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 | 2.4 | ||
Root | \(-53338.0i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.39.b.a.2.9 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 640056.i | − | 1.22081i | −0.792090 | − | 0.610405i | \(-0.791007\pi\) | ||
0.792090 | − | 0.610405i | \(-0.208993\pi\) | |||||||
\(3\) | 2.88152e8 | + | 1.12598e9i | 0.247924 | + | 0.968780i | ||||
\(4\) | −1.34793e11 | −0.490375 | ||||||||
\(5\) | 3.15820e13i | 1.65581i | 0.560871 | + | 0.827903i | \(0.310466\pi\) | ||||
−0.560871 | + | 0.827903i | \(0.689534\pi\) | |||||||
\(6\) | 7.20687e14 | − | 1.84433e14i | 1.18270 | − | 0.302668i | ||||
\(7\) | 9.50531e15 | 0.833880 | 0.416940 | − | 0.908934i | \(-0.363103\pi\) | ||||
0.416940 | + | 0.908934i | \(0.363103\pi\) | |||||||
\(8\) | − | 8.96619e16i | − | 0.622154i | ||||||
\(9\) | −1.18479e18 | + | 6.48904e17i | −0.877068 | + | 0.480367i | ||||
\(10\) | 2.02142e19 | 2.02142 | ||||||||
\(11\) | 6.59450e19i | 1.07825i | 0.842225 | + | 0.539127i | \(0.181246\pi\) | ||||
−0.842225 | + | 0.539127i | \(0.818754\pi\) | |||||||
\(12\) | −3.88410e19 | − | 1.51774e20i | −0.121576 | − | 0.475066i | ||||
\(13\) | −1.55676e21 | −1.06487 | −0.532436 | − | 0.846470i | \(-0.678723\pi\) | ||||
−0.532436 | + | 0.846470i | \(0.678723\pi\) | |||||||
\(14\) | − | 6.08393e21i | − | 1.01801i | ||||||
\(15\) | −3.55605e22 | + | 9.10042e21i | −1.60411 | + | 0.410514i | ||||
\(16\) | −9.44403e22 | −1.24991 | ||||||||
\(17\) | − | 2.67217e23i | − | 1.11773i | −0.829260 | − | 0.558863i | \(-0.811238\pi\) | ||
0.829260 | − | 0.558863i | \(-0.188762\pi\) | |||||||
\(18\) | 4.15335e23 | + | 7.58331e23i | 0.586436 | + | 1.07073i | ||||
\(19\) | −1.27892e24 | −0.646436 | −0.323218 | − | 0.946325i | \(-0.604765\pi\) | ||||
−0.323218 | + | 0.946325i | \(0.604765\pi\) | |||||||
\(20\) | − | 4.25704e24i | − | 0.811967i | ||||||
\(21\) | 2.73898e24 | + | 1.07027e25i | 0.206739 | + | 0.807846i | ||||
\(22\) | 4.22085e25 | 1.31634 | ||||||||
\(23\) | 4.27683e25i | 0.573183i | 0.958053 | + | 0.286592i | \(0.0925223\pi\) | ||||
−0.958053 | + | 0.286592i | \(0.907478\pi\) | |||||||
\(24\) | 1.00957e26 | − | 2.58363e25i | 0.602731 | − | 0.154247i | ||||
\(25\) | −6.33625e26 | −1.74170 | ||||||||
\(26\) | 9.96411e26i | 1.30001i | ||||||||
\(27\) | −1.07205e27 | − | 1.14706e27i | −0.682815 | − | 0.730591i | ||||
\(28\) | −1.28125e27 | −0.408914 | ||||||||
\(29\) | 6.33374e27i | 1.03776i | 0.854846 | + | 0.518881i | \(0.173651\pi\) | ||||
−0.854846 | + | 0.518881i | \(0.826349\pi\) | |||||||
\(30\) | 5.82478e27 | + | 2.27607e28i | 0.501159 | + | 1.95831i | ||||
\(31\) | 2.54059e28 | 1.17236 | 0.586182 | − | 0.810179i | \(-0.300630\pi\) | ||||
0.586182 | + | 0.810179i | \(0.300630\pi\) | |||||||
\(32\) | 3.58010e28i | 0.903744i | ||||||||
\(33\) | −7.42524e28 | + | 1.90022e28i | −1.04459 | + | 0.267325i | ||||
\(34\) | −1.71034e29 | −1.36453 | ||||||||
\(35\) | 3.00197e29i | 1.38074i | ||||||||
\(36\) | 1.59702e29 | − | 8.74680e28i | 0.430092 | − | 0.235560i | ||||
\(37\) | −9.87322e28 | −0.157989 | −0.0789944 | − | 0.996875i | \(-0.525171\pi\) | ||||
−0.0789944 | + | 0.996875i | \(0.525171\pi\) | |||||||
\(38\) | 8.18580e29i | 0.789175i | ||||||||
\(39\) | −4.48583e29 | − | 1.75287e30i | −0.264007 | − | 1.03163i | ||||
\(40\) | 2.83170e30 | 1.03017 | ||||||||
\(41\) | − | 3.57778e30i | − | 0.814180i | −0.913388 | − | 0.407090i | \(-0.866543\pi\) | ||
0.913388 | − | 0.407090i | \(-0.133457\pi\) | |||||||
\(42\) | 6.85035e30 | − | 1.75310e30i | 0.986226 | − | 0.252388i | ||||
\(43\) | −8.11666e30 | −0.747269 | −0.373634 | − | 0.927576i | \(-0.621889\pi\) | ||||
−0.373634 | + | 0.927576i | \(0.621889\pi\) | |||||||
\(44\) | − | 8.88895e30i | − | 0.528749i | ||||||
\(45\) | −2.04937e31 | − | 3.74180e31i | −0.795394 | − | 1.45225i | ||||
\(46\) | 2.73741e31 | 0.699747 | ||||||||
\(47\) | 7.20582e31i | 1.22412i | 0.790811 | + | 0.612060i | \(0.209659\pi\) | ||||
−0.790811 | + | 0.612060i | \(0.790341\pi\) | |||||||
\(48\) | −2.72132e31 | − | 1.06337e32i | −0.309882 | − | 1.21088i | ||||
\(49\) | −3.95839e31 | −0.304644 | ||||||||
\(50\) | 4.05555e32i | 2.12628i | ||||||||
\(51\) | 3.00880e32 | − | 7.69993e31i | 1.08283 | − | 0.277111i | ||||
\(52\) | 2.09841e32 | 0.522187 | ||||||||
\(53\) | 4.09843e32i | 0.710192i | 0.934830 | + | 0.355096i | \(0.115552\pi\) | ||||
−0.934830 | + | 0.355096i | \(0.884448\pi\) | |||||||
\(54\) | −7.34182e32 | + | 6.86171e32i | −0.891912 | + | 0.833587i | ||||
\(55\) | −2.08268e33 | −1.78538 | ||||||||
\(56\) | − | 8.52264e32i | − | 0.518802i | ||||||
\(57\) | −3.68524e32 | − | 1.44003e33i | −0.160267 | − | 0.626254i | ||||
\(58\) | 4.05394e33 | 1.26691 | ||||||||
\(59\) | 1.03957e33i | 0.234783i | 0.993086 | + | 0.117392i | \(0.0374532\pi\) | ||||
−0.993086 | + | 0.117392i | \(0.962547\pi\) | |||||||
\(60\) | 4.79333e33 | − | 1.22668e33i | 0.786617 | − | 0.201306i | ||||
\(61\) | 5.64098e33 | 0.676220 | 0.338110 | − | 0.941107i | \(-0.390212\pi\) | ||||
0.338110 | + | 0.941107i | \(0.390212\pi\) | |||||||
\(62\) | − | 1.62612e34i | − | 1.43123i | ||||||
\(63\) | −1.12618e34 | + | 6.16804e33i | −0.731369 | + | 0.400568i | ||||
\(64\) | −3.04493e33 | −0.146608 | ||||||||
\(65\) | − | 4.91655e34i | − | 1.76322i | ||||||
\(66\) | 1.21625e34 | + | 4.75257e34i | 0.326352 | + | 1.27525i | ||||
\(67\) | −6.14474e34 | −1.23903 | −0.619515 | − | 0.784984i | \(-0.712671\pi\) | ||||
−0.619515 | + | 0.784984i | \(0.712671\pi\) | |||||||
\(68\) | 3.60191e34i | 0.548105i | ||||||||
\(69\) | −4.81561e34 | + | 1.23238e34i | −0.555288 | + | 0.142106i | ||||
\(70\) | 1.92143e35 | 1.68562 | ||||||||
\(71\) | 1.97414e35i | 1.32272i | 0.750068 | + | 0.661361i | \(0.230021\pi\) | ||||
−0.750068 | + | 0.661361i | \(0.769979\pi\) | |||||||
\(72\) | 5.81820e34 | + | 1.06230e35i | 0.298862 | + | 0.545672i | ||||
\(73\) | −1.80385e35 | −0.712962 | −0.356481 | − | 0.934303i | \(-0.616023\pi\) | ||||
−0.356481 | + | 0.934303i | \(0.616023\pi\) | |||||||
\(74\) | 6.31941e34i | 0.192874i | ||||||||
\(75\) | −1.82580e35 | − | 7.13446e35i | −0.431807 | − | 1.68732i | ||||
\(76\) | 1.72390e35 | 0.316996 | ||||||||
\(77\) | 6.26828e35i | 0.899134i | ||||||||
\(78\) | −1.12193e36 | + | 2.87118e35i | −1.25942 | + | 0.322302i | ||||
\(79\) | 1.59780e36 | 1.40802 | 0.704009 | − | 0.710191i | \(-0.251392\pi\) | ||||
0.704009 | + | 0.710191i | \(0.251392\pi\) | |||||||
\(80\) | − | 2.98261e36i | − | 2.06960i | ||||||
\(81\) | 9.82647e35 | − | 1.53763e36i | 0.538495 | − | 0.842628i | ||||
\(82\) | −2.28998e36 | −0.993959 | ||||||||
\(83\) | 2.62427e36i | 0.904744i | 0.891829 | + | 0.452372i | \(0.149422\pi\) | ||||
−0.891829 | + | 0.452372i | \(0.850578\pi\) | |||||||
\(84\) | −3.69196e35 | − | 1.44266e36i | −0.101379 | − | 0.396148i | ||||
\(85\) | 8.43926e36 | 1.85074 | ||||||||
\(86\) | 5.19512e36i | 0.912273i | ||||||||
\(87\) | −7.13163e36 | + | 1.82508e36i | −1.00536 | + | 0.257286i | ||||
\(88\) | 5.91276e36 | 0.670840 | ||||||||
\(89\) | − | 3.89397e36i | − | 0.356437i | −0.983991 | − | 0.178218i | \(-0.942967\pi\) | ||
0.983991 | − | 0.178218i | \(-0.0570333\pi\) | |||||||
\(90\) | −2.39496e37 | + | 1.31171e37i | −1.77293 | + | 0.971025i | ||||
\(91\) | −1.47975e37 | −0.887975 | ||||||||
\(92\) | − | 5.76489e36i | − | 0.281075i | ||||||
\(93\) | 7.32076e36 | + | 2.86064e37i | 0.290657 | + | 1.13576i | ||||
\(94\) | 4.61213e37 | 1.49442 | ||||||||
\(95\) | − | 4.03909e37i | − | 1.07037i | ||||||
\(96\) | −4.03110e37 | + | 1.03161e37i | −0.875529 | + | 0.224060i | ||||
\(97\) | 8.00800e37 | 1.42844 | 0.714219 | − | 0.699923i | \(-0.246782\pi\) | ||||
0.714219 | + | 0.699923i | \(0.246782\pi\) | |||||||
\(98\) | 2.53359e37i | 0.371913i | ||||||||
\(99\) | −4.27920e37 | − | 7.81309e37i | −0.517957 | − | 0.945701i | ||||
\(100\) | 8.54084e37 | 0.854084 | ||||||||
\(101\) | − | 5.86969e37i | − | 0.485858i | −0.970044 | − | 0.242929i | \(-0.921892\pi\) | ||
0.970044 | − | 0.242929i | \(-0.0781082\pi\) | |||||||
\(102\) | −4.92838e37 | − | 1.92580e38i | −0.338299 | − | 1.32193i | ||||
\(103\) | −1.79233e38 | −1.02214 | −0.511071 | − | 0.859539i | \(-0.670751\pi\) | ||||
−0.511071 | + | 0.859539i | \(0.670751\pi\) | |||||||
\(104\) | 1.39582e38i | 0.662515i | ||||||||
\(105\) | −3.38014e38 | + | 8.65023e37i | −1.33764 | + | 0.342319i | ||||
\(106\) | 2.62322e38 | 0.867009 | ||||||||
\(107\) | − | 1.11640e38i | − | 0.308694i | −0.988017 | − | 0.154347i | \(-0.950673\pi\) | ||
0.988017 | − | 0.154347i | \(-0.0493274\pi\) | |||||||
\(108\) | 1.44505e38 | + | 1.54616e38i | 0.334836 | + | 0.358264i | ||||
\(109\) | 9.48509e38 | 1.84475 | 0.922376 | − | 0.386294i | \(-0.126245\pi\) | ||||
0.922376 | + | 0.386294i | \(0.126245\pi\) | |||||||
\(110\) | 1.33303e39i | 2.17961i | ||||||||
\(111\) | −2.84499e37 | − | 1.11170e38i | −0.0391691 | − | 0.153056i | ||||
\(112\) | −8.97684e38 | −1.04227 | ||||||||
\(113\) | − | 2.89986e38i | − | 0.284372i | −0.989840 | − | 0.142186i | \(-0.954587\pi\) | ||
