Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,16,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(11.4154804080\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 6354 x^{12} + 136110 x^{11} + 41390651 x^{10} - 1368564777 x^{9} - 361745089708 x^{8} + 52039630950804 x^{7} + \cdots + 24\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{91}\cdot 3^{6}\cdot 5^{4}\cdot 31^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(85.4255 + 19.3112i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.16.b.a.5.2 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −176.851 | − | 38.6225i | −0.976973 | − | 0.213361i | ||||
\(3\) | 4900.64i | 1.29373i | 0.762605 | + | 0.646864i | \(0.223920\pi\) | ||||
−0.762605 | + | 0.646864i | \(0.776080\pi\) | |||||||
\(4\) | 29784.6 | + | 13660.8i | 0.908954 | + | 0.416896i | ||||
\(5\) | 174283.i | 0.997654i | 0.866702 | + | 0.498827i | \(0.166236\pi\) | ||||
−0.866702 | + | 0.498827i | \(0.833764\pi\) | |||||||
\(6\) | 189275. | − | 866683.i | 0.276031 | − | 1.26394i | ||||
\(7\) | 3.39868e6 | 1.55982 | 0.779911 | − | 0.625891i | \(-0.215265\pi\) | ||||
0.779911 | + | 0.625891i | \(0.215265\pi\) | |||||||
\(8\) | −4.73983e6 | − | 3.56629e6i | −0.799075 | − | 0.601232i | ||||
\(9\) | −9.66732e6 | −0.673732 | ||||||||
\(10\) | 6.73124e6 | − | 3.08221e7i | 0.212860 | − | 0.974682i | ||||
\(11\) | 8.19468e7i | 1.26791i | 0.773372 | + | 0.633953i | \(0.218569\pi\) | ||||
−0.773372 | + | 0.633953i | \(0.781431\pi\) | |||||||
\(12\) | −6.69468e7 | + | 1.45964e8i | −0.539350 | + | 1.17594i | ||||
\(13\) | 1.80132e8i | 0.796187i | 0.917345 | + | 0.398094i | \(0.130328\pi\) | ||||
−0.917345 | + | 0.398094i | \(0.869672\pi\) | |||||||
\(14\) | −6.01060e8 | − | 1.31265e8i | −1.52390 | − | 0.332805i | ||||
\(15\) | −8.54097e8 | −1.29069 | ||||||||
\(16\) | 7.00504e8 | + | 8.13766e8i | 0.652395 | + | 0.757879i | ||||
\(17\) | −1.02640e9 | −0.606665 | −0.303332 | − | 0.952885i | \(-0.598099\pi\) | ||||
−0.303332 | + | 0.952885i | \(0.598099\pi\) | |||||||
\(18\) | 1.70968e9 | + | 3.73376e8i | 0.658218 | + | 0.143748i | ||||
\(19\) | − | 5.87020e9i | − | 1.50661i | −0.657671 | − | 0.753306i | \(-0.728458\pi\) | ||
0.657671 | − | 0.753306i | \(-0.271542\pi\) | |||||||
\(20\) | −2.38085e9 | + | 5.19095e9i | −0.415918 | + | 0.906822i | ||||
\(21\) | 1.66557e10i | 2.01798i | ||||||||
\(22\) | 3.16499e9 | − | 1.44924e10i | 0.270521 | − | 1.23871i | ||||
\(23\) | −9.43109e9 | −0.577568 | −0.288784 | − | 0.957394i | \(-0.593251\pi\) | ||||
−0.288784 | + | 0.957394i | \(0.593251\pi\) | |||||||
\(24\) | 1.74771e10 | − | 2.32282e10i | 0.777830 | − | 1.03379i | ||||
\(25\) | 1.43006e8 | 0.00468602 | ||||||||
\(26\) | 6.95713e9 | − | 3.18565e10i | 0.169875 | − | 0.777854i | ||||
\(27\) | 2.29428e10i | 0.422102i | ||||||||
\(28\) | 1.01228e11 | + | 4.64288e10i | 1.41781 | + | 0.650283i | ||||
\(29\) | − | 7.53397e10i | − | 0.811033i | −0.914088 | − | 0.405517i | \(-0.867092\pi\) | ||
0.914088 | − | 0.405517i | \(-0.132908\pi\) | |||||||
\(30\) | 1.51048e11 | + | 3.29873e10i | 1.26097 | + | 0.275384i | ||||
\(31\) | −1.68086e11 | −1.09728 | −0.548640 | − | 0.836059i | \(-0.684854\pi\) | ||||
−0.548640 | + | 0.836059i | \(0.684854\pi\) | |||||||
\(32\) | −9.24553e10 | − | 1.70971e11i | −0.475671 | − | 0.879623i | ||||
\(33\) | −4.01591e11 | −1.64032 | ||||||||
\(34\) | 1.81520e11 | + | 3.96420e10i | 0.592696 | + | 0.129439i | ||||
\(35\) | 5.92332e11i | 1.55616i | ||||||||
\(36\) | −2.87937e11 | − | 1.32064e11i | −0.612391 | − | 0.280876i | ||||
\(37\) | 3.21169e11i | 0.556187i | 0.960554 | + | 0.278093i | \(0.0897025\pi\) | ||||
−0.960554 | + | 0.278093i | \(0.910297\pi\) | |||||||
\(38\) | −2.26722e11 | + | 1.03815e12i | −0.321452 | + | 1.47192i | ||||
\(39\) | −8.82760e11 | −1.03005 | ||||||||
\(40\) | 6.21544e11 | − | 8.26071e11i | 0.599821 | − | 0.797200i | ||||
\(41\) | 1.60362e12 | 1.28594 | 0.642972 | − | 0.765889i | \(-0.277701\pi\) | ||||
0.642972 | + | 0.765889i | \(0.277701\pi\) | |||||||
\(42\) | 6.43284e11 | − | 2.94558e12i | 0.430559 | − | 1.97152i | ||||
\(43\) | − | 1.36491e12i | − | 0.765758i | −0.923799 | − | 0.382879i | \(-0.874933\pi\) | ||
0.923799 | − | 0.382879i | \(-0.125067\pi\) | |||||||
\(44\) | −1.11946e12 | + | 2.44075e12i | −0.528585 | + | 1.15247i | ||||
\(45\) | − | 1.68485e12i | − | 0.672152i | ||||||
\(46\) | 1.66790e12 | + | 3.64252e11i | 0.564269 | + | 0.123231i | ||||
\(47\) | 1.39788e12 | 0.402472 | 0.201236 | − | 0.979543i | \(-0.435504\pi\) | ||||
0.201236 | + | 0.979543i | \(0.435504\pi\) | |||||||
\(48\) | −3.98797e12 | + | 3.43292e12i | −0.980489 | + | 0.844022i | ||||
\(49\) | 6.80345e12 | 1.43304 | ||||||||
\(50\) | −2.52908e10 | − | 5.52325e9i | −0.00457812 | − | 0.000999814i | ||||
\(51\) | − | 5.03000e12i | − | 0.784859i | ||||||
\(52\) | −2.46075e12 | + | 5.36515e12i | −0.331927 | + | 0.723698i | ||||
\(53\) | 2.31639e12i | 0.270858i | 0.990787 | + | 0.135429i | \(0.0432413\pi\) | ||||
−0.990787 | + | 0.135429i | \(0.956759\pi\) | |||||||
\(54\) | 8.86106e11 | − | 4.05745e12i | 0.0900601 | − | 0.412383i | ||||
\(55\) | −1.42819e13 | −1.26493 | ||||||||
\(56\) | −1.61091e13 | − | 1.21207e13i | −1.24641 | − | 0.937814i | ||||
\(57\) | 2.87677e13 | 1.94914 | ||||||||
\(58\) | −2.90980e12 | + | 1.33239e13i | −0.173043 | + | 0.792358i | ||||
\(59\) | 2.85735e13i | 1.49477i | 0.664393 | + | 0.747384i | \(0.268690\pi\) | ||||
−0.664393 | + | 0.747384i | \(0.731310\pi\) | |||||||
\(60\) | −2.54390e13 | − | 1.16677e13i | −1.17318 | − | 0.538085i | ||||
\(61\) | − | 2.15410e13i | − | 0.877591i | −0.898587 | − | 0.438795i | \(-0.855405\pi\) | ||
0.898587 | − | 0.438795i | \(-0.144595\pi\) | |||||||
\(62\) | 2.97261e13 | + | 6.49188e12i | 1.07201 | + | 0.234117i | ||||
\(63\) | −3.28561e13 | −1.05090 | ||||||||
\(64\) | 9.74751e12 | + | 3.38072e13i | 0.277041 | + | 0.960858i | ||||
\(65\) | −3.13939e13 | −0.794319 | ||||||||
\(66\) | 7.10218e13 | + | 1.55104e13i | 1.60255 | + | 0.349981i | ||||
\(67\) | 7.75964e12i | 0.156416i | 0.996937 | + | 0.0782079i | \(0.0249198\pi\) | ||||
−0.996937 | + | 0.0782079i | \(0.975080\pi\) | |||||||
\(68\) | −3.05709e13 | − | 1.40215e13i | −0.551431 | − | 0.252916i | ||||
\(69\) | − | 4.62183e13i | − | 0.747216i | ||||||
\(70\) | 2.28773e13 | − | 1.04755e14i | 0.332024 | − | 1.52033i | ||||
\(71\) | −9.37922e13 | −1.22385 | −0.611926 | − | 0.790915i | \(-0.709605\pi\) | ||||
−0.611926 | + | 0.790915i | \(0.709605\pi\) | |||||||
\(72\) | 4.58214e13 | + | 3.44765e13i | 0.538362 | + | 0.405069i | ||||
\(73\) | 1.79919e14 | 1.90614 | 0.953072 | − | 0.302745i | \(-0.0979030\pi\) | ||||
0.953072 | + | 0.302745i | \(0.0979030\pi\) | |||||||
\(74\) | 1.24043e13 | − | 5.67991e13i | 0.118669 | − | 0.543380i | ||||
\(75\) | 7.00821e11i | 0.00606244i | ||||||||
\(76\) | 8.01920e13 | − | 1.74842e14i | 0.628100 | − | 1.36944i | ||||
\(77\) | 2.78511e14i | 1.97771i | ||||||||
\(78\) | 1.56117e14 | + | 3.40944e13i | 1.00633 | + | 0.219772i | ||||
\(79\) | −1.28657e14 | −0.753753 | −0.376876 | − | 0.926264i | \(-0.623002\pi\) | ||||
−0.376876 | + | 0.926264i | \(0.623002\pi\) | |||||||
\(80\) | −1.41826e14 | + | 1.22086e14i | −0.756101 | + | 0.650865i | ||||
\(81\) | −2.51150e14 | −1.21982 | ||||||||
\(82\) | −2.83602e14 | − | 6.19357e13i | −1.25633 | − | 0.274370i | ||||
\(83\) | − | 2.32762e14i | − | 0.941514i | −0.882263 | − | 0.470757i | \(-0.843981\pi\) | ||
0.882263 | − | 0.470757i | \(-0.156019\pi\) | |||||||
\(84\) | −2.27531e14 | + | 4.96083e14i | −0.841290 | + | 1.83426i | ||||
\(85\) | − | 1.78884e14i | − | 0.605242i | ||||||
\(86\) | −5.27163e13 | + | 2.41386e14i | −0.163383 | + | 0.748125i | ||||
\(87\) | 3.69212e14 | 1.04926 | ||||||||
\(88\) | 2.92246e14 | − | 3.88413e14i | 0.762305 | − | 1.01315i | ||||
\(89\) | 4.72336e12 | 0.0113195 | 0.00565974 | − | 0.999984i | \(-0.498198\pi\) | ||||
0.00565974 | + | 0.999984i | \(0.498198\pi\) | |||||||
\(90\) | −6.50730e13 | + | 2.97967e14i | −0.143411 | + | 0.656674i | ||||
\(91\) | 6.12210e14i | 1.24191i | ||||||||
\(92\) | −2.80901e14 | − | 1.28837e14i | −0.524983 | − | 0.240786i | ||||
\(93\) | − | 8.23726e14i | − | 1.41958i | ||||||
\(94\) | −2.47216e14 | − | 5.39895e13i | −0.393204 | − | 0.0858717i | ||||
\(95\) | 1.02308e15 | 1.50308 | ||||||||
\(96\) | 8.37865e14 | − | 4.53090e14i | 1.13799 | − | 0.615389i | ||||
\(97\) | 4.41963e14 | 0.555390 | 0.277695 | − | 0.960669i | \(-0.410430\pi\) | ||||
0.277695 | + | 0.960669i | \(0.410430\pi\) | |||||||
\(98\) | −1.20320e15 | − | 2.62766e14i | −1.40004 | − | 0.305755i | ||||
\(99\) | − | 7.92205e14i | − | 0.854228i | ||||||
\(100\) | 4.25938e12 | + | 1.95358e12i | 0.00425938 | + | 0.00195358i | ||||
\(101\) | 7.48993e14i | 0.695132i | 0.937655 | + | 0.347566i | \(0.112992\pi\) | ||||
−0.937655 | + | 0.347566i | \(0.887008\pi\) | |||||||
\(102\) | −1.94271e14 | + | 8.89561e14i | −0.167458 | + | 0.766787i | ||||
\(103\) | 1.47544e15 | 1.18207 | 0.591034 | − | 0.806647i | \(-0.298720\pi\) | ||||
0.591034 | + | 0.806647i | \(0.298720\pi\) | |||||||
\(104\) | 6.42402e14 | − | 8.53793e14i | 0.478693 | − | 0.636213i | ||||
\(105\) | −2.90280e15 | −2.01325 | ||||||||
\(106\) | 8.94646e13 | − | 4.09656e14i | 0.0577906 | − | 0.264621i | ||||
\(107\) | − | 5.49539e14i | − | 0.330842i | −0.986223 | − | 0.165421i | \(-0.947102\pi\) | ||
0.986223 | − | 0.165421i | \(-0.0528982\pi\) | |||||||
\(108\) | −3.13418e14 | + | 6.83341e14i | −0.175973 | + | 0.383671i | ||||
\(109\) | 2.46207e15i | 1.29003i | 0.764168 | + | 0.645017i | \(0.223150\pi\) | ||||
−0.764168 | + | 0.645017i | \(0.776850\pi\) | |||||||
\(110\) | 2.52578e15 | + | 5.51603e14i | 1.23580 | + | 0.269887i | ||||
