Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,15,Mod(22,23)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(23, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.22");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
Character orbit: | \([\chi]\) | \(=\) | 23.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.5956626749\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.20 | ||
Character | \(\chi\) | \(=\) | 23.22 |
Dual form | 23.15.b.b.22.19 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/23\mathbb{Z}\right)^\times\).
\(n\) | \(5\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 137.789 | 1.07648 | 0.538239 | − | 0.842793i | \(-0.319090\pi\) | ||||
0.538239 | + | 0.842793i | \(0.319090\pi\) | |||||||
\(3\) | 2037.01 | 0.931419 | 0.465709 | − | 0.884938i | \(-0.345799\pi\) | ||||
0.465709 | + | 0.884938i | \(0.345799\pi\) | |||||||
\(4\) | 2601.83 | 0.158803 | ||||||||
\(5\) | 58362.5i | 0.747040i | 0.927622 | + | 0.373520i | \(0.121849\pi\) | ||||
−0.927622 | + | 0.373520i | \(0.878151\pi\) | |||||||
\(6\) | 280678. | 1.00265 | ||||||||
\(7\) | 1.12900e6i | 1.37090i | 0.728119 | + | 0.685451i | \(0.240395\pi\) | ||||
−0.728119 | + | 0.685451i | \(0.759605\pi\) | |||||||
\(8\) | −1.89903e6 | −0.905529 | ||||||||
\(9\) | −633549. | −0.132459 | ||||||||
\(10\) | 8.04171e6i | 0.804171i | ||||||||
\(11\) | − | 7.80142e6i | − | 0.400336i | −0.979762 | − | 0.200168i | \(-0.935851\pi\) | ||
0.979762 | − | 0.200168i | \(-0.0641488\pi\) | |||||||
\(12\) | 5.29996e6 | 0.147912 | ||||||||
\(13\) | −7.61695e7 | −1.21388 | −0.606942 | − | 0.794746i | \(-0.707604\pi\) | ||||
−0.606942 | + | 0.794746i | \(0.707604\pi\) | |||||||
\(14\) | 1.55563e8i | 1.47574i | ||||||||
\(15\) | 1.18885e8i | 0.695807i | ||||||||
\(16\) | −3.04294e8 | −1.13358 | ||||||||
\(17\) | 4.29810e8i | 1.04745i | 0.851887 | + | 0.523726i | \(0.175459\pi\) | ||||
−0.851887 | + | 0.523726i | \(0.824541\pi\) | |||||||
\(18\) | −8.72962e7 | −0.142590 | ||||||||
\(19\) | − | 8.27065e8i | − | 0.925261i | −0.886551 | − | 0.462631i | \(-0.846906\pi\) | ||
0.886551 | − | 0.462631i | \(-0.153094\pi\) | |||||||
\(20\) | 1.51849e8i | 0.118632i | ||||||||
\(21\) | 2.29978e9i | 1.27688i | ||||||||
\(22\) | − | 1.07495e9i | − | 0.430953i | ||||||
\(23\) | 1.95836e9 | + | 2.78526e9i | 0.575172 | + | 0.818032i | ||||
\(24\) | −3.86835e9 | −0.843427 | ||||||||
\(25\) | 2.69734e9 | 0.441932 | ||||||||
\(26\) | −1.04953e10 | −1.30672 | ||||||||
\(27\) | −1.10335e10 | −1.05479 | ||||||||
\(28\) | 2.93746e9i | 0.217703i | ||||||||
\(29\) | 1.59943e10 | 0.927210 | 0.463605 | − | 0.886042i | \(-0.346556\pi\) | ||||
0.463605 | + | 0.886042i | \(0.346556\pi\) | |||||||
\(30\) | 1.63811e10i | 0.749020i | ||||||||
\(31\) | 2.16761e10 | 0.787861 | 0.393930 | − | 0.919140i | \(-0.371115\pi\) | ||||
0.393930 | + | 0.919140i | \(0.371115\pi\) | |||||||
\(32\) | −1.08147e10 | −0.314749 | ||||||||
\(33\) | − | 1.58916e10i | − | 0.372880i | ||||||
\(34\) | 5.92232e10i | 1.12756i | ||||||||
\(35\) | −6.58910e10 | −1.02412 | ||||||||
\(36\) | −1.64839e9 | −0.0210350 | ||||||||
\(37\) | 9.88060e10i | 1.04081i | 0.853920 | + | 0.520404i | \(0.174219\pi\) | ||||
−0.853920 | + | 0.520404i | \(0.825781\pi\) | |||||||
\(38\) | − | 1.13961e11i | − | 0.996023i | ||||||
\(39\) | −1.55158e11 | −1.13063 | ||||||||
\(40\) | − | 1.10832e11i | − | 0.676466i | ||||||
\(41\) | 1.77934e10 | 0.0913635 | 0.0456818 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456818 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(42\) | 3.16885e11i | 1.37454i | ||||||||
\(43\) | 4.10966e11i | 1.51191i | 0.654621 | + | 0.755957i | \(0.272828\pi\) | ||||
−0.654621 | + | 0.755957i | \(0.727172\pi\) | |||||||
\(44\) | − | 2.02980e10i | − | 0.0635746i | ||||||
\(45\) | − | 3.69755e10i | − | 0.0989524i | ||||||
\(46\) | 2.69841e11 | + | 3.83778e11i | 0.619160 | + | 0.880593i | ||||
\(47\) | −3.61631e11 | −0.713806 | −0.356903 | − | 0.934141i | \(-0.616167\pi\) | ||||
−0.356903 | + | 0.934141i | \(0.616167\pi\) | |||||||
\(48\) | −6.19851e11 | −1.05584 | ||||||||
\(49\) | −5.96410e11 | −0.879372 | ||||||||
\(50\) | 3.71664e11 | 0.475729 | ||||||||
\(51\) | 8.75529e11i | 0.975617i | ||||||||
\(52\) | −1.98180e11 | −0.192769 | ||||||||
\(53\) | 1.13469e12i | 0.965932i | 0.875639 | + | 0.482966i | \(0.160441\pi\) | ||||
−0.875639 | + | 0.482966i | \(0.839559\pi\) | |||||||
\(54\) | −1.52030e12 | −1.13546 | ||||||||
\(55\) | 4.55310e11 | 0.299067 | ||||||||
\(56\) | − | 2.14400e12i | − | 1.24139i | ||||||
\(57\) | − | 1.68474e12i | − | 0.861806i | ||||||
\(58\) | 2.20383e12 | 0.998120 | ||||||||
\(59\) | 3.54124e12 | 1.42295 | 0.711477 | − | 0.702709i | \(-0.248026\pi\) | ||||
0.711477 | + | 0.702709i | \(0.248026\pi\) | |||||||
\(60\) | 3.09319e11i | 0.110496i | ||||||||
\(61\) | − | 5.08379e12i | − | 1.61763i | −0.588065 | − | 0.808814i | \(-0.700110\pi\) | ||
0.588065 | − | 0.808814i | \(-0.299890\pi\) | |||||||
\(62\) | 2.98673e12 | 0.848114 | ||||||||
\(63\) | − | 7.15275e11i | − | 0.181589i | ||||||
\(64\) | 3.49541e12 | 0.794765 | ||||||||
\(65\) | − | 4.44544e12i | − | 0.906820i | ||||||
\(66\) | − | 2.18969e12i | − | 0.401397i | ||||||
\(67\) | − | 9.73344e12i | − | 1.60599i | −0.595986 | − | 0.802995i | \(-0.703239\pi\) | ||
0.595986 | − | 0.802995i | \(-0.296761\pi\) | |||||||
\(68\) | 1.11829e12i | 0.166339i | ||||||||
\(69\) | 3.98920e12 | + | 5.67360e12i | 0.535726 | + | 0.761931i | ||||
\(70\) | −9.07907e12 | −1.10244 | ||||||||
\(71\) | −4.25884e12 | −0.468255 | −0.234127 | − | 0.972206i | \(-0.575223\pi\) | ||||
−0.234127 | + | 0.972206i | \(0.575223\pi\) | |||||||
\(72\) | 1.20313e12 | 0.119946 | ||||||||
\(73\) | 6.04556e12 | 0.547239 | 0.273619 | − | 0.961838i | \(-0.411779\pi\) | ||||
0.273619 | + | 0.961838i | \(0.411779\pi\) | |||||||
\(74\) | 1.36144e13i | 1.12041i | ||||||||
\(75\) | 5.49451e12 | 0.411623 | ||||||||
\(76\) | − | 2.15188e12i | − | 0.146934i | ||||||
\(77\) | 8.80777e12 | 0.548821 | ||||||||
\(78\) | −2.13791e13 | −1.21710 | ||||||||
\(79\) | 2.57109e13i | 1.33884i | 0.742885 | + | 0.669419i | \(0.233457\pi\) | ||||
−0.742885 | + | 0.669419i | \(0.766543\pi\) | |||||||
\(80\) | − | 1.77594e13i | − | 0.846833i | ||||||
\(81\) | −1.94452e13 | −0.849995 | ||||||||
\(82\) | 2.45174e12 | 0.0983507 | ||||||||
\(83\) | − | 8.42299e12i | − | 0.310399i | −0.987883 | − | 0.155199i | \(-0.950398\pi\) | ||
0.987883 | − | 0.155199i | \(-0.0496020\pi\) | |||||||
\(84\) | 5.98364e12i | 0.202773i | ||||||||
\(85\) | −2.50848e13 | −0.782489 | ||||||||
\(86\) | 5.66267e13i | 1.62754i | ||||||||
\(87\) | 3.25805e13 | 0.863620 | ||||||||
\(88\) | 1.48151e13i | 0.362516i | ||||||||
\(89\) | − | 9.49852e11i | − | 0.0214746i | −0.999942 | − | 0.0107373i | \(-0.996582\pi\) | ||
0.999942 | − | 0.0107373i | \(-0.00341786\pi\) | |||||||
\(90\) | − | 5.09482e12i | − | 0.106520i | ||||||
\(91\) | − | 8.59951e13i | − | 1.66412i | ||||||
\(92\) | 5.09532e12 | + | 7.24677e12i | 0.0913391 | + | 0.129906i | ||||
\(93\) | 4.41545e13 | 0.733828 | ||||||||
\(94\) | −4.98287e13 | −0.768396 | ||||||||
\(95\) | 4.82696e13 | 0.691207 | ||||||||
\(96\) | −2.20297e13 | −0.293163 | ||||||||
\(97\) | − | 3.57714e13i | − | 0.442725i | −0.975192 | − | 0.221363i | \(-0.928950\pi\) | ||
0.975192 | − | 0.221363i | \(-0.0710504\pi\) | |||||||
\(98\) | −8.21788e13 | −0.946624 | ||||||||
\(99\) | 4.94258e12i | 0.0530283i | ||||||||
\(100\) | 7.01801e12 | 0.0701801 | ||||||||
\(101\) | −8.62056e13 | −0.804055 | −0.402028 | − | 0.915628i | \(-0.631694\pi\) | ||||
−0.402028 | + | 0.915628i | \(0.631694\pi\) | |||||||
\(102\) | 1.20638e14i | 1.05023i | ||||||||
\(103\) | 2.14857e14i | 1.74698i | 0.486838 | + | 0.873492i | \(0.338150\pi\) | ||||
−0.486838 | + | 0.873492i | \(0.661850\pi\) | |||||||
\(104\) | 1.44648e14 | 1.09921 | ||||||||
\(105\) | −1.34221e14 | −0.953883 | ||||||||
\(106\) | 1.56348e14i | 1.03980i | ||||||||
\(107\) | − | 3.81103e13i | − | 0.237332i | −0.992934 | − | 0.118666i | \(-0.962138\pi\) | ||
