Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −81.8884 | −1.80950 | −0.904748 | − | 0.425947i | \(-0.859941\pi\) | ||||
−0.904748 | + | 0.425947i | \(0.859941\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | 4657.72 | 2.27428 | ||||||||
\(5\) | −12268.5 | −1.75572 | −0.877861 | − | 0.478915i | \(-0.841030\pi\) | ||||
−0.877861 | + | 0.478915i | \(0.841030\pi\) | |||||||
\(6\) | 19898.9 | 1.04471 | ||||||||
\(7\) | −65634.7 | −1.47603 | −0.738013 | − | 0.674786i | \(-0.764236\pi\) | ||||
−0.738013 | + | 0.674786i | \(0.764236\pi\) | |||||||
\(8\) | −213706. | −2.30580 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 1.00465e6 | 3.17697 | ||||||||
\(11\) | 614467. | 1.15037 | 0.575187 | − | 0.818022i | \(-0.304929\pi\) | ||||
0.575187 | + | 0.818022i | \(0.304929\pi\) | |||||||
\(12\) | −1.13182e6 | −1.31305 | ||||||||
\(13\) | 1.74232e6 | 1.30149 | 0.650744 | − | 0.759297i | \(-0.274457\pi\) | ||||
0.650744 | + | 0.759297i | \(0.274457\pi\) | |||||||
\(14\) | 5.37472e6 | 2.67086 | ||||||||
\(15\) | 2.98124e6 | 1.01367 | ||||||||
\(16\) | 7.96101e6 | 1.89805 | ||||||||
\(17\) | −1.11473e6 | −0.190415 | −0.0952076 | − | 0.995457i | \(-0.530351\pi\) | ||||
−0.0952076 | + | 0.995457i | \(0.530351\pi\) | |||||||
\(18\) | −4.83543e6 | −0.603165 | ||||||||
\(19\) | 1.46733e7 | 1.35951 | 0.679756 | − | 0.733438i | \(-0.262086\pi\) | ||||
0.679756 | + | 0.733438i | \(0.262086\pi\) | |||||||
\(20\) | −5.71431e7 | −3.99300 | ||||||||
\(21\) | 1.59492e7 | 0.852184 | ||||||||
\(22\) | −5.03177e7 | −2.08160 | ||||||||
\(23\) | 5.31182e7 | 1.72084 | 0.860419 | − | 0.509587i | \(-0.170202\pi\) | ||||
0.860419 | + | 0.509587i | \(0.170202\pi\) | |||||||
\(24\) | 5.19304e7 | 1.33125 | ||||||||
\(25\) | 1.01688e8 | 2.08256 | ||||||||
\(26\) | −1.42676e8 | −2.35504 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | −3.05708e8 | −3.35689 | ||||||||
\(29\) | −1.59287e8 | −1.44209 | −0.721043 | − | 0.692891i | \(-0.756337\pi\) | ||||
−0.721043 | + | 0.692891i | \(0.756337\pi\) | |||||||
\(30\) | −2.44129e8 | −1.83423 | ||||||||
\(31\) | 4.50702e7 | 0.282749 | 0.141374 | − | 0.989956i | \(-0.454848\pi\) | ||||
0.141374 | + | 0.989956i | \(0.454848\pi\) | |||||||
\(32\) | −2.14246e8 | −1.12872 | ||||||||
\(33\) | −1.49315e8 | −0.664168 | ||||||||
\(34\) | 9.12837e7 | 0.344556 | ||||||||
\(35\) | 8.05238e8 | 2.59149 | ||||||||
\(36\) | 2.75033e8 | 0.758092 | ||||||||
\(37\) | 7.33231e8 | 1.73833 | 0.869163 | − | 0.494526i | \(-0.164658\pi\) | ||||
0.869163 | + | 0.494526i | \(0.164658\pi\) | |||||||
\(38\) | −1.20157e9 | −2.46003 | ||||||||
\(39\) | −4.23385e8 | −0.751415 | ||||||||
\(40\) | 2.62184e9 | 4.04834 | ||||||||
\(41\) | −3.90985e7 | −0.0527046 | −0.0263523 | − | 0.999653i | \(-0.508389\pi\) | ||||
−0.0263523 | + | 0.999653i | \(0.508389\pi\) | |||||||
\(42\) | −1.30606e9 | −1.54202 | ||||||||
\(43\) | 9.67989e8 | 1.00414 | 0.502070 | − | 0.864827i | \(-0.332572\pi\) | ||||
0.502070 | + | 0.864827i | \(0.332572\pi\) | |||||||
\(44\) | 2.86201e9 | 2.61627 | ||||||||
\(45\) | −7.24442e8 | −0.585241 | ||||||||
\(46\) | −4.34976e9 | −3.11385 | ||||||||
\(47\) | 1.84099e9 | 1.17088 | 0.585440 | − | 0.810716i | \(-0.300922\pi\) | ||||
0.585440 | + | 0.810716i | \(0.300922\pi\) | |||||||
\(48\) | −1.93453e9 | −1.09584 | ||||||||
\(49\) | 2.33058e9 | 1.17865 | ||||||||
\(50\) | −8.32704e9 | −3.76839 | ||||||||
\(51\) | 2.70880e8 | 0.109936 | ||||||||
\(52\) | 8.11525e9 | 2.95994 | ||||||||
\(53\) | 3.64445e9 | 1.19706 | 0.598528 | − | 0.801102i | \(-0.295752\pi\) | ||||
0.598528 | + | 0.801102i | \(0.295752\pi\) | |||||||
\(54\) | 1.17501e9 | 0.348238 | ||||||||
\(55\) | −7.53858e9 | −2.01974 | ||||||||
\(56\) | 1.40265e10 | 3.40342 | ||||||||
\(57\) | −3.56561e9 | −0.784915 | ||||||||
\(58\) | 1.30438e10 | 2.60945 | ||||||||
\(59\) | −7.14924e8 | −0.130189 | ||||||||
\(60\) | 1.38858e10 | 2.30536 | ||||||||
\(61\) | 1.84441e9 | 0.279604 | 0.139802 | − | 0.990179i | \(-0.455353\pi\) | ||||
0.139802 | + | 0.990179i | \(0.455353\pi\) | |||||||
\(62\) | −3.69073e9 | −0.511633 | ||||||||
\(63\) | −3.87566e9 | −0.492009 | ||||||||
\(64\) | 1.24009e9 | 0.144366 | ||||||||
\(65\) | −2.13757e10 | −2.28505 | ||||||||
\(66\) | 1.22272e10 | 1.20181 | ||||||||
\(67\) | −1.36376e10 | −1.23403 | −0.617017 | − | 0.786950i | \(-0.711659\pi\) | ||||
−0.617017 | + | 0.786950i | \(0.711659\pi\) | |||||||
\(68\) | −5.19211e9 | −0.433057 | ||||||||
\(69\) | −1.29077e10 | −0.993526 | ||||||||
\(70\) | −6.59397e10 | −4.68930 | ||||||||
\(71\) | −2.07952e10 | −1.36786 | −0.683930 | − | 0.729548i | \(-0.739731\pi\) | ||||
−0.683930 | + | 0.729548i | \(0.739731\pi\) | |||||||
\(72\) | −1.26191e10 | −0.768599 | ||||||||
\(73\) | 1.69766e10 | 0.958465 | 0.479232 | − | 0.877688i | \(-0.340915\pi\) | ||||
0.479232 | + | 0.877688i | \(0.340915\pi\) | |||||||
\(74\) | −6.00431e10 | −3.14549 | ||||||||
\(75\) | −2.47101e10 | −1.20237 | ||||||||
\(76\) | 6.83441e10 | 3.09191 | ||||||||
\(77\) | −4.03303e10 | −1.69798 | ||||||||
\(78\) | 3.46703e10 | 1.35968 | ||||||||
\(79\) | 3.36122e10 | 1.22899 | 0.614494 | − | 0.788922i | \(-0.289360\pi\) | ||||
0.614494 | + | 0.788922i | \(0.289360\pi\) | |||||||
\(80\) | −9.76695e10 | −3.33245 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 3.20171e9 | 0.0953688 | ||||||||
\(83\) | 2.76507e10 | 0.770507 | 0.385254 | − | 0.922811i | \(-0.374114\pi\) | ||||
0.385254 | + | 0.922811i | \(0.374114\pi\) | |||||||
\(84\) | 7.42870e10 | 1.93810 | ||||||||
\(85\) | 1.36761e10 | 0.334316 | ||||||||
\(86\) | −7.92671e10 | −1.81699 | ||||||||
\(87\) | 3.87067e10 | 0.832588 | ||||||||
\(88\) | −1.31315e11 | −2.65253 | ||||||||
\(89\) | −1.44161e10 | −0.273655 | −0.136827 | − | 0.990595i | \(-0.543691\pi\) | ||||
−0.136827 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(90\) | 5.93234e10 | 1.05899 | ||||||||
\(91\) | −1.14357e11 | −1.92103 | ||||||||
\(92\) | 2.47409e11 | 3.91366 | ||||||||
\(93\) | −1.09521e10 | −0.163245 | ||||||||
\(94\) | −1.50755e11 | −2.11870 | ||||||||
\(95\) | −1.80019e11 | −2.38693 | ||||||||
\(96\) | 5.20617e10 | 0.651668 | ||||||||
\(97\) | 1.18137e11 | 1.39683 | 0.698413 | − | 0.715695i | \(-0.253890\pi\) | ||||
0.698413 | + | 0.715695i | \(0.253890\pi\) | |||||||
\(98\) | −1.90848e11 | −2.13277 | ||||||||
\(99\) | 3.62837e10 | 0.383458 | ||||||||
\(100\) | 4.73632e11 | 4.73632 | ||||||||
\(101\) | −3.07269e10 | −0.290905 | −0.145453 | − | 0.989365i | \(-0.546464\pi\) | ||||
−0.145453 | + | 0.989365i | \(0.546464\pi\) | |||||||
\(102\) | −2.21819e10 | −0.198929 | ||||||||
\(103\) | 4.65828e10 | 0.395932 | 0.197966 | − | 0.980209i | \(-0.436566\pi\) | ||||
0.197966 | + | 0.980209i | \(0.436566\pi\) | |||||||
\(104\) | −3.72344e11 | −3.00097 | ||||||||
\(105\) | −1.95673e11 | −1.49620 | ||||||||
\(106\) | −2.98438e11 | −2.16607 | ||||||||
\(107\) | −1.33118e11 | −0.917542 | −0.458771 | − | 0.888555i | \(-0.651710\pi\) | ||||
−0.458771 | + | 0.888555i | \(0.651710\pi\) | |||||||
\(108\) | −6.68331e10 | −0.437684 | ||||||||
\(109\) | 1.35886e11 | 0.845921 | 0.422960 | − | 0.906148i | \(-0.360991\pi\) | ||||
0.422960 | + | 0.906148i | \(0.360991\pi\) | |||||||
\(110\) | 6.17322e11 | 3.65470 | ||||||||
\(111\) | −1.78175e11 | −1.00362 | ||||||||
\(112\) | −5.22518e11 | −2.80158 | ||||||||
\(113\) | 1.99811e11 | 1.02020 | 0.510102 | − | 0.860114i | \(-0.329608\pi\) | ||||
0.510102 | + | 0.860114i | \(0.329608\pi\) | |||||||
\(114\) | 2.91982e11 | 1.42030 | ||||||||
