Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,54,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 54, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 54);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 54 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(17.7903107608\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2315873743412x^{2} - 421178019174503472x + 612167648493870378955584 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{27}\cdot 3^{8}\cdot 5^{3}\cdot 7\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-708531.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.51381e7 | −0.897075 | −0.448538 | − | 0.893764i | \(-0.648055\pi\) | ||||
−0.448538 | + | 0.893764i | \(0.648055\pi\) | |||||||
\(3\) | 6.54009e12 | 1.48549 | 0.742746 | − | 0.669573i | \(-0.233523\pi\) | ||||
0.742746 | + | 0.669573i | \(0.233523\pi\) | |||||||
\(4\) | −1.75871e15 | −0.195256 | ||||||||
\(5\) | 2.26338e17 | 0.0679285 | 0.0339643 | − | 0.999423i | \(-0.489187\pi\) | ||||
0.0339643 | + | 0.999423i | \(0.489187\pi\) | |||||||
\(6\) | −5.56810e20 | −1.33260 | ||||||||
\(7\) | −3.24923e22 | −1.30822 | −0.654112 | − | 0.756398i | \(-0.726957\pi\) | ||||
−0.654112 | + | 0.756398i | \(0.726957\pi\) | |||||||
\(8\) | 9.16589e23 | 1.07223 | ||||||||
\(9\) | 2.33895e25 | 1.20669 | ||||||||
\(10\) | −1.92700e25 | −0.0609370 | ||||||||
\(11\) | 4.70740e27 | 1.19090 | 0.595449 | − | 0.803393i | \(-0.296974\pi\) | ||||
0.595449 | + | 0.803393i | \(0.296974\pi\) | |||||||
\(12\) | −1.15021e28 | −0.290051 | ||||||||
\(13\) | −5.49891e29 | −1.66256 | −0.831282 | − | 0.555852i | \(-0.812392\pi\) | ||||
−0.831282 | + | 0.555852i | \(0.812392\pi\) | |||||||
\(14\) | 2.76633e30 | 1.17357 | ||||||||
\(15\) | 1.48027e30 | 0.100907 | ||||||||
\(16\) | −6.21955e31 | −0.766619 | ||||||||
\(17\) | −1.83884e32 | −0.454620 | −0.227310 | − | 0.973823i | \(-0.572993\pi\) | ||||
−0.227310 | + | 0.973823i | \(0.572993\pi\) | |||||||
\(18\) | −1.99134e33 | −1.08249 | ||||||||
\(19\) | −8.16294e33 | −1.05895 | −0.529476 | − | 0.848325i | \(-0.677611\pi\) | ||||
−0.529476 | + | 0.848325i | \(0.677611\pi\) | |||||||
\(20\) | −3.98062e32 | −0.0132634 | ||||||||
\(21\) | −2.12502e35 | −1.94336 | ||||||||
\(22\) | −4.00779e35 | −1.06833 | ||||||||
\(23\) | 8.36591e35 | 0.686635 | 0.343317 | − | 0.939219i | \(-0.388449\pi\) | ||||
0.343317 | + | 0.939219i | \(0.388449\pi\) | |||||||
\(24\) | 5.99457e36 | 1.59280 | ||||||||
\(25\) | −1.10510e37 | −0.995386 | ||||||||
\(26\) | 4.68167e37 | 1.49144 | ||||||||
\(27\) | 2.62013e37 | 0.307032 | ||||||||
\(28\) | 5.71444e37 | 0.255438 | ||||||||
\(29\) | −7.80382e38 | −1.37645 | −0.688224 | − | 0.725498i | \(-0.741610\pi\) | ||||
−0.688224 | + | 0.725498i | \(0.741610\pi\) | |||||||
\(30\) | −1.26027e38 | −0.0905214 | ||||||||
\(31\) | −3.24461e39 | −0.977413 | −0.488707 | − | 0.872448i | \(-0.662531\pi\) | ||||
−0.488707 | + | 0.872448i | \(0.662531\pi\) | |||||||
\(32\) | −2.96069e39 | −0.384519 | ||||||||
\(33\) | 3.07868e40 | 1.76907 | ||||||||
\(34\) | 1.56555e40 | 0.407828 | ||||||||
\(35\) | −7.35423e39 | −0.0888657 | ||||||||
\(36\) | −4.11353e40 | −0.235613 | ||||||||
\(37\) | −2.65824e40 | −0.0736628 | −0.0368314 | − | 0.999321i | \(-0.511726\pi\) | ||||
−0.0368314 | + | 0.999321i | \(0.511726\pi\) | |||||||
\(38\) | 6.94977e41 | 0.949960 | ||||||||
\(39\) | −3.59634e42 | −2.46972 | ||||||||
\(40\) | 2.07459e41 | 0.0728353 | ||||||||
\(41\) | 5.60775e41 | 0.102333 | 0.0511666 | − | 0.998690i | \(-0.483706\pi\) | ||||
0.0511666 | + | 0.998690i | \(0.483706\pi\) | |||||||
\(42\) | 1.80920e43 | 1.74334 | ||||||||
\(43\) | 2.91200e42 | 0.150410 | 0.0752050 | − | 0.997168i | \(-0.476039\pi\) | ||||
0.0752050 | + | 0.997168i | \(0.476039\pi\) | |||||||
\(44\) | −8.27894e42 | −0.232530 | ||||||||
\(45\) | 5.29393e42 | 0.0819684 | ||||||||
\(46\) | −7.12258e43 | −0.615963 | ||||||||
\(47\) | −3.43769e43 | −0.168141 | −0.0840705 | − | 0.996460i | \(-0.526792\pi\) | ||||
−0.0840705 | + | 0.996460i | \(0.526792\pi\) | |||||||
\(48\) | −4.06764e44 | −1.13881 | ||||||||
\(49\) | 4.38874e44 | 0.711448 | ||||||||
\(50\) | 9.40861e44 | 0.892936 | ||||||||
\(51\) | −1.20262e45 | −0.675334 | ||||||||
\(52\) | 9.67099e44 | 0.324625 | ||||||||
\(53\) | 5.37279e45 | 1.08865 | 0.544327 | − | 0.838873i | \(-0.316785\pi\) | ||||
0.544327 | + | 0.838873i | \(0.316785\pi\) | |||||||
\(54\) | −2.23073e45 | −0.275430 | ||||||||
\(55\) | 1.06546e45 | 0.0808959 | ||||||||
\(56\) | −2.97820e46 | −1.40272 | ||||||||
\(57\) | −5.33864e46 | −1.57307 | ||||||||
\(58\) | 6.64402e46 | 1.23478 | ||||||||
\(59\) | 1.17524e47 | 1.38851 | 0.694256 | − | 0.719728i | \(-0.255733\pi\) | ||||
0.694256 | + | 0.719728i | \(0.255733\pi\) | |||||||
\(60\) | −2.60336e45 | −0.0197027 | ||||||||
\(61\) | −6.10529e46 | −0.298171 | −0.149086 | − | 0.988824i | \(-0.547633\pi\) | ||||
−0.149086 | + | 0.988824i | \(0.547633\pi\) | |||||||
\(62\) | 2.76240e47 | 0.876813 | ||||||||
\(63\) | −7.59978e47 | −1.57862 | ||||||||
\(64\) | 8.12275e47 | 1.11156 | ||||||||
\(65\) | −1.24461e47 | −0.112935 | ||||||||
\(66\) | −2.62113e48 | −1.58699 | ||||||||
\(67\) | 5.08562e47 | 0.206710 | 0.103355 | − | 0.994645i | \(-0.467042\pi\) | ||||
0.103355 | + | 0.994645i | \(0.467042\pi\) | |||||||
\(68\) | 3.23399e47 | 0.0887671 | ||||||||
\(69\) | 5.47138e48 | 1.01999 | ||||||||
\(70\) | 6.26125e47 | 0.0797192 | ||||||||
\(71\) | −2.80926e48 | −0.245610 | −0.122805 | − | 0.992431i | \(-0.539189\pi\) | ||||
−0.122805 | + | 0.992431i | \(0.539189\pi\) | |||||||
\(72\) | 2.14386e49 | 1.29385 | ||||||||
\(73\) | −1.95202e49 | −0.817389 | −0.408695 | − | 0.912671i | \(-0.634016\pi\) | ||||
−0.408695 | + | 0.912671i | \(0.634016\pi\) | |||||||
\(74\) | 2.26317e48 | 0.0660811 | ||||||||
\(75\) | −7.22745e49 | −1.47864 | ||||||||
\(76\) | 1.43562e49 | 0.206767 | ||||||||
\(77\) | −1.52954e50 | −1.55796 | ||||||||
\(78\) | 3.06185e50 | 2.21553 | ||||||||
\(79\) | 1.95888e50 | 1.01132 | 0.505662 | − | 0.862732i | \(-0.331248\pi\) | ||||
0.505662 | + | 0.862732i | \(0.331248\pi\) | |||||||
\(80\) | −1.40772e49 | −0.0520753 | ||||||||
\(81\) | −2.82006e50 | −0.750594 | ||||||||
\(82\) | −4.77433e49 | −0.0918005 | ||||||||
\(83\) | −9.78793e49 | −0.136496 | −0.0682482 | − | 0.997668i | \(-0.521741\pi\) | ||||
−0.0682482 | + | 0.997668i | \(0.521741\pi\) | |||||||
\(84\) | 3.73730e50 | 0.379452 | ||||||||
\(85\) | −4.16200e49 | −0.0308816 | ||||||||
\(86\) | −2.47922e50 | −0.134929 | ||||||||
\(87\) | −5.10376e51 | −2.04470 | ||||||||
\(88\) | 4.31475e51 | 1.27692 | ||||||||
\(89\) | 4.98452e50 | 0.109342 | 0.0546712 | − | 0.998504i | \(-0.482589\pi\) | ||||
0.0546712 | + | 0.998504i | \(0.482589\pi\) | |||||||
\(90\) | −4.50715e50 | −0.0735318 | ||||||||
\(91\) | 1.78672e52 | 2.17500 | ||||||||
\(92\) | −1.47132e51 | −0.134069 | ||||||||
\(93\) | −2.12201e52 | −1.45194 | ||||||||
\(94\) | 2.92678e51 | 0.150835 | ||||||||
\(95\) | −1.84758e51 | −0.0719330 | ||||||||
\(96\) | −1.93632e52 | −0.571200 | ||||||||
\(97\) | −1.99451e52 | −0.447079 | −0.223540 | − | 0.974695i | \(-0.571761\pi\) | ||||
−0.223540 | + | 0.974695i | \(0.571761\pi\) | |||||||
\(98\) | −3.73649e52 | −0.638223 | ||||||||
\(99\) | 1.10104e53 | 1.43704 | ||||||||
\(100\) | 1.94355e52 | 0.194355 | ||||||||
\(101\) | 1.70262e52 | 0.130798 | 0.0653990 | − | 0.997859i | \(-0.479168\pi\) | ||||
0.0653990 | + | 0.997859i | \(0.479168\pi\) | |||||||
\(102\) | 1.02389e53 | 0.605825 | ||||||||
\(103\) | 1.87090e53 | 0.854799 | 0.427400 | − | 0.904063i | \(-0.359430\pi\) | ||||
0.427400 | + | 0.904063i | \(0.359430\pi\) | |||||||
