Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,48,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 48, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 48);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 48 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(27.9815325310\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 5897345978580 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{7}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.42844e6\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.38861e6 | −0.707107 | ||||||||
\(3\) | 2.70963e11 | 1.66173 | 0.830864 | − | 0.556476i | \(-0.187847\pi\) | ||||
0.830864 | + | 0.556476i | \(0.187847\pi\) | |||||||
\(4\) | 7.03687e13 | 0.500000 | ||||||||
\(5\) | −1.02521e16 | −0.384607 | −0.192303 | − | 0.981336i | \(-0.561596\pi\) | ||||
−0.192303 | + | 0.981336i | \(0.561596\pi\) | |||||||
\(6\) | −2.27300e18 | −1.17502 | ||||||||
\(7\) | 1.08843e20 | 1.50314 | 0.751568 | − | 0.659655i | \(-0.229298\pi\) | ||||
0.751568 | + | 0.659655i | \(0.229298\pi\) | |||||||
\(8\) | −5.90296e20 | −0.353553 | ||||||||
\(9\) | 4.68319e22 | 1.76134 | ||||||||
\(10\) | 8.60007e22 | 0.271958 | ||||||||
\(11\) | 3.92772e24 | 1.32255 | 0.661276 | − | 0.750143i | \(-0.270015\pi\) | ||||
0.661276 | + | 0.750143i | \(0.270015\pi\) | |||||||
\(12\) | 1.90673e25 | 0.830864 | ||||||||
\(13\) | −2.33551e26 | −1.55136 | −0.775679 | − | 0.631128i | \(-0.782592\pi\) | ||||
−0.775679 | + | 0.631128i | \(0.782592\pi\) | |||||||
\(14\) | −9.13045e26 | −1.06288 | ||||||||
\(15\) | −2.77793e27 | −0.639112 | ||||||||
\(16\) | 4.95176e27 | 0.250000 | ||||||||
\(17\) | 4.05682e28 | 0.492760 | 0.246380 | − | 0.969173i | \(-0.420759\pi\) | ||||
0.246380 | + | 0.969173i | \(0.420759\pi\) | |||||||
\(18\) | −3.92855e29 | −1.24545 | ||||||||
\(19\) | −1.56322e29 | −0.139095 | −0.0695473 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695473 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(20\) | −7.21426e29 | −0.192303 | ||||||||
\(21\) | 2.94925e31 | 2.49780 | ||||||||
\(22\) | −3.29481e31 | −0.935185 | ||||||||
\(23\) | 3.32892e31 | 0.332429 | 0.166215 | − | 0.986090i | \(-0.446846\pi\) | ||||
0.166215 | + | 0.986090i | \(0.446846\pi\) | |||||||
\(24\) | −1.59948e32 | −0.587509 | ||||||||
\(25\) | −6.05438e32 | −0.852078 | ||||||||
\(26\) | 1.95916e33 | 1.09698 | ||||||||
\(27\) | 5.48512e33 | 1.26514 | ||||||||
\(28\) | 7.65918e33 | 0.751568 | ||||||||
\(29\) | 9.92617e32 | 0.0427001 | 0.0213500 | − | 0.999772i | \(-0.493204\pi\) | ||||
0.0213500 | + | 0.999772i | \(0.493204\pi\) | |||||||
\(30\) | 2.33030e34 | 0.451920 | ||||||||
\(31\) | 1.71111e35 | 1.53560 | 0.767799 | − | 0.640690i | \(-0.221352\pi\) | ||||
0.767799 | + | 0.640690i | \(0.221352\pi\) | |||||||
\(32\) | −4.15384e34 | −0.176777 | ||||||||
\(33\) | 1.06427e36 | 2.19772 | ||||||||
\(34\) | −3.40310e35 | −0.348434 | ||||||||
\(35\) | −1.11587e36 | −0.578117 | ||||||||
\(36\) | 3.29550e36 | 0.880669 | ||||||||
\(37\) | 1.08691e37 | 1.52564 | 0.762819 | − | 0.646612i | \(-0.223815\pi\) | ||||
0.762819 | + | 0.646612i | \(0.223815\pi\) | |||||||
\(38\) | 1.31132e36 | 0.0983548 | ||||||||
\(39\) | −6.32835e37 | −2.57793 | ||||||||
\(40\) | 6.05176e36 | 0.135979 | ||||||||
\(41\) | −7.95054e37 | −0.999945 | −0.499972 | − | 0.866041i | \(-0.666656\pi\) | ||||
−0.499972 | + | 0.866041i | \(0.666656\pi\) | |||||||
\(42\) | −2.47401e38 | −1.76621 | ||||||||
\(43\) | 3.70345e38 | 1.52089 | 0.760446 | − | 0.649402i | \(-0.224981\pi\) | ||||
0.760446 | + | 0.649402i | \(0.224981\pi\) | |||||||
\(44\) | 2.76389e38 | 0.661276 | ||||||||
\(45\) | −4.80124e38 | −0.677423 | ||||||||
\(46\) | −2.79250e38 | −0.235063 | ||||||||
\(47\) | −6.30322e38 | −0.320083 | −0.160041 | − | 0.987110i | \(-0.551163\pi\) | ||||
−0.160041 | + | 0.987110i | \(0.551163\pi\) | |||||||
\(48\) | 1.34174e39 | 0.415432 | ||||||||
\(49\) | 6.60357e39 | 1.25942 | ||||||||
\(50\) | 5.07878e39 | 0.602510 | ||||||||
\(51\) | 1.09925e40 | 0.818833 | ||||||||
\(52\) | −1.64347e40 | −0.775679 | ||||||||
\(53\) | 2.32864e40 | 0.702456 | 0.351228 | − | 0.936290i | \(-0.385764\pi\) | ||||
0.351228 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(54\) | −4.60125e40 | −0.894587 | ||||||||
\(55\) | −4.02673e40 | −0.508662 | ||||||||
\(56\) | −6.42499e40 | −0.531439 | ||||||||
\(57\) | −4.23574e40 | −0.231137 | ||||||||
\(58\) | −8.32668e39 | −0.0301935 | ||||||||
\(59\) | −3.80182e41 | −0.922507 | −0.461253 | − | 0.887268i | \(-0.652600\pi\) | ||||
−0.461253 | + | 0.887268i | \(0.652600\pi\) | |||||||
\(60\) | −1.95479e41 | −0.319556 | ||||||||
\(61\) | 1.07627e42 | 1.19308 | 0.596541 | − | 0.802583i | \(-0.296541\pi\) | ||||
0.596541 | + | 0.802583i | \(0.296541\pi\) | |||||||
\(62\) | −1.43538e42 | −1.08583 | ||||||||
\(63\) | 5.09735e42 | 2.64753 | ||||||||
\(64\) | 3.48449e41 | 0.125000 | ||||||||
\(65\) | 2.39438e42 | 0.596663 | ||||||||
\(66\) | −8.92770e42 | −1.55402 | ||||||||
\(67\) | −1.46013e42 | −0.178498 | −0.0892490 | − | 0.996009i | \(-0.528447\pi\) | ||||
−0.0892490 | + | 0.996009i | \(0.528447\pi\) | |||||||
\(68\) | 2.85473e42 | 0.246380 | ||||||||
\(69\) | 9.02012e42 | 0.552406 | ||||||||
\(70\) | 9.36061e42 | 0.408790 | ||||||||
\(71\) | −1.66419e43 | −0.520752 | −0.260376 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260376 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(72\) | −2.76447e43 | −0.622727 | ||||||||
\(73\) | −5.99210e42 | −0.0976095 | −0.0488047 | − | 0.998808i | \(-0.515541\pi\) | ||||
−0.0488047 | + | 0.998808i | \(0.515541\pi\) | |||||||
\(74\) | −9.11763e43 | −1.07879 | ||||||||
\(75\) | −1.64051e44 | −1.41592 | ||||||||
\(76\) | −1.10002e43 | −0.0695473 | ||||||||
\(77\) | 4.27507e44 | 1.98798 | ||||||||
\(78\) | 5.30860e44 | 1.82287 | ||||||||
\(79\) | −1.80688e44 | −0.459931 | −0.229966 | − | 0.973199i | \(-0.573861\pi\) | ||||
−0.229966 | + | 0.973199i | \(0.573861\pi\) | |||||||
\(80\) | −5.07658e43 | −0.0961517 | ||||||||
\(81\) | 2.41058e44 | 0.340975 | ||||||||
\(82\) | 6.66940e44 | 0.707068 | ||||||||
\(83\) | −2.37314e45 | −1.89229 | −0.946144 | − | 0.323745i | \(-0.895058\pi\) | ||||
−0.946144 | + | 0.323745i | \(0.895058\pi\) | |||||||
\(84\) | 2.07535e45 | 1.24890 | ||||||||
\(85\) | −4.15908e44 | −0.189519 | ||||||||
\(86\) | −3.10668e45 | −1.07543 | ||||||||
\(87\) | 2.68962e44 | 0.0709559 | ||||||||
\(88\) | −2.31852e45 | −0.467592 | ||||||||
\(89\) | 1.07890e45 | 0.166846 | 0.0834232 | − | 0.996514i | \(-0.473415\pi\) | ||||
0.0834232 | + | 0.996514i | \(0.473415\pi\) | |||||||
\(90\) | 4.02758e45 | 0.479010 | ||||||||
\(91\) | −2.54205e46 | −2.33190 | ||||||||
\(92\) | 2.34252e45 | 0.166215 | ||||||||
\(93\) | 4.63646e46 | 2.55175 | ||||||||
\(94\) | 5.28752e45 | 0.226333 | ||||||||
\(95\) | 1.60263e45 | 0.0534967 | ||||||||
\(96\) | −1.12553e46 | −0.293755 | ||||||||
\(97\) | −5.98242e45 | −0.122389 | −0.0611943 | − | 0.998126i | \(-0.519491\pi\) | ||||
−0.0611943 | + | 0.998126i | \(0.519491\pi\) | |||||||
\(98\) | −5.53948e46 | −0.890545 | ||||||||
\(99\) | 1.83943e47 | 2.32946 | ||||||||
\(100\) | −4.26039e46 | −0.426039 | ||||||||
\(101\) | −6.21755e46 | −0.492115 | −0.246058 | − | 0.969255i | \(-0.579135\pi\) | ||||
−0.246058 | + | 0.969255i | \(0.579135\pi\) | |||||||
\(102\) | −9.22114e46 | −0.579003 | ||||||||
\(103\) | 1.44306e45 | 0.00720458 | 0.00360229 | − | 0.999994i | \(-0.498853\pi\) | ||||
0.00360229 | + | 0.999994i | \(0.498853\pi\) | |||||||
\(104\) | 1.37864e47 | 0.548488 | ||||||||
\(105\) | −3.02360e47 | −0.960672 | ||||||||
\(106\) | −1.95340e47 | −0.496712 | ||||||||
