\) | 5.45409e24 | 1.11741 | 0.558705 | − | 0.829366i | \(-0.311298\pi\) | ||||
0.558705 | + | 0.829366i | \(0.311298\pi\) | |||||||
\(398\) | 2.55274e24 | 0.510643 | ||||||||
\(399\) | 2.85616e24 | 0.557879 | ||||||||
\(400\) | −3.53364e23 | −0.0673988 | ||||||||
\(401\) | 3.85979e24 | 0.718940 | 0.359470 | − | 0.933157i | \(-0.382958\pi\) | ||||
0.359470 | + | 0.933157i | \(0.382958\pi\) | |||||||
\(402\) | −3.76768e24 | −0.685373 | ||||||||
\(403\) | 1.15487e25 | 2.05179 | ||||||||
\(404\) | 4.21829e24 | 0.732004 | ||||||||
\(405\) | −5.60224e23 | −0.0949597 | ||||||||
\(406\) | −7.55924e24 | −1.25164 | ||||||||
\(407\) | −8.85700e24 | −1.43265 | ||||||||
\(408\) | 1.38196e24 | 0.218385 | ||||||||
\(409\) | 7.54727e24 | 1.16525 | 0.582624 | − | 0.812742i | \(-0.302026\pi\) | ||||
0.582624 | + | 0.812742i | \(0.302026\pi\) | |||||||
\(410\) | 3.57400e24 | 0.539148 | ||||||||
\(411\) | −9.90291e23 | −0.145971 | ||||||||
\(412\) | 3.94160e22 | 0.00567739 | ||||||||
\(413\) | −6.20695e24 | −0.873680 | ||||||||
\(414\) | 2.71430e23 | 0.0373383 | ||||||||
\(415\) | 7.45656e23 | 0.100249 | ||||||||
\(416\) | −2.08427e24 | −0.273884 | ||||||||
\(417\) | 6.25666e24 | 0.803619 | ||||||||
\(418\) | 3.70287e24 | 0.464905 | ||||||||
\(419\) | 1.19281e25 | 1.46400 | 0.731998 | − | 0.681307i | \(-0.238588\pi\) | ||||
0.731998 | + | 0.681307i | \(0.238588\pi\) | |||||||
\(420\) | −2.88251e24 | −0.345861 | ||||||||
\(421\) | 6.32070e24 | 0.741456 | 0.370728 | − | 0.928742i | \(-0.379108\pi\) | ||||
0.370728 | + | 0.928742i | \(0.379108\pi\) | |||||||
\(422\) | −6.95300e24 | −0.797451 | ||||||||
\(423\) | −4.09593e24 | −0.459324 | ||||||||
\(424\) | 4.87799e24 | 0.534891 | ||||||||
\(425\) | −2.68990e24 | −0.288430 | ||||||||
\(426\) | 6.88143e24 | 0.721586 | ||||||||
\(427\) | −2.20764e25 | −2.26393 | ||||||||
\(428\) | 5.34194e24 | 0.535776 | ||||||||
\(429\) | 8.69791e24 | 0.853239 | ||||||||
\(430\) | −2.83537e23 | −0.0272056 | ||||||||
\(431\) | −1.40410e25 | −1.31784 | −0.658921 | − | 0.752212i | \(-0.728987\pi\) | ||||
−0.658921 | + | 0.752212i | \(0.728987\pi\) | |||||||
\(432\) | −5.24027e23 | −0.0481125 | ||||||||
\(433\) | −6.29547e24 | −0.565448 | −0.282724 | − | 0.959201i | \(-0.591238\pi\) | ||||
−0.282724 | + | 0.959201i | \(0.591238\pi\) | |||||||
\(434\) | 1.49396e25 | 1.31277 | ||||||||
\(435\) | −7.24693e24 | −0.623026 | ||||||||
\(436\) | 9.39207e24 | 0.790023 | ||||||||
\(437\) | −1.32664e24 | −0.109189 | ||||||||
\(438\) | −7.00162e23 | −0.0563890 | ||||||||
\(439\) | −3.14113e24 | −0.247556 | −0.123778 | − | 0.992310i | \(-0.539501\pi\) | ||||
−0.123778 | + | 0.992310i | \(0.539501\pi\) | |||||||
\(440\) | −3.73703e24 | −0.288221 | ||||||||
\(441\) | 4.26279e24 | 0.321757 | ||||||||
\(442\) | −1.58660e25 | −1.17208 | ||||||||
\(443\) | 1.93668e25 | 1.40030 | 0.700152 | − | 0.713993i | \(-0.253115\pi\) | ||||
0.700152 | + | 0.713993i | \(0.253115\pi\) | |||||||
\(444\) | −6.12630e24 | −0.433571 | ||||||||
\(445\) | −4.74279e24 | −0.328559 | ||||||||
\(446\) | −1.28161e24 | −0.0869111 | ||||||||
\(447\) | −8.36161e24 | −0.555096 | ||||||||
\(448\) | −2.69626e24 | −0.175235 | ||||||||
\(449\) | −2.12764e25 | −1.35381 | −0.676906 | − | 0.736070i | \(-0.736679\pi\) | ||||
−0.676906 | + | 0.736070i | \(0.736679\pi\) | |||||||
\(450\) | 1.01999e24 | 0.0635442 | ||||||||
\(451\) | −1.39511e25 | −0.851002 | ||||||||
\(452\) | −4.38460e23 | −0.0261888 | ||||||||
\(453\) | 1.13538e25 | 0.664064 | ||||||||
\(454\) | −4.25531e22 | −0.00243726 | ||||||||
\(455\) | 3.30935e25 | 1.85624 | ||||||||
\(456\) | 2.56124e24 | 0.140697 | ||||||||
\(457\) | −2.08995e25 | −1.12443 | −0.562214 | − | 0.826992i | \(-0.690050\pi\) | ||||
−0.562214 | + | 0.826992i | \(0.690050\pi\) | |||||||
\(458\) | −1.66209e23 | −0.00875858 | ||||||||
\(459\) | −3.98903e24 | −0.205895 | ||||||||
\(460\) | 1.33888e24 | 0.0676927 | ||||||||
\(461\) | 3.78803e25 | 1.87609 | 0.938046 | − | 0.346510i | \(-0.112633\pi\) | ||||
0.938046 | + | 0.346510i | \(0.112633\pi\) | |||||||
\(462\) | 1.12518e25 | 0.545915 | ||||||||
\(463\) | −1.09015e25 | −0.518163 | −0.259082 | − | 0.965855i | \(-0.583420\pi\) | ||||
−0.259082 | + | 0.965855i | \(0.583420\pi\) | |||||||
\(464\) | −6.77869e24 | −0.315664 | ||||||||
\(465\) | 1.43224e25 | 0.653450 | ||||||||
\(466\) | 7.11638e24 | 0.318121 | ||||||||
\(467\) | −3.52044e25 | −1.54201 | −0.771004 | − | 0.636830i | \(-0.780245\pi\) | ||||
−0.771004 | + | 0.636830i | \(0.780245\pi\) | |||||||