\(104\) | −5.04024e53 | −1.78266 | ||||||||
\(105\) | −4.80973e52 | −0.132009 | ||||||||
\(106\) | −4.57429e53 | −0.976604 | ||||||||
\(107\) | 1.10378e54 | 1.83743 | 0.918716 | − | 0.394918i | \(-0.129227\pi\) | ||||
0.918716 | + | 0.394918i | \(0.129227\pi\) | |||||||
\(108\) | −4.60804e52 | −0.0599497 | ||||||||
\(109\) | −1.44235e54 | −1.46984 | −0.734919 | − | 0.678155i | \(-0.762780\pi\) | ||||
−0.734919 | + | 0.678155i | \(0.762780\pi\) | |||||||
\(110\) | −9.07114e52 | −0.0725697 | ||||||||
\(111\) | −1.73851e53 | −0.109426 | ||||||||
\(112\) | 2.02087e54 | 1.00291 | ||||||||
\(113\) | 1.79503e53 | 0.0703869 | 0.0351935 | − | 0.999381i | \(-0.488795\pi\) | ||||
0.0351935 | + | 0.999381i | \(0.488795\pi\) | |||||||
\(114\) | 4.54521e54 | 1.41116 | ||||||||
\(115\) | 1.89352e53 | 0.0466421 | ||||||||
\(116\) | 1.37246e54 | 0.268760 | ||||||||
\(117\) | −1.28617e55 | −2.00619 | ||||||||
\(118\) | −1.00058e55 | −1.24560 | ||||||||
\(119\) | 5.97481e54 | 0.594744 | ||||||||
\(120\) | 1.35680e54 | 0.108196 | ||||||||
\(121\) | 6.53486e54 | 0.418238 | ||||||||
\(122\) | 5.19793e54 | 0.267482 | ||||||||
\(123\) | 3.66752e54 | 0.152015 | ||||||||
\(124\) | 5.70633e54 | 0.190846 | ||||||||
\(125\) | −5.01411e54 | −0.135544 | ||||||||
\(126\) | 6.47031e55 | 1.41614 | ||||||||
\(127\) | −4.95049e55 | −0.878719 | −0.439359 | − | 0.898311i | \(-0.644794\pi\) | ||||
−0.439359 | + | 0.898311i | \(0.644794\pi\) | |||||||
\(128\) | −4.24880e55 | −0.612636 | ||||||||
\(129\) | 1.90447e55 | 0.223433 | ||||||||
\(130\) | 1.05964e55 | 0.101312 | ||||||||
\(131\) | −1.71039e56 | −1.33477 | −0.667386 | − | 0.744712i | \(-0.732587\pi\) | ||||
−0.667386 | + | 0.744712i | \(0.732587\pi\) | |||||||
\(132\) | −5.41450e55 | −0.345421 | ||||||||
\(133\) | 2.65233e56 | 1.38535 | ||||||||
\(134\) | −4.32979e55 | −0.185434 | ||||||||
\(135\) | 5.93034e54 | 0.0208562 | ||||||||
\(136\) | −1.68546e56 | −0.487459 | ||||||||
\(137\) | 4.96948e56 | 1.18363 | 0.591815 | − | 0.806074i | \(-0.298412\pi\) | ||||
0.591815 | + | 0.806074i | \(0.298412\pi\) | |||||||
\(138\) | −4.65823e56 | −0.915008 | ||||||||
\(139\) | 9.49018e56 | 1.53951 | 0.769755 | − | 0.638340i | \(-0.220379\pi\) | ||||
0.769755 | + | 0.638340i | \(0.220379\pi\) | |||||||
\(140\) | 1.29339e55 | 0.0173515 | ||||||||
\(141\) | −2.24828e56 | −0.249772 | ||||||||
\(142\) | 2.39175e56 | 0.220331 | ||||||||
\(143\) | −2.58856e57 | −1.97994 | ||||||||
\(144\) | −1.45472e57 | −0.925069 | ||||||||
\(145\) | −1.76630e56 | −0.0935001 | ||||||||
\(146\) | 1.66191e57 | 0.733260 | ||||||||
\(147\) | 2.87027e57 | 1.05685 | ||||||||
\(148\) | 4.67507e55 | 0.0143831 | ||||||||
\(149\) | 3.22647e57 | 0.830407 | 0.415204 | − | 0.909728i | \(-0.363710\pi\) | ||||
0.415204 | + | 0.909728i | \(0.363710\pi\) | |||||||
\(150\) | 6.15331e57 | 1.32645 | ||||||||
\(151\) | −7.49843e57 | −1.35544 | −0.677721 | − | 0.735319i | \(-0.737032\pi\) | ||||
−0.677721 | + | 0.735319i | \(0.737032\pi\) | |||||||
\(152\) | −7.48206e57 | −1.13545 | ||||||||
\(153\) | −4.30096e57 | −0.548583 | ||||||||
\(154\) | 1.30222e58 | 1.39761 | ||||||||
\(155\) | −7.34379e56 | −0.0663942 | ||||||||
\(156\) | 6.32491e57 | 0.482228 | ||||||||
\(157\) | −2.71453e58 | −1.74725 | −0.873624 | − | 0.486602i | \(-0.838236\pi\) | ||||
−0.873624 | + | 0.486602i | \(0.838236\pi\) | |||||||
\(158\) | −1.66775e58 | −0.907233 | ||||||||
\(159\) | 3.51385e58 | 1.61719 | ||||||||
\(160\) | −6.70116e56 | −0.0261198 | ||||||||
\(161\) | −2.71827e58 | −0.898272 | ||||||||
\(162\) | 2.40094e58 | 0.673339 | ||||||||
\(163\) | 5.10046e58 | 1.21517 | 0.607586 | − | 0.794254i | \(-0.292138\pi\) | ||||
0.607586 | + | 0.794254i | \(0.292138\pi\) | |||||||
\(164\) | −9.86239e56 | −0.0199811 | ||||||||
\(165\) | 6.96821e57 | 0.120170 | ||||||||
\(166\) | 8.33325e57 | 0.122448 | ||||||||
\(167\) | −1.89473e58 | −0.237444 | −0.118722 | − | 0.992928i | \(-0.537880\pi\) | ||||
−0.118722 | + | 0.992928i | \(0.537880\pi\) | |||||||
\(168\) | −1.94777e59 | −2.08373 | ||||||||
\(169\) | 1.92986e59 | 1.76412 | ||||||||
\(170\) | 3.54344e57 | 0.0277031 | ||||||||
\(171\) | −1.90927e59 | −1.27782 | ||||||||
\(172\) | −5.12135e57 | −0.0293684 | ||||||||
\(173\) | −3.74302e59 | −1.84078 | −0.920388 | − | 0.391006i | \(-0.872127\pi\) | ||||
−0.920388 | + | 0.391006i | \(0.872127\pi\) | |||||||
\(174\) | 4.34525e59 | 1.83425 | ||||||||
\(175\) | 3.59072e59 | 1.30219 | ||||||||
\(176\) | −2.92779e59 | −0.912965 | ||||||||
\(177\) | 7.68620e59 | 2.06262 | ||||||||
\(178\) | −4.24373e58 | −0.0980883 | ||||||||
\(179\) | −3.52065e59 | −0.701483 | −0.350741 | − | 0.936472i | \(-0.614070\pi\) | ||||
−0.350741 | + | 0.936472i | \(0.614070\pi\) | |||||||
\(180\) | −9.31048e57 | −0.0160048 | ||||||||
\(181\) | 3.15641e58 | 0.0468501 | 0.0234251 | − | 0.999726i | \(-0.492543\pi\) | ||||
0.0234251 | + | 0.999726i | \(0.492543\pi\) | |||||||
\(182\) | −1.52118e60 | −1.95114 | ||||||||
\(183\) | −3.99292e59 | −0.442931 | ||||||||
\(184\) | 7.66810e59 | 0.736233 | ||||||||
\(185\) | −6.01660e57 | −0.00500380 | ||||||||
\(186\) | 1.80664e60 | 1.30250 | ||||||||
\(187\) | −8.65616e59 | −0.541406 | ||||||||
\(188\) | 6.04590e58 | 0.0328305 | ||||||||
\(189\) | −8.51339e59 | −0.401666 | ||||||||
\(190\) | 1.57300e59 | 0.0645294 | ||||||||
\(191\) | −2.50150e60 | −0.892927 | −0.446464 | − | 0.894802i | \(-0.647317\pi\) | ||||
−0.446464 | + | 0.894802i | \(0.647317\pi\) | |||||||
\(192\) | 5.31235e60 | 1.65122 | ||||||||
\(193\) | 1.82350e60 | 0.493899 | 0.246949 | − | 0.969028i | \(-0.420572\pi\) | ||||
0.246949 | + | 0.969028i | \(0.420572\pi\) | |||||||
\(194\) | 1.69808e60 | 0.401064 | ||||||||
\(195\) | −8.13987e59 | −0.167765 | ||||||||
\(196\) | −7.71851e59 | −0.138914 | ||||||||
\(197\) | −4.11846e60 | −0.647709 | −0.323855 | − | 0.946107i | \(-0.604979\pi\) | ||||
−0.323855 | + | 0.946107i | \(0.604979\pi\) | |||||||
\(198\) | −9.37401e60 | −1.28913 | ||||||||
\(199\) | 2.79044e60 | 0.335789 | 0.167895 | − | 0.985805i | \(-0.446303\pi\) | ||||
0.167895 | + | 0.985805i | \(0.446303\pi\) | |||||||
\(200\) | −1.01292e61 | −1.06729 | ||||||||
\(201\) | 3.32604e60 | 0.307066 | ||||||||
\(202\) | −1.44958e60 | −0.117336 | ||||||||
\(203\) | 2.53564e61 | 1.80070 | ||||||||
\(204\) | 2.11506e60 | 0.131863 | ||||||||
\(205\) | 1.26925e59 | 0.00695133 | ||||||||
\(206\) | −1.59285e61 | −0.766819 | ||||||||
\(207\) | 1.95675e61 | 0.828553 | ||||||||
\(208\) | 3.42008e61 | 1.27455 | ||||||||
\(209\) | −3.84262e61 | −1.26110 | ||||||||
\(210\) | 4.09491e60 | 0.118422 | ||||||||
\(211\) | −9.61153e60 | −0.245080 | −0.122540 | − | 0.992464i | \(-0.539104\pi\) | ||||
−0.122540 | + | 0.992464i | \(0.539104\pi\) | |||||||
\(212\) | −9.44918e60 | −0.212566 | ||||||||
\(213\) | −1.83728e61 | −0.364852 | ||||||||
\(214\) | −9.39735e61 | −1.64832 | ||||||||
\(215\) | 6.59095e59 | 0.0102171 | ||||||||
\(216\) | 2.40158e61 | 0.329210 | ||||||||
\(217\) | 1.05425e62 | 1.27867 | ||||||||
\(218\) | 1.22799e62 | 1.31856 | ||||||||
\(219\) | −1.27664e62 | −1.21423 | ||||||||
\(220\) | −1.87384e60 | −0.0157954 | ||||||||
\(221\) | 1.01116e62 | 0.755834 | ||||||||
\(222\) | 1.48014e61 | 0.0981629 | ||||||||
\(223\) | −8.79461e61 | −0.517771 | −0.258885 | − | 0.965908i | \(-0.583355\pi\) | ||||
−0.258885 | + | 0.965908i | \(0.583355\pi\) | |||||||
\(224\) | 9.61994e61 | 0.503037 | ||||||||
\(225\) | −2.58477e62 | −1.20112 | ||||||||
\(226\) | −1.52825e61 | −0.0631424 | ||||||||
\(227\) | 3.14689e62 | 1.15664 | 0.578318 | − | 0.815811i | \(-0.303709\pi\) | ||||
0.578318 | + | 0.815811i | \(0.303709\pi\) | |||||||
\(228\) | 9.38911e61 | 0.307150 | ||||||||
