Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,14,Mod(19,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.19");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.c (of order \(3\), degree \(2\), not 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: | \(57.9047016340\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 344289641 x^{10} - 1721448150 x^{9} + \cdots + 46\!\cdots\!81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{45} \) |
Twist minimal: | no (minimal twist has level 18) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.4 | ||
Root | \(0.500000 + 3035.92i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 54.37 |
Dual form | 54.14.c.a.19.4 |
$q$-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 \(\left(\mathbb{Z}/54\mathbb{Z}\right)^\times\).
\(n\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −32.0000 | − | 55.4256i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2048.00 | + | 3547.24i | −0.250000 | + | 0.433013i | ||||
\(5\) | 10927.3 | − | 18926.7i | 0.312758 | − | 0.541713i | −0.666200 | − | 0.745773i | \(-0.732080\pi\) |
0.978958 | + | 0.204060i | \(0.0654138\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −146006. | − | 252890.i | −0.469066 | − | 0.812446i | 0.530309 | − | 0.847805i | \(-0.322076\pi\) |
−0.999375 | + | 0.0353584i | \(0.988743\pi\) | |||||||
\(8\) | 262144. | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.39870e6 | −0.442307 | ||||||||
\(11\) | −1.12078e6 | − | 1.94125e6i | −0.190751 | − | 0.330391i | 0.754748 | − | 0.656015i | \(-0.227759\pi\) |
−0.945499 | + | 0.325624i | \(0.894426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.69332e6 | − | 1.50573e7i | 0.499521 | − | 0.865196i | −0.500479 | − | 0.865749i | \(-0.666843\pi\) |
1.00000 | 0.000553009i | \(0.000176028\pi\) | ||||||||
\(14\) | −9.34440e6 | + | 1.61850e7i | −0.331680 | + | 0.574486i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.38861e6 | − | 1.45295e7i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.02646e8 | −1.03139 | −0.515697 | − | 0.856771i | \(-0.672467\pi\) | ||||
−0.515697 | + | 0.856771i | \(0.672467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.84600e8 | 1.38783 | 0.693915 | − | 0.720057i | \(-0.255884\pi\) | ||||
0.693915 | + | 0.720057i | \(0.255884\pi\) | |||||||
\(20\) | 4.47583e7 | + | 7.75236e7i | 0.156379 | + | 0.270856i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.17298e7 | + | 1.24240e8i | −0.134882 | + | 0.233622i | ||||
\(23\) | 1.29161e8 | − | 2.23713e8i | 0.181928 | − | 0.315108i | −0.760609 | − | 0.649210i | \(-0.775100\pi\) |
0.942537 | + | 0.334102i | \(0.108433\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.71539e8 | + | 6.43525e8i | 0.304365 | + | 0.527175i | ||||
\(26\) | −1.11274e9 | −0.706429 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.19608e9 | 0.469066 | ||||||||
\(29\) | −1.74217e9 | − | 3.01753e9i | −0.543881 | − | 0.942030i | −0.998676 | − | 0.0514340i | \(-0.983621\pi\) |
0.454795 | − | 0.890596i | \(-0.349713\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.05701e9 | − | 7.02694e9i | 0.821022 | − | 1.42205i | −0.0838996 | − | 0.996474i | \(-0.526738\pi\) |
0.904922 | − | 0.425578i | \(-0.139929\pi\) | |||||||
\(32\) | −5.36871e8 | + | 9.29888e8i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.28468e9 | + | 5.68923e9i | 0.364653 | + | 0.631597i | ||||
\(35\) | −6.38182e9 | −0.586817 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.28194e10 | −0.821405 | −0.410703 | − | 0.911769i | \(-0.634717\pi\) | ||||
−0.410703 | + | 0.911769i | \(0.634717\pi\) | |||||||
\(38\) | −9.10720e9 | − | 1.57741e10i | −0.490672 | − | 0.849869i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.86453e9 | − | 4.96151e9i | 0.110577 | − | 0.191524i | ||||
\(41\) | −2.35711e9 | + | 4.08263e9i | −0.0774970 | + | 0.134229i | −0.902169 | − | 0.431382i | \(-0.858026\pi\) |
0.824672 | + | 0.565611i | \(0.191359\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.66397e10 | − | 2.88208e10i | −0.401422 | − | 0.695283i | 0.592476 | − | 0.805588i | \(-0.298151\pi\) |
−0.993898 | + | 0.110305i | \(0.964817\pi\) | |||||||
\(44\) | 9.18142e9 | 0.190751 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.65326e10 | −0.257285 | ||||||||
\(47\) | −1.52063e9 | − | 2.63380e9i | −0.0205772 | − | 0.0356408i | 0.855553 | − | 0.517715i | \(-0.173217\pi\) |
−0.876131 | + | 0.482074i | \(0.839884\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.80889e9 | − | 1.00613e10i | 0.0599541 | − | 0.103843i | ||||
\(50\) | 2.37785e10 | − | 4.11856e10i | 0.215218 | − | 0.372769i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.56078e10 | + | 6.16746e10i | 0.249761 | + | 0.432598i | ||||
\(53\) | 5.94638e10 | 0.368519 | 0.184259 | − | 0.982878i | \(-0.441011\pi\) | ||||
0.184259 | + | 0.982878i | \(0.441011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.89884e10 | −0.238636 | ||||||||
\(56\) | −3.82746e10 | − | 6.62936e10i | −0.165840 | − | 0.287243i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.11499e11 | + | 1.93122e11i | −0.384582 | + | 0.666116i | ||||
\(59\) | −2.89332e11 | + | 5.01138e11i | −0.893015 | + | 1.54675i | −0.0567738 | + | 0.998387i | \(0.518081\pi\) |
−0.836242 | + | 0.548361i | \(0.815252\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.43544e11 | + | 2.48625e11i | 0.356731 | + | 0.617876i | 0.987413 | − | 0.158166i | \(-0.0505581\pi\) |
−0.630682 | + | 0.776041i | \(0.717225\pi\) | |||||||
\(62\) | −5.19297e11 | −1.16110 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | −1.89989e11 | − | 3.29071e11i | −0.312458 | − | 0.541194i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.37420e11 | + | 7.57634e11i | −0.590762 | + | 1.02323i | 0.403368 | + | 0.915038i | \(0.367839\pi\) |
−0.994130 | + | 0.108192i | \(0.965494\pi\) | |||||||
\(68\) | 2.10219e11 | − | 3.64110e11i | 0.257849 | − | 0.446607i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.04218e11 | + | 3.53716e11i | 0.207471 | + | 0.359350i | ||||
\(71\) | −1.64422e12 | −1.52329 | −0.761644 | − | 0.647996i | \(-0.775607\pi\) | ||||
−0.761644 | + | 0.647996i | \(0.775607\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.62988e12 | −1.26054 | −0.630270 | − | 0.776376i | \(-0.717056\pi\) | ||||
−0.630270 | + | 0.776376i | \(0.717056\pi\) | |||||||
\(74\) | 4.10222e11 | + | 7.10525e11i | 0.290411 | + | 0.503006i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −5.82861e11 | + | 1.00954e12i | −0.346958 | + | 0.600948i | ||||
\(77\) | −3.27281e11 | + | 5.66868e11i | −0.178950 | + | 0.309950i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.51346e12 | + | 2.62139e12i | 0.700478 | + | 1.21326i | 0.968299 | + | 0.249795i | \(0.0803632\pi\) |
−0.267821 | + | 0.963469i | \(0.586304\pi\) | |||||||
\(80\) | −3.66660e11 | −0.156379 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.01710e11 | 0.109597 | ||||||||
\(83\) | 4.62483e11 | + | 8.01045e11i | 0.155270 | + | 0.268936i | 0.933157 | − | 0.359468i | \(-0.117042\pi\) |
−0.777887 | + | 0.628404i | \(0.783708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.12165e12 | + | 1.94275e12i | −0.322577 | + | 0.558719i | ||||
\(86\) | −1.06494e12 | + | 1.84453e12i | −0.283848 | + | 0.491639i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.93805e11 | − | 5.08886e11i | −0.0674408 | − | 0.116811i | ||||
\(89\) | −6.03750e12 | −1.28772 | −0.643861 | − | 0.765143i | \(-0.722668\pi\) | ||||
−0.643861 | + | 0.765143i | \(0.722668\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.07711e12 | −0.937233 | ||||||||
\(92\) | 5.29042e11 | + | 9.16328e11i | 0.0909640 | + | 0.157554i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.73201e10 | + | 1.68563e11i | −0.0145503 | + | 0.0252018i | ||||
\(95\) | 3.10991e12 | − | 5.38653e12i | 0.434055 | − | 0.751805i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.99631e11 | − | 1.03859e12i | −0.0730916 | − | 0.126598i | 0.827163 | − | 0.561962i | \(-0.189953\pi\) |
−0.900255 | + | 0.435363i | \(0.856620\pi\) | |||||||
\(98\) | −7.43538e11 | −0.0847878 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.04365e12 | −0.304365 | ||||||||
\(101\) | −6.16075e12 | − | 1.06707e13i | −0.577490 | − | 1.00024i | −0.995766 | − | 0.0919222i | \(-0.970699\pi\) |
0.418276 | − | 0.908320i | \(-0.362634\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.90932e12 | + | 3.30704e12i | −0.157557 | + | 0.272897i | −0.933987 | − | 0.357307i | \(-0.883695\pi\) |
0.776430 | + | 0.630203i | \(0.217028\pi\) | |||||||
\(104\) | 2.27890e12 | − | 3.94717e12i | 0.176607 | − | 0.305893i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.90284e12 | − | 3.29582e12i | −0.130291 | − | 0.225671i | ||||
\(107\) | −2.89672e13 | −1.86600 | −0.933002 | − | 0.359872i | \(-0.882821\pi\) | ||||
