Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −164.231 | −1.81452 | −0.907259 | − | 0.420572i | \(-0.861829\pi\) | ||||
−0.907259 | + | 0.420572i | \(0.861829\pi\) | |||||||
\(3\) | −1747.83 | −1.38424 | −0.692118 | − | 0.721784i | \(-0.743322\pi\) | ||||
−0.692118 | + | 0.721784i | \(0.743322\pi\) | |||||||
\(4\) | 18780.0 | 2.29248 | ||||||||
\(5\) | −30963.6 | −0.886231 | −0.443116 | − | 0.896465i | \(-0.646127\pi\) | ||||
−0.443116 | + | 0.896465i | \(0.646127\pi\) | |||||||
\(6\) | 287048. | 2.51172 | ||||||||
\(7\) | 120554. | 0.387299 | 0.193649 | − | 0.981071i | \(-0.437968\pi\) | ||||
0.193649 | + | 0.981071i | \(0.437968\pi\) | |||||||
\(8\) | −1.73888e6 | −2.34522 | ||||||||
\(9\) | 1.46057e6 | 0.916109 | ||||||||
\(10\) | 5.08520e6 | 1.60808 | ||||||||
\(11\) | −1.02128e7 | −1.73817 | −0.869084 | − | 0.494665i | \(-0.835291\pi\) | ||||
−0.869084 | + | 0.494665i | \(0.835291\pi\) | |||||||
\(12\) | −3.28241e7 | −3.17333 | ||||||||
\(13\) | 5.41676e6 | 0.311249 | 0.155624 | − | 0.987816i | \(-0.450261\pi\) | ||||
0.155624 | + | 0.987816i | \(0.450261\pi\) | |||||||
\(14\) | −1.97988e7 | −0.702761 | ||||||||
\(15\) | 5.41191e7 | 1.22675 | ||||||||
\(16\) | 1.31733e8 | 1.96298 | ||||||||
\(17\) | 1.78741e8 | 1.79600 | 0.897999 | − | 0.439997i | \(-0.145021\pi\) | ||||
0.897999 | + | 0.439997i | \(0.145021\pi\) | |||||||
\(18\) | −2.39872e8 | −1.66230 | ||||||||
\(19\) | −2.67219e8 | −1.30307 | −0.651536 | − | 0.758617i | \(-0.725875\pi\) | ||||
−0.651536 | + | 0.758617i | \(0.725875\pi\) | |||||||
\(20\) | −5.81496e8 | −2.03166 | ||||||||
\(21\) | −2.10708e8 | −0.536113 | ||||||||
\(22\) | 1.67726e9 | 3.15394 | ||||||||
\(23\) | 5.02187e8 | 0.707350 | 0.353675 | − | 0.935368i | \(-0.384932\pi\) | ||||
0.353675 | + | 0.935368i | \(0.384932\pi\) | |||||||
\(24\) | 3.03926e9 | 3.24634 | ||||||||
\(25\) | −2.61956e8 | −0.214594 | ||||||||
\(26\) | −8.89602e8 | −0.564766 | ||||||||
\(27\) | 2.33771e8 | 0.116125 | ||||||||
\(28\) | 2.26401e9 | 0.887874 | ||||||||
\(29\) | 3.45170e9 | 1.07757 | 0.538785 | − | 0.842443i | \(-0.318883\pi\) | ||||
0.538785 | + | 0.842443i | \(0.318883\pi\) | |||||||
\(30\) | −8.88805e9 | −2.22597 | ||||||||
\(31\) | −8.65904e9 | −1.75234 | −0.876171 | − | 0.482001i | \(-0.839910\pi\) | ||||
−0.876171 | + | 0.482001i | \(0.839910\pi\) | |||||||
\(32\) | −7.38982e9 | −1.21663 | ||||||||
\(33\) | 1.78502e10 | 2.40603 | ||||||||
\(34\) | −2.93549e10 | −3.25887 | ||||||||
\(35\) | −3.73280e9 | −0.343236 | ||||||||
\(36\) | 2.74295e10 | 2.10016 | ||||||||
\(37\) | 7.60282e9 | 0.487151 | 0.243576 | − | 0.969882i | \(-0.421680\pi\) | ||||
0.243576 | + | 0.969882i | \(0.421680\pi\) | |||||||
\(38\) | 4.38857e10 | 2.36445 | ||||||||
\(39\) | −9.46755e9 | −0.430842 | ||||||||
\(40\) | 5.38420e10 | 2.07841 | ||||||||
\(41\) | −4.48741e10 | −1.47537 | −0.737685 | − | 0.675145i | \(-0.764081\pi\) | ||||
−0.737685 | + | 0.675145i | \(0.764081\pi\) | |||||||
\(42\) | 3.46049e10 | 0.972787 | ||||||||
\(43\) | −7.21879e9 | −0.174148 | −0.0870741 | − | 0.996202i | \(-0.527752\pi\) | ||||
−0.0870741 | + | 0.996202i | \(0.527752\pi\) | |||||||
\(44\) | −1.91796e11 | −3.98471 | ||||||||
\(45\) | −4.52247e10 | −0.811884 | ||||||||
\(46\) | −8.24749e10 | −1.28350 | ||||||||
\(47\) | −7.77885e10 | −1.05264 | −0.526319 | − | 0.850287i | \(-0.676428\pi\) | ||||
−0.526319 | + | 0.850287i | \(0.676428\pi\) | |||||||
\(48\) | −2.30247e11 | −2.71722 | ||||||||
\(49\) | −8.23556e10 | −0.850000 | ||||||||
\(50\) | 4.30214e10 | 0.389386 | ||||||||
\(51\) | −3.12408e11 | −2.48609 | ||||||||
\(52\) | 1.01727e11 | 0.713531 | ||||||||
\(53\) | 8.12388e10 | 0.503466 | 0.251733 | − | 0.967797i | \(-0.419000\pi\) | ||||
0.251733 | + | 0.967797i | \(0.419000\pi\) | |||||||
\(54\) | −3.83925e10 | −0.210711 | ||||||||
\(55\) | 3.16225e11 | 1.54042 | ||||||||
\(56\) | −2.09630e11 | −0.908302 | ||||||||
\(57\) | 4.67052e11 | 1.80376 | ||||||||
\(58\) | −5.66877e11 | −1.95527 | ||||||||
\(59\) | −1.94075e11 | −0.599005 | −0.299503 | − | 0.954095i | \(-0.596821\pi\) | ||||
−0.299503 | + | 0.954095i | \(0.596821\pi\) | |||||||
\(60\) | 1.01635e12 | 2.81230 | ||||||||
\(61\) | 2.64439e11 | 0.657175 | 0.328588 | − | 0.944474i | \(-0.393427\pi\) | ||||
0.328588 | + | 0.944474i | \(0.393427\pi\) | |||||||
\(62\) | 1.42209e12 | 3.17966 | ||||||||
\(63\) | 1.76079e11 | 0.354808 | ||||||||
\(64\) | 1.34484e11 | 0.244625 | ||||||||
\(65\) | −1.67722e11 | −0.275838 | ||||||||
\(66\) | −2.93156e12 | −4.36579 | ||||||||
\(67\) | −1.30061e12 | −1.75655 | −0.878275 | − | 0.478157i | \(-0.841305\pi\) | ||||
−0.878275 | + | 0.478157i | \(0.841305\pi\) | |||||||
\(68\) | 3.35675e12 | 4.11729 | ||||||||
\(69\) | −8.77736e11 | −0.979140 | ||||||||
\(70\) | 6.13044e11 | 0.622808 | ||||||||
\(71\) | 1.46842e12 | 1.36041 | 0.680206 | − | 0.733021i | \(-0.261890\pi\) | ||||
0.680206 | + | 0.733021i | \(0.261890\pi\) | |||||||
\(72\) | −2.53976e12 | −2.14848 | ||||||||
\(73\) | −1.62887e11 | −0.125976 | −0.0629881 | − | 0.998014i | \(-0.520063\pi\) | ||||
−0.0629881 | + | 0.998014i | \(0.520063\pi\) | |||||||
\(74\) | −1.24862e12 | −0.883945 | ||||||||
\(75\) | 4.57854e11 | 0.297049 | ||||||||
\(76\) | −5.01836e12 | −2.98727 | ||||||||
\(77\) | −1.23120e12 | −0.673190 | ||||||||
\(78\) | 1.55487e12 | 0.781770 | ||||||||
\(79\) | 9.21802e11 | 0.426640 | 0.213320 | − | 0.976982i | \(-0.431572\pi\) | ||||
0.213320 | + | 0.976982i | \(0.431572\pi\) | |||||||
\(80\) | −4.07894e12 | −1.73965 | ||||||||
\(81\) | −2.73722e12 | −1.07685 | ||||||||
\(82\) | 7.36974e12 | 2.67708 | ||||||||
\(83\) | −5.40648e12 | −1.81513 | −0.907564 | − | 0.419914i | \(-0.862060\pi\) | ||||
−0.907564 | + | 0.419914i | \(0.862060\pi\) | |||||||
\(84\) | −3.95710e12 | −1.22903 | ||||||||
\(85\) | −5.53447e12 | −1.59167 | ||||||||
\(86\) | 1.18555e12 | 0.315995 | ||||||||
\(87\) | −6.03297e12 | −1.49161 | ||||||||
\(88\) | 1.77588e13 | 4.07639 | ||||||||
\(89\) | 3.99862e12 | 0.852855 | 0.426428 | − | 0.904522i | \(-0.359772\pi\) | ||||
0.426428 | + | 0.904522i | \(0.359772\pi\) | |||||||
\(90\) | 7.42731e12 | 1.47318 | ||||||||
\(91\) | 6.53014e11 | 0.120546 | ||||||||
\(92\) | 9.43106e12 | 1.62158 | ||||||||
\(93\) | 1.51345e13 | 2.42565 | ||||||||
\(94\) | 1.27753e13 | 1.91003 | ||||||||
\(95\) | 8.27407e12 | 1.15482 | ||||||||
\(96\) | 1.29161e13 | 1.68411 | ||||||||
\(97\) | −8.17971e11 | −0.0997061 | −0.0498530 | − | 0.998757i | \(-0.515875\pi\) | ||||
−0.0498530 | + | 0.998757i | \(0.515875\pi\) | |||||||
\(98\) | 1.35254e13 | 1.54234 | ||||||||
\(99\) | −1.49165e13 | −1.59235 | ||||||||
\(100\) | −4.91953e12 | −0.491953 | ||||||||
\(101\) | 9.96328e12 | 0.933928 | 0.466964 | − | 0.884276i | \(-0.345348\pi\) | ||||
0.466964 | + | 0.884276i | \(0.345348\pi\) | |||||||
\(102\) | 5.13072e13 | 4.51105 | ||||||||
\(103\) | 3.83298e12 | 0.316297 | 0.158148 | − | 0.987415i | \(-0.449448\pi\) | ||||
0.158148 | + | 0.987415i | \(0.449448\pi\) | |||||||
\(104\) | −9.41908e12 | −0.729948 | ||||||||
\(105\) | 6.52429e12 | 0.475120 | ||||||||
\(106\) | −1.33420e13 | −0.913548 | ||||||||
\(107\) | −1.46504e13 | −0.943743 | −0.471872 | − | 0.881667i | \(-0.656421\pi\) | ||||
−0.471872 | + | 0.881667i | \(0.656421\pi\) | |||||||
\(108\) | 4.39021e12 | 0.266214 | ||||||||
\(109\) | 2.24078e13 | 1.27975 | 0.639877 | − | 0.768477i | \(-0.278985\pi\) | ||||
0.639877 | + | 0.768477i | \(0.278985\pi\) | |||||||
\(110\) | −5.19341e13 | −2.79512 | ||||||||
\(111\) | −1.32884e13 | −0.674332 | ||||||||
