Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,16,Mod(47,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("48.47");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (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: | \(68.4928824480\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 8885809 x^{18} - 79971996 x^{17} + 21106062365235 x^{16} - 168846686224596 x^{15} + \cdots + 85\!\cdots\!61 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{194}\cdot 3^{63}\cdot 5^{6}\cdot 7^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(0.500000 - 67.7098i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.16.c.d.47.1 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3773.75 | + | 328.241i | −0.996239 | + | 0.0866530i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 91619.9i | 0.524463i | 0.965005 | + | 0.262232i | \(0.0844584\pi\) | ||||
−0.965005 | + | 0.262232i | \(0.915542\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.91696e6i | 1.33873i | 0.742932 | + | 0.669367i | \(0.233435\pi\) | ||||
−0.742932 | + | 0.669367i | \(0.766565\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.41334e7 | − | 2.47740e6i | 0.984983 | − | 0.172654i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.20504e8 | −1.86448 | −0.932240 | − | 0.361841i | \(-0.882148\pi\) | ||||
−0.932240 | + | 0.361841i | \(0.882148\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.22828e8 | −0.984906 | −0.492453 | − | 0.870339i | \(-0.663900\pi\) | ||||
−0.492453 | + | 0.870339i | \(0.663900\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −3.00734e7 | − | 3.45750e8i | −0.0454463 | − | 0.522490i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.08506e9i | 1.23240i | 0.787591 | + | 0.616199i | \(0.211328\pi\) | ||||
−0.787591 | + | 0.616199i | \(0.788672\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.74224e9i | 1.73042i | 0.501408 | + | 0.865211i | \(0.332815\pi\) | ||||
−0.501408 | + | 0.865211i | \(0.667185\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −9.57464e8 | − | 1.10079e10i | −0.116005 | − | 1.33370i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.31392e10 | 0.804659 | 0.402329 | − | 0.915495i | \(-0.368201\pi\) | ||||
0.402329 | + | 0.915495i | \(0.368201\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.21234e10 | 0.724938 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.25228e10 | + | 1.39882e10i | −0.966317 | + | 0.257356i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.45712e10i | 1.01806i | 0.860748 | + | 0.509031i | \(0.169996\pi\) | ||||
−0.860748 | + | 0.509031i | \(0.830004\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.50013e11i | 1.63211i | 0.577975 | + | 0.816054i | \(0.303843\pi\) | ||||
−0.577975 | + | 0.816054i | \(0.696157\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.54753e11 | − | 3.95545e10i | 1.85747 | − | 0.161563i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.67251e11 | −0.702117 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.54788e11 | −0.960758 | −0.480379 | − | 0.877061i | \(-0.659501\pi\) | ||||
−0.480379 | + | 0.877061i | \(0.659501\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8.40896e11 | − | 7.31413e10i | 0.981201 | − | 0.0853450i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 1.24374e12i | − | 0.997357i | −0.866787 | − | 0.498679i | \(-0.833819\pi\) | ||
0.866787 | − | 0.498679i | \(-0.166181\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.38035e11i | 0.245751i | 0.992422 | + | 0.122876i | \(0.0392116\pi\) | ||||
−0.992422 | + | 0.122876i | \(0.960788\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.26979e11 | + | 1.29490e12i | 0.0905507 | + | 0.516587i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.15000e12 | −0.619021 | −0.309510 | − | 0.950896i | \(-0.600165\pi\) | ||||
−0.309510 | + | 0.950896i | \(0.600165\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.76107e12 | −0.792210 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.84401e11 | − | 7.86847e12i | −0.106791 | − | 1.22776i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.56397e12i | 0.299808i | 0.988701 | + | 0.149904i | \(0.0478965\pi\) | ||||
−0.988701 | + | 0.149904i | \(0.952103\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.10406e13i | − | 0.977851i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.21308e12 | − | 2.54435e13i | −0.149946 | − | 1.72391i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.44400e12 | −0.127853 | −0.0639264 | − | 0.997955i | \(-0.520362\pi\) | ||||
−0.0639264 | + | 0.997955i | \(0.520362\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.11888e13 | 0.863241 | 0.431620 | − | 0.902055i | \(-0.357942\pi\) | ||||
0.431620 | + | 0.902055i | \(0.357942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.22646e12 | + | 4.12266e13i | 0.231138 | + | 1.31863i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.04155e13i | − | 0.516547i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.84632e12i | 0.117848i | 0.998262 | + | 0.0589239i | \(0.0187669\pi\) | ||||
−0.998262 | + | 0.0589239i | \(0.981233\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.95842e13 | + | 4.31284e12i | −0.801632 | + | 0.0697261i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.30114e14 | −1.69780 | −0.848898 | − | 0.528556i | \(-0.822734\pi\) | ||||
−0.848898 | + | 0.528556i | \(0.822734\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.46179e13 | 0.896480 | 0.448240 | − | 0.893913i | \(-0.352051\pi\) | ||||
0.448240 | + | 0.893913i | \(0.352051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.34880e13 | + | 7.26180e12i | −0.722212 | + | 0.0628181i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.51506e14i | − | 2.49604i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.42970e14i | 0.837608i | 0.908077 | + | 0.418804i | \(0.137551\pi\) | ||||
−0.908077 | + | 0.418804i | \(0.862449\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.93616e14 | − | 7.00282e13i | 0.940381 | − | 0.340122i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.01259e13 | −0.0814083 | −0.0407042 | − | 0.999171i | \(-0.512960\pi\) | ||||
−0.0407042 | + | 0.999171i | \(0.512960\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.91033e14 | −0.646347 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.10421e13 | − | 3.56888e14i | −0.0882180 | − | 1.01423i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 4.59438e14i | − | 1.10104i | −0.834823 | − | 0.550519i | \(-0.814430\pi\) | ||
0.834823 | − | 0.550519i | \(-0.185570\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 6.49979e14i | − | 1.31853i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −8.20644e13 | − | 9.43484e14i | −0.141427 | − | 1.62597i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −6.17723e14 | −0.907542 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.20584e14 | −0.654189 | −0.327094 | − | 0.944992i | \(-0.606070\pi\) | ||||
−0.327094 | + | 0.944992i | \(0.606070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.70314e15 | + | 2.98537e14i | −1.83648 | + | 0.321910i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1.36026e15i | − | 1.26244i | −0.775603 | − | 0.631221i | \(-0.782554\pi\) | ||
0.775603 | − | 0.631221i | \(-0.217446\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.92884e14i | 0.394880i | 0.980315 | + | 0.197440i | \(0.0632628\pi\) | ||||
−0.980315 | + | 0.197440i | \(0.936737\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.00854e15 | − | 8.77228e13i | 0.699476 | − | 0.0608405i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.86968e14 | 0.112561 | 0.0562805 | − | 0.998415i | \(-0.482076\pi\) | ||||