\(107\) | −8.78783e47 | −1.79210 | −0.896051 | − | 0.443951i | \(-0.853577\pi\) | ||||
−0.896051 | + | 0.443951i | \(0.853577\pi\) | |||||||
\(108\) | 3.85981e47 | 0.632569 | ||||||||
\(109\) | −1.77433e45 | −0.00234159 | −0.00117080 | − | 0.999999i | \(-0.500373\pi\) | ||||
−0.00117080 | + | 0.999999i | \(0.500373\pi\) | |||||||
\(110\) | 3.37787e47 | 0.359678 | ||||||||
\(111\) | 2.94511e48 | 2.53520 | ||||||||
\(112\) | 5.38967e47 | 0.375784 | ||||||||
\(113\) | −6.05109e46 | −0.0342365 | −0.0171183 | − | 0.999853i | \(-0.505449\pi\) | ||||
−0.0171183 | + | 0.999853i | \(0.505449\pi\) | |||||||
\(114\) | 3.55320e47 | 0.163439 | ||||||||
\(115\) | −3.41283e47 | −0.127854 | ||||||||
\(116\) | 6.98492e46 | 0.0213500 | ||||||||
\(117\) | −1.09376e49 | −2.73247 | ||||||||
\(118\) | 3.18920e48 | 0.652311 | ||||||||
\(119\) | 4.41558e48 | 0.740686 | ||||||||
\(120\) | 1.63980e48 | 0.225960 | ||||||||
\(121\) | 6.60724e48 | 0.749141 | ||||||||
\(122\) | −9.02840e48 | −0.843636 | ||||||||
\(123\) | −2.15430e49 | −1.66164 | ||||||||
\(124\) | 1.20409e49 | 0.767799 | ||||||||
\(125\) | 1.34915e49 | 0.712321 | ||||||||
\(126\) | −4.27597e49 | −1.87209 | ||||||||
\(127\) | 8.82915e48 | 0.321020 | 0.160510 | − | 0.987034i | \(-0.448686\pi\) | ||||
0.160510 | + | 0.987034i | \(0.448686\pi\) | |||||||
\(128\) | −2.92300e48 | −0.0883883 | ||||||||
\(129\) | 1.00350e50 | 2.52731 | ||||||||
\(130\) | −2.00855e49 | −0.421904 | ||||||||
\(131\) | −1.59705e49 | −0.280183 | −0.140092 | − | 0.990139i | \(-0.544740\pi\) | ||||
−0.140092 | + | 0.990139i | \(0.544740\pi\) | |||||||
\(132\) | 7.48910e49 | 1.09886 | ||||||||
\(133\) | −1.70146e49 | −0.209078 | ||||||||
\(134\) | 1.22485e49 | 0.126217 | ||||||||
\(135\) | −5.62339e49 | −0.486580 | ||||||||
\(136\) | −2.39472e49 | −0.174217 | ||||||||
\(137\) | −6.03702e49 | −0.369734 | −0.184867 | − | 0.982764i | \(-0.559185\pi\) | ||||
−0.184867 | + | 0.982764i | \(0.559185\pi\) | |||||||
\(138\) | −7.56663e49 | −0.390610 | ||||||||
\(139\) | 1.21646e50 | 0.529969 | 0.264985 | − | 0.964253i | \(-0.414633\pi\) | ||||
0.264985 | + | 0.964253i | \(0.414633\pi\) | |||||||
\(140\) | −7.85225e49 | −0.289058 | ||||||||
\(141\) | −1.70794e50 | −0.531891 | ||||||||
\(142\) | 1.39602e50 | 0.368227 | ||||||||
\(143\) | −9.17321e50 | −2.05175 | ||||||||
\(144\) | 2.31900e50 | 0.440335 | ||||||||
\(145\) | −1.01764e49 | −0.0164227 | ||||||||
\(146\) | 5.02654e49 | 0.0690203 | ||||||||
\(147\) | 1.78932e51 | 2.09281 | ||||||||
\(148\) | 7.64843e50 | 0.762819 | ||||||||
\(149\) | −1.57670e51 | −1.34237 | −0.671185 | − | 0.741290i | \(-0.734214\pi\) | ||||
−0.671185 | + | 0.741290i | \(0.734214\pi\) | |||||||
\(150\) | 1.37616e51 | 1.00121 | ||||||||
\(151\) | 1.05031e51 | 0.653674 | 0.326837 | − | 0.945081i | \(-0.394017\pi\) | ||||
0.326837 | + | 0.945081i | \(0.394017\pi\) | |||||||
\(152\) | 9.22762e49 | 0.0491774 | ||||||||
\(153\) | 1.89988e51 | 0.867918 | ||||||||
\(154\) | −3.58619e51 | −1.40571 | ||||||||
\(155\) | −1.75424e51 | −0.590602 | ||||||||
\(156\) | −4.45318e51 | −1.28897 | ||||||||
\(157\) | −3.24813e51 | −0.809081 | −0.404541 | − | 0.914520i | \(-0.632569\pi\) | ||||
−0.404541 | + | 0.914520i | \(0.632569\pi\) | |||||||
\(158\) | 1.51572e51 | 0.325221 | ||||||||
\(159\) | 6.30974e51 | 1.16729 | ||||||||
\(160\) | 4.25855e50 | 0.0679895 | ||||||||
\(161\) | 3.62331e51 | 0.499686 | ||||||||
\(162\) | −2.02214e51 | −0.241106 | ||||||||
\(163\) | −4.29859e51 | −0.443524 | −0.221762 | − | 0.975101i | \(-0.571181\pi\) | ||||
−0.221762 | + | 0.975101i | \(0.571181\pi\) | |||||||
\(164\) | −5.59469e51 | −0.499972 | ||||||||
\(165\) | −1.09109e52 | −0.845258 | ||||||||
\(166\) | 1.99073e52 | 1.33805 | ||||||||
\(167\) | −6.41790e50 | −0.0374590 | −0.0187295 | − | 0.999825i | \(-0.505962\pi\) | ||||
−0.0187295 | + | 0.999825i | \(0.505962\pi\) | |||||||
\(168\) | −1.74093e52 | −0.883107 | ||||||||
\(169\) | 3.18818e52 | 1.40671 | ||||||||
\(170\) | 3.48889e51 | 0.134010 | ||||||||
\(171\) | −7.32086e51 | −0.244993 | ||||||||
\(172\) | 2.60607e52 | 0.760446 | ||||||||
\(173\) | 6.69399e52 | 1.70452 | 0.852259 | − | 0.523120i | \(-0.175232\pi\) | ||||
0.852259 | + | 0.523120i | \(0.175232\pi\) | |||||||
\(174\) | −2.25622e51 | −0.0501734 | ||||||||
\(175\) | −6.58979e52 | −1.28079 | ||||||||
\(176\) | 1.94491e52 | 0.330638 | ||||||||
\(177\) | −1.03015e53 | −1.53296 | ||||||||
\(178\) | −9.05048e51 | −0.117978 | ||||||||
\(179\) | −1.38049e53 | −1.57757 | −0.788784 | − | 0.614671i | \(-0.789289\pi\) | ||||
−0.788784 | + | 0.614671i | \(0.789289\pi\) | |||||||
\(180\) | −3.37858e52 | −0.338711 | ||||||||
\(181\) | −9.26435e52 | −0.815396 | −0.407698 | − | 0.913117i | \(-0.633668\pi\) | ||||
−0.407698 | + | 0.913117i | \(0.633668\pi\) | |||||||
\(182\) | 2.13242e53 | 1.64890 | ||||||||
\(183\) | 2.91629e53 | 1.98258 | ||||||||
\(184\) | −1.96505e52 | −0.117531 | ||||||||
\(185\) | −1.11431e53 | −0.586771 | ||||||||
\(186\) | −3.88935e53 | −1.80436 | ||||||||
\(187\) | 1.59340e53 | 0.651701 | ||||||||
\(188\) | −4.43549e52 | −0.160041 | ||||||||
\(189\) | 5.97020e53 | 1.90168 | ||||||||
\(190\) | −1.34438e52 | −0.0378279 | ||||||||
\(191\) | 3.78107e53 | 0.940439 | 0.470220 | − | 0.882549i | \(-0.344175\pi\) | ||||
0.470220 | + | 0.882549i | \(0.344175\pi\) | |||||||
\(192\) | 9.44167e52 | 0.207716 | ||||||||
\(193\) | −6.95903e53 | −1.35504 | −0.677520 | − | 0.735504i | \(-0.736945\pi\) | ||||
−0.677520 | + | 0.735504i | \(0.736945\pi\) | |||||||
\(194\) | 5.01842e52 | 0.0865418 | ||||||||
\(195\) | 6.48787e53 | 0.991491 | ||||||||
\(196\) | 4.64685e53 | 0.629710 | ||||||||
\(197\) | −7.80244e53 | −0.938155 | −0.469077 | − | 0.883157i | \(-0.655413\pi\) | ||||
−0.469077 | + | 0.883157i | \(0.655413\pi\) | |||||||
\(198\) | −1.54302e54 | −1.64718 | ||||||||
\(199\) | −1.09549e54 | −1.03887 | −0.519434 | − | 0.854510i | \(-0.673857\pi\) | ||||
−0.519434 | + | 0.854510i | \(0.673857\pi\) | |||||||
\(200\) | 3.57387e53 | 0.301255 | ||||||||
\(201\) | −3.95640e53 | −0.296615 | ||||||||
\(202\) | 5.21566e53 | 0.347978 | ||||||||
\(203\) | 1.08040e53 | 0.0641841 | ||||||||
\(204\) | 7.73525e53 | 0.409417 | ||||||||
\(205\) | 8.15095e53 | 0.384585 | ||||||||
\(206\) | −1.21052e52 | −0.00509441 | ||||||||
\(207\) | 1.55900e54 | 0.585520 | ||||||||
\(208\) | −1.15649e54 | −0.387840 | ||||||||
\(209\) | −6.13989e53 | −0.183960 | ||||||||
\(210\) | 2.53638e54 | 0.679298 | ||||||||
\(211\) | −1.93427e54 | −0.463317 | −0.231659 | − | 0.972797i | \(-0.574415\pi\) | ||||
−0.231659 | + | 0.972797i | \(0.574415\pi\) | |||||||
\(212\) | 1.63863e54 | 0.351228 | ||||||||
\(213\) | −4.50932e54 | −0.865348 | ||||||||
\(214\) | 7.37177e54 | 1.26721 | ||||||||
\(215\) | −3.79681e54 | −0.584945 | ||||||||
\(216\) | −3.23784e54 | −0.447294 | ||||||||
\(217\) | 1.86243e55 | 2.30822 | ||||||||
\(218\) | 1.48841e52 | 0.00165575 | ||||||||
\(219\) | −1.62364e54 | −0.162200 | ||||||||
\(220\) | −2.83356e54 | −0.254331 | ||||||||
\(221\) | −9.47471e54 | −0.764448 | ||||||||
\(222\) | −2.47054e55 | −1.79265 | ||||||||
\(223\) | 7.23600e54 | 0.472426 | 0.236213 | − | 0.971701i | \(-0.424094\pi\) | ||||
0.236213 | + | 0.971701i | \(0.424094\pi\) | |||||||
\(224\) | −4.52118e54 | −0.265720 | ||||||||
\(225\) | −2.83538e55 | −1.50080 | ||||||||
\(226\) | 5.07602e53 | 0.0242089 | ||||||||
\(227\) | 2.17948e55 | 0.937013 | 0.468507 | − | 0.883460i | \(-0.344792\pi\) | ||||
0.468507 | + | 0.883460i | \(0.344792\pi\) | |||||||
\(228\) | −2.98064e54 | −0.115569 | ||||||||
\(229\) | −1.86932e55 | −0.653957 | −0.326979 | − | 0.945032i | \(-0.606031\pi\) | ||||
