Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [18,14,Mod(1,18)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(18, 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("18.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 18 = 2 \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 18.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: | \(19.3015672113\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 18.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −64.0000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4096.00 | 0.500000 | ||||||||
\(5\) | −15936.0 | −0.456115 | −0.228057 | − | 0.973648i | \(-0.573237\pi\) | ||||
−0.228057 | + | 0.973648i | \(0.573237\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 98252.0 | 0.315649 | 0.157824 | − | 0.987467i | \(-0.449552\pi\) | ||||
0.157824 | + | 0.987467i | \(0.449552\pi\) | |||||||
\(8\) | −262144. | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.01990e6 | 0.322522 | ||||||||
\(11\) | 1.63046e6 | 0.277497 | 0.138749 | − | 0.990328i | \(-0.455692\pi\) | ||||
0.138749 | + | 0.990328i | \(0.455692\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.23163e7 | 1.28230 | 0.641151 | − | 0.767415i | \(-0.278457\pi\) | ||||
0.641151 | + | 0.767415i | \(0.278457\pi\) | |||||||
\(14\) | −6.28813e6 | −0.223197 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.67772e7 | 0.250000 | ||||||||
\(17\) | −1.22938e8 | −1.23529 | −0.617644 | − | 0.786458i | \(-0.711913\pi\) | ||||
−0.617644 | + | 0.786458i | \(0.711913\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.42730e7 | −0.362187 | −0.181093 | − | 0.983466i | \(-0.557964\pi\) | ||||
−0.181093 | + | 0.983466i | \(0.557964\pi\) | |||||||
\(20\) | −6.52739e7 | −0.228057 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.04350e8 | −0.196220 | ||||||||
\(23\) | −1.06951e9 | −1.50645 | −0.753223 | − | 0.657765i | \(-0.771502\pi\) | ||||
−0.753223 | + | 0.657765i | \(0.771502\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.66747e8 | −0.791959 | ||||||||
\(26\) | −1.42824e9 | −0.906725 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.02440e8 | 0.157824 | ||||||||
\(29\) | −5.60709e9 | −1.75045 | −0.875227 | − | 0.483713i | \(-0.839288\pi\) | ||||
−0.875227 | + | 0.483713i | \(0.839288\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.16203e9 | 0.437533 | 0.218767 | − | 0.975777i | \(-0.429797\pi\) | ||||
0.218767 | + | 0.975777i | \(0.429797\pi\) | |||||||
\(32\) | −1.07374e9 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.86803e9 | 0.873480 | ||||||||
\(35\) | −1.56574e9 | −0.143972 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.95945e9 | −0.381852 | −0.190926 | − | 0.981604i | \(-0.561149\pi\) | ||||
−0.190926 | + | 0.981604i | \(0.561149\pi\) | |||||||
\(38\) | 4.75347e9 | 0.256105 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 4.17753e9 | 0.161261 | ||||||||
\(41\) | 2.16769e10 | 0.712691 | 0.356345 | − | 0.934354i | \(-0.384023\pi\) | ||||
0.356345 | + | 0.934354i | \(0.384023\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.11010e10 | −1.47402 | −0.737010 | − | 0.675881i | \(-0.763763\pi\) | ||||
−0.737010 | + | 0.675881i | \(0.763763\pi\) | |||||||
\(44\) | 6.67838e9 | 0.138749 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.84486e10 | 1.06522 | ||||||||
\(47\) | 1.36472e11 | 1.84675 | 0.923373 | − | 0.383903i | \(-0.125420\pi\) | ||||
0.923373 | + | 0.383903i | \(0.125420\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −8.72356e10 | −0.900366 | ||||||||
\(50\) | 6.18718e10 | 0.560000 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.14076e10 | 0.641151 | ||||||||
\(53\) | 5.57016e8 | 0.00345203 | 0.00172601 | − | 0.999999i | \(-0.499451\pi\) | ||||
0.00172601 | + | 0.999999i | \(0.499451\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.59831e10 | −0.126571 | ||||||||
\(56\) | −2.57562e10 | −0.111599 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.58854e11 | 1.23776 | ||||||||
\(59\) | −3.02212e11 | −0.932768 | −0.466384 | − | 0.884582i | \(-0.654443\pi\) | ||||
−0.466384 | + | 0.884582i | \(0.654443\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.90535e11 | −0.473513 | −0.236756 | − | 0.971569i | \(-0.576084\pi\) | ||||
−0.236756 | + | 0.971569i | \(0.576084\pi\) | |||||||
\(62\) | −1.38370e11 | −0.309383 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | −3.55633e11 | −0.584877 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.18343e11 | −1.24028 | −0.620139 | − | 0.784492i | \(-0.712924\pi\) | ||||
−0.620139 | + | 0.784492i | \(0.712924\pi\) | |||||||
\(68\) | −5.03554e11 | −0.617644 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00208e11 | 0.101804 | ||||||||
\(71\) | −1.08659e12 | −1.00667 | −0.503336 | − | 0.864091i | \(-0.667894\pi\) | ||||
−0.503336 | + | 0.864091i | \(0.667894\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.72759e10 | −0.0597648 | −0.0298824 | − | 0.999553i | \(-0.509513\pi\) | ||||
−0.0298824 | + | 0.999553i | \(0.509513\pi\) | |||||||
\(74\) | 3.81405e11 | 0.270010 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.04222e11 | −0.181093 | ||||||||
\(77\) | 1.60196e11 | 0.0875917 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.62436e12 | 1.21464 | 0.607320 | − | 0.794457i | \(-0.292244\pi\) | ||||
0.607320 | + | 0.794457i | \(0.292244\pi\) | |||||||
\(80\) | −2.67362e11 | −0.114029 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.38732e12 | −0.503948 | ||||||||
\(83\) | 3.26961e12 | 1.09771 | 0.548856 | − | 0.835917i | \(-0.315064\pi\) | ||||
0.548856 | + | 0.835917i | \(0.315064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.95914e12 | 0.563433 | ||||||||
\(86\) | 3.91047e12 | 1.04229 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.27416e11 | −0.0981101 | ||||||||
\(89\) | 5.92223e12 | 1.26314 | 0.631568 | − | 0.775320i | \(-0.282412\pi\) | ||||
0.631568 | + | 0.775320i | \(0.282412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.19262e12 | 0.404757 | ||||||||
\(92\) | −4.38071e12 | −0.753223 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.73420e12 | −1.30585 | ||||||||
\(95\) | 1.18361e12 | 0.165199 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.34013e12 | 0.650932 | 0.325466 | − | 0.945554i | \(-0.394479\pi\) | ||||
0.325466 | + | 0.945554i | \(0.394479\pi\) | |||||||
\(98\) | 5.58308e12 | 0.636655 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.95980e12 | −0.395980 | ||||||||
\(101\) | −7.40002e12 | −0.693656 | −0.346828 | − | 0.937929i | \(-0.612741\pi\) | ||||
−0.346828 | + | 0.937929i | \(0.612741\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.13810e12 | −0.754074 | −0.377037 | − | 0.926198i | \(-0.623057\pi\) | ||||
−0.377037 | + | 0.926198i | \(0.623057\pi\) | |||||||
\(104\) | −5.85009e12 | −0.453362 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.56490e10 | −0.00244095 | ||||||||
\(107\) | −6.61381e12 | −0.426047 | −0.213023 | − | 0.977047i | \(-0.568331\pi\) | ||||