0.0562805 | + | 0.998415i | \(0.482076\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.56133e14 | 0.134204 | 0.0671022 | − | 0.997746i | \(-0.478625\pi\) | ||||
0.0671022 | + | 0.997746i | \(0.478625\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.09363e15 | − | 1.82104e14i | 0.957144 | − | 0.0832525i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 3.67406e15i | − | 1.46912i | −0.678542 | − | 0.734562i | \(-0.737388\pi\) | ||
0.678542 | − | 0.734562i | \(-0.262612\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.20382e15i | 0.422014i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −3.14932e15 | + | 5.52033e14i | −0.970115 | + | 0.170048i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.08201e15 | −1.64985 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.03441e16 | 2.47628 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.08247e14 | + | 4.69356e15i | 0.0864240 | + | 0.993606i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.82296e15i | 0.904667i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.37612e15i | − | 0.395677i | −0.980235 | − | 0.197839i | \(-0.936608\pi\) | ||
0.980235 | − | 0.197839i | \(-0.0633922\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.43781e14 | − | 1.65303e15i | −0.0212951 | − | 0.244827i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.37388e15 | 0.709175 | 0.354588 | − | 0.935023i | \(-0.384621\pi\) | ||||
0.354588 | + | 0.935023i | \(0.384621\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.96668e16 | −2.31658 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.28160e15 | − | 4.81213e15i | −0.134974 | − | 0.506797i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.58771e16i | 1.49750i | 0.662854 | + | 0.748749i | \(0.269345\pi\) | ||||
−0.662854 | + | 0.748749i | \(0.730655\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.08203e16i | − | 0.915439i | −0.889097 | − | 0.457720i | \(-0.848666\pi\) | ||
0.889097 | − | 0.457720i | \(-0.151334\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.11357e15 | − | 7.05719e14i | 0.616692 | − | 0.0536400i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.68517e16 | 1.83634 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.66461e15 | −0.533936 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.41933e16 | − | 1.23454e15i | 0.789231 | − | 0.0686474i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.13166e16i | 0.568614i | 0.958733 | + | 0.284307i | \(0.0917635\pi\) | ||||
−0.958733 | + | 0.284307i | \(0.908236\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71632e16i | 0.780316i | 0.920748 | + | 0.390158i | \(0.127580\pi\) | ||||
−0.920748 | + | 0.390158i | \(0.872420\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 5.16551e15 | + | 2.94690e16i | 0.212778 | + | 1.21389i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.29061e16 | −0.855981 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.00953e16 | 0.342668 | 0.171334 | − | 0.985213i | \(-0.445192\pi\) | ||||
0.171334 | + | 0.985213i | \(0.445192\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.41600e14 | − | 9.67577e15i | −0.0259793 | − | 0.298681i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.83266e16i | 1.07722i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1.83997e16i | − | 0.471416i | −0.971824 | − | 0.235708i | \(-0.924259\pi\) | ||
0.971824 | − | 0.235708i | \(-0.0757409\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.62398e15 | + | 4.16644e16i | 0.0847337 | + | 0.974173i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.03318e16 | 1.07515 | 0.537575 | − | 0.843216i | \(-0.319341\pi\) | ||||
0.537575 | + | 0.843216i | \(0.319341\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.53358e15 | −0.0299610 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.67032e16 | + | 9.52909e16i | 0.298764 | + | 1.70444i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1.75166e15i | − | 0.0287147i | −0.999897 | − | 0.0143574i | \(-0.995430\pi\) | ||
0.999897 | − | 0.0143574i | \(-0.00457025\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.45329e16i | 0.970500i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.22302e15 | − | 8.02220e14i | 0.127372 | − | 0.0110788i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.36164e16 | 0.680613 | 0.340306 | − | 0.940315i | \(-0.389469\pi\) | ||||
0.340306 | + | 0.940315i | \(0.389469\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.26268e16 | 0.147470 | 0.0737351 | − | 0.997278i | \(-0.476508\pi\) | ||||
0.0737351 | + | 0.997278i | \(0.476508\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.99611e16 | + | 6.95502e15i | −0.859994 | + | 0.0748024i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.08296e16i | − | 0.503882i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 2.51258e17i | − | 2.29778i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.08031e16 | − | 1.53207e17i | −0.344532 | − | 1.29364i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.21144e16 | −0.640721 | −0.320361 | − | 0.947296i | \(-0.603804\pi\) | ||||
−0.320361 | + | 0.947296i | \(0.603804\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.08429e16 | −0.655558 | −0.327779 | − | 0.944754i | \(-0.606300\pi\) | ||||
−0.327779 | + | 0.944754i | \(0.606300\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.70120e15 | + | 7.70429e16i | 0.0447603 | + | 0.514604i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.84764e17i | 1.14320i | 0.820533 | + | 0.571599i | \(0.193677\pi\) | ||||
−0.820533 | + | 0.571599i | \(0.806323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.94422e17i | − | 1.11519i | −0.830114 | − | 0.557594i | \(-0.811725\pi\) | ||
0.830114 | − | 0.557594i | \(-0.188275\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.91900e15 | − | 2.20625e16i | −0.0102119 | − | 0.117405i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.75860e17 | −1.36291 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.13951e17 | 0.523077 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.85703e17 | − | 3.25511e16i | 0.792575 | − | 0.138928i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 8.12469e17i | − | 3.22634i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.44613e17i | 0.904401i | 0.891916 | + | 0.452201i | \(0.149361\pi\) | ||||
−0.891916 | + | 0.452201i | \(0.850639\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.91017e17 | − | 4.27087e16i | 1.69141 | − | 0.147119i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.01328e16 | −0.128887 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.29275e17 | −2.18496 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.19326e17 | + | 2.77751e16i | −0.893108 | + | 0.0776827i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.64609e17i | − | 1.21379i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.26598e17i | − | 0.797494i | −0.917061 | − | 0.398747i | \(-0.869445\pi\) | ||
0.917061 | − | 0.398747i | \(-0.130555\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.12679e17 | − | 5.48084e16i | 0.714052 | − | 0.125164i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.27486e17 | −0.699840 | −0.349920 | − | 0.936780i | \(-0.613791\pi\) | ||||
−0.349920 | + | 0.936780i | \(0.613791\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.03248e17 | 0.206593 | 0.103296 | − | 0.994651i | \(-0.467061\pi\) | ||||
