Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.13 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.8994 | −0.240846 | −0.120423 | − | 0.992723i | \(-0.538425\pi\) | ||||
−0.120423 | + | 0.992723i | \(0.538425\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −1929.20 | −0.941993 | ||||||||
\(5\) | 3570.42 | 0.510957 | 0.255478 | − | 0.966815i | \(-0.417767\pi\) | ||||
0.255478 | + | 0.966815i | \(0.417767\pi\) | |||||||
\(6\) | 2648.56 | 0.139052 | ||||||||
\(7\) | −66491.5 | −1.49529 | −0.747647 | − | 0.664096i | \(-0.768817\pi\) | ||||
−0.747647 | + | 0.664096i | \(0.768817\pi\) | |||||||
\(8\) | 43349.2 | 0.467721 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −38915.5 | −0.123062 | ||||||||
\(11\) | −586024. | −1.09712 | −0.548562 | − | 0.836110i | \(-0.684824\pi\) | ||||
−0.548562 | + | 0.836110i | \(0.684824\pi\) | |||||||
\(12\) | 468796. | 0.543860 | ||||||||
\(13\) | −248702. | −0.185776 | −0.0928881 | − | 0.995677i | \(-0.529610\pi\) | ||||
−0.0928881 | + | 0.995677i | \(0.529610\pi\) | |||||||
\(14\) | 724720. | 0.360135 | ||||||||
\(15\) | −867612. | −0.295001 | ||||||||
\(16\) | 3.47852e6 | 0.829345 | ||||||||
\(17\) | 3.17341e6 | 0.542073 | 0.271036 | − | 0.962569i | \(-0.412634\pi\) | ||||
0.271036 | + | 0.962569i | \(0.412634\pi\) | |||||||
\(18\) | −643601. | −0.0802819 | ||||||||
\(19\) | −8.29582e6 | −0.768625 | −0.384312 | − | 0.923203i | \(-0.625561\pi\) | ||||
−0.384312 | + | 0.923203i | \(0.625561\pi\) | |||||||
\(20\) | −6.88806e6 | −0.481318 | ||||||||
\(21\) | 1.61574e7 | 0.863309 | ||||||||
\(22\) | 6.38733e6 | 0.264237 | ||||||||
\(23\) | 4.26559e7 | 1.38190 | 0.690949 | − | 0.722903i | \(-0.257193\pi\) | ||||
0.690949 | + | 0.722903i | \(0.257193\pi\) | |||||||
\(24\) | −1.05339e7 | −0.270039 | ||||||||
\(25\) | −3.60802e7 | −0.738923 | ||||||||
\(26\) | 2.71071e6 | 0.0447434 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 1.28276e8 | 1.40856 | ||||||||
\(29\) | −2.96146e7 | −0.268113 | −0.134056 | − | 0.990974i | \(-0.542800\pi\) | ||||
−0.134056 | + | 0.990974i | \(0.542800\pi\) | |||||||
\(30\) | 9.45648e6 | 0.0710497 | ||||||||
\(31\) | 7.28074e7 | 0.456758 | 0.228379 | − | 0.973572i | \(-0.426657\pi\) | ||||
0.228379 | + | 0.973572i | \(0.426657\pi\) | |||||||
\(32\) | −1.26693e8 | −0.667465 | ||||||||
\(33\) | 1.42404e8 | 0.633425 | ||||||||
\(34\) | −3.45884e7 | −0.130556 | ||||||||
\(35\) | −2.37402e8 | −0.764031 | ||||||||
\(36\) | −1.13917e8 | −0.313998 | ||||||||
\(37\) | 4.75313e8 | 1.12686 | 0.563430 | − | 0.826164i | \(-0.309481\pi\) | ||||
0.563430 | + | 0.826164i | \(0.309481\pi\) | |||||||
\(38\) | 9.04197e7 | 0.185120 | ||||||||
\(39\) | 6.04345e7 | 0.107258 | ||||||||
\(40\) | 1.54775e8 | 0.238985 | ||||||||
\(41\) | 5.12374e7 | 0.0690679 | 0.0345339 | − | 0.999404i | \(-0.489005\pi\) | ||||
0.0345339 | + | 0.999404i | \(0.489005\pi\) | |||||||
\(42\) | −1.76107e8 | −0.207924 | ||||||||
\(43\) | −1.03154e9 | −1.07007 | −0.535033 | − | 0.844831i | \(-0.679701\pi\) | ||||
−0.535033 | + | 0.844831i | \(0.679701\pi\) | |||||||
\(44\) | 1.13056e9 | 1.03348 | ||||||||
\(45\) | 2.10830e8 | 0.170319 | ||||||||
\(46\) | −4.64925e8 | −0.332824 | ||||||||
\(47\) | 2.14124e9 | 1.36185 | 0.680923 | − | 0.732355i | \(-0.261579\pi\) | ||||
0.680923 | + | 0.732355i | \(0.261579\pi\) | |||||||
\(48\) | −8.45281e8 | −0.478822 | ||||||||
\(49\) | 2.44379e9 | 1.23591 | ||||||||
\(50\) | 3.93254e8 | 0.177966 | ||||||||
\(51\) | −7.71139e8 | −0.312966 | ||||||||
\(52\) | 4.79796e8 | 0.175000 | ||||||||
\(53\) | 1.08003e9 | 0.354747 | 0.177373 | − | 0.984144i | \(-0.443240\pi\) | ||||
0.177373 | + | 0.984144i | \(0.443240\pi\) | |||||||
\(54\) | 1.56395e8 | 0.0463508 | ||||||||
\(55\) | −2.09235e9 | −0.560583 | ||||||||
\(56\) | −2.88236e9 | −0.699380 | ||||||||
\(57\) | 2.01588e9 | 0.443766 | ||||||||
\(58\) | 3.22783e8 | 0.0645738 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 1.67380e9 | 0.277889 | ||||||||
\(61\) | 8.65057e9 | 1.31139 | 0.655693 | − | 0.755027i | \(-0.272377\pi\) | ||||
0.655693 | + | 0.755027i | \(0.272377\pi\) | |||||||
\(62\) | −7.93559e8 | −0.110008 | ||||||||
\(63\) | −3.92626e9 | −0.498432 | ||||||||
\(64\) | −5.74313e9 | −0.668589 | ||||||||
\(65\) | −8.87969e8 | −0.0949236 | ||||||||
\(66\) | −1.55212e9 | −0.152558 | ||||||||
\(67\) | 1.80367e10 | 1.63210 | 0.816048 | − | 0.577984i | \(-0.196161\pi\) | ||||
0.816048 | + | 0.577984i | \(0.196161\pi\) | |||||||
\(68\) | −6.12215e9 | −0.510629 | ||||||||
\(69\) | −1.03654e10 | −0.797840 | ||||||||
\(70\) | 2.58755e9 | 0.184014 | ||||||||
\(71\) | −7.45126e9 | −0.490127 | −0.245063 | − | 0.969507i | \(-0.578809\pi\) | ||||
−0.245063 | + | 0.969507i | \(0.578809\pi\) | |||||||
\(72\) | 2.55973e9 | 0.155907 | ||||||||
\(73\) | 2.81179e10 | 1.58748 | 0.793738 | − | 0.608259i | \(-0.208132\pi\) | ||||
0.793738 | + | 0.608259i | \(0.208132\pi\) | |||||||
\(74\) | −5.18064e9 | −0.271400 | ||||||||
\(75\) | 8.76750e9 | 0.426617 | ||||||||
\(76\) | 1.60043e10 | 0.724040 | ||||||||
\(77\) | 3.89656e10 | 1.64052 | ||||||||
\(78\) | −6.58701e8 | −0.0258326 | ||||||||
\(79\) | 1.85738e10 | 0.679128 | 0.339564 | − | 0.940583i | \(-0.389720\pi\) | ||||
0.339564 | + | 0.940583i | \(0.389720\pi\) | |||||||
\(80\) | 1.24198e10 | 0.423759 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −5.58459e8 | −0.0166347 | ||||||||
\(83\) | −2.72476e10 | −0.759273 | −0.379637 | − | 0.925136i | \(-0.623951\pi\) | ||||
−0.379637 | + | 0.925136i | \(0.623951\pi\) | |||||||
\(84\) | −3.11710e10 | −0.813231 | ||||||||
\(85\) | 1.13304e10 | 0.276976 | ||||||||
\(86\) | 1.12432e10 | 0.257721 | ||||||||
\(87\) | 7.19636e9 | 0.154795 | ||||||||
\(88\) | −2.54037e10 | −0.513147 | ||||||||
\(89\) | −4.76941e10 | −0.905356 | −0.452678 | − | 0.891674i | \(-0.649531\pi\) | ||||
−0.452678 | + | 0.891674i | \(0.649531\pi\) | |||||||
\(90\) | −2.29792e9 | −0.0410206 | ||||||||
\(91\) | 1.65365e10 | 0.277790 | ||||||||
\(92\) | −8.22919e10 | −1.30174 | ||||||||
\(93\) | −1.76922e10 | −0.263709 | ||||||||
\(94\) | −2.33383e10 | −0.327995 | ||||||||
\(95\) | −2.96195e10 | −0.392734 | ||||||||
\(96\) | 3.07864e10 | 0.385361 | ||||||||
\(97\) | 4.57032e10 | 0.540384 | 0.270192 | − | 0.962806i | \(-0.412913\pi\) | ||||
0.270192 | + | 0.962806i | \(0.412913\pi\) | |||||||
\(98\) | −2.66359e10 | −0.297663 | ||||||||
\(99\) | −3.46041e10 | −0.365708 | ||||||||
\(100\) | 6.96061e10 | 0.696061 | ||||||||
\(101\) | −1.05361e11 | −0.997499 | −0.498750 | − | 0.866746i | \(-0.666207\pi\) | ||||
−0.498750 | + | 0.866746i | \(0.666207\pi\) | |||||||
\(102\) | 8.40498e9 | 0.0753764 | ||||||||
\(103\) | 2.07637e10 | 0.176482 | 0.0882409 | − | 0.996099i | \(-0.471875\pi\) | ||||
0.0882409 | + | 0.996099i | \(0.471875\pi\) | |||||||
\(104\) | −1.07810e10 | −0.0868914 | ||||||||
\(105\) | 5.76888e10 | 0.441114 | ||||||||
\(106\) | −1.17717e10 | −0.0854393 | ||||||||
\(107\) | −1.61325e11 | −1.11197 | −0.555983 | − | 0.831194i | \(-0.687658\pi\) | ||||
−0.555983 | + | 0.831194i | \(0.687658\pi\) | |||||||
\(108\) | 2.76819e10 | 0.181287 | ||||||||
\(109\) | −8.08431e10 | −0.503265 | −0.251633 | − | 0.967823i | \(-0.580967\pi\) | ||||
−0.251633 | + | 0.967823i | \(0.580967\pi\) | |||||||
\(110\) | 2.28054e10 | 0.135014 | ||||||||
\(111\) | −1.15501e11 | −0.650593 | ||||||||
\(112\) | −2.31292e11 | −1.24012 | ||||||||
\(113\) | −1.96639e11 | −1.00401 | −0.502006 | − | 0.864864i | \(-0.667405\pi\) | ||||
−0.502006 | + | 0.864864i | \(0.667405\pi\) | |||||||
\(114\) | −2.19720e10 | −0.106879 | ||||||||
