Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,18,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(18.3222087345\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{36061}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 9015 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{5}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-94.4487\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −256.000 | −0.707107 | ||||||||
\(3\) | 12037.8 | 1.05929 | 0.529646 | − | 0.848219i | \(-0.322325\pi\) | ||||
0.529646 | + | 0.848219i | \(0.322325\pi\) | |||||||
\(4\) | 65536.0 | 0.500000 | ||||||||
\(5\) | −390625. | −0.447214 | ||||||||
\(6\) | −3.08167e6 | −0.749033 | ||||||||
\(7\) | −9.53475e6 | −0.625138 | −0.312569 | − | 0.949895i | \(-0.601190\pi\) | ||||
−0.312569 | + | 0.949895i | \(0.601190\pi\) | |||||||
\(8\) | −1.67772e7 | −0.353553 | ||||||||
\(9\) | 1.57682e7 | 0.122101 | ||||||||
\(10\) | 1.00000e8 | 0.316228 | ||||||||
\(11\) | 4.01191e8 | 0.564305 | 0.282152 | − | 0.959370i | \(-0.408952\pi\) | ||||
0.282152 | + | 0.959370i | \(0.408952\pi\) | |||||||
\(12\) | 7.88908e8 | 0.529646 | ||||||||
\(13\) | 8.56166e8 | 0.291098 | 0.145549 | − | 0.989351i | \(-0.453505\pi\) | ||||
0.145549 | + | 0.989351i | \(0.453505\pi\) | |||||||
\(14\) | 2.44090e9 | 0.442040 | ||||||||
\(15\) | −4.70226e9 | −0.473730 | ||||||||
\(16\) | 4.29497e9 | 0.250000 | ||||||||
\(17\) | −3.89127e10 | −1.35293 | −0.676465 | − | 0.736475i | \(-0.736489\pi\) | ||||
−0.676465 | + | 0.736475i | \(0.736489\pi\) | |||||||
\(18\) | −4.03665e9 | −0.0863385 | ||||||||
\(19\) | −1.13839e11 | −1.53775 | −0.768876 | − | 0.639398i | \(-0.779184\pi\) | ||||
−0.768876 | + | 0.639398i | \(0.779184\pi\) | |||||||
\(20\) | −2.56000e10 | −0.223607 | ||||||||
\(21\) | −1.14777e11 | −0.662205 | ||||||||
\(22\) | −1.02705e11 | −0.399024 | ||||||||
\(23\) | 1.64834e10 | 0.0438894 | 0.0219447 | − | 0.999759i | \(-0.493014\pi\) | ||||
0.0219447 | + | 0.999759i | \(0.493014\pi\) | |||||||
\(24\) | −2.01961e11 | −0.374517 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | −2.19179e11 | −0.205838 | ||||||||
\(27\) | −1.36475e12 | −0.929952 | ||||||||
\(28\) | −6.24870e11 | −0.312569 | ||||||||
\(29\) | −2.27472e12 | −0.844394 | −0.422197 | − | 0.906504i | \(-0.638741\pi\) | ||||
−0.422197 | + | 0.906504i | \(0.638741\pi\) | |||||||
\(30\) | 1.20378e12 | 0.334978 | ||||||||
\(31\) | −1.63788e12 | −0.344911 | −0.172455 | − | 0.985017i | \(-0.555170\pi\) | ||||
−0.172455 | + | 0.985017i | \(0.555170\pi\) | |||||||
\(32\) | −1.09951e12 | −0.176777 | ||||||||
\(33\) | 4.82946e12 | 0.597764 | ||||||||
\(34\) | 9.96164e12 | 0.956665 | ||||||||
\(35\) | 3.72451e12 | 0.279570 | ||||||||
\(36\) | 1.03338e12 | 0.0610506 | ||||||||
\(37\) | −1.75967e13 | −0.823599 | −0.411799 | − | 0.911275i | \(-0.635100\pi\) | ||||
−0.411799 | + | 0.911275i | \(0.635100\pi\) | |||||||
\(38\) | 2.91428e13 | 1.08735 | ||||||||
\(39\) | 1.03064e13 | 0.308358 | ||||||||
\(40\) | 6.55360e12 | 0.158114 | ||||||||
\(41\) | −2.95532e13 | −0.578018 | −0.289009 | − | 0.957326i | \(-0.593326\pi\) | ||||
−0.289009 | + | 0.957326i | \(0.593326\pi\) | |||||||
\(42\) | 2.93830e13 | 0.468249 | ||||||||
\(43\) | 1.37690e14 | 1.79647 | 0.898233 | − | 0.439519i | \(-0.144851\pi\) | ||||
0.898233 | + | 0.439519i | \(0.144851\pi\) | |||||||
\(44\) | 2.62925e13 | 0.282152 | ||||||||
\(45\) | −6.15944e12 | −0.0546053 | ||||||||
\(46\) | −4.21974e12 | −0.0310345 | ||||||||
\(47\) | −1.65452e14 | −1.01354 | −0.506770 | − | 0.862081i | \(-0.669161\pi\) | ||||
−0.506770 | + | 0.862081i | \(0.669161\pi\) | |||||||
\(48\) | 5.17019e13 | 0.264823 | ||||||||
\(49\) | −1.41719e14 | −0.609202 | ||||||||
\(50\) | −3.90625e13 | −0.141421 | ||||||||
\(51\) | −4.68422e14 | −1.43315 | ||||||||
\(52\) | 5.61097e13 | 0.145549 | ||||||||
\(53\) | −7.25259e14 | −1.60010 | −0.800052 | − | 0.599931i | \(-0.795195\pi\) | ||||
−0.800052 | + | 0.599931i | \(0.795195\pi\) | |||||||
\(54\) | 3.49376e14 | 0.657575 | ||||||||
\(55\) | −1.56715e14 | −0.252365 | ||||||||
\(56\) | 1.59967e14 | 0.221020 | ||||||||
\(57\) | −1.37037e15 | −1.62893 | ||||||||
\(58\) | 5.82328e14 | 0.597076 | ||||||||
\(59\) | 1.62177e15 | 1.43796 | 0.718981 | − | 0.695030i | \(-0.244609\pi\) | ||||
0.718981 | + | 0.695030i | \(0.244609\pi\) | |||||||
\(60\) | −3.08167e14 | −0.236865 | ||||||||
\(61\) | 2.46915e15 | 1.64909 | 0.824545 | − | 0.565796i | \(-0.191431\pi\) | ||||
0.824545 | + | 0.565796i | \(0.191431\pi\) | |||||||
\(62\) | 4.19296e14 | 0.243889 | ||||||||
\(63\) | −1.50346e14 | −0.0763301 | ||||||||
\(64\) | 2.81475e14 | 0.125000 | ||||||||
\(65\) | −3.34440e14 | −0.130183 | ||||||||
\(66\) | −1.23634e15 | −0.422683 | ||||||||
\(67\) | −2.03244e14 | −0.0611479 | −0.0305739 | − | 0.999533i | \(-0.509734\pi\) | ||||
−0.0305739 | + | 0.999533i | \(0.509734\pi\) | |||||||
\(68\) | −2.55018e15 | −0.676465 | ||||||||
\(69\) | 1.98423e14 | 0.0464917 | ||||||||
\(70\) | −9.53475e14 | −0.197686 | ||||||||
\(71\) | 9.39117e15 | 1.72593 | 0.862966 | − | 0.505262i | \(-0.168604\pi\) | ||||
0.862966 | + | 0.505262i | \(0.168604\pi\) | |||||||
\(72\) | −2.64546e14 | −0.0431693 | ||||||||
\(73\) | 1.54865e15 | 0.224754 | 0.112377 | − | 0.993666i | \(-0.464153\pi\) | ||||
0.112377 | + | 0.993666i | \(0.464153\pi\) | |||||||
\(74\) | 4.50475e15 | 0.582372 | ||||||||
\(75\) | 1.83682e15 | 0.211859 | ||||||||
\(76\) | −7.46056e15 | −0.768876 | ||||||||
\(77\) | −3.82526e15 | −0.352769 | ||||||||
\(78\) | −2.63843e15 | −0.218042 | ||||||||
\(79\) | 8.30977e15 | 0.616252 | 0.308126 | − | 0.951345i | \(-0.400298\pi\) | ||||
0.308126 | + | 0.951345i | \(0.400298\pi\) | |||||||
\(80\) | −1.67772e15 | −0.111803 | ||||||||
\(81\) | −1.84648e16 | −1.10719 | ||||||||
\(82\) | 7.56562e15 | 0.408721 | ||||||||
\(83\) | −6.14697e15 | −0.299569 | −0.149785 | − | 0.988719i | \(-0.547858\pi\) | ||||
−0.149785 | + | 0.988719i | \(0.547858\pi\) | |||||||
\(84\) | −7.52205e15 | −0.331102 | ||||||||
\(85\) | 1.52003e16 | 0.605048 | ||||||||
\(86\) | −3.52485e16 | −1.27029 | ||||||||
\(87\) | −2.73826e16 | −0.894460 | ||||||||
\(88\) | −6.73087e15 | −0.199512 | ||||||||
\(89\) | 4.67428e15 | 0.125863 | 0.0629317 | − | 0.998018i | \(-0.479955\pi\) | ||||
0.0629317 | + | 0.998018i | \(0.479955\pi\) | |||||||
\(90\) | 1.57682e15 | 0.0386118 | ||||||||
\(91\) | −8.16334e15 | −0.181977 | ||||||||
\(92\) | 1.08025e15 | 0.0219447 | ||||||||
\(93\) | −1.97164e16 | −0.365362 | ||||||||
\(94\) | 4.23558e16 | 0.716681 | ||||||||
\(95\) | 4.44684e16 | 0.687703 | ||||||||
\(96\) | −1.32357e16 | −0.187258 | ||||||||
\(97\) | 1.01799e17 | 1.31881 | 0.659407 | − | 0.751786i | \(-0.270808\pi\) | ||||
0.659407 | + | 0.751786i | \(0.270808\pi\) | |||||||
\(98\) | 3.62801e16 | 0.430771 | ||||||||
\(99\) | 6.32605e15 | 0.0689023 | ||||||||
\(100\) | 1.00000e16 | 0.100000 | ||||||||
\(101\) | 3.11898e16 | 0.286603 | 0.143302 | − | 0.989679i | \(-0.454228\pi\) | ||||
0.143302 | + | 0.989679i | \(0.454228\pi\) | |||||||
\(102\) | 1.19916e17 | 1.01339 | ||||||||
\(103\) | −1.71633e17 | −1.33501 | −0.667505 | − | 0.744606i | \(-0.732638\pi\) | ||||
−0.667505 | + | 0.744606i | \(0.732638\pi\) | |||||||
\(104\) | −1.43641e16 | −0.102919 | ||||||||
\(105\) | 4.48349e16 | 0.296147 | ||||||||
\(106\) | 1.85666e17 | 1.13144 | ||||||||
\(107\) | −1.64074e17 | −0.923159 | −0.461579 | − | 0.887099i | \(-0.652717\pi\) | ||||
−0.461579 | + | 0.887099i | \(0.652717\pi\) | |||||||
\(108\) | −8.94401e16 | −0.464976 | ||||||||
\(109\) | 2.80332e17 | 1.34756 | 0.673779 | − | 0.738933i | \(-0.264670\pi\) | ||||
0.673779 | + | 0.738933i | \(0.264670\pi\) | |||||||