\(229\) | −4.50545e61 | −0.131250 | −0.0656248 | − | 0.997844i | \(-0.520904\pi\) | ||||
−0.0656248 | + | 0.997844i | \(0.520904\pi\) | |||||||
\(230\) | −1.61211e61 | −0.0418414 | ||||||||
\(231\) | −1.00033e63 | −2.31434 | ||||||||
\(232\) | −7.15289e62 | −1.47588 | ||||||||
\(233\) | 6.26152e62 | 1.15278 | 0.576392 | − | 0.817173i | \(-0.304460\pi\) | ||||
0.576392 | + | 0.817173i | \(0.304460\pi\) | |||||||
\(234\) | 1.09502e63 | 1.79971 | ||||||||
\(235\) | −7.78080e60 | −0.0114216 | ||||||||
\(236\) | −2.06691e62 | −0.271115 | ||||||||
\(237\) | 1.28113e63 | 1.50231 | ||||||||
\(238\) | −5.08684e62 | −0.533530 | ||||||||
\(239\) | 1.59379e63 | 1.49585 | 0.747923 | − | 0.663785i | \(-0.231051\pi\) | ||||
0.747923 | + | 0.663785i | \(0.231051\pi\) | |||||||
\(240\) | −9.20662e61 | −0.0773574 | ||||||||
\(241\) | −1.86546e63 | −1.40390 | −0.701948 | − | 0.712228i | \(-0.747686\pi\) | ||||
−0.701948 | + | 0.712228i | \(0.747686\pi\) | |||||||
\(242\) | −5.56365e62 | −0.375191 | ||||||||
\(243\) | −2.35221e63 | −1.42203 | ||||||||
\(244\) | 1.07374e62 | 0.0582197 | ||||||||
\(245\) | 9.93337e61 | 0.0483276 | ||||||||
\(246\) | −3.12245e62 | −0.136369 | ||||||||
\(247\) | 4.48873e63 | 1.76058 | ||||||||
\(248\) | −2.97398e63 | −1.04802 | ||||||||
\(249\) | −6.40139e62 | −0.202764 | ||||||||
\(250\) | 4.26892e62 | 0.121593 | ||||||||
\(251\) | −1.23471e62 | −0.0316382 | −0.0158191 | − | 0.999875i | \(-0.505036\pi\) | ||||
−0.0158191 | + | 0.999875i | \(0.505036\pi\) | |||||||
\(252\) | 1.33658e63 | 0.308234 | ||||||||
\(253\) | 3.93817e63 | 0.817712 | ||||||||
\(254\) | 4.21475e63 | 0.788277 | ||||||||
\(255\) | −2.72198e62 | −0.0458744 | ||||||||
\(256\) | −3.69897e63 | −0.561982 | ||||||||
\(257\) | −2.57030e63 | −0.352174 | −0.176087 | − | 0.984375i | \(-0.556344\pi\) | ||||
−0.176087 | + | 0.984375i | \(0.556344\pi\) | |||||||
\(258\) | −1.62143e63 | −0.200436 | ||||||||
\(259\) | 8.63722e62 | 0.0963674 | ||||||||
\(260\) | 2.18891e62 | 0.0220513 | ||||||||
\(261\) | −1.82527e64 | −1.66094 | ||||||||
\(262\) | 1.45620e64 | 1.19739 | ||||||||
\(263\) | −1.92105e64 | −1.42794 | −0.713972 | − | 0.700174i | \(-0.753106\pi\) | ||||
−0.713972 | + | 0.700174i | \(0.753106\pi\) | |||||||
\(264\) | 2.82188e64 | 1.89686 | ||||||||
\(265\) | 1.21607e63 | 0.0739506 | ||||||||
\(266\) | −2.25814e64 | −1.24276 | ||||||||
\(267\) | 3.25992e63 | 0.162427 | ||||||||
\(268\) | −8.94411e62 | −0.0403613 | ||||||||
\(269\) | 1.72508e64 | 0.705301 | 0.352651 | − | 0.935755i | \(-0.385280\pi\) | ||||
0.352651 | + | 0.935755i | \(0.385280\pi\) | |||||||
\(270\) | −5.04898e62 | −0.0187096 | ||||||||
\(271\) | −1.11722e64 | −0.375365 | −0.187682 | − | 0.982230i | \(-0.560098\pi\) | ||||
−0.187682 | + | 0.982230i | \(0.560098\pi\) | |||||||
\(272\) | 1.14368e64 | 0.348520 | ||||||||
\(273\) | 1.16853e65 | 3.23095 | ||||||||
\(274\) | −4.23092e64 | −1.06180 | ||||||||
\(275\) | −5.20214e64 | −1.18540 | ||||||||
\(276\) | −9.62256e63 | −0.199159 | ||||||||
\(277\) | −1.05957e64 | −0.199258 | −0.0996291 | − | 0.995025i | \(-0.531766\pi\) | ||||
−0.0996291 | + | 0.995025i | \(0.531766\pi\) | |||||||
\(278\) | −8.07976e64 | −1.38106 | ||||||||
\(279\) | −7.58899e64 | −1.17943 | ||||||||
\(280\) | −6.74080e63 | −0.0952848 | ||||||||
\(281\) | 5.57080e64 | 0.716473 | 0.358237 | − | 0.933631i | \(-0.383378\pi\) | ||||
0.358237 | + | 0.933631i | \(0.383378\pi\) | |||||||
\(282\) | 1.91414e64 | 0.224064 | ||||||||
\(283\) | 1.04527e65 | 1.11401 | 0.557003 | − | 0.830511i | \(-0.311951\pi\) | ||||
0.557003 | + | 0.830511i | \(0.311951\pi\) | |||||||
\(284\) | 4.94067e63 | 0.0479568 | ||||||||
\(285\) | −1.20834e64 | −0.106856 | ||||||||
\(286\) | 2.20385e65 | 1.77616 | ||||||||
\(287\) | −1.82208e64 | −0.133875 | ||||||||
\(288\) | −6.92490e64 | −0.463994 | ||||||||
\(289\) | −1.29790e65 | −0.793321 | ||||||||
\(290\) | 1.50379e64 | 0.0838766 | ||||||||
\(291\) | −1.30442e65 | −0.664132 | ||||||||
\(292\) | 3.43304e64 | 0.159600 | ||||||||
\(293\) | 2.53583e65 | 1.07678 | 0.538392 | − | 0.842694i | \(-0.319032\pi\) | ||||
0.538392 | + | 0.842694i | \(0.319032\pi\) | |||||||
\(294\) | −2.44369e65 | −0.948075 | ||||||||
\(295\) | 2.66002e64 | 0.0943196 | ||||||||
\(296\) | −2.43651e64 | −0.0789838 | ||||||||
\(297\) | 1.23340e65 | 0.365643 | ||||||||
\(298\) | −2.74695e65 | −0.744938 | ||||||||
\(299\) | −4.60034e65 | −1.14157 | ||||||||
\(300\) | 1.27110e65 | 0.288713 | ||||||||
\(301\) | −9.46174e64 | −0.196770 | ||||||||
\(302\) | 6.38402e65 | 1.21593 | ||||||||
\(303\) | 1.11353e65 | 0.194300 | ||||||||
\(304\) | 5.07699e65 | 0.811813 | ||||||||
\(305\) | −1.38186e64 | −0.0202543 | ||||||||
\(306\) | 3.66176e65 | 0.492121 | ||||||||
\(307\) | −1.14760e66 | −1.41457 | −0.707284 | − | 0.706930i | \(-0.750080\pi\) | ||||
−0.707284 | + | 0.706930i | \(0.750080\pi\) | |||||||
\(308\) | 2.69001e65 | 0.304201 | ||||||||
\(309\) | 1.22358e66 | 1.26980 | ||||||||
\(310\) | 6.25236e64 | 0.0595606 | ||||||||
\(311\) | 3.98992e65 | 0.348991 | 0.174496 | − | 0.984658i | \(-0.444171\pi\) | ||||
0.174496 | + | 0.984658i | \(0.444171\pi\) | |||||||
\(312\) | −3.29636e66 | −2.64812 | ||||||||
\(313\) | −1.04506e66 | −0.771291 | −0.385645 | − | 0.922647i | \(-0.626021\pi\) | ||||
−0.385645 | + | 0.922647i | \(0.626021\pi\) | |||||||
\(314\) | 2.31110e66 | 1.56741 | ||||||||
\(315\) | −1.72012e65 | −0.107233 | ||||||||
\(316\) | −3.44510e65 | −0.197467 | ||||||||
\(317\) | 1.24693e66 | 0.657312 | 0.328656 | − | 0.944450i | \(-0.393404\pi\) | ||||
0.328656 | + | 0.944450i | \(0.393404\pi\) | |||||||
\(318\) | −2.99163e66 | −1.45074 | ||||||||
\(319\) | −3.67357e66 | −1.63921 | ||||||||
\(320\) | 1.83849e65 | 0.0755067 | ||||||||
\(321\) | 7.21880e66 | 2.72949 | ||||||||
\(322\) | 2.31429e66 | 0.805817 | ||||||||
\(323\) | 1.50104e66 | 0.481420 | ||||||||
\(324\) | 4.95966e65 | 0.146558 | ||||||||
\(325\) | 6.07685e66 | 1.65489 | ||||||||
\(326\) | −4.34243e66 | −1.09010 | ||||||||
\(327\) | −9.43312e66 | −2.18343 | ||||||||
\(328\) | 5.14000e65 | 0.109725 | ||||||||
\(329\) | 1.11698e66 | 0.219966 | ||||||||
\(330\) | −5.93260e65 | −0.107802 | ||||||||
\(331\) | −7.02324e66 | −1.17787 | −0.588933 | − | 0.808182i | \(-0.700452\pi\) | ||||
−0.588933 | + | 0.808182i | \(0.700452\pi\) | |||||||
\(332\) | 1.72141e65 | 0.0266517 | ||||||||
\(333\) | −6.21749e65 | −0.0888879 | ||||||||
\(334\) | 1.61314e66 | 0.213005 | ||||||||
\(335\) | 1.15107e65 | 0.0140415 | ||||||||
\(336\) | 1.32167e67 | 1.48981 | ||||||||
\(337\) | 7.44919e66 | 0.776098 | 0.388049 | − | 0.921639i | \(-0.373149\pi\) | ||||
0.388049 | + | 0.921639i | \(0.373149\pi\) | |||||||
\(338\) | −1.64304e67 | −1.58254 | ||||||||
\(339\) | 1.17396e66 | 0.104559 | ||||||||
\(340\) | 7.31974e64 | 0.00602982 | ||||||||
\(341\) | −1.52737e67 | −1.16400 | ||||||||
\(342\) | 1.62552e67 | 1.14630 | ||||||||
\(343\) | 5.78362e66 | 0.377490 | ||||||||
\(344\) | 2.66910e66 | 0.161275 | ||||||||
\(345\) | 1.23838e66 | 0.0692864 | ||||||||
\(346\) | 3.18674e67 | 1.65131 | ||||||||
\(347\) | −1.68736e67 | −0.809985 | −0.404993 | − | 0.914320i | \(-0.632726\pi\) | ||||
−0.404993 | + | 0.914320i | \(0.632726\pi\) | |||||||
\(348\) | 8.97603e66 | 0.399240 | ||||||||
\(349\) | −1.94835e67 | −0.803143 | −0.401571 | − | 0.915828i | \(-0.631536\pi\) | ||||
−0.401571 | + | 0.915828i | \(0.631536\pi\) | |||||||
\(350\) | −3.05707e67 | −1.16816 | ||||||||
\(351\) | −1.44079e67 | −0.510459 | ||||||||
\(352\) | −1.39371e67 | −0.457923 | ||||||||
\(353\) | 4.86893e67 | 1.48390 | 0.741948 | − | 0.670457i | \(-0.233902\pi\) | ||||
0.741948 | + | 0.670457i | \(0.233902\pi\) | |||||||