0.989840 | − | 0.142186i | \(-0.0454131\pi\) | |||||||
\(114\) | −9.21701e38 | + | 2.35876e38i | −0.764536 | + | 0.195655i | ||||
\(115\) | −1.35071e39 | −0.949080 | ||||||||
\(116\) | − | 8.53746e38i | − | 0.508893i | ||||||
\(117\) | 1.84443e39 | − | 1.01019e39i | 0.933964 | − | 0.511529i | ||||
\(118\) | 6.65385e38 | 0.286625 | ||||||||
\(119\) | − | 2.53998e39i | − | 0.932049i | ||||||
\(120\) | 8.15961e38 | + | 3.18843e39i | 0.255403 | + | 0.998005i | ||||
\(121\) | −6.08310e38 | −0.162631 | ||||||||
\(122\) | − | 3.61054e39i | − | 0.825536i | ||||||
\(123\) | 4.02849e39 | − | 1.03095e39i | 0.788761 | − | 0.201855i | ||||
\(124\) | −3.42455e39 | −0.574898 | ||||||||
\(125\) | − | 8.52168e39i | − | 1.22810i | ||||||
\(126\) | 3.94789e39 | + | 7.20817e39i | 0.489017 | + | 0.892862i | ||||
\(127\) | 6.95430e39 | 0.741280 | 0.370640 | − | 0.928777i | \(-0.379138\pi\) | ||||
0.370640 | + | 0.928777i | \(0.379138\pi\) | |||||||
\(128\) | 1.17898e40i | 1.08272i | ||||||||
\(129\) | −2.33883e39 | − | 9.13916e39i | −0.185266 | − | 0.723939i | ||||
\(130\) | −3.14687e40 | −2.15256 | ||||||||
\(131\) | 2.23746e40i | 1.32313i | 0.749889 | + | 0.661563i | \(0.230107\pi\) | ||||
−0.749889 | + | 0.661563i | \(0.769893\pi\) | |||||||
\(132\) | 1.00087e40 | − | 2.56137e39i | 0.512241 | − | 0.131089i | ||||
\(133\) | −1.21565e40 | −0.539050 | ||||||||
\(134\) | 3.93297e40i | 1.51262i | ||||||||
\(135\) | 3.62264e40 | − | 3.38575e40i | 1.20972 | − | 1.13061i | ||||
\(136\) | −2.39592e40 | −0.695398 | ||||||||
\(137\) | − | 1.97371e40i | − | 0.498416i | −0.968450 | − | 0.249208i | \(-0.919830\pi\) | ||
0.968450 | − | 0.249208i | \(-0.0801703\pi\) | |||||||
\(138\) | 7.88791e39 | + | 3.08226e40i | 0.173484 | + | 0.677901i | ||||
\(139\) | 3.39057e40 | 0.650117 | 0.325059 | − | 0.945694i | \(-0.394616\pi\) | ||||
0.325059 | + | 0.945694i | \(0.394616\pi\) | |||||||
\(140\) | − | 4.04645e40i | − | 0.677083i | ||||||
\(141\) | −8.11358e40 | + | 2.07637e40i | −1.18590 | + | 0.303488i | ||||
\(142\) | 1.26356e41 | 1.61479 | ||||||||
\(143\) | − | 1.02660e41i | − | 1.14820i | ||||||
\(144\) | 1.11892e41 | − | 6.12827e40i | 1.09625 | − | 0.600414i | ||||
\(145\) | −2.00032e41 | −1.71833 | ||||||||
\(146\) | 1.15456e41i | 0.870390i | ||||||||
\(147\) | −1.14062e40 | − | 4.45705e40i | −0.0755286 | − | 0.295133i | ||||
\(148\) | 1.33084e40 | 0.0774738 | ||||||||
\(149\) | − | 3.13683e41i | − | 1.60676i | −0.595463 | − | 0.803382i | \(-0.703032\pi\) | ||
0.595463 | − | 0.803382i | \(-0.296968\pi\) | |||||||
\(150\) | −4.56645e41 | + | 1.16862e41i | −2.05989 | + | 0.527155i | ||||
\(151\) | 2.49290e41 | 0.991157 | 0.495578 | − | 0.868563i | \(-0.334956\pi\) | ||||
0.495578 | + | 0.868563i | \(0.334956\pi\) | |||||||
\(152\) | 1.14670e41i | 0.402183i | ||||||||
\(153\) | 1.73399e41 | + | 3.16596e41i | 0.536918 | + | 0.980321i | ||||
\(154\) | 4.01205e41 | 1.09767 | ||||||||
\(155\) | 8.02369e41i | 1.94121i | ||||||||
\(156\) | 6.04660e40 | + | 2.36275e41i | 0.129462 | + | 0.505884i | ||||
\(157\) | 3.35685e41 | 0.636559 | 0.318280 | − | 0.947997i | \(-0.396895\pi\) | ||||
0.318280 | + | 0.947997i | \(0.396895\pi\) | |||||||
\(158\) | − | 1.02268e42i | − | 1.71892i | ||||||
\(159\) | −4.61473e41 | + | 1.18097e41i | −0.688020 | + | 0.176073i | ||||
\(160\) | −1.13067e42 | −1.49643 | ||||||||
\(161\) | 4.06526e41i | 0.477966i | ||||||||
\(162\) | −9.84168e41 | − | 6.28949e41i | −1.02869 | − | 0.657400i | ||||
\(163\) | 8.93945e41 | 0.831278 | 0.415639 | − | 0.909530i | \(-0.363558\pi\) | ||||
0.415639 | + | 0.909530i | \(0.363558\pi\) | |||||||
\(164\) | 4.82261e41i | 0.399254i | ||||||||
\(165\) | −6.00127e41 | − | 2.34504e42i | −0.442638 | − | 1.72964i | ||||
\(166\) | 1.67968e42 | 1.10452 | ||||||||
\(167\) | 1.94932e42i | 1.14359i | 0.820396 | + | 0.571795i | \(0.193753\pi\) | ||||
−0.820396 | + | 0.571795i | \(0.806247\pi\) | |||||||
\(168\) | 9.59628e41 | − | 2.45582e41i | 0.502605 | − | 0.128623i | ||||
\(169\) | 2.86282e41 | 0.133951 | ||||||||
\(170\) | − | 5.40160e42i | − | 2.25940i | ||||||
\(171\) | 1.51525e42 | − | 8.29897e41i | 0.566968 | − | 0.310526i | ||||
\(172\) | 1.09407e42 | 0.366442 | ||||||||
\(173\) | 6.41502e42i | 1.92452i | 0.272136 | + | 0.962259i | \(0.412270\pi\) | ||||
−0.272136 | + | 0.962259i | \(0.587730\pi\) | |||||||
\(174\) | 1.16815e42 | + | 4.56464e42i | 0.314097 | + | 1.22736i | ||||
\(175\) | −6.02280e42 | −1.45236 | ||||||||
\(176\) | − | 6.22787e42i | − | 1.34772i | ||||||
\(177\) | −1.17053e42 | + | 2.99555e41i | −0.227453 | + | 0.0582083i | ||||
\(178\) | −2.49236e42 | −0.435141 | ||||||||
\(179\) | − | 1.15790e42i | − | 0.181745i | −0.995863 | − | 0.0908726i | \(-0.971034\pi\) | ||
0.995863 | − | 0.0908726i | \(-0.0289656\pi\) | |||||||
\(180\) | 2.76241e42 | + | 5.04370e42i | 0.390042 | + | 0.712150i | ||||
\(181\) | −1.08797e43 | −1.38269 | −0.691344 | − | 0.722526i | \(-0.742981\pi\) | ||||
−0.691344 | + | 0.722526i | \(0.742981\pi\) | |||||||
\(182\) | 9.47120e42i | 1.08405i | ||||||||
\(183\) | 1.62546e42 | + | 6.35161e42i | 0.167651 | + | 0.655108i | ||||
\(184\) | 3.83469e42 | 0.356609 | ||||||||
\(185\) | − | 3.11816e42i | − | 0.261599i | ||||||
\(186\) | 1.83097e43 | − | 4.68570e42i | 1.38655 | − | 0.354836i | ||||
\(187\) | 1.76217e43 | 1.20519 | ||||||||
\(188\) | − | 9.71297e42i | − | 0.600279i | ||||||
\(189\) | −1.01902e43 | − | 1.09032e43i | −0.569386 | − | 0.609225i | ||||
\(190\) | −2.58524e43 | −1.30672 | ||||||||
\(191\) | 1.16526e43i | 0.533075i | 0.963825 | + | 0.266537i | \(0.0858796\pi\) | ||||
−0.963825 | + | 0.266537i | \(0.914120\pi\) | |||||||
\(192\) | −8.77404e41 | − | 3.42852e42i | −0.0363476 | − | 0.142031i | ||||
\(193\) | −1.38553e43 | −0.520029 | −0.260014 | − | 0.965605i | \(-0.583727\pi\) | ||||
−0.260014 | + | 0.965605i | \(0.583727\pi\) | |||||||
\(194\) | − | 5.12557e43i | − | 1.74385i | ||||||
\(195\) | 5.53591e43 | − | 1.41671e43i | 1.70817 | − | 0.437144i | ||||
\(196\) | 5.33565e42 | 0.149390 | ||||||||
\(197\) | 1.34295e43i | 0.341351i | 0.985327 | + | 0.170676i | \(0.0545950\pi\) | ||||
−0.985327 | + | 0.170676i | \(0.945405\pi\) | |||||||
\(198\) | −5.00081e43 | + | 2.73893e43i | −1.15452 | + | 0.632327i | ||||
\(199\) | 8.89031e42 | 0.186513 | 0.0932563 | − | 0.995642i | \(-0.470272\pi\) | ||||
0.0932563 | + | 0.995642i | \(0.470272\pi\) | |||||||
\(200\) | 5.68120e43i | 1.08360i | ||||||||
\(201\) | −1.77062e43 | − | 6.91882e43i | −0.307185 | − | 1.20035i | ||||
\(202\) | −3.75693e43 | −0.593140 | ||||||||
\(203\) | 6.02041e43i | 0.865369i | ||||||||
\(204\) | −4.05566e43 | + | 1.03790e43i | −0.530993 | + | 0.135888i | ||||
\(205\) | 1.12994e44 | 1.34813 | ||||||||
\(206\) | 1.14719e44i | 1.24784i | ||||||||
\(207\) | −2.77526e43 | − | 5.06714e43i | −0.275338 | − | 0.502720i | ||||
\(208\) | 1.47021e44 | 1.33099 | ||||||||
\(209\) | − | 8.43384e43i | − | 0.697021i | ||||||
\(210\) | 5.53663e43 | + | 2.16348e44i | 0.417906 | + | 1.63300i | ||||
\(211\) | −1.25172e44 | −0.863259 | −0.431629 | − | 0.902051i | \(-0.642061\pi\) | ||||
−0.431629 | + | 0.902051i | \(0.642061\pi\) | |||||||
\(212\) | − | 5.52441e43i | − | 0.348261i | ||||||
\(213\) | −2.22283e44 | + | 5.68852e43i | −1.28143 | + | 0.327934i | ||||
\(214\) | −7.14559e43 | −0.376857 | ||||||||
\(215\) | − | 2.56340e44i | − | 1.23733i | ||||||
\(216\) | −1.02848e44 | + | 9.61220e43i | −0.454540 | + | 0.424817i | ||||
\(217\) | 2.41491e44 | 0.977611 | ||||||||
\(218\) | − | 6.07098e44i | − | 2.25209i | ||||||
\(219\) | −5.19783e43 | − | 2.03109e44i | −0.176760 | − | 0.690703i | ||||
\(220\) | 2.80731e44 | 0.875506 | ||||||||
\(221\) | 4.15993e44i | 1.19023i | ||||||||
\(222\) | −7.11550e43 | + | 1.82095e43i | −0.186852 | + | 0.0478181i | ||||
\(223\) | −6.66529e43 | −0.160704 | −0.0803520 | − | 0.996767i | \(-0.525604\pi\) | ||||
−0.0803520 | + | 0.996767i | \(0.525604\pi\) | |||||||
\(224\) | 3.40299e44i | 0.753614i | ||||||||
\(225\) | 7.50712e44 | − | 4.11162e44i | 1.52758 | − | 0.836652i | ||||
\(226\) | −1.85607e44 | −0.347164 | ||||||||
\(227\) | − | 7.05437e43i | − | 0.121330i | −0.998158 | − | 0.0606648i | \(-0.980678\pi\) | ||
0.998158 | − | 0.0606648i | \(-0.0193221\pi\) | |||||||
\(228\) | 4.96746e43 | + | 1.94107e44i | 0.0785908 | + | 0.307099i | ||||
\(229\) | −9.62962e43 | −0.140196 | −0.0700979 | − | 0.997540i | \(-0.522331\pi\) | ||||
−0.0700979 | + | 0.997540i | \(0.522331\pi\) | |||||||
\(230\) | 8.64529e44i | 1.15865i | ||||||||
\(231\) | −7.05792e44 | + | 1.80622e44i | −0.871063 | + | 0.222917i | ||||
\(232\) | 5.67895e44 | 0.645649 | ||||||||
\(233\) | 4.41342e44i | 0.462395i | 0.972907 | + | 0.231197i | \(0.0742643\pi\) | ||||
−0.972907 | + | 0.231197i | \(0.925736\pi\) | |||||||
\(234\) | −6.46576e44 | − | 1.18054e45i | −0.624479 | − | 1.14019i | ||||
\(235\) | −2.27574e45 | −2.02691 | ||||||||
\(236\) | − | 1.40128e44i | − | 0.115132i | ||||||
\(237\) | 4.60410e44 | + | 1.79908e45i | 0.349081 | + | 1.36406i | ||||