−0.213023 | + | 0.977047i | \(0.568331\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.46236e13 | 0.835185 | 0.417592 | − | 0.908634i | \(-0.362874\pi\) | ||||
0.417592 | + | 0.908634i | \(0.362874\pi\) | |||||||
\(110\) | 1.66292e12 | 0.0894990 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.64840e12 | 0.0789122 | ||||||||
\(113\) | −2.97612e13 | −1.34475 | −0.672374 | − | 0.740212i | \(-0.734725\pi\) | ||||
−0.672374 | + | 0.740212i | \(0.734725\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.70437e13 | 0.687113 | ||||||||
\(116\) | −2.29666e13 | −0.875227 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.93416e13 | 0.659566 | ||||||||
\(119\) | −1.20789e13 | −0.389917 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.18643e13 | −0.922995 | ||||||||
\(122\) | 1.21943e13 | 0.334824 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.85568e12 | 0.218767 | ||||||||
\(125\) | 3.48592e13 | 0.817339 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.79603e13 | −1.22576 | −0.612881 | − | 0.790175i | \(-0.709990\pi\) | ||||
−0.612881 | + | 0.790175i | \(0.709990\pi\) | |||||||
\(128\) | −4.39805e12 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.27605e13 | 0.413571 | ||||||||
\(131\) | 3.17740e13 | 0.549298 | 0.274649 | − | 0.961545i | \(-0.411438\pi\) | ||||
0.274649 | + | 0.961545i | \(0.411438\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.29747e12 | −0.114324 | ||||||||
\(134\) | 5.87740e13 | 0.877008 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.22275e13 | 0.436740 | ||||||||
\(137\) | 6.89176e13 | 0.890526 | 0.445263 | − | 0.895400i | \(-0.353110\pi\) | ||||
0.445263 | + | 0.895400i | \(0.353110\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.18252e14 | −1.39064 | −0.695318 | − | 0.718702i | \(-0.744737\pi\) | ||||
−0.695318 | + | 0.718702i | \(0.744737\pi\) | |||||||
\(140\) | −6.41329e12 | −0.0719861 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.95420e13 | 0.711824 | ||||||||
\(143\) | 3.63859e13 | 0.355836 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.93546e13 | 0.798408 | ||||||||
\(146\) | 4.94566e12 | 0.0422601 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.44099e13 | −0.190926 | ||||||||
\(149\) | 1.55654e12 | 0.0116533 | 0.00582666 | − | 0.999983i | \(-0.498145\pi\) | ||||
0.00582666 | + | 0.999983i | \(0.498145\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.55424e13 | 0.244004 | 0.122002 | − | 0.992530i | \(-0.461069\pi\) | ||||
0.122002 | + | 0.992530i | \(0.461069\pi\) | |||||||
\(152\) | 1.94702e13 | 0.128052 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.02526e13 | −0.0619367 | ||||||||
\(155\) | −3.44541e13 | −0.199565 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.53865e14 | 0.819958 | 0.409979 | − | 0.912095i | \(-0.365536\pi\) | ||||
0.409979 | + | 0.912095i | \(0.365536\pi\) | |||||||
\(158\) | −1.67959e14 | −0.858881 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.71111e13 | 0.0806305 | ||||||||
\(161\) | −1.05081e14 | −0.475508 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.99640e14 | −0.833736 | −0.416868 | − | 0.908967i | \(-0.636872\pi\) | ||||
−0.416868 | + | 0.908967i | \(0.636872\pi\) | |||||||
\(164\) | 8.87884e13 | 0.356345 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.09255e14 | −0.776199 | ||||||||
\(167\) | −4.64940e14 | −1.65859 | −0.829297 | − | 0.558809i | \(-0.811259\pi\) | ||||
−0.829297 | + | 0.558809i | \(0.811259\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.95142e14 | 0.644300 | ||||||||
\(170\) | −1.25385e14 | −0.398407 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.50270e14 | −0.737010 | ||||||||
\(173\) | −3.76731e14 | −1.06840 | −0.534198 | − | 0.845360i | \(-0.679386\pi\) | ||||
−0.534198 | + | 0.845360i | \(0.679386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.49848e13 | −0.249981 | ||||||||
\(176\) | 2.73546e13 | 0.0693743 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.79023e14 | −0.893172 | ||||||||
\(179\) | 7.32554e14 | 1.66454 | 0.832271 | − | 0.554369i | \(-0.187040\pi\) | ||||
0.832271 | + | 0.554369i | \(0.187040\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.37497e14 | 1.55901 | 0.779506 | − | 0.626395i | \(-0.215470\pi\) | ||||
0.779506 | + | 0.626395i | \(0.215470\pi\) | |||||||
\(182\) | −1.40328e14 | −0.286207 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.80365e14 | 0.532609 | ||||||||
\(185\) | 9.49698e13 | 0.174168 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.00446e14 | −0.342789 | ||||||||
\(188\) | 5.58989e14 | 0.923373 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −7.57513e13 | −0.116813 | ||||||||
\(191\) | 2.20757e14 | 0.329001 | 0.164501 | − | 0.986377i | \(-0.447399\pi\) | ||||
0.164501 | + | 0.986377i | \(0.447399\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.11051e15 | 1.54667 | 0.773337 | − | 0.633995i | \(-0.218586\pi\) | ||||
0.773337 | + | 0.633995i | \(0.218586\pi\) | |||||||
\(194\) | −3.41769e14 | −0.460279 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.57317e14 | −0.450183 | ||||||||
\(197\) | 1.37055e15 | 1.67057 | 0.835287 | − | 0.549815i | \(-0.185302\pi\) | ||||
0.835287 | + | 0.549815i | \(0.185302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.76425e14 | −1.11454 | −0.557268 | − | 0.830333i | \(-0.688150\pi\) | ||||
−0.557268 | + | 0.830333i | \(0.688150\pi\) | |||||||
\(200\) | 2.53427e14 | 0.280000 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.73602e14 | 0.490489 | ||||||||
\(203\) | −5.50908e14 | −0.552529 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.45442e14 | −0.325069 | ||||||||
\(206\) | 5.84838e14 | 0.533211 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.74405e14 | 0.320576 | ||||||||
\(209\) | −1.21099e14 | −0.100506 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.13103e15 | −0.882343 | −0.441171 | − | 0.897423i | \(-0.645437\pi\) | ||||
−0.441171 | + | 0.897423i | \(0.645437\pi\) | |||||||
\(212\) | 2.28154e12 | 0.00172601 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.23284e14 | 0.301261 | ||||||||
\(215\) | 9.73706e14 | 0.672323 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.12424e14 | 0.138107 | ||||||||
\(218\) | −9.35912e14 | −0.590565 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.06427e14 | −0.0632853 | ||||||||
\(221\) | −2.74352e15 | −1.58401 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.49575e15 | −1.90352 | −0.951762 | − | 0.306837i | \(-0.900729\pi\) | ||||
−0.951762 | + | 0.306837i | \(0.900729\pi\) | |||||||
\(224\) | −1.05497e14 | −0.0557994 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.90472e15 | 0.950880 | ||||||||
\(227\) | −2.16551e15 | −1.05049 | −0.525245 | − | 0.850951i | \(-0.676027\pi\) | ||||
−0.525245 | + | 0.850951i | \(0.676027\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.65691e15 | 1.21744 | 0.608719 | − | 0.793386i | \(-0.291684\pi\) | ||||
0.608719 | + | 0.793386i | \(0.291684\pi\) | |||||||
\(230\) | −1.09080e15 | −0.485862 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.46987e15 | 0.618879 | ||||||||