\(115\) | −6.51679e11 | −3.02131 | ||||||||
\(116\) | −7.41913e11 | −3.27970 | ||||||||
\(117\) | 1.02882e11 | 0.433830 | ||||||||
\(118\) | 5.85440e10 | 0.235576 | ||||||||
\(119\) | 7.31651e10 | 0.281058 | ||||||||
\(120\) | −6.37108e11 | −2.33731 | ||||||||
\(121\) | 9.22580e10 | 0.323359 | ||||||||
\(122\) | −1.51036e11 | −0.505943 | ||||||||
\(123\) | 9.50093e9 | 0.0304290 | ||||||||
\(124\) | 2.09924e11 | 0.643048 | ||||||||
\(125\) | −6.48505e11 | −1.90068 | ||||||||
\(126\) | 3.17372e11 | 0.890288 | ||||||||
\(127\) | −2.45066e11 | −0.658208 | −0.329104 | − | 0.944294i | \(-0.606747\pi\) | ||||
−0.329104 | + | 0.944294i | \(0.606747\pi\) | |||||||
\(128\) | 3.37226e11 | 0.867493 | ||||||||
\(129\) | −2.35221e11 | −0.579740 | ||||||||
\(130\) | 1.75042e12 | 4.13479 | ||||||||
\(131\) | −3.48684e11 | −0.789659 | −0.394830 | − | 0.918754i | \(-0.629196\pi\) | ||||
−0.394830 | + | 0.918754i | \(0.629196\pi\) | |||||||
\(132\) | −6.95469e11 | −1.51050 | ||||||||
\(133\) | −9.63078e11 | −2.00668 | ||||||||
\(134\) | 1.11676e12 | 2.23298 | ||||||||
\(135\) | 1.76039e11 | 0.337889 | ||||||||
\(136\) | 2.38225e11 | 0.439059 | ||||||||
\(137\) | 7.91794e10 | 0.140168 | 0.0700840 | − | 0.997541i | \(-0.477673\pi\) | ||||
0.0700840 | + | 0.997541i | \(0.477673\pi\) | |||||||
\(138\) | 1.05699e12 | 1.79778 | ||||||||
\(139\) | 5.35686e11 | 0.875646 | 0.437823 | − | 0.899061i | \(-0.355750\pi\) | ||||
0.437823 | + | 0.899061i | \(0.355750\pi\) | |||||||
\(140\) | 3.75057e12 | 5.89377 | ||||||||
\(141\) | −4.47359e11 | −0.676007 | ||||||||
\(142\) | 1.70288e12 | 2.47514 | ||||||||
\(143\) | 1.07060e12 | 1.49720 | ||||||||
\(144\) | 4.70090e11 | 0.632684 | ||||||||
\(145\) | 1.95421e12 | 2.53190 | ||||||||
\(146\) | −1.39019e12 | −1.73434 | ||||||||
\(147\) | −5.66332e11 | −0.680496 | ||||||||
\(148\) | 3.41518e12 | 3.95343 | ||||||||
\(149\) | −1.13785e12 | −1.26928 | −0.634642 | − | 0.772806i | \(-0.718852\pi\) | ||||
−0.634642 | + | 0.772806i | \(0.718852\pi\) | |||||||
\(150\) | 2.02347e12 | 2.17568 | ||||||||
\(151\) | 7.52312e11 | 0.779875 | 0.389937 | − | 0.920841i | \(-0.372497\pi\) | ||||
0.389937 | + | 0.920841i | \(0.372497\pi\) | |||||||
\(152\) | −3.13577e12 | −3.13476 | ||||||||
\(153\) | −6.58239e10 | −0.0634717 | ||||||||
\(154\) | 3.30259e12 | 3.07249 | ||||||||
\(155\) | −5.52944e11 | −0.496428 | ||||||||
\(156\) | −1.97201e12 | −1.70892 | ||||||||
\(157\) | 1.57758e12 | 1.31991 | 0.659954 | − | 0.751306i | \(-0.270576\pi\) | ||||
0.659954 | + | 0.751306i | \(0.270576\pi\) | |||||||
\(158\) | −2.75245e12 | −2.22385 | ||||||||
\(159\) | −8.85602e11 | −0.691121 | ||||||||
\(160\) | 2.62847e12 | 1.98172 | ||||||||
\(161\) | −3.48639e12 | −2.54000 | ||||||||
\(162\) | −2.85527e11 | −0.201055 | ||||||||
\(163\) | 1.11569e12 | 0.759470 | 0.379735 | − | 0.925095i | \(-0.376015\pi\) | ||||
0.379735 | + | 0.925095i | \(0.376015\pi\) | |||||||
\(164\) | −1.82110e11 | −0.119865 | ||||||||
\(165\) | 1.83187e12 | 1.16610 | ||||||||
\(166\) | −2.26427e12 | −1.39423 | ||||||||
\(167\) | 1.00214e12 | 0.597020 | 0.298510 | − | 0.954407i | \(-0.403510\pi\) | ||||
0.298510 | + | 0.954407i | \(0.403510\pi\) | |||||||
\(168\) | −3.40844e12 | −1.96496 | ||||||||
\(169\) | 1.24353e12 | 0.693874 | ||||||||
\(170\) | −1.11991e12 | −0.604944 | ||||||||
\(171\) | 8.66444e11 | 0.453171 | ||||||||
\(172\) | 4.50862e12 | 2.28369 | ||||||||
\(173\) | 1.17842e12 | 0.578156 | 0.289078 | − | 0.957306i | \(-0.406651\pi\) | ||||
0.289078 | + | 0.957306i | \(0.406651\pi\) | |||||||
\(174\) | −3.16963e12 | −1.50657 | ||||||||
\(175\) | −6.67423e12 | −3.07392 | ||||||||
\(176\) | 4.89178e12 | 2.18347 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 1.18051e12 | 0.495177 | ||||||||
\(179\) | −1.28029e12 | −0.520735 | −0.260368 | − | 0.965510i | \(-0.583844\pi\) | ||||
−0.260368 | + | 0.965510i | \(0.583844\pi\) | |||||||
\(180\) | −3.37424e12 | −1.33100 | ||||||||
\(181\) | 2.22754e12 | 0.852302 | 0.426151 | − | 0.904652i | \(-0.359869\pi\) | ||||
0.426151 | + | 0.904652i | \(0.359869\pi\) | |||||||
\(182\) | 9.36450e12 | 3.47610 | ||||||||
\(183\) | −4.48192e11 | −0.161430 | ||||||||
\(184\) | −1.13516e13 | −3.96790 | ||||||||
\(185\) | −8.99563e12 | −3.05202 | ||||||||
\(186\) | 8.96848e11 | 0.295391 | ||||||||
\(187\) | −6.84967e11 | −0.219049 | ||||||||
\(188\) | 8.57479e12 | 2.66290 | ||||||||
\(189\) | 9.41786e11 | 0.284061 | ||||||||
\(190\) | 1.47415e13 | 4.31913 | ||||||||
\(191\) | 1.46958e11 | 0.0418320 | 0.0209160 | − | 0.999781i | \(-0.493342\pi\) | ||||
0.0209160 | + | 0.999781i | \(0.493342\pi\) | |||||||
\(192\) | −3.01343e11 | −0.0833496 | ||||||||
\(193\) | −7.03816e12 | −1.89188 | −0.945941 | − | 0.324338i | \(-0.894859\pi\) | ||||
−0.945941 | + | 0.324338i | \(0.894859\pi\) | |||||||
\(194\) | −9.67407e12 | −2.52755 | ||||||||
\(195\) | 5.19429e12 | 1.31928 | ||||||||
\(196\) | 1.08552e13 | 2.68058 | ||||||||
\(197\) | 4.74360e12 | 1.13905 | 0.569527 | − | 0.821973i | \(-0.307127\pi\) | ||||
0.569527 | + | 0.821973i | \(0.307127\pi\) | |||||||
\(198\) | −2.97121e12 | −0.693865 | ||||||||
\(199\) | −6.90796e12 | −1.56913 | −0.784563 | − | 0.620049i | \(-0.787113\pi\) | ||||
−0.784563 | + | 0.620049i | \(0.787113\pi\) | |||||||
\(200\) | −2.17312e13 | −4.80196 | ||||||||
\(201\) | 3.31394e12 | 0.712470 | ||||||||
\(202\) | 2.51618e12 | 0.526392 | ||||||||
\(203\) | 1.04547e13 | 2.12856 | ||||||||
\(204\) | 1.26168e12 | 0.250025 | ||||||||
\(205\) | 4.79679e11 | 0.0925347 | ||||||||
\(206\) | −3.81459e12 | −0.716438 | ||||||||
\(207\) | 3.13657e12 | 0.573613 | ||||||||
\(208\) | 1.38707e13 | 2.47029 | ||||||||
\(209\) | 9.01626e12 | 1.56395 | ||||||||
\(210\) | 1.60233e13 | 2.70737 | ||||||||
\(211\) | 2.87436e12 | 0.473139 | 0.236569 | − | 0.971615i | \(-0.423977\pi\) | ||||
0.236569 | + | 0.971615i | \(0.423977\pi\) | |||||||
\(212\) | 1.69748e13 | 2.72244 | ||||||||
\(213\) | 5.05323e12 | 0.789734 | ||||||||
\(214\) | 1.09008e13 | 1.66029 | ||||||||
\(215\) | −1.18758e13 | −1.76299 | ||||||||
\(216\) | 3.06644e12 | 0.443751 | ||||||||
\(217\) | −2.95817e12 | −0.417345 | ||||||||
\(218\) | −1.11275e13 | −1.53069 | ||||||||
\(219\) | −4.12532e12 | −0.553370 | ||||||||
\(220\) | −3.51126e13 | −4.59344 | ||||||||
\(221\) | −1.94223e12 | −0.247823 | ||||||||
\(222\) | 1.45905e13 | 1.81605 | ||||||||
\(223\) | −9.28787e11 | −0.112782 | −0.0563910 | − | 0.998409i | \(-0.517959\pi\) | ||||
−0.0563910 | + | 0.998409i | \(0.517959\pi\) | |||||||
\(224\) | 1.40619e13 | 1.66602 | ||||||||
\(225\) | 6.00455e12 | 0.694187 | ||||||||
\(226\) | −1.63622e13 | −1.84606 | ||||||||
\(227\) | 2.76808e11 | 0.0304815 | 0.0152408 | − | 0.999884i | \(-0.495149\pi\) | ||||
0.0152408 | + | 0.999884i | \(0.495149\pi\) | |||||||
\(228\) | −1.66076e13 | −1.78511 | ||||||||
\(229\) | 2.06500e12 | 0.216683 | 0.108341 | − | 0.994114i | \(-0.465446\pi\) | ||||
0.108341 | + | 0.994114i | \(0.465446\pi\) | |||||||
\(230\) | 5.33650e13 | 5.46705 | ||||||||
\(231\) | 9.80027e12 | 0.980330 | ||||||||
\(232\) | 3.40405e13 | 3.32515 | ||||||||
\(233\) | 1.37762e13 | 1.31423 | 0.657117 | − | 0.753788i | \(-0.271776\pi\) | ||||
0.657117 | + | 0.753788i | \(0.271776\pi\) | |||||||
\(234\) | −8.42489e12 | −0.785013 | ||||||||
\(235\) | −2.25861e13 | −2.05574 | ||||||||
\(236\) | −3.32991e12 | −0.296085 | ||||||||
\(237\) | −8.16776e12 | −0.709556 | ||||||||
\(238\) | −5.99138e12 | −0.508573 | ||||||||