\(238\) | −1.62573e45 | −1.13785 | ||||||||
\(239\) | 1.33189e44i | 0.0860813i | 0.999073 | + | 0.0430407i | \(0.0137045\pi\) | ||||
−0.999073 | + | 0.0430407i | \(0.986295\pi\) | |||||||
\(240\) | 3.35835e45 | − | 8.59447e44i | 2.00499 | − | 0.513104i | ||||
\(241\) | 2.28762e45 | 1.26200 | 0.631000 | − | 0.775783i | \(-0.282645\pi\) | ||||
0.631000 | + | 0.775783i | \(0.282645\pi\) | |||||||
\(242\) | 3.89352e44i | 0.198541i | ||||||||
\(243\) | 2.01448e45 | + | 6.63365e44i | 0.949827 | + | 0.312776i | ||||
\(244\) | −7.60367e44 | −0.331602 | ||||||||
\(245\) | − | 1.25014e45i | − | 0.504432i | ||||||
\(246\) | −6.59863e44 | − | 2.57846e45i | −0.246426 | − | 0.962927i | ||||
\(247\) | 1.99097e45 | 0.688371 | ||||||||
\(248\) | − | 2.27794e45i | − | 0.729391i | ||||||
\(249\) | −2.95487e45 | + | 7.56190e44i | −0.876497 | + | 0.224307i | ||||
\(250\) | −5.45435e45 | −1.49928 | ||||||||
\(251\) | − | 3.22130e45i | − | 0.820787i | −0.911908 | − | 0.410394i | \(-0.865391\pi\) | ||
0.911908 | − | 0.410394i | \(-0.134609\pi\) | |||||||
\(252\) | 1.51801e45 | − | 8.31410e44i | 0.358645 | − | 0.196429i | ||||
\(253\) | −2.82036e45 | −0.618037 | ||||||||
\(254\) | − | 4.45114e45i | − | 0.904962i | ||||||
\(255\) | 2.43179e45 | + | 9.50240e45i | 0.458842 | + | 1.79296i | ||||
\(256\) | 6.70916e45 | 1.17519 | ||||||||
\(257\) | 3.34070e45i | 0.543386i | 0.962384 | + | 0.271693i | \(0.0875835\pi\) | ||||
−0.962384 | + | 0.271693i | \(0.912416\pi\) | |||||||
\(258\) | −5.84957e45 | + | 1.49698e45i | −0.883791 | + | 0.226174i | ||||
\(259\) | −9.38480e44 | −0.131744 | ||||||||
\(260\) | 6.62718e45i | 0.864640i | ||||||||
\(261\) | −4.10999e45 | − | 7.50414e45i | −0.498507 | − | 0.910188i | ||||
\(262\) | 1.43210e46 | 1.61529 | ||||||||
\(263\) | 4.17907e45i | 0.438450i | 0.975674 | + | 0.219225i | \(0.0703529\pi\) | ||||
−0.975674 | + | 0.219225i | \(0.929647\pi\) | |||||||
\(264\) | 1.70377e45 | + | 6.65762e45i | 0.166317 | + | 0.649896i | ||||
\(265\) | −1.29437e46 | −1.17594 | ||||||||
\(266\) | 7.78086e45i | 0.658077i | ||||||||
\(267\) | 4.38451e45 | − | 1.12206e45i | 0.345309 | − | 0.0883691i | ||||
\(268\) | 8.28270e45 | 0.607590 | ||||||||
\(269\) | 4.32268e45i | 0.295433i | 0.989030 | + | 0.147717i | \(0.0471924\pi\) | ||||
−0.989030 | + | 0.147717i | \(0.952808\pi\) | |||||||
\(270\) | −2.16707e46 | − | 2.31869e46i | −1.38026 | − | 1.47683i | ||||
\(271\) | 1.17659e46 | 0.698571 | 0.349285 | − | 0.937016i | \(-0.386424\pi\) | ||||
0.349285 | + | 0.937016i | \(0.386424\pi\) | |||||||
\(272\) | 2.52361e46i | 1.39705i | ||||||||
\(273\) | −4.26392e45 | − | 1.66616e46i | −0.220150 | − | 0.860252i | ||||
\(274\) | −1.26328e46 | −0.608471 | ||||||||
\(275\) | − | 4.17844e46i | − | 1.87799i | ||||||
\(276\) | 6.49112e45 | − | 1.66116e45i | 0.272300 | − | 0.0696851i | ||||
\(277\) | 1.48250e46 | 0.580602 | 0.290301 | − | 0.956935i | \(-0.406245\pi\) | ||||
0.290301 | + | 0.956935i | \(0.406245\pi\) | |||||||
\(278\) | − | 2.17016e46i | − | 0.793669i | ||||||
\(279\) | −3.01006e46 | + | 1.64860e46i | −1.02824 | + | 0.563165i | ||||
\(280\) | 2.69162e46 | 0.859036 | ||||||||
\(281\) | − | 1.30765e45i | − | 0.0390005i | −0.999810 | − | 0.0195003i | \(-0.993792\pi\) | ||
0.999810 | − | 0.0195003i | \(-0.00620752\pi\) | |||||||
\(282\) | 1.32899e46 | + | 5.19314e46i | 0.370502 | + | 1.44776i | ||||
\(283\) | 2.61530e46 | 0.681679 | 0.340839 | − | 0.940122i | \(-0.389289\pi\) | ||||
0.340839 | + | 0.940122i | \(0.389289\pi\) | |||||||
\(284\) | − | 2.66100e46i | − | 0.648630i | ||||||
\(285\) | 4.54791e46 | − | 1.16387e46i | 1.03695 | − | 0.265371i | ||||
\(286\) | −6.57084e46 | −1.40174 | ||||||||
\(287\) | − | 3.40079e46i | − | 0.678929i | ||||||
\(288\) | −2.32314e46 | − | 4.24166e46i | −0.434129 | − | 0.792645i | ||||
\(289\) | −1.42495e46 | −0.249311 | ||||||||
\(290\) | 1.28032e47i | 2.09776i | ||||||||
\(291\) | 2.30752e46 | + | 9.01681e46i | 0.354143 | + | 1.38384i | ||||
\(292\) | 2.43147e46 | 0.349619 | ||||||||
\(293\) | 1.80643e46i | 0.243408i | 0.992566 | + | 0.121704i | \(0.0388359\pi\) | ||||
−0.992566 | + | 0.121704i | \(0.961164\pi\) | |||||||
\(294\) | −2.85276e46 | + | 7.30060e45i | −0.360302 | + | 0.0922060i | ||||
\(295\) | −3.28318e46 | −0.388755 | ||||||||
\(296\) | 8.85252e45i | 0.0982934i | ||||||||
\(297\) | 7.56428e46 | − | 7.06963e46i | 0.787762 | − | 0.736248i | ||||
\(298\) | −2.00775e47 | −1.96155 | ||||||||
\(299\) | − | 6.65799e46i | − | 0.610366i | ||||||
\(300\) | 2.46106e46 | + | 9.61678e46i | 0.211748 | + | 0.827419i | ||||
\(301\) | −7.71514e46 | −0.623132 | ||||||||
\(302\) | − | 1.59559e47i | − | 1.21001i | ||||||
\(303\) | 6.60913e46 | − | 1.69136e46i | 0.470689 | − | 0.120456i | ||||
\(304\) | 1.20782e47 | 0.807985 | ||||||||
\(305\) | 1.78154e47i | 1.11969i | ||||||||
\(306\) | 2.02639e47 | − | 1.10985e47i | 1.19679 | − | 0.655475i | ||||
\(307\) | 2.11365e46 | 0.117329 | 0.0586643 | − | 0.998278i | \(-0.481316\pi\) | ||||
0.0586643 | + | 0.998278i | \(0.481316\pi\) | |||||||
\(308\) | − | 8.44922e46i | − | 0.440913i | ||||||
\(309\) | −5.16464e46 | − | 2.01812e47i | −0.253413 | − | 0.990230i | ||||
\(310\) | 5.13561e47 | 2.36984 | ||||||||
\(311\) | 1.90047e47i | 0.824926i | 0.910974 | + | 0.412463i | \(0.135331\pi\) | ||||
−0.910974 | + | 0.412463i | \(0.864669\pi\) | |||||||
\(312\) | −1.57166e47 | + | 4.02208e46i | −0.641831 | + | 0.164253i | ||||
\(313\) | −4.36802e47 | −1.67858 | −0.839290 | − | 0.543684i | \(-0.817029\pi\) | ||||
−0.839290 | + | 0.543684i | \(0.817029\pi\) | |||||||
\(314\) | − | 2.14857e47i | − | 0.777118i | ||||||
\(315\) | −1.94799e47 | − | 3.55670e47i | −0.663263 | − | 1.21101i | ||||
\(316\) | −2.15373e47 | −0.690457 | ||||||||
\(317\) | 2.82613e47i | 0.853229i | 0.904434 | + | 0.426614i | \(0.140294\pi\) | ||||
−0.904434 | + | 0.426614i | \(0.859706\pi\) | |||||||
\(318\) | 7.55887e46 | + | 2.95368e47i | 0.214952 | + | 0.839941i | ||||
\(319\) | −4.17678e47 | −1.11897 | ||||||||
\(320\) | − | 9.61651e46i | − | 0.242755i | ||||||
\(321\) | 1.25704e47 | − | 3.21694e46i | 0.299057 | − | 0.0765327i | ||||
\(322\) | 2.60199e47 | 0.583505 | ||||||||
\(323\) | 3.41750e47i | 0.722538i | ||||||||
\(324\) | −1.32454e47 | + | 2.07262e47i | −0.264065 | + | 0.413204i | ||||
\(325\) | 9.86400e47 | 1.85468 | ||||||||
\(326\) | − | 5.72175e47i | − | 1.01483i | ||||||
\(327\) | 2.73315e47 | + | 1.06800e48i | 0.457358 | + | 1.78716i | ||||
\(328\) | −3.20791e47 | −0.506546 | ||||||||
\(329\) | 6.84936e47i | 1.02077i | ||||||||
\(330\) | −1.50096e48 | + | 3.84115e47i | −2.11156 | + | 0.540376i | ||||
\(331\) | 8.26572e47 | 1.09787 | 0.548933 | − | 0.835867i | \(-0.315034\pi\) | ||||
0.548933 | + | 0.835867i | \(0.315034\pi\) | |||||||
\(332\) | − | 3.53735e47i | − | 0.443664i | ||||||
\(333\) | 1.16977e47 | − | 6.40678e46i | 0.138567 | − | 0.0758925i | ||||
\(334\) | 1.24767e48 | 1.39611 | ||||||||
\(335\) | − | 1.94063e48i | − | 2.05160i | ||||||
\(336\) | −2.58670e47 | − | 1.01077e48i | −0.258404 | − | 1.00973i | ||||
\(337\) | −1.06999e48 | −1.01021 | −0.505105 | − | 0.863058i | \(-0.668546\pi\) | ||||
−0.505105 | + | 0.863058i | \(0.668546\pi\) | |||||||
\(338\) | − | 1.83237e47i | − | 0.163529i | ||||||
\(339\) | 3.26517e47 | − | 8.35601e46i | 0.275494 | − | 0.0705025i | ||||
\(340\) | −1.13756e48 | −0.907556 | ||||||||
\(341\) | 1.67539e48i | 1.26411i | ||||||||
\(342\) | −5.31180e47 | − | 9.69845e47i | −0.379093 | − | 0.692159i | ||||
\(343\) | −1.61133e48 | −1.08792 | ||||||||
\(344\) | 7.27756e47i | 0.464917i | ||||||||
\(345\) | −3.89210e47 | − | 1.52087e48i | −0.235300 | − | 0.919450i | ||||
\(346\) | 4.10597e48 | 2.34947 | ||||||||
\(347\) | − | 2.30805e48i | − | 1.25022i | −0.780539 | − | 0.625108i | \(-0.785055\pi\) | ||
0.780539 | − | 0.625108i | \(-0.214945\pi\) | |||||||
\(348\) | 9.61297e47 | − | 2.46009e47i | 0.493005 | − | 0.126167i | ||||
\(349\) | 2.58261e48 | 1.25423 | 0.627114 | − | 0.778928i | \(-0.284236\pi\) | ||||
0.627114 | + | 0.778928i | \(0.284236\pi\) | |||||||
\(350\) | 3.85493e48i | 1.77306i | ||||||||
\(351\) | 1.66892e48 | + | 1.78569e48i | 0.727111 | + | 0.777985i | ||||
\(352\) | −2.36090e48 | −0.974465 | ||||||||
\(353\) | − | 7.29378e47i | − | 0.285255i | −0.989776 | − | 0.142627i | \(-0.954445\pi\) | ||
0.989776 | − | 0.142627i | \(-0.0455551\pi\) | |||||||
\(354\) | 1.91732e47 | + | 7.49207e47i | 0.0710612 | + | 0.277677i | ||||
\(355\) | −6.23472e48 | −2.19017 | ||||||||
\(356\) | 5.24881e47i | 0.174788i | ||||||||
\(357\) | 2.85996e48 | − | 7.31902e47i | 0.902950 | − | 0.231077i | ||||
\(358\) | −7.41120e47 | −0.221876 | ||||||||
\(359\) | − | 2.35585e47i | − | 0.0668888i | −0.999441 | − | 0.0334444i | \(-0.989352\pi\) | ||
0.999441 | − | 0.0334444i | \(-0.0106477\pi\) | |||||||
\(360\) | −3.35497e48 | + | 1.83750e48i | −0.903527 | + | 0.494858i | ||||
\(361\) | −2.27851e48 | −0.582121 | ||||||||
\(362\) | 6.96361e48i | 1.68800i | ||||||||