0.103296 | + | 0.994651i | \(0.467061\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.15379e17 | + | 1.32649e18i | 0.216290 | + | 2.48665i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 9.99582e17i | 1.75650i | 0.478199 | + | 0.878251i | \(0.341290\pi\) | ||||
−0.478199 | + | 0.878251i | \(0.658710\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1.96983e17i | − | 0.324654i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.69285e16 | − | 5.39532e17i | −0.0725812 | − | 0.834458i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.83454e17 | −0.411622 | −0.205811 | − | 0.978592i | \(-0.565983\pi\) | ||||
−0.205811 | + | 0.978592i | \(0.565983\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.71721e17 | 1.05277 | 0.526384 | − | 0.850247i | \(-0.323547\pi\) | ||||
0.526384 | + | 0.850247i | \(0.323547\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −7.07672e17 | + | 3.27821e17i | −0.907371 | + | 0.420330i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.44589e17i | − | 0.415485i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 1.50236e18i | − | 1.70430i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.59499e16 | − | 6.60613e15i | 0.0811021 | − | 0.00705427i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.43019e18 | 1.43827 | 0.719137 | − | 0.694868i | \(-0.244537\pi\) | ||||
0.719137 | + | 0.694868i | \(0.244537\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.58334e18 | −1.50027 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.20909e17 | − | 6.27048e16i | 0.643916 | − | 0.0560079i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 2.19887e17i | − | 0.185226i | −0.995702 | − | 0.0926128i | \(-0.970478\pi\) | ||
0.995702 | − | 0.0926128i | \(-0.0295219\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1.61829e18i | − | 1.28620i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.34290e17 | + | 1.33661e18i | 0.175772 | + | 1.00277i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.77718e18 | 1.25911 | 0.629553 | − | 0.776957i | \(-0.283238\pi\) | ||||
0.629553 | + | 0.776957i | \(0.283238\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.34911e17 | −0.157238 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.50807e17 | + | 1.73380e18i | 0.0954082 | + | 1.09690i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.21535e18i | 1.32526i | 0.748948 | + | 0.662629i | \(0.230559\pi\) | ||||
−0.748948 | + | 0.662629i | \(0.769441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 8.40929e17i | − | 0.475871i | −0.971281 | − | 0.237936i | \(-0.923529\pi\) | ||
0.971281 | − | 0.237936i | \(-0.0764707\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.13350e17 | + | 2.45286e18i | 0.114254 | + | 1.31357i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.66596e18 | −1.35163 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.37475e18 | −1.14030 | −0.570150 | − | 0.821541i | \(-0.693115\pi\) | ||||
−0.570150 | + | 0.821541i | \(0.693115\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.19380e17 | + | 3.53353e18i | 0.281790 | + | 1.60760i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.29636e17i | 0.357759i | 0.983871 | + | 0.178879i | \(0.0572472\pi\) | ||||
−0.983871 | + | 0.178879i | \(0.942753\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.44669e18i | − | 1.00042i | −0.865905 | − | 0.500209i | \(-0.833257\pi\) | ||
0.865905 | − | 0.500209i | \(-0.166743\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.33113e18 | − | 2.02762e17i | 0.904129 | − | 0.0786412i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.62794e18 | 1.33520 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.48503e18 | −0.518803 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.96455e18 | − | 1.70877e17i | 0.651728 | − | 0.0566874i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.91289e18i | 1.23308i | 0.787324 | + | 0.616539i | \(0.211466\pi\) | ||||
−0.787324 | + | 0.616539i | \(0.788534\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.23919e17i | − | 0.0670541i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 6.32922e18 | − | 1.68564e18i | 1.80168 | − | 0.479836i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.92779e18 | −0.792513 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.27773e18 | −0.328996 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.46493e17 | + | 5.13328e18i | 0.109394 | + | 1.25769i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.94131e18i | 0.452738i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.11807e18i | 0.914441i | 0.889353 | + | 0.457220i | \(0.151155\pi\) | ||||
−0.889353 | + | 0.457220i | \(0.848845\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.61785e17 | − | 1.86002e18i | −0.0342175 | − | 0.393395i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.36299e18 | 1.68523 | 0.842614 | − | 0.538518i | \(-0.181016\pi\) | ||||
0.842614 | + | 0.538518i | \(0.181016\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.51721e17 | −0.0675485 | −0.0337743 | − | 0.999429i | \(-0.510753\pi\) | ||||
−0.0337743 | + | 0.999429i | \(0.510753\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.77718e18 | + | 6.62088e17i | −0.691573 | + | 0.121223i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.22031e18i | − | 0.213072i | −0.994309 | − | 0.106536i | \(-0.966024\pi\) | ||
0.994309 | − | 0.106536i | \(-0.0339760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.13962e19i | − | 1.89815i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.05568e17 | + | 6.13704e16i | −0.112138 | + | 0.00975374i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.40579e19 | −2.13257 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.92970e18 | −0.713996 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.66581e17 | + | 8.40733e16i | −0.133700 | + | 0.0116292i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 6.27146e18i | − | 0.828705i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 1.43269e19i | − | 1.80901i | −0.426461 | − | 0.904506i | \(-0.640240\pi\) | ||
0.426461 | − | 0.904506i | \(-0.359760\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.84105e18 | + | 1.37443e18i | −0.946330 | + | 0.165879i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.35639e17 | −0.0618068 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.54302e17 | 0.105308 | 0.0526540 | − | 0.998613i | \(-0.483232\pi\) | ||||
0.0526540 | + | 0.998613i | \(0.483232\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.20598e18 | + | 1.38650e19i | 0.127304 | + | 1.46360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 3.01276e19i | − | 3.04303i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.87756e18i | 0.278175i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.95142e17 | − | 4.54290e18i | −0.0365688 | − | 0.420426i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.14589e18 | −0.544645 | −0.272322 | − | 0.962206i | \(-0.587792\pi\) | ||||
−0.272322 | + | 0.962206i | \(0.587792\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.53448e19 | 1.30248 | 0.651238 | − | 0.758874i | \(-0.274250\pi\) | ||||
0.651238 | + | 0.758874i | \(0.274250\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.17035e19 | − | 3.11697e18i | 0.951731 | − | 0.253472i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 5.81472e18i | 0.453126i | 0.973997 | + | 0.226563i | \(0.0727489\pi\) | ||||