−0.326979 | + | 0.945032i | \(0.606031\pi\) | |||||||
\(230\) | 2.86289e54 | 0.0904067 | ||||||||
\(231\) | 1.15838e56 | 3.30347 | ||||||||
\(232\) | −5.85938e53 | −0.0150968 | ||||||||
\(233\) | −5.14721e55 | −1.19869 | −0.599346 | − | 0.800490i | \(-0.704573\pi\) | ||||
−0.599346 | + | 0.800490i | \(0.704573\pi\) | |||||||
\(234\) | 9.17514e55 | 1.93215 | ||||||||
\(235\) | 6.46211e54 | 0.123106 | ||||||||
\(236\) | −2.67530e55 | −0.461253 | ||||||||
\(237\) | −4.89597e55 | −0.764281 | ||||||||
\(238\) | −3.70406e55 | −0.523744 | ||||||||
\(239\) | −2.55198e55 | −0.326984 | −0.163492 | − | 0.986545i | \(-0.552276\pi\) | ||||
−0.163492 | + | 0.986545i | \(0.552276\pi\) | |||||||
\(240\) | −1.37556e55 | −0.159778 | ||||||||
\(241\) | 6.85848e55 | 0.722483 | 0.361241 | − | 0.932472i | \(-0.382353\pi\) | ||||
0.361241 | + | 0.932472i | \(0.382353\pi\) | |||||||
\(242\) | −5.54255e55 | −0.529723 | ||||||||
\(243\) | −8.05253e55 | −0.698529 | ||||||||
\(244\) | 7.57357e55 | 0.596541 | ||||||||
\(245\) | −6.77003e55 | −0.484382 | ||||||||
\(246\) | 1.80716e56 | 1.17495 | ||||||||
\(247\) | 3.65091e55 | 0.215786 | ||||||||
\(248\) | −1.01006e56 | −0.542916 | ||||||||
\(249\) | −6.43031e56 | −3.14447 | ||||||||
\(250\) | −1.13175e56 | −0.503687 | ||||||||
\(251\) | 4.26400e56 | 1.72776 | 0.863882 | − | 0.503694i | \(-0.168026\pi\) | ||||
0.863882 | + | 0.503694i | \(0.168026\pi\) | |||||||
\(252\) | 3.58694e56 | 1.32377 | ||||||||
\(253\) | 1.30751e56 | 0.439654 | ||||||||
\(254\) | −7.40643e55 | −0.226995 | ||||||||
\(255\) | −1.12695e56 | −0.314929 | ||||||||
\(256\) | 2.45199e55 | 0.0625000 | ||||||||
\(257\) | 5.48104e56 | 1.27478 | 0.637389 | − | 0.770543i | \(-0.280015\pi\) | ||||
0.637389 | + | 0.770543i | \(0.280015\pi\) | |||||||
\(258\) | −8.41794e56 | −1.78708 | ||||||||
\(259\) | 1.18303e57 | 2.29324 | ||||||||
\(260\) | 1.68489e56 | 0.298331 | ||||||||
\(261\) | 4.64862e55 | 0.0752093 | ||||||||
\(262\) | 1.33970e56 | 0.198119 | ||||||||
\(263\) | −1.18349e57 | −1.60032 | −0.800158 | − | 0.599789i | \(-0.795251\pi\) | ||||
−0.800158 | + | 0.599789i | \(0.795251\pi\) | |||||||
\(264\) | −6.28231e56 | −0.777011 | ||||||||
\(265\) | −2.38734e56 | −0.270169 | ||||||||
\(266\) | 1.42729e56 | 0.147841 | ||||||||
\(267\) | 2.92342e56 | 0.277253 | ||||||||
\(268\) | −1.02747e56 | −0.0892490 | ||||||||
\(269\) | −2.06922e55 | −0.0164675 | −0.00823375 | − | 0.999966i | \(-0.502621\pi\) | ||||
−0.00823375 | + | 0.999966i | \(0.502621\pi\) | |||||||
\(270\) | 4.71724e56 | 0.344064 | ||||||||
\(271\) | 2.88469e57 | 1.92895 | 0.964473 | − | 0.264181i | \(-0.0851015\pi\) | ||||
0.964473 | + | 0.264181i | \(0.0851015\pi\) | |||||||
\(272\) | 2.00884e56 | 0.123190 | ||||||||
\(273\) | −6.88799e57 | −3.87499 | ||||||||
\(274\) | 5.06422e56 | 0.261441 | ||||||||
\(275\) | −2.37799e57 | −1.12692 | ||||||||
\(276\) | 6.34735e56 | 0.276203 | ||||||||
\(277\) | −4.45744e55 | −0.0178160 | −0.00890801 | − | 0.999960i | \(-0.502836\pi\) | ||||
−0.00890801 | + | 0.999960i | \(0.502836\pi\) | |||||||
\(278\) | −1.02044e57 | −0.374745 | ||||||||
\(279\) | 8.01345e57 | 2.70471 | ||||||||
\(280\) | 6.58695e56 | 0.204395 | ||||||||
\(281\) | 6.47805e56 | 0.184861 | 0.0924306 | − | 0.995719i | \(-0.470536\pi\) | ||||
0.0924306 | + | 0.995719i | \(0.470536\pi\) | |||||||
\(282\) | 1.43272e57 | 0.376104 | ||||||||
\(283\) | 4.33569e57 | 1.04731 | 0.523657 | − | 0.851929i | \(-0.324567\pi\) | ||||
0.523657 | + | 0.851929i | \(0.324567\pi\) | |||||||
\(284\) | −1.17107e57 | −0.260376 | ||||||||
\(285\) | 4.34252e56 | 0.0888970 | ||||||||
\(286\) | 7.69505e57 | 1.45081 | ||||||||
\(287\) | −8.65364e57 | −1.50305 | ||||||||
\(288\) | −1.94532e57 | −0.311364 | ||||||||
\(289\) | −5.13219e57 | −0.757187 | ||||||||
\(290\) | 8.53657e55 | 0.0116126 | ||||||||
\(291\) | −1.62101e57 | −0.203377 | ||||||||
\(292\) | −4.21657e56 | −0.0488047 | ||||||||
\(293\) | −1.05782e58 | −1.12986 | −0.564929 | − | 0.825140i | \(-0.691096\pi\) | ||||
−0.564929 | + | 0.825140i | \(0.691096\pi\) | |||||||
\(294\) | −1.50099e58 | −1.47984 | ||||||||
\(295\) | 3.89766e57 | 0.354802 | ||||||||
\(296\) | −6.41596e57 | −0.539395 | ||||||||
\(297\) | 2.15440e58 | 1.67321 | ||||||||
\(298\) | 1.32263e58 | 0.949199 | ||||||||
\(299\) | −7.77470e57 | −0.515716 | ||||||||
\(300\) | −1.15441e58 | −0.707961 | ||||||||
\(301\) | 4.03097e58 | 2.28611 | ||||||||
\(302\) | −8.81067e57 | −0.462217 | ||||||||
\(303\) | −1.68472e58 | −0.817762 | ||||||||
\(304\) | −7.74069e56 | −0.0347737 | ||||||||
\(305\) | −1.10340e58 | −0.458867 | ||||||||
\(306\) | −1.59374e58 | −0.613710 | ||||||||
\(307\) | 2.06877e58 | 0.737837 | 0.368919 | − | 0.929462i | \(-0.379728\pi\) | ||||
0.368919 | + | 0.929462i | \(0.379728\pi\) | |||||||
\(308\) | 3.00831e58 | 0.993988 | ||||||||
\(309\) | 3.91015e56 | 0.0119721 | ||||||||
\(310\) | 1.47156e58 | 0.417618 | ||||||||
\(311\) | −2.39439e58 | −0.629978 | −0.314989 | − | 0.949095i | \(-0.602001\pi\) | ||||
−0.314989 | + | 0.949095i | \(0.602001\pi\) | |||||||
\(312\) | 3.73560e58 | 0.911437 | ||||||||
\(313\) | −9.48940e57 | −0.214757 | −0.107378 | − | 0.994218i | \(-0.534246\pi\) | ||||
−0.107378 | + | 0.994218i | \(0.534246\pi\) | |||||||
\(314\) | 2.72473e58 | 0.572107 | ||||||||
\(315\) | −5.22584e58 | −1.01826 | ||||||||
\(316\) | −1.27148e58 | −0.229966 | ||||||||
\(317\) | 9.13985e58 | 1.53478 | 0.767391 | − | 0.641180i | \(-0.221555\pi\) | ||||
0.767391 | + | 0.641180i | \(0.221555\pi\) | |||||||
\(318\) | −5.29300e58 | −0.825400 | ||||||||
\(319\) | 3.89872e57 | 0.0564731 | ||||||||
\(320\) | −3.57233e57 | −0.0480758 | ||||||||
\(321\) | −2.38117e59 | −2.97799 | ||||||||
\(322\) | −3.03945e58 | −0.353332 | ||||||||
\(323\) | −6.34170e57 | −0.0685403 | ||||||||
\(324\) | 1.69629e58 | 0.170488 | ||||||||
\(325\) | 1.41400e59 | 1.32188 | ||||||||
\(326\) | 3.60592e58 | 0.313619 | ||||||||
\(327\) | −4.80776e56 | −0.00389108 | ||||||||
\(328\) | 4.69317e58 | 0.353534 | ||||||||
\(329\) | −6.86064e58 | −0.481129 | ||||||||
\(330\) | 9.15275e58 | 0.597687 | ||||||||
\(331\) | −1.08997e59 | −0.662911 | −0.331456 | − | 0.943471i | \(-0.607540\pi\) | ||||
−0.331456 | + | 0.943471i | \(0.607540\pi\) | |||||||
\(332\) | −1.66995e59 | −0.946144 | ||||||||
\(333\) | 5.09019e59 | 2.68717 | ||||||||
\(334\) | 5.38372e57 | 0.0264875 | ||||||||
\(335\) | 1.49694e58 | 0.0686516 | ||||||||
\(336\) | 1.46040e59 | 0.624451 | ||||||||
\(337\) | −2.00408e59 | −0.799120 | −0.399560 | − | 0.916707i | \(-0.630837\pi\) | ||||
−0.399560 | + | 0.916707i | \(0.630837\pi\) | |||||||
\(338\) | −2.67444e59 | −0.994695 | ||||||||
\(339\) | −1.63962e58 | −0.0568918 | ||||||||
\(340\) | −2.92669e58 | −0.0947594 | ||||||||
\(341\) | 6.72076e59 | 2.03091 | ||||||||
\(342\) | 6.14118e58 | 0.173236 | ||||||||
\(343\) | 1.48052e59 | 0.389945 | ||||||||
\(344\) | −2.18613e59 | −0.537716 | ||||||||
\(345\) | −9.24750e58 | −0.212459 | ||||||||
\(346\) | −5.61533e59 | −1.20528 | ||||||||
\(347\) | −8.91525e59 | −1.78810 | −0.894048 | − | 0.447971i | \(-0.852147\pi\) | ||||
−0.894048 | + | 0.447971i | \(0.852147\pi\) | |||||||
\(348\) | 1.89265e58 | 0.0354780 | ||||||||
\(349\) | −2.64940e59 | −0.464248 | −0.232124 | − | 0.972686i | \(-0.574567\pi\) | ||||
−0.232124 | + | 0.972686i | \(0.574567\pi\) | |||||||
\(350\) | 5.52792e59 | 0.905655 | ||||||||
\(351\) | −1.28105e60 | −1.96268 | ||||||||
\(352\) | −1.63151e59 | −0.233796 | ||||||||
\(353\) | 6.11122e59 | 0.819261 | 0.409630 | − | 0.912252i | \(-0.365658\pi\) | ||||
0.409630 | + | 0.912252i | \(0.365658\pi\) | |||||||
\(354\) | 8.64154e59 | 1.08396 | ||||||||