\(468\) | 6.01626e24 | 0.258220 | ||||||||
\(469\) | 5.59572e25 | 2.35350 | ||||||||
\(470\) | −2.02040e25 | −0.832735 | ||||||||
\(471\) | −1.09517e25 | −0.442368 | ||||||||
\(472\) | −5.56603e24 | −0.220342 | ||||||||
\(473\) | 1.10678e24 | 0.0429419 | ||||||||
\(474\) | 4.11679e24 | 0.156554 | ||||||||
\(475\) | −4.98530e24 | −0.185824 | ||||||||
\(476\) | −2.05247e25 | −0.749911 | ||||||||
\(477\) | −1.40804e25 | −0.504301 | ||||||||
\(478\) | 3.49056e24 | 0.122555 | ||||||||
\(479\) | 4.63983e25 | 1.59704 | 0.798518 | − | 0.601971i | \(-0.205618\pi\) | ||||
0.798518 | + | 0.601971i | \(0.205618\pi\) | |||||||
\(480\) | −2.58487e24 | −0.0872260 | ||||||||
\(481\) | 7.03349e25 | 2.32698 | ||||||||
\(482\) | 5.64241e24 | 0.183028 | ||||||||
\(483\) | −4.03124e24 | −0.128216 | ||||||||
\(484\) | −1.44504e24 | −0.0450659 | ||||||||
\(485\) | −9.38441e24 | −0.286986 | ||||||||
\(486\) | 1.51261e24 | 0.0453609 | ||||||||
\(487\) | −2.50165e25 | −0.735701 | −0.367851 | − | 0.929885i | \(-0.619906\pi\) | ||||
−0.367851 | + | 0.929885i | \(0.619906\pi\) | |||||||
\(488\) | −1.97968e25 | −0.570961 | ||||||||
\(489\) | −2.94483e25 | −0.832963 | ||||||||
\(490\) | 2.10270e25 | 0.583332 | ||||||||
\(491\) | 1.16110e24 | 0.0315934 | 0.0157967 | − | 0.999875i | \(-0.494972\pi\) | ||||
0.0157967 | + | 0.999875i | \(0.494972\pi\) | |||||||
\(492\) | −9.64982e24 | −0.257543 | ||||||||
\(493\) | −5.16011e25 | −1.35087 | ||||||||
\(494\) | −2.94051e25 | −0.755121 | ||||||||
\(495\) | 1.07870e25 | 0.271738 | ||||||||
\(496\) | 1.33970e25 | 0.331079 | ||||||||
\(497\) | −1.02202e26 | −2.47785 | ||||||||
\(498\) | −2.01328e24 | −0.0478878 | ||||||||
\(499\) | 3.16323e25 | 0.738202 | 0.369101 | − | 0.929389i | \(-0.379666\pi\) | ||||
0.369101 | + | 0.929389i | \(0.379666\pi\) | |||||||
\(500\) | 2.36937e25 | 0.542522 | ||||||||
\(501\) | 1.88798e25 | 0.424168 | ||||||||
\(502\) | −6.58909e24 | −0.145258 | ||||||||
\(503\) | −7.15936e23 | −0.0154874 | −0.00774369 | − | 0.999970i | \(-0.502465\pi\) | ||||
−0.00774369 | + | 0.999970i | \(0.502465\pi\) | |||||||
\(504\) | 7.78278e24 | 0.165213 | ||||||||
\(505\) | −6.00611e25 | −1.25120 | ||||||||
\(506\) | −5.22630e24 | −0.106848 | ||||||||
\(507\) | −4.02965e25 | −0.808522 | ||||||||
\(508\) | −7.94238e24 | −0.156403 | ||||||||
\(509\) | 7.34242e25 | 1.41912 | 0.709562 | − | 0.704643i | \(-0.248893\pi\) | ||||
0.709562 | + | 0.704643i | \(0.248893\pi\) | |||||||
\(510\) | −1.96767e25 | −0.373280 | ||||||||
\(511\) | 1.03987e25 | 0.193634 | ||||||||
\(512\) | −2.41785e24 | −0.0441942 | ||||||||
\(513\) | −7.39303e24 | −0.132650 | ||||||||
\(514\) | 5.68742e25 | 1.00176 | ||||||||
\(515\) | −5.61215e23 | −0.00970422 | ||||||||
\(516\) | 7.65550e23 | 0.0129957 | ||||||||
\(517\) | 7.88659e25 | 1.31440 | ||||||||
\(518\) | 9.09870e25 | 1.48884 | ||||||||
\(519\) | 1.08591e25 | 0.174464 | ||||||||
\(520\) | 2.96763e25 | 0.468143 | ||||||||
\(521\) | −8.40278e25 | −1.30156 | −0.650780 | − | 0.759266i | \(-0.725558\pi\) | ||||
−0.650780 | + | 0.759266i | \(0.725558\pi\) | |||||||
\(522\) | 1.95667e25 | 0.297611 | ||||||||
\(523\) | 2.62032e25 | 0.391371 | 0.195685 | − | 0.980667i | \(-0.437307\pi\) | ||||
0.195685 | + | 0.980667i | \(0.437307\pi\) | |||||||
\(524\) | 4.22582e25 | 0.619818 | ||||||||
\(525\) | −1.51487e25 | −0.218204 | ||||||||
\(526\) | −4.21631e25 | −0.596442 | ||||||||
\(527\) | 1.01981e26 | 1.41684 | ||||||||
\(528\) | 1.00900e25 | 0.137679 | ||||||||
\(529\) | −7.27430e25 | −0.974905 | ||||||||
\(530\) | −6.94541e25 | −0.914276 | ||||||||
\(531\) | 1.60664e25 | 0.207740 | ||||||||
\(532\) | −3.80392e25 | −0.483137 | ||||||||
\(533\) | 1.10788e26 | 1.38224 | ||||||||
\(534\) | 1.28055e25 | 0.156948 | ||||||||
\(535\) | −7.60599e25 | −0.915788 | ||||||||
\(536\) | 5.01791e25 | 0.593550 | ||||||||
\(537\) | 2.61217e25 | 0.303560 | ||||||||
\(538\) | −6.57171e25 | −0.750320 | ||||||||
\(539\) | −8.20788e25 | −0.920742 | ||||||||
\(540\) | 7.46123e24 | 0.0822375 | ||||||||
\(541\) | 8.43002e24 | 0.0912966 | 0.0456483 | − | 0.998958i | \(-0.485465\pi\) | ||||
0.0456483 | + | 0.998958i | \(0.485465\pi\) | |||||||
\(542\) | −1.44689e25 | −0.153972 | ||||||||
\(543\) | 5.80793e25 | 0.607327 | ||||||||
\(544\) | −1.84053e25 | −0.189127 | ||||||||
\(545\) | −1.33727e26 | −1.35037 | ||||||||
\(546\) | −8.93527e25 | −0.886701 | ||||||||
\(547\) | 9.35298e25 | 0.912158 | 0.456079 | − | 0.889939i | \(-0.349253\pi\) | ||||