−0.973997 | + | 0.226563i | \(0.927251\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.19210e19i | − | 0.890432i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.29520e19 | − | 1.99637e18i | 1.64365 | − | 0.142965i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.32500e18 | 0.571710 | 0.285855 | − | 0.958273i | \(-0.407722\pi\) | ||||
0.285855 | + | 0.958273i | \(0.407722\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.02766e19 | −1.99436 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.90358e19 | + | 3.39534e18i | −2.46697 | + | 0.214577i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.75268e18i | 0.470171i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.06582e19i | 1.20253i | 0.799049 | + | 0.601265i | \(0.205337\pi\) | ||||
−0.799049 | + | 0.601265i | \(0.794663\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.08124e18 | − | 1.75783e19i | −0.172198 | − | 0.982380i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.47898e18 | −0.401364 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.76828e19 | 0.911453 | 0.455727 | − | 0.890120i | \(-0.349379\pi\) | ||||
0.455727 | + | 0.890120i | \(0.349379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.58309e18 | − | 1.82006e19i | −0.0783920 | − | 0.901264i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.10731e19i | − | 1.00269i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.53073e19i | 1.15731i | 0.815571 | + | 0.578657i | \(0.196423\pi\) | ||||
−0.815571 | + | 0.578657i | \(0.803577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.79941e17 | + | 8.96689e18i | 0.0342866 | + | 0.394189i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.30319e18 | 0.0550829 | 0.0275414 | − | 0.999621i | \(-0.491232\pi\) | ||||
0.0275414 | + | 0.999621i | \(0.491232\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.22049e19 | 1.30908 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.08519e18 | + | 6.19094e18i | 0.0424299 | + | 0.242061i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.05944e19i | 1.15085i | 0.817853 | + | 0.575427i | \(0.195164\pi\) | ||||
−0.817853 | + | 0.575427i | \(0.804836\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.73961e19i | 0.991659i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.02797e19 | + | 1.76393e18i | −0.706508 | + | 0.0614521i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.30989e19 | −0.439295 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.83722e19 | −1.88485 | −0.942426 | − | 0.334414i | \(-0.891462\pi\) | ||||
−0.942426 | + | 0.334414i | \(0.891462\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.42175e19 | − | 6.45545e18i | 2.30786 | − | 0.200738i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.14385e19i | 0.642112i | 0.947060 | + | 0.321056i | \(0.104038\pi\) | ||||
−0.947060 | + | 0.321056i | \(0.895962\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 5.57098e19i | − | 1.60747i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 6.41598e18 | + | 1.77391e19i | 0.178382 | + | 0.493195i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.68543e19 | 1.79131 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.09849e19 | −0.283709 | −0.141854 | − | 0.989888i | \(-0.545306\pi\) | ||||
−0.141854 | + | 0.989888i | \(0.545306\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.21151e18 | − | 5.99160e19i | −0.129763 | − | 1.49186i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 7.12903e18i | − | 0.171161i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 1.84393e18i | − | 0.0426957i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.55168e18 | + | 4.08332e19i | 0.0793255 | + | 0.911996i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.10414e19 | −1.53076 | −0.765378 | − | 0.643581i | \(-0.777448\pi\) | ||||
−0.765378 | + | 0.643581i | \(0.777448\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.02493e19 | 1.46058 | 0.730291 | − | 0.683136i | \(-0.239384\pi\) | ||||
0.730291 | + | 0.683136i | \(0.239384\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.03869e19 | + | 5.32641e18i | −0.609725 | + | 0.106876i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.61284e19i | 0.893412i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.18067e19i | 1.15565i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −1.01332e20 | + | 8.81384e18i | −1.82943 | + | 0.159124i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.48889e19 | 0.956985 | 0.478492 | − | 0.878092i | \(-0.341183\pi\) | ||||
0.478492 | + | 0.878092i | \(0.341183\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.36612e19 | 1.07205 | 0.536026 | − | 0.844202i | \(-0.319925\pi\) | ||||
0.536026 | + | 0.844202i | \(0.319925\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.26980e19 | − | 2.84408e18i | 0.531927 | − | 0.0462671i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.85879e19i | 1.39240i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 1.34028e18i | − | 0.0203570i | −0.999948 | − | 0.0101785i | \(-0.996760\pi\) | ||
0.999948 | − | 0.0101785i | \(-0.00323997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.31568e19 | + | 9.31766e18i | −0.780313 | + | 0.136778i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.44524e19 | 0.914558 | 0.457279 | − | 0.889323i | \(-0.348824\pi\) | ||||
0.457279 | + | 0.889323i | \(0.348824\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 4.20937e19 | 0.577454 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.71456e18 | − | 4.27058e19i | −0.0492721 | − | 0.566475i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7.19613e19i | 0.923105i | 0.887113 | + | 0.461553i | \(0.152707\pi\) | ||||
−0.887113 | + | 0.461553i | \(0.847293\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.49876e20i | 1.85955i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.63366e18 | − | 6.47695e19i | −0.0676167 | − | 0.777381i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5.95511e19 | 0.691519 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.39947e19 | −0.269615 | −0.134808 | − | 0.990872i | \(-0.543042\pi\) | ||||
−0.134808 | + | 0.990872i | \(0.543042\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.91663e19 | − | 1.09513e20i | −0.317165 | − | 1.19089i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.24275e20i | − | 1.30805i | −0.756471 | − | 0.654027i | \(-0.773078\pi\) | ||
0.756471 | − | 0.654027i | \(-0.226922\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.28962e20i | 1.31403i | 0.753879 | + | 0.657014i | \(0.228181\pi\) | ||||
−0.753879 | + | 0.657014i | \(0.771819\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.64419e19 | − | 7.51873e18i | 0.852761 | − | 0.0741733i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.07767e19 | −0.867157 | −0.433579 | − | 0.901116i | \(-0.642749\pi\) | ||||
−0.433579 | + | 0.901116i | \(0.642749\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.70534e19 | −0.157767 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.80973e19 | + | 3.31371e18i | −0.341379 | + | 0.0296932i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 5.27851e19i | − | 0.458198i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.49161e20i | 1.25445i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.35197e18 | + | 3.62377e19i | 0.0517631 | + | 0.295306i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.21775e19 | −0.648988 | −0.324494 | − | 0.945888i | \(-0.605194\pi\) | ||||
−0.324494 | + | 0.945888i | \(0.605194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.23622e20 | 0.946256 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.25804e19 | − | 1.44635e20i | −0.0933447 | − | 1.07317i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 4.76959e19i | − | 0.343098i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.84649e20i | − | 1.28789i | −0.765071 | − | 0.643946i | \(-0.777296\pi\) | ||