\(112\) | 1.58810e13 | 0.760258 | ||||||||
\(113\) | 3.28909e12 | 0.148616 | 0.0743080 | − | 0.997235i | \(-0.476325\pi\) | ||||
0.0743080 | + | 0.997235i | \(0.476325\pi\) | |||||||
\(114\) | −7.67047e13 | −3.27296 | ||||||||
\(115\) | −1.55495e13 | −0.626876 | ||||||||
\(116\) | 6.48228e13 | 2.47031 | ||||||||
\(117\) | 7.91157e12 | 0.285138 | ||||||||
\(118\) | 3.18732e13 | 1.08691 | ||||||||
\(119\) | 2.15480e13 | 0.695588 | ||||||||
\(120\) | −9.41065e13 | −2.87701 | ||||||||
\(121\) | 6.97783e13 | 2.02123 | ||||||||
\(122\) | −4.34292e13 | −1.19246 | ||||||||
\(123\) | 7.84321e13 | 2.04226 | ||||||||
\(124\) | −1.62617e14 | −4.01720 | ||||||||
\(125\) | 4.59085e13 | 1.07641 | ||||||||
\(126\) | −2.89177e13 | −0.643805 | ||||||||
\(127\) | 1.31246e13 | 0.277564 | 0.138782 | − | 0.990323i | \(-0.455681\pi\) | ||||
0.138782 | + | 0.990323i | \(0.455681\pi\) | |||||||
\(128\) | 3.84509e13 | 0.772755 | ||||||||
\(129\) | 1.26172e13 | 0.241062 | ||||||||
\(130\) | 2.75453e13 | 0.500514 | ||||||||
\(131\) | 7.29776e13 | 1.26161 | 0.630806 | − | 0.775940i | \(-0.282724\pi\) | ||||
0.630806 | + | 0.775940i | \(0.282724\pi\) | |||||||
\(132\) | 3.35226e14 | 5.51578 | ||||||||
\(133\) | −3.22144e13 | −0.504678 | ||||||||
\(134\) | 2.13601e14 | 3.18729 | ||||||||
\(135\) | −7.23840e12 | −0.102914 | ||||||||
\(136\) | −3.10809e14 | −4.21202 | ||||||||
\(137\) | 9.95397e13 | 1.28621 | 0.643106 | − | 0.765777i | \(-0.277645\pi\) | ||||
0.643106 | + | 0.765777i | \(0.277645\pi\) | |||||||
\(138\) | 1.44152e14 | 1.77667 | ||||||||
\(139\) | −1.04292e14 | −1.22646 | −0.613232 | − | 0.789903i | \(-0.710131\pi\) | ||||
−0.613232 | + | 0.789903i | \(0.710131\pi\) | |||||||
\(140\) | −7.01020e13 | −0.786861 | ||||||||
\(141\) | 1.35961e14 | 1.45710 | ||||||||
\(142\) | −2.41160e14 | −2.46849 | ||||||||
\(143\) | −5.53202e13 | −0.541002 | ||||||||
\(144\) | 1.92406e14 | 1.79830 | ||||||||
\(145\) | −1.06877e14 | −0.954977 | ||||||||
\(146\) | 2.67512e13 | 0.228586 | ||||||||
\(147\) | 1.43943e14 | 1.17660 | ||||||||
\(148\) | 1.42781e14 | 1.11678 | ||||||||
\(149\) | 1.55537e14 | 1.16445 | 0.582226 | − | 0.813027i | \(-0.302182\pi\) | ||||
0.582226 | + | 0.813027i | \(0.302182\pi\) | |||||||
\(150\) | −7.51940e13 | −0.539002 | ||||||||
\(151\) | −4.80644e13 | −0.329969 | −0.164985 | − | 0.986296i | \(-0.552757\pi\) | ||||
−0.164985 | + | 0.986296i | \(0.552757\pi\) | |||||||
\(152\) | 4.64661e14 | 3.05600 | ||||||||
\(153\) | 2.61064e14 | 1.64533 | ||||||||
\(154\) | 2.02201e14 | 1.22152 | ||||||||
\(155\) | 2.68115e14 | 1.55298 | ||||||||
\(156\) | −1.77800e14 | −0.987695 | ||||||||
\(157\) | 2.18884e14 | 1.16645 | 0.583226 | − | 0.812310i | \(-0.301790\pi\) | ||||
0.583226 | + | 0.812310i | \(0.301790\pi\) | |||||||
\(158\) | −1.51389e14 | −0.774146 | ||||||||
\(159\) | −1.41991e14 | −0.696916 | ||||||||
\(160\) | 2.28816e14 | 1.07822 | ||||||||
\(161\) | 6.05409e13 | 0.273956 | ||||||||
\(162\) | 4.49537e14 | 1.95397 | ||||||||
\(163\) | 1.30251e13 | 0.0543954 | 0.0271977 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271977 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(164\) | −8.42735e14 | −3.38225 | ||||||||
\(165\) | −5.52706e14 | −2.13230 | ||||||||
\(166\) | 8.87914e14 | 3.29358 | ||||||||
\(167\) | 3.04290e14 | 1.08550 | 0.542751 | − | 0.839893i | \(-0.317383\pi\) | ||||
0.542751 | + | 0.839893i | \(0.317383\pi\) | |||||||
\(168\) | 3.66396e14 | 1.25730 | ||||||||
\(169\) | −2.73534e14 | −0.903124 | ||||||||
\(170\) | 9.08934e14 | 2.88811 | ||||||||
\(171\) | −3.90293e14 | −1.19376 | ||||||||
\(172\) | −1.35569e14 | −0.399231 | ||||||||
\(173\) | −4.56273e14 | −1.29397 | −0.646987 | − | 0.762501i | \(-0.723971\pi\) | ||||
−0.646987 | + | 0.762501i | \(0.723971\pi\) | |||||||
\(174\) | 9.90803e14 | 2.70656 | ||||||||
\(175\) | −3.15800e13 | −0.0831122 | ||||||||
\(176\) | −1.34536e15 | −3.41198 | ||||||||
\(177\) | 3.39209e14 | 0.829165 | ||||||||
\(178\) | −6.56699e14 | −1.54752 | ||||||||
\(179\) | 6.65645e14 | 1.51251 | 0.756255 | − | 0.654277i | \(-0.227027\pi\) | ||||
0.756255 | + | 0.654277i | \(0.227027\pi\) | |||||||
\(180\) | −8.49318e14 | −1.86123 | ||||||||
\(181\) | 1.83594e13 | 0.0388103 | 0.0194052 | − | 0.999812i | \(-0.493823\pi\) | ||||
0.0194052 | + | 0.999812i | \(0.493823\pi\) | |||||||
\(182\) | −1.07245e14 | −0.218733 | ||||||||
\(183\) | −4.62193e14 | −0.909685 | ||||||||
\(184\) | −8.73242e14 | −1.65890 | ||||||||
\(185\) | −2.35411e14 | −0.431729 | ||||||||
\(186\) | −2.48556e15 | −4.40139 | ||||||||
\(187\) | −1.82544e15 | −3.12175 | ||||||||
\(188\) | −1.46087e15 | −2.41315 | ||||||||
\(189\) | 2.81821e13 | 0.0449751 | ||||||||
\(190\) | −1.35886e15 | −2.09545 | ||||||||
\(191\) | −7.49221e14 | −1.11659 | −0.558294 | − | 0.829643i | \(-0.688544\pi\) | ||||
−0.558294 | + | 0.829643i | \(0.688544\pi\) | |||||||
\(192\) | −2.35054e14 | −0.338618 | ||||||||
\(193\) | 1.22802e15 | 1.71034 | 0.855171 | − | 0.518346i | \(-0.173452\pi\) | ||||
0.855171 | + | 0.518346i | \(0.173452\pi\) | |||||||
\(194\) | 1.34337e14 | 0.180919 | ||||||||
\(195\) | 2.93150e14 | 0.381825 | ||||||||
\(196\) | −1.54664e15 | −1.94861 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | 2.44976e15 | 2.88935 | ||||||||
\(199\) | −1.04554e15 | −1.19342 | −0.596712 | − | 0.802456i | \(-0.703526\pi\) | ||||
−0.596712 | + | 0.802456i | \(0.703526\pi\) | |||||||
\(200\) | 4.55510e14 | 0.503272 | ||||||||
\(201\) | 2.27324e15 | 2.43148 | ||||||||
\(202\) | −1.63628e15 | −1.69463 | ||||||||
\(203\) | 4.16118e14 | 0.417342 | ||||||||
\(204\) | −5.86702e15 | −5.69930 | ||||||||
\(205\) | 1.38947e15 | 1.30752 | ||||||||
\(206\) | −6.29496e14 | −0.573926 | ||||||||
\(207\) | 7.33481e14 | 0.648010 | ||||||||
\(208\) | 7.13566e14 | 0.610974 | ||||||||
\(209\) | 2.72905e15 | 2.26496 | ||||||||
\(210\) | −1.07149e15 | −0.862114 | ||||||||
\(211\) | −1.41523e15 | −1.10406 | −0.552028 | − | 0.833825i | \(-0.686146\pi\) | ||||
−0.552028 | + | 0.833825i | \(0.686146\pi\) | |||||||
\(212\) | 1.52566e15 | 1.15418 | ||||||||
\(213\) | −2.56654e15 | −1.88313 | ||||||||
\(214\) | 2.40605e15 | 1.71244 | ||||||||
\(215\) | 2.23520e14 | 0.154336 | ||||||||
\(216\) | −4.06499e14 | −0.272339 | ||||||||
\(217\) | −1.04389e15 | −0.678679 | ||||||||
\(218\) | −3.68006e15 | −2.32214 | ||||||||
\(219\) | 2.84699e14 | 0.174381 | ||||||||
\(220\) | 5.93870e15 | 3.53137 | ||||||||
\(221\) | 9.68196e14 | 0.559002 | ||||||||
\(222\) | 2.18238e15 | 1.22359 | ||||||||
\(223\) | 9.57325e14 | 0.521288 | 0.260644 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260644 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(224\) | −8.90876e14 | −0.471200 | ||||||||
\(225\) | −3.82606e14 | −0.196592 | ||||||||
\(226\) | −5.40172e14 | −0.269667 | ||||||||
\(227\) | 2.20717e15 | 1.07070 | 0.535349 | − | 0.844631i | \(-0.320180\pi\) | ||||
0.535349 | + | 0.844631i | \(0.320180\pi\) | |||||||
\(228\) | 8.77123e15 | 4.13508 | ||||||||
\(229\) | −3.39090e15 | −1.55376 | −0.776880 | − | 0.629649i | \(-0.783199\pi\) | ||||
−0.776880 | + | 0.629649i | \(0.783199\pi\) | |||||||
\(230\) | 2.55372e15 | 1.13748 | ||||||||
\(231\) | 2.15192e15 | 0.931854 | ||||||||
\(232\) | −6.00208e15 | −2.52715 | ||||||||
\(233\) | 2.78688e15 | 1.14105 | 0.570525 | − | 0.821280i | \(-0.306740\pi\) | ||||
0.570525 | + | 0.821280i | \(0.306740\pi\) | |||||||
\(234\) | −1.29933e15 | −0.517388 | ||||||||
\(235\) | 2.40861e15 | 0.932881 | ||||||||