0.456079 | + | 0.889939i | \(0.349253\pi\) | |||||||
\(548\) | 1.31890e25 | 0.126414 | ||||||||
\(549\) | 5.71436e25 | 0.538307 | ||||||||
\(550\) | −1.96396e25 | −0.181839 | ||||||||
\(551\) | −9.56345e25 | −0.870311 | ||||||||
\(552\) | −3.61498e24 | −0.0323359 | ||||||||
\(553\) | −6.11420e25 | −0.537589 | ||||||||
\(554\) | −2.40508e25 | −0.207868 | ||||||||
\(555\) | 8.72278e25 | 0.741091 | ||||||||
\(556\) | −8.33281e25 | −0.695955 | ||||||||
\(557\) | −6.72734e25 | −0.552356 | −0.276178 | − | 0.961107i | \(-0.589068\pi\) | ||||
−0.276178 | + | 0.961107i | \(0.589068\pi\) | |||||||
\(558\) | −3.86705e25 | −0.312144 | ||||||||
\(559\) | −8.78913e24 | −0.0697483 | ||||||||
\(560\) | 3.83901e25 | 0.299525 | ||||||||
\(561\) | 7.68076e25 | 0.589193 | ||||||||
\(562\) | −7.39320e24 | −0.0557619 | ||||||||
\(563\) | 1.94848e26 | 1.44500 | 0.722499 | − | 0.691372i | \(-0.242994\pi\) | ||||
0.722499 | + | 0.691372i | \(0.242994\pi\) | |||||||
\(564\) | 5.45508e25 | 0.397786 | ||||||||
\(565\) | 6.24291e24 | 0.0447638 | ||||||||
\(566\) | 1.30357e26 | 0.919131 | ||||||||
\(567\) | −2.24651e25 | −0.155765 | ||||||||
\(568\) | −9.16490e25 | −0.624911 | ||||||||
\(569\) | −2.11021e25 | −0.141501 | −0.0707504 | − | 0.997494i | \(-0.522539\pi\) | ||||
−0.0707504 | + | 0.997494i | \(0.522539\pi\) | |||||||
\(570\) | −3.64676e25 | −0.240489 | ||||||||
\(571\) | −3.02789e25 | −0.196380 | −0.0981900 | − | 0.995168i | \(-0.531305\pi\) | ||||
−0.0981900 | + | 0.995168i | \(0.531305\pi\) | |||||||
\(572\) | −1.15841e26 | −0.738926 | ||||||||
\(573\) | −8.68923e25 | −0.545146 | ||||||||
\(574\) | 1.43318e26 | 0.884377 | ||||||||
\(575\) | 7.03635e24 | 0.0427074 | ||||||||
\(576\) | 6.97915e24 | 0.0416667 | ||||||||
\(577\) | −1.45327e26 | −0.853446 | −0.426723 | − | 0.904382i | \(-0.640332\pi\) | ||||
−0.426723 | + | 0.904382i | \(0.640332\pi\) | |||||||
\(578\) | −1.77009e25 | −0.102254 | ||||||||
\(579\) | −1.01084e26 | −0.574429 | ||||||||
\(580\) | 9.65167e25 | 0.539556 | ||||||||
\(581\) | 2.99009e25 | 0.164441 | ||||||||
\(582\) | 2.53379e25 | 0.137089 | ||||||||
\(583\) | 2.71114e26 | 1.44311 | ||||||||
\(584\) | 9.32497e24 | 0.0488343 | ||||||||
\(585\) | −8.56610e25 | −0.441370 | ||||||||
\(586\) | −6.16885e23 | −0.00312735 | ||||||||
\(587\) | 1.44980e26 | 0.723178 | 0.361589 | − | 0.932338i | \(-0.382234\pi\) | ||||
0.361589 | + | 0.932338i | \(0.382234\pi\) | |||||||
\(588\) | −5.67731e25 | −0.278649 | ||||||||
\(589\) | 1.89006e26 | 0.912811 | ||||||||
\(590\) | 7.92505e25 | 0.376624 | ||||||||
\(591\) | −1.59123e25 | −0.0744134 | ||||||||
\(592\) | 8.15919e25 | 0.375483 | ||||||||
\(593\) | −9.52077e24 | −0.0431174 | −0.0215587 | − | 0.999768i | \(-0.506863\pi\) | ||||
−0.0215587 | + | 0.999768i | \(0.506863\pi\) | |||||||
\(594\) | −2.91248e25 | −0.129805 | ||||||||
\(595\) | 2.92235e26 | 1.28180 | ||||||||
\(596\) | 1.11362e26 | 0.480728 | ||||||||
\(597\) | 9.81360e25 | 0.416939 | ||||||||
\(598\) | 4.15029e25 | 0.173547 | ||||||||
\(599\) | −3.73628e26 | −1.53775 | −0.768873 | − | 0.639402i | \(-0.779182\pi\) | ||||
−0.768873 | + | 0.639402i | \(0.779182\pi\) | |||||||
\(600\) | −1.35845e25 | −0.0550309 | ||||||||
\(601\) | −2.04542e26 | −0.815597 | −0.407798 | − | 0.913072i | \(-0.633703\pi\) | ||||
−0.407798 | + | 0.913072i | \(0.633703\pi\) | |||||||
\(602\) | −1.13698e25 | −0.0446260 | ||||||||
\(603\) | −1.44842e26 | −0.559605 | ||||||||
\(604\) | −1.51214e26 | −0.575097 | ||||||||
\(605\) | 2.05748e25 | 0.0770300 | ||||||||
\(606\) | 1.62165e26 | 0.597679 | ||||||||
\(607\) | −2.78691e26 | −1.01118 | −0.505591 | − | 0.862773i | \(-0.668726\pi\) | ||||
−0.505591 | + | 0.862773i | \(0.668726\pi\) | |||||||
\(608\) | −3.41113e25 | −0.121847 | ||||||||
\(609\) | −2.90603e26 | −1.02196 | ||||||||
\(610\) | 2.81872e26 | 0.975929 | ||||||||
\(611\) | −6.26287e26 | −2.13492 | ||||||||
\(612\) | 5.31271e25 | 0.178311 | ||||||||
\(613\) | 1.83909e26 | 0.607754 | 0.303877 | − | 0.952711i | \(-0.401719\pi\) | ||||
0.303877 | + | 0.952711i | \(0.401719\pi\) | |||||||
\(614\) | −2.45776e25 | −0.0799724 | ||||||||
\(615\) | 1.37397e26 | 0.440212 | ||||||||
\(616\) | −1.49855e26 | −0.472776 | ||||||||
\(617\) | 5.72893e26 | 1.77977 | 0.889886 | − | 0.456183i | \(-0.150784\pi\) | ||||
0.889886 | + | 0.456183i | \(0.150784\pi\) | |||||||
\(618\) | 1.51528e24 | 0.00463557 | ||||||||
\(619\) | −4.19679e26 | −1.26432 | −0.632159 | − | 0.774838i | \(-0.717831\pi\) | ||||
