Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [23,13,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, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("23.22");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 23 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
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: | \(21.0218577974\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + 3347471347 x^{18} + 50192028136 x^{17} + \cdots + 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | multiple of \( 2^{35}\cdot 3^{11}\cdot 67 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 22.1 | ||
Root | \(-891.853 + 7568.36i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.22 |
Dual form | 23.13.b.c.22.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −111.723 | −1.74567 | −0.872833 | − | 0.488020i | \(-0.837719\pi\) | ||||
−0.872833 | + | 0.488020i | \(0.837719\pi\) | |||||||
\(3\) | 792.131 | 1.08660 | 0.543299 | − | 0.839539i | \(-0.317175\pi\) | ||||
0.543299 | + | 0.839539i | \(0.317175\pi\) | |||||||
\(4\) | 8385.93 | 2.04735 | ||||||||
\(5\) | − | 7568.36i | − | 0.484375i | −0.970229 | − | 0.242187i | \(-0.922135\pi\) | ||
0.970229 | − | 0.242187i | \(-0.0778649\pi\) | |||||||
\(6\) | −88498.9 | −1.89684 | ||||||||
\(7\) | 231962.i | 1.97165i | 0.167786 | + | 0.985823i | \(0.446338\pi\) | ||||
−0.167786 | + | 0.985823i | \(0.553662\pi\) | |||||||
\(8\) | −479282. | −1.82832 | ||||||||
\(9\) | 96030.0 | 0.180697 | ||||||||
\(10\) | 845556.i | 0.845556i | ||||||||
\(11\) | − | 956612.i | − | 0.539983i | −0.962863 | − | 0.269991i | \(-0.912979\pi\) | ||
0.962863 | − | 0.269991i | \(-0.0870208\pi\) | |||||||
\(12\) | 6.64275e6 | 2.22464 | ||||||||
\(13\) | 1.33056e6 | 0.275660 | 0.137830 | − | 0.990456i | \(-0.455987\pi\) | ||||
0.137830 | + | 0.990456i | \(0.455987\pi\) | |||||||
\(14\) | − | 2.59154e7i | − | 3.44184i | ||||||
\(15\) | − | 5.99513e6i | − | 0.526321i | ||||||
\(16\) | 1.91979e7 | 1.14428 | ||||||||
\(17\) | 2.04742e7i | 0.848230i | 0.905608 | + | 0.424115i | \(0.139415\pi\) | ||||
−0.905608 | + | 0.424115i | \(0.860585\pi\) | |||||||
\(18\) | −1.07287e7 | −0.315437 | ||||||||
\(19\) | 1.74722e6i | 0.0371387i | 0.999828 | + | 0.0185694i | \(0.00591115\pi\) | ||||
−0.999828 | + | 0.0185694i | \(0.994089\pi\) | |||||||
\(20\) | − | 6.34677e7i | − | 0.991683i | ||||||
\(21\) | 1.83744e8i | 2.14239i | ||||||||
\(22\) | 1.06875e8i | 0.942629i | ||||||||
\(23\) | −9.91035e7 | − | 1.09969e8i | −0.669456 | − | 0.742852i | ||||
\(24\) | −3.79654e8 | −1.98665 | ||||||||
\(25\) | 1.86861e8 | 0.765381 | ||||||||
\(26\) | −1.48653e8 | −0.481210 | ||||||||
\(27\) | −3.44902e8 | −0.890253 | ||||||||
\(28\) | 1.94522e9i | 4.03664i | ||||||||
\(29\) | −5.12386e8 | −0.861409 | −0.430704 | − | 0.902493i | \(-0.641735\pi\) | ||||
−0.430704 | + | 0.902493i | \(0.641735\pi\) | |||||||
\(30\) | 6.69791e8i | 0.918781i | ||||||||
\(31\) | −1.11066e9 | −1.25144 | −0.625719 | − | 0.780049i | \(-0.715194\pi\) | ||||
−0.625719 | + | 0.780049i | \(0.715194\pi\) | |||||||
\(32\) | −1.81694e8 | −0.169216 | ||||||||
\(33\) | − | 7.57762e8i | − | 0.586744i | ||||||
\(34\) | − | 2.28743e9i | − | 1.48073i | ||||||
\(35\) | 1.75557e9 | 0.955016 | ||||||||
\(36\) | 8.05301e8 | 0.369950 | ||||||||
\(37\) | 2.11420e9i | 0.824016i | 0.911180 | + | 0.412008i | \(0.135172\pi\) | ||||
−0.911180 | + | 0.412008i | \(0.864828\pi\) | |||||||
\(38\) | − | 1.95204e8i | − | 0.0648318i | ||||||
\(39\) | 1.05398e9 | 0.299532 | ||||||||
\(40\) | 3.62738e9i | 0.885590i | ||||||||
\(41\) | 5.34076e8 | 0.112435 | 0.0562173 | − | 0.998419i | \(-0.482096\pi\) | ||||
0.0562173 | + | 0.998419i | \(0.482096\pi\) | |||||||
\(42\) | − | 2.05284e10i | − | 3.73989i | ||||||
\(43\) | 1.05964e10i | 1.67629i | 0.545451 | + | 0.838143i | \(0.316358\pi\) | ||||
−0.545451 | + | 0.838143i | \(0.683642\pi\) | |||||||
\(44\) | − | 8.02208e9i | − | 1.10553i | ||||||
\(45\) | − | 7.26789e8i | − | 0.0875253i | ||||||
\(46\) | 1.10721e10 | + | 1.22860e10i | 1.16865 | + | 1.29677i | ||||
\(47\) | 2.06440e8 | 0.0191517 | 0.00957584 | − | 0.999954i | \(-0.496952\pi\) | ||||
0.00957584 | + | 0.999954i | \(0.496952\pi\) | |||||||
\(48\) | 1.52072e10 | 1.24337 | ||||||||
\(49\) | −3.99652e10 | −2.88739 | ||||||||
\(50\) | −2.08765e10 | −1.33610 | ||||||||
\(51\) | 1.62183e10i | 0.921686i | ||||||||
\(52\) | 1.11580e10 | 0.564371 | ||||||||
\(53\) | 3.93108e10i | 1.77360i | 0.462151 | + | 0.886801i | \(0.347078\pi\) | ||||
−0.462151 | + | 0.886801i | \(0.652922\pi\) | |||||||
\(54\) | 3.85334e10 | 1.55408 | ||||||||
\(55\) | −7.23998e9 | −0.261554 | ||||||||
\(56\) | − | 1.11175e11i | − | 3.60479i | ||||||
\(57\) | 1.38403e9i | 0.0403549i | ||||||||
\(58\) | 5.72451e10 | 1.50373 | ||||||||
\(59\) | −2.74230e10 | −0.650135 | −0.325068 | − | 0.945691i | \(-0.605387\pi\) | ||||
−0.325068 | + | 0.945691i | \(0.605387\pi\) | |||||||
\(60\) | − | 5.02747e10i | − | 1.07756i | ||||||
\(61\) | − | 7.12673e10i | − | 1.38328i | −0.722240 | − | 0.691642i | \(-0.756888\pi\) | ||
0.722240 | − | 0.691642i | \(-0.243112\pi\) | |||||||
\(62\) | 1.24085e11 | 2.18459 | ||||||||
\(63\) | 2.22753e10i | 0.356271i | ||||||||
\(64\) | −5.83351e10 | −0.848887 | ||||||||
\(65\) | − | 1.00701e10i | − | 0.133523i | ||||||
\(66\) | 8.46591e10i | 1.02426i | ||||||||
\(67\) | 1.12785e11i | 1.24681i | 0.781898 | + | 0.623406i | \(0.214252\pi\) | ||||
−0.781898 | + | 0.623406i | \(0.785748\pi\) | |||||||
\(68\) | 1.71695e11i | 1.73662i | ||||||||
\(69\) | −7.85029e10 | − | 8.71096e10i | −0.727430 | − | 0.807182i | ||||
\(70\) | −1.96137e11 | −1.66714 | ||||||||
\(71\) | 1.71752e11 | 1.34076 | 0.670381 | − | 0.742017i | \(-0.266131\pi\) | ||||
0.670381 | + | 0.742017i | \(0.266131\pi\) | |||||||
\(72\) | −4.60255e10 | −0.330372 | ||||||||
\(73\) | −2.22447e11 | −1.46990 | −0.734951 | − | 0.678120i | \(-0.762795\pi\) | ||||
