Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,16,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, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
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: | \(8.56161030600\) |
Analytic rank: | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 128.000 | 0.707107 | ||||||||
\(3\) | −2187.00 | −0.577350 | ||||||||
\(4\) | 16384.0 | 0.500000 | ||||||||
\(5\) | −114810. | −0.657211 | −0.328605 | − | 0.944467i | \(-0.606579\pi\) | ||||
−0.328605 | + | 0.944467i | \(0.606579\pi\) | |||||||
\(6\) | −279936. | −0.408248 | ||||||||
\(7\) | −3.03453e6 | −1.39269 | −0.696347 | − | 0.717705i | \(-0.745193\pi\) | ||||
−0.696347 | + | 0.717705i | \(0.745193\pi\) | |||||||
\(8\) | 2.09715e6 | 0.353553 | ||||||||
\(9\) | 4.78297e6 | 0.333333 | ||||||||
\(10\) | −1.46957e7 | −0.464718 | ||||||||
\(11\) | −1.03452e8 | −1.60064 | −0.800318 | − | 0.599576i | \(-0.795336\pi\) | ||||
−0.800318 | + | 0.599576i | \(0.795336\pi\) | |||||||
\(12\) | −3.58318e7 | −0.288675 | ||||||||
\(13\) | −1.04366e8 | −0.461300 | −0.230650 | − | 0.973037i | \(-0.574085\pi\) | ||||
−0.230650 | + | 0.973037i | \(0.574085\pi\) | |||||||
\(14\) | −3.88420e8 | −0.984784 | ||||||||
\(15\) | 2.51089e8 | 0.379441 | ||||||||
\(16\) | 2.68435e8 | 0.250000 | ||||||||
\(17\) | 9.97690e8 | 0.589697 | 0.294848 | − | 0.955544i | \(-0.404731\pi\) | ||||
0.294848 | + | 0.955544i | \(0.404731\pi\) | |||||||
\(18\) | 6.12220e8 | 0.235702 | ||||||||
\(19\) | 4.93402e9 | 1.26633 | 0.633167 | − | 0.774015i | \(-0.281754\pi\) | ||||
0.633167 | + | 0.774015i | \(0.281754\pi\) | |||||||
\(20\) | −1.88105e9 | −0.328605 | ||||||||
\(21\) | 6.63651e9 | 0.804073 | ||||||||
\(22\) | −1.32418e10 | −1.13182 | ||||||||
\(23\) | 8.32492e9 | 0.509825 | 0.254913 | − | 0.966964i | \(-0.417953\pi\) | ||||
0.254913 | + | 0.966964i | \(0.417953\pi\) | |||||||
\(24\) | −4.58647e9 | −0.204124 | ||||||||
\(25\) | −1.73362e10 | −0.568074 | ||||||||
\(26\) | −1.33588e10 | −0.326188 | ||||||||
\(27\) | −1.04604e10 | −0.192450 | ||||||||
\(28\) | −4.97177e10 | −0.696347 | ||||||||
\(29\) | 1.04128e11 | 1.12094 | 0.560472 | − | 0.828174i | \(-0.310620\pi\) | ||||
0.560472 | + | 0.828174i | \(0.310620\pi\) | |||||||
\(30\) | 3.21395e10 | 0.268305 | ||||||||
\(31\) | −2.96697e11 | −1.93687 | −0.968434 | − | 0.249270i | \(-0.919809\pi\) | ||||
−0.968434 | + | 0.249270i | \(0.919809\pi\) | |||||||
\(32\) | 3.43597e10 | 0.176777 | ||||||||
\(33\) | 2.26249e11 | 0.924127 | ||||||||
\(34\) | 1.27704e11 | 0.416978 | ||||||||
\(35\) | 3.48394e11 | 0.915294 | ||||||||
\(36\) | 7.83642e10 | 0.166667 | ||||||||
\(37\) | −1.78337e11 | −0.308837 | −0.154419 | − | 0.988006i | \(-0.549350\pi\) | ||||
−0.154419 | + | 0.988006i | \(0.549350\pi\) | |||||||
\(38\) | 6.31554e11 | 0.895434 | ||||||||
\(39\) | 2.28248e11 | 0.266332 | ||||||||
\(40\) | −2.40774e11 | −0.232359 | ||||||||
\(41\) | −1.79088e12 | −1.43611 | −0.718056 | − | 0.695986i | \(-0.754968\pi\) | ||||
−0.718056 | + | 0.695986i | \(0.754968\pi\) | |||||||
\(42\) | 8.49474e11 | 0.568565 | ||||||||
\(43\) | −2.86346e12 | −1.60649 | −0.803244 | − | 0.595650i | \(-0.796895\pi\) | ||||
−0.803244 | + | 0.595650i | \(0.796895\pi\) | |||||||
\(44\) | −1.69495e12 | −0.800318 | ||||||||
\(45\) | −5.49133e11 | −0.219070 | ||||||||
\(46\) | 1.06559e12 | 0.360501 | ||||||||
\(47\) | 4.33291e12 | 1.24751 | 0.623757 | − | 0.781618i | \(-0.285605\pi\) | ||||
0.623757 | + | 0.781618i | \(0.285605\pi\) | |||||||
\(48\) | −5.87068e11 | −0.144338 | ||||||||
\(49\) | 4.46080e12 | 0.939598 | ||||||||
\(50\) | −2.21904e12 | −0.401689 | ||||||||
\(51\) | −2.18195e12 | −0.340461 | ||||||||
\(52\) | −1.70993e12 | −0.230650 | ||||||||
\(53\) | 9.73232e12 | 1.13801 | 0.569007 | − | 0.822333i | \(-0.307328\pi\) | ||||
0.569007 | + | 0.822333i | \(0.307328\pi\) | |||||||
\(54\) | −1.33893e12 | −0.136083 | ||||||||
\(55\) | 1.18773e13 | 1.05196 | ||||||||
\(56\) | −6.36387e12 | −0.492392 | ||||||||
\(57\) | −1.07907e13 | −0.731119 | ||||||||
\(58\) | 1.33284e13 | 0.792626 | ||||||||
\(59\) | −1.35148e13 | −0.707002 | −0.353501 | − | 0.935434i | \(-0.615009\pi\) | ||||
−0.353501 | + | 0.935434i | \(0.615009\pi\) | |||||||
\(60\) | 4.11385e12 | 0.189720 | ||||||||
\(61\) | 5.35266e12 | 0.218070 | 0.109035 | − | 0.994038i | \(-0.465224\pi\) | ||||
0.109035 | + | 0.994038i | \(0.465224\pi\) | |||||||
\(62\) | −3.79772e13 | −1.36957 | ||||||||
\(63\) | −1.45141e13 | −0.464231 | ||||||||
\(64\) | 4.39805e12 | 0.125000 | ||||||||
\(65\) | 1.19822e13 | 0.303171 | ||||||||
\(66\) | 2.89599e13 | 0.653457 | ||||||||
\(67\) | −5.32339e13 | −1.07307 | −0.536534 | − | 0.843879i | \(-0.680267\pi\) | ||||
−0.536534 | + | 0.843879i | \(0.680267\pi\) | |||||||
\(68\) | 1.63461e13 | 0.294848 | ||||||||
\(69\) | −1.82066e13 | −0.294348 | ||||||||
\(70\) | 4.45945e13 | 0.647210 | ||||||||
\(71\) | −2.02297e13 | −0.263968 | −0.131984 | − | 0.991252i | \(-0.542135\pi\) | ||||
−0.131984 | + | 0.991252i | \(0.542135\pi\) | |||||||
\(72\) | 1.00306e13 | 0.117851 | ||||||||
\(73\) | 2.62642e13 | 0.278254 | 0.139127 | − | 0.990275i | \(-0.455570\pi\) | ||||
0.139127 | + | 0.990275i | \(0.455570\pi\) | |||||||
\(74\) | −2.28272e13 | −0.218381 | ||||||||
\(75\) | 3.79144e13 | 0.327978 | ||||||||
\(76\) | 8.08389e13 | 0.633167 | ||||||||
\(77\) | 3.13927e14 | 2.22920 | ||||||||
\(78\) | 2.92158e13 | 0.188325 | ||||||||
\(79\) | −3.39031e14 | −1.98626 | −0.993131 | − | 0.117005i | \(-0.962671\pi\) | ||||
−0.993131 | + | 0.117005i | \(0.962671\pi\) | |||||||
\(80\) | −3.08191e13 | −0.164303 | ||||||||
\(81\) | 2.28768e13 | 0.111111 | ||||||||
\(82\) | −2.29233e14 | −1.01548 | ||||||||
\(83\) | 1.31685e14 | 0.532660 | 0.266330 | − | 0.963882i | \(-0.414189\pi\) | ||||
0.266330 | + | 0.963882i | \(0.414189\pi\) | |||||||
\(84\) | 1.08733e14 | 0.402036 | ||||||||
\(85\) | −1.14545e14 | −0.387555 | ||||||||
\(86\) | −3.66523e14 | −1.13596 | ||||||||
\(87\) | −2.27728e14 | −0.647177 | ||||||||
\(88\) | −2.16954e14 | −0.565910 | ||||||||
\(89\) | −3.93521e13 | −0.0943069 | −0.0471534 | − | 0.998888i | \(-0.515015\pi\) | ||||
−0.0471534 | + | 0.998888i | \(0.515015\pi\) | |||||||
\(90\) | −7.02890e13 | −0.154906 | ||||||||
\(91\) | 3.16701e14 | 0.642450 | ||||||||
\(92\) | 1.36395e14 | 0.254913 | ||||||||
\(93\) | 6.48876e14 | 1.11825 | ||||||||
\(94\) | 5.54612e14 | 0.882126 | ||||||||
\(95\) | −5.66474e14 | −0.832249 | ||||||||
\(96\) | −7.51447e13 | −0.102062 | ||||||||
\(97\) | 1.12875e15 | 1.41844 | 0.709219 | − | 0.704989i | \(-0.249048\pi\) | ||||
0.709219 | + | 0.704989i | \(0.249048\pi\) | |||||||
\(98\) | 5.70982e14 | 0.664396 | ||||||||
\(99\) | −4.94806e14 | −0.533545 | ||||||||
\(100\) | −2.84037e14 | −0.284037 | ||||||||
\(101\) | 3.79528e13 | 0.0352236 | 0.0176118 | − | 0.999845i | \(-0.494394\pi\) | ||||
0.0176118 | + | 0.999845i | \(0.494394\pi\) | |||||||
\(102\) | −2.79289e14 | −0.240743 | ||||||||
\(103\) | −2.07297e14 | −0.166079 | −0.0830393 | − | 0.996546i | \(-0.526463\pi\) | ||||
−0.0830393 | + | 0.996546i | \(0.526463\pi\) | |||||||
\(104\) | −2.18871e14 | −0.163094 | ||||||||
\(105\) | −7.61938e14 | −0.528445 | ||||||||
\(106\) | 1.24574e15 | 0.804697 | ||||||||
\(107\) | −1.99692e15 | −1.20221 | −0.601107 | − | 0.799169i | \(-0.705273\pi\) | ||||
−0.601107 | + | 0.799169i | \(0.705273\pi\) | |||||||
\(108\) | −1.71382e14 | −0.0962250 | ||||||||
\(109\) | 1.35603e13 | 0.00710510 | 0.00355255 | − | 0.999994i | \(-0.498869\pi\) | ||||
0.00355255 | + | 0.999994i | \(0.498869\pi\) | |||||||
\(110\) | 1.52029e15 | 0.743845 | ||||||||
\(111\) | 3.90024e14 | 0.178307 | ||||||||