−0.933002 | + | 0.359872i | \(0.882821\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.01531e13 | 1.15099 | 0.575494 | − | 0.817806i | \(-0.304810\pi\) | ||||
0.575494 | + | 0.817806i | \(0.304810\pi\) | |||||||
\(110\) | 1.56763e12 | + | 2.71521e12i | 0.0843705 | + | 0.146134i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.44958e12 | + | 4.24279e12i | −0.117267 | + | 0.203112i | ||||
\(113\) | −7.37102e12 | + | 1.27670e13i | −0.333056 | + | 0.576870i | −0.983110 | − | 0.183018i | \(-0.941413\pi\) |
0.650053 | + | 0.759889i | \(0.274747\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.82276e12 | − | 4.88916e12i | −0.113799 | − | 0.197105i | ||||
\(116\) | 1.42719e13 | 0.543881 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.70345e13 | 1.26291 | ||||||||
\(119\) | 1.49870e13 | + | 2.59582e13i | 0.483792 | + | 0.837952i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.47491e13 | − | 2.55461e13i | 0.427228 | − | 0.739980i | ||||
\(122\) | 9.18680e12 | − | 1.59120e13i | 0.252247 | − | 0.436904i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.66175e13 | + | 2.87824e13i | 0.410511 | + | 0.711026i | ||||
\(125\) | 4.29177e13 | 1.00629 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.27677e13 | −1.32743 | −0.663715 | − | 0.747985i | \(-0.731021\pi\) | ||||
−0.663715 | + | 0.747985i | \(0.731021\pi\) | |||||||
\(128\) | −2.19902e12 | − | 3.80882e12i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.21593e13 | + | 2.10605e13i | −0.220941 | + | 0.382682i | ||||
\(131\) | 2.97023e13 | − | 5.14459e13i | 0.513484 | − | 0.889380i | −0.486394 | − | 0.873740i | \(-0.661688\pi\) |
0.999878 | − | 0.0156407i | \(-0.00497878\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.15533e13 | − | 7.19725e13i | −0.650984 | − | 1.12754i | ||||
\(134\) | 5.59898e13 | 0.835463 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.69081e13 | −0.364653 | ||||||||
\(137\) | 6.70609e13 | + | 1.16153e14i | 0.866535 | + | 1.50088i | 0.865515 | + | 0.500883i | \(0.166991\pi\) |
0.00101949 | + | 0.999999i | \(0.499675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.44053e13 | − | 1.28874e14i | 0.874999 | − | 1.51554i | 0.0182356 | − | 0.999834i | \(-0.494195\pi\) |
0.856764 | − | 0.515709i | \(-0.172472\pi\) | |||||||
\(140\) | 1.30700e13 | − | 2.26379e13i | 0.146704 | − | 0.254099i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.26152e13 | + | 9.11322e13i | 0.538563 | + | 0.932819i | ||||
\(143\) | −3.89731e13 | −0.381137 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.61491e13 | −0.680413 | ||||||||
\(146\) | 5.21561e13 | + | 9.03370e13i | 0.445668 | + | 0.771920i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.62542e13 | − | 4.54736e13i | 0.205351 | − | 0.355679i | ||||
\(149\) | 1.10148e13 | − | 1.90782e13i | 0.0824645 | − | 0.142833i | −0.821843 | − | 0.569713i | \(-0.807054\pi\) |
0.904308 | + | 0.426881i | \(0.140388\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.09503e13 | − | 3.62870e13i | −0.143827 | − | 0.249116i | 0.785108 | − | 0.619359i | \(-0.212608\pi\) |
−0.928935 | + | 0.370244i | \(0.879274\pi\) | |||||||
\(152\) | 7.46062e13 | 0.490672 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.18920e13 | 0.253073 | ||||||||
\(155\) | −8.86644e13 | − | 1.53571e14i | −0.513562 | − | 0.889516i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.74371e13 | − | 1.16805e14i | 0.359378 | − | 0.622461i | −0.628479 | − | 0.777826i | \(-0.716322\pi\) |
0.987857 | + | 0.155366i | \(0.0496556\pi\) | |||||||
\(158\) | 9.68614e13 | − | 1.67769e14i | 0.495313 | − | 0.857907i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.17331e13 | + | 2.03224e13i | 0.0552883 | + | 0.0957622i | ||||
\(161\) | −7.54330e13 | −0.341345 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.65656e14 | 0.691813 | 0.345907 | − | 0.938269i | \(-0.387571\pi\) | ||||
0.345907 | + | 0.938269i | \(0.387571\pi\) | |||||||
\(164\) | −9.65472e12 | − | 1.67225e13i | −0.0387485 | − | 0.0671143i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.95989e13 | − | 5.12669e13i | 0.109793 | − | 0.190167i | ||||
\(167\) | −8.10102e13 | + | 1.40314e14i | −0.288990 | + | 0.500545i | −0.973569 | − | 0.228393i | \(-0.926653\pi\) |
0.684579 | + | 0.728939i | \(0.259986\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.90013e11 | + | 5.02318e11i | 0.000957534 | + | 0.00165850i | ||||
\(170\) | 1.43571e14 | 0.456192 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.36313e14 | 0.401422 | ||||||||
\(173\) | −1.33981e14 | − | 2.32062e14i | −0.379964 | − | 0.658118i | 0.611092 | − | 0.791559i | \(-0.290730\pi\) |
−0.991057 | + | 0.133442i | \(0.957397\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.08494e14 | − | 1.87917e14i | 0.285534 | − | 0.494560i | ||||
\(176\) | −1.88035e13 | + | 3.25687e13i | −0.0476878 | + | 0.0825977i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.93200e14 | + | 3.34632e14i | 0.455278 | + | 0.788565i | ||||
\(179\) | −8.14358e14 | −1.85042 | −0.925211 | − | 0.379454i | \(-0.876112\pi\) | ||||
−0.925211 | + | 0.379454i | \(0.876112\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.82572e14 | −1.44291 | −0.721453 | − | 0.692464i | \(-0.756525\pi\) | ||||
−0.721453 | + | 0.692464i | \(0.756525\pi\) | |||||||
\(182\) | 1.62468e14 | + | 2.81402e14i | 0.331362 | + | 0.573936i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.38587e13 | − | 5.86450e13i | 0.0643212 | − | 0.111408i | ||||
\(185\) | −1.40082e14 | + | 2.42629e14i | −0.256901 | + | 0.444966i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.15044e14 | + | 1.99261e14i | 0.196740 | + | 0.340763i | ||||
\(188\) | 1.24570e13 | 0.0205772 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.98069e14 | −0.613846 | ||||||||
\(191\) | −2.97121e14 | − | 5.14629e14i | −0.442809 | − | 0.766968i | 0.555087 | − | 0.831792i | \(-0.312685\pi\) |
−0.997897 | + | 0.0648238i | \(0.979351\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.17764e14 | + | 7.23589e14i | −0.581847 | + | 1.00779i | 0.413414 | + | 0.910543i | \(0.364336\pi\) |
−0.995260 | + | 0.0972448i | \(0.968997\pi\) | |||||||
\(194\) | −3.83764e13 | + | 6.64698e13i | −0.0516836 | + | 0.0895186i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.37932e13 | + | 4.12111e13i | 0.0299770 | + | 0.0519217i | ||||
\(197\) | 9.13748e14 | 1.11377 | 0.556886 | − | 0.830589i | \(-0.311996\pi\) | ||||
0.556886 | + | 0.830589i | \(0.311996\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.29824e14 | −0.604765 | −0.302382 | − | 0.953187i | \(-0.597782\pi\) | ||||
−0.302382 | + | 0.953187i | \(0.597782\pi\) | |||||||
\(200\) | 9.73968e13 | + | 1.68696e14i | 0.107609 | + | 0.186385i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.94288e14 | + | 6.82927e14i | −0.408347 | + | 0.707278i | ||||
\(203\) | −5.08736e14 | + | 8.81157e14i | −0.510233 | + | 0.883749i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.15138e13 | + | 8.92244e13i | 0.0484756 | + | 0.0839622i | ||||
\(206\) | 2.44393e14 | 0.222819 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.91699e14 | −0.249761 | ||||||||
\(209\) | −3.18974e14 | − | 5.52478e14i | −0.264730 | − | 0.458526i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.98238e13 | − | 3.43358e13i | 0.0154650 | − | 0.0267862i | −0.858189 | − | 0.513333i | \(-0.828410\pi\) |
0.873654 | + | 0.486547i | \(0.161744\pi\) | |||||||
\(212\) | −1.21782e14 | + | 2.10932e14i | −0.0921297 | + | 0.159573i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.26952e14 | + | 1.60553e15i | 0.659732 | + | 1.14269i | ||||
\(215\) | −7.27310e14 | −0.502192 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.36939e15 | −1.54045 | ||||||||
\(218\) | −6.44901e14 | − | 1.11700e15i | −0.406936 | − | 0.704833i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.00328e14 | − | 1.73774e14i | 0.0596590 | − | 0.103332i | ||||
\(221\) | −8.92335e14 | + | 1.54557e15i | −0.515203 | + | 0.892358i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.67180e15 | + | 2.89564e15i | 0.910337 | + | 1.57675i | 0.813588 | + | 0.581442i | \(0.197511\pi\) |
0.0967496 | + | 0.995309i | \(0.469155\pi\) | |||||||
\(224\) | 3.13546e14 | 0.165840 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 9.43490e14 | 0.471013 | ||||||||
\(227\) | 7.83386e14 | + | 1.35686e15i | 0.380021 | + | 0.658216i | 0.991065 | − | 0.133381i | \(-0.0425835\pi\) |
−0.611044 | + | 0.791597i | \(0.709250\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.93486e15 | − | 3.35128e15i | 0.886582 | − | 1.53561i | 0.0426925 | − | 0.999088i | \(-0.486406\pi\) |
0.843890 | − | 0.536517i | \(-0.180260\pi\) | |||||||
\(230\) | −1.80657e14 | + | 3.12906e14i | −0.0804679 | + | 0.139375i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.56700e14 | − | 7.91028e14i | −0.192291 | − | 0.333058i | ||||
\(233\) | −5.09381e14 | −0.208559 | −0.104280 | − | 0.994548i | \(-0.533254\pi\) | ||||
