Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,34,Mod(1,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(34.4914144405\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 1372039866x^{3} - 648067657640x^{2} + 285631173782445856x - 33409741805340964224 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{5}\cdot 5^{4}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-33002.4\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 138106. | 1.49010 | 0.745051 | − | 0.667007i | \(-0.232425\pi\) | ||||
0.745051 | + | 0.667007i | \(0.232425\pi\) | |||||||
\(3\) | −1.45282e7 | −0.194855 | −0.0974273 | − | 0.995243i | \(-0.531061\pi\) | ||||
−0.0974273 | + | 0.995243i | \(0.531061\pi\) | |||||||
\(4\) | 1.04832e10 | 1.22041 | ||||||||
\(5\) | −1.52588e11 | −0.447214 | ||||||||
\(6\) | −2.00642e12 | −0.290353 | ||||||||
\(7\) | 3.75584e13 | 0.427158 | 0.213579 | − | 0.976926i | \(-0.431488\pi\) | ||||
0.213579 | + | 0.976926i | \(0.431488\pi\) | |||||||
\(8\) | 2.61472e14 | 0.328428 | ||||||||
\(9\) | −5.34799e15 | −0.962032 | ||||||||
\(10\) | −2.10732e16 | −0.666394 | ||||||||
\(11\) | −7.18987e16 | −0.471783 | −0.235891 | − | 0.971779i | \(-0.575801\pi\) | ||||
−0.235891 | + | 0.971779i | \(0.575801\pi\) | |||||||
\(12\) | −1.52302e17 | −0.237802 | ||||||||
\(13\) | 1.13201e18 | 0.471830 | 0.235915 | − | 0.971774i | \(-0.424191\pi\) | ||||
0.235915 | + | 0.971774i | \(0.424191\pi\) | |||||||
\(14\) | 5.18702e18 | 0.636510 | ||||||||
\(15\) | 2.21682e18 | 0.0871416 | ||||||||
\(16\) | −5.39393e19 | −0.731014 | ||||||||
\(17\) | −1.70846e20 | −0.851526 | −0.425763 | − | 0.904835i | \(-0.639994\pi\) | ||||
−0.425763 | + | 0.904835i | \(0.639994\pi\) | |||||||
\(18\) | −7.38588e20 | −1.43353 | ||||||||
\(19\) | −8.48651e20 | −0.674986 | −0.337493 | − | 0.941328i | \(-0.609579\pi\) | ||||
−0.337493 | + | 0.941328i | \(0.609579\pi\) | |||||||
\(20\) | −1.59961e21 | −0.545782 | ||||||||
\(21\) | −5.45655e20 | −0.0832338 | ||||||||
\(22\) | −9.92962e21 | −0.703005 | ||||||||
\(23\) | −3.95696e22 | −1.34540 | −0.672702 | − | 0.739914i | \(-0.734866\pi\) | ||||
−0.672702 | + | 0.739914i | \(0.734866\pi\) | |||||||
\(24\) | −3.79872e21 | −0.0639958 | ||||||||
\(25\) | 2.32831e22 | 0.200000 | ||||||||
\(26\) | 1.56337e23 | 0.703075 | ||||||||
\(27\) | 1.58460e23 | 0.382311 | ||||||||
\(28\) | 3.93732e23 | 0.521307 | ||||||||
\(29\) | 9.30999e23 | 0.690848 | 0.345424 | − | 0.938447i | \(-0.387735\pi\) | ||||
0.345424 | + | 0.938447i | \(0.387735\pi\) | |||||||
\(30\) | 3.06156e23 | 0.129850 | ||||||||
\(31\) | −8.60649e23 | −0.212500 | −0.106250 | − | 0.994339i | \(-0.533884\pi\) | ||||
−0.106250 | + | 0.994339i | \(0.533884\pi\) | |||||||
\(32\) | −9.69535e24 | −1.41772 | ||||||||
\(33\) | 1.04456e24 | 0.0919290 | ||||||||
\(34\) | −2.35948e25 | −1.26886 | ||||||||
\(35\) | −5.73095e24 | −0.191031 | ||||||||
\(36\) | −5.60641e25 | −1.17407 | ||||||||
\(37\) | −5.07725e25 | −0.676550 | −0.338275 | − | 0.941047i | \(-0.609843\pi\) | ||||
−0.338275 | + | 0.941047i | \(0.609843\pi\) | |||||||
\(38\) | −1.17203e26 | −1.00580 | ||||||||
\(39\) | −1.64461e25 | −0.0919383 | ||||||||
\(40\) | −3.98975e25 | −0.146878 | ||||||||
\(41\) | −1.78283e26 | −0.436692 | −0.218346 | − | 0.975871i | \(-0.570066\pi\) | ||||
−0.218346 | + | 0.975871i | \(0.570066\pi\) | |||||||
\(42\) | −7.53580e25 | −0.124027 | ||||||||
\(43\) | 8.10579e26 | 0.904827 | 0.452414 | − | 0.891808i | \(-0.350563\pi\) | ||||
0.452414 | + | 0.891808i | \(0.350563\pi\) | |||||||
\(44\) | −7.53730e26 | −0.575767 | ||||||||
\(45\) | 8.16039e26 | 0.430234 | ||||||||
\(46\) | −5.46479e27 | −2.00479 | ||||||||
\(47\) | −5.64217e27 | −1.45155 | −0.725775 | − | 0.687933i | \(-0.758518\pi\) | ||||
−0.725775 | + | 0.687933i | \(0.758518\pi\) | |||||||
\(48\) | 7.83641e26 | 0.142441 | ||||||||
\(49\) | −6.32036e27 | −0.817536 | ||||||||
\(50\) | 3.21552e27 | 0.298021 | ||||||||
\(51\) | 2.48208e27 | 0.165924 | ||||||||
\(52\) | 1.18671e28 | 0.575825 | ||||||||
\(53\) | 5.15002e28 | 1.82497 | 0.912487 | − | 0.409105i | \(-0.134159\pi\) | ||||
0.912487 | + | 0.409105i | \(0.134159\pi\) | |||||||
\(54\) | 2.18842e28 | 0.569682 | ||||||||
\(55\) | 1.09709e28 | 0.210988 | ||||||||
\(56\) | 9.82047e27 | 0.140291 | ||||||||
\(57\) | 1.23294e28 | 0.131524 | ||||||||
\(58\) | 1.28576e29 | 1.02943 | ||||||||
\(59\) | 1.40126e29 | 0.846175 | 0.423088 | − | 0.906089i | \(-0.360946\pi\) | ||||
0.423088 | + | 0.906089i | \(0.360946\pi\) | |||||||
\(60\) | 2.32394e28 | 0.106348 | ||||||||
\(61\) | −8.28448e28 | −0.288618 | −0.144309 | − | 0.989533i | \(-0.546096\pi\) | ||||
−0.144309 | + | 0.989533i | \(0.546096\pi\) | |||||||
\(62\) | −1.18860e29 | −0.316646 | ||||||||
\(63\) | −2.00862e29 | −0.410940 | ||||||||
\(64\) | −8.75647e29 | −1.38153 | ||||||||
\(65\) | −1.72731e29 | −0.211009 | ||||||||
\(66\) | 1.44259e29 | 0.136984 | ||||||||
\(67\) | 2.02520e29 | 0.150049 | 0.0750246 | − | 0.997182i | \(-0.476096\pi\) | ||||
0.0750246 | + | 0.997182i | \(0.476096\pi\) | |||||||
\(68\) | −1.79102e30 | −1.03921 | ||||||||
\(69\) | 5.74875e29 | 0.262158 | ||||||||
\(70\) | −7.91476e29 | −0.284656 | ||||||||
\(71\) | 6.89895e30 | 1.96345 | 0.981726 | − | 0.190302i | \(-0.0609466\pi\) | ||||
0.981726 | + | 0.190302i | \(0.0609466\pi\) | |||||||
\(72\) | −1.39835e30 | −0.315959 | ||||||||
\(73\) | −3.84757e30 | −0.692404 | −0.346202 | − | 0.938160i | \(-0.612529\pi\) | ||||
−0.346202 | + | 0.938160i | \(0.612529\pi\) | |||||||
\(74\) | −7.01196e30 | −1.00813 | ||||||||
\(75\) | −3.38261e29 | −0.0389709 | ||||||||
\(76\) | −8.89659e30 | −0.823757 | ||||||||
\(77\) | −2.70040e30 | −0.201526 | ||||||||
\(78\) | −2.27129e30 | −0.136997 | ||||||||
\(79\) | 9.36491e30 | 0.457780 | 0.228890 | − | 0.973452i | \(-0.426490\pi\) | ||||
0.228890 | + | 0.973452i | \(0.426490\pi\) | |||||||
\(80\) | 8.23049e30 | 0.326920 | ||||||||
\(81\) | 2.74277e31 | 0.887537 | ||||||||
\(82\) | −2.46218e31 | −0.650716 | ||||||||
\(83\) | 7.23102e31 | 1.56463 | 0.782314 | − | 0.622884i | \(-0.214039\pi\) | ||||
0.782314 | + | 0.622884i | \(0.214039\pi\) | |||||||
\(84\) | −5.72021e30 | −0.101579 | ||||||||
\(85\) | 2.60691e31 | 0.380814 | ||||||||
\(86\) | 1.11945e32 | 1.34829 | ||||||||
\(87\) | −1.35257e31 | −0.134615 | ||||||||
\(88\) | −1.87995e31 | −0.154947 | ||||||||
\(89\) | 4.37547e31 | 0.299288 | 0.149644 | − | 0.988740i | \(-0.452187\pi\) | ||||
0.149644 | + | 0.988740i | \(0.452187\pi\) | |||||||
\(90\) | 1.12700e32 | 0.641092 | ||||||||
\(91\) | 4.25165e31 | 0.201546 | ||||||||
\(92\) | −4.14817e32 | −1.64194 | ||||||||
\(93\) | 1.25037e31 | 0.0414065 | ||||||||
\(94\) | −7.79216e32 | −2.16296 | ||||||||
\(95\) | 1.29494e32 | 0.301863 | ||||||||
\(96\) | 1.40856e32 | 0.276248 | ||||||||
\(97\) | −1.02091e33 | −1.68754 | −0.843771 | − | 0.536703i | \(-0.819669\pi\) | ||||
−0.843771 | + | 0.536703i | \(0.819669\pi\) | |||||||
\(98\) | −8.72877e32 | −1.21821 | ||||||||
\(99\) | 3.84514e32 | 0.453870 | ||||||||
\(100\) | 2.44081e32 | 0.244081 | ||||||||
\(101\) | 2.20022e33 | 1.86709 | 0.933543 | − | 0.358466i | \(-0.116700\pi\) | ||||
0.933543 | + | 0.358466i | \(0.116700\pi\) | |||||||
\(102\) | 3.42790e32 | 0.247244 | ||||||||
\(103\) | −1.21369e33 | −0.745234 | −0.372617 | − | 0.927985i | \(-0.621539\pi\) | ||||
−0.372617 | + | 0.927985i | \(0.621539\pi\) | |||||||
\(104\) | 2.95990e32 | 0.154962 | ||||||||
\(105\) | 8.32603e31 | 0.0372233 | ||||||||
\(106\) | 7.11246e33 | 2.71940 | ||||||||
\(107\) | −3.78167e33 | −1.23837 | −0.619187 | − | 0.785244i | \(-0.712538\pi\) | ||||
−0.619187 | + | 0.785244i | \(0.712538\pi\) | |||||||