\(112\) | −8.14575e14 | −0.348174 | ||||||||
\(113\) | −7.08794e14 | −0.283421 | −0.141710 | − | 0.989908i | \(-0.545260\pi\) | ||||
−0.141710 | + | 0.989908i | \(0.545260\pi\) | |||||||
\(114\) | −1.38121e15 | −0.516979 | ||||||||
\(115\) | −9.55784e14 | −0.335063 | ||||||||
\(116\) | 1.70604e15 | 0.560472 | ||||||||
\(117\) | −4.99179e14 | −0.153767 | ||||||||
\(118\) | −1.72990e15 | −0.499926 | ||||||||
\(119\) | −3.02752e15 | −0.821267 | ||||||||
\(120\) | 5.26573e14 | 0.134153 | ||||||||
\(121\) | 6.52501e15 | 1.56203 | ||||||||
\(122\) | 6.85141e14 | 0.154199 | ||||||||
\(123\) | 3.91666e15 | 0.829139 | ||||||||
\(124\) | −4.86108e15 | −0.968434 | ||||||||
\(125\) | 5.49410e15 | 1.03056 | ||||||||
\(126\) | −1.85780e15 | −0.328261 | ||||||||
\(127\) | −1.23021e15 | −0.204858 | −0.102429 | − | 0.994740i | \(-0.532661\pi\) | ||||
−0.102429 | + | 0.994740i | \(0.532661\pi\) | |||||||
\(128\) | 5.62950e14 | 0.0883883 | ||||||||
\(129\) | 6.26239e15 | 0.927507 | ||||||||
\(130\) | 1.53373e15 | 0.214374 | ||||||||
\(131\) | 7.94836e15 | 1.04892 | 0.524460 | − | 0.851435i | \(-0.324267\pi\) | ||||
0.524460 | + | 0.851435i | \(0.324267\pi\) | |||||||
\(132\) | 3.70686e15 | 0.462064 | ||||||||
\(133\) | −1.49724e16 | −1.76362 | ||||||||
\(134\) | −6.81394e15 | −0.758774 | ||||||||
\(135\) | 1.20095e15 | 0.126480 | ||||||||
\(136\) | 2.09231e15 | 0.208489 | ||||||||
\(137\) | −1.78131e16 | −1.68010 | −0.840050 | − | 0.542508i | \(-0.817475\pi\) | ||||
−0.840050 | + | 0.542508i | \(0.817475\pi\) | |||||||
\(138\) | −2.33044e15 | −0.208135 | ||||||||
\(139\) | 3.89941e15 | 0.329904 | 0.164952 | − | 0.986302i | \(-0.447253\pi\) | ||||
0.164952 | + | 0.986302i | \(0.447253\pi\) | |||||||
\(140\) | 5.70809e15 | 0.457647 | ||||||||
\(141\) | −9.47607e15 | −0.720253 | ||||||||
\(142\) | −2.58940e15 | −0.186653 | ||||||||
\(143\) | 1.07968e16 | 0.738373 | ||||||||
\(144\) | 1.28392e15 | 0.0833333 | ||||||||
\(145\) | −1.19550e16 | −0.736696 | ||||||||
\(146\) | 3.36181e15 | 0.196756 | ||||||||
\(147\) | −9.75577e15 | −0.542477 | ||||||||
\(148\) | −2.92188e15 | −0.154419 | ||||||||
\(149\) | −3.48726e15 | −0.175222 | −0.0876108 | − | 0.996155i | \(-0.527923\pi\) | ||||
−0.0876108 | + | 0.996155i | \(0.527923\pi\) | |||||||
\(150\) | 4.85304e15 | 0.231915 | ||||||||
\(151\) | 6.85712e15 | 0.311756 | 0.155878 | − | 0.987776i | \(-0.450179\pi\) | ||||
0.155878 | + | 0.987776i | \(0.450179\pi\) | |||||||
\(152\) | 1.03474e16 | 0.447717 | ||||||||
\(153\) | 4.77192e15 | 0.196566 | ||||||||
\(154\) | 4.01827e16 | 1.57628 | ||||||||
\(155\) | 3.40637e16 | 1.27293 | ||||||||
\(156\) | 3.73962e15 | 0.133166 | ||||||||
\(157\) | 3.69836e16 | 1.25534 | 0.627670 | − | 0.778480i | \(-0.284009\pi\) | ||||
0.627670 | + | 0.778480i | \(0.284009\pi\) | |||||||
\(158\) | −4.33960e16 | −1.40450 | ||||||||
\(159\) | −2.12846e16 | −0.657032 | ||||||||
\(160\) | −3.94484e15 | −0.116180 | ||||||||
\(161\) | −2.52622e16 | −0.710031 | ||||||||
\(162\) | 2.92823e15 | 0.0785674 | ||||||||
\(163\) | 7.42535e15 | 0.190244 | 0.0951218 | − | 0.995466i | \(-0.469676\pi\) | ||||
0.0951218 | + | 0.995466i | \(0.469676\pi\) | |||||||
\(164\) | −2.93418e16 | −0.718056 | ||||||||
\(165\) | −2.59756e16 | −0.607347 | ||||||||
\(166\) | 1.68557e16 | 0.376647 | ||||||||
\(167\) | −1.47365e16 | −0.314789 | −0.157395 | − | 0.987536i | \(-0.550309\pi\) | ||||
−0.157395 | + | 0.987536i | \(0.550309\pi\) | |||||||
\(168\) | 1.39178e16 | 0.284283 | ||||||||
\(169\) | −4.02937e16 | −0.787203 | ||||||||
\(170\) | −1.46617e16 | −0.274043 | ||||||||
\(171\) | 2.35992e16 | 0.422112 | ||||||||
\(172\) | −4.69149e16 | −0.803244 | ||||||||
\(173\) | 3.40039e16 | 0.557421 | 0.278710 | − | 0.960375i | \(-0.410093\pi\) | ||||
0.278710 | + | 0.960375i | \(0.410093\pi\) | |||||||
\(174\) | −2.91492e16 | −0.457623 | ||||||||
\(175\) | 5.26073e16 | 0.791153 | ||||||||
\(176\) | −2.77701e16 | −0.400159 | ||||||||
\(177\) | 2.95569e16 | 0.408188 | ||||||||
\(178\) | −5.03707e15 | −0.0666850 | ||||||||
\(179\) | 3.81276e16 | 0.483996 | 0.241998 | − | 0.970277i | \(-0.422197\pi\) | ||||
0.241998 | + | 0.970277i | \(0.422197\pi\) | |||||||
\(180\) | −8.99699e15 | −0.109535 | ||||||||
\(181\) | −5.14124e16 | −0.600452 | −0.300226 | − | 0.953868i | \(-0.597062\pi\) | ||||
−0.300226 | + | 0.953868i | \(0.597062\pi\) | |||||||
\(182\) | 4.05377e16 | 0.454280 | ||||||||
\(183\) | −1.17063e16 | −0.125903 | ||||||||
\(184\) | 1.74586e16 | 0.180250 | ||||||||
\(185\) | 2.04749e16 | 0.202971 | ||||||||
\(186\) | 8.30561e16 | 0.790723 | ||||||||
\(187\) | −1.03213e17 | −0.943889 | ||||||||
\(188\) | 7.09904e16 | 0.623757 | ||||||||
\(189\) | 3.17422e16 | 0.268024 | ||||||||
\(190\) | −7.25087e16 | −0.588489 | ||||||||
\(191\) | 6.75568e16 | 0.527131 | 0.263566 | − | 0.964641i | \(-0.415101\pi\) | ||||
0.263566 | + | 0.964641i | \(0.415101\pi\) | |||||||
\(192\) | −9.61853e15 | −0.0721688 | ||||||||
\(193\) | −2.07235e16 | −0.149549 | −0.0747746 | − | 0.997200i | \(-0.523824\pi\) | ||||
−0.0747746 | + | 0.997200i | \(0.523824\pi\) | |||||||
\(194\) | 1.44480e17 | 1.00299 | ||||||||
\(195\) | −2.62052e16 | −0.175036 | ||||||||
\(196\) | 7.30857e16 | 0.469799 | ||||||||
\(197\) | 1.71244e16 | 0.105954 | 0.0529772 | − | 0.998596i | \(-0.483129\pi\) | ||||
0.0529772 | + | 0.998596i | \(0.483129\pi\) | |||||||
\(198\) | −6.33352e16 | −0.377273 | ||||||||
\(199\) | −1.05743e17 | −0.606533 | −0.303267 | − | 0.952906i | \(-0.598077\pi\) | ||||
−0.303267 | + | 0.952906i | \(0.598077\pi\) | |||||||
\(200\) | −3.63567e16 | −0.200844 | ||||||||
\(201\) | 1.16423e17 | 0.619536 | ||||||||
\(202\) | 4.85796e15 | 0.0249069 | ||||||||
\(203\) | −3.15980e17 | −1.56113 | ||||||||
\(204\) | −3.57490e16 | −0.170231 | ||||||||
\(205\) | 2.05611e17 | 0.943828 | ||||||||
\(206\) | −2.65340e16 | −0.117435 | ||||||||
\(207\) | 3.98178e16 | 0.169942 | ||||||||
\(208\) | −2.80155e16 | −0.115325 | ||||||||
\(209\) | −5.10432e17 | −2.02694 | ||||||||
\(210\) | −9.75281e16 | −0.373667 | ||||||||
\(211\) | −3.13093e17 | −1.15759 | −0.578795 | − | 0.815473i | \(-0.696477\pi\) | ||||
−0.578795 | + | 0.815473i | \(0.696477\pi\) | |||||||
\(212\) | 1.59454e17 | 0.569007 | ||||||||
\(213\) | 4.42423e16 | 0.152402 | ||||||||
\(214\) | −2.55605e17 | −0.850093 | ||||||||
\(215\) | 3.28754e17 | 1.05580 | ||||||||
\(216\) | −2.19370e16 | −0.0680414 | ||||||||
\(217\) | 9.00334e17 | 2.69747 | ||||||||
\(218\) | 1.73572e15 | 0.00502406 | ||||||||
\(219\) | −5.74397e16 | −0.160650 | ||||||||
\(220\) | 1.94598e17 | 0.525978 | ||||||||
\(221\) | −1.04125e17 | −0.272027 | ||||||||
\(222\) | 4.99231e16 | 0.126082 | ||||||||
\(223\) | 3.35017e17 | 0.818052 | 0.409026 | − | 0.912523i | \(-0.365869\pi\) | ||||
0.409026 | + | 0.912523i | \(0.365869\pi\) | |||||||
\(224\) | −1.04266e17 | −0.246196 | ||||||||
\(225\) | −8.29187e16 | −0.189358 | ||||||||
\(226\) | −9.07256e16 | −0.200409 | ||||||||
\(227\) | 4.67560e17 | 0.999180 | 0.499590 | − | 0.866262i | \(-0.333484\pi\) | ||||
0.499590 | + | 0.866262i | \(0.333484\pi\) | |||||||
\(228\) | −1.76795e17 | −0.365559 | ||||||||
\(229\) | 3.61186e17 | 0.722711 | 0.361355 | − | 0.932428i | \(-0.382314\pi\) | ||||
0.361355 | + | 0.932428i | \(0.382314\pi\) | |||||||
\(230\) | −1.22340e17 | −0.236925 | ||||||||
\(231\) | −6.86559e17 | −1.28703 | ||||||||
\(232\) | 2.18373e17 | 0.396313 | ||||||||
\(233\) | 3.61787e17 | 0.635747 | 0.317873 | − | 0.948133i | \(-0.397031\pi\) | ||||
0.317873 | + | 0.948133i | \(0.397031\pi\) | |||||||
\(234\) | −6.38949e16 | −0.108729 | ||||||||
\(235\) | −4.97461e17 | −0.819880 | ||||||||
\(236\) | −2.21427e17 | −0.353501 | ||||||||