\(110\) | 4.01191e16 | 0.178449 | ||||||||
\(111\) | −2.11825e17 | −0.872432 | ||||||||
\(112\) | −4.09515e16 | −0.156285 | ||||||||
\(113\) | −5.30659e17 | −1.87780 | −0.938899 | − | 0.344193i | \(-0.888153\pi\) | ||||
−0.938899 | + | 0.344193i | \(0.888153\pi\) | |||||||
\(114\) | 3.50815e17 | 1.15183 | ||||||||
\(115\) | −6.43882e15 | −0.0196279 | ||||||||
\(116\) | −1.49076e17 | −0.422197 | ||||||||
\(117\) | 1.35002e16 | 0.0355434 | ||||||||
\(118\) | −4.15173e17 | −1.01679 | ||||||||
\(119\) | 3.71023e17 | 0.845768 | ||||||||
\(120\) | 7.88908e16 | 0.167489 | ||||||||
\(121\) | −3.44493e17 | −0.681560 | ||||||||
\(122\) | −6.32103e17 | −1.16608 | ||||||||
\(123\) | −3.55755e17 | −0.612291 | ||||||||
\(124\) | −1.07340e17 | −0.172455 | ||||||||
\(125\) | −5.96046e16 | −0.0894427 | ||||||||
\(126\) | 3.84885e16 | 0.0539735 | ||||||||
\(127\) | 3.45518e17 | 0.453043 | 0.226522 | − | 0.974006i | \(-0.427265\pi\) | ||||
0.226522 | + | 0.974006i | \(0.427265\pi\) | |||||||
\(128\) | −7.20576e16 | −0.0883883 | ||||||||
\(129\) | 1.65748e18 | 1.90298 | ||||||||
\(130\) | 8.56166e16 | 0.0920534 | ||||||||
\(131\) | −5.92983e17 | −0.597360 | −0.298680 | − | 0.954353i | \(-0.596546\pi\) | ||||
−0.298680 | + | 0.954353i | \(0.596546\pi\) | |||||||
\(132\) | 3.16503e17 | 0.298882 | ||||||||
\(133\) | 1.08543e18 | 0.961307 | ||||||||
\(134\) | 5.20304e16 | 0.0432381 | ||||||||
\(135\) | 5.33105e17 | 0.415887 | ||||||||
\(136\) | 6.52846e17 | 0.478333 | ||||||||
\(137\) | −5.64525e17 | −0.388650 | −0.194325 | − | 0.980937i | \(-0.562252\pi\) | ||||
−0.194325 | + | 0.980937i | \(0.562252\pi\) | |||||||
\(138\) | −5.07964e16 | −0.0328746 | ||||||||
\(139\) | 2.13511e18 | 1.29956 | 0.649778 | − | 0.760124i | \(-0.274862\pi\) | ||||
0.649778 | + | 0.760124i | \(0.274862\pi\) | |||||||
\(140\) | 2.44090e17 | 0.139785 | ||||||||
\(141\) | −1.99168e18 | −1.07364 | ||||||||
\(142\) | −2.40414e18 | −1.22042 | ||||||||
\(143\) | 3.43487e17 | 0.164268 | ||||||||
\(144\) | 6.77237e16 | 0.0305253 | ||||||||
\(145\) | 8.88563e17 | 0.377624 | ||||||||
\(146\) | −3.96454e17 | −0.158925 | ||||||||
\(147\) | −1.70598e18 | −0.645323 | ||||||||
\(148\) | −1.15321e18 | −0.411799 | ||||||||
\(149\) | 2.11167e18 | 0.712103 | 0.356051 | − | 0.934466i | \(-0.384123\pi\) | ||||
0.356051 | + | 0.934466i | \(0.384123\pi\) | |||||||
\(150\) | −4.70226e17 | −0.149807 | ||||||||
\(151\) | 1.09446e18 | 0.329532 | 0.164766 | − | 0.986333i | \(-0.447313\pi\) | ||||
0.164766 | + | 0.986333i | \(0.447313\pi\) | |||||||
\(152\) | 1.90990e18 | 0.543677 | ||||||||
\(153\) | −6.13581e17 | −0.165194 | ||||||||
\(154\) | 9.79267e17 | 0.249445 | ||||||||
\(155\) | 6.39796e17 | 0.154249 | ||||||||
\(156\) | 6.75437e17 | 0.154179 | ||||||||
\(157\) | 2.67975e18 | 0.579359 | 0.289680 | − | 0.957124i | \(-0.406451\pi\) | ||||
0.289680 | + | 0.957124i | \(0.406451\pi\) | |||||||
\(158\) | −2.12730e18 | −0.435756 | ||||||||
\(159\) | −8.73051e18 | −1.69498 | ||||||||
\(160\) | 4.29497e17 | 0.0790569 | ||||||||
\(161\) | −1.57165e17 | −0.0274369 | ||||||||
\(162\) | 4.72700e18 | 0.782903 | ||||||||
\(163\) | −9.47539e18 | −1.48937 | −0.744685 | − | 0.667416i | \(-0.767400\pi\) | ||||
−0.744685 | + | 0.667416i | \(0.767400\pi\) | |||||||
\(164\) | −1.93680e18 | −0.289009 | ||||||||
\(165\) | −1.88651e18 | −0.267328 | ||||||||
\(166\) | 1.57362e18 | 0.211827 | ||||||||
\(167\) | −6.70665e18 | −0.857859 | −0.428929 | − | 0.903338i | \(-0.641109\pi\) | ||||
−0.428929 | + | 0.903338i | \(0.641109\pi\) | |||||||
\(168\) | 1.92564e18 | 0.234125 | ||||||||
\(169\) | −7.91739e18 | −0.915262 | ||||||||
\(170\) | −3.89127e18 | −0.427834 | ||||||||
\(171\) | −1.79503e18 | −0.187761 | ||||||||
\(172\) | 9.02362e18 | 0.898233 | ||||||||
\(173\) | 1.05695e19 | 1.00152 | 0.500762 | − | 0.865585i | \(-0.333053\pi\) | ||||
0.500762 | + | 0.865585i | \(0.333053\pi\) | |||||||
\(174\) | 7.00994e18 | 0.632479 | ||||||||
\(175\) | −1.45489e18 | −0.125028 | ||||||||
\(176\) | 1.72310e18 | 0.141076 | ||||||||
\(177\) | 1.95225e19 | 1.52322 | ||||||||
\(178\) | −1.19662e18 | −0.0889989 | ||||||||
\(179\) | −1.98718e19 | −1.40924 | −0.704621 | − | 0.709583i | \(-0.748883\pi\) | ||||
−0.704621 | + | 0.709583i | \(0.748883\pi\) | |||||||
\(180\) | −4.03665e17 | −0.0273026 | ||||||||
\(181\) | 2.50176e19 | 1.61428 | 0.807138 | − | 0.590363i | \(-0.201015\pi\) | ||||
0.807138 | + | 0.590363i | \(0.201015\pi\) | |||||||
\(182\) | 2.08981e18 | 0.128677 | ||||||||
\(183\) | 2.97231e19 | 1.74687 | ||||||||
\(184\) | −2.76545e17 | −0.0155172 | ||||||||
\(185\) | 6.87370e18 | 0.368324 | ||||||||
\(186\) | 5.04740e18 | 0.258350 | ||||||||
\(187\) | −1.56114e19 | −0.763464 | ||||||||
\(188\) | −1.08431e19 | −0.506770 | ||||||||
\(189\) | 1.30125e19 | 0.581349 | ||||||||
\(190\) | −1.13839e19 | −0.486280 | ||||||||
\(191\) | −2.63385e19 | −1.07599 | −0.537995 | − | 0.842948i | \(-0.680818\pi\) | ||||
−0.537995 | + | 0.842948i | \(0.680818\pi\) | |||||||
\(192\) | 3.38834e18 | 0.132412 | ||||||||
\(193\) | 3.68856e19 | 1.37918 | 0.689589 | − | 0.724201i | \(-0.257791\pi\) | ||||
0.689589 | + | 0.724201i | \(0.257791\pi\) | |||||||
\(194\) | −2.60605e19 | −0.932542 | ||||||||
\(195\) | −4.02592e18 | −0.137902 | ||||||||
\(196\) | −9.28769e18 | −0.304601 | ||||||||
\(197\) | −4.04920e19 | −1.27176 | −0.635882 | − | 0.771786i | \(-0.719364\pi\) | ||||
−0.635882 | + | 0.771786i | \(0.719364\pi\) | |||||||
\(198\) | −1.61947e18 | −0.0487212 | ||||||||
\(199\) | −3.32772e19 | −0.959171 | −0.479586 | − | 0.877495i | \(-0.659213\pi\) | ||||
−0.479586 | + | 0.877495i | \(0.659213\pi\) | |||||||
\(200\) | −2.56000e18 | −0.0707107 | ||||||||
\(201\) | −2.44660e18 | −0.0647735 | ||||||||
\(202\) | −7.98459e18 | −0.202659 | ||||||||
\(203\) | 2.16889e19 | 0.527863 | ||||||||
\(204\) | −3.06985e19 | −0.716574 | ||||||||
\(205\) | 1.15442e19 | 0.258498 | ||||||||
\(206\) | 4.39380e19 | 0.943994 | ||||||||
\(207\) | 2.59912e17 | 0.00535894 | ||||||||
\(208\) | 3.67721e18 | 0.0727746 | ||||||||
\(209\) | −4.56713e19 | −0.867761 | ||||||||
\(210\) | −1.14777e19 | −0.209407 | ||||||||
\(211\) | −2.42162e19 | −0.424331 | −0.212166 | − | 0.977234i | \(-0.568052\pi\) | ||||
−0.212166 | + | 0.977234i | \(0.568052\pi\) | |||||||
\(212\) | −4.75306e19 | −0.800052 | ||||||||
\(213\) | 1.13049e20 | 1.82827 | ||||||||
\(214\) | 4.20028e19 | 0.652772 | ||||||||
\(215\) | −5.37850e19 | −0.803404 | ||||||||
\(216\) | 2.28967e19 | 0.328788 | ||||||||
\(217\) | 1.56168e19 | 0.215617 | ||||||||
\(218\) | −7.17650e19 | −0.952867 | ||||||||
\(219\) | 1.86423e19 | 0.238081 | ||||||||
\(220\) | −1.02705e19 | −0.126182 | ||||||||
\(221\) | −3.33157e19 | −0.393835 | ||||||||
\(222\) | 5.42272e19 | 0.616903 | ||||||||
\(223\) | 7.42273e19 | 0.812779 | 0.406390 | − | 0.913700i | \(-0.366788\pi\) | ||||
0.406390 | + | 0.913700i | \(0.366788\pi\) | |||||||
\(224\) | 1.04836e19 | 0.110510 | ||||||||
\(225\) | 2.40603e18 | 0.0244202 | ||||||||
\(226\) | 1.35849e20 | 1.32780 | ||||||||
\(227\) | 9.57531e18 | 0.0901432 | 0.0450716 | − | 0.998984i | \(-0.485648\pi\) | ||||
0.0450716 | + | 0.998984i | \(0.485648\pi\) | |||||||
\(228\) | −8.98087e19 | −0.814464 | ||||||||
\(229\) | 1.97753e20 | 1.72791 | 0.863955 | − | 0.503569i | \(-0.167980\pi\) | ||||
0.863955 | + | 0.503569i | \(0.167980\pi\) | |||||||
\(230\) | 1.64834e18 | 0.0138790 | ||||||||
\(231\) | −4.60477e19 | −0.373685 | ||||||||
\(232\) | 3.81635e19 | 0.298538 | ||||||||
\(233\) | −1.79778e20 | −1.35585 | −0.677925 | − | 0.735131i | \(-0.737120\pi\) | ||||
−0.677925 | + | 0.735131i | \(0.737120\pi\) | |||||||
