Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [11,18,Mod(1,11)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(11, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("11.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 11 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 11.a (trivial) |
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: | yes |
Analytic conductor: | \(20.1544296079\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 715858 x^{6} - 57426812 x^{5} + 132277346400 x^{4} + 17831801296448 x^{3} + \cdots + 70\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{5}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(713.940\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 11.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −681.940 | −1.88361 | −0.941805 | − | 0.336159i | \(-0.890872\pi\) | ||||
−0.941805 | + | 0.336159i | \(0.890872\pi\) | |||||||
\(3\) | −16808.1 | −1.47907 | −0.739536 | − | 0.673117i | \(-0.764955\pi\) | ||||
−0.739536 | + | 0.673117i | \(0.764955\pi\) | |||||||
\(4\) | 333970. | 2.54799 | ||||||||
\(5\) | 1.17558e6 | 1.34588 | 0.672941 | − | 0.739696i | \(-0.265031\pi\) | ||||
0.672941 | + | 0.739696i | \(0.265031\pi\) | |||||||
\(6\) | 1.14621e7 | 2.78599 | ||||||||
\(7\) | −2.07343e7 | −1.35942 | −0.679712 | − | 0.733479i | \(-0.737895\pi\) | ||||
−0.679712 | + | 0.733479i | \(0.737895\pi\) | |||||||
\(8\) | −1.38364e8 | −2.91581 | ||||||||
\(9\) | 1.53374e8 | 1.18765 | ||||||||
\(10\) | −8.01675e8 | −2.53512 | ||||||||
\(11\) | 2.14359e8 | 0.301511 | ||||||||
\(12\) | −5.61341e9 | −3.76866 | ||||||||
\(13\) | 5.57006e8 | 0.189383 | 0.0946915 | − | 0.995507i | \(-0.469814\pi\) | ||||
0.0946915 | + | 0.995507i | \(0.469814\pi\) | |||||||
\(14\) | 1.41395e10 | 2.56063 | ||||||||
\(15\) | −1.97593e10 | −1.99066 | ||||||||
\(16\) | 5.05819e10 | 2.94425 | ||||||||
\(17\) | −4.13492e10 | −1.43764 | −0.718822 | − | 0.695194i | \(-0.755318\pi\) | ||||
−0.718822 | + | 0.695194i | \(0.755318\pi\) | |||||||
\(18\) | −1.04592e11 | −2.23708 | ||||||||
\(19\) | −7.69786e10 | −1.03983 | −0.519917 | − | 0.854217i | \(-0.674037\pi\) | ||||
−0.519917 | + | 0.854217i | \(0.674037\pi\) | |||||||
\(20\) | 3.92608e11 | 3.42929 | ||||||||
\(21\) | 3.48504e11 | 2.01069 | ||||||||
\(22\) | −1.46180e11 | −0.567930 | ||||||||
\(23\) | −1.06545e11 | −0.283692 | −0.141846 | − | 0.989889i | \(-0.545304\pi\) | ||||
−0.141846 | + | 0.989889i | \(0.545304\pi\) | |||||||
\(24\) | 2.32564e12 | 4.31268 | ||||||||
\(25\) | 6.19049e11 | 0.811400 | ||||||||
\(26\) | −3.79844e11 | −0.356724 | ||||||||
\(27\) | −4.07322e11 | −0.277553 | ||||||||
\(28\) | −6.92461e12 | −3.46380 | ||||||||
\(29\) | −2.21603e12 | −0.822609 | −0.411304 | − | 0.911498i | \(-0.634927\pi\) | ||||
−0.411304 | + | 0.911498i | \(0.634927\pi\) | |||||||
\(30\) | 1.34747e13 | 3.74962 | ||||||||
\(31\) | 1.88738e12 | 0.397452 | 0.198726 | − | 0.980055i | \(-0.436320\pi\) | ||||
0.198726 | + | 0.980055i | \(0.436320\pi\) | |||||||
\(32\) | −1.63581e13 | −2.63002 | ||||||||
\(33\) | −3.60298e12 | −0.445957 | ||||||||
\(34\) | 2.81977e13 | 2.70796 | ||||||||
\(35\) | −2.43748e13 | −1.82963 | ||||||||
\(36\) | 5.12222e13 | 3.02613 | ||||||||
\(37\) | 1.71018e12 | 0.0800435 | 0.0400218 | − | 0.999199i | \(-0.487257\pi\) | ||||
0.0400218 | + | 0.999199i | \(0.487257\pi\) | |||||||
\(38\) | 5.24947e13 | 1.95864 | ||||||||
\(39\) | −9.36223e12 | −0.280111 | ||||||||
\(40\) | −1.62658e14 | −3.92433 | ||||||||
\(41\) | 4.62083e13 | 0.903768 | 0.451884 | − | 0.892077i | \(-0.350752\pi\) | ||||
0.451884 | + | 0.892077i | \(0.350752\pi\) | |||||||
\(42\) | −2.37659e14 | −3.78735 | ||||||||
\(43\) | 3.90310e13 | 0.509246 | 0.254623 | − | 0.967040i | \(-0.418049\pi\) | ||||
0.254623 | + | 0.967040i | \(0.418049\pi\) | |||||||
\(44\) | 7.15894e13 | 0.768247 | ||||||||
\(45\) | 1.80303e14 | 1.59844 | ||||||||
\(46\) | 7.26573e13 | 0.534364 | ||||||||
\(47\) | −1.67719e14 | −1.02743 | −0.513714 | − | 0.857961i | \(-0.671731\pi\) | ||||
−0.513714 | + | 0.857961i | \(0.671731\pi\) | |||||||
\(48\) | −8.50188e14 | −4.35476 | ||||||||
\(49\) | 1.97279e14 | 0.848034 | ||||||||
\(50\) | −4.22154e14 | −1.52836 | ||||||||
\(51\) | 6.95004e14 | 2.12638 | ||||||||
\(52\) | 1.86023e14 | 0.482546 | ||||||||
\(53\) | 2.26137e14 | 0.498915 | 0.249458 | − | 0.968386i | \(-0.419748\pi\) | ||||
0.249458 | + | 0.968386i | \(0.419748\pi\) | |||||||
\(54\) | 2.77769e14 | 0.522801 | ||||||||
\(55\) | 2.51996e14 | 0.405799 | ||||||||
\(56\) | 2.86888e15 | 3.96382 | ||||||||
\(57\) | 1.29387e15 | 1.53799 | ||||||||
\(58\) | 1.51120e15 | 1.54947 | ||||||||
\(59\) | −1.73463e15 | −1.53803 | −0.769017 | − | 0.639229i | \(-0.779254\pi\) | ||||
−0.769017 | + | 0.639229i | \(0.779254\pi\) | |||||||
\(60\) | −6.59902e15 | −5.07217 | ||||||||
\(61\) | 1.80557e15 | 1.20590 | 0.602949 | − | 0.797780i | \(-0.293992\pi\) | ||||
0.602949 | + | 0.797780i | \(0.293992\pi\) | |||||||
\(62\) | −1.28708e15 | −0.748645 | ||||||||
\(63\) | −3.18009e15 | −1.61452 | ||||||||
\(64\) | 4.52539e15 | 2.00968 | ||||||||
\(65\) | 6.54805e14 | 0.254887 | ||||||||
\(66\) | 2.45701e15 | 0.840009 | ||||||||
\(67\) | 3.06974e15 | 0.923563 | 0.461781 | − | 0.886994i | \(-0.347210\pi\) | ||||
0.461781 | + | 0.886994i | \(0.347210\pi\) | |||||||
\(68\) | −1.38094e16 | −3.66310 | ||||||||
\(69\) | 1.79082e15 | 0.419600 | ||||||||
\(70\) | 1.66221e16 | 3.44630 | ||||||||
\(71\) | 1.54669e14 | 0.0284254 | 0.0142127 | − | 0.999899i | \(-0.495476\pi\) | ||||
0.0142127 | + | 0.999899i | \(0.495476\pi\) | |||||||
\(72\) | −2.12214e16 | −3.46297 | ||||||||
\(73\) | 1.32716e16 | 1.92610 | 0.963052 | − | 0.269315i | \(-0.0867973\pi\) | ||||
0.963052 | + | 0.269315i | \(0.0867973\pi\) | |||||||
\(74\) | −1.16624e15 | −0.150771 | ||||||||
\(75\) | −1.04051e16 | −1.20012 | ||||||||
\(76\) | −2.57085e16 | −2.64949 | ||||||||
\(77\) | −4.44457e15 | −0.409882 | ||||||||
\(78\) | 6.38448e15 | 0.527620 | ||||||||
\(79\) | 5.63148e15 | 0.417631 | 0.208815 | − | 0.977955i | \(-0.433039\pi\) | ||||
0.208815 | + | 0.977955i | \(0.433039\pi\) | |||||||
\(80\) | 5.94630e16 | 3.96262 | ||||||||
\(81\) | −1.29604e16 | −0.777133 | ||||||||
\(82\) | −3.15113e16 | −1.70235 | ||||||||
\(83\) | −2.96855e16 | −1.44671 | −0.723353 | − | 0.690478i | \(-0.757400\pi\) | ||||
−0.723353 | + | 0.690478i | \(0.757400\pi\) | |||||||
\(84\) | 1.16390e17 | 5.12320 | ||||||||
\(85\) | −4.86093e16 | −1.93490 | ||||||||
\(86\) | −2.66168e16 | −0.959221 | ||||||||
\(87\) | 3.72474e16 | 1.21670 | ||||||||
\(88\) | −2.96596e16 | −0.879148 | ||||||||
\(89\) | 4.62487e16 | 1.24533 | 0.622665 | − | 0.782488i | \(-0.286050\pi\) | ||||
0.622665 | + | 0.782488i | \(0.286050\pi\) | |||||||
\(90\) | −1.22956e17 | −3.01084 | ||||||||
\(91\) | −1.15491e16 | −0.257452 | ||||||||
\(92\) | −3.55828e16 | −0.722843 | ||||||||
\(93\) | −3.17234e16 | −0.587860 | ||||||||
\(94\) | 1.14375e17 | 1.93527 | ||||||||
\(95\) | −9.04945e16 | −1.39950 | ||||||||
\(96\) | 2.74950e17 | 3.88999 | ||||||||
\(97\) | 1.10934e17 | 1.43716 | 0.718580 | − | 0.695444i | \(-0.244792\pi\) | ||||
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(98\) | −1.34532e17 | −1.59737 | ||||||||
\(99\) | 3.28770e16 | 0.358091 | ||||||||
\(100\) | 2.06744e17 | 2.06744 | ||||||||
\(101\) | 1.99011e17 | 1.82872 | 0.914358 | − | 0.404906i | \(-0.132696\pi\) | ||||
0.914358 | + | 0.404906i | \(0.132696\pi\) | |||||||
\(102\) | −4.73951e17 | −4.00527 | ||||||||
\(103\) | 2.73079e16 | 0.212409 | 0.106204 | − | 0.994344i | \(-0.466130\pi\) | ||||
0.106204 | + | 0.994344i | \(0.466130\pi\) | |||||||