\(363\) | −1.75286e47 | − | 6.84942e47i | −0.0403200 | − | 0.157553i | ||||
\(364\) | 1.99460e48 | 0.435441 | ||||||||
\(365\) | − | 5.69692e48i | − | 1.18053i | ||||||
\(366\) | 4.06538e48 | − | 1.04039e48i | 0.799762 | − | 0.204670i | ||||
\(367\) | 1.34691e48 | 0.251585 | 0.125793 | − | 0.992057i | \(-0.459853\pi\) | ||||
0.125793 | + | 0.992057i | \(0.459853\pi\) | |||||||
\(368\) | − | 4.03906e48i | − | 0.716426i | ||||||
\(369\) | 2.32164e48 | + | 4.23891e48i | 0.391105 | + | 0.714091i | ||||
\(370\) | −1.99580e48 | −0.319362 | ||||||||
\(371\) | 3.89568e48i | 0.592215i | ||||||||
\(372\) | −9.86790e47 | − | 3.85595e48i | −0.142531 | − | 0.556950i | ||||
\(373\) | −9.41851e48 | −1.29275 | −0.646375 | − | 0.763020i | \(-0.723716\pi\) | ||||
−0.646375 | + | 0.763020i | \(0.723716\pi\) | |||||||
\(374\) | − | 1.12788e49i | − | 1.47131i | ||||||
\(375\) | 9.59520e48 | − | 2.45554e48i | 1.18976 | − | 0.304476i | ||||
\(376\) | 6.46088e48 | 0.761592 | ||||||||
\(377\) | − | 9.86009e48i | − | 1.10508i | ||||||
\(378\) | −6.97862e48 | + | 6.52227e48i | −0.743748 | + | 0.695112i | ||||
\(379\) | 1.30347e49 | 1.32116 | 0.660580 | − | 0.750756i | \(-0.270310\pi\) | ||||
0.660580 | + | 0.750756i | \(0.270310\pi\) | |||||||
\(380\) | 5.44442e48i | 0.524884i | ||||||||
\(381\) | 2.00390e48 | + | 7.83037e48i | 0.183781 | + | 0.718137i | ||||
\(382\) | 7.45830e48 | 0.650782 | ||||||||
\(383\) | − | 1.34719e49i | − | 1.11854i | −0.828984 | − | 0.559272i | \(-0.811081\pi\) | ||
0.828984 | − | 0.559272i | \(-0.188919\pi\) | |||||||
\(384\) | −1.32751e49 | + | 3.39726e48i | −1.04892 | + | 0.268433i | ||||
\(385\) | −1.97965e49 | −1.48879 | ||||||||
\(386\) | 8.86817e48i | 0.634856i | ||||||||
\(387\) | 9.61653e48 | − | 5.26694e48i | 0.655405 | − | 0.358963i | ||||
\(388\) | −1.07943e49 | −0.700470 | ||||||||
\(389\) | 3.22298e49i | 1.99166i | 0.0912415 | + | 0.995829i | \(0.470916\pi\) | ||||
−0.0912415 | + | 0.995829i | \(0.529084\pi\) | |||||||
\(390\) | −9.06776e48 | − | 3.54329e49i | −0.533670 | − | 2.08535i | ||||
\(391\) | 1.14284e49 | 0.640662 | ||||||||
\(392\) | 3.54917e48i | 0.189536i | ||||||||
\(393\) | −2.51933e49 | + | 6.44730e48i | −1.28182 | + | 0.328034i | ||||
\(394\) | 8.59563e48 | 0.416725 | ||||||||
\(395\) | 5.04618e49i | 2.33140i | ||||||||
\(396\) | 5.76808e48 | + | 1.05315e49i | 0.253993 | + | 0.463749i | ||||
\(397\) | 1.66907e49 | 0.700574 | 0.350287 | − | 0.936642i | \(-0.386084\pi\) | ||||
0.350287 | + | 0.936642i | \(0.386084\pi\) | |||||||
\(398\) | − | 5.69029e48i | − | 0.227696i | ||||||
\(399\) | −3.50293e48 | − | 1.36880e49i | −0.133643 | − | 0.522220i | ||||
\(400\) | 5.98398e49 | 2.17696 | ||||||||
\(401\) | − | 5.22212e49i | − | 1.81177i | −0.423522 | − | 0.905886i | \(-0.639206\pi\) | ||
0.423522 | − | 0.905886i | \(-0.360794\pi\) | |||||||
\(402\) | −4.42843e49 | + | 1.13330e49i | −1.46540 | + | 0.375014i | ||||
\(403\) | −3.95508e49 | −1.24842 | ||||||||
\(404\) | 7.91195e48i | 0.238253i | ||||||||
\(405\) | 4.85614e49 | + | 3.10340e49i | 1.39523 | + | 0.891644i | ||||
\(406\) | 3.85340e49 | 1.05645 | ||||||||
\(407\) | − | 6.51090e48i | − | 0.170352i | ||||||
\(408\) | −6.90390e48 | − | 2.69775e49i | −0.172406 | − | 0.673687i | ||||
\(409\) | −5.82974e49 | −1.38965 | −0.694826 | − | 0.719178i | \(-0.744519\pi\) | ||||
−0.694826 | + | 0.719178i | \(0.744519\pi\) | |||||||
\(410\) | − | 7.23221e49i | − | 1.64580i | ||||||
\(411\) | 2.22234e49 | − | 5.68728e48i | 0.482855 | − | 0.123569i | ||||
\(412\) | 2.41594e49 | 0.501233 | ||||||||
\(413\) | 9.88146e48i | 0.195781i | ||||||||
\(414\) | −3.24325e49 | + | 1.77632e49i | −0.613726 | + | 0.336135i | ||||
\(415\) | −8.28799e49 | −1.49808 | ||||||||
\(416\) | − | 5.57335e49i | − | 0.962371i | ||||||
\(417\) | 9.77001e48 | + | 3.81770e49i | 0.161180 | + | 0.629820i | ||||
\(418\) | −5.39813e49 | −0.850930 | ||||||||
\(419\) | − | 6.06466e49i | − | 0.913567i | −0.889578 | − | 0.456783i | \(-0.849001\pi\) | ||
0.889578 | − | 0.456783i | \(-0.150999\pi\) | |||||||
\(420\) | 4.55620e49 | − | 1.16599e49i | 0.655944 | − | 0.167865i | ||||
\(421\) | 1.33651e50 | 1.83913 | 0.919564 | − | 0.392941i | \(-0.128542\pi\) | ||||
0.919564 | + | 0.392941i | \(0.128542\pi\) | |||||||
\(422\) | 8.01172e49i | 1.05387i | ||||||||
\(423\) | −4.67589e49 | − | 8.53737e49i | −0.588027 | − | 1.07364i | ||||
\(424\) | 3.67473e49 | 0.441849 | ||||||||
\(425\) | 1.69316e50i | 1.94674i | ||||||||
\(426\) | 3.64097e49 | + | 1.42273e50i | 0.400345 | + | 1.56438i | ||||
\(427\) | 5.36193e49 | 0.563886 | ||||||||
\(428\) | 1.50484e49i | 0.151376i | ||||||||
\(429\) | 1.15593e50 | − | 2.95818e49i | 1.11235 | − | 0.284666i | ||||
\(430\) | −1.64072e50 | −1.51055 | ||||||||
\(431\) | 8.75519e49i | 0.771254i | 0.922655 | + | 0.385627i | \(0.126015\pi\) | ||||
−0.922655 | + | 0.385627i | \(0.873985\pi\) | |||||||
\(432\) | 1.01245e50 | + | 1.08329e50i | 0.853456 | + | 0.913171i | ||||
\(433\) | −2.17140e50 | −1.75174 | −0.875871 | − | 0.482545i | \(-0.839713\pi\) | ||||
−0.875871 | + | 0.482545i | \(0.839713\pi\) | |||||||
\(434\) | − | 1.54568e50i | − | 1.19348i | ||||||
\(435\) | −5.76397e49 | − | 2.25231e50i | −0.426016 | − | 1.66469i | ||||
\(436\) | −1.27853e50 | −0.904621 | ||||||||
\(437\) | − | 5.46973e49i | − | 0.370526i | ||||||
\(438\) | −1.30001e50 | + | 3.32690e49i | −0.843216 | + | 0.215790i | ||||
\(439\) | −6.53351e49 | −0.405808 | −0.202904 | − | 0.979199i | \(-0.565038\pi\) | ||||
−0.202904 | + | 0.979199i | \(0.565038\pi\) | |||||||
\(440\) | 1.86737e50i | 1.11078i | ||||||||
\(441\) | 4.68986e49 | − | 2.56862e49i | 0.267194 | − | 0.146341i | ||||
\(442\) | 2.66258e50 | 1.45305 | ||||||||
\(443\) | − | 1.65500e50i | − | 0.865223i | −0.901580 | − | 0.432612i | \(-0.857592\pi\) | ||
0.901580 | − | 0.432612i | \(-0.142408\pi\) | |||||||
\(444\) | 3.83486e48 | + | 1.49850e49i | 0.0192076 | + | 0.0750550i | ||||
\(445\) | 1.22979e50 | 0.590190 | ||||||||
\(446\) | 4.26616e49i | 0.196189i | ||||||||
\(447\) | 3.53200e50 | − | 9.03885e49i | 1.55660 | − | 0.398355i | ||||
\(448\) | −2.89430e49 | −0.122254 | ||||||||
\(449\) | 1.27526e50i | 0.516321i | 0.966102 | + | 0.258160i | \(0.0831163\pi\) | ||||
−0.966102 | + | 0.258160i | \(0.916884\pi\) | |||||||
\(450\) | −2.63167e50 | − | 4.80497e50i | −1.02139 | − | 1.86489i | ||||
\(451\) | 2.35937e50 | 0.877893 | ||||||||
\(452\) | 3.90882e49i | 0.139449i | ||||||||
\(453\) | 7.18334e49 | + | 2.80694e50i | 0.245731 | + | 0.960213i | ||||
\(454\) | −4.51519e49 | −0.148120 | ||||||||
\(455\) | − | 4.67333e50i | − | 1.47031i | ||||||
\(456\) | −1.29116e50 | + | 3.30425e49i | −0.389626 | + | 0.0997106i | ||||
\(457\) | −1.64482e50 | −0.476112 | −0.238056 | − | 0.971251i | \(-0.576510\pi\) | ||||
−0.238056 | + | 0.971251i | \(0.576510\pi\) | |||||||
\(458\) | 6.16349e49i | 0.171152i | ||||||||
\(459\) | −3.06514e50 | + | 2.86470e50i | −0.816600 | + | 0.763200i | ||||
\(460\) | 1.82067e50 | 0.465406 | ||||||||
\(461\) | 1.38516e50i | 0.339767i | 0.985464 | + | 0.169884i | \(0.0543392\pi\) | ||||
−0.985464 | + | 0.169884i | \(0.945661\pi\) | |||||||
\(462\) | 1.15608e50 | + | 4.51746e50i | 0.272139 | + | 1.06340i | ||||
\(463\) | 2.37863e50 | 0.537387 | 0.268694 | − | 0.963226i | \(-0.413408\pi\) | ||||
0.268694 | + | 0.963226i | \(0.413408\pi\) | |||||||
\(464\) | − | 5.98160e50i | − | 1.29711i | ||||||
\(465\) | −9.03448e50 | + | 2.31204e50i | −1.88060 | + | 0.481271i | ||||
\(466\) | 2.82484e50 | 0.564496 | ||||||||
\(467\) | − | 2.32560e50i | − | 0.446184i | −0.974797 | − | 0.223092i | \(-0.928385\pi\) | ||
0.974797 | − | 0.223092i | \(-0.0716151\pi\) | |||||||
\(468\) | −2.48617e50 | + | 1.36166e50i | −0.457993 | + | 0.250841i | ||||
\(469\) | −5.84076e50 | −1.03320 | ||||||||
\(470\) | 1.45660e51i | 2.47447i | ||||||||
\(471\) | 9.67284e49 | + | 3.77973e50i | 0.157818 | + | 0.616686i | ||||
\(472\) | 9.32101e49 | 0.146071 | ||||||||
\(473\) | − | 5.35253e50i | − | 0.805745i | ||||||
\(474\) | 1.15151e51 | − | 2.94688e50i | 1.66526 | − | 0.426161i | ||||
\(475\) | 8.10356e50 | 1.12589 | ||||||||
\(476\) | 3.42373e50i | 0.457054i | ||||||||
\(477\) | −2.65949e50 | − | 4.85577e50i | −0.341153 | − | 0.622887i | ||||
\(478\) | 8.52485e49 | 0.105089 | ||||||||
\(479\) | 2.65576e50i | 0.314640i | 0.987548 | + | 0.157320i | \(0.0502854\pi\) | ||||
−0.987548 | + | 0.157320i | \(0.949715\pi\) | |||||||
\(480\) | −3.25804e50 | − | 1.27310e51i | −0.370999 | − | 1.44971i | ||||
\(481\) | 1.53702e50 | 0.168238 | ||||||||
\(482\) | − | 1.46420e51i | − | 1.54066i | ||||||
\(483\) | −4.57738e50 | + | 1.17141e50i | −0.463044 | + | 0.118499i | ||||
\(484\) | 8.19961e49 | 0.0797501 | ||||||||
\(485\) | 2.52909e51i | 2.36522i | ||||||||
\(486\) | 4.24590e50 | − | 1.28938e51i | 0.381840 | − | 1.15956i | ||||
\(487\) | −1.00479e51 | −0.869014 | −0.434507 | − | 0.900669i | \(-0.643077\pi\) | ||||
−0.434507 | + | 0.900669i | \(0.643077\pi\) | |||||||
\(488\) | − | 5.05781e50i | − | 0.420713i | ||||||
