Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,54,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 54, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 54);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 54 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(17.7903107608\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2315873743412x^{2} - 421178019174503472x + 612167648493870378955584 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(1.52611e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.29387e8 | 1.36332 | 0.681659 | − | 0.731670i | \(-0.261259\pi\) | ||||
0.681659 | + | 0.731670i | \(0.261259\pi\) | |||||||
\(3\) | 1.34470e12 | 0.305431 | 0.152715 | − | 0.988270i | \(-0.451198\pi\) | ||||
0.152715 | + | 0.988270i | \(0.451198\pi\) | |||||||
\(4\) | 7.73392e15 | 0.858638 | ||||||||
\(5\) | −4.81259e18 | −1.44435 | −0.722177 | − | 0.691708i | \(-0.756858\pi\) | ||||
−0.722177 | + | 0.691708i | \(0.756858\pi\) | |||||||
\(6\) | 1.73988e20 | 0.416400 | ||||||||
\(7\) | −1.66125e22 | −0.668863 | −0.334432 | − | 0.942420i | \(-0.608544\pi\) | ||||
−0.334432 | + | 0.942420i | \(0.608544\pi\) | |||||||
\(8\) | −1.64746e23 | −0.192722 | ||||||||
\(9\) | −1.75750e25 | −0.906712 | ||||||||
\(10\) | −6.22689e26 | −1.96912 | ||||||||
\(11\) | −9.74180e26 | −0.246452 | −0.123226 | − | 0.992379i | \(-0.539324\pi\) | ||||
−0.123226 | + | 0.992379i | \(0.539324\pi\) | |||||||
\(12\) | 1.03998e28 | 0.262254 | ||||||||
\(13\) | 4.82001e29 | 1.45730 | 0.728650 | − | 0.684886i | \(-0.240148\pi\) | ||||
0.728650 | + | 0.684886i | \(0.240148\pi\) | |||||||
\(14\) | −2.14945e30 | −0.911873 | ||||||||
\(15\) | −6.47150e30 | −0.441150 | ||||||||
\(16\) | −9.09771e31 | −1.12138 | ||||||||
\(17\) | 5.02736e32 | 1.24292 | 0.621460 | − | 0.783446i | \(-0.286540\pi\) | ||||
0.621460 | + | 0.783446i | \(0.286540\pi\) | |||||||
\(18\) | −2.27399e33 | −1.23614 | ||||||||
\(19\) | −1.38519e34 | −1.79696 | −0.898479 | − | 0.439017i | \(-0.855327\pi\) | ||||
−0.898479 | + | 0.439017i | \(0.855327\pi\) | |||||||
\(20\) | −3.72202e34 | −1.24018 | ||||||||
\(21\) | −2.23389e34 | −0.204291 | ||||||||
\(22\) | −1.26047e35 | −0.335993 | ||||||||
\(23\) | −5.29051e35 | −0.434220 | −0.217110 | − | 0.976147i | \(-0.569663\pi\) | ||||
−0.217110 | + | 0.976147i | \(0.569663\pi\) | |||||||
\(24\) | −2.21535e35 | −0.0588633 | ||||||||
\(25\) | 1.20588e37 | 1.08616 | ||||||||
\(26\) | 6.23649e37 | 1.98676 | ||||||||
\(27\) | −4.96979e37 | −0.582369 | ||||||||
\(28\) | −1.28480e38 | −0.574311 | ||||||||
\(29\) | −3.32225e38 | −0.585984 | −0.292992 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292992 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(30\) | −8.37331e38 | −0.601429 | ||||||||
\(31\) | 2.69343e39 | 0.811374 | 0.405687 | − | 0.914012i | \(-0.367032\pi\) | ||||
0.405687 | + | 0.914012i | \(0.367032\pi\) | |||||||
\(32\) | −1.02874e40 | −1.33607 | ||||||||
\(33\) | −1.30998e39 | −0.0752742 | ||||||||
\(34\) | 6.50477e40 | 1.69450 | ||||||||
\(35\) | 7.99492e40 | 0.966075 | ||||||||
\(36\) | −1.35924e41 | −0.778537 | ||||||||
\(37\) | 2.08872e41 | 0.578808 | 0.289404 | − | 0.957207i | \(-0.406543\pi\) | ||||
0.289404 | + | 0.957207i | \(0.406543\pi\) | |||||||
\(38\) | −1.79226e42 | −2.44983 | ||||||||
\(39\) | 6.48148e41 | 0.445105 | ||||||||
\(40\) | 7.92857e41 | 0.278359 | ||||||||
\(41\) | 2.96475e42 | 0.541022 | 0.270511 | − | 0.962717i | \(-0.412807\pi\) | ||||
0.270511 | + | 0.962717i | \(0.412807\pi\) | |||||||
\(42\) | −2.89037e42 | −0.278514 | ||||||||
\(43\) | 1.06838e43 | 0.551837 | 0.275919 | − | 0.961181i | \(-0.411018\pi\) | ||||
0.275919 | + | 0.961181i | \(0.411018\pi\) | |||||||
\(44\) | −7.53423e42 | −0.211613 | ||||||||
\(45\) | 8.45814e43 | 1.30961 | ||||||||
\(46\) | −6.84525e43 | −0.591980 | ||||||||
\(47\) | −2.94705e44 | −1.44143 | −0.720716 | − | 0.693230i | \(-0.756187\pi\) | ||||
−0.720716 | + | 0.693230i | \(0.756187\pi\) | |||||||
\(48\) | −1.22337e44 | −0.342504 | ||||||||
\(49\) | −3.40898e44 | −0.552622 | ||||||||
\(50\) | 1.56026e45 | 1.48078 | ||||||||
\(51\) | 6.76030e44 | 0.379626 | ||||||||
\(52\) | 3.72776e45 | 1.25129 | ||||||||
\(53\) | −5.52073e45 | −1.11863 | −0.559314 | − | 0.828956i | \(-0.688936\pi\) | ||||
−0.559314 | + | 0.828956i | \(0.688936\pi\) | |||||||
\(54\) | −6.43028e45 | −0.793954 | ||||||||
\(55\) | 4.68833e45 | 0.355965 | ||||||||
\(56\) | 2.73685e45 | 0.128905 | ||||||||
\(57\) | −1.86266e46 | −0.548846 | ||||||||
\(58\) | −4.29858e46 | −0.798883 | ||||||||
\(59\) | 1.07917e47 | 1.27501 | 0.637503 | − | 0.770448i | \(-0.279967\pi\) | ||||
0.637503 | + | 0.770448i | \(0.279967\pi\) | |||||||
\(60\) | −5.00501e46 | −0.378788 | ||||||||
\(61\) | 3.62994e46 | 0.177280 | 0.0886398 | − | 0.996064i | \(-0.471748\pi\) | ||||
0.0886398 | + | 0.996064i | \(0.471748\pi\) | |||||||
\(62\) | 3.48496e47 | 1.10616 | ||||||||
\(63\) | 2.91965e47 | 0.606466 | ||||||||
\(64\) | −5.11611e47 | −0.700117 | ||||||||
\(65\) | −2.31967e48 | −2.10486 | ||||||||
\(66\) | −1.69495e47 | −0.102623 | ||||||||
\(67\) | 7.15705e47 | 0.290905 | 0.145453 | − | 0.989365i | \(-0.453536\pi\) | ||||
0.145453 | + | 0.989365i | \(0.453536\pi\) | |||||||
\(68\) | 3.88812e48 | 1.06722 | ||||||||
\(69\) | −7.11416e47 | −0.132624 | ||||||||
\(70\) | 1.03444e49 | 1.31707 | ||||||||
\(71\) | −9.79077e48 | −0.855994 | −0.427997 | − | 0.903780i | \(-0.640781\pi\) | ||||
−0.427997 | + | 0.903780i | \(0.640781\pi\) | |||||||
\(72\) | 2.89542e48 | 0.174743 | ||||||||
\(73\) | −2.48596e49 | −1.04097 | −0.520485 | − | 0.853871i | \(-0.674249\pi\) | ||||
−0.520485 | + | 0.853871i | \(0.674249\pi\) | |||||||
\(74\) | 2.70254e49 | 0.789100 | ||||||||
\(75\) | 1.62155e49 | 0.331747 | ||||||||
\(76\) | −1.07129e50 | −1.54294 | ||||||||
\(77\) | 1.61836e49 | 0.164843 | ||||||||
\(78\) | 8.38622e49 | 0.606819 | ||||||||
\(79\) | −2.29029e50 | −1.18242 | −0.591210 | − | 0.806517i | \(-0.701350\pi\) | ||||
−0.591210 | + | 0.806517i | \(0.701350\pi\) | |||||||
\(80\) | 4.37835e50 | 1.61967 | ||||||||
\(81\) | 2.73832e50 | 0.728839 | ||||||||
\(82\) | 3.83601e50 | 0.737586 | ||||||||
\(83\) | −8.70995e50 | −1.21464 | −0.607318 | − | 0.794459i | \(-0.707755\pi\) | ||||
−0.607318 | + | 0.794459i | \(0.707755\pi\) | |||||||
\(84\) | −1.72767e50 | −0.175412 | ||||||||
\(85\) | −2.41946e51 | −1.79522 | ||||||||
\(86\) | 1.38235e51 | 0.752330 | ||||||||
\(87\) | −4.46744e50 | −0.178978 | ||||||||
\(88\) | 1.60493e50 | 0.0474968 | ||||||||
\(89\) | 2.82739e51 | 0.620227 | 0.310114 | − | 0.950700i | \(-0.399633\pi\) | ||||
0.310114 | + | 0.950700i | \(0.399633\pi\) | |||||||
\(90\) | 1.09438e52 | 1.78542 | ||||||||
\(91\) | −8.00725e51 | −0.974734 | ||||||||
\(92\) | −4.09163e51 | −0.372837 | ||||||||
\(93\) | 3.62186e51 | 0.247819 | ||||||||
\(94\) | −3.81311e52 | −1.96513 | ||||||||
\(95\) | 6.66634e52 | 2.59544 | ||||||||
\(96\) | −1.38335e52 | −0.408079 | ||||||||
\(97\) | −5.70641e52 | −1.27912 | −0.639561 | − | 0.768740i | \(-0.720884\pi\) | ||||
−0.639561 | + | 0.768740i | \(0.720884\pi\) | |||||||
\(98\) | −4.41079e52 | −0.753400 | ||||||||
\(99\) | 1.71212e52 | 0.223461 | ||||||||
\(100\) | 9.32617e52 | 0.932617 | ||||||||
\(101\) | 2.16630e52 | 0.166418 | 0.0832092 | − | 0.996532i | \(-0.473483\pi\) | ||||
0.0832092 | + | 0.996532i | \(0.473483\pi\) | |||||||
\(102\) | 8.74698e52 | 0.517552 | ||||||||
\(103\) | 1.64434e53 | 0.751284 | 0.375642 | − | 0.926765i | \(-0.377422\pi\) | ||||
0.375642 | + | 0.926765i | \(0.377422\pi\) | |||||||
\(104\) | −7.94079e52 | −0.280854 | ||||||||
\(105\) | 1.07508e53 | 0.295069 | ||||||||