−0.104280 | + | 0.994548i | \(0.533254\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.64655e13 | −0.0257428 | ||||||||
\(236\) | −1.18511e15 | − | 2.05266e15i | −0.446508 | − | 0.773374i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.59166e14 | − | 1.66132e15i | 0.342093 | − | 0.592522i | ||||
\(239\) | 7.94675e14 | − | 1.37642e15i | 0.275806 | − | 0.477709i | −0.694532 | − | 0.719461i | \(-0.744389\pi\) |
0.970338 | + | 0.241752i | \(0.0777220\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.97767e14 | + | 3.42542e14i | 0.0650193 | + | 0.112617i | 0.896703 | − | 0.442634i | \(-0.145956\pi\) |
−0.831683 | + | 0.555250i | \(0.812622\pi\) | |||||||
\(242\) | −1.88788e15 | −0.604191 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.17591e15 | −0.356731 | ||||||||
\(245\) | −1.26951e14 | − | 2.19886e14i | −0.0375022 | − | 0.0649558i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.47412e15 | − | 4.28530e15i | 0.693250 | − | 1.20074i | ||||
\(248\) | 1.06352e15 | − | 1.84207e15i | 0.290275 | − | 0.502771i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.37337e15 | − | 2.37874e15i | −0.355776 | − | 0.616222i | ||||
\(251\) | 2.94268e15 | 0.742786 | 0.371393 | − | 0.928476i | \(-0.378880\pi\) | ||||
0.371393 | + | 0.928476i | \(0.378880\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.79042e14 | −0.138812 | ||||||||
\(254\) | 2.00857e15 | + | 3.47894e15i | 0.469318 | + | 0.812882i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.40737e14 | + | 2.43764e14i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 4.25116e15 | − | 7.36322e15i | 0.920326 | − | 1.59405i | 0.121416 | − | 0.992602i | \(-0.461257\pi\) |
0.798910 | − | 0.601450i | \(-0.205410\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.87172e15 | + | 3.24191e15i | 0.385293 | + | 0.667348i | ||||
\(260\) | 1.55639e15 | 0.312458 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.80190e15 | −0.726176 | ||||||||
\(263\) | 4.13547e14 | + | 7.16284e14i | 0.0770570 | + | 0.133467i | 0.901979 | − | 0.431780i | \(-0.142114\pi\) |
−0.824922 | + | 0.565247i | \(0.808781\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.49780e14 | − | 1.12545e15i | 0.115257 | − | 0.199631i | ||||
\(266\) | −2.65941e15 | + | 4.60624e15i | −0.460315 | + | 0.797289i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.79167e15 | − | 3.10327e15i | −0.295381 | − | 0.511615i | ||||
\(269\) | 1.21446e16 | 1.95431 | 0.977156 | − | 0.212521i | \(-0.0681674\pi\) | ||||
0.977156 | + | 0.212521i | \(0.0681674\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.66147e14 | −0.132828 | −0.0664142 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664142 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(272\) | 8.61058e14 | + | 1.49140e15i | 0.128924 | + | 0.223303i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.29190e15 | − | 7.43379e15i | 0.612733 | − | 1.06128i | ||||
\(275\) | 8.32826e14 | − | 1.44250e15i | 0.116116 | − | 0.201119i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.11698e15 | + | 1.93467e15i | 0.148569 | + | 0.257329i | 0.930699 | − | 0.365787i | \(-0.119200\pi\) |
−0.782130 | + | 0.623116i | \(0.785867\pi\) | |||||||
\(278\) | −9.52388e15 | −1.23744 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.67296e15 | −0.207471 | ||||||||
\(281\) | 2.37385e15 | + | 4.11163e15i | 0.287649 | + | 0.498222i | 0.973248 | − | 0.229757i | \(-0.0737931\pi\) |
−0.685599 | + | 0.727979i | \(0.740460\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.28026e15 | − | 5.68158e15i | 0.379574 | − | 0.657442i | −0.611426 | − | 0.791302i | \(-0.709404\pi\) |
0.991000 | + | 0.133860i | \(0.0427371\pi\) | |||||||
\(284\) | 3.36737e15 | − | 5.83246e15i | 0.380822 | − | 0.659603i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.24714e15 | + | 2.16011e15i | 0.134752 | + | 0.233398i | ||||
\(287\) | 1.37661e15 | 0.145405 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.31651e14 | 0.0637736 | ||||||||
\(290\) | 2.43677e15 | + | 4.22061e15i | 0.240562 | + | 0.416666i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.33799e15 | − | 5.78157e15i | 0.315135 | − | 0.545830i | ||||
\(293\) | −5.53057e15 | + | 9.57923e15i | −0.510658 | + | 0.884486i | 0.489266 | + | 0.872135i | \(0.337265\pi\) |
−0.999924 | + | 0.0123510i | \(0.996068\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.32325e15 | + | 1.09522e16i | 0.558595 | + | 0.967516i | ||||
\(296\) | −3.36054e15 | −0.290411 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.40990e15 | −0.116622 | ||||||||
\(299\) | −2.24567e15 | − | 3.88961e15i | −0.181754 | − | 0.314807i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.85900e15 | + | 8.41604e15i | −0.376587 | + | 0.652267i | ||||
\(302\) | −1.34082e15 | + | 2.32237e15i | −0.101701 | + | 0.176151i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.38740e15 | − | 4.13509e15i | −0.173479 | − | 0.300474i | ||||
\(305\) | 6.27419e15 | 0.446281 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.85853e15 | −0.331211 | −0.165606 | − | 0.986192i | \(-0.552958\pi\) | ||||
−0.165606 | + | 0.986192i | \(0.552958\pi\) | |||||||
\(308\) | −1.34054e15 | − | 2.32189e15i | −0.0894749 | − | 0.154975i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.67452e15 | + | 9.82856e15i | −0.363144 | + | 0.628983i | ||||
\(311\) | 3.88280e15 | − | 6.72520e15i | 0.243334 | − | 0.421466i | −0.718328 | − | 0.695704i | \(-0.755092\pi\) |
0.961662 | + | 0.274238i | \(0.0884256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.24807e16 | + | 2.16172e16i | 0.750241 | + | 1.29945i | 0.947706 | + | 0.319145i | \(0.103396\pi\) |
−0.197465 | + | 0.980310i | \(0.563271\pi\) | |||||||
\(314\) | −8.63195e15 | −0.508237 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.23983e16 | −0.700478 | ||||||||
\(317\) | 5.36996e14 | + | 9.30105e14i | 0.0297226 | + | 0.0514810i | 0.880504 | − | 0.474039i | \(-0.157204\pi\) |
−0.850782 | + | 0.525520i | \(0.823871\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.90518e15 | + | 6.76397e15i | −0.207492 | + | 0.359387i | ||||
\(320\) | 7.50919e14 | − | 1.30063e15i | 0.0390947 | − | 0.0677141i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.41386e15 | + | 4.18092e15i | 0.120684 | + | 0.209030i | ||||
\(323\) | −2.92131e16 | −1.43140 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.29196e16 | 0.608147 | ||||||||
\(326\) | −5.30101e15 | − | 9.18161e15i | −0.244593 | − | 0.423648i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −6.17902e14 | + | 1.07024e15i | −0.0273993 | + | 0.0474570i | ||||
\(329\) | −4.44042e14 | + | 7.69103e14i | −0.0193041 | + | 0.0334358i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.86953e16 | − | 3.23811e16i | −0.781357 | − | 1.35335i | −0.931152 | − | 0.364632i | \(-0.881195\pi\) |
0.149795 | − | 0.988717i | \(-0.452139\pi\) | |||||||
\(332\) | −3.78866e15 | −0.155270 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.03693e16 | 0.408693 | ||||||||
\(335\) | 9.55965e15 | + | 1.65578e16i | 0.369531 | + | 0.640046i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.45382e15 | + | 7.71424e15i | −0.165630 | + | 0.286879i | −0.936879 | − | 0.349655i | \(-0.886299\pi\) |
0.771249 | + | 0.636533i | \(0.219632\pi\) | |||||||
\(338\) | 1.85608e13 | − | 3.21483e13i | 0.000677079 | − | 0.00117274i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.59426e15 | − | 7.95750e15i | −0.161288 | − | 0.279360i | ||||
\(341\) | −1.81880e16 | −0.626444 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.16853e16 | −1.05062 | ||||||||
\(344\) | −4.36200e15 | − | 7.55521e15i | −0.141924 | − | 0.245820i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −8.57477e15 | + | 1.48519e16i | −0.268675 | + | 0.465359i | ||||
\(347\) | −8.89968e15 | + | 1.54147e16i | −0.273674 | + | 0.474017i | −0.969800 | − | 0.243903i | \(-0.921572\pi\) |
0.696126 | + | 0.717920i | \(0.254905\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.02979e16 | − | 3.51571e16i | −0.601294 | − | 1.04147i | −0.992625 | − | 0.121222i | \(-0.961319\pi\) |
0.391332 | − | 0.920250i | \(-0.372014\pi\) | |||||||
\(350\) | −1.38872e16 | −0.403807 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.40685e15 | 0.0674408 | ||||||||
\(353\) | −2.52713e16 | − | 4.37711e16i | −0.695170 | − | 1.20407i | −0.970123 | − | 0.242613i | \(-0.921996\pi\) |
0.274953 | − | 0.961458i | \(-0.411338\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.79670e16 | + | 3.11197e16i | −0.476420 | + | 0.825184i | ||||
\(356\) | 1.23648e16 | − | 2.14165e16i | 0.321930 | − | 0.557600i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.60595e16 | + | 4.51363e16i | 0.654223 | + | 1.13315i | ||||
\(359\) | 4.12005e16 | 1.01575 | 0.507877 | − | 0.861430i | \(-0.330430\pi\) | ||||