\(236\) | −3.64472e15 | −1.37321 | ||||||||
\(237\) | −1.61115e15 | −0.590571 | ||||||||
\(238\) | −3.53886e15 | −1.26216 | ||||||||
\(239\) | 1.92839e15 | 0.669282 | 0.334641 | − | 0.942346i | \(-0.391385\pi\) | ||||
0.334641 | + | 0.942346i | \(0.391385\pi\) | |||||||
\(240\) | 7.12927e15 | 2.40809 | ||||||||
\(241\) | 9.64137e14 | 0.316977 | 0.158489 | − | 0.987361i | \(-0.449338\pi\) | ||||
0.158489 | + | 0.987361i | \(0.449338\pi\) | |||||||
\(242\) | −1.14598e16 | −3.66756 | ||||||||
\(243\) | 4.41147e15 | 1.37449 | ||||||||
\(244\) | 4.96615e15 | 1.50656 | ||||||||
\(245\) | 2.55003e15 | 0.753296 | ||||||||
\(246\) | −1.28810e16 | −3.70572 | ||||||||
\(247\) | −1.44746e15 | −0.405580 | ||||||||
\(248\) | 1.50570e16 | 4.10963 | ||||||||
\(249\) | 9.44959e15 | 2.51256 | ||||||||
\(250\) | −7.53963e15 | −1.95317 | ||||||||
\(251\) | 4.01969e14 | 0.101464 | 0.0507322 | − | 0.998712i | \(-0.483845\pi\) | ||||
0.0507322 | + | 0.998712i | \(0.483845\pi\) | |||||||
\(252\) | 3.30675e15 | 0.813389 | ||||||||
\(253\) | −5.12873e15 | −1.22949 | ||||||||
\(254\) | −2.15548e15 | −0.503645 | ||||||||
\(255\) | 9.67329e15 | 2.20325 | ||||||||
\(256\) | −7.41655e15 | −1.64680 | ||||||||
\(257\) | −3.39614e15 | −0.735225 | −0.367613 | − | 0.929979i | \(-0.619825\pi\) | ||||
−0.367613 | + | 0.929979i | \(0.619825\pi\) | |||||||
\(258\) | −2.07214e15 | −0.437412 | ||||||||
\(259\) | 9.16554e14 | 0.188673 | ||||||||
\(260\) | −3.14982e15 | −0.632353 | ||||||||
\(261\) | 5.04146e15 | 0.987172 | ||||||||
\(262\) | −1.19852e16 | −2.28922 | ||||||||
\(263\) | 7.87181e15 | 1.46677 | 0.733385 | − | 0.679813i | \(-0.237939\pi\) | ||||
0.733385 | + | 0.679813i | \(0.237939\pi\) | |||||||
\(264\) | −3.10393e16 | −5.64269 | ||||||||
\(265\) | −2.51545e15 | −0.446187 | ||||||||
\(266\) | 5.29062e15 | 0.915748 | ||||||||
\(267\) | −6.98890e15 | −1.18055 | ||||||||
\(268\) | −2.44254e16 | −4.02685 | ||||||||
\(269\) | −2.71709e15 | −0.437234 | −0.218617 | − | 0.975811i | \(-0.570155\pi\) | ||||
−0.218617 | + | 0.975811i | \(0.570155\pi\) | |||||||
\(270\) | 1.18877e15 | 0.186739 | ||||||||
\(271\) | 3.46996e15 | 0.532138 | 0.266069 | − | 0.963954i | \(-0.414275\pi\) | ||||
0.266069 | + | 0.963954i | \(0.414275\pi\) | |||||||
\(272\) | 2.35461e16 | 3.52550 | ||||||||
\(273\) | −1.14136e15 | −0.166864 | ||||||||
\(274\) | −1.63476e16 | −2.33386 | ||||||||
\(275\) | 2.67530e15 | 0.373001 | ||||||||
\(276\) | −1.64839e16 | −2.24466 | ||||||||
\(277\) | 4.83696e15 | 0.643359 | 0.321680 | − | 0.946849i | \(-0.395753\pi\) | ||||
0.321680 | + | 0.946849i | \(0.395753\pi\) | |||||||
\(278\) | 1.71280e16 | 2.22544 | ||||||||
\(279\) | −1.26472e16 | −1.60534 | ||||||||
\(280\) | 6.49090e15 | 0.804966 | ||||||||
\(281\) | 5.65710e15 | 0.685493 | 0.342747 | − | 0.939428i | \(-0.388643\pi\) | ||||
0.342747 | + | 0.939428i | \(0.388643\pi\) | |||||||
\(282\) | −2.23290e16 | −2.64393 | ||||||||
\(283\) | −9.99162e15 | −1.15618 | −0.578088 | − | 0.815974i | \(-0.696201\pi\) | ||||
−0.578088 | + | 0.815974i | \(0.696201\pi\) | |||||||
\(284\) | 2.75768e16 | 3.11871 | ||||||||
\(285\) | −1.44616e16 | −1.59855 | ||||||||
\(286\) | 9.08531e15 | 0.981659 | ||||||||
\(287\) | −5.40977e15 | −0.571409 | ||||||||
\(288\) | −1.07934e16 | −1.11457 | ||||||||
\(289\) | 2.20437e16 | 2.22561 | ||||||||
\(290\) | 1.75526e16 | 1.73282 | ||||||||
\(291\) | 1.42967e15 | 0.138017 | ||||||||
\(292\) | −3.05902e15 | −0.288798 | ||||||||
\(293\) | −1.86990e16 | −1.72655 | −0.863274 | − | 0.504736i | \(-0.831590\pi\) | ||||
−0.863274 | + | 0.504736i | \(0.831590\pi\) | |||||||
\(294\) | −2.36400e16 | −2.13496 | ||||||||
\(295\) | 6.00926e15 | 0.530857 | ||||||||
\(296\) | −1.32204e16 | −1.14248 | ||||||||
\(297\) | −2.38745e15 | −0.201845 | ||||||||
\(298\) | −2.55440e16 | −2.11292 | ||||||||
\(299\) | 2.72022e15 | 0.220162 | ||||||||
\(300\) | 8.59848e15 | 0.680979 | ||||||||
\(301\) | −8.70257e14 | −0.0674474 | ||||||||
\(302\) | 7.89368e15 | 0.598735 | ||||||||
\(303\) | −1.74141e16 | −1.29278 | ||||||||
\(304\) | −3.52016e16 | −2.55790 | ||||||||
\(305\) | −8.18798e15 | −0.582409 | ||||||||
\(306\) | −4.28750e16 | −2.98548 | ||||||||
\(307\) | 1.05970e16 | 0.722408 | 0.361204 | − | 0.932487i | \(-0.382366\pi\) | ||||
0.361204 | + | 0.932487i | \(0.382366\pi\) | |||||||
\(308\) | −2.31218e16 | −1.54327 | ||||||||
\(309\) | −6.69939e15 | −0.437829 | ||||||||
\(310\) | −4.40330e16 | −2.81791 | ||||||||
\(311\) | 2.72333e16 | 1.70670 | 0.853351 | − | 0.521337i | \(-0.174567\pi\) | ||||
0.853351 | + | 0.521337i | \(0.174567\pi\) | |||||||
\(312\) | 1.64629e16 | 1.01042 | ||||||||
\(313\) | −9.42099e15 | −0.566316 | −0.283158 | − | 0.959073i | \(-0.591382\pi\) | ||||
−0.283158 | + | 0.959073i | \(0.591382\pi\) | |||||||
\(314\) | −3.59477e16 | −2.11655 | ||||||||
\(315\) | −5.45204e15 | −0.314442 | ||||||||
\(316\) | 1.73114e16 | 0.978063 | ||||||||
\(317\) | 1.50841e15 | 0.0834902 | 0.0417451 | − | 0.999128i | \(-0.486708\pi\) | ||||
0.0417451 | + | 0.999128i | \(0.486708\pi\) | |||||||
\(318\) | 2.33194e16 | 1.26457 | ||||||||
\(319\) | −3.52515e16 | −1.87300 | ||||||||
\(320\) | −4.16411e15 | −0.216794 | ||||||||
\(321\) | 2.56063e16 | 1.30636 | ||||||||
\(322\) | −9.94272e15 | −0.497098 | ||||||||
\(323\) | −4.77629e16 | −2.34032 | ||||||||
\(324\) | −5.14049e16 | −2.46866 | ||||||||
\(325\) | −1.41895e15 | −0.0667922 | ||||||||
\(326\) | −2.13913e15 | −0.0987015 | ||||||||
\(327\) | −3.91649e16 | −1.77148 | ||||||||
\(328\) | 7.80306e16 | 3.46007 | ||||||||
\(329\) | −9.37775e15 | −0.407685 | ||||||||
\(330\) | 9.07718e16 | 3.86910 | ||||||||
\(331\) | 2.65500e16 | 1.10964 | 0.554821 | − | 0.831970i | \(-0.312787\pi\) | ||||
0.554821 | + | 0.831970i | \(0.312787\pi\) | |||||||
\(332\) | −1.01534e17 | −4.16114 | ||||||||
\(333\) | 1.11045e16 | 0.446284 | ||||||||
\(334\) | −4.99740e16 | −1.96966 | ||||||||
\(335\) | 4.02716e16 | 1.55671 | ||||||||
\(336\) | −2.77572e16 | −1.05238 | ||||||||
\(337\) | 3.97000e16 | 1.47637 | 0.738186 | − | 0.674597i | \(-0.235683\pi\) | ||||
0.738186 | + | 0.674597i | \(0.235683\pi\) | |||||||
\(338\) | 4.49229e16 | 1.63874 | ||||||||
\(339\) | −5.74876e15 | −0.205720 | ||||||||
\(340\) | −1.03937e17 | −3.64887 | ||||||||
\(341\) | 8.84329e16 | 3.04586 | ||||||||
\(342\) | 6.40984e16 | 2.16609 | ||||||||
\(343\) | −2.16087e16 | −0.716502 | ||||||||
\(344\) | 1.25526e16 | 0.408417 | ||||||||
\(345\) | 2.71779e16 | 0.867744 | ||||||||
\(346\) | 7.49344e16 | 2.34794 | ||||||||
\(347\) | 3.08047e15 | 0.0947272 | 0.0473636 | − | 0.998878i | \(-0.484918\pi\) | ||||
0.0473636 | + | 0.998878i | \(0.484918\pi\) | |||||||
\(348\) | −1.13299e17 | −3.41949 | ||||||||
\(349\) | 6.02974e16 | 1.78621 | 0.893106 | − | 0.449846i | \(-0.148521\pi\) | ||||
0.893106 | + | 0.449846i | \(0.148521\pi\) | |||||||
\(350\) | 5.18643e15 | 0.150809 | ||||||||
\(351\) | 1.26628e15 | 0.0361438 | ||||||||
\(352\) | 7.54707e16 | 2.11471 | ||||||||
\(353\) | 3.36289e16 | 0.925077 | 0.462538 | − | 0.886599i | \(-0.346939\pi\) | ||||
0.462538 | + | 0.886599i | \(0.346939\pi\) | |||||||
\(354\) | −5.57088e16 | −1.50453 | ||||||||
\(355\) | −4.54676e16 | −1.20564 | ||||||||
\(356\) | 7.50940e16 | 1.95515 | ||||||||
\(357\) | −3.76622e16 | −0.962858 | ||||||||
\(358\) | −1.09320e17 | −2.74448 | ||||||||
\(359\) | −4.89221e16 | −1.20612 | −0.603060 | − | 0.797695i | \(-0.706052\pi\) | ||||
−0.603060 | + | 0.797695i | \(0.706052\pi\) | |||||||
\(360\) | 7.86402e16 | 1.90405 | ||||||||