\(489\) | 2.57592e50 | + | 1.00656e51i | 0.206094 | + | 0.805325i | ||||
\(490\) | −8.00159e50 | −0.615816 | ||||||||
\(491\) | − | 2.22260e51i | − | 1.64556i | −0.568362 | − | 0.822779i | \(-0.692423\pi\) | ||
0.568362 | − | 0.822779i | \(-0.307577\pi\) | |||||||
\(492\) | −5.43014e50 | + | 1.38965e50i | −0.386789 | + | 0.0989845i | ||||
\(493\) | 1.69248e51 | 1.15993 | ||||||||
\(494\) | − | 1.27433e51i | − | 0.840369i | ||||||
\(495\) | 2.46753e51 | − | 1.35146e51i | 1.56590 | − | 0.857637i | ||||
\(496\) | −2.39934e51 | −1.46535 | ||||||||
\(497\) | 1.87648e51i | 1.10299i | ||||||||
\(498\) | 4.84004e50 | + | 1.89128e51i | 0.273837 | + | 1.07004i | ||||
\(499\) | 2.09860e50 | 0.114293 | 0.0571465 | − | 0.998366i | \(-0.481800\pi\) | ||||
0.0571465 | + | 0.998366i | \(0.481800\pi\) | |||||||
\(500\) | 1.14867e51i | 0.602232i | ||||||||
\(501\) | −2.19489e51 | + | 5.61701e50i | −1.10789 | + | 0.283523i | ||||
\(502\) | −2.06181e51 | −1.00202 | ||||||||
\(503\) | − | 1.59022e51i | − | 0.744157i | −0.928201 | − | 0.372078i | \(-0.878645\pi\) | ||
0.928201 | − | 0.372078i | \(-0.121355\pi\) | |||||||
\(504\) | 5.53038e50 | + | 1.00975e51i | 0.249215 | + | 0.455025i | ||||
\(505\) | 1.85377e51 | 0.804486 | ||||||||
\(506\) | 1.80519e51i | 0.754505i | ||||||||
\(507\) | 8.24928e49 | + | 3.22347e50i | 0.0332097 | + | 0.129769i | ||||
\(508\) | −9.37393e50 | −0.363506 | ||||||||
\(509\) | 4.63601e51i | 1.73183i | 0.500188 | + | 0.865917i | \(0.333264\pi\) | ||||
−0.500188 | + | 0.865917i | \(0.666736\pi\) | |||||||
\(510\) | 6.08206e51 | − | 1.55648e51i | 2.18886 | − | 0.560158i | ||||
\(511\) | −1.71462e51 | −0.594524 | ||||||||
\(512\) | − | 1.05347e51i | − | 0.351961i | ||||||
\(513\) | 1.37107e51 | + | 1.46700e51i | 0.441396 | + | 0.472280i | ||||
\(514\) | 2.13824e51 | 0.663371 | ||||||||
\(515\) | − | 5.66054e51i | − | 1.69247i | ||||||
\(516\) | 3.15259e50 | + | 1.23190e51i | 0.0908497 | + | 0.355002i | ||||
\(517\) | −4.75188e51 | −1.31991 | ||||||||
\(518\) | 6.00680e50i | 0.160834i | ||||||||
\(519\) | −7.22315e51 | + | 1.84850e51i | −1.86443 | + | 0.477133i | ||||
\(520\) | −4.40827e51 | −1.09700 | ||||||||
\(521\) | − | 3.58692e51i | − | 0.860606i | −0.902684 | − | 0.430303i | \(-0.858407\pi\) | ||
0.902684 | − | 0.430303i | \(-0.141593\pi\) | |||||||
\(522\) | −4.80307e51 | + | 2.63062e51i | −1.11117 | + | 0.608582i | ||||
\(523\) | 8.65118e51 | 1.92994 | 0.964969 | − | 0.262365i | \(-0.0845024\pi\) | ||||
0.964969 | + | 0.262365i | \(0.0845024\pi\) | |||||||
\(524\) | − | 3.01595e51i | − | 0.648829i | ||||||
\(525\) | −1.73548e51 | − | 6.78152e51i | −0.360076 | − | 1.40702i | ||||
\(526\) | 2.67484e51 | 0.535264 | ||||||||
\(527\) | − | 6.78890e51i | − | 1.31038i | ||||||
\(528\) | 7.01243e51 | − | 1.79457e51i | 1.30564 | − | 0.334131i | ||||
\(529\) | 3.73834e51 | 0.671461 | ||||||||
\(530\) | 8.28466e51i | 1.43560i | ||||||||
\(531\) | −6.74583e50 | − | 1.23167e51i | −0.112782 | − | 0.205921i | ||||
\(532\) | 1.63862e51 | 0.264337 | ||||||||
\(533\) | 5.56974e51i | 0.866997i | ||||||||
\(534\) | −7.18178e50 | − | 2.80633e51i | −0.107882 | − | 0.421556i | ||||
\(535\) | 3.52582e51 | 0.511138 | ||||||||
\(536\) | 5.50949e51i | 0.770869i | ||||||||
\(537\) | 1.30377e51 | − | 3.33651e50i | 0.176071 | − | 0.0450589i | ||||
\(538\) | 2.76675e51 | 0.360668 | ||||||||
\(539\) | − | 2.61036e51i | − | 0.328484i | ||||||
\(540\) | −4.88308e51 | + | 4.56376e51i | −0.593216 | + | 0.554423i | ||||
\(541\) | −8.93589e51 | −1.04807 | −0.524034 | − | 0.851697i | \(-0.675574\pi\) | ||||
−0.524034 | + | 0.851697i | \(0.675574\pi\) | |||||||
\(542\) | − | 7.53086e51i | − | 0.852821i | ||||||
\(543\) | −3.13501e51 | − | 1.22503e52i | −0.342801 | − | 1.33952i | ||||
\(544\) | 9.56665e51 | 1.01014 | ||||||||
\(545\) | 2.99558e52i | 3.05455i | ||||||||
\(546\) | −1.06643e52 | + | 2.72915e51i | −1.05020 | + | 0.268761i | ||||
\(547\) | 4.41976e51 | 0.420378 | 0.210189 | − | 0.977661i | \(-0.432592\pi\) | ||||
0.210189 | + | 0.977661i | \(0.432592\pi\) | |||||||
\(548\) | 2.66043e51i | 0.244411i | ||||||||
\(549\) | −6.68337e51 | + | 3.66046e51i | −0.593091 | + | 0.324834i | ||||
\(550\) | −2.67443e52 | −2.29267 | ||||||||
\(551\) | − | 8.10035e51i | − | 0.670847i | ||||||
\(552\) | 1.10497e51 | + | 4.31777e51i | 0.0884117 | + | 0.345475i | ||||
\(553\) | 1.51876e52 | 1.17412 | ||||||||
\(554\) | − | 9.48882e51i | − | 0.708805i | ||||||
\(555\) | 3.51097e51 | − | 8.98505e50i | 0.253432 | − | 0.0648565i | ||||
\(556\) | −4.57027e51 | −0.318802 | ||||||||
\(557\) | − | 1.02056e52i | − | 0.688005i | −0.938969 | − | 0.344003i | \(-0.888217\pi\) | ||
0.938969 | − | 0.344003i | \(-0.111783\pi\) | |||||||
\(558\) | 1.05520e52 | + | 1.92661e52i | 0.687517 | + | 1.25529i | ||||
\(559\) | 1.26357e52 | 0.795745 | ||||||||
\(560\) | − | 2.83507e52i | − | 1.72580i | ||||||
\(561\) | 5.07772e51 | + | 1.98415e52i | 0.298796 | + | 1.16757i | ||||
\(562\) | −8.36967e50 | −0.0476122 | ||||||||
\(563\) | 2.11318e52i | 1.16219i | 0.813837 | + | 0.581094i | \(0.197375\pi\) | ||||
−0.813837 | + | 0.581094i | \(0.802625\pi\) | |||||||
\(564\) | 1.09366e52 | − | 2.79881e51i | 0.581538 | − | 0.148823i | ||||
\(565\) | 9.15834e51 | 0.470865 | ||||||||
\(566\) | − | 1.67394e52i | − | 0.832200i | ||||||
\(567\) | 9.34036e51 | − | 1.46156e52i | 0.449040 | − | 0.702651i | ||||
\(568\) | 1.77005e52 | 0.822937 | ||||||||
\(569\) | − | 9.67361e51i | − | 0.434966i | −0.976064 | − | 0.217483i | \(-0.930215\pi\) | ||
0.976064 | − | 0.217483i | \(-0.0697847\pi\) | |||||||
\(570\) | −7.44943e51 | − | 2.91092e52i | −0.323967 | − | 1.26592i | ||||
\(571\) | −3.71935e52 | −1.56452 | −0.782260 | − | 0.622952i | \(-0.785933\pi\) | ||||
−0.782260 | + | 0.622952i | \(0.785933\pi\) | |||||||
\(572\) | 1.38379e52i | 0.563050i | ||||||||
\(573\) | −1.31205e52 | + | 3.35772e51i | −0.516432 | + | 0.132162i | ||||
\(574\) | −2.17670e52 | −0.828842 | ||||||||
\(575\) | − | 2.70991e52i | − | 0.998310i | ||||||
\(576\) | 3.60760e51 | − | 1.97587e51i | 0.128585 | − | 0.0704257i | ||||
\(577\) | −4.10688e52 | −1.41635 | −0.708177 | − | 0.706035i | \(-0.750482\pi\) | ||||
−0.708177 | + | 0.706035i | \(0.750482\pi\) | |||||||
\(578\) | 9.12048e51i | 0.304361i | ||||||||
\(579\) | −3.99244e51 | − | 1.56007e52i | −0.128927 | − | 0.503793i | ||||
\(580\) | 2.69630e52 | 0.842629 | ||||||||
\(581\) | 2.49445e52i | 0.754448i | ||||||||
\(582\) | 5.77126e52 | − | 1.47694e52i | 1.68941 | − | 0.432342i | ||||
\(583\) | −2.70271e52 | −0.765767 | ||||||||
\(584\) | 1.61737e52i | 0.443572i | ||||||||
\(585\) | 3.19037e52 | + | 5.82507e52i | 0.846993 | + | 1.54646i | ||||
\(586\) | 1.15621e52 | 0.297155 | ||||||||
\(587\) | 6.81962e52i | 1.69682i | 0.529338 | + | 0.848411i | \(0.322440\pi\) | ||||
−0.529338 | + | 0.848411i | \(0.677560\pi\) | |||||||
\(588\) | 1.53748e51 | + | 6.00781e51i | 0.0370374 | + | 0.144726i | ||||
\(589\) | −3.24921e52 | −0.757858 | ||||||||
\(590\) | 2.10142e52i | 0.474596i | ||||||||
\(591\) | −1.51213e52 | + | 3.86974e51i | −0.330694 | + | 0.0846291i | ||||
\(592\) | 9.32430e51 | 0.197471 | ||||||||
\(593\) | − | 8.57574e52i | − | 1.75886i | −0.476025 | − | 0.879432i | \(-0.657923\pi\) | ||
0.476025 | − | 0.879432i | \(-0.342077\pi\) | |||||||
\(594\) | −4.52496e52 | − | 4.84156e52i | −0.898819 | − | 0.961708i | ||||
\(595\) | 8.02178e52 | 1.54329 | ||||||||
\(596\) | 4.22824e52i | 0.787918i | ||||||||
\(597\) | 2.56176e51 | + | 1.00103e52i | 0.0462409 | + | 0.180690i | ||||
\(598\) | −4.26149e52 | −0.745141 | ||||||||
\(599\) | 8.74442e51i | 0.148123i | 0.997254 | + | 0.0740613i | \(0.0235960\pi\) | ||||
−0.997254 | + | 0.0740613i | \(0.976404\pi\) | |||||||
\(600\) | −6.39689e52 | + | 1.63705e52i | −1.04977 | + | 0.268651i | ||||
\(601\) | 4.20628e52 | 0.668780 | 0.334390 | − | 0.942435i | \(-0.391470\pi\) | ||||
0.334390 | + | 0.942435i | \(0.391470\pi\) | |||||||
\(602\) | 4.93812e52i | 0.760726i | ||||||||
\(603\) | 7.28022e52 | − | 3.98735e52i | 1.08671 | − | 0.595189i | ||||
\(604\) | −3.36026e52 | −0.486039 | ||||||||
\(605\) | − | 1.92116e52i | − | 0.269285i | ||||||
\(606\) | −1.08257e52 | − | 4.23021e52i | −0.147053 | − | 0.574622i | ||||
\(607\) | −1.96991e52 | −0.259335 | −0.129667 | − | 0.991558i | \(-0.541391\pi\) | ||||
−0.129667 | + | 0.991558i | \(0.541391\pi\) | |||||||
\(608\) | − | 4.57866e52i | − | 0.584212i | ||||||
\(609\) | −6.77884e52 | + | 1.73479e52i | −0.838352 | + | 0.214546i | ||||
\(610\) | 1.14028e53 | 1.36693 | ||||||||
\(611\) | − | 1.12177e53i | − | 1.30353i | ||||||
\(612\) | −2.33730e52 | − | 4.26750e52i | −0.263292 | − | 0.480725i | ||||
\(613\) | −8.00587e52 | −0.874298 | −0.437149 | − | 0.899389i | \(-0.644012\pi\) | ||||
−0.437149 | + | 0.899389i | \(0.644012\pi\) | |||||||
\(614\) | − | 1.35285e52i | − | 0.143236i | ||||||
\(615\) | 3.25593e52 | + | 1.27228e53i | 0.334232 | + | 1.30604i | ||||
\(616\) | 5.62026e52 | 0.559400 | ||||||||
\(617\) | − | 9.48033e52i | − | 0.914966i | −0.889218 | − | 0.457483i | \(-0.848751\pi\) | ||