0.507877 | + | 0.861430i | \(0.330430\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.89441e16 | 0.926073 | ||||||||
\(362\) | 2.18423e16 | + | 3.78320e16i | 0.510144 | + | 0.883595i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.03979e16 | − | 1.80097e16i | 0.234308 | − | 0.405834i | ||||
\(365\) | −1.78102e16 | + | 3.08481e16i | −0.394244 | + | 0.682850i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.92069e16 | + | 3.32673e16i | 0.410325 | + | 0.710703i | 0.994925 | − | 0.100618i | \(-0.0320820\pi\) |
−0.584600 | + | 0.811321i | \(0.698749\pi\) | |||||||
\(368\) | −4.33391e15 | −0.0909640 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.79305e16 | 0.363313 | ||||||||
\(371\) | −8.68209e15 | − | 1.50378e16i | −0.172860 | − | 0.299402i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.62379e16 | − | 4.54454e16i | 0.504455 | − | 0.873741i | −0.495532 | − | 0.868590i | \(-0.665027\pi\) |
0.999987 | − | 0.00515150i | \(-0.00163978\pi\) | |||||||
\(374\) | 7.36279e15 | − | 1.27527e16i | 0.139116 | − | 0.240956i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.98623e14 | − | 6.90436e14i | −0.00727514 | − | 0.0126009i | ||||
\(377\) | −6.05810e16 | −1.08672 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.80121e16 | −0.658820 | −0.329410 | − | 0.944187i | \(-0.606850\pi\) | ||||
−0.329410 | + | 0.944187i | \(0.606850\pi\) | |||||||
\(380\) | 1.27382e16 | + | 2.20632e16i | 0.217027 | + | 0.375903i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.90158e16 | + | 3.29363e16i | −0.313113 | + | 0.542328i | ||||
\(383\) | −9.58764e15 | + | 1.66063e16i | −0.155210 | + | 0.268832i | −0.933135 | − | 0.359525i | \(-0.882939\pi\) |
0.777926 | + | 0.628357i | \(0.216272\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.15261e15 | + | 1.23887e16i | 0.111936 | + | 0.193879i | ||||
\(386\) | 5.34738e16 | 0.822856 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.91218e15 | 0.0730916 | ||||||||
\(389\) | −3.75175e16 | − | 6.49823e16i | −0.548987 | − | 0.950873i | −0.998344 | − | 0.0575208i | \(-0.981680\pi\) |
0.449358 | − | 0.893352i | \(-0.351653\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.32578e16 | + | 2.29633e16i | −0.187639 | + | 0.325001i | ||||
\(392\) | 1.52277e15 | − | 2.63751e15i | 0.0211970 | − | 0.0367142i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.92399e16 | − | 5.06451e16i | −0.393778 | − | 0.682043i | ||||
\(395\) | 6.61522e16 | 0.876320 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.62792e16 | 0.849647 | 0.424824 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424824 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(398\) | 1.69544e16 | + | 2.93658e16i | 0.213817 | + | 0.370341i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.23339e15 | − | 1.07966e16i | 0.0760912 | − | 0.131794i | ||||
\(401\) | −4.76233e15 | + | 8.24860e15i | −0.0571980 | + | 0.0990699i | −0.893207 | − | 0.449646i | \(-0.851550\pi\) |
0.836009 | + | 0.548716i | \(0.184883\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.05377e16 | − | 1.22175e17i | −0.820236 | − | 1.42069i | ||||
\(404\) | 5.04688e16 | 0.577490 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 6.51182e16 | 0.721578 | ||||||||
\(407\) | 1.43677e16 | + | 2.48857e16i | 0.156684 | + | 0.271385i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.61134e15 | + | 1.49153e16i | −0.0909639 | + | 0.157554i | −0.907917 | − | 0.419150i | \(-0.862328\pi\) |
0.816953 | + | 0.576704i | \(0.195661\pi\) | |||||||
\(410\) | 3.29688e15 | − | 5.71036e15i | 0.0342774 | − | 0.0593702i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −7.82059e15 | − | 1.35457e16i | −0.0787784 | − | 0.136448i | ||||
\(413\) | 1.68977e17 | 1.67553 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.02148e16 | 0.194248 | ||||||||
\(416\) | 9.33438e15 | + | 1.61676e16i | 0.0883037 | + | 0.152946i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.04143e16 | + | 3.53586e16i | −0.187193 | + | 0.324227i | ||||
\(419\) | −7.14576e16 | + | 1.23768e17i | −0.645145 | + | 1.11742i | 0.339123 | + | 0.940742i | \(0.389870\pi\) |
−0.984268 | + | 0.176682i | \(0.943463\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.30966e16 | − | 9.19660e16i | −0.464765 | − | 0.804996i | 0.534426 | − | 0.845215i | \(-0.320528\pi\) |
−0.999191 | + | 0.0402192i | \(0.987194\pi\) | |||||||
\(422\) | −2.53744e15 | −0.0218708 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.55881e16 | 0.130291 | ||||||||
\(425\) | −3.81371e16 | − | 6.60553e16i | −0.313920 | − | 0.543726i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.19166e16 | − | 7.26016e16i | 0.334660 | − | 0.579649i | ||||
\(428\) | 5.93249e16 | − | 1.02754e17i | 0.466501 | − | 0.808003i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.32739e16 | + | 4.03116e16i | 0.177552 | + | 0.307528i | ||||
\(431\) | 9.79018e16 | 0.735679 | 0.367840 | − | 0.929889i | \(-0.380098\pi\) | ||||
0.367840 | + | 0.929889i | \(0.380098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.01860e17 | 0.742736 | 0.371368 | − | 0.928486i | \(-0.378889\pi\) | ||||
0.371368 | + | 0.928486i | \(0.378889\pi\) | |||||||
\(434\) | 7.58206e16 | + | 1.31325e17i | 0.544633 | + | 0.943332i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.12736e16 | + | 7.14880e16i | −0.287747 | + | 0.498392i | ||||
\(437\) | 3.67591e16 | − | 6.36687e16i | 0.252485 | − | 0.437317i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.75733e16 | − | 1.34361e17i | −0.517241 | − | 0.895887i | −0.999800 | − | 0.0200235i | \(-0.993626\pi\) |
0.482559 | − | 0.875864i | \(-0.339707\pi\) | |||||||
\(440\) | −1.28420e16 | −0.0843705 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.14219e17 | 0.728607 | ||||||||
\(443\) | −4.10565e15 | − | 7.11119e15i | −0.0258082 | − | 0.0447011i | 0.852833 | − | 0.522184i | \(-0.174883\pi\) |
−0.878641 | + | 0.477483i | \(0.841549\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.59736e16 | + | 1.14270e17i | −0.402745 | + | 0.697575i | ||||
\(446\) | 1.06995e17 | − | 1.85321e17i | 0.643706 | − | 1.11493i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00335e16 | − | 1.73785e16i | −0.0586333 | − | 0.101556i | ||||
\(449\) | 2.94000e16 | 0.169335 | 0.0846675 | − | 0.996409i | \(-0.473017\pi\) | ||||
0.0846675 | + | 0.996409i | \(0.473017\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.05672e16 | 0.0591306 | ||||||||
\(452\) | −3.01917e16 | − | 5.22935e16i | −0.166528 | − | 0.288435i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.01367e16 | − | 8.68393e16i | 0.268715 | − | 0.465429i | ||||
\(455\) | −5.54792e16 | + | 9.60928e16i | −0.293127 | + | 0.507711i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.27616e17 | − | 2.21038e17i | −0.655316 | − | 1.13504i | −0.981815 | − | 0.189842i | \(-0.939202\pi\) |
0.326499 | − | 0.945198i | \(-0.394131\pi\) | |||||||
\(458\) | −2.47662e17 | −1.25382 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.31240e16 | 0.113799 | ||||||||
\(461\) | −6.15012e16 | − | 1.06523e17i | −0.298420 | − | 0.516878i | 0.677355 | − | 0.735656i | \(-0.263126\pi\) |
−0.975775 | + | 0.218778i | \(0.929793\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.63262e16 | − | 4.55984e16i | 0.124197 | − | 0.215116i | −0.797222 | − | 0.603687i | \(-0.793698\pi\) |
0.921419 | + | 0.388571i | \(0.127031\pi\) | |||||||
\(464\) | −2.92288e16 | + | 5.06258e16i | −0.135970 | + | 0.235508i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.63002e16 | + | 2.82328e16i | 0.0737368 | + | 0.127716i | ||||
\(467\) | −3.35303e17 | −1.49581 | −0.747907 | − | 0.663803i | \(-0.768941\pi\) | ||||
−0.747907 | + | 0.663803i | \(0.768941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.55464e17 | 1.10843 | ||||||||
\(470\) | 2.12690e15 | + | 3.68389e15i | 0.00910144 | + | 0.0157642i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −7.58468e16 | + | 1.31370e17i | −0.315729 | + | 0.546858i | ||||
\(473\) | −3.72989e16 | + | 6.46036e16i | −0.153143 | + | 0.265252i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.05740e17 | + | 1.83147e17i | 0.422407 | + | 0.731630i | ||||
\(476\) | −1.22773e17 | −0.483792 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.01718e17 | −0.390048 | ||||||||
\(479\) | −1.28704e17 | − | 2.22922e17i | −0.486869 | − | 0.843282i | 0.513017 | − | 0.858378i | \(-0.328528\pi\) |
−0.999886 | + | 0.0150967i | \(0.995194\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.11443e17 | + | 1.93026e17i | −0.410309 | + | 0.710676i | ||||
\(482\) | 1.26571e16 | − | 2.19227e16i | 0.0459756 | − | 0.0796321i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.04122e16 | + | 1.04637e17i | 0.213614 | + | 0.369990i | ||||
\(485\) | −2.62094e16 | −0.0914400 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.57963e17 | −0.536560 | −0.268280 | − | 0.963341i | \(-0.586455\pi\) | ||||