0.992934 | − | 0.118666i | \(-0.0378617\pi\) | |||||||
\(108\) | −2.87073e13 | −0.167505 | ||||||||
\(109\) | − | 1.41808e14i | − | 0.775738i | −0.921714 | − | 0.387869i | \(-0.873211\pi\) | ||
0.921714 | − | 0.387869i | \(-0.126789\pi\) | |||||||
\(110\) | 6.27367e13 | 0.321939 | ||||||||
\(111\) | 2.01269e14i | 0.969429i | ||||||||
\(112\) | − | 3.43547e14i | − | 1.55403i | ||||||
\(113\) | − | 2.74981e13i | − | 0.116884i | −0.998291 | − | 0.0584418i | \(-0.981387\pi\) | ||
0.998291 | − | 0.0584418i | \(-0.0186132\pi\) | |||||||
\(114\) | − | 2.32139e14i | − | 0.927714i | ||||||
\(115\) | −1.62555e14 | + | 1.14295e14i | −0.611103 | + | 0.429676i | ||||
\(116\) | 4.16143e13 | 0.147244 | ||||||||
\(117\) | 4.82571e13 | 0.160790 | ||||||||
\(118\) | 4.87944e14 | 1.53178 | ||||||||
\(119\) | −4.85254e14 | −1.43595 | ||||||||
\(120\) | − | 2.25767e14i | − | 0.630073i | ||||||
\(121\) | 3.18888e14 | 0.839731 | ||||||||
\(122\) | − | 7.00490e14i | − | 1.74134i | ||||||
\(123\) | 3.62454e13 | 0.0850977 | ||||||||
\(124\) | 5.63976e13 | 0.125115 | ||||||||
\(125\) | 5.13640e14i | 1.07718i | ||||||||
\(126\) | − | 9.85571e13i | − | 0.195476i | ||||||
\(127\) | 5.77041e14 | 1.08288 | 0.541441 | − | 0.840739i | \(-0.317879\pi\) | ||||
0.541441 | + | 0.840739i | \(0.317879\pi\) | |||||||
\(128\) | 6.58817e14 | 1.17029 | ||||||||
\(129\) | 8.37144e14i | 1.40823i | ||||||||
\(130\) | − | 6.12533e14i | − | 0.976171i | ||||||
\(131\) | −1.27284e15 | −1.92254 | −0.961269 | − | 0.275611i | \(-0.911120\pi\) | ||||
−0.961269 | + | 0.275611i | \(0.911120\pi\) | |||||||
\(132\) | − | 4.13472e13i | − | 0.0592146i | ||||||
\(133\) | 9.33753e14 | 1.26844 | ||||||||
\(134\) | − | 1.34116e15i | − | 1.72881i | ||||||
\(135\) | − | 6.43943e14i | − | 0.787973i | ||||||
\(136\) | − | 8.16224e14i | − | 0.948499i | ||||||
\(137\) | 5.61791e14i | 0.620199i | 0.950704 | + | 0.310099i | \(0.100362\pi\) | ||||
−0.950704 | + | 0.310099i | \(0.899638\pi\) | |||||||
\(138\) | 5.49669e14 | + | 7.81761e14i | 0.576697 | + | 0.820201i | ||||
\(139\) | −5.55761e14 | −0.554350 | −0.277175 | − | 0.960819i | \(-0.589398\pi\) | ||||
−0.277175 | + | 0.960819i | \(0.589398\pi\) | |||||||
\(140\) | −1.71437e14 | −0.162633 | ||||||||
\(141\) | −7.36646e14 | −0.664852 | ||||||||
\(142\) | −5.86821e14 | −0.504066 | ||||||||
\(143\) | 5.94230e14i | 0.485962i | ||||||||
\(144\) | 1.92785e14 | 0.150154 | ||||||||
\(145\) | 9.33464e14i | 0.692663i | ||||||||
\(146\) | 8.33013e14 | 0.589090 | ||||||||
\(147\) | −1.21490e15 | −0.819063 | ||||||||
\(148\) | 2.57076e14i | 0.165284i | ||||||||
\(149\) | 1.34502e15i | 0.824946i | 0.910970 | + | 0.412473i | \(0.135335\pi\) | ||||
−0.910970 | + | 0.412473i | \(0.864665\pi\) | |||||||
\(150\) | 7.57083e14 | 0.443103 | ||||||||
\(151\) | −1.32797e15 | −0.741907 | −0.370953 | − | 0.928651i | \(-0.620969\pi\) | ||||
−0.370953 | + | 0.928651i | \(0.620969\pi\) | |||||||
\(152\) | 1.57062e15i | 0.837851i | ||||||||
\(153\) | − | 2.72306e14i | − | 0.138745i | ||||||
\(154\) | 1.21362e15 | 0.590794 | ||||||||
\(155\) | 1.26507e15i | 0.588563i | ||||||||
\(156\) | −4.03695e14 | −0.179548 | ||||||||
\(157\) | − | 3.44722e15i | − | 1.46613i | −0.680160 | − | 0.733064i | \(-0.738090\pi\) | ||
0.680160 | − | 0.733064i | \(-0.261910\pi\) | |||||||
\(158\) | 3.54268e15i | 1.44123i | ||||||||
\(159\) | 2.31138e15i | 0.899687i | ||||||||
\(160\) | − | 6.31172e14i | − | 0.235130i | ||||||
\(161\) | −3.14455e15 | + | 2.21098e15i | −1.12144 | + | 0.788504i | ||||
\(162\) | −2.67933e15 | −0.915000 | ||||||||
\(163\) | −4.32305e15 | −1.41409 | −0.707045 | − | 0.707168i | \(-0.749972\pi\) | ||||
−0.707045 | + | 0.707168i | \(0.749972\pi\) | |||||||
\(164\) | 4.62955e13 | 0.0145088 | ||||||||
\(165\) | 9.27472e14 | 0.278556 | ||||||||
\(166\) | − | 1.16060e15i | − | 0.334137i | ||||||
\(167\) | 3.06701e15 | 0.846643 | 0.423322 | − | 0.905979i | \(-0.360864\pi\) | ||||
0.423322 | + | 0.905979i | \(0.360864\pi\) | |||||||
\(168\) | − | 4.36736e15i | − | 1.15626i | ||||||
\(169\) | 1.86441e15 | 0.473516 | ||||||||
\(170\) | −3.45641e15 | −0.842331 | ||||||||
\(171\) | 5.23986e14i | 0.122560i | ||||||||
\(172\) | 1.06926e15i | 0.240097i | ||||||||
\(173\) | 2.23477e15 | 0.481848 | 0.240924 | − | 0.970544i | \(-0.422550\pi\) | ||||
0.240924 | + | 0.970544i | \(0.422550\pi\) | |||||||
\(174\) | 4.48924e15 | 0.929668 | ||||||||
\(175\) | 3.04528e15i | 0.605845i | ||||||||
\(176\) | 2.37393e15i | 0.453815i | ||||||||
\(177\) | 7.21355e15 | 1.32537 | ||||||||
\(178\) | − | 1.30879e14i | − | 0.0231170i | ||||||
\(179\) | 9.99495e14 | 0.169750 | 0.0848749 | − | 0.996392i | \(-0.472951\pi\) | ||||
0.0848749 | + | 0.996392i | \(0.472951\pi\) | |||||||
\(180\) | − | 9.62040e13i | − | 0.0157140i | ||||||
\(181\) | − | 1.15490e14i | − | 0.0181466i | −0.999959 | − | 0.00907329i | \(-0.997112\pi\) | ||
0.999959 | − | 0.00907329i | \(-0.00288816\pi\) | |||||||
\(182\) | − | 1.18492e16i | − | 1.79138i | ||||||
\(183\) | − | 1.03557e16i | − | 1.50669i | ||||||
\(184\) | −3.71899e15 | − | 5.28930e15i | −0.520835 | − | 0.740752i | ||||
\(185\) | −5.76656e15 | −0.777526 | ||||||||
\(186\) | 6.08401e15 | 0.789949 | ||||||||
\(187\) | 3.35313e15 | 0.419333 | ||||||||
\(188\) | −9.40901e14 | −0.113355 | ||||||||
\(189\) | − | 1.24568e16i | − | 1.44602i | ||||||
\(190\) | 6.65102e15 | 0.744068 | ||||||||
\(191\) | 1.30175e16i | 1.40376i | 0.712296 | + | 0.701879i | \(0.247655\pi\) | ||||
−0.712296 | + | 0.701879i | \(0.752345\pi\) | |||||||
\(192\) | 7.12020e15 | 0.740259 | ||||||||
\(193\) | 4.22945e15 | 0.424016 | 0.212008 | − | 0.977268i | \(-0.432000\pi\) | ||||
0.212008 | + | 0.977268i | \(0.432000\pi\) | |||||||
\(194\) | − | 4.92891e15i | − | 0.476584i | ||||||
\(195\) | − | 9.05541e15i | − | 0.844629i | ||||||
\(196\) | −1.55176e15 | −0.139647 | ||||||||
\(197\) | −4.49025e15 | −0.389948 | −0.194974 | − | 0.980808i | \(-0.562462\pi\) | ||||
−0.194974 | + | 0.980808i | \(0.562462\pi\) | |||||||
\(198\) | 6.81034e14i | 0.0570837i | ||||||||
\(199\) | 1.93481e16i | 1.56555i | 0.622308 | + | 0.782773i | \(0.286195\pi\) | ||||
−0.622308 | + | 0.782773i | \(0.713805\pi\) | |||||||
\(200\) | −5.12233e15 | −0.400182 | ||||||||
\(201\) | − | 1.98271e16i | − | 1.49585i | ||||||
\(202\) | −1.18782e16 | −0.865547 | ||||||||
\(203\) | 1.80575e16i | 1.27111i | ||||||||
\(204\) | 2.27798e15i | 0.154931i | ||||||||
\(205\) | 1.03847e15i | 0.0682522i | ||||||||
\(206\) | 2.96050e16i | 1.88059i | ||||||||
\(207\) | −1.24072e15 | − | 1.76460e15i | −0.0761870 | − | 0.108356i | ||||
\(208\) | 2.31779e16 | 1.37604 | ||||||||
\(209\) | −6.45228e15 | −0.370415 | ||||||||
\(210\) | −1.84942e16 | −1.02683 | ||||||||
\(211\) | −1.18264e16 | −0.635149 | −0.317574 | − | 0.948233i | \(-0.602868\pi\) | ||||
−0.317574 | + | 0.948233i | \(0.602868\pi\) | |||||||
\(212\) | 2.95227e15i | 0.153393i | ||||||||
\(213\) | −8.67530e15 | −0.436141 | ||||||||
\(214\) | − | 5.25118e15i | − | 0.255482i | ||||||
\(215\) | −2.39850e16 | −1.12946 | ||||||||
\(216\) | 2.09530e16 | 0.955147 | ||||||||
\(217\) | 2.44723e16i | 1.08008i | ||||||||
\(218\) | − | 1.95396e16i | − | 0.835064i | ||||||
\(219\) | 1.23149e16 | 0.509708 | ||||||||
\(220\) | 1.18464e15 | 0.0474928 | ||||||||
\(221\) | − | 3.27384e16i | − | 1.27149i | ||||||
\(222\) | 2.77327e16i | 1.04357i | ||||||||
\(223\) | 2.42052e16 | 0.882623 | 0.441312 | − | 0.897354i | \(-0.354513\pi\) | ||||
0.441312 | + | 0.897354i | \(0.354513\pi\) | |||||||
\(224\) | − | 1.22097e16i | − | 0.431490i | ||||||
\(225\) | −1.70890e15 | −0.0585380 | ||||||||
\(226\) | − | 3.78894e15i | − | 0.125822i | ||||||
\(227\) | 2.67934e16i | 0.862673i | 0.902191 | + | 0.431337i | \(0.141958\pi\) | ||||
−0.902191 | + | 0.431337i | \(0.858042\pi\) | |||||||
\(228\) | − | 4.38341e15i | − | 0.136857i | ||||||
\(229\) | − | 2.01899e16i | − | 0.611344i | −0.952137 | − | 0.305672i | \(-0.901119\pi\) | ||
0.952137 | − | 0.305672i | \(-0.0988811\pi\) | |||||||