−0.734951 | + | 0.678120i | \(0.762795\pi\) | |||||||
\(74\) | − | 2.36204e11i | − | 1.43846i | ||||||
\(75\) | 1.48018e11 | 0.831662 | ||||||||
\(76\) | 1.46521e10i | 0.0760359i | ||||||||
\(77\) | 2.21898e11 | 1.06465 | ||||||||
\(78\) | −1.17753e11 | −0.522882 | ||||||||
\(79\) | 2.90410e11i | 1.19467i | 0.801991 | + | 0.597336i | \(0.203774\pi\) | ||||
−0.801991 | + | 0.597336i | \(0.796226\pi\) | |||||||
\(80\) | − | 1.45296e11i | − | 0.554261i | ||||||
\(81\) | −3.24242e11 | −1.14805 | ||||||||
\(82\) | −5.96684e10 | −0.196273 | ||||||||
\(83\) | 1.27559e11i | 0.390161i | 0.980787 | + | 0.195080i | \(0.0624968\pi\) | ||||
−0.980787 | + | 0.195080i | \(0.937503\pi\) | |||||||
\(84\) | 1.54087e12i | 4.38621i | ||||||||
\(85\) | 1.54956e11 | 0.410861 | ||||||||
\(86\) | − | 1.18386e12i | − | 2.92623i | ||||||
\(87\) | −4.05877e11 | −0.936006 | ||||||||
\(88\) | 4.58487e11i | 0.987259i | ||||||||
\(89\) | 1.91239e11i | 0.384801i | 0.981316 | + | 0.192400i | \(0.0616273\pi\) | ||||
−0.981316 | + | 0.192400i | \(0.938373\pi\) | |||||||
\(90\) | 8.11988e10i | 0.152790i | ||||||||
\(91\) | 3.08639e11i | 0.543504i | ||||||||
\(92\) | −8.31075e11 | − | 9.22190e11i | −1.37061 | − | 1.52088i | ||||
\(93\) | −8.79784e11 | −1.35981 | ||||||||
\(94\) | −2.30640e10 | −0.0334324 | ||||||||
\(95\) | 1.32236e10 | 0.0179891 | ||||||||
\(96\) | −1.43925e11 | −0.183870 | ||||||||
\(97\) | − | 9.67574e11i | − | 1.16159i | −0.814049 | − | 0.580796i | \(-0.802741\pi\) | ||
0.814049 | − | 0.580796i | \(-0.197259\pi\) | |||||||
\(98\) | 4.46502e12 | 5.04042 | ||||||||
\(99\) | − | 9.18634e10i | − | 0.0975734i | ||||||
\(100\) | 1.56700e12 | 1.56700 | ||||||||
\(101\) | 6.96867e11 | 0.656480 | 0.328240 | − | 0.944594i | \(-0.393545\pi\) | ||||
0.328240 | + | 0.944594i | \(0.393545\pi\) | |||||||
\(102\) | − | 1.81195e12i | − | 1.60896i | ||||||
\(103\) | − | 1.06863e12i | − | 0.894959i | −0.894294 | − | 0.447479i | \(-0.852322\pi\) | ||
0.894294 | − | 0.447479i | \(-0.147678\pi\) | |||||||
\(104\) | −6.37713e11 | −0.503994 | ||||||||
\(105\) | 1.39064e12 | 1.03772 | ||||||||
\(106\) | − | 4.39190e12i | − | 3.09612i | ||||||
\(107\) | − | 1.74182e11i | − | 0.116065i | −0.998315 | − | 0.0580324i | \(-0.981517\pi\) | ||
0.998315 | − | 0.0580324i | \(-0.0184827\pi\) | |||||||
\(108\) | −2.89233e12 | −1.82266 | ||||||||
\(109\) | 2.46633e12i | 1.47059i | 0.677745 | + | 0.735297i | \(0.262957\pi\) | ||||
−0.677745 | + | 0.735297i | \(0.737043\pi\) | |||||||
\(110\) | 8.08869e11 | 0.456586 | ||||||||
\(111\) | 1.67472e12i | 0.895375i | ||||||||
\(112\) | 4.45318e12i | 2.25612i | ||||||||
\(113\) | − | 1.82230e12i | − | 0.875283i | −0.899149 | − | 0.437642i | \(-0.855814\pi\) | ||
0.899149 | − | 0.437642i | \(-0.144186\pi\) | |||||||
\(114\) | − | 1.54627e11i | − | 0.0704462i | ||||||
\(115\) | −8.32283e11 | + | 7.50051e11i | −0.359819 | + | 0.324268i | ||||
\(116\) | −4.29684e12 | −1.76360 | ||||||||
\(117\) | 1.27773e11 | 0.0498110 | ||||||||
\(118\) | 3.06377e12 | 1.13492 | ||||||||
\(119\) | −4.74925e12 | −1.67241 | ||||||||
\(120\) | 2.87336e12i | 0.962282i | ||||||||
\(121\) | 2.22332e12 | 0.708419 | ||||||||
\(122\) | 7.96217e12i | 2.41475i | ||||||||
\(123\) | 4.23058e11 | 0.122171 | ||||||||
\(124\) | −9.31388e12 | −2.56213 | ||||||||
\(125\) | − | 3.26197e12i | − | 0.855106i | ||||||
\(126\) | − | 2.48866e12i | − | 0.621930i | ||||||
\(127\) | 8.60955e11 | 0.205191 | 0.102595 | − | 0.994723i | \(-0.467285\pi\) | ||||
0.102595 | + | 0.994723i | \(0.467285\pi\) | |||||||
\(128\) | 7.26157e12 | 1.65109 | ||||||||
\(129\) | 8.39374e12i | 1.82145i | ||||||||
\(130\) | 1.12506e12i | 0.233086i | ||||||||
\(131\) | −3.85505e12 | −0.762786 | −0.381393 | − | 0.924413i | \(-0.624556\pi\) | ||||
−0.381393 | + | 0.924413i | \(0.624556\pi\) | |||||||
\(132\) | − | 6.35454e12i | − | 1.20127i | ||||||
\(133\) | −4.05290e11 | −0.0732245 | ||||||||
\(134\) | − | 1.26006e13i | − | 2.17652i | ||||||
\(135\) | 2.61034e12i | 0.431216i | ||||||||
\(136\) | − | 9.81293e12i | − | 1.55083i | ||||||
\(137\) | − | 1.83704e12i | − | 0.277841i | −0.990304 | − | 0.138920i | \(-0.955637\pi\) | ||
0.990304 | − | 0.138920i | \(-0.0443632\pi\) | |||||||
\(138\) | 8.77055e12 | + | 9.73211e12i | 1.26985 | + | 1.40907i | ||||
\(139\) | 4.97123e12 | 0.689247 | 0.344624 | − | 0.938741i | \(-0.388007\pi\) | ||||
0.344624 | + | 0.938741i | \(0.388007\pi\) | |||||||
\(140\) | 1.47221e13 | 1.95525 | ||||||||
\(141\) | 1.63528e11 | 0.0208102 | ||||||||
\(142\) | −1.91886e13 | −2.34052 | ||||||||
\(143\) | − | 1.27283e12i | − | 0.148852i | ||||||
\(144\) | 1.84357e12 | 0.206769 | ||||||||
\(145\) | 3.87792e12i | 0.417245i | ||||||||
\(146\) | 2.48523e13 | 2.56596 | ||||||||
\(147\) | −3.16577e13 | −3.13744 | ||||||||
\(148\) | 1.77295e13i | 1.68705i | ||||||||
\(149\) | − | 9.29618e12i | − | 0.849546i | −0.905300 | − | 0.424773i | \(-0.860354\pi\) | ||
0.905300 | − | 0.424773i | \(-0.139646\pi\) | |||||||
\(150\) | −1.65370e13 | −1.45180 | ||||||||
\(151\) | 5.81772e12 | 0.490784 | 0.245392 | − | 0.969424i | \(-0.421083\pi\) | ||||
0.245392 | + | 0.969424i | \(0.421083\pi\) | |||||||
\(152\) | − | 8.37413e11i | − | 0.0679014i | ||||||
\(153\) | 1.96614e12i | 0.153273i | ||||||||
\(154\) | −2.47910e13 | −1.85853 | ||||||||
\(155\) | 8.40584e12i | 0.606165i | ||||||||
\(156\) | 8.83857e12 | 0.613245 | ||||||||
\(157\) | 1.58296e13i | 1.05699i | 0.848936 | + | 0.528495i | \(0.177243\pi\) | ||||
−0.848936 | + | 0.528495i | \(0.822757\pi\) | |||||||
\(158\) | − | 3.24453e13i | − | 2.08550i | ||||||
\(159\) | 3.11393e13i | 1.92719i | ||||||||
\(160\) | 1.37513e12i | 0.0819638i | ||||||||
\(161\) | 2.55086e13 | − | 2.29883e13i | 1.46464 | − | 1.31993i | ||||
\(162\) | 3.62252e13 | 2.00410 | ||||||||
\(163\) | 7.35237e12 | 0.392014 | 0.196007 | − | 0.980602i | \(-0.437202\pi\) | ||||
0.196007 | + | 0.980602i | \(0.437202\pi\) | |||||||