\(104\) | −7.70696e16 | −0.552204 | ||||||||
\(105\) | 4.09695e17 | 2.70615 | ||||||||
\(106\) | −1.54212e17 | −0.939761 | ||||||||
\(107\) | 5.70109e16 | 0.320772 | 0.160386 | − | 0.987054i | \(-0.448726\pi\) | ||||
0.160386 | + | 0.987054i | \(0.448726\pi\) | |||||||
\(108\) | −1.36033e17 | −0.707201 | ||||||||
\(109\) | 4.34668e16 | 0.208945 | 0.104473 | − | 0.994528i | \(-0.466685\pi\) | ||||
0.104473 | + | 0.994528i | \(0.466685\pi\) | |||||||
\(110\) | −1.71846e17 | −0.764367 | ||||||||
\(111\) | −2.87449e16 | −0.118390 | ||||||||
\(112\) | −1.04878e18 | −4.00249 | ||||||||
\(113\) | −1.72825e17 | −0.611561 | −0.305781 | − | 0.952102i | \(-0.598917\pi\) | ||||
−0.305781 | + | 0.952102i | \(0.598917\pi\) | |||||||
\(114\) | −8.82340e17 | −2.89697 | ||||||||
\(115\) | −1.25252e17 | −0.381816 | ||||||||
\(116\) | −7.40088e17 | −2.09600 | ||||||||
\(117\) | 8.54300e16 | 0.224921 | ||||||||
\(118\) | 1.18292e18 | 2.89706 | ||||||||
\(119\) | 8.57345e17 | 1.95437 | ||||||||
\(120\) | 2.73398e18 | 5.80437 | ||||||||
\(121\) | 4.59497e16 | 0.0909091 | ||||||||
\(122\) | −1.23129e18 | −2.27144 | ||||||||
\(123\) | −7.76676e17 | −1.33674 | ||||||||
\(124\) | 6.30328e17 | 1.01270 | ||||||||
\(125\) | −1.69155e17 | −0.253833 | ||||||||
\(126\) | 2.16863e18 | 3.04114 | ||||||||
\(127\) | 6.39079e17 | 0.837959 | 0.418979 | − | 0.907996i | \(-0.362388\pi\) | ||||
0.418979 | + | 0.907996i | \(0.362388\pi\) | |||||||
\(128\) | −9.41953e17 | −1.15543 | ||||||||
\(129\) | −6.56039e17 | −0.753211 | ||||||||
\(130\) | −4.46537e17 | −0.480108 | ||||||||
\(131\) | −5.08763e17 | −0.512518 | −0.256259 | − | 0.966608i | \(-0.582490\pi\) | ||||
−0.256259 | + | 0.966608i | \(0.582490\pi\) | |||||||
\(132\) | −1.20329e18 | −1.13629 | ||||||||
\(133\) | 1.59609e18 | 1.41358 | ||||||||
\(134\) | −2.09338e18 | −1.73963 | ||||||||
\(135\) | −4.78839e17 | −0.373553 | ||||||||
\(136\) | 5.72124e18 | 4.19189 | ||||||||
\(137\) | 1.75027e18 | 1.20498 | 0.602492 | − | 0.798125i | \(-0.294175\pi\) | ||||
0.602492 | + | 0.798125i | \(0.294175\pi\) | |||||||
\(138\) | −1.22123e18 | −0.790363 | ||||||||
\(139\) | −1.38318e18 | −0.841883 | −0.420942 | − | 0.907088i | \(-0.638300\pi\) | ||||
−0.420942 | + | 0.907088i | \(0.638300\pi\) | |||||||
\(140\) | −8.14044e18 | −4.66186 | ||||||||
\(141\) | 2.81905e18 | 1.51964 | ||||||||
\(142\) | −1.05475e17 | −0.0535423 | ||||||||
\(143\) | 1.19399e17 | 0.0571011 | ||||||||
\(144\) | 7.75793e18 | 3.49675 | ||||||||
\(145\) | −2.60512e18 | −1.10713 | ||||||||
\(146\) | −9.05045e18 | −3.62803 | ||||||||
\(147\) | −3.31589e18 | −1.25430 | ||||||||
\(148\) | 5.71147e17 | 0.203950 | ||||||||
\(149\) | −7.01809e17 | −0.236666 | −0.118333 | − | 0.992974i | \(-0.537755\pi\) | ||||
−0.118333 | + | 0.992974i | \(0.537755\pi\) | |||||||
\(150\) | 7.09563e18 | 2.26056 | ||||||||
\(151\) | −2.47410e18 | −0.744926 | −0.372463 | − | 0.928047i | \(-0.621487\pi\) | ||||
−0.372463 | + | 0.928047i | \(0.621487\pi\) | |||||||
\(152\) | 1.06511e19 | 3.03195 | ||||||||
\(153\) | −6.34188e18 | −1.70742 | ||||||||
\(154\) | 3.03093e18 | 0.772058 | ||||||||
\(155\) | 2.21877e18 | 0.534924 | ||||||||
\(156\) | −3.12670e18 | −0.713719 | ||||||||
\(157\) | 6.25634e18 | 1.35261 | 0.676307 | − | 0.736620i | \(-0.263579\pi\) | ||||
0.676307 | + | 0.736620i | \(0.263579\pi\) | |||||||
\(158\) | −3.84033e18 | −0.786653 | ||||||||
\(159\) | −3.80094e18 | −0.737931 | ||||||||
\(160\) | −1.92303e19 | −3.53970 | ||||||||
\(161\) | 2.20913e18 | 0.385657 | ||||||||
\(162\) | 8.83820e18 | 1.46382 | ||||||||
\(163\) | −6.44391e18 | −1.01287 | −0.506436 | − | 0.862277i | \(-0.669037\pi\) | ||||
−0.506436 | + | 0.862277i | \(0.669037\pi\) | |||||||
\(164\) | 1.54322e19 | 2.30279 | ||||||||
\(165\) | −4.23559e18 | −0.600206 | ||||||||
\(166\) | 2.02437e19 | 2.72503 | ||||||||
\(167\) | 1.11330e19 | 1.42404 | 0.712021 | − | 0.702158i | \(-0.247780\pi\) | ||||
0.712021 | + | 0.702158i | \(0.247780\pi\) | |||||||
\(168\) | −4.82205e19 | −5.86277 | ||||||||
\(169\) | −8.34016e18 | −0.964134 | ||||||||
\(170\) | 3.31486e19 | 3.64460 | ||||||||
\(171\) | −1.18065e19 | −1.23496 | ||||||||
\(172\) | 1.30352e19 | 1.29755 | ||||||||
\(173\) | −4.68185e18 | −0.443635 | −0.221817 | − | 0.975088i | \(-0.571199\pi\) | ||||
−0.221817 | + | 0.975088i | \(0.571199\pi\) | |||||||
\(174\) | −2.54005e19 | −2.29178 | ||||||||
\(175\) | −1.28355e19 | −1.10304 | ||||||||
\(176\) | 1.08427e19 | 0.887726 | ||||||||
\(177\) | 2.91560e19 | 2.27486 | ||||||||
\(178\) | −3.15388e19 | −2.34572 | ||||||||
\(179\) | 2.31874e19 | 1.64438 | 0.822190 | − | 0.569214i | \(-0.192752\pi\) | ||||
0.822190 | + | 0.569214i | \(0.192752\pi\) | |||||||
\(180\) | 6.02158e19 | 4.07281 | ||||||||
\(181\) | 2.69496e18 | 0.173894 | 0.0869469 | − | 0.996213i | \(-0.472289\pi\) | ||||
0.0869469 | + | 0.996213i | \(0.472289\pi\) | |||||||
\(182\) | 7.87579e18 | 0.484939 | ||||||||
\(183\) | −3.03483e19 | −1.78361 | ||||||||
\(184\) | 1.47420e19 | 0.827189 | ||||||||
\(185\) | 2.01045e18 | 0.107729 | ||||||||
\(186\) | 2.16334e19 | 1.10730 | ||||||||
\(187\) | −8.86357e18 | −0.433466 | ||||||||
\(188\) | −5.60132e19 | −2.61787 | ||||||||
\(189\) | 8.44551e18 | 0.377312 | ||||||||
\(190\) | 6.17118e19 | 2.63610 | ||||||||
\(191\) | 1.07776e19 | 0.440291 | 0.220146 | − | 0.975467i | \(-0.429347\pi\) | ||||
0.220146 | + | 0.975467i | \(0.429347\pi\) | |||||||
\(192\) | −7.60635e19 | −2.97246 | ||||||||
\(193\) | 3.71281e18 | 0.138824 | 0.0694122 | − | 0.997588i | \(-0.477888\pi\) | ||||
0.0694122 | + | 0.997588i | \(0.477888\pi\) | |||||||
\(194\) | −7.56504e19 | −2.70705 | ||||||||
\(195\) | −1.10061e19 | −0.376997 | ||||||||
\(196\) | 6.58851e19 | 2.16078 | ||||||||
\(197\) | −3.64967e18 | −0.114628 | −0.0573140 | − | 0.998356i | \(-0.518254\pi\) | ||||
−0.0573140 | + | 0.998356i | \(0.518254\pi\) | |||||||
\(198\) | −2.24201e19 | −0.674504 | ||||||||
\(199\) | 2.71668e19 | 0.783046 | 0.391523 | − | 0.920168i | \(-0.371948\pi\) | ||||
0.391523 | + | 0.920168i | \(0.371948\pi\) | |||||||
\(200\) | −8.56542e19 | −2.36588 | ||||||||
\(201\) | −5.15967e19 | −1.36602 | ||||||||
\(202\) | −1.35714e20 | −3.44459 | ||||||||
\(203\) | 4.59478e19 | 1.11827 | ||||||||
\(204\) | 2.32110e20 | 5.41799 | ||||||||
\(205\) | 5.43215e19 | 1.21637 | ||||||||
\(206\) | −1.86224e19 | −0.400095 | ||||||||
\(207\) | −1.63412e19 | −0.336927 | ||||||||
\(208\) | 2.81744e19 | 0.557591 | ||||||||
\(209\) | −1.65010e19 | −0.313522 | ||||||||
\(210\) | −2.79387e20 | −5.09733 | ||||||||
\(211\) | 7.26013e19 | 1.27217 | 0.636083 | − | 0.771621i | \(-0.280554\pi\) | ||||
0.636083 | + | 0.771621i | \(0.280554\pi\) | |||||||
\(212\) | 7.55229e19 | 1.27123 | ||||||||
\(213\) | −2.59969e18 | −0.0420431 | ||||||||
\(214\) | −3.88780e19 | −0.604209 | ||||||||
\(215\) | 4.58841e19 | 0.685385 | ||||||||
\(216\) | 5.63587e19 | 0.809290 | ||||||||
\(217\) | −3.91334e19 | −0.540306 | ||||||||
\(218\) | −2.96417e19 | −0.393571 | ||||||||
\(219\) | −2.23071e20 | −2.84885 | ||||||||
\(220\) | 8.41591e19 | 1.03397 | ||||||||
\(221\) | −2.30317e19 | −0.272265 | ||||||||
\(222\) | 1.96023e19 | 0.223001 | ||||||||
\(223\) | 1.52861e20 | 1.67381 | 0.836904 | − | 0.547349i | \(-0.184363\pi\) | ||||
0.836904 | + | 0.547349i | \(0.184363\pi\) | |||||||
\(224\) | 3.39174e20 | 3.57531 | ||||||||
\(225\) | 9.49459e19 | 0.963662 | ||||||||
\(226\) | 1.17856e20 | 1.15194 | ||||||||
\(227\) | −1.10733e19 | −0.104246 | −0.0521229 | − | 0.998641i | \(-0.516599\pi\) | ||||
−0.0521229 | + | 0.998641i | \(0.516599\pi\) | |||||||
\(228\) | 4.32113e20 | 3.91878 | ||||||||