\(355\) | 1.70614e59 | 0.200285 | ||||||||
\(356\) | 7.59209e58 | 0.0834232 | ||||||||
\(357\) | 1.19646e60 | 1.23082 | ||||||||
\(358\) | 1.15804e60 | 1.11551 | ||||||||
\(359\) | −2.33703e59 | −0.210836 | −0.105418 | − | 0.994428i | \(-0.533618\pi\) | ||||
−0.105418 | + | 0.994428i | \(0.533618\pi\) | |||||||
\(360\) | 2.83415e59 | 0.239505 | ||||||||
\(361\) | −1.23861e60 | −0.980653 | ||||||||
\(362\) | 7.77150e59 | 0.576572 | ||||||||
\(363\) | 1.79031e60 | 1.24487 | ||||||||
\(364\) | −1.78881e60 | −1.16595 | ||||||||
\(365\) | 6.14315e58 | 0.0375413 | ||||||||
\(366\) | −2.44636e60 | −1.40189 | ||||||||
\(367\) | 7.93168e59 | 0.426298 | 0.213149 | − | 0.977020i | \(-0.431628\pi\) | ||||
0.213149 | + | 0.977020i | \(0.431628\pi\) | |||||||
\(368\) | 1.64840e59 | 0.0831073 | ||||||||
\(369\) | −3.72339e60 | −1.76124 | ||||||||
\(370\) | 9.34747e59 | 0.414910 | ||||||||
\(371\) | 2.53457e60 | 1.05589 | ||||||||
\(372\) | 3.26262e60 | 1.27587 | ||||||||
\(373\) | −2.14688e60 | −0.788224 | −0.394112 | − | 0.919062i | \(-0.628948\pi\) | ||||
−0.394112 | + | 0.919062i | \(0.628948\pi\) | |||||||
\(374\) | −1.33664e60 | −0.460822 | ||||||||
\(375\) | 3.65570e60 | 1.18368 | ||||||||
\(376\) | 3.72076e59 | 0.113166 | ||||||||
\(377\) | −2.31826e59 | −0.0662431 | ||||||||
\(378\) | −5.00816e60 | −1.34469 | ||||||||
\(379\) | −5.45651e60 | −1.37687 | −0.688436 | − | 0.725297i | \(-0.741702\pi\) | ||||
−0.688436 | + | 0.725297i | \(0.741702\pi\) | |||||||
\(380\) | 1.12775e59 | 0.0267484 | ||||||||
\(381\) | 2.39237e60 | 0.533447 | ||||||||
\(382\) | −3.17179e60 | −0.664991 | ||||||||
\(383\) | −2.64466e60 | −0.521434 | −0.260717 | − | 0.965415i | \(-0.583959\pi\) | ||||
−0.260717 | + | 0.965415i | \(0.583959\pi\) | |||||||
\(384\) | −7.92025e59 | −0.146877 | ||||||||
\(385\) | −4.38283e60 | −0.764589 | ||||||||
\(386\) | 5.83766e60 | 0.958158 | ||||||||
\(387\) | 1.73440e61 | 2.67880 | ||||||||
\(388\) | −4.20975e59 | −0.0611943 | ||||||||
\(389\) | 8.47705e60 | 1.15992 | 0.579962 | − | 0.814644i | \(-0.303068\pi\) | ||||
0.579962 | + | 0.814644i | \(0.303068\pi\) | |||||||
\(390\) | −5.44242e60 | −0.701090 | ||||||||
\(391\) | 1.35048e60 | 0.163808 | ||||||||
\(392\) | −3.89806e60 | −0.445272 | ||||||||
\(393\) | −4.32740e60 | −0.465588 | ||||||||
\(394\) | 6.54516e60 | 0.663375 | ||||||||
\(395\) | 1.85243e60 | 0.176893 | ||||||||
\(396\) | 1.29438e61 | 1.16473 | ||||||||
\(397\) | −1.01947e61 | −0.864568 | −0.432284 | − | 0.901738i | \(-0.642292\pi\) | ||||
−0.432284 | + | 0.901738i | \(0.642292\pi\) | |||||||
\(398\) | 9.18963e60 | 0.734591 | ||||||||
\(399\) | −4.61033e60 | −0.347431 | ||||||||
\(400\) | −2.99798e60 | −0.213019 | ||||||||
\(401\) | −2.08710e61 | −1.39846 | −0.699230 | − | 0.714897i | \(-0.746474\pi\) | ||||
−0.699230 | + | 0.714897i | \(0.746474\pi\) | |||||||
\(402\) | 3.31887e60 | 0.209739 | ||||||||
\(403\) | −3.99630e61 | −2.38226 | ||||||||
\(404\) | −4.37521e60 | −0.246058 | ||||||||
\(405\) | −2.47134e60 | −0.131141 | ||||||||
\(406\) | −9.06305e59 | −0.0453850 | ||||||||
\(407\) | 4.26907e61 | 2.01774 | ||||||||
\(408\) | −6.48880e60 | −0.289501 | ||||||||
\(409\) | 2.90356e61 | 1.22302 | 0.611509 | − | 0.791238i | \(-0.290563\pi\) | ||||
0.611509 | + | 0.791238i | \(0.290563\pi\) | |||||||
\(410\) | −6.83752e60 | −0.271943 | ||||||||
\(411\) | −1.63581e61 | −0.614397 | ||||||||
\(412\) | 1.01546e59 | 0.00360229 | ||||||||
\(413\) | −4.13804e61 | −1.38665 | ||||||||
\(414\) | −1.30778e61 | −0.414025 | ||||||||
\(415\) | 2.43296e61 | 0.727787 | ||||||||
\(416\) | 9.70131e60 | 0.274244 | ||||||||
\(417\) | 3.29616e61 | 0.880664 | ||||||||
\(418\) | 5.15051e60 | 0.130079 | ||||||||
\(419\) | 4.51827e61 | 1.07880 | 0.539402 | − | 0.842048i | \(-0.318650\pi\) | ||||
0.539402 | + | 0.842048i | \(0.318650\pi\) | |||||||
\(420\) | −2.12767e61 | −0.480336 | ||||||||
\(421\) | 6.03083e61 | 1.28750 | 0.643751 | − | 0.765235i | \(-0.277377\pi\) | ||||
0.643751 | + | 0.765235i | \(0.277377\pi\) | |||||||
\(422\) | 1.62258e61 | 0.327615 | ||||||||
\(423\) | −2.95192e61 | −0.563775 | ||||||||
\(424\) | −1.37459e61 | −0.248356 | ||||||||
\(425\) | −2.45615e61 | −0.419870 | ||||||||
\(426\) | 3.78270e61 | 0.611894 | ||||||||
\(427\) | 1.17145e62 | 1.79336 | ||||||||
\(428\) | −6.18389e61 | −0.896051 | ||||||||
\(429\) | −2.48560e62 | −3.40945 | ||||||||
\(430\) | 3.18499e61 | 0.413619 | ||||||||
\(431\) | −2.84185e61 | −0.349450 | −0.174725 | − | 0.984617i | \(-0.555904\pi\) | ||||
−0.174725 | + | 0.984617i | \(0.555904\pi\) | |||||||
\(432\) | 2.71610e61 | 0.316284 | ||||||||
\(433\) | 9.49921e61 | 1.04766 | 0.523832 | − | 0.851822i | \(-0.324502\pi\) | ||||
0.523832 | + | 0.851822i | \(0.324502\pi\) | |||||||
\(434\) | −1.56232e62 | −1.63215 | ||||||||
\(435\) | −2.75742e60 | −0.0272901 | ||||||||
\(436\) | −1.24857e59 | −0.00117080 | ||||||||
\(437\) | −5.20383e60 | −0.0462391 | ||||||||
\(438\) | 1.36200e61 | 0.114693 | ||||||||
\(439\) | −8.51566e61 | −0.679676 | −0.339838 | − | 0.940484i | \(-0.610372\pi\) | ||||
−0.339838 | + | 0.940484i | \(0.610372\pi\) | |||||||
\(440\) | 2.37696e61 | 0.179839 | ||||||||
\(441\) | 3.09258e62 | 2.21827 | ||||||||
\(442\) | 7.94797e61 | 0.540546 | ||||||||
\(443\) | −2.00324e62 | −1.29195 | −0.645974 | − | 0.763360i | \(-0.723548\pi\) | ||||
−0.645974 | + | 0.763360i | \(0.723548\pi\) | |||||||
\(444\) | 2.07244e62 | 1.26760 | ||||||||
\(445\) | −1.10610e61 | −0.0641702 | ||||||||
\(446\) | −6.06999e61 | −0.334056 | ||||||||
\(447\) | −4.27227e62 | −2.23065 | ||||||||
\(448\) | 3.79264e61 | 0.187892 | ||||||||
\(449\) | 1.70791e62 | 0.802927 | 0.401463 | − | 0.915875i | \(-0.368502\pi\) | ||||
0.401463 | + | 0.915875i | \(0.368502\pi\) | |||||||
\(450\) | 2.37849e62 | 1.06122 | ||||||||
\(451\) | −3.12275e62 | −1.32248 | ||||||||
\(452\) | −4.25807e60 | −0.0171183 | ||||||||
\(453\) | 2.84596e62 | 1.08623 | ||||||||
\(454\) | −1.82828e62 | −0.662568 | ||||||||
\(455\) | 2.60613e62 | 0.896866 | ||||||||
\(456\) | 2.50034e61 | 0.0817194 | ||||||||
\(457\) | 6.09529e62 | 1.89219 | 0.946093 | − | 0.323895i | \(-0.104993\pi\) | ||||
0.946093 | + | 0.323895i | \(0.104993\pi\) | |||||||
\(458\) | 1.56810e62 | 0.462418 | ||||||||
\(459\) | 2.22521e62 | 0.623409 | ||||||||
\(460\) | −2.40157e61 | −0.0639272 | ||||||||
\(461\) | −6.69058e62 | −1.69236 | −0.846179 | − | 0.532898i | \(-0.821103\pi\) | ||||
−0.846179 | + | 0.532898i | \(0.821103\pi\) | |||||||
\(462\) | −9.71723e62 | −2.33591 | ||||||||
\(463\) | 4.30318e62 | 0.983187 | 0.491593 | − | 0.870825i | \(-0.336415\pi\) | ||||
0.491593 | + | 0.870825i | \(0.336415\pi\) | |||||||
\(464\) | 4.91520e60 | 0.0106750 | ||||||||
\(465\) | −4.75334e62 | −0.981419 | ||||||||
\(466\) | 4.31779e62 | 0.847604 | ||||||||
\(467\) | −5.60104e62 | −1.04550 | −0.522748 | − | 0.852487i | \(-0.675093\pi\) | ||||
−0.522748 | + | 0.852487i | \(0.675093\pi\) | |||||||
\(468\) | −7.69666e62 | −1.36623 | ||||||||
\(469\) | −1.58926e62 | −0.268307 | ||||||||
\(470\) | −5.42081e61 | −0.0870491 | ||||||||
\(471\) | −8.80123e62 | −1.34447 | ||||||||
\(472\) | 2.24420e62 | 0.326155 | ||||||||
\(473\) | 1.45461e63 | 2.01146 | ||||||||
\(474\) | 4.10704e62 | 0.540428 | ||||||||
\(475\) | 9.46432e61 | 0.118519 | ||||||||
\(476\) | 3.10719e62 | 0.370343 | ||||||||
\(477\) | 1.09055e63 | 1.23726 | ||||||||
\(478\) | 2.14076e62 | 0.231213 | ||||||||
\(479\) | 1.45521e63 | 1.49638 | 0.748190 | − | 0.663484i | \(-0.230923\pi\) | ||||
0.748190 | + | 0.663484i | \(0.230923\pi\) | |||||||
\(480\) | 1.15391e62 | 0.112980 | ||||||||
\(481\) | −2.53848e63 | −2.36681 | ||||||||