\(237\) | 7.41462e17 | 1.14677 | ||||||||
\(238\) | −3.87522e17 | −0.580724 | ||||||||
\(239\) | −1.06842e18 | −1.55152 | −0.775762 | − | 0.631026i | \(-0.782634\pi\) | ||||
−0.775762 | + | 0.631026i | \(0.782634\pi\) | |||||||
\(240\) | 6.74013e16 | 0.0948602 | ||||||||
\(241\) | −1.00588e18 | −1.37220 | −0.686102 | − | 0.727505i | \(-0.740680\pi\) | ||||
−0.686102 | + | 0.727505i | \(0.740680\pi\) | |||||||
\(242\) | 8.35201e17 | 1.10453 | ||||||||
\(243\) | −5.00315e16 | −0.0641500 | ||||||||
\(244\) | 8.76980e16 | 0.109035 | ||||||||
\(245\) | −5.12144e17 | −0.617514 | ||||||||
\(246\) | 5.01332e17 | 0.586290 | ||||||||
\(247\) | −5.14943e17 | −0.584160 | ||||||||
\(248\) | −6.22218e17 | −0.684786 | ||||||||
\(249\) | −2.87995e17 | −0.307531 | ||||||||
\(250\) | 7.03244e17 | 0.728713 | ||||||||
\(251\) | 1.74766e18 | 1.75754 | 0.878768 | − | 0.477249i | \(-0.158366\pi\) | ||||
0.878768 | + | 0.477249i | \(0.158366\pi\) | |||||||
\(252\) | −2.37798e17 | −0.232116 | ||||||||
\(253\) | −8.61227e17 | −0.816044 | ||||||||
\(254\) | −1.57467e17 | −0.144856 | ||||||||
\(255\) | 2.50509e17 | 0.223755 | ||||||||
\(256\) | 7.20576e16 | 0.0625000 | ||||||||
\(257\) | −2.77264e17 | −0.233558 | −0.116779 | − | 0.993158i | \(-0.537257\pi\) | ||||
−0.116779 | + | 0.993158i | \(0.537257\pi\) | |||||||
\(258\) | 8.01585e17 | 0.655846 | ||||||||
\(259\) | 5.41170e17 | 0.430116 | ||||||||
\(260\) | 1.96317e17 | 0.151586 | ||||||||
\(261\) | 4.98042e17 | 0.373648 | ||||||||
\(262\) | 1.01739e18 | 0.741699 | ||||||||
\(263\) | 1.73303e18 | 1.22783 | 0.613914 | − | 0.789373i | \(-0.289594\pi\) | ||||
0.613914 | + | 0.789373i | \(0.289594\pi\) | |||||||
\(264\) | 4.74478e17 | 0.326728 | ||||||||
\(265\) | −1.11737e18 | −0.747914 | ||||||||
\(266\) | −1.91647e18 | −1.24707 | ||||||||
\(267\) | 8.60631e16 | 0.0544481 | ||||||||
\(268\) | −8.72184e17 | −0.536534 | ||||||||
\(269\) | −5.11271e16 | −0.0305850 | −0.0152925 | − | 0.999883i | \(-0.504868\pi\) | ||||
−0.0152925 | + | 0.999883i | \(0.504868\pi\) | |||||||
\(270\) | 1.53722e17 | 0.0894351 | ||||||||
\(271\) | 2.08455e17 | 0.117962 | 0.0589812 | − | 0.998259i | \(-0.481215\pi\) | ||||
0.0589812 | + | 0.998259i | \(0.481215\pi\) | |||||||
\(272\) | 2.67815e17 | 0.147424 | ||||||||
\(273\) | −6.92625e17 | −0.370918 | ||||||||
\(274\) | −2.28008e18 | −1.18801 | ||||||||
\(275\) | 1.79346e18 | 0.909279 | ||||||||
\(276\) | −2.98297e17 | −0.147174 | ||||||||
\(277\) | 3.29723e18 | 1.58326 | 0.791628 | − | 0.611003i | \(-0.209234\pi\) | ||||
0.791628 | + | 0.611003i | \(0.209234\pi\) | |||||||
\(278\) | 4.99124e17 | 0.233277 | ||||||||
\(279\) | −1.41909e18 | −0.645623 | ||||||||
\(280\) | 7.30636e17 | 0.323605 | ||||||||
\(281\) | −3.98328e18 | −1.71768 | −0.858841 | − | 0.512242i | \(-0.828815\pi\) | ||||
−0.858841 | + | 0.512242i | \(0.828815\pi\) | |||||||
\(282\) | −1.21294e18 | −0.509296 | ||||||||
\(283\) | −2.19051e18 | −0.895668 | −0.447834 | − | 0.894117i | \(-0.647804\pi\) | ||||
−0.447834 | + | 0.894117i | \(0.647804\pi\) | |||||||
\(284\) | −3.31443e17 | −0.131984 | ||||||||
\(285\) | 1.23888e18 | 0.480499 | ||||||||
\(286\) | 1.38199e18 | 0.522108 | ||||||||
\(287\) | 5.43448e18 | 2.00006 | ||||||||
\(288\) | 1.64342e17 | 0.0589256 | ||||||||
\(289\) | −1.86704e18 | −0.652258 | ||||||||
\(290\) | −1.53024e18 | −0.520923 | ||||||||
\(291\) | −2.46858e18 | −0.818935 | ||||||||
\(292\) | 4.30312e17 | 0.139127 | ||||||||
\(293\) | −5.27183e18 | −1.66132 | −0.830662 | − | 0.556778i | \(-0.812038\pi\) | ||||
−0.830662 | + | 0.556778i | \(0.812038\pi\) | |||||||
\(294\) | −1.24874e18 | −0.383589 | ||||||||
\(295\) | 1.55164e18 | 0.464649 | ||||||||
\(296\) | −3.74001e17 | −0.109190 | ||||||||
\(297\) | 1.08214e18 | 0.308042 | ||||||||
\(298\) | −4.46369e17 | −0.123900 | ||||||||
\(299\) | −8.68837e17 | −0.235182 | ||||||||
\(300\) | 6.21189e17 | 0.163989 | ||||||||
\(301\) | 8.68925e18 | 2.23735 | ||||||||
\(302\) | 8.77712e17 | 0.220445 | ||||||||
\(303\) | −8.30029e16 | −0.0203364 | ||||||||
\(304\) | 1.32446e18 | 0.316584 | ||||||||
\(305\) | −6.14539e17 | −0.143318 | ||||||||
\(306\) | 6.10806e17 | 0.138993 | ||||||||
\(307\) | 4.77067e18 | 1.05935 | 0.529677 | − | 0.848199i | \(-0.322313\pi\) | ||||
0.529677 | + | 0.848199i | \(0.322313\pi\) | |||||||
\(308\) | 5.14338e18 | 1.11460 | ||||||||
\(309\) | 4.53359e17 | 0.0958856 | ||||||||
\(310\) | 4.36016e18 | 0.900098 | ||||||||
\(311\) | −6.46666e18 | −1.30310 | −0.651549 | − | 0.758607i | \(-0.725880\pi\) | ||||
−0.651549 | + | 0.758607i | \(0.725880\pi\) | |||||||
\(312\) | 4.78671e17 | 0.0941624 | ||||||||
\(313\) | −6.00129e18 | −1.15256 | −0.576278 | − | 0.817254i | \(-0.695496\pi\) | ||||
−0.576278 | + | 0.817254i | \(0.695496\pi\) | |||||||
\(314\) | 4.73389e18 | 0.887659 | ||||||||
\(315\) | 1.66636e18 | 0.305098 | ||||||||
\(316\) | −5.55469e18 | −0.993131 | ||||||||
\(317\) | −9.53943e17 | −0.166563 | −0.0832814 | − | 0.996526i | \(-0.526540\pi\) | ||||
−0.0832814 | + | 0.996526i | \(0.526540\pi\) | |||||||
\(318\) | −2.72443e18 | −0.464592 | ||||||||
\(319\) | −1.07722e19 | −1.79422 | ||||||||
\(320\) | −5.04940e17 | −0.0821513 | ||||||||
\(321\) | 4.36726e18 | 0.694098 | ||||||||
\(322\) | −3.23356e18 | −0.502068 | ||||||||
\(323\) | 4.92262e18 | 0.746753 | ||||||||
\(324\) | 3.74813e17 | 0.0555556 | ||||||||
\(325\) | 1.80931e18 | 0.262052 | ||||||||
\(326\) | 9.50445e17 | 0.134523 | ||||||||
\(327\) | −2.96563e16 | −0.00410213 | ||||||||
\(328\) | −3.75575e18 | −0.507742 | ||||||||
\(329\) | −1.31483e19 | −1.73741 | ||||||||
\(330\) | −3.32488e18 | −0.429459 | ||||||||
\(331\) | −5.29071e18 | −0.668042 | −0.334021 | − | 0.942566i | \(-0.608406\pi\) | ||||
−0.334021 | + | 0.942566i | \(0.608406\pi\) | |||||||
\(332\) | 2.15752e18 | 0.266330 | ||||||||
\(333\) | −8.52983e17 | −0.102946 | ||||||||
\(334\) | −1.88627e18 | −0.222590 | ||||||||
\(335\) | 6.11179e18 | 0.705232 | ||||||||
\(336\) | 1.78148e18 | 0.201018 | ||||||||
\(337\) | 6.22409e18 | 0.686834 | 0.343417 | − | 0.939183i | \(-0.388416\pi\) | ||||
0.343417 | + | 0.939183i | \(0.388416\pi\) | |||||||
\(338\) | −5.15759e18 | −0.556636 | ||||||||
\(339\) | 1.55013e18 | 0.163633 | ||||||||
\(340\) | −1.87670e18 | −0.193777 | ||||||||
\(341\) | 3.06938e19 | 3.10022 | ||||||||
\(342\) | 3.02070e18 | 0.298478 | ||||||||
\(343\) | 8.70190e17 | 0.0841217 | ||||||||
\(344\) | −6.00511e18 | −0.567979 | ||||||||
\(345\) | 2.09030e18 | 0.193448 | ||||||||
\(346\) | 4.35250e18 | 0.394156 | ||||||||
\(347\) | −3.22035e18 | −0.285386 | −0.142693 | − | 0.989767i | \(-0.545576\pi\) | ||||
−0.142693 | + | 0.989767i | \(0.545576\pi\) | |||||||
\(348\) | −3.73110e18 | −0.323588 | ||||||||
\(349\) | −6.17407e18 | −0.524060 | −0.262030 | − | 0.965060i | \(-0.584392\pi\) | ||||
−0.262030 | + | 0.965060i | \(0.584392\pi\) | |||||||
\(350\) | 6.73374e18 | 0.559430 | ||||||||
\(351\) | 1.09170e18 | 0.0887772 | ||||||||
\(352\) | −3.55457e18 | −0.282955 | ||||||||
\(353\) | −6.14267e18 | −0.478681 | −0.239341 | − | 0.970936i | \(-0.576931\pi\) | ||||
−0.239341 | + | 0.970936i | \(0.576931\pi\) | |||||||
\(354\) | 3.78329e18 | 0.288632 | ||||||||
\(355\) | 2.32257e18 | 0.173483 | ||||||||
\(356\) | −6.44746e17 | −0.0471534 | ||||||||
\(357\) | 6.62118e18 | 0.474159 | ||||||||
\(358\) | 4.88033e18 | 0.342237 | ||||||||
\(359\) | −5.81103e18 | −0.399066 | −0.199533 | − | 0.979891i | \(-0.563943\pi\) | ||||
−0.199533 | + | 0.979891i | \(0.563943\pi\) | |||||||
\(360\) | −1.15161e18 | −0.0774530 | ||||||||
\(361\) | 9.16338e18 | 0.603603 | ||||||||
\(362\) | −6.58079e18 | −0.424584 | ||||||||
\(363\) | −1.42702e19 | −0.901841 | ||||||||