\(229\) | −1.29979e20 | −1.13572 | −0.567861 | − | 0.823124i | \(-0.692229\pi\) | ||||
−0.567861 | + | 0.823124i | \(0.692229\pi\) | |||||||
\(230\) | 8.54144e19 | 0.719192 | ||||||||
\(231\) | 7.47050e19 | 0.606245 | ||||||||
\(232\) | 3.06619e20 | 2.39857 | ||||||||
\(233\) | −2.35354e20 | −1.77499 | −0.887495 | − | 0.460817i | \(-0.847556\pi\) | ||||
−0.887495 | + | 0.460817i | \(0.847556\pi\) | |||||||
\(234\) | −5.82581e19 | −0.423664 | ||||||||
\(235\) | −1.97168e20 | −1.38280 | ||||||||
\(236\) | −5.79315e20 | −3.91889 | ||||||||
\(237\) | −9.46548e19 | −0.617706 | ||||||||
\(238\) | −5.84658e20 | −3.68127 | ||||||||
\(239\) | 1.09974e19 | 0.0668204 | 0.0334102 | − | 0.999442i | \(-0.489363\pi\) | ||||
0.0334102 | + | 0.999442i | \(0.489363\pi\) | |||||||
\(240\) | −9.99464e20 | −5.86100 | ||||||||
\(241\) | −7.17676e19 | −0.406241 | −0.203120 | − | 0.979154i | \(-0.565108\pi\) | ||||
−0.203120 | + | 0.979154i | \(0.565108\pi\) | |||||||
\(242\) | −3.13349e19 | −0.171237 | ||||||||
\(243\) | 2.70442e20 | 1.42699 | ||||||||
\(244\) | 6.03005e20 | 3.07261 | ||||||||
\(245\) | 2.31917e20 | 1.14135 | ||||||||
\(246\) | 5.29646e20 | 2.51789 | ||||||||
\(247\) | −4.28775e19 | −0.196927 | ||||||||
\(248\) | −2.61145e20 | −1.15889 | ||||||||
\(249\) | 4.98958e20 | 2.13978 | ||||||||
\(250\) | 1.15353e20 | 0.478123 | ||||||||
\(251\) | 3.00496e20 | 1.20396 | 0.601980 | − | 0.798511i | \(-0.294379\pi\) | ||||
0.601980 | + | 0.798511i | \(0.294379\pi\) | |||||||
\(252\) | −1.06205e21 | −4.11379 | ||||||||
\(253\) | −2.28389e19 | −0.0855362 | ||||||||
\(254\) | −4.35813e20 | −1.57839 | ||||||||
\(255\) | 8.17032e20 | 2.86186 | ||||||||
\(256\) | 4.92026e19 | 0.166705 | ||||||||
\(257\) | −2.18500e20 | −0.716177 | −0.358088 | − | 0.933688i | \(-0.616571\pi\) | ||||
−0.358088 | + | 0.933688i | \(0.616571\pi\) | |||||||
\(258\) | 4.47379e20 | 1.41876 | ||||||||
\(259\) | −3.54592e19 | −0.108813 | ||||||||
\(260\) | 2.18685e20 | 0.649450 | ||||||||
\(261\) | −3.39881e20 | −0.976974 | ||||||||
\(262\) | 3.46946e20 | 0.965384 | ||||||||
\(263\) | 3.76045e20 | 1.01301 | 0.506507 | − | 0.862236i | \(-0.330936\pi\) | ||||
0.506507 | + | 0.862236i | \(0.330936\pi\) | |||||||
\(264\) | 4.98523e20 | 1.30032 | ||||||||
\(265\) | 2.65842e20 | 0.671481 | ||||||||
\(266\) | −1.08844e21 | −2.66263 | ||||||||
\(267\) | −7.77355e20 | −1.84193 | ||||||||
\(268\) | 1.02520e21 | 2.35323 | ||||||||
\(269\) | −7.45654e20 | −1.65822 | −0.829111 | − | 0.559083i | \(-0.811153\pi\) | ||||
−0.829111 | + | 0.559083i | \(0.811153\pi\) | |||||||
\(270\) | 3.26539e20 | 0.703629 | ||||||||
\(271\) | 2.17881e20 | 0.454967 | 0.227484 | − | 0.973782i | \(-0.426950\pi\) | ||||
0.227484 | + | 0.973782i | \(0.426950\pi\) | |||||||
\(272\) | −2.09152e21 | −4.23279 | ||||||||
\(273\) | 1.94119e20 | 0.380790 | ||||||||
\(274\) | −1.19358e21 | −2.26972 | ||||||||
\(275\) | 1.32699e20 | 0.244646 | ||||||||
\(276\) | 5.98081e20 | 1.06914 | ||||||||
\(277\) | −4.87360e20 | −0.844835 | −0.422417 | − | 0.906401i | \(-0.638818\pi\) | ||||
−0.422417 | + | 0.906401i | \(0.638818\pi\) | |||||||
\(278\) | 9.43243e20 | 1.58578 | ||||||||
\(279\) | 2.89474e20 | 0.472035 | ||||||||
\(280\) | 3.37259e21 | 5.33483 | ||||||||
\(281\) | 7.81004e20 | 1.19853 | 0.599266 | − | 0.800550i | \(-0.295459\pi\) | ||||
0.599266 | + | 0.800550i | \(0.295459\pi\) | |||||||
\(282\) | −1.92242e21 | −2.86241 | ||||||||
\(283\) | −1.05855e21 | −1.52943 | −0.764713 | − | 0.644371i | \(-0.777119\pi\) | ||||
−0.764713 | + | 0.644371i | \(0.777119\pi\) | |||||||
\(284\) | 5.16546e19 | 0.0724275 | ||||||||
\(285\) | 1.52104e21 | 2.06995 | ||||||||
\(286\) | −8.14230e19 | −0.107556 | ||||||||
\(287\) | −9.58094e20 | −1.22860 | ||||||||
\(288\) | −2.50891e21 | −3.12355 | ||||||||
\(289\) | 8.82516e20 | 1.06682 | ||||||||
\(290\) | 1.77654e21 | 2.08541 | ||||||||
\(291\) | −1.86460e21 | −2.12566 | ||||||||
\(292\) | 4.43232e21 | 4.90769 | ||||||||
\(293\) | 5.06688e20 | 0.544962 | 0.272481 | − | 0.962161i | \(-0.412156\pi\) | ||||
0.272481 | + | 0.962161i | \(0.412156\pi\) | |||||||
\(294\) | 2.26124e21 | 2.36262 | ||||||||
\(295\) | −2.03920e21 | −2.07001 | ||||||||
\(296\) | −2.36627e20 | −0.233391 | ||||||||
\(297\) | −8.73130e19 | −0.0836853 | ||||||||
\(298\) | 4.78592e20 | 0.445786 | ||||||||
\(299\) | −5.93462e19 | −0.0537264 | ||||||||
\(300\) | −3.47498e21 | −3.05789 | ||||||||
\(301\) | −8.09278e20 | −0.692281 | ||||||||
\(302\) | 1.68719e21 | 1.40315 | ||||||||
\(303\) | −3.34501e21 | −2.70480 | ||||||||
\(304\) | −3.89372e21 | −3.06154 | ||||||||
\(305\) | 2.12259e21 | 1.62300 | ||||||||
\(306\) | 4.32478e21 | 3.21612 | ||||||||
\(307\) | 2.00355e21 | 1.44919 | 0.724594 | − | 0.689176i | \(-0.242027\pi\) | ||||
0.724594 | + | 0.689176i | \(0.242027\pi\) | |||||||
\(308\) | −1.48435e21 | −1.04437 | ||||||||
\(309\) | −4.58996e20 | −0.314168 | ||||||||
\(310\) | −1.51306e21 | −1.00759 | ||||||||
\(311\) | −2.52349e21 | −1.63508 | −0.817538 | − | 0.575874i | \(-0.804662\pi\) | ||||
−0.817538 | + | 0.575874i | \(0.804662\pi\) | |||||||
\(312\) | 1.29540e21 | 0.816749 | ||||||||
\(313\) | 2.05053e21 | 1.25817 | 0.629084 | − | 0.777337i | \(-0.283430\pi\) | ||||
0.629084 | + | 0.777337i | \(0.283430\pi\) | |||||||
\(314\) | −4.26645e21 | −2.54780 | ||||||||
\(315\) | −3.73845e21 | −2.17296 | ||||||||
\(316\) | 1.88074e21 | 1.06412 | ||||||||
\(317\) | −2.75915e21 | −1.51975 | −0.759873 | − | 0.650072i | \(-0.774739\pi\) | ||||
−0.759873 | + | 0.650072i | \(0.774739\pi\) | |||||||
\(318\) | 2.59201e21 | 1.38997 | ||||||||
\(319\) | −4.75026e20 | −0.248026 | ||||||||
\(320\) | 5.31996e21 | 2.70479 | ||||||||
\(321\) | −9.58248e20 | −0.474444 | ||||||||
\(322\) | −1.50649e21 | −0.726428 | ||||||||
\(323\) | 3.18300e21 | 1.49491 | ||||||||
\(324\) | −4.32838e21 | −1.98012 | ||||||||
\(325\) | 3.44814e20 | 0.153665 | ||||||||
\(326\) | 4.39436e21 | 1.90786 | ||||||||
\(327\) | −7.30596e20 | −0.309045 | ||||||||
\(328\) | −6.39357e21 | −2.63521 | ||||||||
\(329\) | 3.47754e21 | 1.39671 | ||||||||
\(330\) | 2.88842e21 | 1.13055 | ||||||||
\(331\) | 2.54943e21 | 0.972535 | 0.486268 | − | 0.873810i | \(-0.338358\pi\) | ||||
0.486268 | + | 0.873810i | \(0.338358\pi\) | |||||||
\(332\) | −9.91406e21 | −3.68619 | ||||||||
\(333\) | 2.62296e20 | 0.0950639 | ||||||||
\(334\) | −7.59204e21 | −2.68234 | ||||||||
\(335\) | 3.60873e21 | 1.24301 | ||||||||
\(336\) | 1.76280e22 | 5.91997 | ||||||||
\(337\) | 2.19535e21 | 0.718867 | 0.359434 | − | 0.933171i | \(-0.382970\pi\) | ||||
0.359434 | + | 0.933171i | \(0.382970\pi\) | |||||||
\(338\) | 5.68749e21 | 1.81605 | ||||||||
\(339\) | 2.90487e21 | 0.904543 | ||||||||
\(340\) | −1.62340e22 | −4.93010 | ||||||||
\(341\) | 4.04576e20 | 0.119836 | ||||||||
\(342\) | 8.05132e21 | 2.32619 | ||||||||
\(343\) | 7.32994e20 | 0.206586 | ||||||||
\(344\) | −5.40049e21 | −1.48486 | ||||||||
\(345\) | 2.10526e21 | 0.564733 | ||||||||
\(346\) | 3.19274e21 | 0.835635 | ||||||||
\(347\) | −4.75493e20 | −0.121435 | −0.0607174 | − | 0.998155i | \(-0.519339\pi\) | ||||
−0.0607174 | + | 0.998155i | \(0.519339\pi\) | |||||||
\(348\) | 1.24395e22 | 3.10013 | ||||||||
\(349\) | 3.91716e21 | 0.952697 | 0.476349 | − | 0.879257i | \(-0.341960\pi\) | ||||
0.476349 | + | 0.879257i | \(0.341960\pi\) | |||||||
\(350\) | 8.75305e21 | 2.07769 | ||||||||
\(351\) | −2.26880e20 | −0.0525638 | ||||||||
\(352\) | −3.50651e21 | −0.792981 | ||||||||
\(353\) | −1.24417e21 | −0.274661 | −0.137330 | − | 0.990525i | \(-0.543852\pi\) | ||||
−0.137330 | + | 0.990525i | \(0.543852\pi\) | |||||||
\(354\) | −1.98826e22 | −4.28495 | ||||||||