−0.268280 | + | 0.963341i | \(0.586455\pi\) | |||||||
\(488\) | 3.76291e16 | + | 6.51756e16i | 0.126123 | + | 0.218452i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −8.12487e15 | + | 1.40727e16i | −0.0265181 | + | 0.0459307i | ||||
\(491\) | −9.68006e16 | + | 1.67664e17i | −0.311780 | + | 0.540019i | −0.978748 | − | 0.205068i | \(-0.934259\pi\) |
0.666968 | + | 0.745087i | \(0.267592\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.78827e17 | + | 3.09738e17i | 0.560956 | + | 0.971604i | ||||
\(494\) | −3.16687e17 | −0.980404 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.36131e17 | −0.410511 | ||||||||
\(497\) | 2.40067e17 | + | 4.15808e17i | 0.714522 | + | 1.23759i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.03789e17 | + | 3.52972e17i | −0.590917 | + | 1.02350i | 0.403192 | + | 0.915115i | \(0.367901\pi\) |
−0.994109 | + | 0.108383i | \(0.965433\pi\) | |||||||
\(500\) | −8.78955e16 | + | 1.52239e17i | −0.251572 | + | 0.435735i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −9.41657e16 | − | 1.63100e17i | −0.262615 | − | 0.454862i | ||||
\(503\) | 3.41866e17 | 0.941162 | 0.470581 | − | 0.882357i | \(-0.344044\pi\) | ||||
0.470581 | + | 0.882357i | \(0.344044\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.69282e17 | −0.722458 | ||||||||
\(506\) | 1.85294e16 | + | 3.20938e16i | 0.0490774 | + | 0.0850046i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.28548e17 | − | 2.22652e17i | 0.331858 | − | 0.574794i | ||||
\(509\) | 3.30769e17 | − | 5.72909e17i | 0.843062 | − | 1.46023i | −0.0442315 | − | 0.999021i | \(-0.514084\pi\) |
0.887294 | − | 0.461205i | \(-0.152583\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.37972e17 | + | 4.12180e17i | 0.591276 | + | 1.02412i | ||||
\(512\) | 1.80144e16 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −5.44148e17 | −1.30154 | ||||||||
\(515\) | 4.17275e16 | + | 7.22742e16i | 0.0985543 | + | 0.170701i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.40857e15 | + | 5.90382e15i | −0.00785026 | + | 0.0135970i | ||||
\(518\) | 1.19790e17 | − | 2.07482e17i | 0.272444 | − | 0.471886i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.98045e16 | − | 8.62640e16i | −0.110471 | − | 0.191341i | ||||
\(521\) | −1.27627e17 | −0.279575 | −0.139787 | − | 0.990182i | \(-0.544642\pi\) | ||||
−0.139787 | + | 0.990182i | \(0.544642\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.90574e17 | −0.407196 | −0.203598 | − | 0.979055i | \(-0.565264\pi\) | ||||
−0.203598 | + | 0.979055i | \(0.565264\pi\) | |||||||
\(524\) | 1.21661e17 | + | 2.10723e17i | 0.256742 | + | 0.444690i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.64670e16 | − | 4.58422e16i | 0.0544875 | − | 0.0943752i | ||||
\(527\) | −4.16436e17 | + | 7.21289e17i | −0.846797 | + | 1.46670i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.18653e17 | + | 3.78718e17i | 0.433804 | + | 0.751371i | ||||
\(530\) | −8.31718e16 | −0.162998 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.40405e17 | 0.650984 | ||||||||
\(533\) | 4.09822e16 | + | 7.09833e16i | 0.0774227 | + | 0.134100i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.16534e17 | + | 5.48253e17i | −0.583608 | + | 1.01084i | ||||
\(536\) | −1.14667e17 | + | 1.98609e17i | −0.208866 | + | 0.361766i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −3.88628e17 | − | 6.73123e17i | −0.690954 | − | 1.19677i | ||||
\(539\) | −2.60419e16 | −0.0457453 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.46355e17 | 1.10838 | 0.554191 | − | 0.832390i | \(-0.313028\pi\) | ||||
0.554191 | + | 0.832390i | \(0.313028\pi\) | |||||||
\(542\) | 2.77167e16 | + | 4.80067e16i | 0.0469619 | + | 0.0813405i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 5.51077e16 | − | 9.54494e16i | 0.0911632 | − | 0.157899i | ||||
\(545\) | 2.20220e17 | − | 3.81432e17i | 0.359981 | − | 0.623505i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.79901e17 | − | 3.11598e17i | −0.287155 | − | 0.497367i | 0.685975 | − | 0.727625i | \(-0.259376\pi\) |
−0.973129 | + | 0.230259i | \(0.926043\pi\) | |||||||
\(548\) | −5.49363e17 | −0.866535 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.06602e17 | −0.164213 | ||||||||
\(551\) | −4.95822e17 | − | 8.58789e17i | −0.754815 | − | 1.30738i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.41949e17 | − | 7.65478e17i | 0.657141 | − | 1.13820i | ||||
\(554\) | 7.14869e16 | − | 1.23819e17i | 0.105054 | − | 0.181959i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.04764e17 | + | 5.27867e17i | 0.437500 | + | 0.757772i | ||||
\(557\) | 1.20436e18 | 1.70883 | 0.854413 | − | 0.519595i | \(-0.173917\pi\) | ||||
0.854413 | + | 0.519595i | \(0.173917\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.78617e17 | −0.802075 | ||||||||
\(560\) | 5.35346e16 | + | 9.27247e16i | 0.0733521 | + | 0.127050i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.51926e17 | − | 2.63144e17i | 0.203398 | − | 0.352296i | ||||
\(563\) | 7.49238e15 | − | 1.29772e16i | 0.00991551 | − | 0.0171742i | −0.861025 | − | 0.508563i | \(-0.830177\pi\) |
0.870941 | + | 0.491388i | \(0.163510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.61091e17 | + | 2.79018e17i | 0.208332 | + | 0.360842i | ||||
\(566\) | −4.19874e17 | −0.536799 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.31024e17 | −0.538563 | ||||||||
\(569\) | −3.97144e17 | − | 6.87874e17i | −0.490590 | − | 0.849727i | 0.509351 | − | 0.860559i | \(-0.329885\pi\) |
−0.999941 | + | 0.0108318i | \(0.996552\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.75009e17 | − | 8.22740e17i | 0.573545 | − | 0.993408i | −0.422654 | − | 0.906291i | \(-0.638901\pi\) |
0.996198 | − | 0.0871169i | \(-0.0277654\pi\) | |||||||
\(572\) | 7.98170e16 | − | 1.38247e17i | 0.0952843 | − | 0.165037i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.40515e16 | − | 7.62995e16i | −0.0514084 | − | 0.0890419i | ||||
\(575\) | 1.91953e17 | 0.221490 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.58846e17 | 0.292011 | 0.146005 | − | 0.989284i | \(-0.453358\pi\) | ||||
0.146005 | + | 0.989284i | \(0.453358\pi\) | |||||||
\(578\) | −2.02128e16 | − | 3.50097e16i | −0.0225474 | − | 0.0390532i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.55953e17 | − | 2.70119e17i | 0.170103 | − | 0.294627i | ||||
\(581\) | 1.35051e17 | − | 2.33915e17i | 0.145664 | − | 0.252298i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.66458e16 | − | 1.15434e17i | −0.0702954 | − | 0.121755i | ||||
\(584\) | −4.27263e17 | −0.445668 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.07913e17 | 0.722180 | ||||||||
\(587\) | 6.50180e17 | + | 1.12614e18i | 0.655973 | + | 1.13618i | 0.981649 | + | 0.190697i | \(0.0610747\pi\) |
−0.325676 | + | 0.945481i | \(0.605592\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.15462e18 | − | 1.99987e18i | 1.13944 | − | 1.97357i | ||||
\(590\) | 4.04688e17 | − | 7.00940e17i | 0.394987 | − | 0.684137i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.07537e17 | + | 1.86260e17i | 0.102676 | + | 0.177839i | ||||
\(593\) | 1.53388e18 | 1.44855 | 0.724277 | − | 0.689509i | \(-0.242174\pi\) | ||||
0.724277 | + | 0.689509i | \(0.242174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.55069e17 | 0.605239 | ||||||||
\(596\) | 4.51167e16 | + | 7.81445e16i | 0.0412322 | + | 0.0714163i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.43723e17 | + | 2.48935e17i | −0.128519 | + | 0.222602i | ||||
\(599\) | −4.15847e17 | + | 7.20268e17i | −0.367840 | + | 0.637118i | −0.989228 | − | 0.146386i | \(-0.953236\pi\) |
0.621388 | + | 0.783503i | \(0.286569\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.69383e17 | + | 6.39790e17i | 0.319737 | + | 0.553800i | 0.980433 | − | 0.196853i | \(-0.0630722\pi\) |
−0.660696 | + | 0.750653i | \(0.729739\pi\) | |||||||
\(602\) | 6.21953e17 | 0.532574 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.71625e17 | 0.143827 | ||||||||
\(605\) | −3.22335e17 | − | 5.58301e17i | −0.267238 | − | 0.462870i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.65998e16 | − | 1.67316e17i | 0.0783880 | − | 0.135772i | −0.824167 | − | 0.566347i | \(-0.808356\pi\) |
0.902555 | + | 0.430575i | \(0.141689\pi\) | |||||||
\(608\) | −1.52793e17 | + | 2.64646e17i | −0.122668 | + | 0.212467i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.00774e17 | − | 3.47751e17i | −0.157784 | − | 0.273290i | ||||
\(611\) | −5.28772e16 | −0.0411150 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.81666e18 | −1.38286 | −0.691432 | − | 0.722441i | \(-0.743020\pi\) | ||||
−0.691432 | + | 0.722441i | \(0.743020\pi\) | |||||||
\(614\) | 1.55473e17 | + | 2.69287e17i | 0.117101 | + | 0.202825i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.57948e16 | + | 1.48601e17i | −0.0632683 | + | 0.109584i | ||||