−0.632159 | + | 0.774838i | \(0.717831\pi\) | |||||||
\(620\) | −1.90750e26 | −0.565905 | ||||||||
\(621\) | 1.04347e25 | 0.0304866 | ||||||||
\(622\) | 1.50014e26 | 0.431642 | ||||||||
\(623\) | −1.90186e26 | −0.538943 | ||||||||
\(624\) | −8.01263e25 | −0.223625 | ||||||||
\(625\) | −2.39278e26 | −0.657723 | ||||||||
\(626\) | −4.66860e26 | −1.26395 | ||||||||
\(627\) | 1.42351e26 | 0.379593 | ||||||||
\(628\) | 1.45858e26 | 0.383102 | ||||||||
\(629\) | 6.21098e26 | 1.60686 | ||||||||
\(630\) | −1.10813e26 | −0.282395 | ||||||||
\(631\) | 3.87489e26 | 0.972704 | 0.486352 | − | 0.873763i | \(-0.338327\pi\) | ||||
0.486352 | + | 0.873763i | \(0.338327\pi\) | |||||||
\(632\) | −5.48286e25 | −0.135580 | ||||||||
\(633\) | −2.67297e26 | −0.651116 | ||||||||
\(634\) | −9.36202e25 | −0.224658 | ||||||||
\(635\) | 1.13086e26 | 0.267336 | ||||||||
\(636\) | 1.87526e26 | 0.436737 | ||||||||
\(637\) | 6.51801e26 | 1.49551 | ||||||||
\(638\) | −3.76752e26 | −0.851646 | ||||||||
\(639\) | 2.64545e26 | 0.589172 | ||||||||
\(640\) | 3.44260e25 | 0.0755400 | ||||||||
\(641\) | 2.30520e26 | 0.498376 | 0.249188 | − | 0.968455i | \(-0.419836\pi\) | ||||
0.249188 | + | 0.968455i | \(0.419836\pi\) | |||||||
\(642\) | 2.05362e26 | 0.437459 | ||||||||
\(643\) | −3.49990e26 | −0.734600 | −0.367300 | − | 0.930103i | \(-0.619718\pi\) | ||||
−0.367300 | + | 0.930103i | \(0.619718\pi\) | |||||||
\(644\) | 5.36892e25 | 0.111038 | ||||||||
\(645\) | −1.09001e25 | −0.0222133 | ||||||||
\(646\) | −2.59664e26 | −0.521439 | ||||||||
\(647\) | 3.77903e26 | 0.747808 | 0.373904 | − | 0.927467i | \(-0.378019\pi\) | ||||
0.373904 | + | 0.927467i | \(0.378019\pi\) | |||||||
\(648\) | −2.01454e25 | −0.0392837 | ||||||||
\(649\) | −3.09354e26 | −0.594471 | ||||||||
\(650\) | 1.55961e26 | 0.295352 | ||||||||
\(651\) | 5.74330e26 | 1.07187 | ||||||||
\(652\) | 3.92201e26 | 0.721367 | ||||||||
\(653\) | 8.44532e26 | 1.53088 | 0.765439 | − | 0.643508i | \(-0.222522\pi\) | ||||
0.765439 | + | 0.643508i | \(0.222522\pi\) | |||||||
\(654\) | 3.61063e26 | 0.645051 | ||||||||
\(655\) | −6.01684e26 | −1.05944 | ||||||||
\(656\) | 1.28519e26 | 0.223039 | ||||||||
\(657\) | −2.69166e25 | −0.0460415 | ||||||||
\(658\) | −8.10181e26 | −1.36595 | ||||||||
\(659\) | −2.79794e26 | −0.464972 | −0.232486 | − | 0.972600i | \(-0.574686\pi\) | ||||
−0.232486 | + | 0.972600i | \(0.574686\pi\) | |||||||
\(660\) | −1.43664e26 | −0.235332 | ||||||||
\(661\) | −1.04973e26 | −0.169498 | −0.0847491 | − | 0.996402i | \(-0.527009\pi\) | ||||
−0.0847491 | + | 0.996402i | \(0.527009\pi\) | |||||||
\(662\) | 2.04267e26 | 0.325122 | ||||||||
\(663\) | −6.09942e26 | −0.956996 | ||||||||
\(664\) | 2.68134e25 | 0.0414720 | ||||||||
\(665\) | 5.41612e26 | 0.825814 | ||||||||
\(666\) | −2.35516e26 | −0.354009 | ||||||||
\(667\) | 1.34980e26 | 0.200021 | ||||||||
\(668\) | −2.51446e26 | −0.367340 | ||||||||
\(669\) | −4.92694e25 | −0.0709626 | ||||||||
\(670\) | −7.14463e26 | −1.01454 | ||||||||
\(671\) | −1.10028e27 | −1.54043 | ||||||||
\(672\) | −1.03653e26 | −0.143079 | ||||||||
\(673\) | −8.12980e26 | −1.10646 | −0.553231 | − | 0.833028i | \(-0.686605\pi\) | ||||
−0.553231 | + | 0.833028i | \(0.686605\pi\) | |||||||
\(674\) | 7.26611e26 | 0.975063 | ||||||||
\(675\) | 3.92118e25 | 0.0518837 | ||||||||
\(676\) | 5.36681e26 | 0.700201 | ||||||||
\(677\) | −7.93130e26 | −1.02036 | −0.510178 | − | 0.860069i | \(-0.670421\pi\) | ||||
−0.510178 | + | 0.860069i | \(0.670421\pi\) | |||||||
\(678\) | −1.68559e25 | −0.0213830 | ||||||||
\(679\) | −3.76316e26 | −0.470749 | ||||||||
\(680\) | 2.62060e26 | 0.323270 | ||||||||
\(681\) | −1.63589e24 | −0.00199001 | ||||||||
\(682\) | 7.44590e26 | 0.893235 | ||||||||
\(683\) | 5.15218e26 | 0.609528 | 0.304764 | − | 0.952428i | \(-0.401422\pi\) | ||||
0.304764 | + | 0.952428i | \(0.401422\pi\) | |||||||
\(684\) | 9.84626e25 | 0.114878 | ||||||||
\(685\) | −1.87788e26 | −0.216077 | ||||||||
\(686\) | −3.03377e25 | −0.0344274 | ||||||||
\(687\) | −6.38965e24 | −0.00715135 | ||||||||
\(688\) | −1.01958e25 | −0.0112546 | ||||||||
\(689\) | −2.15296e27 | −2.34397 | ||||||||
\(690\) | 5.14710e25 | 0.0552709 | ||||||||
\(691\) | 9.85717e26 | 1.04402 | 0.522012 | − | 0.852938i | \(-0.325182\pi\) | ||||
0.522012 | + | 0.852938i | \(0.325182\pi\) | |||||||
\(692\) | −1.44625e26 | −0.151090 | ||||||||
\(693\) | 4.32558e26 | 0.445737 | ||||||||
\(694\) | 7.52659e25 | 0.0765039 | ||||||||
\(695\) | 1.18645e27 | 1.18958 | ||||||||