\(108\) | 1.66117e33 | 0.466575 | ||||||||
\(109\) | −4.93974e33 | −1.19170 | −0.595849 | − | 0.803096i | \(-0.703184\pi\) | ||||
−0.595849 | + | 0.803096i | \(0.703184\pi\) | |||||||
\(110\) | 1.51514e33 | 0.314393 | ||||||||
\(111\) | 7.37632e32 | 0.131829 | ||||||||
\(112\) | −2.02587e33 | −0.312259 | ||||||||
\(113\) | −3.63884e33 | −0.484360 | −0.242180 | − | 0.970231i | \(-0.577862\pi\) | ||||
−0.242180 | + | 0.970231i | \(0.577862\pi\) | |||||||
\(114\) | 1.70275e33 | 0.195984 | ||||||||
\(115\) | 6.03785e33 | 0.601683 | ||||||||
\(116\) | 9.75986e33 | 0.843115 | ||||||||
\(117\) | −6.05399e33 | −0.453916 | ||||||||
\(118\) | 1.93522e34 | 1.26089 | ||||||||
\(119\) | −6.41670e33 | −0.363737 | ||||||||
\(120\) | 5.79638e32 | 0.0286198 | ||||||||
\(121\) | −1.80557e34 | −0.777421 | ||||||||
\(122\) | −1.14413e34 | −0.430070 | ||||||||
\(123\) | 2.59012e33 | 0.0850915 | ||||||||
\(124\) | −9.02236e33 | −0.259336 | ||||||||
\(125\) | −3.55271e33 | −0.0894427 | ||||||||
\(126\) | −2.77401e34 | −0.612343 | ||||||||
\(127\) | 3.03012e34 | 0.587082 | 0.293541 | − | 0.955947i | \(-0.405166\pi\) | ||||
0.293541 | + | 0.955947i | \(0.405166\pi\) | |||||||
\(128\) | −3.76492e34 | −0.640902 | ||||||||
\(129\) | −1.17762e34 | −0.176310 | ||||||||
\(130\) | −2.38552e34 | −0.314425 | ||||||||
\(131\) | −7.83378e34 | −0.909903 | −0.454951 | − | 0.890516i | \(-0.650343\pi\) | ||||
−0.454951 | + | 0.890516i | \(0.650343\pi\) | |||||||
\(132\) | 1.09503e34 | 0.112191 | ||||||||
\(133\) | −3.18739e34 | −0.288326 | ||||||||
\(134\) | 2.79691e34 | 0.223589 | ||||||||
\(135\) | −2.41790e34 | −0.170975 | ||||||||
\(136\) | −4.46715e34 | −0.279665 | ||||||||
\(137\) | 1.43675e35 | 0.797060 | 0.398530 | − | 0.917155i | \(-0.369520\pi\) | ||||
0.398530 | + | 0.917155i | \(0.369520\pi\) | |||||||
\(138\) | 7.93934e34 | 0.390642 | ||||||||
\(139\) | 3.03428e35 | 1.32529 | 0.662647 | − | 0.748932i | \(-0.269433\pi\) | ||||
0.662647 | + | 0.748932i | \(0.269433\pi\) | |||||||
\(140\) | −6.00788e34 | −0.233136 | ||||||||
\(141\) | 8.19705e34 | 0.282841 | ||||||||
\(142\) | 9.52783e35 | 2.92574 | ||||||||
\(143\) | −8.13902e34 | −0.222601 | ||||||||
\(144\) | 2.88467e35 | 0.703259 | ||||||||
\(145\) | −1.42059e35 | −0.308957 | ||||||||
\(146\) | −5.31371e35 | −1.03175 | ||||||||
\(147\) | 9.18234e34 | 0.159301 | ||||||||
\(148\) | −5.32259e35 | −0.825666 | ||||||||
\(149\) | −8.47533e35 | −1.17648 | −0.588238 | − | 0.808688i | \(-0.700178\pi\) | ||||
−0.588238 | + | 0.808688i | \(0.700178\pi\) | |||||||
\(150\) | −4.67157e34 | −0.0580707 | ||||||||
\(151\) | −1.42730e36 | −1.59000 | −0.794999 | − | 0.606610i | \(-0.792529\pi\) | ||||
−0.794999 | + | 0.606610i | \(0.792529\pi\) | |||||||
\(152\) | −2.21899e35 | −0.221685 | ||||||||
\(153\) | 9.13684e35 | 0.819195 | ||||||||
\(154\) | −3.72940e35 | −0.300294 | ||||||||
\(155\) | 1.31325e35 | 0.0950327 | ||||||||
\(156\) | −1.72408e35 | −0.112202 | ||||||||
\(157\) | −1.47748e36 | −0.865320 | −0.432660 | − | 0.901557i | \(-0.642425\pi\) | ||||
−0.432660 | + | 0.901557i | \(0.642425\pi\) | |||||||
\(158\) | 1.29335e36 | 0.682139 | ||||||||
\(159\) | −7.48204e35 | −0.355605 | ||||||||
\(160\) | 1.47939e36 | 0.634021 | ||||||||
\(161\) | −1.48617e36 | −0.574701 | ||||||||
\(162\) | 3.78792e36 | 1.32252 | ||||||||
\(163\) | −1.91804e36 | −0.605011 | −0.302505 | − | 0.953148i | \(-0.597823\pi\) | ||||
−0.302505 | + | 0.953148i | \(0.597823\pi\) | |||||||
\(164\) | −1.86897e36 | −0.532942 | ||||||||
\(165\) | −1.59387e35 | −0.0411119 | ||||||||
\(166\) | 9.98644e36 | 2.33146 | ||||||||
\(167\) | −3.91696e36 | −0.828185 | −0.414093 | − | 0.910235i | \(-0.635901\pi\) | ||||
−0.414093 | + | 0.910235i | \(0.635901\pi\) | |||||||
\(168\) | −1.42674e35 | −0.0273363 | ||||||||
\(169\) | −4.47468e36 | −0.777376 | ||||||||
\(170\) | 3.60028e36 | 0.567452 | ||||||||
\(171\) | 4.53858e36 | 0.649358 | ||||||||
\(172\) | 8.49747e36 | 1.10426 | ||||||||
\(173\) | −1.42658e37 | −1.68475 | −0.842375 | − | 0.538892i | \(-0.818843\pi\) | ||||
−0.842375 | + | 0.538892i | \(0.818843\pi\) | |||||||
\(174\) | −1.86798e36 | −0.200590 | ||||||||
\(175\) | 8.74474e35 | 0.0854317 | ||||||||
\(176\) | 3.87817e36 | 0.344880 | ||||||||
\(177\) | −2.03577e36 | −0.164881 | ||||||||
\(178\) | 6.04277e36 | 0.445970 | ||||||||
\(179\) | −1.89294e37 | −1.27368 | −0.636842 | − | 0.770994i | \(-0.719760\pi\) | ||||
−0.636842 | + | 0.770994i | \(0.719760\pi\) | |||||||
\(180\) | 8.55471e36 | 0.525060 | ||||||||
\(181\) | 2.60338e37 | 1.45828 | 0.729140 | − | 0.684365i | \(-0.239920\pi\) | ||||
0.729140 | + | 0.684365i | \(0.239920\pi\) | |||||||
\(182\) | 5.87177e36 | 0.300325 | ||||||||
\(183\) | 1.20358e36 | 0.0562385 | ||||||||
\(184\) | −1.03464e37 | −0.441869 | ||||||||
\(185\) | 7.74727e36 | 0.302562 | ||||||||
\(186\) | 1.72683e36 | 0.0616999 | ||||||||
\(187\) | 1.22836e37 | 0.401735 | ||||||||
\(188\) | −5.91481e37 | −1.77148 | ||||||||
\(189\) | 5.95148e36 | 0.163307 | ||||||||
\(190\) | 1.78838e37 | 0.449807 | ||||||||
\(191\) | −7.37079e37 | −1.70006 | −0.850029 | − | 0.526736i | \(-0.823415\pi\) | ||||
−0.850029 | + | 0.526736i | \(0.823415\pi\) | |||||||
\(192\) | 1.27216e37 | 0.269197 | ||||||||
\(193\) | 9.51744e36 | 0.184852 | 0.0924261 | − | 0.995720i | \(-0.470538\pi\) | ||||
0.0924261 | + | 0.995720i | \(0.470538\pi\) | |||||||
\(194\) | −1.40994e38 | −2.51461 | ||||||||
\(195\) | 2.50947e36 | 0.0411160 | ||||||||
\(196\) | −6.62577e37 | −0.997726 | ||||||||
\(197\) | 5.57117e37 | 0.771353 | 0.385677 | − | 0.922634i | \(-0.373968\pi\) | ||||
0.385677 | + | 0.922634i | \(0.373968\pi\) | |||||||
\(198\) | 5.31035e37 | 0.676313 | ||||||||
\(199\) | 1.97421e37 | 0.231375 | 0.115688 | − | 0.993286i | \(-0.463093\pi\) | ||||
0.115688 | + | 0.993286i | \(0.463093\pi\) | |||||||
\(200\) | 6.08787e36 | 0.0656857 | ||||||||
\(201\) | −2.94225e36 | −0.0292378 | ||||||||
\(202\) | 3.03863e38 | 2.78215 | ||||||||
\(203\) | 3.49668e37 | 0.295101 | ||||||||
\(204\) | 2.60202e37 | 0.202494 | ||||||||
\(205\) | 2.72038e37 | 0.195295 | ||||||||
\(206\) | −1.67617e38 | −1.11048 | ||||||||
\(207\) | 2.11618e38 | 1.29432 | ||||||||
\(208\) | −6.10600e37 | −0.344915 | ||||||||
\(209\) | 6.10169e37 | 0.318447 | ||||||||
\(210\) | 1.14987e37 | 0.0554665 | ||||||||
\(211\) | 1.86677e37 | 0.0832589 | 0.0416294 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416294 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(212\) | 5.39887e38 | 2.22721 | ||||||||
\(213\) | −1.00229e38 | −0.382587 | ||||||||
\(214\) | −5.22270e38 | −1.84530 | ||||||||
\(215\) | −1.23684e38 | −0.404651 | ||||||||
\(216\) | 4.14328e37 | 0.125562 | ||||||||
\(217\) | −3.23246e37 | −0.0907710 | ||||||||
\(218\) | −6.82205e38 | −1.77575 | ||||||||
\(219\) | 5.58983e37 | 0.134918 | ||||||||
\(220\) | 1.15010e38 | 0.257491 | ||||||||
\(221\) | −1.93400e38 | −0.401776 | ||||||||
\(222\) | 1.01871e38 | 0.196439 | ||||||||
\(223\) | −2.13813e38 | −0.382828 | −0.191414 | − | 0.981509i | \(-0.561307\pi\) | ||||
−0.191414 | + | 0.981509i | \(0.561307\pi\) | |||||||
\(224\) | −3.64142e38 | −0.605589 | ||||||||
\(225\) | −1.24518e38 | −0.192406 | ||||||||
\(226\) | −5.02544e38 | −0.721746 | ||||||||
\(227\) | 2.97111e38 | 0.396727 | 0.198364 | − | 0.980128i | \(-0.436437\pi\) | ||||
0.198364 | + | 0.980128i | \(0.436437\pi\) | |||||||
\(228\) | 1.29251e38 | 0.160513 | ||||||||
\(229\) | −6.71382e38 | −0.775683 | −0.387841 | − | 0.921726i | \(-0.626779\pi\) | ||||
−0.387841 | + | 0.921726i | \(0.626779\pi\) | |||||||
\(230\) | 8.33860e38 | 0.896569 | ||||||||
\(231\) | 3.92319e37 | 0.0392683 | ||||||||