0.765071 | − | 0.643946i | \(-0.222704\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.03955e18 | + | 6.94360e19i | 0.0408496 | + | 0.469643i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.65994e20 | −1.08888 | −0.544442 | − | 0.838799i | \(-0.683259\pi\) | ||||
−0.544442 | + | 0.838799i | \(0.683259\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.97186e20 | −1.25466 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.73520e19 | − | 1.56041e20i | −0.168830 | − | 0.963166i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3.79536e20i | − | 2.27290i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 1.51240e20i | − | 0.878844i | −0.898281 | − | 0.439422i | \(-0.855183\pi\) | ||
0.898281 | − | 0.439422i | \(-0.144817\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.89939e20 | + | 1.65210e19i | −1.07111 | + | 0.0931649i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.04561e20 | 1.11960 | 0.559800 | − | 0.828628i | \(-0.310878\pi\) | ||||
0.559800 | + | 0.828628i | \(0.310878\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.24627e20 | 0.662104 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.78735e18 | − | 5.03385e17i | 0.0298483 | − | 0.00259621i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.16643e20i | − | 0.584082i | −0.956406 | − | 0.292041i | \(-0.905666\pi\) | ||
0.956406 | − | 0.292041i | \(-0.0943344\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.46827e20i | 1.20015i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −9.43120e19 | − | 3.54121e20i | −0.445335 | − | 1.67214i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −4.51580e19 | −0.207100 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.59085e20 | 1.15415 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.74968e17 | + | 6.61033e18i | 0.00248822 | + | 0.0286067i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.40159e19i | 0.395292i | 0.980273 | + | 0.197646i | \(0.0633297\pi\) | ||||
−0.980273 | + | 0.197646i | \(0.936670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.02555e20i | 0.418980i | 0.977811 | + | 0.209490i | \(0.0671803\pi\) | ||||
−0.977811 | + | 0.209490i | \(0.932820\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.11823e19 | − | 2.43531e20i | −0.0840967 | − | 0.966850i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.21290e20 | −2.01141 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.39954e19 | −0.352524 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.45420e19 | + | 6.05475e18i | −0.125933 | + | 0.0220743i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.77140e20i | 0.982303i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.71300e19i | 0.0590341i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.02335e20 | + | 1.75991e19i | −0.678053 | + | 0.0589771i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.53225e20 | 1.47706 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.70899e20 | 1.17565 | 0.587823 | − | 0.808989i | \(-0.299985\pi\) | ||||
0.587823 | + | 0.808989i | \(0.299985\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.76504e19 | + | 4.14464e18i | −0.146916 | + | 0.0127787i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.34669e19i | 0.0703852i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.95393e19i | 0.173740i | 0.996220 | + | 0.0868698i | \(0.0276864\pi\) | ||||
−0.996220 | + | 0.0868698i | \(0.972314\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.99470e20 | − | 5.24930e19i | 0.850277 | − | 0.149042i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.37621e20 | −1.76168 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.17036e20 | −1.12134 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.66844e19 | + | 1.91818e20i | 0.0436629 | + | 0.501987i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.19190e20i | 0.303616i | 0.988410 | + | 0.151808i | \(0.0485096\pi\) | ||||
−0.988410 | + | 0.151808i | \(0.951490\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.76065e19i | − | 0.242042i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.24733e19 | + | 9.48185e20i | 0.199109 | + | 2.28914i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.55853e20 | 1.77674 | 0.888371 | − | 0.459127i | \(-0.151838\pi\) | ||||
0.888371 | + | 0.459127i | \(0.151838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.36618e20 | 0.770501 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.04269e20 | + | 5.64770e20i | 0.455334 | + | 1.25892i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.96195e20i | − | 0.425938i | −0.977059 | − | 0.212969i | \(-0.931687\pi\) | ||
0.977059 | − | 0.212969i | \(-0.0683133\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.61066e20i | − | 0.340592i | −0.985393 | − | 0.170296i | \(-0.945528\pi\) | ||
0.985393 | − | 0.170296i | \(-0.0544723\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.09879e20 | − | 2.69533e19i | 0.638311 | − | 0.0555204i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.90684e20 | 0.583328 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.00141e20 | 0.195791 | 0.0978954 | − | 0.995197i | \(-0.468789\pi\) | ||||
0.0978954 | + | 0.995197i | \(0.468789\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.42818e20 | − | 2.98184e19i | 0.653092 | − | 0.0568061i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 5.87062e19i | − | 0.108984i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 3.08969e20i | − | 0.558987i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.05773e19 | − | 2.88541e20i | −0.0891839 | − | 0.508789i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.48320e20 | 0.598677 | 0.299339 | − | 0.954147i | \(-0.403234\pi\) | ||||
0.299339 | + | 0.954147i | \(0.403234\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.68564e21 | −2.82424 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.06473e19 | − | 6.97254e20i | −0.0990616 | − | 1.13890i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.93907e20i | 1.58284i | 0.611276 | + | 0.791418i | \(0.290657\pi\) | ||||
−0.611276 | + | 0.791418i | \(0.709343\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 5.57234e20i | − | 0.865287i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.38174e19 | + | 7.33701e20i | 0.0966344 | + | 1.11099i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.71732e20 | −0.696617 | −0.348308 | − | 0.937380i | \(-0.613244\pi\) | ||||
−0.348308 | + | 0.937380i | \(0.613244\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.09217e21 | −1.57301 | −0.786503 | − | 0.617587i | \(-0.788110\pi\) | ||||
−0.786503 | + | 0.617587i | \(0.788110\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.44837e19 | + | 8.26285e19i | 0.0203469 | + | 0.116078i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 9.47721e20i | 1.29872i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.13358e20i | 0.552600i | 0.961071 | + | 0.276300i | \(0.0891084\pi\) | ||||
−0.961071 | + | 0.276300i | \(0.910892\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.04103e21 | − | 9.05486e19i | 1.35779 | − | 0.118101i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.79081e20 | 0.609677 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.63118e20 | 1.19599 | 0.597993 | − | 0.801502i | \(-0.295965\pi\) | ||||