\(230\) | −2.23982e16 | + | 1.57486e16i | −0.657838 | + | 0.462537i | ||||
\(231\) | 1.79415e16 | 0.511182 | ||||||||
\(232\) | −3.03736e16 | −0.839616 | ||||||||
\(233\) | −9.46251e15 | −0.253814 | −0.126907 | − | 0.991915i | \(-0.540505\pi\) | ||||
−0.126907 | + | 0.991915i | \(0.540505\pi\) | |||||||
\(234\) | 6.64930e15 | 0.173087 | ||||||||
\(235\) | − | 2.11057e16i | − | 0.533241i | ||||||
\(236\) | 9.21370e15 | 0.225970 | ||||||||
\(237\) | 5.23734e16i | 1.24702i | ||||||||
\(238\) | −6.68628e16 | −1.54577 | ||||||||
\(239\) | 2.96264e16 | 0.665110 | 0.332555 | − | 0.943084i | \(-0.392089\pi\) | ||||
0.332555 | + | 0.943084i | \(0.392089\pi\) | |||||||
\(240\) | − | 3.61761e16i | − | 0.788756i | ||||||
\(241\) | 9.61938e15i | 0.203717i | 0.994799 | + | 0.101859i | \(0.0324789\pi\) | ||||
−0.994799 | + | 0.101859i | \(0.967521\pi\) | |||||||
\(242\) | 4.39392e16 | 0.903951 | ||||||||
\(243\) | 1.31629e16 | 0.263093 | ||||||||
\(244\) | − | 1.32272e16i | − | 0.256884i | ||||||
\(245\) | − | 3.48080e16i | − | 0.656926i | ||||||
\(246\) | 4.99423e15 | 0.0916057 | ||||||||
\(247\) | 6.29971e16i | 1.12316i | ||||||||
\(248\) | −4.11636e16 | −0.713431 | ||||||||
\(249\) | − | 1.71577e16i | − | 0.289111i | ||||||
\(250\) | 7.07739e16i | 1.15956i | ||||||||
\(251\) | − | 9.84235e15i | − | 0.156813i | −0.996921 | − | 0.0784066i | \(-0.975017\pi\) | ||
0.996921 | − | 0.0784066i | \(-0.0249832\pi\) | |||||||
\(252\) | − | 1.86102e15i | − | 0.0288369i | ||||||
\(253\) | 2.17290e16 | − | 1.52780e16i | 0.327488 | − | 0.230262i | ||||
\(254\) | 7.95100e16 | 1.16570 | ||||||||
\(255\) | −5.10980e16 | −0.728825 | ||||||||
\(256\) | 3.35090e16 | 0.465031 | ||||||||
\(257\) | 7.06118e15 | 0.0953554 | 0.0476777 | − | 0.998863i | \(-0.484818\pi\) | ||||
0.0476777 | + | 0.998863i | \(0.484818\pi\) | |||||||
\(258\) | 1.15349e17i | 1.51592i | ||||||||
\(259\) | −1.11552e17 | −1.42685 | ||||||||
\(260\) | − | 1.15663e16i | − | 0.144006i | ||||||
\(261\) | −1.01331e16 | −0.122818 | ||||||||
\(262\) | −1.75384e17 | −2.06957 | ||||||||
\(263\) | − | 1.23692e17i | − | 1.42119i | −0.703600 | − | 0.710596i | \(-0.748425\pi\) | ||
0.703600 | − | 0.710596i | \(-0.251575\pi\) | |||||||
\(264\) | 3.01786e16i | 0.337654i | ||||||||
\(265\) | −6.62234e16 | −0.721589 | ||||||||
\(266\) | 1.28661e17 | 1.36545 | ||||||||
\(267\) | − | 1.93486e15i | − | 0.0200019i | ||||||
\(268\) | − | 2.53247e16i | − | 0.255036i | ||||||
\(269\) | 1.79119e17 | 1.75742 | 0.878708 | − | 0.477360i | \(-0.158406\pi\) | ||||
0.878708 | + | 0.477360i | \(0.158406\pi\) | |||||||
\(270\) | − | 8.87283e16i | − | 0.848235i | ||||||
\(271\) | 1.41141e17 | 1.31482 | 0.657411 | − | 0.753532i | \(-0.271651\pi\) | ||||
0.657411 | + | 0.753532i | \(0.271651\pi\) | |||||||
\(272\) | − | 1.30789e17i | − | 1.18738i | ||||||
\(273\) | − | 1.75173e17i | − | 1.54999i | ||||||
\(274\) | 7.74087e16i | 0.667630i | ||||||||
\(275\) | − | 2.10431e16i | − | 0.176921i | ||||||
\(276\) | 1.03792e16 | + | 1.47618e16i | 0.0850749 | + | 0.120997i | ||||
\(277\) | 2.20460e17 | 1.76186 | 0.880930 | − | 0.473247i | \(-0.156918\pi\) | ||||
0.880930 | + | 0.473247i | \(0.156918\pi\) | |||||||
\(278\) | −7.65777e16 | −0.596745 | ||||||||
\(279\) | −1.37329e16 | −0.104360 | ||||||||
\(280\) | 1.25129e17 | 0.927369 | ||||||||
\(281\) | − | 1.31107e17i | − | 0.947724i | −0.880599 | − | 0.473862i | \(-0.842860\pi\) | ||
0.880599 | − | 0.473862i | \(-0.157140\pi\) | |||||||
\(282\) | −1.01502e17 | −0.715698 | ||||||||
\(283\) | − | 1.55980e17i | − | 1.07291i | −0.843929 | − | 0.536455i | \(-0.819763\pi\) | ||
0.843929 | − | 0.536455i | \(-0.180237\pi\) | |||||||
\(284\) | −1.10808e16 | −0.0743603 | ||||||||
\(285\) | 9.83257e16 | 0.643803 | ||||||||
\(286\) | 8.18784e16i | 0.523127i | ||||||||
\(287\) | 2.00887e16i | 0.125250i | ||||||||
\(288\) | 6.85164e15 | 0.0416914 | ||||||||
\(289\) | −1.63591e16 | −0.0971574 | ||||||||
\(290\) | 1.28621e17i | 0.745635i | ||||||||
\(291\) | − | 7.28669e16i | − | 0.412362i | ||||||
\(292\) | 1.57295e16 | 0.0869032 | ||||||||
\(293\) | 2.15234e17i | 1.16101i | 0.814256 | + | 0.580506i | \(0.197145\pi\) | ||||
−0.814256 | + | 0.580506i | \(0.802855\pi\) | |||||||
\(294\) | −1.67399e17 | −0.881703 | ||||||||
\(295\) | 2.06675e17i | 1.06300i | ||||||||
\(296\) | − | 1.87636e17i | − | 0.942483i | ||||||
\(297\) | 8.60771e16i | 0.422272i | ||||||||
\(298\) | 1.85329e17i | 0.888036i | ||||||||
\(299\) | −1.49167e17 | − | 2.12152e17i | −0.698193 | − | 0.992997i | ||||
\(300\) | 1.42958e16 | 0.0653671 | ||||||||
\(301\) | −4.63980e17 | −2.07269 | ||||||||
\(302\) | −1.82980e17 | −0.798646 | ||||||||
\(303\) | −1.75602e17 | −0.748912 | ||||||||
\(304\) | 2.51671e17i | 1.04886i | ||||||||
\(305\) | 2.96702e17 | 1.20843 | ||||||||
\(306\) | − | 3.75208e16i | − | 0.149356i | ||||||
\(307\) | −3.06657e17 | −1.19312 | −0.596560 | − | 0.802568i | \(-0.703466\pi\) | ||||
−0.596560 | + | 0.802568i | \(0.703466\pi\) | |||||||
\(308\) | 2.29163e16 | 0.0871546 | ||||||||
\(309\) | 4.37667e17i | 1.62717i | ||||||||
\(310\) | 1.74313e17i | 0.633575i | ||||||||
\(311\) | 2.83499e17 | 1.00746 | 0.503731 | − | 0.863861i | \(-0.331960\pi\) | ||||
0.503731 | + | 0.863861i | \(0.331960\pi\) | |||||||
\(312\) | 2.94650e17 | 1.02382 | ||||||||
\(313\) | 3.67542e17i | 1.24881i | 0.781101 | + | 0.624405i | \(0.214658\pi\) | ||||
−0.781101 | + | 0.624405i | \(0.785342\pi\) | |||||||
\(314\) | − | 4.74990e17i | − | 1.57825i | ||||||
\(315\) | 4.17452e16 | 0.135654 | ||||||||
\(316\) | 6.68954e16i | 0.212612i | ||||||||
\(317\) | 3.77489e16 | 0.117352 | 0.0586759 | − | 0.998277i | \(-0.481312\pi\) | ||||
0.0586759 | + | 0.998277i | \(0.481312\pi\) | |||||||
\(318\) | 3.18483e17i | 0.968492i | ||||||||
\(319\) | − | 1.24778e17i | − | 0.371196i | ||||||
\(320\) | 2.04001e17i | 0.593721i | ||||||||
\(321\) | − | 7.76311e16i | − | 0.221055i | ||||||
\(322\) | −4.33284e17 | + | 3.04649e17i | −1.20721 | + | 0.848807i | ||||
\(323\) | 3.55481e17 | 0.969167 | ||||||||
\(324\) | −5.05930e16 | −0.134982 | ||||||||
\(325\) | −2.05455e17 | −0.536454 | ||||||||
\(326\) | −5.95669e17 | −1.52224 | ||||||||
\(327\) | − | 2.88865e17i | − | 0.722537i | ||||||
\(328\) | −3.37903e16 | −0.0827323 | ||||||||
\(329\) | − | 4.08280e17i | − | 0.978558i | ||||||
\(330\) | 1.27796e17 | 0.299860 | ||||||||
\(331\) | −3.16425e17 | −0.726899 | −0.363450 | − | 0.931614i | \(-0.618401\pi\) | ||||
−0.363450 | + | 0.931614i | \(0.618401\pi\) | |||||||
\(332\) | − | 2.19152e16i | − | 0.0492923i | ||||||
\(333\) | − | 6.25984e16i | − | 0.137865i | ||||||
\(334\) | 4.22601e17 | 0.911392 | ||||||||
\(335\) | 5.68067e17 | 1.19974 | ||||||||
\(336\) | − | 6.99810e17i | − | 1.44746i | ||||||
\(337\) | 4.86788e16i | 0.0986122i | 0.998784 | + | 0.0493061i | \(0.0157010\pi\) | ||||
−0.998784 | + | 0.0493061i | \(0.984299\pi\) | |||||||
\(338\) | 2.56896e17 | 0.509730 | ||||||||
\(339\) | − | 5.60139e16i | − | 0.108868i | ||||||
\(340\) | −6.52664e16 | −0.124262 | ||||||||
\(341\) | − | 1.69104e17i | − | 0.315409i | ||||||
\(342\) | 7.21996e16i | 0.131933i | ||||||||
\(343\) | 9.23664e16i | 0.165369i | ||||||||
\(344\) | − | 7.80439e17i | − | 1.36908i | ||||||
\(345\) | −3.31126e17 | + | 2.32820e17i | −0.569192 | + | 0.400209i | ||||
\(346\) | 3.07927e17 | 0.518698 | ||||||||
\(347\) | 5.16729e17 | 0.853014 | 0.426507 | − | 0.904484i | \(-0.359744\pi\) | ||||
0.426507 | + | 0.904484i | \(0.359744\pi\) | |||||||
\(348\) | 8.47689e16 | 0.137146 | ||||||||
\(349\) | −7.79449e17 | −1.23598 | −0.617988 | − | 0.786188i | \(-0.712052\pi\) | ||||
−0.617988 | + | 0.786188i | \(0.712052\pi\) | |||||||
\(350\) | 4.19607e17i | 0.652178i | ||||||||
\(351\) | 8.40417e17 | 1.28040 | ||||||||
\(352\) | 8.43699e16i | 0.126005i | ||||||||
\(353\) | 4.53420e17 | 0.663862 | 0.331931 | − | 0.943304i | \(-0.392300\pi\) | ||||
0.331931 | + | 0.943304i | \(0.392300\pi\) | |||||||
\(354\) | 9.93948e17 | 1.42673 | ||||||||
\(355\) | − | 2.48556e17i | − | 0.349805i | ||||||