\(354\) | −6.54388e67 | −1.85033 | ||||||||
\(355\) | −6.35842e65 | −0.0166839 | ||||||||
\(356\) | −8.76632e65 | −0.0213497 | ||||||||
\(357\) | 3.90758e67 | 0.883487 | ||||||||
\(358\) | 2.99741e67 | 0.629283 | ||||||||
\(359\) | 3.23986e67 | 0.631719 | 0.315860 | − | 0.948806i | \(-0.397707\pi\) | ||||
0.315860 | + | 0.948806i | \(0.397707\pi\) | |||||||
\(360\) | 4.85236e66 | 0.0878894 | ||||||||
\(361\) | 7.21254e66 | 0.121380 | ||||||||
\(362\) | −2.68730e66 | −0.0420281 | ||||||||
\(363\) | 4.27385e67 | 0.621290 | ||||||||
\(364\) | −3.14232e67 | −0.424682 | ||||||||
\(365\) | −4.41816e66 | −0.0555240 | ||||||||
\(366\) | 3.39949e67 | 0.397343 | ||||||||
\(367\) | −4.09627e67 | −0.445388 | −0.222694 | − | 0.974888i | \(-0.571485\pi\) | ||||
−0.222694 | + | 0.974888i | \(0.571485\pi\) | |||||||
\(368\) | −5.20323e67 | −0.526387 | ||||||||
\(369\) | 1.31162e67 | 0.123484 | ||||||||
\(370\) | 5.12242e65 | 0.00448879 | ||||||||
\(371\) | −1.74574e68 | −1.42420 | ||||||||
\(372\) | 3.73199e67 | 0.283500 | ||||||||
\(373\) | −1.54943e68 | −1.09619 | −0.548097 | − | 0.836415i | \(-0.684648\pi\) | ||||
−0.548097 | + | 0.836415i | \(0.684648\pi\) | |||||||
\(374\) | 7.36969e67 | 0.485682 | ||||||||
\(375\) | −3.27927e67 | −0.201349 | ||||||||
\(376\) | −3.15095e67 | −0.180287 | ||||||||
\(377\) | 4.29125e68 | 2.28843 | ||||||||
\(378\) | 7.24814e67 | 0.360324 | ||||||||
\(379\) | 1.05294e68 | 0.488049 | 0.244025 | − | 0.969769i | \(-0.421532\pi\) | ||||
0.244025 | + | 0.969769i | \(0.421532\pi\) | |||||||
\(380\) | 3.24936e66 | 0.0140453 | ||||||||
\(381\) | −3.23767e68 | −1.30533 | ||||||||
\(382\) | 2.12973e68 | 0.801023 | ||||||||
\(383\) | 8.24887e67 | 0.289486 | 0.144743 | − | 0.989469i | \(-0.453764\pi\) | ||||
0.144743 | + | 0.989469i | \(0.453764\pi\) | |||||||
\(384\) | −2.77875e68 | −0.910065 | ||||||||
\(385\) | −3.46193e67 | −0.105830 | ||||||||
\(386\) | −1.55250e68 | −0.443064 | ||||||||
\(387\) | 6.81102e67 | 0.181498 | ||||||||
\(388\) | 3.50775e67 | 0.0872948 | ||||||||
\(389\) | 1.89075e68 | 0.439510 | 0.219755 | − | 0.975555i | \(-0.429474\pi\) | ||||
0.219755 | + | 0.975555i | \(0.429474\pi\) | |||||||
\(390\) | 6.93013e67 | 0.150498 | ||||||||
\(391\) | −1.53836e68 | −0.312158 | ||||||||
\(392\) | 4.02267e68 | 0.762840 | ||||||||
\(393\) | −1.11861e69 | −1.98279 | ||||||||
\(394\) | 3.50638e68 | 0.581044 | ||||||||
\(395\) | 4.43369e67 | 0.0686977 | ||||||||
\(396\) | −1.93640e68 | −0.280591 | ||||||||
\(397\) | −1.41885e69 | −1.92304 | −0.961518 | − | 0.274743i | \(-0.911407\pi\) | ||||
−0.961518 | + | 0.274743i | \(0.911407\pi\) | |||||||
\(398\) | −2.37573e68 | −0.301228 | ||||||||
\(399\) | 1.73464e69 | 2.05792 | ||||||||
\(400\) | 6.87323e68 | 0.763082 | ||||||||
\(401\) | 1.07913e69 | 1.12137 | 0.560686 | − | 0.828028i | \(-0.310537\pi\) | ||||
0.560686 | + | 0.828028i | \(0.310537\pi\) | |||||||
\(402\) | −2.83172e68 | −0.275461 | ||||||||
\(403\) | 1.78419e69 | 1.62501 | ||||||||
\(404\) | −2.99441e67 | −0.0255391 | ||||||||
\(405\) | −6.38286e67 | −0.0509867 | ||||||||
\(406\) | −2.15879e69 | −1.61537 | ||||||||
\(407\) | −1.25134e68 | −0.0877249 | ||||||||
\(408\) | −1.10231e69 | −0.724116 | ||||||||
\(409\) | −1.89009e69 | −1.16363 | −0.581814 | − | 0.813322i | \(-0.697657\pi\) | ||||
−0.581814 | + | 0.813322i | \(0.697657\pi\) | |||||||
\(410\) | −1.08061e67 | −0.00623587 | ||||||||
\(411\) | 3.25008e69 | 1.75827 | ||||||||
\(412\) | −3.29037e68 | −0.166905 | ||||||||
\(413\) | −3.81863e69 | −1.81648 | ||||||||
\(414\) | −1.66594e69 | −0.743274 | ||||||||
\(415\) | −2.21538e67 | −0.00927200 | ||||||||
\(416\) | 1.62806e69 | 0.639288 | ||||||||
\(417\) | 6.20666e69 | 2.28693 | ||||||||
\(418\) | 3.27153e69 | 1.13131 | ||||||||
\(419\) | −5.52165e69 | −1.79225 | −0.896123 | − | 0.443807i | \(-0.853628\pi\) | ||||
−0.896123 | + | 0.443807i | \(0.853628\pi\) | |||||||
\(420\) | 8.45891e67 | 0.0257756 | ||||||||
\(421\) | −1.18435e69 | −0.338847 | −0.169424 | − | 0.985543i | \(-0.554191\pi\) | ||||
−0.169424 | + | 0.985543i | \(0.554191\pi\) | |||||||
\(422\) | 8.18307e68 | 0.219855 | ||||||||
\(423\) | −8.04059e68 | −0.202894 | ||||||||
\(424\) | 4.92464e69 | 1.16729 | ||||||||
\(425\) | 2.03210e69 | 0.452522 | ||||||||
\(426\) | 1.56423e69 | 0.327300 | ||||||||
\(427\) | 1.98375e69 | 0.390075 | ||||||||
\(428\) | −1.94122e69 | −0.358769 | ||||||||
\(429\) | −1.69294e70 | −2.94119 | ||||||||
\(430\) | −5.61141e67 | −0.00916554 | ||||||||
\(431\) | 2.27553e69 | 0.349490 | 0.174745 | − | 0.984614i | \(-0.444090\pi\) | ||||
0.174745 | + | 0.984614i | \(0.444090\pi\) | |||||||
\(432\) | −1.62960e69 | −0.235376 | ||||||||
\(433\) | 1.18575e70 | 1.61088 | 0.805440 | − | 0.592677i | \(-0.201929\pi\) | ||||
0.805440 | + | 0.592677i | \(0.201929\pi\) | |||||||
\(434\) | −8.97567e69 | −1.14707 | ||||||||
\(435\) | −1.15517e69 | −0.138894 | ||||||||
\(436\) | 2.53668e69 | 0.286994 | ||||||||
\(437\) | −6.82905e69 | −0.727113 | ||||||||
\(438\) | 1.08691e70 | 1.08925 | ||||||||
\(439\) | −1.92587e69 | −0.181684 | −0.0908422 | − | 0.995865i | \(-0.528956\pi\) | ||||
−0.0908422 | + | 0.995865i | \(0.528956\pi\) | |||||||
\(440\) | 9.76590e68 | 0.0867394 | ||||||||
\(441\) | 1.02650e70 | 0.858495 | ||||||||
\(442\) | −8.60885e69 | −0.678040 | ||||||||
\(443\) | −1.15476e69 | −0.0856626 | −0.0428313 | − | 0.999082i | \(-0.513638\pi\) | ||||
−0.0428313 | + | 0.999082i | \(0.513638\pi\) | |||||||
\(444\) | 3.05754e68 | 0.0213660 | ||||||||
\(445\) | 1.12819e68 | 0.00742746 | ||||||||
\(446\) | 7.48756e69 | 0.464479 | ||||||||
\(447\) | 2.11014e70 | 1.23356 | ||||||||
\(448\) | −2.63926e70 | −1.45417 | ||||||||
\(449\) | 1.26244e70 | 0.655664 | 0.327832 | − | 0.944736i | \(-0.393682\pi\) | ||||
0.327832 | + | 0.944736i | \(0.393682\pi\) | |||||||
\(450\) | 2.20063e70 | 1.07749 | ||||||||
\(451\) | 2.63979e69 | 0.121868 | ||||||||
\(452\) | −3.15693e68 | −0.0137435 | ||||||||
\(453\) | −4.90404e70 | −2.01350 | ||||||||
\(454\) | −2.67921e70 | −1.03759 | ||||||||
\(455\) | 4.04403e69 | 0.147745 | ||||||||
\(456\) | −4.89333e70 | −1.68669 | ||||||||
\(457\) | 1.89960e70 | 0.617848 | 0.308924 | − | 0.951087i | \(-0.400031\pi\) | ||||
0.308924 | + | 0.951087i | \(0.400031\pi\) | |||||||
\(458\) | 3.83586e69 | 0.117741 | ||||||||
\(459\) | −4.81800e69 | −0.139583 | ||||||||
\(460\) | −3.33015e68 | −0.00910714 | ||||||||
\(461\) | 4.91287e70 | 1.26841 | 0.634206 | − | 0.773164i | \(-0.281327\pi\) | ||||
0.634206 | + | 0.773164i | \(0.281327\pi\) | |||||||
\(462\) | 8.51664e70 | 2.07614 | ||||||||
\(463\) | −1.61924e70 | −0.372748 | −0.186374 | − | 0.982479i | \(-0.559674\pi\) | ||||
−0.186374 | + | 0.982479i | \(0.559674\pi\) | |||||||
\(464\) | 4.85363e70 | 1.05521 | ||||||||
\(465\) | −4.80290e69 | −0.0986281 | ||||||||
\(466\) | −5.33094e70 | −1.03413 | ||||||||
\(467\) | 9.60677e68 | 0.0176068 | 0.00880339 | − | 0.999961i | \(-0.497198\pi\) | ||||
0.00880339 | + | 0.999961i | \(0.497198\pi\) | |||||||
\(468\) | 2.26200e70 | 0.391721 | ||||||||
\(469\) | −1.65243e70 | −0.270423 | ||||||||
\(470\) | 6.62442e68 | 0.0102460 | ||||||||
\(471\) | −1.77533e71 | −2.59552 | ||||||||
\(472\) | 1.07722e71 | 1.48881 | ||||||||
\(473\) | 1.37079e70 | 0.179123 | ||||||||
\(474\) | −1.09073e71 | −1.34769 | ||||||||
\(475\) | 9.02087e70 | 1.05407 | ||||||||
\(476\) | −1.05080e70 | −0.116127 | ||||||||
\(477\) | 1.25667e71 | 1.31366 | ||||||||
\(478\) | −1.35692e71 | −1.34189 | ||||||||
\(479\) | −7.16104e70 | −0.670016 | −0.335008 | − | 0.942215i | \(-0.608739\pi\) | ||||
−0.335008 | + | 0.942215i | \(0.608739\pi\) | |||||||
\(480\) | −4.38261e69 | −0.0388008 | ||||||||