0.889218 | − | 0.457483i | \(-0.151249\pi\) | |||||||
\(618\) | −1.29171e53 | + | 3.30566e52i | −1.20888 | + | 0.309369i | ||||
\(619\) | 6.24570e52 | 0.566838 | 0.283419 | − | 0.958996i | \(-0.408531\pi\) | ||||
0.283419 | + | 0.958996i | \(0.408531\pi\) | |||||||
\(620\) | − | 1.08154e53i | − | 0.951920i | ||||||
\(621\) | 4.90578e52 | − | 4.58498e52i | 0.418762 | − | 0.391378i | ||||
\(622\) | 1.21641e53 | 1.00708 | ||||||||
\(623\) | − | 3.70134e52i | − | 0.297225i | ||||||
\(624\) | 4.23643e52 | + | 1.65542e53i | 0.329984 | + | 1.28944i | ||||
\(625\) | 3.86203e52 | 0.291807 | ||||||||
\(626\) | 2.79577e53i | 2.04923i | ||||||||
\(627\) | 9.49630e52 | − | 2.43023e52i | 0.675260 | − | 0.172808i | ||||
\(628\) | −4.52481e52 | −0.312153 | ||||||||
\(629\) | 2.63830e52i | 0.176588i | ||||||||
\(630\) | −2.27648e53 | + | 1.24682e53i | −1.47841 | + | 0.809718i | ||||
\(631\) | −1.78963e53 | −1.12773 | −0.563866 | − | 0.825867i | \(-0.690686\pi\) | ||||
−0.563866 | + | 0.825867i | \(0.690686\pi\) | |||||||
\(632\) | − | 1.43262e53i | − | 0.876005i | ||||||
\(633\) | −3.60686e52 | − | 1.40941e53i | −0.214022 | − | 0.836308i | ||||
\(634\) | 1.80888e53 | 1.04163 | ||||||||
\(635\) | 2.19631e53i | 1.22742i | ||||||||
\(636\) | 6.22035e52 | − | 1.59187e52i | 0.337388 | − | 0.0863421i | ||||
\(637\) | 6.16226e52 | 0.324407 | ||||||||
\(638\) | 2.67337e53i | 1.36605i | ||||||||
\(639\) | −1.28103e53 | − | 2.33893e53i | −0.635392 | − | 1.16012i | ||||
\(640\) | −3.72346e53 | −1.79278 | ||||||||
\(641\) | 2.19558e53i | 1.02624i | 0.858318 | + | 0.513118i | \(0.171510\pi\) | ||||
−0.858318 | + | 0.513118i | \(0.828490\pi\) | |||||||
\(642\) | −2.05902e52 | − | 8.04576e52i | −0.0934318 | − | 0.365091i | ||||
\(643\) | −3.76988e52 | −0.166081 | −0.0830403 | − | 0.996546i | \(-0.526463\pi\) | ||||
−0.0830403 | + | 0.996546i | \(0.526463\pi\) | |||||||
\(644\) | − | 5.47970e52i | − | 0.234383i | ||||||
\(645\) | 2.88633e53 | − | 7.38651e52i | 1.19870 | − | 0.306764i | ||||
\(646\) | 2.18739e53 | 0.882081 | ||||||||
\(647\) | − | 2.71575e52i | − | 0.106343i | −0.998585 | − | 0.0531715i | \(-0.983067\pi\) | ||
0.998585 | − | 0.0531715i | \(-0.0169330\pi\) | |||||||
\(648\) | −1.37867e53 | − | 8.81060e52i | −0.524245 | − | 0.335027i | ||||
\(649\) | −6.85547e52 | −0.253156 | ||||||||
\(650\) | − | 6.31351e53i | − | 2.26421i | ||||||
\(651\) | 6.95861e52 | + | 2.71913e53i | 0.242373 | + | 0.947089i | ||||
\(652\) | −1.20498e53 | −0.407638 | ||||||||
\(653\) | 1.97468e52i | 0.0648852i | 0.999474 | + | 0.0324426i | \(0.0103286\pi\) | ||||
−0.999474 | + | 0.0324426i | \(0.989671\pi\) | |||||||
\(654\) | 6.83578e53 | − | 1.74937e53i | 2.18178 | − | 0.558346i | ||||
\(655\) | −7.06636e53 | −2.19084 | ||||||||
\(656\) | 3.37887e53i | 1.01765i | ||||||||
\(657\) | 2.13718e53 | − | 1.17053e53i | 0.625316 | − | 0.342483i | ||||
\(658\) | 4.38397e53 | 1.24616 | ||||||||
\(659\) | 6.36429e51i | 0.0175763i | 0.999961 | + | 0.00878814i | \(0.00279739\pi\) | ||||
−0.999961 | + | 0.00878814i | \(0.997203\pi\) | |||||||
\(660\) | 8.08932e52 | + | 3.16096e53i | 0.217059 | + | 0.848172i | ||||
\(661\) | 6.25141e53 | 1.62986 | 0.814930 | − | 0.579560i | \(-0.196775\pi\) | ||||
0.814930 | + | 0.579560i | \(0.196775\pi\) | |||||||
\(662\) | − | 5.29052e53i | − | 1.34028i | ||||||
\(663\) | −4.68397e53 | + | 1.19869e53i | −1.15307 | + | 0.295087i | ||||
\(664\) | 2.35297e53 | 0.562890 | ||||||||
\(665\) | − | 3.83928e53i | − | 0.892562i | ||||||
\(666\) | −4.10069e52 | − | 7.48717e52i | −0.0926503 | − | 0.169164i | ||||
\(667\) | −2.70883e53 | −0.594828 | ||||||||
\(668\) | − | 2.62756e53i | − | 0.560789i | ||||||
\(669\) | −1.92062e52 | − | 7.50495e52i | −0.0398423 | − | 0.155687i | ||||
\(670\) | −1.24211e54 | −2.50461 | ||||||||
\(671\) | 3.71995e53i | 0.729137i | ||||||||
\(672\) | −3.83169e53 | + | 9.80580e52i | −0.730086 | + | 0.186839i | ||||
\(673\) | −8.96991e53 | −1.66151 | −0.830753 | − | 0.556641i | \(-0.812090\pi\) | ||||
−0.830753 | + | 0.556641i | \(0.812090\pi\) | |||||||
\(674\) | 6.84854e53i | 1.23327i | ||||||||
\(675\) | 6.79277e53 | + | 7.26805e53i | 1.18926 | + | 1.27247i | ||||
\(676\) | −3.85889e52 | −0.0656864 | ||||||||
\(677\) | 2.57942e53i | 0.426911i | 0.976953 | + | 0.213455i | \(0.0684718\pi\) | ||||
−0.976953 | + | 0.213455i | \(0.931528\pi\) | |||||||
\(678\) | −5.34831e52 | − | 2.08989e53i | −0.0860701 | − | 0.336325i | ||||
\(679\) | 7.61185e53 | 1.19114 | ||||||||
\(680\) | − | 7.56680e53i | − | 1.15144i | ||||||
\(681\) | 7.94305e52 | − | 2.03273e52i | 0.117542 | − | 0.0300805i | ||||
\(682\) | 1.07234e54 | 1.54323 | ||||||||
\(683\) | 7.21883e53i | 1.01035i | 0.863016 | + | 0.505177i | \(0.168573\pi\) | ||||
−0.863016 | + | 0.505177i | \(0.831427\pi\) | |||||||
\(684\) | −2.04246e53 | + | 1.11865e53i | −0.278027 | + | 0.152274i | ||||
\(685\) | 6.23336e53 | 0.825280 | ||||||||
\(686\) | 1.03134e54i | 1.32814i | ||||||||
\(687\) | −2.77480e52 | − | 1.08427e53i | −0.0347579 | − | 0.135819i | ||||
\(688\) | 7.66540e53 | 0.934017 | ||||||||
\(689\) | − | 6.38026e53i | − | 0.756263i | ||||||
\(690\) | −9.73439e53 | + | 2.49116e53i | −1.12247 | + | 0.287256i | ||||
\(691\) | 6.84772e53 | 0.768181 | 0.384090 | − | 0.923296i | \(-0.374515\pi\) | ||||
0.384090 | + | 0.923296i | \(0.374515\pi\) | |||||||
\(692\) | − | 8.64702e53i | − | 0.943736i | ||||||
\(693\) | −4.06751e53 | − | 7.42658e53i | −0.431914 | − | 0.788601i | ||||
\(694\) | −1.47728e54 | −1.52627 | ||||||||
\(695\) | 1.07081e54i | 1.07647i | ||||||||
\(696\) | 1.63640e53 | + | 6.39436e53i | 0.160072 | + | 0.625491i | ||||
\(697\) | −9.56046e53 | −0.910030 | ||||||||
\(698\) | − | 1.65302e54i | − | 1.53117i | ||||||
\(699\) | −4.96940e53 | + | 1.27174e53i | −0.447959 | + | 0.114639i | ||||
\(700\) | 8.11834e53 | 0.712204 | ||||||||
\(701\) | − | 6.20423e53i | − | 0.529719i | −0.964287 | − | 0.264860i | \(-0.914674\pi\) | ||
0.964287 | − | 0.264860i | \(-0.0853256\pi\) | |||||||
\(702\) | 1.14294e54 | − | 1.06820e54i | 0.949772 | − | 0.887663i | ||||
\(703\) | 1.26271e53 | 0.102130 | ||||||||
\(704\) | − | 2.00798e53i | − | 0.158081i | ||||||
\(705\) | −6.55760e53 | − | 2.56243e54i | −0.502518 | − | 1.96363i | ||||
\(706\) | −4.66842e53 | −0.348242 | ||||||||
\(707\) | − | 5.57932e53i | − | 0.405147i | ||||||
\(708\) | 1.57780e53 | − | 4.03781e52i | 0.111537 | − | 0.0285439i | ||||
\(709\) | 1.50676e54 | 1.03697 | 0.518485 | − | 0.855087i | \(-0.326496\pi\) | ||||
0.518485 | + | 0.855087i | \(0.326496\pi\) | |||||||
\(710\) | 3.99057e54i | 2.67378i | ||||||||
\(711\) | −1.89306e54 | + | 1.03682e54i | −1.23493 | + | 0.676365i | ||||
\(712\) | −3.49141e53 | −0.221759 | ||||||||
\(713\) | 1.08657e54i | 0.671979i | ||||||||
\(714\) | −4.68458e53 | − | 1.83053e54i | −0.282101 | − | 1.10233i | ||||
\(715\) | 3.24222e54 | 1.90120 | ||||||||
\(716\) | 1.56077e53i | 0.0891234i | ||||||||
\(717\) | −1.49968e53 | + | 3.83788e52i | −0.0833939 | + | 0.0213416i | ||||
\(718\) | −1.50788e53 | −0.0816584 | ||||||||
\(719\) | − | 2.78504e54i | − | 1.46887i | −0.678681 | − | 0.734434i | \(-0.737448\pi\) | ||
0.678681 | − | 0.734434i | \(-0.262552\pi\) | |||||||
\(720\) | 1.93543e54 | + | 3.53377e54i | 0.994169 | + | 1.81518i | ||||
\(721\) | −1.70367e54 | −0.852343 | ||||||||
\(722\) | 1.45837e54i | 0.710659i | ||||||||
\(723\) | 6.59181e53 | + | 2.57580e54i | 0.312880 | + | 1.22260i | ||||
\(724\) | 1.46651e54 | 0.678036 | ||||||||
\(725\) | − | 4.01321e54i | − | 1.80747i | ||||||
\(726\) | −4.38401e53 | + | 1.12193e53i | −0.192343 | + | 0.0492231i | ||||
\(727\) | −1.29791e54 | −0.554743 | −0.277371 | − | 0.960763i | \(-0.589463\pi\) | ||||
−0.277371 | + | 0.960763i | \(0.589463\pi\) | |||||||
\(728\) | 1.32677e54i | 0.552458i | ||||||||
\(729\) | −1.66455e53 | + | 2.45941e54i | −0.0675263 | + | 0.997717i | ||||
\(730\) | −3.64635e54 | −1.44120 | ||||||||
\(731\) | 2.16891e54i | 0.835242i | ||||||||
\(732\) | −2.19101e53 | − | 8.56155e53i | −0.0822119 | − | 0.321249i | ||||
\(733\) | −3.00923e54 | −1.10022 | −0.550111 | − | 0.835092i | \(-0.685415\pi\) | ||||
−0.550111 | + | 0.835092i | \(0.685415\pi\) | |||||||
\(734\) | − | 8.62100e53i | − | 0.307137i | ||||||
\(735\) | 1.40763e54 | − | 3.60230e53i | 0.488684 | − | 0.125061i | ||||
\(736\) | −1.53115e54 | −0.518011 | ||||||||
\(737\) | − | 4.05215e54i | − | 1.33599i | ||||||
\(738\) | 2.71314e54 | − | 1.48598e54i | 0.871769 | − | 0.477465i | ||||
\(739\) | −3.54901e54 | −1.11138 | −0.555690 | − | 0.831389i | \(-0.687546\pi\) | ||||
−0.555690 | + | 0.831389i | \(0.687546\pi\) | |||||||
\(740\) | 4.20307e53i | 0.128282i | ||||||||
\(741\) | 5.73702e53 | + | 2.24178e54i | 0.170663 | + | 0.666880i | ||||
\(742\) | 2.49345e54 | 0.722982 | ||||||||
\(743\) | − | 7.43135e53i | − | 0.210030i | −0.994471 | − | 0.105015i | \(-0.966511\pi\) | ||
0.994471 | − | 0.105015i | \(-0.0334890\pi\) | |||||||
\(744\) | 2.56491e54 | − | 6.56394e53i | 0.706620 | − | 0.180833i | ||||