\(364\) | 5.18883e18 | 0.321225 | ||||||||
\(365\) | −3.01539e18 | −0.182872 | ||||||||
\(366\) | −1.49840e18 | −0.0890268 | ||||||||
\(367\) | −2.77147e17 | −0.0161330 | −0.00806650 | − | 0.999967i | \(-0.502568\pi\) | ||||
−0.00806650 | + | 0.999967i | \(0.502568\pi\) | |||||||
\(368\) | 2.23470e18 | 0.127456 | ||||||||
\(369\) | −8.56574e18 | −0.478704 | ||||||||
\(370\) | 2.62079e18 | 0.143522 | ||||||||
\(371\) | −2.95330e19 | −1.58490 | ||||||||
\(372\) | 1.06312e19 | 0.559126 | ||||||||
\(373\) | 2.30498e19 | 1.18809 | 0.594047 | − | 0.804430i | \(-0.297529\pi\) | ||||
0.594047 | + | 0.804430i | \(0.297529\pi\) | |||||||
\(374\) | −1.32112e19 | −0.667431 | ||||||||
\(375\) | −1.20156e19 | −0.594991 | ||||||||
\(376\) | 9.08677e18 | 0.441063 | ||||||||
\(377\) | −1.08674e19 | −0.517091 | ||||||||
\(378\) | 4.06301e18 | 0.189522 | ||||||||
\(379\) | −1.34397e19 | −0.614604 | −0.307302 | − | 0.951612i | \(-0.599426\pi\) | ||||
−0.307302 | + | 0.951612i | \(0.599426\pi\) | |||||||
\(380\) | −9.28112e18 | −0.416124 | ||||||||
\(381\) | 2.69048e18 | 0.118275 | ||||||||
\(382\) | 8.64727e18 | 0.372738 | ||||||||
\(383\) | 2.64151e19 | 1.11651 | 0.558254 | − | 0.829670i | \(-0.311471\pi\) | ||||
0.558254 | + | 0.829670i | \(0.311471\pi\) | |||||||
\(384\) | −1.23117e18 | −0.0510310 | ||||||||
\(385\) | −3.60420e19 | −1.46505 | ||||||||
\(386\) | −2.65261e18 | −0.105747 | ||||||||
\(387\) | −1.36958e19 | −0.535496 | ||||||||
\(388\) | 1.84935e19 | 0.709219 | ||||||||
\(389\) | 3.95275e19 | 1.48688 | 0.743442 | − | 0.668800i | \(-0.233192\pi\) | ||||
0.743442 | + | 0.668800i | \(0.233192\pi\) | |||||||
\(390\) | −3.35426e18 | −0.123769 | ||||||||
\(391\) | 8.30569e18 | 0.300642 | ||||||||
\(392\) | 9.35497e18 | 0.332198 | ||||||||
\(393\) | −1.73831e19 | −0.605595 | ||||||||
\(394\) | 2.19192e18 | 0.0749210 | ||||||||
\(395\) | 3.89242e19 | 1.30539 | ||||||||
\(396\) | −8.10691e18 | −0.266773 | ||||||||
\(397\) | 2.82890e18 | 0.0913457 | 0.0456729 | − | 0.998956i | \(-0.485457\pi\) | ||||
0.0456729 | + | 0.998956i | \(0.485457\pi\) | |||||||
\(398\) | −1.35351e19 | −0.428884 | ||||||||
\(399\) | 3.27447e19 | 1.01822 | ||||||||
\(400\) | −4.65366e18 | −0.142018 | ||||||||
\(401\) | −4.63681e19 | −1.38879 | −0.694395 | − | 0.719594i | \(-0.744328\pi\) | ||||
−0.694395 | + | 0.719594i | \(0.744328\pi\) | |||||||
\(402\) | 1.49021e19 | 0.438078 | ||||||||
\(403\) | 3.09650e19 | 0.893477 | ||||||||
\(404\) | 6.21819e17 | 0.0176118 | ||||||||
\(405\) | −2.62648e18 | −0.0730234 | ||||||||
\(406\) | −4.04454e19 | −1.10389 | ||||||||
\(407\) | 1.84493e19 | 0.494336 | ||||||||
\(408\) | −4.57588e18 | −0.120371 | ||||||||
\(409\) | −1.17092e19 | −0.302415 | −0.151207 | − | 0.988502i | \(-0.548316\pi\) | ||||
−0.151207 | + | 0.988502i | \(0.548316\pi\) | |||||||
\(410\) | 2.63182e19 | 0.667387 | ||||||||
\(411\) | 3.89573e19 | 0.970007 | ||||||||
\(412\) | −3.39635e18 | −0.0830393 | ||||||||
\(413\) | 4.10112e19 | 0.984638 | ||||||||
\(414\) | 5.09668e18 | 0.120167 | ||||||||
\(415\) | −1.51187e19 | −0.350070 | ||||||||
\(416\) | −3.58598e18 | −0.0815470 | ||||||||
\(417\) | −8.52801e18 | −0.190470 | ||||||||
\(418\) | −6.53353e19 | −1.43326 | ||||||||
\(419\) | −4.20102e19 | −0.905210 | −0.452605 | − | 0.891711i | \(-0.649505\pi\) | ||||
−0.452605 | + | 0.891711i | \(0.649505\pi\) | |||||||
\(420\) | −1.24836e19 | −0.264223 | ||||||||
\(421\) | −1.59718e19 | −0.332077 | −0.166039 | − | 0.986119i | \(-0.553098\pi\) | ||||
−0.166039 | + | 0.986119i | \(0.553098\pi\) | |||||||
\(422\) | −4.00759e19 | −0.818540 | ||||||||
\(423\) | 2.07242e19 | 0.415838 | ||||||||
\(424\) | 2.04101e19 | 0.402348 | ||||||||
\(425\) | −1.72962e19 | −0.334991 | ||||||||
\(426\) | 5.66301e18 | 0.107764 | ||||||||
\(427\) | −1.62428e19 | −0.303705 | ||||||||
\(428\) | −3.27175e19 | −0.601107 | ||||||||
\(429\) | −2.36127e19 | −0.426300 | ||||||||
\(430\) | 4.20805e19 | 0.746564 | ||||||||
\(431\) | −9.76365e19 | −1.70229 | −0.851143 | − | 0.524934i | \(-0.824090\pi\) | ||||
−0.851143 | + | 0.524934i | \(0.824090\pi\) | |||||||
\(432\) | −2.80793e18 | −0.0481125 | ||||||||
\(433\) | −6.91455e19 | −1.16441 | −0.582204 | − | 0.813043i | \(-0.697809\pi\) | ||||
−0.582204 | + | 0.813043i | \(0.697809\pi\) | |||||||
\(434\) | 1.15243e20 | 1.90740 | ||||||||
\(435\) | 2.61455e19 | 0.425332 | ||||||||
\(436\) | 2.22172e17 | 0.00355255 | ||||||||
\(437\) | 4.10753e19 | 0.645609 | ||||||||
\(438\) | −7.35229e18 | −0.113597 | ||||||||
\(439\) | 5.48990e19 | 0.833836 | 0.416918 | − | 0.908944i | \(-0.363110\pi\) | ||||
0.416918 | + | 0.908944i | \(0.363110\pi\) | |||||||
\(440\) | 2.49085e19 | 0.371922 | ||||||||
\(441\) | 2.13359e19 | 0.313199 | ||||||||
\(442\) | −1.33280e19 | −0.192352 | ||||||||
\(443\) | 3.80504e19 | 0.539923 | 0.269961 | − | 0.962871i | \(-0.412989\pi\) | ||||
0.269961 | + | 0.962871i | \(0.412989\pi\) | |||||||
\(444\) | 6.39015e18 | 0.0891536 | ||||||||
\(445\) | 4.51802e18 | 0.0619795 | ||||||||
\(446\) | 4.28822e19 | 0.578450 | ||||||||
\(447\) | 7.62664e18 | 0.101164 | ||||||||
\(448\) | −1.33460e19 | −0.174087 | ||||||||
\(449\) | 1.11994e18 | 0.0143663 | 0.00718317 | − | 0.999974i | \(-0.497714\pi\) | ||||
0.00718317 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(450\) | −1.06136e19 | −0.133896 | ||||||||
\(451\) | 1.85270e20 | 2.29869 | ||||||||
\(452\) | −1.16129e19 | −0.141710 | ||||||||
\(453\) | −1.49965e19 | −0.179992 | ||||||||
\(454\) | 5.98477e19 | 0.706527 | ||||||||
\(455\) | −3.63604e19 | −0.422225 | ||||||||
\(456\) | −2.26297e19 | −0.258489 | ||||||||
\(457\) | −9.70734e19 | −1.09076 | −0.545379 | − | 0.838189i | \(-0.683614\pi\) | ||||
−0.545379 | + | 0.838189i | \(0.683614\pi\) | |||||||
\(458\) | 4.62318e19 | 0.511034 | ||||||||
\(459\) | −1.04362e19 | −0.113487 | ||||||||
\(460\) | −1.56596e19 | −0.167531 | ||||||||
\(461\) | −9.78165e19 | −1.02957 | −0.514784 | − | 0.857320i | \(-0.672128\pi\) | ||||
−0.514784 | + | 0.857320i | \(0.672128\pi\) | |||||||
\(462\) | −8.78795e19 | −0.910066 | ||||||||
\(463\) | −2.17159e19 | −0.221269 | −0.110634 | − | 0.993861i | \(-0.535288\pi\) | ||||
−0.110634 | + | 0.993861i | \(0.535288\pi\) | |||||||
\(464\) | 2.79517e19 | 0.280236 | ||||||||
\(465\) | −7.44974e19 | −0.734927 | ||||||||
\(466\) | 4.63088e19 | 0.449541 | ||||||||
\(467\) | −1.98443e20 | −1.89565 | −0.947826 | − | 0.318788i | \(-0.896724\pi\) | ||||
−0.947826 | + | 0.318788i | \(0.896724\pi\) | |||||||
\(468\) | −8.17854e18 | −0.0768833 | ||||||||
\(469\) | 1.61540e20 | 1.49446 | ||||||||
\(470\) | −6.36750e19 | −0.579743 | ||||||||
\(471\) | −8.08830e19 | −0.724771 | ||||||||
\(472\) | −2.83427e19 | −0.249963 | ||||||||
\(473\) | 2.96230e20 | 2.57140 | ||||||||
\(474\) | 9.49071e19 | 0.810888 | ||||||||
\(475\) | −8.55373e19 | −0.719372 | ||||||||
\(476\) | −4.96028e19 | −0.410634 | ||||||||
\(477\) | 4.65494e19 | 0.379338 | ||||||||
\(478\) | −1.36758e20 | −1.09709 | ||||||||
\(479\) | −3.78661e19 | −0.299043 | −0.149522 | − | 0.988758i | \(-0.547773\pi\) | ||||
−0.149522 | + | 0.988758i | \(0.547773\pi\) | |||||||
\(480\) | 8.62737e18 | 0.0670763 | ||||||||
\(481\) | 1.86123e19 | 0.142467 | ||||||||
\(482\) | −1.28753e20 | −0.970295 | ||||||||
\(483\) | 5.52484e19 | 0.409936 | ||||||||
\(484\) | 1.06906e20 | 0.781017 | ||||||||
\(485\) | −1.29592e20 | −0.932212 | ||||||||
\(486\) | −6.40404e18 | −0.0453609 | ||||||||
\(487\) | 3.89265e19 | 0.271505 | 0.135752 | − | 0.990743i | \(-0.456655\pi\) | ||||
0.135752 | + | 0.990743i | \(0.456655\pi\) | |||||||
\(488\) | 1.12253e19 | 0.0770994 | ||||||||
\(489\) | −1.62392e19 | −0.109837 | ||||||||