\(106\) | −7.14313e53 | −1.52505 | ||||||||
\(107\) | −6.28499e53 | −1.04625 | −0.523124 | − | 0.852257i | \(-0.675234\pi\) | ||||
−0.523124 | + | 0.852257i | \(0.675234\pi\) | |||||||
\(108\) | −3.84359e53 | −0.500044 | ||||||||
\(109\) | 1.11123e54 | 1.13240 | 0.566201 | − | 0.824267i | \(-0.308412\pi\) | ||||
0.566201 | + | 0.824267i | \(0.308412\pi\) | |||||||
\(110\) | 6.06611e53 | 0.485293 | ||||||||
\(111\) | 2.80871e53 | 0.176786 | ||||||||
\(112\) | 1.51136e54 | 0.750049 | ||||||||
\(113\) | 3.22273e53 | 0.126371 | 0.0631853 | − | 0.998002i | \(-0.479874\pi\) | ||||
0.0631853 | + | 0.998002i | \(0.479874\pi\) | |||||||
\(114\) | −2.41005e54 | −0.748253 | ||||||||
\(115\) | 2.54610e54 | 0.627167 | ||||||||
\(116\) | −2.56940e54 | −0.503148 | ||||||||
\(117\) | −8.47118e54 | −1.32135 | ||||||||
\(118\) | 1.39631e55 | 1.73824 | ||||||||
\(119\) | −8.35170e54 | −0.831344 | ||||||||
\(120\) | 1.06616e54 | 0.0850194 | ||||||||
\(121\) | −1.46757e55 | −0.939261 | ||||||||
\(122\) | 4.69669e54 | 0.241689 | ||||||||
\(123\) | 3.98670e54 | 0.165245 | ||||||||
\(124\) | 2.08308e55 | 0.696676 | ||||||||
\(125\) | −4.60355e54 | −0.124445 | ||||||||
\(126\) | 3.77766e55 | 0.826807 | ||||||||
\(127\) | 1.88562e55 | 0.334700 | 0.167350 | − | 0.985898i | \(-0.446479\pi\) | ||||
0.167350 | + | 0.985898i | \(0.446479\pi\) | |||||||
\(128\) | 2.64645e55 | 0.381593 | ||||||||
\(129\) | 1.43665e55 | 0.168548 | ||||||||
\(130\) | −3.00137e56 | −2.86959 | ||||||||
\(131\) | −7.70511e55 | −0.601298 | −0.300649 | − | 0.953735i | \(-0.597203\pi\) | ||||
−0.300649 | + | 0.953735i | \(0.597203\pi\) | |||||||
\(132\) | −1.01313e55 | −0.0646332 | ||||||||
\(133\) | 2.30114e56 | 1.20192 | ||||||||
\(134\) | 9.26033e55 | 0.396597 | ||||||||
\(135\) | 2.39176e56 | 0.841147 | ||||||||
\(136\) | −8.28239e55 | −0.239538 | ||||||||
\(137\) | 2.23996e56 | 0.533513 | 0.266757 | − | 0.963764i | \(-0.414048\pi\) | ||||
0.266757 | + | 0.963764i | \(0.414048\pi\) | |||||||
\(138\) | −9.20483e55 | −0.180809 | ||||||||
\(139\) | −4.13628e56 | −0.670993 | −0.335496 | − | 0.942042i | \(-0.608904\pi\) | ||||
−0.335496 | + | 0.942042i | \(0.608904\pi\) | |||||||
\(140\) | 6.18321e56 | 0.829509 | ||||||||
\(141\) | −3.96291e56 | −0.440258 | ||||||||
\(142\) | −1.26680e57 | −1.16699 | ||||||||
\(143\) | −4.69556e56 | −0.359155 | ||||||||
\(144\) | 1.59892e57 | 1.01677 | ||||||||
\(145\) | 1.59886e57 | 0.846369 | ||||||||
\(146\) | −3.21652e57 | −1.41917 | ||||||||
\(147\) | −4.58406e56 | −0.168788 | ||||||||
\(148\) | 1.61540e57 | 0.496986 | ||||||||
\(149\) | −2.00904e57 | −0.517073 | −0.258536 | − | 0.966001i | \(-0.583240\pi\) | ||||
−0.258536 | + | 0.966001i | \(0.583240\pi\) | |||||||
\(150\) | 2.09808e57 | 0.452276 | ||||||||
\(151\) | 1.00882e58 | 1.82358 | 0.911790 | − | 0.410656i | \(-0.134700\pi\) | ||||
0.911790 | + | 0.410656i | \(0.134700\pi\) | |||||||
\(152\) | 2.28205e57 | 0.346313 | ||||||||
\(153\) | −8.83559e57 | −1.12697 | ||||||||
\(154\) | 2.09395e57 | 0.224733 | ||||||||
\(155\) | −1.29624e58 | −1.17191 | ||||||||
\(156\) | 5.01272e57 | 0.382183 | ||||||||
\(157\) | −6.27576e57 | −0.403948 | −0.201974 | − | 0.979391i | \(-0.564736\pi\) | ||||
−0.201974 | + | 0.979391i | \(0.564736\pi\) | |||||||
\(158\) | −2.96334e58 | −1.61202 | ||||||||
\(159\) | −7.42374e57 | −0.341664 | ||||||||
\(160\) | 4.95090e58 | 1.92977 | ||||||||
\(161\) | 8.78886e57 | 0.290433 | ||||||||
\(162\) | 3.54304e58 | 0.993639 | ||||||||
\(163\) | 9.18357e55 | 0.00218796 | 0.00109398 | − | 0.999999i | \(-0.499652\pi\) | ||||
0.00109398 | + | 0.999999i | \(0.499652\pi\) | |||||||
\(164\) | 2.29291e58 | 0.464542 | ||||||||
\(165\) | 6.30441e57 | 0.108723 | ||||||||
\(166\) | −1.12696e59 | −1.65594 | ||||||||
\(167\) | −3.13517e58 | −0.392893 | −0.196447 | − | 0.980515i | \(-0.562940\pi\) | ||||
−0.196447 | + | 0.980515i | \(0.562940\pi\) | |||||||
\(168\) | 3.68025e57 | 0.0393715 | ||||||||
\(169\) | 1.22930e59 | 1.12372 | ||||||||
\(170\) | −3.13048e59 | −2.44745 | ||||||||
\(171\) | 2.43447e59 | 1.62932 | ||||||||
\(172\) | 8.26275e58 | 0.473828 | ||||||||
\(173\) | −4.28978e58 | −0.210966 | −0.105483 | − | 0.994421i | \(-0.533639\pi\) | ||||
−0.105483 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(174\) | −5.78031e58 | −0.244004 | ||||||||
\(175\) | −2.00327e59 | −0.726492 | ||||||||
\(176\) | 8.86280e58 | 0.276367 | ||||||||
\(177\) | 1.45117e59 | 0.389426 | ||||||||
\(178\) | 3.65829e59 | 0.845567 | ||||||||
\(179\) | 1.12342e59 | 0.223840 | 0.111920 | − | 0.993717i | \(-0.464300\pi\) | ||||
0.111920 | + | 0.993717i | \(0.464300\pi\) | |||||||
\(180\) | 6.54146e59 | 1.12448 | ||||||||
\(181\) | −6.03513e59 | −0.895786 | −0.447893 | − | 0.894087i | \(-0.647825\pi\) | ||||
−0.447893 | + | 0.894087i | \(0.647825\pi\) | |||||||
\(182\) | −1.03604e60 | −1.32887 | ||||||||
\(183\) | 4.88119e58 | 0.0541467 | ||||||||
\(184\) | 8.71592e58 | 0.0836837 | ||||||||
\(185\) | −1.00522e60 | −0.836004 | ||||||||
\(186\) | 4.68624e59 | 0.337856 | ||||||||
\(187\) | −4.89755e59 | −0.306321 | ||||||||
\(188\) | −2.27922e60 | −1.23767 | ||||||||
\(189\) | 8.25606e59 | 0.389525 | ||||||||
\(190\) | 8.62540e60 | 3.53842 | ||||||||
\(191\) | −1.23426e60 | −0.440577 | −0.220289 | − | 0.975435i | \(-0.570700\pi\) | ||||
−0.220289 | + | 0.975435i | \(0.570700\pi\) | |||||||
\(192\) | −6.87964e59 | −0.213837 | ||||||||
\(193\) | 4.53607e60 | 1.22860 | 0.614301 | − | 0.789072i | \(-0.289438\pi\) | ||||
0.614301 | + | 0.789072i | \(0.289438\pi\) | |||||||
\(194\) | −7.38338e60 | −1.74385 | ||||||||
\(195\) | −3.11927e60 | −0.642889 | ||||||||
\(196\) | −2.63648e60 | −0.474502 | ||||||||
\(197\) | −2.14130e60 | −0.336761 | −0.168381 | − | 0.985722i | \(-0.553854\pi\) | ||||
−0.168381 | + | 0.985722i | \(0.553854\pi\) | |||||||
\(198\) | 2.21527e60 | 0.304649 | ||||||||
\(199\) | 9.14306e59 | 0.110023 | 0.0550117 | − | 0.998486i | \(-0.482480\pi\) | ||||
0.0550117 | + | 0.998486i | \(0.482480\pi\) | |||||||
\(200\) | −1.98664e60 | −0.209327 | ||||||||
\(201\) | 9.62411e59 | 0.0888515 | ||||||||
\(202\) | 2.80292e60 | 0.226881 | ||||||||
\(203\) | 5.51910e60 | 0.391943 | ||||||||
\(204\) | 5.22836e60 | 0.325961 | ||||||||
\(205\) | −1.42681e61 | −0.781428 | ||||||||
\(206\) | 2.12756e61 | 1.02424 | ||||||||
\(207\) | 9.29807e60 | 0.393712 | ||||||||
\(208\) | −4.38510e61 | −1.63419 | ||||||||
\(209\) | 1.34942e61 | 0.442864 | ||||||||
\(210\) | 1.39102e61 | 0.402273 | ||||||||
\(211\) | 6.72523e61 | 1.71483 | 0.857417 | − | 0.514623i | \(-0.172068\pi\) | ||||
0.857417 | + | 0.514623i | \(0.172068\pi\) | |||||||
\(212\) | −4.26969e61 | −0.960497 | ||||||||
\(213\) | −1.31657e61 | −0.261447 | ||||||||
\(214\) | −8.13199e61 | −1.42637 | ||||||||
\(215\) | −5.14167e61 | −0.797049 | ||||||||
\(216\) | 8.18755e60 | 0.112235 | ||||||||
\(217\) | −4.47447e61 | −0.542698 | ||||||||
\(218\) | 1.43779e62 | 1.54383 | ||||||||
\(219\) | −3.34288e61 | −0.317944 | ||||||||
\(220\) | 3.62592e61 | 0.305645 | ||||||||
\(221\) | 2.42319e62 | 1.81131 | ||||||||
\(222\) | 3.63412e61 | 0.241015 | ||||||||
\(223\) | −1.36676e62 | −0.804660 | −0.402330 | − | 0.915495i | \(-0.631799\pi\) | ||||
−0.402330 | + | 0.915495i | \(0.631799\pi\) | |||||||
\(224\) | 1.70899e62 | 0.893651 | ||||||||
\(225\) | −2.11934e62 | −0.984834 | ||||||||
\(226\) | 4.16981e61 | 0.172283 | ||||||||
\(227\) | −4.41921e62 | −1.62427 | −0.812137 | − | 0.583467i | \(-0.801696\pi\) | ||||
−0.812137 | + | 0.583467i | \(0.801696\pi\) | |||||||
\(228\) | −1.44057e62 | −0.471260 | ||||||||
\(229\) | −1.20175e62 | −0.350087 | −0.175043 | − | 0.984561i | \(-0.556007\pi\) | ||||