\(164\) | 4.47873e12 | 0.230193 | ||||||||
\(165\) | −5.73501e12 | −0.284204 | ||||||||
\(166\) | − | 1.42513e13i | − | 0.681090i | ||||||
\(167\) | 8.07303e12 | 0.372167 | 0.186084 | − | 0.982534i | \(-0.440420\pi\) | ||||
0.186084 | + | 0.982534i | \(0.440420\pi\) | |||||||
\(168\) | − | 8.80654e13i | − | 3.91697i | ||||||
\(169\) | −2.15277e13 | −0.924012 | ||||||||
\(170\) | −1.73121e13 | −0.717227 | ||||||||
\(171\) | 1.67786e11i | 0.00671087i | ||||||||
\(172\) | 8.88608e13i | 3.43194i | ||||||||
\(173\) | −3.30970e13 | −1.23456 | −0.617281 | − | 0.786743i | \(-0.711766\pi\) | ||||
−0.617281 | + | 0.786743i | \(0.711766\pi\) | |||||||
\(174\) | 4.53456e13 | 1.63395 | ||||||||
\(175\) | 4.33446e13i | 1.50906i | ||||||||
\(176\) | − | 1.83649e13i | − | 0.617892i | ||||||
\(177\) | −2.17226e13 | −0.706436 | ||||||||
\(178\) | − | 2.13657e13i | − | 0.671734i | ||||||
\(179\) | −1.98742e13 | −0.604188 | −0.302094 | − | 0.953278i | \(-0.597686\pi\) | ||||
−0.302094 | + | 0.953278i | \(0.597686\pi\) | |||||||
\(180\) | − | 6.09480e12i | − | 0.179195i | ||||||
\(181\) | − | 2.26848e13i | − | 0.645154i | −0.946543 | − | 0.322577i | \(-0.895451\pi\) | ||
0.946543 | − | 0.322577i | \(-0.104549\pi\) | |||||||
\(182\) | − | 3.44820e13i | − | 0.948776i | ||||||
\(183\) | − | 5.64530e13i | − | 1.50308i | ||||||
\(184\) | 4.74985e13 | + | 5.27060e13i | 1.22398 | + | 1.35817i | ||||
\(185\) | 1.60010e13 | 0.399133 | ||||||||
\(186\) | 9.82918e13 | 2.37377 | ||||||||
\(187\) | 1.95859e13 | 0.458030 | ||||||||
\(188\) | 1.73119e12 | 0.0392101 | ||||||||
\(189\) | − | 8.00044e13i | − | 1.75527i | ||||||
\(190\) | −1.47738e12 | −0.0314029 | ||||||||
\(191\) | 6.25463e13i | 1.28825i | 0.764919 | + | 0.644127i | \(0.222779\pi\) | ||||
−0.764919 | + | 0.644127i | \(0.777221\pi\) | |||||||
\(192\) | −4.62090e13 | −0.922400 | ||||||||
\(193\) | 5.78720e13 | 1.11976 | 0.559880 | − | 0.828574i | \(-0.310847\pi\) | ||||
0.559880 | + | 0.828574i | \(0.310847\pi\) | |||||||
\(194\) | 1.08100e14i | 2.02775i | ||||||||
\(195\) | − | 7.97687e12i | − | 0.145086i | ||||||
\(196\) | −3.35146e14 | −5.91149 | ||||||||
\(197\) | 9.63702e13 | 1.64871 | 0.824357 | − | 0.566071i | \(-0.191537\pi\) | ||||
0.824357 | + | 0.566071i | \(0.191537\pi\) | |||||||
\(198\) | 1.02632e13i | 0.170330i | ||||||||
\(199\) | − | 1.54021e13i | − | 0.248006i | −0.992282 | − | 0.124003i | \(-0.960427\pi\) | ||
0.992282 | − | 0.124003i | \(-0.0395732\pi\) | |||||||
\(200\) | −8.95589e13 | −1.39936 | ||||||||
\(201\) | 8.93401e13i | 1.35478i | ||||||||
\(202\) | −7.78557e13 | −1.14599 | ||||||||
\(203\) | − | 1.18854e14i | − | 1.69839i | ||||||
\(204\) | 1.36005e14i | 1.88701i | ||||||||
\(205\) | − | 4.04208e12i | − | 0.0544605i | ||||||
\(206\) | 1.19390e14i | 1.56230i | ||||||||
\(207\) | −9.51691e12 | − | 1.05603e13i | −0.120969 | − | 0.134231i | ||||
\(208\) | 2.55439e13 | 0.315433 | ||||||||
\(209\) | 1.67142e12 | 0.0200543 | ||||||||
\(210\) | −1.55366e14 | −1.81151 | ||||||||
\(211\) | 4.65398e13 | 0.527388 | 0.263694 | − | 0.964606i | \(-0.415059\pi\) | ||||
0.263694 | + | 0.964606i | \(0.415059\pi\) | |||||||
\(212\) | 3.29657e14i | 3.63118i | ||||||||
\(213\) | 1.36050e14 | 1.45687 | ||||||||
\(214\) | 1.94601e13i | 0.202610i | ||||||||
\(215\) | 8.01974e13 | 0.811951 | ||||||||
\(216\) | 1.65306e14 | 1.62766 | ||||||||
\(217\) | − | 2.57630e14i | − | 2.46739i | ||||||
\(218\) | − | 2.75545e14i | − | 2.56716i | ||||||
\(219\) | −1.76207e14 | −1.59719 | ||||||||
\(220\) | −6.07140e13 | −0.535492 | ||||||||
\(221\) | 2.72421e13i | 0.233823i | ||||||||
\(222\) | − | 1.87104e14i | − | 1.56303i | ||||||
\(223\) | 1.67886e14 | 1.36517 | 0.682585 | − | 0.730806i | \(-0.260856\pi\) | ||||
0.682585 | + | 0.730806i | \(0.260856\pi\) | |||||||
\(224\) | − | 4.21462e13i | − | 0.333634i | ||||||
\(225\) | 1.79442e13 | 0.138302 | ||||||||
\(226\) | 2.03592e14i | 1.52795i | ||||||||
\(227\) | − | 2.44863e14i | − | 1.78965i | −0.446415 | − | 0.894826i | \(-0.647300\pi\) | ||
0.446415 | − | 0.894826i | \(-0.352700\pi\) | |||||||
\(228\) | 1.16064e13i | 0.0826205i | ||||||||
\(229\) | − | 1.15757e14i | − | 0.802668i | −0.915932 | − | 0.401334i | \(-0.868547\pi\) | ||
0.915932 | − | 0.401334i | \(-0.131453\pi\) | |||||||
\(230\) | 9.29848e13 | − | 8.37976e13i | 0.628123 | − | 0.566063i | ||||
\(231\) | 1.75772e14 | 1.15685 | ||||||||
\(232\) | 2.45578e14 | 1.57493 | ||||||||
\(233\) | −2.01419e14 | −1.25882 | −0.629412 | − | 0.777072i | \(-0.716704\pi\) | ||||
−0.629412 | + | 0.777072i | \(0.716704\pi\) | |||||||
\(234\) | −1.42752e13 | −0.0869534 | ||||||||
\(235\) | − | 1.56241e12i | − | 0.00927660i | ||||||
\(236\) | −2.29968e14 | −1.33105 | ||||||||
\(237\) | 2.30042e14i | 1.29813i | ||||||||
\(238\) | 5.30598e14 | 2.91947 | ||||||||
\(239\) | −7.11653e13 | −0.381840 | −0.190920 | − | 0.981606i | \(-0.561147\pi\) | ||||
−0.190920 | + | 0.981606i | \(0.561147\pi\) | |||||||
\(240\) | − | 1.15094e14i | − | 0.602260i | ||||||
\(241\) | 1.69668e13i | 0.0865961i | 0.999062 | + | 0.0432981i | \(0.0137865\pi\) | ||||
−0.999062 | + | 0.0432981i | \(0.986213\pi\) | |||||||
\(242\) | −2.48395e14 | −1.23666 | ||||||||
\(243\) | −7.35468e13 | −0.357212 | ||||||||
\(244\) | − | 5.97643e14i | − | 2.83206i | ||||||
\(245\) | 3.02471e14i | 1.39858i | ||||||||
\(246\) | −4.72651e13 | −0.213270 | ||||||||
\(247\) | 2.32478e12i | 0.0102377i | ||||||||
\(248\) | 5.32317e14 | 2.28802 | ||||||||
\(249\) | 1.01044e14i | 0.423948i | ||||||||
\(250\) | 3.64436e14i | 1.49273i | ||||||||
\(251\) | 4.79307e13i | 0.191678i | 0.995397 | + | 0.0958388i | \(0.0305533\pi\) | ||||
−0.995397 | + | 0.0958388i | \(0.969447\pi\) | |||||||
\(252\) | 1.86799e14i | 0.729411i | ||||||||
\(253\) | −1.05197e14 | + | 9.48036e13i | −0.401127 | + | 0.361494i | ||||
\(254\) | −9.61881e13 | −0.358194 | ||||||||
\(255\) | 1.22746e14 | 0.446442 | ||||||||
\(256\) | −5.72340e14 | −2.03336 | ||||||||