\(482\) | −5.75331e62 | −0.510872 | ||||||||
\(483\) | 9.81782e62 | 0.830343 | ||||||||
\(484\) | 4.64943e62 | 0.374571 | ||||||||
\(485\) | 6.13322e61 | 0.0470715 | ||||||||
\(486\) | 6.75495e62 | 0.493935 | ||||||||
\(487\) | −1.24716e62 | −0.0868944 | −0.0434472 | − | 0.999056i | \(-0.513834\pi\) | ||||
−0.0434472 | + | 0.999056i | \(0.513834\pi\) | |||||||
\(488\) | −6.35317e62 | −0.421818 | ||||||||
\(489\) | −1.16476e63 | −0.737017 | ||||||||
\(490\) | 5.67911e62 | 0.342510 | ||||||||
\(491\) | 9.69339e62 | 0.557263 | 0.278632 | − | 0.960398i | \(-0.410119\pi\) | ||||
0.278632 | + | 0.960398i | \(0.410119\pi\) | |||||||
\(492\) | −1.51595e63 | −0.830818 | ||||||||
\(493\) | 4.02687e61 | 0.0210409 | ||||||||
\(494\) | −3.06260e62 | −0.152584 | ||||||||
\(495\) | −1.88579e63 | −0.895926 | ||||||||
\(496\) | 8.47300e62 | 0.383900 | ||||||||
\(497\) | −1.81136e63 | −0.782762 | ||||||||
\(498\) | 5.39413e63 | 2.22347 | ||||||||
\(499\) | −3.24859e63 | −1.27742 | −0.638708 | − | 0.769449i | \(-0.720531\pi\) | ||||
−0.638708 | + | 0.769449i | \(0.720531\pi\) | |||||||
\(500\) | 9.49382e62 | 0.356161 | ||||||||
\(501\) | −1.73901e62 | −0.0622466 | ||||||||
\(502\) | −3.57690e63 | −1.22171 | ||||||||
\(503\) | −2.69774e63 | −0.879330 | −0.439665 | − | 0.898162i | \(-0.644903\pi\) | ||||
−0.439665 | + | 0.898162i | \(0.644903\pi\) | |||||||
\(504\) | −3.00894e63 | −0.936044 | ||||||||
\(505\) | 6.37428e62 | 0.189271 | ||||||||
\(506\) | −1.09682e63 | −0.310883 | ||||||||
\(507\) | 8.63877e63 | 2.33757 | ||||||||
\(508\) | 6.21296e62 | 0.160510 | ||||||||
\(509\) | 6.02700e63 | 1.48673 | 0.743366 | − | 0.668884i | \(-0.233228\pi\) | ||||
0.743366 | + | 0.668884i | \(0.233228\pi\) | |||||||
\(510\) | 9.45358e62 | 0.222688 | ||||||||
\(511\) | −6.52201e62 | −0.146720 | ||||||||
\(512\) | −2.05688e62 | −0.0441942 | ||||||||
\(513\) | −8.57445e62 | −0.175974 | ||||||||
\(514\) | −4.59783e63 | −0.901404 | ||||||||
\(515\) | −1.47943e61 | −0.00277093 | ||||||||
\(516\) | 7.06148e63 | 1.26365 | ||||||||
\(517\) | −2.47573e63 | −0.423326 | ||||||||
\(518\) | −9.92395e63 | −1.62157 | ||||||||
\(519\) | 1.81382e64 | 2.83245 | ||||||||
\(520\) | −1.41339e63 | −0.210952 | ||||||||
\(521\) | 1.33678e63 | 0.190710 | 0.0953548 | − | 0.995443i | \(-0.469601\pi\) | ||||
0.0953548 | + | 0.995443i | \(0.469601\pi\) | |||||||
\(522\) | −3.89954e62 | −0.0531810 | ||||||||
\(523\) | −8.20599e63 | −1.06989 | −0.534947 | − | 0.844885i | \(-0.679669\pi\) | ||||
−0.534947 | + | 0.844885i | \(0.679669\pi\) | |||||||
\(524\) | −1.12382e63 | −0.140092 | ||||||||
\(525\) | −1.78559e64 | −2.12832 | ||||||||
\(526\) | 9.92787e63 | 1.13159 | ||||||||
\(527\) | 6.94165e63 | 0.756682 | ||||||||
\(528\) | 5.26999e63 | 0.549430 | ||||||||
\(529\) | −8.91969e63 | −0.889491 | ||||||||
\(530\) | 2.00265e63 | 0.191039 | ||||||||
\(531\) | −1.78047e64 | −1.62485 | ||||||||
\(532\) | −1.19730e63 | −0.104539 | ||||||||
\(533\) | 1.85685e64 | 1.55127 | ||||||||
\(534\) | −2.45234e63 | −0.196048 | ||||||||
\(535\) | 9.00935e63 | 0.689255 | ||||||||
\(536\) | 8.61908e62 | 0.0631086 | ||||||||
\(537\) | −3.74062e64 | −2.62149 | ||||||||
\(538\) | 1.73579e62 | 0.0116443 | ||||||||
\(539\) | 2.59370e64 | 1.66565 | ||||||||
\(540\) | −3.95711e63 | −0.243290 | ||||||||
\(541\) | −6.23992e62 | −0.0367319 | −0.0183660 | − | 0.999831i | \(-0.505846\pi\) | ||||
−0.0183660 | + | 0.999831i | \(0.505846\pi\) | |||||||
\(542\) | −2.41985e64 | −1.36397 | ||||||||
\(543\) | −2.51029e64 | −1.35497 | ||||||||
\(544\) | −1.68514e63 | −0.0871085 | ||||||||
\(545\) | 1.81905e61 | 0.000900591 0 | ||||||||
\(546\) | 5.77807e64 | 2.74003 | ||||||||
\(547\) | 3.05397e64 | 1.38727 | 0.693636 | − | 0.720325i | \(-0.256007\pi\) | ||||
0.693636 | + | 0.720325i | \(0.256007\pi\) | |||||||
\(548\) | −4.24817e63 | −0.184867 | ||||||||
\(549\) | 5.04038e64 | 2.10142 | ||||||||
\(550\) | 1.99480e64 | 0.796850 | ||||||||
\(551\) | −1.55168e62 | −0.00593936 | ||||||||
\(552\) | −5.32454e63 | −0.195305 | ||||||||
\(553\) | −1.96667e64 | −0.691340 | ||||||||
\(554\) | 3.73917e62 | 0.0125978 | ||||||||
\(555\) | −3.01935e64 | −0.975053 | ||||||||
\(556\) | 8.56009e63 | 0.264985 | ||||||||
\(557\) | 3.06228e64 | 0.908758 | 0.454379 | − | 0.890809i | \(-0.349861\pi\) | ||||
0.454379 | + | 0.890809i | \(0.349861\pi\) | |||||||
\(558\) | −6.72217e64 | −1.91252 | ||||||||
\(559\) | −8.64943e64 | −2.35945 | ||||||||
\(560\) | −5.52553e63 | −0.144529 | ||||||||
\(561\) | 4.31753e64 | 1.08295 | ||||||||
\(562\) | −5.43418e63 | −0.130717 | ||||||||
\(563\) | −1.53750e64 | −0.354705 | −0.177353 | − | 0.984147i | \(-0.556753\pi\) | ||||
−0.177353 | + | 0.984147i | \(0.556753\pi\) | |||||||
\(564\) | −1.20185e64 | −0.265945 | ||||||||
\(565\) | 6.20362e62 | 0.0131676 | ||||||||
\(566\) | −3.63704e64 | −0.740563 | ||||||||
\(567\) | 2.62376e64 | 0.512533 | ||||||||
\(568\) | 9.82363e63 | 0.184114 | ||||||||
\(569\) | −9.13382e63 | −0.164253 | −0.0821266 | − | 0.996622i | \(-0.526171\pi\) | ||||
−0.0821266 | + | 0.996622i | \(0.526171\pi\) | |||||||
\(570\) | −3.64277e63 | −0.0628597 | ||||||||
\(571\) | 4.20849e64 | 0.696911 | 0.348456 | − | 0.937325i | \(-0.386706\pi\) | ||||
0.348456 | + | 0.937325i | \(0.386706\pi\) | |||||||
\(572\) | −6.45507e64 | −1.02588 | ||||||||
\(573\) | 1.02453e65 | 1.56275 | ||||||||
\(574\) | 7.25920e64 | 1.06282 | ||||||||
\(575\) | −2.01545e64 | −0.283255 | ||||||||
\(576\) | 1.63185e64 | 0.220167 | ||||||||
\(577\) | 1.16840e65 | 1.51342 | 0.756709 | − | 0.653752i | \(-0.226806\pi\) | ||||
0.756709 | + | 0.653752i | \(0.226806\pi\) | |||||||
\(578\) | 4.30519e64 | 0.535412 | ||||||||
\(579\) | −1.88564e65 | −2.25171 | ||||||||
\(580\) | −7.16100e62 | −0.00821137 | ||||||||
\(581\) | −2.58300e65 | −2.84437 | ||||||||
\(582\) | 1.35980e64 | 0.143809 | ||||||||
\(583\) | 9.14625e64 | 0.929035 | ||||||||
\(584\) | 3.53711e63 | 0.0345102 | ||||||||
\(585\) | 1.12133e65 | 1.05093 | ||||||||
\(586\) | 8.87366e64 | 0.798930 | ||||||||
\(587\) | 1.22823e65 | 1.06239 | 0.531197 | − | 0.847248i | \(-0.321742\pi\) | ||||
0.531197 | + | 0.847248i | \(0.321742\pi\) | |||||||
\(588\) | 1.25912e65 | 1.04641 | ||||||||
\(589\) | −2.67484e64 | −0.213594 | ||||||||
\(590\) | −3.26959e64 | −0.250883 | ||||||||
\(591\) | −2.11417e65 | −1.55896 | ||||||||
\(592\) | 5.38210e64 | 0.381410 | ||||||||
\(593\) | 2.18247e65 | 1.48649 | 0.743245 | − | 0.669019i | \(-0.233286\pi\) | ||||
0.743245 | + | 0.669019i | \(0.233286\pi\) | |||||||
\(594\) | −1.80724e65 | −1.18314 | ||||||||
\(595\) | −4.52689e64 | −0.284873 | ||||||||
\(596\) | −1.10950e65 | −0.671185 | ||||||||
\(597\) | −2.96836e65 | −1.72632 | ||||||||
\(598\) | 6.52189e64 | 0.364667 | ||||||||
\(599\) | 1.76834e65 | 0.950684 | 0.475342 | − | 0.879801i | \(-0.342324\pi\) | ||||
0.475342 | + | 0.879801i | \(0.342324\pi\) | |||||||
\(600\) | 9.68386e64 | 0.500604 | ||||||||
\(601\) | −1.41803e65 | −0.704912 | −0.352456 | − | 0.935828i | \(-0.614653\pi\) | ||||
−0.352456 | + | 0.935828i | \(0.614653\pi\) | |||||||
\(602\) | −3.38142e65 | −1.61652 | ||||||||
\(603\) | −6.83807e64 | −0.314396 | ||||||||
\(604\) | 7.39093e64 | 0.326837 | ||||||||
\(605\) | −6.77379e64 | −0.288125 | ||||||||
\(606\) | 1.41325e65 | 0.578245 | ||||||||
\(607\) | 1.14990e65 | 0.452610 | 0.226305 | − | 0.974056i | \(-0.427335\pi\) | ||||
0.226305 | + | 0.974056i | \(0.427335\pi\) | |||||||
\(608\) | 6.49336e63 | 0.0245887 | ||||||||
\(609\) | 2.92748e64 | 0.106656 | ||||||||
\(610\) | 9.25599e64 | 0.324468 | ||||||||
\(611\) | 1.47212e65 | 0.496563 | ||||||||