\(234\) | −3.45604e18 | −0.0251330 | ||||||||
\(235\) | 6.46298e19 | 0.453269 | ||||||||
\(236\) | 1.06284e20 | 0.718981 | ||||||||
\(237\) | 1.00031e20 | 0.652792 | ||||||||
\(238\) | −9.49818e19 | −0.598048 | ||||||||
\(239\) | −2.00207e20 | −1.21646 | −0.608229 | − | 0.793761i | \(-0.708120\pi\) | ||||
−0.608229 | + | 0.793761i | \(0.708120\pi\) | |||||||
\(240\) | −2.01961e19 | −0.118433 | ||||||||
\(241\) | −1.81616e20 | −1.02804 | −0.514018 | − | 0.857779i | \(-0.671844\pi\) | ||||
−0.514018 | + | 0.857779i | \(0.671844\pi\) | |||||||
\(242\) | 8.81901e19 | 0.481936 | ||||||||
\(243\) | −4.60321e19 | −0.242889 | ||||||||
\(244\) | 1.61818e20 | 0.824545 | ||||||||
\(245\) | 5.53590e19 | 0.272443 | ||||||||
\(246\) | 9.10733e19 | 0.432955 | ||||||||
\(247\) | −9.74653e19 | −0.447637 | ||||||||
\(248\) | 2.74790e19 | 0.121944 | ||||||||
\(249\) | −7.39959e19 | −0.317332 | ||||||||
\(250\) | 1.52588e19 | 0.0632456 | ||||||||
\(251\) | −3.20192e20 | −1.28288 | −0.641438 | − | 0.767175i | \(-0.721662\pi\) | ||||
−0.641438 | + | 0.767175i | \(0.721662\pi\) | |||||||
\(252\) | −9.85304e18 | −0.0381651 | ||||||||
\(253\) | 6.61299e18 | 0.0247670 | ||||||||
\(254\) | −8.84527e19 | −0.320350 | ||||||||
\(255\) | 1.82977e20 | 0.640923 | ||||||||
\(256\) | 1.84467e19 | 0.0625000 | ||||||||
\(257\) | −3.34539e20 | −1.09652 | −0.548259 | − | 0.836309i | \(-0.684709\pi\) | ||||
−0.548259 | + | 0.836309i | \(0.684709\pi\) | |||||||
\(258\) | −4.24314e20 | −1.34561 | ||||||||
\(259\) | 1.67780e20 | 0.514863 | ||||||||
\(260\) | −2.19179e19 | −0.0650916 | ||||||||
\(261\) | −3.58681e19 | −0.103101 | ||||||||
\(262\) | 1.51804e20 | 0.422397 | ||||||||
\(263\) | 2.95034e20 | 0.794782 | 0.397391 | − | 0.917649i | \(-0.369916\pi\) | ||||
0.397391 | + | 0.917649i | \(0.369916\pi\) | |||||||
\(264\) | −8.10248e19 | −0.211341 | ||||||||
\(265\) | 2.83304e20 | 0.715588 | ||||||||
\(266\) | −2.77870e20 | −0.679747 | ||||||||
\(267\) | 5.62680e19 | 0.133326 | ||||||||
\(268\) | −1.33198e19 | −0.0305739 | ||||||||
\(269\) | 7.56967e20 | 1.68338 | 0.841690 | − | 0.539960i | \(-0.181561\pi\) | ||||
0.841690 | + | 0.539960i | \(0.181561\pi\) | |||||||
\(270\) | −1.36475e20 | −0.294077 | ||||||||
\(271\) | −1.18908e20 | −0.248298 | −0.124149 | − | 0.992264i | \(-0.539620\pi\) | ||||
−0.124149 | + | 0.992264i | \(0.539620\pi\) | |||||||
\(272\) | −1.67129e20 | −0.338232 | ||||||||
\(273\) | −9.82685e19 | −0.192767 | ||||||||
\(274\) | 1.44518e20 | 0.274817 | ||||||||
\(275\) | 6.12169e19 | 0.112861 | ||||||||
\(276\) | 1.30039e19 | 0.0232458 | ||||||||
\(277\) | −1.96379e20 | −0.340421 | −0.170211 | − | 0.985408i | \(-0.554445\pi\) | ||||
−0.170211 | + | 0.985408i | \(0.554445\pi\) | |||||||
\(278\) | −5.46589e20 | −0.918925 | ||||||||
\(279\) | −2.58263e19 | −0.0421140 | ||||||||
\(280\) | −6.24870e19 | −0.0988431 | ||||||||
\(281\) | −3.39035e20 | −0.520284 | −0.260142 | − | 0.965570i | \(-0.583769\pi\) | ||||
−0.260142 | + | 0.965570i | \(0.583769\pi\) | |||||||
\(282\) | 5.09870e20 | 0.759175 | ||||||||
\(283\) | 4.03445e20 | 0.582908 | 0.291454 | − | 0.956585i | \(-0.405861\pi\) | ||||
0.291454 | + | 0.956585i | \(0.405861\pi\) | |||||||
\(284\) | 6.15460e20 | 0.862966 | ||||||||
\(285\) | 5.35301e20 | 0.728479 | ||||||||
\(286\) | −8.79326e19 | −0.116155 | ||||||||
\(287\) | 2.81782e20 | 0.361341 | ||||||||
\(288\) | −1.73373e19 | −0.0215846 | ||||||||
\(289\) | 6.86955e20 | 0.830418 | ||||||||
\(290\) | −2.27472e20 | −0.267021 | ||||||||
\(291\) | 1.22543e21 | 1.39701 | ||||||||
\(292\) | 1.01492e20 | 0.112377 | ||||||||
\(293\) | −1.05777e20 | −0.113767 | −0.0568836 | − | 0.998381i | \(-0.518116\pi\) | ||||
−0.0568836 | + | 0.998381i | \(0.518116\pi\) | |||||||
\(294\) | 4.36732e20 | 0.456312 | ||||||||
\(295\) | −6.33504e20 | −0.643076 | ||||||||
\(296\) | 2.95223e20 | 0.291186 | ||||||||
\(297\) | −5.47525e20 | −0.524776 | ||||||||
\(298\) | −5.40587e20 | −0.503533 | ||||||||
\(299\) | 1.41125e19 | 0.0127761 | ||||||||
\(300\) | 1.20378e20 | 0.105929 | ||||||||
\(301\) | −1.31284e21 | −1.12304 | ||||||||
\(302\) | −2.80183e20 | −0.233014 | ||||||||
\(303\) | 3.75456e20 | 0.303597 | ||||||||
\(304\) | −4.88936e20 | −0.384438 | ||||||||
\(305\) | −9.64513e20 | −0.737495 | ||||||||
\(306\) | 1.57077e20 | 0.116810 | ||||||||
\(307\) | −1.82911e21 | −1.32301 | −0.661504 | − | 0.749941i | \(-0.730082\pi\) | ||||
−0.661504 | + | 0.749941i | \(0.730082\pi\) | |||||||
\(308\) | −2.50692e20 | −0.176384 | ||||||||
\(309\) | −2.06608e21 | −1.41417 | ||||||||
\(310\) | −1.63788e20 | −0.109070 | ||||||||
\(311\) | 2.00748e21 | 1.30073 | 0.650366 | − | 0.759621i | \(-0.274616\pi\) | ||||
0.650366 | + | 0.759621i | \(0.274616\pi\) | |||||||
\(312\) | −1.72912e20 | −0.109021 | ||||||||
\(313\) | −2.84834e21 | −1.74769 | −0.873846 | − | 0.486203i | \(-0.838381\pi\) | ||||
−0.873846 | + | 0.486203i | \(0.838381\pi\) | |||||||
\(314\) | −6.86017e20 | −0.409669 | ||||||||
\(315\) | 5.87287e19 | 0.0341359 | ||||||||
\(316\) | 5.44589e20 | 0.308126 | ||||||||
\(317\) | 2.74347e20 | 0.151111 | 0.0755554 | − | 0.997142i | \(-0.475927\pi\) | ||||
0.0755554 | + | 0.997142i | \(0.475927\pi\) | |||||||
\(318\) | 2.23501e21 | 1.19853 | ||||||||
\(319\) | −9.12598e20 | −0.476495 | ||||||||
\(320\) | −1.09951e20 | −0.0559017 | ||||||||
\(321\) | −1.97508e21 | −0.977895 | ||||||||
\(322\) | 4.02342e19 | 0.0194008 | ||||||||
\(323\) | 4.42979e21 | 2.08047 | ||||||||
\(324\) | −1.21011e21 | −0.553596 | ||||||||
\(325\) | 1.30641e20 | 0.0582197 | ||||||||
\(326\) | 2.42570e21 | 1.05314 | ||||||||
\(327\) | 3.37458e21 | 1.42746 | ||||||||
\(328\) | 4.95820e20 | 0.204360 | ||||||||
\(329\) | 1.57755e21 | 0.633603 | ||||||||
\(330\) | 4.82946e20 | 0.189030 | ||||||||
\(331\) | 1.83521e20 | 0.0700082 | 0.0350041 | − | 0.999387i | \(-0.488856\pi\) | ||||
0.0350041 | + | 0.999387i | \(0.488856\pi\) | |||||||
\(332\) | −4.02848e20 | −0.149785 | ||||||||
\(333\) | −2.77467e20 | −0.100562 | ||||||||
\(334\) | 1.71690e21 | 0.606598 | ||||||||
\(335\) | 7.93921e19 | 0.0273462 | ||||||||
\(336\) | −4.92965e20 | −0.165551 | ||||||||
\(337\) | −6.21202e20 | −0.203413 | −0.101706 | − | 0.994814i | \(-0.532430\pi\) | ||||
−0.101706 | + | 0.994814i | \(0.532430\pi\) | |||||||
\(338\) | 2.02685e21 | 0.647188 | ||||||||
\(339\) | −6.38796e21 | −1.98914 | ||||||||
\(340\) | 9.96164e20 | 0.302524 | ||||||||
\(341\) | −6.57102e20 | −0.194635 | ||||||||
\(342\) | 4.59529e20 | 0.132767 | ||||||||
\(343\) | 3.56933e21 | 1.00597 | ||||||||
\(344\) | −2.31005e21 | −0.635147 | ||||||||
\(345\) | −7.75091e19 | −0.0207917 | ||||||||
\(346\) | −2.70579e21 | −0.708185 | ||||||||
\(347\) | 5.08978e21 | 1.29987 | 0.649933 | − | 0.759992i | \(-0.274797\pi\) | ||||
0.649933 | + | 0.759992i | \(0.274797\pi\) | |||||||
\(348\) | −1.79455e21 | −0.447230 | ||||||||
\(349\) | −3.81066e20 | −0.0926796 | −0.0463398 | − | 0.998926i | \(-0.514756\pi\) | ||||
−0.0463398 | + | 0.998926i | \(0.514756\pi\) | |||||||
\(350\) | 3.72451e20 | 0.0884079 | ||||||||
\(351\) | −1.16845e21 | −0.270707 | ||||||||
\(352\) | −4.41115e20 | −0.0997559 | ||||||||
\(353\) | 2.34699e21 | 0.518115 | 0.259058 | − | 0.965862i | \(-0.416588\pi\) | ||||
0.259058 | + | 0.965862i | \(0.416588\pi\) | |||||||
\(354\) | −4.99777e21 | −1.07708 | ||||||||
\(355\) | −3.66842e21 | −0.771860 | ||||||||
\(356\) | 3.06334e20 | 0.0629317 | ||||||||
\(357\) | 4.46629e21 | 0.895916 | ||||||||
\(358\) | 5.08717e21 | 0.996485 | ||||||||
\(359\) | −6.19792e19 | −0.0118561 | −0.00592807 | − | 0.999982i | \(-0.501887\pi\) | ||||
−0.00592807 | + | 0.999982i | \(0.501887\pi\) | |||||||
\(360\) | 1.03338e20 | 0.0193059 | ||||||||