\(696\) | −2.60596e26 | −0.257739 | ||||||||
\(697\) | 9.78321e26 | 0.954487 | ||||||||
\(698\) | −3.92898e26 | −0.378140 | ||||||||
\(699\) | 2.73578e26 | 0.259745 | ||||||||
\(700\) | 2.01755e26 | 0.188970 | ||||||||
\(701\) | 1.32660e27 | 1.22580 | 0.612899 | − | 0.790161i | \(-0.290003\pi\) | ||||
0.612899 | + | 0.790161i | \(0.290003\pi\) | |||||||
\(702\) | 2.31285e26 | 0.210836 | ||||||||
\(703\) | 1.15111e27 | 1.03524 | ||||||||
\(704\) | −1.34382e26 | −0.119234 | ||||||||
\(705\) | −7.76708e26 | −0.679925 | ||||||||
\(706\) | 9.57655e26 | 0.827112 | ||||||||
\(707\) | −2.40846e27 | −2.05236 | ||||||||
\(708\) | −2.13977e26 | −0.179908 | ||||||||
\(709\) | −5.63780e26 | −0.467703 | −0.233851 | − | 0.972272i | \(-0.575133\pi\) | ||||
−0.233851 | + | 0.972272i | \(0.575133\pi\) | |||||||
\(710\) | 1.30492e27 | 1.06814 | ||||||||
\(711\) | 1.58263e26 | 0.127826 | ||||||||
\(712\) | −1.70548e26 | −0.135921 | ||||||||
\(713\) | −2.66767e26 | −0.209789 | ||||||||
\(714\) | −7.89037e26 | −0.612300 | ||||||||
\(715\) | 1.64938e27 | 1.26303 | ||||||||
\(716\) | −3.47896e26 | −0.262891 | ||||||||
\(717\) | 1.34189e26 | 0.100065 | ||||||||
\(718\) | −8.31960e26 | −0.612238 | ||||||||
\(719\) | −1.69545e27 | −1.23129 | −0.615645 | − | 0.788024i | \(-0.711104\pi\) | ||||
−0.615645 | + | 0.788024i | \(0.711104\pi\) | |||||||
\(720\) | −9.93709e25 | −0.0712198 | ||||||||
\(721\) | −2.25048e25 | −0.0159181 | ||||||||
\(722\) | 5.31705e26 | 0.371165 | ||||||||
\(723\) | 2.16913e26 | 0.149442 | ||||||||
\(724\) | −7.73517e26 | −0.525961 | ||||||||
\(725\) | 5.07234e26 | 0.340406 | ||||||||
\(726\) | −5.55521e25 | −0.0367962 | ||||||||
\(727\) | 2.57739e27 | 1.68501 | 0.842507 | − | 0.538685i | \(-0.181079\pi\) | ||||
0.842507 | + | 0.538685i | \(0.181079\pi\) | |||||||
\(728\) | 1.19003e27 | 0.767906 | ||||||||
\(729\) | 5.81497e25 | 0.0370370 | ||||||||
\(730\) | −1.32771e26 | −0.0834713 | ||||||||
\(731\) | −7.76132e25 | −0.0481638 | ||||||||
\(732\) | −7.61055e26 | −0.466188 | ||||||||
\(733\) | −7.00439e26 | −0.423528 | −0.211764 | − | 0.977321i | \(-0.567921\pi\) | ||||
−0.211764 | + | 0.977321i | \(0.567921\pi\) | |||||||
\(734\) | 1.53787e26 | 0.0917925 | ||||||||
\(735\) | 8.08350e26 | 0.476288 | ||||||||
\(736\) | 4.81454e25 | 0.0280037 | ||||||||
\(737\) | 2.78890e27 | 1.60137 | ||||||||
\(738\) | −3.70971e26 | −0.210283 | ||||||||
\(739\) | −2.24718e27 | −1.25752 | −0.628760 | − | 0.777599i | \(-0.716437\pi\) | ||||
−0.628760 | + | 0.777599i | \(0.716437\pi\) | |||||||
\(740\) | −1.16173e27 | −0.641804 | ||||||||
\(741\) | −1.13043e27 | −0.616554 | ||||||||
\(742\) | −2.78512e27 | −1.49971 | ||||||||
\(743\) | −2.12060e26 | −0.112737 | −0.0563683 | − | 0.998410i | \(-0.517952\pi\) | ||||
−0.0563683 | + | 0.998410i | \(0.517952\pi\) | |||||||
\(744\) | 5.15026e26 | 0.270325 | ||||||||
\(745\) | −1.58561e27 | −0.821695 | ||||||||
\(746\) | −1.37696e27 | −0.704532 | ||||||||
\(747\) | −7.73971e25 | −0.0391002 | ||||||||
\(748\) | −1.02295e27 | −0.510256 | ||||||||
\(749\) | −3.05001e27 | −1.50219 | ||||||||
\(750\) | 9.10864e26 | 0.442967 | ||||||||
\(751\) | 3.31814e27 | 1.59337 | 0.796684 | − | 0.604397i | \(-0.206586\pi\) | ||||
0.796684 | + | 0.604397i | \(0.206586\pi\) | |||||||
\(752\) | −7.26523e26 | −0.344493 | ||||||||
\(753\) | −2.53307e26 | −0.118603 | ||||||||
\(754\) | 2.99185e27 | 1.38329 | ||||||||
\(755\) | 2.15302e27 | 0.982998 | ||||||||
\(756\) | 2.99196e26 | 0.134896 | ||||||||
\(757\) | 2.98175e26 | 0.132758 | 0.0663789 | − | 0.997794i | \(-0.478855\pi\) | ||||
0.0663789 | + | 0.997794i | \(0.478855\pi\) | |||||||
\(758\) | 1.26273e25 | 0.00555203 | ||||||||
\(759\) | −2.00917e26 | −0.0872407 | ||||||||
\(760\) | 4.85686e26 | 0.208270 | ||||||||
\(761\) | −7.82078e26 | −0.331204 | −0.165602 | − | 0.986193i | \(-0.552957\pi\) | ||||
−0.165602 | + | 0.986193i | \(0.552957\pi\) | |||||||
\(762\) | −3.05332e26 | −0.127703 | ||||||||
\(763\) | −5.36246e27 | −2.21504 | ||||||||
\(764\) | 1.15726e27 | 0.472110 | ||||||||
\(765\) | −7.56437e26 | −0.304782 | ||||||||
\(766\) | −2.27922e27 | −0.907010 | ||||||||
\(767\) | 2.45663e27 | 0.965569 | ||||||||
\(768\) | −9.29503e25 | −0.0360844 | ||||||||
\(769\) | −1.07371e27 | −0.411706 | −0.205853 | − | 0.978583i | \(-0.565997\pi\) | ||||
−0.205853 | + | 0.978583i | \(0.565997\pi\) | |||||||
\(770\) | 2.13368e27 | 0.808104 | ||||||||
\(771\) | 2.18643e27 | 0.817937 | ||||||||
\(772\) | 1.34627e27 | 0.497470 | ||||||||