\(257\) | −3.35579e14 | −1.16465 | −0.582325 | − | 0.812956i | \(-0.697857\pi\) | ||||
−0.582325 | + | 0.812956i | \(0.697857\pi\) | |||||||
\(258\) | − | 9.37770e14i | − | 3.17964i | ||||||
\(259\) | −4.90415e14 | −1.62467 | ||||||||
\(260\) | − | 8.44475e13i | − | 0.273367i | ||||||
\(261\) | −4.92044e13 | −0.155654 | ||||||||
\(262\) | 4.30696e14 | 1.33157 | ||||||||
\(263\) | 2.25829e14i | 0.682410i | 0.939989 | + | 0.341205i | \(0.110835\pi\) | ||||
−0.939989 | + | 0.341205i | \(0.889165\pi\) | |||||||
\(264\) | 3.63182e14i | 1.07275i | ||||||||
\(265\) | 2.97518e14 | 0.859088 | ||||||||
\(266\) | 4.52801e13 | 0.127825 | ||||||||
\(267\) | 1.51486e14i | 0.418124i | ||||||||
\(268\) | 9.45804e14i | 2.55266i | ||||||||
\(269\) | −7.03869e13 | −0.185771 | −0.0928855 | − | 0.995677i | \(-0.529609\pi\) | ||||
−0.0928855 | + | 0.995677i | \(0.529609\pi\) | |||||||
\(270\) | − | 2.91634e14i | − | 0.752759i | ||||||
\(271\) | 5.91195e14 | 1.49250 | 0.746251 | − | 0.665665i | \(-0.231852\pi\) | ||||
0.746251 | + | 0.665665i | \(0.231852\pi\) | |||||||
\(272\) | 3.93061e14i | 0.970614i | ||||||||
\(273\) | 2.44483e14i | 0.590571i | ||||||||
\(274\) | 2.05239e14i | 0.485017i | ||||||||
\(275\) | − | 1.78753e14i | − | 0.413292i | ||||||
\(276\) | −6.58320e14 | − | 7.30495e14i | −1.48930 | − | 1.65258i | ||||
\(277\) | −4.77761e14 | −1.05763 | −0.528813 | − | 0.848738i | \(-0.677363\pi\) | ||||
−0.528813 | + | 0.848738i | \(0.677363\pi\) | |||||||
\(278\) | −5.55399e14 | −1.20320 | ||||||||
\(279\) | −1.06656e14 | −0.226132 | ||||||||
\(280\) | −8.41415e14 | −1.74607 | ||||||||
\(281\) | 8.18776e14i | 1.66313i | 0.555425 | + | 0.831567i | \(0.312556\pi\) | ||||
−0.555425 | + | 0.831567i | \(0.687444\pi\) | |||||||
\(282\) | −1.82697e13 | −0.0363276 | ||||||||
\(283\) | − | 1.88967e14i | − | 0.367848i | −0.982940 | − | 0.183924i | \(-0.941120\pi\) | ||
0.982940 | − | 0.183924i | \(-0.0588800\pi\) | |||||||
\(284\) | 1.44030e15 | 2.74500 | ||||||||
\(285\) | 1.04748e13 | 0.0195469 | ||||||||
\(286\) | 1.42204e14i | 0.259845i | ||||||||
\(287\) | 1.23886e14i | 0.221681i | ||||||||
\(288\) | −1.74481e13 | −0.0305768 | ||||||||
\(289\) | 1.63429e14 | 0.280505 | ||||||||
\(290\) | − | 4.33251e14i | − | 0.728370i | ||||||
\(291\) | − | 7.66445e14i | − | 1.26219i | ||||||
\(292\) | −1.86542e15 | −3.00940 | ||||||||
\(293\) | − | 6.81718e14i | − | 1.07745i | −0.842480 | − | 0.538727i | \(-0.818905\pi\) | ||
0.842480 | − | 0.538727i | \(-0.181095\pi\) | |||||||
\(294\) | 3.53688e15 | 5.47691 | ||||||||
\(295\) | 2.07547e14i | 0.314909i | ||||||||
\(296\) | − | 1.01330e15i | − | 1.50656i | ||||||
\(297\) | 3.29938e14i | 0.480721i | ||||||||
\(298\) | 1.03859e15i | 1.48302i | ||||||||
\(299\) | −1.31863e14 | − | 1.46320e14i | −0.184542 | − | 0.204775i | ||||
\(300\) | 1.24127e15 | 1.70270 | ||||||||
\(301\) | −2.45797e15 | −3.30504 | ||||||||
\(302\) | −6.49970e14 | −0.856745 | ||||||||
\(303\) | 5.52010e14 | 0.713330 | ||||||||
\(304\) | 3.35430e13i | 0.0424972i | ||||||||
\(305\) | −5.39377e14 | −0.670028 | ||||||||
\(306\) | − | 2.19662e14i | − | 0.267563i | ||||||
\(307\) | 7.45905e14 | 0.890950 | 0.445475 | − | 0.895294i | \(-0.353035\pi\) | ||||
0.445475 | + | 0.895294i | \(0.353035\pi\) | |||||||
\(308\) | 1.86082e15 | 2.17972 | ||||||||
\(309\) | − | 8.46493e14i | − | 0.972461i | ||||||
\(310\) | − | 9.39122e14i | − | 1.05816i | ||||||
\(311\) | 4.61018e14 | 0.509514 | 0.254757 | − | 0.967005i | \(-0.418005\pi\) | ||||
0.254757 | + | 0.967005i | \(0.418005\pi\) | |||||||
\(312\) | −5.05152e14 | −0.547639 | ||||||||
\(313\) | 9.87907e14i | 1.05063i | 0.850908 | + | 0.525315i | \(0.176053\pi\) | ||||
−0.850908 | + | 0.525315i | \(0.823947\pi\) | |||||||
\(314\) | − | 1.76852e15i | − | 1.84515i | ||||||
\(315\) | 1.68588e14 | 0.172569 | ||||||||
\(316\) | 2.43536e15i | 2.44591i | ||||||||
\(317\) | 1.46800e15 | 1.44667 | 0.723337 | − | 0.690495i | \(-0.242607\pi\) | ||||
0.723337 | + | 0.690495i | \(0.242607\pi\) | |||||||
\(318\) | − | 3.47896e15i | − | 3.36424i | ||||||
\(319\) | 4.90155e14i | 0.465146i | ||||||||
\(320\) | 4.41501e14i | 0.411180i | ||||||||
\(321\) | − | 1.37975e14i | − | 0.126116i | ||||||
\(322\) | −2.84989e15 | + | 2.56831e15i | −2.55677 | + | 2.30416i | ||||
\(323\) | −3.57731e13 | −0.0315022 | ||||||||
\(324\) | −2.71907e15 | −2.35045 | ||||||||
\(325\) | 2.48629e14 | 0.210985 | ||||||||
\(326\) | −8.21426e14 | −0.684326 | ||||||||
\(327\) | 1.95366e15i | 1.59795i | ||||||||
\(328\) | −2.55973e14 | −0.205566 | ||||||||
\(329\) | 4.78863e13i | 0.0377604i | ||||||||
\(330\) | 6.40730e14 | 0.496125 | ||||||||
\(331\) | 1.58575e12 | 0.00120578 | 0.000602888 | − | 1.00000i | \(-0.499808\pi\) | ||||
0.000602888 | 1.00000i | \(0.499808\pi\) | ||||||||
\(332\) | 1.06970e15i | 0.798794i | ||||||||
\(333\) | 2.03027e14i | 0.148898i | ||||||||
\(334\) | −9.01940e14 | −0.649679 | ||||||||
\(335\) | 8.53594e14 | 0.603924 | ||||||||
\(336\) | 3.52750e15i | 2.45150i | ||||||||
\(337\) | − | 7.60014e13i | − | 0.0518850i | −0.999663 | − | 0.0259425i | \(-0.991741\pi\) | ||
0.999663 | − | 0.0259425i | \(-0.00825869\pi\) | |||||||
\(338\) | 2.40513e15 | 1.61301 | ||||||||
\(339\) | − | 1.44350e15i | − | 0.951082i | ||||||
\(340\) | 1.29945e15 | 0.841176 | ||||||||
\(341\) | 1.06247e15i | 0.675755i | ||||||||
\(342\) | − | 1.87455e13i | − | 0.0117149i | ||||||
\(343\) | − | 6.05977e15i | − | 3.72127i | ||||||
\(344\) | − | 5.07867e15i | − | 3.06478i | ||||||
\(345\) | −6.59277e14 | + | 5.94138e14i | −0.390979 | + | 0.352349i | ||||
\(346\) | 3.69769e15 | 2.15513 | ||||||||
\(347\) | 1.15982e15 | 0.664377 | 0.332189 | − | 0.943213i | \(-0.392213\pi\) | ||||
0.332189 | + | 0.943213i | \(0.392213\pi\) | |||||||
\(348\) | −3.40365e15 | −1.91633 | ||||||||
\(349\) | 8.12282e14 | 0.449525 | 0.224763 | − | 0.974414i | \(-0.427839\pi\) | ||||
0.224763 | + | 0.974414i | \(0.427839\pi\) | |||||||