\(232\) | 2.43430e38 | 0.226894 | ||||||||
\(233\) | 1.66756e39 | 1.44780 | 0.723899 | − | 0.689906i | \(-0.242348\pi\) | ||||
0.723899 | + | 0.689906i | \(0.242348\pi\) | |||||||
\(234\) | −8.36090e38 | −0.676381 | ||||||||
\(235\) | 8.60927e38 | 0.649153 | ||||||||
\(236\) | 1.46897e39 | 1.03268 | ||||||||
\(237\) | −1.36055e38 | −0.0892005 | ||||||||
\(238\) | −8.86182e38 | −0.542005 | ||||||||
\(239\) | 6.59391e38 | 0.376338 | 0.188169 | − | 0.982137i | \(-0.439745\pi\) | ||||
0.188169 | + | 0.982137i | \(0.439745\pi\) | |||||||
\(240\) | −1.19574e38 | −0.0637018 | ||||||||
\(241\) | 1.79835e39 | 0.894524 | 0.447262 | − | 0.894403i | \(-0.352399\pi\) | ||||
0.447262 | + | 0.894403i | \(0.352399\pi\) | |||||||
\(242\) | −2.49360e39 | −1.15844 | ||||||||
\(243\) | −1.27936e39 | −0.555251 | ||||||||
\(244\) | −8.68479e38 | −0.352231 | ||||||||
\(245\) | 9.64411e38 | 0.365613 | ||||||||
\(246\) | 3.57710e38 | 0.126795 | ||||||||
\(247\) | −9.60683e38 | −0.318479 | ||||||||
\(248\) | −2.25036e38 | −0.0697909 | ||||||||
\(249\) | −1.05054e39 | −0.304875 | ||||||||
\(250\) | −4.90650e38 | −0.133279 | ||||||||
\(251\) | 4.62035e39 | 1.17506 | 0.587528 | − | 0.809204i | \(-0.300101\pi\) | ||||
0.587528 | + | 0.809204i | \(0.300101\pi\) | |||||||
\(252\) | −2.10568e39 | −0.501514 | ||||||||
\(253\) | 2.84501e39 | 0.634738 | ||||||||
\(254\) | 4.18477e39 | 0.874812 | ||||||||
\(255\) | −3.78736e38 | −0.0742034 | ||||||||
\(256\) | 2.32218e39 | 0.426517 | ||||||||
\(257\) | 4.29716e39 | 0.740090 | 0.370045 | − | 0.929014i | \(-0.379342\pi\) | ||||
0.370045 | + | 0.929014i | \(0.379342\pi\) | |||||||
\(258\) | −1.62636e39 | −0.262720 | ||||||||
\(259\) | −1.90693e39 | −0.288994 | ||||||||
\(260\) | −1.81078e39 | −0.257517 | ||||||||
\(261\) | −4.97898e39 | −0.664618 | ||||||||
\(262\) | −1.08189e40 | −1.35585 | ||||||||
\(263\) | −5.41479e39 | −0.637253 | −0.318627 | − | 0.947880i | \(-0.603222\pi\) | ||||
−0.318627 | + | 0.947880i | \(0.603222\pi\) | |||||||
\(264\) | 2.73123e38 | 0.0301921 | ||||||||
\(265\) | −7.85830e39 | −0.816154 | ||||||||
\(266\) | −4.40197e39 | −0.429635 | ||||||||
\(267\) | −6.35677e38 | −0.0583177 | ||||||||
\(268\) | 2.12306e39 | 0.183121 | ||||||||
\(269\) | 9.46661e39 | 0.767860 | 0.383930 | − | 0.923362i | \(-0.374570\pi\) | ||||
0.383930 | + | 0.923362i | \(0.374570\pi\) | |||||||
\(270\) | −3.33926e39 | −0.254770 | ||||||||
\(271\) | −2.02716e40 | −1.45511 | −0.727555 | − | 0.686050i | \(-0.759343\pi\) | ||||
−0.727555 | + | 0.686050i | \(0.759343\pi\) | |||||||
\(272\) | 9.21533e39 | 0.622478 | ||||||||
\(273\) | −6.17688e38 | −0.0392722 | ||||||||
\(274\) | 1.98423e40 | 1.18770 | ||||||||
\(275\) | −1.67402e39 | −0.0943565 | ||||||||
\(276\) | 6.02653e39 | 0.319939 | ||||||||
\(277\) | −2.14513e40 | −1.07285 | −0.536423 | − | 0.843949i | \(-0.680225\pi\) | ||||
−0.536423 | + | 0.843949i | \(0.680225\pi\) | |||||||
\(278\) | 4.19052e40 | 1.97482 | ||||||||
\(279\) | 4.60274e39 | 0.204431 | ||||||||
\(280\) | −1.49848e39 | −0.0627400 | ||||||||
\(281\) | −2.22768e40 | −0.879425 | −0.439712 | − | 0.898139i | \(-0.644920\pi\) | ||||
−0.439712 | + | 0.898139i | \(0.644920\pi\) | |||||||
\(282\) | 1.13206e40 | 0.421462 | ||||||||
\(283\) | 1.45996e40 | 0.512702 | 0.256351 | − | 0.966584i | \(-0.417480\pi\) | ||||
0.256351 | + | 0.966584i | \(0.417480\pi\) | |||||||
\(284\) | 7.23231e40 | 2.39621 | ||||||||
\(285\) | −1.88131e39 | −0.0588193 | ||||||||
\(286\) | −1.12404e40 | −0.331699 | ||||||||
\(287\) | −6.69600e39 | −0.186537 | ||||||||
\(288\) | 5.18507e40 | 1.36389 | ||||||||
\(289\) | −1.10661e40 | −0.274903 | ||||||||
\(290\) | −1.96192e40 | −0.460377 | ||||||||
\(291\) | 1.48320e40 | 0.328825 | ||||||||
\(292\) | −4.03349e40 | −0.845015 | ||||||||
\(293\) | −3.33509e40 | −0.660377 | −0.330188 | − | 0.943915i | \(-0.607112\pi\) | ||||
−0.330188 | + | 0.943915i | \(0.607112\pi\) | |||||||
\(294\) | 1.26813e40 | 0.237374 | ||||||||
\(295\) | −2.13815e40 | −0.378421 | ||||||||
\(296\) | −1.32756e40 | −0.222198 | ||||||||
\(297\) | −1.13931e40 | −0.180368 | ||||||||
\(298\) | −1.17049e41 | −1.75307 | ||||||||
\(299\) | −4.47933e40 | −0.634802 | ||||||||
\(300\) | −3.54606e39 | −0.0475604 | ||||||||
\(301\) | 3.04440e40 | 0.386504 | ||||||||
\(302\) | −1.97119e41 | −2.36926 | ||||||||
\(303\) | −3.19653e40 | −0.363810 | ||||||||
\(304\) | 4.57757e40 | 0.493424 | ||||||||
\(305\) | 1.26411e40 | 0.129074 | ||||||||
\(306\) | 1.26185e41 | 1.22069 | ||||||||
\(307\) | 8.68250e40 | 0.795906 | 0.397953 | − | 0.917406i | \(-0.369721\pi\) | ||||
0.397953 | + | 0.917406i | \(0.369721\pi\) | |||||||
\(308\) | −2.83089e40 | −0.245944 | ||||||||
\(309\) | 1.76327e40 | 0.145212 | ||||||||
\(310\) | 1.81367e40 | 0.141608 | ||||||||
\(311\) | 1.66474e41 | 1.23254 | 0.616270 | − | 0.787535i | \(-0.288643\pi\) | ||||
0.616270 | + | 0.787535i | \(0.288643\pi\) | |||||||
\(312\) | −4.30019e39 | −0.0301951 | ||||||||
\(313\) | 2.38300e41 | 1.58724 | 0.793618 | − | 0.608416i | \(-0.208195\pi\) | ||||
0.793618 | + | 0.608416i | \(0.208195\pi\) | |||||||
\(314\) | −2.04048e41 | −1.28942 | ||||||||
\(315\) | 3.06491e40 | 0.183778 | ||||||||
\(316\) | 9.81743e40 | 0.558677 | ||||||||
\(317\) | −1.03851e41 | −0.560964 | −0.280482 | − | 0.959859i | \(-0.590494\pi\) | ||||
−0.280482 | + | 0.959859i | \(0.590494\pi\) | |||||||
\(318\) | −1.03331e41 | −0.529888 | ||||||||
\(319\) | −6.69377e40 | −0.325930 | ||||||||
\(320\) | 1.33613e41 | 0.617838 | ||||||||
\(321\) | 5.49408e40 | 0.241303 | ||||||||
\(322\) | −2.05248e41 | −0.856363 | ||||||||
\(323\) | 1.44989e41 | 0.574768 | ||||||||
\(324\) | 2.87530e41 | 1.08316 | ||||||||
\(325\) | 2.63567e40 | 0.0943660 | ||||||||
\(326\) | −2.64893e41 | −0.901528 | ||||||||
\(327\) | 7.17654e40 | 0.232208 | ||||||||
\(328\) | −4.66160e40 | −0.143422 | ||||||||
\(329\) | −2.11911e41 | −0.620041 | ||||||||
\(330\) | −2.20122e40 | −0.0612610 | ||||||||
\(331\) | −1.38040e41 | −0.365463 | −0.182732 | − | 0.983163i | \(-0.558494\pi\) | ||||
−0.182732 | + | 0.983163i | \(0.558494\pi\) | |||||||
\(332\) | 7.58043e41 | 1.90948 | ||||||||
\(333\) | 2.71531e41 | 0.650863 | ||||||||
\(334\) | −5.40954e41 | −1.23408 | ||||||||
\(335\) | −3.09021e40 | −0.0671040 | ||||||||
\(336\) | 2.94323e40 | 0.0608451 | ||||||||
\(337\) | 1.52333e40 | 0.0299847 | 0.0149923 | − | 0.999888i | \(-0.495228\pi\) | ||||
0.0149923 | + | 0.999888i | \(0.495228\pi\) | |||||||
\(338\) | −6.17978e41 | −1.15837 | ||||||||
\(339\) | 5.28657e40 | 0.0943798 | ||||||||
\(340\) | 2.73287e41 | 0.464748 | ||||||||
\(341\) | 6.18796e40 | 0.100254 | ||||||||
\(342\) | 6.26803e41 | 0.967610 | ||||||||
\(343\) | −5.27746e41 | −0.776376 | ||||||||
\(344\) | 2.11944e41 | 0.297171 | ||||||||
\(345\) | −8.77189e40 | −0.117241 | ||||||||
\(346\) | −1.97019e42 | −2.51045 | ||||||||
\(347\) | 1.11878e42 | 1.35928 | 0.679639 | − | 0.733547i | \(-0.262136\pi\) | ||||
0.679639 | + | 0.733547i | \(0.262136\pi\) | |||||||
\(348\) | −1.41793e41 | −0.164285 | ||||||||
\(349\) | −6.63572e41 | −0.733278 | −0.366639 | − | 0.930363i | \(-0.619492\pi\) | ||||
−0.366639 | + | 0.930363i | \(0.619492\pi\) | |||||||
\(350\) | 1.20770e41 | 0.127302 | ||||||||
\(351\) | 1.79378e41 | 0.180386 | ||||||||
\(352\) | 6.97084e41 | 0.668853 | ||||||||
\(353\) | 4.28180e41 | 0.392052 | 0.196026 | − | 0.980599i | \(-0.437196\pi\) | ||||
0.196026 | + | 0.980599i | \(0.437196\pi\) | |||||||
\(354\) | −2.81152e41 | −0.245690 | ||||||||
\(355\) | −1.05270e42 | −0.878082 | ||||||||
\(356\) | 4.58690e41 | 0.365253 | ||||||||
\(357\) | 9.32230e40 | 0.0708757 | ||||||||
\(358\) | −2.61426e42 | −1.89792 | ||||||||