\(481\) | 1.46174e70 | 0.122469 | ||||||||
\(482\) | 1.58822e71 | 1.25940 | ||||||||
\(483\) | −1.77778e71 | −1.33438 | ||||||||
\(484\) | −1.14929e70 | −0.0816635 | ||||||||
\(485\) | −4.51432e69 | −0.0303694 | ||||||||
\(486\) | 2.00263e71 | 1.27567 | ||||||||
\(487\) | 8.84962e70 | 0.533835 | 0.266918 | − | 0.963719i | \(-0.413995\pi\) | ||||
0.266918 | + | 0.963719i | \(0.413995\pi\) | |||||||
\(488\) | −5.59604e70 | −0.319710 | ||||||||
\(489\) | 3.33574e71 | 1.80513 | ||||||||
\(490\) | −8.45708e69 | −0.0433535 | ||||||||
\(491\) | −3.37986e71 | −1.64149 | −0.820747 | − | 0.571292i | \(-0.806442\pi\) | ||||
−0.820747 | + | 0.571292i | \(0.806442\pi\) | |||||||
\(492\) | −6.45009e69 | −0.0296818 | ||||||||
\(493\) | 1.43500e71 | 0.625760 | ||||||||
\(494\) | −3.82162e71 | −1.57937 | ||||||||
\(495\) | 2.49206e70 | 0.0976160 | ||||||||
\(496\) | 2.01801e71 | 0.749304 | ||||||||
\(497\) | 9.12793e70 | 0.321313 | ||||||||
\(498\) | 5.45002e70 | 0.181895 | ||||||||
\(499\) | −5.44978e71 | −1.72470 | −0.862352 | − | 0.506310i | \(-0.831009\pi\) | ||||
−0.862352 | + | 0.506310i | \(0.831009\pi\) | |||||||
\(500\) | 8.81836e69 | 0.0264657 | ||||||||
\(501\) | −1.23917e71 | −0.352722 | ||||||||
\(502\) | 1.05121e70 | 0.0283818 | ||||||||
\(503\) | 5.30455e71 | 1.35862 | 0.679308 | − | 0.733853i | \(-0.262280\pi\) | ||||
0.679308 | + | 0.733853i | \(0.262280\pi\) | |||||||
\(504\) | −6.96587e71 | −1.69265 | ||||||||
\(505\) | 3.85367e69 | 0.00888492 | ||||||||
\(506\) | −3.35288e71 | −0.733549 | ||||||||
\(507\) | 1.26214e72 | 2.62058 | ||||||||
\(508\) | 8.70647e70 | 0.171575 | ||||||||
\(509\) | −5.04965e71 | −0.944582 | −0.472291 | − | 0.881443i | \(-0.656573\pi\) | ||||
−0.472291 | + | 0.881443i | \(0.656573\pi\) | |||||||
\(510\) | 2.31744e70 | 0.0411528 | ||||||||
\(511\) | 6.34256e71 | 1.06933 | ||||||||
\(512\) | 6.97622e71 | 1.11678 | ||||||||
\(513\) | −2.13880e71 | −0.325132 | ||||||||
\(514\) | 2.18831e71 | 0.315926 | ||||||||
\(515\) | 4.23455e70 | 0.0580652 | ||||||||
\(516\) | −3.34941e70 | −0.0436266 | ||||||||
\(517\) | −1.61826e71 | −0.200239 | ||||||||
\(518\) | −7.35356e70 | −0.0864488 | ||||||||
\(519\) | −2.44797e72 | −2.73446 | ||||||||
\(520\) | −1.14080e71 | −0.121093 | ||||||||
\(521\) | −1.71481e72 | −1.72989 | −0.864943 | − | 0.501870i | \(-0.832646\pi\) | ||||
−0.864943 | + | 0.501870i | \(0.832646\pi\) | |||||||
\(522\) | 1.55400e72 | 1.48999 | ||||||||
\(523\) | −1.17717e72 | −1.07287 | −0.536433 | − | 0.843943i | \(-0.680228\pi\) | ||||
−0.536433 | + | 0.843943i | \(0.680228\pi\) | |||||||
\(524\) | 3.00808e71 | 0.260622 | ||||||||
\(525\) | 2.34836e72 | 1.93439 | ||||||||
\(526\) | 1.63554e72 | 1.28097 | ||||||||
\(527\) | 5.96633e71 | 0.444351 | ||||||||
\(528\) | −1.91480e72 | −1.35620 | ||||||||
\(529\) | −7.84598e71 | −0.528533 | ||||||||
\(530\) | −1.03534e71 | −0.0663392 | ||||||||
\(531\) | 2.74884e72 | 1.67550 | ||||||||
\(532\) | −4.66467e71 | −0.270497 | ||||||||
\(533\) | −3.08365e71 | −0.170135 | ||||||||
\(534\) | −2.77543e71 | −0.145709 | ||||||||
\(535\) | 2.49827e71 | 0.124814 | ||||||||
\(536\) | 4.66142e71 | 0.221641 | ||||||||
\(537\) | −2.30253e72 | −1.04205 | ||||||||
\(538\) | −1.46870e72 | −0.632708 | ||||||||
\(539\) | 2.06595e72 | 0.847263 | ||||||||
\(540\) | −1.04297e70 | −0.00407229 | ||||||||
\(541\) | 3.05901e72 | 1.13724 | 0.568621 | − | 0.822600i | \(-0.307477\pi\) | ||||
0.568621 | + | 0.822600i | \(0.307477\pi\) | |||||||
\(542\) | 9.51181e71 | 0.336730 | ||||||||
\(543\) | 2.06432e71 | 0.0695955 | ||||||||
\(544\) | 5.44424e71 | 0.174810 | ||||||||
\(545\) | −3.26459e71 | −0.0998439 | ||||||||
\(546\) | −9.94865e72 | −2.89841 | ||||||||
\(547\) | −3.46128e72 | −0.960667 | −0.480333 | − | 0.877086i | \(-0.659484\pi\) | ||||
−0.480333 | + | 0.877086i | \(0.659484\pi\) | |||||||
\(548\) | −8.73986e71 | −0.231111 | ||||||||
\(549\) | −1.42800e72 | −0.359799 | ||||||||
\(550\) | 4.42901e72 | 1.06340 | ||||||||
\(551\) | 6.37021e72 | 1.45759 | ||||||||
\(552\) | 5.01501e72 | 1.09367 | ||||||||
\(553\) | −6.36485e72 | −1.32304 | ||||||||
\(554\) | 9.02098e71 | 0.178750 | ||||||||
\(555\) | −3.93491e70 | −0.00743311 | ||||||||
\(556\) | −1.66905e72 | −0.300598 | ||||||||
\(557\) | 9.15984e72 | 1.57299 | 0.786493 | − | 0.617599i | \(-0.211894\pi\) | ||||
0.786493 | + | 0.617599i | \(0.211894\pi\) | |||||||
\(558\) | 6.46112e72 | 1.05804 | ||||||||
\(559\) | −1.60128e72 | −0.250066 | ||||||||
\(560\) | 4.57400e71 | 0.0681261 | ||||||||
\(561\) | −5.66120e72 | −0.804254 | ||||||||
\(562\) | −4.74287e72 | −0.642730 | ||||||||
\(563\) | 2.99024e72 | 0.386575 | 0.193288 | − | 0.981142i | \(-0.438085\pi\) | ||||
0.193288 | + | 0.981142i | \(0.438085\pi\) | |||||||
\(564\) | 3.95407e71 | 0.0487695 | ||||||||
\(565\) | 4.06282e70 | 0.00478128 | ||||||||
\(566\) | −8.89922e72 | −0.999347 | ||||||||
\(567\) | 9.16301e72 | 0.981944 | ||||||||
\(568\) | −2.57494e72 | −0.263352 | ||||||||
\(569\) | −1.95493e73 | −1.90834 | −0.954169 | − | 0.299270i | \(-0.903257\pi\) | ||||
−0.954169 | + | 0.299270i | \(0.903257\pi\) | |||||||
\(570\) | 1.02875e72 | 0.0958579 | ||||||||
\(571\) | 6.21208e72 | 0.552561 | 0.276280 | − | 0.961077i | \(-0.410898\pi\) | ||||
0.276280 | + | 0.961077i | \(0.410898\pi\) | |||||||
\(572\) | 4.55252e72 | 0.386595 | ||||||||
\(573\) | −1.63600e73 | −1.32644 | ||||||||
\(574\) | 1.55129e72 | 0.120096 | ||||||||
\(575\) | −9.24517e72 | −0.683466 | ||||||||
\(576\) | 1.89987e73 | 1.34131 | ||||||||
\(577\) | 3.44976e72 | 0.232611 | 0.116305 | − | 0.993213i | \(-0.462895\pi\) | ||||
0.116305 | + | 0.993213i | \(0.462895\pi\) | |||||||
\(578\) | 1.10501e73 | 0.711669 | ||||||||
\(579\) | 1.19259e73 | 0.733682 | ||||||||
\(580\) | 3.10640e71 | 0.0182564 | ||||||||
\(581\) | 3.18032e72 | 0.178568 | ||||||||
\(582\) | 1.11056e73 | 0.595777 | ||||||||
\(583\) | 2.52919e73 | 1.29647 | ||||||||
\(584\) | −1.78920e73 | −0.876433 | ||||||||
\(585\) | −2.91109e72 | −0.136278 | ||||||||
\(586\) | −2.15896e73 | −0.965957 | ||||||||
\(587\) | −3.91303e73 | −1.67341 | −0.836707 | − | 0.547650i | \(-0.815522\pi\) | ||||
−0.836707 | + | 0.547650i | \(0.815522\pi\) | |||||||
\(588\) | −5.04797e72 | −0.206356 | ||||||||
\(589\) | 2.64856e73 | 1.03503 | ||||||||
\(590\) | −2.26469e72 | −0.0846118 | ||||||||
\(591\) | −2.69351e73 | −0.962167 | ||||||||
\(592\) | 1.65331e72 | 0.0564713 | ||||||||
\(593\) | 3.03919e73 | 0.992679 | 0.496340 | − | 0.868128i | \(-0.334677\pi\) | ||||
0.496340 | + | 0.868128i | \(0.334677\pi\) | |||||||
\(594\) | −1.05009e73 | −0.328010 | ||||||||
\(595\) | 1.35233e72 | 0.0404001 | ||||||||
\(596\) | −5.67442e72 | −0.162142 | ||||||||
\(597\) | 1.82497e73 | 0.498812 | ||||||||
\(598\) | 3.91664e73 | 1.02408 | ||||||||
\(599\) | −4.69569e73 | −1.17460 | −0.587298 | − | 0.809371i | \(-0.699808\pi\) | ||||
−0.587298 | + | 0.809371i | \(0.699808\pi\) | |||||||
\(600\) | −6.62460e73 | −1.58545 | ||||||||
\(601\) | 3.32571e73 | 0.761572 | 0.380786 | − | 0.924663i | \(-0.375653\pi\) | ||||
0.380786 | + | 0.924663i | \(0.375653\pi\) | |||||||
\(602\) | 8.05554e72 | 0.176517 | ||||||||
\(603\) | 1.18950e73 | 0.249434 | ||||||||
\(604\) | 1.31875e73 | 0.264658 | ||||||||
\(605\) | 1.47909e72 | 0.0284103 | ||||||||
\(606\) | −9.48037e72 | −0.174301 | ||||||||
\(607\) | −4.03134e73 | −0.709495 | −0.354747 | − | 0.934962i | \(-0.615433\pi\) | ||||
−0.354747 | + | 0.934962i | \(0.615433\pi\) | |||||||
\(608\) | 2.41679e73 | 0.407188 | ||||||||
\(609\) | 1.65833e74 | 2.67493 | ||||||||
\(610\) | 1.17649e72 | 0.0181697 | ||||||||
\(611\) | 1.89036e73 | 0.279545 | ||||||||
\(612\) | 7.56414e72 | 0.107114 | ||||||||