\(115\) | 1.52299e11 | 0.706090 | ||||||||
\(116\) | 5.71326e10 | 0.252560 | ||||||||
\(117\) | −1.46856e10 | −0.0619254 | ||||||||
\(118\) | −7.79227e9 | −0.0313554 | ||||||||
\(119\) | −2.11005e11 | −0.810558 | ||||||||
\(120\) | −3.76103e10 | −0.137978 | ||||||||
\(121\) | 5.81123e10 | 0.203680 | ||||||||
\(122\) | −9.42863e10 | −0.315842 | ||||||||
\(123\) | −1.24507e10 | −0.0398763 | ||||||||
\(124\) | −1.40460e11 | −0.430263 | ||||||||
\(125\) | −3.03158e11 | −0.888515 | ||||||||
\(126\) | 4.27940e10 | 0.120045 | ||||||||
\(127\) | 3.45018e11 | 0.926662 | 0.463331 | − | 0.886185i | \(-0.346654\pi\) | ||||
0.463331 | + | 0.886185i | \(0.346654\pi\) | |||||||
\(128\) | 3.22065e11 | 0.828492 | ||||||||
\(129\) | 2.50665e11 | 0.617803 | ||||||||
\(130\) | 9.67835e9 | 0.0228619 | ||||||||
\(131\) | 5.10254e11 | 1.15556 | 0.577782 | − | 0.816191i | \(-0.303918\pi\) | ||||
0.577782 | + | 0.816191i | \(0.303918\pi\) | |||||||
\(132\) | −2.74726e11 | −0.596682 | ||||||||
\(133\) | 5.51601e11 | 1.14932 | ||||||||
\(134\) | −1.96590e11 | −0.393083 | ||||||||
\(135\) | −5.12316e10 | −0.0983337 | ||||||||
\(136\) | 1.37565e11 | 0.253539 | ||||||||
\(137\) | 5.34579e11 | 0.946344 | 0.473172 | − | 0.880970i | \(-0.343109\pi\) | ||||
0.473172 | + | 0.880970i | \(0.343109\pi\) | |||||||
\(138\) | 1.12977e11 | 0.192156 | ||||||||
\(139\) | 5.71369e11 | 0.933974 | 0.466987 | − | 0.884264i | \(-0.345339\pi\) | ||||
0.466987 | + | 0.884264i | \(0.345339\pi\) | |||||||
\(140\) | 4.57997e11 | 0.719712 | ||||||||
\(141\) | −5.20322e11 | −0.786262 | ||||||||
\(142\) | 8.12145e10 | 0.118045 | ||||||||
\(143\) | 1.45745e11 | 0.203819 | ||||||||
\(144\) | 2.05403e11 | 0.276448 | ||||||||
\(145\) | −1.05737e11 | −0.136994 | ||||||||
\(146\) | −3.06469e11 | −0.382337 | ||||||||
\(147\) | −5.93841e11 | −0.713551 | ||||||||
\(148\) | −9.16975e11 | −1.06150 | ||||||||
\(149\) | 6.11636e11 | 0.682289 | 0.341145 | − | 0.940011i | \(-0.389185\pi\) | ||||
0.341145 | + | 0.940011i | \(0.389185\pi\) | |||||||
\(150\) | −9.55607e10 | −0.102749 | ||||||||
\(151\) | −9.59349e11 | −0.994497 | −0.497248 | − | 0.867608i | \(-0.665656\pi\) | ||||
−0.497248 | + | 0.867608i | \(0.665656\pi\) | |||||||
\(152\) | −3.59617e11 | −0.359502 | ||||||||
\(153\) | 1.87387e11 | 0.180691 | ||||||||
\(154\) | −4.24703e11 | −0.395113 | ||||||||
\(155\) | 2.59953e11 | 0.233384 | ||||||||
\(156\) | −1.16590e11 | −0.101036 | ||||||||
\(157\) | −1.46027e12 | −1.22175 | −0.610877 | − | 0.791725i | \(-0.709183\pi\) | ||||
−0.610877 | + | 0.791725i | \(0.709183\pi\) | |||||||
\(158\) | −2.02444e11 | −0.163565 | ||||||||
\(159\) | −2.62447e11 | −0.204813 | ||||||||
\(160\) | −4.52348e11 | −0.341046 | ||||||||
\(161\) | −2.83626e12 | −2.06635 | ||||||||
\(162\) | −3.80040e10 | −0.0267606 | ||||||||
\(163\) | −2.01632e12 | −1.37255 | −0.686273 | − | 0.727344i | \(-0.740755\pi\) | ||||
−0.686273 | + | 0.727344i | \(0.740755\pi\) | |||||||
\(164\) | −9.88473e10 | −0.0650615 | ||||||||
\(165\) | 5.08441e11 | 0.323653 | ||||||||
\(166\) | 2.96983e11 | 0.182868 | ||||||||
\(167\) | −2.14766e12 | −1.27946 | −0.639728 | − | 0.768601i | \(-0.720953\pi\) | ||||
−0.639728 | + | 0.768601i | \(0.720953\pi\) | |||||||
\(168\) | 7.00413e11 | 0.403788 | ||||||||
\(169\) | −1.73031e12 | −0.965487 | ||||||||
\(170\) | −1.23495e11 | −0.0667084 | ||||||||
\(171\) | −4.89860e11 | −0.256208 | ||||||||
\(172\) | 1.99005e12 | 1.00799 | ||||||||
\(173\) | 3.00631e12 | 1.47496 | 0.737481 | − | 0.675368i | \(-0.236015\pi\) | ||||
0.737481 | + | 0.675368i | \(0.236015\pi\) | |||||||
\(174\) | −7.84362e10 | −0.0372817 | ||||||||
\(175\) | 2.39903e12 | 1.10491 | ||||||||
\(176\) | −2.03850e12 | −0.909894 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | 5.19839e11 | 0.218051 | ||||||||
\(179\) | −2.89437e12 | −1.17723 | −0.588617 | − | 0.808412i | \(-0.700327\pi\) | ||||
−0.588617 | + | 0.808412i | \(0.700327\pi\) | |||||||
\(180\) | −4.06733e11 | −0.160439 | ||||||||
\(181\) | −4.77947e12 | −1.82872 | −0.914361 | − | 0.404899i | \(-0.867307\pi\) | ||||
−0.914361 | + | 0.404899i | \(0.867307\pi\) | |||||||
\(182\) | −1.80239e11 | −0.0669046 | ||||||||
\(183\) | −2.10209e12 | −0.757129 | ||||||||
\(184\) | 1.84910e12 | 0.646343 | ||||||||
\(185\) | 1.69707e12 | 0.575777 | ||||||||
\(186\) | 1.92835e11 | 0.0635133 | ||||||||
\(187\) | −1.85970e12 | −0.594721 | ||||||||
\(188\) | −4.13089e12 | −1.28285 | ||||||||
\(189\) | 9.54080e11 | 0.287770 | ||||||||
\(190\) | 3.22836e11 | 0.0945883 | ||||||||
\(191\) | −4.41995e12 | −1.25815 | −0.629077 | − | 0.777343i | \(-0.716567\pi\) | ||||
−0.629077 | + | 0.777343i | \(0.716567\pi\) | |||||||
\(192\) | 1.39558e12 | 0.386010 | ||||||||
\(193\) | 3.26145e12 | 0.876688 | 0.438344 | − | 0.898807i | \(-0.355565\pi\) | ||||
0.438344 | + | 0.898807i | \(0.355565\pi\) | |||||||
\(194\) | −4.98139e11 | −0.130149 | ||||||||
\(195\) | 2.15776e11 | 0.0548042 | ||||||||
\(196\) | −4.71457e12 | −1.16422 | ||||||||
\(197\) | 1.75273e12 | 0.420873 | 0.210437 | − | 0.977608i | \(-0.432511\pi\) | ||||
0.210437 | + | 0.977608i | \(0.432511\pi\) | |||||||
\(198\) | 3.77165e11 | 0.0880792 | ||||||||
\(199\) | 1.26489e12 | 0.287317 | 0.143658 | − | 0.989627i | \(-0.454113\pi\) | ||||
0.143658 | + | 0.989627i | \(0.454113\pi\) | |||||||
\(200\) | −1.56405e12 | −0.345610 | ||||||||
\(201\) | −4.38292e12 | −0.942291 | ||||||||
\(202\) | 1.14838e12 | 0.240243 | ||||||||
\(203\) | 1.96912e12 | 0.400908 | ||||||||
\(204\) | 1.48768e12 | 0.294812 | ||||||||
\(205\) | 1.82939e11 | 0.0352907 | ||||||||
\(206\) | −2.26313e11 | −0.0425049 | ||||||||
\(207\) | 2.51879e12 | 0.460633 | ||||||||
\(208\) | −8.65114e11 | −0.154072 | ||||||||
\(209\) | 4.86155e12 | 0.843276 | ||||||||
\(210\) | −6.28775e11 | −0.106240 | ||||||||
\(211\) | −9.77199e12 | −1.60853 | −0.804266 | − | 0.594270i | \(-0.797441\pi\) | ||||
−0.804266 | + | 0.594270i | \(0.797441\pi\) | |||||||
\(212\) | −2.08360e12 | −0.334169 | ||||||||
\(213\) | 1.81066e12 | 0.282975 | ||||||||
\(214\) | 1.75835e12 | 0.267812 | ||||||||
\(215\) | −3.68304e12 | −0.546757 | ||||||||
\(216\) | −6.22014e11 | −0.0900129 | ||||||||
\(217\) | −4.84107e12 | −0.682988 | ||||||||
\(218\) | 8.81143e11 | 0.121209 | ||||||||
\(219\) | −6.83265e12 | −0.916530 | ||||||||
\(220\) | 4.03657e12 | 0.528065 | ||||||||
\(221\) | −7.89232e11 | −0.100704 | ||||||||
\(222\) | 1.25890e12 | 0.156693 | ||||||||
\(223\) | 9.61626e11 | 0.116770 | 0.0583848 | − | 0.998294i | \(-0.481405\pi\) | ||||
0.0583848 | + | 0.998294i | \(0.481405\pi\) | |||||||
\(224\) | 8.42402e12 | 0.998057 | ||||||||
\(225\) | −2.13050e12 | −0.246308 | ||||||||
\(226\) | 2.14326e12 | 0.241812 | ||||||||
\(227\) | −1.49335e13 | −1.64444 | −0.822221 | − | 0.569168i | \(-0.807265\pi\) | ||||
−0.822221 | + | 0.569168i | \(0.807265\pi\) | |||||||
\(228\) | −3.88905e12 | −0.418024 | ||||||||
\(229\) | 3.29995e12 | 0.346268 | 0.173134 | − | 0.984898i | \(-0.444611\pi\) | ||||
0.173134 | + | 0.984898i | \(0.444611\pi\) | |||||||
\(230\) | −1.65998e12 | −0.170059 | ||||||||
\(231\) | −9.46864e12 | −0.947157 | ||||||||
\(232\) | −1.28377e12 | −0.125402 | ||||||||
\(233\) | 5.24978e12 | 0.500822 | 0.250411 | − | 0.968140i | \(-0.419434\pi\) | ||||
0.250411 | + | 0.968140i | \(0.419434\pi\) | |||||||
\(234\) | 1.60064e11 | 0.0149145 | ||||||||
\(235\) | 7.64514e12 | 0.695844 | ||||||||
\(236\) | −1.37923e12 | −0.122637 | ||||||||
\(237\) | −4.51343e12 | −0.392095 | ||||||||
\(238\) | 2.29983e12 | 0.195219 | ||||||||