\(361\) | 2.93529e16 | 0.697999 | ||||||||
\(362\) | −3.01519e15 | −0.0704220 | ||||||||
\(363\) | −1.21960e17 | −2.79786 | ||||||||
\(364\) | 1.22636e16 | 0.276349 | ||||||||
\(365\) | 5.04358e15 | 0.111644 | ||||||||
\(366\) | 7.59066e16 | 1.65064 | ||||||||
\(367\) | 2.08663e16 | 0.445775 | 0.222888 | − | 0.974844i | \(-0.428452\pi\) | ||||
0.222888 | + | 0.974844i | \(0.428452\pi\) | |||||||
\(368\) | 6.61546e16 | 1.38851 | ||||||||
\(369\) | −6.55419e16 | −1.35160 | ||||||||
\(370\) | 3.86619e16 | 0.783379 | ||||||||
\(371\) | 9.79369e15 | 0.194992 | ||||||||
\(372\) | 2.84225e17 | 5.56076 | ||||||||
\(373\) | −6.90621e16 | −1.32780 | −0.663899 | − | 0.747822i | \(-0.731100\pi\) | ||||
−0.663899 | + | 0.747822i | \(0.731100\pi\) | |||||||
\(374\) | 2.99795e17 | 5.66447 | ||||||||
\(375\) | −8.02401e16 | −1.49001 | ||||||||
\(376\) | 1.35265e17 | 2.46867 | ||||||||
\(377\) | 1.86970e16 | 0.335392 | ||||||||
\(378\) | −4.62839e15 | −0.0816081 | ||||||||
\(379\) | 4.82810e16 | 0.836800 | 0.418400 | − | 0.908263i | \(-0.362591\pi\) | ||||
0.418400 | + | 0.908263i | \(0.362591\pi\) | |||||||
\(380\) | 1.55387e17 | 2.64741 | ||||||||
\(381\) | −2.29396e16 | −0.384214 | ||||||||
\(382\) | 1.23046e17 | 2.02607 | ||||||||
\(383\) | −7.25637e16 | −1.17470 | −0.587351 | − | 0.809333i | \(-0.699829\pi\) | ||||
−0.587351 | + | 0.809333i | \(0.699829\pi\) | |||||||
\(384\) | −6.72056e16 | −1.06968 | ||||||||
\(385\) | 3.81223e16 | 0.596602 | ||||||||
\(386\) | −2.01680e17 | −3.10345 | ||||||||
\(387\) | −1.05436e16 | −0.159539 | ||||||||
\(388\) | −1.53615e16 | −0.228574 | ||||||||
\(389\) | −9.04859e15 | −0.132406 | −0.0662031 | − | 0.997806i | \(-0.521089\pi\) | ||||
−0.0662031 | + | 0.997806i | \(0.521089\pi\) | |||||||
\(390\) | −4.81444e16 | −0.692829 | ||||||||
\(391\) | 8.97614e16 | 1.27040 | ||||||||
\(392\) | 1.43206e17 | 1.99344 | ||||||||
\(393\) | −1.27552e17 | −1.74637 | ||||||||
\(394\) | 9.59961e15 | 0.129279 | ||||||||
\(395\) | −2.85424e16 | −0.378102 | ||||||||
\(396\) | −2.80132e17 | −3.65043 | ||||||||
\(397\) | 5.87080e16 | 0.752591 | 0.376295 | − | 0.926500i | \(-0.377198\pi\) | ||||
0.376295 | + | 0.926500i | \(0.377198\pi\) | |||||||
\(398\) | 1.71710e17 | 2.16549 | ||||||||
\(399\) | 5.63052e16 | 0.698594 | ||||||||
\(400\) | −3.45083e16 | −0.421244 | ||||||||
\(401\) | 7.57878e16 | 0.910251 | 0.455125 | − | 0.890427i | \(-0.349594\pi\) | ||||
0.455125 | + | 0.890427i | \(0.349594\pi\) | |||||||
\(402\) | −3.73337e17 | −4.41196 | ||||||||
\(403\) | −4.69039e16 | −0.545414 | ||||||||
\(404\) | 1.87110e17 | 2.14101 | ||||||||
\(405\) | 8.47542e16 | 0.954341 | ||||||||
\(406\) | −6.83396e16 | −0.757274 | ||||||||
\(407\) | −7.76460e16 | −0.846751 | ||||||||
\(408\) | 5.43240e17 | 5.83043 | ||||||||
\(409\) | −6.14465e16 | −0.649076 | −0.324538 | − | 0.945873i | \(-0.605209\pi\) | ||||
−0.324538 | + | 0.945873i | \(0.605209\pi\) | |||||||
\(410\) | −2.28194e17 | −2.37252 | ||||||||
\(411\) | −1.73978e17 | −1.78042 | ||||||||
\(412\) | 7.19833e16 | 0.725103 | ||||||||
\(413\) | −2.33966e16 | −0.231994 | ||||||||
\(414\) | −1.20461e17 | −1.17583 | ||||||||
\(415\) | 1.67404e17 | 1.60862 | ||||||||
\(416\) | −4.00289e16 | −0.378675 | ||||||||
\(417\) | 1.82284e17 | 1.69772 | ||||||||
\(418\) | −4.48196e17 | −4.10981 | ||||||||
\(419\) | 1.56464e17 | 1.41261 | 0.706306 | − | 0.707907i | \(-0.250360\pi\) | ||||
0.706306 | + | 0.707907i | \(0.250360\pi\) | |||||||
\(420\) | 1.22526e17 | 1.08920 | ||||||||
\(421\) | −1.28104e17 | −1.12132 | −0.560661 | − | 0.828045i | \(-0.689453\pi\) | ||||
−0.560661 | + | 0.828045i | \(0.689453\pi\) | |||||||
\(422\) | 2.32425e17 | 2.00333 | ||||||||
\(423\) | −1.13616e17 | −0.964331 | ||||||||
\(424\) | −1.41264e17 | −1.18074 | ||||||||
\(425\) | −4.68223e16 | −0.385411 | ||||||||
\(426\) | 4.21506e17 | 3.41698 | ||||||||
\(427\) | 3.18793e16 | 0.254523 | ||||||||
\(428\) | −2.75133e17 | −2.16351 | ||||||||
\(429\) | 9.66900e16 | 0.748875 | ||||||||
\(430\) | −3.67090e16 | −0.280045 | ||||||||
\(431\) | 1.14344e17 | 0.859235 | 0.429617 | − | 0.903011i | \(-0.358648\pi\) | ||||
0.429617 | + | 0.903011i | \(0.358648\pi\) | |||||||
\(432\) | 3.07954e16 | 0.227951 | ||||||||
\(433\) | 2.25765e17 | 1.64621 | 0.823105 | − | 0.567889i | \(-0.192240\pi\) | ||||
0.823105 | + | 0.567889i | \(0.192240\pi\) | |||||||
\(434\) | 1.71439e17 | 1.23148 | ||||||||
\(435\) | 1.86803e17 | 1.32191 | ||||||||
\(436\) | 4.20817e17 | 2.93381 | ||||||||
\(437\) | −1.34194e17 | −0.921729 | ||||||||
\(438\) | −4.67565e16 | −0.316417 | ||||||||
\(439\) | −9.07134e16 | −0.604856 | −0.302428 | − | 0.953172i | \(-0.597797\pi\) | ||||
−0.302428 | + | 0.953172i | \(0.597797\pi\) | |||||||
\(440\) | −5.49877e17 | −3.61263 | ||||||||
\(441\) | −1.20286e17 | −0.778692 | ||||||||
\(442\) | −1.59008e17 | −1.01432 | ||||||||
\(443\) | −2.41413e17 | −1.51753 | −0.758765 | − | 0.651365i | \(-0.774197\pi\) | ||||
−0.758765 | + | 0.651365i | \(0.774197\pi\) | |||||||
\(444\) | −2.49556e17 | −1.54589 | ||||||||
\(445\) | −1.23812e17 | −0.755827 | ||||||||
\(446\) | −1.57223e17 | −0.945887 | ||||||||
\(447\) | −2.71851e17 | −1.61188 | ||||||||
\(448\) | 1.62126e16 | 0.0947428 | ||||||||
\(449\) | 7.03138e16 | 0.404986 | 0.202493 | − | 0.979284i | \(-0.435096\pi\) | ||||
0.202493 | + | 0.979284i | \(0.435096\pi\) | |||||||
\(450\) | 6.28360e16 | 0.356720 | ||||||||
\(451\) | 4.58290e17 | 2.56444 | ||||||||
\(452\) | 6.17690e16 | 0.340699 | ||||||||
\(453\) | 8.40082e16 | 0.456755 | ||||||||
\(454\) | −3.62486e17 | −1.94280 | ||||||||
\(455\) | −2.02197e16 | −0.106832 | ||||||||
\(456\) | −8.12147e17 | −4.23022 | ||||||||
\(457\) | −2.57859e16 | −0.132412 | −0.0662060 | − | 0.997806i | \(-0.521089\pi\) | ||||
−0.0662060 | + | 0.997806i | \(0.521089\pi\) | |||||||
\(458\) | 5.56892e17 | 2.81933 | ||||||||
\(459\) | 4.17844e16 | 0.208560 | ||||||||
\(460\) | −2.92020e17 | −1.43710 | ||||||||
\(461\) | −7.49441e16 | −0.363648 | −0.181824 | − | 0.983331i | \(-0.558200\pi\) | ||||
−0.181824 | + | 0.983331i | \(0.558200\pi\) | |||||||
\(462\) | −3.53413e17 | −1.69087 | ||||||||
\(463\) | 2.39300e17 | 1.12893 | 0.564464 | − | 0.825457i | \(-0.309083\pi\) | ||||
0.564464 | + | 0.825457i | \(0.309083\pi\) | |||||||
\(464\) | 4.54703e17 | 2.11525 | ||||||||
\(465\) | −4.68619e17 | −2.14969 | ||||||||
\(466\) | −4.57694e17 | −2.07046 | ||||||||
\(467\) | −2.99998e16 | −0.133832 | −0.0669158 | − | 0.997759i | \(-0.521316\pi\) | ||||
−0.0669158 | + | 0.997759i | \(0.521316\pi\) | |||||||
\(468\) | 1.48579e17 | 0.653672 | ||||||||
\(469\) | −1.56794e17 | −0.680309 | ||||||||
\(470\) | −3.95570e17 | −1.69273 | ||||||||
\(471\) | −3.82572e17 | −1.61464 | ||||||||
\(472\) | 3.37472e17 | 1.40480 | ||||||||
\(473\) | 7.37239e16 | 0.302699 | ||||||||
\(474\) | 2.64602e17 | 1.07160 | ||||||||
\(475\) | 6.99996e16 | 0.279632 | ||||||||
\(476\) | 4.04671e17 | 1.59462 | ||||||||
\(477\) | 1.18655e17 | 0.461230 | ||||||||
\(478\) | −3.16703e17 | −1.21442 | ||||||||
\(479\) | −2.32445e17 | −0.879304 | −0.439652 | − | 0.898168i | \(-0.644898\pi\) | ||||
−0.439652 | + | 0.898168i | \(0.644898\pi\) | |||||||
\(480\) | −3.99930e17 | −1.49251 | ||||||||
\(481\) | 4.11826e16 | 0.151625 | ||||||||
\(482\) | −1.58342e17 | −0.575161 | ||||||||
\(483\) | −1.05815e17 | −0.379219 | ||||||||
\(484\) | 1.31043e18 | 4.63362 | ||||||||
\(485\) | 2.53274e16 | 0.0883626 | ||||||||
\(486\) | −7.24503e17 | −2.49404 | ||||||||