\(490\) | −6.55545e19 | −0.436648 | ||||||||
\(491\) | 1.40516e20 | 0.921753 | 0.460876 | − | 0.887464i | \(-0.347535\pi\) | ||||
0.460876 | + | 0.887464i | \(0.347535\pi\) | |||||||
\(492\) | 6.41706e19 | 0.414570 | ||||||||
\(493\) | 1.03888e20 | 0.661016 | ||||||||
\(494\) | −6.59127e19 | −0.413063 | ||||||||
\(495\) | 5.68087e19 | 0.350652 | ||||||||
\(496\) | −7.96439e19 | −0.484217 | ||||||||
\(497\) | 6.13875e19 | 0.367627 | ||||||||
\(498\) | −3.68633e19 | −0.217457 | ||||||||
\(499\) | −1.53703e20 | −0.893157 | −0.446578 | − | 0.894745i | \(-0.647358\pi\) | ||||
−0.446578 | + | 0.894745i | \(0.647358\pi\) | |||||||
\(500\) | 9.00153e19 | 0.515278 | ||||||||
\(501\) | 3.22287e19 | 0.181744 | ||||||||
\(502\) | 2.23701e20 | 1.24277 | ||||||||
\(503\) | 5.62265e18 | 0.0307738 | 0.0153869 | − | 0.999882i | \(-0.495102\pi\) | ||||
0.0153869 | + | 0.999882i | \(0.495102\pi\) | |||||||
\(504\) | −3.04382e19 | −0.164131 | ||||||||
\(505\) | −4.35737e18 | −0.0231493 | ||||||||
\(506\) | −1.10237e20 | −0.577031 | ||||||||
\(507\) | 8.81222e19 | 0.454492 | ||||||||
\(508\) | −2.01558e19 | −0.102429 | ||||||||
\(509\) | 3.29307e20 | 1.64899 | 0.824495 | − | 0.565869i | \(-0.191459\pi\) | ||||
0.824495 | + | 0.565869i | \(0.191459\pi\) | |||||||
\(510\) | 3.20652e19 | 0.158219 | ||||||||
\(511\) | −7.96993e19 | −0.387523 | ||||||||
\(512\) | 9.22337e18 | 0.0441942 | ||||||||
\(513\) | −5.16115e19 | −0.243706 | ||||||||
\(514\) | −3.54898e19 | −0.165151 | ||||||||
\(515\) | 2.37998e19 | 0.109149 | ||||||||
\(516\) | 1.02603e20 | 0.463753 | ||||||||
\(517\) | −4.48247e20 | −1.99682 | ||||||||
\(518\) | 6.92698e19 | 0.304138 | ||||||||
\(519\) | −7.43666e19 | −0.321827 | ||||||||
\(520\) | 2.51286e19 | 0.107187 | ||||||||
\(521\) | 1.71775e20 | 0.722231 | 0.361116 | − | 0.932521i | \(-0.382396\pi\) | ||||
0.361116 | + | 0.932521i | \(0.382396\pi\) | |||||||
\(522\) | 6.37494e19 | 0.264209 | ||||||||
\(523\) | −1.59414e20 | −0.651275 | −0.325637 | − | 0.945495i | \(-0.605579\pi\) | ||||
−0.325637 | + | 0.945495i | \(0.605579\pi\) | |||||||
\(524\) | 1.30226e20 | 0.524460 | ||||||||
\(525\) | −1.15052e20 | −0.456773 | ||||||||
\(526\) | 2.21828e20 | 0.868205 | ||||||||
\(527\) | −2.96011e20 | −1.14216 | ||||||||
\(528\) | 6.07332e19 | 0.231032 | ||||||||
\(529\) | −1.97331e20 | −0.740078 | ||||||||
\(530\) | −1.43023e20 | −0.528855 | ||||||||
\(531\) | −6.46410e19 | −0.235667 | ||||||||
\(532\) | −2.45308e20 | −0.881809 | ||||||||
\(533\) | 1.86907e20 | 0.662478 | ||||||||
\(534\) | 1.10161e19 | 0.0385006 | ||||||||
\(535\) | 2.29266e20 | 0.790108 | ||||||||
\(536\) | −1.11640e20 | −0.379387 | ||||||||
\(537\) | −8.33851e19 | −0.279435 | ||||||||
\(538\) | −6.54427e18 | −0.0216269 | ||||||||
\(539\) | −4.61477e20 | −1.50395 | ||||||||
\(540\) | 1.96764e19 | 0.0632401 | ||||||||
\(541\) | 4.74121e19 | 0.150283 | 0.0751415 | − | 0.997173i | \(-0.476059\pi\) | ||||
0.0751415 | + | 0.997173i | \(0.476059\pi\) | |||||||
\(542\) | 2.66823e19 | 0.0834120 | ||||||||
\(543\) | 1.12439e20 | 0.346671 | ||||||||
\(544\) | 3.42804e19 | 0.104245 | ||||||||
\(545\) | −1.55686e18 | −0.00466955 | ||||||||
\(546\) | −8.86560e19 | −0.262279 | ||||||||
\(547\) | −2.80986e20 | −0.819934 | −0.409967 | − | 0.912100i | \(-0.634460\pi\) | ||||
−0.409967 | + | 0.912100i | \(0.634460\pi\) | |||||||
\(548\) | −2.91850e20 | −0.840050 | ||||||||
\(549\) | 2.56016e19 | 0.0726900 | ||||||||
\(550\) | 2.29563e20 | 0.642958 | ||||||||
\(551\) | 5.13770e20 | 1.41949 | ||||||||
\(552\) | −3.81820e19 | −0.104068 | ||||||||
\(553\) | 1.02880e21 | 2.76626 | ||||||||
\(554\) | 4.22046e20 | 1.11953 | ||||||||
\(555\) | −4.47787e19 | −0.117185 | ||||||||
\(556\) | 6.38879e19 | 0.164952 | ||||||||
\(557\) | −3.49642e20 | −0.890654 | −0.445327 | − | 0.895368i | \(-0.646913\pi\) | ||||
−0.445327 | + | 0.895368i | \(0.646913\pi\) | |||||||
\(558\) | −1.81644e20 | −0.456524 | ||||||||
\(559\) | 2.98847e20 | 0.741073 | ||||||||
\(560\) | 9.35213e19 | 0.228823 | ||||||||
\(561\) | 2.25726e20 | 0.544955 | ||||||||
\(562\) | −5.09859e20 | −1.21459 | ||||||||
\(563\) | 2.68215e20 | 0.630479 | 0.315240 | − | 0.949012i | \(-0.397915\pi\) | ||||
0.315240 | + | 0.949012i | \(0.397915\pi\) | |||||||
\(564\) | −1.55256e20 | −0.360126 | ||||||||
\(565\) | 8.13766e19 | 0.186267 | ||||||||
\(566\) | −2.80385e20 | −0.633333 | ||||||||
\(567\) | −6.94203e19 | −0.154744 | ||||||||
\(568\) | −4.24247e19 | −0.0933267 | ||||||||
\(569\) | −7.95691e20 | −1.72744 | −0.863719 | − | 0.503974i | \(-0.831871\pi\) | ||||
−0.863719 | + | 0.503974i | \(0.831871\pi\) | |||||||
\(570\) | 1.58577e20 | 0.339764 | ||||||||
\(571\) | 8.84470e20 | 1.87030 | 0.935152 | − | 0.354246i | \(-0.115262\pi\) | ||||
0.935152 | + | 0.354246i | \(0.115262\pi\) | |||||||
\(572\) | 1.76895e20 | 0.369186 | ||||||||
\(573\) | −1.47747e20 | −0.304339 | ||||||||
\(574\) | 6.95614e20 | 1.41426 | ||||||||
\(575\) | −1.44323e20 | −0.289618 | ||||||||
\(576\) | 2.10357e19 | 0.0416667 | ||||||||
\(577\) | 3.15722e20 | 0.617286 | 0.308643 | − | 0.951178i | \(-0.400125\pi\) | ||||
0.308643 | + | 0.951178i | \(0.400125\pi\) | |||||||
\(578\) | −2.38981e20 | −0.461216 | ||||||||
\(579\) | 4.53224e19 | 0.0863423 | ||||||||
\(580\) | −1.95870e20 | −0.368348 | ||||||||
\(581\) | −3.99601e20 | −0.741832 | ||||||||
\(582\) | −3.15978e20 | −0.579075 | ||||||||
\(583\) | −1.00682e21 | −1.82154 | ||||||||
\(584\) | 5.50799e19 | 0.0983778 | ||||||||
\(585\) | 5.73107e19 | 0.101057 | ||||||||
\(586\) | −6.74794e20 | −1.17473 | ||||||||
\(587\) | 7.33397e20 | 1.26053 | 0.630265 | − | 0.776380i | \(-0.282946\pi\) | ||||
0.630265 | + | 0.776380i | \(0.282946\pi\) | |||||||
\(588\) | −1.59838e20 | −0.271239 | ||||||||
\(589\) | −1.46391e21 | −2.45272 | ||||||||
\(590\) | 1.98610e20 | 0.328557 | ||||||||
\(591\) | −3.74511e19 | −0.0611728 | ||||||||
\(592\) | −4.78721e19 | −0.0772093 | ||||||||
\(593\) | −3.25571e20 | −0.518485 | −0.259242 | − | 0.965812i | \(-0.583473\pi\) | ||||
−0.259242 | + | 0.965812i | \(0.583473\pi\) | |||||||
\(594\) | 1.38514e20 | 0.217819 | ||||||||
\(595\) | 3.47589e20 | 0.539746 | ||||||||
\(596\) | −5.71353e19 | −0.0876108 | ||||||||
\(597\) | 2.31261e20 | 0.350182 | ||||||||
\(598\) | −1.11211e20 | −0.166299 | ||||||||
\(599\) | 6.61173e20 | 0.976368 | 0.488184 | − | 0.872741i | \(-0.337659\pi\) | ||||
0.488184 | + | 0.872741i | \(0.337659\pi\) | |||||||
\(600\) | 7.95122e19 | 0.115958 | ||||||||
\(601\) | −2.49467e20 | −0.359297 | −0.179649 | − | 0.983731i | \(-0.557496\pi\) | ||||
−0.179649 | + | 0.983731i | \(0.557496\pi\) | |||||||
\(602\) | 1.11222e21 | 1.58204 | ||||||||
\(603\) | −2.54616e20 | −0.357689 | ||||||||
\(604\) | 1.12347e20 | 0.155878 | ||||||||
\(605\) | −7.49136e20 | −1.02659 | ||||||||
\(606\) | −1.06244e19 | −0.0143800 | ||||||||
\(607\) | 1.08917e21 | 1.45606 | 0.728031 | − | 0.685544i | \(-0.240436\pi\) | ||||
0.728031 | + | 0.685544i | \(0.240436\pi\) | |||||||
\(608\) | 1.69531e20 | 0.223858 | ||||||||
\(609\) | 6.91048e20 | 0.901320 | ||||||||
\(610\) | −7.86610e19 | −0.101341 | ||||||||
\(611\) | −4.52208e20 | −0.575478 | ||||||||
\(612\) | 7.81831e19 | 0.0982828 | ||||||||
\(613\) | 1.99450e20 | 0.247674 | 0.123837 | − | 0.992303i | \(-0.460480\pi\) | ||||
0.123837 | + | 0.992303i | \(0.460480\pi\) | |||||||
\(614\) | 6.10645e20 | 0.749076 | ||||||||
\(615\) | −4.49672e20 | −0.544919 | ||||||||
\(616\) | 6.58353e20 | 0.788140 | ||||||||
\(617\) | 4.21127e20 | 0.498052 | 0.249026 | − | 0.968497i | \(-0.419890\pi\) | ||||
0.249026 | + | 0.968497i | \(0.419890\pi\) | |||||||
\(618\) | 5.80299e19 | 0.0678013 | ||||||||