\(612\) | 1.33692e65 | 0.433959 | ||||||||
\(613\) | −9.28200e64 | −0.289948 | −0.144974 | − | 0.989435i | \(-0.546310\pi\) | ||||
−0.144974 | + | 0.989435i | \(0.546310\pi\) | |||||||
\(614\) | −1.73541e65 | −0.521730 | ||||||||
\(615\) | 2.20860e65 | 0.639076 | ||||||||
\(616\) | −2.52355e65 | −0.702855 | ||||||||
\(617\) | 5.27493e65 | 1.41421 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(618\) | −3.28007e63 | −0.00846552 | ||||||||
\(619\) | −1.15047e65 | −0.285854 | −0.142927 | − | 0.989733i | \(-0.545651\pi\) | ||||
−0.142927 | + | 0.989733i | \(0.545651\pi\) | |||||||
\(620\) | −1.23444e65 | −0.295301 | ||||||||
\(621\) | 1.82595e65 | 0.420568 | ||||||||
\(622\) | 2.00856e65 | 0.445462 | ||||||||
\(623\) | 1.17431e65 | 0.250793 | ||||||||
\(624\) | −3.13364e65 | −0.644484 | ||||||||
\(625\) | 2.91873e65 | 0.578114 | ||||||||
\(626\) | 7.96029e64 | 0.151856 | ||||||||
\(627\) | −1.66368e65 | −0.305691 | ||||||||
\(628\) | −2.28567e65 | −0.404541 | ||||||||
\(629\) | 4.40938e65 | 0.751774 | ||||||||
\(630\) | 4.38375e65 | 0.720018 | ||||||||
\(631\) | −4.57574e65 | −0.724054 | −0.362027 | − | 0.932168i | \(-0.617915\pi\) | ||||
−0.362027 | + | 0.932168i | \(0.617915\pi\) | |||||||
\(632\) | 1.06659e65 | 0.162610 | ||||||||
\(633\) | −5.24114e65 | −0.769907 | ||||||||
\(634\) | −7.66706e65 | −1.08525 | ||||||||
\(635\) | −9.05172e64 | −0.123466 | ||||||||
\(636\) | 4.44009e65 | 0.583646 | ||||||||
\(637\) | −1.54227e66 | −1.95381 | ||||||||
\(638\) | −3.27049e64 | −0.0399325 | ||||||||
\(639\) | −7.79371e65 | −0.917221 | ||||||||
\(640\) | 2.99669e64 | 0.0339948 | ||||||||
\(641\) | −9.71867e65 | −1.06278 | −0.531390 | − | 0.847128i | \(-0.678330\pi\) | ||||
−0.531390 | + | 0.847128i | \(0.678330\pi\) | |||||||
\(642\) | 1.99747e66 | 2.10575 | ||||||||
\(643\) | 2.57162e65 | 0.261366 | 0.130683 | − | 0.991424i | \(-0.458283\pi\) | ||||
0.130683 | + | 0.991424i | \(0.458283\pi\) | |||||||
\(644\) | 2.54968e65 | 0.249843 | ||||||||
\(645\) | −1.02879e66 | −0.972019 | ||||||||
\(646\) | 5.31980e64 | 0.0484653 | ||||||||
\(647\) | 2.26973e66 | 1.99400 | 0.996998 | − | 0.0774314i | \(-0.0246719\pi\) | ||||
0.996998 | + | 0.0774314i | \(0.0246719\pi\) | |||||||
\(648\) | −1.42295e65 | −0.120553 | ||||||||
\(649\) | −1.49325e66 | −1.22006 | ||||||||
\(650\) | −1.18615e66 | −0.934709 | ||||||||
\(651\) | 5.04649e66 | 3.83563 | ||||||||
\(652\) | −3.02487e65 | −0.221762 | ||||||||
\(653\) | 1.60777e66 | 1.13701 | 0.568504 | − | 0.822681i | \(-0.307522\pi\) | ||||
0.568504 | + | 0.822681i | \(0.307522\pi\) | |||||||
\(654\) | 4.03304e63 | 0.00275141 | ||||||||
\(655\) | 1.63730e65 | 0.107760 | ||||||||
\(656\) | −3.93692e65 | −0.249986 | ||||||||
\(657\) | −2.80622e65 | −0.171923 | ||||||||
\(658\) | 5.75512e65 | 0.340209 | ||||||||
\(659\) | −3.20448e66 | −1.82789 | −0.913946 | − | 0.405835i | \(-0.866981\pi\) | ||||
−0.913946 | + | 0.405835i | \(0.866981\pi\) | |||||||
\(660\) | −7.67789e65 | −0.422629 | ||||||||
\(661\) | 6.38586e65 | 0.339223 | 0.169611 | − | 0.985511i | \(-0.445749\pi\) | ||||
0.169611 | + | 0.985511i | \(0.445749\pi\) | |||||||
\(662\) | 9.14330e65 | 0.468749 | ||||||||
\(663\) | −2.56729e66 | −1.27030 | ||||||||
\(664\) | 1.40085e66 | 0.669025 | ||||||||
\(665\) | 1.74435e65 | 0.0804129 | ||||||||
\(666\) | −4.26996e66 | −1.90011 | ||||||||
\(667\) | 3.30434e64 | 0.0141948 | ||||||||
\(668\) | −4.51619e64 | −0.0187295 | ||||||||
\(669\) | 1.96068e66 | 0.785044 | ||||||||
\(670\) | −1.25572e65 | −0.0485440 | ||||||||
\(671\) | 4.22729e66 | 1.57791 | ||||||||
\(672\) | −1.22507e66 | −0.441554 | ||||||||
\(673\) | −2.24978e66 | −0.783043 | −0.391521 | − | 0.920169i | \(-0.628051\pi\) | ||||
−0.391521 | + | 0.920169i | \(0.628051\pi\) | |||||||
\(674\) | 1.68114e66 | 0.565063 | ||||||||
\(675\) | −3.32090e66 | −1.07800 | ||||||||
\(676\) | 2.24348e66 | 0.703356 | ||||||||
\(677\) | −4.79933e65 | −0.145327 | −0.0726636 | − | 0.997357i | \(-0.523150\pi\) | ||||
−0.0726636 | + | 0.997357i | \(0.523150\pi\) | |||||||
\(678\) | 1.37541e65 | 0.0402286 | ||||||||
\(679\) | −6.51147e65 | −0.183967 | ||||||||
\(680\) | 2.45509e65 | 0.0670050 | ||||||||
\(681\) | 5.90558e66 | 1.55706 | ||||||||
\(682\) | −5.63778e66 | −1.43607 | ||||||||
\(683\) | −4.30311e66 | −1.05900 | −0.529500 | − | 0.848310i | \(-0.677621\pi\) | ||||
−0.529500 | + | 0.848310i | \(0.677621\pi\) | |||||||
\(684\) | −5.15160e65 | −0.122496 | ||||||||
\(685\) | 6.18920e65 | 0.142202 | ||||||||
\(686\) | −1.24195e66 | −0.275733 | ||||||||
\(687\) | −5.06515e66 | −1.08670 | ||||||||
\(688\) | 1.83386e66 | 0.380223 | ||||||||
\(689\) | −5.43855e66 | −1.08976 | ||||||||
\(690\) | 7.75737e65 | 0.150231 | ||||||||
\(691\) | 8.37771e66 | 1.56816 | 0.784081 | − | 0.620658i | \(-0.213135\pi\) | ||||
0.784081 | + | 0.620658i | \(0.213135\pi\) | |||||||
\(692\) | 4.71048e66 | 0.852259 | ||||||||
\(693\) | 2.00210e67 | 3.50150 | ||||||||
\(694\) | 7.47865e66 | 1.26437 | ||||||||
\(695\) | −1.24713e66 | −0.203830 | ||||||||
\(696\) | −1.58767e65 | −0.0250867 | ||||||||
\(697\) | −3.22539e66 | −0.492733 | ||||||||
\(698\) | 2.22248e66 | 0.328273 | ||||||||
\(699\) | −1.39470e67 | −1.99190 | ||||||||
\(700\) | −4.63716e66 | −0.640395 | ||||||||
\(701\) | −1.18236e67 | −1.57898 | −0.789489 | − | 0.613765i | \(-0.789654\pi\) | ||||
−0.789489 | + | 0.613765i | \(0.789654\pi\) | |||||||
\(702\) | 1.07463e67 | 1.38783 | ||||||||
\(703\) | −1.69907e66 | −0.212208 | ||||||||
\(704\) | 1.36861e66 | 0.165319 | ||||||||
\(705\) | 1.75099e66 | 0.204569 | ||||||||
\(706\) | −5.12646e66 | −0.579305 | ||||||||
\(707\) | −6.76740e66 | −0.739717 | ||||||||
\(708\) | −7.24905e66 | −0.766478 | ||||||||
\(709\) | 8.35736e66 | 0.854836 | 0.427418 | − | 0.904054i | \(-0.359423\pi\) | ||||
0.427418 | + | 0.904054i | \(0.359423\pi\) | |||||||
\(710\) | −1.43121e66 | −0.141623 | ||||||||
\(711\) | −8.46197e66 | −0.810095 | ||||||||
\(712\) | −6.36871e65 | −0.0589891 | ||||||||
\(713\) | 5.69614e66 | 0.510478 | ||||||||
\(714\) | −1.00366e67 | −0.870320 | ||||||||
\(715\) | 9.40445e66 | 0.789117 | ||||||||
\(716\) | −9.71436e66 | −0.788784 | ||||||||
\(717\) | −6.91492e66 | −0.543359 | ||||||||
\(718\) | 1.96045e66 | 0.149084 | ||||||||
\(719\) | 1.29585e67 | 0.953731 | 0.476865 | − | 0.878976i | \(-0.341773\pi\) | ||||
0.476865 | + | 0.878976i | \(0.341773\pi\) | |||||||
\(720\) | −2.37746e66 | −0.169356 | ||||||||
\(721\) | 1.57067e65 | 0.0108295 | ||||||||
\(722\) | 1.03902e67 | 0.693426 | ||||||||
\(723\) | 1.85839e67 | 1.20057 | ||||||||
\(724\) | −6.51921e66 | −0.407698 | ||||||||
\(725\) | −6.00968e65 | −0.0363838 | ||||||||
\(726\) | −1.50182e67 | −0.880255 | ||||||||
\(727\) | 6.75407e66 | 0.383272 | 0.191636 | − | 0.981466i | \(-0.438621\pi\) | ||||
0.191636 | + | 0.981466i | \(0.438621\pi\) | |||||||
\(728\) | 1.50056e67 | 0.824452 | ||||||||
\(729\) | −2.82288e67 | −1.50174 | ||||||||
\(730\) | −5.15325e65 | −0.0265457 | ||||||||
\(731\) | 1.50242e67 | 0.749435 | ||||||||
\(732\) | 2.05216e67 | 0.991288 | ||||||||
\(733\) | 3.49174e67 | 1.63342 | 0.816711 | − | 0.577047i | \(-0.195795\pi\) | ||||
0.816711 | + | 0.577047i | \(0.195795\pi\) | |||||||
\(734\) | −6.65358e66 | −0.301438 | ||||||||
\(735\) | −1.83443e67 | −0.804910 | ||||||||
\(736\) | −1.38278e66 | −0.0587657 | ||||||||
\(737\) | −5.73498e66 | −0.236073 | ||||||||
\(738\) | 3.12341e67 | 1.24539 | ||||||||
\(739\) | 2.87820e66 | 0.111167 | 0.0555835 | − | 0.998454i | \(-0.482298\pi\) | ||||
0.0555835 | + | 0.998454i | \(0.482298\pi\) | |||||||
\(740\) | −7.84123e66 | −0.293385 | ||||||||
\(741\) | 9.89260e66 | 0.358577 | ||||||||
