Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,39,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(27.4390407101\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 17353504902 x^{10} + \cdots + 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{75}\cdot 3^{91}\cdot 5^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.2 | ||
Root | \(-65373.8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.39.b.a.2.11 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 784486.i | − | 1.49629i | −0.663537 | − | 0.748144i | \(-0.730945\pi\) | ||
0.663537 | − | 0.748144i | \(-0.269055\pi\) | |||||||
\(3\) | 1.15997e9 | + | 7.30136e7i | 0.998025 | + | 0.0628202i | ||||
\(4\) | −3.40540e11 | −1.23888 | ||||||||
\(5\) | − | 3.07374e13i | − | 1.61153i | −0.592237 | − | 0.805764i | \(-0.701755\pi\) | ||
0.592237 | − | 0.805764i | \(-0.298245\pi\) | |||||||
\(6\) | 5.72781e13 | − | 9.09976e14i | 0.0939971 | − | 1.49333i | ||||
\(7\) | 1.07708e16 | 0.944899 | 0.472449 | − | 0.881358i | \(-0.343370\pi\) | ||||
0.472449 | + | 0.881358i | \(0.343370\pi\) | |||||||
\(8\) | 5.15107e16i | 0.357427i | ||||||||
\(9\) | 1.34019e18 | + | 1.69386e17i | 0.992107 | + | 0.125392i | ||||
\(10\) | −2.41131e19 | −2.41131 | ||||||||
\(11\) | − | 2.63951e19i | − | 0.431580i | −0.976440 | − | 0.215790i | \(-0.930767\pi\) | ||
0.976440 | − | 0.215790i | \(-0.0692327\pi\) | |||||||
\(12\) | −3.95014e20 | − | 2.48640e19i | −1.23643 | − | 0.0778265i | ||||
\(13\) | 2.34737e21 | 1.60568 | 0.802839 | − | 0.596196i | \(-0.203322\pi\) | ||||
0.802839 | + | 0.596196i | \(0.203322\pi\) | |||||||
\(14\) | − | 8.44954e21i | − | 1.41384i | ||||||
\(15\) | 2.24425e21 | − | 3.56544e22i | 0.101237 | − | 1.60834i | ||||
\(16\) | −5.31974e22 | −0.704062 | ||||||||
\(17\) | − | 1.67135e23i | − | 0.699099i | −0.936918 | − | 0.349550i | \(-0.886335\pi\) | ||
0.936918 | − | 0.349550i | \(-0.113665\pi\) | |||||||
\(18\) | 1.32881e23 | − | 1.05136e24i | 0.187623 | − | 1.48448i | ||||
\(19\) | −9.52513e23 | −0.481451 | −0.240726 | − | 0.970593i | \(-0.577385\pi\) | ||||
−0.240726 | + | 0.970593i | \(0.577385\pi\) | |||||||
\(20\) | 1.04673e25i | 1.99648i | ||||||||
\(21\) | 1.24938e25 | + | 7.86415e23i | 0.943033 | + | 0.0593588i | ||||
\(22\) | −2.07065e25 | −0.645768 | ||||||||
\(23\) | 4.84019e25i | 0.648684i | 0.945940 | + | 0.324342i | \(0.105143\pi\) | ||||
−0.945940 | + | 0.324342i | \(0.894857\pi\) | |||||||
\(24\) | −3.76098e24 | + | 5.97506e25i | −0.0224537 | + | 0.356721i | ||||
\(25\) | −5.80992e26 | −1.59702 | ||||||||
\(26\) | − | 1.84148e27i | − | 2.40255i | ||||||
\(27\) | 1.54221e27 | + | 2.94335e26i | 0.982271 | + | 0.187469i | ||||
\(28\) | −3.66789e27 | −1.17061 | ||||||||
\(29\) | 8.06134e27i | 1.32083i | 0.750903 | + | 0.660413i | \(0.229619\pi\) | ||||
−0.750903 | + | 0.660413i | \(0.770381\pi\) | |||||||
\(30\) | −2.79703e28 | − | 1.76058e27i | −2.40655 | − | 0.151479i | ||||
\(31\) | −1.15899e28 | −0.534821 | −0.267411 | − | 0.963583i | \(-0.586168\pi\) | ||||
−0.267411 | + | 0.963583i | \(0.586168\pi\) | |||||||
\(32\) | 5.58918e28i | 1.41091i | ||||||||
\(33\) | 1.92720e27 | − | 3.06174e28i | 0.0271120 | − | 0.430728i | ||||
\(34\) | −1.31115e29 | −1.04605 | ||||||||
\(35\) | − | 3.31067e29i | − | 1.52273i | ||||||
\(36\) | −4.56388e29 | − | 5.76828e28i | −1.22910 | − | 0.155346i | ||||
\(37\) | −4.26694e29 | −0.682785 | −0.341393 | − | 0.939921i | \(-0.610899\pi\) | ||||
−0.341393 | + | 0.939921i | \(0.610899\pi\) | |||||||
\(38\) | 7.47233e29i | 0.720390i | ||||||||
\(39\) | 2.72287e30 | + | 1.71390e29i | 1.60251 | + | 0.100869i | ||||
\(40\) | 1.58331e30 | 0.576003 | ||||||||
\(41\) | 7.27638e30i | 1.65585i | 0.560835 | + | 0.827927i | \(0.310480\pi\) | ||||
−0.560835 | + | 0.827927i | \(0.689520\pi\) | |||||||
\(42\) | 6.16931e29 | − | 9.80118e30i | 0.0888178 | − | 1.41105i | ||||
\(43\) | 9.82872e30 | 0.904891 | 0.452446 | − | 0.891792i | \(-0.350552\pi\) | ||||
0.452446 | + | 0.891792i | \(0.350552\pi\) | |||||||
\(44\) | 8.98856e30i | 0.534674i | ||||||||
\(45\) | 5.20651e30 | − | 4.11940e31i | 0.202073 | − | 1.59881i | ||||
\(46\) | 3.79706e31 | 0.970618 | ||||||||
\(47\) | − | 8.44918e29i | − | 0.0143534i | −0.999974 | − | 0.00717671i | \(-0.997716\pi\) | ||
0.999974 | − | 0.00717671i | \(-0.00228444\pi\) | |||||||
\(48\) | −6.17072e31 | − | 3.88413e30i | −0.702672 | − | 0.0442294i | ||||
\(49\) | −1.39246e31 | −0.107166 | ||||||||
\(50\) | 4.55780e32i | 2.38960i | ||||||||
\(51\) | 1.22031e31 | − | 1.93871e32i | 0.0439176 | − | 0.697718i | ||||
\(52\) | −7.99373e32 | −1.98923 | ||||||||
\(53\) | 6.22306e31i | 0.107836i | 0.998545 | + | 0.0539178i | \(0.0171709\pi\) | ||||
−0.998545 | + | 0.0539178i | \(0.982829\pi\) | |||||||
\(54\) | 2.30901e32 | − | 1.20984e33i | 0.280508 | − | 1.46976i | ||||
\(55\) | −8.11317e32 | −0.695503 | ||||||||
\(56\) | 5.54811e32i | 0.337732i | ||||||||
\(57\) | −1.10488e33 | − | 6.95464e31i | −0.480501 | − | 0.0302449i | ||||
\(58\) | 6.32401e33 | 1.97633 | ||||||||
\(59\) | − | 5.85547e33i | − | 1.32243i | −0.750195 | − | 0.661217i | \(-0.770040\pi\) | ||
0.750195 | − | 0.661217i | \(-0.229960\pi\) | |||||||
\(60\) | −7.64256e32 | + | 1.21417e34i | −0.125420 | + | 1.99254i | ||||
\(61\) | −2.26498e33 | −0.271518 | −0.135759 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135759 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(62\) | 9.09213e33i | 0.800246i | ||||||||
\(63\) | 1.44349e34 | + | 1.82443e33i | 0.937441 | + | 0.118483i | ||||
\(64\) | 2.92235e34 | 1.40706 | ||||||||
\(65\) | − | 7.21522e34i | − | 2.58759i | ||||||
\(66\) | −2.40189e34 | − | 1.51186e33i | −0.644493 | − | 0.0405673i | ||||
\(67\) | −2.71859e34 | −0.548180 | −0.274090 | − | 0.961704i | \(-0.588377\pi\) | ||||
−0.274090 | + | 0.961704i | \(0.588377\pi\) | |||||||
\(68\) | 5.69162e34i | 0.866097i | ||||||||
\(69\) | −3.53399e33 | + | 5.61445e34i | −0.0407505 | + | 0.647403i | ||||
\(70\) | −2.59717e35 | −2.27844 | ||||||||
\(71\) | − | 6.76007e34i | − | 0.452942i | −0.974018 | − | 0.226471i | \(-0.927281\pi\) | ||
0.974018 | − | 0.226471i | \(-0.0727189\pi\) | |||||||
\(72\) | −8.72521e33 | + | 6.90341e34i | −0.0448186 | + | 0.354606i | ||||
\(73\) | 4.44073e35 | 1.75517 | 0.877587 | − | 0.479417i | \(-0.159152\pi\) | ||||
0.877587 | + | 0.479417i | \(0.159152\pi\) | |||||||
\(74\) | 3.34736e35i | 1.02164i | ||||||||
\(75\) | −6.73931e35 | − | 4.24203e34i | −1.59387 | − | 0.100325i | ||||
\(76\) | 3.24368e35 | 0.596459 | ||||||||
\(77\) | − | 2.84296e35i | − | 0.407800i | ||||||
\(78\) | 1.34453e35 | − | 2.13605e36i | 0.150929 | − | 2.39781i | ||||
\(79\) | −1.68762e35 | −0.148717 | −0.0743584 | − | 0.997232i | \(-0.523691\pi\) | ||||
−0.0743584 | + | 0.997232i | \(0.523691\pi\) | |||||||
\(80\) | 1.63515e36i | 1.13462i | ||||||||
\(81\) | 1.76742e36 | + | 4.54020e35i | 0.968554 | + | 0.248805i | ||||
\(82\) | 5.70822e36 | 2.47763 | ||||||||
\(83\) | 3.55603e36i | 1.22598i | 0.790092 | + | 0.612988i | \(0.210032\pi\) | ||||
−0.790092 | + | 0.612988i | \(0.789968\pi\) | |||||||
\(84\) | −4.25462e36 | − | 2.67805e35i | −1.16830 | − | 0.0735382i | ||||
\(85\) | −5.13731e36 | −1.12662 | ||||||||
\(86\) | − | 7.71049e36i | − | 1.35398i | ||||||
\(87\) | −5.88587e35 | + | 9.35088e36i | −0.0829746 | + | 1.31822i | ||||
\(88\) | 1.35963e36 | 0.154258 | ||||||||
\(89\) | − | 7.51232e36i | − | 0.687644i | −0.939035 | − | 0.343822i | \(-0.888278\pi\) | ||
0.939035 | − | 0.343822i | \(-0.111722\pi\) | |||||||
\(90\) | −3.23161e37 | − | 4.08443e36i | −2.39228 | − | 0.302360i | ||||
\(91\) | 2.52831e37 | 1.51720 | ||||||||
\(92\) | − | 1.64828e37i | − | 0.803639i | ||||||
\(93\) | −1.34439e37 | − | 8.46222e35i | −0.533765 | − | 0.0335976i | ||||
\(94\) | −6.62826e35 | −0.0214768 | ||||||||
\(95\) | 2.92778e37i | 0.775872i | ||||||||
\(96\) | −4.08086e36 | + | 6.48325e37i | −0.0886335 | + | 1.40812i | ||||
\(97\) | 2.81399e37 | 0.501948 | 0.250974 | − | 0.967994i | \(-0.419249\pi\) | ||||
0.250974 | + | 0.967994i | \(0.419249\pi\) | |||||||
\(98\) | 1.09236e37i | 0.160351i | ||||||||
\(99\) | 4.47096e36 | − | 3.53744e37i | 0.0541169 | − | 0.428174i | ||||
\(100\) | 1.97851e38 | 1.97851 | ||||||||
\(101\) | − | 1.58783e38i | − | 1.31431i | −0.753757 | − | 0.657153i | \(-0.771760\pi\) | ||
0.753757 | − | 0.657153i | \(-0.228240\pi\) | |||||||
\(102\) | −1.52089e38 | − | 9.57319e36i | −1.04399 | − | 0.0657133i | ||||
\(103\) | 1.04178e38 | 0.594110 | 0.297055 | − | 0.954860i | \(-0.403995\pi\) | ||||
0.297055 | + | 0.954860i | \(0.403995\pi\) | |||||||
\(104\) | 1.20915e38i | 0.573912i | ||||||||
\(105\) | 2.41724e37 | − | 3.84026e38i | 0.0956583 | − | 1.51972i | ||||
\(106\) | 4.88190e37 | 0.161353 | ||||||||
\(107\) | 5.90450e38i | 1.63264i | 0.577597 | + | 0.816322i | \(0.303991\pi\) | ||||
−0.577597 | + | 0.816322i | \(0.696009\pi\) | |||||||
\(108\) | −5.25183e38 | − | 1.00233e38i | −1.21691 | − | 0.232251i | ||||
\(109\) | −1.13397e38 | −0.220546 | −0.110273 | − | 0.993901i | \(-0.535172\pi\) | ||||