−0.175043 | + | 0.984561i | \(0.556007\pi\) | |||||||
\(230\) | 3.29434e62 | 0.855029 | ||||||||
\(231\) | 2.17621e61 | 0.0503481 | ||||||||
\(232\) | 5.47329e61 | 0.112932 | ||||||||
\(233\) | 3.74033e62 | 0.688618 | 0.344309 | − | 0.938856i | \(-0.388113\pi\) | ||||
0.344309 | + | 0.938856i | \(0.388113\pi\) | |||||||
\(234\) | −1.09606e63 | −1.80142 | ||||||||
\(235\) | 1.41829e63 | 2.08194 | ||||||||
\(236\) | 8.34623e62 | 1.09477 | ||||||||
\(237\) | −3.07975e62 | −0.361148 | ||||||||
\(238\) | −1.08061e63 | −1.13339 | ||||||||
\(239\) | −2.03152e62 | −0.190668 | −0.0953339 | − | 0.995445i | \(-0.530392\pi\) | ||||
−0.0953339 | + | 0.995445i | \(0.530392\pi\) | |||||||
\(240\) | 5.88758e62 | 0.494697 | ||||||||
\(241\) | 2.85110e62 | 0.214566 | 0.107283 | − | 0.994229i | \(-0.465785\pi\) | ||||
0.107283 | + | 0.994229i | \(0.465785\pi\) | |||||||
\(242\) | −1.89885e63 | −1.28051 | ||||||||
\(243\) | 1.33153e63 | 0.804979 | ||||||||
\(244\) | 2.80737e62 | 0.152219 | ||||||||
\(245\) | 1.64060e63 | 0.798182 | ||||||||
\(246\) | 5.15829e62 | 0.225282 | ||||||||
\(247\) | −6.67661e63 | −2.61871 | ||||||||
\(248\) | −4.43733e62 | −0.156370 | ||||||||
\(249\) | −1.17123e63 | −0.370987 | ||||||||
\(250\) | −5.95642e62 | −0.169658 | ||||||||
\(251\) | 7.65328e63 | 1.96107 | 0.980537 | − | 0.196336i | \(-0.0629045\pi\) | ||||
0.980537 | + | 0.196336i | \(0.0629045\pi\) | |||||||
\(252\) | 2.25804e63 | 0.520735 | ||||||||
\(253\) | 5.15390e62 | 0.107014 | ||||||||
\(254\) | 2.43976e63 | 0.456302 | ||||||||
\(255\) | −3.25346e63 | −0.548315 | ||||||||
\(256\) | 8.03236e63 | 1.22035 | ||||||||
\(257\) | −3.77322e63 | −0.516993 | −0.258496 | − | 0.966012i | \(-0.583227\pi\) | ||||
−0.258496 | + | 0.966012i | \(0.583227\pi\) | |||||||
\(258\) | 1.85885e63 | 0.229785 | ||||||||
\(259\) | −3.46989e63 | −0.387143 | ||||||||
\(260\) | −1.79402e64 | −1.80731 | ||||||||
\(261\) | 5.83887e63 | 0.531319 | ||||||||
\(262\) | −9.96945e63 | −0.819761 | ||||||||
\(263\) | −2.00429e64 | −1.48982 | −0.744911 | − | 0.667164i | \(-0.767508\pi\) | ||||
−0.744911 | + | 0.667164i | \(0.767508\pi\) | |||||||
\(264\) | 2.15815e62 | 0.0145070 | ||||||||
\(265\) | 2.65690e64 | 1.61570 | ||||||||
\(266\) | 2.97739e64 | 1.63860 | ||||||||
\(267\) | 3.80200e63 | 0.189437 | ||||||||
\(268\) | 5.53521e63 | 0.249782 | ||||||||
\(269\) | −3.27370e64 | −1.33846 | −0.669228 | − | 0.743058i | \(-0.733375\pi\) | ||||
−0.669228 | + | 0.743058i | \(0.733375\pi\) | |||||||
\(270\) | 3.09463e64 | 1.14675 | ||||||||
\(271\) | 1.33847e64 | 0.449699 | 0.224849 | − | 0.974394i | \(-0.427811\pi\) | ||||
0.224849 | + | 0.974394i | \(0.427811\pi\) | |||||||
\(272\) | −4.57374e64 | −1.39379 | ||||||||
\(273\) | −1.07674e64 | −0.297714 | ||||||||
\(274\) | 2.89823e64 | 0.727348 | ||||||||
\(275\) | −1.17474e64 | −0.267687 | ||||||||
\(276\) | −5.50203e63 | −0.113876 | ||||||||
\(277\) | 4.06188e64 | 0.763858 | 0.381929 | − | 0.924192i | \(-0.375260\pi\) | ||||
0.381929 | + | 0.924192i | \(0.375260\pi\) | |||||||
\(278\) | −5.35183e64 | −0.914777 | ||||||||
\(279\) | −4.73371e64 | −0.735682 | ||||||||
\(280\) | −1.31713e64 | −0.186184 | ||||||||
\(281\) | 7.96754e64 | 1.02472 | 0.512362 | − | 0.858770i | \(-0.328771\pi\) | ||||
0.512362 | + | 0.858770i | \(0.328771\pi\) | |||||||
\(282\) | −5.12750e64 | −0.600212 | ||||||||
\(283\) | 4.10609e64 | 0.437611 | 0.218806 | − | 0.975768i | \(-0.429784\pi\) | ||||
0.218806 | + | 0.975768i | \(0.429784\pi\) | |||||||
\(284\) | −7.57210e64 | −0.734988 | ||||||||
\(285\) | 8.96424e64 | 0.792729 | ||||||||
\(286\) | −6.07546e64 | −0.489643 | ||||||||
\(287\) | −4.92519e64 | −0.361870 | ||||||||
\(288\) | 1.80801e65 | 1.21144 | ||||||||
\(289\) | 8.91397e64 | 0.544852 | ||||||||
\(290\) | 2.06873e65 | 1.15387 | ||||||||
\(291\) | −7.67342e64 | −0.390683 | ||||||||
\(292\) | −1.92262e65 | −0.893816 | ||||||||
\(293\) | 1.54719e65 | 0.656980 | 0.328490 | − | 0.944507i | \(-0.393460\pi\) | ||||
0.328490 | + | 0.944507i | \(0.393460\pi\) | |||||||
\(294\) | −5.93120e64 | −0.230112 | ||||||||
\(295\) | −5.19361e65 | −1.84156 | ||||||||
\(296\) | −3.44109e64 | −0.111549 | ||||||||
\(297\) | 4.84147e64 | 0.143526 | ||||||||
\(298\) | −2.59944e65 | −0.704935 | ||||||||
\(299\) | −2.55003e65 | −0.632788 | ||||||||
\(300\) | 1.25409e65 | 0.284850 | ||||||||
\(301\) | −1.77484e65 | −0.369104 | ||||||||
\(302\) | 1.30529e66 | 2.48612 | ||||||||
\(303\) | 2.91302e64 | 0.0508293 | ||||||||
\(304\) | 1.26020e66 | 2.01507 | ||||||||
\(305\) | −1.74694e65 | −0.256055 | ||||||||
\(306\) | −1.14321e66 | −1.53642 | ||||||||
\(307\) | −5.91230e64 | −0.0728769 | −0.0364384 | − | 0.999336i | \(-0.511601\pi\) | ||||
−0.0364384 | + | 0.999336i | \(0.511601\pi\) | |||||||
\(308\) | 1.25162e65 | 0.141540 | ||||||||
\(309\) | 2.21114e65 | 0.229465 | ||||||||
\(310\) | −1.67717e66 | −1.59769 | ||||||||
\(311\) | 6.42175e63 | 0.00561699 | 0.00280849 | − | 0.999996i | \(-0.499106\pi\) | ||||
0.00280849 | + | 0.999996i | \(0.499106\pi\) | |||||||
\(312\) | −1.06780e65 | −0.0857815 | ||||||||
\(313\) | 1.94924e66 | 1.43860 | 0.719302 | − | 0.694698i | \(-0.244462\pi\) | ||||
0.719302 | + | 0.694698i | \(0.244462\pi\) | |||||||
\(314\) | −8.12005e65 | −0.550710 | ||||||||
\(315\) | −1.40511e66 | −0.875952 | ||||||||
\(316\) | −1.77129e66 | −1.01527 | ||||||||
\(317\) | 3.17927e66 | 1.67593 | 0.837967 | − | 0.545721i | \(-0.183744\pi\) | ||||
0.837967 | + | 0.545721i | \(0.183744\pi\) | |||||||
\(318\) | −9.60539e65 | −0.465797 | ||||||||
\(319\) | 3.23647e65 | 0.144417 | ||||||||
\(320\) | 2.46217e66 | 1.01122 | ||||||||
\(321\) | −8.45145e65 | −0.319557 | ||||||||
\(322\) | 1.13717e66 | 0.395953 | ||||||||
\(323\) | −6.96383e66 | −2.23348 | ||||||||
\(324\) | 2.11780e66 | 0.625808 | ||||||||
\(325\) | 5.81235e66 | 1.58286 | ||||||||
\(326\) | 1.18824e64 | 0.00298289 | ||||||||
\(327\) | 1.49427e66 | 0.345871 | ||||||||
\(328\) | −4.88431e65 | −0.104267 | ||||||||
\(329\) | 4.89579e66 | 0.964121 | ||||||||
\(330\) | 8.15711e65 | 0.148224 | ||||||||
\(331\) | −9.10692e66 | −1.52732 | −0.763659 | − | 0.645620i | \(-0.776599\pi\) | ||||
−0.763659 | + | 0.645620i | \(0.776599\pi\) | |||||||
\(332\) | −6.73621e66 | −1.04293 | ||||||||
\(333\) | −3.67093e66 | −0.524812 | ||||||||
\(334\) | −4.05651e66 | −0.535638 | ||||||||
\(335\) | −3.44440e66 | −0.420171 | ||||||||
\(336\) | 2.03233e66 | 0.229088 | ||||||||
\(337\) | 6.75654e66 | 0.703934 | 0.351967 | − | 0.936012i | \(-0.385513\pi\) | ||||
0.351967 | + | 0.936012i | \(0.385513\pi\) | |||||||
\(338\) | 1.59056e67 | 1.53199 | ||||||||
\(339\) | 4.33362e65 | 0.0385975 | ||||||||
\(340\) | −1.87119e67 | −1.54144 | ||||||||
\(341\) | −2.62389e66 | −0.199965 | ||||||||
\(342\) | 3.14990e67 | 2.22129 | ||||||||
\(343\) | 1.59110e67 | 1.03849 | ||||||||
\(344\) | −1.76012e66 | −0.106351 | ||||||||
\(345\) | 3.42375e66 | 0.191556 | ||||||||
\(346\) | −5.55043e66 | −0.287614 | ||||||||
\(347\) | −3.44317e67 | −1.65283 | −0.826413 | − | 0.563064i | \(-0.809622\pi\) | ||||
−0.826413 | + | 0.563064i | \(0.809622\pi\) | |||||||
\(348\) | −3.45508e66 | −0.153677 | ||||||||
\(349\) | 3.11481e66 | 0.128398 | 0.0641989 | − | 0.997937i | \(-0.479551\pi\) | ||||
0.0641989 | + | 0.997937i | \(0.479551\pi\) | |||||||
\(350\) | −2.59198e67 | −0.990440 | ||||||||
\(351\) | −2.39544e67 | −0.848686 | ||||||||
\(352\) | 1.00218e67 | 0.329279 | ||||||||
\(353\) | −8.64866e66 | −0.263584 | −0.131792 | − | 0.991277i | \(-0.542073\pi\) | ||||
−0.131792 | + | 0.991277i | \(0.542073\pi\) | |||||||
\(354\) | 1.87763e67 | 0.530912 | ||||||||
\(355\) | 4.71190e67 | 1.23636 | ||||||||