\(361\) | 7.47897e21 | 1.36468 | ||||||||
\(362\) | −6.40451e21 | −1.14147 | ||||||||
\(363\) | −4.14693e21 | −0.721972 | ||||||||
\(364\) | −5.34992e20 | −0.0909884 | ||||||||
\(365\) | −6.04941e20 | −0.100513 | ||||||||
\(366\) | −7.60912e21 | −1.23522 | ||||||||
\(367\) | −3.40565e21 | −0.540180 | −0.270090 | − | 0.962835i | \(-0.587054\pi\) | ||||
−0.270090 | + | 0.962835i | \(0.587054\pi\) | |||||||
\(368\) | 7.07955e19 | 0.0109723 | ||||||||
\(369\) | −4.65999e20 | −0.0705767 | ||||||||
\(370\) | −1.75967e21 | −0.260445 | ||||||||
\(371\) | 6.91517e21 | 1.00029 | ||||||||
\(372\) | −1.29213e21 | −0.182681 | ||||||||
\(373\) | −6.44986e21 | −0.891302 | −0.445651 | − | 0.895207i | \(-0.647028\pi\) | ||||
−0.445651 | + | 0.895207i | \(0.647028\pi\) | |||||||
\(374\) | 3.99652e21 | 0.539851 | ||||||||
\(375\) | −7.17508e20 | −0.0947460 | ||||||||
\(376\) | 2.77583e21 | 0.358340 | ||||||||
\(377\) | −1.94754e21 | −0.245802 | ||||||||
\(378\) | −3.33121e21 | −0.411076 | ||||||||
\(379\) | −5.68235e21 | −0.685638 | −0.342819 | − | 0.939401i | \(-0.611382\pi\) | ||||
−0.342819 | + | 0.939401i | \(0.611382\pi\) | |||||||
\(380\) | 2.91428e21 | 0.343852 | ||||||||
\(381\) | 4.15928e21 | 0.479905 | ||||||||
\(382\) | 6.74266e21 | 0.760839 | ||||||||
\(383\) | −1.28548e22 | −1.41865 | −0.709327 | − | 0.704879i | \(-0.751001\pi\) | ||||
−0.709327 | + | 0.704879i | \(0.751001\pi\) | |||||||
\(384\) | −8.67414e20 | −0.0936291 | ||||||||
\(385\) | 1.49424e21 | 0.157763 | ||||||||
\(386\) | −9.44272e21 | −0.975226 | ||||||||
\(387\) | 2.17111e21 | 0.219351 | ||||||||
\(388\) | 6.67149e21 | 0.659407 | ||||||||
\(389\) | 1.70189e22 | 1.64573 | 0.822867 | − | 0.568234i | \(-0.192373\pi\) | ||||
0.822867 | + | 0.568234i | \(0.192373\pi\) | |||||||
\(390\) | 1.03064e21 | 0.0975115 | ||||||||
\(391\) | −6.41412e20 | −0.0593792 | ||||||||
\(392\) | 2.37765e21 | 0.215385 | ||||||||
\(393\) | −7.13820e21 | −0.632779 | ||||||||
\(394\) | 1.03660e22 | 0.899273 | ||||||||
\(395\) | −3.24600e21 | −0.275596 | ||||||||
\(396\) | 4.14584e20 | 0.0344511 | ||||||||
\(397\) | −1.81182e22 | −1.47365 | −0.736827 | − | 0.676081i | \(-0.763677\pi\) | ||||
−0.736827 | + | 0.676081i | \(0.763677\pi\) | |||||||
\(398\) | 8.51897e21 | 0.678236 | ||||||||
\(399\) | 1.30662e22 | 1.01831 | ||||||||
\(400\) | 6.55360e20 | 0.0500000 | ||||||||
\(401\) | 1.75008e22 | 1.30717 | 0.653585 | − | 0.756853i | \(-0.273264\pi\) | ||||
0.653585 | + | 0.756853i | \(0.273264\pi\) | |||||||
\(402\) | 6.26331e20 | 0.0458018 | ||||||||
\(403\) | −1.40230e21 | −0.100403 | ||||||||
\(404\) | 2.04406e21 | 0.143302 | ||||||||
\(405\) | 7.21283e21 | 0.495152 | ||||||||
\(406\) | −5.55236e21 | −0.373255 | ||||||||
\(407\) | −7.05963e21 | −0.464761 | ||||||||
\(408\) | 7.85882e21 | 0.506694 | ||||||||
\(409\) | 9.06225e21 | 0.572253 | 0.286127 | − | 0.958192i | \(-0.407632\pi\) | ||||
0.286127 | + | 0.958192i | \(0.407632\pi\) | |||||||
\(410\) | −2.95532e21 | −0.182785 | ||||||||
\(411\) | −6.79563e21 | −0.411694 | ||||||||
\(412\) | −1.12481e22 | −0.667505 | ||||||||
\(413\) | −1.54632e22 | −0.898925 | ||||||||
\(414\) | −6.65376e19 | −0.00378934 | ||||||||
\(415\) | 2.40116e21 | 0.133971 | ||||||||
\(416\) | −9.41365e20 | −0.0514594 | ||||||||
\(417\) | 2.57020e22 | 1.37661 | ||||||||
\(418\) | 1.16919e22 | 0.613599 | ||||||||
\(419\) | 7.49706e21 | 0.385542 | 0.192771 | − | 0.981244i | \(-0.438253\pi\) | ||||
0.192771 | + | 0.981244i | \(0.438253\pi\) | |||||||
\(420\) | 2.93830e21 | 0.148073 | ||||||||
\(421\) | −2.95580e22 | −1.45975 | −0.729873 | − | 0.683583i | \(-0.760421\pi\) | ||||
−0.729873 | + | 0.683583i | \(0.760421\pi\) | |||||||
\(422\) | 6.19935e21 | 0.300048 | ||||||||
\(423\) | −2.60888e21 | −0.123754 | ||||||||
\(424\) | 1.21678e22 | 0.565722 | ||||||||
\(425\) | −5.93760e21 | −0.270586 | ||||||||
\(426\) | −2.89405e22 | −1.29278 | ||||||||
\(427\) | −2.35428e22 | −1.03091 | ||||||||
\(428\) | −1.07527e22 | −0.461579 | ||||||||
\(429\) | 4.13482e21 | 0.174008 | ||||||||
\(430\) | 1.37690e22 | 0.568093 | ||||||||
\(431\) | −7.37016e21 | −0.298140 | −0.149070 | − | 0.988827i | \(-0.547628\pi\) | ||||
−0.149070 | + | 0.988827i | \(0.547628\pi\) | |||||||
\(432\) | −5.86155e21 | −0.232488 | ||||||||
\(433\) | 1.77584e21 | 0.0690650 | 0.0345325 | − | 0.999404i | \(-0.489006\pi\) | ||||
0.0345325 | + | 0.999404i | \(0.489006\pi\) | |||||||
\(434\) | −3.99789e21 | −0.152464 | ||||||||
\(435\) | 1.06963e22 | 0.400015 | ||||||||
\(436\) | 1.83718e22 | 0.673779 | ||||||||
\(437\) | −1.87645e21 | −0.0674909 | ||||||||
\(438\) | −4.77243e21 | −0.168349 | ||||||||
\(439\) | −2.92011e22 | −1.01030 | −0.505151 | − | 0.863031i | \(-0.668563\pi\) | ||||
−0.505151 | + | 0.863031i | \(0.668563\pi\) | |||||||
\(440\) | 2.62925e21 | 0.0892244 | ||||||||
\(441\) | −2.23465e21 | −0.0743842 | ||||||||
\(442\) | 8.52882e21 | 0.278484 | ||||||||
\(443\) | −4.06554e22 | −1.30223 | −0.651113 | − | 0.758980i | \(-0.725698\pi\) | ||||
−0.651113 | + | 0.758980i | \(0.725698\pi\) | |||||||
\(444\) | −1.38822e22 | −0.436216 | ||||||||
\(445\) | −1.82589e21 | −0.0562879 | ||||||||
\(446\) | −1.90022e22 | −0.574722 | ||||||||
\(447\) | 2.54198e22 | 0.754325 | ||||||||
\(448\) | −2.68379e21 | −0.0781423 | ||||||||
\(449\) | 4.62783e21 | 0.132216 | 0.0661079 | − | 0.997812i | \(-0.478942\pi\) | ||||
0.0661079 | + | 0.997812i | \(0.478942\pi\) | |||||||
\(450\) | −6.15944e20 | −0.0172677 | ||||||||
\(451\) | −1.18565e22 | −0.326179 | ||||||||
\(452\) | −3.47773e22 | −0.938899 | ||||||||
\(453\) | 1.31749e22 | 0.349071 | ||||||||
\(454\) | −2.45128e21 | −0.0637409 | ||||||||
\(455\) | 3.18880e21 | 0.0813825 | ||||||||
\(456\) | 2.29910e22 | 0.575913 | ||||||||
\(457\) | 6.30841e22 | 1.55107 | 0.775536 | − | 0.631303i | \(-0.217480\pi\) | ||||
0.775536 | + | 0.631303i | \(0.217480\pi\) | |||||||
\(458\) | −5.06247e22 | −1.22182 | ||||||||
\(459\) | 5.31060e22 | 1.25816 | ||||||||
\(460\) | −4.21974e20 | −0.00981396 | ||||||||
\(461\) | 5.62982e22 | 1.28539 | 0.642697 | − | 0.766120i | \(-0.277815\pi\) | ||||
0.642697 | + | 0.766120i | \(0.277815\pi\) | |||||||
\(462\) | 1.17882e22 | 0.264235 | ||||||||
\(463\) | 5.90180e21 | 0.129881 | 0.0649405 | − | 0.997889i | \(-0.479314\pi\) | ||||
0.0649405 | + | 0.997889i | \(0.479314\pi\) | |||||||
\(464\) | −9.76985e21 | −0.211098 | ||||||||
\(465\) | 7.70172e21 | 0.163395 | ||||||||
\(466\) | 4.60232e22 | 0.958730 | ||||||||
\(467\) | 2.51115e22 | 0.513663 | 0.256832 | − | 0.966456i | \(-0.417321\pi\) | ||||
0.256832 | + | 0.966456i | \(0.417321\pi\) | |||||||
\(468\) | 8.84747e20 | 0.0177717 | ||||||||
\(469\) | 1.93788e21 | 0.0382259 | ||||||||
\(470\) | −1.65452e22 | −0.320509 | ||||||||
\(471\) | 3.22583e22 | 0.613711 | ||||||||
\(472\) | −2.72088e22 | −0.508396 | ||||||||
\(473\) | 5.52399e22 | 1.01375 | ||||||||
\(474\) | −2.56080e22 | −0.461594 | ||||||||
\(475\) | −1.73705e22 | −0.307550 | ||||||||
\(476\) | 2.43153e22 | 0.422884 | ||||||||
\(477\) | −1.14360e22 | −0.195375 | ||||||||
\(478\) | 5.12530e22 | 0.860166 | ||||||||
\(479\) | −3.54309e22 | −0.584158 | −0.292079 | − | 0.956394i | \(-0.594347\pi\) | ||||
−0.292079 | + | 0.956394i | \(0.594347\pi\) | |||||||
\(480\) | 5.17019e21 | 0.0837444 | ||||||||
\(481\) | −1.50657e22 | −0.239748 | ||||||||
\(482\) | 4.64936e22 | 0.726931 | ||||||||
\(483\) | −1.89192e21 | −0.0290637 | ||||||||
\(484\) | −2.25767e22 | −0.340780 | ||||||||
\(485\) | −3.97652e22 | −0.589791 | ||||||||
\(486\) | 1.17842e22 | 0.171748 | ||||||||
\(487\) | −1.51696e22 | −0.217259 | −0.108629 | − | 0.994082i | \(-0.534646\pi\) | ||||