\(619\) | −1.27272e21 | −1.46910 | −0.734552 | − | 0.678552i | \(-0.762608\pi\) | ||||
−0.734552 | + | 0.678552i | \(0.762608\pi\) | |||||||
\(620\) | 5.58100e20 | 0.636465 | ||||||||
\(621\) | −8.70816e19 | −0.0981159 | ||||||||
\(622\) | −8.27732e20 | −0.921429 | ||||||||
\(623\) | 1.19415e20 | 0.131341 | ||||||||
\(624\) | 6.12699e19 | 0.0665829 | ||||||||
\(625\) | −1.01717e20 | −0.109218 | ||||||||
\(626\) | −7.68165e20 | −0.814980 | ||||||||
\(627\) | 1.11632e21 | 1.17025 | ||||||||
\(628\) | 6.05938e20 | 0.627670 | ||||||||
\(629\) | −1.77925e20 | −0.182120 | ||||||||
\(630\) | 2.13294e20 | 0.215737 | ||||||||
\(631\) | −3.42884e20 | −0.342711 | −0.171355 | − | 0.985209i | \(-0.554815\pi\) | ||||
−0.171355 | + | 0.985209i | \(0.554815\pi\) | |||||||
\(632\) | −7.11000e20 | −0.702250 | ||||||||
\(633\) | 6.84735e20 | 0.668335 | ||||||||
\(634\) | −1.22105e20 | −0.117778 | ||||||||
\(635\) | 1.41241e20 | 0.134635 | ||||||||
\(636\) | −3.48727e20 | −0.328516 | ||||||||
\(637\) | −4.65555e20 | −0.433436 | ||||||||
\(638\) | −1.37885e21 | −1.26871 | ||||||||
\(639\) | −9.67578e19 | −0.0879893 | ||||||||
\(640\) | −6.46323e19 | −0.0580898 | ||||||||
\(641\) | 1.00075e21 | 0.888980 | 0.444490 | − | 0.895784i | \(-0.353385\pi\) | ||||
0.444490 | + | 0.895784i | \(0.353385\pi\) | |||||||
\(642\) | 5.59009e20 | 0.490802 | ||||||||
\(643\) | −1.35729e20 | −0.117785 | −0.0588927 | − | 0.998264i | \(-0.518757\pi\) | ||||
−0.0588927 | + | 0.998264i | \(0.518757\pi\) | |||||||
\(644\) | −4.13896e20 | −0.355015 | ||||||||
\(645\) | −7.18985e20 | −0.609567 | ||||||||
\(646\) | 6.30095e20 | 0.528034 | ||||||||
\(647\) | 2.15462e21 | 1.78479 | 0.892397 | − | 0.451251i | \(-0.149022\pi\) | ||||
0.892397 | + | 0.451251i | \(0.149022\pi\) | |||||||
\(648\) | 4.79761e19 | 0.0392837 | ||||||||
\(649\) | 1.39813e21 | 1.13165 | ||||||||
\(650\) | 2.31592e20 | 0.185299 | ||||||||
\(651\) | −1.96903e21 | −1.55738 | ||||||||
\(652\) | 1.21657e20 | 0.0951218 | ||||||||
\(653\) | −2.06101e21 | −1.59306 | −0.796529 | − | 0.604601i | \(-0.793333\pi\) | ||||
−0.796529 | + | 0.604601i | \(0.793333\pi\) | |||||||
\(654\) | −3.79601e18 | −0.00290064 | ||||||||
\(655\) | −9.12551e20 | −0.689362 | ||||||||
\(656\) | −4.80736e20 | −0.359028 | ||||||||
\(657\) | 1.25621e20 | 0.0927515 | ||||||||
\(658\) | −1.68299e21 | −1.22853 | ||||||||
\(659\) | −1.61309e21 | −1.16418 | −0.582089 | − | 0.813125i | \(-0.697764\pi\) | ||||
−0.582089 | + | 0.813125i | \(0.697764\pi\) | |||||||
\(660\) | −4.25585e20 | −0.303673 | ||||||||
\(661\) | 1.60888e21 | 1.13504 | 0.567521 | − | 0.823359i | \(-0.307903\pi\) | ||||
0.567521 | + | 0.823359i | \(0.307903\pi\) | |||||||
\(662\) | −6.77211e20 | −0.472377 | ||||||||
\(663\) | 2.27721e20 | 0.157055 | ||||||||
\(664\) | 2.76163e20 | 0.188324 | ||||||||
\(665\) | 1.71898e21 | 1.15907 | ||||||||
\(666\) | −1.09182e20 | −0.0727936 | ||||||||
\(667\) | 8.66859e20 | 0.571485 | ||||||||
\(668\) | −2.41442e20 | −0.157395 | ||||||||
\(669\) | −7.32683e20 | −0.472303 | ||||||||
\(670\) | 7.82309e20 | 0.498674 | ||||||||
\(671\) | −5.53742e20 | −0.349051 | ||||||||
\(672\) | 2.28029e20 | 0.142141 | ||||||||
\(673\) | 1.67294e21 | 1.03126 | 0.515628 | − | 0.856812i | \(-0.327559\pi\) | ||||
0.515628 | + | 0.856812i | \(0.327559\pi\) | |||||||
\(674\) | 7.96684e20 | 0.485665 | ||||||||
\(675\) | 1.81343e20 | 0.109326 | ||||||||
\(676\) | −6.60171e20 | −0.393601 | ||||||||
\(677\) | 7.27000e20 | 0.428666 | 0.214333 | − | 0.976761i | \(-0.431242\pi\) | ||||
0.214333 | + | 0.976761i | \(0.431242\pi\) | |||||||
\(678\) | 1.98417e20 | 0.115706 | ||||||||
\(679\) | −3.42523e21 | −1.97545 | ||||||||
\(680\) | −2.40218e20 | −0.137021 | ||||||||
\(681\) | −1.02255e21 | −0.576877 | ||||||||
\(682\) | 3.92880e21 | 2.19219 | ||||||||
\(683\) | 2.85909e21 | 1.57787 | 0.788936 | − | 0.614475i | \(-0.210632\pi\) | ||||
0.788936 | + | 0.614475i | \(0.210632\pi\) | |||||||
\(684\) | 3.86650e20 | 0.211056 | ||||||||
\(685\) | 2.04512e21 | 1.10418 | ||||||||
\(686\) | 1.11384e20 | 0.0594830 | ||||||||
\(687\) | −7.89913e20 | −0.417257 | ||||||||
\(688\) | −7.68654e20 | −0.401622 | ||||||||
\(689\) | −1.01572e21 | −0.524965 | ||||||||
\(690\) | 2.67558e20 | 0.136789 | ||||||||
\(691\) | 1.71274e21 | 0.866178 | 0.433089 | − | 0.901351i | \(-0.357424\pi\) | ||||
0.433089 | + | 0.901351i | \(0.357424\pi\) | |||||||
\(692\) | 5.57120e20 | 0.278710 | ||||||||
\(693\) | 1.50150e21 | 0.743065 | ||||||||
\(694\) | −4.12205e20 | −0.201798 | ||||||||
\(695\) | −4.47691e20 | −0.216817 | ||||||||
\(696\) | −4.77581e20 | −0.228812 | ||||||||
\(697\) | −1.78675e21 | −0.846870 | ||||||||
\(698\) | −7.90281e20 | −0.370566 | ||||||||
\(699\) | −7.91229e20 | −0.367049 | ||||||||
\(700\) | 8.61918e20 | 0.395577 | ||||||||
\(701\) | −8.95519e20 | −0.406621 | −0.203311 | − | 0.979114i | \(-0.565170\pi\) | ||||
−0.203311 | + | 0.979114i | \(0.565170\pi\) | |||||||
\(702\) | 1.39738e20 | 0.0627749 | ||||||||
\(703\) | −8.79920e20 | −0.391091 | ||||||||
\(704\) | −4.54985e20 | −0.200079 | ||||||||
\(705\) | 1.08795e21 | 0.473358 | ||||||||
\(706\) | −7.86261e20 | −0.338479 | ||||||||
\(707\) | −1.15169e20 | −0.0490557 | ||||||||
\(708\) | 4.84261e20 | 0.204094 | ||||||||
\(709\) | −3.99642e21 | −1.66657 | −0.833286 | − | 0.552842i | \(-0.813543\pi\) | ||||
−0.833286 | + | 0.552842i | \(0.813543\pi\) | |||||||
\(710\) | 2.97289e20 | 0.122671 | ||||||||
\(711\) | −1.62158e21 | −0.662088 | ||||||||
\(712\) | −8.25274e19 | −0.0333425 | ||||||||
\(713\) | −2.46998e21 | −0.987464 | ||||||||
\(714\) | 8.47511e20 | 0.335281 | ||||||||
\(715\) | −1.23958e21 | −0.485267 | ||||||||
\(716\) | 6.24683e20 | 0.241998 | ||||||||
\(717\) | 2.33664e21 | 0.895772 | ||||||||
\(718\) | −7.43812e20 | −0.282183 | ||||||||
\(719\) | −2.66669e20 | −0.100117 | −0.0500583 | − | 0.998746i | \(-0.515941\pi\) | ||||
−0.0500583 | + | 0.998746i | \(0.515941\pi\) | |||||||
\(720\) | −1.47407e20 | −0.0547676 | ||||||||
\(721\) | 6.29049e20 | 0.231297 | ||||||||
\(722\) | 1.17291e21 | 0.426812 | ||||||||
\(723\) | 2.19986e21 | 0.792242 | ||||||||
\(724\) | −8.42341e20 | −0.300226 | ||||||||
\(725\) | −1.80519e21 | −0.636779 | ||||||||
\(726\) | −1.82658e21 | −0.637698 | ||||||||
\(727\) | −1.69447e21 | −0.585499 | −0.292750 | − | 0.956189i | \(-0.594570\pi\) | ||||
−0.292750 | + | 0.956189i | \(0.594570\pi\) | |||||||
\(728\) | 6.64170e20 | 0.227140 | ||||||||
\(729\) | 1.09419e20 | 0.0370370 | ||||||||
\(730\) | −3.85970e20 | −0.129310 | ||||||||
\(731\) | −2.85684e21 | −0.947341 | ||||||||
\(732\) | −1.91796e20 | −0.0629514 | ||||||||
\(733\) | 3.16239e21 | 1.02739 | 0.513695 | − | 0.857973i | \(-0.328276\pi\) | ||||
0.513695 | + | 0.857973i | \(0.328276\pi\) | |||||||
\(734\) | −3.54749e19 | −0.0114078 | ||||||||
\(735\) | 1.12006e21 | 0.356522 | ||||||||
\(736\) | 2.86042e20 | 0.0901252 | ||||||||
\(737\) | 5.50714e21 | 1.71759 | ||||||||
\(738\) | −1.09641e21 | −0.338495 | ||||||||
\(739\) | 2.01381e21 | 0.615440 | 0.307720 | − | 0.951477i | \(-0.400434\pi\) | ||||
0.307720 | + | 0.951477i | \(0.400434\pi\) | |||||||
\(740\) | 3.35461e20 | 0.101486 | ||||||||
\(741\) | 1.12618e21 | 0.337265 | ||||||||
\(742\) | −3.78022e21 | −1.12070 | ||||||||
\(743\) | 2.11411e21 | 0.620458 | 0.310229 | − | 0.950662i | \(-0.399594\pi\) | ||||
0.310229 | + | 0.950662i | \(0.399594\pi\) | |||||||
\(744\) | 1.36079e21 | 0.395361 | ||||||||
\(745\) | 4.00372e20 | 0.115157 | ||||||||
\(746\) | 2.95038e21 | 0.840110 | ||||||||
\(747\) | 6.29844e20 | 0.177553 | ||||||||
\(748\) | −1.69104e21 | −0.471945 | ||||||||
\(749\) | 6.05970e21 | 1.67432 | ||||||||
\(750\) | −1.53800e21 | −0.420722 | ||||||||