\(239\) | −1.06137e13 | −0.880400 | −0.440200 | − | 0.897900i | \(-0.645092\pi\) | ||||
−0.440200 | + | 0.897900i | \(0.645092\pi\) | |||||||
\(240\) | −3.01801e12 | −0.244658 | ||||||||
\(241\) | 6.93809e12 | 0.549726 | 0.274863 | − | 0.961483i | \(-0.411368\pi\) | ||||
0.274863 | + | 0.961483i | \(0.411368\pi\) | |||||||
\(242\) | −6.33391e11 | −0.0490555 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | −1.66887e13 | −1.23532 | ||||||||
\(245\) | 8.72536e12 | 0.631495 | ||||||||
\(246\) | 1.35705e11 | 0.00960405 | ||||||||
\(247\) | 2.06318e12 | 0.142792 | ||||||||
\(248\) | 3.15615e12 | 0.213635 | ||||||||
\(249\) | 6.62116e12 | 0.438367 | ||||||||
\(250\) | 3.30425e12 | 0.213995 | ||||||||
\(251\) | 1.08474e13 | 0.687258 | 0.343629 | − | 0.939106i | \(-0.388344\pi\) | ||||
0.343629 | + | 0.939106i | \(0.388344\pi\) | |||||||
\(252\) | 7.57454e12 | 0.469519 | ||||||||
\(253\) | −2.49974e13 | −1.51611 | ||||||||
\(254\) | −3.76050e12 | −0.223183 | ||||||||
\(255\) | −2.75329e12 | −0.159912 | ||||||||
\(256\) | 8.25162e12 | 0.469050 | ||||||||
\(257\) | −5.95164e12 | −0.331135 | −0.165567 | − | 0.986198i | \(-0.552945\pi\) | ||||
−0.165567 | + | 0.986198i | \(0.552945\pi\) | |||||||
\(258\) | −2.73210e12 | −0.148795 | ||||||||
\(259\) | −3.16043e13 | −1.68499 | ||||||||
\(260\) | 1.71307e12 | 0.0894174 | ||||||||
\(261\) | −1.74871e12 | −0.0893709 | ||||||||
\(262\) | −5.56148e12 | −0.278313 | ||||||||
\(263\) | −8.89001e12 | −0.435658 | −0.217829 | − | 0.975987i | \(-0.569897\pi\) | ||||
−0.217829 | + | 0.975987i | \(0.569897\pi\) | |||||||
\(264\) | 6.17310e12 | 0.296266 | ||||||||
\(265\) | 3.85616e12 | 0.181260 | ||||||||
\(266\) | −6.01214e12 | −0.276809 | ||||||||
\(267\) | 1.15897e13 | 0.522708 | ||||||||
\(268\) | −3.47964e13 | −1.53742 | ||||||||
\(269\) | 4.16303e13 | 1.80207 | 0.901037 | − | 0.433743i | \(-0.142807\pi\) | ||||
0.901037 | + | 0.433743i | \(0.142807\pi\) | |||||||
\(270\) | 5.58396e11 | 0.0236832 | ||||||||
\(271\) | −3.20752e13 | −1.33302 | −0.666512 | − | 0.745494i | \(-0.732213\pi\) | ||||
−0.666512 | + | 0.745494i | \(0.732213\pi\) | |||||||
\(272\) | 1.10388e13 | 0.449565 | ||||||||
\(273\) | −4.01838e12 | −0.160382 | ||||||||
\(274\) | −5.82661e12 | −0.227923 | ||||||||
\(275\) | 2.11439e13 | 0.810690 | ||||||||
\(276\) | 1.99969e13 | 0.751560 | ||||||||
\(277\) | 3.14801e13 | 1.15984 | 0.579919 | − | 0.814674i | \(-0.303084\pi\) | ||||
0.579919 | + | 0.814674i | \(0.303084\pi\) | |||||||
\(278\) | −6.22759e12 | −0.224944 | ||||||||
\(279\) | 4.29920e12 | 0.152253 | ||||||||
\(280\) | −1.02912e13 | −0.357353 | ||||||||
\(281\) | −1.35973e13 | −0.462987 | −0.231493 | − | 0.972836i | \(-0.574361\pi\) | ||||
−0.231493 | + | 0.972836i | \(0.574361\pi\) | |||||||
\(282\) | 5.67122e12 | 0.189368 | ||||||||
\(283\) | 2.32657e13 | 0.761886 | 0.380943 | − | 0.924598i | \(-0.375599\pi\) | ||||
0.380943 | + | 0.924598i | \(0.375599\pi\) | |||||||
\(284\) | 1.43750e13 | 0.461696 | ||||||||
\(285\) | 7.19755e12 | 0.226745 | ||||||||
\(286\) | −1.58854e12 | −0.0490890 | ||||||||
\(287\) | −3.40685e12 | −0.103277 | ||||||||
\(288\) | −7.48111e12 | −0.222488 | ||||||||
\(289\) | −2.42014e13 | −0.706157 | ||||||||
\(290\) | 1.15247e12 | 0.0329944 | ||||||||
\(291\) | −1.11059e13 | −0.311991 | ||||||||
\(292\) | −5.42451e13 | −1.49539 | ||||||||
\(293\) | 3.24702e13 | 0.878442 | 0.439221 | − | 0.898379i | \(-0.355255\pi\) | ||||
0.439221 | + | 0.898379i | \(0.355255\pi\) | |||||||
\(294\) | 6.47253e12 | 0.171856 | ||||||||
\(295\) | 2.55258e12 | 0.0665209 | ||||||||
\(296\) | 2.06045e13 | 0.527056 | ||||||||
\(297\) | 8.40880e12 | 0.211142 | ||||||||
\(298\) | −6.66648e12 | −0.164326 | ||||||||
\(299\) | −1.06086e13 | −0.256724 | ||||||||
\(300\) | −1.69143e13 | −0.401871 | ||||||||
\(301\) | 6.85888e13 | 1.60006 | ||||||||
\(302\) | 1.04564e13 | 0.239520 | ||||||||
\(303\) | 2.56027e13 | 0.575907 | ||||||||
\(304\) | −2.88572e13 | −0.637455 | ||||||||
\(305\) | 3.08862e13 | 0.670062 | ||||||||
\(306\) | −2.04241e12 | −0.0435186 | ||||||||
\(307\) | 2.27591e13 | 0.476315 | 0.238158 | − | 0.971226i | \(-0.423456\pi\) | ||||
0.238158 | + | 0.971226i | \(0.423456\pi\) | |||||||
\(308\) | −7.51725e13 | −1.54536 | ||||||||
\(309\) | −5.04558e12 | −0.101892 | ||||||||
\(310\) | −2.83334e12 | −0.0562094 | ||||||||
\(311\) | 5.49995e13 | 1.07195 | 0.535977 | − | 0.844233i | \(-0.319943\pi\) | ||||
0.535977 | + | 0.844233i | \(0.319943\pi\) | |||||||
\(312\) | 2.61979e12 | 0.0501668 | ||||||||
\(313\) | −1.78455e13 | −0.335765 | −0.167882 | − | 0.985807i | \(-0.553693\pi\) | ||||
−0.167882 | + | 0.985807i | \(0.553693\pi\) | |||||||
\(314\) | 1.59161e13 | 0.294254 | ||||||||
\(315\) | −1.40184e13 | −0.254677 | ||||||||
\(316\) | −3.58326e13 | −0.639734 | ||||||||
\(317\) | 4.88368e13 | 0.856882 | 0.428441 | − | 0.903570i | \(-0.359063\pi\) | ||||
0.428441 | + | 0.903570i | \(0.359063\pi\) | |||||||
\(318\) | 2.86053e12 | 0.0493284 | ||||||||
\(319\) | 1.73549e13 | 0.294153 | ||||||||
\(320\) | −2.05054e13 | −0.341620 | ||||||||
\(321\) | 3.92020e13 | 0.641994 | ||||||||
\(322\) | 3.09136e13 | 0.497671 | ||||||||
\(323\) | −2.63261e13 | −0.416650 | ||||||||
\(324\) | −6.72671e12 | −0.104666 | ||||||||
\(325\) | 8.97321e12 | 0.137274 | ||||||||
\(326\) | 2.19767e13 | 0.330572 | ||||||||
\(327\) | 1.96449e13 | 0.290560 | ||||||||
\(328\) | 2.22110e12 | 0.0323045 | ||||||||
\(329\) | −1.42374e14 | −2.03636 | ||||||||
\(330\) | −5.54172e12 | −0.0779503 | ||||||||
\(331\) | 1.00303e14 | 1.38758 | 0.693791 | − | 0.720177i | \(-0.255939\pi\) | ||||
0.693791 | + | 0.720177i | \(0.255939\pi\) | |||||||
\(332\) | 5.25661e13 | 0.715230 | ||||||||
\(333\) | 2.80668e13 | 0.375620 | ||||||||
\(334\) | 2.34083e13 | 0.308151 | ||||||||
\(335\) | 6.43986e13 | 0.833930 | ||||||||
\(336\) | 5.62040e13 | 0.715981 | ||||||||
\(337\) | 5.21287e12 | 0.0653299 | 0.0326650 | − | 0.999466i | \(-0.489601\pi\) | ||||
0.0326650 | + | 0.999466i | \(0.489601\pi\) | |||||||
\(338\) | 1.88594e13 | 0.232533 | ||||||||
\(339\) | 4.77834e13 | 0.579667 | ||||||||
\(340\) | −2.18587e13 | −0.260909 | ||||||||
\(341\) | −4.26669e13 | −0.501120 | ||||||||
\(342\) | 5.33919e12 | 0.0617067 | ||||||||
\(343\) | −3.10160e13 | −0.352750 | ||||||||
\(344\) | −4.47166e13 | −0.500492 | ||||||||
\(345\) | −3.70088e13 | −0.407662 | ||||||||
\(346\) | −3.27671e13 | −0.355238 | ||||||||
\(347\) | −8.57886e12 | −0.0915413 | −0.0457707 | − | 0.998952i | \(-0.514574\pi\) | ||||
−0.0457707 | + | 0.998952i | \(0.514574\pi\) | |||||||
\(348\) | −1.38832e13 | −0.145816 | ||||||||
\(349\) | 6.67566e13 | 0.690167 | 0.345083 | − | 0.938572i | \(-0.387851\pi\) | ||||
0.345083 | + | 0.938572i | \(0.387851\pi\) | |||||||
\(350\) | −2.61480e13 | −0.266112 | ||||||||
\(351\) | 3.56859e12 | 0.0357526 | ||||||||
\(352\) | 7.42452e13 | 0.732291 | ||||||||
\(353\) | −3.88466e13 | −0.377218 | −0.188609 | − | 0.982052i | \(-0.560398\pi\) | ||||
−0.188609 | + | 0.982052i | \(0.560398\pi\) | |||||||
\(354\) | 1.89352e12 | 0.0181031 | ||||||||
\(355\) | −2.66041e13 | −0.250434 | ||||||||
\(356\) | 9.20116e13 | 0.852840 | ||||||||
\(357\) | 5.12742e13 | 0.467976 | ||||||||
\(358\) | 3.15470e13 | 0.283532 | ||||||||
\(359\) | 1.06909e14 | 0.946226 | 0.473113 | − | 0.881002i | \(-0.343130\pi\) | ||||
0.473113 | + | 0.881002i | \(0.343130\pi\) | |||||||
\(360\) | 9.13931e12 | 0.0796617 | ||||||||
\(361\) | −4.76697e13 | −0.409216 | ||||||||
\(362\) | 5.20935e13 | 0.440440 | ||||||||
\(363\) | −1.41213e13 | −0.117595 | ||||||||