\(239\) | 1.12934e13 | 0.936776 | 0.468388 | − | 0.883523i | \(-0.344835\pi\) | ||||
0.468388 | + | 0.883523i | \(0.344835\pi\) | |||||||
\(240\) | 2.37337e13 | 1.92399 | ||||||||
\(241\) | 1.59171e13 | 1.26116 | 0.630581 | − | 0.776123i | \(-0.282817\pi\) | ||||
0.630581 | + | 0.776123i | \(0.282817\pi\) | |||||||
\(242\) | −7.55487e12 | −0.585116 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 8.59075e12 | 0.635897 | ||||||||
\(245\) | −2.85927e13 | −2.06939 | ||||||||
\(246\) | −7.78016e11 | −0.0550612 | ||||||||
\(247\) | 2.55657e13 | 1.76939 | ||||||||
\(248\) | −9.63176e12 | −0.651961 | ||||||||
\(249\) | −6.71912e12 | −0.444853 | ||||||||
\(250\) | 5.31051e13 | 3.43927 | ||||||||
\(251\) | 1.23833e12 | 0.0784569 | 0.0392284 | − | 0.999230i | \(-0.487510\pi\) | ||||
0.0392284 | + | 0.999230i | \(0.487510\pi\) | |||||||
\(252\) | −1.80517e13 | −1.11896 | ||||||||
\(253\) | 3.26394e13 | 1.97961 | ||||||||
\(254\) | 2.00681e13 | 1.19102 | ||||||||
\(255\) | −3.32329e12 | −0.193018 | ||||||||
\(256\) | −3.01546e13 | −1.71409 | ||||||||
\(257\) | −2.89910e13 | −1.61299 | −0.806494 | − | 0.591242i | \(-0.798638\pi\) | ||||
−0.806494 | + | 0.591242i | \(0.798638\pi\) | |||||||
\(258\) | 1.92619e13 | 1.04904 | ||||||||
\(259\) | −4.81253e13 | −2.56581 | ||||||||
\(260\) | −9.95618e13 | −5.19684 | ||||||||
\(261\) | −9.40573e12 | −0.480695 | ||||||||
\(262\) | 2.85532e13 | 1.42889 | ||||||||
\(263\) | 2.19744e13 | 1.07686 | 0.538432 | − | 0.842669i | \(-0.319017\pi\) | ||||
0.538432 | + | 0.842669i | \(0.319017\pi\) | |||||||
\(264\) | 3.19095e13 | 1.53144 | ||||||||
\(265\) | −4.47119e13 | −2.10170 | ||||||||
\(266\) | 7.88649e13 | 3.63107 | ||||||||
\(267\) | 3.50312e12 | 0.157995 | ||||||||
\(268\) | −6.35201e13 | −2.80653 | ||||||||
\(269\) | 1.88848e13 | 0.817476 | 0.408738 | − | 0.912652i | \(-0.365969\pi\) | ||||
0.408738 | + | 0.912652i | \(0.365969\pi\) | |||||||
\(270\) | −1.44156e13 | −0.611409 | ||||||||
\(271\) | −2.90121e13 | −1.20573 | −0.602863 | − | 0.797845i | \(-0.705973\pi\) | ||||
−0.602863 | + | 0.797845i | \(0.705973\pi\) | |||||||
\(272\) | −8.87440e12 | −0.361418 | ||||||||
\(273\) | 2.77887e13 | 1.10911 | ||||||||
\(274\) | −6.48387e12 | −0.253633 | ||||||||
\(275\) | 6.24837e13 | 2.39572 | ||||||||
\(276\) | −6.01205e13 | −2.25955 | ||||||||
\(277\) | 4.19714e13 | 1.54638 | 0.773188 | − | 0.634177i | \(-0.218661\pi\) | ||||
0.773188 | + | 0.634177i | \(0.218661\pi\) | |||||||
\(278\) | −4.38665e13 | −1.58448 | ||||||||
\(279\) | 2.66135e12 | 0.0942496 | ||||||||
\(280\) | −1.72084e14 | −5.97545 | ||||||||
\(281\) | 3.40504e13 | 1.15941 | 0.579706 | − | 0.814826i | \(-0.303167\pi\) | ||||
0.579706 | + | 0.814826i | \(0.303167\pi\) | |||||||
\(282\) | 3.66336e13 | 1.22323 | ||||||||
\(283\) | 2.11301e12 | 0.0691951 | 0.0345976 | − | 0.999401i | \(-0.488985\pi\) | ||||
0.0345976 | + | 0.999401i | \(0.488985\pi\) | |||||||
\(284\) | −9.68580e13 | −3.11089 | ||||||||
\(285\) | 4.37447e13 | 1.37809 | ||||||||
\(286\) | −8.76698e13 | −2.70917 | ||||||||
\(287\) | 2.56622e12 | 0.0777934 | ||||||||
\(288\) | −1.26510e13 | −0.376241 | ||||||||
\(289\) | −3.30293e13 | −0.963742 | ||||||||
\(290\) | −1.60027e14 | −4.58147 | ||||||||
\(291\) | −2.87073e13 | −0.806457 | ||||||||
\(292\) | 7.90724e13 | 2.17981 | ||||||||
\(293\) | −1.32074e13 | −0.357311 | −0.178656 | − | 0.983912i | \(-0.557175\pi\) | ||||
−0.178656 | + | 0.983912i | \(0.557175\pi\) | |||||||
\(294\) | 4.63760e13 | 1.23135 | ||||||||
\(295\) | 8.77104e12 | 0.228576 | ||||||||
\(296\) | −1.56695e14 | −4.00822 | ||||||||
\(297\) | −8.81693e12 | −0.221389 | ||||||||
\(298\) | 9.31763e13 | 2.29676 | ||||||||
\(299\) | 9.25490e13 | 2.23965 | ||||||||
\(300\) | −1.15093e14 | −2.73451 | ||||||||
\(301\) | −6.35336e13 | −1.48214 | ||||||||
\(302\) | −6.16057e13 | −1.41118 | ||||||||
\(303\) | 7.46664e12 | 0.167954 | ||||||||
\(304\) | 1.16814e14 | 2.58043 | ||||||||
\(305\) | −2.26281e13 | −0.490908 | ||||||||
\(306\) | 5.39021e12 | 0.114852 | ||||||||
\(307\) | 2.80769e13 | 0.587608 | 0.293804 | − | 0.955866i | \(-0.405079\pi\) | ||||
0.293804 | + | 0.955866i | \(0.405079\pi\) | |||||||
\(308\) | −1.87847e14 | −3.86168 | ||||||||
\(309\) | −1.13196e13 | −0.228592 | ||||||||
\(310\) | 4.52797e13 | 0.898285 | ||||||||
\(311\) | −1.42706e13 | −0.278139 | −0.139069 | − | 0.990283i | \(-0.544411\pi\) | ||||
−0.139069 | + | 0.990283i | \(0.544411\pi\) | |||||||
\(312\) | 9.04797e13 | 1.73261 | ||||||||
\(313\) | −6.35564e13 | −1.19582 | −0.597910 | − | 0.801564i | \(-0.704002\pi\) | ||||
−0.597910 | + | 0.801564i | \(0.704002\pi\) | |||||||
\(314\) | −1.29186e14 | −2.38837 | ||||||||
\(315\) | 4.75485e13 | 0.863831 | ||||||||
\(316\) | 1.56556e14 | 2.79506 | ||||||||
\(317\) | 8.71235e13 | 1.52866 | 0.764328 | − | 0.644828i | \(-0.223071\pi\) | ||||
0.764328 | + | 0.644828i | \(0.223071\pi\) | |||||||
\(318\) | 7.25205e13 | 1.25058 | ||||||||
\(319\) | −9.78765e13 | −1.65894 | ||||||||
\(320\) | −1.52141e13 | −0.253466 | ||||||||
\(321\) | 3.23477e13 | 0.529743 | ||||||||
\(322\) | 2.85495e14 | 4.59612 | ||||||||
\(323\) | −1.63568e13 | −0.258872 | ||||||||
\(324\) | 1.62404e13 | 0.252697 | ||||||||
\(325\) | 1.77173e14 | 2.71043 | ||||||||
\(326\) | −9.13618e13 | −1.37426 | ||||||||
\(327\) | −3.30203e13 | −0.488393 | ||||||||
\(328\) | 8.35556e12 | 0.121526 | ||||||||
\(329\) | −1.20832e14 | −1.72825 | ||||||||
\(330\) | −1.50009e14 | −2.11004 | ||||||||
\(331\) | 7.31864e13 | 1.01246 | 0.506229 | − | 0.862399i | \(-0.331039\pi\) | ||||
0.506229 | + | 0.862399i | \(0.331039\pi\) | |||||||
\(332\) | 1.28789e14 | 1.75235 | ||||||||
\(333\) | 4.32965e13 | 0.579442 | ||||||||
\(334\) | −8.20638e13 | −1.08030 | ||||||||
\(335\) | 1.67313e14 | 2.16662 | ||||||||
\(336\) | 1.26972e14 | 1.61749 | ||||||||
\(337\) | −7.55866e13 | −0.947284 | −0.473642 | − | 0.880717i | \(-0.657061\pi\) | ||||
−0.473642 | + | 0.880717i | \(0.657061\pi\) | |||||||
\(338\) | −1.01831e14 | −1.25556 | ||||||||
\(339\) | −4.85540e13 | −0.589015 | ||||||||
\(340\) | 6.36993e13 | 0.760327 | ||||||||
\(341\) | 2.76942e13 | 0.325267 | ||||||||
\(342\) | −7.09517e13 | −0.820011 | ||||||||
\(343\) | −2.31859e13 | −0.263698 | ||||||||
\(344\) | −2.06865e14 | −2.31534 | ||||||||
\(345\) | 1.58358e14 | 1.74436 | ||||||||
\(346\) | −9.64987e13 | −1.04617 | ||||||||
\(347\) | 9.47376e13 | 1.01090 | 0.505452 | − | 0.862854i | \(-0.331326\pi\) | ||||
0.505452 | + | 0.862854i | \(0.331326\pi\) | |||||||
\(348\) | 1.80285e14 | 1.89354 | ||||||||
\(349\) | −6.81483e12 | −0.0704556 | −0.0352278 | − | 0.999379i | \(-0.511216\pi\) | ||||
−0.0352278 | + | 0.999379i | \(0.511216\pi\) | |||||||
\(350\) | 5.46542e14 | 5.56224 | ||||||||
\(351\) | −2.50004e13 | −0.250472 | ||||||||
\(352\) | −1.31647e14 | −1.29845 | ||||||||
\(353\) | −8.85389e13 | −0.859752 | −0.429876 | − | 0.902888i | \(-0.641443\pi\) | ||||
−0.429876 | + | 0.902888i | \(0.641443\pi\) | |||||||
\(354\) | −1.42262e13 | −0.136010 | ||||||||
\(355\) | 2.55125e14 | 2.40158 | ||||||||
\(356\) | −6.71462e13 | −0.622366 | ||||||||
\(357\) | −1.77791e13 | −0.162269 | ||||||||
\(358\) | 1.04841e14 | 0.942269 | ||||||||
\(359\) | 1.09759e14 | 0.971449 | 0.485724 | − | 0.874112i | \(-0.338556\pi\) | ||||
0.485724 | + | 0.874112i | \(0.338556\pi\) | |||||||
\(360\) | 1.54817e14 | 1.34945 | ||||||||
\(361\) | 9.88156e13 | 0.848274 | ||||||||
\(362\) | −1.82410e14 | −1.54224 | ||||||||
\(363\) | −2.24187e13 | −0.186691 | ||||||||