\(233\) | 1.28597e15 | 0.526525 | 0.263262 | − | 0.964724i | \(-0.415202\pi\) | ||||
0.263262 | + | 0.964724i | \(0.415202\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.17482e15 | −0.842329 | ||||||||
\(236\) | −1.23786e15 | −0.466384 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.73050e14 | 0.275713 | ||||||||
\(239\) | −3.90092e15 | −1.35388 | −0.676940 | − | 0.736038i | \(-0.736694\pi\) | ||||
−0.676940 | + | 0.736038i | \(0.736694\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.93072e15 | 1.29229 | 0.646147 | − | 0.763213i | \(-0.276379\pi\) | ||||
0.646147 | + | 0.763213i | \(0.276379\pi\) | |||||||
\(242\) | 2.03932e15 | 0.652656 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −7.80433e14 | −0.236756 | ||||||||
\(245\) | 1.39019e15 | 0.410670 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.65750e15 | −0.464433 | ||||||||
\(248\) | −5.66763e14 | −0.154691 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.23099e15 | −0.577946 | ||||||||
\(251\) | 6.50267e15 | 1.64139 | 0.820696 | − | 0.571365i | \(-0.193586\pi\) | ||||
0.820696 | + | 0.571365i | \(0.193586\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.74380e15 | −0.418035 | ||||||||
\(254\) | 3.70946e15 | 0.866745 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.81475e14 | 0.0625000 | ||||||||
\(257\) | −2.69802e15 | −0.584090 | −0.292045 | − | 0.956405i | \(-0.594336\pi\) | ||||
−0.292045 | + | 0.956405i | \(0.594336\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.85528e14 | −0.120531 | ||||||||
\(260\) | −1.45667e15 | −0.292439 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −2.03353e15 | −0.388412 | ||||||||
\(263\) | 5.08958e15 | 0.948352 | 0.474176 | − | 0.880430i | \(-0.342746\pi\) | ||||
0.474176 | + | 0.880430i | \(0.342746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.87660e12 | −0.00157452 | ||||||||
\(266\) | 4.67038e14 | 0.0808391 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −3.76153e15 | −0.620139 | ||||||||
\(269\) | 7.06228e15 | 1.13646 | 0.568231 | − | 0.822869i | \(-0.307628\pi\) | ||||
0.568231 | + | 0.822869i | \(0.307628\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.25952e15 | 0.806576 | 0.403288 | − | 0.915073i | \(-0.367867\pi\) | ||||
0.403288 | + | 0.915073i | \(0.367867\pi\) | |||||||
\(272\) | −2.06256e15 | −0.308822 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.41073e15 | −0.629697 | ||||||||
\(275\) | −1.57625e15 | −0.219767 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.34084e16 | 1.78344 | 0.891722 | − | 0.452584i | \(-0.149498\pi\) | ||||
0.891722 | + | 0.452584i | \(0.149498\pi\) | |||||||
\(278\) | 7.56815e15 | 0.983329 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.10450e14 | 0.0509018 | ||||||||
\(281\) | −1.82029e15 | −0.220572 | −0.110286 | − | 0.993900i | \(-0.535177\pi\) | ||||
−0.110286 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.56765e15 | −0.528544 | −0.264272 | − | 0.964448i | \(-0.585132\pi\) | ||||
−0.264272 | + | 0.964448i | \(0.585132\pi\) | |||||||
\(284\) | −4.45069e15 | −0.503336 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.32870e15 | −0.251614 | ||||||||
\(287\) | 2.12979e15 | 0.224960 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.20917e15 | 0.525936 | ||||||||
\(290\) | −5.71869e15 | −0.564560 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −3.16522e14 | −0.0298824 | ||||||||
\(293\) | −1.34769e16 | −1.24437 | −0.622186 | − | 0.782869i | \(-0.713755\pi\) | ||||
−0.622186 | + | 0.782869i | \(0.713755\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.81605e15 | 0.425449 | ||||||||
\(296\) | 1.56223e15 | 0.135005 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.96186e13 | −0.00824014 | ||||||||
\(299\) | −2.38675e16 | −1.93172 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00330e15 | −0.465273 | ||||||||
\(302\) | −2.27472e15 | −0.172537 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.24609e15 | −0.0905467 | ||||||||
\(305\) | 3.03637e15 | 0.215976 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.20152e15 | −0.218252 | −0.109126 | − | 0.994028i | \(-0.534805\pi\) | ||||
−0.109126 | + | 0.994028i | \(0.534805\pi\) | |||||||
\(308\) | 6.56164e14 | 0.0437958 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.20506e15 | 0.141114 | ||||||||
\(311\) | 2.27156e15 | 0.142358 | 0.0711789 | − | 0.997464i | \(-0.477324\pi\) | ||||
0.0711789 | + | 0.997464i | \(0.477324\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.03562e16 | −1.22365 | −0.611827 | − | 0.790991i | \(-0.709565\pi\) | ||||
−0.611827 | + | 0.790991i | \(0.709565\pi\) | |||||||
\(314\) | −9.84735e15 | −0.579798 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.07494e16 | 0.607320 | ||||||||
\(317\) | 4.16681e15 | 0.230631 | 0.115316 | − | 0.993329i | \(-0.463212\pi\) | ||||
0.115316 | + | 0.993329i | \(0.463212\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.14216e15 | −0.485746 | ||||||||
\(320\) | −1.09511e15 | −0.0570144 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 6.72521e15 | 0.336235 | ||||||||
\(323\) | 9.13097e15 | 0.447405 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.15742e16 | −1.01553 | ||||||||
\(326\) | 1.27770e16 | 0.589541 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.68246e15 | −0.251974 | ||||||||
\(329\) | 1.34086e16 | 0.582923 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.19092e16 | 1.75157 | 0.875785 | − | 0.482702i | \(-0.160344\pi\) | ||||
0.875785 | + | 0.482702i | \(0.160344\pi\) | |||||||
\(332\) | 1.33923e16 | 0.548856 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.97562e16 | 1.17280 | ||||||||
\(335\) | 1.46347e16 | 0.565709 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.06740e16 | −0.396946 | −0.198473 | − | 0.980106i | \(-0.563598\pi\) | ||||
−0.198473 | + | 0.980106i | \(0.563598\pi\) | |||||||
\(338\) | −1.24891e16 | −0.455589 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 8.02464e15 | 0.281717 | ||||||||
\(341\) | 3.52511e15 | 0.121414 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.80906e16 | −0.599848 | ||||||||
\(344\) | 1.60173e16 | 0.521145 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.41108e16 | 0.755470 | ||||||||
\(347\) | 2.04361e16 | 0.628429 | 0.314214 | − | 0.949352i | \(-0.398259\pi\) | ||||
0.314214 | + | 0.949352i | \(0.398259\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.64023e16 | −0.485893 | −0.242947 | − | 0.970040i | \(-0.578114\pi\) | ||||
−0.242947 | + | 0.970040i | \(0.578114\pi\) | |||||||
\(350\) | 6.07903e15 | 0.176763 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.75070e15 | −0.0490551 | ||||||||
\(353\) | 1.55775e16 | 0.428510 | 0.214255 | − | 0.976778i | \(-0.431268\pi\) | ||||
0.214255 | + | 0.976778i | \(0.431268\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.73160e16 | 0.459158 | ||||||||
\(356\) | 2.42575e16 | 0.631568 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.68834e16 | −1.17701 | ||||||||
\(359\) | −1.79339e16 | −0.442140 | −0.221070 | − | 0.975258i | \(-0.570955\pi\) | ||||