\(359\) | −9.04901e41 | −0.627397 | −0.313698 | − | 0.949523i | \(-0.601568\pi\) | ||||
−0.313698 | + | 0.949523i | \(0.601568\pi\) | |||||||
\(360\) | 2.13371e41 | 0.141301 | ||||||||
\(361\) | −8.60562e41 | −0.544394 | ||||||||
\(362\) | 3.59541e42 | 2.17299 | ||||||||
\(363\) | 2.62317e41 | 0.151484 | ||||||||
\(364\) | 4.45710e41 | 0.245968 | ||||||||
\(365\) | 5.87093e41 | 0.309653 | ||||||||
\(366\) | 1.66222e41 | 0.0838011 | ||||||||
\(367\) | −2.16128e41 | −0.104165 | −0.0520823 | − | 0.998643i | \(-0.516586\pi\) | ||||
−0.0520823 | + | 0.998643i | \(0.516586\pi\) | |||||||
\(368\) | 2.13436e42 | 0.983510 | ||||||||
\(369\) | 9.53454e41 | 0.420112 | ||||||||
\(370\) | 1.06994e42 | 0.450849 | ||||||||
\(371\) | 1.93426e42 | 0.779553 | ||||||||
\(372\) | 1.31079e41 | 0.0505328 | ||||||||
\(373\) | 3.17253e42 | 1.17007 | 0.585033 | − | 0.811009i | \(-0.301081\pi\) | ||||
0.585033 | + | 0.811009i | \(0.301081\pi\) | |||||||
\(374\) | 1.69644e42 | 0.598627 | ||||||||
\(375\) | 5.16145e40 | 0.0174283 | ||||||||
\(376\) | −1.47527e42 | −0.476730 | ||||||||
\(377\) | 1.05390e42 | 0.325963 | ||||||||
\(378\) | 8.21933e41 | 0.243345 | ||||||||
\(379\) | −5.62885e42 | −1.59541 | −0.797705 | − | 0.603048i | \(-0.793953\pi\) | ||||
−0.797705 | + | 0.603048i | \(0.793953\pi\) | |||||||
\(380\) | 1.35751e42 | 0.368395 | ||||||||
\(381\) | −4.40221e41 | −0.114396 | ||||||||
\(382\) | −1.01795e43 | −2.53326 | ||||||||
\(383\) | 1.01197e42 | 0.241205 | 0.120603 | − | 0.992701i | \(-0.461517\pi\) | ||||
0.120603 | + | 0.992701i | \(0.461517\pi\) | |||||||
\(384\) | 5.46975e41 | 0.124883 | ||||||||
\(385\) | 4.12048e41 | 0.0901251 | ||||||||
\(386\) | 1.31441e42 | 0.275449 | ||||||||
\(387\) | −4.33497e42 | −0.870472 | ||||||||
\(388\) | −1.07024e43 | −2.05949 | ||||||||
\(389\) | −9.74782e42 | −1.79779 | −0.898896 | − | 0.438163i | \(-0.855629\pi\) | ||||
−0.898896 | + | 0.438163i | \(0.855629\pi\) | |||||||
\(390\) | 3.46572e41 | 0.0612671 | ||||||||
\(391\) | 6.76032e42 | 1.14565 | ||||||||
\(392\) | −1.65260e42 | −0.268502 | ||||||||
\(393\) | 1.13811e42 | 0.177299 | ||||||||
\(394\) | 7.69409e42 | 1.14940 | ||||||||
\(395\) | −1.42897e42 | −0.204725 | ||||||||
\(396\) | 4.03094e42 | 0.553906 | ||||||||
\(397\) | −5.84553e42 | −0.770514 | −0.385257 | − | 0.922809i | \(-0.625887\pi\) | ||||
−0.385257 | + | 0.922809i | \(0.625887\pi\) | |||||||
\(398\) | 2.72649e42 | 0.344773 | ||||||||
\(399\) | 4.63070e41 | 0.0561816 | ||||||||
\(400\) | −1.25587e42 | −0.146203 | ||||||||
\(401\) | 6.82021e42 | 0.761931 | 0.380966 | − | 0.924589i | \(-0.375592\pi\) | ||||
0.380966 | + | 0.924589i | \(0.375592\pi\) | |||||||
\(402\) | −4.06341e41 | −0.0435673 | ||||||||
\(403\) | −9.74265e41 | −0.100264 | ||||||||
\(404\) | 2.30654e43 | 2.27860 | ||||||||
\(405\) | −4.18513e42 | −0.396918 | ||||||||
\(406\) | 4.82911e42 | 0.439732 | ||||||||
\(407\) | 3.65048e42 | 0.319185 | ||||||||
\(408\) | 6.48996e41 | 0.0544941 | ||||||||
\(409\) | −7.09650e42 | −0.572281 | −0.286141 | − | 0.958188i | \(-0.592372\pi\) | ||||
−0.286141 | + | 0.958188i | \(0.592372\pi\) | |||||||
\(410\) | 3.75699e42 | 0.291009 | ||||||||
\(411\) | −2.08733e42 | −0.155311 | ||||||||
\(412\) | −1.27233e43 | −0.909488 | ||||||||
\(413\) | 5.26290e42 | 0.361451 | ||||||||
\(414\) | 2.92256e43 | 1.92867 | ||||||||
\(415\) | −1.10337e43 | −0.699723 | ||||||||
\(416\) | −1.09753e43 | −0.668921 | ||||||||
\(417\) | −4.40826e42 | −0.258239 | ||||||||
\(418\) | 8.42678e42 | 0.474518 | ||||||||
\(419\) | −1.41115e43 | −0.763912 | −0.381956 | − | 0.924181i | \(-0.624749\pi\) | ||||
−0.381956 | + | 0.924181i | \(0.624749\pi\) | |||||||
\(420\) | 8.72835e41 | 0.0454275 | ||||||||
\(421\) | −9.28037e42 | −0.464420 | −0.232210 | − | 0.972666i | \(-0.574596\pi\) | ||||
−0.232210 | + | 0.972666i | \(0.574596\pi\) | |||||||
\(422\) | 2.57811e42 | 0.124064 | ||||||||
\(423\) | 3.01743e43 | 1.39644 | ||||||||
\(424\) | 1.34659e43 | 0.599374 | ||||||||
\(425\) | −3.97782e42 | −0.170305 | ||||||||
\(426\) | −1.38422e43 | −0.570095 | ||||||||
\(427\) | −3.11151e42 | −0.123285 | ||||||||
\(428\) | −3.96441e43 | −1.51132 | ||||||||
\(429\) | 1.18245e42 | 0.0433749 | ||||||||
\(430\) | −1.70815e43 | −0.602972 | ||||||||
\(431\) | −2.40707e43 | −0.817738 | −0.408869 | − | 0.912593i | \(-0.634077\pi\) | ||||
−0.408869 | + | 0.912593i | \(0.634077\pi\) | |||||||
\(432\) | −8.54721e42 | −0.279475 | ||||||||
\(433\) | 4.96426e43 | 1.56244 | 0.781222 | − | 0.624253i | \(-0.214597\pi\) | ||||
0.781222 | + | 0.624253i | \(0.214597\pi\) | |||||||
\(434\) | −4.46420e42 | −0.135258 | ||||||||
\(435\) | 2.06386e42 | 0.0602016 | ||||||||
\(436\) | −5.17843e43 | −1.45436 | ||||||||
\(437\) | 3.35808e43 | 0.908128 | ||||||||
\(438\) | 7.71986e42 | 0.201042 | ||||||||
\(439\) | 4.80839e43 | 1.20597 | 0.602984 | − | 0.797754i | \(-0.293978\pi\) | ||||
0.602984 | + | 0.797754i | \(0.293978\pi\) | |||||||
\(440\) | 2.86858e42 | 0.0692943 | ||||||||
\(441\) | 3.38013e43 | 0.786495 | ||||||||
\(442\) | −2.67096e43 | −0.598687 | ||||||||
\(443\) | −8.49113e42 | −0.183360 | −0.0916799 | − | 0.995789i | \(-0.529224\pi\) | ||||
−0.0916799 | + | 0.995789i | \(0.529224\pi\) | |||||||
\(444\) | 7.73275e42 | 0.160885 | ||||||||
\(445\) | −6.67644e42 | −0.133846 | ||||||||
\(446\) | −2.95287e43 | −0.570453 | ||||||||
\(447\) | 1.23131e43 | 0.229242 | ||||||||
\(448\) | −3.28879e43 | −0.590131 | ||||||||
\(449\) | −8.15651e43 | −1.41072 | −0.705359 | − | 0.708851i | \(-0.749214\pi\) | ||||
−0.705359 | + | 0.708851i | \(0.749214\pi\) | |||||||
\(450\) | −1.71966e43 | −0.286705 | ||||||||
\(451\) | 1.28183e43 | 0.206024 | ||||||||
\(452\) | −3.81467e43 | −0.591116 | ||||||||
\(453\) | 2.07361e43 | 0.309819 | ||||||||
\(454\) | 4.10327e43 | 0.591165 | ||||||||
\(455\) | −6.48751e42 | −0.0901342 | ||||||||
\(456\) | 3.22378e42 | 0.0431962 | ||||||||
\(457\) | 3.82156e43 | 0.493882 | 0.246941 | − | 0.969030i | \(-0.420575\pi\) | ||||
0.246941 | + | 0.969030i | \(0.420575\pi\) | |||||||
\(458\) | −9.27216e43 | −1.15585 | ||||||||
\(459\) | −2.70722e43 | −0.325548 | ||||||||
\(460\) | 6.32960e43 | 0.734298 | ||||||||
\(461\) | 1.42045e44 | 1.58987 | 0.794933 | − | 0.606698i | \(-0.207506\pi\) | ||||
0.794933 | + | 0.606698i | \(0.207506\pi\) | |||||||
\(462\) | 5.41814e42 | 0.0585137 | ||||||||
\(463\) | 1.76412e43 | 0.183841 | 0.0919203 | − | 0.995766i | \(-0.470700\pi\) | ||||
0.0919203 | + | 0.995766i | \(0.470700\pi\) | |||||||
\(464\) | −5.02175e43 | −0.505020 | ||||||||
\(465\) | −1.90791e42 | −0.0185176 | ||||||||
\(466\) | 2.30299e44 | 2.15737 | ||||||||
\(467\) | 1.44747e44 | 1.30882 | 0.654410 | − | 0.756140i | \(-0.272917\pi\) | ||||
0.654410 | + | 0.756140i | \(0.272917\pi\) | |||||||
\(468\) | −6.34653e43 | −0.553962 | ||||||||
\(469\) | 7.60631e42 | 0.0640947 | ||||||||
\(470\) | 1.18899e44 | 0.967304 | ||||||||
\(471\) | 2.14651e43 | 0.168612 | ||||||||
\(472\) | 3.66390e43 | 0.277908 | ||||||||
\(473\) | −5.82796e43 | −0.426882 | ||||||||
\(474\) | −1.87900e43 | −0.132918 | ||||||||
\(475\) | −1.97592e43 | −0.134997 | ||||||||
\(476\) | −6.72677e43 | −0.443907 | ||||||||
\(477\) | −2.75423e44 | −1.75568 | ||||||||
\(478\) | 9.10656e43 | 0.560782 | ||||||||
\(479\) | −2.82253e44 | −1.67920 | −0.839602 | − | 0.543203i | \(-0.817212\pi\) | ||||
−0.839602 | + | 0.543203i | \(0.817212\pi\) | |||||||
\(480\) | −2.14929e43 | −0.123542 | ||||||||
\(481\) | −5.74751e43 | −0.319217 | ||||||||
\(482\) | 2.48362e44 | 1.33293 | ||||||||
\(483\) | 2.15914e43 | 0.111983 | ||||||||
\(484\) | −1.89282e44 | −0.948770 | ||||||||