\(364\) | −5.32642e14 | −4.36896 | ||||||||
\(365\) | −2.08278e14 | −1.68280 | ||||||||
\(366\) | 3.67018e13 | 0.292106 | ||||||||
\(367\) | −1.27385e14 | −0.998745 | −0.499373 | − | 0.866387i | \(-0.666436\pi\) | ||||
−0.499373 | + | 0.866387i | \(0.666436\pi\) | |||||||
\(368\) | 4.22874e14 | 3.26624 | ||||||||
\(369\) | −2.30873e12 | −0.0175682 | ||||||||
\(370\) | 7.36638e14 | 5.52261 | ||||||||
\(371\) | −2.39202e14 | −1.76689 | ||||||||
\(372\) | −5.10116e13 | −0.371264 | ||||||||
\(373\) | −1.67487e14 | −1.20111 | −0.600554 | − | 0.799584i | \(-0.705053\pi\) | ||||
−0.600554 | + | 0.799584i | \(0.705053\pi\) | |||||||
\(374\) | 5.60908e13 | 0.396368 | ||||||||
\(375\) | 1.57587e14 | 1.09736 | ||||||||
\(376\) | −3.93429e14 | −2.69981 | ||||||||
\(377\) | −2.77529e14 | −1.87686 | ||||||||
\(378\) | −7.71214e13 | −0.514008 | ||||||||
\(379\) | 8.74232e13 | 0.574263 | 0.287132 | − | 0.957891i | \(-0.407298\pi\) | ||||
0.287132 | + | 0.957891i | \(0.407298\pi\) | |||||||
\(380\) | −8.38478e14 | −5.42853 | ||||||||
\(381\) | 5.95511e13 | 0.380016 | ||||||||
\(382\) | −1.20341e13 | −0.0756949 | ||||||||
\(383\) | 1.33470e14 | 0.827541 | 0.413770 | − | 0.910381i | \(-0.364212\pi\) | ||||
0.413770 | + | 0.910381i | \(0.364212\pi\) | |||||||
\(384\) | −8.19459e13 | −0.500847 | ||||||||
\(385\) | 4.94792e14 | 2.98118 | ||||||||
\(386\) | 5.76344e14 | 3.42335 | ||||||||
\(387\) | 5.71588e13 | 0.334713 | ||||||||
\(388\) | 5.50249e14 | 3.17676 | ||||||||
\(389\) | −2.38319e14 | −1.35655 | −0.678276 | − | 0.734808i | \(-0.737272\pi\) | ||||
−0.678276 | + | 0.734808i | \(0.737272\pi\) | |||||||
\(390\) | −4.25352e14 | −2.38722 | ||||||||
\(391\) | −5.92126e13 | −0.327674 | ||||||||
\(392\) | −4.98059e14 | −2.71773 | ||||||||
\(393\) | 8.47302e13 | 0.455910 | ||||||||
\(394\) | −3.88446e14 | −2.06111 | ||||||||
\(395\) | −4.12370e14 | −2.15776 | ||||||||
\(396\) | 1.68999e14 | 0.872088 | ||||||||
\(397\) | 3.31386e14 | 1.68650 | 0.843249 | − | 0.537523i | \(-0.180640\pi\) | ||||
0.843249 | + | 0.537523i | \(0.180640\pi\) | |||||||
\(398\) | 5.65682e14 | 2.83933 | ||||||||
\(399\) | 2.34028e14 | 1.15855 | ||||||||
\(400\) | 8.09536e14 | 3.95281 | ||||||||
\(401\) | −2.88745e14 | −1.39066 | −0.695330 | − | 0.718691i | \(-0.744742\pi\) | ||||
−0.695330 | + | 0.718691i | \(0.744742\pi\) | |||||||
\(402\) | −2.71373e14 | −1.28921 | ||||||||
\(403\) | 7.85270e13 | 0.367994 | ||||||||
\(404\) | −1.43117e14 | −0.661599 | ||||||||
\(405\) | −4.27776e13 | −0.195080 | ||||||||
\(406\) | −8.56122e14 | −3.85161 | ||||||||
\(407\) | 4.50546e14 | 1.99972 | ||||||||
\(408\) | −5.78886e13 | −0.253491 | ||||||||
\(409\) | 3.50854e14 | 1.51582 | 0.757911 | − | 0.652358i | \(-0.226220\pi\) | ||||
0.757911 | + | 0.652358i | \(0.226220\pi\) | |||||||
\(410\) | −3.92802e13 | −0.167441 | ||||||||
\(411\) | −1.92406e13 | −0.0809260 | ||||||||
\(412\) | 2.16970e14 | 0.900459 | ||||||||
\(413\) | 4.69238e13 | 0.192162 | ||||||||
\(414\) | −2.56849e14 | −1.03795 | ||||||||
\(415\) | −3.39232e14 | −1.35280 | ||||||||
\(416\) | −3.73285e14 | −1.46902 | ||||||||
\(417\) | −1.30172e14 | −0.505555 | ||||||||
\(418\) | −7.38328e14 | −2.82996 | ||||||||
\(419\) | −8.89563e13 | −0.336511 | −0.168256 | − | 0.985743i | \(-0.553813\pi\) | ||||
−0.168256 | + | 0.985743i | \(0.553813\pi\) | |||||||
\(420\) | −9.11388e14 | −3.40277 | ||||||||
\(421\) | −1.68005e14 | −0.619113 | −0.309556 | − | 0.950881i | \(-0.600181\pi\) | ||||
−0.309556 | + | 0.950881i | \(0.600181\pi\) | |||||||
\(422\) | −2.35377e14 | −0.856142 | ||||||||
\(423\) | 1.08708e14 | 0.390293 | ||||||||
\(424\) | −7.78839e14 | −2.76017 | ||||||||
\(425\) | −1.13354e14 | −0.396551 | ||||||||
\(426\) | −4.13801e14 | −1.42902 | ||||||||
\(427\) | −1.21057e14 | −0.412703 | ||||||||
\(428\) | −6.20026e14 | −2.08674 | ||||||||
\(429\) | −2.60156e14 | −0.864408 | ||||||||
\(430\) | 9.72487e14 | 3.19012 | ||||||||
\(431\) | −1.33060e14 | −0.430946 | −0.215473 | − | 0.976510i | \(-0.569129\pi\) | ||||
−0.215473 | + | 0.976510i | \(0.569129\pi\) | |||||||
\(432\) | −1.14232e14 | −0.365280 | ||||||||
\(433\) | −3.10508e14 | −0.980370 | −0.490185 | − | 0.871619i | \(-0.663071\pi\) | ||||
−0.490185 | + | 0.871619i | \(0.663071\pi\) | |||||||
\(434\) | 2.42240e14 | 0.755183 | ||||||||
\(435\) | −4.74873e14 | −1.46179 | ||||||||
\(436\) | 6.32919e14 | 1.92386 | ||||||||
\(437\) | 7.79419e14 | 2.33950 | ||||||||
\(438\) | 3.37816e14 | 1.00132 | ||||||||
\(439\) | 5.94518e14 | 1.74024 | 0.870122 | − | 0.492837i | \(-0.164040\pi\) | ||||
0.870122 | + | 0.492837i | \(0.164040\pi\) | |||||||
\(440\) | 1.61104e15 | 4.65710 | ||||||||
\(441\) | 1.37619e14 | 0.392885 | ||||||||
\(442\) | 1.59046e14 | 0.448435 | ||||||||
\(443\) | −6.10093e14 | −1.69893 | −0.849465 | − | 0.527645i | \(-0.823075\pi\) | ||||
−0.849465 | + | 0.527645i | \(0.823075\pi\) | |||||||
\(444\) | −8.29889e14 | −2.28251 | ||||||||
\(445\) | 1.76864e14 | 0.480462 | ||||||||
\(446\) | 7.60569e13 | 0.204078 | ||||||||
\(447\) | 2.76496e14 | 0.732821 | ||||||||
\(448\) | −8.13931e13 | −0.213088 | ||||||||
\(449\) | 3.25417e14 | 0.841560 | 0.420780 | − | 0.907163i | \(-0.361756\pi\) | ||||
0.420780 | + | 0.907163i | \(0.361756\pi\) | |||||||
\(450\) | −4.91703e14 | −1.25613 | ||||||||
\(451\) | −2.40247e13 | −0.0606300 | ||||||||
\(452\) | 9.30661e14 | 2.32023 | ||||||||
\(453\) | −1.82812e14 | −0.450261 | ||||||||
\(454\) | −2.26674e13 | −0.0551562 | ||||||||
\(455\) | 1.40299e15 | 3.37280 | ||||||||
\(456\) | 7.61991e14 | 1.80985 | ||||||||
\(457\) | −5.63579e14 | −1.32256 | −0.661281 | − | 0.750139i | \(-0.729987\pi\) | ||||
−0.661281 | + | 0.750139i | \(0.729987\pi\) | |||||||
\(458\) | −1.69100e14 | −0.392087 | ||||||||
\(459\) | 1.59952e13 | 0.0366454 | ||||||||
\(460\) | −3.03534e15 | −6.87130 | ||||||||
\(461\) | 1.78681e14 | 0.399691 | 0.199846 | − | 0.979827i | \(-0.435956\pi\) | ||||
0.199846 | + | 0.979827i | \(0.435956\pi\) | |||||||
\(462\) | −8.02529e14 | −1.77390 | ||||||||
\(463\) | 5.69718e14 | 1.24441 | 0.622207 | − | 0.782853i | \(-0.286236\pi\) | ||||
0.622207 | + | 0.782853i | \(0.286236\pi\) | |||||||
\(464\) | −1.26808e15 | −2.73715 | ||||||||
\(465\) | 1.34365e14 | 0.286613 | ||||||||
\(466\) | −1.12811e15 | −2.37810 | ||||||||
\(467\) | −3.81172e13 | −0.0794105 | −0.0397052 | − | 0.999211i | \(-0.512642\pi\) | ||||
−0.0397052 | + | 0.999211i | \(0.512642\pi\) | |||||||
\(468\) | 4.79197e14 | 0.986648 | ||||||||
\(469\) | 8.95101e14 | 1.82147 | ||||||||
\(470\) | 1.84954e15 | 3.71985 | ||||||||
\(471\) | −3.83352e14 | −0.762049 | ||||||||
\(472\) | 1.52783e14 | 0.300189 | ||||||||
\(473\) | 5.94797e14 | 1.15514 | ||||||||
\(474\) | 6.68845e14 | 1.28394 | ||||||||
\(475\) | 1.49209e15 | 2.83127 | ||||||||
\(476\) | 3.40782e14 | 0.639203 | ||||||||
\(477\) | 2.15201e14 | 0.399019 | ||||||||
\(478\) | −9.24798e14 | −1.69509 | ||||||||
\(479\) | −8.91177e13 | −0.161480 | −0.0807400 | − | 0.996735i | \(-0.525728\pi\) | ||||
−0.0807400 | + | 0.996735i | \(0.525728\pi\) | |||||||
\(480\) | −6.38718e14 | −1.14415 | ||||||||
\(481\) | 1.27753e15 | 2.26241 | ||||||||
\(482\) | −1.30343e15 | −2.28207 | ||||||||
\(483\) | 8.47193e14 | 1.46647 | ||||||||
\(484\) | 4.29712e14 | 0.735407 | ||||||||
\(485\) | −1.44936e15 | −2.45244 | ||||||||
\(486\) | 6.93831e13 | 0.116079 | ||||||||
\(487\) | −1.20100e15 | −1.98670 | −0.993350 | − | 0.115137i | \(-0.963269\pi\) | ||||
−0.993350 | + | 0.115137i | \(0.963269\pi\) | |||||||