\(487\) | 3.80963e17 | 1.29403 | 0.647016 | − | 0.762477i | \(-0.276017\pi\) | ||||
0.647016 | + | 0.762477i | \(0.276017\pi\) | |||||||
\(488\) | −4.59827e17 | −1.54122 | ||||||||
\(489\) | −2.27656e16 | −0.0752961 | ||||||||
\(490\) | −4.18795e17 | −1.36687 | ||||||||
\(491\) | 2.77787e17 | 0.894711 | 0.447355 | − | 0.894356i | \(-0.352366\pi\) | ||||
0.447355 | + | 0.894356i | \(0.352366\pi\) | |||||||
\(492\) | 1.47295e18 | 4.68183 | ||||||||
\(493\) | 6.16960e17 | 1.93532 | ||||||||
\(494\) | 2.37718e17 | 0.735932 | ||||||||
\(495\) | 4.61870e17 | 1.41119 | ||||||||
\(496\) | −1.14068e18 | −3.43980 | ||||||||
\(497\) | 1.77024e17 | 0.526886 | ||||||||
\(498\) | −1.55192e18 | −4.55909 | ||||||||
\(499\) | 2.25995e16 | 0.0655308 | 0.0327654 | − | 0.999463i | \(-0.489569\pi\) | ||||
0.0327654 | + | 0.999463i | \(0.489569\pi\) | |||||||
\(500\) | 8.62161e17 | 2.46765 | ||||||||
\(501\) | −5.31846e17 | −1.50259 | ||||||||
\(502\) | −6.60160e16 | −0.184109 | ||||||||
\(503\) | 5.95996e16 | 0.164078 | 0.0820392 | − | 0.996629i | \(-0.473857\pi\) | ||||
0.0820392 | + | 0.996629i | \(0.473857\pi\) | |||||||
\(504\) | −3.06179e17 | −0.832104 | ||||||||
\(505\) | −3.08499e17 | −0.827676 | ||||||||
\(506\) | 8.42299e17 | 2.23094 | ||||||||
\(507\) | 4.78090e17 | 1.25014 | ||||||||
\(508\) | 2.46480e17 | 0.636309 | ||||||||
\(509\) | 3.04966e17 | 0.777294 | 0.388647 | − | 0.921387i | \(-0.372943\pi\) | ||||
0.388647 | + | 0.921387i | \(0.372943\pi\) | |||||||
\(510\) | −1.58866e18 | −3.99783 | ||||||||
\(511\) | −1.96368e16 | −0.0487904 | ||||||||
\(512\) | 9.03040e17 | 2.21540 | ||||||||
\(513\) | −6.24680e16 | −0.151319 | ||||||||
\(514\) | 5.57753e17 | 1.33408 | ||||||||
\(515\) | −1.18683e17 | −0.280312 | ||||||||
\(516\) | 2.36950e17 | 0.552630 | ||||||||
\(517\) | 7.94437e17 | 1.82966 | ||||||||
\(518\) | −1.50527e17 | −0.342351 | ||||||||
\(519\) | 7.97486e17 | 1.79116 | ||||||||
\(520\) | 2.91649e17 | 0.646903 | ||||||||
\(521\) | −5.62230e17 | −1.23160 | −0.615799 | − | 0.787904i | \(-0.711167\pi\) | ||||
−0.615799 | + | 0.787904i | \(0.711167\pi\) | |||||||
\(522\) | −8.27966e17 | −1.79124 | ||||||||
\(523\) | −5.72007e17 | −1.22220 | −0.611098 | − | 0.791555i | \(-0.709272\pi\) | ||||
−0.611098 | + | 0.791555i | \(0.709272\pi\) | |||||||
\(524\) | 1.37052e18 | 2.89222 | ||||||||
\(525\) | 5.51963e16 | 0.115047 | ||||||||
\(526\) | −1.29280e18 | −2.66148 | ||||||||
\(527\) | −1.54772e18 | −3.14720 | ||||||||
\(528\) | 2.35146e18 | 4.72299 | ||||||||
\(529\) | −2.51845e17 | −0.499656 | ||||||||
\(530\) | 4.13116e17 | 0.809615 | ||||||||
\(531\) | −2.83460e17 | −0.548754 | ||||||||
\(532\) | −6.04986e17 | −1.15696 | ||||||||
\(533\) | −2.43072e17 | −0.459207 | ||||||||
\(534\) | 1.14780e18 | 2.14213 | ||||||||
\(535\) | 4.53628e17 | 0.836374 | ||||||||
\(536\) | 2.26160e18 | 4.11950 | ||||||||
\(537\) | −1.16343e18 | −2.09367 | ||||||||
\(538\) | 4.46232e17 | 0.793370 | ||||||||
\(539\) | 8.41080e17 | 1.47744 | ||||||||
\(540\) | −1.35937e17 | −0.235927 | ||||||||
\(541\) | −5.51264e17 | −0.945318 | −0.472659 | − | 0.881245i | \(-0.656706\pi\) | ||||
−0.472659 | + | 0.881245i | \(0.656706\pi\) | |||||||
\(542\) | −5.69877e17 | −0.965574 | ||||||||
\(543\) | −3.20890e16 | −0.0537226 | ||||||||
\(544\) | −1.32086e18 | −2.18507 | ||||||||
\(545\) | −6.93826e17 | −1.13416 | ||||||||
\(546\) | 1.87446e17 | 0.302778 | ||||||||
\(547\) | 4.15668e16 | 0.0663481 | 0.0331741 | − | 0.999450i | \(-0.489438\pi\) | ||||
0.0331741 | + | 0.999450i | \(0.489438\pi\) | |||||||
\(548\) | 1.86935e18 | 2.94861 | ||||||||
\(549\) | 3.86232e17 | 0.602044 | ||||||||
\(550\) | −4.39369e17 | −0.676818 | ||||||||
\(551\) | −9.22359e17 | −1.40415 | ||||||||
\(552\) | 1.52628e18 | 2.29630 | ||||||||
\(553\) | 1.11127e17 | 0.165237 | ||||||||
\(554\) | −7.94380e17 | −1.16739 | ||||||||
\(555\) | 4.11458e17 | 0.597614 | ||||||||
\(556\) | −1.95860e18 | −2.81164 | ||||||||
\(557\) | −6.66203e17 | −0.945252 | −0.472626 | − | 0.881263i | \(-0.656694\pi\) | ||||
−0.472626 | + | 0.881263i | \(0.656694\pi\) | |||||||
\(558\) | 2.07706e18 | 2.91291 | ||||||||
\(559\) | −3.91024e16 | −0.0542034 | ||||||||
\(560\) | −4.91734e17 | −0.673764 | ||||||||
\(561\) | 3.19056e18 | 4.32123 | ||||||||
\(562\) | −9.29075e17 | −1.24384 | ||||||||
\(563\) | −1.40923e18 | −1.86499 | −0.932495 | − | 0.361183i | \(-0.882373\pi\) | ||||
−0.932495 | + | 0.361183i | \(0.882373\pi\) | |||||||
\(564\) | 2.55334e18 | 3.34037 | ||||||||
\(565\) | −1.01842e17 | −0.131708 | ||||||||
\(566\) | 1.64094e18 | 2.09790 | ||||||||
\(567\) | −3.29984e17 | −0.417064 | ||||||||
\(568\) | −2.55340e18 | −3.19047 | ||||||||
\(569\) | −1.10068e18 | −1.35966 | −0.679831 | − | 0.733369i | \(-0.737947\pi\) | ||||
−0.679831 | + | 0.733369i | \(0.737947\pi\) | |||||||
\(570\) | 2.37506e18 | 2.90060 | ||||||||
\(571\) | −4.64559e17 | −0.560927 | −0.280464 | − | 0.959865i | \(-0.590488\pi\) | ||||
−0.280464 | + | 0.959865i | \(0.590488\pi\) | |||||||
\(572\) | −1.03891e18 | −1.24024 | ||||||||
\(573\) | 1.30951e18 | 1.54562 | ||||||||
\(574\) | 8.88455e17 | 1.03683 | ||||||||
\(575\) | −1.31551e17 | −0.151793 | ||||||||
\(576\) | 1.96424e17 | 0.224103 | ||||||||
\(577\) | −2.50781e17 | −0.282912 | −0.141456 | − | 0.989945i | \(-0.545178\pi\) | ||||
−0.141456 | + | 0.989945i | \(0.545178\pi\) | |||||||
\(578\) | −3.62027e18 | −4.03841 | ||||||||
\(579\) | −2.14637e18 | −2.36752 | ||||||||
\(580\) | −2.00715e18 | −2.18926 | ||||||||
\(581\) | −6.51775e17 | −0.702996 | ||||||||
\(582\) | −2.34797e17 | −0.250434 | ||||||||
\(583\) | −8.29674e17 | −0.875108 | ||||||||
\(584\) | 2.83241e17 | 0.295443 | ||||||||
\(585\) | −2.44971e17 | −0.252698 | ||||||||
\(586\) | 3.07096e18 | 3.13285 | ||||||||
\(587\) | −1.08453e17 | −0.109419 | −0.0547096 | − | 0.998502i | \(-0.517423\pi\) | ||||
−0.0547096 | + | 0.998502i | \(0.517423\pi\) | |||||||
\(588\) | 2.70325e18 | 2.69733 | ||||||||
\(589\) | 2.31386e18 | 2.28343 | ||||||||
\(590\) | −9.86909e17 | −0.963250 | ||||||||
\(591\) | 1.02163e17 | 0.0986227 | ||||||||
\(592\) | 1.00154e18 | 0.956266 | ||||||||
\(593\) | −1.11060e18 | −1.04883 | −0.524413 | − | 0.851464i | \(-0.675715\pi\) | ||||
−0.524413 | + | 0.851464i | \(0.675715\pi\) | |||||||
\(594\) | 3.92095e17 | 0.366251 | ||||||||
\(595\) | −6.67205e17 | −0.616452 | ||||||||
\(596\) | 2.92097e18 | 2.66948 | ||||||||
\(597\) | 1.82742e18 | 1.65198 | ||||||||
\(598\) | −4.46746e17 | −0.399488 | ||||||||
\(599\) | 1.09969e18 | 0.972742 | 0.486371 | − | 0.873752i | \(-0.338320\pi\) | ||||
0.486371 | + | 0.873752i | \(0.338320\pi\) | |||||||
\(600\) | −7.96152e17 | −0.696648 | ||||||||
\(601\) | −1.58647e18 | −1.37324 | −0.686621 | − | 0.727015i | \(-0.740907\pi\) | ||||
−0.686621 | + | 0.727015i | \(0.740907\pi\) | |||||||
\(602\) | 1.42924e17 | 0.122385 | ||||||||
\(603\) | −1.89963e18 | −1.60919 | ||||||||
\(604\) | −9.02648e17 | −0.756447 | ||||||||
\(605\) | −2.16059e18 | −1.79128 | ||||||||
\(606\) | 2.85994e18 | 2.34577 | ||||||||
\(607\) | −6.04036e17 | −0.490158 | −0.245079 | − | 0.969503i | \(-0.578814\pi\) | ||||
−0.245079 | + | 0.969503i | \(0.578814\pi\) | |||||||
\(608\) | 1.97470e18 | 1.58536 | ||||||||
\(609\) | −7.27301e17 | −0.577699 | ||||||||
\(610\) | 1.34472e18 | 1.05679 | ||||||||
\(611\) | −4.21361e17 | −0.327632 | ||||||||
\(612\) | 4.90278e18 | 3.77188 | ||||||||
\(613\) | 5.37012e17 | 0.408781 | 0.204391 | − | 0.978889i | \(-0.434479\pi\) | ||||
0.204391 | + | 0.978889i | \(0.434479\pi\) | |||||||