\(613\) | −1.16967e74 | −1.58621 | −0.793103 | − | 0.609087i | \(-0.791536\pi\) | ||||
−0.793103 | + | 0.609087i | \(0.791536\pi\) | |||||||
\(614\) | 9.77045e73 | 1.26897 | ||||||||
\(615\) | 8.30098e71 | 0.0103262 | ||||||||
\(616\) | −1.40196e74 | −1.67050 | ||||||||
\(617\) | −8.47254e73 | −0.967067 | −0.483534 | − | 0.875326i | \(-0.660647\pi\) | ||||
−0.483534 | + | 0.875326i | \(0.660647\pi\) | |||||||
\(618\) | −1.04174e74 | −1.13910 | ||||||||
\(619\) | −4.01420e73 | −0.420529 | −0.210265 | − | 0.977644i | \(-0.567433\pi\) | ||||
−0.210265 | + | 0.977644i | \(0.567433\pi\) | |||||||
\(620\) | 1.29156e72 | 0.0129639 | ||||||||
\(621\) | 2.19198e73 | 0.210818 | ||||||||
\(622\) | −3.39694e73 | −0.313071 | ||||||||
\(623\) | −1.61958e73 | −0.143044 | ||||||||
\(624\) | 2.23676e74 | 1.89334 | ||||||||
\(625\) | 1.21556e74 | 0.986178 | ||||||||
\(626\) | 8.89748e73 | 0.691906 | ||||||||
\(627\) | −2.51311e74 | −1.87336 | ||||||||
\(628\) | 4.77407e73 | 0.341160 | ||||||||
\(629\) | 4.88808e72 | 0.0334886 | ||||||||
\(630\) | 1.46447e73 | 0.0961961 | ||||||||
\(631\) | 1.79458e74 | 1.13028 | 0.565139 | − | 0.824996i | \(-0.308823\pi\) | ||||
0.565139 | + | 0.824996i | \(0.308823\pi\) | |||||||
\(632\) | 1.79549e74 | 1.08438 | ||||||||
\(633\) | −6.28603e73 | −0.364064 | ||||||||
\(634\) | −1.06161e74 | −0.589658 | ||||||||
\(635\) | −1.12048e73 | −0.0596900 | ||||||||
\(636\) | −6.17984e73 | −0.315765 | ||||||||
\(637\) | −2.41333e74 | −1.18283 | ||||||||
\(638\) | 3.12760e74 | 1.47050 | ||||||||
\(639\) | −6.57073e73 | −0.296374 | ||||||||
\(640\) | −9.61665e72 | −0.0416154 | ||||||||
\(641\) | 9.16136e73 | 0.380384 | 0.190192 | − | 0.981747i | \(-0.439089\pi\) | ||||
0.190192 | + | 0.981747i | \(0.439089\pi\) | |||||||
\(642\) | −6.14595e74 | −2.44856 | ||||||||
\(643\) | 2.41149e74 | 0.921924 | 0.460962 | − | 0.887420i | \(-0.347504\pi\) | ||||
0.460962 | + | 0.887420i | \(0.347504\pi\) | |||||||
\(644\) | 4.78065e73 | 0.175393 | ||||||||
\(645\) | 4.31054e72 | 0.0151775 | ||||||||
\(646\) | −1.27795e74 | −0.431870 | ||||||||
\(647\) | −2.73867e74 | −0.888334 | −0.444167 | − | 0.895944i | \(-0.646500\pi\) | ||||
−0.444167 | + | 0.895944i | \(0.646500\pi\) | |||||||
\(648\) | −2.58483e74 | −0.804813 | ||||||||
\(649\) | 5.53234e74 | 1.65358 | ||||||||
\(650\) | −5.17371e74 | −1.48456 | ||||||||
\(651\) | 6.89488e74 | 1.89946 | ||||||||
\(652\) | −8.97021e73 | −0.237269 | ||||||||
\(653\) | 2.24596e74 | 0.570430 | 0.285215 | − | 0.958464i | \(-0.407935\pi\) | ||||
0.285215 | + | 0.958464i | \(0.407935\pi\) | |||||||
\(654\) | 8.03117e74 | 1.95870 | ||||||||
\(655\) | −3.87127e73 | −0.0906690 | ||||||||
\(656\) | −3.48777e73 | −0.0784505 | ||||||||
\(657\) | −4.56568e74 | −0.986333 | ||||||||
\(658\) | −9.50979e73 | −0.197326 | ||||||||
\(659\) | −7.20835e74 | −1.43672 | −0.718361 | − | 0.695671i | \(-0.755107\pi\) | ||||
−0.718361 | + | 0.695671i | \(0.755107\pi\) | |||||||
\(660\) | −1.22551e73 | −0.0234639 | ||||||||
\(661\) | 2.05504e73 | 0.0377992 | 0.0188996 | − | 0.999821i | \(-0.493984\pi\) | ||||
0.0188996 | + | 0.999821i | \(0.493984\pi\) | |||||||
\(662\) | 5.97945e74 | 1.05663 | ||||||||
\(663\) | 6.61310e74 | 1.12278 | ||||||||
\(664\) | −8.97150e73 | −0.146356 | ||||||||
\(665\) | 6.00322e73 | 0.0941045 | ||||||||
\(666\) | 5.29345e73 | 0.0797392 | ||||||||
\(667\) | −6.52861e74 | −0.945118 | ||||||||
\(668\) | 3.33228e73 | 0.0463624 | ||||||||
\(669\) | −5.75175e74 | −0.769144 | ||||||||
\(670\) | −9.79996e72 | −0.0125963 | ||||||||
\(671\) | −2.87400e74 | −0.355092 | ||||||||
\(672\) | 6.29153e74 | 0.747258 | ||||||||
\(673\) | −8.58844e73 | −0.0980652 | −0.0490326 | − | 0.998797i | \(-0.515614\pi\) | ||||
−0.0490326 | + | 0.998797i | \(0.515614\pi\) | |||||||
\(674\) | −6.34209e74 | −0.696218 | ||||||||
\(675\) | −2.89551e74 | −0.305615 | ||||||||
\(676\) | −3.39405e74 | −0.344454 | ||||||||
\(677\) | −1.28702e75 | −1.25599 | −0.627993 | − | 0.778219i | \(-0.716123\pi\) | ||||
−0.627993 | + | 0.778219i | \(0.716123\pi\) | |||||||
\(678\) | −9.99489e73 | −0.0937975 | ||||||||
\(679\) | 6.48060e74 | 0.584879 | ||||||||
\(680\) | −3.81484e73 | −0.0331123 | ||||||||
\(681\) | 2.05810e75 | 1.71817 | ||||||||
\(682\) | 1.30037e75 | 1.04420 | ||||||||
\(683\) | 2.32106e75 | 1.79283 | 0.896414 | − | 0.443218i | \(-0.146163\pi\) | ||||
0.896414 | + | 0.443218i | \(0.146163\pi\) | |||||||
\(684\) | 3.35785e74 | 0.249503 | ||||||||
\(685\) | 1.12478e74 | 0.0804022 | ||||||||
\(686\) | −4.92406e74 | −0.338637 | ||||||||
\(687\) | −2.94661e74 | −0.194970 | ||||||||
\(688\) | −1.81113e74 | −0.115307 | ||||||||
\(689\) | −2.95445e75 | −1.80995 | ||||||||
\(690\) | −1.05433e74 | −0.0621551 | ||||||||
\(691\) | 4.45634e74 | 0.252819 | 0.126410 | − | 0.991978i | \(-0.459655\pi\) | ||||
0.126410 | + | 0.991978i | \(0.459655\pi\) | |||||||
\(692\) | 6.58289e74 | 0.359422 | ||||||||
\(693\) | −3.57752e75 | −1.87997 | ||||||||
\(694\) | 1.43659e75 | 0.726618 | ||||||||
\(695\) | 2.14799e74 | 0.104577 | ||||||||
\(696\) | −4.67805e75 | −2.19240 | ||||||||
\(697\) | −1.03118e74 | −0.0465226 | ||||||||
\(698\) | 1.65879e75 | 0.720480 | ||||||||
\(699\) | 4.09509e75 | 1.71245 | ||||||||
\(700\) | −6.31503e74 | −0.254260 | ||||||||
\(701\) | −1.68252e75 | −0.652276 | −0.326138 | − | 0.945322i | \(-0.605747\pi\) | ||||
−0.326138 | + | 0.945322i | \(0.605747\pi\) | |||||||
\(702\) | 1.22666e75 | 0.457920 | ||||||||
\(703\) | 2.16991e74 | 0.0780054 | ||||||||
\(704\) | 3.82370e75 | 1.32376 | ||||||||
\(705\) | −5.08871e73 | −0.0169667 | ||||||||
\(706\) | −4.14531e75 | −1.33117 | ||||||||
\(707\) | −5.53220e74 | −0.171113 | ||||||||
\(708\) | −1.35178e75 | −0.402739 | ||||||||
\(709\) | 4.03690e75 | 1.15857 | 0.579286 | − | 0.815124i | \(-0.303331\pi\) | ||||
0.579286 | + | 0.815124i | \(0.303331\pi\) | |||||||
\(710\) | 5.41344e73 | 0.0149667 | ||||||||
\(711\) | 4.58173e75 | 1.22035 | ||||||||
\(712\) | 4.56876e74 | 0.117241 | ||||||||
\(713\) | −2.71442e75 | −0.671126 | ||||||||
\(714\) | −3.32684e75 | −0.792555 | ||||||||
\(715\) | −5.85888e74 | −0.134495 | ||||||||
\(716\) | 6.19179e74 | 0.136969 | ||||||||
\(717\) | 1.04235e76 | 2.22207 | ||||||||
\(718\) | −2.75836e75 | −0.566700 | ||||||||
\(719\) | −2.29058e75 | −0.453555 | −0.226778 | − | 0.973947i | \(-0.572819\pi\) | ||||
−0.226778 | + | 0.973947i | \(0.572819\pi\) | |||||||
\(720\) | −3.29259e74 | −0.0628386 | ||||||||
\(721\) | −6.07898e75 | −1.11827 | ||||||||
\(722\) | −6.14062e74 | −0.108887 | ||||||||
\(723\) | −1.22003e76 | −2.08548 | ||||||||
\(724\) | −5.55120e73 | −0.00914776 | ||||||||
\(725\) | 8.62400e75 | 1.37010 | ||||||||
\(726\) | −3.63868e75 | −0.557344 | ||||||||
\(727\) | −1.58967e75 | −0.234772 | −0.117386 | − | 0.993086i | \(-0.537451\pi\) | ||||
−0.117386 | + | 0.993086i | \(0.537451\pi\) | |||||||
\(728\) | 1.63769e76 | 2.33211 | ||||||||
\(729\) | −9.91746e75 | −1.36182 | ||||||||
\(730\) | 3.76154e74 | 0.0498092 | ||||||||
\(731\) | −5.35470e74 | −0.0683793 | ||||||||
\(732\) | 7.02237e74 | 0.0864849 | ||||||||
\(733\) | 8.19933e74 | 0.0973919 | 0.0486959 | − | 0.998814i | \(-0.484493\pi\) | ||||
0.0486959 | + | 0.998814i | \(0.484493\pi\) | |||||||
\(734\) | 3.48749e75 | 0.399546 | ||||||||
\(735\) | 6.49651e74 | 0.0717903 | ||||||||
\(736\) | −2.47689e75 | −0.264024 | ||||||||
\(737\) | 2.39400e75 | 0.246170 | ||||||||
\(738\) | −1.11669e75 | −0.110774 | ||||||||
\(739\) | −5.66664e75 | −0.542310 | −0.271155 | − | 0.962536i | \(-0.587406\pi\) | ||||
−0.271155 | + | 0.962536i | \(0.587406\pi\) | |||||||
\(740\) | 1.05814e73 | 0.000977022 0 | ||||||||