\(111\) | −1.57393e15 | −0.719555 | ||||||||
\(112\) | 2.38079e15 | + | 2.76573e15i | 1.01762 | + | 1.18216i | ||||
\(113\) | −9.16605e14 | −0.366517 | −0.183259 | − | 0.983065i | \(-0.558665\pi\) | ||||
−0.183259 | + | 0.983065i | \(0.558665\pi\) | |||||||
\(114\) | −5.08760e15 | − | 1.11108e15i | −1.90426 | − | 0.415871i | ||||
\(115\) | − | 1.64368e15i | − | 0.576213i | ||||||
\(116\) | 1.02920e15 | − | 2.24396e15i | 0.338117 | − | 0.737192i | ||||
\(117\) | − | 1.74139e15i | − | 0.536417i | ||||||
\(118\) | 1.10358e15 | − | 5.05326e15i | 0.318925 | − | 1.46035i | ||||
\(119\) | −3.48840e15 | −0.946289 | ||||||||
\(120\) | 4.04827e15 | + | 3.04596e15i | 1.03136 | + | 0.776006i | ||||
\(121\) | −2.53803e15 | −0.607583 | ||||||||
\(122\) | −8.31966e14 | + | 3.80955e15i | −0.187244 | + | 0.857383i | ||||
\(123\) | 7.85875e15i | 1.66366i | ||||||||
\(124\) | −5.00636e15 | − | 2.29619e15i | −0.997378 | − | 0.457452i | ||||
\(125\) | 5.34362e15i | 1.00233i | ||||||||
\(126\) | 5.81064e15 | + | 1.26898e15i | 1.02670 | + | 0.224221i | ||||
\(127\) | 5.63341e15 | 0.938088 | 0.469044 | − | 0.883175i | \(-0.344599\pi\) | ||||
0.469044 | + | 0.883175i | \(0.344599\pi\) | |||||||
\(128\) | −4.18141e14 | − | 6.35531e15i | −0.0656520 | − | 0.997843i | ||||
\(129\) | 6.68894e15 | 0.990682 | ||||||||
\(130\) | 5.55205e15 | + | 1.21251e15i | 0.776029 | + | 0.169477i | ||||
\(131\) | − | 2.82994e15i | − | 0.373458i | −0.982411 | − | 0.186729i | \(-0.940211\pi\) | ||
0.982411 | − | 0.186729i | \(-0.0597887\pi\) | |||||||
\(132\) | −1.19612e16 | − | 5.48608e15i | −1.49098 | − | 0.683845i | ||||
\(133\) | − | 1.99509e16i | − | 2.35004i | ||||||
\(134\) | 2.99696e14 | − | 1.37230e15i | 0.0333730 | − | 0.152814i | ||||
\(135\) | −3.99853e15 | −0.421112 | ||||||||
\(136\) | 4.86495e15 | + | 3.66043e15i | 0.484771 | + | 0.364746i | ||||
\(137\) | 1.39509e16 | 1.31583 | 0.657913 | − | 0.753094i | \(-0.271439\pi\) | ||||
0.657913 | + | 0.753094i | \(0.271439\pi\) | |||||||
\(138\) | −1.78507e15 | + | 8.17376e15i | −0.159427 | + | 0.730010i | ||||
\(139\) | − | 1.36091e16i | − | 1.15138i | −0.817669 | − | 0.575689i | \(-0.804734\pi\) | ||
0.817669 | − | 0.575689i | \(-0.195266\pi\) | |||||||
\(140\) | −8.09176e15 | + | 1.76424e16i | −0.648758 | + | 1.41448i | ||||
\(141\) | 6.85049e15i | 0.520689i | ||||||||
\(142\) | 1.65872e16 | + | 3.62248e15i | 1.19567 | + | 0.261122i | ||||
\(143\) | −1.47612e16 | −1.00949 | ||||||||
\(144\) | −6.77200e15 | − | 7.86693e15i | −0.439540 | − | 0.510607i | ||||
\(145\) | 1.31304e16 | 0.809131 | ||||||||
\(146\) | −3.18189e16 | − | 6.94891e15i | −1.86225 | − | 0.406697i | ||||
\(147\) | 3.33412e16i | 1.85397i | ||||||||
\(148\) | −4.38744e15 | + | 9.56590e15i | −0.231872 | + | 0.505548i | ||||
\(149\) | 2.14670e14i | 0.0107863i | 0.999985 | + | 0.00539317i | \(0.00171671\pi\) | ||||
−0.999985 | + | 0.00539317i | \(0.998283\pi\) | |||||||
\(150\) | 2.70674e13 | − | 1.23941e14i | 0.00129349 | − | 0.00592284i | ||||
\(151\) | −2.98047e15 | −0.135506 | −0.0677529 | − | 0.997702i | \(-0.521583\pi\) | ||||
−0.0677529 | + | 0.997702i | \(0.521583\pi\) | |||||||
\(152\) | −2.09349e16 | + | 2.78237e16i | −0.905822 | + | 1.20389i | ||||
\(153\) | 9.92252e15 | 0.408730 | ||||||||
\(154\) | 1.07568e16 | − | 4.92549e16i | 0.421965 | − | 1.93217i | ||||
\(155\) | − | 2.92945e16i | − | 1.09471i | ||||||
\(156\) | −2.62927e16 | − | 1.20593e16i | −0.936268 | − | 0.429424i | ||||
\(157\) | 4.50242e16i | 1.52827i | 0.645059 | + | 0.764133i | \(0.276833\pi\) | ||||
−0.645059 | + | 0.764133i | \(0.723167\pi\) | |||||||
\(158\) | 2.27531e16 | + | 4.96903e15i | 0.736396 | + | 0.160821i | ||||
\(159\) | −1.13518e16 | −0.350417 | ||||||||
\(160\) | 2.97973e16 | − | 1.61134e16i | 0.877560 | − | 0.474555i | ||||
\(161\) | −3.20533e16 | −0.900903 | ||||||||
\(162\) | 4.44161e16 | + | 9.70001e15i | 1.19173 | + | 0.260261i | ||||
\(163\) | − | 2.75686e16i | − | 0.706331i | −0.935561 | − | 0.353165i | \(-0.885105\pi\) | ||
0.935561 | − | 0.353165i | \(-0.114895\pi\) | |||||||
\(164\) | 4.77632e16 | + | 2.19068e16i | 1.16886 | + | 0.536105i | ||||
\(165\) | − | 6.99905e16i | − | 1.63648i | ||||||
\(166\) | −8.98985e15 | + | 4.11642e16i | −0.200882 | + | 0.919834i | ||||
\(167\) | 2.90393e15 | 0.0620315 | 0.0310157 | − | 0.999519i | \(-0.490126\pi\) | ||||
0.0310157 | + | 0.999519i | \(0.490126\pi\) | |||||||
\(168\) | 5.93990e16 | − | 7.89450e16i | 1.21328 | − | 1.61252i | ||||
\(169\) | 1.87384e16 | 0.366086 | ||||||||
\(170\) | −6.90893e15 | + | 3.16358e16i | −0.129135 | + | 0.591305i | ||||
\(171\) | 5.67491e16i | 1.01505i | ||||||||
\(172\) | 1.86459e16 | − | 4.06534e16i | 0.319241 | − | 0.696039i | ||||
\(173\) | 2.57418e16i | 0.421982i | 0.977488 | + | 0.210991i | \(0.0676690\pi\) | ||||
−0.977488 | + | 0.210991i | \(0.932331\pi\) | |||||||
\(174\) | −6.52956e16 | − | 1.42599e16i | −1.02510 | − | 0.223870i | ||||
\(175\) | 4.86032e14 | 0.00730936 | ||||||||
\(176\) | −6.66855e16 | + | 5.74041e16i | −0.960918 | + | 0.827176i | ||||
\(177\) | −1.40028e17 | −1.93382 | ||||||||
\(178\) | −8.35332e14 | − | 1.82428e14i | −0.0110588 | − | 0.00241513i | ||||
\(179\) | 8.37590e16i | 1.06325i | 0.846981 | + | 0.531623i | \(0.178418\pi\) | ||||
−0.846981 | + | 0.531623i | \(0.821582\pi\) | |||||||
\(180\) | 2.30165e16 | − | 5.01826e16i | 0.280217 | − | 0.610955i | ||||
\(181\) | − | 3.60190e15i | − | 0.0420671i | −0.999779 | − | 0.0210336i | \(-0.993304\pi\) | ||
0.999779 | − | 0.0210336i | \(-0.00669568\pi\) | |||||||
\(182\) | 2.36451e16 | − | 1.08270e17i | 0.264975 | − | 1.21331i | ||||
\(183\) | 1.05565e17 | 1.13536 | ||||||||
\(184\) | 4.47017e16 | + | 3.36340e16i | 0.461520 | + | 0.347252i | ||||
\(185\) | −5.59743e16 | −0.554882 | ||||||||
\(186\) | −3.18143e16 | + | 1.45677e17i | −0.302883 | + | 1.38689i | ||||
\(187\) | − | 8.41100e16i | − | 0.769194i | ||||||
\(188\) | 4.16352e16 | + | 1.90962e16i | 0.365828 | + | 0.167789i | ||||
\(189\) | 7.79751e16i | 0.658404i | ||||||||
\(190\) | −1.80932e17 | − | 3.95137e16i | −1.46847 | − | 0.320698i | ||||
\(191\) | 1.83863e17 | 1.43464 | 0.717322 | − | 0.696742i | \(-0.245368\pi\) | ||||
0.717322 | + | 0.696742i | \(0.245368\pi\) | |||||||
\(192\) | −1.65677e17 | + | 4.77690e16i | −1.24309 | + | 0.358416i | ||||
\(193\) | 7.85347e16 | 0.566737 | 0.283369 | − | 0.959011i | \(-0.408548\pi\) | ||||
0.283369 | + | 0.959011i | \(0.408548\pi\) | |||||||
\(194\) | −7.81617e16 | − | 1.70697e16i | −0.542601 | − | 0.118499i | ||||
\(195\) | − | 1.53850e17i | − | 1.02763i | ||||||
\(196\) | 2.02638e17 | + | 9.29410e16i | 1.30257 | + | 0.597429i | ||||
\(197\) | − | 7.29349e16i | − | 0.451272i | −0.974212 | − | 0.225636i | \(-0.927554\pi\) | ||
0.974212 | − | 0.225636i | \(-0.0724460\pi\) | |||||||
\(198\) | −3.05969e16 | + | 1.40102e17i | −0.182259 | + | 0.834558i | ||||
\(199\) | −1.32290e17 | −0.758802 | −0.379401 | − | 0.925232i | \(-0.623870\pi\) | ||||
−0.379401 | + | 0.925232i | \(0.623870\pi\) | |||||||
\(200\) | −6.77824e14 | − | 5.10001e14i | −0.00374448 | − | 0.00281739i | ||||
\(201\) | −3.80272e16 | −0.202359 | ||||||||
\(202\) | 2.89280e16 | − | 1.32460e17i | 0.148314 | − | 0.679126i | ||||
\(203\) | − | 2.56055e17i | − | 1.26507i | ||||||
\(204\) | 6.87141e16 | − | 1.49817e17i | 0.327205 | − | 0.713401i | ||||
\(205\) | 2.79484e17i | 1.28293i | ||||||||
\(206\) | −2.60933e17 | − | 5.69851e16i | −1.15485 | − | 0.252207i | ||||
\(207\) | 9.11734e16 | 0.389126 | ||||||||
\(208\) | −1.46585e17 | + | 1.26183e17i | −0.603413 | + | 0.519429i | ||||
\(209\) | 4.81044e17 | 1.91024 | ||||||||
\(210\) | 5.13364e17 | + | 1.12113e17i | 1.96689 | + | 0.429549i | ||||
\(211\) | 1.35103e17i | 0.499513i | 0.968309 | + | 0.249756i | \(0.0803506\pi\) | ||||
−0.968309 | + | 0.249756i | \(0.919649\pi\) | |||||||
\(212\) | −3.16438e16 | + | 6.89927e16i | −0.112920 | + | 0.246198i | ||||
\(213\) | − | 4.59641e17i | − | 1.58333i | ||||||
\(214\) | −2.12245e16 | + | 9.71866e16i | −0.0705887 | + | 0.323223i | ||||
\(215\) | 2.37881e17 | 0.763961 | ||||||||
\(216\) | 8.18206e16 | − | 1.08745e17i | 0.253781 | − | 0.337291i | ||||
\(217\) | −5.71269e17 | −1.71156 | ||||||||
\(218\) | 9.50911e16 | − | 4.35419e17i | 0.275243 | − | 1.26033i | ||||
\(219\) | 8.81717e17i | 2.46603i | ||||||||
\(220\) | −4.25382e17 | − | 1.95103e17i | −1.14976 | − | 0.527345i | ||||
\(221\) | − | 1.84887e17i | − | 0.483019i | ||||||
\(222\) | 2.78352e17 | + | 6.07891e16i | 0.702986 | + | 0.153525i | ||||
\(223\) | −6.20180e17 | −1.51437 | −0.757183 | − | 0.653202i | \(-0.773425\pi\) | ||||
−0.757183 | + | 0.653202i | \(0.773425\pi\) | |||||||
\(224\) | −3.14226e17 | − | 5.81074e17i | −0.741962 | − | 1.37205i | ||||
\(225\) | −1.38248e15 | −0.00315712 | ||||||||
\(226\) | 1.62103e17 | + | 3.54016e16i | 0.358077 | + | 0.0782004i | ||||
\(227\) | − | 2.33485e17i | − | 0.498960i | −0.968380 | − | 0.249480i | \(-0.919740\pi\) | ||
0.968380 | − | 0.249480i | \(-0.0802597\pi\) | |||||||
\(228\) | 8.56835e17 | + | 3.92992e17i | 1.77168 | + | 0.812591i | ||||
\(229\) | 5.46593e17i | 1.09370i | 0.837231 | + | 0.546850i | \(0.184173\pi\) | ||||
−0.837231 | + | 0.546850i | \(0.815827\pi\) | |||||||
\(230\) | −6.34829e16 | + | 2.90686e17i | −0.122941 | + | 0.562945i | ||||
\(231\) | −1.36488e18 | −2.55861 | ||||||||
\(232\) | −2.68683e17 | + | 3.57097e17i | −0.487619 | + | 0.648076i | ||||
\(233\) | 8.18025e17 | 1.43746 | 0.718732 | − | 0.695287i | \(-0.244723\pi\) | ||||
0.718732 | + | 0.695287i | \(0.244723\pi\) | |||||||
\(234\) | −6.72568e16 | + | 3.07967e17i | −0.114450 | + | 0.524065i | ||||
\(235\) | 2.43626e17i | 0.401527i | ||||||||