−0.110273 | + | 0.993901i | \(0.535172\pi\) | |||||||
\(110\) | 6.36466e38i | 1.04067i | ||||||||
\(111\) | −4.94951e38 | − | 3.11545e37i | −0.681437 | − | 0.0428927i | ||||
\(112\) | −5.72979e38 | −0.665268 | ||||||||
\(113\) | − | 6.92711e38i | − | 0.679300i | −0.940552 | − | 0.339650i | \(-0.889691\pi\) | ||
0.940552 | − | 0.339650i | \(-0.110309\pi\) | |||||||
\(114\) | −5.45581e37 | + | 8.66764e38i | −0.0452551 | + | 0.718967i | ||||
\(115\) | 1.48775e39 | 1.04537 | ||||||||
\(116\) | − | 2.74521e39i | − | 1.63634i | ||||||
\(117\) | 3.14592e39 | + | 3.97613e38i | 1.59300 | + | 0.201340i | ||||
\(118\) | −4.59353e39 | −1.97874 | ||||||||
\(119\) | − | 1.80018e39i | − | 0.660578i | ||||||
\(120\) | 1.83658e39 | + | 1.15603e38i | 0.574866 | + | 0.0361847i | ||||
\(121\) | 3.04374e39 | 0.813738 | ||||||||
\(122\) | 1.77685e39i | 0.406269i | ||||||||
\(123\) | −5.31274e38 | + | 8.44035e39i | −0.104021 | + | 1.65258i | ||||
\(124\) | 3.94683e39 | 0.662577 | ||||||||
\(125\) | 6.67601e39i | 0.962114i | ||||||||
\(126\) | 1.43124e39 | − | 1.13240e40i | 0.177285 | − | 1.40268i | ||||
\(127\) | 6.02500e39 | 0.642224 | 0.321112 | − | 0.947041i | \(-0.395943\pi\) | ||||
0.321112 | + | 0.947041i | \(0.395943\pi\) | |||||||
\(128\) | − | 7.56199e39i | − | 0.694459i | ||||||
\(129\) | 1.14010e40 | + | 7.17630e38i | 0.903104 | + | 0.0568455i | ||||
\(130\) | −5.66024e40 | −3.87178 | ||||||||
\(131\) | − | 1.13980e40i | − | 0.674021i | −0.941501 | − | 0.337011i | \(-0.890584\pi\) | ||
0.941501 | − | 0.337011i | \(-0.109416\pi\) | |||||||
\(132\) | −6.56287e38 | + | 1.04264e40i | −0.0335884 | + | 0.533618i | ||||
\(133\) | −1.02593e40 | −0.454923 | ||||||||
\(134\) | 2.13270e40i | 0.820235i | ||||||||
\(135\) | 9.04709e39 | − | 4.74035e40i | 0.302112 | − | 1.58296i | ||||
\(136\) | 8.60925e39 | 0.249877 | ||||||||
\(137\) | 2.61641e40i | 0.660715i | 0.943856 | + | 0.330358i | \(0.107169\pi\) | ||||
−0.943856 | + | 0.330358i | \(0.892831\pi\) | |||||||
\(138\) | 4.40446e40 | + | 2.77237e39i | 0.968701 | + | 0.0609745i | ||||
\(139\) | 1.77183e40 | 0.339735 | 0.169867 | − | 0.985467i | \(-0.445666\pi\) | ||||
0.169867 | + | 0.985467i | \(0.445666\pi\) | |||||||
\(140\) | 1.12741e41i | 1.88647i | ||||||||
\(141\) | 6.16905e37 | − | 9.80076e38i | 0.000901686 | − | 0.0143251i | ||||
\(142\) | −5.30318e40 | −0.677732 | ||||||||
\(143\) | − | 6.19590e40i | − | 0.692979i | ||||||
\(144\) | −7.12947e40 | − | 9.01093e39i | −0.698505 | − | 0.0882840i | ||||
\(145\) | 2.47785e41 | 2.12855 | ||||||||
\(146\) | − | 3.48369e41i | − | 2.62625i | ||||||
\(147\) | −1.61520e40 | − | 1.01668e39i | −0.106954 | − | 0.00673219i | ||||
\(148\) | 1.45306e41 | 0.845886 | ||||||||
\(149\) | 1.85063e40i | 0.0947938i | 0.998876 | + | 0.0473969i | \(0.0150926\pi\) | ||||
−0.998876 | + | 0.0473969i | \(0.984907\pi\) | |||||||
\(150\) | −3.32781e40 | + | 5.28689e41i | −0.150115 | + | 2.38488i | ||||
\(151\) | −2.58190e41 | −1.02654 | −0.513272 | − | 0.858226i | \(-0.671567\pi\) | ||||
−0.513272 | + | 0.858226i | \(0.671567\pi\) | |||||||
\(152\) | − | 4.90646e40i | − | 0.172084i | ||||||
\(153\) | 2.83105e40 | − | 2.23993e41i | 0.0876617 | − | 0.693581i | ||||
\(154\) | −2.23026e41 | −0.610186 | ||||||||
\(155\) | 3.56245e41i | 0.861879i | ||||||||
\(156\) | −9.27246e41 | − | 5.83651e40i | −1.98531 | − | 0.124964i | ||||
\(157\) | −6.27539e40 | −0.119000 | −0.0595001 | − | 0.998228i | \(-0.518951\pi\) | ||||
−0.0595001 | + | 0.998228i | \(0.518951\pi\) | |||||||
\(158\) | 1.32391e41i | 0.222523i | ||||||||
\(159\) | −4.54368e39 | + | 7.21854e40i | −0.00677426 | + | 0.107623i | ||||
\(160\) | 1.71797e42 | 2.27371 | ||||||||
\(161\) | 5.21327e41i | 0.612941i | ||||||||
\(162\) | 3.56172e41 | − | 1.38651e42i | 0.372284 | − | 1.44923i | ||||
\(163\) | −1.58317e42 | −1.47219 | −0.736094 | − | 0.676879i | \(-0.763332\pi\) | ||||
−0.736094 | + | 0.676879i | \(0.763332\pi\) | |||||||
\(164\) | − | 2.47790e42i | − | 2.05140i | ||||||
\(165\) | −9.41099e41 | − | 5.92371e40i | −0.694130 | − | 0.0436917i | ||||
\(166\) | 2.78965e42 | 1.83441 | ||||||||
\(167\) | 2.76798e42i | 1.62387i | 0.583749 | + | 0.811934i | \(0.301585\pi\) | ||||
−0.583749 | + | 0.811934i | \(0.698415\pi\) | |||||||
\(168\) | −4.05087e40 | + | 6.43562e41i | −0.0212164 | + | 0.337065i | ||||
\(169\) | 3.37294e42 | 1.57820 | ||||||||
\(170\) | 4.03015e42i | 1.68574i | ||||||||
\(171\) | −1.27655e42 | − | 1.61343e41i | −0.477651 | − | 0.0603703i | ||||
\(172\) | −3.34707e42 | −1.12105 | ||||||||
\(173\) | − | 4.23364e42i | − | 1.27010i | −0.772471 | − | 0.635050i | \(-0.780979\pi\) | ||
0.772471 | − | 0.635050i | \(-0.219021\pi\) | |||||||
\(174\) | 7.33563e42 | + | 4.61738e41i | 1.97243 | + | 0.124154i | ||||
\(175\) | −6.25776e42 | −1.50902 | ||||||||
\(176\) | 1.40415e42i | 0.303859i | ||||||||
\(177\) | 4.27529e41 | − | 6.79215e42i | 0.0830756 | − | 1.31982i | ||||
\(178\) | −5.89330e42 | −1.02891 | ||||||||
\(179\) | − | 2.84670e42i | − | 0.446821i | −0.974724 | − | 0.223411i | \(-0.928281\pi\) | ||
0.974724 | − | 0.223411i | \(-0.0717191\pi\) | |||||||
\(180\) | −1.77302e42 | + | 1.40282e43i | −0.250344 | + | 1.98072i | ||||
\(181\) | −2.20401e42 | −0.280105 | −0.140052 | − | 0.990144i | \(-0.544727\pi\) | ||||
−0.140052 | + | 0.990144i | \(0.544727\pi\) | |||||||
\(182\) | − | 1.98342e43i | − | 2.27017i | ||||||
\(183\) | −2.62730e42 | − | 1.65375e41i | −0.270981 | − | 0.0170568i | ||||
\(184\) | −2.49321e42 | −0.231857 | ||||||||
\(185\) | 1.31155e43i | 1.10033i | ||||||||
\(186\) | −6.63849e41 | + | 1.05466e43i | −0.0502717 | + | 0.798666i | ||||
\(187\) | −4.41155e42 | −0.301717 | ||||||||
\(188\) | 2.87728e41i | 0.0177821i | ||||||||
\(189\) | 1.66108e43 | + | 3.17022e42i | 0.928146 | + | 0.177139i | ||||
\(190\) | 2.29680e43 | 1.16093 | ||||||||
\(191\) | 1.70688e43i | 0.780852i | 0.920634 | + | 0.390426i | \(0.127672\pi\) | ||||
−0.920634 | + | 0.390426i | \(0.872328\pi\) | |||||||
\(192\) | 3.38982e43 | + | 2.13371e42i | 1.40428 | + | 0.0883918i | ||||
\(193\) | −2.36210e43 | −0.886562 | −0.443281 | − | 0.896383i | \(-0.646186\pi\) | ||||
−0.443281 | + | 0.896383i | \(0.646186\pi\) | |||||||
\(194\) | − | 2.20753e43i | − | 0.751059i | ||||||
\(195\) | 5.26809e42 | − | 8.36941e43i | 0.162553 | − | 2.58248i | ||||
\(196\) | 4.74187e42 | 0.132765 | ||||||||
\(197\) | 5.31510e43i | 1.35099i | 0.737363 | + | 0.675497i | \(0.236071\pi\) | ||||
−0.737363 | + | 0.675497i | \(0.763929\pi\) | |||||||
\(198\) | −2.77507e43 | − | 3.50741e42i | −0.640671 | − | 0.0809744i | ||||
\(199\) | 2.82826e43 | 0.593350 | 0.296675 | − | 0.954978i | \(-0.404122\pi\) | ||||
0.296675 | + | 0.954978i | \(0.404122\pi\) | |||||||
\(200\) | − | 2.99273e43i | − | 0.570818i | ||||||
\(201\) | −3.15348e43 | − | 1.98494e42i | −0.547097 | − | 0.0344368i | ||||
\(202\) | −1.24563e44 | −1.96658 | ||||||||
\(203\) | 8.68271e43i | 1.24805i | ||||||||
\(204\) | −4.15565e42 | + | 6.60209e43i | −0.0544084 | + | 0.864386i | ||||
\(205\) | 2.23657e44 | 2.66845 | ||||||||
\(206\) | − | 8.17258e43i | − | 0.888960i | ||||||
\(207\) | −8.19862e42 | + | 6.48677e43i | −0.0813400 | + | 0.643564i | ||||
\(208\) | −1.24874e44 | −1.13050 | ||||||||
\(209\) | 2.51416e43i | 0.207785i | ||||||||
\(210\) | −3.01263e44 | − | 1.89629e43i | −2.27394 | − | 0.143132i | ||||
\(211\) | −7.14319e43 | −0.492636 | −0.246318 | − | 0.969189i | \(-0.579221\pi\) | ||||
−0.246318 | + | 0.969189i | \(0.579221\pi\) | |||||||
\(212\) | − | 2.11920e43i | − | 0.133595i | ||||||
\(213\) | 4.93577e42 | − | 7.84145e43i | 0.0284539 | − | 0.452047i | ||||
\(214\) | 4.63200e44 | 2.44290 | ||||||||
\(215\) | − | 3.02110e44i | − | 1.45826i | ||||||
\(216\) | −1.51614e43 | + | 7.94401e43i | −0.0670065 | + | 0.351090i | ||||
\(217\) | −1.24833e44 | −0.505352 | ||||||||
\(218\) | 8.89584e43i | 0.330000i | ||||||||
\(219\) | 5.15110e44 | + | 3.24234e43i | 1.75171 | + | 0.110260i | ||||
\(220\) | 2.76285e44 | 0.861642 | ||||||||
\(221\) | − | 3.92329e44i | − | 1.12253i | ||||||
\(222\) | −2.44402e43 | + | 3.88282e44i | −0.0641799 | + | 1.01962i | ||||
\(223\) | 2.38406e44 | 0.574811 | 0.287405 | − | 0.957809i | \(-0.407207\pi\) | ||||
0.287405 | + | 0.957809i | \(0.407207\pi\) | |||||||
\(224\) | 6.01999e44i | 1.33316i | ||||||||
\(225\) | −7.78640e44 | − | 9.84122e43i | −1.58441 | − | 0.200254i | ||||
\(226\) | −5.43421e44 | −1.01643 | ||||||||
\(227\) | 7.53137e44i | 1.29534i | 0.761922 | + | 0.647668i | \(0.224256\pi\) | ||||
−0.761922 | + | 0.647668i | \(0.775744\pi\) | |||||||
\(228\) | 3.76256e44 | + | 2.36833e43i | 0.595281 | + | 0.0374697i | ||||
\(229\) | −1.95667e44 | −0.284867 | −0.142434 | − | 0.989804i | \(-0.545493\pi\) | ||||
−0.142434 | + | 0.989804i | \(0.545493\pi\) | |||||||
\(230\) | − | 1.16712e45i | − | 1.56418i | ||||||
\(231\) | 2.07575e43 | − | 3.29774e44i | 0.0256181 | − | 0.406994i | ||||
\(232\) | −4.15245e44 | −0.472099 | ||||||||
\(233\) | 8.52785e43i | 0.0893464i | 0.999002 | + | 0.0446732i | \(0.0142246\pi\) | ||||
−0.999002 | + | 0.0446732i | \(0.985775\pi\) | |||||||