\(745\) | 9.90675e54 | 2.66049 | ||||||||
\(746\) | 6.02837e54i | 1.57820i | ||||||||
\(747\) | −1.70290e54 | − | 3.10921e54i | −0.434609 | − | 0.793521i | ||||
\(748\) | −2.37528e54 | −0.590996 | ||||||||
\(749\) | − | 1.06117e54i | − | 0.257414i | ||||||
\(750\) | −1.57168e54 | − | 6.14146e54i | −0.371707 | − | 1.45247i | ||||
\(751\) | −5.13765e54 | −1.18469 | −0.592346 | − | 0.805684i | \(-0.701798\pi\) | ||||
−0.592346 | + | 0.805684i | \(0.701798\pi\) | |||||||
\(752\) | − | 6.80520e54i | − | 1.53004i | ||||||
\(753\) | 3.62711e54 | − | 9.28225e53i | 0.795162 | − | 0.203493i | ||||
\(754\) | −6.31101e54 | −1.34910 | ||||||||
\(755\) | 7.87307e54i | 1.64116i | ||||||||
\(756\) | 1.37357e54 | + | 1.46967e54i | 0.279213 | + | 0.298749i | ||||
\(757\) | 8.88483e54 | 1.76128 | 0.880638 | − | 0.473789i | \(-0.157114\pi\) | ||||
0.880638 | + | 0.473789i | \(0.157114\pi\) | |||||||
\(758\) | − | 8.34292e54i | − | 1.61288i | ||||||
\(759\) | −8.12692e53 | − | 3.17565e54i | −0.153226 | − | 0.598741i | ||||
\(760\) | −3.62152e54 | −0.665937 | ||||||||
\(761\) | 8.14284e54i | 1.46039i | 0.683241 | + | 0.730193i | \(0.260570\pi\) | ||||
−0.683241 | + | 0.730193i | \(0.739430\pi\) | |||||||
\(762\) | 5.01187e54 | − | 1.28260e54i | 0.876709 | − | 0.224362i | ||||
\(763\) | 9.01587e54 | 1.53830 | ||||||||
\(764\) | − | 1.57069e54i | − | 0.261407i | ||||||
\(765\) | −9.99874e54 | + | 5.47627e54i | −1.62322 | + | 0.889033i | ||||
\(766\) | −8.62278e54 | −1.36553 | ||||||||
\(767\) | − | 1.61836e54i | − | 0.250014i | ||||||
\(768\) | 1.93326e54 | + | 7.55435e54i | 0.291358 | + | 1.13850i | ||||
\(769\) | 2.06056e54 | 0.302959 | 0.151480 | − | 0.988460i | \(-0.451596\pi\) | ||||
0.151480 | + | 0.988460i | \(0.451596\pi\) | |||||||
\(770\) | 1.26708e55i | 1.81753i | ||||||||
\(771\) | −3.76155e54 | + | 9.62630e53i | −0.526421 | + | 0.134718i | ||||
\(772\) | 1.86760e54 | 0.255009 | ||||||||
\(773\) | − | 4.04901e52i | − | 0.00539434i | −0.999996 | − | 0.00269717i | \(-0.999141\pi\) | ||
0.999996 | − | 0.00269717i | \(-0.000858537\pi\) | |||||||
\(774\) | −3.37113e54 | − | 6.15511e54i | −0.438226 | − | 0.800125i | ||||
\(775\) | −1.60978e55 | −2.04190 | ||||||||
\(776\) | − | 7.18013e54i | − | 0.888709i | ||||||
\(777\) | −2.70425e53 | − | 1.05671e54i | −0.0326624 | − | 0.127631i | ||||
\(778\) | 2.06288e55 | 2.43143 | ||||||||
\(779\) | 4.57570e54i | 0.526315i | ||||||||
\(780\) | −7.46204e54 | + | 1.90964e54i | −0.837646 | + | 0.214365i | ||||
\(781\) | −1.30184e55 | −1.42623 | ||||||||
\(782\) | − | 7.31484e54i | − | 0.782126i | ||||||
\(783\) | 7.26517e54 | − | 6.79008e54i | 0.758180 | − | 0.708600i | ||||
\(784\) | 3.73832e54 | 0.380777 | ||||||||
\(785\) | 1.06016e55i | 1.05402i | ||||||||
\(786\) | 4.12663e54 | + | 1.61251e55i | 0.400467 | + | 1.56486i | ||||
\(787\) | 9.33817e54 | 0.884589 | 0.442295 | − | 0.896870i | \(-0.354165\pi\) | ||||
0.442295 | + | 0.896870i | \(0.354165\pi\) | |||||||
\(788\) | − | 1.81021e54i | − | 0.167390i | ||||||
\(789\) | −4.70553e54 | + | 1.20421e54i | −0.424762 | + | 0.108702i | ||||
\(790\) | 3.22983e55 | 2.84620 | ||||||||
\(791\) | − | 2.75641e54i | − | 0.237132i | ||||||
\(792\) | −7.00536e54 | + | 3.83681e54i | −0.588372 | + | 0.322249i | ||||
\(793\) | −8.78164e54 | −0.720087 | ||||||||
\(794\) | − | 1.06830e55i | − | 0.855267i | ||||||
\(795\) | −3.72974e54 | − | 1.45742e55i | −0.291544 | − | 1.13923i | ||||
\(796\) | −1.19835e54 | −0.0914612 | ||||||||
\(797\) | − | 9.06547e54i | − | 0.675589i | −0.941220 | − | 0.337794i | \(-0.890319\pi\) | ||
0.941220 | − | 0.337794i | \(-0.109681\pi\) | |||||||
\(798\) | −8.76106e54 | + | 2.24207e54i | −0.637531 | + | 0.163153i | ||||
\(799\) | 1.92552e55 | 1.36823 | ||||||||
\(800\) | − | 2.26844e55i | − | 1.57405i | ||||||
\(801\) | 2.52681e54 | + | 4.61353e54i | 0.171220 | + | 0.312619i | ||||
\(802\) | −3.34245e55 | −2.21183 | ||||||||
\(803\) | − | 1.18955e55i | − | 0.768753i | ||||||
\(804\) | 2.38668e54 | + | 9.32611e54i | 0.150636 | + | 0.588621i | ||||
\(805\) | −1.28389e55 | −0.791419 | ||||||||
\(806\) | 2.53147e55i | 1.52408i | ||||||||
\(807\) | −4.86723e54 | + | 1.24559e54i | −0.286210 | + | 0.0732449i | ||||
\(808\) | −5.26288e54 | −0.302279 | ||||||||
\(809\) | − | 1.36999e55i | − | 0.768591i | −0.923210 | − | 0.384296i | \(-0.874444\pi\) | ||
0.923210 | − | 0.384296i | \(-0.125556\pi\) | |||||||
\(810\) | 1.98635e55 | − | 3.10820e55i | 1.08853 | − | 1.70331i | ||||
\(811\) | 1.50149e55 | 0.803761 | 0.401880 | − | 0.915692i | \(-0.368357\pi\) | ||||
0.401880 | + | 0.915692i | \(0.368357\pi\) | |||||||
\(812\) | − | 8.11512e54i | − | 0.424356i | ||||||
\(813\) | 3.39038e54 | + | 1.32482e55i | 0.173192 | + | 0.676761i | ||||
\(814\) | −4.16734e54 | −0.207967 | ||||||||
\(815\) | 2.82326e55i | 1.37644i | ||||||||
\(816\) | −2.84152e55 | + | 7.27184e54i | −1.35344 | + | 0.346363i | ||||
\(817\) | 1.03806e55 | 0.483061 | ||||||||
\(818\) | 3.73136e55i | 1.69650i | ||||||||
\(819\) | 1.75319e55 | − | 9.60213e54i | 0.778814 | − | 0.426554i | ||||
\(820\) | −1.52308e55 | −0.661087 | ||||||||
\(821\) | 3.10003e55i | 1.31476i | 0.753560 | + | 0.657380i | \(0.228335\pi\) | ||||
−0.753560 | + | 0.657380i | \(0.771665\pi\) | |||||||
\(822\) | −3.64017e54 | − | 1.42242e55i | −0.150854 | − | 0.589474i | ||||
\(823\) | 1.06953e55 | 0.433107 | 0.216554 | − | 0.976271i | \(-0.430518\pi\) | ||||
0.216554 | + | 0.976271i | \(0.430518\pi\) | |||||||
\(824\) | 1.60704e55i | 0.635930i | ||||||||
\(825\) | 4.70482e55 | − | 1.20403e55i | 1.81936 | − | 0.465598i | ||||
\(826\) | 6.32469e54 | 0.239011 | ||||||||
\(827\) | − | 4.53445e55i | − | 1.67464i | −0.546716 | − | 0.837318i | \(-0.684122\pi\) | ||
0.546716 | − | 0.837318i | \(-0.315878\pi\) | |||||||
\(828\) | 3.74086e54 | + | 6.83017e54i | 0.135019 | + | 0.246522i | ||||
\(829\) | −2.66453e55 | −0.939906 | −0.469953 | − | 0.882691i | \(-0.655729\pi\) | ||||
−0.469953 | + | 0.882691i | \(0.655729\pi\) | |||||||
\(830\) | 5.30477e55i | 1.82887i | ||||||||
\(831\) | 4.27185e54 | + | 1.66926e55i | 0.143945 | + | 0.562475i | ||||
\(832\) | 4.74022e54 | 0.156119 | ||||||||
\(833\) | 1.05775e55i | 0.340509i | ||||||||
\(834\) | 2.44354e55 | − | 6.25335e54i | 0.768891 | − | 0.196769i | ||||
\(835\) | −6.15635e55 | −1.89357 | ||||||||
\(836\) | 1.13683e55i | 0.341802i | ||||||||
\(837\) | −2.72364e55 | − | 2.91421e55i | −0.800508 | − | 0.856518i | ||||
\(838\) | −3.88172e55 | −1.11529 | ||||||||
\(839\) | − | 6.89502e55i | − | 1.93668i | −0.249630 | − | 0.968341i | \(-0.580309\pi\) | ||
0.249630 | − | 0.968341i | \(-0.419691\pi\) | |||||||
\(840\) | 7.75596e54 | + | 3.03070e55i | 0.212975 | + | 0.832216i | ||||
\(841\) | −2.86644e54 | −0.0769517 | ||||||||
\(842\) | − | 8.55440e55i | − | 2.24522i | ||||||
\(843\) | 1.47238e54 | − | 3.76802e53i | 0.0377829 | − | 0.00966916i | ||||
\(844\) | 1.68724e55 | 0.423321 | ||||||||
\(845\) | 9.04137e54i | 0.221797i | ||||||||
\(846\) | −5.46439e55 | + | 2.99283e55i | −1.31071 | + | 0.717869i | ||||
\(847\) | −5.78217e54 | −0.135615 | ||||||||
\(848\) | − | 3.87057e55i | − | 0.887675i | ||||||
\(849\) | 7.53605e54 | + | 2.94477e55i | 0.169004 | + | 0.660397i | ||||
\(850\) | 1.08371e56 | 2.37660 | ||||||||
\(851\) | − | 4.22261e54i | − | 0.0905565i | ||||||
\(852\) | 2.99622e55 | − | 7.66774e54i | 0.628380 | − | 0.160811i | ||||
\(853\) | 4.16393e55 | 0.854026 | 0.427013 | − | 0.904245i | \(-0.359566\pi\) | ||||
0.427013 | + | 0.904245i | \(0.359566\pi\) | |||||||
\(854\) | − | 3.43193e55i | − | 0.688398i | ||||||
\(855\) | 2.62098e55 | + | 4.78546e55i | 0.514171 | + | 0.938789i | ||||
\(856\) | −1.00099e55 | −0.192056 | ||||||||
\(857\) | 4.14276e55i | 0.777416i | 0.921361 | + | 0.388708i | \(0.127079\pi\) | ||||
−0.921361 | + | 0.388708i | \(0.872921\pi\) | |||||||
\(858\) | −1.89340e55 | − | 7.39860e55i | −0.347523 | − | 1.35797i | ||||
\(859\) | 2.72913e54 | 0.0489952 | 0.0244976 | − | 0.999700i | \(-0.492201\pi\) | ||||
0.0244976 | + | 0.999700i | \(0.492201\pi\) | |||||||
\(860\) | 3.45530e55i | 0.606757i | ||||||||
\(861\) | 3.82921e55 | − | 9.79946e54i | 0.657732 | − | 0.168322i | ||||
\(862\) | 5.60381e55 | 0.941554 | ||||||||
\(863\) | − | 7.71673e55i | − | 1.26832i | −0.773203 | − | 0.634159i | \(-0.781346\pi\) | ||
0.773203 | − | 0.634159i | \(-0.218654\pi\) | |||||||
\(864\) | 4.10659e55 | − | 3.83804e55i | 0.660267 | − | 0.617090i | ||||
\(865\) | −2.02599e56 | −3.18663 | ||||||||
\(866\) | 1.38982e56i | 2.13854i | ||||||||
\(867\) | −4.10603e54 | − | 1.60446e55i | −0.0618100 | − | 0.241527i | ||||
\(868\) | −3.25514e55 | −0.479396 | ||||||||
\(869\) | 1.05367e56i | 1.51820i | ||||||||
\(870\) | −1.44161e56 | + | 3.68926e55i | −2.03227 | + | 0.520084i | ||||
\(871\) | 9.56587e55 | 1.31941 | ||||||||
\(872\) | − | 8.50451e55i | − | 1.14772i | ||||||
\(873\) | −9.48779e55 | + | 5.19643e55i | −1.25284 | + | 0.686174i | ||||
\(874\) | −3.50093e55 | −0.452342 | ||||||||