\(350\) | − | 4.84257e15i | − | 2.63432i | ||||||
\(351\) | −4.58913e14 | −0.245407 | ||||||||
\(352\) | 1.73811e14i | 0.0913735i | ||||||||
\(353\) | 1.28013e15 | 0.661615 | 0.330807 | − | 0.943698i | \(-0.392679\pi\) | ||||
0.330807 | + | 0.943698i | \(0.392679\pi\) | |||||||
\(354\) | 2.42691e15 | 1.23320 | ||||||||
\(355\) | − | 1.29988e15i | − | 0.649431i | ||||||
\(356\) | 1.60372e15i | 0.787821i | ||||||||
\(357\) | −3.76202e15 | −1.81724 | ||||||||
\(358\) | 2.22040e15 | 1.05471 | ||||||||
\(359\) | 1.55094e14i | 0.0724485i | 0.999344 | + | 0.0362243i | \(0.0115331\pi\) | ||||
−0.999344 | + | 0.0362243i | \(0.988467\pi\) | |||||||
\(360\) | 3.48337e14i | 0.160024i | ||||||||
\(361\) | 2.21026e15 | 0.998621 | ||||||||
\(362\) | 2.53440e15i | 1.12622i | ||||||||
\(363\) | 1.76116e15 | 0.769767 | ||||||||
\(364\) | 2.58823e15i | 1.11274i | ||||||||
\(365\) | 1.68355e15i | 0.711984i | ||||||||
\(366\) | 6.30708e15i | 2.62387i | ||||||||
\(367\) | 3.46051e15i | 1.41626i | 0.706080 | + | 0.708132i | \(0.250462\pi\) | ||||
−0.706080 | + | 0.708132i | \(0.749538\pi\) | |||||||
\(368\) | −1.90257e15 | − | 2.11116e15i | −0.766046 | − | 0.850031i | ||||
\(369\) | 5.12873e13 | 0.0203166 | ||||||||
\(370\) | −1.78768e15 | −0.696752 | ||||||||
\(371\) | −9.11861e15 | −3.49692 | ||||||||
\(372\) | −7.37781e15 | −2.78400 | ||||||||
\(373\) | 2.87796e15i | 1.06864i | 0.845282 | + | 0.534320i | \(0.179432\pi\) | ||||
−0.845282 | + | 0.534320i | \(0.820568\pi\) | |||||||
\(374\) | −2.18819e15 | −0.799566 | ||||||||
\(375\) | − | 2.58391e15i | − | 0.929158i | ||||||
\(376\) | −9.89431e13 | −0.0350153 | ||||||||
\(377\) | −6.81760e14 | −0.237456 | ||||||||
\(378\) | 8.93829e15i | 3.06411i | ||||||||
\(379\) | 4.91863e15i | 1.65962i | 0.558046 | + | 0.829810i | \(0.311551\pi\) | ||||
−0.558046 | + | 0.829810i | \(0.688449\pi\) | |||||||
\(380\) | 1.10892e14 | 0.0368299 | ||||||||
\(381\) | 6.81989e14 | 0.222960 | ||||||||
\(382\) | − | 6.98783e15i | − | 2.24886i | ||||||
\(383\) | − | 1.34592e15i | − | 0.426411i | −0.977007 | − | 0.213205i | \(-0.931610\pi\) | ||
0.977007 | − | 0.213205i | \(-0.0683903\pi\) | |||||||
\(384\) | 5.75211e15 | 1.79407 | ||||||||
\(385\) | − | 1.67940e15i | − | 0.515692i | ||||||
\(386\) | −6.46561e15 | −1.95472 | ||||||||
\(387\) | 1.01757e15i | 0.302900i | ||||||||
\(388\) | − | 8.11401e15i | − | 2.37818i | ||||||
\(389\) | 1.76711e15i | 0.509995i | 0.966942 | + | 0.254998i | \(0.0820747\pi\) | ||||
−0.966942 | + | 0.254998i | \(0.917925\pi\) | |||||||
\(390\) | 8.91196e14i | 0.253271i | ||||||||
\(391\) | 2.25152e15 | − | 2.02907e15i | 0.630109 | − | 0.567853i | ||||
\(392\) | 1.91546e16 | 5.27907 | ||||||||
\(393\) | −3.05371e15 | −0.828842 | ||||||||
\(394\) | −1.07667e16 | −2.87810 | ||||||||
\(395\) | 2.19792e15 | 0.578669 | ||||||||
\(396\) | − | 7.70360e14i | − | 0.199767i | ||||||
\(397\) | 2.47007e15 | 0.630908 | 0.315454 | − | 0.948941i | \(-0.397843\pi\) | ||||
0.315454 | + | 0.948941i | \(0.397843\pi\) | |||||||
\(398\) | 1.72076e15i | 0.432935i | ||||||||
\(399\) | −3.21043e14 | −0.0795656 | ||||||||
\(400\) | 3.58732e15 | 0.875811 | ||||||||
\(401\) | 9.25290e14i | 0.222542i | 0.993790 | + | 0.111271i | \(0.0354921\pi\) | ||||
−0.993790 | + | 0.111271i | \(0.964508\pi\) | |||||||
\(402\) | − | 9.98131e15i | − | 2.36500i | ||||||
\(403\) | −1.47779e15 | −0.344971 | ||||||||
\(404\) | 5.84388e15 | 1.34404 | ||||||||
\(405\) | 2.45398e15i | 0.556085i | ||||||||
\(406\) | 1.32787e16i | 2.96483i | ||||||||
\(407\) | 2.02247e15 | 0.444954 | ||||||||
\(408\) | − | 7.77312e15i | − | 1.68513i | ||||||
\(409\) | −1.94278e15 | −0.415034 | −0.207517 | − | 0.978231i | \(-0.566538\pi\) | ||||
−0.207517 | + | 0.978231i | \(0.566538\pi\) | |||||||
\(410\) | 4.51591e14i | 0.0950698i | ||||||||
\(411\) | − | 1.45518e15i | − | 0.301901i | ||||||
\(412\) | − | 8.96144e15i | − | 1.83229i | ||||||
\(413\) | − | 6.36111e15i | − | 1.28184i | ||||||
\(414\) | 1.06325e15 | + | 1.17982e15i | 0.211171 | + | 0.234323i | ||||
\(415\) | 9.65415e14 | 0.188984 | ||||||||
\(416\) | −2.41754e14 | −0.0466460 | ||||||||
\(417\) | 3.93786e15 | 0.748936 | ||||||||
\(418\) | −1.86735e14 | −0.0350080 | ||||||||
\(419\) | − | 1.47609e15i | − | 0.272791i | −0.990654 | − | 0.136396i | \(-0.956448\pi\) | ||
0.990654 | − | 0.136396i | \(-0.0435518\pi\) | |||||||
\(420\) | 1.16618e16 | 2.12457 | ||||||||
\(421\) | − | 2.20439e15i | − | 0.395909i | −0.980211 | − | 0.197955i | \(-0.936570\pi\) | ||
0.980211 | − | 0.197955i | \(-0.0634299\pi\) | |||||||
\(422\) | −5.19955e15 | −0.920642 | ||||||||
\(423\) | 1.98244e13 | 0.00346066 | ||||||||
\(424\) | − | 1.88409e16i | − | 3.24271i | ||||||
\(425\) | 3.82582e15i | 0.649219i | ||||||||
\(426\) | −1.51999e16 | −2.54321 | ||||||||
\(427\) | 1.65313e16 | 2.72735 | ||||||||
\(428\) | − | 1.46068e15i | − | 0.237625i | ||||||
\(429\) | − | 1.00825e15i | − | 0.161742i | ||||||
\(430\) | −8.95986e15 | −1.41739 | ||||||||
\(431\) | − | 7.55030e15i | − | 1.17788i | −0.808177 | − | 0.588939i | \(-0.799546\pi\) | ||
0.808177 | − | 0.588939i | \(-0.200454\pi\) | |||||||
\(432\) | −6.62139e15 | −1.01870 | ||||||||
\(433\) | − | 4.52905e15i | − | 0.687195i | −0.939117 | − | 0.343597i | \(-0.888354\pi\) | ||
0.939117 | − | 0.343597i | \(-0.111646\pi\) | |||||||
\(434\) | 2.87831e16i | 4.30724i | ||||||||
\(435\) | 3.07182e15i | 0.453378i | ||||||||
\(436\) | 2.06825e16i | 3.01081i | ||||||||
\(437\) | 1.92140e14 | − | 1.73156e14i | 0.0275886 | − | 0.0248627i | ||||
\(438\) | 1.96863e16 | 2.78817 | ||||||||
\(439\) | −1.51533e15 | −0.211700 | −0.105850 | − | 0.994382i | \(-0.533756\pi\) | ||||
−0.105850 | + | 0.994382i | \(0.533756\pi\) | |||||||
\(440\) | 3.46999e15 | 0.478203 | ||||||||
\(441\) | −3.83786e15 | −0.521744 | ||||||||
\(442\) | − | 3.04356e15i | − | 0.408177i | ||||||
\(443\) | −4.08853e15 | −0.540934 | −0.270467 | − | 0.962729i | \(-0.587178\pi\) | ||||