\(773\) | 3.25274e27 | 1.18725 | 0.593627 | − | 0.804740i | \(-0.297696\pi\) | ||||
0.593627 | + | 0.804740i | \(0.297696\pi\) | |||||||
\(774\) | 2.94303e25 | 0.0106110 | ||||||||
\(775\) | −1.00247e27 | −0.357029 | ||||||||
\(776\) | −3.37458e26 | −0.118723 | ||||||||
\(777\) | 3.49785e27 | 1.21563 | ||||||||
\(778\) | 3.59524e27 | 1.23430 | ||||||||
\(779\) | 1.81316e27 | 0.614937 | ||||||||
\(780\) | 1.14086e27 | 0.382237 | ||||||||
\(781\) | −5.09375e27 | −1.68598 | ||||||||
\(782\) | 3.66495e26 | 0.119841 | ||||||||
\(783\) | 7.52211e26 | 0.242998 | ||||||||
\(784\) | 7.56121e26 | 0.241317 | ||||||||
\(785\) | −2.07677e27 | −0.654827 | ||||||||
\(786\) | 1.62455e27 | 0.506079 | ||||||||
\(787\) | 1.32360e27 | 0.407378 | 0.203689 | − | 0.979036i | \(-0.434707\pi\) | ||||
0.203689 | + | 0.979036i | \(0.434707\pi\) | |||||||
\(788\) | 2.11924e26 | 0.0644439 | ||||||||
\(789\) | −1.62089e27 | −0.486993 | ||||||||
\(790\) | 7.80663e26 | 0.231743 | ||||||||
\(791\) | 2.50342e26 | 0.0734271 | ||||||||
\(792\) | 3.87893e26 | 0.112415 | ||||||||
\(793\) | 8.73753e27 | 2.50204 | ||||||||
\(794\) | −2.79250e27 | −0.790129 | ||||||||
\(795\) | −2.67005e27 | −0.746503 | ||||||||
\(796\) | −1.30700e27 | −0.361079 | ||||||||
\(797\) | −5.29249e27 | −1.44480 | −0.722398 | − | 0.691478i | \(-0.756960\pi\) | ||||
−0.722398 | + | 0.691478i | \(0.756960\pi\) | |||||||
\(798\) | −1.46235e27 | −0.394480 | ||||||||
\(799\) | −5.53048e27 | −1.47424 | ||||||||
\(800\) | 1.80922e26 | 0.0476582 | ||||||||
\(801\) | 4.92288e26 | 0.128148 | ||||||||
\(802\) | −1.97621e27 | −0.508367 | ||||||||
\(803\) | 5.18271e26 | 0.131753 | ||||||||
\(804\) | 1.92905e27 | 0.484632 | ||||||||
\(805\) | −7.64441e26 | −0.189794 | ||||||||
\(806\) | −5.91291e27 | −1.45084 | ||||||||
\(807\) | −2.52639e27 | −0.612634 | ||||||||
\(808\) | −2.15976e27 | −0.517605 | ||||||||
\(809\) | 8.43529e26 | 0.199797 | 0.0998986 | − | 0.994998i | \(-0.468148\pi\) | ||||
0.0998986 | + | 0.994998i | \(0.468148\pi\) | |||||||
\(810\) | 2.86835e26 | 0.0671466 | ||||||||
\(811\) | 2.58962e27 | 0.599153 | 0.299576 | − | 0.954072i | \(-0.403155\pi\) | ||||
0.299576 | + | 0.954072i | \(0.403155\pi\) | |||||||
\(812\) | 3.87033e27 | 0.885046 | ||||||||
\(813\) | −5.56234e26 | −0.125718 | ||||||||
\(814\) | 4.53479e27 | 1.01304 | ||||||||
\(815\) | −5.58426e27 | −1.23301 | ||||||||
\(816\) | −7.07562e26 | −0.154422 | ||||||||
\(817\) | −1.43844e26 | −0.0310300 | ||||||||
\(818\) | −3.86420e27 | −0.823955 | ||||||||
\(819\) | −3.43502e27 | −0.723989 | ||||||||
\(820\) | −1.82989e27 | −0.381235 | ||||||||
\(821\) | 6.26683e27 | 1.29059 | 0.645294 | − | 0.763934i | \(-0.276735\pi\) | ||||
0.645294 | + | 0.763934i | \(0.276735\pi\) | |||||||
\(822\) | 5.07029e26 | 0.103217 | ||||||||
\(823\) | −4.11316e27 | −0.827709 | −0.413854 | − | 0.910343i | \(-0.635818\pi\) | ||||
−0.413854 | + | 0.910343i | \(0.635818\pi\) | |||||||
\(824\) | −2.01810e25 | −0.00401452 | ||||||||
\(825\) | −7.55012e26 | −0.148471 | ||||||||
\(826\) | 3.17796e27 | 0.617785 | ||||||||
\(827\) | 5.78083e27 | 1.11093 | 0.555466 | − | 0.831539i | \(-0.312540\pi\) | ||||
0.555466 | + | 0.831539i | \(0.312540\pi\) | |||||||
\(828\) | −1.38972e26 | −0.0264021 | ||||||||
\(829\) | 4.03871e27 | 0.758534 | 0.379267 | − | 0.925287i | \(-0.376176\pi\) | ||||
0.379267 | + | 0.925287i | \(0.376176\pi\) | |||||||
\(830\) | −3.81776e26 | −0.0708870 | ||||||||
\(831\) | −9.24595e26 | −0.169723 | ||||||||
\(832\) | 1.06715e27 | 0.193665 | ||||||||
\(833\) | 5.75579e27 | 1.03271 | ||||||||
\(834\) | −3.20341e27 | −0.568245 | ||||||||
\(835\) | 3.58016e27 | 0.627886 | ||||||||
\(836\) | −1.89587e27 | −0.328737 | ||||||||
\(837\) | −1.48663e27 | −0.254865 | ||||||||
\(838\) | −6.10721e27 | −1.03520 | ||||||||
\(839\) | 7.16187e27 | 1.20030 | 0.600148 | − | 0.799889i | \(-0.295108\pi\) | ||||
0.600148 | + | 0.799889i | \(0.295108\pi\) | |||||||
\(840\) | 1.47584e27 | 0.244561 | ||||||||
\(841\) | 3.62716e27 | 0.594299 | ||||||||
\(842\) | −3.23620e27 | −0.524289 | ||||||||
\(843\) | −2.84220e26 | −0.0455294 | ||||||||
\(844\) | 3.55994e27 | 0.563883 | ||||||||
\(845\) | −7.64140e27 | −1.19683 | ||||||||
\(846\) | 2.09711e27 | 0.324791 | ||||||||
\(847\) | 8.25052e26 | 0.126354 | ||||||||
\(848\) | −2.49753e27 | −0.378225 | ||||||||
\(849\) | 5.01135e27 | 0.750468 | ||||||||
\(850\) | 1.37723e27 | 0.203951 | ||||||||
\(851\) | −1.62470e27 | −0.237926 | ||||||||
\(852\) | −3.52329e27 | −0.510238 | ||||||||