\(356\) | 2.18668e67 | 0.532550 | ||||||||
\(357\) | −1.12306e67 | −0.253918 | ||||||||
\(358\) | 1.45357e67 | 0.305166 | ||||||||
\(359\) | −5.93891e67 | −1.15799 | −0.578993 | − | 0.815332i | \(-0.696554\pi\) | ||||
−0.578993 | + | 0.815332i | \(0.696554\pi\) | |||||||
\(360\) | −1.39345e67 | −0.252391 | ||||||||
\(361\) | 1.32453e68 | 2.22906 | ||||||||
\(362\) | −7.80870e67 | −1.22124 | ||||||||
\(363\) | −1.97344e67 | −0.286879 | ||||||||
\(364\) | −6.19274e67 | −0.836944 | ||||||||
\(365\) | 1.19639e68 | 1.50353 | ||||||||
\(366\) | 6.31565e66 | 0.0738192 | ||||||||
\(367\) | 1.25080e66 | 0.0136000 | 0.00679999 | − | 0.999977i | \(-0.497835\pi\) | ||||
0.00679999 | + | 0.999977i | \(0.497835\pi\) | |||||||
\(368\) | 4.81315e67 | 0.486925 | ||||||||
\(369\) | −5.21055e67 | −0.490551 | ||||||||
\(370\) | −1.30062e68 | −1.13974 | ||||||||
\(371\) | 9.17132e67 | 0.748209 | ||||||||
\(372\) | 2.80112e67 | 0.212786 | ||||||||
\(373\) | −2.22554e68 | −1.57453 | −0.787267 | − | 0.616613i | \(-0.788504\pi\) | ||||
−0.787267 | + | 0.616613i | \(0.788504\pi\) | |||||||
\(374\) | −6.33682e67 | −0.417613 | ||||||||
\(375\) | −6.19041e66 | −0.0380094 | ||||||||
\(376\) | 4.85516e67 | 0.277796 | ||||||||
\(377\) | −1.60133e68 | −0.853955 | ||||||||
\(378\) | 1.06823e68 | 0.531047 | ||||||||
\(379\) | 1.79817e68 | 0.833474 | 0.416737 | − | 0.909027i | \(-0.363174\pi\) | ||||
0.416737 | + | 0.909027i | \(0.363174\pi\) | |||||||
\(380\) | 5.15569e68 | 2.22855 | ||||||||
\(381\) | 2.53560e67 | 0.102228 | ||||||||
\(382\) | −1.59698e68 | −0.600647 | ||||||||
\(383\) | −7.96579e67 | −0.279551 | −0.139776 | − | 0.990183i | \(-0.544638\pi\) | ||||
−0.139776 | + | 0.990183i | \(0.544638\pi\) | |||||||
\(384\) | 3.55869e67 | 0.116550 | ||||||||
\(385\) | −7.78849e67 | −0.238092 | ||||||||
\(386\) | 5.86911e68 | 1.67498 | ||||||||
\(387\) | −1.87768e68 | −0.500357 | ||||||||
\(388\) | −4.41329e68 | −1.09830 | ||||||||
\(389\) | −4.61806e68 | −1.07348 | −0.536741 | − | 0.843747i | \(-0.680345\pi\) | ||||
−0.536741 | + | 0.843747i | \(0.680345\pi\) | |||||||
\(390\) | −4.03595e68 | −0.876462 | ||||||||
\(391\) | −2.65973e68 | −0.539701 | ||||||||
\(392\) | 5.61617e67 | 0.106502 | ||||||||
\(393\) | −1.03611e68 | −0.183655 | ||||||||
\(394\) | −2.77057e68 | −0.459113 | ||||||||
\(395\) | 1.10222e69 | 1.70783 | ||||||||
\(396\) | 1.32414e68 | 0.191872 | ||||||||
\(397\) | 9.49592e68 | 1.28703 | 0.643515 | − | 0.765434i | \(-0.277475\pi\) | ||||
0.643515 | + | 0.765434i | \(0.277475\pi\) | |||||||
\(398\) | 1.18300e68 | 0.149997 | ||||||||
\(399\) | 3.09435e68 | 0.367103 | ||||||||
\(400\) | −1.09707e69 | −1.21800 | ||||||||
\(401\) | −4.54047e68 | −0.471818 | −0.235909 | − | 0.971775i | \(-0.575807\pi\) | ||||
−0.235909 | + | 0.971775i | \(0.575807\pi\) | |||||||
\(402\) | 1.24524e68 | 0.121133 | ||||||||
\(403\) | 1.29824e69 | 1.18242 | ||||||||
\(404\) | 1.67540e68 | 0.142893 | ||||||||
\(405\) | −1.31784e69 | −1.05270 | ||||||||
\(406\) | 7.14102e68 | 0.534343 | ||||||||
\(407\) | −2.03479e68 | −0.142649 | ||||||||
\(408\) | −1.11374e68 | −0.0731624 | ||||||||
\(409\) | −4.09199e68 | −0.251923 | −0.125961 | − | 0.992035i | \(-0.540202\pi\) | ||||
−0.125961 | + | 0.992035i | \(0.540202\pi\) | |||||||
\(410\) | −1.84611e69 | −1.06534 | ||||||||
\(411\) | 3.01208e68 | 0.162951 | ||||||||
\(412\) | 1.27172e69 | 0.645080 | ||||||||
\(413\) | −1.79278e69 | −0.852805 | ||||||||
\(414\) | 1.20305e69 | 0.536755 | ||||||||
\(415\) | 4.19174e69 | 1.75437 | ||||||||
\(416\) | −4.95853e69 | −1.94706 | ||||||||
\(417\) | −5.56207e68 | −0.204942 | ||||||||
\(418\) | 1.74598e69 | 0.603765 | ||||||||
\(419\) | −3.39626e69 | −1.10238 | −0.551188 | − | 0.834381i | \(-0.685825\pi\) | ||||
−0.551188 | + | 0.834381i | \(0.685825\pi\) | |||||||
\(420\) | 8.31457e68 | 0.253358 | ||||||||
\(421\) | −5.62917e69 | −1.61053 | −0.805264 | − | 0.592916i | \(-0.797977\pi\) | ||||
−0.805264 | + | 0.592916i | \(0.797977\pi\) | |||||||
\(422\) | 8.70160e69 | 2.33786 | ||||||||
\(423\) | 5.17945e69 | 1.30696 | ||||||||
\(424\) | 9.09521e68 | 0.215584 | ||||||||
\(425\) | 6.06239e69 | 1.35001 | ||||||||
\(426\) | −1.70347e69 | −0.356435 | ||||||||
\(427\) | −6.03024e68 | −0.118576 | ||||||||
\(428\) | −4.86076e69 | −0.898348 | ||||||||
\(429\) | −6.31413e68 | −0.109697 | ||||||||
\(430\) | −6.65267e69 | −1.08663 | ||||||||
\(431\) | −4.87848e69 | −0.749267 | −0.374633 | − | 0.927173i | \(-0.622231\pi\) | ||||
−0.374633 | + | 0.927173i | \(0.622231\pi\) | |||||||
\(432\) | 4.52137e69 | 0.653056 | ||||||||
\(433\) | −1.12249e70 | −1.52494 | −0.762469 | − | 0.647025i | \(-0.776013\pi\) | ||||
−0.762469 | + | 0.647025i | \(0.776013\pi\) | |||||||
\(434\) | −5.78940e69 | −0.739870 | ||||||||
\(435\) | 2.15000e69 | 0.258507 | ||||||||
\(436\) | 8.59415e69 | 0.972323 | ||||||||
\(437\) | 7.32834e69 | 0.780274 | ||||||||
\(438\) | −4.32526e69 | −0.433460 | ||||||||
\(439\) | −1.69286e68 | −0.0159702 | −0.00798509 | − | 0.999968i | \(-0.502542\pi\) | ||||
−0.00798509 | + | 0.999968i | \(0.502542\pi\) | |||||||
\(440\) | −7.72385e68 | −0.0686022 | ||||||||
\(441\) | 5.99129e69 | 0.501069 | ||||||||
\(442\) | 3.13531e70 | 2.46939 | ||||||||
\(443\) | −1.39750e69 | −0.103670 | −0.0518351 | − | 0.998656i | \(-0.516507\pi\) | ||||
−0.0518351 | + | 0.998656i | \(0.516507\pi\) | |||||||
\(444\) | 2.17223e69 | 0.151795 | ||||||||
\(445\) | −1.36071e70 | −0.895828 | ||||||||
\(446\) | −1.76841e70 | −1.09701 | ||||||||
\(447\) | −2.70156e69 | −0.157930 | ||||||||
\(448\) | 8.49914e69 | 0.468282 | ||||||||
\(449\) | 1.04380e70 | 0.542110 | 0.271055 | − | 0.962564i | \(-0.412627\pi\) | ||||
0.271055 | + | 0.962564i | \(0.412627\pi\) | |||||||
\(450\) | −2.74215e70 | −1.34264 | ||||||||
\(451\) | −2.88820e69 | −0.133336 | ||||||||
\(452\) | 2.49244e69 | 0.108506 | ||||||||
\(453\) | 1.35656e70 | 0.556978 | ||||||||
\(454\) | −5.71790e70 | −2.21440 | ||||||||
\(455\) | 3.85356e70 | 1.40786 | ||||||||
\(456\) | 3.06867e69 | 0.105775 | ||||||||
\(457\) | 3.06454e70 | 0.996751 | 0.498376 | − | 0.866961i | \(-0.333930\pi\) | ||||
0.498376 | + | 0.866961i | \(0.333930\pi\) | |||||||
\(458\) | −1.55492e70 | −0.477280 | ||||||||
\(459\) | −2.49849e70 | −0.723838 | ||||||||
\(460\) | 1.96914e70 | 0.538509 | ||||||||
\(461\) | −1.38267e70 | −0.356979 | −0.178489 | − | 0.983942i | \(-0.557121\pi\) | ||||
−0.178489 | + | 0.983942i | \(0.557121\pi\) | |||||||
\(462\) | 2.81574e69 | 0.0686405 | ||||||||
\(463\) | −2.87526e69 | −0.0661882 | −0.0330941 | − | 0.999452i | \(-0.510536\pi\) | ||||
−0.0330941 | + | 0.999452i | \(0.510536\pi\) | |||||||
\(464\) | 3.02249e70 | 0.657110 | ||||||||
\(465\) | −1.74305e70 | −0.357938 | ||||||||
\(466\) | 4.83952e70 | 0.938805 | ||||||||
\(467\) | −3.27527e69 | −0.0600275 | −0.0300137 | − | 0.999549i | \(-0.509555\pi\) | ||||
−0.0300137 | + | 0.999549i | \(0.509555\pi\) | |||||||
\(468\) | −6.55154e70 | −1.13456 | ||||||||
\(469\) | −1.18897e70 | −0.194576 | ||||||||
\(470\) | 1.83510e71 | 2.83835 | ||||||||
\(471\) | −8.43903e69 | −0.123378 | ||||||||
\(472\) | −1.77790e70 | −0.245722 | ||||||||
\(473\) | −1.04079e70 | −0.136002 | ||||||||
\(474\) | −3.98482e70 | −0.492359 | ||||||||
\(475\) | −1.67037e71 | −1.95178 | ||||||||
\(476\) | −6.45914e70 | −0.713823 | ||||||||
\(477\) | 9.70269e70 | 1.01427 | ||||||||
\(478\) | −2.62854e70 | −0.259941 | ||||||||
\(479\) | −1.92415e71 | −1.80032 | −0.900158 | − | 0.435564i | \(-0.856549\pi\) | ||||
−0.900158 | + | 0.435564i | \(0.856549\pi\) | |||||||
\(480\) | 6.65749e70 | 0.589410 | ||||||||
\(481\) | 1.00677e71 | 0.843497 | ||||||||