\(355\) | 1.81825e20 | 0.0382572 | ||||||||
\(356\) | 1.54457e22 | 3.17309 | ||||||||
\(357\) | −1.44104e22 | −2.89065 | ||||||||
\(358\) | −1.58124e22 | −3.09737 | ||||||||
\(359\) | 3.07812e20 | 0.0588820 | 0.0294410 | − | 0.999567i | \(-0.490627\pi\) | ||||
0.0294410 | + | 0.999567i | \(0.490627\pi\) | |||||||
\(360\) | −2.49475e22 | −4.66075 | ||||||||
\(361\) | 4.45314e20 | 0.0812560 | ||||||||
\(362\) | −1.83780e21 | −0.327548 | ||||||||
\(363\) | −7.72330e20 | −0.134461 | ||||||||
\(364\) | −3.85705e21 | −0.655984 | ||||||||
\(365\) | 1.56019e22 | 2.59231 | ||||||||
\(366\) | 2.06957e22 | 3.35962 | ||||||||
\(367\) | −1.70106e21 | −0.269811 | −0.134905 | − | 0.990858i | \(-0.543073\pi\) | ||||
−0.134905 | + | 0.990858i | \(0.543073\pi\) | |||||||
\(368\) | −5.38925e21 | −0.835260 | ||||||||
\(369\) | 7.08714e21 | 1.07336 | ||||||||
\(370\) | −1.37100e21 | −0.202920 | ||||||||
\(371\) | −4.68878e21 | −0.678237 | ||||||||
\(372\) | −1.05946e22 | −1.49786 | ||||||||
\(373\) | −1.88241e21 | −0.260129 | −0.130065 | − | 0.991506i | \(-0.541518\pi\) | ||||
−0.130065 | + | 0.991506i | \(0.541518\pi\) | |||||||
\(374\) | 6.04442e21 | 0.816481 | ||||||||
\(375\) | 2.84318e21 | 0.375438 | ||||||||
\(376\) | 2.32063e22 | 2.99578 | ||||||||
\(377\) | −1.23434e21 | −0.155788 | ||||||||
\(378\) | −5.75933e21 | −0.710709 | ||||||||
\(379\) | 2.24229e21 | 0.270557 | 0.135278 | − | 0.990808i | \(-0.456807\pi\) | ||||
0.135278 | + | 0.990808i | \(0.456807\pi\) | |||||||
\(380\) | −3.02224e22 | −3.56590 | ||||||||
\(381\) | −1.07417e22 | −1.23940 | ||||||||
\(382\) | −7.34970e21 | −0.829337 | ||||||||
\(383\) | −3.53424e21 | −0.390038 | −0.195019 | − | 0.980799i | \(-0.562477\pi\) | ||||
−0.195019 | + | 0.980799i | \(0.562477\pi\) | |||||||
\(384\) | 1.58325e22 | 1.70897 | ||||||||
\(385\) | −5.22495e21 | −0.551653 | ||||||||
\(386\) | −2.53191e21 | −0.261491 | ||||||||
\(387\) | 5.98633e21 | 0.604808 | ||||||||
\(388\) | 3.70486e22 | 3.66187 | ||||||||
\(389\) | −3.71170e21 | −0.358923 | −0.179461 | − | 0.983765i | \(-0.557435\pi\) | ||||
−0.179461 | + | 0.983765i | \(0.557435\pi\) | |||||||
\(390\) | 7.50547e21 | 0.710115 | ||||||||
\(391\) | 4.40555e21 | 0.407848 | ||||||||
\(392\) | −2.72963e22 | −2.47270 | ||||||||
\(393\) | 8.55136e21 | 0.758051 | ||||||||
\(394\) | 2.48886e21 | 0.215915 | ||||||||
\(395\) | 6.62026e21 | 0.562082 | ||||||||
\(396\) | 1.09799e22 | 0.912411 | ||||||||
\(397\) | 6.48398e21 | 0.527379 | 0.263689 | − | 0.964608i | \(-0.415061\pi\) | ||||
0.263689 | + | 0.964608i | \(0.415061\pi\) | |||||||
\(398\) | −1.85261e22 | −1.47495 | ||||||||
\(399\) | −2.68274e22 | −2.09078 | ||||||||
\(400\) | 3.13127e22 | 2.38897 | ||||||||
\(401\) | 1.54416e22 | 1.15336 | 0.576680 | − | 0.816970i | \(-0.304348\pi\) | ||||
0.576680 | + | 0.816970i | \(0.304348\pi\) | |||||||
\(402\) | 3.51859e22 | 2.57304 | ||||||||
\(403\) | 1.05128e21 | 0.0752707 | ||||||||
\(404\) | 6.64638e22 | 4.65955 | ||||||||
\(405\) | −1.52360e22 | −1.04593 | ||||||||
\(406\) | −3.13336e22 | −2.10639 | ||||||||
\(407\) | 3.66591e20 | 0.0241340 | ||||||||
\(408\) | −9.61635e22 | −6.20011 | ||||||||
\(409\) | 2.99028e21 | 0.188827 | 0.0944134 | − | 0.995533i | \(-0.469902\pi\) | ||||
0.0944134 | + | 0.995533i | \(0.469902\pi\) | |||||||
\(410\) | −3.70440e22 | −2.29116 | ||||||||
\(411\) | −2.94189e22 | −1.78226 | ||||||||
\(412\) | 9.12002e21 | 0.541214 | ||||||||
\(413\) | 3.59663e22 | 2.09084 | ||||||||
\(414\) | 1.11437e22 | 0.634640 | ||||||||
\(415\) | −3.48977e22 | −1.94710 | ||||||||
\(416\) | −9.11157e21 | −0.498081 | ||||||||
\(417\) | 2.32486e22 | 1.24521 | ||||||||
\(418\) | 1.12527e22 | 0.590553 | ||||||||
\(419\) | 1.94485e22 | 1.00015 | 0.500076 | − | 0.865981i | \(-0.333305\pi\) | ||||
0.500076 | + | 0.865981i | \(0.333305\pi\) | |||||||
\(420\) | 1.36826e23 | 6.89523 | ||||||||
\(421\) | 3.85665e21 | 0.190464 | 0.0952320 | − | 0.995455i | \(-0.469641\pi\) | ||||
0.0952320 | + | 0.995455i | \(0.469641\pi\) | |||||||
\(422\) | −4.95097e22 | −2.39626 | ||||||||
\(423\) | −2.57238e22 | −1.22023 | ||||||||
\(424\) | −3.12892e22 | −1.45474 | ||||||||
\(425\) | −2.55972e22 | −1.16650 | ||||||||
\(426\) | 1.77283e21 | 0.0791929 | ||||||||
\(427\) | −3.74371e22 | −1.63933 | ||||||||
\(428\) | 1.90399e22 | 0.817322 | ||||||||
\(429\) | −2.00688e21 | −0.0844567 | ||||||||
\(430\) | −3.12902e22 | −1.29100 | ||||||||
\(431\) | −1.17839e22 | −0.476686 | −0.238343 | − | 0.971181i | \(-0.576604\pi\) | ||||
−0.238343 | + | 0.971181i | \(0.576604\pi\) | |||||||
\(432\) | −2.06031e22 | −0.817185 | ||||||||
\(433\) | −2.89668e22 | −1.12656 | −0.563280 | − | 0.826266i | \(-0.690461\pi\) | ||||
−0.563280 | + | 0.826266i | \(0.690461\pi\) | |||||||
\(434\) | 2.66866e22 | 1.01773 | ||||||||
\(435\) | 4.37873e22 | 1.63753 | ||||||||
\(436\) | 1.45166e22 | 0.532389 | ||||||||
\(437\) | 8.20168e21 | 0.294992 | ||||||||
\(438\) | 1.52121e23 | 5.36612 | ||||||||
\(439\) | −2.18950e22 | −0.757524 | −0.378762 | − | 0.925494i | \(-0.623650\pi\) | ||||
−0.378762 | + | 0.925494i | \(0.623650\pi\) | |||||||
\(440\) | −3.48672e22 | −1.18323 | ||||||||
\(441\) | 3.02574e22 | 1.00717 | ||||||||
\(442\) | 1.57063e22 | 0.512842 | ||||||||
\(443\) | 6.03618e22 | 1.93344 | 0.966720 | − | 0.255839i | \(-0.0823516\pi\) | ||||
0.966720 | + | 0.255839i | \(0.0823516\pi\) | |||||||
\(444\) | −9.59993e21 | −0.301656 | ||||||||
\(445\) | 5.43691e22 | 1.67607 | ||||||||
\(446\) | −1.04242e23 | −3.15280 | ||||||||
\(447\) | 1.17961e22 | 0.350046 | ||||||||
\(448\) | −9.38307e22 | −2.73201 | ||||||||
\(449\) | −1.87858e22 | −0.536704 | −0.268352 | − | 0.963321i | \(-0.586479\pi\) | ||||
−0.268352 | + | 0.963321i | \(0.586479\pi\) | |||||||
\(450\) | −6.47474e22 | −1.81516 | ||||||||
\(451\) | 9.90515e21 | 0.272496 | ||||||||
\(452\) | −5.77184e22 | −1.55825 | ||||||||
\(453\) | 4.15851e22 | 1.10180 | ||||||||
\(454\) | 7.55134e21 | 0.196358 | ||||||||
\(455\) | −1.35769e22 | −0.346500 | ||||||||
\(456\) | −1.79025e23 | −4.48448 | ||||||||
\(457\) | −1.04123e22 | −0.256010 | −0.128005 | − | 0.991774i | \(-0.540857\pi\) | ||||
−0.128005 | + | 0.991774i | \(0.540857\pi\) | |||||||
\(458\) | 8.86379e22 | 2.13926 | ||||||||
\(459\) | 1.68424e22 | 0.399022 | ||||||||
\(460\) | −4.18305e22 | −0.972861 | ||||||||
\(461\) | −4.41492e22 | −1.00801 | −0.504005 | − | 0.863701i | \(-0.668141\pi\) | ||||
−0.504005 | + | 0.863701i | \(0.668141\pi\) | |||||||
\(462\) | −5.09443e22 | −1.14193 | ||||||||
\(463\) | −1.91173e21 | −0.0420716 | −0.0210358 | − | 0.999779i | \(-0.506696\pi\) | ||||
−0.0210358 | + | 0.999779i | \(0.506696\pi\) | |||||||
\(464\) | −1.12091e23 | −2.42197 | ||||||||
\(465\) | −3.72933e22 | −0.791191 | ||||||||
\(466\) | 1.60497e23 | 3.34339 | ||||||||
\(467\) | −1.96144e21 | −0.0401220 | −0.0200610 | − | 0.999799i | \(-0.506386\pi\) | ||||
−0.0200610 | + | 0.999799i | \(0.506386\pi\) | |||||||
\(468\) | 2.85310e22 | 0.573097 | ||||||||
\(469\) | −6.36488e22 | −1.25551 | ||||||||
\(470\) | 1.34456e23 | 2.60465 | ||||||||
\(471\) | −1.05158e23 | −2.00061 | ||||||||
\(472\) | 2.40011e23 | 4.48461 | ||||||||
\(473\) | 8.36664e21 | 0.153543 | ||||||||
\(474\) | 6.45488e22 | 1.16352 | ||||||||
\(475\) | −4.76535e22 | −0.843722 | ||||||||
\(476\) | 2.86327e23 | 4.97971 | ||||||||
\(477\) | 3.46835e22 | 0.592538 | ||||||||
\(478\) | −7.49959e21 | −0.125864 | ||||||||
\(479\) | −9.08054e22 | −1.49713 | −0.748565 | − | 0.663061i | \(-0.769257\pi\) | ||||
−0.748565 | + | 0.663061i | \(0.769257\pi\) | |||||||
\(480\) | 3.23226e23 | 5.23547 | ||||||||