\(488\) | −3.94161e14 | −0.644711 | ||||||||
\(489\) | −2.71112e14 | −0.438480 | ||||||||
\(490\) | 2.34141e15 | 3.74455 | ||||||||
\(491\) | −4.53460e14 | −0.717118 | −0.358559 | − | 0.933507i | \(-0.616732\pi\) | ||||
−0.358559 | + | 0.933507i | \(0.616732\pi\) | |||||||
\(492\) | 4.42526e13 | 0.0692040 | ||||||||
\(493\) | 1.77562e14 | 0.274595 | ||||||||
\(494\) | −2.09353e15 | −3.20170 | ||||||||
\(495\) | −4.45146e14 | −0.673245 | ||||||||
\(496\) | 3.58805e14 | 0.536672 | ||||||||
\(497\) | 1.36488e15 | 2.01900 | ||||||||
\(498\) | 5.50218e14 | 0.804959 | ||||||||
\(499\) | −2.32270e13 | −0.0336079 | −0.0168039 | − | 0.999859i | \(-0.505349\pi\) | ||||
−0.0168039 | + | 0.999859i | \(0.505349\pi\) | |||||||
\(500\) | −3.02055e15 | −4.32266 | ||||||||
\(501\) | −2.43520e14 | −0.344689 | ||||||||
\(502\) | −1.01405e14 | −0.141967 | ||||||||
\(503\) | −1.06144e15 | −1.46985 | −0.734926 | − | 0.678148i | \(-0.762783\pi\) | ||||
−0.734926 | + | 0.678148i | \(0.762783\pi\) | |||||||
\(504\) | 8.28250e14 | 1.13447 | ||||||||
\(505\) | 3.76973e14 | 0.510749 | ||||||||
\(506\) | −2.67279e15 | −3.58209 | ||||||||
\(507\) | −3.02178e14 | −0.400608 | ||||||||
\(508\) | −1.14145e15 | −1.49695 | ||||||||
\(509\) | 4.13158e14 | 0.536005 | 0.268002 | − | 0.963418i | \(-0.413636\pi\) | ||||
0.268002 | + | 0.963418i | \(0.413636\pi\) | |||||||
\(510\) | 2.72139e14 | 0.349265 | ||||||||
\(511\) | −1.11426e15 | −1.41472 | ||||||||
\(512\) | 1.77867e15 | 2.23415 | ||||||||
\(513\) | −2.10546e14 | −0.261638 | ||||||||
\(514\) | 2.37403e15 | 2.91870 | ||||||||
\(515\) | −5.71501e14 | −0.695148 | ||||||||
\(516\) | −1.09559e15 | −1.31849 | ||||||||
\(517\) | 1.13122e15 | 1.34695 | ||||||||
\(518\) | 3.94091e15 | 4.64283 | ||||||||
\(519\) | −2.86355e14 | −0.333799 | ||||||||
\(520\) | 4.56810e15 | 5.26887 | ||||||||
\(521\) | 1.20058e15 | 1.37019 | 0.685097 | − | 0.728452i | \(-0.259760\pi\) | ||||
0.685097 | + | 0.728452i | \(0.259760\pi\) | |||||||
\(522\) | 7.70220e14 | 0.869816 | ||||||||
\(523\) | −2.39919e14 | −0.268105 | −0.134052 | − | 0.990974i | \(-0.542799\pi\) | ||||
−0.134052 | + | 0.990974i | \(0.542799\pi\) | |||||||
\(524\) | −1.62407e15 | −1.79590 | ||||||||
\(525\) | 1.62184e15 | 1.77473 | ||||||||
\(526\) | −1.79945e15 | −1.94858 | ||||||||
\(527\) | −5.02413e13 | −0.0538397 | ||||||||
\(528\) | −1.18870e15 | −1.26063 | ||||||||
\(529\) | 1.86873e15 | 1.96128 | ||||||||
\(530\) | 3.66139e15 | 3.80302 | ||||||||
\(531\) | −4.22156e13 | −0.0433963 | ||||||||
\(532\) | −4.48574e15 | −4.56373 | ||||||||
\(533\) | −6.81222e13 | −0.0685945 | ||||||||
\(534\) | −2.86865e14 | −0.285891 | ||||||||
\(535\) | 1.63316e15 | 1.61095 | ||||||||
\(536\) | 2.91443e15 | 2.84543 | ||||||||
\(537\) | 3.11111e14 | 0.300647 | ||||||||
\(538\) | −1.54645e15 | −1.47922 | ||||||||
\(539\) | 1.43207e15 | 1.35589 | ||||||||
\(540\) | 8.19941e14 | 0.768452 | ||||||||
\(541\) | −1.53994e15 | −1.42862 | −0.714312 | − | 0.699827i | \(-0.753260\pi\) | ||||
−0.714312 | + | 0.699827i | \(0.753260\pi\) | |||||||
\(542\) | 2.37576e15 | 2.18176 | ||||||||
\(543\) | −5.41292e14 | −0.492077 | ||||||||
\(544\) | 2.38827e14 | 0.214926 | ||||||||
\(545\) | −1.66712e15 | −1.48520 | ||||||||
\(546\) | −2.27557e15 | −2.00693 | ||||||||
\(547\) | −1.77377e15 | −1.54870 | −0.774349 | − | 0.632759i | \(-0.781923\pi\) | ||||
−0.774349 | + | 0.632759i | \(0.781923\pi\) | |||||||
\(548\) | 3.68795e14 | 0.318781 | ||||||||
\(549\) | 1.08911e14 | 0.0932015 | ||||||||
\(550\) | −5.11669e15 | −4.33505 | ||||||||
\(551\) | −2.33726e15 | −1.96053 | ||||||||
\(552\) | 2.75845e15 | 2.29087 | ||||||||
\(553\) | −2.20612e15 | −1.81402 | ||||||||
\(554\) | −3.43697e15 | −2.79816 | ||||||||
\(555\) | 2.18594e15 | 1.76208 | ||||||||
\(556\) | 2.49507e15 | 1.99146 | ||||||||
\(557\) | −1.34692e15 | −1.06448 | −0.532242 | − | 0.846592i | \(-0.678650\pi\) | ||||
−0.532242 | + | 0.846592i | \(0.678650\pi\) | |||||||
\(558\) | −2.17934e14 | −0.170544 | ||||||||
\(559\) | 1.68655e15 | 1.30688 | ||||||||
\(560\) | 6.41051e15 | 4.91879 | ||||||||
\(561\) | 1.66447e14 | 0.126468 | ||||||||
\(562\) | −2.78834e15 | −2.09795 | ||||||||
\(563\) | −5.37127e14 | −0.400204 | −0.200102 | − | 0.979775i | \(-0.564127\pi\) | ||||
−0.200102 | + | 0.979775i | \(0.564127\pi\) | |||||||
\(564\) | −2.08367e15 | −1.53743 | ||||||||
\(565\) | −2.45137e15 | −1.79120 | ||||||||
\(566\) | −1.73031e14 | −0.125208 | ||||||||
\(567\) | −2.28854e14 | −0.164003 | ||||||||
\(568\) | 4.44404e15 | 3.15401 | ||||||||
\(569\) | 8.67485e14 | 0.609740 | 0.304870 | − | 0.952394i | \(-0.401387\pi\) | ||||
0.304870 | + | 0.952394i | \(0.401387\pi\) | |||||||
\(570\) | −3.58218e15 | −2.49365 | ||||||||
\(571\) | 6.22355e14 | 0.429081 | 0.214541 | − | 0.976715i | \(-0.431175\pi\) | ||||
0.214541 | + | 0.976715i | \(0.431175\pi\) | |||||||
\(572\) | 4.98655e15 | 3.40504 | ||||||||
\(573\) | −3.57107e13 | −0.0241517 | ||||||||
\(574\) | −2.10143e14 | −0.140767 | ||||||||
\(575\) | 5.40146e15 | 3.58375 | ||||||||
\(576\) | 7.32262e13 | 0.0481219 | ||||||||
\(577\) | −2.49549e15 | −1.62438 | −0.812191 | − | 0.583392i | \(-0.801725\pi\) | ||||
−0.812191 | + | 0.583392i | \(0.801725\pi\) | |||||||
\(578\) | 2.70471e15 | 1.74389 | ||||||||
\(579\) | 1.71027e15 | 1.09228 | ||||||||
\(580\) | 9.10215e15 | 5.75824 | ||||||||
\(581\) | −1.81485e15 | −1.13729 | ||||||||
\(582\) | 2.35080e15 | 1.45928 | ||||||||
\(583\) | 2.23939e15 | 1.37706 | ||||||||
\(584\) | −3.62800e15 | −2.21002 | ||||||||
\(585\) | −1.26221e15 | −0.761684 | ||||||||
\(586\) | 1.08154e15 | 0.646553 | ||||||||
\(587\) | −4.10477e14 | −0.243097 | −0.121549 | − | 0.992585i | \(-0.538786\pi\) | ||||
−0.121549 | + | 0.992585i | \(0.538786\pi\) | |||||||
\(588\) | −2.63781e15 | −1.54764 | ||||||||
\(589\) | 6.61330e14 | 0.384400 | ||||||||
\(590\) | −7.18247e14 | −0.413607 | ||||||||
\(591\) | −1.15270e15 | −0.657633 | ||||||||
\(592\) | 5.83725e15 | 3.29943 | ||||||||
\(593\) | 3.87690e14 | 0.217112 | 0.108556 | − | 0.994090i | \(-0.465377\pi\) | ||||
0.108556 | + | 0.994090i | \(0.465377\pi\) | |||||||
\(594\) | 7.22005e14 | 0.400603 | ||||||||
\(595\) | −8.97625e14 | −0.493460 | ||||||||
\(596\) | −5.29976e15 | −2.88670 | ||||||||
\(597\) | 1.67863e15 | 0.905935 | ||||||||
\(598\) | −7.57870e15 | −4.05264 | ||||||||
\(599\) | −3.99439e14 | −0.211642 | −0.105821 | − | 0.994385i | \(-0.533747\pi\) | ||||
−0.105821 | + | 0.994385i | \(0.533747\pi\) | |||||||
\(600\) | 5.28068e15 | 2.77241 | ||||||||
\(601\) | −1.59334e15 | −0.828896 | −0.414448 | − | 0.910073i | \(-0.636025\pi\) | ||||
−0.414448 | + | 0.910073i | \(0.636025\pi\) | |||||||
\(602\) | 5.20267e15 | 2.68192 | ||||||||
\(603\) | −8.05288e14 | −0.411345 | ||||||||
\(604\) | 3.50406e15 | 1.77365 | ||||||||
\(605\) | −1.13187e15 | −0.567728 | ||||||||
\(606\) | −6.11432e14 | −0.303913 | ||||||||
\(607\) | −1.83861e15 | −0.905631 | −0.452816 | − | 0.891604i | \(-0.649580\pi\) | ||||
−0.452816 | + | 0.891604i | \(0.649580\pi\) | |||||||
\(608\) | −3.14369e15 | −1.53451 | ||||||||
\(609\) | −2.54050e15 | −1.22892 | ||||||||
\(610\) | 1.85298e15 | 0.888295 | ||||||||
\(611\) | 3.20759e15 | 1.52389 | ||||||||
\(612\) | −3.06589e14 | −0.144352 | ||||||||
\(613\) | −2.85879e15 | −1.33398 | −0.666992 | − | 0.745065i | \(-0.732418\pi\) | ||||
−0.666992 | + | 0.745065i | \(0.732418\pi\) | |||||||
\(614\) | −2.29917e15 | −1.06327 | ||||||||
\(615\) | −1.16562e14 | −0.0534249 | ||||||||