−0.221070 | + | 0.975258i | \(0.570955\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.65365e16 | −0.868821 | ||||||||
\(362\) | −4.71998e16 | −1.10239 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.98098e15 | 0.202379 | ||||||||
\(365\) | 1.23147e15 | 0.0272596 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.84657e16 | 1.03539 | 0.517697 | − | 0.855564i | \(-0.326790\pi\) | ||||
0.517697 | + | 0.855564i | \(0.326790\pi\) | |||||||
\(368\) | −1.79434e16 | −0.376611 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −6.07807e15 | −0.123156 | ||||||||
\(371\) | 5.47279e13 | 0.00108963 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.64940e16 | −0.701640 | −0.350820 | − | 0.936443i | \(-0.614097\pi\) | ||||
−0.350820 | + | 0.936443i | \(0.614097\pi\) | |||||||
\(374\) | 1.28285e16 | 0.242388 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.57753e16 | −0.652924 | ||||||||
\(377\) | −1.25130e17 | −2.24461 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.25386e16 | 0.563955 | 0.281977 | − | 0.959421i | \(-0.409010\pi\) | ||||
0.281977 | + | 0.959421i | \(0.409010\pi\) | |||||||
\(380\) | 4.84808e15 | 0.0825994 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.41284e16 | −0.232639 | ||||||||
\(383\) | −3.03495e16 | −0.491314 | −0.245657 | − | 0.969357i | \(-0.579004\pi\) | ||||
−0.245657 | + | 0.969357i | \(0.579004\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.55289e15 | −0.0399519 | ||||||||
\(386\) | −7.10724e16 | −1.09366 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.18732e16 | 0.325466 | ||||||||
\(389\) | 4.62220e15 | 0.0676358 | 0.0338179 | − | 0.999428i | \(-0.489233\pi\) | ||||
0.0338179 | + | 0.999428i | \(0.489233\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.31483e17 | 1.86089 | ||||||||
\(392\) | 2.28683e16 | 0.318327 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.77154e16 | −1.18127 | ||||||||
\(395\) | −4.18219e16 | −0.554016 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.28843e15 | 0.0549743 | 0.0274872 | − | 0.999622i | \(-0.491249\pi\) | ||||
0.0274872 | + | 0.999622i | \(0.491249\pi\) | |||||||
\(398\) | 6.24912e16 | 0.788096 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.62193e16 | −0.197990 | ||||||||
\(401\) | 1.12464e17 | 1.35075 | 0.675376 | − | 0.737473i | \(-0.263981\pi\) | ||||
0.675376 | + | 0.737473i | \(0.263981\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.82485e16 | 0.561050 | ||||||||
\(404\) | −3.03105e16 | −0.346828 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.52581e16 | 0.390697 | ||||||||
\(407\) | −9.71667e15 | −0.105963 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.47607e16 | 0.472820 | 0.236410 | − | 0.971653i | \(-0.424029\pi\) | ||||
0.236410 | + | 0.971653i | \(0.424029\pi\) | |||||||
\(410\) | 2.21083e16 | 0.229858 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.74296e16 | −0.377037 | ||||||||
\(413\) | −2.96929e16 | −0.294427 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.21045e16 | −0.500682 | ||||||||
\(416\) | −2.39620e16 | −0.226681 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.75036e15 | 0.0710683 | ||||||||
\(419\) | 1.39060e17 | 1.25549 | 0.627743 | − | 0.778421i | \(-0.283979\pi\) | ||||
0.627743 | + | 0.778421i | \(0.283979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.69201e16 | −0.410700 | −0.205350 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205350 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(422\) | 7.23858e16 | 0.623911 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.46018e14 | −0.00122048 | ||||||||
\(425\) | 1.18850e17 | 0.978297 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.87205e16 | −0.149464 | ||||||||
\(428\) | −2.70902e16 | −0.213023 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −6.23172e16 | −0.475404 | ||||||||
\(431\) | 3.57649e16 | 0.268754 | 0.134377 | − | 0.990930i | \(-0.457097\pi\) | ||||
0.134377 | + | 0.990930i | \(0.457097\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.90804e17 | −1.39129 | −0.695644 | − | 0.718386i | \(-0.744881\pi\) | ||||
−0.695644 | + | 0.718386i | \(0.744881\pi\) | |||||||
\(434\) | −1.35951e16 | −0.0976563 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.98984e16 | 0.417592 | ||||||||
\(437\) | 7.94356e16 | 0.545615 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.80923e16 | 0.120635 | 0.0603176 | − | 0.998179i | \(-0.480789\pi\) | ||||
0.0603176 | + | 0.998179i | \(0.480789\pi\) | |||||||
\(440\) | 6.81131e15 | 0.0447495 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.75585e17 | 1.12007 | ||||||||
\(443\) | −2.24850e16 | −0.141341 | −0.0706705 | − | 0.997500i | \(-0.522514\pi\) | ||||
−0.0706705 | + | 0.997500i | \(0.522514\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.43767e16 | −0.576135 | ||||||||
\(446\) | 2.23728e17 | 1.34599 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.75183e15 | 0.0394561 | ||||||||
\(449\) | −1.74031e17 | −1.00236 | −0.501181 | − | 0.865343i | \(-0.667101\pi\) | ||||
−0.501181 | + | 0.865343i | \(0.667101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.53433e16 | 0.197770 | ||||||||
\(452\) | −1.21902e17 | −0.672374 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.38593e17 | 0.742809 | ||||||||
\(455\) | −3.49416e16 | −0.184616 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.39682e17 | 1.23078 | 0.615389 | − | 0.788224i | \(-0.288999\pi\) | ||||
0.615389 | + | 0.788224i | \(0.288999\pi\) | |||||||
\(458\) | −1.70042e17 | −0.860858 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.98110e16 | 0.343556 | ||||||||
\(461\) | −4.80424e16 | −0.233114 | −0.116557 | − | 0.993184i | \(-0.537186\pi\) | ||||
−0.116557 | + | 0.993184i | \(0.537186\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.34366e17 | −1.10565 | −0.552825 | − | 0.833298i | \(-0.686450\pi\) | ||||
−0.552825 | + | 0.833298i | \(0.686450\pi\) | |||||||
\(464\) | −9.40714e16 | −0.437613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.23023e16 | −0.372309 | ||||||||
\(467\) | −3.01241e17 | −1.34386 | −0.671931 | − | 0.740614i | \(-0.734535\pi\) | ||||
−0.671931 | + | 0.740614i | \(0.734535\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.02290e16 | −0.391492 | ||||||||
\(470\) | 1.39188e17 | 0.595616 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 7.92230e16 | 0.329783 | ||||||||
\(473\) | −9.96230e16 | −0.409037 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 7.18032e16 | 0.286837 | ||||||||
\(476\) | −4.94752e16 | −0.194959 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.49659e17 | 0.957338 | ||||||||
\(479\) | −1.06328e17 | −0.402224 | −0.201112 | − | 0.979568i | \(-0.564456\pi\) | ||||
−0.201112 | + | 0.979568i | \(0.564456\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.32993e17 | −0.489650 | ||||||||
\(482\) | −2.51566e17 | −0.913790 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.30516e17 | −0.461498 | ||||||||