\(356\) | − | 2.47135e15i | − | 0.00341024i | ||||||
\(357\) | −9.88469e17 | −1.33748 | ||||||||
\(358\) | 1.37720e17 | 0.182732 | ||||||||
\(359\) | − | 9.69024e17i | − | 1.26088i | −0.776238 | − | 0.630439i | \(-0.782875\pi\) | ||
0.776238 | − | 0.630439i | \(-0.217125\pi\) | |||||||
\(360\) | 7.02177e16i | 0.0896043i | ||||||||
\(361\) | 1.14970e17 | 0.143892 | ||||||||
\(362\) | − | 1.59133e16i | − | 0.0195344i | ||||||
\(363\) | 6.49578e17 | 0.782141 | ||||||||
\(364\) | − | 2.23745e17i | − | 0.264267i | ||||||
\(365\) | 3.52834e17i | 0.408809i | ||||||||
\(366\) | − | 1.42691e18i | − | 1.62192i | ||||||
\(367\) | 8.63965e17i | 0.963460i | 0.876320 | + | 0.481730i | \(0.159991\pi\) | ||||
−0.876320 | + | 0.481730i | \(0.840009\pi\) | |||||||
\(368\) | −5.95918e17 | − | 8.47538e17i | −0.652006 | − | 0.927309i | ||||
\(369\) | −1.12730e16 | −0.0121020 | ||||||||
\(370\) | −7.94569e17 | −0.836989 | ||||||||
\(371\) | −1.28106e18 | −1.32420 | ||||||||
\(372\) | 1.14883e17 | 0.116534 | ||||||||
\(373\) | 8.42416e17i | 0.838620i | 0.907843 | + | 0.419310i | \(0.137728\pi\) | ||||
−0.907843 | + | 0.419310i | \(0.862272\pi\) | |||||||
\(374\) | 4.62025e17 | 0.451403 | ||||||||
\(375\) | 1.04629e18i | 1.00331i | ||||||||
\(376\) | 6.86748e17 | 0.646372 | ||||||||
\(377\) | −1.21827e18 | −1.12553 | ||||||||
\(378\) | − | 1.71641e18i | − | 1.55661i | ||||||
\(379\) | 1.62272e17i | 0.144467i | 0.997388 | + | 0.0722334i | \(0.0230126\pi\) | ||||
−0.997388 | + | 0.0722334i | \(0.976987\pi\) | |||||||
\(380\) | 1.25589e17 | 0.109766 | ||||||||
\(381\) | 1.17544e18 | 1.00862 | ||||||||
\(382\) | 1.79366e18i | 1.51111i | ||||||||
\(383\) | 5.04550e17i | 0.417362i | 0.977984 | + | 0.208681i | \(0.0669170\pi\) | ||||
−0.977984 | + | 0.208681i | \(0.933083\pi\) | |||||||
\(384\) | 1.34202e18 | 1.09003 | ||||||||
\(385\) | 5.14043e17i | 0.409991i | ||||||||
\(386\) | 5.82771e17 | 0.456444 | ||||||||
\(387\) | − | 2.60368e17i | − | 0.200267i | ||||||
\(388\) | − | 9.30712e16i | − | 0.0703061i | ||||||
\(389\) | 5.34673e17i | 0.396681i | 0.980133 | + | 0.198340i | \(0.0635552\pi\) | ||||
−0.980133 | + | 0.198340i | \(0.936445\pi\) | |||||||
\(390\) | − | 1.24774e18i | − | 0.909224i | ||||||
\(391\) | −1.19713e18 | + | 8.41724e17i | −0.856850 | + | 0.602466i | ||||
\(392\) | 1.13260e18 | 0.796297 | ||||||||
\(393\) | −2.59279e18 | −1.79069 | ||||||||
\(394\) | −6.18708e17 | −0.419771 | ||||||||
\(395\) | −1.50055e18 | −1.00016 | ||||||||
\(396\) | 1.28598e16i | 0.00842106i | ||||||||
\(397\) | −1.02854e18 | −0.661740 | −0.330870 | − | 0.943676i | \(-0.607342\pi\) | ||||
−0.330870 | + | 0.943676i | \(0.607342\pi\) | |||||||
\(398\) | 2.66595e18i | 1.68527i | ||||||||
\(399\) | 1.90207e18 | 1.18145 | ||||||||
\(400\) | −8.20784e17 | −0.500967 | ||||||||
\(401\) | 2.01703e18i | 1.20977i | 0.796313 | + | 0.604884i | \(0.206781\pi\) | ||||
−0.796313 | + | 0.604884i | \(0.793219\pi\) | |||||||
\(402\) | − | 2.73196e18i | − | 1.61025i | ||||||
\(403\) | −1.65106e18 | −0.956372 | ||||||||
\(404\) | −2.24292e17 | −0.127686 | ||||||||
\(405\) | − | 1.13487e18i | − | 0.634980i | ||||||
\(406\) | 2.48812e18i | 1.36832i | ||||||||
\(407\) | 7.70826e17 | 0.416673 | ||||||||
\(408\) | − | 1.66266e18i | − | 0.883450i | ||||||
\(409\) | 1.95903e18 | 1.02324 | 0.511621 | − | 0.859211i | \(-0.329045\pi\) | ||||
0.511621 | + | 0.859211i | \(0.329045\pi\) | |||||||
\(410\) | 1.43090e17i | 0.0734719i | ||||||||
\(411\) | 1.14438e18i | 0.577665i | ||||||||
\(412\) | 5.59022e17i | 0.277427i | ||||||||
\(413\) | 3.99805e18i | 1.95073i | ||||||||
\(414\) | −1.70957e17 | − | 2.43142e17i | −0.0820135 | − | 0.116643i | ||||
\(415\) | 4.91587e17 | 0.231880 | ||||||||
\(416\) | 8.23749e17 | 0.382069 | ||||||||
\(417\) | −1.13209e18 | −0.516332 | ||||||||
\(418\) | −8.89053e17 | −0.398744 | ||||||||
\(419\) | − | 4.15676e18i | − | 1.83340i | −0.399579 | − | 0.916699i | \(-0.630844\pi\) | ||
0.399579 | − | 0.916699i | \(-0.369156\pi\) | |||||||
\(420\) | −3.49220e17 | −0.151480 | ||||||||
\(421\) | − | 2.76660e18i | − | 1.18025i | −0.807314 | − | 0.590123i | \(-0.799079\pi\) | ||
0.807314 | − | 0.590123i | \(-0.200921\pi\) | |||||||
\(422\) | −1.62955e18 | −0.683723 | ||||||||
\(423\) | 2.29111e17 | 0.0945503 | ||||||||
\(424\) | − | 2.15482e18i | − | 0.874680i | ||||||
\(425\) | 1.15934e18i | 0.462903i | ||||||||
\(426\) | −1.19536e18 | −0.469496 | ||||||||
\(427\) | 5.73958e18 | 2.21761 | ||||||||
\(428\) | − | 9.91565e16i | − | 0.0376890i | ||||||
\(429\) | 1.21045e18i | 0.452634i | ||||||||
\(430\) | −3.30487e18 | −1.21584 | ||||||||
\(431\) | − | 3.54954e18i | − | 1.28479i | −0.766375 | − | 0.642393i | \(-0.777942\pi\) | ||
0.766375 | − | 0.642393i | \(-0.222058\pi\) | |||||||
\(432\) | 3.35744e18 | 1.19570 | ||||||||
\(433\) | − | 9.99469e17i | − | 0.350230i | −0.984548 | − | 0.175115i | \(-0.943970\pi\) | ||
0.984548 | − | 0.175115i | \(-0.0560298\pi\) | |||||||
\(434\) | 3.37201e18i | 1.16268i | ||||||||
\(435\) | 1.90148e18i | 0.645159i | ||||||||
\(436\) | − | 3.68960e17i | − | 0.123190i | ||||||
\(437\) | 2.30359e18 | − | 1.61969e18i | 0.756894 | − | 0.532184i | ||||
\(438\) | 1.69686e18 | 0.548689 | ||||||||
\(439\) | 6.16885e17 | 0.196315 | 0.0981573 | − | 0.995171i | \(-0.468705\pi\) | ||||
0.0981573 | + | 0.995171i | \(0.468705\pi\) | |||||||
\(440\) | −8.64649e17 | −0.270814 | ||||||||
\(441\) | 3.77855e17 | 0.116481 | ||||||||
\(442\) | − | 4.51100e18i | − | 1.36873i | ||||||
\(443\) | −4.96476e18 | −1.48276 | −0.741382 | − | 0.671083i | \(-0.765829\pi\) | ||||
−0.741382 | + | 0.671083i | \(0.765829\pi\) | |||||||
\(444\) | 5.23668e17i | 0.153948i | ||||||||
\(445\) | 5.54357e16 | 0.0160424 | ||||||||
\(446\) | 3.33522e18 | 0.950124 | ||||||||
\(447\) | 2.73983e18i | 0.768370i | ||||||||
\(448\) | 3.94631e18i | 1.08954i | ||||||||
\(449\) | −6.59082e18 | −1.79149 | −0.895746 | − | 0.444566i | \(-0.853358\pi\) | ||||
−0.895746 | + | 0.444566i | \(0.853358\pi\) | |||||||
\(450\) | −2.35467e17 | −0.0630148 | ||||||||
\(451\) | − | 1.38814e17i | − | 0.0365761i | ||||||
\(452\) | − | 7.15454e16i | − | 0.0185615i | ||||||
\(453\) | −2.70509e18 | −0.691026 | ||||||||
\(454\) | 3.69183e18i | 0.928648i | ||||||||
\(455\) | 5.01889e18 | 1.24316 | ||||||||
\(456\) | 3.19938e18i | 0.780390i | ||||||||
\(457\) | − | 1.50674e18i | − | 0.361930i | −0.983490 | − | 0.180965i | \(-0.942078\pi\) | ||
0.983490 | − | 0.180965i | \(-0.0579221\pi\) | |||||||
\(458\) | − | 2.78195e18i | − | 0.658098i | ||||||
\(459\) | − | 4.74232e18i | − | 1.10485i | ||||||
\(460\) | −4.22939e17 | + | 2.97376e17i | −0.0970450 | + | 0.0682339i | ||||
\(461\) | 8.19334e18 | 1.85163 | 0.925816 | − | 0.377975i | \(-0.123379\pi\) | ||||
0.925816 | + | 0.377975i | \(0.123379\pi\) | |||||||
\(462\) | 2.47215e18 | 0.550276 | ||||||||
\(463\) | −5.62016e18 | −1.23220 | −0.616101 | − | 0.787667i | \(-0.711289\pi\) | ||||
−0.616101 | + | 0.787667i | \(0.711289\pi\) | |||||||
\(464\) | −4.86696e18 | −1.05107 | ||||||||
\(465\) | 2.57697e18i | 0.548199i | ||||||||
\(466\) | −1.30383e18 | −0.273225 | ||||||||
\(467\) | − | 4.43115e18i | − | 0.914741i | −0.889276 | − | 0.457371i | \(-0.848791\pi\) | ||
0.889276 | − | 0.457371i | \(-0.151209\pi\) | |||||||
\(468\) | 1.25557e17 | 0.0255340 | ||||||||
\(469\) | 1.09890e19 | 2.20165 | ||||||||
\(470\) | − | 2.90813e18i | − | 0.574022i | ||||||
\(471\) | − | 7.02204e18i | − | 1.36558i | ||||||
\(472\) | −6.72493e18 | −1.28853 | ||||||||
\(473\) | 3.20612e18 | 0.605274 | ||||||||
\(474\) | 7.21649e18i | 1.34239i | ||||||||
\(475\) | − | 2.23087e18i | − | 0.408902i | ||||||
\(476\) | −1.26255e18 | −0.228034 | ||||||||
\(477\) | − | 7.18883e17i | − | 0.127947i | ||||||
\(478\) | 4.08219e18 | 0.715976 | ||||||||
\(479\) | − | 7.29563e18i | − | 1.26100i | −0.776190 | − | 0.630499i | \(-0.782850\pi\) | ||
0.776190 | − | 0.630499i | \(-0.217150\pi\) | |||||||
\(480\) | − | 1.28570e18i | − | 0.219004i | ||||||
\(481\) | − | 7.52600e18i | − | 1.26342i | ||||||
\(482\) | 1.32545e18i | 0.219297i | ||||||||