\(616\) | 8.61882e15 | 3.91520 | ||||||||
\(617\) | 4.04258e15 | 1.82008 | 0.910040 | − | 0.414520i | \(-0.136051\pi\) | ||||
0.910040 | + | 0.414520i | \(0.136051\pi\) | |||||||
\(618\) | 9.26947e14 | 0.413636 | ||||||||
\(619\) | 1.66600e15 | 0.736847 | 0.368423 | − | 0.929658i | \(-0.379898\pi\) | ||||
0.368423 | + | 0.929658i | \(0.379898\pi\) | |||||||
\(620\) | −2.57545e15 | −1.12901 | ||||||||
\(621\) | −7.62188e14 | −0.331175 | ||||||||
\(622\) | 1.16860e15 | 0.503291 | ||||||||
\(623\) | 9.46197e14 | 0.403922 | ||||||||
\(624\) | −3.37057e15 | −1.42623 | ||||||||
\(625\) | 2.99096e15 | 1.25450 | ||||||||
\(626\) | 5.20454e15 | 2.16383 | ||||||||
\(627\) | −2.19095e15 | −0.902945 | ||||||||
\(628\) | 7.34793e15 | 3.00183 | ||||||||
\(629\) | −8.17356e14 | −0.331004 | ||||||||
\(630\) | −3.89367e15 | −1.56310 | ||||||||
\(631\) | −2.22420e15 | −0.885140 | −0.442570 | − | 0.896734i | \(-0.645933\pi\) | ||||
−0.442570 | + | 0.896734i | \(0.645933\pi\) | |||||||
\(632\) | −7.18311e15 | −2.83379 | ||||||||
\(633\) | −6.98471e14 | −0.273167 | ||||||||
\(634\) | −7.13441e15 | −2.76610 | ||||||||
\(635\) | 3.00659e15 | 1.15563 | ||||||||
\(636\) | −4.12488e15 | −1.57180 | ||||||||
\(637\) | 4.06063e15 | 1.53400 | ||||||||
\(638\) | 8.01496e15 | 3.00184 | ||||||||
\(639\) | −1.22793e15 | −0.455953 | ||||||||
\(640\) | −4.13725e15 | −1.52308 | ||||||||
\(641\) | −3.13841e15 | −1.14549 | −0.572743 | − | 0.819735i | \(-0.694121\pi\) | ||||
−0.572743 | + | 0.819735i | \(0.694121\pi\) | |||||||
\(642\) | −2.64890e15 | −0.958568 | ||||||||
\(643\) | −2.20899e15 | −0.792563 | −0.396281 | − | 0.918129i | \(-0.629700\pi\) | ||||
−0.396281 | + | 0.918129i | \(0.629700\pi\) | |||||||
\(644\) | −1.62386e16 | −5.77666 | ||||||||
\(645\) | 2.88581e15 | 1.01786 | ||||||||
\(646\) | 1.33943e15 | 0.468428 | ||||||||
\(647\) | −2.86406e15 | −0.993137 | −0.496568 | − | 0.867998i | \(-0.665407\pi\) | ||||
−0.496568 | + | 0.867998i | \(0.665407\pi\) | |||||||
\(648\) | −7.45145e14 | −0.256200 | ||||||||
\(649\) | −4.39297e14 | −0.149766 | ||||||||
\(650\) | −1.45084e16 | −4.90451 | ||||||||
\(651\) | 7.18836e14 | 0.240954 | ||||||||
\(652\) | 5.19655e15 | 1.72724 | ||||||||
\(653\) | 2.31705e15 | 0.763681 | 0.381841 | − | 0.924228i | \(-0.375290\pi\) | ||||
0.381841 | + | 0.924228i | \(0.375290\pi\) | |||||||
\(654\) | 2.70398e15 | 0.883744 | ||||||||
\(655\) | 4.27782e15 | 1.38642 | ||||||||
\(656\) | −3.11263e14 | −0.100036 | ||||||||
\(657\) | 1.00245e15 | 0.319488 | ||||||||
\(658\) | 9.89478e15 | 3.12726 | ||||||||
\(659\) | −1.43478e14 | −0.0449691 | −0.0224846 | − | 0.999747i | \(-0.507158\pi\) | ||||
−0.0224846 | + | 0.999747i | \(0.507158\pi\) | |||||||
\(660\) | 8.53235e15 | 2.65202 | ||||||||
\(661\) | 3.98885e15 | 1.22953 | 0.614766 | − | 0.788710i | \(-0.289250\pi\) | ||||
0.614766 | + | 0.788710i | \(0.289250\pi\) | |||||||
\(662\) | −5.99312e15 | −1.83204 | ||||||||
\(663\) | 4.71961e14 | 0.143081 | ||||||||
\(664\) | −5.90911e15 | −1.77663 | ||||||||
\(665\) | 1.18155e16 | 3.52317 | ||||||||
\(666\) | −3.54549e15 | −1.04850 | ||||||||
\(667\) | −8.46102e15 | −2.48159 | ||||||||
\(668\) | 4.66769e15 | 1.35779 | ||||||||
\(669\) | 2.25695e14 | 0.0651147 | ||||||||
\(670\) | −1.37010e16 | −3.92049 | ||||||||
\(671\) | 1.13333e15 | 0.321649 | ||||||||
\(672\) | −3.41705e15 | −0.961879 | ||||||||
\(673\) | −5.12540e14 | −0.143102 | −0.0715509 | − | 0.997437i | \(-0.522795\pi\) | ||||
−0.0715509 | + | 0.997437i | \(0.522795\pi\) | |||||||
\(674\) | 6.18967e15 | 1.71411 | ||||||||
\(675\) | −1.45911e15 | −0.400789 | ||||||||
\(676\) | 5.79202e15 | 1.57806 | ||||||||
\(677\) | 2.83003e15 | 0.764809 | 0.382405 | − | 0.923995i | \(-0.375096\pi\) | ||||
0.382405 | + | 0.923995i | \(0.375096\pi\) | |||||||
\(678\) | 3.97601e15 | 1.06582 | ||||||||
\(679\) | −7.75390e15 | −2.06175 | ||||||||
\(680\) | −2.92265e15 | −0.770865 | ||||||||
\(681\) | −6.72644e13 | −0.0175985 | ||||||||
\(682\) | −2.26783e15 | −0.588568 | ||||||||
\(683\) | 1.48113e15 | 0.381312 | 0.190656 | − | 0.981657i | \(-0.438938\pi\) | ||||
0.190656 | + | 0.981657i | \(0.438938\pi\) | |||||||
\(684\) | 4.03565e15 | 1.03064 | ||||||||
\(685\) | −9.71411e14 | −0.246096 | ||||||||
\(686\) | 1.89866e15 | 0.477160 | ||||||||
\(687\) | −5.01795e14 | −0.125102 | ||||||||
\(688\) | 7.70617e15 | 1.90591 | ||||||||
\(689\) | 6.34981e15 | 1.55796 | ||||||||
\(690\) | −1.29677e16 | −3.15641 | ||||||||
\(691\) | 6.00640e15 | 1.45039 | 0.725195 | − | 0.688544i | \(-0.241750\pi\) | ||||
0.725195 | + | 0.688544i | \(0.241750\pi\) | |||||||
\(692\) | 5.48873e15 | 1.31489 | ||||||||
\(693\) | −2.38147e15 | −0.565994 | ||||||||
\(694\) | −7.75791e15 | −1.82923 | ||||||||
\(695\) | −6.57205e15 | −1.53739 | ||||||||
\(696\) | −8.27184e15 | −1.91978 | ||||||||
\(697\) | 4.35844e13 | 0.0100358 | ||||||||
\(698\) | 5.58056e14 | 0.127489 | ||||||||
\(699\) | −3.34762e15 | −0.758774 | ||||||||
\(700\) | −3.10867e16 | −6.99093 | ||||||||
\(701\) | 1.87164e15 | 0.417613 | 0.208806 | − | 0.977957i | \(-0.433042\pi\) | ||||
0.208806 | + | 0.977957i | \(0.433042\pi\) | |||||||
\(702\) | 2.04725e15 | 0.453227 | ||||||||
\(703\) | 1.07589e16 | 2.36327 | ||||||||
\(704\) | 7.61996e14 | 0.166075 | ||||||||
\(705\) | 5.48842e15 | 1.18688 | ||||||||
\(706\) | 7.25031e15 | 1.55572 | ||||||||
\(707\) | 2.01675e15 | 0.429384 | ||||||||
\(708\) | 8.09169e14 | 0.170945 | ||||||||
\(709\) | 6.18607e15 | 1.29676 | 0.648382 | − | 0.761315i | \(-0.275446\pi\) | ||||
0.648382 | + | 0.761315i | \(0.275446\pi\) | |||||||
\(710\) | −2.08918e16 | −4.34565 | ||||||||
\(711\) | 1.98476e15 | 0.409663 | ||||||||
\(712\) | 3.08080e15 | 0.630992 | ||||||||
\(713\) | 2.39405e15 | 0.486565 | ||||||||
\(714\) | 1.45590e15 | 0.293625 | ||||||||
\(715\) | −1.31346e16 | −2.62866 | ||||||||
\(716\) | −5.96323e15 | −1.18430 | ||||||||
\(717\) | −2.74429e15 | −0.540848 | ||||||||
\(718\) | −8.98798e15 | −1.75783 | ||||||||
\(719\) | −3.83167e14 | −0.0743668 | −0.0371834 | − | 0.999308i | \(-0.511839\pi\) | ||||
−0.0371834 | + | 0.999308i | \(0.511839\pi\) | |||||||
\(720\) | −5.76729e15 | −1.11082 | ||||||||
\(721\) | −3.05745e15 | −0.584407 | ||||||||
\(722\) | −8.09186e15 | −1.53495 | ||||||||
\(723\) | −3.86786e15 | −0.728133 | ||||||||
\(724\) | 1.03752e16 | 1.93837 | ||||||||
\(725\) | −1.61975e16 | −3.00323 | ||||||||
\(726\) | 1.83583e15 | 0.337817 | ||||||||
\(727\) | −5.51247e15 | −1.00672 | −0.503358 | − | 0.864078i | \(-0.667902\pi\) | ||||
−0.503358 | + | 0.864078i | \(0.667902\pi\) | |||||||
\(728\) | 2.44387e16 | 4.42951 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 1.70555e16 | 3.04502 | ||||||||
\(731\) | −1.07905e15 | −0.191203 | ||||||||
\(732\) | −2.08755e15 | −0.367135 | ||||||||
\(733\) | 5.39658e15 | 0.941991 | 0.470995 | − | 0.882136i | \(-0.343895\pi\) | ||||
0.470995 | + | 0.882136i | \(0.343895\pi\) | |||||||
\(734\) | 1.04314e16 | 1.80722 | ||||||||
\(735\) | 6.94803e15 | 1.19476 | ||||||||
\(736\) | −1.13803e16 | −1.94235 | ||||||||
\(737\) | −8.37987e15 | −1.41960 | ||||||||
\(738\) | 1.89058e14 | 0.0317896 | ||||||||
\(739\) | −4.28606e15 | −0.715342 | −0.357671 | − | 0.933848i | \(-0.616429\pi\) | ||||
−0.357671 | + | 0.933848i | \(0.616429\pi\) | |||||||
\(740\) | −4.18991e16 | −6.94113 | ||||||||
\(741\) | −6.21245e15 | −1.02156 | ||||||||
\(742\) | 1.95879e16 | 3.19718 | ||||||||
\(743\) | −3.44325e15 | −0.557866 | −0.278933 | − | 0.960311i | \(-0.589981\pi\) | ||||