\(741\) | 2.93567e76 | 2.61532 | ||||||||
\(742\) | 1.48629e76 | 1.27762 | ||||||||
\(743\) | −1.25772e76 | −1.04323 | −0.521615 | − | 0.853181i | \(-0.674670\pi\) | ||||
−0.521615 | + | 0.853181i | \(0.674670\pi\) | |||||||
\(744\) | −1.94501e76 | −1.55682 | ||||||||
\(745\) | 7.30272e74 | 0.0564083 | ||||||||
\(746\) | 1.31915e76 | 0.983369 | ||||||||
\(747\) | −2.28935e75 | −0.164708 | ||||||||
\(748\) | 1.52237e75 | 0.105713 | ||||||||
\(749\) | −3.58642e76 | −2.40377 | ||||||||
\(750\) | 2.79191e75 | 0.180625 | ||||||||
\(751\) | −5.86096e75 | −0.366025 | −0.183012 | − | 0.983111i | \(-0.558585\pi\) | ||||
−0.183012 | + | 0.983111i | \(0.558585\pi\) | |||||||
\(752\) | 2.13809e75 | 0.128900 | ||||||||
\(753\) | −8.07512e74 | −0.0469983 | ||||||||
\(754\) | −3.65349e76 | −2.05290 | ||||||||
\(755\) | −1.69718e75 | −0.0920732 | ||||||||
\(756\) | 1.49726e75 | 0.0784276 | ||||||||
\(757\) | 3.11946e76 | 1.57775 | 0.788877 | − | 0.614551i | \(-0.210663\pi\) | ||||
0.788877 | + | 0.614551i | \(0.210663\pi\) | |||||||
\(758\) | −8.96451e75 | −0.437817 | ||||||||
\(759\) | 2.57560e76 | 1.21470 | ||||||||
\(760\) | −1.69347e75 | −0.0771291 | ||||||||
\(761\) | 7.11505e75 | 0.312957 | 0.156478 | − | 0.987681i | \(-0.449986\pi\) | ||||
0.156478 | + | 0.987681i | \(0.449986\pi\) | |||||||
\(762\) | 2.75649e76 | 1.17098 | ||||||||
\(763\) | 4.68653e76 | 1.92288 | ||||||||
\(764\) | 4.39941e75 | 0.174349 | ||||||||
\(765\) | −9.73470e74 | −0.0372644 | ||||||||
\(766\) | −7.02293e75 | −0.259691 | ||||||||
\(767\) | −6.46257e76 | −2.30849 | ||||||||
\(768\) | −2.41916e76 | −0.834819 | ||||||||
\(769\) | 2.10631e76 | 0.702223 | 0.351112 | − | 0.936334i | \(-0.385804\pi\) | ||||
0.351112 | + | 0.936334i | \(0.385804\pi\) | |||||||
\(770\) | 2.94742e75 | 0.0949374 | ||||||||
\(771\) | −1.68100e76 | −0.523151 | ||||||||
\(772\) | −3.20701e75 | −0.0964366 | ||||||||
\(773\) | 3.92297e75 | 0.113988 | 0.0569938 | − | 0.998375i | \(-0.481848\pi\) | ||||
0.0569938 | + | 0.998375i | \(0.481848\pi\) | |||||||
\(774\) | −5.79877e75 | −0.162817 | ||||||||
\(775\) | 3.58562e76 | 0.972903 | ||||||||
\(776\) | −1.82814e76 | −0.479374 | ||||||||
\(777\) | 5.64882e75 | 0.143153 | ||||||||
\(778\) | −1.60975e76 | −0.394274 | ||||||||
\(779\) | −4.57757e75 | −0.108366 | ||||||||
\(780\) | 1.43157e75 | 0.0327570 | ||||||||
\(781\) | −1.32243e76 | −0.292497 | ||||||||
\(782\) | 1.30973e76 | 0.280029 | ||||||||
\(783\) | −2.04470e76 | −0.422613 | ||||||||
\(784\) | −2.72960e76 | −0.545410 | ||||||||
\(785\) | −6.14402e75 | −0.118688 | ||||||||
\(786\) | 9.52365e76 | 1.77871 | ||||||||
\(787\) | −2.38560e76 | −0.430792 | −0.215396 | − | 0.976527i | \(-0.569104\pi\) | ||||
−0.215396 | + | 0.976527i | \(0.569104\pi\) | |||||||
\(788\) | 7.24317e75 | 0.126469 | ||||||||
\(789\) | −1.25638e77 | −2.12120 | ||||||||
\(790\) | −3.77476e75 | −0.0616270 | ||||||||
\(791\) | −5.83244e75 | −0.0920818 | ||||||||
\(792\) | 1.00920e77 | 1.54084 | ||||||||
\(793\) | 3.35725e76 | 0.495729 | ||||||||
\(794\) | 1.20798e77 | 1.72511 | ||||||||
\(795\) | 7.95318e75 | 0.109853 | ||||||||
\(796\) | −4.90758e75 | −0.0655648 | ||||||||
\(797\) | 9.89205e76 | 1.27832 | 0.639162 | − | 0.769072i | \(-0.279281\pi\) | ||||
0.639162 | + | 0.769072i | \(0.279281\pi\) | |||||||
\(798\) | −1.47684e77 | −1.84611 | ||||||||
\(799\) | 6.32137e75 | 0.0764402 | ||||||||
\(800\) | 3.27186e76 | 0.382745 | ||||||||
\(801\) | 1.16586e76 | 0.131942 | ||||||||
\(802\) | −9.18754e76 | −1.00596 | ||||||||
\(803\) | −9.18894e76 | −0.973427 | ||||||||
\(804\) | −5.84953e75 | −0.0599564 | ||||||||
\(805\) | −6.15248e75 | −0.0610182 | ||||||||
\(806\) | −1.51902e77 | −1.45776 | ||||||||
\(807\) | 1.12822e77 | 1.04772 | ||||||||
\(808\) | 1.56060e76 | 0.140246 | ||||||||
\(809\) | 1.59609e77 | 1.38810 | 0.694050 | − | 0.719927i | \(-0.255825\pi\) | ||||
0.694050 | + | 0.719927i | \(0.255825\pi\) | |||||||
\(810\) | 5.43424e75 | 0.0457389 | ||||||||
\(811\) | −2.38631e77 | −1.94390 | −0.971952 | − | 0.235181i | \(-0.924432\pi\) | ||||
−0.971952 | + | 0.235181i | \(0.924432\pi\) | |||||||
\(812\) | −4.45944e76 | −0.351598 | ||||||||
\(813\) | −7.30673e76 | −0.557601 | ||||||||
\(814\) | 1.06537e76 | 0.0786959 | ||||||||
\(815\) | 1.15443e76 | 0.0825448 | ||||||||
\(816\) | 7.47976e76 | 0.517724 | ||||||||
\(817\) | −2.37705e76 | −0.159277 | ||||||||
\(818\) | 1.60918e77 | 1.04386 | ||||||||
\(819\) | 4.17905e77 | 2.62455 | ||||||||
\(820\) | −2.23223e74 | −0.00135729 | ||||||||
\(821\) | −2.72431e77 | −1.60385 | −0.801924 | − | 0.597425i | \(-0.796190\pi\) | ||||
−0.801924 | + | 0.597425i | \(0.796190\pi\) | |||||||
\(822\) | −2.76706e77 | −1.57730 | ||||||||
\(823\) | 2.80427e77 | 1.54784 | 0.773918 | − | 0.633286i | \(-0.218294\pi\) | ||||
0.773918 | + | 0.633286i | \(0.218294\pi\) | |||||||
\(824\) | 1.71485e77 | 0.916545 | ||||||||
\(825\) | −3.40225e77 | −1.76091 | ||||||||
\(826\) | 3.25111e77 | 1.62952 | ||||||||
\(827\) | 3.27438e77 | 1.58940 | 0.794700 | − | 0.607002i | \(-0.207628\pi\) | ||||
0.794700 | + | 0.607002i | \(0.207628\pi\) | |||||||
\(828\) | −3.44135e76 | −0.161780 | ||||||||
\(829\) | −1.12060e77 | −0.510216 | −0.255108 | − | 0.966913i | \(-0.582111\pi\) | ||||
−0.255108 | + | 0.966913i | \(0.582111\pi\) | |||||||
\(830\) | 1.88613e75 | 0.00831768 | ||||||||
\(831\) | −6.92969e76 | −0.295996 | ||||||||
\(832\) | −4.46663e77 | −1.84804 | ||||||||
\(833\) | −8.07019e76 | −0.323438 | ||||||||
\(834\) | −5.28423e77 | −2.05155 | ||||||||
\(835\) | −4.28850e75 | −0.0161292 | ||||||||
\(836\) | 6.75805e76 | 0.246238 | ||||||||
\(837\) | −8.50131e76 | −0.300097 | ||||||||
\(838\) | 4.70103e77 | 1.60778 | ||||||||
\(839\) | −2.49923e77 | −0.828159 | −0.414079 | − | 0.910241i | \(-0.635896\pi\) | ||||
−0.414079 | + | 0.910241i | \(0.635896\pi\) | |||||||
\(840\) | −4.40854e76 | −0.141545 | ||||||||
\(841\) | 2.87560e77 | 0.894611 | ||||||||
\(842\) | 1.00833e77 | 0.303972 | ||||||||
\(843\) | 3.64335e77 | 1.06432 | ||||||||
\(844\) | 1.69039e76 | 0.0478533 | ||||||||
\(845\) | 4.36799e76 | 0.119834 | ||||||||
\(846\) | 6.84560e76 | 0.182011 | ||||||||
\(847\) | −2.12332e77 | −0.547149 | ||||||||
\(848\) | −3.34164e77 | −0.834583 | ||||||||
\(849\) | 6.83615e77 | 1.65485 | ||||||||
\(850\) | −1.73009e77 | −0.405946 | ||||||||
\(851\) | −2.22386e76 | −0.0505794 | ||||||||
\(852\) | 3.23124e76 | 0.0712394 | ||||||||
\(853\) | −7.69577e77 | −1.64476 | −0.822381 | − | 0.568937i | \(-0.807355\pi\) | ||||
−0.822381 | + | 0.568937i | \(0.807355\pi\) | |||||||
\(854\) | −1.68892e77 | −0.349926 | ||||||||
\(855\) | −4.32141e76 | −0.0868007 | ||||||||
\(856\) | 1.01171e78 | 1.97016 | ||||||||
\(857\) | −4.56317e77 | −0.861539 | −0.430769 | − | 0.902462i | \(-0.641758\pi\) | ||||
−0.430769 | + | 0.902462i | \(0.641758\pi\) | |||||||
\(858\) | 1.44134e78 | 2.63847 | ||||||||
\(859\) | −5.50005e77 | −0.976219 | −0.488110 | − | 0.872782i | \(-0.662313\pi\) | ||||
−0.488110 | + | 0.872782i | \(0.662313\pi\) | |||||||
\(860\) | −1.15916e75 | −0.00199495 | ||||||||
\(861\) | −1.19166e77 | −0.198870 | ||||||||
\(862\) | −1.93734e77 | −0.313519 | ||||||||
\(863\) | 2.27402e77 | 0.356868 | 0.178434 | − | 0.983952i | \(-0.442897\pi\) | ||||
0.178434 | + | 0.983952i | \(0.442897\pi\) | |||||||
\(864\) | −7.75738e76 | −0.118060 | ||||||||
\(865\) | −8.47188e76 | −0.125041 | ||||||||
\(866\) | −1.00952e78 | −1.44508 | ||||||||
\(867\) | −8.48839e77 | −1.17847 | ||||||||
\(868\) | −1.85412e77 | −0.249669 | ||||||||
\(869\) | 9.22123e77 | 1.20438 | ||||||||
\(870\) | 9.83494e76 | 0.124598 | ||||||||
\(871\) | −2.79654e77 | −0.343668 | ||||||||