\(614\) | −1.74036e18 | −1.31082 | ||||||||
\(615\) | −2.42854e18 | −1.80991 | ||||||||
\(616\) | 2.14090e18 | 1.57878 | ||||||||
\(617\) | −1.55039e18 | −1.13132 | −0.565662 | − | 0.824637i | \(-0.691379\pi\) | ||||
−0.565662 | + | 0.824637i | \(0.691379\pi\) | |||||||
\(618\) | 1.10025e18 | 0.794450 | ||||||||
\(619\) | 8.75786e17 | 0.625762 | 0.312881 | − | 0.949792i | \(-0.398706\pi\) | ||||
0.312881 | + | 0.949792i | \(0.398706\pi\) | |||||||
\(620\) | 5.03520e18 | 3.56017 | ||||||||
\(621\) | 1.17397e17 | 0.0821411 | ||||||||
\(622\) | −4.47256e18 | −3.09684 | ||||||||
\(623\) | 4.82052e17 | 0.330310 | ||||||||
\(624\) | −1.24719e18 | −0.845732 | ||||||||
\(625\) | −1.10172e18 | −0.739355 | ||||||||
\(626\) | 1.54722e18 | 1.02759 | ||||||||
\(627\) | −4.76990e18 | −3.13524 | ||||||||
\(628\) | 4.11064e18 | 2.67406 | ||||||||
\(629\) | 1.35894e18 | 0.874923 | ||||||||
\(630\) | 8.95396e17 | 0.570560 | ||||||||
\(631\) | −5.68638e17 | −0.358629 | −0.179314 | − | 0.983792i | \(-0.557388\pi\) | ||||
−0.179314 | + | 0.983792i | \(0.557388\pi\) | |||||||
\(632\) | −1.60290e18 | −1.00057 | ||||||||
\(633\) | 2.47358e18 | 1.52827 | ||||||||
\(634\) | −2.47729e17 | −0.151494 | ||||||||
\(635\) | −4.06387e17 | −0.245986 | ||||||||
\(636\) | −2.66659e18 | −1.59766 | ||||||||
\(637\) | −4.46100e17 | −0.264561 | ||||||||
\(638\) | 5.78940e18 | 3.39859 | ||||||||
\(639\) | 2.14473e18 | 1.24629 | ||||||||
\(640\) | −1.19058e18 | −0.684840 | ||||||||
\(641\) | 2.67922e18 | 1.52557 | 0.762784 | − | 0.646654i | \(-0.223832\pi\) | ||||
0.762784 | + | 0.646654i | \(0.223832\pi\) | |||||||
\(642\) | −4.20536e18 | −2.37042 | ||||||||
\(643\) | −1.98256e17 | −0.110626 | −0.0553128 | − | 0.998469i | \(-0.517616\pi\) | ||||
−0.0553128 | + | 0.998469i | \(0.517616\pi\) | |||||||
\(644\) | 1.13696e18 | 0.628038 | ||||||||
\(645\) | −3.90674e17 | −0.213637 | ||||||||
\(646\) | 7.84418e18 | 4.24655 | ||||||||
\(647\) | 1.70529e18 | 0.913945 | 0.456973 | − | 0.889481i | \(-0.348934\pi\) | ||||
0.456973 | + | 0.889481i | \(0.348934\pi\) | |||||||
\(648\) | 4.75969e18 | 2.52546 | ||||||||
\(649\) | 1.98204e18 | 1.04117 | ||||||||
\(650\) | 2.33037e17 | 0.121196 | ||||||||
\(651\) | 1.82453e18 | 0.939452 | ||||||||
\(652\) | 2.44611e17 | 0.124700 | ||||||||
\(653\) | −2.26552e18 | −1.14349 | −0.571746 | − | 0.820431i | \(-0.693734\pi\) | ||||
−0.571746 | + | 0.820431i | \(0.693734\pi\) | |||||||
\(654\) | 6.43211e18 | 3.21439 | ||||||||
\(655\) | −2.25965e18 | −1.11808 | ||||||||
\(656\) | −5.91140e18 | −2.89611 | ||||||||
\(657\) | −2.37909e17 | −0.115408 | ||||||||
\(658\) | 1.54012e18 | 0.739753 | ||||||||
\(659\) | 1.06435e18 | 0.506210 | 0.253105 | − | 0.967439i | \(-0.418548\pi\) | ||||
0.253105 | + | 0.967439i | \(0.418548\pi\) | |||||||
\(660\) | −1.03798e19 | −4.88826 | ||||||||
\(661\) | −2.82204e18 | −1.31599 | −0.657996 | − | 0.753021i | \(-0.728596\pi\) | ||||
−0.657996 | + | 0.753021i | \(0.728596\pi\) | |||||||
\(662\) | −4.36035e18 | −2.01347 | ||||||||
\(663\) | −1.69224e18 | −0.773791 | ||||||||
\(664\) | 9.40122e18 | 4.25688 | ||||||||
\(665\) | 9.97476e17 | 0.447262 | ||||||||
\(666\) | −1.82371e18 | −0.809790 | ||||||||
\(667\) | 1.73340e18 | 0.762220 | ||||||||
\(668\) | 5.71456e18 | 2.48849 | ||||||||
\(669\) | −1.67324e18 | −0.721586 | ||||||||
\(670\) | −6.61386e18 | −2.82468 | ||||||||
\(671\) | −2.70066e18 | −1.14228 | ||||||||
\(672\) | 1.55710e18 | 0.652252 | ||||||||
\(673\) | 2.07422e18 | 0.860511 | 0.430255 | − | 0.902707i | \(-0.358424\pi\) | ||||
0.430255 | + | 0.902707i | \(0.358424\pi\) | |||||||
\(674\) | −6.51998e18 | −2.67890 | ||||||||
\(675\) | −6.12377e16 | −0.0249198 | ||||||||
\(676\) | −5.13696e18 | −2.07039 | ||||||||
\(677\) | 4.05470e18 | 1.61857 | 0.809286 | − | 0.587415i | \(-0.199854\pi\) | ||||
0.809286 | + | 0.587415i | \(0.199854\pi\) | |||||||
\(678\) | 9.44127e17 | 0.373282 | ||||||||
\(679\) | −9.86101e16 | −0.0386160 | ||||||||
\(680\) | 9.62377e18 | 3.73282 | ||||||||
\(681\) | −3.85775e18 | −1.48210 | ||||||||
\(682\) | −1.45235e19 | −5.52678 | ||||||||
\(683\) | −1.88066e18 | −0.708886 | −0.354443 | − | 0.935078i | \(-0.615330\pi\) | ||||
−0.354443 | + | 0.935078i | \(0.615330\pi\) | |||||||
\(684\) | −7.32969e18 | −2.73666 | ||||||||
\(685\) | −3.08211e18 | −1.13988 | ||||||||
\(686\) | 3.54884e18 | 1.30011 | ||||||||
\(687\) | 5.92670e18 | 2.15077 | ||||||||
\(688\) | −9.50953e17 | −0.341849 | ||||||||
\(689\) | 4.40050e17 | 0.156703 | ||||||||
\(690\) | −4.46346e18 | −1.57454 | ||||||||
\(691\) | −1.84402e18 | −0.644406 | −0.322203 | − | 0.946671i | \(-0.604423\pi\) | ||||
−0.322203 | + | 0.946671i | \(0.604423\pi\) | |||||||
\(692\) | −8.56880e18 | −2.96640 | ||||||||
\(693\) | −1.79825e18 | −0.616716 | ||||||||
\(694\) | −5.05910e17 | −0.171884 | ||||||||
\(695\) | 3.22926e18 | 1.08693 | ||||||||
\(696\) | 1.04906e19 | 3.49817 | ||||||||
\(697\) | −8.02084e18 | −2.64976 | ||||||||
\(698\) | −9.90272e18 | −3.24111 | ||||||||
\(699\) | −4.87098e18 | −1.57948 | ||||||||
\(700\) | −5.93071e17 | −0.190533 | ||||||||
\(701\) | 1.05721e18 | 0.336507 | 0.168253 | − | 0.985744i | \(-0.446187\pi\) | ||||
0.168253 | + | 0.985744i | \(0.446187\pi\) | |||||||
\(702\) | −2.07963e17 | −0.0655835 | ||||||||
\(703\) | −2.03162e18 | −0.634793 | ||||||||
\(704\) | −1.37345e18 | −0.425199 | ||||||||
\(705\) | −4.20984e18 | −1.29133 | ||||||||
\(706\) | −5.52293e18 | −1.67857 | ||||||||
\(707\) | 1.20112e18 | 0.361709 | ||||||||
\(708\) | 6.37033e18 | 1.90084 | ||||||||
\(709\) | −3.47406e18 | −1.02716 | −0.513579 | − | 0.858042i | \(-0.671681\pi\) | ||||
−0.513579 | + | 0.858042i | \(0.671681\pi\) | |||||||
\(710\) | 7.46720e18 | 2.18765 | ||||||||
\(711\) | 1.34636e18 | 0.390849 | ||||||||
\(712\) | −6.95312e18 | −2.00014 | ||||||||
\(713\) | −4.34846e18 | −1.23952 | ||||||||
\(714\) | 6.18532e18 | 1.74712 | ||||||||
\(715\) | 1.71291e18 | 0.479453 | ||||||||
\(716\) | 1.25008e19 | 3.46740 | ||||||||
\(717\) | −3.37049e18 | −0.926444 | ||||||||
\(718\) | 8.03454e18 | 2.18853 | ||||||||
\(719\) | 3.18904e18 | 0.860839 | 0.430420 | − | 0.902629i | \(-0.358366\pi\) | ||||
0.430420 | + | 0.902629i | \(0.358366\pi\) | |||||||
\(720\) | −5.95759e18 | −1.59371 | ||||||||
\(721\) | 4.62083e17 | 0.122501 | ||||||||
\(722\) | −4.82067e18 | −1.26653 | ||||||||
\(723\) | −1.68514e18 | −0.438771 | ||||||||
\(724\) | 3.44789e17 | 0.0889718 | ||||||||
\(725\) | −9.04194e17 | −0.231241 | ||||||||
\(726\) | 2.00297e19 | 5.07676 | ||||||||
\(727\) | 6.45840e18 | 1.62238 | 0.811188 | − | 0.584786i | \(-0.198821\pi\) | ||||
0.811188 | + | 0.584786i | \(0.198821\pi\) | |||||||
\(728\) | −1.13551e18 | −0.282708 | ||||||||
\(729\) | −3.34648e18 | −0.825770 | ||||||||
\(730\) | −8.28315e17 | −0.202580 | ||||||||
\(731\) | −1.29029e18 | −0.312770 | ||||||||
\(732\) | −8.67997e18 | −2.08543 | ||||||||
\(733\) | −3.06499e18 | −0.729883 | −0.364941 | − | 0.931031i | \(-0.618911\pi\) | ||||
−0.364941 | + | 0.931031i | \(0.618911\pi\) | |||||||
\(734\) | −3.42690e18 | −0.808867 | ||||||||
\(735\) | −4.45701e18 | −1.04274 | ||||||||
\(736\) | −3.71107e18 | −0.860585 | ||||||||
\(737\) | 1.32828e19 | 3.05318 | ||||||||
\(738\) | 1.07640e19 | 2.45250 | ||||||||
\(739\) | −2.66860e18 | −0.602691 | −0.301345 | − | 0.953515i | \(-0.597436\pi\) | ||||
−0.301345 | + | 0.953515i | \(0.597436\pi\) | |||||||
\(740\) | −4.42102e18 | −0.989728 | ||||||||
\(741\) | 2.52991e18 | 0.561418 | ||||||||
\(742\) | −1.60843e18 | −0.353816 | ||||||||