\(483\) | −6.40548e18 | + | 4.50380e18i | −1.04453 | + | 0.734428i | ||||
\(484\) | 8.29692e17 | 0.133352 | ||||||||
\(485\) | 2.08771e18 | 0.330733 | ||||||||
\(486\) | 1.81371e18 | 0.283213 | ||||||||
\(487\) | 3.34405e18 | 0.514719 | 0.257359 | − | 0.966316i | \(-0.417148\pi\) | ||||
0.257359 | + | 0.966316i | \(0.417148\pi\) | |||||||
\(488\) | 9.65428e18i | 1.46481i | ||||||||
\(489\) | −8.80611e18 | −1.31711 | ||||||||
\(490\) | − | 4.79616e18i | − | 0.707165i | ||||||
\(491\) | 1.15300e19 | 1.67594 | 0.837969 | − | 0.545718i | \(-0.183743\pi\) | ||||
0.837969 | + | 0.545718i | \(0.183743\pi\) | |||||||
\(492\) | 9.43045e16 | 0.0135138 | ||||||||
\(493\) | 6.87450e18i | 0.971208i | ||||||||
\(494\) | 8.68031e18i | 1.20906i | ||||||||
\(495\) | −2.88461e17 | −0.0396142 | ||||||||
\(496\) | −6.59592e18 | −0.893107 | ||||||||
\(497\) | − | 4.80821e18i | − | 0.641932i | ||||||
\(498\) | − | 2.36415e18i | − | 0.311221i | ||||||
\(499\) | 2.63099e18 | 0.341520 | 0.170760 | − | 0.985313i | \(-0.445378\pi\) | ||||
0.170760 | + | 0.985313i | \(0.445378\pi\) | |||||||
\(500\) | 1.33640e18i | 0.171060i | ||||||||
\(501\) | 6.24755e18 | 0.788579 | ||||||||
\(502\) | − | 1.35617e18i | − | 0.168806i | ||||||
\(503\) | − | 6.37067e17i | − | 0.0782004i | −0.999235 | − | 0.0391002i | \(-0.987551\pi\) | ||
0.999235 | − | 0.0391002i | \(-0.0124492\pi\) | |||||||
\(504\) | 1.35833e18i | 0.164434i | ||||||||
\(505\) | − | 5.03117e18i | − | 0.600661i | ||||||
\(506\) | 2.99401e18 | − | 2.10514e18i | 0.352533 | − | 0.247872i | ||||
\(507\) | 3.79783e18 | 0.441042 | ||||||||
\(508\) | 1.50136e18 | 0.171965 | ||||||||
\(509\) | −1.18529e19 | −1.33906 | −0.669528 | − | 0.742787i | \(-0.733504\pi\) | ||||
−0.669528 | + | 0.742787i | \(0.733504\pi\) | |||||||
\(510\) | −7.04075e18 | −0.784563 | ||||||||
\(511\) | 6.82542e18i | 0.750210i | ||||||||
\(512\) | −6.17689e18 | −0.669700 | ||||||||
\(513\) | 9.12543e18i | 0.975960i | ||||||||
\(514\) | 9.72953e17 | 0.102648 | ||||||||
\(515\) | −1.25396e19 | −1.30507 | ||||||||
\(516\) | 2.17811e18i | 0.223631i | ||||||||
\(517\) | 2.82123e18i | 0.285762i | ||||||||
\(518\) | −1.53706e19 | −1.53597 | ||||||||
\(519\) | 4.55225e18 | 0.448802 | ||||||||
\(520\) | 8.44203e18i | 0.821152i | ||||||||
\(521\) | − | 8.24803e18i | − | 0.791565i | −0.918344 | − | 0.395782i | \(-0.870473\pi\) | ||
0.918344 | − | 0.395782i | \(-0.129527\pi\) | |||||||
\(522\) | −1.39624e18 | −0.132210 | ||||||||
\(523\) | 1.82691e19i | 1.70689i | 0.521185 | + | 0.853444i | \(0.325490\pi\) | ||||
−0.521185 | + | 0.853444i | \(0.674510\pi\) | |||||||
\(524\) | −3.31172e18 | −0.305305 | ||||||||
\(525\) | 6.20328e18i | 0.564295i | ||||||||
\(526\) | − | 1.70435e19i | − | 1.52988i | ||||||
\(527\) | 9.31662e18i | 0.825247i | ||||||||
\(528\) | 4.83572e18i | 0.422692i | ||||||||
\(529\) | −3.92249e18 | + | 1.09091e19i | −0.338354 | + | 0.941019i | ||||
\(530\) | −9.12486e18 | −0.776775 | ||||||||
\(531\) | −2.24355e18 | −0.188484 | ||||||||
\(532\) | 2.42947e18 | 0.201433 | ||||||||
\(533\) | −1.35532e18 | −0.110905 | ||||||||
\(534\) | − | 2.66603e17i | − | 0.0215316i | ||||||
\(535\) | 2.22421e18 | 0.177296 | ||||||||
\(536\) | 1.84841e19i | 1.45427i | ||||||||
\(537\) | 2.03598e18 | 0.158108 | ||||||||
\(538\) | 2.46806e19 | 1.89182 | ||||||||
\(539\) | 4.65285e18i | 0.352044i | ||||||||
\(540\) | − | 1.67543e18i | − | 0.125133i | ||||||
\(541\) | −2.44163e19 | −1.80011 | −0.900053 | − | 0.435780i | \(-0.856473\pi\) | ||||
−0.900053 | + | 0.435780i | \(0.856473\pi\) | |||||||
\(542\) | 1.94476e19 | 1.41538 | ||||||||
\(543\) | − | 2.35255e17i | − | 0.0169021i | ||||||
\(544\) | − | 4.64826e18i | − | 0.329685i | ||||||
\(545\) | 8.27626e18 | 0.579507 | ||||||||
\(546\) | − | 2.41369e19i | − | 1.66853i | ||||||
\(547\) | 2.53778e19 | 1.73198 | 0.865990 | − | 0.500061i | \(-0.166689\pi\) | ||||
0.865990 | + | 0.500061i | \(0.166689\pi\) | |||||||
\(548\) | 1.46168e18i | 0.0984895i | ||||||||
\(549\) | 3.22083e18i | 0.214270i | ||||||||
\(550\) | − | 2.89950e18i | − | 0.190452i | ||||||
\(551\) | − | 1.32283e19i | − | 0.857911i | ||||||
\(552\) | −7.57563e18 | − | 1.07744e19i | −0.485115 | − | 0.689951i | ||||
\(553\) | −2.90275e19 | −1.83541 | ||||||||
\(554\) | 3.03770e19 | 1.89660 | ||||||||
\(555\) | −1.17466e19 | −0.724202 | ||||||||
\(556\) | −1.44599e18 | −0.0880325 | ||||||||
\(557\) | − | 2.07893e19i | − | 1.24984i | −0.780689 | − | 0.624920i | \(-0.785132\pi\) | ||
0.780689 | − | 0.624920i | \(-0.214868\pi\) | |||||||
\(558\) | −1.89224e18 | −0.112341 | ||||||||
\(559\) | − | 3.13031e19i | − | 1.83529i | ||||||
\(560\) | 2.00503e19 | 1.16092 | ||||||||
\(561\) | 6.83037e18 | 0.390575 | ||||||||
\(562\) | − | 1.80651e19i | − | 1.02020i | ||||||
\(563\) | − | 2.61350e19i | − | 1.45769i | −0.684681 | − | 0.728843i | \(-0.740058\pi\) | ||
0.684681 | − | 0.728843i | \(-0.259942\pi\) | |||||||
\(564\) | −1.91663e18 | −0.105581 | ||||||||
\(565\) | 1.60486e18 | 0.0873166 | ||||||||
\(566\) | − | 2.14923e19i | − | 1.15496i | ||||||
\(567\) | − | 2.19535e19i | − | 1.16526i | ||||||
\(568\) | 8.08767e18 | 0.424019 | ||||||||
\(569\) | 2.59722e19i | 1.34500i | 0.740097 | + | 0.672500i | \(0.234780\pi\) | ||||
−0.740097 | + | 0.672500i | \(0.765220\pi\) | |||||||
\(570\) | 1.35482e19 | 0.693039 | ||||||||
\(571\) | 1.54450e19i | 0.780430i | 0.920724 | + | 0.390215i | \(0.127599\pi\) | ||||
−0.920724 | + | 0.390215i | \(0.872401\pi\) | |||||||
\(572\) | 1.54609e18i | 0.0771723i | ||||||||
\(573\) | 2.65167e19i | 1.30749i | ||||||||
\(574\) | 2.76801e18i | 0.134829i | ||||||||
\(575\) | 5.28236e18 | + | 7.51278e18i | 0.254187 | + | 0.361515i | ||||
\(576\) | −2.21452e18 | −0.105274 | ||||||||
\(577\) | −8.16943e18 | −0.383673 | −0.191836 | − | 0.981427i | \(-0.561444\pi\) | ||||
−0.191836 | + | 0.981427i | \(0.561444\pi\) | |||||||
\(578\) | −2.25411e18 | −0.104588 | ||||||||
\(579\) | 8.61543e18 | 0.394936 | ||||||||
\(580\) | 2.42872e18i | 0.109997i | ||||||||
\(581\) | 9.50953e18 | 0.425526 | ||||||||
\(582\) | − | 1.00403e19i | − | 0.443899i | ||||||
\(583\) | 8.85220e18 | 0.386697 | ||||||||
\(584\) | −1.14807e19 | −0.495541 | ||||||||
\(585\) | 2.81640e18i | 0.120117i | ||||||||
\(586\) | 2.96568e19i | 1.24980i | ||||||||
\(587\) | 2.20336e19 | 0.917528 | 0.458764 | − | 0.888558i | \(-0.348292\pi\) | ||||
0.458764 | + | 0.888558i | \(0.348292\pi\) | |||||||
\(588\) | −3.16095e18 | −0.130070 | ||||||||
\(589\) | − | 1.79276e19i | − | 0.728977i | ||||||
\(590\) | 2.84776e19i | 1.14430i | ||||||||
\(591\) | −9.14670e18 | −0.363205 | ||||||||
\(592\) | − | 3.00661e19i | − | 1.17985i | ||||||
\(593\) | 1.65096e19 | 0.640258 | 0.320129 | − | 0.947374i | \(-0.396274\pi\) | ||||
0.320129 | + | 0.947374i | \(0.396274\pi\) | |||||||
\(594\) | 1.18605e19i | 0.454566i | ||||||||
\(595\) | − | 2.83207e19i | − | 1.07272i | ||||||
\(596\) | 3.49952e18i | 0.131004i | ||||||||
\(597\) | 3.94122e19i | 1.45818i | ||||||||
\(598\) | −2.05536e19 | − | 2.92322e19i | −0.751588 | − | 1.06894i | ||||
\(599\) | −2.68291e19 | −0.969656 | −0.484828 | − | 0.874610i | \(-0.661118\pi\) | ||||
−0.484828 | + | 0.874610i | \(0.661118\pi\) | |||||||
\(600\) | −1.04343e19 | −0.372737 | ||||||||
\(601\) | 7.15467e18 | 0.252620 | 0.126310 | − | 0.991991i | \(-0.459687\pi\) | ||||
0.126310 | + | 0.991991i | \(0.459687\pi\) | |||||||
\(602\) | −6.39313e19 | −2.23120 | ||||||||
\(603\) | 6.16661e18i | 0.212728i | ||||||||
\(604\) | −3.45515e18 | −0.117817 | ||||||||
\(605\) | 1.86111e19i | 0.627312i | ||||||||
\(606\) | −2.41960e19 | −0.806187 | ||||||||
\(607\) | −2.88767e18 | −0.0951102 | −0.0475551 | − | 0.998869i | \(-0.515143\pi\) | ||||
−0.0475551 | + | 0.998869i | \(0.515143\pi\) | |||||||
\(608\) | 8.94445e18i | 0.291225i | ||||||||
\(609\) | 3.67833e19i | 1.18394i | ||||||||
\(610\) | 4.08824e19 | 1.30085 | ||||||||
\(611\) | 2.75452e19 | 0.866478 | ||||||||
\(612\) | − | 7.08494e17i | − | 0.0220331i | ||||||