0.597993 | + | 0.801502i | \(0.295965\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −4.30024e20 | + | 3.74035e19i | −0.521110 | + | 0.0453262i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.09668e20i | 0.839299i | 0.907686 | + | 0.419650i | \(0.137847\pi\) | ||||
−0.907686 | + | 0.419650i | \(0.862153\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 6.48141e20i | − | 0.748152i | −0.927398 | − | 0.374076i | \(-0.877960\pi\) | ||
0.927398 | − | 0.374076i | \(-0.122040\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −6.90110e20 | + | 1.83795e20i | −0.777555 | + | 0.207084i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.34016e21 | 1.47400 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.33272e20 | 0.250474 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.66686e20 | + | 3.06605e21i | 0.279572 | + | 3.21420i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.15676e21i | − | 1.18404i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1.26945e21i | − | 1.26881i | −0.773001 | − | 0.634405i | \(-0.781245\pi\) | ||
0.773001 | − | 0.634405i | \(-0.218755\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.02920e19 | − | 9.23108e20i | −0.0783690 | − | 0.900999i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.17700e20 | 0.207518 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.38071e20 | 0.780253 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.83895e21 | + | 3.22344e20i | −1.67230 | + | 0.293132i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 7.33282e20i | − | 0.651382i | −0.945476 | − | 0.325691i | \(-0.894403\pi\) | ||
0.945476 | − | 0.325691i | \(-0.105597\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.36465e21i | − | 1.18424i | −0.805850 | − | 0.592119i | \(-0.798291\pi\) | ||
0.805850 | − | 0.592119i | \(-0.201709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.51451e20 | − | 1.31732e19i | 0.128403 | − | 0.0111685i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.20674e21 | −1.82797 | −0.913987 | − | 0.405744i | \(-0.867013\pi\) | ||||
−0.913987 | + | 0.405744i | \(0.867013\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.94512e20 | 0.238379 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 2.75210e21 | − | 2.39378e20i | 2.17674 | − | 0.189333i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.50941e20i | 0.271260i | 0.990760 | + | 0.135630i | \(0.0433058\pi\) | ||||
−0.990760 | + | 0.135630i | \(0.956694\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.92355e20i | 0.371936i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.19594e21 | − | 2.09632e20i | 0.883017 | − | 0.154781i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 6.05839e19 | 0.0437237 | 0.0218618 | − | 0.999761i | \(-0.493041\pi\) | ||||
0.0218618 | + | 0.999761i | \(0.493041\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.53243e20 | −0.601952 | −0.300976 | − | 0.953632i | \(-0.597312\pi\) | ||||
−0.300976 | + | 0.953632i | \(0.597312\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.52504e20 | + | 1.75332e21i | 0.105179 | + | 1.20923i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.80187e21i | − | 1.21496i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.24259e21i | 0.819192i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.07203e20 | + | 1.23250e21i | 0.0691052 | + | 0.794494i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.55334e21 | −1.60949 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.72542e21 | −1.06361 | −0.531803 | − | 0.846868i | \(-0.678485\pi\) | ||||
−0.531803 | + | 0.846868i | \(0.678485\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.16198e21 | + | 3.09467e20i | −0.700520 | + | 0.186567i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.87672e20i | − | 0.582368i | −0.956667 | − | 0.291184i | \(-0.905951\pi\) | ||
0.956667 | − | 0.291184i | \(-0.0940492\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 1.51852e21i | − | 0.875785i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.23585e21 | − | 1.07494e20i | 0.697208 | − | 0.0606432i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.20150e21 | −1.21496 | −0.607482 | − | 0.794333i | \(-0.707820\pi\) | ||||
−0.607482 | + | 0.794333i | \(0.707820\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.45466e21 | −0.785382 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.89631e20 | + | 3.38902e19i | −0.205816 | + | 0.0179019i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 5.71324e20i | − | 0.295283i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1.24816e21i | − | 0.631228i | −0.948888 | − | 0.315614i | \(-0.897790\pi\) | ||
0.948888 | − | 0.315614i | \(-0.102210\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.70820e20 | − | 4.96798e21i | −0.430952 | − | 2.45856i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 9.91358e20 | 0.480114 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.59327e21 | 1.22914 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.28104e20 | − | 3.77217e21i | −0.152206 | − | 1.74990i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 4.24355e21i | − | 1.92683i | −0.268009 | − | 0.963416i | \(-0.586366\pi\) | ||
0.268009 | − | 0.963416i | \(-0.413634\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.74051e21i | − | 1.66252i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.46580e19 | + | 7.43365e20i | 0.0281322 | + | 0.323432i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.96782e21 | 1.69008 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.57825e21 | −1.49219 | −0.746094 | − | 0.665841i | \(-0.768073\pi\) | ||||
−0.746094 | + | 0.665841i | \(0.768073\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.54193e20 | + | 2.02065e21i | 0.144616 | + | 0.825029i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.28498e21i | 1.31329i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.46015e21i | 0.963091i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.06968e21 | − | 9.30413e19i | 0.410074 | − | 0.0356683i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.97493e20 | 0.149232 | 0.0746162 | − | 0.997212i | \(-0.476227\pi\) | ||||
0.0746162 | + | 0.997212i | \(0.476227\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.43772e21 | −0.528640 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.91228e21 | + | 2.53311e20i | −1.04881 | + | 0.0912255i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.09223e21i | 0.738032i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.33381e21i | 0.460877i | 0.973087 | + | 0.230438i | \(0.0740160\pi\) | ||||
−0.973087 | + | 0.230438i | \(0.925984\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.56297e21 | − | 1.46940e21i | 0.867535 | − | 0.497375i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.13328e20 | −0.302863 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.44650e21 | 1.44457 | 0.722285 | − | 0.691596i | \(-0.243092\pi\) | ||||
0.722285 | + | 0.691596i | \(0.243092\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.13108e20 | + | 1.30039e21i | 0.0360030 | + | 0.413922i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 7.04507e20i | − | 0.219725i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 5.39016e20i | − | 0.164728i | −0.996602 | − | 0.0823642i | \(-0.973753\pi\) | ||
0.996602 | − | 0.0823642i | \(-0.0262471\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.93136e20 | + | 5.66952e21i | 0.147683 | + | 1.69789i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.73352e21 | −0.508759 | −0.254380 | − | 0.967104i | \(-0.581871\pi\) | ||||