−0.278933 | + | 0.960311i | \(0.589981\pi\) | |||||||
\(744\) | 2.34052e15 | 0.376410 | ||||||||
\(745\) | 1.39596e16 | 2.22851 | ||||||||
\(746\) | 1.37152e16 | 2.17340 | ||||||||
\(747\) | 1.63275e15 | 0.256836 | ||||||||
\(748\) | −3.19038e15 | −0.498177 | ||||||||
\(749\) | 8.73715e15 | 1.35432 | ||||||||
\(750\) | −1.29045e16 | −1.98566 | ||||||||
\(751\) | −1.02592e16 | −1.56709 | −0.783547 | − | 0.621332i | \(-0.786592\pi\) | ||||
−0.783547 | + | 0.621332i | \(0.786592\pi\) | |||||||
\(752\) | 1.46561e16 | 2.22239 | ||||||||
\(753\) | −3.00914e14 | −0.0452971 | ||||||||
\(754\) | 2.27264e16 | 3.39617 | ||||||||
\(755\) | −9.22973e15 | −1.36924 | ||||||||
\(756\) | 4.38657e15 | 0.646034 | ||||||||
\(757\) | −8.42991e15 | −1.23252 | −0.616262 | − | 0.787541i | \(-0.711354\pi\) | ||||
−0.616262 | + | 0.787541i | \(0.711354\pi\) | |||||||
\(758\) | −7.15895e15 | −1.03913 | ||||||||
\(759\) | −7.93136e15 | −1.14293 | ||||||||
\(760\) | 3.84711e16 | 5.50376 | ||||||||
\(761\) | −1.18345e16 | −1.68088 | −0.840439 | − | 0.541907i | \(-0.817703\pi\) | ||||
−0.840439 | + | 0.541907i | \(0.817703\pi\) | |||||||
\(762\) | −4.87654e15 | −0.687638 | ||||||||
\(763\) | −8.91885e15 | −1.24860 | ||||||||
\(764\) | 6.84487e14 | 0.0951376 | ||||||||
\(765\) | 8.07559e14 | 0.111439 | ||||||||
\(766\) | −1.09296e16 | −1.49743 | ||||||||
\(767\) | −1.24563e15 | −0.169439 | ||||||||
\(768\) | 7.32757e15 | 0.989631 | ||||||||
\(769\) | −8.62931e15 | −1.15713 | −0.578564 | − | 0.815637i | \(-0.696387\pi\) | ||||
−0.578564 | + | 0.815637i | \(0.696387\pi\) | |||||||
\(770\) | −4.05178e16 | −5.39444 | ||||||||
\(771\) | 7.04482e15 | 0.931260 | ||||||||
\(772\) | −3.27818e16 | −4.30266 | ||||||||
\(773\) | −3.26142e15 | −0.425030 | −0.212515 | − | 0.977158i | \(-0.568165\pi\) | ||||
−0.212515 | + | 0.977158i | \(0.568165\pi\) | |||||||
\(774\) | −4.68064e15 | −0.605662 | ||||||||
\(775\) | 4.58308e15 | 0.588842 | ||||||||
\(776\) | −2.52466e16 | −3.22079 | ||||||||
\(777\) | 1.16945e16 | 1.48137 | ||||||||
\(778\) | 1.95156e16 | 2.45467 | ||||||||
\(779\) | −5.73704e14 | −0.0716526 | ||||||||
\(780\) | 2.41935e16 | 3.00040 | ||||||||
\(781\) | −1.27779e16 | −1.57355 | ||||||||
\(782\) | 4.84882e15 | 0.592924 | ||||||||
\(783\) | 2.28559e15 | 0.277529 | ||||||||
\(784\) | 1.85538e16 | 2.23715 | ||||||||
\(785\) | −1.93545e16 | −2.31739 | ||||||||
\(786\) | −6.93842e15 | −0.824967 | ||||||||
\(787\) | 2.49094e15 | 0.294105 | 0.147053 | − | 0.989129i | \(-0.453021\pi\) | ||||
0.147053 | + | 0.989129i | \(0.453021\pi\) | |||||||
\(788\) | 2.20943e16 | 2.59052 | ||||||||
\(789\) | −5.33978e15 | −0.621728 | ||||||||
\(790\) | 3.37684e16 | 3.90446 | ||||||||
\(791\) | −1.31145e16 | −1.50585 | ||||||||
\(792\) | −7.75402e15 | −0.884175 | ||||||||
\(793\) | 3.21356e15 | 0.363902 | ||||||||
\(794\) | −2.71367e16 | −3.05171 | ||||||||
\(795\) | 1.08650e16 | 1.21342 | ||||||||
\(796\) | −3.21753e16 | −3.56862 | ||||||||
\(797\) | 2.02263e15 | 0.222790 | 0.111395 | − | 0.993776i | \(-0.464468\pi\) | ||||
0.111395 | + | 0.993776i | \(0.464468\pi\) | |||||||
\(798\) | −1.91642e16 | −2.09640 | ||||||||
\(799\) | −2.05221e15 | −0.222953 | ||||||||
\(800\) | −2.17861e16 | −2.35063 | ||||||||
\(801\) | −8.51257e14 | −0.0912183 | ||||||||
\(802\) | 2.36449e16 | 2.51639 | ||||||||
\(803\) | 1.04316e16 | 1.10259 | ||||||||
\(804\) | 1.54354e16 | 1.62035 | ||||||||
\(805\) | 4.27728e16 | 4.45954 | ||||||||
\(806\) | −6.43045e15 | −0.665884 | ||||||||
\(807\) | −4.58901e15 | −0.471970 | ||||||||
\(808\) | 6.56651e15 | 0.670768 | ||||||||
\(809\) | 7.96662e15 | 0.808272 | 0.404136 | − | 0.914699i | \(-0.367572\pi\) | ||||
0.404136 | + | 0.914699i | \(0.367572\pi\) | |||||||
\(810\) | 3.50299e15 | 0.352997 | ||||||||
\(811\) | −2.21596e15 | −0.221793 | −0.110896 | − | 0.993832i | \(-0.535372\pi\) | ||||
−0.110896 | + | 0.993832i | \(0.535372\pi\) | |||||||
\(812\) | 4.86952e16 | 4.84092 | ||||||||
\(813\) | 7.04995e15 | 0.696126 | ||||||||
\(814\) | −3.68945e16 | −3.61849 | ||||||||
\(815\) | −1.36878e16 | −1.33342 | ||||||||
\(816\) | 2.15648e15 | 0.208665 | ||||||||
\(817\) | 1.42036e16 | 1.36514 | ||||||||
\(818\) | −2.87309e16 | −2.74287 | ||||||||
\(819\) | −6.75266e15 | −0.640344 | ||||||||
\(820\) | 2.23421e15 | 0.210449 | ||||||||
\(821\) | 7.19699e15 | 0.673385 | 0.336692 | − | 0.941615i | \(-0.390692\pi\) | ||||
0.336692 | + | 0.941615i | \(0.390692\pi\) | |||||||
\(822\) | 1.57558e15 | 0.146435 | ||||||||
\(823\) | 2.87425e15 | 0.265354 | 0.132677 | − | 0.991159i | \(-0.457643\pi\) | ||||
0.132677 | + | 0.991159i | \(0.457643\pi\) | |||||||
\(824\) | −9.95501e15 | −0.912939 | ||||||||
\(825\) | −1.51835e16 | −1.38317 | ||||||||
\(826\) | −3.84252e15 | −0.347717 | ||||||||
\(827\) | 8.45798e15 | 0.760302 | 0.380151 | − | 0.924924i | \(-0.375872\pi\) | ||||
0.380151 | + | 0.924924i | \(0.375872\pi\) | |||||||
\(828\) | 1.46093e16 | 1.30455 | ||||||||
\(829\) | 4.09434e15 | 0.363190 | 0.181595 | − | 0.983373i | \(-0.441874\pi\) | ||||
0.181595 | + | 0.983373i | \(0.441874\pi\) | |||||||
\(830\) | 2.77792e16 | 2.44788 | ||||||||
\(831\) | −1.01991e16 | −0.892800 | ||||||||
\(832\) | 2.16064e15 | 0.187890 | ||||||||
\(833\) | −2.59798e15 | −0.224434 | ||||||||
\(834\) | 1.06596e16 | 0.914799 | ||||||||
\(835\) | −1.22948e16 | −1.04820 | ||||||||
\(836\) | 4.19952e16 | 3.55685 | ||||||||
\(837\) | −6.46709e14 | −0.0544150 | ||||||||
\(838\) | 7.28449e15 | 0.608915 | ||||||||
\(839\) | 2.31251e15 | 0.192040 | 0.0960201 | − | 0.995379i | \(-0.469389\pi\) | ||||
0.0960201 | + | 0.995379i | \(0.469389\pi\) | |||||||
\(840\) | 4.18164e16 | 3.44993 | ||||||||
\(841\) | 1.31718e16 | 1.07961 | ||||||||
\(842\) | 1.37576e16 | 1.12028 | ||||||||
\(843\) | −8.27426e15 | −0.669387 | ||||||||
\(844\) | 1.33880e16 | 1.07605 | ||||||||
\(845\) | −1.52563e16 | −1.21825 | ||||||||
\(846\) | −8.90196e15 | −0.706234 | ||||||||
\(847\) | −6.05533e15 | −0.477286 | ||||||||
\(848\) | 2.90135e16 | 2.27208 | ||||||||
\(849\) | −5.13461e14 | −0.0399498 | ||||||||
\(850\) | 9.28242e15 | 0.717558 | ||||||||
\(851\) | 3.89479e16 | 2.99138 | ||||||||
\(852\) | 2.35365e16 | 1.79607 | ||||||||
\(853\) | −2.06938e15 | −0.156899 | −0.0784496 | − | 0.996918i | \(-0.524997\pi\) | ||||
−0.0784496 | + | 0.996918i | \(0.524997\pi\) | |||||||
\(854\) | 9.91320e15 | 0.746785 | ||||||||
\(855\) | −1.06300e16 | −0.795642 | ||||||||
\(856\) | 2.84480e16 | 2.11566 | ||||||||
\(857\) | 1.04644e16 | 0.773248 | 0.386624 | − | 0.922237i | \(-0.373641\pi\) | ||||
0.386624 | + | 0.922237i | \(0.373641\pi\) | |||||||
\(858\) | 2.13038e16 | 1.56414 | ||||||||
\(859\) | 7.94158e15 | 0.579354 | 0.289677 | − | 0.957124i | \(-0.406452\pi\) | ||||
0.289677 | + | 0.957124i | \(0.406452\pi\) | |||||||
\(860\) | −5.53139e16 | −4.00952 | ||||||||
\(861\) | −6.23590e14 | −0.0449140 | ||||||||
\(862\) | 1.08961e16 | 0.779796 | ||||||||
\(863\) | 1.14766e16 | 0.816122 | 0.408061 | − | 0.912955i | \(-0.366205\pi\) | ||||
0.408061 | + | 0.912955i | \(0.366205\pi\) | |||||||
\(864\) | 3.07419e15 | 0.217223 | ||||||||
\(865\) | −1.44574e16 | −1.01508 | ||||||||
\(866\) | 2.54270e16 | 1.77397 | ||||||||
\(867\) | 8.02611e15 | 0.556417 | ||||||||
\(868\) | −1.37783e16 | −0.949156 | ||||||||
\(869\) | 2.06536e16 | 1.41379 | ||||||||
\(870\) | 3.88866e16 | 2.64511 | ||||||||
\(871\) | −2.37611e16 | −1.60608 | ||||||||
\(872\) | −2.90396e16 | −1.95052 | ||||||||