\(236\) | −3.90339e17 | + | 8.51051e17i | −0.623163 | + | 1.35868i | ||||
\(237\) | − | 6.30499e17i | − | 0.975151i | ||||||
\(238\) | 6.16927e17 | + | 1.34730e17i | 0.924499 | + | 0.201901i | ||||
\(239\) | −1.12195e17 | −0.162925 | −0.0814625 | − | 0.996676i | \(-0.525959\pi\) | ||||
−0.0814625 | + | 0.996676i | \(0.525959\pi\) | |||||||
\(240\) | −5.98299e17 | − | 6.95036e17i | −0.842042 | − | 0.978189i | ||||
\(241\) | −4.88568e17 | −0.666496 | −0.333248 | − | 0.942839i | \(-0.608145\pi\) | ||||
−0.333248 | + | 0.942839i | \(0.608145\pi\) | |||||||
\(242\) | 4.48853e17 | + | 9.80248e16i | 0.593593 | + | 0.129635i | ||||
\(243\) | − | 9.01589e17i | − | 1.15601i | ||||||
\(244\) | 2.94268e17 | − | 6.41590e17i | 0.365864 | − | 0.797690i | ||||
\(245\) | 1.18573e18i | 1.42968i | ||||||||
\(246\) | 3.03524e17 | − | 1.38983e18i | 0.354961 | − | 1.62535i | ||||
\(247\) | 1.05741e18 | 1.19954 | ||||||||
\(248\) | 7.96696e17 | + | 5.99442e17i | 0.876809 | + | 0.659720i | ||||
\(249\) | 1.14068e18 | 1.21806 | ||||||||
\(250\) | 2.06384e17 | − | 9.45025e17i | 0.213858 | − | 0.979249i | ||||
\(251\) | − | 7.31956e17i | − | 0.736092i | −0.929808 | − | 0.368046i | \(-0.880027\pi\) | ||
0.929808 | − | 0.368046i | \(-0.119973\pi\) | |||||||
\(252\) | −9.78606e17 | − | 4.48842e17i | −0.955221 | − | 0.438117i | ||||
\(253\) | − | 7.72848e17i | − | 0.732302i | ||||||
\(254\) | −9.96275e17 | − | 2.17576e17i | −0.916487 | − | 0.200151i | ||||
\(255\) | 8.76644e17 | 0.783018 | ||||||||
\(256\) | −1.71509e17 | + | 1.14009e18i | −0.148760 | + | 0.988873i | ||||
\(257\) | 7.41815e17 | 0.624881 | 0.312440 | − | 0.949937i | \(-0.398854\pi\) | ||||
0.312440 | + | 0.949937i | \(0.398854\pi\) | |||||||
\(258\) | −1.18295e18 | − | 2.58343e17i | −0.967870 | − | 0.211373i | ||||
\(259\) | 1.09155e18i | 0.867552i | ||||||||
\(260\) | −9.35055e17 | − | 4.28867e17i | −0.722000 | − | 0.331149i | ||||
\(261\) | 7.28333e17i | 0.546419i | ||||||||
\(262\) | −1.09299e17 | + | 5.00478e17i | −0.0796815 | + | 0.364859i | ||||
\(263\) | 1.76442e17 | 0.125007 | 0.0625036 | − | 0.998045i | \(-0.480092\pi\) | ||||
0.0625036 | + | 0.998045i | \(0.480092\pi\) | |||||||
\(264\) | 1.90347e18 | + | 1.43219e18i | 1.31074 | + | 0.986215i | ||||
\(265\) | −4.03707e17 | −0.270223 | ||||||||
\(266\) | −7.70554e17 | + | 3.52834e18i | −0.501408 | + | 2.29593i | ||||
\(267\) | 2.31475e16i | 0.0146443i | ||||||||
\(268\) | −1.06003e17 | + | 2.31118e17i | −0.0652091 | + | 0.142175i | ||||
\(269\) | − | 3.11629e18i | − | 1.86422i | −0.362179 | − | 0.932108i | \(-0.617967\pi\) | ||
0.362179 | − | 0.932108i | \(-0.382033\pi\) | |||||||
\(270\) | 7.07145e17 | + | 1.54433e17i | 0.411415 | + | 0.0898489i | ||||
\(271\) | −4.73577e17 | −0.267992 | −0.133996 | − | 0.990982i | \(-0.542781\pi\) | ||||
−0.133996 | + | 0.990982i | \(0.542781\pi\) | |||||||
\(272\) | −7.18996e17 | − | 8.35248e17i | −0.395785 | − | 0.459778i | ||||
\(273\) | −3.00022e18 | −1.60669 | ||||||||
\(274\) | −2.46724e18 | − | 5.38819e17i | −1.28553 | − | 0.280746i | ||||
\(275\) | 1.17189e16i | 0.00594143i | ||||||||
\(276\) | 6.31382e17 | − | 1.37660e18i | 0.311511 | − | 0.679185i | ||||
\(277\) | 4.14576e17i | 0.199070i | 0.995034 | + | 0.0995350i | \(0.0317355\pi\) | ||||
−0.995034 | + | 0.0995350i | \(0.968264\pi\) | |||||||
\(278\) | −5.25616e17 | + | 2.40678e18i | −0.245659 | + | 1.12486i | ||||
\(279\) | 1.62494e18 | 0.739273 | ||||||||
\(280\) | 2.11243e18 | − | 2.80755e18i | 0.935614 | − | 1.24349i | ||||
\(281\) | −1.18027e18 | −0.508959 | −0.254479 | − | 0.967078i | \(-0.581904\pi\) | ||||
−0.254479 | + | 0.967078i | \(0.581904\pi\) | |||||||
\(282\) | 2.64583e17 | − | 1.21152e18i | 0.111095 | − | 0.508699i | ||||
\(283\) | − | 8.15996e17i | − | 0.333649i | −0.985987 | − | 0.166824i | \(-0.946649\pi\) | ||
0.985987 | − | 0.166824i | \(-0.0533513\pi\) | |||||||
\(284\) | −2.79356e18 | − | 1.28128e18i | −1.11243 | − | 0.510219i | ||||
\(285\) | 5.01373e18i | 1.94457i | ||||||||
\(286\) | 2.61054e18 | + | 5.70115e17i | 0.986245 | + | 0.215386i | ||||
\(287\) | 5.45019e18 | 2.00584 | ||||||||
\(288\) | 8.93795e17 | + | 1.65283e18i | 0.320475 | + | 0.592630i | ||||
\(289\) | −1.80893e18 | −0.631958 | ||||||||
\(290\) | −2.32213e18 | − | 5.07129e17i | −0.790499 | − | 0.172637i | ||||
\(291\) | 2.16590e18i | 0.718524i | ||||||||
\(292\) | 5.35882e18 | + | 2.45785e18i | 1.73260 | + | 0.794664i | ||||
\(293\) | − | 2.76770e17i | − | 0.0872190i | −0.999049 | − | 0.0436095i | \(-0.986114\pi\) | ||
0.999049 | − | 0.0436095i | \(-0.0138857\pi\) | |||||||
\(294\) | 1.28772e18 | − | 5.89644e18i | 0.395564 | − | 1.81128i | ||||
\(295\) | −4.97988e18 | −1.49126 | ||||||||
\(296\) | 1.14538e18 | − | 1.52229e18i | 0.334397 | − | 0.444435i | ||||
\(297\) | −1.88009e18 | −0.535185 | ||||||||
\(298\) | 8.29107e15 | − | 3.79646e16i | 0.00230138 | − | 0.0105380i | ||||
\(299\) | − | 1.69884e18i | − | 0.459852i | ||||||
\(300\) | −9.57380e15 | + | 2.08737e16i | −0.00252741 | + | 0.00551048i | ||||
\(301\) | − | 4.63890e18i | − | 1.19444i | ||||||
\(302\) | 5.27100e17 | + | 1.15113e17i | 0.132386 | + | 0.0289117i | ||||
\(303\) | −3.67054e18 | −0.899312 | ||||||||
\(304\) | 4.77697e18 | − | 4.11210e18i | 1.14183 | − | 0.982906i | ||||
\(305\) | 3.75423e18 | 0.875532 | ||||||||
\(306\) | −1.75481e18 | − | 3.83232e17i | −0.399318 | − | 0.0872069i | ||||
\(307\) | − | 1.17318e18i | − | 0.260512i | −0.991480 | − | 0.130256i | \(-0.958420\pi\) | ||
0.991480 | − | 0.130256i | \(-0.0415800\pi\) | |||||||
\(308\) | −3.80469e18 | + | 8.29533e18i | −0.824497 | + | 1.79764i | ||||
\(309\) | 7.23059e18i | 1.52927i | ||||||||
\(310\) | −1.13142e18 | + | 5.18076e18i | −0.233568 | + | 1.06950i | ||||
\(311\) | 1.01267e18 | 0.204064 | 0.102032 | − | 0.994781i | \(-0.467466\pi\) | ||||
0.102032 | + | 0.994781i | \(0.467466\pi\) | |||||||
\(312\) | 4.18413e18 | + | 3.14818e18i | 0.823087 | + | 0.619298i | ||||
\(313\) | −2.17123e18 | −0.416988 | −0.208494 | − | 0.978024i | \(-0.566856\pi\) | ||||
−0.208494 | + | 0.978024i | \(0.566856\pi\) | |||||||
\(314\) | 1.73895e18 | − | 7.96259e18i | 0.326072 | − | 1.49308i | ||||
\(315\) | − | 5.72626e18i | − | 1.04844i | ||||||
\(316\) | −3.83199e18 | − | 1.75756e18i | −0.685127 | − | 0.314236i | ||||
\(317\) | − | 3.39592e18i | − | 0.592943i | −0.955042 | − | 0.296471i | \(-0.904190\pi\) | ||
0.955042 | − | 0.296471i | \(-0.0958099\pi\) | |||||||
\(318\) | 2.00757e18 | + | 4.38433e17i | 0.342348 | + | 0.0747653i | ||||
\(319\) | 6.17384e18 | 1.02831 | ||||||||
\(320\) | −5.89202e18 | + | 1.69883e18i | −0.958604 | + | 0.276391i | ||||
\(321\) | 2.69309e18 | 0.428019 | ||||||||
\(322\) | 5.66865e18 | + | 1.23798e18i | 0.880158 | + | 0.192218i | ||||
\(323\) | 6.02517e18i | 0.914008i | ||||||||
\(324\) | −7.48039e18 | − | 3.43092e18i | −1.10876 | − | 0.508537i | ||||
\(325\) | 2.57599e16i | 0.00373095i | ||||||||
\(326\) | −1.06477e18 | + | 4.87554e18i | −0.150703 | + | 0.690066i | ||||
\(327\) | −1.20657e19 | −1.66895 | ||||||||
\(328\) | −7.60087e18 | − | 5.71897e18i | −1.02757 | − | 0.773151i | ||||
\(329\) | 4.75094e18 | 0.627784 | ||||||||
\(330\) | −2.70321e18 | + | 1.23779e19i | −0.349160 | + | 1.59879i | ||||
\(331\) | 9.91491e18i | 1.25193i | 0.779852 | + | 0.625963i | \(0.215294\pi\) | ||||
−0.779852 | + | 0.625963i | \(0.784706\pi\) | |||||||
\(332\) | 3.17973e18 | − | 6.93273e18i | 0.392513 | − | 0.855793i | ||||
\(333\) | − | 3.10484e18i | − | 0.374721i | ||||||
\(334\) | −5.13563e17 | − | 1.12157e17i | −0.0606031 | − | 0.0132351i | ||||
\(335\) | −1.35237e18 | −0.156049 | ||||||||
\(336\) | −1.35538e19 | + | 1.16674e19i | −1.52939 | + | 1.31652i | ||||
\(337\) | 1.37021e19 | 1.51203 | 0.756017 | − | 0.654552i | \(-0.227143\pi\) | ||||
0.756017 | + | 0.654552i | \(0.227143\pi\) | |||||||
\(338\) | −3.31391e18 | − | 7.23725e17i | −0.357656 | − | 0.0781085i | ||||
\(339\) | − | 4.49195e18i | − | 0.474173i | ||||||
\(340\) | 2.44370e18 | − | 5.32798e18i | 0.252323 | − | 0.550137i | ||||
\(341\) | − | 1.37741e19i | − | 1.39125i | ||||||
\(342\) | 2.19179e18 | − | 1.00361e19i | 0.216572 | − | 0.991679i | ||||
\(343\) | 6.98732e18 | 0.675468 | ||||||||
\(344\) | −4.86767e18 | + | 6.46944e18i | −0.460398 | + | 0.611898i | ||||
\(345\) | 8.05507e18 | 0.745463 | ||||||||
\(346\) | 9.94212e17 | − | 4.55247e18i | 0.0900344 | − | 0.412265i | ||||
\(347\) | 8.09568e18i | 0.717435i | 0.933446 | + | 0.358717i | \(0.116786\pi\) | ||||
−0.933446 | + | 0.358717i | \(0.883214\pi\) | |||||||
\(348\) | 1.09968e19 | + | 5.04375e18i | 0.953726 | + | 0.437431i | ||||
\(349\) | 6.14623e18i | 0.521697i | 0.965380 | + | 0.260848i | \(0.0840023\pi\) | ||||
−0.965380 | + | 0.260848i | \(0.915998\pi\) | |||||||
\(350\) | −8.59552e16 | − | 1.87717e16i | −0.00714105 | − | 0.00155953i | ||||
\(351\) | −4.13272e18 | −0.336072 | ||||||||
\(352\) | 1.40105e19 | − | 7.57641e18i | 1.11528 | − | 0.603106i | ||||
\(353\) | 2.71644e18 | 0.211685 | 0.105842 | − | 0.994383i | \(-0.466246\pi\) | ||||
0.105842 | + | 0.994383i | \(0.466246\pi\) | |||||||
\(354\) | 2.47642e19 | + | 5.40824e18i | 1.88929 | + | 0.412602i | ||||
\(355\) | − | 1.63464e19i | − | 1.22098i | ||||||
\(356\) | 1.40684e17 | + | 6.45252e16i | 0.0102889 | + | 0.00471904i | ||||
\(357\) | − | 1.70954e19i | − | 1.22424i | ||||||
\(358\) | 3.23498e18 | − | 1.48129e19i | 0.226855 | − | 1.03876i | ||||
\(359\) | −1.18069e19 | −0.810824 | −0.405412 | − | 0.914134i | \(-0.632872\pi\) | ||||
−0.405412 | + | 0.914134i | \(0.632872\pi\) | |||||||
\(360\) | −6.00866e18 | + | 7.98589e18i | −0.404119 | + | 0.537099i | ||||
\(361\) | −1.92782e19 | −1.26988 | ||||||||