\(364\) | −3.19023e13 | −0.261676 | ||||||||
\(365\) | 1.00393e14 | 0.811132 | ||||||||
\(366\) | 2.29116e13 | 0.182351 | ||||||||
\(367\) | −1.74287e14 | −1.36648 | −0.683239 | − | 0.730195i | \(-0.739429\pi\) | ||||
−0.683239 | + | 0.730195i | \(0.739429\pi\) | |||||||
\(368\) | 1.48380e14 | 1.14607 | ||||||||
\(369\) | 3.02552e12 | 0.0230226 | ||||||||
\(370\) | −1.84971e13 | −0.138673 | ||||||||
\(371\) | −7.18128e13 | −0.530451 | ||||||||
\(372\) | 3.41318e13 | 0.248412 | ||||||||
\(373\) | 1.81954e14 | 1.30486 | 0.652429 | − | 0.757850i | \(-0.273750\pi\) | ||||
0.652429 | + | 0.757850i | \(0.273750\pi\) | |||||||
\(374\) | 2.02696e13 | 0.143236 | ||||||||
\(375\) | 7.36675e13 | 0.512984 | ||||||||
\(376\) | 9.28213e13 | 0.636963 | ||||||||
\(377\) | 7.36520e12 | 0.0498089 | ||||||||
\(378\) | −1.03989e13 | −0.0693081 | ||||||||
\(379\) | −1.00579e14 | −0.660678 | −0.330339 | − | 0.943862i | \(-0.607163\pi\) | ||||
−0.330339 | + | 0.943862i | \(0.607163\pi\) | |||||||
\(380\) | 5.71421e13 | 0.369953 | ||||||||
\(381\) | −8.38394e13 | −0.535008 | ||||||||
\(382\) | 4.81750e13 | 0.303021 | ||||||||
\(383\) | −3.59629e13 | −0.222978 | −0.111489 | − | 0.993766i | \(-0.535562\pi\) | ||||
−0.111489 | + | 0.993766i | \(0.535562\pi\) | |||||||
\(384\) | −7.82617e13 | −0.478330 | ||||||||
\(385\) | 1.39124e14 | 0.838237 | ||||||||
\(386\) | −3.55479e13 | −0.211147 | ||||||||
\(387\) | −6.09115e13 | −0.356688 | ||||||||
\(388\) | −8.81708e13 | −0.509038 | ||||||||
\(389\) | 3.31371e14 | 1.88622 | 0.943110 | − | 0.332482i | \(-0.107886\pi\) | ||||
0.943110 | + | 0.332482i | \(0.107886\pi\) | |||||||
\(390\) | −2.35184e12 | −0.0131993 | ||||||||
\(391\) | 1.35365e14 | 0.749089 | ||||||||
\(392\) | 1.05937e14 | 0.578059 | ||||||||
\(393\) | −1.23992e14 | −0.667165 | ||||||||
\(394\) | −1.91038e13 | −0.101365 | ||||||||
\(395\) | 6.63163e13 | 0.347005 | ||||||||
\(396\) | 6.67584e13 | 0.344494 | ||||||||
\(397\) | 2.27606e14 | 1.15834 | 0.579170 | − | 0.815207i | \(-0.303377\pi\) | ||||
0.579170 | + | 0.815207i | \(0.303377\pi\) | |||||||
\(398\) | −1.37866e13 | −0.0691990 | ||||||||
\(399\) | −1.34039e14 | −0.663561 | ||||||||
\(400\) | −1.25506e14 | −0.612822 | ||||||||
\(401\) | −1.66902e14 | −0.803838 | −0.401919 | − | 0.915675i | \(-0.631657\pi\) | ||||
−0.401919 | + | 0.915675i | \(0.631657\pi\) | |||||||
\(402\) | 4.77713e13 | 0.226947 | ||||||||
\(403\) | −1.81073e13 | −0.0848547 | ||||||||
\(404\) | 2.03263e14 | 0.939638 | ||||||||
\(405\) | 1.24493e13 | 0.0567730 | ||||||||
\(406\) | −2.14623e13 | −0.0965569 | ||||||||
\(407\) | −2.78545e14 | −1.23631 | ||||||||
\(408\) | −3.34283e13 | −0.146381 | ||||||||
\(409\) | 1.21687e14 | 0.525732 | 0.262866 | − | 0.964832i | \(-0.415332\pi\) | ||||
0.262866 | + | 0.964832i | \(0.415332\pi\) | |||||||
\(410\) | −1.99393e12 | −0.00849961 | ||||||||
\(411\) | −1.29903e14 | −0.546372 | ||||||||
\(412\) | −4.00574e13 | −0.166245 | ||||||||
\(413\) | −4.75364e13 | −0.194671 | ||||||||
\(414\) | −2.74534e13 | −0.110941 | ||||||||
\(415\) | −9.72852e13 | −0.387956 | ||||||||
\(416\) | 3.15088e13 | 0.123999 | ||||||||
\(417\) | −1.38843e14 | −0.539230 | ||||||||
\(418\) | −5.29881e13 | −0.203100 | ||||||||
\(419\) | −4.64645e14 | −1.75770 | −0.878848 | − | 0.477101i | \(-0.841688\pi\) | ||||
−0.878848 | + | 0.477101i | \(0.841688\pi\) | |||||||
\(420\) | −1.11293e14 | −0.415526 | ||||||||
\(421\) | 3.06553e14 | 1.12968 | 0.564838 | − | 0.825202i | \(-0.308939\pi\) | ||||
0.564838 | + | 0.825202i | \(0.308939\pi\) | |||||||
\(422\) | 1.06509e14 | 0.387408 | ||||||||
\(423\) | 1.26438e14 | 0.453948 | ||||||||
\(424\) | 4.68185e13 | 0.165922 | ||||||||
\(425\) | −1.14497e14 | −0.400550 | ||||||||
\(426\) | −1.97351e13 | −0.0681533 | ||||||||
\(427\) | −5.75189e14 | −1.96091 | ||||||||
\(428\) | 3.11229e14 | 1.04746 | ||||||||
\(429\) | −3.54160e13 | −0.117675 | ||||||||
\(430\) | 4.01430e13 | 0.131684 | ||||||||
\(431\) | −3.15623e14 | −1.02222 | −0.511109 | − | 0.859516i | \(-0.670765\pi\) | ||||
−0.511109 | + | 0.859516i | \(0.670765\pi\) | |||||||
\(432\) | −4.99130e13 | −0.159607 | ||||||||
\(433\) | −5.21759e13 | −0.164735 | −0.0823675 | − | 0.996602i | \(-0.526248\pi\) | ||||
−0.0823675 | + | 0.996602i | \(0.526248\pi\) | |||||||
\(434\) | 5.27649e13 | 0.164495 | ||||||||
\(435\) | 2.56940e13 | 0.0790935 | ||||||||
\(436\) | 1.55963e14 | 0.474073 | ||||||||
\(437\) | −3.53866e14 | −1.06216 | ||||||||
\(438\) | 7.44720e13 | 0.220742 | ||||||||
\(439\) | −4.75814e14 | −1.39278 | −0.696390 | − | 0.717664i | \(-0.745211\pi\) | ||||
−0.696390 | + | 0.717664i | \(0.745211\pi\) | |||||||
\(440\) | −9.07018e13 | −0.262196 | ||||||||
\(441\) | 1.44303e14 | 0.411969 | ||||||||
\(442\) | 8.60218e12 | 0.0242542 | ||||||||
\(443\) | −2.38581e14 | −0.664378 | −0.332189 | − | 0.943213i | \(-0.607787\pi\) | ||||
−0.332189 | + | 0.943213i | \(0.607787\pi\) | |||||||
\(444\) | 2.22825e14 | 0.612854 | ||||||||
\(445\) | −1.70288e14 | −0.462598 | ||||||||
\(446\) | −1.04812e13 | −0.0281234 | ||||||||
\(447\) | −1.48627e14 | −0.393920 | ||||||||
\(448\) | 3.81870e14 | 0.999737 | ||||||||
\(449\) | 2.52988e14 | 0.654251 | 0.327125 | − | 0.944981i | \(-0.393920\pi\) | ||||
0.327125 | + | 0.944981i | \(0.393920\pi\) | |||||||
\(450\) | 2.32213e13 | 0.0593222 | ||||||||
\(451\) | −3.00263e13 | −0.0757760 | ||||||||
\(452\) | 3.79357e14 | 0.945773 | ||||||||
\(453\) | 2.33122e14 | 0.574173 | ||||||||
\(454\) | 1.62766e14 | 0.396057 | ||||||||
\(455\) | 5.90424e13 | 0.141939 | ||||||||
\(456\) | 8.73871e13 | 0.207558 | ||||||||
\(457\) | −1.80008e14 | −0.422428 | −0.211214 | − | 0.977440i | \(-0.567742\pi\) | ||||
−0.211214 | + | 0.977440i | \(0.567742\pi\) | |||||||
\(458\) | −3.59676e13 | −0.0833972 | ||||||||
\(459\) | −4.55350e13 | −0.104322 | ||||||||
\(460\) | −2.93817e14 | −0.665133 | ||||||||
\(461\) | 8.67632e14 | 1.94080 | 0.970400 | − | 0.241504i | \(-0.0776407\pi\) | ||||
0.970400 | + | 0.241504i | \(0.0776407\pi\) | |||||||
\(462\) | 1.03203e14 | 0.228119 | ||||||||
\(463\) | 6.99011e14 | 1.52682 | 0.763411 | − | 0.645913i | \(-0.223523\pi\) | ||||
0.763411 | + | 0.645913i | \(0.223523\pi\) | |||||||
\(464\) | −1.03015e14 | −0.222358 | ||||||||
\(465\) | −6.31685e13 | −0.134744 | ||||||||
\(466\) | −5.72196e13 | −0.120621 | ||||||||
\(467\) | −3.20026e14 | −0.666718 | −0.333359 | − | 0.942800i | \(-0.608182\pi\) | ||||
−0.333359 | + | 0.942800i | \(0.608182\pi\) | |||||||
\(468\) | 2.83314e13 | 0.0583333 | ||||||||
\(469\) | −1.19929e15 | −2.44046 | ||||||||
\(470\) | −8.33276e13 | −0.167591 | ||||||||
\(471\) | 3.54845e14 | 0.705380 | ||||||||
\(472\) | 3.09914e13 | 0.0608921 | ||||||||
\(473\) | 6.04508e14 | 1.17399 | ||||||||
\(474\) | 4.91939e13 | 0.0944344 | ||||||||
\(475\) | 2.99315e14 | 0.567955 | ||||||||
\(476\) | 4.07071e14 | 0.763541 | ||||||||
\(477\) | 6.37747e13 | 0.118249 | ||||||||
\(478\) | 1.15684e14 | 0.212040 | ||||||||
\(479\) | −2.51037e14 | −0.454875 | −0.227438 | − | 0.973793i | \(-0.573035\pi\) | ||||
−0.227438 | + | 0.973793i | \(0.573035\pi\) | |||||||
\(480\) | 1.09921e14 | 0.196903 | ||||||||
\(481\) | −1.18211e14 | −0.209344 | ||||||||
\(482\) | −7.56212e13 | −0.132399 | ||||||||
\(483\) | 6.89210e14 | 1.19301 | ||||||||
\(484\) | −1.12110e14 | −0.191865 | ||||||||
\(485\) | 1.63180e14 | 0.276113 | ||||||||
\(486\) | 9.23496e12 | 0.0154503 | ||||||||
\(487\) | −2.64352e14 | −0.437294 | −0.218647 | − | 0.975804i | \(-0.570164\pi\) | ||||
−0.218647 | + | 0.975804i | \(0.570164\pi\) | |||||||