\(873\) | 6.97588e15 | 0.465608 | ||||||||
\(874\) | −6.38254e16 | −4.23332 | ||||||||
\(875\) | 4.25644e16 | 2.80545 | ||||||||
\(876\) | −1.92146e16 | −1.25852 | ||||||||
\(877\) | −2.61506e16 | −1.70209 | −0.851046 | − | 0.525090i | \(-0.824031\pi\) | ||||
−0.851046 | + | 0.525090i | \(0.824031\pi\) | |||||||
\(878\) | −4.86841e16 | −3.14896 | ||||||||
\(879\) | 3.20941e15 | 0.206294 | ||||||||
\(880\) | −6.00147e16 | −3.83357 | ||||||||
\(881\) | 9.22917e14 | 0.0585862 | 0.0292931 | − | 0.999571i | \(-0.490674\pi\) | ||||
0.0292931 | + | 0.999571i | \(0.490674\pi\) | |||||||
\(882\) | −1.12694e16 | −0.710923 | ||||||||
\(883\) | 6.31286e15 | 0.395769 | 0.197885 | − | 0.980225i | \(-0.436593\pi\) | ||||
0.197885 | + | 0.980225i | \(0.436593\pi\) | |||||||
\(884\) | −9.04634e15 | −0.563618 | ||||||||
\(885\) | −2.13136e15 | −0.131968 | ||||||||
\(886\) | 4.99596e16 | 3.07421 | ||||||||
\(887\) | 2.29576e16 | 1.40393 | 0.701966 | − | 0.712211i | \(-0.252306\pi\) | ||||
0.701966 | + | 0.712211i | \(0.252306\pi\) | |||||||
\(888\) | 3.80770e16 | 2.31415 | ||||||||
\(889\) | 1.60848e16 | 0.971532 | ||||||||
\(890\) | −1.44831e16 | −0.869394 | ||||||||
\(891\) | 2.14251e15 | 0.127819 | ||||||||
\(892\) | −4.32603e15 | −0.256497 | ||||||||
\(893\) | 2.70133e16 | 1.59182 | ||||||||
\(894\) | −2.26419e16 | −1.32604 | ||||||||
\(895\) | 1.57072e16 | 0.914267 | ||||||||
\(896\) | −2.21337e16 | −1.28044 | ||||||||
\(897\) | −2.24894e16 | −1.29306 | ||||||||
\(898\) | −2.66479e16 | −1.52280 | ||||||||
\(899\) | −7.17910e15 | −0.407748 | ||||||||
\(900\) | 2.79675e16 | 1.57877 | ||||||||
\(901\) | −4.06259e15 | −0.227938 | ||||||||
\(902\) | 1.96735e15 | 0.109710 | ||||||||
\(903\) | 1.54387e16 | 0.855712 | ||||||||
\(904\) | −4.27006e16 | −2.35238 | ||||||||
\(905\) | −2.73285e16 | −1.49641 | ||||||||
\(906\) | 1.49702e16 | 0.814745 | ||||||||
\(907\) | −1.33216e16 | −0.720636 | −0.360318 | − | 0.932830i | \(-0.617332\pi\) | ||||
−0.360318 | + | 0.932830i | \(0.617332\pi\) | |||||||
\(908\) | 1.28929e15 | 0.0693234 | ||||||||
\(909\) | −1.81439e15 | −0.0969684 | ||||||||
\(910\) | −1.14888e17 | −6.10307 | ||||||||
\(911\) | −4.14245e15 | −0.218729 | −0.109364 | − | 0.994002i | \(-0.534882\pi\) | ||||
−0.109364 | + | 0.994002i | \(0.534882\pi\) | |||||||
\(912\) | −2.83859e16 | −1.48981 | ||||||||
\(913\) | 1.69904e16 | 0.886371 | ||||||||
\(914\) | 4.61506e16 | 2.39317 | ||||||||
\(915\) | 5.49864e15 | 0.283426 | ||||||||
\(916\) | 9.61818e15 | 0.492797 | ||||||||
\(917\) | 2.28858e16 | 1.16556 | ||||||||
\(918\) | −1.30982e15 | −0.0663098 | ||||||||
\(919\) | −2.51113e16 | −1.26367 | −0.631836 | − | 0.775102i | \(-0.717698\pi\) | ||||
−0.631836 | + | 0.775102i | \(0.717698\pi\) | |||||||
\(920\) | 1.39267e17 | 6.96653 | ||||||||
\(921\) | −6.82268e15 | −0.339256 | ||||||||
\(922\) | −1.46319e16 | −0.723239 | ||||||||
\(923\) | −3.62319e16 | −1.78025 | ||||||||
\(924\) | 4.56469e16 | 2.22954 | ||||||||
\(925\) | 7.45604e16 | 3.62017 | ||||||||
\(926\) | −4.66534e16 | −2.25176 | ||||||||
\(927\) | 2.75067e15 | 0.131977 | ||||||||
\(928\) | 3.41265e16 | 1.62771 | ||||||||
\(929\) | 2.94286e16 | 1.39535 | 0.697675 | − | 0.716415i | \(-0.254218\pi\) | ||||
0.697675 | + | 0.716415i | \(0.254218\pi\) | |||||||
\(930\) | −1.10030e16 | −0.518625 | ||||||||
\(931\) | 3.41974e16 | 1.60239 | ||||||||
\(932\) | 6.41658e16 | 2.98893 | ||||||||
\(933\) | 3.46777e15 | 0.160584 | ||||||||
\(934\) | 3.12136e15 | 0.143693 | ||||||||
\(935\) | 8.40350e15 | 0.384589 | ||||||||
\(936\) | −2.19866e16 | −1.00032 | ||||||||
\(937\) | −1.14822e16 | −0.519347 | −0.259673 | − | 0.965697i | \(-0.583615\pi\) | ||||
−0.259673 | + | 0.965697i | \(0.583615\pi\) | |||||||
\(938\) | −7.32984e16 | −3.29594 | ||||||||
\(939\) | 1.54442e16 | 0.690407 | ||||||||
\(940\) | −1.05200e17 | −4.67532 | ||||||||
\(941\) | −3.44099e16 | −1.52034 | −0.760171 | − | 0.649724i | \(-0.774885\pi\) | ||||
−0.760171 | + | 0.649724i | \(0.774885\pi\) | |||||||
\(942\) | 3.13921e16 | 1.37893 | ||||||||
\(943\) | −2.07684e15 | −0.0906961 | ||||||||
\(944\) | −5.69152e15 | −0.247105 | ||||||||
\(945\) | −1.15543e16 | −0.498733 | ||||||||
\(946\) | −4.87070e16 | −2.09021 | ||||||||
\(947\) | 1.75216e16 | 0.747563 | 0.373782 | − | 0.927517i | \(-0.378061\pi\) | ||||
0.373782 | + | 0.927517i | \(0.378061\pi\) | |||||||
\(948\) | −3.80431e16 | −1.61373 | ||||||||
\(949\) | 2.95788e16 | 1.24743 | ||||||||
\(950\) | −1.22185e17 | −5.12317 | ||||||||
\(951\) | −2.11710e16 | −0.882570 | ||||||||
\(952\) | −1.56358e16 | −0.648062 | ||||||||
\(953\) | 2.42597e16 | 0.999713 | 0.499856 | − | 0.866108i | \(-0.333386\pi\) | ||||
0.499856 | + | 0.866108i | \(0.333386\pi\) | |||||||
\(954\) | −1.76225e16 | −0.722023 | ||||||||
\(955\) | −1.80295e15 | −0.0734455 | ||||||||
\(956\) | 5.26014e16 | 2.13049 | ||||||||
\(957\) | 2.37840e16 | 0.957787 | ||||||||
\(958\) | 7.29771e15 | 0.292197 | ||||||||
\(959\) | −5.19691e15 | −0.206892 | ||||||||
\(960\) | 3.69702e15 | 0.146339 | ||||||||
\(961\) | −2.33771e16 | −0.920053 | ||||||||
\(962\) | −1.04615e17 | −4.09382 | ||||||||
\(963\) | −7.86048e15 | −0.305847 | ||||||||
\(964\) | 7.41375e16 | 2.86823 | ||||||||
\(965\) | 8.63476e16 | 3.32162 | ||||||||
\(966\) | −6.93753e16 | −2.65357 | ||||||||
\(967\) | −9.87645e15 | −0.375626 | −0.187813 | − | 0.982205i | \(-0.560140\pi\) | ||||
−0.187813 | + | 0.982205i | \(0.560140\pi\) | |||||||
\(968\) | −1.97161e16 | −0.745599 | ||||||||
\(969\) | 3.97471e15 | 0.149460 | ||||||||
\(970\) | 1.18686e17 | 4.43768 | ||||||||
\(971\) | 9.14735e15 | 0.340087 | 0.170043 | − | 0.985437i | \(-0.445609\pi\) | ||||
0.170043 | + | 0.985437i | \(0.445609\pi\) | |||||||
\(972\) | −3.94643e15 | −0.145895 | ||||||||
\(973\) | −3.51596e16 | −1.29248 | ||||||||
\(974\) | 9.83476e16 | 3.59492 | ||||||||
\(975\) | −4.30530e16 | −1.56487 | ||||||||
\(976\) | 1.46834e16 | 0.530704 | ||||||||
\(977\) | −2.21369e16 | −0.795603 | −0.397801 | − | 0.917472i | \(-0.630227\pi\) | ||||
−0.397801 | + | 0.917472i | \(0.630227\pi\) | |||||||
\(978\) | 2.22009e16 | 0.793428 | ||||||||
\(979\) | −8.85823e15 | −0.314805 | ||||||||
\(980\) | −1.33177e17 | −4.70636 | ||||||||
\(981\) | 8.02394e15 | 0.281974 | ||||||||
\(982\) | 3.71331e16 | 1.29762 | ||||||||
\(983\) | 1.98996e16 | 0.691513 | 0.345756 | − | 0.938324i | \(-0.387622\pi\) | ||||
0.345756 | + | 0.938324i | \(0.387622\pi\) | |||||||
\(984\) | −2.03040e15 | −0.0701631 | ||||||||
\(985\) | −5.81968e16 | −1.99986 | ||||||||
\(986\) | −1.45403e16 | −0.496879 | ||||||||
\(987\) | 2.93623e16 | 0.997805 | ||||||||
\(988\) | 1.19078e17 | 4.02408 | ||||||||
\(989\) | 5.14178e16 | 1.72796 | ||||||||
\(990\) | 3.64523e16 | 1.21823 | ||||||||
\(991\) | 2.64736e16 | 0.879849 | 0.439925 | − | 0.898035i | \(-0.355005\pi\) | ||||
0.439925 | + | 0.898035i | \(0.355005\pi\) | |||||||
\(992\) | −9.65610e15 | −0.319145 | ||||||||
\(993\) | −1.77843e16 | −0.584542 | ||||||||
\(994\) | −1.11768e17 | −3.65337 | ||||||||
\(995\) | 8.47502e16 | 2.75495 | ||||||||
\(996\) | −3.12958e16 | −1.01172 | ||||||||
\(997\) | 3.83411e16 | 1.23265 | 0.616327 | − | 0.787491i | \(-0.288620\pi\) | ||||
0.616327 | + | 0.787491i | \(0.288620\pi\) | |||||||
\(998\) | 1.90203e15 | 0.0608133 | ||||||||
\(999\) | −1.05211e16 | −0.334541 |
(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 | 177.12.a.c.1.2 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.c.1.2 | ✓ | 27 | 1.1 | even | 1 | trivial |