\(362\) | −1.39114e17 | + | 6.37001e17i | −0.00897548 | + | 0.0410985i | ||||
\(363\) | − | 1.24379e19i | − | 0.786048i | ||||||
\(364\) | −8.36331e18 | + | 1.82344e19i | −0.517747 | + | 1.12884i | ||||
\(365\) | 3.13568e19i | 1.90167i | ||||||||
\(366\) | −1.86692e19 | − | 4.07716e18i | −1.10922 | − | 0.242242i | ||||
\(367\) | 1.15057e19 | 0.669756 | 0.334878 | − | 0.942262i | \(-0.391305\pi\) | ||||
0.334878 | + | 0.942262i | \(0.391305\pi\) | |||||||
\(368\) | −6.60652e18 | − | 7.67470e18i | −0.376803 | − | 0.437727i | ||||
\(369\) | −1.55027e19 | −0.866382 | ||||||||
\(370\) | 9.89912e18 | + | 2.16187e18i | 0.542105 | + | 0.118390i | ||||
\(371\) | 7.87266e18i | 0.422490i | ||||||||
\(372\) | 1.12528e19 | − | 2.45344e19i | 0.591818 | − | 1.29034i | ||||
\(373\) | 2.65732e19i | 1.36971i | 0.728680 | + | 0.684854i | \(0.240134\pi\) | ||||
−0.728680 | + | 0.684854i | \(0.759866\pi\) | |||||||
\(374\) | −3.24854e18 | + | 1.48749e19i | −0.164116 | + | 0.751482i | ||||
\(375\) | −2.61871e19 | −1.29674 | ||||||||
\(376\) | −6.62570e18 | − | 4.98524e18i | −0.321605 | − | 0.241979i | ||||
\(377\) | 1.35711e19 | 0.645734 | ||||||||
\(378\) | 3.01159e18 | − | 1.37900e19i | 0.140478 | − | 0.643243i | ||||
\(379\) | 1.87597e19i | 0.857891i | 0.903330 | + | 0.428945i | \(0.141115\pi\) | ||||
−0.903330 | + | 0.428945i | \(0.858885\pi\) | |||||||
\(380\) | 3.04719e19 | + | 1.39761e19i | 1.36623 | + | 0.626627i | ||||
\(381\) | 2.76073e19i | 1.21363i | ||||||||
\(382\) | −3.25164e19 | − | 7.10125e18i | −1.40161 | − | 0.306097i | ||||
\(383\) | 1.00414e19 | 0.424428 | 0.212214 | − | 0.977223i | \(-0.431933\pi\) | ||||
0.212214 | + | 0.977223i | \(0.431933\pi\) | |||||||
\(384\) | 3.11451e19 | − | 2.04916e18i | 1.29094 | − | 0.0849359i | ||||
\(385\) | −4.85397e19 | −1.97307 | ||||||||
\(386\) | −1.38889e19 | − | 3.03320e18i | −0.553687 | − | 0.120920i | ||||
\(387\) | 1.31950e19i | 0.515915i | ||||||||
\(388\) | 1.31637e19 | + | 6.03759e18i | 0.504824 | + | 0.231540i | ||||
\(389\) | − | 5.26344e19i | − | 1.97992i | −0.141344 | − | 0.989961i | \(-0.545142\pi\) | ||
0.141344 | − | 0.989961i | \(-0.454858\pi\) | |||||||
\(390\) | −5.94207e18 | + | 2.72086e19i | −0.219257 | + | 1.00397i | ||||
\(391\) | 9.68006e18 | 0.350390 | ||||||||
\(392\) | −3.22472e19 | − | 2.42631e19i | −1.14511 | − | 0.861590i | ||||
\(393\) | 1.38685e19 | 0.483154 | ||||||||
\(394\) | −2.81693e18 | + | 1.28986e19i | −0.0962839 | + | 0.440881i | ||||
\(395\) | − | 2.24227e19i | − | 0.751984i | ||||||
\(396\) | 1.08222e19 | − | 2.35955e19i | 0.356124 | − | 0.776454i | ||||
\(397\) | − | 4.83129e19i | − | 1.56003i | −0.625758 | − | 0.780017i | \(-0.715210\pi\) | ||
0.625758 | − | 0.780017i | \(-0.284790\pi\) | |||||||
\(398\) | 2.33956e19 | + | 5.10936e18i | 0.741330 | + | 0.161899i | ||||
\(399\) | 9.77722e19 | 3.04032 | ||||||||
\(400\) | 1.00176e17 | + | 1.16373e17i | 0.00305714 | + | 0.00355144i | ||||
\(401\) | −2.99975e19 | −0.898467 | −0.449234 | − | 0.893414i | \(-0.648303\pi\) | ||||
−0.449234 | + | 0.893414i | \(0.648303\pi\) | |||||||
\(402\) | 6.72514e18 | + | 1.46870e18i | 0.197700 | + | 0.0431756i | ||||
\(403\) | − | 3.02775e19i | − | 0.873641i | ||||||
\(404\) | −1.02319e19 | + | 2.23085e19i | −0.289798 | + | 0.631843i | ||||
\(405\) | − | 4.37711e19i | − | 1.21696i | ||||||
\(406\) | −9.88949e18 | + | 4.52837e19i | −0.269916 | + | 1.23594i | ||||
\(407\) | −2.63188e19 | −0.705192 | ||||||||
\(408\) | −1.79385e19 | + | 2.38413e19i | −0.471882 | + | 0.627161i | ||||
\(409\) | 1.07765e18 | 0.0278325 | 0.0139163 | − | 0.999903i | \(-0.495570\pi\) | ||||
0.0139163 | + | 0.999903i | \(0.495570\pi\) | |||||||
\(410\) | 1.07943e19 | − | 4.94270e19i | 0.273727 | − | 1.25339i | ||||
\(411\) | 6.83684e19i | 1.70232i | ||||||||
\(412\) | 4.39454e19 | + | 2.01558e19i | 1.07445 | + | 0.492799i | ||||
\(413\) | 9.71122e19i | 2.33157i | ||||||||
\(414\) | −1.61241e19 | − | 3.52134e18i | −0.380166 | − | 0.0830243i | ||||
\(415\) | 4.05665e19 | 0.939305 | ||||||||
\(416\) | 3.07972e19 | − | 1.66541e19i | 0.700345 | − | 0.378723i | ||||
\(417\) | 6.66931e19 | 1.48957 | ||||||||
\(418\) | −8.50732e19 | − | 1.85791e19i | −1.86625 | − | 0.407571i | ||||
\(419\) | − | 5.32812e19i | − | 1.14807i | −0.818830 | − | 0.574036i | \(-0.805377\pi\) | ||
0.818830 | − | 0.574036i | \(-0.194623\pi\) | |||||||
\(420\) | −8.64589e19 | − | 3.96547e19i | −1.82995 | − | 0.839316i | ||||
\(421\) | 5.14025e19i | 1.06873i | 0.845253 | + | 0.534366i | \(0.179449\pi\) | ||||
−0.845253 | + | 0.534366i | \(0.820551\pi\) | |||||||
\(422\) | 5.21801e18 | − | 2.38931e19i | 0.106577 | − | 0.488011i | ||||
\(423\) | −1.35137e19 | −0.271158 | ||||||||
\(424\) | 8.26091e18 | − | 1.09793e19i | 0.162849 | − | 0.216436i | ||||
\(425\) | −1.46781e17 | −0.00284285 | ||||||||
\(426\) | −1.77525e19 | + | 8.12881e19i | −0.337821 | + | 1.54687i | ||||
\(427\) | − | 7.32109e19i | − | 1.36888i | ||||||
\(428\) | 7.50717e18 | − | 1.63678e19i | 0.137927 | − | 0.300720i | ||||
\(429\) | − | 7.23393e19i | − | 1.30601i | ||||||
\(430\) | −4.20695e19 | − | 9.18755e18i | −0.746370 | − | 0.163000i | ||||
\(431\) | −3.85909e19 | −0.672829 | −0.336415 | − | 0.941714i | \(-0.609214\pi\) | ||||
−0.336415 | + | 0.941714i | \(0.609214\pi\) | |||||||
\(432\) | −1.86700e19 | + | 1.60715e19i | −0.319902 | + | 0.275377i | ||||
\(433\) | 3.87254e19 | 0.652133 | 0.326067 | − | 0.945347i | \(-0.394277\pi\) | ||||
0.326067 | + | 0.945347i | \(0.394277\pi\) | |||||||
\(434\) | 1.01029e20 | + | 2.20638e19i | 1.67215 | + | 0.365180i | ||||
\(435\) | 6.43474e19i | 1.04680i | ||||||||
\(436\) | −3.36339e19 | + | 7.33317e19i | −0.537810 | + | 1.17258i | ||||
\(437\) | 5.53624e19i | 0.870171i | ||||||||
\(438\) | 3.40541e19 | − | 1.55933e20i | 0.526155 | − | 2.40925i | ||||
\(439\) | −1.11031e20 | −1.68640 | −0.843201 | − | 0.537599i | \(-0.819332\pi\) | ||||
−0.843201 | + | 0.537599i | \(0.819332\pi\) | |||||||
\(440\) | 6.76939e19 | + | 5.09335e19i | 1.01077 | + | 0.760517i | ||||
\(441\) | −6.57712e19 | −0.965486 | ||||||||
\(442\) | −7.14079e18 | + | 3.26974e19i | −0.103057 | + | 0.471897i | ||||
\(443\) | − | 4.75682e19i | − | 0.674976i | −0.941330 | − | 0.337488i | \(-0.890423\pi\) | ||
0.941330 | − | 0.337488i | \(-0.109577\pi\) | |||||||
\(444\) | −4.68790e19 | − | 2.15013e19i | −0.654042 | − | 0.299979i | ||||
\(445\) | 8.23202e17i | 0.0112929i | ||||||||
\(446\) | 1.09679e20 | + | 2.39529e19i | 1.47950 | + | 0.323107i | ||||
\(447\) | −1.05202e18 | −0.0139546 | ||||||||
\(448\) | 3.31287e19 | + | 1.14900e20i | 0.432134 | + | 1.49877i | ||||
\(449\) | 2.88459e19 | 0.370029 | 0.185015 | − | 0.982736i | \(-0.440767\pi\) | ||||
0.185015 | + | 0.982736i | \(0.440767\pi\) | |||||||
\(450\) | 2.44494e17 | + | 5.33950e16i | 0.00308443 | + | 0.000673607i | ||||
\(451\) | 1.31411e20i | 1.63046i | ||||||||
\(452\) | −2.73007e19 | − | 1.25216e19i | −0.333147 | − | 0.152799i | ||||
\(453\) | − | 1.46062e19i | − | 0.175308i | ||||||
\(454\) | −9.01778e18 | + | 4.12921e19i | −0.106459 | + | 0.487471i | ||||
\(455\) | −1.06698e20 | −1.23900 | ||||||||
\(456\) | −1.36354e20 | − | 1.02594e20i | −1.55751 | − | 1.17189i | ||||
\(457\) | −6.84233e19 | −0.768834 | −0.384417 | − | 0.923160i | \(-0.625597\pi\) | ||||
−0.384417 | + | 0.923160i | \(0.625597\pi\) | |||||||
\(458\) | 2.11108e19 | − | 9.66656e19i | 0.233353 | − | 1.06852i | ||||
\(459\) | − | 2.35484e19i | − | 0.256075i | ||||||
\(460\) | 2.24541e19 | − | 4.89564e19i | 0.240221 | − | 0.523752i | ||||
\(461\) | − | 1.37605e20i | − | 1.44836i | −0.689610 | − | 0.724181i | \(-0.742218\pi\) | ||
0.689610 | − | 0.724181i | \(-0.257782\pi\) | |||||||
\(462\) | 2.41380e20 | + | 5.27150e19i | 2.49970 | + | 0.545908i | ||||
\(463\) | 1.42820e20 | 1.45523 | 0.727615 | − | 0.685985i | \(-0.240629\pi\) | ||||
0.727615 | + | 0.685985i | \(0.240629\pi\) | |||||||
\(464\) | 6.13089e19 | − | 5.27758e19i | 0.614665 | − | 0.529115i | ||||
\(465\) | 1.43561e20 | 1.41625 | ||||||||
\(466\) | −1.44669e20 | − | 3.15941e19i | −1.40436 | − | 0.306699i | ||||
\(467\) | 1.24349e20i | 1.18786i | 0.804517 | + | 0.593930i | \(0.202424\pi\) | ||||
−0.804517 | + | 0.593930i | \(0.797576\pi\) | |||||||
\(468\) | 2.37889e19 | − | 5.18666e19i | 0.223630 | − | 0.487578i | ||||
\(469\) | 2.63725e19i | 0.243981i | ||||||||
\(470\) | 9.40945e18 | − | 4.30856e19i | 0.0856703 | − | 0.392282i | ||||
\(471\) | −2.20647e20 | −1.97716 | ||||||||
\(472\) | 1.01901e20 | − | 1.35433e20i | 0.898702 | − | 1.19443i | ||||
\(473\) | 1.11850e20 | 0.970908 | ||||||||
\(474\) | −2.43514e19 | + | 1.11504e20i | −0.208059 | + | 0.952696i | ||||
\(475\) | − | 8.39475e17i | − | 0.00706001i | ||||||
\(476\) | −1.03901e20 | − | 4.76545e19i | −0.860133 | − | 0.394504i | ||||
\(477\) | − | 2.23932e19i | − | 0.182486i | ||||||
\(478\) | 1.98417e19 | + | 4.33323e18i | 0.159173 | + | 0.0347618i | ||||
\(479\) | −2.59178e19 | −0.204683 | −0.102341 | − | 0.994749i | \(-0.532633\pi\) | ||||
−0.102341 | + | 0.994749i | \(0.532633\pi\) | |||||||
\(480\) | 7.89658e19 | + | 1.46026e20i | 0.613946 | + | 1.13532i | ||||
\(481\) | −5.78528e19 | −0.442829 | ||||||||
\(482\) | 8.64039e19 | + | 1.88697e19i | 0.651149 | + | 0.142204i | ||||
\(483\) | − | 1.57081e20i | − | 1.16552i | ||||||
\(484\) | −7.55941e19 | − | 3.46716e19i | −0.552265 | − | 0.253299i | ||||
\(485\) | 7.70267e19i | 0.554087i | ||||||||
\(486\) | −3.48216e19 | + | 1.59447e20i | −0.246647 | + | 1.12939i | ||||
\(487\) | 2.25603e20 | 1.57354 | 0.786770 | − | 0.617247i | \(-0.211752\pi\) | ||||
0.786770 | + | 0.617247i | \(0.211752\pi\) | |||||||
\(488\) | −7.68215e19 | + | 1.02101e20i | −0.527635 | + | 0.701261i | ||||