\(485\) | 1.55779e44 | 0.754692 | ||||||||
\(486\) | −1.76687e44 | −0.827382 | ||||||||
\(487\) | −2.41873e44 | −1.09486 | −0.547432 | − | 0.836850i | \(-0.684395\pi\) | ||||
−0.547432 | + | 0.836850i | \(0.684395\pi\) | |||||||
\(488\) | −2.16616e43 | −0.0947902 | ||||||||
\(489\) | 2.78657e43 | 0.117889 | ||||||||
\(490\) | 1.33191e44 | 0.544801 | ||||||||
\(491\) | −3.36324e44 | −1.33019 | −0.665095 | − | 0.746759i | \(-0.731609\pi\) | ||||
−0.665095 | + | 0.746759i | \(0.731609\pi\) | |||||||
\(492\) | 2.71528e43 | 0.103846 | ||||||||
\(493\) | −1.59058e44 | −0.588275 | ||||||||
\(494\) | −1.32676e44 | −0.474566 | ||||||||
\(495\) | −5.86722e43 | −0.202977 | ||||||||
\(496\) | 4.64228e43 | 0.155340 | ||||||||
\(497\) | 2.59113e44 | 0.838705 | ||||||||
\(498\) | −1.45085e44 | −0.454295 | ||||||||
\(499\) | −8.01313e43 | −0.242741 | −0.121371 | − | 0.992607i | \(-0.538729\pi\) | ||||
−0.121371 | + | 0.992607i | \(0.538729\pi\) | |||||||
\(500\) | −3.72439e43 | −0.109156 | ||||||||
\(501\) | 5.69063e43 | 0.161376 | ||||||||
\(502\) | 6.38096e44 | 1.75095 | ||||||||
\(503\) | 2.08304e44 | 0.553129 | 0.276565 | − | 0.960995i | \(-0.410804\pi\) | ||||
0.276565 | + | 0.960995i | \(0.410804\pi\) | |||||||
\(504\) | −5.25198e43 | −0.134964 | ||||||||
\(505\) | −3.35728e44 | −0.834986 | ||||||||
\(506\) | 3.92911e44 | 0.945825 | ||||||||
\(507\) | 6.50090e43 | 0.151475 | ||||||||
\(508\) | 3.17654e44 | 0.716478 | ||||||||
\(509\) | 3.65736e44 | 0.798591 | 0.399296 | − | 0.916822i | \(-0.369255\pi\) | ||||
0.399296 | + | 0.916822i | \(0.369255\pi\) | |||||||
\(510\) | −5.23056e43 | −0.110571 | ||||||||
\(511\) | −1.44509e44 | −0.295766 | ||||||||
\(512\) | 6.44110e44 | 1.27646 | ||||||||
\(513\) | −1.34477e44 | −0.258054 | ||||||||
\(514\) | 5.93461e44 | 1.10281 | ||||||||
\(515\) | 1.85194e44 | 0.333279 | ||||||||
\(516\) | −1.23453e44 | −0.215169 | ||||||||
\(517\) | 4.05665e44 | 0.684816 | ||||||||
\(518\) | −2.63358e44 | −0.430631 | ||||||||
\(519\) | 2.07256e44 | 0.328281 | ||||||||
\(520\) | −4.51644e43 | −0.0693013 | ||||||||
\(521\) | −3.73678e44 | −0.555488 | −0.277744 | − | 0.960655i | \(-0.589587\pi\) | ||||
−0.277744 | + | 0.960655i | \(0.589587\pi\) | |||||||
\(522\) | −6.87625e44 | −0.990349 | ||||||||
\(523\) | −2.43582e44 | −0.339913 | −0.169957 | − | 0.985452i | \(-0.554363\pi\) | ||||
−0.169957 | + | 0.985452i | \(0.554363\pi\) | |||||||
\(524\) | −8.21232e44 | −1.11045 | ||||||||
\(525\) | −1.27045e43 | −0.0166468 | ||||||||
\(526\) | −7.47813e44 | −0.949573 | ||||||||
\(527\) | 1.47039e44 | 0.180949 | ||||||||
\(528\) | −5.63428e43 | −0.0672014 | ||||||||
\(529\) | 7.00750e44 | 0.810111 | ||||||||
\(530\) | −1.08528e45 | −1.21615 | ||||||||
\(531\) | −7.49392e44 | −0.814047 | ||||||||
\(532\) | −3.34141e44 | −0.351875 | ||||||||
\(533\) | −2.01818e44 | −0.206045 | ||||||||
\(534\) | −8.77905e43 | −0.0868994 | ||||||||
\(535\) | 5.77037e44 | 0.553817 | ||||||||
\(536\) | 5.29533e43 | 0.0492804 | ||||||||
\(537\) | 2.75010e44 | 0.248183 | ||||||||
\(538\) | 1.30739e45 | 1.14419 | ||||||||
\(539\) | 4.54426e44 | 0.385699 | ||||||||
\(540\) | −2.53474e44 | −0.208659 | ||||||||
\(541\) | 1.83384e45 | 1.46422 | 0.732112 | − | 0.681184i | \(-0.238535\pi\) | ||||
0.732112 | + | 0.681184i | \(0.238535\pi\) | |||||||
\(542\) | −2.79963e45 | −2.16826 | ||||||||
\(543\) | −3.78224e44 | −0.284153 | ||||||||
\(544\) | 1.65641e45 | 1.20722 | ||||||||
\(545\) | 7.53744e44 | 0.532944 | ||||||||
\(546\) | −8.53061e43 | −0.0585196 | ||||||||
\(547\) | −2.32228e45 | −1.54570 | −0.772848 | − | 0.634592i | \(-0.781168\pi\) | ||||
−0.772848 | + | 0.634592i | \(0.781168\pi\) | |||||||
\(548\) | 1.50617e45 | 0.972738 | ||||||||
\(549\) | 4.43053e44 | 0.277659 | ||||||||
\(550\) | −2.31192e44 | −0.140601 | ||||||||
\(551\) | −7.90093e44 | −0.466312 | ||||||||
\(552\) | 1.50314e44 | 0.0861002 | ||||||||
\(553\) | 3.51731e44 | 0.195544 | ||||||||
\(554\) | −2.96255e45 | −1.59865 | ||||||||
\(555\) | −1.12554e44 | −0.0589557 | ||||||||
\(556\) | 3.18090e45 | 1.61740 | ||||||||
\(557\) | −2.15312e45 | −1.06281 | −0.531406 | − | 0.847117i | \(-0.678336\pi\) | ||||
−0.531406 | + | 0.847117i | \(0.678336\pi\) | |||||||
\(558\) | 6.35664e44 | 0.304624 | ||||||||
\(559\) | 9.17585e44 | 0.426925 | ||||||||
\(560\) | 3.09124e44 | 0.139646 | ||||||||
\(561\) | −1.78459e44 | −0.0782800 | ||||||||
\(562\) | −3.07655e45 | −1.31043 | ||||||||
\(563\) | −2.18829e45 | −0.905142 | −0.452571 | − | 0.891728i | \(-0.649493\pi\) | ||||
−0.452571 | + | 0.891728i | \(0.649493\pi\) | |||||||
\(564\) | 8.59314e44 | 0.345181 | ||||||||
\(565\) | 5.55242e44 | 0.216612 | ||||||||
\(566\) | 2.01629e45 | 0.763979 | ||||||||
\(567\) | 1.03014e45 | 0.379119 | ||||||||
\(568\) | 1.80388e45 | 0.644853 | ||||||||
\(569\) | 3.69991e45 | 1.28481 | 0.642404 | − | 0.766366i | \(-0.277937\pi\) | ||||
0.642404 | + | 0.766366i | \(0.277937\pi\) | |||||||
\(570\) | −2.59819e44 | −0.0876469 | ||||||||
\(571\) | 4.09741e44 | 0.134281 | 0.0671403 | − | 0.997744i | \(-0.478612\pi\) | ||||
0.0671403 | + | 0.997744i | \(0.478612\pi\) | |||||||
\(572\) | −8.53231e44 | −0.271664 | ||||||||
\(573\) | 1.07084e45 | 0.331264 | ||||||||
\(574\) | −9.24755e44 | −0.277959 | ||||||||
\(575\) | −9.21302e44 | −0.269081 | ||||||||
\(576\) | 4.68295e45 | 1.32907 | ||||||||
\(577\) | 2.41392e45 | 0.665767 | 0.332884 | − | 0.942968i | \(-0.391978\pi\) | ||||
0.332884 | + | 0.942968i | \(0.391978\pi\) | |||||||
\(578\) | −1.52829e45 | −0.409634 | ||||||||
\(579\) | −1.38271e44 | −0.0360193 | ||||||||
\(580\) | −1.48924e45 | −0.377053 | ||||||||
\(581\) | 2.71585e45 | 0.668344 | ||||||||
\(582\) | 2.04838e45 | 0.489983 | ||||||||
\(583\) | −3.70280e45 | −0.860992 | ||||||||
\(584\) | −1.00603e45 | −0.227405 | ||||||||
\(585\) | 9.23766e44 | 0.202997 | ||||||||
\(586\) | −4.60594e45 | −0.984029 | ||||||||
\(587\) | −3.30502e45 | −0.686507 | −0.343253 | − | 0.939243i | \(-0.611529\pi\) | ||||
−0.343253 | + | 0.939243i | \(0.611529\pi\) | |||||||
\(588\) | 9.62604e44 | 0.194411 | ||||||||
\(589\) | 7.30390e44 | 0.143434 | ||||||||
\(590\) | −2.95291e45 | −0.563886 | ||||||||
\(591\) | −8.09389e44 | −0.150302 | ||||||||
\(592\) | 2.73863e45 | 0.494568 | ||||||||
\(593\) | 3.04911e45 | 0.535514 | 0.267757 | − | 0.963486i | \(-0.413718\pi\) | ||||
0.267757 | + | 0.963486i | \(0.413718\pi\) | |||||||
\(594\) | −1.57344e45 | −0.268766 | ||||||||
\(595\) | 9.79111e44 | 0.162668 | ||||||||
\(596\) | −8.88487e45 | −1.43578 | ||||||||
\(597\) | −2.86816e44 | −0.0450845 | ||||||||
\(598\) | −6.18620e45 | −0.945920 | ||||||||
\(599\) | 4.77681e45 | 0.710551 | 0.355276 | − | 0.934762i | \(-0.384387\pi\) | ||||
0.355276 | + | 0.934762i | \(0.384387\pi\) | |||||||
\(600\) | −8.84457e43 | −0.0127992 | ||||||||
\(601\) | −1.11023e46 | −1.56310 | −0.781549 | − | 0.623844i | \(-0.785570\pi\) | ||||
−0.781549 | + | 0.623844i | \(0.785570\pi\) | |||||||
\(602\) | 4.20449e45 | 0.575931 | ||||||||
\(603\) | −1.08307e45 | −0.144352 | ||||||||
\(604\) | −1.49627e46 | −1.94045 | ||||||||
\(605\) | 2.75508e45 | 0.347673 | ||||||||
\(606\) | −4.41458e45 | −0.542115 | ||||||||
\(607\) | 9.37646e44 | 0.112054 | 0.0560268 | − | 0.998429i | \(-0.482157\pi\) | ||||
0.0560268 | + | 0.998429i | \(0.482157\pi\) | |||||||
\(608\) | 8.22797e45 | 0.956937 | ||||||||
\(609\) | −5.08004e44 | −0.0575019 | ||||||||
\(610\) | 1.74581e45 | 0.192333 | ||||||||
\(611\) | −6.38701e45 | −0.684885 | ||||||||
\(612\) | 9.57834e45 | 0.999751 | ||||||||
\(613\) | 3.40725e45 | 0.346183 | 0.173092 | − | 0.984906i | \(-0.444624\pi\) | ||||
0.173092 | + | 0.984906i | \(0.444624\pi\) | |||||||