−0.270467 | + | 0.962729i | \(0.587178\pi\) | |||||||
\(444\) | 1.40441e16i | 1.83314i | ||||||||
\(445\) | 1.44736e15 | 0.186388 | ||||||||
\(446\) | −1.87567e16 | −2.38313 | ||||||||
\(447\) | − | 7.36379e15i | − | 0.923116i | ||||||
\(448\) | − | 1.35315e16i | − | 1.67371i | ||||||
\(449\) | −9.15793e15 | −1.11768 | −0.558842 | − | 0.829274i | \(-0.688754\pi\) | ||||
−0.558842 | + | 0.829274i | \(0.688754\pi\) | |||||||
\(450\) | −2.00477e15 | −0.241430 | ||||||||
\(451\) | − | 5.10904e14i | − | 0.0607127i | ||||||
\(452\) | − | 1.52817e16i | − | 1.79201i | ||||||
\(453\) | 4.60839e15 | 0.533286 | ||||||||
\(454\) | 2.73568e16i | 3.12413i | ||||||||
\(455\) | 2.33589e15 | 0.263260 | ||||||||
\(456\) | − | 6.63341e14i | − | 0.0737815i | ||||||
\(457\) | − | 1.01341e16i | − | 1.11247i | −0.831026 | − | 0.556234i | \(-0.812246\pi\) | ||
0.831026 | − | 0.556234i | \(-0.187754\pi\) | |||||||
\(458\) | 1.29327e16i | 1.40119i | ||||||||
\(459\) | − | 7.06161e15i | − | 0.755140i | ||||||
\(460\) | −6.97947e15 | + | 6.28987e15i | −0.736674 | + | 0.663888i | ||||
\(461\) | −4.10442e15 | −0.427608 | −0.213804 | − | 0.976877i | \(-0.568585\pi\) | ||||
−0.213804 | + | 0.976877i | \(0.568585\pi\) | |||||||
\(462\) | −1.96377e16 | −2.01948 | ||||||||
\(463\) | 1.11295e16 | 1.12977 | 0.564886 | − | 0.825169i | \(-0.308920\pi\) | ||||
0.564886 | + | 0.825169i | \(0.308920\pi\) | |||||||
\(464\) | −9.83672e15 | −0.985694 | ||||||||
\(465\) | 6.65852e15i | 0.658658i | ||||||||
\(466\) | 2.25030e16 | 2.19748 | ||||||||
\(467\) | 1.62066e16i | 1.56239i | 0.624284 | + | 0.781197i | \(0.285391\pi\) | ||||
−0.624284 | + | 0.781197i | \(0.714609\pi\) | |||||||
\(468\) | 1.07150e15 | 0.101980 | ||||||||
\(469\) | −2.61618e16 | −2.45827 | ||||||||
\(470\) | 1.74557e14i | 0.0161938i | ||||||||
\(471\) | 1.25391e16i | 1.14852i | ||||||||
\(472\) | 1.31434e16 | 1.18865 | ||||||||
\(473\) | 1.01367e16 | 0.905165 | ||||||||
\(474\) | − | 2.57009e16i | − | 2.26610i | ||||||
\(475\) | 3.26487e14i | 0.0284253i | ||||||||
\(476\) | −3.98269e16 | −3.42400 | ||||||||
\(477\) | 3.77501e15i | 0.320485i | ||||||||
\(478\) | 7.95078e15 | 0.666564 | ||||||||
\(479\) | 2.24795e15i | 0.186111i | 0.995661 | + | 0.0930557i | \(0.0296635\pi\) | ||||
−0.995661 | + | 0.0930557i | \(0.970337\pi\) | |||||||
\(480\) | 1.08928e15i | 0.0890618i | ||||||||
\(481\) | 2.81307e15i | 0.227148i | ||||||||
\(482\) | − | 1.89558e15i | − | 0.151168i | ||||||
\(483\) | 2.02061e16 | − | 1.82097e16i | 1.59148 | − | 1.43424i | ||||
\(484\) | 1.86446e16 | 1.45038 | ||||||||
\(485\) | −7.32295e15 | −0.562646 | ||||||||
\(486\) | 8.21683e15 | 0.623572 | ||||||||
\(487\) | 8.99200e15 | 0.674035 | 0.337018 | − | 0.941498i | \(-0.390582\pi\) | ||||
0.337018 | + | 0.941498i | \(0.390582\pi\) | |||||||
\(488\) | 3.41572e16i | 2.52908i | ||||||||
\(489\) | 5.82404e15 | 0.425962 | ||||||||
\(490\) | − | 3.37928e16i | − | 2.44145i | ||||||
\(491\) | 1.31958e16 | 0.941772 | 0.470886 | − | 0.882194i | \(-0.343934\pi\) | ||||
0.470886 | + | 0.882194i | \(0.343934\pi\) | |||||||
\(492\) | 3.54774e15 | 0.250127 | ||||||||
\(493\) | − | 1.04907e16i | − | 0.730673i | ||||||
\(494\) | − | 2.59731e14i | − | 0.0178715i | ||||||
\(495\) | −6.95255e14 | −0.0472621 | ||||||||
\(496\) | −2.13222e16 | −1.43200 | ||||||||
\(497\) | 3.98400e16i | 2.64351i | ||||||||
\(498\) | − | 1.12889e16i | − | 0.740072i | ||||||
\(499\) | 3.42307e13 | 0.00221724 | 0.00110862 | − | 0.999999i | \(-0.499647\pi\) | ||||
0.00110862 | + | 0.999999i | \(0.499647\pi\) | |||||||
\(500\) | − | 2.73547e16i | − | 1.75070i | ||||||
\(501\) | 6.39490e15 | 0.404396 | ||||||||
\(502\) | − | 5.35494e15i | − | 0.334605i | ||||||
\(503\) | − | 1.90470e16i | − | 1.17603i | −0.808849 | − | 0.588016i | \(-0.799909\pi\) | ||
0.808849 | − | 0.588016i | \(-0.200091\pi\) | |||||||
\(504\) | − | 1.06762e16i | − | 0.651377i | ||||||
\(505\) | − | 5.27414e15i | − | 0.317982i | ||||||
\(506\) | 1.17529e16 | − | 1.05917e16i | 0.700233 | − | 0.631048i | ||||
\(507\) | −1.70528e16 | −1.00403 | ||||||||
\(508\) | 7.21991e15 | 0.420097 | ||||||||
\(509\) | −3.15135e16 | −1.81213 | −0.906066 | − | 0.423137i | \(-0.860929\pi\) | ||||
−0.906066 | + | 0.423137i | \(0.860929\pi\) | |||||||
\(510\) | −1.37134e16 | −0.779338 | ||||||||
\(511\) | − | 5.15992e16i | − | 2.89813i | ||||||
\(512\) | 3.41999e16 | 1.89848 | ||||||||
\(513\) | − | 6.02622e14i | − | 0.0330629i | ||||||
\(514\) | 3.74917e16 | 2.03309 | ||||||||
\(515\) | −8.08776e15 | −0.433496 | ||||||||
\(516\) | 7.03893e16i | 3.72914i | ||||||||
\(517\) | − | 1.97483e14i | − | 0.0103416i | ||||||
\(518\) | 5.47904e16 | 2.83613 | ||||||||
\(519\) | −2.62172e16 | −1.34147 | ||||||||
\(520\) | 4.82644e15i | 0.244122i | ||||||||
\(521\) | 3.67283e16i | 1.83643i | 0.396082 | + | 0.918215i | \(0.370370\pi\) | ||||
−0.396082 | + | 0.918215i | \(0.629630\pi\) | |||||||
\(522\) | 5.49725e15 | 0.271720 | ||||||||
\(523\) | 2.06476e16i | 1.00892i | 0.863434 | + | 0.504462i | \(0.168309\pi\) | ||||
−0.863434 | + | 0.504462i | \(0.831691\pi\) | |||||||
\(524\) | −3.23282e16 | −1.56169 | ||||||||
\(525\) | 3.43346e16i | 1.63974i | ||||||||
\(526\) | − | 2.52302e16i | − | 1.19126i | ||||||
\(527\) | − | 2.27398e16i | − | 1.06151i | ||||||
\(528\) | − | 1.45474e16i | − | 0.671401i | ||||||
\(529\) | −2.27162e15 | + | 2.17966e16i | −0.103658 | + | 0.994613i | ||||
\(530\) | −3.32395e16 | −1.49968 | ||||||||
\(531\) | −2.63343e15 | −0.117478 | ||||||||
\(532\) | −3.39874e15 | −0.149916 | ||||||||
\(533\) | 7.10619e14 | 0.0309937 | ||||||||
\(534\) | − | 1.69244e16i | − | 0.729905i | ||||||
\(535\) | −1.31827e15 | −0.0562189 | ||||||||
\(536\) | − | 5.40556e16i | − | 2.27957i | ||||||
\(537\) | −1.57430e16 | −0.656510 | ||||||||
\(538\) | 7.86380e15 | 0.324294 | ||||||||
\(539\) | 3.82312e16i | 1.55914i | ||||||||
\(540\) | 2.18902e16i | 0.882849i | ||||||||