\(234\) | 3.11922e44 | − | 2.46793e45i | 0.301262 | − | 2.38359i | ||||
\(235\) | −2.59706e43 | −0.0231309 | ||||||||
\(236\) | 1.99402e45i | 1.63833i | ||||||||
\(237\) | −1.95758e44 | − | 1.23219e43i | −0.148423 | − | 0.00934242i | ||||
\(238\) | −1.41222e45 | −0.988415 | ||||||||
\(239\) | 1.01935e45i | 0.658812i | 0.944188 | + | 0.329406i | \(0.106849\pi\) | ||||
−0.944188 | + | 0.329406i | \(0.893151\pi\) | |||||||
\(240\) | −1.19388e44 | + | 1.89672e45i | −0.0712768 | + | 1.13237i | ||||
\(241\) | −1.47874e45 | −0.815769 | −0.407884 | − | 0.913034i | \(-0.633733\pi\) | ||||
−0.407884 | + | 0.913034i | \(0.633733\pi\) | |||||||
\(242\) | − | 2.38777e45i | − | 1.21759i | ||||||
\(243\) | 2.01699e45 | + | 6.55693e44i | 0.951010 | + | 0.309159i | ||||
\(244\) | 7.71317e44 | 0.336377 | ||||||||
\(245\) | 4.28006e44i | 0.172701i | ||||||||
\(246\) | 6.62134e45 | + | 4.16777e44i | 2.47274 | + | 0.155646i | ||||
\(247\) | −2.23590e45 | −0.773056 | ||||||||
\(248\) | − | 5.97005e44i | − | 0.191160i | ||||||
\(249\) | −2.59638e44 | + | 4.12487e45i | −0.0770161 | + | 1.22355i | ||||
\(250\) | 5.23723e45 | 1.43960 | ||||||||
\(251\) | − | 5.02297e45i | − | 1.27985i | −0.768436 | − | 0.639926i | \(-0.778965\pi\) | ||
0.768436 | − | 0.639926i | \(-0.221035\pi\) | |||||||
\(252\) | −4.91566e45 | − | 6.21290e44i | −1.16137 | − | 0.146786i | ||||
\(253\) | 1.27757e45 | 0.279959 | ||||||||
\(254\) | − | 4.72653e45i | − | 0.960952i | ||||||
\(255\) | −5.95911e45 | − | 3.75093e44i | −1.12439 | − | 0.0707744i | ||||
\(256\) | 2.10062e45 | 0.367950 | ||||||||
\(257\) | − | 4.58230e45i | − | 0.745340i | −0.927964 | − | 0.372670i | \(-0.878442\pi\) | ||
0.927964 | − | 0.372670i | \(-0.121558\pi\) | |||||||
\(258\) | 5.62970e44 | − | 8.94390e45i | 0.0850572 | − | 1.35130i | ||||
\(259\) | −4.59584e45 | −0.645163 | ||||||||
\(260\) | 2.45707e46i | 3.20571i | ||||||||
\(261\) | −1.36548e45 | + | 1.08037e46i | −0.165621 | + | 1.31040i | ||||
\(262\) | −8.94155e45 | −1.00853 | ||||||||
\(263\) | − | 3.11142e45i | − | 0.326437i | −0.986590 | − | 0.163219i | \(-0.947812\pi\) | ||
0.986590 | − | 0.163219i | \(-0.0521876\pi\) | |||||||
\(264\) | 1.57712e45 | + | 9.92712e43i | 0.153954 | + | 0.00969056i | ||||
\(265\) | 1.91281e45 | 0.173780 | ||||||||
\(266\) | 8.04830e45i | 0.680696i | ||||||||
\(267\) | 5.48501e44 | − | 8.71403e45i | 0.0431980 | − | 0.686286i | ||||
\(268\) | 9.25789e45 | 0.679127 | ||||||||
\(269\) | − | 2.16658e46i | − | 1.48075i | −0.672193 | − | 0.740376i | \(-0.734648\pi\) | ||
0.672193 | − | 0.740376i | \(-0.265352\pi\) | |||||||
\(270\) | −3.71874e46 | − | 7.09731e45i | −2.36856 | − | 0.452046i | ||||
\(271\) | 1.16365e46 | 0.690887 | 0.345444 | − | 0.938440i | \(-0.387728\pi\) | ||||
0.345444 | + | 0.938440i | \(0.387728\pi\) | |||||||
\(272\) | 8.89117e45i | 0.492209i | ||||||||
\(273\) | 2.93275e46 | + | 1.84601e45i | 1.51421 | + | 0.0953110i | ||||
\(274\) | 2.05253e46 | 0.988620 | ||||||||
\(275\) | 1.53353e46i | 0.689242i | ||||||||
\(276\) | 1.20346e45 | − | 1.91194e46i | 0.0504848 | − | 0.802052i | ||||
\(277\) | −5.19583e45 | −0.203488 | −0.101744 | − | 0.994811i | \(-0.532442\pi\) | ||||
−0.101744 | + | 0.994811i | \(0.532442\pi\) | |||||||
\(278\) | − | 1.38997e46i | − | 0.508341i | ||||||
\(279\) | −1.55327e46 | − | 1.96318e45i | −0.530600 | − | 0.0670625i | ||||
\(280\) | 1.70535e46 | 0.544265 | ||||||||
\(281\) | − | 3.03870e45i | − | 0.0906292i | −0.998973 | − | 0.0453146i | \(-0.985571\pi\) | ||
0.998973 | − | 0.0453146i | \(-0.0144290\pi\) | |||||||
\(282\) | −7.68856e44 | − | 4.83953e43i | −0.0214344 | − | 0.00134918i | ||||
\(283\) | 4.82432e46 | 1.25746 | 0.628729 | − | 0.777624i | \(-0.283575\pi\) | ||||
0.628729 | + | 0.777624i | \(0.283575\pi\) | |||||||
\(284\) | 2.30207e46i | 0.561139i | ||||||||
\(285\) | −2.13768e45 | + | 3.39613e46i | −0.0487405 | + | 0.774340i | ||||
\(286\) | −4.86060e46 | −1.03690 | ||||||||
\(287\) | 7.83725e46i | 1.56462i | ||||||||
\(288\) | −9.46731e45 | + | 7.49056e46i | −0.176917 | + | 1.39977i | ||||
\(289\) | 2.92214e46 | 0.511260 | ||||||||
\(290\) | − | 1.94384e47i | − | 3.18492i | ||||||
\(291\) | 3.26413e46 | + | 2.05459e45i | 0.500957 | + | 0.0315325i | ||||
\(292\) | −1.51225e47 | −2.17444 | ||||||||
\(293\) | − | 8.65440e46i | − | 1.16614i | −0.812421 | − | 0.583072i | \(-0.801851\pi\) | ||
0.812421 | − | 0.583072i | \(-0.198149\pi\) | |||||||
\(294\) | −7.97573e44 | + | 1.26710e46i | −0.0100733 | + | 0.160034i | ||||
\(295\) | −1.79982e47 | −2.13114 | ||||||||
\(296\) | − | 2.19793e46i | − | 0.244046i | ||||||
\(297\) | 7.76898e45 | − | 4.07066e46i | 0.0809080 | − | 0.423929i | ||||
\(298\) | 1.45179e46 | 0.141839 | ||||||||
\(299\) | 1.13617e47i | 1.04158i | ||||||||
\(300\) | 2.29500e47 | + | 1.44458e46i | 1.97460 | + | 0.124290i | ||||
\(301\) | 1.05863e47 | 0.855031 | ||||||||
\(302\) | 2.02546e47i | 1.53600i | ||||||||
\(303\) | 1.15933e46 | − | 1.84182e47i | 0.0825651 | − | 1.31171i | ||||
\(304\) | 5.06713e46 | 0.338972 | ||||||||
\(305\) | 6.96198e46i | 0.437558i | ||||||||
\(306\) | −1.75719e47 | − | 2.22091e46i | −1.03780 | − | 0.131167i | ||||
\(307\) | 1.80284e46 | 0.100076 | 0.0500379 | − | 0.998747i | \(-0.484066\pi\) | ||||
0.0500379 | + | 0.998747i | \(0.484066\pi\) | |||||||
\(308\) | 9.68141e46i | 0.505213i | ||||||||
\(309\) | 1.20842e47 | + | 7.60638e45i | 0.592937 | + | 0.0373222i | ||||
\(310\) | 2.79469e47 | 1.28962 | ||||||||
\(311\) | − | 5.09327e46i | − | 0.221080i | −0.993872 | − | 0.110540i | \(-0.964742\pi\) | ||
0.993872 | − | 0.110540i | \(-0.0352580\pi\) | |||||||
\(312\) | −8.82841e45 | + | 1.40257e47i | −0.0360533 | + | 0.572779i | ||||
\(313\) | −3.91522e47 | −1.50458 | −0.752288 | − | 0.658835i | \(-0.771050\pi\) | ||||
−0.752288 | + | 0.658835i | \(0.771050\pi\) | |||||||
\(314\) | 4.92295e46i | 0.178058i | ||||||||
\(315\) | 5.60783e46 | − | 4.43693e47i | 0.190939 | − | 1.51071i | ||||
\(316\) | 5.74701e46 | 0.184242 | ||||||||
\(317\) | − | 1.16993e47i | − | 0.353212i | −0.984282 | − | 0.176606i | \(-0.943488\pi\) | ||
0.984282 | − | 0.176606i | \(-0.0565118\pi\) | |||||||
\(318\) | 5.66284e46 | + | 3.56445e45i | 0.161034 | + | 0.0101362i | ||||
\(319\) | 2.12780e47 | 0.570042 | ||||||||
\(320\) | − | 8.98255e47i | − | 2.26751i | ||||||
\(321\) | −4.31109e46 | + | 6.84902e47i | −0.102563 | + | 1.62942i | ||||
\(322\) | 4.08974e47 | 0.917136 | ||||||||
\(323\) | 1.59199e47i | 0.336582i | ||||||||
\(324\) | −6.01875e47 | − | 1.54612e47i | −1.19992 | − | 0.308239i | ||||
\(325\) | −1.36381e48 | −2.56430 | ||||||||
\(326\) | 1.24197e48i | 2.20282i | ||||||||
\(327\) | −1.31537e47 | − | 8.27953e45i | −0.220110 | − | 0.0138547i | ||||
\(328\) | −3.74811e47 | −0.591847 | ||||||||
\(329\) | − | 9.10045e45i | − | 0.0135625i | ||||||
\(330\) | −4.64706e46 | + | 7.38279e47i | −0.0653753 | + | 1.03862i | ||||
\(331\) | 8.09163e47 | 1.07474 | 0.537371 | − | 0.843346i | \(-0.319418\pi\) | ||||
0.537371 | + | 0.843346i | \(0.319418\pi\) | |||||||
\(332\) | − | 1.21097e48i | − | 1.51883i | ||||||
\(333\) | −5.71851e47 | − | 7.22762e46i | −0.677396 | − | 0.0856160i | ||||
\(334\) | 2.17144e48 | 2.42977 | ||||||||
\(335\) | 8.35626e47i | 0.883407i | ||||||||
\(336\) | −6.64636e47 | − | 4.18353e46i | −0.663954 | − | 0.0417923i | ||||
\(337\) | 7.40101e47 | 0.698751 | 0.349376 | − | 0.936983i | \(-0.386394\pi\) | ||||
0.349376 | + | 0.936983i | \(0.386394\pi\) | |||||||
\(338\) | − | 2.64603e48i | − | 2.36144i | ||||||
\(339\) | 5.05773e46 | − | 8.03521e47i | 0.0426738 | − | 0.677958i | ||||
\(340\) | 1.74946e48 | 1.39574 | ||||||||
\(341\) | 3.05917e47i | 0.230818i | ||||||||
\(342\) | −1.26571e47 | + | 1.00143e48i | −0.0903314 | + | 0.714704i | ||||
\(343\) | −1.54948e48 | −1.04616 | ||||||||
\(344\) | 5.06284e47i | 0.323433i | ||||||||
\(345\) | 1.72574e48 | + | 1.08626e47i | 1.04331 | + | 0.0656705i | ||||
\(346\) | −3.32123e48 | −1.90044 | ||||||||
\(347\) | 1.40857e48i | 0.762992i | 0.924371 | + | 0.381496i | \(0.124591\pi\) | ||||
−0.924371 | + | 0.381496i | \(0.875409\pi\) | |||||||
\(348\) | 2.00437e47 | − | 3.18435e48i | 0.102795 | − | 1.63311i | ||||
\(349\) | 1.01432e48 | 0.492597 | 0.246299 | − | 0.969194i | \(-0.420786\pi\) | ||||
0.246299 | + | 0.969194i | \(0.420786\pi\) | |||||||
\(350\) | 4.90912e48i | 2.25793i | ||||||||
\(351\) | 3.62013e48 | + | 6.90913e47i | 1.57721 | + | 0.301015i | ||||
\(352\) | 1.47527e48 | 0.608919 | ||||||||
\(353\) | − | 1.52516e48i | − | 0.596479i | −0.954491 | − | 0.298240i | \(-0.903601\pi\) | ||
0.954491 | − | 0.298240i | \(-0.0963995\pi\) | |||||||
\(354\) | −5.32834e48 | − | 3.35390e47i | −1.97483 | − | 0.124305i | ||||
\(355\) | −2.07787e48 | −0.729929 | ||||||||
\(356\) | 2.55824e48i | 0.851906i | ||||||||
\(357\) | 1.31438e47 | − | 2.08815e48i | 0.0414977 | − | 0.659273i | ||||
\(358\) | −2.23319e48 | −0.668573 | ||||||||
\(359\) | − | 2.00126e48i | − | 0.568209i | −0.958793 | − | 0.284105i | \(-0.908304\pi\) | ||
0.958793 | − | 0.284105i | \(-0.0916963\pi\) | |||||||