\(614\) | 1.19910e46 | 1.18598 | ||||||||
\(615\) | −3.95221e44 | −0.0380541 | ||||||||
\(616\) | −7.06079e44 | −0.0661869 | ||||||||
\(617\) | 1.51984e46 | 1.38705 | 0.693525 | − | 0.720432i | \(-0.256057\pi\) | ||||
0.693525 | + | 0.720432i | \(0.256057\pi\) | |||||||
\(618\) | 2.43517e45 | 0.216381 | ||||||||
\(619\) | −3.99242e45 | −0.345415 | −0.172707 | − | 0.984973i | \(-0.555251\pi\) | ||||
−0.172707 | + | 0.984973i | \(0.555251\pi\) | |||||||
\(620\) | 1.37670e45 | 0.115979 | ||||||||
\(621\) | −6.27019e45 | −0.514362 | ||||||||
\(622\) | 2.29910e46 | 1.83661 | ||||||||
\(623\) | 1.64336e45 | 0.127844 | ||||||||
\(624\) | 8.87091e44 | 0.0672082 | ||||||||
\(625\) | 5.42101e44 | 0.0400000 | ||||||||
\(626\) | 3.29105e46 | 2.36515 | ||||||||
\(627\) | −8.86465e44 | −0.0620508 | ||||||||
\(628\) | −1.54887e46 | −1.05604 | ||||||||
\(629\) | 8.67429e45 | 0.576100 | ||||||||
\(630\) | 4.23281e45 | 0.273848 | ||||||||
\(631\) | −8.68878e45 | −0.547614 | −0.273807 | − | 0.961785i | \(-0.588283\pi\) | ||||
−0.273807 | + | 0.961785i | \(0.588283\pi\) | |||||||
\(632\) | 2.44866e45 | 0.150348 | ||||||||
\(633\) | −2.71208e44 | −0.0162234 | ||||||||
\(634\) | −1.43425e46 | −0.835894 | ||||||||
\(635\) | −4.62360e45 | −0.262551 | ||||||||
\(636\) | −7.84358e45 | −0.433982 | ||||||||
\(637\) | −7.15473e45 | −0.385738 | ||||||||
\(638\) | −9.24447e45 | −0.485669 | ||||||||
\(639\) | −3.68955e46 | −1.88890 | ||||||||
\(640\) | 5.74482e45 | 0.286620 | ||||||||
\(641\) | 1.75762e46 | 0.854609 | 0.427305 | − | 0.904108i | \(-0.359463\pi\) | ||||
0.427305 | + | 0.904108i | \(0.359463\pi\) | |||||||
\(642\) | 7.58763e45 | 0.359566 | ||||||||
\(643\) | −3.90754e46 | −1.80477 | −0.902386 | − | 0.430928i | \(-0.858186\pi\) | ||||
−0.902386 | + | 0.430928i | \(0.858186\pi\) | |||||||
\(644\) | −1.55798e46 | −0.701368 | ||||||||
\(645\) | 1.79691e45 | 0.0788481 | ||||||||
\(646\) | 2.00238e46 | 0.856464 | ||||||||
\(647\) | −3.44345e46 | −1.43573 | −0.717865 | − | 0.696182i | \(-0.754881\pi\) | ||||
−0.717865 | + | 0.696182i | \(0.754881\pi\) | |||||||
\(648\) | 7.17158e45 | 0.291492 | ||||||||
\(649\) | −1.00749e46 | −0.399211 | ||||||||
\(650\) | 3.64001e45 | 0.140615 | ||||||||
\(651\) | 4.69617e44 | 0.0176871 | ||||||||
\(652\) | −2.01073e46 | −0.738359 | ||||||||
\(653\) | 4.09793e46 | 1.46723 | 0.733613 | − | 0.679567i | \(-0.237832\pi\) | ||||
0.733613 | + | 0.679567i | \(0.237832\pi\) | |||||||
\(654\) | 9.91120e45 | 0.346014 | ||||||||
\(655\) | 1.19534e46 | 0.406921 | ||||||||
\(656\) | 9.61645e45 | 0.319228 | ||||||||
\(657\) | 2.05768e46 | 0.666115 | ||||||||
\(658\) | −2.92661e46 | −0.923926 | ||||||||
\(659\) | 7.05687e44 | 0.0217271 | 0.0108636 | − | 0.999941i | \(-0.496542\pi\) | ||||
0.0108636 | + | 0.999941i | \(0.496542\pi\) | |||||||
\(660\) | −1.67089e45 | −0.0501732 | ||||||||
\(661\) | 5.13888e45 | 0.150503 | 0.0752514 | − | 0.997165i | \(-0.476024\pi\) | ||||
0.0752514 | + | 0.997165i | \(0.476024\pi\) | |||||||
\(662\) | −1.90641e46 | −0.544578 | ||||||||
\(663\) | 2.80975e45 | 0.0782878 | ||||||||
\(664\) | 1.89071e46 | 0.513868 | ||||||||
\(665\) | 4.86358e45 | 0.128943 | ||||||||
\(666\) | 3.74999e46 | 0.969852 | ||||||||
\(667\) | −3.68393e46 | −0.929469 | ||||||||
\(668\) | −4.10623e46 | −1.01072 | ||||||||
\(669\) | 3.10631e45 | 0.0745958 | ||||||||
\(670\) | −4.26775e45 | −0.0999919 | ||||||||
\(671\) | 5.95644e45 | 0.136165 | ||||||||
\(672\) | 5.29031e45 | 0.118002 | ||||||||
\(673\) | 8.48563e46 | 1.84687 | 0.923434 | − | 0.383758i | \(-0.125370\pi\) | ||||
0.923434 | + | 0.383758i | \(0.125370\pi\) | |||||||
\(674\) | 2.10380e45 | 0.0446803 | ||||||||
\(675\) | 3.68943e45 | 0.0764622 | ||||||||
\(676\) | −4.69090e46 | −0.948715 | ||||||||
\(677\) | 1.97690e46 | 0.390185 | 0.195093 | − | 0.980785i | \(-0.437499\pi\) | ||||
0.195093 | + | 0.980785i | \(0.437499\pi\) | |||||||
\(678\) | 7.30105e45 | 0.140636 | ||||||||
\(679\) | −3.83438e46 | −0.720848 | ||||||||
\(680\) | 6.81633e45 | 0.125070 | ||||||||
\(681\) | −4.31648e45 | −0.0773042 | ||||||||
\(682\) | 8.54591e45 | 0.149388 | ||||||||
\(683\) | 1.05640e47 | 1.80254 | 0.901272 | − | 0.433254i | \(-0.142635\pi\) | ||||
0.901272 | + | 0.433254i | \(0.142635\pi\) | |||||||
\(684\) | 4.75789e46 | 0.792480 | ||||||||
\(685\) | −2.19230e46 | −0.356456 | ||||||||
\(686\) | −7.28847e46 | −1.15688 | ||||||||
\(687\) | 9.75396e45 | 0.151145 | ||||||||
\(688\) | −4.37221e46 | −0.661442 | ||||||||
\(689\) | 5.82988e46 | 0.861078 | ||||||||
\(690\) | −1.21145e46 | −0.174701 | ||||||||
\(691\) | −2.86100e46 | −0.402838 | −0.201419 | − | 0.979505i | \(-0.564555\pi\) | ||||
−0.201419 | + | 0.979505i | \(0.564555\pi\) | |||||||
\(692\) | −1.49551e47 | −2.05608 | ||||||||
\(693\) | 1.44417e46 | 0.193874 | ||||||||
\(694\) | 1.54510e47 | 2.02546 | ||||||||
\(695\) | −4.62995e46 | −0.592689 | ||||||||
\(696\) | −3.53660e45 | −0.0442113 | ||||||||
\(697\) | 3.04589e46 | 0.371855 | ||||||||
\(698\) | −9.16430e46 | −1.09266 | ||||||||
\(699\) | −2.42266e46 | −0.282110 | ||||||||
\(700\) | 9.16729e45 | 0.104261 | ||||||||
\(701\) | 5.94385e46 | 0.660269 | 0.330134 | − | 0.943934i | \(-0.392906\pi\) | ||||
0.330134 | + | 0.943934i | \(0.392906\pi\) | |||||||
\(702\) | 2.47731e46 | 0.268793 | ||||||||
\(703\) | 4.30881e46 | 0.456662 | ||||||||
\(704\) | 6.29579e46 | 0.651781 | ||||||||
\(705\) | −1.25077e46 | −0.126490 | ||||||||
\(706\) | 5.91340e46 | 0.584197 | ||||||||
\(707\) | 8.26368e46 | 0.797541 | ||||||||
\(708\) | −2.13415e46 | −0.201222 | ||||||||
\(709\) | 6.13936e46 | 0.565536 | 0.282768 | − | 0.959188i | \(-0.408747\pi\) | ||||
0.282768 | + | 0.959188i | \(0.408747\pi\) | |||||||
\(710\) | −1.45383e47 | −1.30843 | ||||||||
\(711\) | −5.00835e46 | −0.440399 | ||||||||
\(712\) | 1.14406e46 | 0.0982948 | ||||||||
\(713\) | 3.40555e46 | 0.285898 | ||||||||
\(714\) | 1.28746e46 | 0.105612 | ||||||||
\(715\) | 1.24192e46 | 0.0995503 | ||||||||
\(716\) | −1.98441e47 | −1.55441 | ||||||||
\(717\) | −9.57976e45 | −0.0733311 | ||||||||
\(718\) | −1.24972e47 | −0.934886 | ||||||||
\(719\) | −2.54160e47 | −1.85815 | −0.929075 | − | 0.369891i | \(-0.879395\pi\) | ||||
−0.929075 | + | 0.369891i | \(0.879395\pi\) | |||||||
\(720\) | −4.40166e46 | −0.314507 | ||||||||
\(721\) | −4.55841e46 | −0.318333 | ||||||||
\(722\) | −1.18848e47 | −0.811203 | ||||||||
\(723\) | −2.61267e46 | −0.174302 | ||||||||
\(724\) | 2.72918e47 | 1.77969 | ||||||||
\(725\) | 2.16765e46 | 0.138170 | ||||||||
\(726\) | 3.62274e46 | 0.225727 | ||||||||
\(727\) | −1.41220e47 | −0.860157 | −0.430079 | − | 0.902791i | \(-0.641514\pi\) | ||||
−0.430079 | + | 0.902791i | \(0.641514\pi\) | |||||||
\(728\) | 1.11169e46 | 0.0661935 | ||||||||
\(729\) | −1.33885e47 | −0.779343 | ||||||||
\(730\) | 8.10808e46 | 0.461414 | ||||||||
\(731\) | −1.38484e47 | −0.770484 | ||||||||
\(732\) | 1.26174e46 | 0.0686338 | ||||||||
\(733\) | 1.82342e47 | 0.969778 | 0.484889 | − | 0.874576i | \(-0.338860\pi\) | ||||
0.484889 | + | 0.874576i | \(0.338860\pi\) | |||||||
\(734\) | −2.98484e46 | −0.155216 | ||||||||
\(735\) | −1.40111e46 | −0.0712414 | ||||||||
\(736\) | 3.83641e47 | 1.90740 | ||||||||
\(737\) | −1.45609e46 | −0.0707906 | ||||||||
\(738\) | 1.31677e47 | 0.626010 | ||||||||
\(739\) | 5.23297e46 | 0.243285 | 0.121642 | − | 0.992574i | \(-0.461184\pi\) | ||||
0.121642 | + | 0.992574i | \(0.461184\pi\) | |||||||
\(740\) | 8.12162e46 | 0.369249 | ||||||||
\(741\) | 1.39570e46 | 0.0620570 | ||||||||
\(742\) | 2.67132e47 | 1.16161 | ||||||||
\(743\) | 2.92156e47 | 1.24251 | 0.621255 | − | 0.783609i | \(-0.286623\pi\) | ||||