\(485\) | −8.51004e16 | −0.296900 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5.55030e17 | −1.88529 | −0.942646 | − | 0.333795i | \(-0.891671\pi\) | ||||
−0.942646 | + | 0.333795i | \(0.891671\pi\) | |||||||
\(488\) | 4.99477e16 | 0.167412 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.89719e16 | −0.290388 | ||||||||
\(491\) | 4.75553e17 | 1.53168 | 0.765841 | − | 0.643029i | \(-0.222323\pi\) | ||||
0.765841 | + | 0.643029i | \(0.222323\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.89324e17 | 2.16231 | ||||||||
\(494\) | 1.06080e17 | 0.328404 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.62729e16 | 0.109383 | ||||||||
\(497\) | −1.06760e17 | −0.317755 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.85876e17 | −0.538977 | −0.269489 | − | 0.963004i | \(-0.586855\pi\) | ||||
−0.269489 | + | 0.963004i | \(0.586855\pi\) | |||||||
\(500\) | 1.42783e17 | 0.408670 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.16171e17 | −1.16064 | ||||||||
\(503\) | 1.23322e17 | 0.339508 | 0.169754 | − | 0.985486i | \(-0.445703\pi\) | ||||
0.169754 | + | 0.985486i | \(0.445703\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.17927e17 | 0.316387 | ||||||||
\(506\) | 1.11603e17 | 0.295595 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.37405e17 | −0.612881 | ||||||||
\(509\) | −7.00587e16 | −0.178565 | −0.0892826 | − | 0.996006i | \(-0.528457\pi\) | ||||
−0.0892826 | + | 0.996006i | \(0.528457\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.59251e15 | −0.0188647 | ||||||||
\(512\) | −1.80144e16 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.72673e17 | 0.413014 | ||||||||
\(515\) | 1.45625e17 | 0.343944 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.22513e17 | 0.512467 | ||||||||
\(518\) | 3.74738e16 | 0.0852284 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.32270e16 | 0.206785 | ||||||||
\(521\) | 8.63330e17 | 1.89118 | 0.945588 | − | 0.325368i | \(-0.105488\pi\) | ||||
0.945588 | + | 0.325368i | \(0.105488\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.05623e17 | 0.866685 | 0.433343 | − | 0.901229i | \(-0.357334\pi\) | ||||
0.433343 | + | 0.901229i | \(0.357334\pi\) | |||||||
\(524\) | 1.30146e17 | 0.274649 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.25733e17 | −0.670586 | ||||||||
\(527\) | −2.65796e17 | −0.540479 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.39813e17 | 1.26938 | ||||||||
\(530\) | 5.68102e14 | 0.00111335 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.98904e16 | −0.0571619 | ||||||||
\(533\) | 4.83747e17 | 0.913885 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.05398e17 | 0.194326 | ||||||||
\(536\) | 2.40738e17 | 0.438504 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4.51986e17 | −0.803601 | ||||||||
\(539\) | −1.42234e17 | −0.249849 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.11068e16 | 0.156232 | 0.0781158 | − | 0.996944i | \(-0.475110\pi\) | ||||
0.0781158 | + | 0.996944i | \(0.475110\pi\) | |||||||
\(542\) | −3.36609e17 | −0.570335 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.32004e17 | 0.218370 | ||||||||
\(545\) | −2.33042e17 | −0.380940 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.00896e17 | −0.320667 | −0.160334 | − | 0.987063i | \(-0.551257\pi\) | ||||
−0.160334 | + | 0.987063i | \(0.551257\pi\) | |||||||
\(548\) | 2.82286e17 | 0.445263 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.00880e17 | 0.155398 | ||||||||
\(551\) | 4.16455e17 | 0.633991 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.57849e17 | 0.383400 | ||||||||
\(554\) | −8.58139e17 | −1.26109 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.84362e17 | −0.695318 | ||||||||
\(557\) | −6.99866e17 | −0.993016 | −0.496508 | − | 0.868032i | \(-0.665385\pi\) | ||||
−0.496508 | + | 0.868032i | \(0.665385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.36355e18 | −1.89014 | ||||||||
\(560\) | −2.62688e16 | −0.0359930 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.16499e17 | 0.155968 | ||||||||
\(563\) | −1.36211e18 | −1.80263 | −0.901317 | − | 0.433161i | \(-0.857398\pi\) | ||||
−0.901317 | + | 0.433161i | \(0.857398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.74275e17 | 0.613359 | ||||||||
\(566\) | 2.92330e17 | 0.373737 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.84844e17 | 0.355912 | ||||||||
\(569\) | −1.39312e18 | −1.72091 | −0.860455 | − | 0.509526i | \(-0.829821\pi\) | ||||
−0.860455 | + | 0.509526i | \(0.829821\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.08264e17 | −0.855186 | −0.427593 | − | 0.903971i | \(-0.640638\pi\) | ||||
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(572\) | 1.49037e17 | 0.177918 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.36307e17 | −0.159071 | ||||||||
\(575\) | 1.03394e18 | 1.19304 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.33945e17 | 0.263920 | 0.131960 | − | 0.991255i | \(-0.457873\pi\) | ||||
0.131960 | + | 0.991255i | \(0.457873\pi\) | |||||||
\(578\) | −3.33387e17 | −0.371893 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.65996e17 | 0.399204 | ||||||||
\(581\) | 3.21246e17 | 0.346491 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 9.08194e14 | 0.000957928 0 | ||||||||
\(584\) | 2.02574e16 | 0.0211300 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.62521e17 | 0.879904 | ||||||||
\(587\) | −1.11658e18 | −1.12653 | −0.563264 | − | 0.826277i | \(-0.690455\pi\) | ||||
−0.563264 | + | 0.826277i | \(0.690455\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.60581e17 | −0.158469 | ||||||||
\(590\) | −3.08227e17 | −0.300838 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.99830e16 | −0.0954630 | ||||||||
\(593\) | 1.28180e18 | 1.21050 | 0.605251 | − | 0.796034i | \(-0.293073\pi\) | ||||
0.605251 | + | 0.796034i | \(0.293073\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.92489e17 | 0.177847 | ||||||||
\(596\) | 6.37559e15 | 0.00582666 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.52752e18 | 1.36593 | ||||||||
\(599\) | −6.88211e17 | −0.608761 | −0.304381 | − | 0.952550i | \(-0.598449\pi\) | ||||
−0.304381 | + | 0.952550i | \(0.598449\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.33658e17 | −0.808172 | −0.404086 | − | 0.914721i | \(-0.632410\pi\) | ||||
−0.404086 | + | 0.914721i | \(0.632410\pi\) | |||||||
\(602\) | 3.84211e17 | 0.328998 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.45582e17 | 0.122002 | ||||||||
\(605\) | 5.07789e17 | 0.420992 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.16897e17 | −0.338300 | −0.169150 | − | 0.985590i | \(-0.554102\pi\) | ||||
−0.169150 | + | 0.985590i | \(0.554102\pi\) | |||||||
\(608\) | 7.97500e16 | 0.0640262 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.94328e17 | −0.152718 | ||||||||
\(611\) | 3.04555e18 | 2.36809 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.83422e17 | −0.367988 | −0.183994 | − | 0.982927i | \(-0.558903\pi\) | ||||
−0.183994 | + | 0.982927i | \(0.558903\pi\) | |||||||