\(541\) | 4.00081e16 | 1.59575 | 0.797874 | − | 0.602824i | \(-0.205958\pi\) | ||||
0.797874 | + | 0.602824i | \(0.205958\pi\) | |||||||
\(542\) | −6.60498e16 | −2.60541 | ||||||||
\(543\) | − | 1.79693e16i | − | 0.701024i | ||||||
\(544\) | − | 3.72004e15i | − | 0.143534i | ||||||
\(545\) | 1.86661e16 | 0.712319 | ||||||||
\(546\) | − | 2.73142e16i | − | 1.03094i | ||||||
\(547\) | −8.35881e15 | −0.312047 | −0.156024 | − | 0.987753i | \(-0.549868\pi\) | ||||
−0.156024 | + | 0.987753i | \(0.549868\pi\) | |||||||
\(548\) | − | 1.54053e16i | − | 0.568836i | ||||||
\(549\) | − | 6.84380e15i | − | 0.249956i | ||||||
\(550\) | 1.99708e16i | 0.721470i | ||||||||
\(551\) | − | 8.95254e14i | − | 0.0319916i | ||||||
\(552\) | 3.76250e16 | + | 4.17501e16i | 1.32997 | + | 1.47578i | ||||
\(553\) | −6.73641e16 | −2.35547 | ||||||||
\(554\) | 5.33767e16 | 1.84626 | ||||||||
\(555\) | 1.26749e16 | 0.433697 | ||||||||
\(556\) | 4.16884e16 | 1.41113 | ||||||||
\(557\) | 4.12739e16i | 1.38212i | 0.722799 | + | 0.691058i | \(0.242855\pi\) | ||||
−0.722799 | + | 0.691058i | \(0.757145\pi\) | |||||||
\(558\) | 1.19159e16 | 0.394750 | ||||||||
\(559\) | 1.40991e16i | 0.462085i | ||||||||
\(560\) | 3.37032e16 | 1.09281 | ||||||||
\(561\) | 1.55146e16 | 0.497694 | ||||||||
\(562\) | − | 9.14757e16i | − | 2.90327i | ||||||
\(563\) | − | 6.30566e15i | − | 0.198007i | −0.995087 | − | 0.0990035i | \(-0.968435\pi\) | ||
0.995087 | − | 0.0990035i | \(-0.0315655\pi\) | |||||||
\(564\) | 1.37133e15 | 0.0426057 | ||||||||
\(565\) | −1.37918e16 | −0.423965 | ||||||||
\(566\) | 2.11119e16i | 0.642139i | ||||||||
\(567\) | − | 7.52119e16i | − | 2.26354i | ||||||
\(568\) | −8.23176e16 | −2.45134 | ||||||||
\(569\) | 1.79769e16i | 0.529713i | 0.964288 | + | 0.264857i | \(0.0853246\pi\) | ||||
−0.964288 | + | 0.264857i | \(0.914675\pi\) | |||||||
\(570\) | −1.17028e15 | −0.0341223 | ||||||||
\(571\) | 1.05021e16i | 0.303013i | 0.988456 | + | 0.151507i | \(0.0484125\pi\) | ||||
−0.988456 | + | 0.151507i | \(0.951588\pi\) | |||||||
\(572\) | − | 1.06738e16i | − | 0.304751i | ||||||
\(573\) | 4.95448e16i | 1.39981i | ||||||||
\(574\) | − | 1.38408e16i | − | 0.386981i | ||||||
\(575\) | −1.85185e16 | − | 2.05488e16i | −0.512389 | − | 0.568565i | ||||
\(576\) | −5.60192e15 | −0.153392 | ||||||||
\(577\) | −3.21060e16 | −0.870025 | −0.435013 | − | 0.900424i | \(-0.643256\pi\) | ||||
−0.435013 | + | 0.900424i | \(0.643256\pi\) | |||||||
\(578\) | −1.82587e16 | −0.489668 | ||||||||
\(579\) | 4.58422e16 | 1.21673 | ||||||||
\(580\) | 3.25200e16i | 0.854245i | ||||||||
\(581\) | −2.95890e16 | −0.769259 | ||||||||
\(582\) | 8.56292e16i | 2.20335i | ||||||||
\(583\) | 3.76051e16 | 0.957714 | ||||||||
\(584\) | 1.06615e17 | 2.68745 | ||||||||
\(585\) | − | 9.67035e14i | − | 0.0241272i | ||||||
\(586\) | 7.61633e16i | 1.88087i | ||||||||
\(587\) | −3.87006e16 | −0.945996 | −0.472998 | − | 0.881064i | \(-0.656828\pi\) | ||||
−0.472998 | + | 0.881064i | \(0.656828\pi\) | |||||||
\(588\) | −2.65479e17 | −6.42342 | ||||||||
\(589\) | − | 1.94056e15i | − | 0.0464768i | ||||||
\(590\) | − | 2.31877e16i | − | 0.549726i | ||||||
\(591\) | 7.63378e16 | 1.79149 | ||||||||
\(592\) | 4.05881e16i | 0.942906i | ||||||||
\(593\) | −4.69375e16 | −1.07942 | −0.539711 | − | 0.841850i | \(-0.681467\pi\) | ||||
−0.539711 | + | 0.841850i | \(0.681467\pi\) | |||||||
\(594\) | − | 3.68615e16i | − | 0.839178i | ||||||
\(595\) | 3.59440e16i | 0.810074i | ||||||||
\(596\) | − | 7.79571e16i | − | 1.73931i | ||||||
\(597\) | − | 1.22005e16i | − | 0.269483i | ||||||
\(598\) | 1.47321e16 | + | 1.63472e16i | 0.322149 | + | 0.357468i | ||||
\(599\) | 1.08593e16 | 0.235093 | 0.117546 | − | 0.993067i | \(-0.462497\pi\) | ||||
0.117546 | + | 0.993067i | \(0.462497\pi\) | |||||||
\(600\) | −7.09424e16 | −1.52054 | ||||||||
\(601\) | −1.24364e15 | −0.0263905 | −0.0131953 | − | 0.999913i | \(-0.504200\pi\) | ||||
−0.0131953 | + | 0.999913i | \(0.504200\pi\) | |||||||
\(602\) | 2.74610e17 | 5.76950 | ||||||||
\(603\) | 1.08307e16i | 0.225296i | ||||||||
\(604\) | 4.87870e16 | 1.00481 | ||||||||
\(605\) | − | 1.68269e16i | − | 0.343140i | ||||||
\(606\) | −6.16719e16 | −1.24524 | ||||||||
\(607\) | 5.40600e16 | 1.08080 | 0.540398 | − | 0.841409i | \(-0.318274\pi\) | ||||
0.540398 | + | 0.841409i | \(0.318274\pi\) | |||||||
\(608\) | − | 3.17460e14i | − | 0.00628446i | ||||||
\(609\) | − | 9.41481e16i | − | 1.84547i | ||||||
\(610\) | 6.02605e16 | 1.16964 | ||||||||
\(611\) | 2.74681e14 | 0.00527935 | ||||||||
\(612\) | 1.64879e16i | 0.313803i | ||||||||
\(613\) | − | 4.01852e15i | − | 0.0757361i | −0.999283 | − | 0.0378680i | \(-0.987943\pi\) | ||
0.999283 | − | 0.0378680i | \(-0.0120567\pi\) | |||||||
\(614\) | −8.33344e16 | −1.55530 | ||||||||
\(615\) | − | 3.20185e15i | − | 0.0591767i | ||||||
\(616\) | −1.06352e17 | −1.94653 | ||||||||
\(617\) | − | 9.62972e16i | − | 1.74543i | −0.488230 | − | 0.872715i | \(-0.662357\pi\) | ||
0.488230 | − | 0.872715i | \(-0.337643\pi\) | |||||||
\(618\) | 9.45723e16i | 1.69759i | ||||||||
\(619\) | − | 3.34623e16i | − | 0.594856i | −0.954744 | − | 0.297428i | \(-0.903871\pi\) | ||
0.954744 | − | 0.297428i | \(-0.0961288\pi\) | |||||||
\(620\) | 7.04908e16i | 1.24103i | ||||||||
\(621\) | 3.41810e16 | + | 3.79285e16i | 0.595985 | + | 0.661326i | ||||
\(622\) | −5.15062e16 | −0.889440 | ||||||||
\(623\) | −4.43602e16 | −0.758692 | ||||||||
\(624\) | 2.02341e16 | 0.342749 | ||||||||
\(625\) | 2.09325e16 | 0.351189 | ||||||||
\(626\) | − | 1.10371e17i | − | 1.83405i | ||||||
\(627\) | 1.32398e15 | 0.0217909 | ||||||||
\(628\) | 1.32746e17i | 2.16402i | ||||||||
\(629\) | −4.32866e16 | −0.698956 | ||||||||
\(630\) | −1.88350e16 | −0.301248 | ||||||||
\(631\) | 7.00985e16i | 1.11054i | 0.831672 | + | 0.555268i | \(0.187384\pi\) | ||||
−0.831672 | + | 0.555268i | \(0.812616\pi\) | |||||||