\(875\) | − | 8.10012e55i | − | 1.02409i | ||||||
\(876\) | 7.00633e54 | + | 2.73778e55i | 0.0866788 | + | 0.338704i | ||||
\(877\) | 1.33125e56 | 1.61164 | 0.805820 | − | 0.592160i | \(-0.201725\pi\) | ||||
0.805820 | + | 0.592160i | \(0.201725\pi\) | |||||||
\(878\) | 4.18181e55i | 0.495414i | ||||||||
\(879\) | −2.03399e55 | + | 5.20526e54i | −0.235809 | + | 0.0603467i | ||||
\(880\) | 1.96689e56 | 2.23156 | ||||||||
\(881\) | 1.40199e56i | 1.55669i | 0.627834 | + | 0.778347i | \(0.283942\pi\) | ||||
−0.627834 | + | 0.778347i | \(0.716058\pi\) | |||||||
\(882\) | −1.64406e55 | − | 3.00177e55i | −0.178655 | − | 0.326193i | ||||
\(883\) | −1.26801e56 | −1.34855 | −0.674277 | − | 0.738479i | \(-0.735545\pi\) | ||||
−0.674277 | + | 0.738479i | \(0.735545\pi\) | |||||||
\(884\) | − | 5.60730e55i | − | 0.583662i | ||||||
\(885\) | −9.46055e54 | − | 3.69678e55i | −0.0963817 | − | 0.376618i | ||||
\(886\) | −1.05929e56 | −1.05627 | ||||||||
\(887\) | 9.99145e55i | 0.975169i | 0.873076 | + | 0.487585i | \(0.162122\pi\) | ||||
−0.873076 | + | 0.487585i | \(0.837878\pi\) | |||||||
\(888\) | −9.96772e54 | + | 2.55087e54i | −0.0952246 | + | 0.0243693i | ||||
\(889\) | 6.61027e55 | 0.618139 | ||||||||
\(890\) | − | 7.87136e55i | − | 0.720509i | ||||||
\(891\) | 1.01399e56 | + | 6.48006e55i | 0.908567 | + | 0.580635i | ||||
\(892\) | 8.98437e54 | 0.0788053 | ||||||||
\(893\) | − | 9.21567e55i | − | 0.791315i | ||||||
\(894\) | −5.78537e55 | − | 2.26067e56i | −0.486316 | − | 1.90031i | ||||
\(895\) | 3.65688e55 | 0.300935 | ||||||||
\(896\) | 1.12066e56i | 0.902862i | ||||||||
\(897\) | 7.49673e55 | − | 1.91851e55i | 0.591311 | − | 0.151324i | ||||
\(898\) | 8.16240e55 | 0.630329 | ||||||||
\(899\) | 1.60914e56i | 1.21664i | ||||||||
\(900\) | −1.01191e56 | + | 5.54219e55i | −0.749090 | + | 0.410274i | ||||
\(901\) | 1.09517e56 | 0.793800 | ||||||||
\(902\) | − | 1.51013e56i | − | 1.07174i | ||||||
\(903\) | −2.22313e55 | − | 8.68706e55i | −0.154489 | − | 0.603678i | ||||
\(904\) | −2.60007e55 | −0.176923 | ||||||||
\(905\) | − | 3.43603e56i | − | 2.28946i | ||||||
\(906\) | 1.79660e56 | − | 4.59774e55i | 1.17224 | − | 0.299991i | ||||
\(907\) | −4.50442e55 | −0.287806 | −0.143903 | − | 0.989592i | \(-0.545965\pi\) | ||||
−0.143903 | + | 0.989592i | \(0.545965\pi\) | |||||||
\(908\) | 9.50882e54i | 0.0594971i | ||||||||
\(909\) | 3.80887e55 | + | 6.95434e55i | 0.233390 | + | 0.426130i | ||||
\(910\) | −2.99119e56 | −1.79497 | ||||||||
\(911\) | − | 1.25668e56i | − | 0.738541i | −0.929322 | − | 0.369271i | \(-0.879608\pi\) | ||
0.929322 | − | 0.369271i | \(-0.120392\pi\) | |||||||
\(912\) | 3.48035e55 | + | 1.35997e56i | 0.200319 | + | 0.782759i | ||||
\(913\) | −1.73058e56 | −0.975543 | ||||||||
\(914\) | 1.05277e56i | 0.581242i | ||||||||
\(915\) | −2.00597e56 | + | 5.13353e55i | −1.08473 | + | 0.277598i | ||||
\(916\) | 1.29801e55 | 0.0687486 | ||||||||
\(917\) | 2.12678e56i | 1.10333i | ||||||||
\(918\) | 1.83357e56 | + | 1.96186e56i | 0.931722 | + | 0.996913i | ||||
\(919\) | −5.34481e55 | −0.266034 | −0.133017 | − | 0.991114i | \(-0.542467\pi\) | ||||
−0.133017 | + | 0.991114i | \(0.542467\pi\) | |||||||
\(920\) | 1.21107e56i | 0.590475i | ||||||||
\(921\) | 6.09052e54 | + | 2.37992e55i | 0.0290885 | + | 0.113665i | ||||
\(922\) | 8.86578e55 | 0.414791 | ||||||||
\(923\) | − | 3.07325e56i | − | 1.40853i | ||||||
\(924\) | 9.51361e55 | − | 2.43466e55i | 0.427148 | − | 0.109313i | ||||
\(925\) | 6.25592e55 | 0.275168 | ||||||||
\(926\) | − | 1.52245e56i | − | 0.656047i | ||||||
\(927\) | 2.12353e56 | − | 1.16305e56i | 0.896487 | − | 0.491003i | ||||
\(928\) | −2.26754e56 | −0.937872 | ||||||||
\(929\) | − | 1.02772e55i | − | 0.0416463i | −0.999783 | − | 0.0208231i | \(-0.993371\pi\) | ||
0.999783 | − | 0.0208231i | \(-0.00662869\pi\) | |||||||
\(930\) | 1.47984e56 | + | 5.78257e56i | 0.587541 | + | 2.29586i | ||||
\(931\) | 5.06247e55 | 0.196933 | ||||||||
\(932\) | − | 5.94900e55i | − | 0.226747i | ||||||
\(933\) | −2.13989e56 | + | 5.47626e55i | −0.799171 | + | 0.204519i | ||||
\(934\) | −1.48851e56 | −0.544706 | ||||||||
\(935\) | 5.56527e56i | 1.99556i | ||||||||
\(936\) | −9.05753e55 | − | 1.65375e56i | −0.318250 | − | 0.581070i | ||||
\(937\) | −5.35132e55 | −0.184251 | −0.0921253 | − | 0.995747i | \(-0.529366\pi\) | ||||
−0.0921253 | + | 0.995747i | \(0.529366\pi\) | |||||||
\(938\) | 3.73841e56i | 1.26134i | ||||||||
\(939\) | −1.25865e56 | − | 4.91828e56i | −0.416160 | − | 1.62617i | ||||
\(940\) | 3.06755e56 | 0.993945 | ||||||||
\(941\) | − | 7.35304e55i | − | 0.233488i | −0.993162 | − | 0.116744i | \(-0.962754\pi\) | ||
0.993162 | − | 0.116744i | \(-0.0372457\pi\) | |||||||
\(942\) | 2.41924e56 | − | 6.19116e55i | 0.752856 | − | 0.192666i | ||||
\(943\) | 1.53016e56 | 0.466675 | ||||||||
\(944\) | − | 9.81776e55i | − | 0.293457i | ||||||
\(945\) | 3.44343e56 | − | 3.21826e56i | 1.00876 | − | 0.942793i | ||||
\(946\) | −3.42592e56 | −0.983661 | ||||||||
\(947\) | 4.43729e56i | 1.24873i | 0.781133 | + | 0.624365i | \(0.214642\pi\) | ||||
−0.781133 | + | 0.624365i | \(0.785358\pi\) | |||||||
\(948\) | −6.20602e55 | − | 2.42505e56i | −0.171181 | − | 0.668901i | ||||
\(949\) | 2.80816e56 | 0.759213 | ||||||||
\(950\) | − | 5.18673e56i | − | 1.37450i | ||||||
\(951\) | −3.18215e56 | + | 8.14354e55i | −0.826590 | + | 0.211536i | ||||
\(952\) | −2.27740e56 | −0.579878 | ||||||||
\(953\) | − | 2.15698e56i | − | 0.538371i | −0.963088 | − | 0.269185i | \(-0.913246\pi\) | ||
0.963088 | − | 0.269185i | \(-0.0867545\pi\) | |||||||
\(954\) | −3.10796e56 | + | 1.70222e56i | −0.760426 | + | 0.416482i | ||||
\(955\) | −3.68012e56 | −0.882668 | ||||||||
\(956\) | − | 1.79530e55i | − | 0.0422122i | ||||||
\(957\) | −1.20355e56 | − | 4.70295e56i | −0.277420 | − | 1.08404i | ||||
\(958\) | 1.69983e56 | 0.384115 | ||||||||
\(959\) | − | 1.87607e56i | − | 0.415619i | ||||||
\(960\) | 1.08279e56 | − | 2.77102e55i | 0.235176 | − | 0.0601847i | ||||
\(961\) | 1.75842e56 | 0.374437 | ||||||||
\(962\) | − | 9.83779e55i | − | 0.205386i | ||||||
\(963\) | 7.24438e55 | + | 1.32270e56i | 0.148287 | + | 0.270746i | ||||
\(964\) | −3.08355e56 | −0.618854 | ||||||||
\(965\) | − | 4.37578e56i | − | 0.861067i | ||||||
\(966\) | 7.49770e55 | + | 2.92978e56i | 0.144665 | + | 0.565288i | ||||
\(967\) | 6.13156e56 | 1.16003 | 0.580014 | − | 0.814607i | \(-0.303047\pi\) | ||||
0.580014 | + | 0.814607i | \(0.303047\pi\) | |||||||
\(968\) | 5.45422e55i | 0.101181i | ||||||||
\(969\) | −3.84802e56 | + | 9.84760e55i | −0.699980 | + | 0.179134i | ||||
\(970\) | 1.61876e57 | 2.88748 | ||||||||
\(971\) | 6.07445e56i | 1.06253i | 0.847205 | + | 0.531266i | \(0.178283\pi\) | ||||
−0.847205 | + | 0.531266i | \(0.821717\pi\) | |||||||
\(972\) | −2.71539e56 | − | 8.94172e55i | −0.465772 | − | 0.153378i | ||||
\(973\) | 3.22284e56 | 0.542120 | ||||||||
\(974\) | 6.43124e56i | 1.06090i | ||||||||
\(975\) | 2.84233e56 | + | 1.11066e57i | 0.459819 | + | 1.79678i | ||||
\(976\) | −5.32736e56 | −0.845212 | ||||||||
\(977\) | − | 7.49738e56i | − | 1.16658i | −0.812266 | − | 0.583288i | \(-0.801766\pi\) | ||
0.812266 | − | 0.583288i | \(-0.198234\pi\) | |||||||
\(978\) | 6.44254e56 | − | 1.64873e56i | 0.983149 | − | 0.251601i | ||||
\(979\) | 2.56788e56 | 0.384329 | ||||||||
\(980\) | 1.68510e56i | 0.247361i | ||||||||
\(981\) | −1.12378e57 | + | 6.15491e56i | −1.61797 | + | 0.886157i | ||||
\(982\) | −1.42259e57 | −2.00891 | ||||||||
\(983\) | 8.64716e56i | 1.19772i | 0.800852 | + | 0.598862i | \(0.204380\pi\) | ||||
−0.800852 | + | 0.598862i | \(0.795620\pi\) | |||||||
\(984\) | −9.24366e55 | − | 3.61202e56i | −0.125585 | − | 0.490731i | ||||
\(985\) | −4.24131e56 | −0.565212 | ||||||||
\(986\) | − | 1.08328e57i | − | 1.41606i | ||||||
\(987\) | −7.71220e56 | + | 1.97366e56i | −0.988901 | + | 0.253073i | ||||
\(988\) | −2.68369e56 | −0.337560 | ||||||||
\(989\) | − | 3.47136e56i | − | 0.428322i | ||||||
\(990\) | −8.65008e56 | − | 1.57936e57i | −1.04701 | − | 1.91166i | ||||
\(991\) | 1.11029e57 | 1.31836 | 0.659182 | − | 0.751983i | \(-0.270903\pi\) | ||||
0.659182 | + | 0.751983i | \(0.270903\pi\) | |||||||
\(992\) | 9.09556e56i | 1.05952i | ||||||||
\(993\) | 2.38179e56 | + | 9.30700e56i | 0.272187 | + | 1.06359i | ||||
\(994\) | 1.20105e57 | 1.34654 | ||||||||
\(995\) | 2.80774e56i | 0.308829i | ||||||||
\(996\) | 3.98297e56 | − | 1.01929e56i | 0.429813 | − | 0.109995i | ||||
\(997\) | −6.64488e56 | −0.703524 | −0.351762 | − | 0.936089i | \(-0.614417\pi\) | ||||
−0.351762 | + | 0.936089i | \(0.614417\pi\) | |||||||
\(998\) | − | 1.34322e56i | − | 0.139530i | ||||||
\(999\) | 1.05846e56 | + | 1.13252e56i | 0.107877 | + | 0.115425i |
(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.2.4 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.39.b.a.2.9 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.39.b.a.2.4 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.39.b.a.2.9 | yes | 12 | 3.2 | odd | 2 | inner |