\(482\) | 3.68897e70 | 0.292522 | ||||||||
\(483\) | 1.18184e70 | 0.0887074 | ||||||||
\(484\) | −1.13501e71 | −0.806485 | ||||||||
\(485\) | 2.74626e71 | 1.84751 | ||||||||
\(486\) | 1.72283e71 | 1.09744 | ||||||||
\(487\) | −1.33015e71 | −0.802388 | −0.401194 | − | 0.915993i | \(-0.631405\pi\) | ||||
−0.401194 | + | 0.915993i | \(0.631405\pi\) | |||||||
\(488\) | −5.98020e69 | −0.0341657 | ||||||||
\(489\) | 1.23492e68 | 0.000668272 0 | ||||||||
\(490\) | 2.12273e71 | 1.08818 | ||||||||
\(491\) | 3.09725e71 | 1.50424 | 0.752120 | − | 0.659027i | \(-0.229032\pi\) | ||||
0.752120 | + | 0.659027i | \(0.229032\pi\) | |||||||
\(492\) | 3.08328e70 | 0.141886 | ||||||||
\(493\) | −1.67022e71 | −0.728332 | ||||||||
\(494\) | −8.63870e71 | −3.57013 | ||||||||
\(495\) | −8.23975e70 | −0.322757 | ||||||||
\(496\) | −2.45041e71 | −0.909858 | ||||||||
\(497\) | 1.62649e71 | 0.572543 | ||||||||
\(498\) | −1.51542e71 | −0.505774 | ||||||||
\(499\) | 4.41016e71 | 1.39569 | 0.697847 | − | 0.716247i | \(-0.254142\pi\) | ||||
0.697847 | + | 0.716247i | \(0.254142\pi\) | |||||||
\(500\) | −3.56035e70 | −0.106853 | ||||||||
\(501\) | −4.21587e70 | −0.120002 | ||||||||
\(502\) | 9.90238e71 | 2.67357 | ||||||||
\(503\) | −6.61525e71 | −1.69432 | −0.847158 | − | 0.531341i | \(-0.821688\pi\) | ||||
−0.847158 | + | 0.531341i | \(0.821688\pi\) | |||||||
\(504\) | −4.81002e70 | −0.116879 | ||||||||
\(505\) | −1.04255e71 | −0.240367 | ||||||||
\(506\) | 6.66851e70 | 0.145895 | ||||||||
\(507\) | 1.65304e71 | 0.343220 | ||||||||
\(508\) | 1.45832e71 | 0.287386 | ||||||||
\(509\) | −3.73962e71 | −0.699530 | −0.349765 | − | 0.936837i | \(-0.613739\pi\) | ||||
−0.349765 | + | 0.936837i | \(0.613739\pi\) | |||||||
\(510\) | −4.20956e71 | −0.747528 | ||||||||
\(511\) | 4.12980e71 | 0.696267 | ||||||||
\(512\) | 8.00916e71 | 1.28213 | ||||||||
\(513\) | 6.88408e71 | 1.04649 | ||||||||
\(514\) | −4.88208e71 | −0.704826 | ||||||||
\(515\) | −7.91351e71 | −1.08512 | ||||||||
\(516\) | 1.11109e71 | 0.144722 | ||||||||
\(517\) | 2.87096e71 | 0.355244 | ||||||||
\(518\) | −4.48960e71 | −0.527800 | ||||||||
\(519\) | −5.76847e70 | −0.0644356 | ||||||||
\(520\) | 3.82158e71 | 0.405653 | ||||||||
\(521\) | −8.23378e71 | −0.830614 | −0.415307 | − | 0.909681i | \(-0.636326\pi\) | ||||
−0.415307 | + | 0.909681i | \(0.636326\pi\) | |||||||
\(522\) | 7.55476e71 | 0.724357 | ||||||||
\(523\) | −1.56757e71 | −0.142867 | −0.0714336 | − | 0.997445i | \(-0.522757\pi\) | ||||
−0.0714336 | + | 0.997445i | \(0.522757\pi\) | |||||||
\(524\) | −5.95907e71 | −0.516297 | ||||||||
\(525\) | −2.69380e71 | −0.221893 | ||||||||
\(526\) | −2.59331e72 | −2.03110 | ||||||||
\(527\) | 1.35408e72 | 1.00847 | ||||||||
\(528\) | 1.19178e71 | 0.0844109 | ||||||||
\(529\) | −1.20459e72 | −0.811453 | ||||||||
\(530\) | 3.43770e72 | 2.20271 | ||||||||
\(531\) | −1.89665e72 | −1.15606 | ||||||||
\(532\) | 1.77969e72 | 1.03201 | ||||||||
\(533\) | 1.42901e72 | 0.788432 | ||||||||
\(534\) | 4.91931e71 | 0.258262 | ||||||||
\(535\) | 3.02471e72 | 1.51115 | ||||||||
\(536\) | −1.17910e71 | −0.0560639 | ||||||||
\(537\) | 1.51067e71 | 0.0683678 | ||||||||
\(538\) | −4.23576e72 | −1.82474 | ||||||||
\(539\) | 3.32096e71 | 0.136195 | ||||||||
\(540\) | 1.84976e72 | 0.722240 | ||||||||
\(541\) | −3.10699e72 | −1.15508 | −0.577541 | − | 0.816362i | \(-0.695987\pi\) | ||||
−0.577541 | + | 0.816362i | \(0.695987\pi\) | |||||||
\(542\) | 1.73181e72 | 0.613082 | ||||||||
\(543\) | −8.11545e71 | −0.273601 | ||||||||
\(544\) | −5.17184e72 | −1.66063 | ||||||||
\(545\) | −5.34788e72 | −1.63559 | ||||||||
\(546\) | −1.39316e72 | −0.405879 | ||||||||
\(547\) | 6.13544e72 | 1.70287 | 0.851435 | − | 0.524460i | \(-0.175733\pi\) | ||||
0.851435 | + | 0.524460i | \(0.175733\pi\) | |||||||
\(548\) | 1.73237e72 | 0.458094 | ||||||||
\(549\) | −6.37963e71 | −0.160742 | ||||||||
\(550\) | −1.51997e72 | −0.364942 | ||||||||
\(551\) | 4.60194e72 | 1.05299 | ||||||||
\(552\) | 1.17203e71 | 0.0255596 | ||||||||
\(553\) | 3.80474e72 | 0.790877 | ||||||||
\(554\) | 5.25556e72 | 1.04138 | ||||||||
\(555\) | −1.35172e72 | −0.255341 | ||||||||
\(556\) | −3.19897e72 | −0.576140 | ||||||||
\(557\) | 3.45443e72 | 0.593217 | 0.296608 | − | 0.954999i | \(-0.404144\pi\) | ||||
0.296608 | + | 0.954999i | \(0.404144\pi\) | |||||||
\(558\) | −6.12483e72 | −1.00297 | ||||||||
\(559\) | 5.14959e72 | 0.804193 | ||||||||
\(560\) | −7.27355e72 | −1.08334 | ||||||||
\(561\) | −6.58575e71 | −0.0935598 | ||||||||
\(562\) | 1.03090e73 | 1.39702 | ||||||||
\(563\) | −7.65255e72 | −0.989313 | −0.494656 | − | 0.869089i | \(-0.664706\pi\) | ||||
−0.494656 | + | 0.869089i | \(0.664706\pi\) | |||||||
\(564\) | −3.06488e72 | −0.378022 | ||||||||
\(565\) | −1.55097e72 | −0.182524 | ||||||||
\(566\) | 5.31277e72 | 0.596603 | ||||||||
\(567\) | −4.54904e72 | −0.487493 | ||||||||
\(568\) | 1.61299e72 | 0.164969 | ||||||||
\(569\) | −1.06701e73 | −1.04158 | −0.520789 | − | 0.853686i | \(-0.674362\pi\) | ||||
−0.520789 | + | 0.853686i | \(0.674362\pi\) | |||||||
\(570\) | 1.15986e73 | 1.08074 | ||||||||
\(571\) | 4.28488e72 | 0.381137 | 0.190569 | − | 0.981674i | \(-0.438967\pi\) | ||||
0.190569 | + | 0.981674i | \(0.438967\pi\) | |||||||
\(572\) | −3.63151e72 | −0.308384 | ||||||||
\(573\) | −1.65971e72 | −0.134566 | ||||||||
\(574\) | −6.37257e72 | −0.493344 | ||||||||
\(575\) | −6.37971e72 | −0.471632 | ||||||||
\(576\) | 8.99157e72 | 0.634804 | ||||||||
\(577\) | −2.73962e73 | −1.84727 | −0.923636 | − | 0.383271i | \(-0.874798\pi\) | ||||
−0.923636 | + | 0.383271i | \(0.874798\pi\) | |||||||
\(578\) | 1.15336e73 | 0.742806 | ||||||||
\(579\) | 6.09966e72 | 0.375253 | ||||||||
\(580\) | 1.23655e73 | 0.726724 | ||||||||
\(581\) | 1.44694e73 | 0.812425 | ||||||||
\(582\) | −9.92845e72 | −0.532626 | ||||||||
\(583\) | 5.37818e72 | 0.275689 | ||||||||
\(584\) | 4.09553e72 | 0.200618 | ||||||||
\(585\) | 4.07683e73 | 1.90850 | ||||||||
\(586\) | 2.00187e73 | 0.895673 | ||||||||
\(587\) | −1.81383e72 | −0.0775689 | −0.0387844 | − | 0.999248i | \(-0.512349\pi\) | ||||
−0.0387844 | + | 0.999248i | \(0.512349\pi\) | |||||||
\(588\) | −3.54528e72 | −0.144928 | ||||||||
\(589\) | −3.73091e73 | −1.45800 | ||||||||
\(590\) | −6.71988e73 | −2.51063 | ||||||||
\(591\) | −2.87941e72 | −0.102857 | ||||||||
\(592\) | −1.90026e73 | −0.649063 | ||||||||
\(593\) | 4.87506e72 | 0.159232 | 0.0796161 | − | 0.996826i | \(-0.474631\pi\) | ||||
0.0796161 | + | 0.996826i | \(0.474631\pi\) | |||||||
\(594\) | 6.26425e72 | 0.195672 | ||||||||
\(595\) | 4.01933e73 | 1.20075 | ||||||||
\(596\) | −1.55377e73 | −0.443978 | ||||||||
\(597\) | 1.22947e72 | 0.0336045 | ||||||||
\(598\) | −3.29942e73 | −0.862692 | ||||||||
\(599\) | −1.49187e73 | −0.373181 | −0.186590 | − | 0.982438i | \(-0.559744\pi\) | ||||
−0.186590 | + | 0.982438i | \(0.559744\pi\) | |||||||
\(600\) | −2.67144e72 | −0.0639349 | ||||||||
\(601\) | 7.02936e73 | 1.60969 | 0.804845 | − | 0.593485i | \(-0.202248\pi\) | ||||
0.804845 | + | 0.593485i | \(0.202248\pi\) | |||||||
\(602\) | −2.29643e73 | −0.503206 | ||||||||
\(603\) | −1.25785e73 | −0.263767 | ||||||||
\(604\) | 7.80214e73 | 1.56579 | ||||||||
\(605\) | 7.06281e73 | 1.35663 | ||||||||
\(606\) | 3.76909e72 | 0.0692966 | ||||||||
\(607\) | −9.09644e73 | −1.60093 | −0.800463 | − | 0.599382i | \(-0.795413\pi\) | ||||
−0.800463 | + | 0.599382i | \(0.795413\pi\) | |||||||
\(608\) | 1.42500e74 | 2.40087 | ||||||||
\(609\) | 7.42154e72 | 0.119712 | ||||||||
\(610\) | −2.26032e73 | −0.349084 | ||||||||
\(611\) | −1.42048e74 | −2.10060 | ||||||||
\(612\) | −6.83338e73 | −0.967660 | ||||||||