\(617\) | −1.96368e17 | + | 3.40119e17i | −0.143290 | + | 0.248186i | −0.928734 | − | 0.370747i | \(-0.879102\pi\) |
0.785443 | + | 0.618934i | \(0.212435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.15858e17 | − | 2.00672e17i | −0.0827822 | − | 0.143383i | 0.821662 | − | 0.569975i | \(-0.193047\pi\) |
−0.904444 | + | 0.426592i | \(0.859714\pi\) | |||||||
\(620\) | 7.26339e17 | 0.513562 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.96998e17 | −0.344126 | ||||||||
\(623\) | 8.81512e17 | + | 1.52682e18i | 0.604026 | + | 1.04620i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.54363e16 | − | 2.67365e16i | 0.0103591 | − | 0.0179426i | ||||
\(626\) | 7.98764e17 | − | 1.38350e18i | 0.530500 | − | 0.918853i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.76222e17 | + | 4.78431e17i | 0.179689 | + | 0.311230i | ||||
\(629\) | 1.31586e18 | 0.847193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.03856e18 | −1.91636 | −0.958180 | − | 0.286165i | \(-0.907620\pi\) | ||||
−0.958180 | + | 0.286165i | \(0.907620\pi\) | |||||||
\(632\) | 3.96744e17 | + | 6.87181e17i | 0.247656 | + | 0.428953i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.43678e16 | − | 5.95267e16i | 0.0210170 | − | 0.0364026i | ||||
\(635\) | −6.85882e17 | + | 1.18798e18i | −0.415165 | + | 0.719086i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00997e17 | − | 1.74932e17i | −0.0598966 | − | 0.103744i | ||||
\(638\) | 4.99863e17 | 0.293438 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −9.61177e16 | −0.0552883 | ||||||||
\(641\) | −1.47678e18 | − | 2.55785e18i | −0.840887 | − | 1.45646i | −0.889145 | − | 0.457625i | \(-0.848700\pi\) |
0.0482578 | − | 0.998835i | \(-0.484633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.96115e17 | + | 1.03250e18i | −0.332628 | + | 0.576129i | −0.983026 | − | 0.183465i | \(-0.941269\pi\) |
0.650398 | + | 0.759593i | \(0.274602\pi\) | |||||||
\(644\) | 1.54487e17 | − | 2.67579e17i | 0.0853362 | − | 0.147807i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.34819e17 | + | 1.61915e18i | 0.506076 | + | 0.876550i | ||||
\(647\) | −2.23653e18 | −1.19866 | −0.599331 | − | 0.800502i | \(-0.704567\pi\) | ||||
−0.599331 | + | 0.800502i | \(0.704567\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.29711e18 | 0.681375 | ||||||||
\(650\) | −4.13428e17 | − | 7.16079e17i | −0.215012 | − | 0.372412i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.39264e17 | + | 5.87623e17i | −0.172953 | + | 0.299564i | ||||
\(653\) | −2.19229e17 | + | 3.79715e17i | −0.110653 | + | 0.191656i | −0.916034 | − | 0.401102i | \(-0.868627\pi\) |
0.805381 | + | 0.592758i | \(0.201961\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.49133e17 | − | 1.12433e18i | −0.321192 | − | 0.556322i | ||||
\(656\) | 7.90915e16 | 0.0387485 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.68374e16 | 0.0273002 | ||||||||
\(659\) | 6.64942e17 | + | 1.15171e18i | 0.316248 | + | 0.547758i | 0.979702 | − | 0.200459i | \(-0.0642434\pi\) |
−0.663454 | + | 0.748217i | \(0.730910\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.57315e17 | + | 4.45682e17i | −0.119993 | + | 0.207834i | −0.919765 | − | 0.392471i | \(-0.871620\pi\) |
0.799772 | + | 0.600304i | \(0.204954\pi\) | |||||||
\(662\) | −1.19650e18 | + | 2.07239e18i | −0.552503 | + | 0.956963i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.21237e17 | + | 2.09989e17i | 0.0548964 | + | 0.0950833i | ||||
\(665\) | −1.81627e18 | −0.814402 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9.00081e17 | −0.395789 | ||||||||
\(668\) | −3.31818e17 | − | 5.74725e17i | −0.144495 | − | 0.250273i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 6.11818e17 | − | 1.05970e18i | 0.261298 | − | 0.452581i | ||||
\(671\) | 3.21762e17 | − | 5.57307e17i | 0.136094 | − | 0.235721i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.89072e18 | + | 3.27482e18i | 0.784384 | + | 1.35859i | 0.929366 | + | 0.369159i | \(0.120354\pi\) |
−0.144982 | + | 0.989434i | \(0.546312\pi\) | |||||||
\(674\) | 5.70089e17 | 0.234236 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.37579e15 | −0.000957534 | ||||||||
\(677\) | −8.47886e17 | − | 1.46858e18i | −0.338463 | − | 0.586235i | 0.645681 | − | 0.763607i | \(-0.276574\pi\) |
−0.984144 | + | 0.177372i | \(0.943240\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.75100e17 | + | 3.03282e17i | −0.0685696 | + | 0.118766i | ||||
\(680\) | −2.94033e17 | + | 5.09280e17i | −0.114048 | + | 0.197537i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.82017e17 | + | 1.00808e18i | 0.221481 | + | 0.383617i | ||||
\(683\) | −3.06899e18 | −1.15681 | −0.578404 | − | 0.815750i | \(-0.696324\pi\) | ||||
−0.578404 | + | 0.815750i | \(0.696324\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.93118e18 | 1.08406 | ||||||||
\(686\) | 1.01393e18 | + | 1.75618e18i | 0.371451 | + | 0.643372i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.79168e17 | + | 4.83533e17i | −0.100355 | + | 0.173821i | ||||
\(689\) | 5.16938e17 | − | 8.95363e17i | 0.184083 | − | 0.318841i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.86999e17 | + | 4.97097e17i | 0.100294 | + | 0.173714i | 0.911806 | − | 0.410622i | \(-0.134688\pi\) |
−0.811512 | + | 0.584336i | \(0.801355\pi\) | |||||||
\(692\) | 1.09757e18 | 0.379964 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.13916e18 | 0.387033 | ||||||||
\(695\) | −1.62610e18 | − | 2.81649e18i | −0.547326 | − | 0.947996i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.41948e17 | − | 4.19067e17i | 0.0799299 | − | 0.138443i | ||||
\(698\) | −1.29907e18 | + | 2.25005e18i | −0.425179 | + | 0.736431i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.44392e17 | + | 7.69709e17i | 0.142767 | + | 0.247280i | ||||
\(701\) | −5.78307e18 | −1.84073 | −0.920367 | − | 0.391056i | \(-0.872110\pi\) | ||||
−0.920367 | + | 0.391056i | \(0.872110\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −3.64841e18 | −1.13997 | ||||||||
\(704\) | −7.70193e16 | − | 1.33401e17i | −0.0238439 | − | 0.0412989i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.61736e18 | + | 2.80135e18i | −0.491560 | + | 0.851406i | ||||
\(707\) | −1.79901e18 | + | 3.11598e18i | −0.541762 | + | 0.938359i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.04576e18 | − | 1.81130e18i | −0.309193 | − | 0.535538i | 0.668993 | − | 0.743269i | \(-0.266726\pi\) |
−0.978186 | + | 0.207731i | \(0.933392\pi\) | |||||||
\(710\) | 2.29977e18 | 0.673760 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.58269e18 | −0.455278 | ||||||||
\(713\) | −1.04801e18 | − | 1.81521e18i | −0.298734 | − | 0.517422i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.25872e17 | + | 7.37632e17i | −0.119204 | + | 0.206467i | ||||
\(716\) | 1.66781e18 | − | 2.88872e18i | 0.462605 | − | 0.801256i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.31842e18 | − | 2.28356e18i | −0.359123 | − | 0.622020i | ||||
\(719\) | 2.54253e18 | 0.686321 | 0.343161 | − | 0.939277i | \(-0.388502\pi\) | ||||
0.343161 | + | 0.939277i | \(0.388502\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.11509e18 | 0.295618 | ||||||||
\(722\) | −1.24621e18 | − | 2.15850e18i | −0.327416 | − | 0.567101i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.39791e18 | − | 2.42125e18i | 0.360726 | − | 0.624796i | ||||
\(725\) | 1.29457e18 | − | 2.24226e18i | 0.331077 | − | 0.573442i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −2.67471e18 | − | 4.63273e18i | −0.671897 | − | 1.16376i | −0.977366 | − | 0.211557i | \(-0.932147\pi\) |
0.305469 | − | 0.952202i | \(-0.401187\pi\) | |||||||
\(728\) | −1.33093e18 | −0.331362 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.27970e18 | 0.557545 | ||||||||
\(731\) | 1.70800e18 | + | 2.95835e18i | 0.414024 | + | 0.717111i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.07526e17 | − | 8.79060e17i | 0.120860 | − | 0.209335i | −0.799247 | − | 0.601003i | \(-0.794768\pi\) |
0.920107 | + | 0.391667i | \(0.128101\pi\) | |||||||
\(734\) | 1.22924e18 | − | 2.12911e18i | 0.290143 | − | 0.502543i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.38685e17 | + | 2.40210e17i | 0.0321606 | + | 0.0557038i | ||||
\(737\) | 1.96100e18 | 0.450754 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.21697e18 | −0.952384 | −0.476192 | − | 0.879341i | \(-0.657983\pi\) | ||||
−0.476192 | + | 0.879341i | \(0.657983\pi\) | |||||||
\(740\) | −5.73776e17 | − | 9.93809e17i | −0.128451 | − | 0.222483i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.55654e17 | + | 9.62420e17i | −0.122230 | + | 0.211709i | ||||
\(743\) | 6.27655e17 | − | 1.08713e18i | 0.136865 | − | 0.237058i | −0.789443 | − | 0.613824i | \(-0.789631\pi\) |
0.926309 | + | 0.376766i | \(0.122964\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.40725e17 | − | 4.16948e17i | −0.0515829 | − | 0.0893441i | ||||