\(481\) | 9.52577e20 | 0.0151589 | ||||||||
\(482\) | 4.89412e22 | 0.765199 | ||||||||
\(483\) | −3.71314e22 | −0.570415 | ||||||||
\(484\) | 1.53458e22 | 0.231635 | ||||||||
\(485\) | 1.30412e23 | 1.93425 | ||||||||
\(486\) | −1.84425e23 | −2.68789 | ||||||||
\(487\) | −3.00468e22 | −0.430331 | −0.215165 | − | 0.976578i | \(-0.569029\pi\) | ||||
−0.215165 | + | 0.976578i | \(0.569029\pi\) | |||||||
\(488\) | −2.49826e23 | −3.51616 | ||||||||
\(489\) | 1.08310e23 | 1.49811 | ||||||||
\(490\) | −1.58153e23 | −2.14987 | ||||||||
\(491\) | 3.39667e22 | 0.453796 | 0.226898 | − | 0.973918i | \(-0.427142\pi\) | ||||
0.226898 | + | 0.973918i | \(0.427142\pi\) | |||||||
\(492\) | −2.59386e23 | −3.40599 | ||||||||
\(493\) | 9.16312e22 | 1.18262 | ||||||||
\(494\) | 2.92399e22 | 0.370934 | ||||||||
\(495\) | 3.86496e22 | 0.481948 | ||||||||
\(496\) | 9.54672e22 | 1.17020 | ||||||||
\(497\) | −3.20694e21 | −0.0386421 | ||||||||
\(498\) | −3.40259e23 | −4.03052 | ||||||||
\(499\) | −1.22594e23 | −1.42762 | −0.713811 | − | 0.700338i | \(-0.753033\pi\) | ||||
−0.713811 | + | 0.700338i | \(0.753033\pi\) | |||||||
\(500\) | −5.64925e22 | −0.646764 | ||||||||
\(501\) | −1.87125e23 | −2.10626 | ||||||||
\(502\) | −2.04920e23 | −2.26779 | ||||||||
\(503\) | 1.04506e23 | 1.13714 | 0.568569 | − | 0.822636i | \(-0.307497\pi\) | ||||
0.568569 | + | 0.822636i | \(0.307497\pi\) | |||||||
\(504\) | 4.40010e23 | 4.70764 | ||||||||
\(505\) | 2.33954e23 | 2.46124 | ||||||||
\(506\) | 1.55747e22 | 0.161117 | ||||||||
\(507\) | 1.40183e23 | 1.42602 | ||||||||
\(508\) | 2.13433e23 | 2.13511 | ||||||||
\(509\) | 5.57313e21 | 0.0548275 | 0.0274137 | − | 0.999624i | \(-0.491273\pi\) | ||||
0.0274137 | + | 0.999624i | \(0.491273\pi\) | |||||||
\(510\) | −5.57167e23 | −5.39062 | ||||||||
\(511\) | −2.75177e23 | −2.61839 | ||||||||
\(512\) | 8.99104e22 | 0.841425 | ||||||||
\(513\) | 3.13550e22 | 0.288609 | ||||||||
\(514\) | 1.49004e23 | 1.34900 | ||||||||
\(515\) | 3.21026e22 | 0.285877 | ||||||||
\(516\) | −2.19097e23 | −1.91917 | ||||||||
\(517\) | −3.59521e22 | −0.309781 | ||||||||
\(518\) | 2.41810e22 | 0.204961 | ||||||||
\(519\) | 7.86932e22 | 0.656168 | ||||||||
\(520\) | −9.06014e22 | −0.743202 | ||||||||
\(521\) | 1.52614e23 | 1.23161 | 0.615804 | − | 0.787899i | \(-0.288831\pi\) | ||||
0.615804 | + | 0.787899i | \(0.288831\pi\) | |||||||
\(522\) | 2.31779e23 | 1.84024 | ||||||||
\(523\) | −3.85396e22 | −0.301053 | −0.150526 | − | 0.988606i | \(-0.548097\pi\) | ||||
−0.150526 | + | 0.988606i | \(0.548097\pi\) | |||||||
\(524\) | −1.69911e23 | −1.30589 | ||||||||
\(525\) | 2.15741e23 | 1.63147 | ||||||||
\(526\) | −2.56440e23 | −1.90813 | ||||||||
\(527\) | −7.80416e22 | −0.571395 | ||||||||
\(528\) | −1.82245e23 | −1.31301 | ||||||||
\(529\) | −1.29698e23 | −0.919519 | ||||||||
\(530\) | −1.81288e23 | −1.26481 | ||||||||
\(531\) | −2.66047e23 | −1.82665 | ||||||||
\(532\) | 5.33047e23 | 3.60177 | ||||||||
\(533\) | 2.57383e22 | 0.171158 | ||||||||
\(534\) | 5.30109e23 | 3.46948 | ||||||||
\(535\) | 6.70209e22 | 0.431721 | ||||||||
\(536\) | −4.24742e23 | −2.69293 | ||||||||
\(537\) | −3.89738e23 | −2.43215 | ||||||||
\(538\) | 5.08491e23 | 3.12345 | ||||||||
\(539\) | 4.22884e22 | 0.255692 | ||||||||
\(540\) | −1.59918e23 | −0.951809 | ||||||||
\(541\) | 7.66558e22 | 0.449126 | 0.224563 | − | 0.974460i | \(-0.427905\pi\) | ||||
0.224563 | + | 0.974460i | \(0.427905\pi\) | |||||||
\(542\) | −1.48582e23 | −0.856981 | ||||||||
\(543\) | −4.52973e22 | −0.257201 | ||||||||
\(544\) | 6.76396e23 | 3.78103 | ||||||||
\(545\) | 5.10987e22 | 0.281215 | ||||||||
\(546\) | −1.32377e23 | −0.717260 | ||||||||
\(547\) | 2.41503e23 | 1.28834 | 0.644171 | − | 0.764882i | \(-0.277203\pi\) | ||||
0.644171 | + | 0.764882i | \(0.277203\pi\) | |||||||
\(548\) | 5.84538e23 | 3.07028 | ||||||||
\(549\) | 2.76927e23 | 1.43219 | ||||||||
\(550\) | −9.04925e22 | −0.460818 | ||||||||
\(551\) | 1.70587e23 | 0.855377 | ||||||||
\(552\) | −2.47786e23 | −1.22347 | ||||||||
\(553\) | −1.16765e23 | −0.567737 | ||||||||
\(554\) | 3.32350e23 | 1.59134 | ||||||||
\(555\) | −3.37919e22 | −0.159339 | ||||||||
\(556\) | −4.61939e23 | −2.14511 | ||||||||
\(557\) | −2.40237e23 | −1.09868 | −0.549340 | − | 0.835599i | \(-0.685121\pi\) | ||||
−0.549340 | + | 0.835599i | \(0.685121\pi\) | |||||||
\(558\) | −1.97404e23 | −0.889130 | ||||||||
\(559\) | 2.17405e22 | 0.0964425 | ||||||||
\(560\) | −1.23292e24 | −5.38688 | ||||||||
\(561\) | 1.48980e23 | 0.641127 | ||||||||
\(562\) | −5.32598e23 | −2.25757 | ||||||||
\(563\) | 1.12536e23 | 0.469862 | 0.234931 | − | 0.972012i | \(-0.424514\pi\) | ||||
0.234931 | + | 0.972012i | \(0.424514\pi\) | |||||||
\(564\) | 9.41479e23 | 3.87202 | ||||||||
\(565\) | −2.03170e23 | −0.823090 | ||||||||
\(566\) | 7.21870e23 | 2.88084 | ||||||||
\(567\) | 2.68724e23 | 1.05645 | ||||||||
\(568\) | −2.14006e22 | −0.0828828 | ||||||||
\(569\) | 1.53285e23 | 0.584853 | 0.292426 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292426 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(570\) | −1.03726e24 | −3.89899 | ||||||||
\(571\) | 1.14055e23 | 0.422383 | 0.211191 | − | 0.977445i | \(-0.432266\pi\) | ||||
0.211191 | + | 0.977445i | \(0.432266\pi\) | |||||||
\(572\) | 3.98757e22 | 0.145493 | ||||||||
\(573\) | −1.81152e23 | −0.651222 | ||||||||
\(574\) | 6.53362e23 | 2.31421 | ||||||||
\(575\) | −6.59566e22 | −0.230187 | ||||||||
\(576\) | 6.94077e23 | 2.38680 | ||||||||
\(577\) | −9.95652e22 | −0.337375 | −0.168688 | − | 0.985670i | \(-0.553953\pi\) | ||||
−0.168688 | + | 0.985670i | \(0.553953\pi\) | |||||||
\(578\) | −6.01823e23 | −2.00947 | ||||||||
\(579\) | −6.24055e22 | −0.205331 | ||||||||
\(580\) | −8.70033e23 | −2.82097 | ||||||||
\(581\) | 6.15506e23 | 1.96669 | ||||||||
\(582\) | 1.27154e24 | 4.00392 | ||||||||
\(583\) | 4.84745e22 | 0.150429 | ||||||||
\(584\) | −1.83632e24 | −5.61614 | ||||||||
\(585\) | 1.00430e23 | 0.302718 | ||||||||
\(586\) | −3.45531e23 | −1.02650 | ||||||||
\(587\) | −1.09270e22 | −0.0319946 | −0.0159973 | − | 0.999872i | \(-0.505092\pi\) | ||||
−0.0159973 | + | 0.999872i | \(0.505092\pi\) | |||||||
\(588\) | −1.10741e24 | −3.19595 | ||||||||
\(589\) | −1.45288e23 | −0.413284 | ||||||||
\(590\) | 1.39061e24 | 3.89910 | ||||||||
\(591\) | 6.13442e22 | 0.169543 | ||||||||
\(592\) | 8.65039e22 | 0.235668 | ||||||||
\(593\) | −7.16856e23 | −1.92516 | −0.962581 | − | 0.270994i | \(-0.912648\pi\) | ||||
−0.962581 | + | 0.270994i | \(0.912648\pi\) | |||||||
\(594\) | 5.95422e22 | 0.157630 | ||||||||
\(595\) | 1.00788e24 | 2.63035 | ||||||||
\(596\) | −2.34383e23 | −0.603022 | ||||||||
\(597\) | −4.56623e23 | −1.15818 | ||||||||
\(598\) | 4.04705e22 | 0.101200 | ||||||||
\(599\) | −4.47207e23 | −1.10250 | −0.551252 | − | 0.834339i | \(-0.685850\pi\) | ||||
−0.551252 | + | 0.834339i | \(0.685850\pi\) | |||||||
\(600\) | 1.43969e24 | 3.49931 | ||||||||
\(601\) | −2.21734e23 | −0.531374 | −0.265687 | − | 0.964059i | \(-0.585599\pi\) | ||||
−0.265687 | + | 0.964059i | \(0.585599\pi\) | |||||||
\(602\) | 5.51879e23 | 1.30399 | ||||||||
\(603\) | 4.70818e23 | 1.09687 | ||||||||
\(604\) | −8.26275e23 | −1.89806 | ||||||||
\(605\) | 5.40176e22 | 0.122353 | ||||||||
\(606\) | 2.28110e24 | 5.09479 | ||||||||
\(607\) | −8.29393e21 | −0.0182666 | −0.00913328 | − | 0.999958i | \(-0.502907\pi\) | ||||
−0.00913328 | + | 0.999958i | \(0.502907\pi\) | |||||||
\(608\) | 1.25923e24 | 2.73479 | ||||||||
\(609\) | −7.72297e23 | −1.65401 | ||||||||
\(610\) | −1.44748e24 | −3.05709 | ||||||||
\(611\) | −9.34206e22 | −0.194577 | ||||||||
\(612\) | −2.11800e24 | −4.35049 | ||||||||