\(853\) | 1.17165e28 | 1.67796 | 0.838982 | − | 0.544159i | \(-0.183151\pi\) | ||||
0.838982 | + | 0.544159i | \(0.183151\pi\) | |||||||
\(854\) | 1.13031e28 | 1.60084 | ||||||||
\(855\) | −1.40194e27 | −0.196359 | ||||||||
\(856\) | −2.73507e27 | −0.378851 | ||||||||
\(857\) | −1.10156e28 | −1.50901 | −0.754505 | − | 0.656295i | \(-0.772123\pi\) | ||||
−0.754505 | + | 0.656295i | \(0.772123\pi\) | |||||||
\(858\) | −4.45333e27 | −0.603331 | ||||||||
\(859\) | 3.04449e27 | 0.407924 | 0.203962 | − | 0.978979i | \(-0.434618\pi\) | ||||
0.203962 | + | 0.978979i | \(0.434618\pi\) | |||||||
\(860\) | 1.45171e26 | 0.0192373 | ||||||||
\(861\) | 5.50962e27 | 0.722090 | ||||||||
\(862\) | 7.18898e27 | 0.931855 | ||||||||
\(863\) | −2.46553e26 | −0.0316088 | −0.0158044 | − | 0.999875i | \(-0.505031\pi\) | ||||
−0.0158044 | + | 0.999875i | \(0.505031\pi\) | |||||||
\(864\) | 2.68302e26 | 0.0340207 | ||||||||
\(865\) | 2.05921e27 | 0.258254 | ||||||||
\(866\) | 3.22328e27 | 0.399832 | ||||||||
\(867\) | −6.80482e26 | −0.0834902 | ||||||||
\(868\) | −7.64909e27 | −0.928266 | ||||||||
\(869\) | −3.04731e27 | −0.365788 | ||||||||
\(870\) | 3.71043e27 | 0.440546 | ||||||||
\(871\) | −2.21471e28 | −2.60102 | ||||||||
\(872\) | −4.80874e27 | −0.558631 | ||||||||
\(873\) | 9.74076e26 | 0.111933 | ||||||||
\(874\) | 6.79240e26 | 0.0772085 | ||||||||
\(875\) | −1.35280e28 | −1.52110 | ||||||||
\(876\) | 3.58483e26 | 0.0398731 | ||||||||
\(877\) | −1.08028e28 | −1.18861 | −0.594303 | − | 0.804241i | \(-0.702572\pi\) | ||||
−0.594303 | + | 0.804241i | \(0.702572\pi\) | |||||||
\(878\) | 1.60826e27 | 0.175048 | ||||||||
\(879\) | −2.37151e25 | −0.00255347 | ||||||||
\(880\) | 1.91336e27 | 0.203803 | ||||||||
\(881\) | 1.28087e28 | 1.34969 | 0.674847 | − | 0.737958i | \(-0.264210\pi\) | ||||
0.674847 | + | 0.737958i | \(0.264210\pi\) | |||||||
\(882\) | −2.18255e27 | −0.227516 | ||||||||
\(883\) | 9.95748e26 | 0.102689 | 0.0513443 | − | 0.998681i | \(-0.483649\pi\) | ||||
0.0513443 | + | 0.998681i | \(0.483649\pi\) | |||||||
\(884\) | 8.12339e27 | 0.828782 | ||||||||
\(885\) | 3.04666e27 | 0.307512 | ||||||||
\(886\) | −9.91580e27 | −0.990165 | ||||||||
\(887\) | 4.91403e27 | 0.485471 | 0.242736 | − | 0.970092i | \(-0.421955\pi\) | ||||
0.242736 | + | 0.970092i | \(0.421955\pi\) | |||||||
\(888\) | 3.13667e27 | 0.306581 | ||||||||
\(889\) | 4.53475e27 | 0.438517 | ||||||||
\(890\) | 2.42831e27 | 0.232326 | ||||||||
\(891\) | −1.11966e27 | −0.105986 | ||||||||
\(892\) | 6.56185e26 | 0.0614554 | ||||||||
\(893\) | −1.02499e28 | −0.949794 | ||||||||
\(894\) | 4.28114e27 | 0.392512 | ||||||||
\(895\) | 4.95343e27 | 0.449353 | ||||||||
\(896\) | 1.38049e27 | 0.123910 | ||||||||
\(897\) | 1.59551e27 | 0.141701 | ||||||||
\(898\) | 1.08935e28 | 0.957289 | ||||||||
\(899\) | −1.92306e28 | −1.67215 | ||||||||
\(900\) | −5.22234e26 | −0.0449326 | ||||||||
\(901\) | −1.90119e28 | −1.61860 | ||||||||
\(902\) | 7.14295e27 | 0.601749 | ||||||||
\(903\) | −4.37095e26 | −0.0364370 | ||||||||
\(904\) | 2.24492e26 | 0.0185183 | ||||||||
\(905\) | 1.10135e28 | 0.899011 | ||||||||
\(906\) | −5.81317e27 | −0.469564 | ||||||||
\(907\) | −4.38931e27 | −0.350854 | −0.175427 | − | 0.984492i | \(-0.556131\pi\) | ||||
−0.175427 | + | 0.984492i | \(0.556131\pi\) | |||||||
\(908\) | 2.17872e25 | 0.00172340 | ||||||||
\(909\) | 6.23418e27 | 0.488003 | ||||||||
\(910\) | −1.69439e28 | −1.31256 | ||||||||
\(911\) | 1.44663e28 | 1.10900 | 0.554500 | − | 0.832183i | \(-0.312909\pi\) | ||||
0.554500 | + | 0.832183i | \(0.312909\pi\) | |||||||
\(912\) | −1.31135e27 | −0.0994876 | ||||||||
\(913\) | 1.49026e27 | 0.111890 | ||||||||
\(914\) | 1.07005e28 | 0.795091 | ||||||||
\(915\) | 1.08361e28 | 0.796843 | ||||||||
\(916\) | 8.50992e25 | 0.00619325 | ||||||||
\(917\) | −2.41276e28 | −1.73782 | ||||||||
\(918\) | 2.04238e27 | 0.145590 | ||||||||
\(919\) | 2.02703e28 | 1.43009 | 0.715044 | − | 0.699079i | \(-0.246406\pi\) | ||||
0.715044 | + | 0.699079i | \(0.246406\pi\) | |||||||
\(920\) | −6.85506e26 | −0.0478660 | ||||||||
\(921\) | −9.44846e26 | −0.0652972 | ||||||||
\(922\) | −1.93947e28 | −1.32660 | ||||||||
\(923\) | 4.04503e28 | 2.73845 | ||||||||
\(924\) | −5.76094e27 | −0.386020 | ||||||||
\(925\) | −6.10534e27 | −0.404914 | ||||||||
\(926\) | 5.58157e27 | 0.366397 | ||||||||
\(927\) | 5.82526e25 | 0.00378493 | ||||||||
\(928\) | 3.47069e27 | 0.223208 | ||||||||
\(929\) | 1.69685e27 | 0.108017 | 0.0540087 | − | 0.998540i | \(-0.482800\pi\) | ||||