\(489\) | 1.35104e20 | 0.913800 | ||||||||
\(490\) | 4.57957e19 | − | 2.09697e20i | 0.305038 | − | 1.39676i | ||||
\(491\) | 8.41823e19i | 0.552217i | 0.961126 | + | 0.276109i | \(0.0890449\pi\) | ||||
−0.961126 | + | 0.276109i | \(0.910955\pi\) | |||||||
\(492\) | −1.07357e20 | + | 2.34070e20i | −0.693574 | + | 1.51219i | ||||
\(493\) | 7.73285e19i | 0.492026i | ||||||||
\(494\) | −1.87004e20 | − | 4.08398e19i | −1.17192 | − | 0.255936i | ||||
\(495\) | 1.38068e20 | 0.852224 | ||||||||
\(496\) | −1.17745e20 | − | 1.36782e20i | −0.715861 | − | 0.831606i | ||||
\(497\) | −3.18769e20 | −1.90899 | ||||||||
\(498\) | −2.01731e20 | − | 4.40560e19i | −1.19001 | − | 0.259887i | ||||
\(499\) | − | 3.32246e20i | − | 1.93066i | −0.261035 | − | 0.965329i | \(-0.584064\pi\) | ||
0.261035 | − | 0.965329i | \(-0.415936\pi\) | |||||||
\(500\) | −7.29984e19 | + | 1.59158e20i | −0.417867 | + | 0.911071i | ||||
\(501\) | 1.42311e19i | 0.0802519i | ||||||||
\(502\) | −2.82699e19 | + | 1.29447e20i | −0.157053 | + | 0.719142i | ||||
\(503\) | −3.33944e20 | −1.82774 | −0.913870 | − | 0.406007i | \(-0.866921\pi\) | ||||
−0.913870 | + | 0.406007i | \(0.866921\pi\) | |||||||
\(504\) | 1.55732e20 | + | 1.17174e20i | 0.839749 | + | 0.631835i | ||||
\(505\) | −1.30537e20 | −0.693502 | ||||||||
\(506\) | −2.98493e19 | + | 1.36679e20i | −0.156245 | + | 0.715439i | ||||
\(507\) | 9.18303e19i | 0.473616i | ||||||||
\(508\) | 1.67789e20 | + | 7.69572e19i | 0.852679 | + | 0.391085i | ||||
\(509\) | − | 1.32906e20i | − | 0.665521i | −0.943011 | − | 0.332761i | \(-0.892020\pi\) | ||
0.943011 | − | 0.332761i | \(-0.107980\pi\) | |||||||
\(510\) | −1.55035e20 | − | 3.38582e19i | −0.764988 | − | 0.167066i | ||||
\(511\) | 6.11487e20 | 2.97324 | ||||||||
\(512\) | 7.43648e19 | − | 1.95003e20i | 0.356322 | − | 0.934363i | ||||
\(513\) | 1.34679e20 | 0.635944 | ||||||||
\(514\) | −1.31191e20 | − | 2.86507e19i | −0.610492 | − | 0.133325i | ||||
\(515\) | 2.57144e20i | 1.17929i | ||||||||
\(516\) | 1.99227e20 | + | 9.13765e19i | 0.900484 | + | 0.413011i | ||||
\(517\) | 1.14552e20i | 0.510296i | ||||||||
\(518\) | 4.21584e19 | − | 1.93042e20i | 0.185102 | − | 0.847575i | ||||
\(519\) | −1.26151e20 | −0.545929 | ||||||||
\(520\) | 1.48802e20 | + | 1.11960e20i | 0.634721 | + | 0.477570i | ||||
\(521\) | 2.73640e20 | 1.15053 | 0.575264 | − | 0.817968i | \(-0.304899\pi\) | ||||
0.575264 | + | 0.817968i | \(0.304899\pi\) | |||||||
\(522\) | 2.81300e19 | − | 1.28806e20i | 0.116585 | − | 0.533837i | ||||
\(523\) | − | 3.08487e20i | − | 1.26030i | −0.776474 | − | 0.630149i | \(-0.782994\pi\) | ||
0.776474 | − | 0.630149i | \(-0.217006\pi\) | |||||||
\(524\) | 3.86594e19 | − | 8.42886e19i | 0.155693 | − | 0.339457i | ||||
\(525\) | 2.38186e18i | 0.00945632i | ||||||||
\(526\) | −3.12040e19 | − | 6.81464e18i | −0.122129 | − | 0.0266717i | ||||
\(527\) | 1.72523e20 | 0.665682 | ||||||||
\(528\) | −2.81316e20 | − | 3.26801e20i | −1.07014 | − | 1.24317i | ||||
\(529\) | −1.77690e20 | −0.666415 | ||||||||
\(530\) | 7.13960e19 | + | 1.55922e19i | 0.264001 | + | 0.0576550i | ||||
\(531\) | − | 2.76229e20i | − | 1.00707i | ||||||
\(532\) | 2.72547e20 | − | 5.94231e20i | 0.979724 | − | 2.13608i | ||||
\(533\) | 2.88863e20i | 1.02385i | ||||||||
\(534\) | 8.94013e17 | − | 4.09366e18i | 0.00312453 | − | 0.0143071i | ||||
\(535\) | 9.57753e19 | 0.330066 | ||||||||
\(536\) | 2.76731e19 | − | 3.67793e19i | 0.0940421 | − | 0.124988i | ||||
\(537\) | −4.10472e20 | −1.37555 | ||||||||
\(538\) | −1.20359e20 | + | 5.51120e20i | −0.397751 | + | 1.82129i | ||||
\(539\) | 5.57521e20i | 1.81696i | ||||||||
\(540\) | −1.19095e20 | − | 5.46234e19i | −0.382771 | − | 0.175560i | ||||
\(541\) | − | 5.48913e20i | − | 1.73990i | −0.493142 | − | 0.869949i | \(-0.664152\pi\) | ||
0.493142 | − | 0.869949i | \(-0.335848\pi\) | |||||||
\(542\) | 8.37527e19 | + | 1.82907e19i | 0.261821 | + | 0.0571790i | ||||
\(543\) | 1.76516e19 | 0.0544234 | ||||||||
\(544\) | 9.48959e19 | + | 1.75484e20i | 0.288573 | + | 0.533637i | ||||
\(545\) | −4.29097e20 | −1.28701 | ||||||||
\(546\) | 5.30592e20 | + | 1.15876e20i | 1.56970 | + | 0.342806i | ||||
\(547\) | 3.73838e20i | 1.09088i | 0.838149 | + | 0.545442i | \(0.183638\pi\) | ||||
−0.838149 | + | 0.545442i | \(0.816362\pi\) | |||||||
\(548\) | 4.15523e20 | + | 1.90581e20i | 1.19603 | + | 0.548563i | ||||
\(549\) | 2.08244e20i | 0.591261i | ||||||||
\(550\) | 4.52612e17 | − | 2.07250e18i | 0.00126767 | − | 0.00580462i | ||||
\(551\) | −4.42259e20 | −1.22191 | ||||||||
\(552\) | −1.64828e20 | + | 2.19067e20i | −0.449250 | + | 0.597082i | ||||
\(553\) | −4.37262e20 | −1.17572 | ||||||||
\(554\) | 1.60119e19 | − | 7.33182e19i | 0.0424738 | − | 0.194486i | ||||
\(555\) | − | 2.74310e20i | − | 0.717867i | ||||||
\(556\) | 1.85912e20 | − | 4.05341e20i | 0.480005 | − | 1.04655i | ||||
\(557\) | − | 9.58954e19i | − | 0.244278i | −0.992513 | − | 0.122139i | \(-0.961025\pi\) | ||
0.992513 | − | 0.122139i | \(-0.0389753\pi\) | |||||||
\(558\) | −2.87372e20 | − | 6.27590e19i | −0.722250 | − | 0.157732i | ||||
\(559\) | 2.45864e20 | 0.609686 | ||||||||
\(560\) | −4.82020e20 | + | 4.14931e20i | −1.17938 | + | 1.01523i | ||||
\(561\) | 4.12193e20 | 0.995127 | ||||||||
\(562\) | 2.08731e20 | + | 4.55848e19i | 0.497239 | + | 0.108592i | ||||
\(563\) | − | 5.14407e20i | − | 1.20919i | −0.796533 | − | 0.604595i | \(-0.793335\pi\) | ||
0.796533 | − | 0.604595i | \(-0.206665\pi\) | |||||||
\(564\) | −9.35835e19 | + | 2.04039e20i | −0.217073 | + | 0.473282i | ||||
\(565\) | − | 1.59749e20i | − | 0.365657i | ||||||
\(566\) | −3.15158e19 | + | 1.44310e20i | −0.0711877 | + | 0.325966i | ||||
\(567\) | −8.53577e20 | −1.90270 | ||||||||
\(568\) | 4.44559e20 | + | 3.34490e20i | 0.977950 | + | 0.735819i | ||||
\(569\) | 8.71846e20 | 1.89277 | 0.946385 | − | 0.323041i | \(-0.104705\pi\) | ||||
0.946385 | + | 0.323041i | \(0.104705\pi\) | |||||||
\(570\) | 1.93642e20 | − | 8.86683e20i | 0.414896 | − | 1.89980i | ||||
\(571\) | 7.82822e20i | 1.65536i | 0.561202 | + | 0.827679i | \(0.310339\pi\) | ||||
−0.561202 | + | 0.827679i | \(0.689661\pi\) | |||||||
\(572\) | −4.39657e20 | − | 2.01651e20i | −0.917580 | − | 0.420852i | ||||
\(573\) | 9.01046e20i | 1.85604i | ||||||||
\(574\) | −9.63871e20 | − | 2.10500e20i | −1.95966 | − | 0.427969i | ||||
\(575\) | −1.34870e18 | −0.00270650 | ||||||||
\(576\) | −9.42323e19 | − | 3.26825e20i | −0.186651 | − | 0.647361i | ||||
\(577\) | 5.77728e19 | 0.112955 | 0.0564774 | − | 0.998404i | \(-0.482013\pi\) | ||||
0.0564774 | + | 0.998404i | \(0.482013\pi\) | |||||||
\(578\) | 3.19911e20 | + | 6.98653e19i | 0.617406 | + | 0.134835i | ||||
\(579\) | 3.84870e20i | 0.733204i | ||||||||
\(580\) | 3.91085e20 | + | 1.79373e20i | 0.735463 | + | 0.337323i | ||||
\(581\) | − | 7.91084e20i | − | 1.46859i | ||||||
\(582\) | 8.36524e19 | − | 3.83042e20i | 0.153305 | − | 0.701979i | ||||
\(583\) | −1.89820e20 | −0.343423 | ||||||||
\(584\) | −8.52785e20 | − | 6.41643e20i | −1.52315 | − | 1.14603i | ||||
\(585\) | 3.03495e20 | 0.535158 | ||||||||
\(586\) | −1.06895e19 | + | 4.89470e19i | −0.0186091 | + | 0.0852107i | ||||
\(587\) | − | 1.10291e21i | − | 1.89564i | −0.318807 | − | 0.947820i | \(-0.603282\pi\) | ||
0.318807 | − | 0.947820i | \(-0.396718\pi\) | |||||||
\(588\) | −4.55470e20 | + | 9.93056e20i | −0.772911 | + | 1.68517i | ||||
\(589\) | 9.86696e20i | 1.65317i | ||||||||
\(590\) | 8.80697e20 | + | 1.92335e20i | 1.45692 | + | 0.318177i | ||||
\(591\) | 3.57427e20 | 0.583824 | ||||||||
\(592\) | −2.61357e20 | + | 2.24980e20i | −0.421522 | + | 0.362854i | ||||
\(593\) | 9.27288e20 | 1.47674 | 0.738370 | − | 0.674395i | \(-0.235596\pi\) | ||||
0.738370 | + | 0.674395i | \(0.235596\pi\) | |||||||
\(594\) | 3.32495e20 | + | 7.26135e19i | 0.522862 | + | 0.114188i | ||||
\(595\) | − | 6.07968e20i | − | 0.944069i | ||||||
\(596\) | −2.93257e18 | + | 6.39386e18i | −0.00449678 | + | 0.00980428i | ||||
\(597\) | − | 6.48304e20i | − | 0.981683i | ||||||
\(598\) | −6.56134e19 | + | 3.00442e20i | −0.0981146 | + | 0.449264i | ||||
\(599\) | 9.48773e20 | 1.40107 | 0.700537 | − | 0.713616i | \(-0.252944\pi\) | ||||
0.700537 | + | 0.713616i | \(0.252944\pi\) | |||||||
\(600\) | 2.49933e18 | − | 3.32177e18i | 0.00364493 | − | 0.00484434i | ||||
\(601\) | −6.01318e20 | −0.866056 | −0.433028 | − | 0.901380i | \(-0.642555\pi\) | ||||
−0.433028 | + | 0.901380i | \(0.642555\pi\) | |||||||
\(602\) | −1.79166e20 | + | 8.20394e20i | −0.254848 | + | 1.16694i | ||||
\(603\) | − | 7.50149e19i | − | 0.105382i | ||||||
\(604\) | −8.87722e19 | − | 4.07158e19i | −0.123169 | − | 0.0564918i | ||||
\(605\) | − | 4.42335e20i | − | 0.606158i | ||||||
\(606\) | 6.49139e20 | + | 1.41765e20i | 0.878604 | + | 0.191878i | ||||
\(607\) | −5.61388e20 | −0.750495 | −0.375248 | − | 0.926925i | \(-0.622442\pi\) | ||||
−0.375248 | + | 0.926925i | \(0.622442\pi\) | |||||||
\(608\) | −1.00363e21 | + | 5.42731e20i | −1.32525 | + | 0.716652i | ||||
\(609\) | 1.25483e21 | 1.63665 | ||||||||
\(610\) | −6.63940e20 | − | 1.44998e20i | −0.855372 | − | 0.186804i | ||||
\(611\) | 2.51802e20i | 0.320443i | ||||||||
\(612\) | 2.95538e20 | + | 1.35550e20i | 0.371516 | + | 0.170398i | ||||
\(613\) | − | 8.99740e20i | − | 1.11728i | −0.829409 | − | 0.558642i | \(-0.811323\pi\) | ||
0.829409 | − | 0.558642i | \(-0.188677\pi\) | |||||||
\(614\) | −4.53113e19 | + | 2.07479e20i | −0.0555832 | + | 0.254514i | ||||
\(615\) | −1.36965e21 | −1.65976 | ||||||||
\(616\) | 9.93250e20 | − | 1.32009e21i | 1.18906 | − | 1.58033i | ||||
\(617\) | 1.77760e20 | 0.210230 | 0.105115 | − | 0.994460i | \(-0.466479\pi\) | ||||
0.105115 | + | 0.994460i | \(0.466479\pi\) | |||||||