−0.108629 | + | 0.994082i | \(0.534646\pi\) | |||||||
\(488\) | −4.14255e22 | −0.583041 | ||||||||
\(489\) | −1.14063e23 | −1.57768 | ||||||||
\(490\) | −1.41719e22 | −0.192647 | ||||||||
\(491\) | −6.96906e22 | −0.931068 | −0.465534 | − | 0.885030i | \(-0.654138\pi\) | ||||
−0.465534 | + | 0.885030i | \(0.654138\pi\) | |||||||
\(492\) | −2.33148e22 | −0.306145 | ||||||||
\(493\) | 8.85154e22 | 1.14240 | ||||||||
\(494\) | 2.49511e22 | 0.316527 | ||||||||
\(495\) | −2.47111e21 | −0.0308140 | ||||||||
\(496\) | −7.03463e21 | −0.0862277 | ||||||||
\(497\) | −8.95425e22 | −1.07895 | ||||||||
\(498\) | 1.89430e22 | 0.224387 | ||||||||
\(499\) | −5.10974e22 | −0.595037 | −0.297518 | − | 0.954716i | \(-0.596159\pi\) | ||||
−0.297518 | + | 0.954716i | \(0.596159\pi\) | |||||||
\(500\) | −3.90625e21 | −0.0447214 | ||||||||
\(501\) | −8.07332e22 | −0.908723 | ||||||||
\(502\) | 8.19693e22 | 0.907130 | ||||||||
\(503\) | 6.26474e21 | 0.0681671 | 0.0340836 | − | 0.999419i | \(-0.489149\pi\) | ||||
0.0340836 | + | 0.999419i | \(0.489149\pi\) | |||||||
\(504\) | 2.52238e21 | 0.0269868 | ||||||||
\(505\) | −1.21835e22 | −0.128173 | ||||||||
\(506\) | −1.69292e21 | −0.0175129 | ||||||||
\(507\) | −9.53079e22 | −0.969530 | ||||||||
\(508\) | 2.26439e22 | 0.226522 | ||||||||
\(509\) | −7.41555e22 | −0.729528 | −0.364764 | − | 0.931100i | \(-0.618850\pi\) | ||||
−0.364764 | + | 0.931100i | \(0.618850\pi\) | |||||||
\(510\) | −4.68422e22 | −0.453201 | ||||||||
\(511\) | −1.47660e22 | −0.140503 | ||||||||
\(512\) | −4.72237e21 | −0.0441942 | ||||||||
\(513\) | 1.55362e23 | 1.43003 | ||||||||
\(514\) | 8.56421e22 | 0.775355 | ||||||||
\(515\) | 6.70441e22 | 0.597034 | ||||||||
\(516\) | 1.08624e23 | 0.951492 | ||||||||
\(517\) | −6.63780e22 | −0.571945 | ||||||||
\(518\) | −4.29516e22 | −0.364063 | ||||||||
\(519\) | 1.27233e23 | 1.06091 | ||||||||
\(520\) | 5.61097e21 | 0.0460267 | ||||||||
\(521\) | 9.53386e21 | 0.0769393 | 0.0384696 | − | 0.999260i | \(-0.487752\pi\) | ||||
0.0384696 | + | 0.999260i | \(0.487752\pi\) | |||||||
\(522\) | 9.18225e21 | 0.0729037 | ||||||||
\(523\) | 1.49123e23 | 1.16487 | 0.582437 | − | 0.812876i | \(-0.302099\pi\) | ||||
0.582437 | + | 0.812876i | \(0.302099\pi\) | |||||||
\(524\) | −3.88617e22 | −0.298680 | ||||||||
\(525\) | −1.75136e22 | −0.132441 | ||||||||
\(526\) | −7.55287e22 | −0.561996 | ||||||||
\(527\) | 6.37341e22 | 0.466640 | ||||||||
\(528\) | 2.07424e22 | 0.149441 | ||||||||
\(529\) | −1.40778e23 | −0.998074 | ||||||||
\(530\) | −7.25259e22 | −0.505997 | ||||||||
\(531\) | 2.55723e22 | 0.175577 | ||||||||
\(532\) | 7.11347e22 | 0.480654 | ||||||||
\(533\) | −2.53025e22 | −0.168260 | ||||||||
\(534\) | −1.44046e22 | −0.0942759 | ||||||||
\(535\) | 6.40912e22 | 0.412849 | ||||||||
\(536\) | 3.40986e21 | 0.0216190 | ||||||||
\(537\) | −2.39212e23 | −1.49280 | ||||||||
\(538\) | −1.93783e23 | −1.19033 | ||||||||
\(539\) | −5.68564e22 | −0.343776 | ||||||||
\(540\) | 3.49376e22 | 0.207944 | ||||||||
\(541\) | 8.46775e22 | 0.496125 | 0.248063 | − | 0.968744i | \(-0.420206\pi\) | ||||
0.248063 | + | 0.968744i | \(0.420206\pi\) | |||||||
\(542\) | 3.04405e22 | 0.175573 | ||||||||
\(543\) | 3.01157e23 | 1.70999 | ||||||||
\(544\) | 4.27849e22 | 0.239166 | ||||||||
\(545\) | −1.09505e23 | −0.602646 | ||||||||
\(546\) | 2.51567e22 | 0.136307 | ||||||||
\(547\) | 4.72359e22 | 0.251988 | 0.125994 | − | 0.992031i | \(-0.459788\pi\) | ||||
0.125994 | + | 0.992031i | \(0.459788\pi\) | |||||||
\(548\) | −3.69967e22 | −0.194325 | ||||||||
\(549\) | 3.89340e22 | 0.201356 | ||||||||
\(550\) | −1.56715e22 | −0.0798048 | ||||||||
\(551\) | 2.58952e23 | 1.29847 | ||||||||
\(552\) | −3.32899e21 | −0.0164373 | ||||||||
\(553\) | −7.92316e22 | −0.385243 | ||||||||
\(554\) | 5.02730e22 | 0.240714 | ||||||||
\(555\) | 8.27441e22 | 0.390163 | ||||||||
\(556\) | 1.39927e23 | 0.649778 | ||||||||
\(557\) | 3.77820e23 | 1.72789 | 0.863945 | − | 0.503587i | \(-0.167987\pi\) | ||||
0.863945 | + | 0.503587i | \(0.167987\pi\) | |||||||
\(558\) | 6.61153e21 | 0.0297791 | ||||||||
\(559\) | 1.17885e23 | 0.522949 | ||||||||
\(560\) | 1.59967e22 | 0.0698926 | ||||||||
\(561\) | −1.87927e23 | −0.808732 | ||||||||
\(562\) | 8.67929e22 | 0.367896 | ||||||||
\(563\) | −4.35959e23 | −1.82022 | −0.910112 | − | 0.414363i | \(-0.864005\pi\) | ||||
−0.910112 | + | 0.414363i | \(0.864005\pi\) | |||||||
\(564\) | −1.30527e23 | −0.536818 | ||||||||
\(565\) | 2.07289e23 | 0.839777 | ||||||||
\(566\) | −1.03282e23 | −0.412178 | ||||||||
\(567\) | 1.76058e23 | 0.692149 | ||||||||
\(568\) | −1.57558e23 | −0.610209 | ||||||||
\(569\) | −1.25095e23 | −0.477293 | −0.238647 | − | 0.971106i | \(-0.576704\pi\) | ||||
−0.238647 | + | 0.971106i | \(0.576704\pi\) | |||||||
\(570\) | −1.37037e23 | −0.515113 | ||||||||
\(571\) | −3.10316e23 | −1.14920 | −0.574602 | − | 0.818433i | \(-0.694843\pi\) | ||||
−0.574602 | + | 0.818433i | \(0.694843\pi\) | |||||||
\(572\) | 2.25107e22 | 0.0821341 | ||||||||
\(573\) | −3.17058e23 | −1.13979 | ||||||||
\(574\) | −7.21363e22 | −0.255507 | ||||||||
\(575\) | 2.51516e21 | 0.00877787 | ||||||||
\(576\) | 4.43834e21 | 0.0152626 | ||||||||
\(577\) | −2.11578e23 | −0.716928 | −0.358464 | − | 0.933544i | \(-0.616699\pi\) | ||||
−0.358464 | + | 0.933544i | \(0.616699\pi\) | |||||||
\(578\) | −1.75860e23 | −0.587194 | ||||||||
\(579\) | 4.44021e23 | 1.46095 | ||||||||
\(580\) | 5.82328e22 | 0.188812 | ||||||||
\(581\) | 5.86099e22 | 0.187272 | ||||||||
\(582\) | −3.13711e23 | −0.987835 | ||||||||
\(583\) | −2.90968e23 | −0.902947 | ||||||||
\(584\) | −2.59820e22 | −0.0794627 | ||||||||
\(585\) | −5.27350e21 | −0.0158955 | ||||||||
\(586\) | 2.70790e22 | 0.0804456 | ||||||||
\(587\) | 2.15996e23 | 0.632443 | 0.316222 | − | 0.948685i | \(-0.397586\pi\) | ||||
0.316222 | + | 0.948685i | \(0.397586\pi\) | |||||||
\(588\) | −1.11803e23 | −0.322662 | ||||||||
\(589\) | 1.86455e23 | 0.530387 | ||||||||
\(590\) | 1.62177e23 | 0.454723 | ||||||||
\(591\) | −4.87434e23 | −1.34717 | ||||||||
\(592\) | −7.55771e22 | −0.205900 | ||||||||
\(593\) | 3.56471e23 | 0.957326 | 0.478663 | − | 0.877999i | \(-0.341122\pi\) | ||||
0.478663 | + | 0.877999i | \(0.341122\pi\) | |||||||
\(594\) | 1.40166e23 | 0.371073 | ||||||||
\(595\) | −1.44931e23 | −0.378239 | ||||||||
\(596\) | 1.38390e23 | 0.356051 | ||||||||
\(597\) | −4.00584e23 | −1.01604 | ||||||||
\(598\) | −3.61280e21 | −0.00903408 | ||||||||
\(599\) | 3.17118e23 | 0.781796 | 0.390898 | − | 0.920434i | \(-0.372165\pi\) | ||||
0.390898 | + | 0.920434i | \(0.372165\pi\) | |||||||
\(600\) | −3.08167e22 | −0.0749033 | ||||||||
\(601\) | −2.47473e23 | −0.593055 | −0.296528 | − | 0.955024i | \(-0.595829\pi\) | ||||
−0.296528 | + | 0.955024i | \(0.595829\pi\) | |||||||
\(602\) | 3.36086e23 | 0.794109 | ||||||||
\(603\) | −3.20478e21 | −0.00746622 | ||||||||
\(604\) | 7.17268e22 | 0.164766 | ||||||||
\(605\) | 1.34567e23 | 0.304803 | ||||||||
\(606\) | −9.61168e22 | −0.214675 | ||||||||
\(607\) | 1.27464e23 | 0.280726 | 0.140363 | − | 0.990100i | \(-0.455173\pi\) | ||||
0.140363 | + | 0.990100i | \(0.455173\pi\) | |||||||
\(608\) | 1.25168e23 | 0.271839 | ||||||||
\(609\) | 2.61086e23 | 0.559161 | ||||||||
\(610\) | 2.46915e23 | 0.521488 | ||||||||
\(611\) | −1.41655e23 | −0.295040 | ||||||||
\(612\) | −4.02116e22 | −0.0825971 | ||||||||
\(613\) | 2.08992e23 | 0.423366 | 0.211683 | − | 0.977338i | \(-0.432105\pi\) | ||||
0.211683 | + | 0.977338i | \(0.432105\pi\) | |||||||
\(614\) | 4.68251e23 | 0.935508 | ||||||||
\(615\) | 1.38967e23 | 0.273825 | ||||||||
\(616\) | 6.41772e22 | 0.124723 | ||||||||
\(617\) | 2.52173e23 | 0.483364 | 0.241682 | − | 0.970356i | \(-0.422301\pi\) | ||||