\(614\) | 2.04898e17 | 0.154327 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.19945e16 | −0.0309683 | ||||||||
\(617\) | −1.45200e18 | −1.05953 | −0.529764 | − | 0.848145i | \(-0.677719\pi\) | ||||
−0.529764 | + | 0.848145i | \(0.677719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.42177e18 | 1.01588 | 0.507938 | − | 0.861394i | \(-0.330408\pi\) | ||||
0.507938 | + | 0.861394i | \(0.330408\pi\) | |||||||
\(620\) | −1.41124e17 | −0.0997827 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.45380e17 | −0.100662 | ||||||||
\(623\) | 5.81871e17 | 0.398708 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.24595e17 | 0.419158 | ||||||||
\(626\) | 1.30280e18 | 0.865254 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.30230e17 | 0.409979 | ||||||||
\(629\) | 7.32643e17 | 0.471697 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.75897e18 | −1.74003 | −0.870013 | − | 0.493029i | \(-0.835890\pi\) | ||||
−0.870013 | + | 0.493029i | \(0.835890\pi\) | |||||||
\(632\) | −6.87961e17 | −0.429440 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.66676e17 | −0.163081 | ||||||||
\(635\) | 9.23655e17 | 0.559089 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.94678e18 | −1.15454 | ||||||||
\(638\) | 5.85098e17 | 0.343474 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.00873e16 | 0.0403152 | ||||||||
\(641\) | 2.14378e18 | 1.22068 | 0.610341 | − | 0.792139i | \(-0.291033\pi\) | ||||
0.610341 | + | 0.792139i | \(0.291033\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.18189e18 | 1.21748 | 0.608739 | − | 0.793371i | \(-0.291676\pi\) | ||||
0.608739 | + | 0.793371i | \(0.291676\pi\) | |||||||
\(644\) | −4.30413e17 | −0.237754 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.84382e17 | −0.316363 | ||||||||
\(647\) | −2.20644e18 | −1.18254 | −0.591269 | − | 0.806475i | \(-0.701373\pi\) | ||||
−0.591269 | + | 0.806475i | \(0.701373\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.92746e17 | −0.258841 | ||||||||
\(650\) | 1.38075e18 | 0.718089 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.17727e17 | −0.416868 | ||||||||
\(653\) | −1.68563e18 | −0.850797 | −0.425398 | − | 0.905006i | \(-0.639866\pi\) | ||||
−0.425398 | + | 0.905006i | \(0.639866\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.06350e17 | −0.250543 | ||||||||
\(656\) | 3.63677e17 | 0.178173 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.58153e17 | −0.412189 | ||||||||
\(659\) | −1.13582e18 | −0.540198 | −0.270099 | − | 0.962833i | \(-0.587056\pi\) | ||||
−0.270099 | + | 0.962833i | \(0.587056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.50291e18 | 0.700850 | 0.350425 | − | 0.936591i | \(-0.386037\pi\) | ||||
0.350425 | + | 0.936591i | \(0.386037\pi\) | |||||||
\(662\) | −2.68219e18 | −1.23855 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.57108e17 | −0.388100 | ||||||||
\(665\) | 1.16292e17 | 0.0521448 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.99683e18 | 2.63696 | ||||||||
\(668\) | −1.90439e18 | −0.829297 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −9.36622e17 | −0.400017 | ||||||||
\(671\) | −3.10661e17 | −0.131399 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.18721e17 | −0.0907387 | −0.0453693 | − | 0.998970i | \(-0.514446\pi\) | ||||
−0.0453693 | + | 0.998970i | \(0.514446\pi\) | |||||||
\(674\) | 6.83134e17 | 0.280683 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.99303e17 | 0.322150 | ||||||||
\(677\) | −3.22640e18 | −1.28793 | −0.643965 | − | 0.765055i | \(-0.722712\pi\) | ||||
−0.643965 | + | 0.765055i | \(0.722712\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.24679e17 | 0.205466 | ||||||||
\(680\) | −5.13577e17 | −0.199204 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.25607e17 | −0.0858528 | ||||||||
\(683\) | −2.67590e18 | −1.00864 | −0.504319 | − | 0.863517i | \(-0.668257\pi\) | ||||
−0.504319 | + | 0.863517i | \(0.668257\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.09827e18 | −0.406182 | ||||||||
\(686\) | 1.15780e18 | 0.424157 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.02511e18 | −0.368505 | ||||||||
\(689\) | 1.24305e16 | 0.00442654 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.91753e18 | 1.36900 | 0.684502 | − | 0.729011i | \(-0.260020\pi\) | ||||
0.684502 | + | 0.729011i | \(0.260020\pi\) | |||||||
\(692\) | −1.54309e18 | −0.534198 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.30791e18 | −0.444366 | ||||||||
\(695\) | 1.88447e18 | 0.634290 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.66491e18 | −0.880378 | ||||||||
\(698\) | 1.04975e18 | 0.343578 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.89058e17 | −0.124990 | ||||||||
\(701\) | 3.13316e18 | 0.997277 | 0.498638 | − | 0.866810i | \(-0.333834\pi\) | ||||
0.498638 | + | 0.866810i | \(0.333834\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.42626e17 | 0.138302 | ||||||||
\(704\) | 1.12045e17 | 0.0346872 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.96957e17 | −0.303002 | ||||||||
\(707\) | −7.27067e17 | −0.218952 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.61211e18 | −0.476643 | −0.238322 | − | 0.971186i | \(-0.576597\pi\) | ||||
−0.238322 | + | 0.971186i | \(0.576597\pi\) | |||||||
\(710\) | −1.10822e18 | −0.324674 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.55248e18 | −0.446586 | ||||||||
\(713\) | −2.31231e18 | −0.659120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.79846e17 | −0.162302 | ||||||||
\(716\) | 3.00054e18 | 0.832271 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.14777e18 | 0.312640 | ||||||||
\(719\) | −2.04122e18 | −0.551000 | −0.275500 | − | 0.961301i | \(-0.588843\pi\) | ||||
−0.275500 | + | 0.961301i | \(0.588843\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.97836e17 | −0.238022 | ||||||||
\(722\) | 2.33834e18 | 0.614349 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.02079e18 | 0.779506 | ||||||||
\(725\) | 5.42064e18 | 1.38629 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.72741e18 | −0.433932 | −0.216966 | − | 0.976179i | \(-0.569616\pi\) | ||||
−0.216966 | + | 0.976179i | \(0.569616\pi\) | |||||||
\(728\) | −5.74783e17 | −0.143103 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.88140e16 | −0.0192755 | ||||||||
\(731\) | 7.51164e18 | 1.82084 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.12183e18 | −0.743419 | −0.371709 | − | 0.928349i | \(-0.621228\pi\) | ||||
−0.371709 | + | 0.928349i | \(0.621228\pi\) | |||||||
\(734\) | −3.10181e18 | −0.732133 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.14838e18 | 0.266305 | ||||||||
\(737\) | −1.49733e18 | −0.344174 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.01232e18 | 0.906164 | 0.453082 | − | 0.891469i | \(-0.350325\pi\) | ||||
0.453082 | + | 0.891469i | \(0.350325\pi\) | |||||||
\(740\) | 3.88996e17 | 0.0870842 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.50259e15 | −0.000770484 0 | ||||||||
\(743\) | 4.94213e18 | 1.07767 | 0.538837 | − | 0.842410i | \(-0.318864\pi\) | ||||