−0.254380 | + | 0.967104i | \(0.581871\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.03682e21 | −0.298217 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.84447e20 | + | 4.98598e19i | −0.0801858 | + | 0.0140555i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.45376e20i | 0.150689i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.43093e21i | 0.658375i | 0.944265 | + | 0.329188i | \(0.106775\pi\) | ||||
−0.944265 | + | 0.329188i | \(0.893225\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.39718e21 | + | 4.69448e20i | −1.43286 | + | 0.124631i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.57249e21 | −0.409247 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.58554e21 | 0.404538 | 0.202269 | − | 0.979330i | \(-0.435169\pi\) | ||||
0.202269 | + | 0.979330i | \(0.435169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.97511e21 | − | 5.19716e20i | 1.49463 | − | 0.130003i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.50338e21i | − | 0.613964i | −0.951715 | − | 0.306982i | \(-0.900681\pi\) | ||
0.951715 | − | 0.306982i | \(-0.0993191\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.47128e20i | 0.179664i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2.69995e21 | + | 4.73264e20i | −0.636640 | + | 0.111594i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.44591e20 | 0.125923 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.95350e21 | −0.442961 | −0.221481 | − | 0.975165i | \(-0.571089\pi\) | ||||
−0.221481 | + | 0.975165i | \(0.571089\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.21759e19 | + | 8.29798e20i | 0.0160504 | + | 0.184529i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.08728e21i | 1.76383i | 0.471410 | + | 0.881914i | \(0.343745\pi\) | ||||
−0.471410 | + | 0.881914i | \(0.656255\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.53112e21i | 1.18318i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.31189e20 | + | 6.10702e21i | 0.111453 | + | 1.28136i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.38559e21 | 1.72585 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.56793e22 | 3.16551 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.32288e21 | − | 4.96714e21i | −0.262004 | − | 0.983770i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.24935e20i | 0.179717i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.39098e21i | 0.646420i | 0.946327 | + | 0.323210i | \(0.104762\pi\) | ||||
−0.946327 | + | 0.323210i | \(0.895238\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.70662e21 | + | 5.83343e20i | −1.25437 | + | 0.109105i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.07171e22 | 1.96677 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.72145e21 | −0.850211 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.86493e20 | − | 7.71073e19i | 0.156647 | − | 0.0136252i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.65124e20i | 0.132677i | 0.997797 | + | 0.0663383i | \(0.0211317\pi\) | ||||
−0.997797 | + | 0.0663383i | \(0.978868\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 4.48288e21i | − | 0.762879i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.13821e21 | − | 6.49344e21i | −0.190099 | − | 1.08450i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.01968e22 | −1.67147 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.51148e21 | −0.564965 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.27169e20 | − | 8.36017e21i | −0.114838 | − | 1.32027i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.27093e22i | 1.97019i | 0.172018 | + | 0.985094i | \(0.444971\pi\) | ||||
−0.172018 | + | 0.985094i | \(0.555029\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.54863e21i | 0.235662i | 0.993034 | + | 0.117831i | \(0.0375942\pi\) | ||||
−0.993034 | + | 0.117831i | \(0.962406\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.76027e20 | + | 3.17345e21i | 0.0412357 | + | 0.474081i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.68578e21 | 0.247240 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.95334e21 | −0.425253 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.61026e21 | − | 9.18643e21i | −0.227649 | − | 1.29873i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.11147e21i | 0.431908i | 0.976404 | + | 0.215954i | \(0.0692862\pi\) | ||||
−0.976404 | + | 0.215954i | \(0.930714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 3.90247e21i | − | 0.531913i | −0.963985 | − | 0.265957i | \(-0.914312\pi\) | ||
0.963985 | − | 0.265957i | \(-0.0856878\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.00607e22 | − | 8.75078e20i | 1.34655 | − | 0.117123i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.97423e21 | −1.17952 | −0.589761 | − | 0.807578i | \(-0.700778\pi\) | ||||
−0.589761 | + | 0.807578i | \(0.700778\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.22258e21 | −1.06133 | −0.530664 | − | 0.847583i | \(-0.678057\pi\) | ||||
−0.530664 | + | 0.847583i | \(0.678057\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.96169e21 | − | 7.79489e20i | 1.13601 | − | 0.0988104i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 7.84204e21i | − | 0.976318i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.61140e21i | 0.563876i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.49723e21 | − | 1.31314e22i | −0.420033 | − | 1.57713i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.94628e21 | 0.701505 | 0.350753 | − | 0.936468i | \(-0.385926\pi\) | ||||
0.350753 | + | 0.936468i | \(0.385926\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.14524e20 | −0.0364488 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.72321e20 | − | 3.13084e21i | −0.0310008 | − | 0.356413i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1.40507e20i | − | 0.0157135i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.01731e22i | 3.31509i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.03105e20 | + | 9.23320e21i | 0.0866892 | + | 0.996655i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.28949e21 | −0.773082 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.86722e22 | 1.94571 | 0.972855 | − | 0.231415i | \(-0.0743355\pi\) | ||||
0.972855 | + | 0.231415i | \(0.0743355\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −8.73054e21 | + | 1.53035e21i | −0.893913 | + | 0.156691i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.20113e22i | − | 1.20847i | −0.796806 | − | 0.604235i | \(-0.793479\pi\) | ||
0.796806 | − | 0.604235i | \(-0.206521\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1.77679e21i | − | 0.175665i | −0.996135 | − | 0.0878327i | \(-0.972006\pi\) | ||
0.996135 | − | 0.0878327i | \(-0.0279941\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.36909e22 | + | 1.19084e21i | −1.33017 | + | 0.115699i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.70387e21 | 0.926540 | 0.463270 | − | 0.886217i | \(-0.346676\pi\) | ||||
0.463270 | + | 0.886217i | \(0.346676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.60487e20 | 0.0150598 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 5.60414e21 | − | 4.87449e20i | 0.516852 | − | 0.0449558i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.72285e22i | − | 1.56170i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.30272e21i | − | 0.116069i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −7.35764e21 | + | 1.28969e21i | −0.644365 | + | 0.112948i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.40684e22 | −1.21111 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.66780e22 | 1.41139 | 0.705693 | − | 0.708517i | \(-0.250636\pi\) | ||||