0.241682 | + | 0.970356i | \(0.422301\pi\) | |||||||
\(618\) | 5.28917e23 | 0.999966 | ||||||||
\(619\) | −8.32171e23 | −1.55182 | −0.775911 | − | 0.630842i | \(-0.782709\pi\) | ||||
−0.775911 | + | 0.630842i | \(0.782709\pi\) | |||||||
\(620\) | 4.19296e22 | 0.0771244 | ||||||||
\(621\) | −2.24956e22 | −0.0408150 | ||||||||
\(622\) | −5.13915e23 | −0.919756 | ||||||||
\(623\) | −4.45681e22 | −0.0786821 | ||||||||
\(624\) | 4.42654e22 | 0.0770896 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | 7.29175e23 | 1.23580 | ||||||||
\(627\) | −5.49781e23 | −0.919212 | ||||||||
\(628\) | 1.75620e23 | 0.289680 | ||||||||
\(629\) | 6.84733e23 | 1.11427 | ||||||||
\(630\) | −1.50346e22 | −0.0241377 | ||||||||
\(631\) | 2.44878e23 | 0.387883 | 0.193942 | − | 0.981013i | \(-0.437873\pi\) | ||||
0.193942 | + | 0.981013i | \(0.437873\pi\) | |||||||
\(632\) | −1.39415e23 | −0.217878 | ||||||||
\(633\) | −2.91510e23 | −0.449491 | ||||||||
\(634\) | −7.02327e22 | −0.106852 | ||||||||
\(635\) | −1.34968e23 | −0.202607 | ||||||||
\(636\) | −5.72163e23 | −0.847489 | ||||||||
\(637\) | −1.21335e23 | −0.177338 | ||||||||
\(638\) | 2.33625e23 | 0.336933 | ||||||||
\(639\) | 1.48081e23 | 0.210738 | ||||||||
\(640\) | 2.81475e22 | 0.0395285 | ||||||||
\(641\) | 8.76132e23 | 1.21416 | 0.607081 | − | 0.794640i | \(-0.292340\pi\) | ||||
0.607081 | + | 0.794640i | \(0.292340\pi\) | |||||||
\(642\) | 5.05621e23 | 0.691477 | ||||||||
\(643\) | −3.14015e23 | −0.423796 | −0.211898 | − | 0.977292i | \(-0.567964\pi\) | ||||
−0.211898 | + | 0.977292i | \(0.567964\pi\) | |||||||
\(644\) | −1.03000e22 | −0.0137185 | ||||||||
\(645\) | −6.47452e23 | −0.851040 | ||||||||
\(646\) | −1.13403e24 | −1.47111 | ||||||||
\(647\) | −7.19139e22 | −0.0920718 | −0.0460359 | − | 0.998940i | \(-0.514659\pi\) | ||||
−0.0460359 | + | 0.998940i | \(0.514659\pi\) | |||||||
\(648\) | 3.09789e23 | 0.391452 | ||||||||
\(649\) | 6.50640e23 | 0.811448 | ||||||||
\(650\) | −3.34440e22 | −0.0411675 | ||||||||
\(651\) | 1.87991e23 | 0.228402 | ||||||||
\(652\) | −6.20979e23 | −0.744685 | ||||||||
\(653\) | −7.53337e23 | −0.891717 | −0.445858 | − | 0.895103i | \(-0.647102\pi\) | ||||
−0.445858 | + | 0.895103i | \(0.647102\pi\) | |||||||
\(654\) | −8.63892e23 | −1.00937 | ||||||||
\(655\) | 2.31634e23 | 0.267148 | ||||||||
\(656\) | −1.26930e23 | −0.144505 | ||||||||
\(657\) | 2.44193e22 | 0.0274428 | ||||||||
\(658\) | −4.03852e23 | −0.448025 | ||||||||
\(659\) | −1.78954e24 | −1.95981 | −0.979906 | − | 0.199459i | \(-0.936081\pi\) | ||||
−0.979906 | + | 0.199459i | \(0.936081\pi\) | |||||||
\(660\) | −1.23634e23 | −0.133664 | ||||||||
\(661\) | 3.55263e23 | 0.379173 | 0.189586 | − | 0.981864i | \(-0.439285\pi\) | ||||
0.189586 | + | 0.981864i | \(0.439285\pi\) | |||||||
\(662\) | −4.69815e22 | −0.0495033 | ||||||||
\(663\) | −4.01047e23 | −0.417187 | ||||||||
\(664\) | 1.03129e23 | 0.105914 | ||||||||
\(665\) | −4.23996e23 | −0.429910 | ||||||||
\(666\) | 7.10315e22 | 0.0711083 | ||||||||
\(667\) | −3.74951e22 | −0.0370599 | ||||||||
\(668\) | −4.39527e23 | −0.428929 | ||||||||
\(669\) | 8.93533e23 | 0.860971 | ||||||||
\(670\) | −2.03244e22 | −0.0193367 | ||||||||
\(671\) | 9.90603e23 | 0.930589 | ||||||||
\(672\) | 1.26199e23 | 0.117062 | ||||||||
\(673\) | 5.15130e23 | 0.471833 | 0.235917 | − | 0.971773i | \(-0.424191\pi\) | ||||
0.235917 | + | 0.971773i | \(0.424191\pi\) | |||||||
\(674\) | 1.59028e23 | 0.143835 | ||||||||
\(675\) | −2.08244e23 | −0.185990 | ||||||||
\(676\) | −5.18874e23 | −0.457631 | ||||||||
\(677\) | 1.69205e23 | 0.147370 | 0.0736851 | − | 0.997282i | \(-0.476524\pi\) | ||||
0.0736851 | + | 0.997282i | \(0.476524\pi\) | |||||||
\(678\) | 1.63532e24 | 1.40653 | ||||||||
\(679\) | −9.70628e23 | −0.824441 | ||||||||
\(680\) | −2.55018e23 | −0.213917 | ||||||||
\(681\) | 1.15265e23 | 0.0954880 | ||||||||
\(682\) | 1.68218e23 | 0.137628 | ||||||||
\(683\) | 1.97763e23 | 0.159797 | 0.0798987 | − | 0.996803i | \(-0.474540\pi\) | ||||
0.0798987 | + | 0.996803i | \(0.474540\pi\) | |||||||
\(684\) | −1.17639e23 | −0.0938806 | ||||||||
\(685\) | 2.20518e23 | 0.173809 | ||||||||
\(686\) | −9.13749e23 | −0.711331 | ||||||||
\(687\) | 2.38051e24 | 1.83036 | ||||||||
\(688\) | 5.91372e23 | 0.449117 | ||||||||
\(689\) | −6.20943e23 | −0.465788 | ||||||||
\(690\) | 1.98423e22 | 0.0147020 | ||||||||
\(691\) | 2.62293e24 | 1.91966 | 0.959828 | − | 0.280589i | \(-0.0905298\pi\) | ||||
0.959828 | + | 0.280589i | \(0.0905298\pi\) | |||||||
\(692\) | 6.92681e23 | 0.500762 | ||||||||
\(693\) | −6.03173e22 | −0.0430734 | ||||||||
\(694\) | −1.30298e24 | −0.919144 | ||||||||
\(695\) | −8.34028e23 | −0.581179 | ||||||||
\(696\) | 4.59404e23 | 0.316239 | ||||||||
\(697\) | 1.14999e24 | 0.782018 | ||||||||
\(698\) | 9.75529e22 | 0.0655344 | ||||||||
\(699\) | −2.16413e24 | −1.43624 | ||||||||
\(700\) | −9.53475e22 | −0.0625138 | ||||||||
\(701\) | −4.05441e22 | −0.0262618 | −0.0131309 | − | 0.999914i | \(-0.504180\pi\) | ||||
−0.0131309 | + | 0.999914i | \(0.504180\pi\) | |||||||
\(702\) | 2.99124e23 | 0.191419 | ||||||||
\(703\) | 2.00319e24 | 1.26649 | ||||||||
\(704\) | 1.12925e23 | 0.0705381 | ||||||||
\(705\) | 7.78000e23 | 0.480144 | ||||||||
\(706\) | −6.00830e23 | −0.366363 | ||||||||
\(707\) | −2.97387e23 | −0.179167 | ||||||||
\(708\) | 1.27943e24 | 0.761611 | ||||||||
\(709\) | −7.92278e23 | −0.465999 | −0.232999 | − | 0.972477i | \(-0.574854\pi\) | ||||
−0.232999 | + | 0.972477i | \(0.574854\pi\) | |||||||
\(710\) | 9.39117e23 | 0.545788 | ||||||||
\(711\) | 1.31030e23 | 0.0752451 | ||||||||
\(712\) | −7.84214e22 | −0.0444995 | ||||||||
\(713\) | −2.69977e22 | −0.0151379 | ||||||||
\(714\) | −1.14337e24 | −0.633508 | ||||||||
\(715\) | −1.34174e23 | −0.0734630 | ||||||||
\(716\) | −1.30232e24 | −0.704621 | ||||||||
\(717\) | −2.41005e24 | −1.28859 | ||||||||
\(718\) | 1.58667e22 | 0.00838355 | ||||||||
\(719\) | −7.47670e23 | −0.390404 | −0.195202 | − | 0.980763i | \(-0.562536\pi\) | ||||
−0.195202 | + | 0.980763i | \(0.562536\pi\) | |||||||
\(720\) | −2.64546e22 | −0.0136513 | ||||||||
\(721\) | 1.63648e24 | 0.834566 | ||||||||
\(722\) | −1.91462e24 | −0.964974 | ||||||||
\(723\) | −2.18625e24 | −1.08899 | ||||||||
\(724\) | 1.63955e24 | 0.807138 | ||||||||
\(725\) | −3.47095e23 | −0.168879 | ||||||||
\(726\) | 1.06161e24 | 0.510511 | ||||||||
\(727\) | 5.40980e23 | 0.257122 | 0.128561 | − | 0.991702i | \(-0.458964\pi\) | ||||
0.128561 | + | 0.991702i | \(0.458964\pi\) | |||||||
\(728\) | 1.36958e23 | 0.0643385 | ||||||||
\(729\) | 1.83043e24 | 0.849902 | ||||||||
\(730\) | 1.54865e23 | 0.0710736 | ||||||||
\(731\) | −5.35787e24 | −2.43049 | ||||||||
\(732\) | 1.94794e24 | 0.873435 | ||||||||
\(733\) | 2.02014e24 | 0.895361 | 0.447680 | − | 0.894194i | \(-0.352250\pi\) | ||||
0.447680 | + | 0.894194i | \(0.352250\pi\) | |||||||
\(734\) | 8.71847e23 | 0.381965 | ||||||||
\(735\) | 6.66400e23 | 0.288597 | ||||||||
\(736\) | −1.81237e22 | −0.00775862 | ||||||||
\(737\) | −8.15396e22 | −0.0345060 | ||||||||
\(738\) | 1.19296e23 | 0.0499053 | ||||||||
\(739\) | −2.11021e24 | −0.872666 | −0.436333 | − | 0.899785i | \(-0.643723\pi\) | ||||
−0.436333 | + | 0.899785i | \(0.643723\pi\) | |||||||
\(740\) | 4.50475e23 | 0.184162 | ||||||||
\(741\) | −1.17327e24 | −0.474179 | ||||||||
\(742\) | −1.77028e24 | −0.707309 | ||||||||
\(743\) | 1.34376e24 | 0.530784 | 0.265392 | − | 0.964141i | \(-0.414499\pi\) | ||||
0.265392 | + | 0.964141i | \(0.414499\pi\) | |||||||
\(744\) | 3.30786e23 | 0.129175 | ||||||||
\(745\) | −8.24871e23 | −0.318462 | ||||||||
\(746\) | 1.65116e24 | 0.630246 | ||||||||