\(488\) | 3.74996e14 | 0.613363 | ||||||||
\(489\) | 4.89965e14 | 0.792440 | ||||||||
\(490\) | −9.51015e13 | −0.152093 | ||||||||
\(491\) | −1.63858e14 | −0.259132 | −0.129566 | − | 0.991571i | \(-0.541358\pi\) | ||||
−0.129566 | + | 0.991571i | \(0.541358\pi\) | |||||||
\(492\) | 2.40199e13 | 0.0375633 | ||||||||
\(493\) | −9.39794e13 | −0.145337 | ||||||||
\(494\) | −2.24875e13 | −0.0343909 | ||||||||
\(495\) | −1.23551e14 | −0.186861 | ||||||||
\(496\) | 2.53262e14 | 0.378810 | ||||||||
\(497\) | 4.95445e14 | 0.732884 | ||||||||
\(498\) | −7.21669e13 | −0.105579 | ||||||||
\(499\) | −1.30857e13 | −0.0189340 | −0.00946701 | − | 0.999955i | \(-0.503013\pi\) | ||||
−0.00946701 | + | 0.999955i | \(0.503013\pi\) | |||||||
\(500\) | 5.84854e14 | 0.836975 | ||||||||
\(501\) | 5.21882e14 | 0.738694 | ||||||||
\(502\) | −1.18230e14 | −0.165523 | ||||||||
\(503\) | 6.57715e14 | 0.910781 | 0.455390 | − | 0.890292i | \(-0.349500\pi\) | ||||
0.455390 | + | 0.890292i | \(0.349500\pi\) | |||||||
\(504\) | −1.70200e14 | −0.233127 | ||||||||
\(505\) | −3.76183e14 | −0.509679 | ||||||||
\(506\) | 2.72457e14 | 0.365149 | ||||||||
\(507\) | 4.20465e14 | 0.557424 | ||||||||
\(508\) | −6.65609e14 | −0.872909 | ||||||||
\(509\) | 4.66671e14 | 0.605429 | 0.302714 | − | 0.953081i | \(-0.402107\pi\) | ||||
0.302714 | + | 0.953081i | \(0.402107\pi\) | |||||||
\(510\) | 3.00093e13 | 0.0385141 | ||||||||
\(511\) | −1.86960e15 | −2.37375 | ||||||||
\(512\) | −7.49526e14 | −0.941460 | ||||||||
\(513\) | 1.19036e14 | 0.147922 | ||||||||
\(514\) | 6.48695e13 | 0.0797523 | ||||||||
\(515\) | 7.41351e13 | 0.0901746 | ||||||||
\(516\) | −4.83583e14 | −0.581966 | ||||||||
\(517\) | −1.25482e15 | −1.49411 | ||||||||
\(518\) | 3.44469e14 | 0.405822 | ||||||||
\(519\) | −7.30534e14 | −0.851570 | ||||||||
\(520\) | −3.84928e13 | −0.0443977 | ||||||||
\(521\) | −1.66453e15 | −1.89970 | −0.949849 | − | 0.312709i | \(-0.898764\pi\) | ||||
−0.949849 | + | 0.312709i | \(0.898764\pi\) | |||||||
\(522\) | 1.90600e13 | 0.0215246 | ||||||||
\(523\) | −1.49774e15 | −1.67369 | −0.836847 | − | 0.547436i | \(-0.815604\pi\) | ||||
−0.836847 | + | 0.547436i | \(0.815604\pi\) | |||||||
\(524\) | −9.84383e14 | −1.08853 | ||||||||
\(525\) | −5.82964e14 | −0.637919 | ||||||||
\(526\) | 9.68960e13 | 0.104926 | ||||||||
\(527\) | 2.31048e14 | 0.247596 | ||||||||
\(528\) | 4.95355e14 | 0.525327 | ||||||||
\(529\) | 8.66717e14 | 0.909644 | ||||||||
\(530\) | −4.20300e13 | −0.0436558 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −1.06415e15 | −1.08265 | ||||||||
\(533\) | −1.27428e13 | −0.0128312 | ||||||||
\(534\) | −1.26321e14 | −0.125892 | ||||||||
\(535\) | −5.75999e14 | −0.568166 | ||||||||
\(536\) | 7.81877e14 | 0.763365 | ||||||||
\(537\) | 7.03333e14 | 0.679677 | ||||||||
\(538\) | −4.53747e14 | −0.434022 | ||||||||
\(539\) | −1.43212e15 | −1.35594 | ||||||||
\(540\) | 9.88361e13 | 0.0926297 | ||||||||
\(541\) | 3.51108e14 | 0.325729 | 0.162864 | − | 0.986648i | \(-0.447927\pi\) | ||||
0.162864 | + | 0.986648i | \(0.447927\pi\) | |||||||
\(542\) | 3.49601e14 | 0.321053 | ||||||||
\(543\) | 1.16141e15 | 1.05581 | ||||||||
\(544\) | −4.02050e14 | −0.361814 | ||||||||
\(545\) | −2.88644e14 | −0.257147 | ||||||||
\(546\) | 4.37980e13 | 0.0386274 | ||||||||
\(547\) | −8.72037e14 | −0.761385 | −0.380693 | − | 0.924702i | \(-0.624314\pi\) | ||||
−0.380693 | + | 0.924702i | \(0.624314\pi\) | |||||||
\(548\) | −1.03131e15 | −0.891449 | ||||||||
\(549\) | 5.10808e14 | 0.437129 | ||||||||
\(550\) | −2.30456e14 | −0.195251 | ||||||||
\(551\) | 2.45678e14 | 0.206078 | ||||||||
\(552\) | −4.49332e14 | −0.373166 | ||||||||
\(553\) | −1.23500e15 | −1.01550 | ||||||||
\(554\) | −3.43115e14 | −0.279342 | ||||||||
\(555\) | −4.12387e14 | −0.332425 | ||||||||
\(556\) | −1.10229e15 | −0.879798 | ||||||||
\(557\) | −1.24034e15 | −0.980248 | −0.490124 | − | 0.871653i | \(-0.663048\pi\) | ||||
−0.490124 | + | 0.871653i | \(0.663048\pi\) | |||||||
\(558\) | −4.68589e13 | −0.0366694 | ||||||||
\(559\) | 2.56546e14 | 0.198793 | ||||||||
\(560\) | −8.25810e14 | −0.633645 | ||||||||
\(561\) | 4.51906e14 | 0.343362 | ||||||||
\(562\) | 1.48203e14 | 0.111508 | ||||||||
\(563\) | −3.60595e13 | −0.0268673 | −0.0134336 | − | 0.999910i | \(-0.504276\pi\) | ||||
−0.0134336 | + | 0.999910i | \(0.504276\pi\) | |||||||
\(564\) | 1.00381e15 | 0.740653 | ||||||||
\(565\) | −7.02085e14 | −0.513007 | ||||||||
\(566\) | −2.53583e14 | −0.183497 | ||||||||
\(567\) | −2.31841e14 | −0.166144 | ||||||||
\(568\) | −3.23006e14 | −0.229243 | ||||||||
\(569\) | 1.14019e15 | 0.801421 | 0.400710 | − | 0.916205i | \(-0.368763\pi\) | ||||
0.400710 | + | 0.916205i | \(0.368763\pi\) | |||||||
\(570\) | −7.84492e13 | −0.0546106 | ||||||||
\(571\) | 7.03830e14 | 0.485254 | 0.242627 | − | 0.970120i | \(-0.421991\pi\) | ||||
0.242627 | + | 0.970120i | \(0.421991\pi\) | |||||||
\(572\) | −2.81172e14 | −0.191997 | ||||||||
\(573\) | 1.07405e15 | 0.726396 | ||||||||
\(574\) | 3.71328e13 | 0.0248738 | ||||||||
\(575\) | −1.53904e15 | −1.02112 | ||||||||
\(576\) | −3.39126e14 | −0.222863 | ||||||||
\(577\) | −1.63485e15 | −1.06417 | −0.532086 | − | 0.846690i | \(-0.678592\pi\) | ||||
−0.532086 | + | 0.846690i | \(0.678592\pi\) | |||||||
\(578\) | 2.63781e14 | 0.170075 | ||||||||
\(579\) | −7.92532e14 | −0.506156 | ||||||||
\(580\) | 2.03987e14 | 0.129047 | ||||||||
\(581\) | 1.81173e15 | 1.13534 | ||||||||
\(582\) | 1.21048e14 | 0.0751417 | ||||||||
\(583\) | −6.32923e14 | −0.389201 | ||||||||
\(584\) | 1.21889e15 | 0.742496 | ||||||||
\(585\) | −5.24337e13 | −0.0316412 | ||||||||
\(586\) | −3.53907e14 | −0.211569 | ||||||||
\(587\) | −2.17586e14 | −0.128861 | −0.0644305 | − | 0.997922i | \(-0.520523\pi\) | ||||
−0.0644305 | + | 0.997922i | \(0.520523\pi\) | |||||||
\(588\) | 1.14564e15 | 0.672160 | ||||||||
\(589\) | −6.03997e14 | −0.351076 | ||||||||
\(590\) | −2.78217e13 | −0.0160213 | ||||||||
\(591\) | −4.25914e14 | −0.242991 | ||||||||
\(592\) | 1.65339e15 | 0.934556 | ||||||||
\(593\) | −2.13126e15 | −1.19354 | −0.596769 | − | 0.802413i | \(-0.703549\pi\) | ||||
−0.596769 | + | 0.802413i | \(0.703549\pi\) | |||||||
\(594\) | −9.16512e13 | −0.0508525 | ||||||||
\(595\) | −7.53376e14 | −0.414160 | ||||||||
\(596\) | −1.17997e15 | −0.642712 | ||||||||
\(597\) | −3.07368e14 | −0.165882 | ||||||||
\(598\) | 1.15628e14 | 0.0618308 | ||||||||
\(599\) | 7.51937e14 | 0.398413 | 0.199207 | − | 0.979958i | \(-0.436164\pi\) | ||||
0.199207 | + | 0.979958i | \(0.436164\pi\) | |||||||
\(600\) | 3.80064e14 | 0.199538 | ||||||||
\(601\) | −1.89694e14 | −0.0986833 | −0.0493416 | − | 0.998782i | \(-0.515712\pi\) | ||||
−0.0493416 | + | 0.998782i | \(0.515712\pi\) | |||||||
\(602\) | −7.47579e14 | −0.385368 | ||||||||
\(603\) | 1.06505e15 | 0.544032 | ||||||||
\(604\) | 1.85078e15 | 0.936809 | ||||||||
\(605\) | 2.07485e14 | 0.104072 | ||||||||
\(606\) | −2.79055e14 | −0.138705 | ||||||||
\(607\) | 6.99157e14 | 0.344379 | 0.172190 | − | 0.985064i | \(-0.444916\pi\) | ||||
0.172190 | + | 0.985064i | \(0.444916\pi\) | |||||||
\(608\) | 1.05102e15 | 0.513030 | ||||||||
\(609\) | −4.78496e14 | −0.231464 | ||||||||
\(610\) | −3.36642e14 | −0.161381 | ||||||||
\(611\) | −5.32530e14 | −0.252998 | ||||||||
\(612\) | −3.61507e14 | −0.170210 | ||||||||
\(613\) | −3.50244e15 | −1.63432 | −0.817162 | − | 0.576408i | \(-0.804454\pi\) | ||||
−0.817162 | + | 0.576408i | \(0.804454\pi\) | |||||||
\(614\) | −2.48062e14 | −0.114719 | ||||||||
\(615\) | −4.44542e13 | −0.0203751 | ||||||||