\(360\) | 2.12193e48 | + | 2.68191e47i | 0.571457 | + | 0.0722264i | ||||
\(361\) | −3.00686e48 | −0.768204 | ||||||||
\(362\) | 1.72901e48i | 0.419117i | ||||||||
\(363\) | 3.53063e48 | + | 2.22234e47i | 0.812131 | + | 0.0511193i | ||||
\(364\) | −8.60989e48 | −1.87963 | ||||||||
\(365\) | − | 1.36497e49i | − | 2.82851i | ||||||
\(366\) | −1.29734e47 | + | 2.06108e48i | −0.0255219 | + | 0.405466i | ||||
\(367\) | 1.39146e48 | 0.259905 | 0.129953 | − | 0.991520i | \(-0.458517\pi\) | ||||
0.129953 | + | 0.991520i | \(0.458517\pi\) | |||||||
\(368\) | − | 2.57486e48i | − | 0.456714i | ||||||
\(369\) | −1.23252e48 | + | 9.75173e48i | −0.207631 | + | 1.64279i | ||||
\(370\) | 1.02889e49 | 1.64641 | ||||||||
\(371\) | 6.70274e47i | 0.101894i | ||||||||
\(372\) | 4.57819e48 | + | 2.88172e47i | 0.661268 | + | 0.0416233i | ||||
\(373\) | 9.04311e48 | 1.24122 | 0.620612 | − | 0.784118i | \(-0.286884\pi\) | ||||
0.620612 | + | 0.784118i | \(0.286884\pi\) | |||||||
\(374\) | 3.46079e48i | 0.451456i | ||||||||
\(375\) | −4.87439e47 | + | 7.74394e48i | −0.0604402 | + | 0.960213i | ||||
\(376\) | 4.35223e46 | 0.00513030 | ||||||||
\(377\) | 1.89230e49i | 2.12082i | ||||||||
\(378\) | 2.48699e48 | − | 1.30309e49i | 0.265051 | − | 1.38877i | ||||
\(379\) | −1.74074e49 | −1.76437 | −0.882184 | − | 0.470904i | \(-0.843928\pi\) | ||||
−0.882184 | + | 0.470904i | \(0.843928\pi\) | |||||||
\(380\) | − | 9.97026e48i | − | 0.961209i | ||||||
\(381\) | 6.98880e48 | + | 4.39907e47i | 0.640956 | + | 0.0403447i | ||||
\(382\) | 1.33902e49 | 1.16838 | ||||||||
\(383\) | − | 2.24202e49i | − | 1.86150i | −0.365662 | − | 0.930748i | \(-0.619157\pi\) | ||
0.365662 | − | 0.930748i | \(-0.380843\pi\) | |||||||
\(384\) | 5.52127e47 | − | 8.77165e48i | 0.0436261 | − | 0.693087i | ||||
\(385\) | −8.73853e48 | −0.657180 | ||||||||
\(386\) | 1.85303e49i | 1.32655i | ||||||||
\(387\) | 1.31724e49 | + | 1.66485e48i | 0.897749 | + | 0.113466i | ||||
\(388\) | −9.58274e48 | −0.621852 | ||||||||
\(389\) | 6.09185e48i | 0.376449i | 0.982126 | + | 0.188225i | \(0.0602733\pi\) | ||||
−0.982126 | + | 0.188225i | \(0.939727\pi\) | |||||||
\(390\) | −6.56568e49 | − | 4.13274e48i | −3.86413 | − | 0.243226i | ||||
\(391\) | 8.08966e48 | 0.453495 | ||||||||
\(392\) | − | 7.17265e47i | − | 0.0383040i | ||||||
\(393\) | 8.32207e47 | − | 1.32213e49i | 0.0423422 | − | 0.672690i | ||||
\(394\) | 4.16962e49 | 2.02147 | ||||||||
\(395\) | 5.18731e48i | 0.239661i | ||||||||
\(396\) | −1.52254e48 | + | 1.20464e49i | −0.0670441 | + | 0.530454i | ||||
\(397\) | −2.98327e49 | −1.25220 | −0.626098 | − | 0.779744i | \(-0.715349\pi\) | ||||
−0.626098 | + | 0.779744i | \(0.715349\pi\) | |||||||
\(398\) | − | 2.21873e49i | − | 0.887823i | ||||||
\(399\) | −1.19005e49 | − | 7.49070e47i | −0.454024 | − | 0.0285784i | ||||
\(400\) | 3.09073e49 | 1.12440 | ||||||||
\(401\) | 5.09325e49i | 1.76706i | 0.468371 | + | 0.883532i | \(0.344841\pi\) | ||||
−0.468371 | + | 0.883532i | \(0.655159\pi\) | |||||||
\(402\) | −1.55716e48 | + | 2.47386e49i | −0.0515274 | + | 0.818615i | ||||
\(403\) | −2.72059e49 | −0.858750 | ||||||||
\(404\) | 5.40717e49i | 1.62826i | ||||||||
\(405\) | 1.39554e49 | − | 5.43259e49i | 0.400956 | − | 1.56085i | ||||
\(406\) | 6.81146e49 | 1.86744 | ||||||||
\(407\) | 1.12626e49i | 0.294677i | ||||||||
\(408\) | 9.98644e48 | + | 6.28592e47i | 0.249383 | + | 0.0156973i | ||||
\(409\) | −4.95505e49 | −1.18115 | −0.590575 | − | 0.806983i | \(-0.701099\pi\) | ||||
−0.590575 | + | 0.806983i | \(0.701099\pi\) | |||||||
\(410\) | − | 1.75456e50i | − | 3.99277i | ||||||
\(411\) | −1.91033e48 | + | 3.03494e49i | −0.0415063 | + | 0.659410i | ||||
\(412\) | −3.54766e49 | −0.736029 | ||||||||
\(413\) | − | 6.30682e49i | − | 1.24957i | ||||||
\(414\) | 5.08878e49 | + | 6.43170e48i | 0.962957 | + | 0.121708i | ||||
\(415\) | 1.09303e50 | 1.97569 | ||||||||
\(416\) | 1.31199e50i | 2.26546i | ||||||||
\(417\) | 2.05526e49 | + | 1.29367e48i | 0.339064 | + | 0.0213422i | ||||
\(418\) | 1.97232e49 | 0.310906 | ||||||||
\(419\) | − | 1.15930e50i | − | 1.74634i | −0.487415 | − | 0.873170i | \(-0.662060\pi\) | ||
0.487415 | − | 0.873170i | \(-0.337940\pi\) | |||||||
\(420\) | −8.23165e48 | + | 1.30776e50i | −0.118509 | + | 1.88275i | ||||
\(421\) | −1.23857e50 | −1.70436 | −0.852179 | − | 0.523251i | \(-0.824719\pi\) | ||||
−0.852179 | + | 0.523251i | \(0.824719\pi\) | |||||||
\(422\) | 5.60373e49i | 0.737125i | ||||||||
\(423\) | 1.43118e47 | − | 1.13235e48i | 0.00179981 | − | 0.0142401i | ||||
\(424\) | −3.20554e48 | −0.0385434 | ||||||||
\(425\) | 9.71044e49i | 1.11648i | ||||||||
\(426\) | −6.15151e49 | − | 3.87204e48i | −0.676393 | − | 0.0425753i | ||||
\(427\) | −2.43957e49 | −0.256557 | ||||||||
\(428\) | − | 2.01072e50i | − | 2.02264i | ||||||
\(429\) | 4.52385e48 | − | 7.18703e49i | 0.0435331 | − | 0.691610i | ||||
\(430\) | −2.37001e50 | −2.18197 | ||||||||
\(431\) | 2.16186e50i | 1.90441i | 0.305463 | + | 0.952204i | \(0.401189\pi\) | ||||
−0.305463 | + | 0.952204i | \(0.598811\pi\) | |||||||
\(432\) | −8.20415e49 | − | 1.56578e49i | −0.691580 | − | 0.131990i | ||||
\(433\) | 2.59340e48 | 0.0209218 | 0.0104609 | − | 0.999945i | \(-0.496670\pi\) | ||||
0.0104609 | + | 0.999945i | \(0.496670\pi\) | |||||||
\(434\) | 9.79296e49i | 0.756152i | ||||||||
\(435\) | 2.87422e50 | + | 1.80917e49i | 2.12434 | + | 0.133716i | ||||
\(436\) | 3.86162e49 | 0.273229 | ||||||||
\(437\) | − | 4.61034e49i | − | 0.312310i | ||||||
\(438\) | 2.54357e49 | − | 4.04096e50i | 0.164981 | − | 2.62106i | ||||
\(439\) | 2.42061e50 | 1.50348 | 0.751742 | − | 0.659457i | \(-0.229214\pi\) | ||||
0.751742 | + | 0.659457i | \(0.229214\pi\) | |||||||
\(440\) | − | 4.17915e49i | − | 0.248592i | ||||||
\(441\) | −1.86616e49 | − | 2.35864e48i | −0.106320 | − | 0.0134378i | ||||
\(442\) | −3.07776e50 | −1.67962 | ||||||||
\(443\) | 8.62313e49i | 0.450811i | 0.974265 | + | 0.225405i | \(0.0723707\pi\) | ||||
−0.974265 | + | 0.225405i | \(0.927629\pi\) | |||||||
\(444\) | 1.68550e50 | + | 1.06093e49i | 0.844215 | + | 0.0531388i | ||||
\(445\) | −2.30909e50 | −1.10816 | ||||||||
\(446\) | − | 1.87026e50i | − | 0.860082i | ||||||
\(447\) | −1.35121e48 | + | 2.14667e49i | −0.00595497 | + | 0.0946066i | ||||
\(448\) | 3.14760e50 | 1.32953 | ||||||||
\(449\) | 3.61936e50i | 1.46538i | 0.680560 | + | 0.732692i | \(0.261736\pi\) | ||||
−0.680560 | + | 0.732692i | \(0.738264\pi\) | |||||||
\(450\) | −7.72030e49 | + | 6.10832e50i | −0.299638 | + | 2.37074i | ||||
\(451\) | 1.92060e50 | 0.714634 | ||||||||
\(452\) | 2.35895e50i | 0.841568i | ||||||||
\(453\) | −2.99492e50 | − | 1.88514e49i | −1.02452 | − | 0.0644877i | ||||
\(454\) | 5.90825e50 | 1.93820 | ||||||||
\(455\) | − | 7.77137e50i | − | 2.44501i | ||||||
\(456\) | 3.58238e48 | − | 5.69132e49i | 0.0108103 | − | 0.171744i | ||||
\(457\) | 2.96698e50 | 0.858830 | 0.429415 | − | 0.903107i | \(-0.358720\pi\) | ||||
0.429415 | + | 0.903107i | \(0.358720\pi\) | |||||||
\(458\) | 1.53498e50i | 0.426243i | ||||||||
\(459\) | 4.91937e49 | − | 2.57757e50i | 0.131059 | − | 0.686704i | ||||
\(460\) | −5.06638e50 | −1.29509 | ||||||||
\(461\) | − | 2.23978e50i | − | 0.549399i | −0.961530 | − | 0.274700i | \(-0.911422\pi\) | ||
0.961530 | − | 0.274700i | \(-0.0885784\pi\) | |||||||
\(462\) | −2.58703e50 | − | 1.62839e49i | −0.608980 | − | 0.0383320i | ||||
\(463\) | −3.71785e50 | −0.839948 | −0.419974 | − | 0.907536i | \(-0.637961\pi\) | ||||
−0.419974 | + | 0.907536i | \(0.637961\pi\) | |||||||
\(464\) | − | 4.28843e50i | − | 0.929943i | ||||||
\(465\) | −2.60107e49 | + | 4.13232e50i | −0.0541434 | + | 0.860177i | ||||
\(466\) | 6.68997e49 | 0.133688 | ||||||||
\(467\) | 3.00718e50i | 0.576950i | 0.957487 | + | 0.288475i | \(0.0931482\pi\) | ||||
−0.957487 | + | 0.288475i | \(0.906852\pi\) | |||||||
\(468\) | −1.07131e51 | − | 1.35403e50i | −1.97353 | − | 0.249435i | ||||
\(469\) | −2.92815e50 | −0.517975 | ||||||||
\(470\) | 2.03736e49i | 0.0346105i | ||||||||
\(471\) | −7.27924e49 | − | 4.58189e48i | −0.118765 | − | 0.00747562i | ||||
\(472\) | 3.01619e50 | 0.472673 | ||||||||
\(473\) | − | 2.59430e50i | − | 0.390533i | ||||||
\(474\) | −9.66636e48 | + | 1.53569e50i | −0.0139789 | + | 0.222083i | ||||
\(475\) | 5.53403e50 | 0.768888 | ||||||||
\(476\) | 6.13033e50i | 0.818374i | ||||||||
\(477\) | −1.05410e49 | + | 8.34008e49i | −0.0135218 | + | 0.106985i | ||||
\(478\) | 7.99662e50 | 0.985772 | ||||||||
\(479\) | − | 1.86336e49i | − | 0.0220760i | −0.999939 | − | 0.0110380i | \(-0.996486\pi\) | ||
0.999939 | − | 0.0110380i | \(-0.00351358\pi\) | |||||||
\(480\) | 1.99279e51 | + | 1.25435e50i | 2.26922 | + | 0.142835i | ||||
\(481\) | −1.00161e51 | −1.09633 | ||||||||
\(482\) | 1.16005e51i | 1.22062i | ||||||||
\(483\) | −3.80639e49 | + | 6.04722e50i | −0.0385051 | + | 0.611730i | ||||
\(484\) | −1.03651e51 | −1.00812 | ||||||||
\(485\) | − | 8.64947e50i | − | 0.808903i | ||||||
\(486\) | 5.14382e50 | − | 1.58230e51i | 0.462590 | − | 1.42298i | ||||