\(613\) | −1.39239e73 | −0.188825 | −0.0944125 | − | 0.995533i | \(-0.530097\pi\) | ||||
−0.0944125 | + | 0.995533i | \(0.530097\pi\) | |||||||
\(614\) | −7.64978e72 | −0.0993544 | ||||||||
\(615\) | −1.91864e73 | −0.238672 | ||||||||
\(616\) | −2.66619e72 | −0.0317689 | ||||||||
\(617\) | 1.12495e73 | 0.128403 | 0.0642015 | − | 0.997937i | \(-0.479550\pi\) | ||||
0.0642015 | + | 0.997937i | \(0.479550\pi\) | |||||||
\(618\) | 2.86094e73 | 0.312834 | ||||||||
\(619\) | 1.38480e74 | 1.45072 | 0.725360 | − | 0.688369i | \(-0.241673\pi\) | ||||
0.725360 | + | 0.688369i | \(0.241673\pi\) | |||||||
\(620\) | −1.00250e74 | −1.00625 | ||||||||
\(621\) | 2.62927e73 | 0.252876 | ||||||||
\(622\) | 8.30895e71 | 0.00765774 | ||||||||
\(623\) | −4.69701e73 | −0.414847 | ||||||||
\(624\) | −5.89666e73 | −0.499131 | ||||||||
\(625\) | −1.11725e74 | −0.906417 | ||||||||
\(626\) | 2.52208e74 | 1.96127 | ||||||||
\(627\) | 1.81457e73 | 0.135264 | ||||||||
\(628\) | −4.85362e73 | −0.346845 | ||||||||
\(629\) | 1.05007e74 | 0.719412 | ||||||||
\(630\) | −1.81803e74 | −1.19420 | ||||||||
\(631\) | −8.85014e73 | −0.557406 | −0.278703 | − | 0.960377i | \(-0.589905\pi\) | ||||
−0.278703 | + | 0.960377i | \(0.589905\pi\) | |||||||
\(632\) | 3.77317e73 | 0.227878 | ||||||||
\(633\) | 9.04343e73 | 0.523763 | ||||||||
\(634\) | 4.11358e74 | 2.28483 | ||||||||
\(635\) | −9.07471e73 | −0.483425 | ||||||||
\(636\) | −5.74146e73 | −0.293365 | ||||||||
\(637\) | −1.64313e74 | −0.805337 | ||||||||
\(638\) | 4.18759e73 | 0.196887 | ||||||||
\(639\) | 1.72073e74 | 0.776140 | ||||||||
\(640\) | −1.27363e74 | −0.551155 | ||||||||
\(641\) | 1.61877e74 | 0.672122 | 0.336061 | − | 0.941840i | \(-0.390905\pi\) | ||||
0.336061 | + | 0.941840i | \(0.390905\pi\) | |||||||
\(642\) | −1.09351e74 | −0.435657 | ||||||||
\(643\) | −1.44296e74 | −0.551648 | −0.275824 | − | 0.961208i | \(-0.588951\pi\) | ||||
−0.275824 | + | 0.961208i | \(0.588951\pi\) | |||||||
\(644\) | 6.79723e73 | 0.249377 | ||||||||
\(645\) | −6.91401e73 | −0.243443 | ||||||||
\(646\) | −9.01032e74 | −3.04494 | ||||||||
\(647\) | 3.96918e72 | 0.0128747 | 0.00643735 | − | 0.999979i | \(-0.497951\pi\) | ||||
0.00643735 | + | 0.999979i | \(0.497951\pi\) | |||||||
\(648\) | −4.51129e73 | −0.140463 | ||||||||
\(649\) | −1.05131e74 | −0.314228 | ||||||||
\(650\) | 7.52045e74 | 2.15794 | ||||||||
\(651\) | −6.01683e73 | −0.165757 | ||||||||
\(652\) | 7.10250e71 | 0.00187867 | ||||||||
\(653\) | 1.24882e74 | 0.317175 | 0.158588 | − | 0.987345i | \(-0.449306\pi\) | ||||
0.158588 | + | 0.987345i | \(0.449306\pi\) | |||||||
\(654\) | 1.93340e74 | 0.471532 | ||||||||
\(655\) | 3.70815e74 | 0.868487 | ||||||||
\(656\) | −2.69724e74 | −0.606691 | ||||||||
\(657\) | 4.36908e74 | 0.943860 | ||||||||
\(658\) | 6.33454e74 | 1.31440 | ||||||||
\(659\) | −1.41749e74 | −0.282524 | −0.141262 | − | 0.989972i | \(-0.545116\pi\) | ||||
−0.141262 | + | 0.989972i | \(0.545116\pi\) | |||||||
\(660\) | 4.87578e73 | 0.0933533 | ||||||||
\(661\) | 3.68248e74 | 0.677333 | 0.338666 | − | 0.940906i | \(-0.390024\pi\) | ||||
0.338666 | + | 0.940906i | \(0.390024\pi\) | |||||||
\(662\) | −1.17832e75 | −2.08222 | ||||||||
\(663\) | 3.25847e74 | 0.553230 | ||||||||
\(664\) | 1.43493e74 | 0.234087 | ||||||||
\(665\) | −1.10745e75 | −1.73600 | ||||||||
\(666\) | −4.74972e74 | −0.715486 | ||||||||
\(667\) | 1.75764e74 | 0.254446 | ||||||||
\(668\) | −2.42471e74 | −0.337353 | ||||||||
\(669\) | −1.83788e74 | −0.245768 | ||||||||
\(670\) | −4.45662e74 | −0.572826 | ||||||||
\(671\) | −3.53622e73 | −0.0436910 | ||||||||
\(672\) | 2.29809e74 | 0.272949 | ||||||||
\(673\) | 1.04283e75 | 1.19073 | 0.595366 | − | 0.803455i | \(-0.297007\pi\) | ||||
0.595366 | + | 0.803455i | \(0.297007\pi\) | |||||||
\(674\) | 8.74211e74 | 0.959686 | ||||||||
\(675\) | −5.99296e74 | −0.632545 | ||||||||
\(676\) | 9.50730e74 | 0.964872 | ||||||||
\(677\) | −1.67343e75 | −1.63309 | −0.816543 | − | 0.577285i | \(-0.804112\pi\) | ||||
−0.816543 | + | 0.577285i | \(0.804112\pi\) | |||||||
\(678\) | 5.60716e73 | 0.0526206 | ||||||||
\(679\) | 9.47978e74 | 0.855558 | ||||||||
\(680\) | 3.98598e74 | 0.345978 | ||||||||
\(681\) | −5.94252e74 | −0.496103 | ||||||||
\(682\) | −3.39498e74 | −0.272616 | ||||||||
\(683\) | −1.24036e74 | −0.0958078 | −0.0479039 | − | 0.998852i | \(-0.515254\pi\) | ||||
−0.0479039 | + | 0.998852i | \(0.515254\pi\) | |||||||
\(684\) | 1.88280e75 | 1.39900 | ||||||||
\(685\) | −1.07800e75 | −0.770582 | ||||||||
\(686\) | 2.05868e75 | 1.41579 | ||||||||
\(687\) | −1.61600e74 | −0.106927 | ||||||||
\(688\) | −9.71979e74 | −0.618819 | ||||||||
\(689\) | −2.66100e75 | −1.63018 | ||||||||
\(690\) | 4.42991e74 | 0.261152 | ||||||||
\(691\) | 2.95439e75 | 1.67610 | 0.838049 | − | 0.545595i | \(-0.183696\pi\) | ||||
0.838049 | + | 0.545595i | \(0.183696\pi\) | |||||||
\(692\) | −3.31768e74 | −0.181144 | ||||||||
\(693\) | −2.84427e74 | −0.149465 | ||||||||
\(694\) | −4.45503e75 | −2.25333 | ||||||||
\(695\) | 1.99062e75 | 0.969151 | ||||||||
\(696\) | 7.35995e73 | 0.0344929 | ||||||||
\(697\) | 1.49048e75 | 0.672448 | ||||||||
\(698\) | 4.03017e74 | 0.175047 | ||||||||
\(699\) | 5.02963e74 | 0.210325 | ||||||||
\(700\) | −1.54931e75 | −0.623793 | ||||||||
\(701\) | −6.43274e74 | −0.249384 | −0.124692 | − | 0.992196i | \(-0.539794\pi\) | ||||
−0.124692 | + | 0.992196i | \(0.539794\pi\) | |||||||
\(702\) | −3.09940e75 | −1.15703 | ||||||||
\(703\) | −2.89327e75 | −1.04009 | ||||||||
\(704\) | 4.98401e74 | 0.172545 | ||||||||
\(705\) | 1.90718e75 | 0.635889 | ||||||||
\(706\) | −1.11903e75 | −0.359349 | ||||||||
\(707\) | −3.59876e74 | −0.111311 | ||||||||
\(708\) | 1.12232e75 | 0.334376 | ||||||||
\(709\) | 5.30581e75 | 1.52274 | 0.761372 | − | 0.648315i | \(-0.224526\pi\) | ||||
0.761372 | + | 0.648315i | \(0.224526\pi\) | |||||||
\(710\) | 6.09660e75 | 1.68555 | ||||||||
\(711\) | 4.02518e75 | 1.07211 | ||||||||
\(712\) | −4.65803e74 | −0.119531 | ||||||||
\(713\) | −1.42496e75 | −0.352315 | ||||||||
\(714\) | −1.45309e75 | −0.346171 | ||||||||
\(715\) | 2.25978e75 | 0.518747 | ||||||||
\(716\) | 8.68847e74 | 0.192198 | ||||||||
\(717\) | −2.73179e74 | −0.0582358 | ||||||||
\(718\) | −7.68420e75 | −1.57870 | ||||||||
\(719\) | −7.52021e75 | −1.48907 | −0.744534 | − | 0.667585i | \(-0.767328\pi\) | ||||
−0.744534 | + | 0.667585i | \(0.767328\pi\) | |||||||
\(720\) | −7.69497e75 | −1.46857 | ||||||||
\(721\) | −2.73165e75 | −0.502506 | ||||||||
\(722\) | 1.71378e76 | 3.03891 | ||||||||
\(723\) | 3.83388e74 | 0.0655351 | ||||||||
\(724\) | −4.66752e75 | −0.769156 | ||||||||
\(725\) | −4.00624e75 | −0.636472 | ||||||||
\(726\) | −2.55339e75 | −0.391108 | ||||||||
\(727\) | −9.24803e75 | −1.36580 | −0.682900 | − | 0.730512i | \(-0.739282\pi\) | ||||
−0.682900 | + | 0.730512i | \(0.739282\pi\) | |||||||
\(728\) | 1.31917e75 | 0.187853 | ||||||||
\(729\) | −3.51724e75 | −0.482973 | ||||||||
\(730\) | 1.54798e76 | 2.04979 | ||||||||
\(731\) | 5.37112e75 | 0.685890 | ||||||||
\(732\) | 3.77507e74 | 0.0464924 | ||||||||
\(733\) | 1.08537e76 | 1.28921 | 0.644603 | − | 0.764517i | \(-0.277023\pi\) | ||||
0.644603 | + | 0.764517i | \(0.277023\pi\) | |||||||
\(734\) | 1.61838e74 | 0.0185411 | ||||||||
\(735\) | 2.20612e75 | 0.243790 | ||||||||
\(736\) | 5.44255e75 | 0.580150 | ||||||||
\(737\) | −6.97226e74 | −0.0716943 | ||||||||
\(738\) | −6.74179e75 | −0.668778 | ||||||||
\(739\) | −3.55012e75 | −0.339755 | −0.169877 | − | 0.985465i | \(-0.554337\pi\) | ||||
−0.169877 | + | 0.985465i | \(0.554337\pi\) | |||||||
\(740\) | −7.77425e75 | −0.717824 | ||||||||
\(741\) | −8.97806e75 | −0.799834 | ||||||||