\(616\) | 1.68913e15 | 0.767307 | ||||||||
\(617\) | −1.88470e15 | −0.848542 | −0.424271 | − | 0.905535i | \(-0.639470\pi\) | ||||
−0.424271 | + | 0.905535i | \(0.639470\pi\) | |||||||
\(618\) | 5.49939e13 | 0.0245402 | ||||||||
\(619\) | −1.49500e15 | −0.661215 | −0.330607 | − | 0.943768i | \(-0.607254\pi\) | ||||
−0.330607 | + | 0.943768i | \(0.607254\pi\) | |||||||
\(620\) | −5.01502e14 | −0.219846 | ||||||||
\(621\) | −6.12066e14 | −0.265947 | ||||||||
\(622\) | −5.99463e14 | −0.258176 | ||||||||
\(623\) | 3.17125e15 | 1.35377 | ||||||||
\(624\) | 2.10223e14 | 0.0889538 | ||||||||
\(625\) | 6.79327e14 | 0.284931 | ||||||||
\(626\) | 1.94506e14 | 0.0808675 | ||||||||
\(627\) | −1.18136e15 | −0.486866 | ||||||||
\(628\) | 2.81715e15 | 1.15088 | ||||||||
\(629\) | 1.50836e15 | 0.610840 | ||||||||
\(630\) | 1.52792e14 | 0.0613379 | ||||||||
\(631\) | −2.92460e15 | −1.16387 | −0.581937 | − | 0.813234i | \(-0.697705\pi\) | ||||
−0.581937 | + | 0.813234i | \(0.697705\pi\) | |||||||
\(632\) | 8.05160e14 | 0.317642 | ||||||||
\(633\) | 2.37459e15 | 0.928686 | ||||||||
\(634\) | −5.32293e14 | −0.206376 | ||||||||
\(635\) | 1.23186e15 | 0.473484 | ||||||||
\(636\) | 5.06314e14 | 0.192933 | ||||||||
\(637\) | −6.07775e14 | −0.229602 | ||||||||
\(638\) | −1.89158e14 | −0.0708454 | ||||||||
\(639\) | −4.39989e14 | −0.163376 | ||||||||
\(640\) | 1.14991e15 | 0.423323 | ||||||||
\(641\) | −3.97230e15 | −1.44985 | −0.724925 | − | 0.688828i | \(-0.758126\pi\) | ||||
−0.724925 | + | 0.688828i | \(0.758126\pi\) | |||||||
\(642\) | −4.27280e14 | −0.154621 | ||||||||
\(643\) | 2.53653e15 | 0.910081 | 0.455040 | − | 0.890471i | \(-0.349625\pi\) | ||||
0.455040 | + | 0.890471i | \(0.349625\pi\) | |||||||
\(644\) | 5.47171e15 | 1.94648 | ||||||||
\(645\) | 8.94978e14 | 0.315670 | ||||||||
\(646\) | 2.86939e14 | 0.100348 | ||||||||
\(647\) | 1.99270e15 | 0.690985 | 0.345493 | − | 0.938421i | \(-0.387712\pi\) | ||||
0.345493 | + | 0.938421i | \(0.387712\pi\) | |||||||
\(648\) | 1.51149e14 | 0.0519690 | ||||||||
\(649\) | −4.18963e14 | −0.142833 | ||||||||
\(650\) | −9.78029e13 | −0.0330619 | ||||||||
\(651\) | 1.17638e15 | 0.394323 | ||||||||
\(652\) | 3.88988e15 | 1.29293 | ||||||||
\(653\) | 3.16053e15 | 1.04169 | 0.520844 | − | 0.853652i | \(-0.325618\pi\) | ||||
0.520844 | + | 0.853652i | \(0.325618\pi\) | |||||||
\(654\) | −2.14118e14 | −0.0699802 | ||||||||
\(655\) | 1.82182e15 | 0.590444 | ||||||||
\(656\) | 1.78231e14 | 0.0572811 | ||||||||
\(657\) | 1.66033e15 | 0.529159 | ||||||||
\(658\) | 1.55180e15 | 0.490449 | ||||||||
\(659\) | 2.29959e15 | 0.720744 | 0.360372 | − | 0.932809i | \(-0.382650\pi\) | ||||
0.360372 | + | 0.932809i | \(0.382650\pi\) | |||||||
\(660\) | −9.80886e14 | −0.304879 | ||||||||
\(661\) | 3.49964e14 | 0.107874 | 0.0539368 | − | 0.998544i | \(-0.482823\pi\) | ||||
0.0539368 | + | 0.998544i | \(0.482823\pi\) | |||||||
\(662\) | −1.09324e15 | −0.334193 | ||||||||
\(663\) | 1.91783e14 | 0.0581416 | ||||||||
\(664\) | −1.18116e15 | −0.355128 | ||||||||
\(665\) | 1.96945e15 | 0.587253 | ||||||||
\(666\) | −3.05912e14 | −0.0904665 | ||||||||
\(667\) | −1.26324e15 | −0.370505 | ||||||||
\(668\) | 4.14327e15 | 1.20524 | ||||||||
\(669\) | −2.33675e14 | −0.0674169 | ||||||||
\(670\) | −7.01908e14 | −0.200849 | ||||||||
\(671\) | −5.06944e15 | −1.43875 | ||||||||
\(672\) | −2.04704e15 | −0.576228 | ||||||||
\(673\) | −5.14921e15 | −1.43766 | −0.718832 | − | 0.695184i | \(-0.755323\pi\) | ||||
−0.718832 | + | 0.695184i | \(0.755323\pi\) | |||||||
\(674\) | −5.68173e13 | −0.0157344 | ||||||||
\(675\) | 5.17712e14 | 0.142206 | ||||||||
\(676\) | 3.33811e15 | 0.909483 | ||||||||
\(677\) | −2.04118e15 | −0.551626 | −0.275813 | − | 0.961211i | \(-0.588947\pi\) | ||||
−0.275813 | + | 0.961211i | \(0.588947\pi\) | |||||||
\(678\) | −5.20812e14 | −0.139610 | ||||||||
\(679\) | −3.03888e15 | −0.808033 | ||||||||
\(680\) | 4.91165e14 | 0.129547 | ||||||||
\(681\) | 3.62883e15 | 0.949419 | ||||||||
\(682\) | 4.65045e14 | 0.120693 | ||||||||
\(683\) | 2.53084e15 | 0.651554 | 0.325777 | − | 0.945447i | \(-0.394374\pi\) | ||||
0.325777 | + | 0.945447i | \(0.394374\pi\) | |||||||
\(684\) | 9.45039e14 | 0.241347 | ||||||||
\(685\) | 1.90867e15 | 0.483541 | ||||||||
\(686\) | 3.38056e14 | 0.0849584 | ||||||||
\(687\) | −8.01889e14 | −0.199918 | ||||||||
\(688\) | −3.58824e15 | −0.887453 | ||||||||
\(689\) | −2.68605e14 | −0.0659035 | ||||||||
\(690\) | 4.03375e14 | 0.0981835 | ||||||||
\(691\) | −2.87994e15 | −0.695430 | −0.347715 | − | 0.937600i | \(-0.613042\pi\) | ||||
−0.347715 | + | 0.937600i | \(0.613042\pi\) | |||||||
\(692\) | −5.79979e15 | −1.38940 | ||||||||
\(693\) | 2.30088e15 | 0.546841 | ||||||||
\(694\) | 9.35047e13 | 0.0220473 | ||||||||
\(695\) | 2.04003e15 | 0.477221 | ||||||||
\(696\) | 3.11957e14 | 0.0724008 | ||||||||
\(697\) | 1.62597e14 | 0.0374398 | ||||||||
\(698\) | −7.27609e14 | −0.166224 | ||||||||
\(699\) | −1.27570e15 | −0.289150 | ||||||||
\(700\) | −4.62821e15 | −1.04082 | ||||||||
\(701\) | 8.64233e14 | 0.192833 | 0.0964166 | − | 0.995341i | \(-0.469262\pi\) | ||||
0.0964166 | + | 0.995341i | \(0.469262\pi\) | |||||||
\(702\) | −3.88957e13 | −0.00861087 | ||||||||
\(703\) | −3.94311e15 | −0.866133 | ||||||||
\(704\) | 3.36561e15 | 0.733524 | ||||||||
\(705\) | −1.85777e15 | −0.401746 | ||||||||
\(706\) | 4.23406e14 | 0.0908512 | ||||||||
\(707\) | 7.00561e15 | 1.49156 | ||||||||
\(708\) | 3.35154e14 | 0.0708046 | ||||||||
\(709\) | 5.64182e15 | 1.18267 | 0.591337 | − | 0.806424i | \(-0.298600\pi\) | ||||
0.591337 | + | 0.806424i | \(0.298600\pi\) | |||||||
\(710\) | 2.89970e14 | 0.0603159 | ||||||||
\(711\) | 1.09676e15 | 0.226376 | ||||||||
\(712\) | −2.06750e15 | −0.423454 | ||||||||
\(713\) | 3.10567e15 | 0.631193 | ||||||||
\(714\) | −5.58860e14 | −0.112710 | ||||||||
\(715\) | 5.20371e14 | 0.104143 | ||||||||
\(716\) | 5.58383e15 | 1.10895 | ||||||||
\(717\) | 2.57914e15 | 0.508299 | ||||||||
\(718\) | −1.16525e15 | −0.227894 | ||||||||
\(719\) | 8.02417e15 | 1.55737 | 0.778684 | − | 0.627416i | \(-0.215888\pi\) | ||||
0.778684 | + | 0.627416i | \(0.215888\pi\) | |||||||
\(720\) | 7.33376e14 | 0.141253 | ||||||||
\(721\) | −1.38061e15 | −0.263892 | ||||||||
\(722\) | 5.19572e14 | 0.0985579 | ||||||||
\(723\) | −1.68596e15 | −0.317384 | ||||||||
\(724\) | 9.22057e15 | 1.72264 | ||||||||
\(725\) | 1.06850e15 | 0.198115 | ||||||||
\(726\) | 1.53914e14 | 0.0283222 | ||||||||
\(727\) | 4.28976e15 | 0.783419 | 0.391710 | − | 0.920089i | \(-0.371884\pi\) | ||||
0.391710 | + | 0.920089i | \(0.371884\pi\) | |||||||
\(728\) | 7.16846e14 | 0.129928 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −1.09422e15 | −0.195358 | ||||||||
\(731\) | −3.27351e15 | −0.580053 | ||||||||
\(732\) | 4.05535e15 | 0.713211 | ||||||||
\(733\) | 8.93218e15 | 1.55914 | 0.779571 | − | 0.626314i | \(-0.215437\pi\) | ||||
0.779571 | + | 0.626314i | \(0.215437\pi\) | |||||||
\(734\) | 1.89963e15 | 0.329110 | ||||||||
\(735\) | −2.12026e15 | −0.364594 | ||||||||
\(736\) | −5.40421e15 | −0.922369 | ||||||||
\(737\) | −1.05699e16 | −1.79061 | ||||||||
\(738\) | −3.29764e13 | −0.00554490 | ||||||||
\(739\) | −2.28468e15 | −0.381313 | −0.190657 | − | 0.981657i | \(-0.561062\pi\) | ||||
−0.190657 | + | 0.981657i | \(0.561062\pi\) | |||||||
\(740\) | −3.27398e15 | −0.542378 | ||||||||
\(741\) | −5.01353e14 | −0.0824411 | ||||||||
\(742\) | 7.82719e14 | 0.127757 | ||||||||
\(743\) | −1.52362e15 | −0.246853 | −0.123427 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123427 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(744\) | −7.66943e14 | −0.123342 | ||||||||