\(743\) | 1.17551e18 | 0.256330 | 0.128165 | − | 0.991753i | \(-0.459091\pi\) | ||||
0.128165 | + | 0.991753i | \(0.459091\pi\) | |||||||
\(744\) | −2.63171e19 | −5.68870 | ||||||||
\(745\) | −4.81598e18 | −1.03197 | ||||||||
\(746\) | 1.13422e19 | 2.40932 | ||||||||
\(747\) | −7.89656e18 | −1.66285 | ||||||||
\(748\) | −3.42818e19 | −7.15654 | ||||||||
\(749\) | −1.76617e18 | −0.365510 | ||||||||
\(750\) | 1.31780e19 | 2.70365 | ||||||||
\(751\) | −7.80250e18 | −1.58699 | −0.793495 | − | 0.608577i | \(-0.791741\pi\) | ||||
−0.793495 | + | 0.608577i | \(0.791741\pi\) | |||||||
\(752\) | −1.02473e19 | −2.06630 | ||||||||
\(753\) | −7.02572e17 | −0.140451 | ||||||||
\(754\) | −3.07064e18 | −0.608576 | ||||||||
\(755\) | 1.48825e18 | 0.292429 | ||||||||
\(756\) | 5.29260e17 | 0.103104 | ||||||||
\(757\) | −1.89110e18 | −0.365251 | −0.182625 | − | 0.983183i | \(-0.558460\pi\) | ||||
−0.182625 | + | 0.983183i | \(0.558460\pi\) | |||||||
\(758\) | −7.92926e18 | −1.51839 | ||||||||
\(759\) | 8.96413e18 | 1.70191 | ||||||||
\(760\) | −1.43876e19 | −2.70832 | ||||||||
\(761\) | 4.11499e18 | 0.768014 | 0.384007 | − | 0.923330i | \(-0.374544\pi\) | ||||
0.384007 | + | 0.923330i | \(0.374544\pi\) | |||||||
\(762\) | 3.76740e18 | 0.697163 | ||||||||
\(763\) | 2.70136e18 | 0.495647 | ||||||||
\(764\) | −1.40703e19 | −2.55975 | ||||||||
\(765\) | −8.08350e18 | −1.45814 | ||||||||
\(766\) | 1.19172e19 | 2.13152 | ||||||||
\(767\) | −1.05126e18 | −0.186440 | ||||||||
\(768\) | 1.29628e19 | 2.27957 | ||||||||
\(769\) | 5.53905e18 | 0.965860 | 0.482930 | − | 0.875659i | \(-0.339572\pi\) | ||||
0.482930 | + | 0.875659i | \(0.339572\pi\) | |||||||
\(770\) | −6.26089e18 | −1.08255 | ||||||||
\(771\) | 5.93586e18 | 1.01772 | ||||||||
\(772\) | 2.30622e19 | 3.92092 | ||||||||
\(773\) | −1.59242e18 | −0.268466 | −0.134233 | − | 0.990950i | \(-0.542857\pi\) | ||||
−0.134233 | + | 0.990950i | \(0.542857\pi\) | |||||||
\(774\) | 1.73159e18 | 0.289486 | ||||||||
\(775\) | 2.26829e18 | 0.376043 | ||||||||
\(776\) | 1.42235e18 | 0.233833 | ||||||||
\(777\) | −1.60198e18 | −0.261168 | ||||||||
\(778\) | 1.48606e18 | 0.240254 | ||||||||
\(779\) | 1.19912e19 | 1.92251 | ||||||||
\(780\) | 5.50535e18 | 0.875326 | ||||||||
\(781\) | −1.49966e19 | −2.36462 | ||||||||
\(782\) | −1.47416e19 | −2.30516 | ||||||||
\(783\) | 8.06906e17 | 0.125133 | ||||||||
\(784\) | −1.08490e19 | −1.66853 | ||||||||
\(785\) | −6.77745e18 | −1.03375 | ||||||||
\(786\) | 2.09481e19 | 3.16882 | ||||||||
\(787\) | 1.13209e19 | 1.69842 | 0.849211 | − | 0.528054i | \(-0.177078\pi\) | ||||
0.849211 | + | 0.528054i | \(0.177078\pi\) | |||||||
\(788\) | −1.09772e18 | −0.163332 | ||||||||
\(789\) | −1.37586e19 | −2.03036 | ||||||||
\(790\) | 4.68755e18 | 0.686073 | ||||||||
\(791\) | 3.96514e17 | 0.0575588 | ||||||||
\(792\) | 2.59380e19 | 3.73442 | ||||||||
\(793\) | 1.43240e18 | 0.204545 | ||||||||
\(794\) | −9.64170e18 | −1.36559 | ||||||||
\(795\) | 4.39656e18 | 0.617628 | ||||||||
\(796\) | −1.96352e19 | −2.73590 | ||||||||
\(797\) | 5.73943e18 | 0.793212 | 0.396606 | − | 0.917989i | \(-0.370188\pi\) | ||||
0.396606 | + | 0.917989i | \(0.370188\pi\) | |||||||
\(798\) | −9.24709e18 | −1.26761 | ||||||||
\(799\) | −1.39040e19 | −1.89054 | ||||||||
\(800\) | 1.93581e18 | 0.261082 | ||||||||
\(801\) | 5.84028e18 | 0.781308 | ||||||||
\(802\) | −1.24467e19 | −1.65167 | ||||||||
\(803\) | 1.66353e18 | 0.218968 | ||||||||
\(804\) | 4.26913e19 | 5.57411 | ||||||||
\(805\) | −1.87457e18 | −0.242788 | ||||||||
\(806\) | 7.70310e18 | 0.989663 | ||||||||
\(807\) | 4.74900e18 | 0.605236 | ||||||||
\(808\) | −1.73249e19 | −2.19027 | ||||||||
\(809\) | 5.01001e18 | 0.628309 | 0.314155 | − | 0.949372i | \(-0.398279\pi\) | ||||
0.314155 | + | 0.949372i | \(0.398279\pi\) | |||||||
\(810\) | −1.39193e19 | −1.73167 | ||||||||
\(811\) | −2.87604e18 | −0.354944 | −0.177472 | − | 0.984126i | \(-0.556792\pi\) | ||||
−0.177472 | + | 0.984126i | \(0.556792\pi\) | |||||||
\(812\) | 7.81468e18 | 0.956747 | ||||||||
\(813\) | −6.06489e18 | −0.736604 | ||||||||
\(814\) | 1.27519e19 | 1.53644 | ||||||||
\(815\) | −4.03305e17 | −0.0482069 | ||||||||
\(816\) | −4.11545e19 | −4.88013 | ||||||||
\(817\) | 1.92900e18 | 0.226928 | ||||||||
\(818\) | 1.00914e19 | 1.17776 | ||||||||
\(819\) | 9.53775e17 | 0.110433 | ||||||||
\(820\) | 2.60941e19 | 2.99746 | ||||||||
\(821\) | −3.04163e18 | −0.346638 | −0.173319 | − | 0.984866i | \(-0.555449\pi\) | ||||
−0.173319 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(822\) | 2.85727e19 | 3.23061 | ||||||||
\(823\) | 8.88153e18 | 0.996297 | 0.498148 | − | 0.867092i | \(-0.334013\pi\) | ||||
0.498148 | + | 0.867092i | \(0.334013\pi\) | |||||||
\(824\) | −6.66509e18 | −0.741787 | ||||||||
\(825\) | −4.67596e18 | −0.516322 | ||||||||
\(826\) | 3.84245e18 | 0.420957 | ||||||||
\(827\) | 1.32121e19 | 1.43610 | 0.718050 | − | 0.695992i | \(-0.245035\pi\) | ||||
0.718050 | + | 0.695992i | \(0.245035\pi\) | |||||||
\(828\) | 1.37748e19 | 1.48555 | ||||||||
\(829\) | −1.05788e19 | −1.13196 | −0.565979 | − | 0.824419i | \(-0.691502\pi\) | ||||
−0.565979 | + | 0.824419i | \(0.691502\pi\) | |||||||
\(830\) | −2.74931e19 | −2.91887 | ||||||||
\(831\) | −8.45416e18 | −0.890561 | ||||||||
\(832\) | 7.28466e17 | 0.0761391 | ||||||||
\(833\) | −1.47203e19 | −1.52660 | ||||||||
\(834\) | −2.99368e19 | −3.08054 | ||||||||
\(835\) | −9.42193e18 | −0.962006 | ||||||||
\(836\) | 5.12515e19 | 5.19237 | ||||||||
\(837\) | −2.02423e18 | −0.203491 | ||||||||
\(838\) | −2.56963e19 | −2.56321 | ||||||||
\(839\) | 3.91972e18 | 0.387974 | 0.193987 | − | 0.981004i | \(-0.437858\pi\) | ||||
0.193987 | + | 0.981004i | \(0.437858\pi\) | |||||||
\(840\) | −1.13450e19 | −1.11426 | ||||||||
\(841\) | 1.65359e18 | 0.161159 | ||||||||
\(842\) | 2.10388e19 | 2.03466 | ||||||||
\(843\) | −9.88764e18 | −0.948884 | ||||||||
\(844\) | −2.65780e19 | −2.53103 | ||||||||
\(845\) | 8.46960e18 | 0.800377 | ||||||||
\(846\) | 1.86593e19 | 1.74980 | ||||||||
\(847\) | 8.41208e18 | 0.782819 | ||||||||
\(848\) | 1.07018e19 | 0.988291 | ||||||||
\(849\) | 1.74636e19 | 1.60042 | ||||||||
\(850\) | 7.68969e18 | 0.699336 | ||||||||
\(851\) | 3.81804e18 | 0.344587 | ||||||||
\(852\) | −4.81995e19 | −4.31703 | ||||||||
\(853\) | −1.56876e19 | −1.39440 | −0.697200 | − | 0.716876i | \(-0.745571\pi\) | ||||
−0.697200 | + | 0.716876i | \(0.745571\pi\) | |||||||
\(854\) | −5.23558e18 | −0.461837 | ||||||||
\(855\) | 1.20849e19 | 1.05794 | ||||||||
\(856\) | 2.54752e19 | 2.21329 | ||||||||
\(857\) | −1.02998e19 | −0.888083 | −0.444041 | − | 0.896006i | \(-0.646456\pi\) | ||||
−0.444041 | + | 0.896006i | \(0.646456\pi\) | |||||||
\(858\) | −1.58795e19 | −1.35885 | ||||||||
\(859\) | 8.47145e18 | 0.719453 | 0.359726 | − | 0.933058i | \(-0.382870\pi\) | ||||
0.359726 | + | 0.933058i | \(0.382870\pi\) | |||||||
\(860\) | 4.19770e18 | 0.353811 | ||||||||
\(861\) | 9.45534e18 | 0.790964 | ||||||||
\(862\) | −1.87789e19 | −1.55910 | ||||||||
\(863\) | −3.58662e18 | −0.295539 | −0.147770 | − | 0.989022i | \(-0.547209\pi\) | ||||
−0.147770 | + | 0.989022i | \(0.547209\pi\) | |||||||
\(864\) | −1.72753e18 | −0.141281 | ||||||||
\(865\) | 1.41279e19 | 1.14676 | ||||||||
\(866\) | −3.70777e19 | −2.98708 | ||||||||
\(867\) | −3.85286e19 | −3.08077 | ||||||||
\(868\) | −1.96041e19 | −1.55586 | ||||||||
\(869\) | −9.41417e18 | −0.741572 | ||||||||
\(870\) | −3.06789e19 | −2.39864 | ||||||||
\(871\) | −7.04508e18 | −0.546724 | ||||||||