0.538837 | + | 0.842410i | \(0.318864\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.48050e16 | −0.00531525 | ||||||||
\(746\) | 2.33562e18 | 0.496134 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.21027e17 | −0.171394 | ||||||||
\(749\) | −6.49820e17 | −0.134481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.93899e18 | −0.394381 | −0.197191 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197191 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(752\) | 2.28962e18 | 0.461687 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00829e18 | 1.58718 | ||||||||
\(755\) | −5.66404e17 | −0.111294 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.50167e17 | −0.0869461 | −0.0434730 | − | 0.999055i | \(-0.513842\pi\) | ||||
−0.0434730 | + | 0.999055i | \(0.513842\pi\) | |||||||
\(758\) | −2.08247e18 | −0.398776 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.10277e17 | −0.0584066 | ||||||||
\(761\) | 5.48520e18 | 1.02375 | 0.511873 | − | 0.859061i | \(-0.328952\pi\) | ||||
0.511873 | + | 0.859061i | \(0.328952\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.43680e18 | 0.263625 | ||||||||
\(764\) | 9.04220e17 | 0.164501 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.94237e18 | 0.347411 | ||||||||
\(767\) | −6.74425e18 | −1.19609 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.62553e18 | −1.15531 | −0.577656 | − | 0.816280i | \(-0.696033\pi\) | ||||
−0.577656 | + | 0.816280i | \(0.696033\pi\) | |||||||
\(770\) | 1.63385e17 | 0.0282502 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.54864e18 | 0.773337 | ||||||||
\(773\) | −7.66142e18 | −1.29164 | −0.645822 | − | 0.763488i | \(-0.723485\pi\) | ||||
−0.645822 | + | 0.763488i | \(0.723485\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.09014e18 | −0.346508 | ||||||||
\(776\) | −1.39988e18 | −0.230139 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.95821e17 | −0.0478257 | ||||||||
\(779\) | −1.61000e18 | −0.258127 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.77165e18 | −0.279349 | ||||||||
\(782\) | −8.41493e18 | −1.31585 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.46357e18 | −0.225091 | ||||||||
\(785\) | −2.45199e18 | −0.373995 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.71301e18 | 1.45720 | 0.728598 | − | 0.684941i | \(-0.240172\pi\) | ||||
0.728598 | + | 0.684941i | \(0.240172\pi\) | |||||||
\(788\) | 5.61379e18 | 0.835287 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 2.67660e18 | 0.391748 | ||||||||
\(791\) | −2.92410e18 | −0.424468 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.25205e18 | −0.607187 | ||||||||
\(794\) | −2.74459e17 | −0.0388727 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.99944e18 | −0.557268 | ||||||||
\(797\) | −7.05558e18 | −0.975110 | −0.487555 | − | 0.873092i | \(-0.662111\pi\) | ||||
−0.487555 | + | 0.873092i | \(0.662111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.67776e19 | −2.28126 | ||||||||
\(800\) | 1.03804e18 | 0.140000 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.19771e18 | −0.955126 | ||||||||
\(803\) | −1.25996e17 | −0.0165846 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.67458e18 | 0.216886 | ||||||||
\(806\) | −3.08791e18 | −0.396722 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.93987e18 | 0.245244 | ||||||||
\(809\) | −7.32496e18 | −0.918628 | −0.459314 | − | 0.888274i | \(-0.651905\pi\) | ||||
−0.459314 | + | 0.888274i | \(0.651905\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.06716e19 | 1.31703 | 0.658513 | − | 0.752570i | \(-0.271186\pi\) | ||||
0.658513 | + | 0.752570i | \(0.271186\pi\) | |||||||
\(812\) | −2.25652e18 | −0.276264 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.21867e17 | 0.0749271 | ||||||||
\(815\) | 3.18147e18 | 0.380280 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.53816e18 | 0.533871 | ||||||||
\(818\) | −2.86469e18 | −0.334334 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.41493e18 | −0.162534 | ||||||||
\(821\) | 1.68217e19 | 1.91707 | 0.958537 | − | 0.284969i | \(-0.0919832\pi\) | ||||
0.958537 | + | 0.284969i | \(0.0919832\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.47808e19 | −1.65806 | −0.829028 | − | 0.559207i | \(-0.811106\pi\) | ||||
−0.829028 | + | 0.559207i | \(0.811106\pi\) | |||||||
\(824\) | 2.39550e18 | 0.266605 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.90035e18 | 0.208191 | ||||||||
\(827\) | −7.19689e18 | −0.782274 | −0.391137 | − | 0.920332i | \(-0.627918\pi\) | ||||
−0.391137 | + | 0.920332i | \(0.627918\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.66095e19 | 1.77727 | 0.888634 | − | 0.458617i | \(-0.151655\pi\) | ||||
0.888634 | + | 0.458617i | \(0.151655\pi\) | |||||||
\(830\) | 3.33469e18 | 0.354036 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.53356e18 | 0.160288 | ||||||||
\(833\) | 1.07246e19 | 1.11221 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.40928e18 | 0.756509 | ||||||||
\(836\) | −4.96023e17 | −0.0502529 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.89986e18 | −0.887763 | ||||||||
\(839\) | −2.37199e18 | −0.234779 | −0.117390 | − | 0.993086i | \(-0.537453\pi\) | ||||
−0.117390 | + | 0.993086i | \(0.537453\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.11788e19 | 2.06409 | ||||||||
\(842\) | 3.00288e18 | 0.290409 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −4.63269e18 | −0.441171 | ||||||||
\(845\) | −3.10979e18 | −0.293875 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.13073e18 | −0.291342 | ||||||||
\(848\) | 9.34517e15 | 0.000863007 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −7.60640e18 | −0.691761 | ||||||||
\(851\) | 6.37369e18 | 0.575240 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9.23784e18 | −0.821111 | −0.410556 | − | 0.911836i | \(-0.634665\pi\) | ||||
−0.410556 | + | 0.911836i | \(0.634665\pi\) | |||||||
\(854\) | 1.19811e18 | 0.105687 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.73377e18 | 0.150630 | ||||||||
\(857\) | 4.40680e18 | 0.379969 | 0.189984 | − | 0.981787i | \(-0.439156\pi\) | ||||
0.189984 | + | 0.981787i | \(0.439156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.82119e18 | 0.834082 | 0.417041 | − | 0.908888i | \(-0.363067\pi\) | ||||
0.417041 | + | 0.908888i | \(0.363067\pi\) | |||||||
\(860\) | 3.98830e18 | 0.336161 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.28895e18 | −0.190038 | ||||||||
\(863\) | 1.47168e19 | 1.21267 | 0.606334 | − | 0.795210i | \(-0.292639\pi\) | ||||
0.606334 | + | 0.795210i | \(0.292639\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.00359e18 | 0.487311 | ||||||||
\(866\) | 1.22115e19 | 0.983790 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.70088e17 | 0.0690534 | ||||||||
\(869\) | 4.27893e18 | 0.337060 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.04940e19 | −1.59041 | ||||||||
\(872\) | −3.83349e18 | −0.295282 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.08388e18 | −0.385808 | ||||||||
\(875\) | 3.42499e18 | 0.257992 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.14468e19 | 0.849548 | 0.424774 | − | 0.905300i | \(-0.360354\pi\) | ||||