\(745\) | 2.18380e15 | 0.348620 | ||||||||
\(746\) | −1.98320e15 | −0.314270 | ||||||||
\(747\) | −1.60894e15 | −0.253091 | ||||||||
\(748\) | 3.58773e15 | 0.560223 | ||||||||
\(749\) | 1.07268e16 | 1.66272 | ||||||||
\(750\) | −8.02934e14 | −0.123550 | ||||||||
\(751\) | −6.85472e15 | −1.04706 | −0.523528 | − | 0.852008i | \(-0.675385\pi\) | ||||
−0.523528 | + | 0.852008i | \(0.675385\pi\) | |||||||
\(752\) | 7.44837e15 | 1.12944 | ||||||||
\(753\) | −2.63591e15 | −0.396788 | ||||||||
\(754\) | −8.02765e13 | −0.0119963 | ||||||||
\(755\) | −3.42528e15 | −0.508145 | ||||||||
\(756\) | −1.84061e15 | −0.271077 | ||||||||
\(757\) | −1.54090e15 | −0.225293 | −0.112647 | − | 0.993635i | \(-0.535933\pi\) | ||||
−0.112647 | + | 0.993635i | \(0.535933\pi\) | |||||||
\(758\) | 1.09625e15 | 0.159122 | ||||||||
\(759\) | 6.07436e15 | 0.875329 | ||||||||
\(760\) | −1.28399e15 | −0.183690 | ||||||||
\(761\) | 1.02518e16 | 1.45607 | 0.728037 | − | 0.685538i | \(-0.240433\pi\) | ||||
0.728037 | + | 0.685538i | \(0.240433\pi\) | |||||||
\(762\) | 9.13801e14 | 0.128854 | ||||||||
\(763\) | 5.37538e15 | 0.752530 | ||||||||
\(764\) | 8.52698e15 | 1.18517 | ||||||||
\(765\) | 6.69049e14 | 0.0923252 | ||||||||
\(766\) | 3.91975e14 | 0.0537032 | ||||||||
\(767\) | −1.77803e14 | −0.0241860 | ||||||||
\(768\) | −2.00514e15 | −0.270806 | ||||||||
\(769\) | −1.26692e16 | −1.69884 | −0.849421 | − | 0.527715i | \(-0.823049\pi\) | ||||
−0.849421 | + | 0.527715i | \(0.823049\pi\) | |||||||
\(770\) | −1.51637e15 | −0.201886 | ||||||||
\(771\) | 1.44625e15 | 0.191181 | ||||||||
\(772\) | −6.29199e15 | −0.825834 | ||||||||
\(773\) | −9.49478e15 | −1.23736 | −0.618682 | − | 0.785641i | \(-0.712333\pi\) | ||||
−0.618682 | + | 0.785641i | \(0.712333\pi\) | |||||||
\(774\) | 6.63901e14 | 0.0859069 | ||||||||
\(775\) | −2.62691e15 | −0.337509 | ||||||||
\(776\) | 1.98120e15 | 0.252749 | ||||||||
\(777\) | 7.67984e15 | 0.972829 | ||||||||
\(778\) | −3.61176e15 | −0.454288 | ||||||||
\(779\) | −4.25056e14 | −0.0530873 | ||||||||
\(780\) | −4.16276e14 | −0.0516252 | ||||||||
\(781\) | 4.36661e15 | 0.537730 | ||||||||
\(782\) | −1.47540e15 | −0.180415 | ||||||||
\(783\) | 4.24938e14 | 0.0515983 | ||||||||
\(784\) | 8.50079e15 | 1.02499 | ||||||||
\(785\) | −5.21376e15 | −0.624264 | ||||||||
\(786\) | 1.35144e15 | 0.160684 | ||||||||
\(787\) | −8.98457e15 | −1.06081 | −0.530403 | − | 0.847745i | \(-0.677960\pi\) | ||||
−0.530403 | + | 0.847745i | \(0.677960\pi\) | |||||||
\(788\) | −3.38137e15 | −0.396460 | ||||||||
\(789\) | 2.16027e15 | 0.251527 | ||||||||
\(790\) | −7.22810e14 | −0.0835747 | ||||||||
\(791\) | 1.30748e16 | 1.50129 | ||||||||
\(792\) | −1.50006e15 | −0.171049 | ||||||||
\(793\) | −2.15141e15 | −0.243624 | ||||||||
\(794\) | −2.48078e15 | −0.278981 | ||||||||
\(795\) | −9.37047e14 | −0.104651 | ||||||||
\(796\) | −2.44023e15 | −0.270650 | ||||||||
\(797\) | −6.11982e15 | −0.674090 | −0.337045 | − | 0.941488i | \(-0.609428\pi\) | ||||
−0.337045 | + | 0.941488i | \(0.609428\pi\) | |||||||
\(798\) | 1.46095e15 | 0.159816 | ||||||||
\(799\) | 6.79505e15 | 0.738219 | ||||||||
\(800\) | 4.57112e15 | 0.493205 | ||||||||
\(801\) | −2.81629e15 | −0.301785 | ||||||||
\(802\) | 1.81914e15 | 0.193601 | ||||||||
\(803\) | −1.64778e16 | −1.74166 | ||||||||
\(804\) | 8.45554e15 | 0.887632 | ||||||||
\(805\) | −1.01266e16 | −1.05581 | ||||||||
\(806\) | 1.97359e14 | 0.0204369 | ||||||||
\(807\) | −1.01162e16 | −1.04043 | ||||||||
\(808\) | −4.56732e15 | −0.466551 | ||||||||
\(809\) | 2.16381e15 | 0.219534 | 0.109767 | − | 0.993957i | \(-0.464990\pi\) | ||||
0.109767 | + | 0.993957i | \(0.464990\pi\) | |||||||
\(810\) | −1.35690e14 | −0.0136735 | ||||||||
\(811\) | 6.81862e15 | 0.682467 | 0.341233 | − | 0.939979i | \(-0.389155\pi\) | ||||
0.341233 | + | 0.939979i | \(0.389155\pi\) | |||||||
\(812\) | −3.79883e15 | −0.377652 | ||||||||
\(813\) | 7.79427e15 | 0.769622 | ||||||||
\(814\) | 3.03598e15 | 0.297759 | ||||||||
\(815\) | −7.19910e15 | −0.701312 | ||||||||
\(816\) | −2.68243e15 | −0.259556 | ||||||||
\(817\) | 8.55748e15 | 0.822479 | ||||||||
\(818\) | −1.32632e15 | −0.126620 | ||||||||
\(819\) | 9.76466e14 | 0.0925967 | ||||||||
\(820\) | −3.52926e14 | −0.0332436 | ||||||||
\(821\) | −1.02535e16 | −0.959370 | −0.479685 | − | 0.877441i | \(-0.659249\pi\) | ||||
−0.479685 | + | 0.877441i | \(0.659249\pi\) | |||||||
\(822\) | 1.41587e15 | 0.131591 | ||||||||
\(823\) | −1.50827e16 | −1.39245 | −0.696227 | − | 0.717822i | \(-0.745139\pi\) | ||||
−0.696227 | + | 0.717822i | \(0.745139\pi\) | |||||||
\(824\) | 9.00091e14 | 0.0825442 | ||||||||
\(825\) | −5.13796e15 | −0.468052 | ||||||||
\(826\) | 5.18120e14 | 0.0468856 | ||||||||
\(827\) | −1.09528e16 | −0.984562 | −0.492281 | − | 0.870436i | \(-0.663837\pi\) | ||||
−0.492281 | + | 0.870436i | \(0.663837\pi\) | |||||||
\(828\) | −4.85925e15 | −0.433913 | ||||||||
\(829\) | 1.00515e15 | 0.0891620 | 0.0445810 | − | 0.999006i | \(-0.485805\pi\) | ||||
0.0445810 | + | 0.999006i | \(0.485805\pi\) | |||||||
\(830\) | 1.06035e15 | 0.0934375 | ||||||||
\(831\) | −7.64966e15 | −0.669633 | ||||||||
\(832\) | 1.42833e15 | 0.124208 | ||||||||
\(833\) | 7.75516e15 | 0.669951 | ||||||||
\(834\) | 1.51331e15 | 0.129871 | ||||||||
\(835\) | −7.66805e15 | −0.653747 | ||||||||
\(836\) | −9.37891e15 | −0.794361 | ||||||||
\(837\) | −1.04471e15 | −0.0879031 | ||||||||
\(838\) | 5.06436e15 | 0.423334 | ||||||||
\(839\) | 1.23063e16 | 1.02196 | 0.510982 | − | 0.859591i | \(-0.329282\pi\) | ||||
0.510982 | + | 0.859591i | \(0.329282\pi\) | |||||||
\(840\) | 2.50077e15 | 0.206318 | ||||||||
\(841\) | −1.13235e16 | −0.928116 | ||||||||
\(842\) | −3.34125e15 | −0.272077 | ||||||||
\(843\) | 3.30415e15 | 0.267306 | ||||||||
\(844\) | 1.88522e16 | 1.51523 | ||||||||
\(845\) | −6.17792e15 | −0.493322 | ||||||||
\(846\) | −1.37811e15 | −0.109332 | ||||||||
\(847\) | −3.86397e15 | −0.304562 | ||||||||
\(848\) | 3.75691e15 | 0.294207 | ||||||||
\(849\) | −5.65356e15 | −0.439875 | ||||||||
\(850\) | 1.24796e15 | 0.0964707 | ||||||||
\(851\) | 2.02749e16 | 1.55721 | ||||||||
\(852\) | −3.49312e15 | −0.266560 | ||||||||
\(853\) | 1.92488e16 | 1.45943 | 0.729716 | − | 0.683750i | \(-0.239652\pi\) | ||||
0.729716 | + | 0.683750i | \(0.239652\pi\) | |||||||
\(854\) | 6.26924e15 | 0.472277 | ||||||||
\(855\) | −1.74900e15 | −0.130911 | ||||||||
\(856\) | −6.99333e15 | −0.520089 | ||||||||
\(857\) | 1.82821e13 | 0.00135093 | 0.000675463 | − | 1.00000i | \(-0.499785\pi\) | ||||
0.000675463 | 1.00000i | \(0.499785\pi\) | ||||||||
\(858\) | 3.86015e14 | 0.0283416 | ||||||||
\(859\) | 8.50521e15 | 0.620472 | 0.310236 | − | 0.950660i | \(-0.399592\pi\) | ||||
0.310236 | + | 0.950660i | \(0.399592\pi\) | |||||||
\(860\) | 7.10532e15 | 0.515042 | ||||||||
\(861\) | 8.27865e14 | 0.0596269 | ||||||||
\(862\) | 3.44011e15 | 0.246197 | ||||||||
\(863\) | −1.21922e16 | −0.867005 | −0.433502 | − | 0.901152i | \(-0.642722\pi\) | ||||
−0.433502 | + | 0.901152i | \(0.642722\pi\) | |||||||
\(864\) | 1.81791e15 | 0.128454 | ||||||||
\(865\) | 1.07338e16 | 0.753642 | ||||||||
\(866\) | 5.68687e14 | 0.0396757 | ||||||||
\(867\) | 5.88093e15 | 0.407700 | ||||||||
\(868\) | 9.33941e15 | 0.643370 | ||||||||
\(869\) | −1.08847e16 | −0.745088 | ||||||||
\(870\) | −2.80050e14 | −0.0190493 | ||||||||
\(871\) | −4.48575e15 | −0.303204 | ||||||||
\(872\) | −3.50449e15 | −0.235388 | ||||||||