\(618\) | 2.79263e20 | − | 1.27874e21i | 0.326287 | − | 1.49406i | ||||
\(619\) | 2.01875e20i | 0.233025i | 0.993189 | + | 0.116513i | \(0.0371716\pi\) | ||||
−0.993189 | + | 0.116513i | \(0.962828\pi\) | |||||||
\(620\) | 4.00187e20 | − | 8.72524e20i | 0.456379 | − | 0.995038i | ||||
\(621\) | − | 2.16375e20i | − | 0.243793i | ||||||
\(622\) | −1.79093e20 | − | 3.91120e19i | −0.199365 | − | 0.0435393i | ||||
\(623\) | 1.60532e19 | 0.0176564 | ||||||||
\(624\) | −6.18377e20 | − | 7.18360e20i | −0.672000 | − | 0.780653i | ||||
\(625\) | −9.26938e20 | −0.995292 | ||||||||
\(626\) | 3.83985e20 | + | 8.38583e19i | 0.407386 | + | 0.0889690i | ||||
\(627\) | 2.35742e21i | 2.47133i | ||||||||
\(628\) | −6.15069e20 | + | 1.34103e21i | −0.637128 | + | 1.38912i | ||||
\(629\) | − | 3.29647e20i | − | 0.337419i | ||||||
\(630\) | −2.21162e20 | + | 1.01270e21i | −0.223695 | + | 1.02429i | ||||
\(631\) | 8.66955e20 | 0.866516 | 0.433258 | − | 0.901270i | \(-0.357364\pi\) | ||||
0.433258 | + | 0.901270i | \(0.357364\pi\) | |||||||
\(632\) | 6.09810e20 | + | 4.58827e20i | 0.602305 | + | 0.453180i | ||||
\(633\) | −6.62091e20 | −0.646234 | ||||||||
\(634\) | −1.31159e20 | + | 6.00572e20i | −0.126511 | + | 0.579289i | ||||
\(635\) | 9.81808e20i | 0.935887i | ||||||||
\(636\) | −3.38108e20 | − | 1.55075e20i | −0.318513 | − | 0.146087i | ||||
\(637\) | 1.22552e21i | 1.14097i | ||||||||
\(638\) | −1.09185e21 | − | 2.38449e20i | −1.00463 | − | 0.219402i | ||||
\(639\) | 9.06719e20 | 0.824548 | ||||||||
\(640\) | 1.10762e21 | − | 7.28749e19i | 0.995502 | − | 0.0654980i | ||||
\(641\) | −5.75049e20 | −0.510822 | −0.255411 | − | 0.966833i | \(-0.582211\pi\) | ||||
−0.255411 | + | 0.966833i | \(0.582211\pi\) | |||||||
\(642\) | −4.76276e20 | − | 1.04014e20i | −0.418163 | − | 0.0913226i | ||||
\(643\) | − | 5.75046e20i | − | 0.499023i | −0.968372 | − | 0.249511i | \(-0.919730\pi\) | ||
0.968372 | − | 0.249511i | \(-0.0802700\pi\) | |||||||
\(644\) | −9.54694e20 | − | 4.37875e20i | −0.818880 | − | 0.375583i | ||||
\(645\) | 1.16577e21i | 0.988358i | ||||||||
\(646\) | 2.32707e20 | − | 1.06556e21i | 0.195014 | − | 0.892962i | ||||
\(647\) | −1.86103e21 | −1.54159 | −0.770797 | − | 0.637080i | \(-0.780142\pi\) | ||||
−0.770797 | + | 0.637080i | \(0.780142\pi\) | |||||||
\(648\) | 1.19040e21 | + | 8.95672e20i | 0.974725 | + | 0.733393i | ||||
\(649\) | −2.34151e21 | −1.89522 | ||||||||
\(650\) | 9.94912e17 | − | 4.55567e18i | 0.000796039 | − | 0.00364504i | ||||
\(651\) | − | 2.79958e21i | − | 2.21429i | ||||||
\(652\) | 3.76611e20 | − | 8.21121e20i | 0.294466 | − | 0.642022i | ||||
\(653\) | 1.47506e21i | 1.14015i | 0.821593 | + | 0.570074i | \(0.193085\pi\) | ||||
−0.821593 | + | 0.570074i | \(0.806915\pi\) | |||||||
\(654\) | 2.13383e21 | + | 4.66007e20i | 1.63052 | + | 0.356090i | ||||
\(655\) | 4.93210e20 | 0.372582 | ||||||||
\(656\) | 1.12334e21 | + | 1.30497e21i | 0.838944 | + | 0.974590i | ||||
\(657\) | −1.73933e21 | −1.28423 | ||||||||
\(658\) | −8.40208e20 | − | 1.83493e20i | −0.613328 | − | 0.133945i | ||||
\(659\) | − | 1.67485e21i | − | 1.20875i | −0.796701 | − | 0.604373i | \(-0.793424\pi\) | ||
0.796701 | − | 0.604373i | \(-0.206576\pi\) | |||||||
\(660\) | 9.56130e20 | − | 2.08464e21i | 0.682240 | − | 1.48748i | ||||
\(661\) | 1.79249e20i | 0.126458i | 0.997999 | + | 0.0632288i | \(0.0201398\pi\) | ||||
−0.997999 | + | 0.0632288i | \(0.979860\pi\) | |||||||
\(662\) | 3.82938e20 | − | 1.75346e21i | 0.267112 | − | 1.22310i | ||||
\(663\) | 9.06063e20 | 0.624895 | ||||||||
\(664\) | −8.30098e20 | + | 1.10325e21i | −0.566068 | + | 0.752340i | ||||
\(665\) | 3.47711e21 | 2.34453 | ||||||||
\(666\) | −1.19917e20 | + | 5.49095e20i | −0.0799508 | + | 0.366092i | ||||
\(667\) | 7.10536e20i | 0.468427i | ||||||||
\(668\) | 8.64924e19 | + | 3.96701e19i | 0.0563838 | + | 0.0258607i | ||||
\(669\) | − | 3.03927e21i | − | 1.95918i | ||||||
\(670\) | 2.39169e20 | + | 5.22320e19i | 0.152456 | + | 0.0332947i | ||||
\(671\) | 1.76522e21 | 1.11270 | ||||||||
\(672\) | 2.84763e21 | − | 1.53991e21i | 1.77507 | − | 0.959897i | ||||
\(673\) | −1.18737e21 | −0.731933 | −0.365967 | − | 0.930628i | \(-0.619262\pi\) | ||||
−0.365967 | + | 0.930628i | \(0.619262\pi\) | |||||||
\(674\) | −2.42322e21 | − | 5.29207e20i | −1.47722 | − | 0.322609i | ||||
\(675\) | 3.28095e18i | 0.00197798i | ||||||||
\(676\) | 5.58117e20 | + | 2.55983e20i | 0.332755 | + | 0.152620i | ||||
\(677\) | 1.27444e21i | 0.751455i | 0.926730 | + | 0.375728i | \(0.122607\pi\) | ||||
−0.926730 | + | 0.375728i | \(0.877393\pi\) | |||||||
\(678\) | −1.73490e20 | + | 7.94406e20i | −0.101170 | + | 0.463255i | ||||
\(679\) | 1.50209e21 | 0.866309 | ||||||||
\(680\) | −6.37952e20 | + | 8.47878e20i | −0.363891 | + | 0.483634i | ||||
\(681\) | 1.14423e21 | 0.645518 | ||||||||
\(682\) | −5.31988e20 | + | 2.43596e21i | −0.296838 | + | 1.35921i | ||||
\(683\) | − | 1.00010e21i | − | 0.551937i | −0.961167 | − | 0.275969i | \(-0.911001\pi\) | ||
0.961167 | − | 0.275969i | \(-0.0889986\pi\) | |||||||
\(684\) | −7.75241e20 | + | 1.69025e21i | −0.423171 | + | 0.922636i | ||||
\(685\) | 2.43141e21i | 1.31274i | ||||||||
\(686\) | −1.23572e21 | − | 2.69868e20i | −0.659914 | − | 0.144119i | ||||
\(687\) | −2.67865e21 | −1.41495 | ||||||||
\(688\) | 1.11072e21 | − | 9.56127e20i | 0.580351 | − | 0.499577i | ||||
\(689\) | −4.17255e20 | −0.215654 | ||||||||
\(690\) | −1.42455e21 | − | 3.11107e20i | −0.728298 | − | 0.159053i | ||||
\(691\) | 1.92165e20i | 0.0971827i | 0.998819 | + | 0.0485913i | \(0.0154732\pi\) | ||||
−0.998819 | + | 0.0485913i | \(0.984527\pi\) | |||||||
\(692\) | −3.51655e20 | + | 7.66710e20i | −0.175922 | + | 0.383562i | ||||
\(693\) | − | 2.69245e21i | − | 1.33244i | ||||||
\(694\) | 3.12675e20 | − | 1.43173e21i | 0.153073 | − | 0.700915i | ||||
\(695\) | 2.37183e21 | 1.14868 | ||||||||
\(696\) | −1.75000e21 | − | 1.31672e21i | −0.838434 | − | 0.630846i | ||||
\(697\) | −1.64595e21 | −0.780138 | ||||||||
\(698\) | 2.37383e20 | − | 1.08697e21i | 0.111310 | − | 0.509684i | ||||
\(699\) | 4.00884e21i | 1.85969i | ||||||||
\(700\) | 1.44763e19 | + | 6.63960e18i | 0.00664387 | + | 0.00304724i | ||||
\(701\) | − | 1.99733e21i | − | 0.906913i | −0.891278 | − | 0.453456i | \(-0.850191\pi\) | ||
0.891278 | − | 0.453456i | \(-0.149809\pi\) | |||||||
\(702\) | 7.30876e20 | + | 1.59616e20i | 0.328334 | + | 0.0717047i | ||||
\(703\) | 1.88533e21 | 0.837957 | ||||||||
\(704\) | −2.77039e21 | + | 7.98777e20i | −1.21828 | + | 0.351262i | ||||
\(705\) | −1.19392e21 | −0.519467 | ||||||||
\(706\) | −4.80405e20 | − | 1.04916e20i | −0.206810 | − | 0.0451653i | ||||
\(707\) | 2.54559e21i | 1.08428i | ||||||||
\(708\) | −4.17069e21 | − | 1.91291e21i | −1.75776 | − | 0.806203i | ||||
\(709\) | 5.38038e20i | 0.224371i | 0.993687 | + | 0.112185i | \(0.0357850\pi\) | ||||
−0.993687 | + | 0.112185i | \(0.964215\pi\) | |||||||
\(710\) | −6.31338e20 | + | 2.89088e21i | −0.260510 | + | 1.19287i | ||||
\(711\) | 1.24376e21 | 0.507827 | ||||||||
\(712\) | −2.23879e19 | − | 1.68449e19i | −0.00904511 | − | 0.00680563i | ||||
\(713\) | 1.58523e21 | 0.633754 | ||||||||
\(714\) | −6.60265e20 | + | 3.02333e21i | −0.261205 | + | 1.19605i | ||||
\(715\) | − | 2.57263e21i | − | 1.00712i | ||||||
\(716\) | −1.14422e21 | + | 2.49473e21i | −0.443263 | + | 0.966442i | ||||
\(717\) | − | 5.49825e20i | − | 0.210781i | ||||||
\(718\) | 2.08806e21 | + | 4.56010e20i | 0.792153 | + | 0.172998i | ||||
\(719\) | −3.14522e21 | −1.18082 | −0.590410 | − | 0.807103i | \(-0.701034\pi\) | ||||
−0.590410 | + | 0.807103i | \(0.701034\pi\) | |||||||
\(720\) | 1.37107e21 | − | 1.18024e21i | 0.509409 | − | 0.438509i | ||||
\(721\) | 5.01454e21 | 1.84381 | ||||||||
\(722\) | 3.40936e21 | + | 7.44570e20i | 1.24064 | + | 0.270942i | ||||
\(723\) | − | 2.39430e21i | − | 0.862265i | ||||||
\(724\) | 4.92051e19 | − | 1.07281e20i | 0.0175376 | − | 0.0382371i | ||||
\(725\) | − | 1.07740e19i | − | 0.00380052i | ||||||
\(726\) | −4.80384e20 | + | 2.19966e21i | −0.167712 | + | 0.767948i | ||||
\(727\) | −2.87779e21 | −0.994376 | −0.497188 | − | 0.867643i | \(-0.665634\pi\) | ||||
−0.497188 | + | 0.867643i | \(0.665634\pi\) | |||||||
\(728\) | 2.18332e21 | − | 2.90177e21i | 0.746675 | − | 0.992379i | ||||
\(729\) | 8.14636e20 | 0.275745 | ||||||||
\(730\) | 1.21108e21 | − | 5.54549e21i | 0.405743 | − | 1.85788i | ||||
\(731\) | 1.40094e21i | 0.464558i | ||||||||
\(732\) | 3.14420e21 | + | 1.44210e21i | 1.03199 | + | 0.473329i | ||||
\(733\) | − | 2.26001e21i | − | 0.734227i | −0.930176 | − | 0.367114i | \(-0.880346\pi\) | ||
0.930176 | − | 0.367114i | \(-0.119654\pi\) | |||||||
\(734\) | −2.03479e21 | − | 4.44377e20i | −0.654333 | − | 0.142900i | ||||
\(735\) | −5.81081e21 | −1.84962 | ||||||||
\(736\) | 8.71954e20 | + | 1.61244e21i | 0.274733 | + | 0.508042i | ||||
\(737\) | −6.35877e20 | −0.198320 | ||||||||
\(738\) | 2.74167e21 | + | 5.98752e20i | 0.846432 | + | 0.184852i | ||||
\(739\) | − | 5.11782e21i | − | 1.56406i | −0.623244 | − | 0.782028i | \(-0.714186\pi\) | ||
0.623244 | − | 0.782028i | \(-0.285814\pi\) | |||||||
\(740\) | −1.66717e21 | − | 7.64657e20i | −0.504363 | − | 0.231328i | ||||
\(741\) | 5.18198e21i | 1.55188i | ||||||||
\(742\) | 3.04061e20 | − | 1.39229e21i | 0.0901430 | − | 0.412762i | ||||
\(743\) | 1.70440e21 | 0.500213 | 0.250106 | − | 0.968218i | \(-0.419534\pi\) | ||||
0.250106 | + | 0.968218i | \(0.419534\pi\) | |||||||
\(744\) | −2.93765e21 | + | 3.90432e21i | −0.853498 | + | 1.13435i | ||||
\(745\) | −3.74133e19 | −0.0107610 | ||||||||
\(746\) | 1.02632e21 | − | 4.69951e21i | 0.292242 | − | 1.33817i | ||||