\(742\) | 1.18665e76 | 1.02005 | ||||||||
\(743\) | −1.21666e75 | −0.100917 | −0.0504586 | − | 0.998726i | \(-0.516068\pi\) | ||||
−0.0504586 | + | 0.998726i | \(0.516068\pi\) | |||||||
\(744\) | −5.96689e74 | −0.0477601 | ||||||||
\(745\) | 9.66867e75 | 0.746837 | ||||||||
\(746\) | −2.87957e76 | −2.14659 | ||||||||
\(747\) | 1.53078e76 | 1.10133 | ||||||||
\(748\) | −3.78773e75 | −0.263018 | ||||||||
\(749\) | 1.04410e76 | 0.699797 | ||||||||
\(750\) | −8.00961e74 | −0.0518189 | ||||||||
\(751\) | −1.83232e76 | −1.14431 | −0.572153 | − | 0.820147i | \(-0.693892\pi\) | ||||
−0.572153 | + | 0.820147i | \(0.693892\pi\) | |||||||
\(752\) | 2.68114e76 | 1.61639 | ||||||||
\(753\) | 1.02914e76 | 0.598972 | ||||||||
\(754\) | −2.07192e76 | −1.16421 | ||||||||
\(755\) | −4.85504e76 | −2.63390 | ||||||||
\(756\) | 6.38517e75 | 0.334461 | ||||||||
\(757\) | 1.67987e76 | 0.849639 | 0.424819 | − | 0.905278i | \(-0.360338\pi\) | ||||
0.424819 | + | 0.905278i | \(0.360338\pi\) | |||||||
\(758\) | 2.32661e76 | 1.13629 | ||||||||
\(759\) | 6.93047e74 | 0.0326855 | ||||||||
\(760\) | −1.09826e76 | −0.500199 | ||||||||
\(761\) | −6.65143e74 | −0.0292565 | −0.0146282 | − | 0.999893i | \(-0.504656\pi\) | ||||
−0.0146282 | + | 0.999893i | \(0.504656\pi\) | |||||||
\(762\) | 3.28075e75 | 0.139369 | ||||||||
\(763\) | −1.84603e76 | −0.757422 | ||||||||
\(764\) | −9.54566e75 | −0.378296 | ||||||||
\(765\) | 4.25221e76 | 1.62775 | ||||||||
\(766\) | −1.03067e76 | −0.381117 | ||||||||
\(767\) | 5.20162e76 | 1.85807 | ||||||||
\(768\) | 1.08011e76 | 0.372732 | ||||||||
\(769\) | 1.78455e75 | 0.0594952 | 0.0297476 | − | 0.999557i | \(-0.490530\pi\) | ||||
0.0297476 | + | 0.999557i | \(0.490530\pi\) | |||||||
\(770\) | −1.00773e76 | −0.324595 | ||||||||
\(771\) | −5.07386e75 | −0.157906 | ||||||||
\(772\) | 3.50816e76 | 1.05492 | ||||||||
\(773\) | −6.01277e76 | −1.74710 | −0.873550 | − | 0.486735i | \(-0.838188\pi\) | ||||
−0.873550 | + | 0.486735i | \(0.838188\pi\) | |||||||
\(774\) | −2.42948e76 | −0.682147 | ||||||||
\(775\) | 3.24795e76 | 0.881282 | ||||||||
\(776\) | 9.40111e75 | 0.246515 | ||||||||
\(777\) | −4.66597e75 | −0.118246 | ||||||||
\(778\) | −5.97519e76 | −1.46350 | ||||||||
\(779\) | −4.10673e76 | −0.972194 | ||||||||
\(780\) | −2.41242e76 | −0.552008 | ||||||||
\(781\) | 9.53797e75 | 0.210962 | ||||||||
\(782\) | −3.44135e76 | −0.735784 | ||||||||
\(783\) | 1.65109e76 | 0.341259 | ||||||||
\(784\) | 3.10139e76 | 0.619699 | ||||||||
\(785\) | 3.02027e76 | 0.583444 | ||||||||
\(786\) | −1.34059e76 | −0.250380 | ||||||||
\(787\) | 7.06315e75 | 0.127546 | 0.0637732 | − | 0.997964i | \(-0.479687\pi\) | ||||
0.0637732 | + | 0.997964i | \(0.479687\pi\) | |||||||
\(788\) | −1.65606e76 | −0.289156 | ||||||||
\(789\) | −2.69518e76 | −0.455037 | ||||||||
\(790\) | 1.42614e77 | 2.32832 | ||||||||
\(791\) | −5.35377e75 | −0.0845246 | ||||||||
\(792\) | −2.82066e75 | −0.0430659 | ||||||||
\(793\) | 1.74963e76 | 0.258350 | ||||||||
\(794\) | 1.22865e77 | 1.75463 | ||||||||
\(795\) | 3.57274e76 | 0.493484 | ||||||||
\(796\) | 7.07117e75 | 0.0944702 | ||||||||
\(797\) | −5.54535e76 | −0.716612 | −0.358306 | − | 0.933604i | \(-0.616645\pi\) | ||||
−0.358306 | + | 0.933604i | \(0.616645\pi\) | |||||||
\(798\) | 4.00370e76 | 0.500478 | ||||||||
\(799\) | −1.48159e77 | −1.79159 | ||||||||
\(800\) | −1.24054e77 | −1.45119 | ||||||||
\(801\) | −4.96915e76 | −0.562367 | ||||||||
\(802\) | −5.87479e76 | −0.643238 | ||||||||
\(803\) | 2.42177e76 | 0.256550 | ||||||||
\(804\) | 7.44321e75 | 0.0762912 | ||||||||
\(805\) | −4.22972e76 | −0.419489 | ||||||||
\(806\) | 1.67976e77 | 1.61201 | ||||||||
\(807\) | −4.40216e76 | −0.408806 | ||||||||
\(808\) | −3.56890e75 | −0.0320725 | ||||||||
\(809\) | 7.38311e76 | 0.642101 | 0.321050 | − | 0.947062i | \(-0.395964\pi\) | ||||
0.321050 | + | 0.947062i | \(0.395964\pi\) | |||||||
\(810\) | −1.70512e77 | −1.43517 | ||||||||
\(811\) | 1.49559e77 | 1.21832 | 0.609159 | − | 0.793048i | \(-0.291507\pi\) | ||||
0.609159 | + | 0.793048i | \(0.291507\pi\) | |||||||
\(812\) | 4.26842e76 | 0.336537 | ||||||||
\(813\) | 1.79984e76 | 0.137352 | ||||||||
\(814\) | −2.63276e76 | −0.194475 | ||||||||
\(815\) | −4.41968e74 | −0.00316019 | ||||||||
\(816\) | −6.15032e76 | −0.425705 | ||||||||
\(817\) | −1.47990e77 | −0.991628 | ||||||||
\(818\) | −5.29453e76 | −0.343451 | ||||||||
\(819\) | 1.40728e77 | 0.883803 | ||||||||
\(820\) | −1.10348e77 | −0.670963 | ||||||||
\(821\) | 2.15004e77 | 1.26576 | 0.632881 | − | 0.774249i | \(-0.281872\pi\) | ||||
0.632881 | + | 0.774249i | \(0.281872\pi\) | |||||||
\(822\) | 3.89725e76 | 0.222155 | ||||||||
\(823\) | 2.98860e77 | 1.64958 | 0.824788 | − | 0.565442i | \(-0.191294\pi\) | ||||
0.824788 | + | 0.565442i | \(0.191294\pi\) | |||||||
\(824\) | −2.70898e76 | −0.144789 | ||||||||
\(825\) | −1.57968e76 | −0.0817598 | ||||||||
\(826\) | −2.31963e77 | −1.16264 | ||||||||
\(827\) | −1.03100e77 | −0.500451 | −0.250226 | − | 0.968188i | \(-0.580505\pi\) | ||||
−0.250226 | + | 0.968188i | \(0.580505\pi\) | |||||||
\(828\) | 7.19106e76 | 0.338056 | ||||||||
\(829\) | −1.73661e77 | −0.790692 | −0.395346 | − | 0.918532i | \(-0.629375\pi\) | ||||
−0.395346 | + | 0.918532i | \(0.629375\pi\) | |||||||
\(830\) | 5.42359e77 | 2.39176 | ||||||||
\(831\) | 5.46202e76 | 0.233306 | ||||||||
\(832\) | −2.46597e77 | −1.02028 | ||||||||
\(833\) | −1.71382e77 | −0.686866 | ||||||||
\(834\) | −7.19662e76 | −0.279401 | ||||||||
\(835\) | 1.50883e77 | 0.567477 | ||||||||
\(836\) | 1.04363e77 | 0.380260 | ||||||||
\(837\) | −1.33858e77 | −0.472519 | ||||||||
\(838\) | −4.39434e77 | −1.50289 | ||||||||
\(839\) | 1.10592e77 | 0.366464 | 0.183232 | − | 0.983070i | \(-0.441344\pi\) | ||||
0.183232 | + | 0.983070i | \(0.441344\pi\) | |||||||
\(840\) | −1.77115e76 | −0.0568664 | ||||||||
\(841\) | −2.11062e77 | −0.656623 | ||||||||
\(842\) | −7.28344e77 | −2.19566 | ||||||||
\(843\) | 1.07140e77 | 0.312982 | ||||||||
\(844\) | 5.20124e77 | 1.47242 | ||||||||
\(845\) | −5.91611e77 | −1.62306 | ||||||||
\(846\) | 6.70155e77 | 1.78181 | ||||||||
\(847\) | 2.43800e77 | 0.628237 | ||||||||
\(848\) | 5.02260e77 | 1.25441 | ||||||||
\(849\) | 5.52147e76 | 0.133660 | ||||||||
\(850\) | 7.84397e77 | 1.84049 | ||||||||
\(851\) | −1.10504e77 | −0.251330 | ||||||||
\(852\) | −1.01822e77 | −0.224488 | ||||||||
\(853\) | 4.30141e77 | 0.919309 | 0.459655 | − | 0.888098i | \(-0.347973\pi\) | ||||
0.459655 | + | 0.888098i | \(0.347973\pi\) | |||||||
\(854\) | −7.80238e76 | −0.161657 | ||||||||
\(855\) | −1.17161e78 | −2.35332 | ||||||||
\(856\) | 1.03543e77 | 0.201635 | ||||||||
\(857\) | 4.39078e77 | 0.828992 | 0.414496 | − | 0.910051i | \(-0.363958\pi\) | ||||
0.414496 | + | 0.910051i | \(0.363958\pi\) | |||||||
\(858\) | −8.16969e76 | −0.149552 | ||||||||
\(859\) | 2.05806e77 | 0.365291 | 0.182646 | − | 0.983179i | \(-0.441534\pi\) | ||||
0.182646 | + | 0.983179i | \(0.441534\pi\) | |||||||
\(860\) | −3.97652e77 | −0.684376 | ||||||||
\(861\) | −6.62291e76 | −0.110526 | ||||||||
\(862\) | −6.31214e77 | −1.02149 | ||||||||
\(863\) | −4.32424e77 | −0.678615 | −0.339307 | − | 0.940676i | \(-0.610193\pi\) | ||||
−0.339307 | + | 0.940676i | \(0.610193\pi\) | |||||||
\(864\) | 5.11261e77 | 0.778088 | ||||||||
\(865\) | 2.06449e77 | 0.304710 | ||||||||
\(866\) | −1.45236e78 | −2.07898 | ||||||||
\(867\) | 1.19866e77 | 0.166414 | ||||||||
\(868\) | −3.46052e77 | −0.465981 | ||||||||
\(869\) | 2.23115e77 | 0.291410 | ||||||||
\(870\) | 2.78183e77 | 0.352428 | ||||||||
\(871\) | 3.44971e77 | 0.423937 | ||||||||
\(872\) | −1.83071e77 | −0.218239 | ||||||||