0.621255 | + | 0.783609i | \(0.286623\pi\) | |||||||
\(744\) | 3.26936e45 | 0.0135991 | ||||||||
\(745\) | 1.29323e47 | 0.526136 | ||||||||
\(746\) | 4.38145e47 | 1.74352 | ||||||||
\(747\) | −3.86715e47 | −1.50522 | ||||||||
\(748\) | 1.28772e47 | 0.490281 | ||||||||
\(749\) | −1.42033e47 | −0.528982 | ||||||||
\(750\) | 7.12825e45 | 0.0259700 | ||||||||
\(751\) | −3.59878e47 | −1.28261 | −0.641307 | − | 0.767284i | \(-0.721608\pi\) | ||||
−0.641307 | + | 0.767284i | \(0.721608\pi\) | |||||||
\(752\) | 3.04335e47 | 1.06110 | ||||||||
\(753\) | −6.71252e46 | −0.228965 | ||||||||
\(754\) | 1.45550e47 | 0.485718 | ||||||||
\(755\) | 2.17789e47 | 0.711069 | ||||||||
\(756\) | 6.23907e46 | 0.199301 | ||||||||
\(757\) | −3.31803e47 | −1.03705 | −0.518524 | − | 0.855063i | \(-0.673518\pi\) | ||||
−0.518524 | + | 0.855063i | \(0.673518\pi\) | |||||||
\(758\) | −7.77375e47 | −2.37733 | ||||||||
\(759\) | −4.13328e46 | −0.123682 | ||||||||
\(760\) | 3.38590e46 | 0.0991403 | ||||||||
\(761\) | 4.31914e47 | 1.23752 | 0.618758 | − | 0.785582i | \(-0.287636\pi\) | ||||
0.618758 | + | 0.785582i | \(0.287636\pi\) | |||||||
\(762\) | −6.07970e46 | −0.170461 | ||||||||
\(763\) | −1.85528e47 | −0.509044 | ||||||||
\(764\) | −7.72696e47 | −2.07476 | ||||||||
\(765\) | −1.39417e47 | −0.366355 | ||||||||
\(766\) | 1.39758e47 | 0.359420 | ||||||||
\(767\) | 1.58624e47 | 0.399251 | ||||||||
\(768\) | −3.37370e46 | −0.0831087 | ||||||||
\(769\) | −7.36766e46 | −0.177642 | −0.0888209 | − | 0.996048i | \(-0.528310\pi\) | ||||
−0.0888209 | + | 0.996048i | \(0.528310\pi\) | |||||||
\(770\) | 5.69062e46 | 0.134296 | ||||||||
\(771\) | −6.24299e46 | −0.144210 | ||||||||
\(772\) | 9.97733e46 | 0.225595 | ||||||||
\(773\) | 3.43337e47 | 0.759904 | 0.379952 | − | 0.925006i | \(-0.375941\pi\) | ||||
0.379952 | + | 0.925006i | \(0.375941\pi\) | |||||||
\(774\) | −5.98683e47 | −1.29709 | ||||||||
\(775\) | −2.00385e46 | −0.0424999 | ||||||||
\(776\) | −2.66940e47 | −0.554237 | ||||||||
\(777\) | 2.77042e46 | 0.0563118 | ||||||||
\(778\) | −1.34623e48 | −2.67889 | ||||||||
\(779\) | 1.51300e47 | 0.294761 | ||||||||
\(780\) | 2.63073e46 | 0.0501783 | ||||||||
\(781\) | −4.96026e47 | −0.926322 | ||||||||
\(782\) | 9.33638e47 | 1.70713 | ||||||||
\(783\) | 1.47526e47 | 0.264119 | ||||||||
\(784\) | 3.40916e47 | 0.597630 | ||||||||
\(785\) | 2.25445e47 | 0.386983 | ||||||||
\(786\) | 1.57179e47 | 0.264193 | ||||||||
\(787\) | 2.31817e47 | 0.381560 | 0.190780 | − | 0.981633i | \(-0.438898\pi\) | ||||
0.190780 | + | 0.981633i | \(0.438898\pi\) | |||||||
\(788\) | 5.84037e47 | 0.941365 | ||||||||
\(789\) | 7.86671e46 | 0.124172 | ||||||||
\(790\) | −1.97349e47 | −0.305062 | ||||||||
\(791\) | −1.36669e47 | −0.206898 | ||||||||
\(792\) | 1.00540e47 | 0.149064 | ||||||||
\(793\) | −9.37813e46 | −0.136179 | ||||||||
\(794\) | −8.07300e47 | −1.14815 | ||||||||
\(795\) | 1.14167e47 | 0.159031 | ||||||||
\(796\) | 2.06960e47 | 0.282372 | ||||||||
\(797\) | 9.59340e47 | 1.28206 | 0.641032 | − | 0.767514i | \(-0.278506\pi\) | ||||
0.641032 | + | 0.767514i | \(0.278506\pi\) | |||||||
\(798\) | 6.39526e46 | 0.0837164 | ||||||||
\(799\) | 9.63944e47 | 1.23603 | ||||||||
\(800\) | −2.25738e47 | −0.283543 | ||||||||
\(801\) | −2.34000e47 | −0.287925 | ||||||||
\(802\) | 9.41909e47 | 1.13536 | ||||||||
\(803\) | 2.76636e47 | 0.326664 | ||||||||
\(804\) | −3.08442e46 | −0.0356819 | ||||||||
\(805\) | 2.26772e47 | 0.257014 | ||||||||
\(806\) | −1.34551e47 | −0.149403 | ||||||||
\(807\) | −1.37533e47 | −0.149621 | ||||||||
\(808\) | 5.75297e47 | 0.613204 | ||||||||
\(809\) | −2.85029e47 | −0.297672 | −0.148836 | − | 0.988862i | \(-0.547553\pi\) | ||||
−0.148836 | + | 0.988862i | \(0.547553\pi\) | |||||||
\(810\) | −5.77990e47 | −0.591449 | ||||||||
\(811\) | −1.46166e48 | −1.46555 | −0.732777 | − | 0.680469i | \(-0.761776\pi\) | ||||
−0.732777 | + | 0.680469i | \(0.761776\pi\) | |||||||
\(812\) | 3.66565e47 | 0.360144 | ||||||||
\(813\) | 2.94510e47 | 0.283535 | ||||||||
\(814\) | 5.04151e47 | 0.475618 | ||||||||
\(815\) | 2.92670e47 | 0.270569 | ||||||||
\(816\) | −1.33882e47 | −0.121293 | ||||||||
\(817\) | −6.87898e47 | −0.610745 | ||||||||
\(818\) | −9.80066e47 | −0.852758 | ||||||||
\(819\) | −2.27378e47 | −0.193894 | ||||||||
\(820\) | 2.85183e47 | 0.238339 | ||||||||
\(821\) | −1.92594e48 | −1.57754 | −0.788771 | − | 0.614687i | \(-0.789282\pi\) | ||||
−0.788771 | + | 0.614687i | \(0.789282\pi\) | |||||||
\(822\) | −2.88272e47 | −0.231429 | ||||||||
\(823\) | 4.92693e47 | 0.387685 | 0.193842 | − | 0.981033i | \(-0.437905\pi\) | ||||
0.193842 | + | 0.981033i | \(0.437905\pi\) | |||||||
\(824\) | −3.17345e47 | −0.244756 | ||||||||
\(825\) | 2.43205e46 | 0.0183858 | ||||||||
\(826\) | 7.26836e47 | 0.538599 | ||||||||
\(827\) | −4.17990e46 | −0.0303616 | −0.0151808 | − | 0.999885i | \(-0.504832\pi\) | ||||
−0.0151808 | + | 0.999885i | \(0.504832\pi\) | |||||||
\(828\) | 2.21844e48 | 1.57960 | ||||||||
\(829\) | 1.71716e48 | 1.19857 | 0.599283 | − | 0.800538i | \(-0.295453\pi\) | ||||
0.599283 | + | 0.800538i | \(0.295453\pi\) | |||||||
\(830\) | −1.52381e48 | −1.04266 | ||||||||
\(831\) | 3.11649e47 | 0.209049 | ||||||||
\(832\) | −9.91243e47 | −0.651846 | ||||||||
\(833\) | 1.07981e48 | 0.696153 | ||||||||
\(834\) | −6.08806e47 | −0.384803 | ||||||||
\(835\) | 5.97681e47 | 0.370376 | ||||||||
\(836\) | 6.39653e47 | 0.388634 | ||||||||
\(837\) | −1.36378e47 | −0.0812409 | ||||||||
\(838\) | −1.94888e48 | −1.13831 | ||||||||
\(839\) | 4.33094e46 | 0.0248033 | 0.0124016 | − | 0.999923i | \(-0.496052\pi\) | ||||
0.0124016 | + | 0.999923i | \(0.496052\pi\) | |||||||
\(840\) | 2.17703e46 | 0.0122252 | ||||||||
\(841\) | −9.49316e47 | −0.522729 | ||||||||
\(842\) | −1.28167e48 | −0.692033 | ||||||||
\(843\) | 3.23641e47 | 0.171360 | ||||||||
\(844\) | 1.95698e47 | 0.101610 | ||||||||
\(845\) | 6.82782e47 | 0.347653 | ||||||||
\(846\) | 4.16724e48 | 2.08083 | ||||||||
\(847\) | −6.78143e47 | −0.332082 | ||||||||
\(848\) | −2.77789e48 | −1.33408 | ||||||||
\(849\) | −2.12106e47 | −0.0999024 | ||||||||
\(850\) | −5.49359e47 | −0.253772 | ||||||||
\(851\) | 2.00905e48 | 0.910233 | ||||||||
\(852\) | −1.05072e48 | −0.466912 | ||||||||
\(853\) | −3.98289e48 | −1.73596 | −0.867979 | − | 0.496601i | \(-0.834581\pi\) | ||||
−0.867979 | + | 0.496601i | \(0.834581\pi\) | |||||||
\(854\) | −4.29717e47 | −0.183708 | ||||||||
\(855\) | −6.92532e47 | −0.290402 | ||||||||
\(856\) | −9.88802e47 | −0.406717 | ||||||||
\(857\) | −3.66149e48 | −1.47732 | −0.738660 | − | 0.674078i | \(-0.764541\pi\) | ||||
−0.738660 | + | 0.674078i | \(0.764541\pi\) | |||||||
\(858\) | 1.63303e47 | 0.0646330 | ||||||||
\(859\) | 4.14441e48 | 1.60907 | 0.804536 | − | 0.593904i | \(-0.202414\pi\) | ||||
0.804536 | + | 0.593904i | \(0.202414\pi\) | |||||||
\(860\) | −1.29661e48 | −0.493839 | ||||||||
\(861\) | 9.72808e46 | 0.0363475 | ||||||||
\(862\) | −3.32430e48 | −1.21851 | ||||||||
\(863\) | 2.44535e48 | 0.879353 | 0.439676 | − | 0.898156i | \(-0.355093\pi\) | ||||
0.439676 | + | 0.898156i | \(0.355093\pi\) | |||||||
\(864\) | −1.53632e48 | −0.542008 | ||||||||
\(865\) | 2.17679e48 | 0.753443 | ||||||||
\(866\) | 6.85593e48 | 2.32820 | ||||||||
\(867\) | 1.60770e47 | 0.0535661 | ||||||||
\(868\) | −3.38865e47 | −0.110777 | ||||||||
\(869\) | −6.73325e47 | −0.215973 | ||||||||
\(870\) | 2.85031e47 | 0.0897066 | ||||||||
\(871\) | 2.29255e47 | 0.0707977 | ||||||||
\(872\) | −1.29160e48 | −0.391388 | ||||||||
\(873\) | 5.45983e48 | 1.62347 | ||||||||
\(874\) | 4.63769e48 | 1.35320 | ||||||||
\(875\) | −1.33434e47 | −0.0382062 | ||||||||
\(876\) | 5.85993e47 | 0.164655 | ||||||||