\(613\) | 7.73224e23 | 1.56636 | 0.783179 | − | 0.621796i | \(-0.213597\pi\) | ||||
0.783179 | + | 0.621796i | \(0.213597\pi\) | |||||||
\(614\) | −1.36630e24 | −2.72971 | ||||||||
\(615\) | −9.13044e23 | −1.79909 | ||||||||
\(616\) | 6.14969e23 | 1.19514 | ||||||||
\(617\) | −9.48149e23 | −1.81741 | −0.908705 | − | 0.417439i | \(-0.862928\pi\) | ||||
−0.908705 | + | 0.417439i | \(0.862928\pi\) | |||||||
\(618\) | 3.13007e23 | 0.591769 | ||||||||
\(619\) | −5.21614e23 | −0.972699 | −0.486350 | − | 0.873764i | \(-0.661672\pi\) | ||||
−0.486350 | + | 0.873764i | \(0.661672\pi\) | |||||||
\(620\) | 7.41001e23 | 1.36298 | ||||||||
\(621\) | 4.33981e22 | 0.0787394 | ||||||||
\(622\) | 1.72087e24 | 3.07985 | ||||||||
\(623\) | −9.58932e23 | −1.69293 | ||||||||
\(624\) | −4.73559e23 | −0.824718 | ||||||||
\(625\) | −6.71152e23 | −1.15303 | ||||||||
\(626\) | −1.39834e24 | −2.36990 | ||||||||
\(627\) | 2.77352e23 | 0.463721 | ||||||||
\(628\) | 2.08943e24 | 3.44644 | ||||||||
\(629\) | −7.07144e22 | −0.115074 | ||||||||
\(630\) | 2.54940e24 | 4.09301 | ||||||||
\(631\) | −5.47428e23 | −0.867116 | −0.433558 | − | 0.901126i | \(-0.642742\pi\) | ||||
−0.433558 | + | 0.901126i | \(0.642742\pi\) | |||||||
\(632\) | −7.79194e23 | −1.21773 | ||||||||
\(633\) | −1.22029e24 | −1.88162 | ||||||||
\(634\) | 1.88157e24 | 2.86261 | ||||||||
\(635\) | 7.51288e23 | 1.12779 | ||||||||
\(636\) | −1.26940e24 | −1.88024 | ||||||||
\(637\) | 1.09885e23 | 0.160603 | ||||||||
\(638\) | 3.23939e23 | 0.467184 | ||||||||
\(639\) | 2.37221e22 | 0.0337595 | ||||||||
\(640\) | −1.10734e24 | −1.55508 | ||||||||
\(641\) | 1.04352e24 | 1.44614 | 0.723068 | − | 0.690776i | \(-0.242731\pi\) | ||||
0.723068 | + | 0.690776i | \(0.242731\pi\) | |||||||
\(642\) | 6.53468e23 | 0.893668 | ||||||||
\(643\) | 1.48086e24 | 1.99857 | 0.999287 | − | 0.0377577i | \(-0.0120215\pi\) | ||||
0.999287 | + | 0.0377577i | \(0.0120215\pi\) | |||||||
\(644\) | 7.37783e23 | 0.982650 | ||||||||
\(645\) | −7.71226e23 | −1.01373 | ||||||||
\(646\) | −2.17062e24 | −2.81583 | ||||||||
\(647\) | 1.06979e24 | 1.36965 | 0.684827 | − | 0.728705i | \(-0.259878\pi\) | ||||
0.684827 | + | 0.728705i | \(0.259878\pi\) | |||||||
\(648\) | 1.79325e24 | 2.26597 | ||||||||
\(649\) | −3.71834e23 | −0.463735 | ||||||||
\(650\) | −2.35142e23 | −0.289446 | ||||||||
\(651\) | 6.57760e23 | 0.799151 | ||||||||
\(652\) | −2.15207e24 | −2.58079 | ||||||||
\(653\) | −1.36660e24 | −1.61763 | −0.808815 | − | 0.588064i | \(-0.799890\pi\) | ||||
−0.808815 | + | 0.588064i | \(0.799890\pi\) | |||||||
\(654\) | 4.98222e23 | 0.582120 | ||||||||
\(655\) | −5.98091e23 | −0.689789 | ||||||||
\(656\) | 2.33730e24 | 2.66092 | ||||||||
\(657\) | 2.03552e24 | 2.28754 | ||||||||
\(658\) | −2.37147e24 | −2.63086 | ||||||||
\(659\) | 1.19225e24 | 1.30570 | 0.652849 | − | 0.757488i | \(-0.273574\pi\) | ||||
0.652849 | + | 0.757488i | \(0.273574\pi\) | |||||||
\(660\) | −1.41456e24 | −1.52932 | ||||||||
\(661\) | 1.29055e23 | 0.137741 | 0.0688703 | − | 0.997626i | \(-0.478061\pi\) | ||||
0.0688703 | + | 0.997626i | \(0.478061\pi\) | |||||||
\(662\) | −1.73856e24 | −1.83188 | ||||||||
\(663\) | 3.87121e23 | 0.402700 | ||||||||
\(664\) | 4.10741e24 | 4.21831 | ||||||||
\(665\) | 1.87634e24 | 1.90251 | ||||||||
\(666\) | −1.78870e23 | −0.179063 | ||||||||
\(667\) | 2.36107e23 | 0.233367 | ||||||||
\(668\) | 3.71809e24 | 3.62844 | ||||||||
\(669\) | −2.56931e24 | −2.47568 | ||||||||
\(670\) | −2.46094e24 | −2.34134 | ||||||||
\(671\) | 3.87040e23 | 0.363592 | ||||||||
\(672\) | −5.70088e24 | −5.28814 | ||||||||
\(673\) | 7.96311e23 | 0.729382 | 0.364691 | − | 0.931129i | \(-0.381175\pi\) | ||||
0.364691 | + | 0.931129i | \(0.381175\pi\) | |||||||
\(674\) | −1.49709e24 | −1.35407 | ||||||||
\(675\) | −2.52152e23 | −0.225206 | ||||||||
\(676\) | −2.78536e24 | −2.45660 | ||||||||
\(677\) | 2.36216e23 | 0.205734 | 0.102867 | − | 0.994695i | \(-0.467198\pi\) | ||||
0.102867 | + | 0.994695i | \(0.467198\pi\) | |||||||
\(678\) | −1.98095e24 | −1.70381 | ||||||||
\(679\) | −2.30014e24 | −1.95371 | ||||||||
\(680\) | 6.72578e24 | 5.64179 | ||||||||
\(681\) | 1.86122e23 | 0.154187 | ||||||||
\(682\) | −2.75897e23 | −0.225725 | ||||||||
\(683\) | −7.98251e23 | −0.645006 | −0.322503 | − | 0.946568i | \(-0.604524\pi\) | ||||
−0.322503 | + | 0.946568i | \(0.604524\pi\) | |||||||
\(684\) | −3.94301e24 | −3.14667 | ||||||||
\(685\) | 2.05759e24 | 1.62177 | ||||||||
\(686\) | −4.99858e23 | −0.389127 | ||||||||
\(687\) | 2.18471e24 | 1.67981 | ||||||||
\(688\) | 1.97426e24 | 1.49935 | ||||||||
\(689\) | 1.25960e23 | 0.0944860 | ||||||||
\(690\) | −1.43566e24 | −1.06374 | ||||||||
\(691\) | 1.84393e24 | 1.34953 | 0.674764 | − | 0.738034i | \(-0.264245\pi\) | ||||
0.674764 | + | 0.738034i | \(0.264245\pi\) | |||||||
\(692\) | −1.56360e24 | −1.13038 | ||||||||
\(693\) | −6.81680e23 | −0.486798 | ||||||||
\(694\) | 3.24257e23 | 0.228736 | ||||||||
\(695\) | −1.62604e24 | −1.13308 | ||||||||
\(696\) | −5.15371e24 | −3.54765 | ||||||||
\(697\) | −1.91068e24 | −1.29930 | ||||||||
\(698\) | −2.67126e24 | −1.79451 | ||||||||
\(699\) | 3.95586e24 | 2.62534 | ||||||||
\(700\) | −4.28668e24 | −2.81052 | ||||||||
\(701\) | 1.27061e24 | 0.823021 | 0.411510 | − | 0.911405i | \(-0.365001\pi\) | ||||
0.411510 | + | 0.911405i | \(0.365001\pi\) | |||||||
\(702\) | 1.54719e23 | 0.0990097 | ||||||||
\(703\) | −1.31647e23 | −0.0832320 | ||||||||
\(704\) | 9.70059e23 | 0.605941 | ||||||||
\(705\) | 3.31402e24 | 2.04526 | ||||||||
\(706\) | 8.48452e23 | 0.517354 | ||||||||
\(707\) | −4.12635e24 | −2.48600 | ||||||||
\(708\) | 9.73722e24 | 5.79632 | ||||||||
\(709\) | 9.86619e23 | 0.580305 | 0.290153 | − | 0.956980i | \(-0.406294\pi\) | ||||
0.290153 | + | 0.956980i | \(0.406294\pi\) | |||||||
\(710\) | −1.23994e23 | −0.0720616 | ||||||||
\(711\) | 8.63721e23 | 0.496000 | ||||||||
\(712\) | −6.39916e24 | −3.63114 | ||||||||
\(713\) | −2.01091e23 | −0.112754 | ||||||||
\(714\) | 9.82701e24 | 5.44486 | ||||||||
\(715\) | 1.40363e23 | 0.0768514 | ||||||||
\(716\) | 7.74390e24 | 4.18986 | ||||||||
\(717\) | −1.84846e23 | −0.0988322 | ||||||||
\(718\) | −2.09909e23 | −0.110911 | ||||||||
\(719\) | 3.10705e23 | 0.162238 | 0.0811189 | − | 0.996704i | \(-0.474151\pi\) | ||||
0.0811189 | + | 0.996704i | \(0.474151\pi\) | |||||||
\(720\) | 9.12007e24 | 4.70622 | ||||||||
\(721\) | −5.66209e23 | −0.288753 | ||||||||
\(722\) | −3.03677e23 | −0.153055 | ||||||||
\(723\) | 1.20628e24 | 0.600859 | ||||||||
\(724\) | 9.00035e23 | 0.443079 | ||||||||
\(725\) | −1.37183e24 | −0.667465 | ||||||||
\(726\) | 5.26682e23 | 0.253272 | ||||||||
\(727\) | −9.91632e22 | −0.0471312 | −0.0235656 | − | 0.999722i | \(-0.507502\pi\) | ||||
−0.0235656 | + | 0.999722i | \(0.507502\pi\) | |||||||
\(728\) | 1.59798e24 | 0.750679 | ||||||||
\(729\) | −2.87192e24 | −1.33348 | ||||||||
\(730\) | −1.06395e25 | −4.88290 | ||||||||
\(731\) | −1.61390e24 | −0.732114 | ||||||||
\(732\) | −1.01354e25 | −4.54461 | ||||||||
\(733\) | 9.22202e22 | 0.0408736 | 0.0204368 | − | 0.999791i | \(-0.493494\pi\) | ||||
0.0204368 | + | 0.999791i | \(0.493494\pi\) | |||||||
\(734\) | 1.16002e24 | 0.508218 | ||||||||
\(735\) | −3.89809e24 | −1.68815 | ||||||||
\(736\) | 1.74288e24 | 0.746114 | ||||||||
\(737\) | 6.58027e23 | 0.278465 | ||||||||
\(738\) | −4.83300e24 | −2.02180 | ||||||||
\(739\) | 3.12320e24 | 1.29158 | 0.645790 | − | 0.763515i | \(-0.276528\pi\) | ||||
0.645790 | + | 0.763515i | \(0.276528\pi\) | |||||||
\(740\) | 6.71429e23 | 0.274493 | ||||||||
\(741\) | 7.20691e23 | 0.291269 | ||||||||
\(742\) | 3.19747e24 | 1.27753 | ||||||||