\(751\) | 4.95087e21 | 1.34086 | 0.670428 | − | 0.741974i | \(-0.266110\pi\) | ||||
0.670428 | + | 0.741974i | \(0.266110\pi\) | |||||||
\(752\) | 1.16311e21 | 0.311879 | ||||||||
\(753\) | −3.82213e21 | −1.01471 | ||||||||
\(754\) | −1.39103e21 | −0.365638 | ||||||||
\(755\) | −7.87266e20 | −0.204889 | ||||||||
\(756\) | 5.20065e20 | 0.134012 | ||||||||
\(757\) | −4.85879e21 | −1.23968 | −0.619839 | − | 0.784729i | \(-0.712802\pi\) | ||||
−0.619839 | + | 0.784729i | \(0.712802\pi\) | |||||||
\(758\) | −1.72028e21 | −0.434590 | ||||||||
\(759\) | 1.88350e21 | 0.471143 | ||||||||
\(760\) | −1.18798e21 | −0.294244 | ||||||||
\(761\) | −3.69092e21 | −0.905211 | −0.452605 | − | 0.891711i | \(-0.649505\pi\) | ||||
−0.452605 | + | 0.891711i | \(0.649505\pi\) | |||||||
\(762\) | 3.44381e20 | 0.0836329 | ||||||||
\(763\) | −4.11491e19 | −0.00989523 | ||||||||
\(764\) | 1.10685e21 | 0.263566 | ||||||||
\(765\) | −5.47864e20 | −0.129185 | ||||||||
\(766\) | 3.38114e21 | 0.789491 | ||||||||
\(767\) | 1.41049e21 | 0.326140 | ||||||||
\(768\) | −1.57590e20 | −0.0360844 | ||||||||
\(769\) | −2.33815e21 | −0.530181 | −0.265091 | − | 0.964224i | \(-0.585402\pi\) | ||||
−0.265091 | + | 0.964224i | \(0.585402\pi\) | |||||||
\(770\) | −4.61337e21 | −1.03595 | ||||||||
\(771\) | 6.06376e20 | 0.134845 | ||||||||
\(772\) | −3.39534e20 | −0.0747746 | ||||||||
\(773\) | −5.20682e21 | −1.13560 | −0.567801 | − | 0.823166i | \(-0.692206\pi\) | ||||
−0.567801 | + | 0.823166i | \(0.692206\pi\) | |||||||
\(774\) | −1.75307e21 | −0.378653 | ||||||||
\(775\) | 5.14361e21 | 1.10028 | ||||||||
\(776\) | 2.36716e21 | 0.501493 | ||||||||
\(777\) | −1.18354e21 | −0.248328 | ||||||||
\(778\) | 5.05952e21 | 1.05139 | ||||||||
\(779\) | −8.83624e21 | −1.81860 | ||||||||
\(780\) | −4.29345e20 | −0.0875180 | ||||||||
\(781\) | 2.09279e21 | 0.422516 | ||||||||
\(782\) | 1.06313e21 | 0.212586 | ||||||||
\(783\) | −1.08922e21 | −0.215726 | ||||||||
\(784\) | 1.19744e21 | 0.234899 | ||||||||
\(785\) | −4.24608e21 | −0.825023 | ||||||||
\(786\) | −2.22503e21 | −0.428220 | ||||||||
\(787\) | −1.92196e21 | −0.366381 | −0.183191 | − | 0.983077i | \(-0.558643\pi\) | ||||
−0.183191 | + | 0.983077i | \(0.558643\pi\) | |||||||
\(788\) | 2.80566e20 | 0.0529772 | ||||||||
\(789\) | −3.79013e21 | −0.708887 | ||||||||
\(790\) | 4.98230e21 | 0.923052 | ||||||||
\(791\) | 2.15085e21 | 0.394718 | ||||||||
\(792\) | −1.03768e21 | −0.188637 | ||||||||
\(793\) | −5.58635e20 | −0.100596 | ||||||||
\(794\) | 3.62099e20 | 0.0645912 | ||||||||
\(795\) | 2.44368e21 | 0.431809 | ||||||||
\(796\) | −1.73250e21 | −0.303267 | ||||||||
\(797\) | −6.23880e20 | −0.108184 | −0.0540921 | − | 0.998536i | \(-0.517226\pi\) | ||||
−0.0540921 | + | 0.998536i | \(0.517226\pi\) | |||||||
\(798\) | 4.19132e21 | 0.719994 | ||||||||
\(799\) | 4.32290e21 | 0.735655 | ||||||||
\(800\) | −5.95669e20 | −0.100422 | ||||||||
\(801\) | −1.88220e20 | −0.0314356 | ||||||||
\(802\) | −5.93511e21 | −0.982022 | ||||||||
\(803\) | −2.71707e21 | −0.445384 | ||||||||
\(804\) | 1.90747e21 | 0.309768 | ||||||||
\(805\) | 2.90035e21 | 0.466640 | ||||||||
\(806\) | 3.96352e21 | 0.631783 | ||||||||
\(807\) | 1.11815e20 | 0.0176583 | ||||||||
\(808\) | 7.95929e19 | 0.0124534 | ||||||||
\(809\) | 5.72858e21 | 0.888042 | 0.444021 | − | 0.896016i | \(-0.353552\pi\) | ||||
0.444021 | + | 0.896016i | \(0.353552\pi\) | |||||||
\(810\) | −3.36190e20 | −0.0516354 | ||||||||
\(811\) | 4.80014e21 | 0.730462 | 0.365231 | − | 0.930917i | \(-0.380990\pi\) | ||||
0.365231 | + | 0.930917i | \(0.380990\pi\) | |||||||
\(812\) | −5.17702e21 | −0.780566 | ||||||||
\(813\) | −4.55892e20 | −0.0681056 | ||||||||
\(814\) | 2.36151e21 | 0.349548 | ||||||||
\(815\) | −8.52505e20 | −0.125030 | ||||||||
\(816\) | −5.85712e20 | −0.0851154 | ||||||||
\(817\) | −1.41284e22 | −2.03435 | ||||||||
\(818\) | −1.49878e21 | −0.213840 | ||||||||
\(819\) | 1.51477e21 | 0.214150 | ||||||||
\(820\) | 3.36873e21 | 0.471914 | ||||||||
\(821\) | 8.89775e21 | 1.23511 | 0.617556 | − | 0.786527i | \(-0.288123\pi\) | ||||
0.617556 | + | 0.786527i | \(0.288123\pi\) | |||||||
\(822\) | 4.98653e21 | 0.685898 | ||||||||
\(823\) | −1.39946e21 | −0.190749 | −0.0953744 | − | 0.995441i | \(-0.530405\pi\) | ||||
−0.0953744 | + | 0.995441i | \(0.530405\pi\) | |||||||
\(824\) | −4.34733e20 | −0.0587177 | ||||||||
\(825\) | −3.92231e21 | −0.524973 | ||||||||
\(826\) | 5.24943e21 | 0.696244 | ||||||||
\(827\) | 6.61343e21 | 0.869232 | 0.434616 | − | 0.900616i | \(-0.356884\pi\) | ||||
0.434616 | + | 0.900616i | \(0.356884\pi\) | |||||||
\(828\) | 6.52375e20 | 0.0849709 | ||||||||
\(829\) | 4.14735e21 | 0.535318 | 0.267659 | − | 0.963514i | \(-0.413750\pi\) | ||||
0.267659 | + | 0.963514i | \(0.413750\pi\) | |||||||
\(830\) | −1.93520e21 | −0.247537 | ||||||||
\(831\) | −7.21105e21 | −0.914093 | ||||||||
\(832\) | −4.59006e20 | −0.0576625 | ||||||||
\(833\) | 4.45049e21 | 0.554078 | ||||||||
\(834\) | −1.09158e21 | −0.134683 | ||||||||
\(835\) | 1.69190e21 | 0.206883 | ||||||||
\(836\) | −8.36292e21 | −1.01347 | ||||||||
\(837\) | 3.10355e21 | 0.372750 | ||||||||
\(838\) | −5.37730e21 | −0.640080 | ||||||||
\(839\) | 9.57811e21 | 1.12997 | 0.564983 | − | 0.825103i | \(-0.308883\pi\) | ||||
0.564983 | + | 0.825103i | \(0.308883\pi\) | |||||||
\(840\) | −1.59790e21 | −0.186834 | ||||||||
\(841\) | 2.21350e21 | 0.256513 | ||||||||
\(842\) | −2.04440e21 | −0.234814 | ||||||||
\(843\) | 8.71142e21 | 0.991705 | ||||||||
\(844\) | −5.12972e21 | −0.578795 | ||||||||
\(845\) | 4.62612e21 | 0.517358 | ||||||||
\(846\) | 2.65269e21 | 0.294042 | ||||||||
\(847\) | −1.98003e22 | −2.17544 | ||||||||
\(848\) | 2.61250e21 | 0.284503 | ||||||||
\(849\) | 4.79065e21 | 0.517114 | ||||||||
\(850\) | −2.21391e21 | −0.236875 | ||||||||
\(851\) | −1.48465e21 | −0.157453 | ||||||||
\(852\) | 7.24865e20 | 0.0762009 | ||||||||
\(853\) | −8.15361e21 | −0.849634 | −0.424817 | − | 0.905279i | \(-0.639662\pi\) | ||||
−0.424817 | + | 0.905279i | \(0.639662\pi\) | |||||||
\(854\) | −2.07908e21 | −0.214752 | ||||||||
\(855\) | −2.70943e21 | −0.277416 | ||||||||
\(856\) | −4.18784e21 | −0.425047 | ||||||||
\(857\) | −1.53552e22 | −1.54490 | −0.772449 | − | 0.635076i | \(-0.780969\pi\) | ||||
−0.772449 | + | 0.635076i | \(0.780969\pi\) | |||||||
\(858\) | −3.02242e21 | −0.301439 | ||||||||
\(859\) | −4.87617e21 | −0.482092 | −0.241046 | − | 0.970514i | \(-0.577490\pi\) | ||||
−0.241046 | + | 0.970514i | \(0.577490\pi\) | |||||||
\(860\) | 5.38630e21 | 0.527901 | ||||||||
\(861\) | −1.18852e22 | −1.15474 | ||||||||
\(862\) | −1.24975e22 | −1.20370 | ||||||||
\(863\) | −4.76667e21 | −0.455128 | −0.227564 | − | 0.973763i | \(-0.573076\pi\) | ||||
−0.227564 | + | 0.973763i | \(0.573076\pi\) | |||||||
\(864\) | −3.59415e20 | −0.0340207 | ||||||||
\(865\) | −3.90399e21 | −0.366343 | ||||||||
\(866\) | −8.85063e21 | −0.823360 | ||||||||
\(867\) | 4.08321e21 | 0.376581 | ||||||||
\(868\) | 1.47511e22 | 1.34873 | ||||||||
\(869\) | 3.50734e22 | 3.17928 | ||||||||
\(870\) | 3.34662e21 | 0.300755 | ||||||||
\(871\) | 5.55580e21 | 0.495006 | ||||||||
\(872\) | 2.84380e19 | 0.00251203 | ||||||||
\(873\) | 5.39878e21 | 0.472812 | ||||||||
\(874\) | 5.25764e21 | 0.456515 | ||||||||
\(875\) | −1.66720e22 | −1.43525 | ||||||||
\(876\) | −9.41093e20 | −0.0803252 | ||||||||
\(877\) | 1.57944e22 | 1.33661 | 0.668306 | − | 0.743887i | \(-0.267020\pi\) | ||||
0.668306 | + | 0.743887i | \(0.267020\pi\) | |||||||
\(878\) | 7.02707e21 | 0.589611 | ||||||||
\(879\) | 1.15295e22 | 0.959165 | ||||||||
\(880\) | 3.18829e21 | 0.262989 | ||||||||