\(872\) | −3.89644e19 | −3.00131 | ||||||||
\(873\) | −1.19471e18 | −0.0913416 | ||||||||
\(874\) | 2.20388e19 | 1.67249 | ||||||||
\(875\) | 5.53448e18 | 0.416893 | ||||||||
\(876\) | 5.34664e18 | 0.399764 | ||||||||
\(877\) | −2.00115e19 | −1.48519 | −0.742594 | − | 0.669742i | \(-0.766405\pi\) | ||||
−0.742594 | + | 0.669742i | \(0.766405\pi\) | |||||||
\(878\) | 1.48980e19 | 1.09752 | ||||||||
\(879\) | 3.26826e19 | 2.38995 | ||||||||
\(880\) | 4.16573e19 | 3.02380 | ||||||||
\(881\) | −2.31276e19 | −1.66643 | −0.833216 | − | 0.552947i | \(-0.813503\pi\) | ||||
−0.833216 | + | 0.552947i | \(0.813503\pi\) | |||||||
\(882\) | 1.97548e19 | 1.41295 | ||||||||
\(883\) | 4.18896e18 | 0.297414 | 0.148707 | − | 0.988881i | \(-0.452489\pi\) | ||||
0.148707 | + | 0.988881i | \(0.452489\pi\) | |||||||
\(884\) | 1.81827e19 | 1.28150 | ||||||||
\(885\) | −1.05031e19 | −0.734832 | ||||||||
\(886\) | 3.96477e19 | 2.75359 | ||||||||
\(887\) | 1.02860e19 | 0.709156 | 0.354578 | − | 0.935026i | \(-0.384625\pi\) | ||||
0.354578 | + | 0.935026i | \(0.384625\pi\) | |||||||
\(888\) | 2.31069e19 | 1.58146 | ||||||||
\(889\) | 1.58223e18 | 0.107500 | ||||||||
\(890\) | 2.03338e19 | 1.37146 | ||||||||
\(891\) | 2.79546e19 | 1.87175 | ||||||||
\(892\) | 1.79785e19 | 1.19504 | ||||||||
\(893\) | 2.07865e19 | 1.37166 | ||||||||
\(894\) | 4.46465e19 | 2.92478 | ||||||||
\(895\) | −2.06108e19 | −1.34043 | ||||||||
\(896\) | 4.63543e18 | 0.299287 | ||||||||
\(897\) | −4.75448e18 | −0.304756 | ||||||||
\(898\) | −1.15477e19 | −0.734854 | ||||||||
\(899\) | −2.98884e19 | −1.88827 | ||||||||
\(900\) | −7.18534e18 | −0.450683 | ||||||||
\(901\) | 1.45207e19 | 0.904224 | ||||||||
\(902\) | −7.52656e19 | −4.65322 | ||||||||
\(903\) | 1.52106e18 | 0.0933631 | ||||||||
\(904\) | −5.71933e18 | −0.348538 | ||||||||
\(905\) | −5.68473e17 | −0.0343949 | ||||||||
\(906\) | −1.37968e19 | −0.828790 | ||||||||
\(907\) | −2.94735e18 | −0.175786 | −0.0878929 | − | 0.996130i | \(-0.528013\pi\) | ||||
−0.0878929 | + | 0.996130i | \(0.528013\pi\) | |||||||
\(908\) | 4.14506e19 | 2.45455 | ||||||||
\(909\) | 1.45521e19 | 0.855580 | ||||||||
\(910\) | 3.32071e18 | 0.193848 | ||||||||
\(911\) | 8.76223e18 | 0.507861 | 0.253931 | − | 0.967222i | \(-0.418276\pi\) | ||||
0.253931 | + | 0.967222i | \(0.418276\pi\) | |||||||
\(912\) | 6.15262e19 | 3.54074 | ||||||||
\(913\) | 5.52152e19 | 3.15500 | ||||||||
\(914\) | 4.23486e18 | 0.240264 | ||||||||
\(915\) | 1.43112e19 | 0.806191 | ||||||||
\(916\) | −6.36810e19 | −3.56196 | ||||||||
\(917\) | 8.79777e18 | 0.488621 | ||||||||
\(918\) | −6.86232e18 | −0.378437 | ||||||||
\(919\) | 2.22512e19 | 1.21844 | 0.609218 | − | 0.793003i | \(-0.291484\pi\) | ||||
0.609218 | + | 0.793003i | \(0.291484\pi\) | |||||||
\(920\) | 2.70388e19 | 1.47016 | ||||||||
\(921\) | −1.85217e19 | −0.999983 | ||||||||
\(922\) | 1.23082e19 | 0.659846 | ||||||||
\(923\) | 7.95406e18 | 0.423426 | ||||||||
\(924\) | 4.04130e19 | 2.13625 | ||||||||
\(925\) | −1.99161e18 | −0.104540 | ||||||||
\(926\) | −3.93006e19 | −2.04846 | ||||||||
\(927\) | 5.59835e18 | 0.289762 | ||||||||
\(928\) | −2.55074e19 | −1.31101 | ||||||||
\(929\) | 2.18098e19 | 1.11314 | 0.556570 | − | 0.830801i | \(-0.312117\pi\) | ||||
0.556570 | + | 0.830801i | \(0.312117\pi\) | |||||||
\(930\) | 7.69620e19 | 3.90065 | ||||||||
\(931\) | 2.20070e19 | 1.10761 | ||||||||
\(932\) | 5.23376e19 | 2.61583 | ||||||||
\(933\) | −4.75991e19 | −2.36248 | ||||||||
\(934\) | 4.92691e18 | 0.242840 | ||||||||
\(935\) | 5.65223e19 | 2.76659 | ||||||||
\(936\) | −1.37573e19 | −0.668712 | ||||||||
\(937\) | 3.47028e18 | 0.167517 | 0.0837583 | − | 0.996486i | \(-0.473308\pi\) | ||||
0.0837583 | + | 0.996486i | \(0.473308\pi\) | |||||||
\(938\) | 2.57505e19 | 1.23443 | ||||||||
\(939\) | 1.64663e19 | 0.783914 | ||||||||
\(940\) | 4.52337e19 | 2.13861 | ||||||||
\(941\) | −9.03591e18 | −0.424267 | −0.212134 | − | 0.977241i | \(-0.568041\pi\) | ||||
−0.212134 | + | 0.977241i | \(0.568041\pi\) | |||||||
\(942\) | 6.28303e19 | 2.92980 | ||||||||
\(943\) | −2.25352e19 | −1.04360 | ||||||||
\(944\) | −2.55661e19 | −1.17583 | ||||||||
\(945\) | −8.72621e17 | −0.0398583 | ||||||||
\(946\) | −1.21078e19 | −0.549253 | ||||||||
\(947\) | −2.42336e18 | −0.109180 | −0.0545901 | − | 0.998509i | \(-0.517385\pi\) | ||||
−0.0545901 | + | 0.998509i | \(0.517385\pi\) | |||||||
\(948\) | −3.02574e19 | −1.35387 | ||||||||
\(949\) | −8.82321e17 | −0.0392099 | ||||||||
\(950\) | −1.14961e19 | −0.507398 | ||||||||
\(951\) | −2.63645e18 | −0.115570 | ||||||||
\(952\) | −3.74694e19 | −1.63131 | ||||||||
\(953\) | −2.10889e18 | −0.0911907 | −0.0455954 | − | 0.998960i | \(-0.514518\pi\) | ||||
−0.0455954 | + | 0.998960i | \(0.514518\pi\) | |||||||
\(954\) | −1.94869e19 | −0.836910 | ||||||||
\(955\) | 2.31986e19 | 0.989555 | ||||||||
\(956\) | 3.62152e19 | 1.53431 | ||||||||
\(957\) | 6.16134e19 | 2.59267 | ||||||||
\(958\) | 3.81748e19 | 1.59551 | ||||||||
\(959\) | 1.20000e19 | 0.498148 | ||||||||
\(960\) | 7.27814e18 | 0.300094 | ||||||||
\(961\) | 5.05614e19 | 2.07070 | ||||||||
\(962\) | −6.76349e18 | −0.275127 | ||||||||
\(963\) | −2.13979e19 | −0.864571 | ||||||||
\(964\) | 1.81065e19 | 0.726663 | ||||||||
\(965\) | −3.80240e19 | −1.51576 | ||||||||
\(966\) | 1.73781e19 | 0.688101 | ||||||||
\(967\) | 2.53391e19 | 0.996596 | 0.498298 | − | 0.867006i | \(-0.333959\pi\) | ||||
0.498298 | + | 0.867006i | \(0.333959\pi\) | |||||||
\(968\) | −1.21336e20 | −4.74023 | ||||||||
\(969\) | 8.34813e19 | 3.23955 | ||||||||
\(970\) | −4.15955e18 | −0.160336 | ||||||||
\(971\) | −2.98802e19 | −1.14408 | −0.572042 | − | 0.820224i | \(-0.693849\pi\) | ||||
−0.572042 | + | 0.820224i | \(0.693849\pi\) | |||||||
\(972\) | 8.28474e19 | 3.15100 | ||||||||
\(973\) | −1.25729e19 | −0.475008 | ||||||||
\(974\) | −6.25661e19 | −2.34804 | ||||||||
\(975\) | 2.48008e18 | 0.0924562 | ||||||||
\(976\) | 3.48353e19 | 1.29002 | ||||||||
\(977\) | −5.02894e18 | −0.184996 | −0.0924979 | − | 0.995713i | \(-0.529485\pi\) | ||||
−0.0924979 | + | 0.995713i | \(0.529485\pi\) | |||||||
\(978\) | 3.73884e18 | 0.136626 | ||||||||
\(979\) | −4.08371e19 | −1.48241 | ||||||||
\(980\) | 4.78895e19 | 1.72691 | ||||||||
\(981\) | 3.27282e19 | 1.17239 | ||||||||
\(982\) | −4.56214e19 | −1.62347 | ||||||||
\(983\) | 6.49435e18 | 0.229582 | 0.114791 | − | 0.993390i | \(-0.463380\pi\) | ||||
0.114791 | + | 0.993390i | \(0.463380\pi\) | |||||||
\(984\) | −1.36384e20 | −4.78956 | ||||||||
\(985\) | 1.80988e18 | 0.0631413 | ||||||||
\(986\) | −1.01324e20 | −3.51167 | ||||||||
\(987\) | 1.63907e19 | 0.564333 | ||||||||
\(988\) | −2.71833e19 | −0.929782 | ||||||||
\(989\) | −3.62518e18 | −0.123184 | ||||||||
\(990\) | −7.58536e19 | −2.56063 | ||||||||
\(991\) | 3.22546e19 | 1.08172 | 0.540858 | − | 0.841114i | \(-0.318100\pi\) | ||||
0.540858 | + | 0.841114i | \(0.318100\pi\) | |||||||
\(992\) | 6.39887e19 | 2.13195 | ||||||||
\(993\) | −4.64048e19 | −1.53601 | ||||||||
\(994\) | −2.90730e19 | −0.956044 | ||||||||
\(995\) | 3.23736e19 | 1.05765 | ||||||||
\(996\) | 1.77463e20 | 5.76000 | ||||||||
\(997\) | 8.49999e17 | 0.0274094 | 0.0137047 | − | 0.999906i | \(-0.495638\pi\) | ||||
0.0137047 | + | 0.999906i | \(0.495638\pi\) | |||||||
\(998\) | −3.71155e18 | −0.118907 | ||||||||
\(999\) | 1.77732e18 | 0.0565705 |
(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 | 197.14.a.a.1.6 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.6 | ✓ | 104 | 1.1 | even | 1 | trivial |