\(746\) | −3.35846e18 | −0.713407 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.42437e17 | −0.196740 | ||||||||
\(749\) | 4.22940e18 | + | 7.32553e18i | 0.875279 | + | 1.51603i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.76700e18 | + | 8.25669e18i | −0.969584 | + | 1.67937i | −0.272826 | + | 0.962064i | \(0.587958\pi\) |
−0.696759 | + | 0.717306i | \(0.745375\pi\) | |||||||
\(752\) | −2.55119e16 | + | 4.41879e16i | −0.00514430 | + | 0.00891020i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.93859e18 | + | 3.35774e18i | 0.384214 | + | 0.665478i | ||||
\(755\) | −9.15722e17 | −0.179932 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.60869e18 | 1.66270 | 0.831350 | − | 0.555749i | \(-0.187569\pi\) | ||||
0.831350 | + | 0.555749i | \(0.187569\pi\) | |||||||
\(758\) | 1.21639e18 | + | 2.10684e18i | 0.232928 | + | 0.403443i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.15245e17 | − | 1.41205e18i | 0.153462 | − | 0.265803i | ||||
\(761\) | 2.59150e18 | − | 4.48862e18i | 0.483673 | − | 0.837746i | −0.516151 | − | 0.856497i | \(-0.672636\pi\) |
0.999824 | + | 0.0187517i | \(0.00596919\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.94248e18 | − | 5.09653e18i | −0.539889 | − | 0.935116i | ||||
\(764\) | 2.43402e18 | 0.442809 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.22722e18 | 0.219500 | ||||||||
\(767\) | 5.03052e18 | + | 8.71311e18i | 0.892160 | + | 1.54527i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.02951e18 | − | 3.51522e18i | 0.353892 | − | 0.612959i | −0.633036 | − | 0.774123i | \(-0.718191\pi\) |
0.986928 | + | 0.161164i | \(0.0515247\pi\) | |||||||
\(770\) | 4.57767e17 | − | 7.92876e17i | 0.0791507 | − | 0.137093i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.71116e18 | − | 2.96382e18i | −0.290923 | − | 0.503894i | ||||
\(773\) | −1.51385e18 | −0.255221 | −0.127610 | − | 0.991824i | \(-0.540731\pi\) | ||||
−0.127610 | + | 0.991824i | \(0.540731\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.02935e18 | 0.999561 | ||||||||
\(776\) | −1.57190e17 | − | 2.72260e17i | −0.0258418 | − | 0.0447593i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.40112e18 | + | 4.15886e18i | −0.388192 | + | 0.672369i | ||||
\(779\) | −6.70833e17 | + | 1.16192e18i | −0.107553 | + | 0.186287i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.84281e18 | + | 3.19184e18i | 0.290569 | + | 0.503280i | ||||
\(782\) | 1.69700e18 | 0.265362 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.94914e17 | −0.0299770 | ||||||||
\(785\) | −1.47381e18 | − | 2.55272e18i | −0.224797 | − | 0.389359i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.55698e18 | − | 4.42882e18i | 0.383612 | − | 0.664435i | −0.607964 | − | 0.793965i | \(-0.708013\pi\) |
0.991576 | + | 0.129530i | \(0.0413467\pi\) | |||||||
\(788\) | −1.87136e18 | + | 3.24128e18i | −0.278443 | + | 0.482277i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.11687e18 | − | 3.66652e18i | −0.309826 | − | 0.536634i | ||||
\(791\) | 4.30486e18 | 0.624902 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.99149e18 | 0.712778 | ||||||||
\(794\) | −2.12093e18 | − | 3.67356e18i | −0.300396 | − | 0.520301i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.08508e18 | − | 1.87941e18i | 0.151191 | − | 0.261871i | ||||
\(797\) | 5.54336e18 | − | 9.60138e18i | 0.766115 | − | 1.32695i | −0.173540 | − | 0.984827i | \(-0.555521\pi\) |
0.939655 | − | 0.342123i | \(-0.111146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.56086e17 | + | 2.70350e17i | 0.0212232 | + | 0.0367597i | ||||
\(800\) | −7.97874e17 | −0.107609 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.09578e17 | 0.0808902 | ||||||||
\(803\) | 1.82673e18 | + | 3.16399e18i | 0.240449 | + | 0.416471i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −8.24281e17 | + | 1.42770e18i | −0.106758 | + | 0.184911i | ||||
\(806\) | −4.51441e18 | + | 7.81919e18i | −0.579994 | + | 1.00458i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.61500e18 | − | 2.79727e18i | −0.204174 | − | 0.353639i | ||||
\(809\) | 1.01551e19 | 1.27356 | 0.636778 | − | 0.771047i | \(-0.280267\pi\) | ||||
0.636778 | + | 0.771047i | \(0.280267\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.70589e18 | 1.07443 | 0.537214 | − | 0.843446i | \(-0.319477\pi\) | ||||
0.537214 | + | 0.843446i | \(0.319477\pi\) | |||||||
\(812\) | −2.08378e18 | − | 3.60922e18i | −0.255116 | − | 0.441874i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 9.19536e17 | − | 1.59268e18i | 0.110792 | − | 0.191898i | ||||
\(815\) | 1.81018e18 | − | 3.13532e18i | 0.216370 | − | 0.374764i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.73566e18 | − | 8.20241e18i | −0.557105 | − | 0.964935i | ||||
\(818\) | 1.10225e18 | 0.128642 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.22001e17 | −0.0484756 | ||||||||
\(821\) | 3.57522e17 | + | 6.19247e17i | 0.0407448 | + | 0.0705721i | 0.885679 | − | 0.464299i | \(-0.153694\pi\) |
−0.844934 | + | 0.534871i | \(0.820360\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.22452e18 | + | 1.07812e19i | −0.698244 | + | 1.20939i | 0.270831 | + | 0.962627i | \(0.412701\pi\) |
−0.969075 | + | 0.246767i | \(0.920632\pi\) | |||||||
\(824\) | −5.00517e17 | + | 8.66922e17i | −0.0557048 | + | 0.0964835i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.40727e18 | − | 9.36567e18i | −0.592390 | − | 1.02605i | ||||
\(827\) | −4.42505e18 | −0.480986 | −0.240493 | − | 0.970651i | \(-0.577309\pi\) | ||||
−0.240493 | + | 0.970651i | \(0.577309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.96050e18 | 0.209779 | 0.104890 | − | 0.994484i | \(-0.466551\pi\) | ||||
0.104890 | + | 0.994484i | \(0.466551\pi\) | |||||||
\(830\) | −6.46874e17 | − | 1.12042e18i | −0.0686771 | − | 0.118952i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.97400e17 | − | 1.03473e18i | 0.0624401 | − | 0.108149i | ||||
\(833\) | −5.96260e17 | + | 1.03275e18i | −0.0618363 | + | 0.107104i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.77045e18 | + | 3.06651e18i | 0.180768 | + | 0.313099i | ||||
\(836\) | 2.61303e18 | 0.264730 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.14658e18 | 0.912373 | ||||||||
\(839\) | −4.88000e18 | − | 8.45241e18i | −0.483022 | − | 0.836619i | 0.516788 | − | 0.856114i | \(-0.327128\pi\) |
−0.999810 | + | 0.0194945i | \(0.993794\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.40017e17 | + | 1.62816e18i | −0.0916139 | + | 0.158680i | ||||
\(842\) | −3.39818e18 | + | 5.88582e18i | −0.328638 | + | 0.569218i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.11981e16 | + | 1.40639e17i | 0.00773250 | + | 0.0133931i | ||||
\(845\) | 1.26763e16 | 0.00119791 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.61382e18 | −0.801592 | ||||||||
\(848\) | −4.98819e17 | − | 8.63980e17i | −0.0460649 | − | 0.0797867i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.44077e18 | + | 4.22754e18i | −0.221975 | + | 0.384472i | ||||
\(851\) | −1.65577e18 | + | 2.86787e18i | −0.149437 | + | 0.258832i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.17246e18 | + | 2.03076e18i | 0.104215 | + | 0.180506i | 0.913417 | − | 0.407025i | \(-0.133434\pi\) |
−0.809202 | + | 0.587530i | \(0.800100\pi\) | |||||||
\(854\) | −5.36532e18 | −0.473281 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.59359e18 | −0.659732 | ||||||||
\(857\) | 5.33861e18 | + | 9.24675e18i | 0.460313 | + | 0.797285i | 0.998976 | − | 0.0452360i | \(-0.0144040\pi\) |
−0.538664 | + | 0.842521i | \(0.681071\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.60207e18 | − | 1.48992e19i | 0.730546 | − | 1.26534i | −0.226105 | − | 0.974103i | \(-0.572599\pi\) |
0.956650 | − | 0.291239i | \(-0.0940675\pi\) | |||||||
\(860\) | 1.48953e18 | − | 2.57994e18i | 0.125548 | − | 0.217455i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.13286e18 | − | 5.42627e18i | −0.260102 | − | 0.450510i | ||||
\(863\) | 1.42851e18 | 0.117710 | 0.0588548 | − | 0.998267i | \(-0.481255\pi\) | ||||
0.0588548 | + | 0.998267i | \(0.481255\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.85620e18 | −0.475348 | ||||||||
\(866\) | −3.25953e18 | − | 5.64568e18i | −0.262597 | − | 0.454831i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.85252e18 | − | 8.40481e18i | 0.385114 | − | 0.667036i | ||||
\(869\) | 3.39250e18 | − | 5.87599e18i | 0.267234 | − | 0.462863i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.60526e18 | + | 1.31727e19i | 0.590196 | + | 1.02225i | ||||
\(872\) | 5.28303e18 | 0.406936 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.70517e18 | −0.357068 | ||||||||
\(875\) | −6.26625e18 | − | 1.08535e19i | −0.472015 | − | 0.817553i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.22801e18 | + | 1.07872e19i | −0.462223 | + | 0.800594i | −0.999071 | − | 0.0430847i | \(-0.986281\pi\) |