\(742\) | −2.12615e67 | −0.746626 | ||||||||
\(743\) | −1.55726e66 | −0.0529814 | −0.0264907 | − | 0.999649i | \(-0.508433\pi\) | ||||
−0.0264907 | + | 0.999649i | \(0.508433\pi\) | |||||||
\(744\) | −2.73689e67 | −0.902179 | ||||||||
\(745\) | 1.61645e67 | 0.516284 | ||||||||
\(746\) | 1.80093e67 | 0.557359 | ||||||||
\(747\) | −1.11138e68 | −3.33296 | ||||||||
\(748\) | 1.12126e67 | 0.325850 | ||||||||
\(749\) | −9.56498e67 | −2.69378 | ||||||||
\(750\) | −3.06662e67 | −0.836991 | ||||||||
\(751\) | 4.80070e67 | 1.26989 | 0.634946 | − | 0.772557i | \(-0.281023\pi\) | ||||
0.634946 | + | 0.772557i | \(0.281023\pi\) | |||||||
\(752\) | −3.12120e66 | −0.0800207 | ||||||||
\(753\) | 1.15538e68 | 2.87107 | ||||||||
\(754\) | 1.94470e66 | 0.0468410 | ||||||||
\(755\) | −1.07679e67 | −0.251407 | ||||||||
\(756\) | 4.20115e67 | 0.950838 | ||||||||
\(757\) | −3.04494e67 | −0.668076 | −0.334038 | − | 0.942560i | \(-0.608411\pi\) | ||||
−0.334038 | + | 0.942560i | \(0.608411\pi\) | |||||||
\(758\) | 4.57725e67 | 0.973595 | ||||||||
\(759\) | 3.54285e67 | 0.730586 | ||||||||
\(760\) | −9.46023e65 | −0.0189140 | ||||||||
\(761\) | −8.19495e67 | −1.58857 | −0.794286 | − | 0.607544i | \(-0.792155\pi\) | ||||
−0.794286 | + | 0.607544i | \(0.792155\pi\) | |||||||
\(762\) | −2.00687e67 | −0.377204 | ||||||||
\(763\) | −1.93124e65 | −0.00351973 | ||||||||
\(764\) | 2.66069e67 | 0.470220 | ||||||||
\(765\) | −1.94778e67 | −0.333807 | ||||||||
\(766\) | 2.21850e67 | 0.368709 | ||||||||
\(767\) | 8.87918e67 | 1.43114 | ||||||||
\(768\) | 6.64398e66 | 0.103858 | ||||||||
\(769\) | −8.58726e67 | −1.30192 | −0.650962 | − | 0.759110i | \(-0.725634\pi\) | ||||
−0.650962 | + | 0.759110i | \(0.725634\pi\) | |||||||
\(770\) | 3.67659e67 | 0.540646 | ||||||||
\(771\) | 1.48516e68 | 2.11833 | ||||||||
\(772\) | −4.89698e67 | −0.677520 | ||||||||
\(773\) | −5.74418e67 | −0.770921 | −0.385460 | − | 0.922724i | \(-0.625957\pi\) | ||||
−0.385460 | + | 0.922724i | \(0.625957\pi\) | |||||||
\(774\) | −1.45492e68 | −1.89420 | ||||||||
\(775\) | −1.03597e68 | −1.30845 | ||||||||
\(776\) | 3.53140e66 | 0.0432709 | ||||||||
\(777\) | 3.20556e68 | 3.81075 | ||||||||
\(778\) | −7.11107e67 | −0.820189 | ||||||||
\(779\) | 1.24284e67 | 0.139087 | ||||||||
\(780\) | 4.56543e67 | 0.495745 | ||||||||
\(781\) | −6.53646e67 | −0.688721 | ||||||||
\(782\) | −1.13287e67 | −0.115830 | ||||||||
\(783\) | 5.44463e66 | 0.0540215 | ||||||||
\(784\) | 3.26993e67 | 0.314855 | ||||||||
\(785\) | 3.33001e67 | 0.311178 | ||||||||
\(786\) | 3.63008e67 | 0.329221 | ||||||||
\(787\) | 1.78281e68 | 1.56928 | 0.784638 | − | 0.619954i | \(-0.212849\pi\) | ||||
0.784638 | + | 0.619954i | \(0.212849\pi\) | |||||||
\(788\) | −5.49048e67 | −0.469077 | ||||||||
\(789\) | −3.20683e68 | −2.65929 | ||||||||
\(790\) | −1.55393e67 | −0.125082 | ||||||||
\(791\) | −6.58621e66 | −0.0514622 | ||||||||
\(792\) | −1.08581e68 | −0.823589 | ||||||||
\(793\) | −2.51363e68 | −1.85090 | ||||||||
\(794\) | 8.55196e67 | 0.611342 | ||||||||
\(795\) | −6.46880e67 | −0.448948 | ||||||||
\(796\) | −7.70882e67 | −0.519434 | ||||||||
\(797\) | 7.67558e67 | 0.502158 | 0.251079 | − | 0.967967i | \(-0.419215\pi\) | ||||
0.251079 | + | 0.967967i | \(0.419215\pi\) | |||||||
\(798\) | 3.86742e67 | 0.245671 | ||||||||
\(799\) | −2.55710e67 | −0.157724 | ||||||||
\(800\) | 2.51489e67 | 0.150627 | ||||||||
\(801\) | 5.05270e67 | 0.293873 | ||||||||
\(802\) | 1.75078e68 | 0.988860 | ||||||||
\(803\) | −2.35353e67 | −0.129094 | ||||||||
\(804\) | −2.78407e67 | −0.148308 | ||||||||
\(805\) | −3.71465e67 | −0.192183 | ||||||||
\(806\) | 3.35234e68 | 1.68451 | ||||||||
\(807\) | −5.60681e66 | −0.0273645 | ||||||||
\(808\) | 3.67019e67 | 0.173989 | ||||||||
\(809\) | 1.39305e68 | 0.641472 | 0.320736 | − | 0.947169i | \(-0.396070\pi\) | ||||
0.320736 | + | 0.947169i | \(0.396070\pi\) | |||||||
\(810\) | 2.07311e67 | 0.0927310 | ||||||||
\(811\) | 6.57381e67 | 0.285645 | 0.142823 | − | 0.989748i | \(-0.454382\pi\) | ||||
0.142823 | + | 0.989748i | \(0.454382\pi\) | |||||||
\(812\) | 7.60263e66 | 0.0320920 | ||||||||
\(813\) | 7.81642e68 | 3.20538 | ||||||||
\(814\) | −3.58115e68 | −1.42675 | ||||||||
\(815\) | 4.40695e67 | 0.170582 | ||||||||
\(816\) | 5.44320e67 | 0.204708 | ||||||||
\(817\) | −5.78931e67 | −0.211548 | ||||||||
\(818\) | −2.43568e68 | −0.864804 | ||||||||
\(819\) | −1.19049e69 | −4.10727 | ||||||||
\(820\) | 5.73572e67 | 0.192293 | ||||||||
\(821\) | 2.60915e68 | 0.850030 | 0.425015 | − | 0.905186i | \(-0.360269\pi\) | ||||
0.425015 | + | 0.905186i | \(0.360269\pi\) | |||||||
\(822\) | 1.37221e68 | 0.434444 | ||||||||
\(823\) | 2.86763e68 | 0.882322 | 0.441161 | − | 0.897428i | \(-0.354567\pi\) | ||||
0.441161 | + | 0.897428i | \(0.354567\pi\) | |||||||
\(824\) | −8.51831e65 | −0.00254720 | ||||||||
\(825\) | −6.44346e68 | −1.87263 | ||||||||
\(826\) | 3.47124e68 | 0.980513 | ||||||||
\(827\) | −2.35931e68 | −0.647747 | −0.323873 | − | 0.946100i | \(-0.604985\pi\) | ||||
−0.323873 | + | 0.946100i | \(0.604985\pi\) | |||||||
\(828\) | 1.09705e68 | 0.292760 | ||||||||
\(829\) | 8.80819e67 | 0.228484 | 0.114242 | − | 0.993453i | \(-0.463556\pi\) | ||||
0.114242 | + | 0.993453i | \(0.463556\pi\) | |||||||
\(830\) | −2.04091e68 | −0.514623 | ||||||||
\(831\) | −1.20780e67 | −0.0296054 | ||||||||
\(832\) | −8.13805e67 | −0.193920 | ||||||||
\(833\) | 2.67895e68 | 0.620592 | ||||||||
\(834\) | −2.76502e68 | −0.622724 | ||||||||
\(835\) | 6.57968e66 | 0.0144070 | ||||||||
\(836\) | −4.32056e67 | −0.0919799 | ||||||||
\(837\) | 9.38564e68 | 1.94274 | ||||||||
\(838\) | −3.79020e68 | −0.762830 | ||||||||
\(839\) | −2.99608e68 | −0.586337 | −0.293168 | − | 0.956061i | \(-0.594710\pi\) | ||||
−0.293168 | + | 0.956061i | \(0.594710\pi\) | |||||||
\(840\) | 1.78482e68 | 0.339649 | ||||||||
\(841\) | −5.39403e68 | −0.998177 | ||||||||
\(842\) | −5.05903e68 | −0.910401 | ||||||||
\(843\) | 1.75531e68 | 0.307189 | ||||||||
\(844\) | −1.36112e68 | −0.231659 | ||||||||
\(845\) | −3.26855e68 | −0.541031 | ||||||||
\(846\) | 2.47625e68 | 0.398649 | ||||||||
\(847\) | 7.19155e68 | 1.12606 | ||||||||
\(848\) | 1.15309e68 | 0.175614 | ||||||||
\(849\) | 1.17481e69 | 1.74035 | ||||||||
\(850\) | 2.06037e68 | 0.296893 | ||||||||
\(851\) | 3.61822e68 | 0.507167 | ||||||||
\(852\) | −3.17316e68 | −0.432674 | ||||||||
\(853\) | 9.47738e68 | 1.25715 | 0.628573 | − | 0.777750i | \(-0.283639\pi\) | ||||
0.628573 | + | 0.777750i | \(0.283639\pi\) | |||||||
\(854\) | −9.82683e68 | −1.26810 | ||||||||
\(855\) | 7.50540e67 | 0.0942259 | ||||||||
\(856\) | 5.18742e68 | 0.633604 | ||||||||
\(857\) | −9.55995e68 | −1.13607 | −0.568037 | − | 0.823003i | \(-0.692297\pi\) | ||||
−0.568037 | + | 0.823003i | \(0.692297\pi\) | |||||||
\(858\) | 2.08507e69 | 2.41085 | ||||||||
\(859\) | −4.21759e68 | −0.474488 | −0.237244 | − | 0.971450i | \(-0.576244\pi\) | ||||
−0.237244 | + | 0.971450i | \(0.576244\pi\) | |||||||
\(860\) | −2.67177e68 | −0.292472 | ||||||||
\(861\) | −2.34481e69 | −2.49767 | ||||||||
\(862\) | 2.38391e68 | 0.247098 | ||||||||
\(863\) | 9.19093e68 | 0.927055 | 0.463528 | − | 0.886082i | \(-0.346583\pi\) | ||||
0.463528 | + | 0.886082i | \(0.346583\pi\) | |||||||
\(864\) | −2.27843e68 | −0.223647 | ||||||||
\(865\) | −6.86273e68 | −0.655569 | ||||||||
\(866\) | −7.96851e68 | −0.740810 | ||||||||
\(867\) | −1.39063e69 | −1.25824 | ||||||||
\(868\) | 1.31057e69 | 1.15411 | ||||||||
\(869\) | −7.09693e68 | −0.608283 | ||||||||
\(870\) | 2.31309e67 | 0.0192970 | ||||||||
\(871\) | 3.41014e68 | 0.276914 | ||||||||
\(872\) | 1.04738e66 | 0.000827877 0 | ||||||||