\(747\) | 2.25019e21i | 0.634328i | ||||||||
\(748\) | 1.14901e21 | − | 2.50518e21i | 0.320674 | − | 0.699162i | ||||
\(749\) | − | 1.86771e21i | − | 0.516054i | ||||||
\(750\) | 4.63122e21 | + | 1.01141e21i | 1.26688 | + | 0.276674i | ||||
\(751\) | −2.99833e21 | −0.812045 | −0.406023 | − | 0.913863i | \(-0.633085\pi\) | ||||
−0.406023 | + | 0.913863i | \(0.633085\pi\) | |||||||
\(752\) | 9.79219e20 | + | 1.13755e21i | 0.262571 | + | 0.305025i | ||||
\(753\) | 3.58705e21 | 0.952302 | ||||||||
\(754\) | −2.40006e21 | − | 5.24148e20i | −0.630865 | − | 0.137775i | ||||
\(755\) | − | 5.19446e20i | − | 0.135188i | ||||||
\(756\) | −1.06521e21 | + | 2.32246e21i | −0.274486 | + | 0.598459i | ||||
\(757\) | 4.05028e21i | 1.03339i | 0.856168 | + | 0.516697i | \(0.172839\pi\) | ||||
−0.856168 | + | 0.516697i | \(0.827161\pi\) | |||||||
\(758\) | 7.24546e20 | − | 3.31767e21i | 0.183040 | − | 0.838136i | ||||
\(759\) | 3.78744e21 | 0.947399 | ||||||||
\(760\) | −4.84920e21 | − | 3.64859e21i | −1.20107 | − | 0.903697i | ||||
\(761\) | −5.55950e21 | −1.36349 | −0.681743 | − | 0.731592i | \(-0.738778\pi\) | ||||
−0.681743 | + | 0.731592i | \(0.738778\pi\) | |||||||
\(762\) | 1.06626e21 | − | 4.88238e21i | 0.258941 | − | 1.18568i | ||||
\(763\) | 8.36778e21i | 2.01222i | ||||||||
\(764\) | 5.47629e21 | + | 2.51173e21i | 1.30403 | + | 0.598098i | ||||
\(765\) | 1.72933e21i | 0.407771i | ||||||||
\(766\) | −1.77584e21 | − | 3.87824e20i | −0.414655 | − | 0.0905564i | ||||
\(767\) | −5.14700e21 | −1.19011 | ||||||||
\(768\) | −5.58718e21 | − | 8.40503e20i | −1.27933 | − | 0.192455i | ||||
\(769\) | 7.86521e21 | 1.78346 | 0.891729 | − | 0.452570i | \(-0.149493\pi\) | ||||
0.891729 | + | 0.452570i | \(0.149493\pi\) | |||||||
\(770\) | 8.58430e21 | + | 1.87472e21i | 1.92763 | + | 0.420975i | ||||
\(771\) | 3.63536e21i | 0.808426i | ||||||||
\(772\) | 2.33913e21 | + | 1.07285e21i | 0.515138 | + | 0.236271i | ||||
\(773\) | − | 1.26435e21i | − | 0.275753i | −0.990449 | − | 0.137876i | \(-0.955972\pi\) | ||
0.990449 | − | 0.137876i | \(-0.0440277\pi\) | |||||||
\(774\) | 5.09625e20 | − | 2.33356e21i | 0.110076 | − | 0.504036i | ||||
\(775\) | −2.40373e19 | −0.00514188 | ||||||||
\(776\) | −2.09483e21 | − | 1.57617e21i | −0.443798 | − | 0.333918i | ||||
\(777\) | −5.34929e21 | −1.12238 | ||||||||
\(778\) | −2.03287e21 | + | 9.30846e21i | −0.422438 | + | 1.93433i | ||||
\(779\) | − | 9.41357e21i | − | 1.93742i | ||||||
\(780\) | 2.10172e21 | − | 4.58237e21i | 0.428416 | − | 0.934072i | ||||
\(781\) | − | 7.68597e21i | − | 1.55173i | ||||||
\(782\) | −1.71193e21 | − | 3.73868e20i | −0.342322 | − | 0.0747596i | ||||
\(783\) | 1.72850e21 | 0.342339 | ||||||||
\(784\) | 4.76585e21 | + | 5.53642e21i | 0.934910 | + | 1.08607i | ||||
\(785\) | −7.84696e21 | −1.52468 | ||||||||
\(786\) | −2.45266e21 | − | 5.35635e20i | −0.472028 | − | 0.103086i | ||||
\(787\) | − | 2.89214e21i | − | 0.551327i | −0.961254 | − | 0.275663i | \(-0.911102\pi\) | ||
0.961254 | − | 0.275663i | \(-0.0888975\pi\) | |||||||
\(788\) | 9.96353e20 | − | 2.17234e21i | 0.188134 | − | 0.410186i | ||||
\(789\) | 8.64680e20i | 0.161725i | ||||||||
\(790\) | −8.66018e20 | + | 3.96547e21i | −0.160444 | + | 0.734669i | ||||
\(791\) | −3.11525e21 | −0.571701 | ||||||||
\(792\) | −2.82524e21 | + | 3.75492e21i | −0.513589 | + | 0.682592i | ||||
\(793\) | 3.88022e21 | 0.698727 | ||||||||
\(794\) | −1.86596e21 | + | 8.54418e21i | −0.332850 | + | 1.52411i | ||||
\(795\) | − | 1.97842e21i | − | 0.349595i | ||||||
\(796\) | −3.94020e21 | − | 1.80719e21i | −0.689716 | − | 0.316342i | ||||
\(797\) | 2.93789e21i | 0.509447i | 0.967014 | + | 0.254723i | \(0.0819844\pi\) | ||||
−0.967014 | + | 0.254723i | \(0.918016\pi\) | |||||||
\(798\) | −1.72911e22 | − | 3.77620e21i | −2.97031 | − | 0.648685i | ||||
\(799\) | −1.43478e21 | −0.244165 | ||||||||
\(800\) | −1.32217e19 | − | 2.44498e19i | −0.00222901 | − | 0.00412193i | ||||
\(801\) | −4.56623e19 | −0.00762629 | ||||||||
\(802\) | 5.30509e21 | + | 1.15858e21i | 0.877779 | + | 0.191698i | ||||
\(803\) | 1.47438e22i | 2.41681i | ||||||||
\(804\) | −1.13262e21 | − | 5.19483e20i | −0.183935 | − | 0.0843628i | ||||
\(805\) | − | 5.58634e21i | − | 0.898790i | ||||||
\(806\) | −1.16939e21 | + | 5.35462e21i | −0.186401 | + | 0.853524i | ||||
\(807\) | 1.52718e22 | 2.41179 | ||||||||
\(808\) | 2.67113e21 | − | 3.55010e21i | 0.417936 | − | 0.555463i | ||||
\(809\) | 7.69701e21 | 1.19319 | 0.596593 | − | 0.802544i | \(-0.296521\pi\) | ||||
0.596593 | + | 0.802544i | \(0.296521\pi\) | |||||||
\(810\) | −1.69055e21 | + | 7.74097e21i | −0.259651 | + | 1.18893i | ||||
\(811\) | − | 2.38886e21i | − | 0.363525i | −0.983342 | − | 0.181762i | \(-0.941820\pi\) | ||
0.983342 | − | 0.181762i | \(-0.0581802\pi\) | |||||||
\(812\) | 3.49793e21 | − | 7.62651e21i | 0.527401 | − | 1.14989i | ||||
\(813\) | − | 2.32083e21i | − | 0.346708i | ||||||
\(814\) | 4.65450e21 | + | 1.01650e21i | 0.688954 | + | 0.150461i | ||||
\(815\) | 4.80474e21 | 0.704674 | ||||||||
\(816\) | 4.09325e21 | − | 3.52354e21i | 0.594828 | − | 0.512039i | ||||
\(817\) | −8.01231e21 | −1.15370 | ||||||||
\(818\) | −1.90584e20 | − | 4.16215e19i | −0.0271916 | − | 0.00593838i | ||||
\(819\) | − | 5.91843e21i | − | 0.836714i | ||||||
\(820\) | −3.81798e21 | + | 8.32431e21i | −0.534848 | + | 1.16612i | ||||
\(821\) | 1.33122e22i | 1.84789i | 0.382525 | + | 0.923945i | \(0.375055\pi\) | ||||
−0.382525 | + | 0.923945i | \(0.624945\pi\) | |||||||
\(822\) | 2.64055e21 | − | 1.20910e22i | 0.363209 | − | 1.66312i | ||||
\(823\) | 1.29945e22 | 1.77117 | 0.885584 | − | 0.464479i | \(-0.153759\pi\) | ||||
0.885584 | + | 0.464479i | \(0.153759\pi\) | |||||||
\(824\) | −6.99332e21 | − | 5.26185e21i | −0.944560 | − | 0.710696i | ||||
\(825\) | −5.74300e19 | −0.00768660 | ||||||||
\(826\) | 3.75071e21 | − | 1.71744e22i | 0.497466 | − | 2.27788i | ||||
\(827\) | − | 7.92255e21i | − | 1.04130i | −0.853772 | − | 0.520648i | \(-0.825691\pi\) | ||
0.853772 | − | 0.520648i | \(-0.174309\pi\) | |||||||
\(828\) | 2.71556e21 | + | 1.24551e21i | 0.353698 | + | 0.162225i | ||||
\(829\) | − | 5.85648e21i | − | 0.755924i | −0.925821 | − | 0.377962i | \(-0.876625\pi\) | ||
0.925821 | − | 0.377962i | \(-0.123375\pi\) | |||||||
\(830\) | −7.17423e21 | − | 1.56678e21i | −0.917676 | − | 0.200411i | ||||
\(831\) | −2.03168e21 | −0.257542 | ||||||||
\(832\) | −6.08975e21 | + | 1.75584e21i | −0.765023 | + | 0.220576i | ||||
\(833\) | −6.98305e21 | −0.869376 | ||||||||
\(834\) | −1.17947e22 | − | 2.57585e21i | −1.45527 | − | 0.317816i | ||||
\(835\) | 5.06105e20i | 0.0618860i | ||||||||
\(836\) | 1.43277e22 | + | 6.57147e21i | 1.73632 | + | 0.796371i | ||||
\(837\) | − | 3.85635e21i | − | 0.463164i | ||||||
\(838\) | −2.05785e21 | + | 9.42284e21i | −0.244954 | + | 1.12163i | ||||
\(839\) | 8.12948e21 | 0.959065 | 0.479532 | − | 0.877524i | \(-0.340806\pi\) | ||||
0.479532 | + | 0.877524i | \(0.340806\pi\) | |||||||
\(840\) | 1.37588e22 | + | 1.03522e22i | 1.60874 | + | 1.21043i | ||||
\(841\) | 2.95312e21 | 0.342225 | ||||||||
\(842\) | 1.98529e21 | − | 9.09059e21i | 0.228026 | − | 1.04412i | ||||
\(843\) | − | 5.78406e21i | − | 0.658454i | ||||||
\(844\) | −1.84562e21 | + | 4.02399e21i | −0.208245 | + | 0.454034i | ||||
\(845\) | 3.26579e21i | 0.365227i | ||||||||
\(846\) | 2.38992e21 | + | 5.21933e20i | 0.264914 | + | 0.0578545i | ||||
\(847\) | −8.62594e21 | −0.947721 | ||||||||
\(848\) | −1.88500e21 | + | 1.62264e21i | −0.205278 | + | 0.176707i | ||||
\(849\) | 3.99890e21 | 0.431651 | ||||||||
\(850\) | 2.59584e19 | + | 5.66905e18i | 0.00277739 | + | 0.000606552i | ||||
\(851\) | − | 3.02898e21i | − | 0.321236i | ||||||
\(852\) | 6.27909e21 | − | 1.36902e22i | 0.660085 | − | 1.43918i | ||||
\(853\) | − | 3.59973e21i | − | 0.375105i | −0.982255 | − | 0.187552i | \(-0.939945\pi\) | ||
0.982255 | − | 0.187552i | \(-0.0600554\pi\) | |||||||
\(854\) | −2.82759e21 | + | 1.29474e22i | −0.292067 | + | 1.33736i | ||||
\(855\) | −9.89041e21 | −1.01267 | ||||||||
\(856\) | −1.95982e21 | + | 2.60472e21i | −0.198912 | + | 0.264367i | ||||
\(857\) | −1.21594e22 | −1.22336 | −0.611681 | − | 0.791105i | \(-0.709506\pi\) | ||||
−0.611681 | + | 0.791105i | \(0.709506\pi\) | |||||||
\(858\) | −2.79392e21 | + | 1.27933e22i | −0.278651 | + | 1.27593i | ||||
\(859\) | 1.14000e22i | 1.12708i | 0.826088 | + | 0.563541i | \(0.190561\pi\) | ||||
−0.826088 | + | 0.563541i | \(0.809439\pi\) | |||||||
\(860\) | 7.08519e21 | + | 3.24966e21i | 0.694406 | + | 0.318492i | ||||
\(861\) | 2.67094e22i | 2.59502i | ||||||||
\(862\) | 6.82484e21 | + | 1.49047e21i | 0.657336 | + | 0.143556i | ||||
\(863\) | −1.71131e22 | −1.63399 | −0.816994 | − | 0.576647i | \(-0.804361\pi\) | ||||
−0.816994 | + | 0.576647i | \(0.804361\pi\) | |||||||
\(864\) | 3.92254e21 | − | 2.12118e21i | 0.371291 | − | 0.200782i | ||||
\(865\) | −4.48636e21 | −0.420992 | ||||||||
\(866\) | −6.84862e21 | − | 1.49567e21i | −0.637117 | − | 0.139140i | ||||
\(867\) | − | 8.86491e21i | − | 0.817581i | ||||||
\(868\) | −1.70150e22 | − | 7.80402e21i | −1.55573 | − | 0.713543i | ||||
\(869\) | − | 1.05430e22i | − | 0.955687i | ||||||
\(870\) | 2.48526e21 | − | 1.13799e22i | 0.223345 | − | 1.02269i | ||||
\(871\) | −1.39776e21 | −0.124536 | ||||||||
\(872\) | 8.78045e21 | − | 1.16698e22i | 0.775610 | − | 1.03083i | ||||
\(873\) | −4.27260e21 | −0.374184 | ||||||||
\(874\) | 2.13823e21 | − | 9.79091e21i | 0.185660 | − | 0.850134i | ||||
\(875\) | 1.81612e22i | 1.56345i | ||||||||
\(876\) | −1.20450e22 | + | 2.62616e22i | −1.02808 | + | 2.24151i | ||||
\(877\) | 1.57451e22i | 1.33244i | 0.745755 | + | 0.666220i | \(0.232089\pi\) | ||||