0.536848 | + | 0.843679i | \(0.319615\pi\) | |||||||
\(878\) | −4.96469e18 | + | 8.59909e18i | −0.365744 | + | 0.633488i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.10945e17 | + | 7.11777e17i | 0.0298295 | + | 0.0516662i | ||||
\(881\) | 3.63494e18 | 0.261911 | 0.130956 | − | 0.991388i | \(-0.458195\pi\) | ||||
0.130956 | + | 0.991388i | \(0.458195\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.55878e18 | −0.110673 | −0.0553364 | − | 0.998468i | \(-0.517623\pi\) | ||||
−0.0553364 | + | 0.998468i | \(0.517623\pi\) | |||||||
\(884\) | −3.65501e18 | − | 6.33066e18i | −0.257601 | − | 0.446179i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.62762e17 | + | 4.55116e17i | −0.0182491 | + | 0.0316085i | ||||
\(887\) | 4.28354e18 | − | 7.41931e18i | 0.295325 | − | 0.511517i | −0.679736 | − | 0.733457i | \(-0.737906\pi\) |
0.975060 | + | 0.221940i | \(0.0712389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9.16447e18 | + | 1.58733e19i | 0.622653 | + | 1.07847i | ||||
\(890\) | 8.44462e18 | 0.569568 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.36954e19 | −0.910337 | ||||||||
\(893\) | −4.32770e17 | − | 7.49580e17i | −0.0285577 | − | 0.0494634i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.89875e18 | + | 1.54131e19i | −0.578734 | + | 1.00240i | ||||
\(896\) | −6.42142e17 | + | 1.11222e18i | −0.0414600 | + | 0.0718108i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −9.40801e17 | − | 1.62952e18i | −0.0598690 | − | 0.103696i | ||||
\(899\) | −2.82720e19 | −1.78615 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.10373e18 | −0.380088 | ||||||||
\(902\) | −3.38150e17 | − | 5.85693e17i | −0.0209058 | − | 0.0362099i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.93227e18 | + | 3.34679e18i | −0.117753 | + | 0.203954i | ||||
\(905\) | −7.45868e18 | + | 1.29188e19i | −0.451280 | + | 0.781640i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.41915e18 | − | 5.92214e18i | −0.203925 | − | 0.353209i | 0.745865 | − | 0.666098i | \(-0.232037\pi\) |
−0.949790 | + | 0.312889i | \(0.898703\pi\) | |||||||
\(908\) | −6.41749e18 | −0.380021 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.10134e18 | 0.414545 | ||||||||
\(911\) | 2.67920e18 | + | 4.64050e18i | 0.155287 | + | 0.268965i | 0.933163 | − | 0.359452i | \(-0.117036\pi\) |
−0.777876 | + | 0.628417i | \(0.783703\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.03668e18 | − | 1.79559e18i | 0.0592360 | − | 0.102600i | ||||
\(914\) | −8.16744e18 | + | 1.41464e19i | −0.463378 | + | 0.802594i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 7.92519e18 | + | 1.37268e19i | 0.443291 | + | 0.767803i | ||||
\(917\) | −1.73469e19 | −0.963432 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.65287e19 | 1.45266 | 0.726332 | − | 0.687344i | \(-0.241224\pi\) | ||||
0.726332 | + | 0.687344i | \(0.241224\pi\) | |||||||
\(920\) | −7.39969e17 | − | 1.28166e18i | −0.0402340 | − | 0.0696873i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.93608e18 | + | 6.81748e18i | −0.211015 | + | 0.365488i | ||||
\(923\) | −1.42938e19 | + | 2.47575e19i | −0.760914 | + | 1.31794i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.76292e18 | − | 8.24962e18i | −0.250007 | − | 0.433025i | ||||
\(926\) | −3.36976e18 | −0.175642 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.74129e18 | 0.192291 | ||||||||
\(929\) | 1.11800e18 | + | 1.93644e18i | 0.0570613 | + | 0.0988330i | 0.893145 | − | 0.449769i | \(-0.148494\pi\) |
−0.836084 | + | 0.548602i | \(0.815160\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.65321e18 | − | 2.86344e18i | 0.0832061 | − | 0.144117i | ||||
\(932\) | 1.04321e18 | − | 1.80690e18i | 0.0521398 | − | 0.0903087i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.07297e19 | + | 1.85844e19i | 0.528850 | + | 0.915996i | ||||
\(935\) | 5.02847e18 | 0.246128 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.93409e18 | −0.479536 | −0.239768 | − | 0.970830i | \(-0.577071\pi\) | ||||
−0.239768 | + | 0.970830i | \(0.577071\pi\) | |||||||
\(938\) | −8.17485e18 | − | 1.41593e19i | −0.391888 | − | 0.678769i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.36121e17 | − | 2.35769e17i | 0.00643569 | − | 0.0111469i | ||||
\(941\) | 1.37093e18 | − | 2.37453e18i | 0.0643700 | − | 0.111492i | −0.832044 | − | 0.554709i | \(-0.812830\pi\) |
0.896414 | + | 0.443217i | \(0.146163\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.08892e17 | + | 1.05463e18i | 0.0281977 | + | 0.0488399i | ||||
\(944\) | 9.70838e18 | 0.446508 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.77426e18 | 0.216578 | ||||||||
\(947\) | 6.52057e18 | + | 1.12940e19i | 0.293772 | + | 0.508828i | 0.974698 | − | 0.223524i | \(-0.0717560\pi\) |
−0.680926 | + | 0.732352i | \(0.738423\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.41690e19 | + | 2.45415e19i | −0.629666 | + | 1.09061i | ||||
\(950\) | 6.76736e18 | − | 1.17214e19i | 0.298687 | − | 0.517341i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.92874e18 | + | 6.80479e18i | 0.171046 | + | 0.296261i | ||||
\(953\) | −1.23319e19 | −0.533243 | −0.266621 | − | 0.963801i | \(-0.585907\pi\) | ||||
−0.266621 | + | 0.963801i | \(0.585907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.29869e19 | −0.553969 | ||||||||
\(956\) | 3.25499e18 | + | 5.63781e18i | 0.137903 | + | 0.238855i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.23707e18 | + | 1.42670e19i | −0.344268 | + | 0.596290i | ||||
\(959\) | 1.95826e19 | − | 3.39181e19i | 0.812924 | − | 1.40803i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.07099e19 | − | 3.58705e19i | −0.848155 | − | 1.46905i | ||||
\(962\) | 1.42648e19 | 0.580265 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.62010e18 | −0.0650193 | ||||||||
\(965\) | 9.13008e18 | + | 1.58138e19i | 0.363954 | + | 0.630388i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.53868e19 | − | 2.66507e19i | 0.605167 | − | 1.04818i | −0.386858 | − | 0.922139i | \(-0.626440\pi\) |
0.992025 | − | 0.126041i | \(-0.0402270\pi\) | |||||||
\(968\) | 3.86638e18 | − | 6.69677e18i | 0.151048 | − | 0.261623i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.38702e17 | + | 1.45267e18i | 0.0323289 | + | 0.0559953i | ||||
\(971\) | 2.27430e19 | 0.870809 | 0.435404 | − | 0.900235i | \(-0.356605\pi\) | ||||
0.435404 | + | 0.900235i | \(0.356605\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.34545e19 | −1.64173 | ||||||||
\(974\) | 5.05483e18 | + | 8.75521e18i | 0.189702 | + | 0.328574i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.40826e18 | − | 4.17124e18i | 0.0891827 | − | 0.154469i | ||||
\(977\) | −1.35929e18 | + | 2.35436e18i | −0.0500033 | + | 0.0866082i | −0.889944 | − | 0.456070i | \(-0.849257\pi\) |
0.839940 | + | 0.542679i | \(0.182590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.76670e18 | + | 1.17203e19i | 0.245634 | + | 0.425451i | ||||
\(980\) | 1.03998e18 | 0.0375022 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.23905e19 | 0.440924 | ||||||||
\(983\) | −1.05770e19 | − | 1.83199e19i | −0.373908 | − | 0.647627i | 0.616255 | − | 0.787546i | \(-0.288649\pi\) |
−0.990163 | + | 0.139920i | \(0.955316\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.98481e18 | − | 1.72942e19i | 0.348341 | − | 0.603344i | ||||
\(986\) | 1.14449e19 | − | 1.98232e19i | 0.396656 | − | 0.687028i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.01340e19 | + | 1.75526e19i | 0.346625 | + | 0.600372i | ||||
\(989\) | −8.59679e18 | −0.292119 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.51495e19 | −0.843434 | −0.421717 | − | 0.906727i | \(-0.638572\pi\) | ||||
−0.421717 | + | 0.906727i | \(0.638572\pi\) | |||||||
\(992\) | 4.35618e18 | + | 7.54512e18i | 0.145138 | + | 0.251386i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.53643e19 | − | 2.66117e19i | 0.505244 | − | 0.875108i | ||||
\(995\) | −5.78955e18 | + | 1.00278e19i | −0.189145 | + | 0.327609i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.35308e18 | + | 4.07565e18i | 0.0758783 | + | 0.131425i | 0.901468 | − | 0.432846i | \(-0.142491\pi\) |
−0.825590 | + | 0.564271i | \(0.809157\pi\) | |||||||
\(998\) | 2.60849e19 | 0.835683 | ||||||||
\(999\) | 0 | 0 |
(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 | 54.14.c.a.37.4 | 12 | ||
3.2 | odd | 2 | 18.14.c.a.13.1 | yes | 12 | ||
9.2 | odd | 6 | 18.14.c.a.7.1 | ✓ | 12 | ||
9.4 | even | 3 | 162.14.a.h.1.3 | 6 | |||
9.5 | odd | 6 | 162.14.a.e.1.4 | 6 | |||
9.7 | even | 3 | inner | 54.14.c.a.19.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
18.14.c.a.7.1 | ✓ | 12 | 9.2 | odd | 6 | ||
18.14.c.a.13.1 | yes | 12 | 3.2 | odd | 2 | ||
54.14.c.a.19.4 | 12 | 9.7 | even | 3 | inner | ||
54.14.c.a.37.4 | 12 | 1.1 | even | 1 | trivial | ||
162.14.a.e.1.4 | 6 | 9.5 | odd | 6 | |||
162.14.a.h.1.3 | 6 | 9.4 | even | 3 |