\(487\) | 1.36286e51 | 1.17869 | 0.589347 | − | 0.807880i | \(-0.299385\pi\) | ||||
0.589347 | + | 0.807880i | \(0.299385\pi\) | |||||||
\(488\) | − | 1.16671e50i | − | 0.0970478i | ||||||
\(489\) | −1.83642e51 | − | 1.15593e50i | −1.46928 | − | 0.0924832i | ||||
\(490\) | 3.35765e50 | 0.258410 | ||||||||
\(491\) | 2.61038e50i | 0.193266i | 0.995320 | + | 0.0966330i | \(0.0308073\pi\) | ||||
−0.995320 | + | 0.0966330i | \(0.969193\pi\) | |||||||
\(492\) | 1.80920e50 | − | 2.87428e51i | 0.128869 | − | 2.04735i | ||||
\(493\) | 1.34733e51 | 0.923388 | ||||||||
\(494\) | 1.75403e51i | 1.15671i | ||||||||
\(495\) | −1.08732e51 | − | 1.37426e50i | −0.690014 | − | 0.0872108i | ||||
\(496\) | 6.16555e50 | 0.376547 | ||||||||
\(497\) | − | 7.28114e50i | − | 0.427985i | ||||||
\(498\) | 3.23590e51 | + | 2.03683e50i | 1.83079 | + | 0.115238i | ||||
\(499\) | −1.22608e51 | −0.667740 | −0.333870 | − | 0.942619i | \(-0.608355\pi\) | ||||
−0.333870 | + | 0.942619i | \(0.608355\pi\) | |||||||
\(500\) | − | 2.27344e51i | − | 1.19194i | ||||||
\(501\) | −2.02100e50 | + | 3.21077e51i | −0.102012 | + | 1.62066i | ||||
\(502\) | −3.94045e51 | −1.91503 | ||||||||
\(503\) | 4.03344e51i | 1.88749i | 0.330680 | + | 0.943743i | \(0.392722\pi\) | ||||
−0.330680 | + | 0.943743i | \(0.607278\pi\) | |||||||
\(504\) | −9.39775e49 | + | 7.43553e50i | −0.0423491 | + | 0.335067i | ||||
\(505\) | −4.88057e51 | −2.11804 | ||||||||
\(506\) | − | 1.00224e51i | − | 0.418900i | ||||||
\(507\) | 3.91250e51 | + | 2.46271e50i | 1.57508 | + | 0.0991429i | ||||
\(508\) | −2.05175e51 | −0.795636 | ||||||||
\(509\) | − | 2.06249e51i | − | 0.770467i | −0.922819 | − | 0.385234i | \(-0.874121\pi\) | ||
0.922819 | − | 0.385234i | \(-0.125879\pi\) | |||||||
\(510\) | −2.94255e50 | + | 4.67483e51i | −0.105899 | + | 1.68241i | ||||
\(511\) | 4.78303e51 | 1.65846 | ||||||||
\(512\) | − | 3.72653e51i | − | 1.24502i | ||||||
\(513\) | −1.46897e51 | − | 2.80357e50i | −0.472916 | − | 0.0902573i | ||||
\(514\) | −3.59475e51 | −1.11524 | ||||||||
\(515\) | − | 3.20215e51i | − | 0.957425i | ||||||
\(516\) | −3.88249e51 | − | 2.44381e50i | −1.11883 | − | 0.0704245i | ||||
\(517\) | −2.23017e49 | −0.00619465 | ||||||||
\(518\) | 3.60537e51i | 0.965349i | ||||||||
\(519\) | 3.09113e50 | − | 4.91088e51i | 0.0797881 | − | 1.26759i | ||||
\(520\) | 3.71661e51 | 0.924876 | ||||||||
\(521\) | − | 4.54680e51i | − | 1.09091i | −0.838140 | − | 0.545455i | \(-0.816357\pi\) | ||
0.838140 | − | 0.545455i | \(-0.183643\pi\) | |||||||
\(522\) | 8.47537e51 | + | 1.07120e51i | 1.96074 | + | 0.247817i | ||||
\(523\) | 7.86068e51 | 1.75359 | 0.876795 | − | 0.480865i | \(-0.159677\pi\) | ||||
0.876795 | + | 0.480865i | \(0.159677\pi\) | |||||||
\(524\) | 3.88147e51i | 0.835028i | ||||||||
\(525\) | −7.25878e51 | − | 4.56901e50i | −1.50604 | − | 0.0947972i | ||||
\(526\) | −2.44087e51 | −0.488444 | ||||||||
\(527\) | 1.93709e51i | 0.373893i | ||||||||
\(528\) | −1.02522e50 | + | 1.62877e51i | −0.0190885 | + | 0.303259i | ||||
\(529\) | 3.22473e51 | 0.579209 | ||||||||
\(530\) | − | 1.50057e51i | − | 0.260025i | ||||||
\(531\) | 9.91838e50 | − | 7.84744e51i | 0.165823 | − | 1.31200i | ||||
\(532\) | 3.49371e51 | 0.563593 | ||||||||
\(533\) | 1.70804e52i | 2.65877i | ||||||||
\(534\) | −6.83603e51 | − | 4.30291e50i | −1.02688 | − | 0.0646366i | ||||
\(535\) | 1.81489e52 | 2.63105 | ||||||||
\(536\) | − | 1.40037e51i | − | 0.195934i | ||||||
\(537\) | 2.07848e50 | − | 3.30207e51i | 0.0280694 | − | 0.445939i | ||||
\(538\) | −1.69965e52 | −2.21563 | ||||||||
\(539\) | 3.67540e50i | 0.0462507i | ||||||||
\(540\) | −3.08089e51 | + | 1.61428e52i | −0.374279 | + | 1.96109i | ||||
\(541\) | −1.20983e52 | −1.41898 | −0.709488 | − | 0.704717i | \(-0.751074\pi\) | ||||
−0.709488 | + | 0.704717i | \(0.751074\pi\) | |||||||
\(542\) | − | 9.12869e51i | − | 1.03377i | ||||||
\(543\) | −2.55657e51 | − | 1.60922e50i | −0.279551 | − | 0.0175962i | ||||
\(544\) | 9.34149e51 | 0.986364 | ||||||||
\(545\) | 3.48554e51i | 0.355415i | ||||||||
\(546\) | 1.44817e51 | − | 2.30070e52i | 0.142613 | − | 2.26569i | ||||
\(547\) | −1.38323e52 | −1.31563 | −0.657817 | − | 0.753178i | \(-0.728520\pi\) | ||||
−0.657817 | + | 0.753178i | \(0.728520\pi\) | |||||||
\(548\) | − | 8.90990e51i | − | 0.818545i | ||||||
\(549\) | −3.03551e51 | − | 3.83658e50i | −0.269375 | − | 0.0340462i | ||||
\(550\) | 1.20303e52 | 1.03130 | ||||||||
\(551\) | − | 7.67853e51i | − | 0.635913i | ||||||
\(552\) | −2.89204e51 | − | 1.82038e50i | −0.231399 | − | 0.0145653i | ||||
\(553\) | −1.81770e51 | −0.140522 | ||||||||
\(554\) | 4.07606e51i | 0.304477i | ||||||||
\(555\) | −9.57609e50 | + | 1.52135e52i | −0.0691228 | + | 1.09815i | ||||
\(556\) | −6.03377e51 | −0.420889 | ||||||||
\(557\) | − | 5.55345e50i | − | 0.0374382i | −0.999825 | − | 0.0187191i | \(-0.994041\pi\) | ||
0.999825 | − | 0.0187191i | \(-0.00595882\pi\) | |||||||
\(558\) | −1.54008e51 | + | 1.21852e52i | −0.100345 | + | 0.793930i | ||||
\(559\) | 2.30717e52 | 1.45296 | ||||||||
\(560\) | 1.76119e52i | 1.07210i | ||||||||
\(561\) | −5.11724e51 | − | 3.22103e50i | −0.301121 | − | 0.0189540i | ||||
\(562\) | −2.38382e51 | −0.135607 | ||||||||
\(563\) | 2.22042e52i | 1.22117i | 0.791950 | + | 0.610585i | \(0.209066\pi\) | ||||
−0.791950 | + | 0.610585i | \(0.790934\pi\) | |||||||
\(564\) | −2.10081e49 | + | 3.33755e50i | −0.00111708 | + | 0.0177470i | ||||
\(565\) | −2.12922e52 | −1.09471 | ||||||||
\(566\) | − | 3.78461e52i | − | 1.88152i | ||||||
\(567\) | 1.90365e52 | + | 4.89016e51i | 0.915185 | + | 0.235096i | ||||
\(568\) | 3.48216e51 | 0.161894 | ||||||||
\(569\) | − | 3.40546e52i | − | 1.53124i | −0.643295 | − | 0.765618i | \(-0.722433\pi\) | ||
0.643295 | − | 0.765618i | \(-0.277567\pi\) | |||||||
\(570\) | 2.66421e52 | + | 1.67698e51i | 1.15863 | + | 0.0729298i | ||||
\(571\) | 1.11181e52 | 0.467676 | 0.233838 | − | 0.972276i | \(-0.424871\pi\) | ||||
0.233838 | + | 0.972276i | \(0.424871\pi\) | |||||||
\(572\) | 2.10995e52i | 0.858514i | ||||||||
\(573\) | −1.24625e51 | + | 1.97992e52i | −0.0490533 | + | 0.779310i | ||||
\(574\) | 6.14821e52 | 2.34111 | ||||||||
\(575\) | − | 2.81211e52i | − | 1.03596i | ||||||
\(576\) | 3.91650e52 | + | 4.95006e51i | 1.39595 | + | 0.176434i | ||||
\(577\) | −4.20380e52 | −1.44978 | −0.724889 | − | 0.688866i | \(-0.758109\pi\) | ||||
−0.724889 | + | 0.688866i | \(0.758109\pi\) | |||||||
\(578\) | − | 2.29238e52i | − | 0.764992i | ||||||
\(579\) | −2.73995e52 | − | 1.72465e51i | −0.884811 | − | 0.0556941i | ||||
\(580\) | −8.43806e52 | −2.63700 | ||||||||
\(581\) | 3.83013e52i | 1.15842i | ||||||||
\(582\) | 1.61180e51 | − | 2.56066e52i | 0.0471817 | − | 0.749575i | ||||
\(583\) | 1.64258e51 | 0.0465398 | ||||||||
\(584\) | 2.28745e52i | 0.627347i | ||||||||
\(585\) | 1.22216e52 | − | 9.66977e52i | 0.324464 | − | 2.56717i | ||||
\(586\) | −6.78925e52 | −1.74489 | ||||||||
\(587\) | − | 2.39246e52i | − | 0.595280i | −0.954678 | − | 0.297640i | \(-0.903800\pi\) | ||
0.954678 | − | 0.297640i | \(-0.0961996\pi\) | |||||||
\(588\) | 5.50041e51 | + | 3.46221e50i | 0.132503 | + | 0.00834035i | ||||
\(589\) | 1.10396e52 | 0.257490 | ||||||||
\(590\) | 1.41193e53i | 3.18879i | ||||||||
\(591\) | −3.88074e51 | + | 6.16534e52i | −0.0848697 | + | 1.34832i | ||||
\(592\) | 2.26990e52 | 0.480723 | ||||||||
\(593\) | 3.91007e52i | 0.801946i | 0.916090 | + | 0.400973i | \(0.131328\pi\) | ||||
−0.916090 | + | 0.400973i | \(0.868672\pi\) | |||||||
\(594\) | −3.19338e52 | − | 6.09465e51i | −0.634319 | − | 0.121062i | ||||
\(595\) | −5.53330e52 | −1.06454 | ||||||||
\(596\) | − | 6.30212e51i | − | 0.117438i | ||||||
\(597\) | 3.28069e52 | + | 2.06502e51i | 0.592179 | + | 0.0372744i | ||||
\(598\) | 8.91311e52 | 1.55850 | ||||||||
\(599\) | − | 2.82304e52i | − | 0.478197i | −0.970995 | − | 0.239099i | \(-0.923148\pi\) | ||
0.970995 | − | 0.239099i | \(-0.0768519\pi\) | |||||||
\(600\) | 2.18510e51 | − | 3.47147e52i | 0.0358589 | − | 0.569691i | ||||
\(601\) | 5.62593e52 | 0.894497 | 0.447249 | − | 0.894410i | \(-0.352404\pi\) | ||||
0.447249 | + | 0.894410i | \(0.352404\pi\) | |||||||
\(602\) | − | 8.30482e52i | − | 1.27937i | ||||||
\(603\) | −3.64343e52 | − | 4.60493e51i | −0.543853 | − | 0.0687376i | ||||
\(604\) | 8.79240e52 | 1.27176 | ||||||||
\(605\) | − | 9.35566e52i | − | 1.31136i | ||||||
\(606\) | −1.44488e53 | − | 9.09476e51i | −1.96270 | − | 0.123541i | ||||
\(607\) | −1.00427e53 | −1.32210 | −0.661051 | − | 0.750341i | \(-0.729889\pi\) | ||||
−0.661051 | + | 0.750341i | \(0.729889\pi\) | |||||||
\(608\) | − | 5.32376e52i | − | 0.679283i | ||||||
\(609\) | −6.33956e51 | + | 1.00716e53i | −0.0784026 | + | 1.24558i | ||||
\(610\) | 5.46157e52 | 0.654713 | ||||||||
\(611\) | − | 1.98334e51i | − | 0.0230470i | ||||||
\(612\) | −9.64083e51 | + | 7.62785e52i | −0.108602 | + | 0.859261i | ||||
\(613\) | 9.17938e52 | 1.00245 | 0.501227 | − | 0.865316i | \(-0.332882\pi\) | ||||
0.501227 | + | 0.865316i | \(0.332882\pi\) | |||||||
\(614\) | − | 1.41430e52i | − | 0.149742i | ||||||