\(873\) | 2.69873e15 | 0.180128 | ||||||||
\(874\) | 3.85694e15 | 0.255817 | ||||||||
\(875\) | 2.01575e16 | 1.32859 | ||||||||
\(876\) | 1.31816e16 | 0.863365 | ||||||||
\(877\) | 1.97025e16 | 1.28240 | 0.641202 | − | 0.767373i | \(-0.278436\pi\) | ||||
0.641202 | + | 0.767373i | \(0.278436\pi\) | |||||||
\(878\) | 5.18610e15 | 0.335445 | ||||||||
\(879\) | −7.89026e15 | −0.507169 | ||||||||
\(880\) | −7.27829e15 | −0.464916 | ||||||||
\(881\) | 1.51238e16 | 0.960047 | 0.480023 | − | 0.877256i | \(-0.340628\pi\) | ||||
0.480023 | + | 0.877256i | \(0.340628\pi\) | |||||||
\(882\) | −1.57283e15 | −0.0992210 | ||||||||
\(883\) | −7.01193e15 | −0.439596 | −0.219798 | − | 0.975545i | \(-0.570540\pi\) | ||||
−0.219798 | + | 0.975545i | \(0.570540\pi\) | |||||||
\(884\) | 1.52259e15 | 0.0948626 | ||||||||
\(885\) | −6.20277e14 | −0.0384059 | ||||||||
\(886\) | 2.60040e15 | 0.160013 | ||||||||
\(887\) | −1.24879e15 | −0.0763677 | −0.0381839 | − | 0.999271i | \(-0.512157\pi\) | ||||
−0.0381839 | + | 0.999271i | \(0.512157\pi\) | |||||||
\(888\) | −5.00688e15 | −0.304296 | ||||||||
\(889\) | −2.29408e16 | −1.38563 | ||||||||
\(890\) | 1.85604e15 | 0.111415 | ||||||||
\(891\) | −2.04334e15 | −0.121903 | ||||||||
\(892\) | −1.85517e15 | −0.109996 | ||||||||
\(893\) | −1.77634e16 | −1.04675 | ||||||||
\(894\) | 1.61996e15 | 0.0948739 | ||||||||
\(895\) | −1.03341e16 | −0.601516 | ||||||||
\(896\) | −2.14146e16 | −1.23884 | ||||||||
\(897\) | 2.57789e15 | 0.148220 | ||||||||
\(898\) | −2.75742e15 | −0.157574 | ||||||||
\(899\) | −2.15616e15 | −0.122463 | ||||||||
\(900\) | 4.11017e15 | 0.232020 | ||||||||
\(901\) | 3.42738e15 | 0.192299 | ||||||||
\(902\) | 3.27270e14 | 0.0182503 | ||||||||
\(903\) | −1.66671e16 | −0.923797 | ||||||||
\(904\) | −8.52417e15 | −0.469598 | ||||||||
\(905\) | −1.70647e16 | −0.934398 | ||||||||
\(906\) | −2.54089e15 | −0.138287 | ||||||||
\(907\) | 9.02571e15 | 0.488249 | 0.244124 | − | 0.969744i | \(-0.421499\pi\) | ||||
0.244124 | + | 0.969744i | \(0.421499\pi\) | |||||||
\(908\) | 2.88097e16 | 1.54905 | ||||||||
\(909\) | −6.22147e15 | −0.332500 | ||||||||
\(910\) | −6.43528e14 | −0.0341853 | ||||||||
\(911\) | −1.08368e16 | −0.572201 | −0.286101 | − | 0.958200i | \(-0.592359\pi\) | ||||
−0.286101 | + | 0.958200i | \(0.592359\pi\) | |||||||
\(912\) | 7.01230e15 | 0.368035 | ||||||||
\(913\) | 1.59677e16 | 0.833017 | ||||||||
\(914\) | 1.96198e15 | 0.101740 | ||||||||
\(915\) | −7.50534e15 | −0.386860 | ||||||||
\(916\) | −6.36628e15 | −0.326182 | ||||||||
\(917\) | −3.39275e16 | −1.72791 | ||||||||
\(918\) | 4.96306e14 | 0.0251255 | ||||||||
\(919\) | −1.63964e16 | −0.825112 | −0.412556 | − | 0.910932i | \(-0.635364\pi\) | ||||
−0.412556 | + | 0.910932i | \(0.635364\pi\) | |||||||
\(920\) | 6.60207e15 | 0.330253 | ||||||||
\(921\) | −5.53047e15 | −0.275001 | ||||||||
\(922\) | −9.45670e15 | −0.467433 | ||||||||
\(923\) | 1.85314e15 | 0.0910539 | ||||||||
\(924\) | 1.82669e16 | 0.892215 | ||||||||
\(925\) | −1.71494e16 | −0.832663 | ||||||||
\(926\) | −7.61882e15 | −0.367729 | ||||||||
\(927\) | 1.22608e15 | 0.0588273 | ||||||||
\(928\) | 3.75197e15 | 0.178956 | ||||||||
\(929\) | 3.91452e16 | 1.85606 | 0.928031 | − | 0.372504i | \(-0.121501\pi\) | ||||
0.928031 | + | 0.372504i | \(0.121501\pi\) | |||||||
\(930\) | 6.88501e14 | 0.0324525 | ||||||||
\(931\) | −2.02733e16 | −0.949949 | ||||||||
\(932\) | −1.01279e16 | −0.471771 | ||||||||
\(933\) | −1.33649e16 | −0.618893 | ||||||||
\(934\) | 3.48810e15 | 0.160576 | ||||||||
\(935\) | −6.63989e15 | −0.303876 | ||||||||
\(936\) | −6.36609e14 | −0.0289638 | ||||||||
\(937\) | −1.21357e15 | −0.0548906 | −0.0274453 | − | 0.999623i | \(-0.508737\pi\) | ||||
−0.0274453 | + | 0.999623i | \(0.508737\pi\) | |||||||
\(938\) | 1.30715e16 | 0.587775 | ||||||||
\(939\) | 4.33646e15 | 0.193854 | ||||||||
\(940\) | −1.47490e16 | −0.655481 | ||||||||
\(941\) | −9.02660e15 | −0.398824 | −0.199412 | − | 0.979916i | \(-0.563903\pi\) | ||||
−0.199412 | + | 0.979916i | \(0.563903\pi\) | |||||||
\(942\) | −3.86761e15 | −0.169888 | ||||||||
\(943\) | 2.18558e15 | 0.0954448 | ||||||||
\(944\) | 2.48688e15 | 0.107971 | ||||||||
\(945\) | 3.40647e15 | 0.147038 | ||||||||
\(946\) | −6.58880e15 | −0.282751 | ||||||||
\(947\) | −3.18898e15 | −0.136059 | −0.0680295 | − | 0.997683i | \(-0.521671\pi\) | ||||
−0.0680295 | + | 0.997683i | \(0.521671\pi\) | |||||||
\(948\) | 8.70733e15 | 0.369351 | ||||||||
\(949\) | −6.99297e15 | −0.294915 | ||||||||
\(950\) | −3.26236e15 | −0.136789 | ||||||||
\(951\) | −1.18673e16 | −0.494721 | ||||||||
\(952\) | −9.14690e15 | −0.379115 | ||||||||
\(953\) | −2.20951e16 | −0.910510 | −0.455255 | − | 0.890361i | \(-0.650452\pi\) | ||||
−0.455255 | + | 0.890361i | \(0.650452\pi\) | |||||||
\(954\) | −6.95108e14 | −0.0284798 | ||||||||
\(955\) | −1.57811e16 | −0.642863 | ||||||||
\(956\) | 2.04760e16 | 0.829330 | ||||||||
\(957\) | −4.21724e15 | −0.169829 | ||||||||
\(958\) | 2.73616e15 | 0.109555 | ||||||||
\(959\) | −3.55450e16 | −1.41506 | ||||||||
\(960\) | 4.98281e15 | 0.197234 | ||||||||
\(961\) | −2.01076e16 | −0.791372 | ||||||||
\(962\) | 1.28843e15 | 0.0504196 | ||||||||
\(963\) | −9.52609e15 | −0.370655 | ||||||||
\(964\) | −1.33850e16 | −0.517838 | ||||||||
\(965\) | 1.16447e16 | 0.447950 | ||||||||
\(966\) | −7.51200e15 | −0.287330 | ||||||||
\(967\) | 2.73879e16 | 1.04163 | 0.520814 | − | 0.853670i | \(-0.325629\pi\) | ||||
0.520814 | + | 0.853670i | \(0.325629\pi\) | |||||||
\(968\) | 2.51912e15 | 0.0952654 | ||||||||
\(969\) | 6.39723e15 | 0.240553 | ||||||||
\(970\) | −1.77857e15 | −0.0665006 | ||||||||
\(971\) | −4.51755e16 | −1.67957 | −0.839784 | − | 0.542921i | \(-0.817318\pi\) | ||||
−0.839784 | + | 0.542921i | \(0.817318\pi\) | |||||||
\(972\) | 1.63459e15 | 0.0604289 | ||||||||
\(973\) | −3.79911e16 | −1.39657 | ||||||||
\(974\) | 2.88129e15 | 0.105320 | ||||||||
\(975\) | −2.18049e15 | −0.0792554 | ||||||||
\(976\) | 3.00912e16 | 1.08759 | ||||||||
\(977\) | −2.54411e16 | −0.914356 | −0.457178 | − | 0.889375i | \(-0.651140\pi\) | ||||
−0.457178 | + | 0.889375i | \(0.651140\pi\) | |||||||
\(978\) | −5.34034e15 | −0.190856 | ||||||||
\(979\) | 2.79499e16 | 0.993288 | ||||||||
\(980\) | −1.68330e16 | −0.594864 | ||||||||
\(981\) | −4.77370e15 | −0.167755 | ||||||||
\(982\) | 1.78596e15 | 0.0624107 | ||||||||
\(983\) | 2.71225e16 | 0.942508 | 0.471254 | − | 0.881997i | \(-0.343801\pi\) | ||||
0.471254 | + | 0.881997i | \(0.343801\pi\) | |||||||
\(984\) | −5.39728e14 | −0.0186510 | ||||||||
\(985\) | 6.25799e15 | 0.215048 | ||||||||
\(986\) | 1.02432e15 | 0.0350037 | ||||||||
\(987\) | 3.45970e16 | 1.17569 | ||||||||
\(988\) | −3.98030e15 | −0.134509 | ||||||||
\(989\) | −4.40014e16 | −1.47872 | ||||||||
\(990\) | 1.34664e15 | 0.0450046 | ||||||||
\(991\) | 5.91660e16 | 1.96638 | 0.983189 | − | 0.182591i | \(-0.0584483\pi\) | ||||
0.983189 | + | 0.182591i | \(0.0584483\pi\) | |||||||
\(992\) | −9.22420e15 | −0.304870 | ||||||||
\(993\) | −2.43735e16 | −0.801121 | ||||||||
\(994\) | −5.40007e15 | −0.176512 | ||||||||
\(995\) | 4.51619e15 | 0.146806 | ||||||||
\(996\) | −1.27736e16 | −0.412938 | ||||||||
\(997\) | 1.87920e16 | 0.604158 | 0.302079 | − | 0.953283i | \(-0.402319\pi\) | ||||
0.302079 | + | 0.953283i | \(0.402319\pi\) | |||||||
\(998\) | 1.42626e14 | 0.00456018 | ||||||||
\(999\) | −6.82022e15 | −0.216864 |
(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 | 177.12.a.a.1.13 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.a.1.13 | ✓ | 26 | 1.1 | even | 1 | trivial |