\(613\) | 5.05757e19i | 1.55496i | 0.628910 | + | 0.777478i | \(0.283501\pi\) | ||||
−0.628910 | + | 0.777478i | \(0.716499\pi\) | |||||||
\(614\) | −4.22540e19 | −1.28437 | ||||||||
\(615\) | 2.11537e18i | 0.0635713i | ||||||||
\(616\) | −1.67262e19 | −0.496974 | ||||||||
\(617\) | − | 3.52476e19i | − | 1.03546i | −0.855544 | − | 0.517730i | \(-0.826777\pi\) | ||
0.855544 | − | 0.517730i | \(-0.173223\pi\) | |||||||
\(618\) | 6.03057e19i | 1.75162i | ||||||||
\(619\) | − | 2.23761e19i | − | 0.642613i | −0.946975 | − | 0.321307i | \(-0.895878\pi\) | ||
0.946975 | − | 0.321307i | \(-0.104122\pi\) | |||||||
\(620\) | 3.29150e18i | 0.0934657i | ||||||||
\(621\) | −2.16076e19 | − | 3.07312e19i | −0.606688 | − | 0.862856i | ||||
\(622\) | 3.90630e19 | 1.08451 | ||||||||
\(623\) | 1.07238e18 | 0.0294396 | ||||||||
\(624\) | 4.72137e19 | 1.28167 | ||||||||
\(625\) | −1.35140e19 | −0.362765 | ||||||||
\(626\) | 5.06432e19i | 1.34431i | ||||||||
\(627\) | −1.31434e19 | −0.345012 | ||||||||
\(628\) | − | 8.96909e18i | − | 0.232826i | ||||||
\(629\) | −4.24678e19 | −1.09020 | ||||||||
\(630\) | 5.75204e18 | 0.146029 | ||||||||
\(631\) | − | 5.32087e19i | − | 1.33591i | −0.744202 | − | 0.667955i | \(-0.767170\pi\) | ||
0.744202 | − | 0.667955i | \(-0.232830\pi\) | |||||||
\(632\) | − | 4.88259e19i | − | 1.21236i | ||||||
\(633\) | −2.40905e19 | −0.591589 | ||||||||
\(634\) | 5.20139e18 | 0.126326 | ||||||||
\(635\) | 3.36776e19i | 0.808955i | ||||||||
\(636\) | 6.01382e18i | 0.142873i | ||||||||
\(637\) | 4.54283e19 | 1.06746 | ||||||||
\(638\) | − | 1.71930e19i | − | 0.399583i | ||||||
\(639\) | 2.69818e18 | 0.0620248 | ||||||||
\(640\) | 3.84502e19i | 0.874257i | ||||||||
\(641\) | 4.52785e19i | 1.01832i | 0.860671 | + | 0.509162i | \(0.170045\pi\) | ||||
−0.860671 | + | 0.509162i | \(0.829955\pi\) | |||||||
\(642\) | − | 1.06967e19i | − | 0.237961i | ||||||
\(643\) | 1.88343e19i | 0.414451i | 0.978293 | + | 0.207225i | \(0.0664434\pi\) | ||||
−0.978293 | + | 0.207225i | \(0.933557\pi\) | |||||||
\(644\) | −8.18158e18 | + | 5.75260e18i | −0.178089 | + | 0.125217i | ||||
\(645\) | −4.88578e19 | −1.05200 | ||||||||
\(646\) | 4.89814e19 | 1.04329 | ||||||||
\(647\) | 7.80559e19 | 1.64466 | 0.822329 | − | 0.569013i | \(-0.192674\pi\) | ||||
0.822329 | + | 0.569013i | \(0.192674\pi\) | |||||||
\(648\) | 3.69270e19 | 0.769695 | ||||||||
\(649\) | − | 2.76267e19i | − | 0.569660i | ||||||
\(650\) | −2.83094e19 | −0.577481 | ||||||||
\(651\) | 4.98503e19i | 1.00601i | ||||||||
\(652\) | −1.12478e19 | −0.224562 | ||||||||
\(653\) | −7.58993e19 | −1.49915 | −0.749576 | − | 0.661918i | \(-0.769743\pi\) | ||||
−0.749576 | + | 0.661918i | \(0.769743\pi\) | |||||||
\(654\) | − | 3.98024e19i | − | 0.777794i | ||||||
\(655\) | − | 7.42862e19i | − | 1.43621i | ||||||
\(656\) | −5.41444e18 | −0.103568 | ||||||||
\(657\) | −3.83016e18 | −0.0724869 | ||||||||
\(658\) | − | 5.62565e19i | − | 1.05340i | ||||||
\(659\) | − | 4.77947e19i | − | 0.885487i | −0.896648 | − | 0.442744i | \(-0.854005\pi\) | ||
0.896648 | − | 0.442744i | \(-0.145995\pi\) | |||||||
\(660\) | 2.41313e18 | 0.0442356 | ||||||||
\(661\) | 5.44299e19i | 0.987250i | 0.869675 | + | 0.493625i | \(0.164329\pi\) | ||||
−0.869675 | + | 0.493625i | \(0.835671\pi\) | |||||||
\(662\) | −4.35998e19 | −0.782490 | ||||||||
\(663\) | − | 6.66886e19i | − | 1.18429i | ||||||
\(664\) | 1.59955e19i | 0.281075i | ||||||||
\(665\) | 5.44962e19i | 0.947577i | ||||||||
\(666\) | − | 8.62538e18i | − | 0.148408i | ||||||
\(667\) | 3.13225e19 | + | 4.45481e19i | 0.533305 | + | 0.758488i | ||||
\(668\) | 7.97985e18 | 0.134450 | ||||||||
\(669\) | 4.93064e19 | 0.822092 | ||||||||
\(670\) | 7.82735e19 | 1.29149 | ||||||||
\(671\) | −3.96607e19 | −0.647595 | ||||||||
\(672\) | − | 2.48714e19i | − | 0.401898i | ||||||
\(673\) | −9.01741e19 | −1.44204 | −0.721018 | − | 0.692916i | \(-0.756326\pi\) | ||||
−0.721018 | + | 0.692916i | \(0.756326\pi\) | |||||||
\(674\) | 6.70741e18i | 0.106154i | ||||||||
\(675\) | −2.97611e19 | −0.466147 | ||||||||
\(676\) | 4.85088e18 | 0.0751959 | ||||||||
\(677\) | 8.16439e19i | 1.25257i | 0.779593 | + | 0.626286i | \(0.215426\pi\) | ||||
−0.779593 | + | 0.626286i | \(0.784574\pi\) | |||||||
\(678\) | − | 7.71811e18i | − | 0.117193i | ||||||
\(679\) | 4.03858e19 | 0.606933 | ||||||||
\(680\) | 4.76368e19 | 0.708567 | ||||||||
\(681\) | 5.45784e19i | 0.803510i | ||||||||
\(682\) | − | 2.33007e19i | − | 0.339531i | ||||||
\(683\) | 9.14636e19 | 1.31918 | 0.659589 | − | 0.751626i | \(-0.270730\pi\) | ||||
0.659589 | + | 0.751626i | \(0.270730\pi\) | |||||||
\(684\) | 1.36332e18i | 0.0194628i | ||||||||
\(685\) | −3.27875e19 | −0.463313 | ||||||||
\(686\) | 1.27271e19i | 0.178016i | ||||||||
\(687\) | − | 4.11271e19i | − | 0.569417i | ||||||
\(688\) | − | 1.25055e20i | − | 1.71388i | ||||||
\(689\) | − | 8.64288e19i | − | 1.17253i | ||||||
\(690\) | −4.56255e19 | + | 3.20800e19i | −0.612723 | + | 0.430815i | ||||
\(691\) | 4.85514e18 | 0.0645439 | 0.0322720 | − | 0.999479i | \(-0.489726\pi\) | ||||
0.0322720 | + | 0.999479i | \(0.489726\pi\) | |||||||
\(692\) | 5.81449e18 | 0.0765189 | ||||||||
\(693\) | −5.58016e18 | −0.0726966 | ||||||||
\(694\) | 7.11996e19 | 0.918250 | ||||||||
\(695\) | − | 3.24356e19i | − | 0.414122i | ||||||
\(696\) | −6.18714e19 | −0.782034 | ||||||||
\(697\) | 7.64780e18i | 0.0956990i | ||||||||
\(698\) | −1.07400e20 | −1.33050 | ||||||||
\(699\) | −1.92753e19 | −0.236407 | ||||||||
\(700\) | 7.92331e18i | 0.0962101i | ||||||||
\(701\) | 9.49951e19i | 1.14202i | 0.820942 | + | 0.571012i | \(0.193449\pi\) | ||||
−0.820942 | + | 0.571012i | \(0.806551\pi\) | |||||||
\(702\) | 1.15800e20 | 1.37832 | ||||||||
\(703\) | 8.17189e19 | 0.963020 | ||||||||
\(704\) | − | 2.72692e19i | − | 0.318173i | ||||||
\(705\) | − | 4.29925e19i | − | 0.496671i | ||||||
\(706\) | 6.24763e19 | 0.714632 | ||||||||
\(707\) | − | 9.73258e19i | − | 1.10228i | ||||||
\(708\) | 1.87684e19 | 0.210472 | ||||||||
\(709\) | 3.80305e19i | 0.422287i | 0.977455 | + | 0.211144i | \(0.0677188\pi\) | ||||
−0.977455 | + | 0.211144i | \(0.932281\pi\) | |||||||
\(710\) | − | 3.42483e19i | − | 0.376557i | ||||||
\(711\) | − | 1.62891e19i | − | 0.177342i | ||||||
\(712\) | 1.80380e18i | 0.0194459i | ||||||||
\(713\) | 4.24496e19 | + | 6.03736e19i | 0.453156 | + | 0.644496i | ||||
\(714\) | −1.36200e20 | −1.43976 | ||||||||
\(715\) | −3.46807e19 | −0.363033 | ||||||||
\(716\) | 2.60052e18 | 0.0269568 | ||||||||
\(717\) | 6.03493e19 | 0.619496 | ||||||||
\(718\) | − | 1.33521e20i | − | 1.35731i | ||||||
\(719\) | 1.16463e20 | 1.17243 | 0.586215 | − | 0.810156i | \(-0.300617\pi\) | ||||
0.586215 | + | 0.810156i | \(0.300617\pi\) | |||||||
\(720\) | 1.12514e19i | 0.112171i | ||||||||
\(721\) | −2.42573e20 | −2.39494 | ||||||||
\(722\) | 1.58417e19 | 0.154896 | ||||||||
\(723\) | 1.95948e19i | 0.189746i | ||||||||
\(724\) | − | 3.00486e17i | − | 0.00288173i | ||||||
\(725\) | 4.31419e19 | 0.409763 | ||||||||
\(726\) | 8.95048e19 | 0.841957 | ||||||||
\(727\) | 1.06408e20i | 0.991363i | 0.868504 | + | 0.495682i | \(0.165082\pi\) | ||||
−0.868504 | + | 0.495682i | \(0.834918\pi\) | |||||||
\(728\) | 1.63307e20i | 1.50691i | ||||||||
\(729\) | 1.19819e20 | 1.09504 | ||||||||
\(730\) | 4.86167e19i | 0.440074i | ||||||||
\(731\) | −1.76638e20 | −1.58366 | ||||||||
\(732\) | − | 2.69439e19i | − | 0.239267i | ||||||
\(733\) | − | 1.13276e20i | − | 0.996347i | −0.867077 | − | 0.498174i | \(-0.834004\pi\) | ||
0.867077 | − | 0.498174i | \(-0.165996\pi\) | |||||||
\(734\) | 1.19045e20i | 1.03714i | ||||||||
\(735\) | − | 7.09043e19i | − | 0.611873i | ||||||
\(736\) | −2.11791e19 | − | 3.01217e19i | −0.181035 | − | 0.257475i | ||||
\(737\) | −7.59346e19 | −0.642935 | ||||||||
\(738\) | −1.55330e18 | −0.0130275 | ||||||||
\(739\) | 1.18974e20 | 0.988419 | 0.494209 | − | 0.869343i | \(-0.335458\pi\) | ||||
0.494209 | + | 0.869343i | \(0.335458\pi\) | |||||||
\(740\) | −1.50036e19 | −0.123473 | ||||||||
\(741\) | 1.28326e20i | 1.04613i | ||||||||