\(743\) | 9.03411e23 | 0.356846 | 0.178423 | − | 0.983954i | \(-0.442900\pi\) | ||||
0.178423 | + | 0.983954i | \(0.442900\pi\) | |||||||
\(744\) | 4.38937e24 | 1.71409 | ||||||||
\(745\) | −8.25033e23 | −0.318525 | ||||||||
\(746\) | 1.28369e24 | 0.489982 | ||||||||
\(747\) | −4.55297e24 | −1.71819 | ||||||||
\(748\) | −2.96016e24 | −1.10447 | ||||||||
\(749\) | −1.18208e24 | −0.436065 | ||||||||
\(750\) | −1.93888e24 | −0.707179 | ||||||||
\(751\) | 2.52046e24 | 0.908951 | 0.454476 | − | 0.890759i | \(-0.349827\pi\) | ||||
0.454476 | + | 0.890759i | \(0.349827\pi\) | |||||||
\(752\) | −8.48356e24 | −3.02501 | ||||||||
\(753\) | −5.05078e24 | −1.78074 | ||||||||
\(754\) | 8.41747e23 | 0.293444 | ||||||||
\(755\) | −2.90850e24 | −1.00258 | ||||||||
\(756\) | 2.82055e24 | 0.961386 | ||||||||
\(757\) | 3.50173e24 | 1.18023 | 0.590117 | − | 0.807318i | \(-0.299082\pi\) | ||||
0.590117 | + | 0.807318i | \(0.299082\pi\) | |||||||
\(758\) | −1.52911e24 | −0.509624 | ||||||||
\(759\) | 3.83879e23 | 0.126514 | ||||||||
\(760\) | 1.25212e25 | 4.08066 | ||||||||
\(761\) | −1.67830e24 | −0.540878 | −0.270439 | − | 0.962737i | \(-0.587169\pi\) | ||||
−0.270439 | + | 0.962737i | \(0.587169\pi\) | |||||||
\(762\) | 7.32521e24 | 2.33455 | ||||||||
\(763\) | −9.01251e23 | −0.284045 | ||||||||
\(764\) | 3.59940e24 | 1.12186 | ||||||||
\(765\) | −7.45539e24 | −2.29799 | ||||||||
\(766\) | 2.41014e24 | 0.734680 | ||||||||
\(767\) | −9.66201e23 | −0.291277 | ||||||||
\(768\) | −8.27005e23 | −0.246569 | ||||||||
\(769\) | 4.76727e24 | 1.40571 | 0.702855 | − | 0.711333i | \(-0.251908\pi\) | ||||
0.702855 | + | 0.711333i | \(0.251908\pi\) | |||||||
\(770\) | 3.56310e24 | 1.03910 | ||||||||
\(771\) | 3.67258e24 | 1.05928 | ||||||||
\(772\) | 1.23997e24 | 0.353723 | ||||||||
\(773\) | −9.44535e23 | −0.266497 | −0.133249 | − | 0.991083i | \(-0.542541\pi\) | ||||
−0.133249 | + | 0.991083i | \(0.542541\pi\) | |||||||
\(774\) | −4.08232e24 | −1.13922 | ||||||||
\(775\) | 1.16838e24 | 0.322493 | ||||||||
\(776\) | −1.53493e25 | −4.19048 | ||||||||
\(777\) | 5.96004e23 | 0.160942 | ||||||||
\(778\) | 2.53115e24 | 0.676070 | ||||||||
\(779\) | −3.55705e24 | −0.939769 | ||||||||
\(780\) | −3.67569e24 | −0.960583 | ||||||||
\(781\) | 3.31546e22 | 0.00857057 | ||||||||
\(782\) | −3.00432e24 | −0.768226 | ||||||||
\(783\) | 9.02638e23 | 0.228317 | ||||||||
\(784\) | 9.97873e24 | 2.49683 | ||||||||
\(785\) | 7.35483e24 | 1.82046 | ||||||||
\(786\) | −5.83151e24 | −1.42787 | ||||||||
\(787\) | 3.45699e24 | 0.837360 | 0.418680 | − | 0.908134i | \(-0.362493\pi\) | ||||
0.418680 | + | 0.908134i | \(0.362493\pi\) | |||||||
\(788\) | −1.21888e24 | −0.292071 | ||||||||
\(789\) | −6.32062e24 | −1.49832 | ||||||||
\(790\) | −4.51462e24 | −1.05874 | ||||||||
\(791\) | 3.58340e24 | 0.831371 | ||||||||
\(792\) | −4.54900e24 | −1.04412 | ||||||||
\(793\) | 1.00571e24 | 0.228377 | ||||||||
\(794\) | −4.42169e24 | −0.993376 | ||||||||
\(795\) | −4.46831e24 | −0.993169 | ||||||||
\(796\) | 9.07289e24 | 1.99519 | ||||||||
\(797\) | −4.45740e24 | −0.969808 | −0.484904 | − | 0.874567i | \(-0.661146\pi\) | ||||
−0.484904 | + | 0.874567i | \(0.661146\pi\) | |||||||
\(798\) | 1.82947e25 | 3.93822 | ||||||||
\(799\) | 6.93506e24 | 1.47708 | ||||||||
\(800\) | −1.01265e25 | −2.13400 | ||||||||
\(801\) | 7.09334e24 | 1.47902 | ||||||||
\(802\) | −1.05302e25 | −2.17248 | ||||||||
\(803\) | 2.84489e24 | 0.580742 | ||||||||
\(804\) | −1.72317e25 | −3.48059 | ||||||||
\(805\) | 2.59701e24 | 0.519049 | ||||||||
\(806\) | −7.16910e23 | −0.141781 | ||||||||
\(807\) | 1.25331e25 | 2.45263 | ||||||||
\(808\) | −2.75360e25 | −5.33218 | ||||||||
\(809\) | −9.65318e24 | −1.84973 | −0.924864 | − | 0.380297i | \(-0.875822\pi\) | ||||
−0.924864 | + | 0.380297i | \(0.875822\pi\) | |||||||
\(810\) | 1.03900e25 | 1.97012 | ||||||||
\(811\) | 2.41658e24 | 0.453444 | 0.226722 | − | 0.973960i | \(-0.427199\pi\) | ||||
0.226722 | + | 0.973960i | \(0.427199\pi\) | |||||||
\(812\) | 1.53452e25 | 2.84935 | ||||||||
\(813\) | −3.66217e24 | −0.672929 | ||||||||
\(814\) | −2.49993e23 | −0.0454591 | ||||||||
\(815\) | −7.57533e24 | −1.36321 | ||||||||
\(816\) | 3.51546e25 | 6.26060 | ||||||||
\(817\) | −3.00455e24 | −0.529532 | ||||||||
\(818\) | −2.03919e24 | −0.355676 | ||||||||
\(819\) | −1.77133e24 | −0.305764 | ||||||||
\(820\) | 1.81418e25 | 3.09928 | ||||||||
\(821\) | 4.17116e24 | 0.705245 | 0.352622 | − | 0.935766i | \(-0.385290\pi\) | ||||
0.352622 | + | 0.935766i | \(0.385290\pi\) | |||||||
\(822\) | 2.00619e25 | 3.35708 | ||||||||
\(823\) | 5.89474e24 | 0.976261 | 0.488131 | − | 0.872771i | \(-0.337679\pi\) | ||||
0.488131 | + | 0.872771i | \(0.337679\pi\) | |||||||
\(824\) | −3.77843e24 | −0.619342 | ||||||||
\(825\) | −2.23042e24 | −0.361849 | ||||||||
\(826\) | −2.45269e25 | −3.93833 | ||||||||
\(827\) | −9.04242e24 | −1.43710 | −0.718552 | − | 0.695474i | \(-0.755195\pi\) | ||||
−0.718552 | + | 0.695474i | \(0.755195\pi\) | |||||||
\(828\) | −5.45747e24 | −0.858486 | ||||||||
\(829\) | −8.31631e24 | −1.29484 | −0.647422 | − | 0.762132i | \(-0.724153\pi\) | ||||
−0.647422 | + | 0.762132i | \(0.724153\pi\) | |||||||
\(830\) | 2.37981e25 | 3.66757 | ||||||||
\(831\) | 8.19162e24 | 1.24957 | ||||||||
\(832\) | 2.52067e24 | 0.380599 | ||||||||
\(833\) | −8.15732e24 | −1.21917 | ||||||||
\(834\) | −1.58542e25 | −2.34548 | ||||||||
\(835\) | 1.30878e25 | 1.91659 | ||||||||
\(836\) | −5.51085e24 | −0.798850 | ||||||||
\(837\) | −7.68770e23 | −0.110314 | ||||||||
\(838\) | −1.32627e25 | −1.88390 | ||||||||
\(839\) | 4.62141e24 | 0.649827 | 0.324913 | − | 0.945744i | \(-0.394665\pi\) | ||||
0.324913 | + | 0.945744i | \(0.394665\pi\) | |||||||
\(840\) | −5.66871e25 | −7.89060 | ||||||||
\(841\) | −2.34634e24 | −0.323315 | ||||||||
\(842\) | −2.63001e24 | −0.358760 | ||||||||
\(843\) | −1.31272e25 | −1.77272 | ||||||||
\(844\) | 2.42466e25 | 3.24146 | ||||||||
\(845\) | −9.80453e24 | −1.29761 | ||||||||
\(846\) | 1.75421e25 | 2.29844 | ||||||||
\(847\) | −9.52733e23 | −0.123584 | ||||||||
\(848\) | 1.14384e25 | 1.46893 | ||||||||
\(849\) | 1.77923e25 | 2.26213 | ||||||||
\(850\) | 1.74557e25 | 2.19724 | ||||||||
\(851\) | −1.82211e23 | −0.0227077 | ||||||||
\(852\) | −8.68219e23 | −0.107125 | ||||||||
\(853\) | −4.20936e24 | −0.514221 | −0.257110 | − | 0.966382i | \(-0.582770\pi\) | ||||
−0.257110 | + | 0.966382i | \(0.582770\pi\) | |||||||
\(854\) | 2.55299e25 | 3.08785 | ||||||||
\(855\) | −1.38795e25 | −1.66212 | ||||||||
\(856\) | −7.88826e24 | −0.935308 | ||||||||
\(857\) | 1.04305e25 | 1.22452 | 0.612261 | − | 0.790656i | \(-0.290260\pi\) | ||||
0.612261 | + | 0.790656i | \(0.290260\pi\) | |||||||
\(858\) | 1.36857e24 | 0.159083 | ||||||||
\(859\) | −4.56105e24 | −0.524956 | −0.262478 | − | 0.964938i | \(-0.584540\pi\) | ||||
−0.262478 | + | 0.964938i | \(0.584540\pi\) | |||||||
\(860\) | 1.53239e25 | 1.74635 | ||||||||
\(861\) | 1.61038e25 | 1.81719 | ||||||||
\(862\) | 8.03591e24 | 0.897890 | ||||||||
\(863\) | −1.21177e25 | −1.34069 | −0.670343 | − | 0.742052i | \(-0.733853\pi\) | ||||
−0.670343 | + | 0.742052i | \(0.733853\pi\) | |||||||
\(864\) | 6.66302e24 | 0.729969 | ||||||||
\(865\) | −5.50389e24 | −0.597080 | ||||||||
\(866\) | 1.97536e25 | 2.12200 | ||||||||
\(867\) | −1.48335e25 | −1.57790 | ||||||||
\(868\) | −1.30694e25 | −1.37669 | ||||||||
\(869\) | 1.20716e24 | 0.125920 | ||||||||
\(870\) | −2.98603e25 | −3.08447 | ||||||||
\(871\) | 1.70986e24 | 0.174907 | ||||||||
\(872\) | −6.01424e24 | −0.609243 | ||||||||
\(873\) | 1.70144e25 | 1.70685 | ||||||||