\(615\) | 2.59435e53 | + | 1.63300e52i | 2.66318 | + | 0.167633i | ||||
\(616\) | 1.46443e52 | 0.145759 | ||||||||
\(617\) | 1.23754e53i | 1.19438i | 0.802101 | + | 0.597189i | \(0.203716\pi\) | ||||
−0.802101 | + | 0.597189i | \(0.796284\pi\) | |||||||
\(618\) | 5.96709e51 | − | 9.47992e52i | 0.0558447 | − | 0.887204i | ||||
\(619\) | 1.86035e52 | 0.168839 | 0.0844195 | − | 0.996430i | \(-0.473096\pi\) | ||||
0.0844195 | + | 0.996430i | \(0.473096\pi\) | |||||||
\(620\) | − | 1.21315e53i | − | 1.06776i | ||||||
\(621\) | −1.42463e52 | + | 7.46457e52i | −0.121608 | + | 0.637183i | ||||
\(622\) | −3.99560e52 | −0.330799 | ||||||||
\(623\) | − | 8.09137e52i | − | 0.649754i | ||||||
\(624\) | −1.44850e53 | − | 9.11751e51i | −1.12826 | − | 0.0710181i | ||||
\(625\) | −6.16050e51 | −0.0465474 | ||||||||
\(626\) | 3.07143e53i | 2.25128i | ||||||||
\(627\) | −1.83568e51 | + | 2.91634e52i | −0.0130531 | + | 0.207375i | ||||
\(628\) | 2.13702e52 | 0.147426 | ||||||||
\(629\) | 7.13157e52i | 0.477335i | ||||||||
\(630\) | −3.48070e53 | − | 4.39926e52i | −2.26046 | − | 0.285699i | ||||
\(631\) | 7.67791e52 | 0.483822 | 0.241911 | − | 0.970298i | \(-0.422226\pi\) | ||||
0.241911 | + | 0.970298i | \(0.422226\pi\) | |||||||
\(632\) | − | 8.69304e51i | − | 0.0531554i | ||||||
\(633\) | −8.28586e52 | − | 5.21550e51i | −0.491663 | − | 0.0309475i | ||||
\(634\) | −9.17796e52 | −0.528507 | ||||||||
\(635\) | − | 1.85193e53i | − | 1.03496i | ||||||
\(636\) | 1.54730e51 | − | 2.45820e52i | 0.00839247 | − | 0.133331i | ||||
\(637\) | −3.26862e52 | −0.172074 | ||||||||
\(638\) | − | 1.66922e53i | − | 0.852947i | ||||||
\(639\) | 1.14506e52 | − | 9.05978e52i | 0.0567955 | − | 0.449367i | ||||
\(640\) | −2.32436e53 | −1.11914 | ||||||||
\(641\) | − | 8.05357e52i | − | 0.376431i | −0.982128 | − | 0.188216i | \(-0.939730\pi\) | ||
0.982128 | − | 0.188216i | \(-0.0602704\pi\) | |||||||
\(642\) | 5.37296e53 | + | 3.38199e52i | 2.43808 | + | 0.153464i | ||||
\(643\) | −4.12888e52 | −0.181896 | −0.0909481 | − | 0.995856i | \(-0.528990\pi\) | ||||
−0.0909481 | + | 0.995856i | \(0.528990\pi\) | |||||||
\(644\) | − | 1.77533e53i | − | 0.759358i | ||||||
\(645\) | 2.20581e52 | − | 3.50437e53i | 0.0916080 | − | 1.45538i | ||||
\(646\) | 1.24889e53 | 0.503624 | ||||||||
\(647\) | 4.04774e53i | 1.58501i | 0.609867 | + | 0.792504i | \(0.291223\pi\) | ||||
−0.609867 | + | 0.792504i | \(0.708777\pi\) | |||||||
\(648\) | −2.33869e52 | + | 9.10408e52i | −0.0889297 | + | 0.346187i | ||||
\(649\) | −1.54556e53 | −0.570736 | ||||||||
\(650\) | 1.06989e54i | 3.83693i | ||||||||
\(651\) | −1.44802e53 | − | 9.11449e51i | −0.504354 | − | 0.0317463i | ||||
\(652\) | 5.39133e53 | 1.82386 | ||||||||
\(653\) | − | 4.23994e53i | − | 1.39319i | −0.717466 | − | 0.696593i | \(-0.754698\pi\) | ||
0.717466 | − | 0.696593i | \(-0.245302\pi\) | |||||||
\(654\) | −6.49517e51 | + | 1.03189e53i | −0.0207307 | + | 0.329348i | ||||
\(655\) | −3.50345e53 | −1.08620 | ||||||||
\(656\) | − | 3.87085e53i | − | 1.16582i | ||||||
\(657\) | 5.95142e53 | + | 7.52200e52i | 1.74132 | + | 0.220085i | ||||
\(658\) | −7.13917e51 | −0.0202934 | ||||||||
\(659\) | 5.50402e53i | 1.52005i | 0.649895 | + | 0.760024i | \(0.274813\pi\) | ||||
−0.649895 | + | 0.760024i | \(0.725187\pi\) | |||||||
\(660\) | 3.20482e53 | + | 2.01726e52i | 0.859940 | + | 0.0541286i | ||||
\(661\) | −2.36596e53 | −0.616850 | −0.308425 | − | 0.951249i | \(-0.599802\pi\) | ||||
−0.308425 | + | 0.951249i | \(0.599802\pi\) | |||||||
\(662\) | − | 6.34776e53i | − | 1.60812i | ||||||
\(663\) | 2.86453e52 | − | 4.55088e53i | 0.0705175 | − | 1.12031i | ||||
\(664\) | −1.83174e53 | −0.438197 | ||||||||
\(665\) | 3.15346e53i | 0.733121i | ||||||||
\(666\) | −5.66997e52 | + | 4.48609e53i | −0.128106 | + | 1.01358i | ||||
\(667\) | −3.90184e53 | −0.856798 | ||||||||
\(668\) | − | 9.42608e53i | − | 2.01177i | ||||||
\(669\) | 2.76543e53 | + | 1.74069e52i | 0.573675 | + | 0.0361098i | ||||
\(670\) | 6.55537e53 | 1.32183 | ||||||||
\(671\) | 5.97844e52i | 0.117182i | ||||||||
\(672\) | −4.39541e52 | + | 6.98299e53i | −0.0837497 | + | 1.33053i | ||||
\(673\) | 1.52102e53 | 0.281740 | 0.140870 | − | 0.990028i | \(-0.455010\pi\) | ||||
0.140870 | + | 0.990028i | \(0.455010\pi\) | |||||||
\(674\) | − | 5.80598e53i | − | 1.04553i | ||||||
\(675\) | −8.96011e53 | − | 1.71006e53i | −1.56871 | − | 0.299392i | ||||
\(676\) | −1.14862e54 | −1.95519 | ||||||||
\(677\) | − | 4.27880e53i | − | 0.708169i | −0.935213 | − | 0.354084i | \(-0.884793\pi\) | ||
0.935213 | − | 0.354084i | \(-0.115207\pi\) | |||||||
\(678\) | −6.30350e53 | − | 3.96771e52i | −1.01442 | − | 0.0638522i | ||||
\(679\) | 3.03089e53 | 0.474290 | ||||||||
\(680\) | − | 2.64626e53i | − | 0.402684i | ||||||
\(681\) | −5.49892e52 | + | 8.73613e53i | −0.0813734 | + | 1.29278i | ||||
\(682\) | 2.39987e53 | 0.345370 | ||||||||
\(683\) | 6.97682e53i | 0.976482i | 0.872709 | + | 0.488241i | \(0.162361\pi\) | ||||
−0.872709 | + | 0.488241i | \(0.837639\pi\) | |||||||
\(684\) | 4.34715e53 | + | 5.49436e52i | 0.591751 | + | 0.0747913i | ||||
\(685\) | 8.04217e53 | 1.06476 | ||||||||
\(686\) | 1.21555e54i | 1.56536i | ||||||||
\(687\) | −2.26966e53 | − | 1.42863e52i | −0.284305 | − | 0.0178954i | ||||
\(688\) | −5.22863e53 | −0.637100 | ||||||||
\(689\) | 1.46078e53i | 0.173149i | ||||||||
\(690\) | 8.52154e52 | − | 1.35382e54i | 0.0982620 | − | 1.56109i | ||||
\(691\) | −1.52764e54 | −1.71372 | −0.856859 | − | 0.515552i | \(-0.827587\pi\) | ||||
−0.856859 | + | 0.515552i | \(0.827587\pi\) | |||||||
\(692\) | 1.44172e54i | 1.57350i | ||||||||
\(693\) | 4.81559e52 | − | 3.81011e53i | 0.0511350 | − | 0.404581i | ||||
\(694\) | 1.10501e54 | 1.14165 | ||||||||
\(695\) | − | 5.44614e53i | − | 0.547492i | ||||||
\(696\) | −4.81670e53 | − | 3.03185e52i | −0.471166 | − | 0.0296574i | ||||
\(697\) | 1.21614e54 | 1.15761 | ||||||||
\(698\) | − | 7.95719e53i | − | 0.737067i | ||||||
\(699\) | −6.22648e51 | + | 9.89201e52i | −0.00561276 | + | 0.0891699i | ||||
\(700\) | 2.13101e54 | 1.86949 | ||||||||
\(701\) | 8.65568e53i | 0.739024i | 0.929226 | + | 0.369512i | \(0.120475\pi\) | ||||
−0.929226 | + | 0.369512i | \(0.879525\pi\) | |||||||
\(702\) | 5.42011e53 | − | 2.83994e54i | 0.450405 | − | 2.35996i | ||||
\(703\) | 4.06432e53 | 0.328728 | ||||||||
\(704\) | − | 7.71355e53i | − | 0.607259i | ||||||
\(705\) | −3.01250e52 | − | 1.89621e51i | −0.0230852 | − | 0.00145309i | ||||
\(706\) | −1.19646e54 | −0.892504 | ||||||||
\(707\) | − | 1.71022e54i | − | 1.24189i | ||||||
\(708\) | −1.45591e53 | + | 2.31300e54i | −0.102920 | + | 1.63509i | ||||
\(709\) | 1.69444e54 | 1.16613 | 0.583066 | − | 0.812425i | \(-0.301853\pi\) | ||||
0.583066 | + | 0.812425i | \(0.301853\pi\) | |||||||
\(710\) | 1.63006e54i | 1.09218i | ||||||||
\(711\) | −2.26173e53 | − | 2.85860e52i | −0.147543 | − | 0.0186479i | ||||
\(712\) | 3.86964e53 | 0.245783 | ||||||||
\(713\) | − | 5.60974e53i | − | 0.346930i | ||||||
\(714\) | −1.63812e54 | − | 1.03111e53i | −0.986462 | − | 0.0620925i | ||||
\(715\) | −1.90446e54 | −1.11675 | ||||||||
\(716\) | 9.69414e53i | 0.553556i | ||||||||
\(717\) | −7.44261e52 | + | 1.18241e54i | −0.0413867 | + | 0.657511i | ||||
\(718\) | −1.56996e54 | −0.850205 | ||||||||
\(719\) | 4.81902e53i | 0.254162i | 0.991892 | + | 0.127081i | \(0.0405608\pi\) | ||||
−0.991892 | + | 0.127081i | \(0.959439\pi\) | |||||||
\(720\) | −2.76973e53 | + | 2.19142e54i | −0.142272 | + | 1.12566i | ||||
\(721\) | 1.12208e54 | 0.561374 | ||||||||
\(722\) | 2.35884e54i | 1.14945i | ||||||||
\(723\) | −1.71528e54 | − | 1.07968e53i | −0.814157 | − | 0.0512468i | ||||
\(724\) | 7.50552e53 | 0.347015 | ||||||||
\(725\) | − | 4.68358e54i | − | 2.10938i | ||||||
\(726\) | 1.74339e53 | − | 2.76973e54i | 0.0764891 | − | 1.21518i | ||||
\(727\) | 3.91570e54 | 1.67361 | 0.836807 | − | 0.547498i | \(-0.184420\pi\) | ||||
0.836807 | + | 0.547498i | \(0.184420\pi\) | |||||||
\(728\) | 1.30235e54i | 0.542289i | ||||||||
\(729\) | 2.29177e54 | + | 9.07849e53i | 0.929711 | + | 0.368291i | ||||
\(730\) | −1.07080e55 | −4.23227 | ||||||||
\(731\) | − | 1.64273e54i | − | 0.632609i | ||||||
\(732\) | 8.94701e53 | + | 5.63166e52i | 0.335712 | + | 0.0211313i | ||||
\(733\) | 3.14878e54 | 1.15124 | 0.575621 | − | 0.817716i | \(-0.304760\pi\) | ||||
0.575621 | + | 0.817716i | \(0.304760\pi\) | |||||||
\(734\) | − | 1.09158e54i | − | 0.388893i | ||||||
\(735\) | −3.12502e52 | + | 4.96472e53i | −0.0108491 | + | 0.172360i | ||||
\(736\) | −2.70527e54 | −0.915233 | ||||||||
\(737\) | 7.17575e53i | 0.236584i | ||||||||
\(738\) | 7.65009e54 | + | 9.66894e53i | 2.45808 | + | 0.310676i | ||||
\(739\) | −5.09600e54 | −1.59582 | −0.797912 | − | 0.602774i | \(-0.794062\pi\) | ||||
−0.797912 | + | 0.602774i | \(0.794062\pi\) | |||||||
\(740\) | − | 4.46634e54i | − | 1.36317i | ||||||
\(741\) | −2.59357e54 | − | 1.63251e53i | −0.771529 | − | 0.0485635i | ||||
\(742\) | 5.25820e53 | 0.152462 | ||||||||
\(743\) | 3.04691e54i | 0.861137i | 0.902558 | + | 0.430569i | \(0.141687\pi\) | ||||