\(742\) | −1.76516e20 | −1.42547 | ||||||||
\(743\) | − | 1.46518e20i | − | 1.17212i | −0.810269 | − | 0.586058i | \(-0.800679\pi\) | ||
0.810269 | − | 0.586058i | \(-0.199321\pi\) | |||||||
\(744\) | −8.38508e19 | −0.664503 | ||||||||
\(745\) | −7.84988e19 | −0.616267 | ||||||||
\(746\) | 1.16076e20i | 0.902755i | ||||||||
\(747\) | 5.33638e18i | 0.0411152i | ||||||||
\(748\) | 8.72428e18 | 0.0665914 | ||||||||
\(749\) | 4.30264e19 | 0.325359 | ||||||||
\(750\) | 1.44167e20i | 1.08004i | ||||||||
\(751\) | 1.97365e19i | 0.146484i | 0.997314 | + | 0.0732420i | \(0.0233345\pi\) | ||||
−0.997314 | + | 0.0732420i | \(0.976665\pi\) | |||||||
\(752\) | 1.10042e20 | 0.809159 | ||||||||
\(753\) | − | 2.00490e19i | − | 0.146059i | ||||||
\(754\) | −1.67865e20 | −1.21160 | ||||||||
\(755\) | − | 7.75036e19i | − | 0.554234i | ||||||
\(756\) | − | 3.24105e19i | − | 0.229632i | ||||||
\(757\) | − | 1.51607e20i | − | 1.06426i | −0.846661 | − | 0.532132i | \(-0.821391\pi\) | ||
0.846661 | − | 0.532132i | \(-0.178609\pi\) | |||||||
\(758\) | 2.23593e19i | 0.155515i | ||||||||
\(759\) | 4.42622e19 | − | 3.11214e19i | 0.305028 | − | 0.214470i | ||||
\(760\) | −9.16654e19 | −0.625908 | ||||||||
\(761\) | 2.71683e20 | 1.83810 | 0.919051 | − | 0.394139i | \(-0.128957\pi\) | ||||
0.919051 | + | 0.394139i | \(0.128957\pi\) | |||||||
\(762\) | 1.61963e20 | 1.08575 | ||||||||
\(763\) | 1.60101e20 | 1.06346 | ||||||||
\(764\) | 3.38692e19i | 0.222921i | ||||||||
\(765\) | 1.58925e19 | 0.103648 | ||||||||
\(766\) | 6.95215e19i | 0.449280i | ||||||||
\(767\) | −2.69734e20 | −1.72730 | ||||||||
\(768\) | 6.82583e19 | 0.433139 | ||||||||
\(769\) | 1.88496e20i | 1.18527i | 0.805471 | + | 0.592635i | \(0.201912\pi\) | ||||
−0.805471 | + | 0.592635i | \(0.798088\pi\) | |||||||
\(770\) | 7.08296e19i | 0.441346i | ||||||||
\(771\) | 1.43837e19 | 0.0888158 | ||||||||
\(772\) | 1.10043e19 | 0.0673351 | ||||||||
\(773\) | − | 1.32572e20i | − | 0.803890i | −0.915664 | − | 0.401945i | \(-0.868334\pi\) | ||
0.915664 | − | 0.401945i | \(-0.131666\pi\) | |||||||
\(774\) | − | 3.58758e19i | − | 0.215583i | ||||||
\(775\) | 5.84678e19 | 0.348181 | ||||||||
\(776\) | 6.79311e19i | 0.400901i | ||||||||
\(777\) | −2.27232e20 | −1.32899 | ||||||||
\(778\) | 7.36721e19i | 0.427018i | ||||||||
\(779\) | − | 1.47163e19i | − | 0.0845351i | ||||||
\(780\) | − | 2.35607e19i | − | 0.134130i | ||||||
\(781\) | 3.32249e19i | 0.187459i | ||||||||
\(782\) | −1.64952e20 | + | 1.15980e20i | −0.922380 | + | 0.648540i | ||||
\(783\) | −1.76473e20 | −0.978015 | ||||||||
\(784\) | 1.81484e20 | 0.996842 | ||||||||
\(785\) | 2.01188e20 | 1.09526 | ||||||||
\(786\) | −3.57259e20 | −1.92764 | ||||||||
\(787\) | 1.85324e20i | 0.991082i | 0.868585 | + | 0.495541i | \(0.165030\pi\) | ||||
−0.868585 | + | 0.495541i | \(0.834970\pi\) | |||||||
\(788\) | −1.16829e19 | −0.0619250 | ||||||||
\(789\) | − | 2.51963e20i | − | 1.32372i | ||||||
\(790\) | −2.06760e20 | −1.07665 | ||||||||
\(791\) | 3.10452e19 | 0.160236 | ||||||||
\(792\) | − | 9.38612e18i | − | 0.0480187i | ||||||
\(793\) | 3.87229e20i | 1.96361i | ||||||||
\(794\) | −1.41721e20 | −0.712348 | ||||||||
\(795\) | −1.34898e20 | −0.672102 | ||||||||
\(796\) | 5.03403e19i | 0.248613i | ||||||||
\(797\) | − | 1.76047e20i | − | 0.861825i | −0.902394 | − | 0.430913i | \(-0.858192\pi\) | ||
0.902394 | − | 0.430913i | \(-0.141808\pi\) | |||||||
\(798\) | 2.62084e20 | 1.27180 | ||||||||
\(799\) | − | 1.55433e20i | − | 0.747678i | ||||||
\(800\) | −2.91709e19 | −0.139097 | ||||||||
\(801\) | 6.01778e17i | 0.00284452i | ||||||||
\(802\) | 2.77925e20i | 1.30229i | ||||||||
\(803\) | − | 4.71640e19i | − | 0.219079i | ||||||
\(804\) | − | 5.15868e19i | − | 0.237545i | ||||||
\(805\) | −1.29038e20 | − | 1.83524e20i | −0.589044 | − | 0.837762i | ||||
\(806\) | −2.27498e20 | −1.02951 | ||||||||
\(807\) | 3.64867e20 | 1.63689 | ||||||||
\(808\) | 1.63707e20 | 0.728096 | ||||||||
\(809\) | 1.96550e20 | 0.866632 | 0.433316 | − | 0.901242i | \(-0.357343\pi\) | ||||
0.433316 | + | 0.901242i | \(0.357343\pi\) | |||||||
\(810\) | − | 1.56372e20i | − | 0.683542i | ||||||
\(811\) | −3.18086e20 | −1.37847 | −0.689236 | − | 0.724536i | \(-0.742054\pi\) | ||||
−0.689236 | + | 0.724536i | \(0.742054\pi\) | |||||||
\(812\) | 4.69824e19i | 0.201857i | ||||||||
\(813\) | 2.87505e20 | 1.22465 | ||||||||
\(814\) | 1.06211e20 | 0.448539 | ||||||||
\(815\) | − | 2.52304e20i | − | 1.05638i | ||||||
\(816\) | − | 2.66419e20i | − | 1.10594i | ||||||
\(817\) | 3.39896e20 | 1.39892 | ||||||||
\(818\) | 2.69933e20 | 1.10150 | ||||||||
\(819\) | 5.44821e19i | 0.220428i | ||||||||
\(820\) | 2.70192e18i | 0.0108387i | ||||||||
\(821\) | −1.05029e20 | −0.417741 | −0.208870 | − | 0.977943i | \(-0.566979\pi\) | ||||
−0.208870 | + | 0.977943i | \(0.566979\pi\) | |||||||
\(822\) | 1.57682e20i | 0.621843i | ||||||||
\(823\) | 3.47206e20 | 1.35765 | 0.678826 | − | 0.734299i | \(-0.262489\pi\) | ||||
0.678826 | + | 0.734299i | \(0.262489\pi\) | |||||||
\(824\) | − | 4.08021e20i | − | 1.58195i | ||||||
\(825\) | − | 4.28650e19i | − | 0.164788i | ||||||
\(826\) | 5.50887e20i | 2.09992i | ||||||||
\(827\) | 1.11144e20i | 0.420095i | 0.977691 | + | 0.210047i | \(0.0673618\pi\) | ||||
−0.977691 | + | 0.210047i | \(0.932638\pi\) | |||||||
\(828\) | −3.22814e18 | − | 4.59119e18i | −0.0120987 | − | 0.0172073i | ||||
\(829\) | −3.71470e20 | −1.38052 | −0.690259 | − | 0.723563i | \(-0.742503\pi\) | ||||
−0.690259 | + | 0.723563i | \(0.742503\pi\) | |||||||
\(830\) | 6.77353e19 | 0.249614 | ||||||||
\(831\) | 4.49080e20 | 1.64103 | ||||||||
\(832\) | −2.66244e20 | −0.964753 | ||||||||
\(833\) | − | 2.56343e20i | − | 0.921100i | ||||||
\(834\) | −1.55990e20 | −0.555820 | ||||||||
\(835\) | 1.78999e20i | 0.632476i | ||||||||
\(836\) | −1.67877e19 | −0.0588231 | ||||||||
\(837\) | −2.39164e20 | −0.831031 | ||||||||
\(838\) | − | 5.72756e20i | − | 1.97361i | ||||||
\(839\) | − | 4.53957e20i | − | 1.55125i | −0.631195 | − | 0.775624i | \(-0.717435\pi\) | ||
0.631195 | − | 0.775624i | \(-0.282565\pi\) | |||||||
\(840\) | 2.54890e20 | 0.863769 | ||||||||
\(841\) | −4.17421e19 | −0.140282 | ||||||||
\(842\) | − | 3.81208e20i | − | 1.27051i | ||||||
\(843\) | − | 2.67067e20i | − | 0.882728i | ||||||
\(844\) | −3.07703e19 | −0.100864 | ||||||||
\(845\) | 1.08812e20i | 0.353735i | ||||||||
\(846\) | 3.15690e19 | 0.101781 | ||||||||
\(847\) | 3.60023e20i | 1.15119i | ||||||||
\(848\) | − | 3.45280e20i | − | 1.09497i | ||||||
\(849\) | − | 3.17733e20i | − | 0.999328i | ||||||
\(850\) | 1.59745e20i | 0.498304i | ||||||||
\(851\) | −2.75200e20 | + | 1.93498e20i | −0.851416 | + | 0.598644i | ||||
\(852\) | −2.25717e19 | −0.0692606 | ||||||||
\(853\) | 1.50373e20 | 0.457644 | 0.228822 | − | 0.973468i | \(-0.426513\pi\) | ||||
0.228822 | + | 0.973468i | \(0.426513\pi\) | |||||||
\(854\) | 7.90851e20 | 2.38721 | ||||||||
\(855\) | −3.05811e19 | −0.0915569 | ||||||||
\(856\) | 7.23727e19i | 0.214911i | ||||||||
\(857\) | 1.03203e20 | 0.303966 | 0.151983 | − | 0.988383i | \(-0.451434\pi\) | ||||
0.151983 | + | 0.988383i | \(0.451434\pi\) | |||||||
\(858\) | 1.66787e20i | 0.487250i | ||||||||
\(859\) | −5.26547e20 | −1.52576 | −0.762878 | − | 0.646542i | \(-0.776214\pi\) | ||||
−0.762878 | + | 0.646542i | \(0.776214\pi\) | |||||||
\(860\) | −6.24049e19 | −0.179362 | ||||||||
\(861\) | 4.09210e19i | 0.116661i | ||||||||
\(862\) | − | 4.89088e20i | − | 1.38304i | ||||||
\(863\) | 1.72159e20 | 0.482896 | 0.241448 | − | 0.970414i | \(-0.422378\pi\) | ||||
0.241448 | + | 0.970414i | \(0.422378\pi\) | |||||||
\(864\) | 1.19324e20 | 0.331995 | ||||||||
\(865\) | 1.30427e20i | 0.359959i | ||||||||
\(866\) | − | 1.37716e20i | − | 0.377015i | ||||||
\(867\) | −3.33238e19 | −0.0904942 | ||||||||
\(868\) | 6.36727e19i | 0.171520i | ||||||||
\(869\) | 2.00582e20 | 0.535985 | ||||||||
\(870\) | 2.62003e20i | 0.694499i | ||||||||
\(871\) | 7.41391e20i | 1.94949i | ||||||||
\(872\) | 2.69298e20i | 0.702454i | ||||||||