−0.745755 | + | 0.666220i | \(0.767911\pi\) | |||||||
\(878\) | 1.96360e22 | + | 4.28830e21i | 1.64757 | + | 0.359812i | ||||
\(879\) | 1.35635e21 | 0.112838 | ||||||||
\(880\) | −1.00046e22 | − | 1.16222e22i | −0.825235 | − | 0.958664i | ||||
\(881\) | −6.09608e21 | −0.498576 | −0.249288 | − | 0.968429i | \(-0.580197\pi\) | ||||
−0.249288 | + | 0.968429i | \(0.580197\pi\) | |||||||
\(882\) | 1.16317e22 | + | 2.54024e21i | 0.943254 | + | 0.205997i | ||||
\(883\) | 9.32569e21i | 0.749853i | 0.927055 | + | 0.374926i | \(0.122332\pi\) | ||||
−0.927055 | + | 0.374926i | \(0.877668\pi\) | |||||||
\(884\) | 2.52571e21 | − | 5.50678e21i | 0.201369 | − | 0.439042i | ||||
\(885\) | − | 2.44046e22i | − | 1.92929i | ||||||
\(886\) | −1.83720e21 | + | 8.41248e21i | −0.144014 | + | 0.659434i | ||||
\(887\) | 5.68335e21 | 0.441751 | 0.220875 | − | 0.975302i | \(-0.429109\pi\) | ||||
0.220875 | + | 0.975302i | \(0.429109\pi\) | |||||||
\(888\) | 7.46016e21 | + | 5.61310e21i | 0.574978 | + | 0.432619i | ||||
\(889\) | 1.91462e22 | 1.46325 | ||||||||
\(890\) | 3.17941e19 | − | 1.45584e20i | 0.00240947 | − | 0.0110329i | ||||
\(891\) | − | 2.05809e22i | − | 1.54661i | ||||||
\(892\) | −1.84718e22 | − | 8.47218e21i | −1.37649 | − | 0.631333i | ||||
\(893\) | − | 8.20583e21i | − | 0.606368i | ||||||
\(894\) | 1.86051e20 | + | 4.06315e19i | 0.0136333 | + | 0.00297736i | ||||
\(895\) | −1.45978e22 | −1.06075 | ||||||||
\(896\) | −1.42113e21 | − | 2.15997e22i | −0.102405 | − | 1.55646i | ||||
\(897\) | 8.32539e21 | 0.594924 | ||||||||
\(898\) | −5.10142e21 | − | 1.11410e21i | −0.361509 | − | 0.0789498i | ||||
\(899\) | 1.26635e22i | 0.889931i | ||||||||
\(900\) | −4.11768e19 | − | 1.88859e19i | −0.00286968 | − | 0.00131619i | ||||
\(901\) | − | 2.37754e21i | − | 0.164320i | ||||||
\(902\) | 5.07543e21 | − | 2.32402e22i | 0.347876 | − | 1.59291i | ||||
\(903\) | 2.27335e22 | 1.54529 | ||||||||
\(904\) | 4.34455e21 | + | 3.26888e21i | 0.292874 | + | 0.220362i | ||||
\(905\) | 6.27751e20 | 0.0419684 | ||||||||
\(906\) | −5.64128e20 | + | 2.58312e21i | −0.0374038 | + | 0.171271i | ||||
\(907\) | 1.47040e22i | 0.966897i | 0.875373 | + | 0.483449i | \(0.160616\pi\) | ||||
−0.875373 | + | 0.483449i | \(0.839384\pi\) | |||||||
\(908\) | 3.18961e21 | − | 6.95427e21i | 0.208014 | − | 0.453532i | ||||
\(909\) | − | 7.24075e21i | − | 0.468333i | ||||||
\(910\) | 1.88696e22 | + | 4.12093e21i | 1.21047 | + | 0.264353i | ||||
\(911\) | −2.92800e21 | −0.186287 | −0.0931437 | − | 0.995653i | \(-0.529692\pi\) | ||||
−0.0931437 | + | 0.995653i | \(0.529692\pi\) | |||||||
\(912\) | 2.01519e22 | + | 2.34102e22i | 1.27161 | + | 1.47722i | ||||
\(913\) | 1.90741e22 | 1.19375 | ||||||||
\(914\) | 1.21007e22 | + | 2.64268e21i | 0.751130 | + | 0.164039i | ||||
\(915\) | 1.83981e22i | 1.13270i | ||||||||
\(916\) | −7.46693e21 | + | 1.62801e22i | −0.455959 | + | 0.994123i | ||||
\(917\) | − | 9.61805e21i | − | 0.582528i | ||||||
\(918\) | −9.09498e20 | + | 4.16456e21i | −0.0546363 | + | 0.250178i | ||||
\(919\) | −2.37414e22 | −1.41462 | −0.707309 | − | 0.706904i | \(-0.750091\pi\) | ||||
−0.707309 | + | 0.706904i | \(0.750091\pi\) | |||||||
\(920\) | −5.86184e21 | + | 7.79075e21i | −0.346438 | + | 0.460438i | ||||
\(921\) | 5.74935e21 | 0.337032 | ||||||||
\(922\) | −5.31464e21 | + | 2.43356e22i | −0.309024 | + | 1.41501i | ||||
\(923\) | − | 1.68950e22i | − | 0.974416i | ||||||
\(924\) | −4.06524e22 | − | 1.86454e22i | −2.32566 | − | 1.06668i | ||||
\(925\) | 4.59291e19i | 0.00260630i | ||||||||
\(926\) | −2.52579e22 | − | 5.51606e21i | −1.42172 | − | 0.310490i | ||||
\(927\) | −1.42635e22 | −0.796396 | ||||||||
\(928\) | −1.28809e22 | + | 6.96555e21i | −0.713404 | + | 0.385785i | ||||
\(929\) | 2.40850e22 | 1.32321 | 0.661606 | − | 0.749852i | \(-0.269875\pi\) | ||||
0.661606 | + | 0.749852i | \(0.269875\pi\) | |||||||
\(930\) | −2.53890e22 | − | 5.54470e21i | −1.38364 | − | 0.302173i | ||||
\(931\) | − | 3.99377e22i | − | 2.15904i | ||||||
\(932\) | 2.43646e22 | + | 1.11749e22i | 1.30659 | + | 0.599273i | ||||
\(933\) | 4.96275e21i | 0.264004i | ||||||||
\(934\) | 4.80266e21 | − | 2.19912e22i | 0.253443 | − | 1.16051i | ||||
\(935\) | 1.46589e22 | 0.767389 | ||||||||
\(936\) | −6.21031e21 | + | 8.25389e21i | −0.322511 | + | 0.428637i | ||||
\(937\) | 1.45880e22 | 0.751535 | 0.375768 | − | 0.926714i | \(-0.377379\pi\) | ||||
0.375768 | + | 0.926714i | \(0.377379\pi\) | |||||||
\(938\) | 1.01857e21 | − | 4.66401e21i | 0.0520559 | − | 0.238363i | ||||
\(939\) | − | 1.06404e22i | − | 0.539469i | ||||||
\(940\) | −3.32814e21 | + | 7.25632e21i | −0.167395 | + | 0.364970i | ||||
\(941\) | − | 2.69089e21i | − | 0.134268i | −0.997744 | − | 0.0671342i | \(-0.978614\pi\) | ||
0.997744 | − | 0.0671342i | \(-0.0213856\pi\) | |||||||
\(942\) | 3.90217e22 | + | 8.52195e21i | 1.93163 | + | 0.421849i | ||||
\(943\) | −1.51239e22 | −0.742721 | ||||||||
\(944\) | −2.32522e22 | + | 2.00159e22i | −1.13285 | + | 0.975179i | ||||
\(945\) | −1.35897e22 | −0.656859 | ||||||||
\(946\) | −1.97808e22 | − | 4.31993e21i | −0.948551 | − | 0.207154i | ||||
\(947\) | − | 2.17487e22i | − | 1.03469i | −0.855778 | − | 0.517344i | \(-0.826921\pi\) | ||
0.855778 | − | 0.517344i | \(-0.173079\pi\) | |||||||
\(948\) | 8.61315e21 | − | 1.87792e22i | 0.406536 | − | 0.886367i | ||||
\(949\) | 3.24091e22i | 1.51765i | ||||||||
\(950\) | −3.24226e19 | + | 1.48462e20i | −0.00150633 | + | 0.00689745i | ||||
\(951\) | 1.66421e22 | 0.767106 | ||||||||
\(952\) | 1.65344e22 | + | 1.24406e22i | 0.756156 | + | 0.568939i | ||||
\(953\) | −2.99084e22 | −1.35705 | −0.678527 | − | 0.734576i | \(-0.737381\pi\) | ||||
−0.678527 | + | 0.734576i | \(0.737381\pi\) | |||||||
\(954\) | −8.64882e20 | + | 3.96027e21i | −0.0389354 | + | 0.178284i | ||||
\(955\) | 3.20442e22i | 1.43128i | ||||||||
\(956\) | −3.34167e21 | − | 1.53267e21i | −0.148091 | − | 0.0679228i | ||||
\(957\) | 3.02558e22i | 1.33036i | ||||||||
\(958\) | 4.58359e21 | + | 1.00101e21i | 0.199970 | + | 0.0436713i | ||||
\(959\) | 4.74147e22 | 2.05245 | ||||||||
\(960\) | −8.32533e21 | − | 2.88746e22i | −0.357575 | − | 1.24017i | ||||
\(961\) | 4.78749e21 | 0.204024 | ||||||||
\(962\) | 1.02313e22 | + | 2.23442e21i | 0.432632 | + | 0.0944824i | ||||
\(963\) | 5.31257e21i | 0.222899i | ||||||||
\(964\) | −1.45518e22 | − | 6.67426e21i | −0.605814 | − | 0.277860i | ||||
\(965\) | 1.36873e22i | 0.565408i | ||||||||
\(966\) | −6.06687e21 | + | 2.77800e22i | −0.248677 | + | 1.13869i | ||||
\(967\) | −3.74766e22 | −1.52427 | −0.762134 | − | 0.647420i | \(-0.775848\pi\) | ||||
−0.762134 | + | 0.647420i | \(0.775848\pi\) | |||||||
\(968\) | 1.20298e22 | + | 9.05134e21i | 0.485505 | + | 0.365298i | ||||
\(969\) | −2.95271e22 | −1.18248 | ||||||||
\(970\) | 2.97496e21 | − | 1.36223e22i | 0.118221 | − | 0.541329i | ||||
\(971\) | 2.48699e22i | 0.980687i | 0.871529 | + | 0.490344i | \(0.163129\pi\) | ||||
−0.871529 | + | 0.490344i | \(0.836871\pi\) | |||||||
\(972\) | 1.23165e22 | − | 2.68535e22i | 0.481936 | − | 1.05076i | ||||
\(973\) | − | 4.62529e22i | − | 1.79594i | ||||||
\(974\) | −3.98981e22 | − | 8.71334e21i | −1.53731 | − | 0.335732i | ||||
\(975\) | −1.26240e20 | −0.00482684 | ||||||||
\(976\) | 1.75293e22 | − | 1.50896e22i | 0.665107 | − | 0.572536i | ||||
\(977\) | 1.45139e22 | 0.546481 | 0.273240 | − | 0.961946i | \(-0.411905\pi\) | ||||
0.273240 | + | 0.961946i | \(0.411905\pi\) | |||||||
\(978\) | −2.38933e22 | − | 5.21804e21i | −0.892758 | − | 0.194969i | ||||
\(979\) | 3.87064e20i | 0.0143520i | ||||||||
\(980\) | −1.61980e22 | + | 3.53164e22i | −0.596028 | + | 1.29951i | ||||
\(981\) | − | 2.38016e22i | − | 0.869137i | ||||||
\(982\) | 3.25133e21 | − | 1.48877e22i | 0.117822 | − | 0.539501i | ||||
\(983\) | 3.45371e21 | 0.124204 | 0.0621018 | − | 0.998070i | \(-0.480220\pi\) | ||||
0.0621018 | + | 0.998070i | \(0.480220\pi\) | |||||||
\(984\) | 2.80266e22 | − | 3.72491e22i | 1.00025 | − | 1.32939i | ||||
\(985\) | 1.27113e22 | 0.450214 | ||||||||
\(986\) | 2.98662e21 | − | 1.36756e22i | 0.104979 | − | 0.480696i | ||||
\(987\) | 2.32826e22i | 0.812181i | ||||||||
\(988\) | 3.14945e22 | + | 1.44451e22i | 1.09033 | + | 0.500085i | ||||
\(989\) | 1.28726e22i | 0.442277i | ||||||||
\(990\) | −2.44175e22 | − | 5.33252e21i | −0.832601 | − | 0.181831i | ||||
\(991\) | 3.77091e21 | 0.127613 | 0.0638064 | − | 0.997962i | \(-0.479676\pi\) | ||||
0.0638064 | + | 0.997962i | \(0.479676\pi\) | |||||||
\(992\) | 1.55404e22 | + | 2.87377e22i | 0.521945 | + | 0.965193i | ||||
\(993\) | −4.85894e22 | −1.61965 | ||||||||
\(994\) | 5.63747e22 | + | 1.23117e22i | 1.86503 | + | 0.407304i | ||||
\(995\) | − | 2.30559e22i | − | 0.757022i | ||||||
\(996\) | 3.39748e22 | + | 1.55827e22i | 1.10716 | + | 0.507805i | ||||
\(997\) | − | 3.32273e22i | − | 1.07469i | −0.843364 | − | 0.537343i | \(-0.819428\pi\) | ||
0.843364 | − | 0.537343i | \(-0.180572\pi\) | |||||||
\(998\) | −1.28322e22 | + | 5.87580e22i | −0.411927 | + | 1.88620i | ||||
\(999\) | −7.36851e21 | −0.234768 |
(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 | 8.16.b.a.5.1 | ✓ | 14 | |
3.2 | odd | 2 | 72.16.d.b.37.14 | 14 | |||
4.3 | odd | 2 | 32.16.b.a.17.3 | 14 | |||
8.3 | odd | 2 | 32.16.b.a.17.12 | 14 | |||
8.5 | even | 2 | inner | 8.16.b.a.5.2 | yes | 14 | |
24.5 | odd | 2 | 72.16.d.b.37.13 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.16.b.a.5.1 | ✓ | 14 | 1.1 | even | 1 | trivial | |
8.16.b.a.5.2 | yes | 14 | 8.5 | even | 2 | inner | |
32.16.b.a.17.3 | 14 | 4.3 | odd | 2 | |||
32.16.b.a.17.12 | 14 | 8.3 | odd | 2 | |||
72.16.d.b.37.13 | 14 | 24.5 | odd | 2 | |||
72.16.d.b.37.14 | 14 | 3.2 | odd | 2 |