0.705693 | + | 0.708517i | \(0.250636\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −1.28437e21 | − | 1.47663e22i | −0.106850 | − | 1.22844i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 4.95738e21i | − | 0.405446i | −0.979236 | − | 0.202723i | \(-0.935021\pi\) | ||
0.979236 | − | 0.202723i | \(-0.0649791\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.65431e20i | 0.0213425i | 0.999943 | + | 0.0106713i | \(0.00339683\pi\) | ||||
−0.999943 | + | 0.0106713i | \(0.996603\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.34993e19 | + | 8.45013e20i | 0.00581044 | + | 0.0668019i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.55057e21 | −0.198249 | −0.0991244 | − | 0.995075i | \(-0.531604\pi\) | ||||
−0.0991244 | + | 0.995075i | \(0.531604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.93105e21 | 0.529707 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.33316e22 | + | 8.43870e21i | −1.75332 | + | 0.634151i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.44958e22i | − | 1.07117i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.91233e21i | 0.356956i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.10487e22 | − | 9.61022e20i | 0.789532 | − | 0.0686736i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.36440e22 | −1.66159 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.34602e21 | −0.369483 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.82183e21 | − | 4.19403e20i | 0.327758 | − | 0.0285084i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.15687e21i | 0.0773427i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.22756e21i | 0.0807210i | 0.999185 | + | 0.0403605i | \(0.0128506\pi\) | ||||
−0.999185 | + | 0.0403605i | \(0.987149\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.36990e21 | − | 1.92251e22i | −0.217966 | − | 1.24348i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.39285e21 | 0.152239 | 0.0761197 | − | 0.997099i | \(-0.475747\pi\) | ||||
0.0761197 | + | 0.997099i | \(0.475747\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.42525e21 | 0.151784 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.37219e20 | − | 7.32603e21i | −0.0392311 | − | 0.451035i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.56754e22i | 0.949397i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 5.70944e21i | − | 0.340194i | −0.985427 | − | 0.170097i | \(-0.945592\pi\) | ||
0.985427 | − | 0.170097i | \(-0.0544082\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.35172e21 | − | 1.55405e22i | −0.0792390 | − | 0.911001i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.89930e22 | 1.67217 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.22738e22 | −0.696490 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.22107e21 | + | 6.96613e21i | 0.0681776 | + | 0.388950i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 5.33097e21i | − | 0.292879i | −0.989220 | − | 0.146440i | \(-0.953219\pi\) | ||
0.989220 | − | 0.146440i | \(-0.0467814\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 2.53580e22i | − | 1.37086i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.15598e22 | + | 2.74508e21i | −1.67889 | + | 0.146030i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.30203e22 | 1.20510 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.68116e21 | 0.447230 | 0.223615 | − | 0.974678i | \(-0.428214\pi\) | ||||
0.223615 | + | 0.974678i | \(0.428214\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.32731e21 | − | 1.15449e20i | 0.0672945 | − | 0.00585328i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.42716e22i | 0.712117i | 0.934464 | + | 0.356059i | \(0.115880\pi\) | ||||
−0.934464 | + | 0.356059i | \(0.884120\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1.63418e22i | − | 0.802532i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.40368e22 | − | 3.73837e21i | 0.678467 | − | 0.180694i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.61533e21 | 0.0768489 | 0.0384244 | − | 0.999262i | \(-0.487766\pi\) | ||||
0.0384244 | + | 0.999262i | \(0.487766\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.88552e22 | −0.882948 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.00557e20 | + | 4.60516e21i | 0.0184634 | + | 0.212271i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.78749e22i | − | 0.811049i | −0.914084 | − | 0.405524i | \(-0.867089\pi\) | ||
0.914084 | − | 0.405524i | \(-0.132911\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 7.52332e21i | − | 0.336035i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.74071e21 | + | 4.30065e22i | 0.164481 | + | 1.89101i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.63127e22 | −2.00475 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.90410e22 | −1.66378 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 2.64249e21 | − | 4.63193e20i | 0.110871 | − | 0.0194341i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 8.32302e21i | − | 0.343816i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.09074e22i | 1.25708i | 0.777776 | + | 0.628542i | \(0.216348\pi\) | ||||
−0.777776 | + | 0.628542i | \(0.783652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.30511e22 | − | 4.61439e21i | 2.12455 | − | 0.184793i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.32111e21 | −0.170393 | −0.0851964 | − | 0.996364i | \(-0.527152\pi\) | ||||
−0.0851964 | + | 0.996364i | \(0.527152\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.15624e22 | 1.22553 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.86035e22 | − | 1.61813e21i | 0.711310 | − | 0.0618699i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.14164e22i | 1.55942i | 0.626140 | + | 0.779710i | \(0.284634\pi\) | ||||
−0.626140 | + | 0.779710i | \(0.715366\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.53643e22i | 2.05286i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.62003e21 | − | 6.34543e20i | 0.132189 | − | 0.0231709i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.15037e22 | 0.773325 | 0.386662 | − | 0.922221i | \(-0.373628\pi\) | ||||
0.386662 | + | 0.922221i | \(0.373628\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.69281e22 | −0.599566 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.05855e21 | + | 2.36669e22i | 0.0718097 | + | 0.825587i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.75545e21i | 0.197746i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.90628e22i | − | 1.66035i | −0.557503 | − | 0.830175i | \(-0.688240\pi\) | ||
0.557503 | − | 0.830175i | \(-0.311760\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.70267e21 | + | 5.40660e22i | 0.156756 | + | 1.80221i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.78130e22 | 0.584875 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.79757e22 | 0.581396 | 0.290698 | − | 0.956815i | \(-0.406113\pi\) | ||||
0.290698 | + | 0.956815i | \(0.406113\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.91390e22 | − | 7.76050e21i | 0.928396 | − | 0.247257i |
(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 | 48.16.c.d.47.2 | yes | 20 | |
3.2 | odd | 2 | inner | 48.16.c.d.47.20 | yes | 20 | |
4.3 | odd | 2 | inner | 48.16.c.d.47.19 | yes | 20 | |
12.11 | even | 2 | inner | 48.16.c.d.47.1 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.16.c.d.47.1 | ✓ | 20 | 12.11 | even | 2 | inner | |
48.16.c.d.47.2 | yes | 20 | 1.1 | even | 1 | trivial | |
48.16.c.d.47.19 | yes | 20 | 4.3 | odd | 2 | inner | |
48.16.c.d.47.20 | yes | 20 | 3.2 | odd | 2 | inner |