\(747\) | −9.69264e22 | −0.0365777 | ||||||||
\(748\) | −1.02311e24 | −0.381732 | ||||||||
\(749\) | 1.56440e24 | 0.577102 | ||||||||
\(750\) | 1.83682e23 | 0.0669956 | ||||||||
\(751\) | 2.72368e24 | 0.982236 | 0.491118 | − | 0.871093i | \(-0.336588\pi\) | ||||
0.491118 | + | 0.871093i | \(0.336588\pi\) | |||||||
\(752\) | −7.10612e23 | −0.253385 | ||||||||
\(753\) | −3.85441e24 | −1.35894 | ||||||||
\(754\) | 4.98570e23 | 0.173808 | ||||||||
\(755\) | −4.27525e23 | −0.147371 | ||||||||
\(756\) | 8.52790e23 | 0.290674 | ||||||||
\(757\) | −3.29400e24 | −1.11022 | −0.555109 | − | 0.831777i | \(-0.687324\pi\) | ||||
−0.555109 | + | 0.831777i | \(0.687324\pi\) | |||||||
\(758\) | 1.45468e24 | 0.484819 | ||||||||
\(759\) | 7.96057e22 | 0.0262355 | ||||||||
\(760\) | −7.46056e23 | −0.243140 | ||||||||
\(761\) | −4.29576e24 | −1.38443 | −0.692215 | − | 0.721692i | \(-0.743365\pi\) | ||||
−0.692215 | + | 0.721692i | \(0.743365\pi\) | |||||||
\(762\) | −1.06477e24 | −0.339344 | ||||||||
\(763\) | −2.67290e24 | −0.842410 | ||||||||
\(764\) | −1.72612e24 | −0.537995 | ||||||||
\(765\) | 2.39680e23 | 0.0738771 | ||||||||
\(766\) | 3.29083e24 | 1.00314 | ||||||||
\(767\) | 1.38851e24 | 0.418588 | ||||||||
\(768\) | 2.22058e23 | 0.0662058 | ||||||||
\(769\) | 5.93781e24 | 1.75086 | 0.875432 | − | 0.483341i | \(-0.160577\pi\) | ||||
0.875432 | + | 0.483341i | \(0.160577\pi\) | |||||||
\(770\) | −3.82526e23 | −0.111555 | ||||||||
\(771\) | −4.02711e24 | −1.16153 | ||||||||
\(772\) | 2.41734e24 | 0.689589 | ||||||||
\(773\) | −1.98352e24 | −0.559642 | −0.279821 | − | 0.960052i | \(-0.590275\pi\) | ||||
−0.279821 | + | 0.960052i | \(0.590275\pi\) | |||||||
\(774\) | −5.55804e23 | −0.155104 | ||||||||
\(775\) | −2.49920e23 | −0.0689822 | ||||||||
\(776\) | −1.70790e24 | −0.466271 | ||||||||
\(777\) | 2.01970e24 | 0.545391 | ||||||||
\(778\) | −4.35684e24 | −1.16371 | ||||||||
\(779\) | 3.36431e24 | 0.888849 | ||||||||
\(780\) | −2.63843e23 | −0.0689510 | ||||||||
\(781\) | 3.76766e24 | 0.973952 | ||||||||
\(782\) | 1.64201e23 | 0.0419874 | ||||||||
\(783\) | 3.10442e24 | 0.785246 | ||||||||
\(784\) | −6.08678e23 | −0.152300 | ||||||||
\(785\) | −1.04678e24 | −0.259097 | ||||||||
\(786\) | 1.82738e24 | 0.447442 | ||||||||
\(787\) | 3.61371e24 | 0.875322 | 0.437661 | − | 0.899140i | \(-0.355807\pi\) | ||||
0.437661 | + | 0.899140i | \(0.355807\pi\) | |||||||
\(788\) | −2.65369e24 | −0.635882 | ||||||||
\(789\) | 3.55156e24 | 0.841907 | ||||||||
\(790\) | 8.30977e23 | 0.194876 | ||||||||
\(791\) | 5.05970e24 | 1.17388 | ||||||||
\(792\) | −1.06133e23 | −0.0243606 | ||||||||
\(793\) | 2.11401e24 | 0.480047 | ||||||||
\(794\) | 4.63826e24 | 1.04203 | ||||||||
\(795\) | 3.41036e24 | 0.758018 | ||||||||
\(796\) | −2.18086e24 | −0.479586 | ||||||||
\(797\) | −4.63064e24 | −1.00750 | −0.503751 | − | 0.863849i | \(-0.668047\pi\) | ||||
−0.503751 | + | 0.863849i | \(0.668047\pi\) | |||||||
\(798\) | −3.34494e24 | −0.720051 | ||||||||
\(799\) | 6.43819e24 | 1.37125 | ||||||||
\(800\) | −1.67772e23 | −0.0353553 | ||||||||
\(801\) | 7.37048e22 | 0.0153681 | ||||||||
\(802\) | −4.48022e24 | −0.924308 | ||||||||
\(803\) | 6.21304e23 | 0.126830 | ||||||||
\(804\) | −1.60341e23 | −0.0323867 | ||||||||
\(805\) | 6.13925e22 | 0.0122702 | ||||||||
\(806\) | 3.58988e23 | 0.0709956 | ||||||||
\(807\) | 9.11220e24 | 1.78319 | ||||||||
\(808\) | −5.23278e23 | −0.101330 | ||||||||
\(809\) | −1.22642e24 | −0.235005 | −0.117502 | − | 0.993073i | \(-0.537489\pi\) | ||||
−0.117502 | + | 0.993073i | \(0.537489\pi\) | |||||||
\(810\) | −1.84648e24 | −0.350125 | ||||||||
\(811\) | −2.42686e24 | −0.455373 | −0.227686 | − | 0.973735i | \(-0.573116\pi\) | ||||
−0.227686 | + | 0.973735i | \(0.573116\pi\) | |||||||
\(812\) | 1.42140e24 | 0.263931 | ||||||||
\(813\) | −1.43139e24 | −0.263020 | ||||||||
\(814\) | 1.80726e24 | 0.328635 | ||||||||
\(815\) | 3.70132e24 | 0.666066 | ||||||||
\(816\) | −2.01186e24 | −0.358287 | ||||||||
\(817\) | −1.56745e25 | −2.76252 | ||||||||
\(818\) | −2.31994e24 | −0.404644 | ||||||||
\(819\) | −1.28721e23 | −0.0222196 | ||||||||
\(820\) | 7.56562e23 | 0.129249 | ||||||||
\(821\) | −9.87401e24 | −1.66946 | −0.834731 | − | 0.550658i | \(-0.814377\pi\) | ||||
−0.834731 | + | 0.550658i | \(0.814377\pi\) | |||||||
\(822\) | 1.73968e24 | 0.291111 | ||||||||
\(823\) | −3.09810e24 | −0.513094 | −0.256547 | − | 0.966532i | \(-0.582585\pi\) | ||||
−0.256547 | + | 0.966532i | \(0.582585\pi\) | |||||||
\(824\) | 2.87952e24 | 0.471997 | ||||||||
\(825\) | 7.36917e23 | 0.119553 | ||||||||
\(826\) | 3.95857e24 | 0.635636 | ||||||||
\(827\) | −3.89248e24 | −0.618628 | −0.309314 | − | 0.950960i | \(-0.600099\pi\) | ||||
−0.309314 | + | 0.950960i | \(0.600099\pi\) | |||||||
\(828\) | 1.70336e22 | 0.00267947 | ||||||||
\(829\) | −1.04208e25 | −1.62251 | −0.811256 | − | 0.584691i | \(-0.801216\pi\) | ||||
−0.811256 | + | 0.584691i | \(0.801216\pi\) | |||||||
\(830\) | −6.14697e23 | −0.0947321 | ||||||||
\(831\) | −2.36397e24 | −0.360606 | ||||||||
\(832\) | 2.40989e23 | 0.0363873 | ||||||||
\(833\) | 5.51466e24 | 0.824207 | ||||||||
\(834\) | −6.57972e24 | −0.973410 | ||||||||
\(835\) | 2.61979e24 | 0.383646 | ||||||||
\(836\) | −2.99311e24 | −0.433880 | ||||||||
\(837\) | 2.23529e24 | 0.320750 | ||||||||
\(838\) | −1.91925e24 | −0.272619 | ||||||||
\(839\) | −6.67595e24 | −0.938721 | −0.469360 | − | 0.883007i | \(-0.655515\pi\) | ||||
−0.469360 | + | 0.883007i | \(0.655515\pi\) | |||||||
\(840\) | −7.52205e23 | −0.104704 | ||||||||
\(841\) | −2.08280e24 | −0.286999 | ||||||||
\(842\) | 7.56685e24 | 1.03220 | ||||||||
\(843\) | −4.08123e24 | −0.551133 | ||||||||
\(844\) | −1.58703e24 | −0.212166 | ||||||||
\(845\) | 3.09273e24 | 0.409318 | ||||||||
\(846\) | 6.67873e23 | 0.0875075 | ||||||||
\(847\) | 3.28465e24 | 0.426069 | ||||||||
\(848\) | −3.11496e24 | −0.400026 | ||||||||
\(849\) | 4.85659e24 | 0.617470 | ||||||||
\(850\) | 1.52003e24 | 0.191333 | ||||||||
\(851\) | −2.90052e23 | −0.0361472 | ||||||||
\(852\) | 7.40877e24 | 0.914134 | ||||||||
\(853\) | 9.79573e24 | 1.19666 | 0.598329 | − | 0.801250i | \(-0.295831\pi\) | ||||
0.598329 | + | 0.801250i | \(0.295831\pi\) | |||||||
\(854\) | 6.02695e24 | 0.728963 | ||||||||
\(855\) | 7.01185e23 | 0.0839694 | ||||||||
\(856\) | 2.75270e24 | 0.326386 | ||||||||
\(857\) | −4.38126e24 | −0.514354 | −0.257177 | − | 0.966364i | \(-0.582792\pi\) | ||||
−0.257177 | + | 0.966364i | \(0.582792\pi\) | |||||||
\(858\) | −1.05851e24 | −0.123042 | ||||||||
\(859\) | −1.50626e25 | −1.73364 | −0.866821 | − | 0.498620i | \(-0.833841\pi\) | ||||
−0.866821 | + | 0.498620i | \(0.833841\pi\) | |||||||
\(860\) | −3.52485e24 | −0.401702 | ||||||||
\(861\) | 3.39204e24 | 0.382766 | ||||||||
\(862\) | 1.88676e24 | 0.210817 | ||||||||
\(863\) | 1.37694e25 | 1.52344 | 0.761718 | − | 0.647909i | \(-0.224356\pi\) | ||||
0.761718 | + | 0.647909i | \(0.224356\pi\) | |||||||
\(864\) | 1.50056e24 | 0.164394 | ||||||||
\(865\) | −4.12870e24 | −0.447896 | ||||||||
\(866\) | −4.54616e23 | −0.0488363 | ||||||||
\(867\) | 8.26942e24 | 0.879655 | ||||||||
\(868\) | 1.02346e24 | 0.107808 | ||||||||
\(869\) | 3.33381e24 | 0.347754 | ||||||||
\(870\) | −2.73826e24 | −0.282853 | ||||||||
\(871\) | −1.74010e23 | −0.0178000 | ||||||||
\(872\) | −4.70319e24 | −0.476434 | ||||||||
\(873\) | 1.60518e24 | 0.161029 | ||||||||
\(874\) | 4.80372e23 | 0.0477233 | ||||||||
\(875\) | 5.68316e23 | 0.0559141 | ||||||||
\(876\) | 1.22174e24 | 0.119040 | ||||||||
\(877\) | −7.56082e24 | −0.729579 | −0.364790 | − | 0.931090i | \(-0.618859\pi\) | ||||
−0.364790 | + | 0.931090i | \(0.618859\pi\) | |||||||