\(873\) | 1.00290e78 | 1.15980 | ||||||||
\(874\) | 9.48195e77 | 1.06376 | ||||||||
\(875\) | 7.64765e76 | 0.0832367 | ||||||||
\(876\) | −2.58535e77 | −0.272999 | ||||||||
\(877\) | 3.01916e77 | 0.309313 | 0.154656 | − | 0.987968i | \(-0.450573\pi\) | ||||
0.154656 | + | 0.987968i | \(0.450573\pi\) | |||||||
\(878\) | −2.19034e76 | −0.0217725 | ||||||||
\(879\) | 2.08051e77 | 0.200662 | ||||||||
\(880\) | −4.26530e77 | −0.399171 | ||||||||
\(881\) | −9.08145e77 | −0.824696 | −0.412348 | − | 0.911026i | \(-0.635291\pi\) | ||||
−0.412348 | + | 0.911026i | \(0.635291\pi\) | |||||||
\(882\) | 7.75198e77 | 0.683117 | ||||||||
\(883\) | −1.16332e78 | −0.994812 | −0.497406 | − | 0.867518i | \(-0.665714\pi\) | ||||
−0.497406 | + | 0.867518i | \(0.665714\pi\) | |||||||
\(884\) | 1.87408e78 | 1.55526 | ||||||||
\(885\) | −6.98386e77 | −0.562470 | ||||||||
\(886\) | −1.80819e77 | −0.141336 | ||||||||
\(887\) | 7.38531e77 | 0.560264 | 0.280132 | − | 0.959962i | \(-0.409622\pi\) | ||||
0.280132 | + | 0.959962i | \(0.409622\pi\) | |||||||
\(888\) | −4.62725e76 | −0.0340705 | ||||||||
\(889\) | −3.13249e77 | −0.223868 | ||||||||
\(890\) | −1.76059e78 | −1.22130 | ||||||||
\(891\) | −2.66762e77 | −0.179624 | ||||||||
\(892\) | −1.05704e78 | −0.690911 | ||||||||
\(893\) | 4.08221e78 | 2.59019 | ||||||||
\(894\) | −3.49548e77 | −0.215309 | ||||||||
\(895\) | −5.40658e77 | −0.323305 | ||||||||
\(896\) | −4.39643e77 | −0.255233 | ||||||||
\(897\) | −3.42903e77 | −0.193273 | ||||||||
\(898\) | 1.35054e78 | 0.739069 | ||||||||
\(899\) | −8.94826e77 | −0.475452 | ||||||||
\(900\) | −1.63908e78 | −0.845615 | ||||||||
\(901\) | −2.77547e78 | −1.39037 | ||||||||
\(902\) | −3.73696e77 | −0.181780 | ||||||||
\(903\) | −2.38664e77 | −0.112736 | ||||||||
\(904\) | −5.30934e76 | −0.0243544 | ||||||||
\(905\) | 2.90446e78 | 1.29383 | ||||||||
\(906\) | 1.75522e78 | 0.759338 | ||||||||
\(907\) | −2.54346e78 | −1.06864 | −0.534321 | − | 0.845281i | \(-0.679433\pi\) | ||||
−0.534321 | + | 0.845281i | \(0.679433\pi\) | |||||||
\(908\) | −3.41778e78 | −1.39466 | ||||||||
\(909\) | −3.80727e77 | −0.150894 | ||||||||
\(910\) | 4.98602e78 | 1.91936 | ||||||||
\(911\) | 4.02246e78 | 1.50403 | 0.752013 | − | 0.659149i | \(-0.229083\pi\) | ||||
0.752013 | + | 0.659149i | \(0.229083\pi\) | |||||||
\(912\) | 1.69460e78 | 0.615465 | ||||||||
\(913\) | 8.48506e77 | 0.299350 | ||||||||
\(914\) | 3.96514e78 | 1.35889 | ||||||||
\(915\) | −2.34912e77 | −0.0782070 | ||||||||
\(916\) | −9.29427e77 | −0.300598 | ||||||||
\(917\) | 1.28001e78 | 0.402186 | ||||||||
\(918\) | −3.23273e78 | −0.986822 | ||||||||
\(919\) | −4.43829e78 | −1.31630 | −0.658150 | − | 0.752887i | \(-0.728661\pi\) | ||||
−0.658150 | + | 0.752887i | \(0.728661\pi\) | |||||||
\(920\) | −4.19461e77 | −0.120869 | ||||||||
\(921\) | −7.95029e76 | −0.0222588 | ||||||||
\(922\) | −1.78900e78 | −0.486676 | ||||||||
\(923\) | −4.71916e78 | −1.24744 | ||||||||
\(924\) | 1.68306e77 | 0.0432308 | ||||||||
\(925\) | 2.51874e78 | 0.628678 | ||||||||
\(926\) | −3.72023e77 | −0.0902357 | ||||||||
\(927\) | −2.88992e78 | −0.681198 | ||||||||
\(928\) | 3.41773e78 | 0.782919 | ||||||||
\(929\) | −8.06660e78 | −1.79587 | −0.897934 | − | 0.440131i | \(-0.854932\pi\) | ||||
−0.897934 | + | 0.440131i | \(0.854932\pi\) | |||||||
\(930\) | −2.25529e78 | −0.487984 | ||||||||
\(931\) | 4.72207e78 | 0.993039 | ||||||||
\(932\) | 2.89274e78 | 0.591273 | ||||||||
\(933\) | 8.63535e75 | 0.00171560 | ||||||||
\(934\) | −4.23779e77 | −0.0818366 | ||||||||
\(935\) | 2.35699e78 | 0.442436 | ||||||||
\(936\) | 1.39560e78 | 0.254654 | ||||||||
\(937\) | 8.82372e76 | 0.0156514 | 0.00782569 | − | 0.999969i | \(-0.497509\pi\) | ||||
0.00782569 | + | 0.999969i | \(0.497509\pi\) | |||||||
\(938\) | −1.53837e78 | −0.265269 | ||||||||
\(939\) | 2.62115e78 | 0.439394 | ||||||||
\(940\) | 1.09690e79 | 1.78763 | ||||||||
\(941\) | 1.02741e79 | 1.62787 | 0.813937 | − | 0.580954i | \(-0.197320\pi\) | ||||
0.813937 | + | 0.580954i | \(0.197320\pi\) | |||||||
\(942\) | −1.09190e78 | −0.168204 | ||||||||
\(943\) | −1.56850e78 | −0.234923 | ||||||||
\(944\) | −9.81799e78 | −1.42977 | ||||||||
\(945\) | −3.97331e78 | −0.562612 | ||||||||
\(946\) | −1.34666e78 | −0.185413 | ||||||||
\(947\) | 1.04239e79 | 1.39558 | 0.697792 | − | 0.716301i | \(-0.254166\pi\) | ||||
0.697792 | + | 0.716301i | \(0.254166\pi\) | |||||||
\(948\) | −2.38186e78 | −0.310095 | ||||||||
\(949\) | −1.19824e79 | −1.51701 | ||||||||
\(950\) | −2.16125e79 | −2.66090 | ||||||||
\(951\) | 4.27517e78 | 0.511882 | ||||||||
\(952\) | 1.37591e78 | 0.160218 | ||||||||
\(953\) | 1.23008e79 | 1.39306 | 0.696532 | − | 0.717526i | \(-0.254725\pi\) | ||||
0.696532 | + | 0.717526i | \(0.254725\pi\) | |||||||
\(954\) | 1.25541e79 | 1.38278 | ||||||||
\(955\) | 5.93998e78 | 0.636349 | ||||||||
\(956\) | −1.57116e78 | −0.163714 | ||||||||
\(957\) | 4.35209e77 | 0.0441095 | ||||||||
\(958\) | −2.48961e79 | −2.45440 | ||||||||
\(959\) | −3.72113e78 | −0.356847 | ||||||||
\(960\) | 3.31089e78 | 0.308857 | ||||||||
\(961\) | −3.76513e78 | −0.341672 | ||||||||
\(962\) | 1.30263e79 | 1.14996 | ||||||||
\(963\) | 1.10459e79 | 0.948646 | ||||||||
\(964\) | 2.20502e78 | 0.184235 | ||||||||
\(965\) | −2.18302e79 | −1.77454 | ||||||||
\(966\) | 1.52915e78 | 0.120936 | ||||||||
\(967\) | −1.31832e79 | −1.01442 | −0.507211 | − | 0.861822i | \(-0.669324\pi\) | ||||
−0.507211 | + | 0.861822i | \(0.669324\pi\) | |||||||
\(968\) | 2.41777e78 | 0.181016 | ||||||||
\(969\) | −9.36428e78 | −0.682173 | ||||||||
\(970\) | 3.55332e79 | 2.51874 | ||||||||
\(971\) | 5.52826e77 | 0.0381311 | 0.0190655 | − | 0.999818i | \(-0.493931\pi\) | ||||
0.0190655 | + | 0.999818i | \(0.493931\pi\) | |||||||
\(972\) | 1.02979e79 | 0.691185 | ||||||||
\(973\) | 6.87140e78 | 0.448802 | ||||||||
\(974\) | −1.72105e79 | −1.09391 | ||||||||
\(975\) | 7.81588e78 | 0.483455 | ||||||||
\(976\) | −3.30241e78 | −0.198798 | ||||||||
\(977\) | −1.64164e78 | −0.0961772 | −0.0480886 | − | 0.998843i | \(-0.515313\pi\) | ||||
−0.0480886 | + | 0.998843i | \(0.515313\pi\) | |||||||
\(978\) | 1.59783e76 | 0.000911067 0 | ||||||||
\(979\) | −2.75439e78 | −0.152856 | ||||||||
\(980\) | 1.26883e79 | 0.685349 | ||||||||
\(981\) | −1.95299e79 | −1.02676 | ||||||||
\(982\) | 4.00746e79 | 2.05076 | ||||||||
\(983\) | 9.35921e77 | 0.0466198 | 0.0233099 | − | 0.999728i | \(-0.492580\pi\) | ||||
0.0233099 | + | 0.999728i | \(0.492580\pi\) | |||||||
\(984\) | −6.56795e77 | −0.0318463 | ||||||||
\(985\) | 1.03052e79 | 0.486402 | ||||||||
\(986\) | −2.16105e79 | −0.992948 | ||||||||
\(987\) | 6.58338e78 | 0.294472 | ||||||||
\(988\) | −5.16364e79 | −2.24852 | ||||||||
\(989\) | −5.65226e78 | −0.239619 | ||||||||
\(990\) | −1.06612e79 | −0.440021 | ||||||||
\(991\) | −1.55923e79 | −0.626553 | −0.313277 | − | 0.949662i | \(-0.601427\pi\) | ||||
−0.313277 | + | 0.949662i | \(0.601427\pi\) | |||||||
\(992\) | −2.77084e79 | −1.08406 | ||||||||
\(993\) | −1.22461e79 | −0.466490 | ||||||||
\(994\) | 2.10448e79 | 0.780558 | ||||||||
\(995\) | −4.40018e78 | −0.158913 | ||||||||
\(996\) | −9.05819e78 | −0.318544 | ||||||||
\(997\) | 3.05684e79 | 1.04677 | 0.523385 | − | 0.852097i | \(-0.324669\pi\) | ||||
0.523385 | + | 0.852097i | \(0.324669\pi\) | |||||||
\(998\) | 5.70620e79 | 1.90278 | ||||||||
\(999\) | −1.03805e79 | −0.337080 |
(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 | 1.54.a.a.1.4 | ✓ | 4 | |
3.2 | odd | 2 | 9.54.a.b.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.54.a.a.1.4 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.54.a.b.1.1 | 4 | 3.2 | odd | 2 |