\(881\) | −1.12789e22 | −0.922461 | −0.461230 | − | 0.887280i | \(-0.652592\pi\) | ||||
−0.461230 | + | 0.887280i | \(0.652592\pi\) | |||||||
\(882\) | 2.73099e21 | 0.221465 | ||||||||
\(883\) | 4.48307e21 | 0.360471 | 0.180236 | − | 0.983623i | \(-0.442314\pi\) | ||||
0.180236 | + | 0.983623i | \(0.442314\pi\) | |||||||
\(884\) | −1.70598e21 | −0.136013 | ||||||||
\(885\) | −3.39343e21 | −0.268265 | ||||||||
\(886\) | 4.87045e21 | 0.381783 | ||||||||
\(887\) | −8.56246e21 | −0.665536 | −0.332768 | − | 0.943009i | \(-0.607983\pi\) | ||||
−0.332768 | + | 0.943009i | \(0.607983\pi\) | |||||||
\(888\) | 8.17940e20 | 0.0630411 | ||||||||
\(889\) | 3.73312e21 | 0.285304 | ||||||||
\(890\) | 5.78307e20 | 0.0438261 | ||||||||
\(891\) | −2.36664e21 | −0.177848 | ||||||||
\(892\) | 5.48893e21 | 0.409026 | ||||||||
\(893\) | 2.13786e22 | 1.57977 | ||||||||
\(894\) | 9.76210e20 | 0.0715339 | ||||||||
\(895\) | −4.37743e21 | −0.318087 | ||||||||
\(896\) | −1.70829e21 | −0.123098 | ||||||||
\(897\) | 1.90015e21 | 0.135783 | ||||||||
\(898\) | 1.43352e20 | 0.0101585 | ||||||||
\(899\) | −3.08945e22 | −2.17112 | ||||||||
\(900\) | −1.35854e21 | −0.0946790 | ||||||||
\(901\) | 9.70983e21 | 0.671082 | ||||||||
\(902\) | 2.37145e22 | 1.62542 | ||||||||
\(903\) | −1.90034e22 | −1.29173 | ||||||||
\(904\) | −1.48645e21 | −0.100204 | ||||||||
\(905\) | 5.90266e21 | 0.394624 | ||||||||
\(906\) | −1.91956e21 | −0.127274 | ||||||||
\(907\) | 7.34638e21 | 0.483079 | 0.241540 | − | 0.970391i | \(-0.422348\pi\) | ||||
0.241540 | + | 0.970391i | \(0.422348\pi\) | |||||||
\(908\) | 7.66051e21 | 0.499590 | ||||||||
\(909\) | 1.81527e20 | 0.0117412 | ||||||||
\(910\) | −4.65414e21 | −0.298558 | ||||||||
\(911\) | −1.18999e22 | −0.757106 | −0.378553 | − | 0.925580i | \(-0.623578\pi\) | ||||
−0.378553 | + | 0.925580i | \(0.623578\pi\) | |||||||
\(912\) | −2.89660e21 | −0.182780 | ||||||||
\(913\) | −1.36230e22 | −0.852594 | ||||||||
\(914\) | −1.24254e22 | −0.771283 | ||||||||
\(915\) | 1.34400e21 | 0.0827447 | ||||||||
\(916\) | 5.91767e21 | 0.361355 | ||||||||
\(917\) | −2.41195e22 | −1.46083 | ||||||||
\(918\) | −1.33583e21 | −0.0802475 | ||||||||
\(919\) | 1.92629e22 | 1.14777 | 0.573886 | − | 0.818935i | \(-0.305435\pi\) | ||||
0.573886 | + | 0.818935i | \(0.305435\pi\) | |||||||
\(920\) | −2.00442e21 | −0.118463 | ||||||||
\(921\) | −1.04334e22 | −0.611618 | ||||||||
\(922\) | −1.25205e22 | −0.728015 | ||||||||
\(923\) | 2.11129e21 | 0.121768 | ||||||||
\(924\) | −1.12486e22 | −0.643514 | ||||||||
\(925\) | 3.09170e21 | 0.175442 | ||||||||
\(926\) | −2.77964e21 | −0.156461 | ||||||||
\(927\) | −9.91495e20 | −0.0553596 | ||||||||
\(928\) | 3.57782e21 | 0.198157 | ||||||||
\(929\) | 8.78109e21 | 0.482426 | 0.241213 | − | 0.970472i | \(-0.422455\pi\) | ||||
0.241213 | + | 0.970472i | \(0.422455\pi\) | |||||||
\(930\) | −9.53567e21 | −0.519672 | ||||||||
\(931\) | 2.20096e22 | 1.18985 | ||||||||
\(932\) | 5.92753e21 | 0.317873 | ||||||||
\(933\) | 1.41426e22 | 0.752343 | ||||||||
\(934\) | −2.54007e22 | −1.34043 | ||||||||
\(935\) | 1.18499e22 | 0.620334 | ||||||||
\(936\) | −1.04685e21 | −0.0543647 | ||||||||
\(937\) | −2.35424e22 | −1.21284 | −0.606421 | − | 0.795144i | \(-0.707395\pi\) | ||||
−0.606421 | + | 0.795144i | \(0.707395\pi\) | |||||||
\(938\) | 2.06771e22 | 1.05674 | ||||||||
\(939\) | 1.31248e22 | 0.665429 | ||||||||
\(940\) | −8.15040e21 | −0.409940 | ||||||||
\(941\) | −2.31660e22 | −1.15592 | −0.577961 | − | 0.816064i | \(-0.696152\pi\) | ||||
−0.577961 | + | 0.816064i | \(0.696152\pi\) | |||||||
\(942\) | −1.03530e22 | −0.512490 | ||||||||
\(943\) | −1.49090e22 | −0.732166 | ||||||||
\(944\) | −3.62786e21 | −0.176751 | ||||||||
\(945\) | −3.64433e21 | −0.176148 | ||||||||
\(946\) | 3.79174e22 | 1.81826 | ||||||||
\(947\) | 2.02578e22 | 0.963755 | 0.481877 | − | 0.876239i | \(-0.339955\pi\) | ||||
0.481877 | + | 0.876239i | \(0.339955\pi\) | |||||||
\(948\) | 1.21481e22 | 0.573385 | ||||||||
\(949\) | −2.74108e21 | −0.128359 | ||||||||
\(950\) | −1.09488e22 | −0.508673 | ||||||||
\(951\) | 2.08627e21 | 0.0961651 | ||||||||
\(952\) | −6.34916e21 | −0.290362 | ||||||||
\(953\) | −1.66351e22 | −0.754794 | −0.377397 | − | 0.926052i | \(-0.623181\pi\) | ||||
−0.377397 | + | 0.926052i | \(0.623181\pi\) | |||||||
\(954\) | 5.95832e21 | 0.268232 | ||||||||
\(955\) | −7.75620e21 | −0.346436 | ||||||||
\(956\) | −1.75050e22 | −0.775762 | ||||||||
\(957\) | 2.35589e22 | 1.03589 | ||||||||
\(958\) | −4.84686e21 | −0.211456 | ||||||||
\(959\) | 5.40544e22 | 2.33987 | ||||||||
\(960\) | 1.10430e21 | 0.0474301 | ||||||||
\(961\) | 6.45637e22 | 2.75146 | ||||||||
\(962\) | 2.38238e21 | 0.100739 | ||||||||
\(963\) | −9.55119e21 | −0.400738 | ||||||||
\(964\) | −1.64804e22 | −0.686102 | ||||||||
\(965\) | 2.37927e21 | 0.0982853 | ||||||||
\(966\) | 7.07180e21 | 0.289869 | ||||||||
\(967\) | −2.10794e22 | −0.857355 | −0.428677 | − | 0.903458i | \(-0.641020\pi\) | ||||
−0.428677 | + | 0.903458i | \(0.641020\pi\) | |||||||
\(968\) | 1.36839e22 | 0.552263 | ||||||||
\(969\) | −1.07658e22 | −0.431138 | ||||||||
\(970\) | −1.65878e22 | −0.659174 | ||||||||
\(971\) | −3.09261e22 | −1.21950 | −0.609749 | − | 0.792594i | \(-0.708730\pi\) | ||||
−0.609749 | + | 0.792594i | \(0.708730\pi\) | |||||||
\(972\) | −8.19717e20 | −0.0320750 | ||||||||
\(973\) | −1.18329e22 | −0.459456 | ||||||||
\(974\) | 4.98259e21 | 0.191983 | ||||||||
\(975\) | −3.95696e21 | −0.151296 | ||||||||
\(976\) | 1.43684e21 | 0.0545175 | ||||||||
\(977\) | 7.85725e21 | 0.295843 | 0.147922 | − | 0.988999i | \(-0.452742\pi\) | ||||
0.147922 | + | 0.988999i | \(0.452742\pi\) | |||||||
\(978\) | −2.07862e21 | −0.0776666 | ||||||||
\(979\) | 4.07105e21 | 0.150951 | ||||||||
\(980\) | −8.39097e21 | −0.308757 | ||||||||
\(981\) | 6.48584e19 | 0.00236837 | ||||||||
\(982\) | 1.79860e22 | 0.651778 | ||||||||
\(983\) | 1.27981e22 | 0.460251 | 0.230125 | − | 0.973161i | \(-0.426086\pi\) | ||||
0.230125 | + | 0.973161i | \(0.426086\pi\) | |||||||
\(984\) | 8.21383e21 | 0.293145 | ||||||||
\(985\) | −1.96605e21 | −0.0696343 | ||||||||
\(986\) | 1.32976e22 | 0.467409 | ||||||||
\(987\) | 2.87554e22 | 1.00309 | ||||||||
\(988\) | −8.43682e21 | −0.292080 | ||||||||
\(989\) | −2.38381e22 | −0.819028 | ||||||||
\(990\) | 7.27151e21 | 0.247948 | ||||||||
\(991\) | −5.39385e22 | −1.82535 | −0.912675 | − | 0.408686i | \(-0.865987\pi\) | ||||
−0.912675 | + | 0.408686i | \(0.865987\pi\) | |||||||
\(992\) | −1.01944e22 | −0.342393 | ||||||||
\(993\) | 1.15708e22 | 0.385694 | ||||||||
\(994\) | 7.85760e21 | 0.259951 | ||||||||
\(995\) | 1.21404e22 | 0.398620 | ||||||||
\(996\) | −4.71850e21 | −0.153766 | ||||||||
\(997\) | −1.99678e22 | −0.645828 | −0.322914 | − | 0.946428i | \(-0.604663\pi\) | ||||
−0.322914 | + | 0.946428i | \(0.604663\pi\) | |||||||
\(998\) | −1.96740e22 | −0.631557 | ||||||||
\(999\) | 1.86547e21 | 0.0594358 |
(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 | 6.16.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.16.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 48.16.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 150.16.c.a.49.2 | 2 | |||
5.3 | odd | 4 | 150.16.c.a.49.1 | 2 | |||
5.4 | even | 2 | 150.16.a.f.1.1 | 1 | |||
12.11 | even | 2 | 144.16.a.j.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.16.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.16.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
48.16.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
144.16.a.j.1.1 | 1 | 12.11 | even | 2 | |||
150.16.a.f.1.1 | 1 | 5.4 | even | 2 | |||
150.16.c.a.49.1 | 2 | 5.3 | odd | 4 | |||
150.16.c.a.49.2 | 2 | 5.2 | odd | 4 |