\(878\) | 7.47549e24 | 0.714391 | ||||||||
\(879\) | −1.27332e24 | −0.120513 | ||||||||
\(880\) | −6.73087e23 | −0.0630912 | ||||||||
\(881\) | 5.11196e24 | 0.474561 | 0.237281 | − | 0.971441i | \(-0.423744\pi\) | ||||
0.237281 | + | 0.971441i | \(0.423744\pi\) | |||||||
\(882\) | 5.72070e23 | 0.0525976 | ||||||||
\(883\) | −1.37334e25 | −1.25058 | −0.625289 | − | 0.780393i | \(-0.715019\pi\) | ||||
−0.625289 | + | 0.780393i | \(0.715019\pi\) | |||||||
\(884\) | −2.18338e24 | −0.196918 | ||||||||
\(885\) | −7.62599e24 | −0.681206 | ||||||||
\(886\) | 1.04078e25 | 0.920813 | ||||||||
\(887\) | 1.15450e25 | 1.01168 | 0.505838 | − | 0.862628i | \(-0.331183\pi\) | ||||
0.505838 | + | 0.862628i | \(0.331183\pi\) | |||||||
\(888\) | 3.55383e24 | 0.308451 | ||||||||
\(889\) | −3.29443e24 | −0.283215 | ||||||||
\(890\) | 4.67428e23 | 0.0398015 | ||||||||
\(891\) | −7.40794e24 | −0.624794 | ||||||||
\(892\) | 4.86456e24 | 0.406390 | ||||||||
\(893\) | 1.88349e25 | 1.55857 | ||||||||
\(894\) | −6.50748e24 | −0.533389 | ||||||||
\(895\) | 7.76241e24 | 0.630233 | ||||||||
\(896\) | 6.87051e23 | 0.0552550 | ||||||||
\(897\) | 1.69883e23 | 0.0135337 | ||||||||
\(898\) | −1.18472e24 | −0.0934907 | ||||||||
\(899\) | 3.72571e24 | 0.291240 | ||||||||
\(900\) | 1.57682e23 | 0.0122101 | ||||||||
\(901\) | 2.82218e25 | 2.16483 | ||||||||
\(902\) | 3.03526e24 | 0.230643 | ||||||||
\(903\) | −1.58036e25 | −1.18963 | ||||||||
\(904\) | 8.90298e24 | 0.663902 | ||||||||
\(905\) | −9.77250e24 | −0.721926 | ||||||||
\(906\) | −3.37278e24 | −0.246830 | ||||||||
\(907\) | −1.74990e25 | −1.26868 | −0.634338 | − | 0.773056i | \(-0.718727\pi\) | ||||
−0.634338 | + | 0.773056i | \(0.718727\pi\) | |||||||
\(908\) | 6.27527e23 | 0.0450716 | ||||||||
\(909\) | 4.91806e23 | 0.0349946 | ||||||||
\(910\) | −8.16334e23 | −0.0575461 | ||||||||
\(911\) | −1.12560e25 | −0.786102 | −0.393051 | − | 0.919517i | \(-0.628580\pi\) | ||||
−0.393051 | + | 0.919517i | \(0.628580\pi\) | |||||||
\(912\) | −5.88570e24 | −0.407232 | ||||||||
\(913\) | −2.46611e24 | −0.169048 | ||||||||
\(914\) | −1.61495e25 | −1.09677 | ||||||||
\(915\) | −1.16106e25 | −0.781224 | ||||||||
\(916\) | 1.29599e25 | 0.863955 | ||||||||
\(917\) | 5.65395e24 | 0.373433 | ||||||||
\(918\) | −1.35951e25 | −0.889653 | ||||||||
\(919\) | −2.33947e24 | −0.151682 | −0.0758412 | − | 0.997120i | \(-0.524164\pi\) | ||||
−0.0758412 | + | 0.997120i | \(0.524164\pi\) | |||||||
\(920\) | 1.08025e23 | 0.00693952 | ||||||||
\(921\) | −2.20184e25 | −1.40145 | ||||||||
\(922\) | −1.44123e25 | −0.908911 | ||||||||
\(923\) | 8.04040e24 | 0.502416 | ||||||||
\(924\) | −3.01778e24 | −0.186843 | ||||||||
\(925\) | −2.68504e24 | −0.164720 | ||||||||
\(926\) | −1.51086e24 | −0.0918398 | ||||||||
\(927\) | −2.70634e24 | −0.163006 | ||||||||
\(928\) | 2.50108e24 | 0.149269 | ||||||||
\(929\) | 3.62091e24 | 0.214133 | 0.107067 | − | 0.994252i | \(-0.465854\pi\) | ||||
0.107067 | + | 0.994252i | \(0.465854\pi\) | |||||||
\(930\) | −1.97164e24 | −0.115537 | ||||||||
\(931\) | 1.61332e25 | 0.936801 | ||||||||
\(932\) | −1.17819e25 | −0.677925 | ||||||||
\(933\) | 2.41656e25 | 1.37786 | ||||||||
\(934\) | −6.42853e24 | −0.363215 | ||||||||
\(935\) | 6.09821e24 | 0.341432 | ||||||||
\(936\) | −2.26495e23 | −0.0125665 | ||||||||
\(937\) | 4.50917e24 | 0.247919 | 0.123960 | − | 0.992287i | \(-0.460441\pi\) | ||||
0.123960 | + | 0.992287i | \(0.460441\pi\) | |||||||
\(938\) | −4.96097e23 | −0.0270298 | ||||||||
\(939\) | −3.42877e25 | −1.85132 | ||||||||
\(940\) | 4.23558e24 | 0.226634 | ||||||||
\(941\) | 2.46547e25 | 1.30734 | 0.653669 | − | 0.756780i | \(-0.273229\pi\) | ||||
0.653669 | + | 0.756780i | \(0.273229\pi\) | |||||||
\(942\) | −8.25812e24 | −0.433959 | ||||||||
\(943\) | −4.87136e23 | −0.0253689 | ||||||||
\(944\) | 6.96545e24 | 0.359490 | ||||||||
\(945\) | −5.08302e24 | −0.259987 | ||||||||
\(946\) | −1.41414e25 | −0.716833 | ||||||||
\(947\) | 2.52153e25 | 1.26675 | 0.633373 | − | 0.773847i | \(-0.281670\pi\) | ||||
0.633373 | + | 0.773847i | \(0.281670\pi\) | |||||||
\(948\) | 6.55565e24 | 0.326396 | ||||||||
\(949\) | 1.32590e24 | 0.0654257 | ||||||||
\(950\) | 4.44684e24 | 0.217471 | ||||||||
\(951\) | 3.30253e24 | 0.160071 | ||||||||
\(952\) | −6.22473e24 | −0.299024 | ||||||||
\(953\) | 2.22635e25 | 1.05999 | 0.529996 | − | 0.848000i | \(-0.322193\pi\) | ||||
0.529996 | + | 0.848000i | \(0.322193\pi\) | |||||||
\(954\) | 2.92762e24 | 0.138151 | ||||||||
\(955\) | 1.02885e25 | 0.481197 | ||||||||
\(956\) | −1.31208e25 | −0.608229 | ||||||||
\(957\) | −1.09857e25 | −0.504748 | ||||||||
\(958\) | 9.07031e24 | 0.413062 | ||||||||
\(959\) | 5.38261e24 | 0.242960 | ||||||||
\(960\) | −1.32357e24 | −0.0592163 | ||||||||
\(961\) | −1.98675e25 | −0.881037 | ||||||||
\(962\) | 3.85681e24 | 0.169528 | ||||||||
\(963\) | −2.58714e24 | −0.112719 | ||||||||
\(964\) | −1.19024e25 | −0.514018 | ||||||||
\(965\) | −1.44085e25 | −0.616787 | ||||||||
\(966\) | 4.84331e23 | 0.0205512 | ||||||||
\(967\) | −4.73776e24 | −0.199273 | −0.0996363 | − | 0.995024i | \(-0.531768\pi\) | ||||
−0.0996363 | + | 0.995024i | \(0.531768\pi\) | |||||||
\(968\) | 5.77963e24 | 0.240968 | ||||||||
\(969\) | 5.33248e25 | 2.20383 | ||||||||
\(970\) | 1.01799e25 | 0.417045 | ||||||||
\(971\) | −3.41703e25 | −1.38767 | −0.693833 | − | 0.720136i | \(-0.744079\pi\) | ||||
−0.693833 | + | 0.720136i | \(0.744079\pi\) | |||||||
\(972\) | −3.01676e24 | −0.121445 | ||||||||
\(973\) | −2.03578e25 | −0.812402 | ||||||||
\(974\) | 3.88341e24 | 0.153625 | ||||||||
\(975\) | 1.57262e24 | 0.0616717 | ||||||||
\(976\) | 1.06049e25 | 0.412273 | ||||||||
\(977\) | 6.32382e24 | 0.243711 | 0.121856 | − | 0.992548i | \(-0.461116\pi\) | ||||
0.121856 | + | 0.992548i | \(0.461116\pi\) | |||||||
\(978\) | 2.92001e25 | 1.11559 | ||||||||
\(979\) | 1.87528e24 | 0.0710254 | ||||||||
\(980\) | 3.62801e24 | 0.136222 | ||||||||
\(981\) | 4.42032e24 | 0.164538 | ||||||||
\(982\) | 1.78408e25 | 0.658365 | ||||||||
\(983\) | −5.13743e25 | −1.87949 | −0.939747 | − | 0.341870i | \(-0.888940\pi\) | ||||
−0.939747 | + | 0.341870i | \(0.888940\pi\) | |||||||
\(984\) | 5.96858e24 | 0.216477 | ||||||||
\(985\) | 1.58172e25 | 0.568750 | ||||||||
\(986\) | −2.26599e25 | −0.807802 | ||||||||
\(987\) | 1.89902e25 | 0.671171 | ||||||||
\(988\) | −6.38749e24 | −0.223818 | ||||||||
\(989\) | 2.26959e24 | 0.0788458 | ||||||||
\(990\) | 6.32605e23 | 0.0217888 | ||||||||
\(991\) | 3.11936e25 | 1.06522 | 0.532610 | − | 0.846361i | \(-0.321211\pi\) | ||||
0.532610 | + | 0.846361i | \(0.321211\pi\) | |||||||
\(992\) | 1.80086e24 | 0.0609722 | ||||||||
\(993\) | 2.20919e24 | 0.0741592 | ||||||||
\(994\) | 2.29229e25 | 0.762930 | ||||||||
\(995\) | 1.29989e25 | 0.428954 | ||||||||
\(996\) | −4.84940e24 | −0.158666 | ||||||||
\(997\) | −4.66217e25 | −1.51244 | −0.756222 | − | 0.654315i | \(-0.772957\pi\) | ||||
−0.756222 | + | 0.654315i | \(0.772957\pi\) | |||||||
\(998\) | 1.30809e25 | 0.420755 | ||||||||
\(999\) | 2.40150e25 | 0.765907 |
(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 | 10.18.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 90.18.a.n.1.1 | 2 | |||
4.3 | odd | 2 | 80.18.a.e.1.1 | 2 | |||
5.2 | odd | 4 | 50.18.b.e.49.1 | 4 | |||
5.3 | odd | 4 | 50.18.b.e.49.4 | 4 | |||
5.4 | even | 2 | 50.18.a.g.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.18.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.18.a.g.1.1 | 2 | 5.4 | even | 2 | |||
50.18.b.e.49.1 | 4 | 5.2 | odd | 4 | |||
50.18.b.e.49.4 | 4 | 5.3 | odd | 4 | |||
80.18.a.e.1.1 | 2 | 4.3 | odd | 2 | |||
90.18.a.n.1.1 | 2 | 3.2 | odd | 2 |