\(873\) | −2.80168e68 | −0.215568 | ||||||||
\(874\) | 4.36529e67 | 0.0326960 | ||||||||
\(875\) | 1.46847e69 | 1.07072 | ||||||||
\(876\) | −1.14253e68 | −0.0811002 | ||||||||
\(877\) | 1.86631e69 | 1.28971 | 0.644855 | − | 0.764305i | \(-0.276918\pi\) | ||||
0.644855 | + | 0.764305i | \(0.276918\pi\) | |||||||
\(878\) | 7.14346e68 | 0.480604 | ||||||||
\(879\) | −2.86630e69 | −1.87752 | ||||||||
\(880\) | −1.99394e68 | −0.127166 | ||||||||
\(881\) | 6.60423e68 | 0.410098 | 0.205049 | − | 0.978752i | \(-0.434265\pi\) | ||||
0.205049 | + | 0.978752i | \(0.434265\pi\) | |||||||
\(882\) | −2.59424e69 | −1.56855 | ||||||||
\(883\) | −8.14396e68 | −0.479467 | −0.239734 | − | 0.970839i | \(-0.577060\pi\) | ||||
−0.239734 | + | 0.970839i | \(0.577060\pi\) | |||||||
\(884\) | −6.66724e68 | −0.382224 | ||||||||
\(885\) | 1.05612e69 | 0.589585 | ||||||||
\(886\) | 1.68044e69 | 0.913545 | ||||||||
\(887\) | −1.87041e68 | −0.0990221 | −0.0495110 | − | 0.998774i | \(-0.515766\pi\) | ||||
−0.0495110 | + | 0.998774i | \(0.515766\pi\) | |||||||
\(888\) | −1.73849e69 | −0.896327 | ||||||||
\(889\) | 9.60996e68 | 0.482537 | ||||||||
\(890\) | 9.27863e67 | 0.0453752 | ||||||||
\(891\) | 9.46807e68 | 0.450957 | ||||||||
\(892\) | 5.09188e68 | 0.236213 | ||||||||
\(893\) | 9.85332e67 | 0.0445218 | ||||||||
\(894\) | 3.58384e69 | 1.57731 | ||||||||
\(895\) | 1.41529e69 | 0.606743 | ||||||||
\(896\) | −3.18150e68 | −0.132860 | ||||||||
\(897\) | −2.10665e69 | −0.856980 | ||||||||
\(898\) | −1.43270e69 | −0.567755 | ||||||||
\(899\) | 1.69848e68 | 0.0655702 | ||||||||
\(900\) | −1.99522e69 | −0.750399 | ||||||||
\(901\) | 9.44686e68 | 0.346143 | ||||||||
\(902\) | 2.61955e69 | 0.935133 | ||||||||
\(903\) | 1.09224e70 | 3.79889 | ||||||||
\(904\) | 3.57193e67 | 0.0121044 | ||||||||
\(905\) | 9.49788e68 | 0.313607 | ||||||||
\(906\) | −2.38736e69 | −0.768079 | ||||||||
\(907\) | −6.31631e69 | −1.98012 | −0.990062 | − | 0.140631i | \(-0.955087\pi\) | ||||
−0.990062 | + | 0.140631i | \(0.955087\pi\) | |||||||
\(908\) | 1.53367e69 | 0.468507 | ||||||||
\(909\) | −2.91180e69 | −0.866782 | ||||||||
\(910\) | −2.18618e69 | −0.634180 | ||||||||
\(911\) | 2.58489e69 | 0.730736 | 0.365368 | − | 0.930863i | \(-0.380943\pi\) | ||||
0.365368 | + | 0.930863i | \(0.380943\pi\) | |||||||
\(912\) | −2.09744e68 | −0.0577844 | ||||||||
\(913\) | −9.32101e69 | −2.50265 | ||||||||
\(914\) | −5.11310e69 | −1.33798 | ||||||||
\(915\) | −2.98980e69 | −0.762512 | ||||||||
\(916\) | −1.31542e69 | −0.326979 | ||||||||
\(917\) | −1.73828e69 | −0.421154 | ||||||||
\(918\) | −1.86664e69 | −0.440817 | ||||||||
\(919\) | 8.65693e68 | 0.199273 | 0.0996367 | − | 0.995024i | \(-0.468232\pi\) | ||||
0.0996367 | + | 0.995024i | \(0.468232\pi\) | |||||||
\(920\) | 2.01458e68 | 0.0452034 | ||||||||
\(921\) | 5.60559e69 | 1.22608 | ||||||||
\(922\) | 5.61247e69 | 1.19668 | ||||||||
\(923\) | 3.88672e69 | 0.807873 | ||||||||
\(924\) | 8.15140e69 | 1.65174 | ||||||||
\(925\) | −6.58054e69 | −1.29996 | ||||||||
\(926\) | −3.60977e69 | −0.695218 | ||||||||
\(927\) | 6.75811e67 | 0.0126897 | ||||||||
\(928\) | −4.12317e67 | −0.00754838 | ||||||||
\(929\) | 7.30808e69 | 1.30447 | 0.652235 | − | 0.758017i | \(-0.273831\pi\) | ||||
0.652235 | + | 0.758017i | \(0.273831\pi\) | |||||||
\(930\) | 3.98739e69 | 0.693968 | ||||||||
\(931\) | −1.03228e69 | −0.175179 | ||||||||
\(932\) | −3.62203e69 | −0.599346 | ||||||||
\(933\) | −6.48789e69 | −1.04685 | ||||||||
\(934\) | 4.69850e69 | 0.739277 | ||||||||
\(935\) | −1.63357e69 | −0.250648 | ||||||||
\(936\) | 6.45643e69 | 0.966073 | ||||||||
\(937\) | 8.40248e69 | 1.22610 | 0.613052 | − | 0.790043i | \(-0.289942\pi\) | ||||
0.613052 | + | 0.790043i | \(0.289942\pi\) | |||||||
\(938\) | 1.33316e69 | 0.189722 | ||||||||
\(939\) | −2.57127e69 | −0.356867 | ||||||||
\(940\) | 4.54730e68 | 0.0615530 | ||||||||
\(941\) | −4.67075e69 | −0.616638 | −0.308319 | − | 0.951283i | \(-0.599766\pi\) | ||||
−0.308319 | + | 0.951283i | \(0.599766\pi\) | |||||||
\(942\) | 7.38300e69 | 0.950686 | ||||||||
\(943\) | −2.64667e69 | −0.332411 | ||||||||
\(944\) | −1.88257e69 | −0.230627 | ||||||||
\(945\) | −6.12069e69 | −0.731397 | ||||||||
\(946\) | −1.22022e70 | −1.42231 | ||||||||
\(947\) | −1.91649e69 | −0.217912 | −0.108956 | − | 0.994047i | \(-0.534751\pi\) | ||||
−0.108956 | + | 0.994047i | \(0.534751\pi\) | |||||||
\(948\) | −3.44523e69 | −0.382140 | ||||||||
\(949\) | 1.39946e69 | 0.151427 | ||||||||
\(950\) | −7.93925e68 | −0.0838059 | ||||||||
\(951\) | 2.47656e70 | 2.55039 | ||||||||
\(952\) | −2.60650e69 | −0.261872 | ||||||||
\(953\) | 8.83831e69 | 0.866336 | 0.433168 | − | 0.901313i | \(-0.357396\pi\) | ||||
0.433168 | + | 0.901313i | \(0.357396\pi\) | |||||||
\(954\) | −9.14817e69 | −0.874878 | ||||||||
\(955\) | −3.87638e69 | −0.361699 | ||||||||
\(956\) | −1.79580e69 | −0.163492 | ||||||||
\(957\) | 1.05641e69 | 0.0938428 | ||||||||
\(958\) | −1.22072e70 | −1.05810 | ||||||||
\(959\) | −6.57090e69 | −0.555761 | ||||||||
\(960\) | −9.67967e68 | −0.0798889 | ||||||||
\(961\) | 1.68624e70 | 1.35806 | ||||||||
\(962\) | 2.12943e70 | 1.67359 | ||||||||
\(963\) | −4.11551e70 | −3.15650 | ||||||||
\(964\) | 4.82623e69 | 0.361241 | ||||||||
\(965\) | 7.13445e69 | 0.521157 | ||||||||
\(966\) | −8.23578e69 | −0.587141 | ||||||||
\(967\) | −1.45957e70 | −1.01556 | −0.507778 | − | 0.861488i | \(-0.669533\pi\) | ||||
−0.507778 | + | 0.861488i | \(0.669533\pi\) | |||||||
\(968\) | −3.90023e69 | −0.264862 | ||||||||
\(969\) | −1.71836e69 | −0.113895 | ||||||||
\(970\) | −5.14492e68 | −0.0332846 | ||||||||
\(971\) | −1.63771e70 | −1.03415 | −0.517077 | − | 0.855939i | \(-0.672980\pi\) | ||||
−0.517077 | + | 0.855939i | \(0.672980\pi\) | |||||||
\(972\) | −5.66646e69 | −0.349265 | ||||||||
\(973\) | 1.32404e70 | 0.796616 | ||||||||
\(974\) | 1.04619e69 | 0.0614436 | ||||||||
\(975\) | 3.83142e70 | 2.19660 | ||||||||
\(976\) | 5.32943e69 | 0.298270 | ||||||||
\(977\) | 2.81412e70 | 1.53752 | 0.768758 | − | 0.639540i | \(-0.220875\pi\) | ||||
0.768758 | + | 0.639540i | \(0.220875\pi\) | |||||||
\(978\) | 9.77070e69 | 0.521150 | ||||||||
\(979\) | 4.23762e69 | 0.220663 | ||||||||
\(980\) | −4.76399e69 | −0.242191 | ||||||||
\(981\) | −8.30951e67 | −0.00412433 | ||||||||
\(982\) | −8.13140e69 | −0.394045 | ||||||||
\(983\) | −2.50839e70 | −1.18683 | −0.593414 | − | 0.804898i | \(-0.702220\pi\) | ||||
−0.593414 | + | 0.804898i | \(0.702220\pi\) | |||||||
\(984\) | 1.27167e70 | 0.587477 | ||||||||
\(985\) | 7.99913e69 | 0.360821 | ||||||||
\(986\) | −3.37798e68 | −0.0148782 | ||||||||
\(987\) | −1.85898e70 | −0.799505 | ||||||||
\(988\) | 2.56910e69 | 0.107893 | ||||||||
\(989\) | 1.23285e70 | 0.505588 | ||||||||
\(990\) | 1.58192e70 | 0.633515 | ||||||||
\(991\) | 1.15349e70 | 0.451111 | 0.225556 | − | 0.974230i | \(-0.427580\pi\) | ||||
0.225556 | + | 0.974230i | \(0.427580\pi\) | |||||||
\(992\) | −7.10767e69 | −0.271458 | ||||||||
\(993\) | −2.95340e70 | −1.10158 | ||||||||
\(994\) | 1.51948e70 | 0.553496 | ||||||||
\(995\) | 1.12310e70 | 0.399556 | ||||||||
\(996\) | −4.52493e70 | −1.57223 | ||||||||
\(997\) | −1.95619e70 | −0.663858 | −0.331929 | − | 0.943304i | \(-0.607699\pi\) | ||||
−0.331929 | + | 0.943304i | \(0.607699\pi\) | |||||||
\(998\) | 2.72512e70 | 0.903270 | ||||||||
\(999\) | 5.96181e70 | 1.93014 |
(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 | 2.48.a.b.1.2 | ✓ | 2 | |
4.3 | odd | 2 | 16.48.a.b.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.48.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
16.48.a.b.1.1 | 2 | 4.3 | odd | 2 |