0.0540087 | + | 0.998540i | \(0.482800\pi\) | |||||||
\(930\) | −7.33307e27 | −0.462059 | ||||||||
\(931\) | 1.06674e28 | 0.665332 | ||||||||
\(932\) | −3.64359e27 | −0.224946 | ||||||||
\(933\) | 5.76705e27 | 0.352434 | ||||||||
\(934\) | 1.80247e28 | 1.09036 | ||||||||
\(935\) | 1.45650e28 | 0.872167 | ||||||||
\(936\) | −3.08032e27 | −0.182589 | ||||||||
\(937\) | 1.88106e28 | 1.10377 | 0.551883 | − | 0.833922i | \(-0.313910\pi\) | ||||
0.551883 | + | 0.833922i | \(0.313910\pi\) | |||||||
\(938\) | −2.86501e28 | −1.66417 | ||||||||
\(939\) | −1.79477e28 | −1.03201 | ||||||||
\(940\) | 1.03444e28 | 0.588832 | ||||||||
\(941\) | −2.39592e28 | −1.35012 | −0.675058 | − | 0.737765i | \(-0.735881\pi\) | ||||
−0.675058 | + | 0.737765i | \(0.735881\pi\) | |||||||
\(942\) | 5.60728e27 | 0.312802 | ||||||||
\(943\) | −2.55913e27 | −0.141329 | ||||||||
\(944\) | 2.84981e27 | 0.155805 | ||||||||
\(945\) | −4.26003e27 | −0.230574 | ||||||||
\(946\) | −5.66672e26 | −0.0303645 | ||||||||
\(947\) | 1.03960e28 | 0.551495 | 0.275748 | − | 0.961230i | \(-0.411075\pi\) | ||||
0.275748 | + | 0.961230i | \(0.411075\pi\) | |||||||
\(948\) | −2.10779e27 | −0.110700 | ||||||||
\(949\) | −4.11568e27 | −0.213999 | ||||||||
\(950\) | 2.55247e27 | 0.131397 | ||||||||
\(951\) | −3.59907e27 | −0.183432 | ||||||||
\(952\) | 1.05086e28 | 0.530267 | ||||||||
\(953\) | −1.88398e28 | −0.941227 | −0.470614 | − | 0.882339i | \(-0.655967\pi\) | ||||
−0.470614 | + | 0.882339i | \(0.655967\pi\) | |||||||
\(954\) | 7.20915e27 | 0.356594 | ||||||||
\(955\) | −1.64773e28 | −0.806965 | ||||||||
\(956\) | −1.78716e27 | −0.0866592 | ||||||||
\(957\) | −1.44836e28 | −0.695366 | ||||||||
\(958\) | −2.37559e28 | −1.12927 | ||||||||
\(959\) | −7.53033e27 | −0.354436 | ||||||||
\(960\) | 1.32345e27 | 0.0616781 | ||||||||
\(961\) | 1.63356e28 | 0.753812 | ||||||||
\(962\) | −3.60115e28 | −1.64542 | ||||||||
\(963\) | 7.89481e27 | 0.357184 | ||||||||
\(964\) | −2.88891e27 | −0.129420 | ||||||||
\(965\) | −1.91685e28 | −0.850313 | ||||||||
\(966\) | 2.06399e27 | 0.0906621 | ||||||||
\(967\) | −2.13424e28 | −0.928308 | −0.464154 | − | 0.885754i | \(-0.653642\pi\) | ||||
−0.464154 | + | 0.885754i | \(0.653642\pi\) | |||||||
\(968\) | 7.39859e26 | 0.0318664 | ||||||||
\(969\) | −9.98236e27 | −0.425753 | ||||||||
\(970\) | 4.80482e27 | 0.202930 | ||||||||
\(971\) | −1.04800e28 | −0.438306 | −0.219153 | − | 0.975691i | \(-0.570329\pi\) | ||||
−0.219153 | + | 0.975691i | \(0.570329\pi\) | |||||||
\(972\) | −7.74455e26 | −0.0320750 | ||||||||
\(973\) | 4.75767e28 | 1.95129 | ||||||||
\(974\) | 1.28084e28 | 0.520219 | ||||||||
\(975\) | 5.99567e27 | 0.241154 | ||||||||
\(976\) | 1.01360e28 | 0.403730 | ||||||||
\(977\) | −3.66937e27 | −0.144742 | −0.0723708 | − | 0.997378i | \(-0.523056\pi\) | ||||
−0.0723708 | + | 0.997378i | \(0.523056\pi\) | |||||||
\(978\) | 1.50775e28 | 0.588994 | ||||||||
\(979\) | −9.47887e27 | −0.366708 | ||||||||
\(980\) | −1.07658e28 | −0.412478 | ||||||||
\(981\) | 1.38805e28 | 0.526682 | ||||||||
\(982\) | −5.94485e26 | −0.0223399 | ||||||||
\(983\) | 2.27156e28 | 0.845407 | 0.422703 | − | 0.906268i | \(-0.361081\pi\) | ||||
0.422703 | + | 0.906268i | \(0.361081\pi\) | |||||||
\(984\) | 4.94071e27 | 0.182111 | ||||||||
\(985\) | −3.01743e27 | −0.110152 | ||||||||
\(986\) | 2.64198e28 | 0.955209 | ||||||||
\(987\) | −3.11461e28 | −1.11530 | ||||||||
\(988\) | 1.50554e28 | 0.533951 | ||||||||
\(989\) | 2.03024e26 | 0.00713152 | ||||||||
\(990\) | −5.52292e27 | −0.192148 | ||||||||
\(991\) | 4.05166e28 | 1.39615 | 0.698077 | − | 0.716022i | \(-0.254039\pi\) | ||||
0.698077 | + | 0.716022i | \(0.254039\pi\) | |||||||
\(992\) | −6.85926e27 | −0.234108 | ||||||||
\(993\) | 7.85269e27 | 0.265461 | ||||||||
\(994\) | 5.23275e28 | 1.75210 | ||||||||
\(995\) | 1.86095e28 | 0.617184 | ||||||||
\(996\) | 1.03080e27 | 0.0338618 | ||||||||
\(997\) | −4.63139e28 | −1.50698 | −0.753489 | − | 0.657460i | \(-0.771631\pi\) | ||||
−0.753489 | + | 0.657460i | \(0.771631\pi\) | |||||||
\(998\) | −1.61957e28 | −0.521987 | ||||||||
\(999\) | −9.05401e27 | −0.289047 |
(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 | 6.20.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.20.a.f.1.1 | 1 | |||
4.3 | odd | 2 | 48.20.a.d.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.20.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.20.a.f.1.1 | 1 | 3.2 | odd | 2 | |||
48.20.a.d.1.1 | 1 | 4.3 | odd | 2 |