\(874\) | −5.59305e24 | −0.555651 | ||||||||
\(875\) | 3.50729e24 | 0.345067 | ||||||||
\(876\) | −7.44991e25 | −7.25883 | ||||||||
\(877\) | −6.90979e24 | −0.666758 | −0.333379 | − | 0.942793i | \(-0.608189\pi\) | ||||
−0.333379 | + | 0.942793i | \(0.608189\pi\) | |||||||
\(878\) | 1.49311e25 | 1.42688 | ||||||||
\(879\) | −8.51649e24 | −0.806037 | ||||||||
\(880\) | 1.27464e25 | 1.19477 | ||||||||
\(881\) | −3.14171e24 | −0.291656 | −0.145828 | − | 0.989310i | \(-0.546585\pi\) | ||||
−0.145828 | + | 0.989310i | \(0.546585\pi\) | |||||||
\(882\) | −2.06337e25 | −1.89712 | ||||||||
\(883\) | −1.31965e24 | −0.120169 | −0.0600845 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600845 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(884\) | −7.69190e24 | −0.693729 | ||||||||
\(885\) | 3.42752e25 | 3.06170 | ||||||||
\(886\) | −4.11631e25 | −3.64185 | ||||||||
\(887\) | −9.68039e24 | −0.848286 | −0.424143 | − | 0.905595i | \(-0.639425\pi\) | ||||
−0.424143 | + | 0.905595i | \(0.639425\pi\) | |||||||
\(888\) | 3.97726e24 | 0.345202 | ||||||||
\(889\) | −1.32508e25 | −1.13914 | ||||||||
\(890\) | −3.70764e25 | −3.15706 | ||||||||
\(891\) | −2.77817e24 | −0.234314 | ||||||||
\(892\) | 5.10510e25 | 4.26484 | ||||||||
\(893\) | 1.29108e25 | 1.06836 | ||||||||
\(894\) | −8.04424e24 | −0.659350 | ||||||||
\(895\) | 2.72587e25 | 2.21314 | ||||||||
\(896\) | 1.95307e25 | 1.57072 | ||||||||
\(897\) | 9.97499e23 | 0.0794652 | ||||||||
\(898\) | 1.28108e25 | 1.01094 | ||||||||
\(899\) | −4.18250e24 | −0.326948 | ||||||||
\(900\) | 3.17091e25 | 2.45540 | ||||||||
\(901\) | −9.35058e24 | −0.717262 | ||||||||
\(902\) | −6.75472e24 | −0.513277 | ||||||||
\(903\) | 1.36025e25 | 1.02393 | ||||||||
\(904\) | 2.39128e25 | 1.78319 | ||||||||
\(905\) | 3.16814e24 | 0.234041 | ||||||||
\(906\) | −2.83585e25 | −2.07536 | ||||||||
\(907\) | −5.92079e24 | −0.429257 | −0.214629 | − | 0.976696i | \(-0.568854\pi\) | ||||
−0.214629 | + | 0.976696i | \(0.568854\pi\) | |||||||
\(908\) | −3.69816e24 | −0.265617 | ||||||||
\(909\) | 3.05231e25 | 2.17188 | ||||||||
\(910\) | 9.25862e24 | 0.652671 | ||||||||
\(911\) | 6.95449e23 | 0.0485690 | 0.0242845 | − | 0.999705i | \(-0.492269\pi\) | ||||
0.0242845 | + | 0.999705i | \(0.492269\pi\) | |||||||
\(912\) | 6.54462e25 | 4.52823 | ||||||||
\(913\) | −6.36335e24 | −0.436198 | ||||||||
\(914\) | 7.10053e24 | 0.482223 | ||||||||
\(915\) | −3.56768e25 | −2.40053 | ||||||||
\(916\) | −4.34091e25 | −2.89381 | ||||||||
\(917\) | 1.05488e25 | 0.696730 | ||||||||
\(918\) | −1.14855e25 | −0.751602 | ||||||||
\(919\) | 1.22171e24 | 0.0792110 | 0.0396055 | − | 0.999215i | \(-0.487390\pi\) | ||||
0.0396055 | + | 0.999215i | \(0.487390\pi\) | |||||||
\(920\) | 1.73304e25 | 1.11330 | ||||||||
\(921\) | −3.36760e25 | −2.14345 | ||||||||
\(922\) | 3.01071e25 | 1.89870 | ||||||||
\(923\) | 8.61512e22 | 0.00538328 | ||||||||
\(924\) | 2.49492e25 | 1.54470 | ||||||||
\(925\) | 1.05868e24 | 0.0649473 | ||||||||
\(926\) | 1.30369e24 | 0.0792465 | ||||||||
\(927\) | 4.18832e24 | 0.252268 | ||||||||
\(928\) | 3.62502e25 | 2.16348 | ||||||||
\(929\) | −3.60079e24 | −0.212944 | −0.106472 | − | 0.994316i | \(-0.533955\pi\) | ||||
−0.106472 | + | 0.994316i | \(0.533955\pi\) | |||||||
\(930\) | 2.54318e25 | 1.49029 | ||||||||
\(931\) | −1.51862e25 | −0.881815 | ||||||||
\(932\) | −7.86011e25 | −4.52265 | ||||||||
\(933\) | 4.24152e25 | 2.41840 | ||||||||
\(934\) | 1.33759e24 | 0.0755742 | ||||||||
\(935\) | −1.04198e25 | −0.583394 | ||||||||
\(936\) | −1.18204e25 | −0.655827 | ||||||||
\(937\) | 2.05869e25 | 1.13189 | 0.565946 | − | 0.824442i | \(-0.308511\pi\) | ||||
0.565946 | + | 0.824442i | \(0.308511\pi\) | |||||||
\(938\) | 4.34047e25 | 2.36490 | ||||||||
\(939\) | −3.44656e25 | −1.86092 | ||||||||
\(940\) | −6.58480e25 | −3.52335 | ||||||||
\(941\) | 1.57986e25 | 0.837735 | 0.418867 | − | 0.908047i | \(-0.362427\pi\) | ||||
0.418867 | + | 0.908047i | \(0.362427\pi\) | |||||||
\(942\) | 7.17111e25 | 3.76837 | ||||||||
\(943\) | −4.92326e24 | −0.256391 | ||||||||
\(944\) | −8.77410e25 | −4.52836 | ||||||||
\(945\) | 9.92837e24 | 0.507818 | ||||||||
\(946\) | −5.70554e24 | −0.289216 | ||||||||
\(947\) | 6.49895e24 | 0.326489 | 0.163244 | − | 0.986586i | \(-0.447804\pi\) | ||||
0.163244 | + | 0.986586i | \(0.447804\pi\) | |||||||
\(948\) | −3.16118e25 | −1.57391 | ||||||||
\(949\) | 7.39237e24 | 0.364771 | ||||||||
\(950\) | 3.24968e25 | 1.58924 | ||||||||
\(951\) | 4.63761e25 | 2.24781 | ||||||||
\(952\) | −1.18626e26 | −5.69856 | ||||||||
\(953\) | 3.84574e25 | 1.83101 | 0.915504 | − | 0.402309i | \(-0.131792\pi\) | ||||
0.915504 | + | 0.402309i | \(0.131792\pi\) | |||||||
\(954\) | −2.36520e25 | −1.11611 | ||||||||
\(955\) | 1.26700e25 | 0.592580 | ||||||||
\(956\) | 3.67281e24 | 0.170258 | ||||||||
\(957\) | 7.98432e24 | 0.366848 | ||||||||
\(958\) | 6.19238e25 | 2.82001 | ||||||||
\(959\) | −3.62906e25 | −1.63808 | ||||||||
\(960\) | −8.94187e25 | −4.00058 | ||||||||
\(961\) | −1.89879e25 | −0.842032 | ||||||||
\(962\) | −6.49600e23 | −0.0285534 | ||||||||
\(963\) | 8.74398e24 | 0.380966 | ||||||||
\(964\) | −2.39682e25 | −1.03510 | ||||||||
\(965\) | 4.36471e24 | 0.186841 | ||||||||
\(966\) | 2.53214e25 | 1.07444 | ||||||||
\(967\) | −2.88586e25 | −1.21381 | −0.606905 | − | 0.794774i | \(-0.707589\pi\) | ||||
−0.606905 | + | 0.794774i | \(0.707589\pi\) | |||||||
\(968\) | −6.35779e24 | −0.265073 | ||||||||
\(969\) | −5.35004e25 | −2.21108 | ||||||||
\(970\) | −8.89331e25 | −3.64337 | ||||||||
\(971\) | −2.30275e25 | −0.935153 | −0.467576 | − | 0.883953i | \(-0.654873\pi\) | ||||
−0.467576 | + | 0.883953i | \(0.654873\pi\) | |||||||
\(972\) | 9.03194e25 | 3.63595 | ||||||||
\(973\) | 2.86791e25 | 1.14448 | ||||||||
\(974\) | 2.04901e25 | 0.810576 | ||||||||
\(975\) | −5.79568e24 | −0.227282 | ||||||||
\(976\) | 9.13290e25 | 3.55047 | ||||||||
\(977\) | 1.73913e24 | 0.0670238 | 0.0335119 | − | 0.999438i | \(-0.489331\pi\) | ||||
0.0335119 | + | 0.999438i | \(0.489331\pi\) | |||||||
\(978\) | −7.38610e25 | −2.82186 | ||||||||
\(979\) | 9.91382e24 | 0.375481 | ||||||||
\(980\) | 7.74532e25 | 2.90816 | ||||||||
\(981\) | 6.66666e24 | 0.248154 | ||||||||
\(982\) | −2.31633e25 | −0.854776 | ||||||||
\(983\) | 5.37513e25 | 1.96645 | 0.983227 | − | 0.182387i | \(-0.0583824\pi\) | ||||
0.983227 | + | 0.182387i | \(0.0583824\pi\) | |||||||
\(984\) | 1.07464e26 | 3.89767 | ||||||||
\(985\) | −4.29048e24 | −0.154276 | ||||||||
\(986\) | −6.24870e25 | −2.22759 | ||||||||
\(987\) | −5.84510e25 | −2.06584 | ||||||||
\(988\) | −1.43198e25 | −0.501768 | ||||||||
\(989\) | −4.15856e24 | −0.144469 | ||||||||
\(990\) | −2.63567e25 | −0.907803 | ||||||||
\(991\) | −4.37853e25 | −1.49521 | −0.747605 | − | 0.664144i | \(-0.768796\pi\) | ||||
−0.747605 | + | 0.664144i | \(0.768796\pi\) | |||||||
\(992\) | −3.08740e25 | −1.04531 | ||||||||
\(993\) | −4.28512e25 | −1.43845 | ||||||||
\(994\) | 2.18694e24 | 0.0727867 | ||||||||
\(995\) | 3.19367e25 | 1.05389 | ||||||||
\(996\) | 1.66637e26 | 5.45214 | ||||||||
\(997\) | 1.18208e25 | 0.383474 | 0.191737 | − | 0.981446i | \(-0.438588\pi\) | ||||
0.191737 | + | 0.981446i | \(0.438588\pi\) | |||||||
\(998\) | 8.36015e25 | 2.68908 | ||||||||
\(999\) | −6.96592e23 | −0.0222163 |
(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 | 11.18.a.b.1.1 | ✓ | 8 | |
3.2 | odd | 2 | 99.18.a.e.1.8 | 8 | |||
11.10 | odd | 2 | 121.18.a.d.1.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
11.18.a.b.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
99.18.a.e.1.8 | 8 | 3.2 | odd | 2 | |||
121.18.a.d.1.8 | 8 | 11.10 | odd | 2 |