−0.902558 | + | 0.430569i | \(0.858313\pi\) | |||||||
\(744\) | 4.35895e52 | − | 6.92505e53i | 0.0120087 | − | 0.190782i | ||||
\(745\) | 5.68836e53 | 0.152763 | ||||||||
\(746\) | − | 7.09419e54i | − | 1.85723i | ||||||
\(747\) | −6.02343e53 | + | 4.76576e54i | −0.153728 | + | 1.21630i | ||||
\(748\) | 1.50231e54 | 0.373790 | ||||||||
\(749\) | 6.35962e54i | 1.54268i | ||||||||
\(750\) | 6.07501e54 | + | 3.82389e53i | 1.43676 | + | 0.0904359i | ||||
\(751\) | 2.68533e54 | 0.619211 | 0.309606 | − | 0.950865i | \(-0.399803\pi\) | ||||
0.309606 | + | 0.950865i | \(0.399803\pi\) | |||||||
\(752\) | 4.49475e52i | 0.0101057i | ||||||||
\(753\) | 3.66745e53 | − | 5.82647e54i | 0.0804006 | − | 1.27732i | ||||
\(754\) | 1.48448e55 | 3.17335 | ||||||||
\(755\) | 7.93610e54i | 1.65430i | ||||||||
\(756\) | −5.65664e54 | − | 1.07959e54i | −1.14986 | − | 0.219454i | ||||
\(757\) | −2.41058e54 | −0.477858 | −0.238929 | − | 0.971037i | \(-0.576796\pi\) | ||||
−0.238929 | + | 0.971037i | \(0.576796\pi\) | |||||||
\(758\) | 1.36559e55i | 2.64000i | ||||||||
\(759\) | 1.48194e54 | + | 9.32799e52i | 0.279406 | + | 0.0175871i | ||||
\(760\) | −1.50812e54 | −0.277318 | ||||||||
\(761\) | − | 5.21893e54i | − | 0.935994i | −0.883730 | − | 0.467997i | \(-0.844976\pi\) | ||
0.883730 | − | 0.467997i | \(-0.155024\pi\) | |||||||
\(762\) | 3.45101e53 | − | 5.48261e54i | 0.0603672 | − | 0.959054i | ||||
\(763\) | −1.22138e54 | −0.208393 | ||||||||
\(764\) | − | 5.81260e54i | − | 0.967379i | ||||||
\(765\) | −6.88497e54 | − | 8.70191e53i | −1.11773 | − | 0.141269i | ||||
\(766\) | −1.75883e55 | −2.78533 | ||||||||
\(767\) | − | 1.37450e55i | − | 2.12340i | ||||||
\(768\) | 2.43665e54 | + | 1.53374e53i | 0.367223 | + | 0.0231147i | ||||
\(769\) | −9.27367e54 | −1.36349 | −0.681744 | − | 0.731591i | \(-0.738778\pi\) | ||||
−0.681744 | + | 0.731591i | \(0.738778\pi\) | |||||||
\(770\) | 6.85525e54i | 0.983331i | ||||||||
\(771\) | 3.34570e53 | − | 5.31531e54i | 0.0468224 | − | 0.743868i | ||||
\(772\) | 8.04388e54 | 1.09834 | ||||||||
\(773\) | 1.03769e55i | 1.38248i | 0.722626 | + | 0.691239i | \(0.242935\pi\) | ||||
−0.722626 | + | 0.691239i | \(0.757065\pi\) | |||||||
\(774\) | 1.30605e54 | − | 1.03335e55i | 0.169778 | − | 1.34329i | ||||
\(775\) | 6.73366e54 | 0.854120 | ||||||||
\(776\) | 1.44950e54i | 0.179410i | ||||||||
\(777\) | −5.33102e54 | − | 3.35559e53i | −0.643889 | − | 0.0405293i | ||||
\(778\) | 4.77896e54 | 0.563276 | ||||||||
\(779\) | − | 6.93085e54i | − | 0.797214i | ||||||
\(780\) | −1.79399e54 | + | 2.85012e55i | −0.201383 | + | 3.19937i | ||||
\(781\) | −1.78432e54 | −0.195481 | ||||||||
\(782\) | − | 6.34622e54i | − | 0.678558i | ||||||
\(783\) | −2.37273e54 | + | 1.24323e55i | −0.247614 | + | 1.29741i | ||||
\(784\) | 7.40752e53 | 0.0754515 | ||||||||
\(785\) | 1.92890e54i | 0.191772i | ||||||||
\(786\) | −1.03719e55 | − | 6.52855e53i | −1.00654 | − | 0.0633561i | ||||
\(787\) | 1.45876e55 | 1.38186 | 0.690929 | − | 0.722922i | \(-0.257202\pi\) | ||||
0.690929 | + | 0.722922i | \(0.257202\pi\) | |||||||
\(788\) | − | 1.81000e55i | − | 1.67371i | ||||||
\(789\) | 2.27176e53 | − | 3.60915e54i | 0.0205069 | − | 0.325793i | ||||
\(790\) | 4.06937e54 | 0.358602 | ||||||||
\(791\) | − | 7.46105e54i | − | 0.641870i | ||||||
\(792\) | 1.82216e54 | + | 2.30302e53i | 0.153041 | + | 0.0193428i | ||||
\(793\) | −5.31676e54 | −0.435970 | ||||||||
\(794\) | 2.34033e55i | 1.87365i | ||||||||
\(795\) | 2.21879e54 | + | 1.39661e53i | 0.173437 | + | 0.0109169i | ||||
\(796\) | −9.63136e54 | −0.735088 | ||||||||
\(797\) | 1.87556e55i | 1.39773i | 0.715253 | + | 0.698866i | \(0.246311\pi\) | ||||
−0.715253 | + | 0.698866i | \(0.753689\pi\) | |||||||
\(798\) | −5.87635e53 | + | 9.33575e54i | −0.0427615 | + | 0.679351i | ||||
\(799\) | −1.41216e53 | −0.0100345 | ||||||||
\(800\) | − | 3.24727e55i | − | 2.25325i | ||||||
\(801\) | 1.27248e54 | − | 1.00679e55i | 0.0862253 | − | 0.682217i | ||||
\(802\) | 3.99558e55 | 2.64403 | ||||||||
\(803\) | − | 1.17213e55i | − | 0.757499i | ||||||
\(804\) | 1.07388e55 | + | 6.75952e53i | 0.677786 | + | 0.0426629i | ||||
\(805\) | 1.60243e55 | 0.987771 | ||||||||
\(806\) | 2.13426e55i | 1.28494i | ||||||||
\(807\) | 1.58190e54 | − | 2.51316e55i | 0.0930212 | − | 1.47783i | ||||
\(808\) | 8.17899e54 | 0.469769 | ||||||||
\(809\) | − | 1.55621e55i | − | 0.873066i | −0.899688 | − | 0.436533i | \(-0.856206\pi\) | ||
0.899688 | − | 0.436533i | \(-0.143794\pi\) | |||||||
\(810\) | −4.26179e55 | − | 1.09478e55i | −2.33548 | − | 0.599946i | ||||
\(811\) | −3.06479e55 | −1.64061 | −0.820304 | − | 0.571928i | \(-0.806196\pi\) | ||||
−0.820304 | + | 0.571928i | \(0.806196\pi\) | |||||||
\(812\) | − | 2.95681e55i | − | 1.54617i | ||||||
\(813\) | 1.34980e55 | + | 8.49625e53i | 0.689522 | + | 0.0434017i | ||||
\(814\) | 8.83536e54 | 0.440921 | ||||||||
\(815\) | 4.86626e55i | 2.37247i | ||||||||
\(816\) | −6.49176e53 | + | 1.03135e55i | −0.0309207 | + | 0.491237i | ||||
\(817\) | −9.36198e54 | −0.435661 | ||||||||
\(818\) | 3.88716e55i | 1.76734i | ||||||||
\(819\) | 3.38841e55 | + | 4.28261e54i | 1.50523 | + | 0.190246i | ||||
\(820\) | −7.61642e55 | −3.30588 | ||||||||
\(821\) | 1.63860e55i | 0.694951i | 0.937689 | + | 0.347475i | \(0.112961\pi\) | ||||
−0.937689 | + | 0.347475i | \(0.887039\pi\) | |||||||
\(822\) | 2.38087e55 | + | 1.49863e54i | 0.986668 | + | 0.0621054i | ||||
\(823\) | −5.01161e54 | −0.202946 | −0.101473 | − | 0.994838i | \(-0.532356\pi\) | ||||
−0.101473 | + | 0.994838i | \(0.532356\pi\) | |||||||
\(824\) | 5.36626e54i | 0.212351i | ||||||||
\(825\) | −1.11969e54 | + | 1.77885e55i | −0.0432984 | + | 0.687881i | ||||
\(826\) | −4.94761e55 | −1.86971 | ||||||||
\(827\) | 1.88297e55i | 0.695407i | 0.937605 | + | 0.347704i | \(0.113038\pi\) | ||||
−0.937605 | + | 0.347704i | \(0.886962\pi\) | |||||||
\(828\) | 2.79196e54 | − | 2.20900e55i | 0.100770 | − | 0.797296i | ||||
\(829\) | −2.14483e55 | −0.756585 | −0.378292 | − | 0.925686i | \(-0.623489\pi\) | ||||
−0.378292 | + | 0.925686i | \(0.623489\pi\) | |||||||
\(830\) | − | 8.57468e55i | − | 2.95620i | ||||||
\(831\) | −6.02699e54 | − | 3.79366e53i | −0.203086 | − | 0.0127832i | ||||
\(832\) | 6.85984e55 | 2.25928 | ||||||||
\(833\) | 2.32729e54i | 0.0749196i | ||||||||
\(834\) | 1.01487e54 | − | 1.61232e55i | 0.0319341 | − | 0.507337i | ||||
\(835\) | 8.50808e55 | 2.61691 | ||||||||
\(836\) | − | 8.56172e54i | − | 0.257420i | ||||||
\(837\) | −1.78741e55 | − | 3.41132e54i | −0.525339 | − | 0.100262i | ||||
\(838\) | −9.09453e55 | −2.61303 | ||||||||
\(839\) | 2.48552e54i | 0.0698136i | 0.999391 | + | 0.0349068i | \(0.0111134\pi\) | ||||
−0.999391 | + | 0.0349068i | \(0.988887\pi\) | |||||||
\(840\) | 1.97815e55 | + | 1.24514e54i | 0.543190 | + | 0.0341909i | ||||
\(841\) | −2.77354e55 | −0.744579 | ||||||||
\(842\) | 9.71640e55i | 2.55021i | ||||||||
\(843\) | 2.21867e53 | − | 3.52479e54i | 0.00569335 | − | 0.0904502i | ||||
\(844\) | 2.43254e55 | 0.610314 | ||||||||
\(845\) | − | 1.03676e56i | − | 2.54331i | ||||||
\(846\) | −8.88313e53 | − | 1.12274e53i | −0.0213073 | − | 0.00269303i | ||||
\(847\) | 3.27835e55 | 0.768901 | ||||||||
\(848\) | − | 3.31051e54i | − | 0.0759230i | ||||||
\(849\) | 5.59604e55 | + | 3.52240e54i | 1.25497 | + | 0.0789938i | ||||
\(850\) | 7.61770e55 | 1.67057 | ||||||||
\(851\) | − | 2.06528e55i | − | 0.442912i | ||||||
\(852\) | −1.68082e54 | + | 2.67033e55i | −0.0352509 | + | 0.560031i | ||||
\(853\) | −1.68012e55 | −0.344594 | −0.172297 | − | 0.985045i | \(-0.555119\pi\) | ||||
−0.172297 | + | 0.985045i | \(0.555119\pi\) | |||||||
\(854\) | 1.91381e55i | 0.383883i | ||||||||
\(855\) | −4.95927e54 | + | 3.92378e55i | −0.0972884 | + | 0.769748i | ||||
\(856\) | −3.04145e55 | −0.583551 | ||||||||
\(857\) | − | 5.32727e55i | − | 0.999699i | −0.866112 | − | 0.499850i | \(-0.833389\pi\) | ||
0.866112 | − | 0.499850i | \(-0.166611\pi\) | |||||||
\(858\) | −5.63812e55 | − | 3.54889e54i | −1.03485 | − | 0.0651380i | ||||
\(859\) | −5.11449e55 | −0.918190 | −0.459095 | − | 0.888387i | \(-0.651826\pi\) | ||||
−0.459095 | + | 0.888387i | \(0.651826\pi\) | |||||||
\(860\) | 1.02880e56i | 1.80660i | ||||||||
\(861\) | −5.72225e54 | + | 9.09094e55i | −0.0982895 | + | 1.56152i | ||||
\(862\) | 1.69595e56 | 2.84954 | ||||||||
\(863\) | − | 8.75182e55i | − | 1.43845i | −0.694780 | − | 0.719223i | \(-0.744498\pi\) | ||
0.694780 | − | 0.719223i | \(-0.255502\pi\) | |||||||
\(864\) | −1.64509e55 | + | 8.61967e55i | −0.264501 | + | 1.38589i | ||||
\(865\) | −1.30131e56 | −2.04680 | ||||||||
\(866\) | − | 2.03448e54i | − | 0.0313050i | ||||||
\(867\) | 3.38958e55 | + | 2.13356e54i | 0.510251 | + | 0.0321175i | ||||
\(868\) | 4.25105e55 | 0.626068 | ||||||||
\(869\) | 4.45448e54i | 0.0641832i | ||||||||
\(870\) | 1.41926e55 | − | 2.25478e56i | 0.200077 | − | 3.17863i | ||||
\(871\) | −6.38155e55 | −0.880200 | ||||||||
\(872\) | − | 5.84116e54i | − | 0.0788290i | ||||||
\(873\) | 3.77128e55 | + | 4.76651e54i | 0.497987 | + | 0.0629405i | ||||