\(873\) | 2.26630e19i | 0.0586431i | ||||||||
\(874\) | 3.17409e20 | − | 2.23176e20i | 0.814779 | − | 0.572884i | ||||
\(875\) | −5.79897e20 | −1.47671 | ||||||||
\(876\) | 3.20412e19 | 0.0809433 | ||||||||
\(877\) | −4.28662e20 | −1.07428 | −0.537141 | − | 0.843492i | \(-0.680496\pi\) | ||||
−0.537141 | + | 0.843492i | \(0.680496\pi\) | |||||||
\(878\) | 8.50000e19 | 0.211328 | ||||||||
\(879\) | 4.38434e20i | 1.08139i | ||||||||
\(880\) | −1.38548e20 | −0.339018 | ||||||||
\(881\) | 2.99471e20i | 0.726982i | 0.931598 | + | 0.363491i | \(0.118415\pi\) | ||||
−0.931598 | + | 0.363491i | \(0.881585\pi\) | |||||||
\(882\) | 5.20643e19 | 0.125389 | ||||||||
\(883\) | −2.41781e20 | −0.577694 | −0.288847 | − | 0.957375i | \(-0.593272\pi\) | ||||
−0.288847 | + | 0.957375i | \(0.593272\pi\) | |||||||
\(884\) | − | 8.51798e19i | − | 0.201916i | ||||||
\(885\) | 4.21001e20i | 0.990101i | ||||||||
\(886\) | −6.84089e20 | −1.59616 | ||||||||
\(887\) | 3.50368e20 | 0.811071 | 0.405535 | − | 0.914079i | \(-0.367085\pi\) | ||||
0.405535 | + | 0.914079i | \(0.367085\pi\) | |||||||
\(888\) | − | 3.82216e20i | − | 0.877846i | ||||||
\(889\) | 6.51478e20i | 1.48452i | ||||||||
\(890\) | 7.63844e18 | 0.0172693 | ||||||||
\(891\) | 1.51700e20i | 0.340284i | ||||||||
\(892\) | 6.29779e19 | 0.140163 | ||||||||
\(893\) | 2.99092e20i | 0.660457i | ||||||||
\(894\) | 3.77518e20i | 0.827133i | ||||||||
\(895\) | 5.83330e19i | 0.126810i | ||||||||
\(896\) | 7.43803e20i | 1.60436i | ||||||||
\(897\) | −3.03856e20 | − | 4.32155e20i | −0.650310 | − | 0.924896i | ||||
\(898\) | −9.08143e20 | −1.92850 | ||||||||
\(899\) | 3.46693e20 | 0.730512 | ||||||||
\(900\) | −4.44626e18 | −0.00929602 | ||||||||
\(901\) | −4.87702e20 | −1.01177 | ||||||||
\(902\) | − | 1.91271e19i | − | 0.0393733i | ||||||
\(903\) | −9.45132e20 | −1.93054 | ||||||||
\(904\) | 5.22198e19i | 0.105841i | ||||||||
\(905\) | 6.74029e18 | 0.0135562 | ||||||||
\(906\) | −3.72732e20 | −0.743874 | ||||||||
\(907\) | 3.62231e20i | 0.717357i | 0.933461 | + | 0.358678i | \(0.116772\pi\) | ||||
−0.933461 | + | 0.358678i | \(0.883228\pi\) | |||||||
\(908\) | 6.97118e19i | 0.136995i | ||||||||
\(909\) | 5.46155e19 | 0.106505 | ||||||||
\(910\) | 6.91548e20 | 1.33823 | ||||||||
\(911\) | 1.46755e20i | 0.281814i | 0.990023 | + | 0.140907i | \(0.0450019\pi\) | ||||
−0.990023 | + | 0.140907i | \(0.954998\pi\) | |||||||
\(912\) | 5.12657e20i | 0.976930i | ||||||||
\(913\) | −6.57113e19 | −0.124264 | ||||||||
\(914\) | − | 2.07612e20i | − | 0.389610i | ||||||
\(915\) | 6.04387e20 | 1.12556 | ||||||||
\(916\) | − | 5.25307e19i | − | 0.0970833i | ||||||
\(917\) | − | 1.43703e21i | − | 2.63561i | ||||||
\(918\) | − | 6.53440e20i | − | 1.18934i | ||||||
\(919\) | − | 5.88168e20i | − | 1.06241i | −0.847243 | − | 0.531206i | \(-0.821739\pi\) | ||
0.847243 | − | 0.531206i | \(-0.178261\pi\) | |||||||
\(920\) | 3.08696e20 | − | 2.17049e20i | 0.553371 | − | 0.389084i | ||||
\(921\) | −6.24664e20 | −1.11129 | ||||||||
\(922\) | 1.12895e21 | 1.99324 | ||||||||
\(923\) | 3.24393e20 | 0.568408 | ||||||||
\(924\) | 4.66809e19 | 0.0811774 | ||||||||
\(925\) | 2.66513e20i | 0.459967i | ||||||||
\(926\) | −7.74397e20 | −1.32644 | ||||||||
\(927\) | − | 1.36123e20i | − | 0.231405i | ||||||
\(928\) | −1.72973e20 | −0.291838 | ||||||||
\(929\) | 7.29333e20 | 1.22128 | 0.610641 | − | 0.791908i | \(-0.290912\pi\) | ||||
0.610641 | + | 0.791908i | \(0.290912\pi\) | |||||||
\(930\) | 3.55078e20i | 0.590124i | ||||||||
\(931\) | 4.93270e20i | 0.813649i | ||||||||
\(932\) | −2.46198e19 | −0.0403064 | ||||||||
\(933\) | 5.77491e20 | 0.938369 | ||||||||
\(934\) | − | 6.10564e20i | − | 0.984698i | ||||||
\(935\) | 1.95697e20i | 0.313258i | ||||||||
\(936\) | −9.16418e19 | −0.145600 | ||||||||
\(937\) | − | 1.03045e21i | − | 1.62499i | −0.582965 | − | 0.812497i | \(-0.698108\pi\) | ||
0.582965 | − | 0.812497i | \(-0.301892\pi\) | |||||||
\(938\) | 1.51417e21 | 2.37003 | ||||||||
\(939\) | 7.48687e20i | 1.16316i | ||||||||
\(940\) | − | 5.49133e19i | − | 0.0846804i | ||||||
\(941\) | 8.79559e20i | 1.34629i | 0.739512 | + | 0.673144i | \(0.235056\pi\) | ||||
−0.739512 | + | 0.673144i | \(0.764944\pi\) | |||||||
\(942\) | − | 9.67560e20i | − | 1.47001i | ||||||
\(943\) | 3.48460e19 | + | 4.95593e19i | 0.0525497 | + | 0.0747383i | ||||
\(944\) | −1.07758e21 | −1.61304 | ||||||||
\(945\) | 7.27010e20 | 1.08023 | ||||||||
\(946\) | 4.41768e20 | 0.651563 | ||||||||
\(947\) | −3.32817e20 | −0.487254 | −0.243627 | − | 0.969869i | \(-0.578337\pi\) | ||||
−0.243627 | + | 0.969869i | \(0.578337\pi\) | |||||||
\(948\) | 1.36267e20i | 0.198030i | ||||||||
\(949\) | −4.60487e20 | −0.664285 | ||||||||
\(950\) | − | 3.07390e20i | − | 0.440174i | ||||||
\(951\) | 7.68950e19 | 0.109304 | ||||||||
\(952\) | 9.21514e20 | 1.30030 | ||||||||
\(953\) | − | 7.83606e20i | − | 1.09761i | −0.835951 | − | 0.548804i | \(-0.815083\pi\) | ||
0.835951 | − | 0.548804i | \(-0.184917\pi\) | |||||||
\(954\) | − | 9.90542e19i | − | 0.137732i | ||||||
\(955\) | −7.59731e20 | −1.04866 | ||||||||
\(956\) | 7.70829e19 | 0.105622 | ||||||||
\(957\) | − | 2.54174e20i | − | 0.345738i | ||||||
\(958\) | − | 1.00526e21i | − | 1.35743i | ||||||
\(959\) | −6.34260e20 | −0.850231 | ||||||||
\(960\) | 4.15552e20i | 0.553003i | ||||||||
\(961\) | −2.87090e20 | −0.379275 | ||||||||
\(962\) | − | 1.03700e21i | − | 1.36005i | ||||||
\(963\) | 2.41447e19i | 0.0314368i | ||||||||
\(964\) | 2.50280e19i | 0.0323509i | ||||||||
\(965\) | 2.46841e20i | 0.316757i | ||||||||
\(966\) | −8.82605e20 | + | 6.20574e20i | −1.12442 | + | 0.790595i | ||||
\(967\) | 1.33489e21 | 1.68834 | 0.844168 | − | 0.536079i | \(-0.180095\pi\) | ||||
0.844168 | + | 0.536079i | \(0.180095\pi\) | |||||||
\(968\) | −6.05578e20 | −0.760401 | ||||||||
\(969\) | 7.24119e20 | 0.902701 | ||||||||
\(970\) | 2.87664e20 | 0.356027 | ||||||||
\(971\) | − | 7.59002e20i | − | 0.932627i | −0.884619 | − | 0.466314i | \(-0.845582\pi\) | ||
0.884619 | − | 0.466314i | \(-0.154418\pi\) | |||||||
\(972\) | 3.42477e19 | 0.0417799 | ||||||||
\(973\) | − | 6.27452e20i | − | 0.759960i | ||||||
\(974\) | 4.60773e20 | 0.554083 | ||||||||
\(975\) | −4.18514e20 | −0.499663 | ||||||||
\(976\) | 1.54697e21i | 1.83372i | ||||||||
\(977\) | 6.28594e20i | 0.739789i | 0.929074 | + | 0.369895i | \(0.120606\pi\) | ||||
−0.929074 | + | 0.369895i | \(0.879394\pi\) | |||||||
\(978\) | −1.21339e21 | −1.41784 | ||||||||
\(979\) | −7.41019e18 | −0.00859707 | ||||||||
\(980\) | − | 9.05645e19i | − | 0.104322i | ||||||
\(981\) | 8.98423e19i | 0.102754i | ||||||||
\(982\) | 1.58870e21 | 1.80411 | ||||||||
\(983\) | 7.23188e20i | 0.815412i | 0.913113 | + | 0.407706i | \(0.133671\pi\) | ||||
−0.913113 | + | 0.407706i | \(0.866329\pi\) | |||||||
\(984\) | −6.88313e19 | −0.0770584 | ||||||||
\(985\) | − | 2.62062e20i | − | 0.291307i | ||||||
\(986\) | 9.47231e20i | 1.04548i | ||||||||
\(987\) | − | 8.31671e20i | − | 0.911447i | ||||||
\(988\) | 1.63908e20i | 0.178361i | ||||||||
\(989\) | −1.14465e21 | + | 8.04820e20i | −1.23680 | + | 0.869611i | ||||
\(990\) | −3.97468e19 | −0.0426438 | ||||||||
\(991\) | 1.29131e21 | 1.37567 | 0.687836 | − | 0.725866i | \(-0.258561\pi\) | ||||
0.687836 | + | 0.725866i | \(0.258561\pi\) | |||||||
\(992\) | −2.34420e20 | −0.247978 | ||||||||
\(993\) | −6.44561e20 | −0.677047 | ||||||||
\(994\) | − | 6.62519e20i | − | 0.691025i | ||||||
\(995\) | −1.12920e21 | −1.16952 | ||||||||
\(996\) | − | 4.46415e19i | − | 0.0459117i | ||||||
\(997\) | −3.27971e20 | −0.334942 | −0.167471 | − | 0.985877i | \(-0.553560\pi\) | ||||
−0.167471 | + | 0.985877i | \(0.553560\pi\) | |||||||
\(998\) | 3.62522e20 | 0.367639 | ||||||||
\(999\) | − | 1.09018e21i | − | 1.09784i |
(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 | 23.15.b.b.22.20 | yes | 24 | |
23.22 | odd | 2 | inner | 23.15.b.b.22.19 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.15.b.b.22.19 | ✓ | 24 | 23.22 | odd | 2 | inner | |
23.15.b.b.22.20 | yes | 24 | 1.1 | even | 1 | trivial |