\(877\) | −5.05120e48 | −1.39284 | −0.696420 | − | 0.717635i | \(-0.745225\pi\) | ||||
−0.696420 | + | 0.717635i | \(0.745225\pi\) | |||||||
\(878\) | 6.64066e48 | 1.79702 | ||||||||
\(879\) | 4.84528e47 | 0.128677 | ||||||||
\(880\) | −5.91762e47 | −0.154235 | ||||||||
\(881\) | −3.16644e48 | −0.809971 | −0.404985 | − | 0.914323i | \(-0.632723\pi\) | ||||
−0.404985 | + | 0.914323i | \(0.632723\pi\) | |||||||
\(882\) | 4.66814e48 | 1.17196 | ||||||||
\(883\) | −1.69432e48 | −0.417489 | −0.208744 | − | 0.977970i | \(-0.566938\pi\) | ||||
−0.208744 | + | 0.977970i | \(0.566938\pi\) | |||||||
\(884\) | −2.02745e48 | −0.490330 | ||||||||
\(885\) | 3.10635e47 | 0.0737371 | ||||||||
\(886\) | −1.17267e48 | −0.273225 | ||||||||
\(887\) | 3.16518e48 | 0.723868 | 0.361934 | − | 0.932204i | \(-0.382117\pi\) | ||||
0.361934 | + | 0.932204i | \(0.382117\pi\) | |||||||
\(888\) | 1.92870e47 | 0.0432964 | ||||||||
\(889\) | 1.13806e48 | 0.250777 | ||||||||
\(890\) | −9.22054e47 | −0.199444 | ||||||||
\(891\) | −1.97202e48 | −0.418724 | ||||||||
\(892\) | −2.24145e48 | −0.467206 | ||||||||
\(893\) | 4.78823e48 | 0.979775 | ||||||||
\(894\) | 1.70051e48 | 0.341594 | ||||||||
\(895\) | 2.88840e48 | 0.569609 | ||||||||
\(896\) | −1.41404e48 | −0.273767 | ||||||||
\(897\) | 6.50765e47 | 0.123694 | ||||||||
\(898\) | −1.12646e49 | −2.10211 | ||||||||
\(899\) | −8.01263e47 | −0.146805 | ||||||||
\(900\) | −1.30535e48 | −0.234814 | ||||||||
\(901\) | −8.79861e48 | −1.55401 | ||||||||
\(902\) | 1.77028e48 | 0.306997 | ||||||||
\(903\) | −4.42296e47 | −0.0753122 | ||||||||
\(904\) | −9.51455e47 | −0.159078 | ||||||||
\(905\) | −3.97244e48 | −0.652163 | ||||||||
\(906\) | 2.86378e48 | 0.461661 | ||||||||
\(907\) | 1.08873e48 | 0.172346 | 0.0861731 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861731 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(908\) | 3.11468e48 | 0.484169 | ||||||||
\(909\) | −1.17668e49 | −1.79620 | ||||||||
\(910\) | −8.95961e47 | −0.134309 | ||||||||
\(911\) | −4.59000e48 | −0.675708 | −0.337854 | − | 0.941199i | \(-0.609701\pi\) | ||||
−0.337854 | + | 0.941199i | \(0.609701\pi\) | |||||||
\(912\) | −6.65037e47 | −0.0961460 | ||||||||
\(913\) | −5.19901e48 | −0.738165 | ||||||||
\(914\) | 5.27779e48 | 0.735935 | ||||||||
\(915\) | −1.83652e47 | −0.0251506 | ||||||||
\(916\) | −7.03824e48 | −0.946648 | ||||||||
\(917\) | −2.94224e48 | −0.388673 | ||||||||
\(918\) | −3.73883e48 | −0.485100 | ||||||||
\(919\) | −2.32948e48 | −0.296861 | −0.148431 | − | 0.988923i | \(-0.547422\pi\) | ||||
−0.148431 | + | 0.988923i | \(0.547422\pi\) | |||||||
\(920\) | 1.57873e48 | 0.197610 | ||||||||
\(921\) | −1.26141e48 | −0.155086 | ||||||||
\(922\) | 1.96172e49 | 2.36906 | ||||||||
\(923\) | 7.80969e48 | 0.926416 | ||||||||
\(924\) | 4.11276e47 | 0.0479232 | ||||||||
\(925\) | −1.18214e48 | −0.135310 | ||||||||
\(926\) | 2.43634e48 | 0.273941 | ||||||||
\(927\) | 6.49079e48 | 0.716939 | ||||||||
\(928\) | −9.02637e48 | −0.979425 | ||||||||
\(929\) | −3.31257e48 | −0.353107 | −0.176553 | − | 0.984291i | \(-0.556495\pi\) | ||||
−0.176553 | + | 0.984291i | \(0.556495\pi\) | |||||||
\(930\) | −2.63493e47 | −0.0275931 | ||||||||
\(931\) | 5.36378e48 | 0.551825 | ||||||||
\(932\) | 1.74814e49 | 1.76690 | ||||||||
\(933\) | −2.41857e48 | −0.240166 | ||||||||
\(934\) | 1.99903e49 | 1.95028 | ||||||||
\(935\) | −1.87433e48 | −0.179662 | ||||||||
\(936\) | −1.58295e48 | −0.149079 | ||||||||
\(937\) | 8.43738e48 | 0.780737 | 0.390368 | − | 0.920659i | \(-0.372348\pi\) | ||||
0.390368 | + | 0.920659i | \(0.372348\pi\) | |||||||
\(938\) | 1.05047e48 | 0.0955078 | ||||||||
\(939\) | −3.46206e48 | −0.309280 | ||||||||
\(940\) | 9.02528e48 | 0.792230 | ||||||||
\(941\) | 1.19866e49 | 1.03387 | 0.516937 | − | 0.856023i | \(-0.327072\pi\) | ||||
0.516937 | + | 0.856023i | \(0.327072\pi\) | |||||||
\(942\) | 2.96445e48 | 0.251249 | ||||||||
\(943\) | 7.05458e48 | 0.587527 | ||||||||
\(944\) | −7.55830e48 | −0.618566 | ||||||||
\(945\) | −9.08125e47 | −0.0730332 | ||||||||
\(946\) | −8.04873e48 | −0.636098 | ||||||||
\(947\) | −1.53140e49 | −1.18936 | −0.594681 | − | 0.803961i | \(-0.702722\pi\) | ||||
−0.594681 | + | 0.803961i | \(0.702722\pi\) | |||||||
\(948\) | −1.42629e48 | −0.108861 | ||||||||
\(949\) | −4.35550e48 | −0.326697 | ||||||||
\(950\) | −2.72885e48 | −0.201160 | ||||||||
\(951\) | 1.50877e48 | 0.109306 | ||||||||
\(952\) | −1.67779e48 | −0.119461 | ||||||||
\(953\) | 4.05106e48 | 0.283488 | 0.141744 | − | 0.989903i | \(-0.454729\pi\) | ||||
0.141744 | + | 0.989903i | \(0.454729\pi\) | |||||||
\(954\) | −3.80374e49 | −2.61615 | ||||||||
\(955\) | 1.12469e49 | 0.760289 | ||||||||
\(956\) | 6.91254e48 | 0.459285 | ||||||||
\(957\) | 9.72483e47 | 0.0635090 | ||||||||
\(958\) | −3.89808e49 | −2.50219 | ||||||||
\(959\) | 5.39619e48 | 0.340471 | ||||||||
\(960\) | −1.94116e48 | −0.120388 | ||||||||
\(961\) | −1.56628e49 | −0.954844 | ||||||||
\(962\) | −7.93763e48 | −0.475666 | ||||||||
\(963\) | 2.02244e49 | 1.19135 | ||||||||
\(964\) | 1.88525e49 | 1.09168 | ||||||||
\(965\) | −1.45225e48 | −0.0826684 | ||||||||
\(966\) | 2.98189e48 | 0.166866 | ||||||||
\(967\) | 1.43741e49 | 0.790757 | 0.395378 | − | 0.918518i | \(-0.370613\pi\) | ||||
0.395378 | + | 0.918518i | \(0.370613\pi\) | |||||||
\(968\) | −4.72107e48 | −0.255327 | ||||||||
\(969\) | −2.10642e48 | −0.111996 | ||||||||
\(970\) | 2.15139e49 | 1.12457 | ||||||||
\(971\) | 1.56174e49 | 0.802585 | 0.401293 | − | 0.915950i | \(-0.368561\pi\) | ||||
0.401293 | + | 0.915950i | \(0.368561\pi\) | |||||||
\(972\) | −1.34118e49 | −0.677632 | ||||||||
\(973\) | 1.13963e49 | 0.566110 | ||||||||
\(974\) | −3.34041e49 | −1.63146 | ||||||||
\(975\) | −3.82915e47 | −0.0183877 | ||||||||
\(976\) | 4.46859e48 | 0.210984 | ||||||||
\(977\) | −1.09477e49 | −0.508235 | −0.254117 | − | 0.967173i | \(-0.581785\pi\) | ||||
−0.254117 | + | 0.967173i | \(0.581785\pi\) | |||||||
\(978\) | 3.84841e48 | 0.175667 | ||||||||
\(979\) | −3.14591e48 | −0.141199 | ||||||||
\(980\) | 1.01101e49 | 0.446197 | ||||||||
\(981\) | 2.64177e49 | 1.14645 | ||||||||
\(982\) | −4.64482e49 | −1.98212 | ||||||||
\(983\) | 1.92109e49 | 0.806150 | 0.403075 | − | 0.915167i | \(-0.367941\pi\) | ||||
0.403075 | + | 0.915167i | \(0.367941\pi\) | |||||||
\(984\) | 6.77245e47 | 0.0279465 | ||||||||
\(985\) | −8.50092e48 | −0.344960 | ||||||||
\(986\) | −2.19668e49 | −0.876591 | ||||||||
\(987\) | 3.07868e48 | 0.120818 | ||||||||
\(988\) | −1.00710e49 | −0.388673 | ||||||||
\(989\) | −3.20743e49 | −1.21736 | ||||||||
\(990\) | −8.10295e48 | −0.302456 | ||||||||
\(991\) | 2.18652e49 | 0.802672 | 0.401336 | − | 0.915931i | \(-0.368546\pi\) | ||||
0.401336 | + | 0.915931i | \(0.368546\pi\) | |||||||
\(992\) | 8.34429e48 | 0.301264 | ||||||||
\(993\) | 2.00547e48 | 0.0712122 | ||||||||
\(994\) | 3.57850e49 | 1.24976 | ||||||||
\(995\) | −3.01240e48 | −0.103474 | ||||||||
\(996\) | −1.10130e49 | −0.372071 | ||||||||
\(997\) | 1.75251e49 | 0.582357 | 0.291179 | − | 0.956669i | \(-0.405953\pi\) | ||||
0.291179 | + | 0.956669i | \(0.405953\pi\) | |||||||
\(998\) | −1.10666e49 | −0.361709 | ||||||||
\(999\) | −8.04539e48 | −0.258652 |
(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 | 5.34.a.a.1.5 | ✓ | 5 | |
5.2 | odd | 4 | 25.34.b.b.24.10 | 10 | |||
5.3 | odd | 4 | 25.34.b.b.24.1 | 10 | |||
5.4 | even | 2 | 25.34.a.b.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.a.1.5 | ✓ | 5 | 1.1 | even | 1 | trivial | |
25.34.a.b.1.1 | 5 | 5.4 | even | 2 | |||
25.34.b.b.24.1 | 10 | 5.3 | odd | 4 | |||
25.34.b.b.24.10 | 10 | 5.2 | odd | 4 |