\(872\) | −1.32204e78 | −1.57601 | ||||||||
\(873\) | −4.66505e77 | −0.539484 | ||||||||
\(874\) | 5.81412e77 | 0.652276 | ||||||||
\(875\) | 1.62920e77 | 0.177321 | ||||||||
\(876\) | 2.24524e77 | 0.237085 | ||||||||
\(877\) | 1.67020e78 | 1.71111 | 0.855556 | − | 0.517711i | \(-0.173216\pi\) | ||||
0.855556 | + | 0.517711i | \(0.173216\pi\) | |||||||
\(878\) | 1.63965e77 | 0.162985 | ||||||||
\(879\) | 1.65846e78 | 1.59955 | ||||||||
\(880\) | −6.62670e76 | −0.0620164 | ||||||||
\(881\) | 1.51231e78 | 1.37334 | 0.686672 | − | 0.726967i | \(-0.259071\pi\) | ||||
0.686672 | + | 0.726967i | \(0.259071\pi\) | |||||||
\(882\) | −8.73946e77 | −0.770135 | ||||||||
\(883\) | −7.53014e77 | −0.643938 | −0.321969 | − | 0.946750i | \(-0.604345\pi\) | ||||
−0.321969 | + | 0.946750i | \(0.604345\pi\) | |||||||
\(884\) | −1.77834e77 | −0.147581 | ||||||||
\(885\) | 1.73968e77 | 0.140111 | ||||||||
\(886\) | 9.83137e76 | 0.0768458 | ||||||||
\(887\) | −2.01497e78 | −1.52859 | −0.764296 | − | 0.644865i | \(-0.776914\pi\) | ||||
−0.764296 | + | 0.644865i | \(0.776914\pi\) | |||||||
\(888\) | −1.59350e77 | −0.117330 | ||||||||
\(889\) | 1.60853e78 | 1.14956 | ||||||||
\(890\) | −9.60516e75 | −0.00666299 | ||||||||
\(891\) | −1.32751e78 | −0.893881 | ||||||||
\(892\) | 1.54671e77 | 0.101098 | ||||||||
\(893\) | 2.80617e77 | 0.178053 | ||||||||
\(894\) | −1.79653e78 | −1.10660 | ||||||||
\(895\) | −7.96855e76 | −0.0476507 | ||||||||
\(896\) | 1.38053e78 | 0.801464 | ||||||||
\(897\) | −3.00867e78 | −1.69580 | ||||||||
\(898\) | −1.07481e78 | −0.588180 | ||||||||
\(899\) | 2.53204e78 | 1.34536 | ||||||||
\(900\) | 4.54586e77 | 0.234525 | ||||||||
\(901\) | −9.87972e77 | −0.494923 | ||||||||
\(902\) | −2.24746e77 | −0.109325 | ||||||||
\(903\) | −6.18806e77 | −0.292300 | ||||||||
\(904\) | 1.64530e77 | 0.0754713 | ||||||||
\(905\) | 7.14414e75 | 0.00318246 | ||||||||
\(906\) | 4.17520e78 | 1.80626 | ||||||||
\(907\) | 8.47265e77 | 0.355980 | 0.177990 | − | 0.984032i | \(-0.443040\pi\) | ||||
0.177990 | + | 0.984032i | \(0.443040\pi\) | |||||||
\(908\) | −5.53447e77 | −0.225840 | ||||||||
\(909\) | 3.98234e77 | 0.157832 | ||||||||
\(910\) | −3.44301e77 | −0.132538 | ||||||||
\(911\) | −5.35967e77 | −0.200402 | −0.100201 | − | 0.994967i | \(-0.531949\pi\) | ||||
−0.100201 | + | 0.994967i | \(0.531949\pi\) | |||||||
\(912\) | 3.32039e78 | 1.20594 | ||||||||
\(913\) | −4.60756e77 | −0.162553 | ||||||||
\(914\) | −1.61728e78 | −0.554256 | ||||||||
\(915\) | −9.03748e76 | −0.0300877 | ||||||||
\(916\) | 7.92378e76 | 0.0256273 | ||||||||
\(917\) | 5.55746e78 | 1.74618 | ||||||||
\(918\) | 4.10196e77 | 0.125216 | ||||||||
\(919\) | −5.43292e78 | −1.61129 | −0.805643 | − | 0.592402i | \(-0.798180\pi\) | ||||
−0.805643 | + | 0.592402i | \(0.798180\pi\) | |||||||
\(920\) | 1.73558e77 | 0.0500112 | ||||||||
\(921\) | −7.50541e78 | −2.10133 | ||||||||
\(922\) | −4.18272e78 | −1.13786 | ||||||||
\(923\) | 1.54479e78 | 0.408342 | ||||||||
\(924\) | 1.75929e78 | 0.451888 | ||||||||
\(925\) | 2.93762e77 | 0.0733229 | ||||||||
\(926\) | 1.37859e78 | 0.334383 | ||||||||
\(927\) | 4.37594e78 | 1.03147 | ||||||||
\(928\) | 2.31047e78 | 0.529271 | ||||||||
\(929\) | −1.48878e78 | −0.331446 | −0.165723 | − | 0.986172i | \(-0.552996\pi\) | ||||
−0.165723 | + | 0.986172i | \(0.552996\pi\) | |||||||
\(930\) | 4.08910e77 | 0.0884768 | ||||||||
\(931\) | −3.58250e78 | −0.753390 | ||||||||
\(932\) | −1.10122e78 | −0.225088 | ||||||||
\(933\) | 2.60945e78 | 0.518423 | ||||||||
\(934\) | −8.17902e76 | −0.0157946 | ||||||||
\(935\) | −1.95922e77 | −0.0367769 | ||||||||
\(936\) | −1.17889e79 | −2.15111 | ||||||||
\(937\) | 5.58551e78 | 0.990749 | 0.495374 | − | 0.868680i | \(-0.335031\pi\) | ||||
0.495374 | + | 0.868680i | \(0.335031\pi\) | |||||||
\(938\) | 1.40685e78 | 0.242590 | ||||||||
\(939\) | −6.83481e78 | −1.14575 | ||||||||
\(940\) | 1.36842e76 | 0.00223013 | ||||||||
\(941\) | 9.38809e78 | 1.48748 | 0.743742 | − | 0.668467i | \(-0.233049\pi\) | ||||
0.743742 | + | 0.668467i | \(0.233049\pi\) | |||||||
\(942\) | 1.51148e79 | 2.32838 | ||||||||
\(943\) | 4.69139e77 | 0.0702655 | ||||||||
\(944\) | −7.30950e78 | −1.06446 | ||||||||
\(945\) | −1.92690e77 | −0.0272846 | ||||||||
\(946\) | −1.16707e78 | −0.160687 | ||||||||
\(947\) | 7.56797e78 | 1.01322 | 0.506611 | − | 0.862174i | \(-0.330898\pi\) | ||||
0.506611 | + | 0.862174i | \(0.330898\pi\) | |||||||
\(948\) | −2.25313e78 | −0.293335 | ||||||||
\(949\) | 1.07340e79 | 1.35896 | ||||||||
\(950\) | −7.68020e78 | −0.945577 | ||||||||
\(951\) | 8.15503e78 | 0.976431 | ||||||||
\(952\) | 5.47645e78 | 0.637705 | ||||||||
\(953\) | −1.45966e79 | −1.65306 | −0.826530 | − | 0.562892i | \(-0.809689\pi\) | ||||
−0.826530 | + | 0.562892i | \(0.809689\pi\) | |||||||
\(954\) | −1.06990e79 | −1.17845 | ||||||||
\(955\) | −5.66184e77 | −0.0606552 | ||||||||
\(956\) | −2.80301e78 | −0.292073 | ||||||||
\(957\) | −2.40254e79 | −2.43503 | ||||||||
\(958\) | 6.09677e78 | 0.601055 | ||||||||
\(959\) | −1.61470e79 | −1.54845 | ||||||||
\(960\) | 1.20239e78 | 0.112165 | ||||||||
\(961\) | −4.92178e77 | −0.0446634 | ||||||||
\(962\) | −1.24450e78 | −0.109864 | ||||||||
\(963\) | 2.58168e79 | 2.21721 | ||||||||
\(964\) | 3.28080e78 | 0.274119 | ||||||||
\(965\) | 4.12728e77 | 0.0335498 | ||||||||
\(966\) | 1.51356e79 | 1.19704 | ||||||||
\(967\) | 1.29544e78 | 0.0996821 | 0.0498411 | − | 0.998757i | \(-0.484129\pi\) | ||||
0.0498411 | + | 0.998757i | \(0.484129\pi\) | |||||||
\(968\) | 5.98978e78 | 0.448450 | ||||||||
\(969\) | 9.81691e78 | 0.715146 | ||||||||
\(970\) | 3.84341e77 | 0.0272436 | ||||||||
\(971\) | −1.09632e79 | −0.756185 | −0.378092 | − | 0.925768i | \(-0.623420\pi\) | ||||
−0.378092 | + | 0.925768i | \(0.623420\pi\) | |||||||
\(972\) | 4.13685e78 | 0.277660 | ||||||||
\(973\) | −3.08357e79 | −2.01402 | ||||||||
\(974\) | −7.53440e78 | −0.478891 | ||||||||
\(975\) | 3.97431e79 | 2.45833 | ||||||||
\(976\) | 3.79722e78 | 0.228584 | ||||||||
\(977\) | 2.12309e79 | 1.24384 | 0.621918 | − | 0.783083i | \(-0.286354\pi\) | ||||
0.621918 | + | 0.783083i | \(0.286354\pi\) | |||||||
\(978\) | −2.83999e79 | −1.61933 | ||||||||
\(979\) | 2.34641e78 | 0.130216 | ||||||||
\(980\) | −1.74699e77 | −0.00943625 | ||||||||
\(981\) | −3.37359e79 | −1.77363 | ||||||||
\(982\) | 2.87755e79 | 1.47254 | ||||||||
\(983\) | −1.67774e79 | −0.835710 | −0.417855 | − | 0.908514i | \(-0.637218\pi\) | ||||
−0.417855 | + | 0.908514i | \(0.637218\pi\) | |||||||
\(984\) | 3.36160e78 | 0.162996 | ||||||||
\(985\) | −9.32164e77 | −0.0439979 | ||||||||
\(986\) | −1.22173e79 | −0.561354 | ||||||||
\(987\) | 7.30517e78 | 0.326758 | ||||||||
\(988\) | −7.89437e78 | −0.343763 | ||||||||
\(989\) | 2.43615e78 | 0.103277 | ||||||||
\(990\) | −2.12169e78 | −0.0875689 | ||||||||
\(991\) | 1.19328e79 | 0.479502 | 0.239751 | − | 0.970834i | \(-0.422934\pi\) | ||||
0.239751 | + | 0.970834i | \(0.422934\pi\) | |||||||
\(992\) | 9.60629e78 | 0.375834 | ||||||||
\(993\) | −4.59326e79 | −1.74971 | ||||||||
\(994\) | −7.77134e78 | −0.288242 | ||||||||
\(995\) | 6.31583e77 | 0.0228097 | ||||||||
\(996\) | 1.12582e78 | 0.0395909 | ||||||||
\(997\) | −2.54279e79 | −0.870739 | −0.435370 | − | 0.900252i | \(-0.643382\pi\) | ||||
−0.435370 | + | 0.900252i | \(0.643382\pi\) | |||||||
\(998\) | 4.63984e79 | 1.54719 | ||||||||
\(999\) | −6.96493e77 | −0.0226168 |
(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 | 1.54.a.a.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.54.a.b.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.54.a.a.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.54.a.b.1.3 | 4 | 3.2 | odd | 2 |