\(874\) | −3.61675e55 | −0.467305 | ||||||||
\(875\) | 7.19059e55i | 0.909100i | ||||||||
\(876\) | −1.75415e56 | − | 1.10414e55i | −2.17015 | − | 0.136599i | ||||
\(877\) | −6.75242e55 | −0.817461 | −0.408731 | − | 0.912655i | \(-0.634028\pi\) | ||||
−0.408731 | + | 0.912655i | \(0.634028\pi\) | |||||||
\(878\) | − | 1.89893e56i | − | 2.24964i | ||||||
\(879\) | 6.31888e54 | − | 1.00388e56i | 0.0732574 | − | 1.16384i | ||||
\(880\) | 4.31600e55 | 0.489678 | ||||||||
\(881\) | 1.35710e56i | 1.50685i | 0.657533 | + | 0.753426i | \(0.271600\pi\) | ||||
−0.657533 | + | 0.753426i | \(0.728400\pi\) | |||||||
\(882\) | −1.85032e54 | + | 1.46397e55i | −0.0201068 | + | 0.159085i | ||||
\(883\) | 1.63496e56 | 1.73881 | 0.869407 | − | 0.494096i | \(-0.164501\pi\) | ||||
0.869407 | + | 0.494096i | \(0.164501\pi\) | |||||||
\(884\) | 1.33604e56i | 1.39067i | ||||||||
\(885\) | −2.08773e56 | − | 1.31411e55i | −2.12693 | − | 0.133879i | ||||
\(886\) | 6.76472e55 | 0.674543 | ||||||||
\(887\) | 5.14800e55i | 0.502446i | 0.967929 | + | 0.251223i | \(0.0808328\pi\) | ||||
−0.967929 | + | 0.251223i | \(0.919167\pi\) | |||||||
\(888\) | 1.60479e54 | − | 2.54952e55i | 0.0153310 | − | 0.243564i | ||||
\(889\) | 6.48941e55 | 0.606837 | ||||||||
\(890\) | 1.81145e56i | 1.65812i | ||||||||
\(891\) | 1.19839e55 | − | 4.66511e55i | 0.107379 | − | 0.418009i | ||||
\(892\) | −8.11867e55 | −0.712119 | ||||||||
\(893\) | 8.04796e53i | 0.00691048i | ||||||||
\(894\) | 1.68403e55 | + | 1.06000e54i | 0.141559 | + | 0.00891035i | ||||
\(895\) | −8.75002e55 | −0.720065 | ||||||||
\(896\) | − | 8.14487e55i | − | 0.656193i | ||||||
\(897\) | −8.29560e54 | + | 1.31792e56i | −0.0654321 | + | 1.03952i | ||||
\(898\) | 2.83934e56 | 2.19264 | ||||||||
\(899\) | − | 9.34304e55i | − | 0.706405i | ||||||
\(900\) | 2.65158e56 | + | 3.35133e55i | 1.96289 | + | 0.248090i | ||||
\(901\) | 1.04009e55 | 0.0753878 | ||||||||
\(902\) | − | 1.50669e56i | − | 1.06930i | ||||||
\(903\) | 1.22798e56 | + | 7.72945e54i | 0.853342 | + | 0.0537132i | ||||
\(904\) | 3.56820e55 | 0.242800 | ||||||||
\(905\) | 6.77456e55i | 0.451396i | ||||||||
\(906\) | −1.47886e55 | + | 2.34947e56i | −0.0964922 | + | 1.53297i | ||||
\(907\) | 7.75407e55 | 0.495440 | 0.247720 | − | 0.968832i | \(-0.420319\pi\) | ||||
0.247720 | + | 0.968832i | \(0.420319\pi\) | |||||||
\(908\) | − | 2.56473e56i | − | 1.60476i | ||||||
\(909\) | 2.68956e55 | − | 2.12799e56i | 0.164804 | − | 1.30393i | ||||
\(910\) | −6.09653e56 | −3.65844 | ||||||||
\(911\) | 1.76900e56i | 1.03963i | 0.854279 | + | 0.519815i | \(0.173999\pi\) | ||||
−0.854279 | + | 0.519815i | \(0.826001\pi\) | |||||||
\(912\) | 5.87769e55 | + | 3.69969e54i | 0.338302 | + | 0.0212943i | ||||
\(913\) | 9.38616e55 | 0.529107 | ||||||||
\(914\) | − | 2.32756e56i | − | 1.28506i | ||||||
\(915\) | −5.08319e54 | + | 8.07566e55i | −0.0274875 | + | 0.436694i | ||||
\(916\) | 6.66322e55 | 0.352915 | ||||||||
\(917\) | − | 1.22765e56i | − | 0.636882i | ||||||
\(918\) | −2.02207e56 | − | 3.85917e55i | −1.02751 | − | 0.196103i | ||||
\(919\) | −1.34682e56 | −0.670370 | −0.335185 | − | 0.942152i | \(-0.608799\pi\) | ||||
−0.335185 | + | 0.942152i | \(0.608799\pi\) | |||||||
\(920\) | 7.66350e55i | 0.373644i | ||||||||
\(921\) | 2.09124e55 | + | 1.31632e54i | 0.0998781 | + | 0.00628678i | ||||
\(922\) | −1.75708e56 | −0.822059 | ||||||||
\(923\) | − | 1.58684e56i | − | 0.727279i | ||||||
\(924\) | −7.06874e54 | + | 1.12301e56i | −0.0317376 | + | 0.504215i | ||||
\(925\) | 2.47906e56 | 1.09042 | ||||||||
\(926\) | 2.91660e56i | 1.25680i | ||||||||
\(927\) | 1.39618e56 | + | 1.76463e55i | 0.589421 | + | 0.0744969i | ||||
\(928\) | −4.50563e56 | −1.86356 | ||||||||
\(929\) | 2.18020e56i | 0.883484i | 0.897142 | + | 0.441742i | \(0.145639\pi\) | ||||
−0.897142 | + | 0.441742i | \(0.854361\pi\) | |||||||
\(930\) | 3.24174e56 | + | 2.04050e55i | 1.28707 | + | 0.0810141i | ||||
\(931\) | 1.32633e55 | 0.0515952 | ||||||||
\(932\) | − | 2.90407e55i | − | 0.110689i | ||||||
\(933\) | 3.71878e54 | − | 5.90802e55i | 0.0138883 | − | 0.220643i | ||||
\(934\) | 2.35909e56 | 0.863283 | ||||||||
\(935\) | 1.35600e56i | 0.486226i | ||||||||
\(936\) | −2.04813e55 | + | 1.62049e56i | −0.0719642 | + | 0.569383i | ||||
\(937\) | −2.73306e56 | −0.941017 | −0.470509 | − | 0.882395i | \(-0.655929\pi\) | ||||
−0.470509 | + | 0.882395i | \(0.655929\pi\) | |||||||
\(938\) | 2.29709e56i | 0.775039i | ||||||||
\(939\) | −4.54152e56 | − | 2.85864e55i | −1.50160 | − | 0.0945178i | ||||
\(940\) | 8.84403e54 | 0.0286564 | ||||||||
\(941\) | − | 4.80036e56i | − | 1.52430i | −0.647400 | − | 0.762151i | \(-0.724144\pi\) | ||
0.647400 | − | 0.762151i | \(-0.275856\pi\) | |||||||
\(942\) | −3.59442e54 | + | 5.71046e55i | −0.0111857 | + | 0.177707i | ||||
\(943\) | −3.52191e56 | −1.07413 | ||||||||
\(944\) | 3.11496e56i | 0.931075i | ||||||||
\(945\) | 9.74444e55 | − | 5.10574e56i | 0.285465 | − | 1.49573i | ||||
\(946\) | −2.03519e56 | −0.584350 | ||||||||
\(947\) | − | 1.20587e56i | − | 0.339353i | −0.985500 | − | 0.169676i | \(-0.945728\pi\) | ||
0.985500 | − | 0.169676i | \(-0.0542723\pi\) | |||||||
\(948\) | 6.66634e55 | + | 4.19610e54i | 0.183878 | + | 0.0115741i | ||||
\(949\) | 1.04241e57 | 2.81824 | ||||||||
\(950\) | − | 4.34137e56i | − | 1.15048i | ||||||
\(951\) | 8.54211e54 | − | 1.35708e56i | 0.0221889 | − | 0.352514i | ||||
\(952\) | 9.27286e55 | 0.236108 | ||||||||
\(953\) | 1.71835e56i | 0.428891i | 0.976736 | + | 0.214446i | \(0.0687945\pi\) | ||||
−0.976736 | + | 0.214446i | \(0.931206\pi\) | |||||||
\(954\) | 6.54267e55 | + | 8.26928e54i | 0.160080 | + | 0.0202325i | ||||
\(955\) | 5.24651e56 | 1.25836 | ||||||||
\(956\) | − | 3.47128e56i | − | 0.816187i | ||||||
\(957\) | 2.46817e56 | + | 1.55358e55i | 0.568916 | + | 0.0358102i | ||||
\(958\) | −1.46178e55 | −0.0330321 | ||||||||
\(959\) | 2.81808e56i | 0.624309i | ||||||||
\(960\) | 6.55848e55 | − | 1.04195e57i | 0.142446 | − | 2.26304i | ||||
\(961\) | −3.35291e56 | −0.713966 | ||||||||
\(962\) | 7.85749e56i | 1.64043i | ||||||||
\(963\) | −1.00014e56 | + | 7.91315e56i | −0.204721 | + | 1.61976i | ||||
\(964\) | 5.03568e56 | 1.01064 | ||||||||
\(965\) | 7.26049e56i | 1.42872i | ||||||||
\(966\) | 4.74395e56 | + | 2.98606e55i | 0.915325 | + | 0.0576147i | ||||
\(967\) | −1.46743e56 | −0.277623 | −0.138812 | − | 0.990319i | \(-0.544328\pi\) | ||||
−0.138812 | + | 0.990319i | \(0.544328\pi\) | |||||||
\(968\) | 1.56785e56i | 0.290852i | ||||||||
\(969\) | −1.16237e55 | + | 1.84665e56i | −0.0211442 | + | 0.335918i | ||||
\(970\) | −6.78539e56 | −1.21035 | ||||||||
\(971\) | − | 1.46891e56i | − | 0.256939i | −0.991713 | − | 0.128470i | \(-0.958994\pi\) | ||
0.991713 | − | 0.128470i | \(-0.0410064\pi\) | |||||||
\(972\) | −6.86866e56 | − | 2.23289e56i | −1.17818 | − | 0.383009i | ||||
\(973\) | 1.90840e56 | 0.321015 | ||||||||
\(974\) | − | 1.06914e57i | − | 1.76367i | ||||||
\(975\) | −1.58197e57 | − | 9.95763e55i | −2.55923 | − | 0.161090i | ||||
\(976\) | 1.20491e56 | 0.191165 | ||||||||
\(977\) | 1.36285e56i | 0.212057i | 0.994363 | + | 0.106028i | \(0.0338134\pi\) | ||||
−0.994363 | + | 0.106028i | \(0.966187\pi\) | |||||||
\(978\) | −9.06810e55 | + | 1.44065e57i | −0.138381 | + | 2.19847i | ||||
\(979\) | −1.98288e56 | −0.296774 | ||||||||
\(980\) | − | 1.45753e56i | − | 0.213955i | ||||||
\(981\) | −1.51974e56 | − | 1.92079e55i | −0.218805 | − | 0.0276547i | ||||
\(982\) | 2.04781e56 | 0.289181 | ||||||||
\(983\) | − | 7.83108e56i | − | 1.08469i | −0.840157 | − | 0.542344i | \(-0.817537\pi\) | ||
0.840157 | − | 0.542344i | \(-0.182463\pi\) | |||||||
\(984\) | −4.34768e56 | − | 2.73663e55i | −0.590678 | − | 0.0371800i | ||||
\(985\) | 1.63373e57 | 2.17716 | ||||||||
\(986\) | − | 1.05696e57i | − | 1.38165i | ||||||
\(987\) | 6.64456e53 | − | 1.05562e55i | 0.000852002 | − | 0.0135357i | ||||
\(988\) | 7.61413e56 | 0.957720 | ||||||||
\(989\) | 4.75729e56i | 0.586989i | ||||||||
\(990\) | −1.07809e56 | + | 8.52985e56i | −0.130492 | + | 1.03246i | ||||
\(991\) | −1.27416e57 | −1.51295 | −0.756477 | − | 0.654021i | \(-0.773081\pi\) | ||||
−0.756477 | + | 0.654021i | \(0.773081\pi\) | |||||||
\(992\) | − | 6.47782e56i | − | 0.754583i | ||||||
\(993\) | 9.38601e56 | + | 5.90798e55i | 1.07262 | + | 0.0675155i | ||||
\(994\) | −5.71195e56 | −0.640388 | ||||||||
\(995\) | − | 8.69336e56i | − | 0.956200i | ||||||
\(996\) | 8.84172e55 | − | 1.40468e57i | 0.0954134 | − | 1.51583i | ||||
\(997\) | −1.45879e57 | −1.54449 | −0.772246 | − | 0.635324i | \(-0.780867\pi\) | ||||
−0.772246 | + | 0.635324i | \(0.780867\pi\) | |||||||
\(998\) | 9.61840e56i | 0.999131i | ||||||||
\(999\) | −6.58051e56 | − | 1.25591e56i | −0.670680 | − | 0.128001i |
(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 | 3.39.b.a.2.2 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.39.b.a.2.11 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.39.b.a.2.2 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.39.b.a.2.11 | yes | 12 | 3.2 | odd | 2 | inner |