0.424774 | + | 0.905300i | \(0.360354\pi\) | |||||||
\(878\) | −1.15791e18 | −0.0853019 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.35924e17 | −0.0316427 | ||||||||
\(881\) | −6.44660e18 | −0.464502 | −0.232251 | − | 0.972656i | \(-0.574609\pi\) | ||||
−0.232251 | + | 0.972656i | \(0.574609\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.62047e18 | 0.115053 | 0.0575263 | − | 0.998344i | \(-0.481679\pi\) | ||||
0.0575263 | + | 0.998344i | \(0.481679\pi\) | |||||||
\(884\) | −1.12375e19 | −0.792006 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.43904e18 | 0.0999432 | ||||||||
\(887\) | 5.24274e18 | 0.361455 | 0.180728 | − | 0.983533i | \(-0.442155\pi\) | ||||
0.180728 | + | 0.983533i | \(0.442155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.69471e18 | −0.386910 | ||||||||
\(890\) | 6.04011e18 | 0.407389 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.43186e19 | −0.951762 | ||||||||
\(893\) | −1.01362e19 | −0.668867 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.16740e19 | −0.759223 | ||||||||
\(896\) | −4.32117e17 | −0.0278997 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.11380e19 | 0.708777 | ||||||||
\(899\) | −1.21227e19 | −0.765881 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.84784e16 | −0.00426425 | ||||||||
\(902\) | −2.26197e18 | −0.139844 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.80172e18 | 0.475440 | ||||||||
\(905\) | −1.17527e19 | −0.711088 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.17095e18 | −0.129480 | −0.0647399 | − | 0.997902i | \(-0.520622\pi\) | ||||
−0.0647399 | + | 0.997902i | \(0.520622\pi\) | |||||||
\(908\) | −8.86993e18 | −0.525245 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.23626e18 | 0.130543 | ||||||||
\(911\) | −8.79267e18 | −0.509626 | −0.254813 | − | 0.966990i | \(-0.582014\pi\) | ||||
−0.254813 | + | 0.966990i | \(0.582014\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.33098e18 | 0.304612 | ||||||||
\(914\) | −1.53396e19 | −0.870291 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.08827e19 | 0.608719 | ||||||||
\(917\) | 3.12185e18 | 0.173385 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.51608e19 | −1.37776 | −0.688880 | − | 0.724876i | \(-0.741897\pi\) | ||||
−0.688880 | + | 0.724876i | \(0.741897\pi\) | |||||||
\(920\) | −4.46790e18 | −0.242931 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.07471e18 | 0.164837 | ||||||||
\(923\) | −2.42487e19 | −1.29086 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.76128e18 | 0.302411 | ||||||||
\(926\) | 1.49994e19 | 0.781812 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 6.02057e18 | 0.309439 | ||||||||
\(929\) | −1.29149e18 | −0.0659157 | −0.0329579 | − | 0.999457i | \(-0.510493\pi\) | ||||
−0.0329579 | + | 0.999457i | \(0.510493\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.47924e18 | 0.326101 | ||||||||
\(932\) | 5.26735e18 | 0.263262 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.92794e19 | 0.950254 | ||||||||
\(935\) | 3.19431e18 | 0.156351 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.58468e19 | 1.24767 | 0.623835 | − | 0.781556i | \(-0.285574\pi\) | ||||
0.623835 | + | 0.781556i | \(0.285574\pi\) | |||||||
\(938\) | 5.77466e18 | 0.276827 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −8.90805e18 | −0.421164 | ||||||||
\(941\) | −1.64109e19 | −0.770550 | −0.385275 | − | 0.922802i | \(-0.625893\pi\) | ||||
−0.385275 | + | 0.922802i | \(0.625893\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.31836e19 | −1.07363 | ||||||||
\(944\) | −5.07028e18 | −0.233192 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.37587e18 | 0.289233 | ||||||||
\(947\) | 6.99992e18 | 0.315369 | 0.157684 | − | 0.987490i | \(-0.449597\pi\) | ||||
0.157684 | + | 0.987490i | \(0.449597\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.72451e18 | −0.0766366 | ||||||||
\(950\) | −4.59540e18 | −0.202824 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.16641e18 | 0.137856 | ||||||||
\(953\) | 2.33363e19 | 1.00909 | 0.504543 | − | 0.863387i | \(-0.331661\pi\) | ||||
0.504543 | + | 0.863387i | \(0.331661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.51798e18 | −0.150062 | ||||||||
\(956\) | −1.59782e19 | −0.676940 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.80501e18 | 0.284415 | ||||||||
\(959\) | 6.77129e18 | 0.281093 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.97432e19 | −0.808565 | ||||||||
\(962\) | 8.51155e18 | 0.346235 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.61002e19 | 0.646147 | ||||||||
\(965\) | −1.76970e19 | −0.705461 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.71778e19 | −1.06891 | −0.534456 | − | 0.845197i | \(-0.679483\pi\) | ||||
−0.534456 | + | 0.845197i | \(0.679483\pi\) | |||||||
\(968\) | 8.35303e18 | 0.326328 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.44642e18 | 0.209940 | ||||||||
\(971\) | 3.52698e19 | 1.35045 | 0.675225 | − | 0.737612i | \(-0.264047\pi\) | ||||
0.675225 | + | 0.737612i | \(0.264047\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.16185e19 | −0.438953 | ||||||||
\(974\) | 3.55219e19 | 1.33310 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.19665e18 | −0.118378 | ||||||||
\(977\) | 1.34520e18 | 0.0494849 | 0.0247424 | − | 0.999694i | \(-0.492123\pi\) | ||||
0.0247424 | + | 0.999694i | \(0.492123\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.65598e18 | 0.350517 | ||||||||
\(980\) | 5.69420e18 | 0.205335 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.04354e19 | −1.08306 | ||||||||
\(983\) | −1.07665e19 | −0.380607 | −0.190304 | − | 0.981725i | \(-0.560947\pi\) | ||||
−0.190304 | + | 0.981725i | \(0.560947\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.18411e19 | −0.761973 | ||||||||
\(986\) | −4.41168e19 | −1.52899 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.78911e18 | −0.232216 | ||||||||
\(989\) | 6.53481e19 | 2.22053 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.52510e18 | 0.218831 | 0.109415 | − | 0.993996i | \(-0.465102\pi\) | ||||
0.109415 | + | 0.993996i | \(0.465102\pi\) | |||||||
\(992\) | −2.32146e18 | −0.0773457 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.83264e18 | 0.224686 | ||||||||
\(995\) | 1.55603e19 | 0.508356 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.97797e19 | 0.960290 | 0.480145 | − | 0.877189i | \(-0.340584\pi\) | ||||
0.480145 | + | 0.877189i | \(0.340584\pi\) | |||||||
\(998\) | 1.18961e19 | 0.381115 | ||||||||
\(999\) | 0 | 0 |
(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 | 18.14.a.b.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.14.a.e.1.1 | yes | 1 | ||
4.3 | odd | 2 | 144.14.a.c.1.1 | 1 | |||
12.11 | even | 2 | 144.14.a.h.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.14.a.b.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.14.a.e.1.1 | yes | 1 | 3.2 | odd | 2 | ||
144.14.a.c.1.1 | 1 | 4.3 | odd | 2 | |||
144.14.a.h.1.1 | 1 | 12.11 | even | 2 |