\(632\) | − | 1.39188e17i | − | 2.18424i | ||||||
\(633\) | 3.68656e16 | 0.573059 | ||||||||
\(634\) | −1.64009e17 | −2.52541 | ||||||||
\(635\) | − | 6.51601e15i | − | 0.0993893i | ||||||
\(636\) | 2.61132e17i | 3.94563i | ||||||||
\(637\) | −5.31760e16 | −0.795938 | ||||||||
\(638\) | − | 5.47613e16i | − | 0.811989i | ||||||
\(639\) | 1.64933e16 | 0.242272 | ||||||||
\(640\) | − | 5.49581e16i | − | 0.799746i | ||||||
\(641\) | 3.96040e16i | 0.570941i | 0.958388 | + | 0.285470i | \(0.0921498\pi\) | ||||
−0.958388 | + | 0.285470i | \(0.907850\pi\) | |||||||
\(642\) | 1.54149e16i | 0.220156i | ||||||||
\(643\) | 2.71327e16i | 0.383908i | 0.981404 | + | 0.191954i | \(0.0614824\pi\) | ||||
−0.981404 | + | 0.191954i | \(0.938518\pi\) | |||||||
\(644\) | 2.13913e17 | − | 1.92778e17i | 2.99863 | − | 2.70236i | ||||
\(645\) | 6.35268e16 | 0.882265 | ||||||||
\(646\) | 3.99666e15 | 0.0549923 | ||||||||
\(647\) | 1.10223e17 | 1.50262 | 0.751309 | − | 0.659951i | \(-0.229423\pi\) | ||||
0.751309 | + | 0.659951i | \(0.229423\pi\) | |||||||
\(648\) | 1.55403e17 | 2.09899 | ||||||||
\(649\) | 2.62332e16i | 0.351062i | ||||||||
\(650\) | −2.77775e16 | −0.368309 | ||||||||
\(651\) | − | 2.04077e17i | − | 2.68107i | ||||||
\(652\) | 6.16565e16 | 0.802589 | ||||||||
\(653\) | 7.33584e16 | 0.946173 | 0.473087 | − | 0.881016i | \(-0.343140\pi\) | ||||
0.473087 | + | 0.881016i | \(0.343140\pi\) | |||||||
\(654\) | − | 2.18268e17i | − | 2.78948i | ||||||
\(655\) | 2.91764e16i | 0.369474i | ||||||||
\(656\) | 1.02531e16 | 0.128657 | ||||||||
\(657\) | −2.13615e16 | −0.265607 | ||||||||
\(658\) | − | 5.34998e15i | − | 0.0659169i | ||||||
\(659\) | 4.26852e16i | 0.521153i | 0.965453 | + | 0.260576i | \(0.0839126\pi\) | ||||
−0.965453 | + | 0.260576i | \(0.916087\pi\) | |||||||
\(660\) | −4.80934e16 | −0.581865 | ||||||||
\(661\) | − | 9.61409e16i | − | 1.15265i | −0.817219 | − | 0.576327i | \(-0.804485\pi\) | ||
0.817219 | − | 0.576327i | \(-0.195515\pi\) | |||||||
\(662\) | −1.77164e14 | −0.00210488 | ||||||||
\(663\) | 2.15793e16i | 0.254072i | ||||||||
\(664\) | − | 6.11369e16i | − | 0.713337i | ||||||
\(665\) | 3.06738e15i | 0.0354681i | ||||||||
\(666\) | − | 2.26827e16i | − | 0.259925i | ||||||
\(667\) | 5.07793e16 | + | 5.63465e16i | 0.576675 | + | 0.639899i | ||||
\(668\) | 6.76999e16 | 0.761955 | ||||||||
\(669\) | 1.32988e17 | 1.48339 | ||||||||
\(670\) | −9.53657e16 | −1.05425 | ||||||||
\(671\) | −6.81752e16 | −0.746949 | ||||||||
\(672\) | − | 3.33853e16i | − | 0.362526i | ||||||
\(673\) | −9.04138e16 | −0.973070 | −0.486535 | − | 0.873661i | \(-0.661739\pi\) | ||||
−0.486535 | + | 0.873661i | \(0.661739\pi\) | |||||||
\(674\) | 8.49107e15i | 0.0905739i | ||||||||
\(675\) | −6.44487e16 | −0.681383 | ||||||||
\(676\) | −1.80530e17 | −1.89177 | ||||||||
\(677\) | − | 3.70409e16i | − | 0.384724i | −0.981324 | − | 0.192362i | \(-0.938385\pi\) | ||
0.981324 | − | 0.192362i | \(-0.0616148\pi\) | |||||||
\(678\) | 1.61271e17i | 1.66027i | ||||||||
\(679\) | 2.24441e17 | 2.29025 | ||||||||
\(680\) | −7.42677e16 | −0.751185 | ||||||||
\(681\) | − | 1.93964e17i | − | 1.94463i | ||||||
\(682\) | − | 1.18701e17i | − | 1.17964i | ||||||
\(683\) | −9.57659e16 | −0.943380 | −0.471690 | − | 0.881764i | \(-0.656356\pi\) | ||||
−0.471690 | + | 0.881764i | \(0.656356\pi\) | |||||||
\(684\) | 1.40704e15i | 0.0137395i | ||||||||
\(685\) | −1.39034e16 | −0.134579 | ||||||||
\(686\) | 6.77013e17i | 6.49609i | ||||||||
\(687\) | − | 9.16950e16i | − | 0.872179i | ||||||
\(688\) | 2.03428e17i | 1.91814i | ||||||||
\(689\) | 5.23052e16i | 0.488911i | ||||||||
\(690\) | 7.36561e16 | − | 6.63786e16i | 0.682518 | − | 0.615083i | ||||
\(691\) | −1.26258e17 | −1.15982 | −0.579908 | − | 0.814682i | \(-0.696911\pi\) | ||||
−0.579908 | + | 0.814682i | \(0.696911\pi\) | |||||||
\(692\) | −2.77550e17 | −2.52757 | ||||||||
\(693\) | 2.13089e16 | 0.192380 | ||||||||
\(694\) | −1.29578e17 | −1.15978 | ||||||||
\(695\) | − | 3.76241e16i | − | 0.333854i | ||||||
\(696\) | 1.94529e17 | 1.71132 | ||||||||
\(697\) | 1.09348e16i | 0.0953704i | ||||||||
\(698\) | −9.07502e16 | −0.784721 | ||||||||
\(699\) | −1.59550e17 | −1.36784 | ||||||||
\(700\) | 3.63485e17i | 3.08957i | ||||||||
\(701\) | 5.24413e16i | 0.441942i | 0.975280 | + | 0.220971i | \(0.0709226\pi\) | ||||
−0.975280 | + | 0.220971i | \(0.929077\pi\) | |||||||
\(702\) | 5.12709e16 | 0.428399 | ||||||||
\(703\) | −3.69398e15 | −0.0306029 | ||||||||
\(704\) | 5.58041e16i | 0.458384i | ||||||||
\(705\) | − | 1.23764e15i | − | 0.0100799i | ||||||
\(706\) | −1.43019e17 | −1.15496 | ||||||||
\(707\) | 1.61647e17i | 1.29435i | ||||||||
\(708\) | −1.82165e17 | −1.44632 | ||||||||
\(709\) | − | 2.09036e17i | − | 1.64567i | −0.568278 | − | 0.822836i | \(-0.692390\pi\) | ||
0.568278 | − | 0.822836i | \(-0.307610\pi\) | |||||||
\(710\) | 1.45226e17i | 1.13369i | ||||||||
\(711\) | 2.78880e16i | 0.215874i | ||||||||
\(712\) | − | 9.16574e16i | − | 0.703538i | ||||||
\(713\) | 1.10070e17 | + | 1.22137e17i | 0.837782 | + | 0.929633i | ||||
\(714\) | 4.20303e17 | 3.17229 | ||||||||
\(715\) | −9.63322e15 | −0.0721000 | ||||||||
\(716\) | −1.66664e17 | −1.23698 | ||||||||
\(717\) | −5.63723e16 | −0.414907 | ||||||||
\(718\) | − | 1.73275e16i | − | 0.126471i | ||||||
\(719\) | −2.06929e16 | −0.149778 | −0.0748890 | − | 0.997192i | \(-0.523860\pi\) | ||||
−0.0748890 | + | 0.997192i | \(0.523860\pi\) | |||||||
\(720\) | − | 1.39528e16i | − | 0.100154i | ||||||
\(721\) | 2.47881e17 | 1.76454 | ||||||||
\(722\) | −2.46936e17 | −1.74326 | ||||||||
\(723\) | 1.34399e16i | 0.0940952i | ||||||||
\(724\) | − | 1.90233e17i | − | 1.32085i | ||||||
\(725\) | −9.57448e16 | −0.659306 | ||||||||
\(726\) | −1.96761e17 | −1.34376 | ||||||||
\(727\) | − | 4.60296e16i | − | 0.311767i | −0.987775 | − | 0.155884i | \(-0.950178\pi\) | ||
0.987775 | − | 0.155884i | \(-0.0498225\pi\) | |||||||
\(728\) | − | 1.47925e17i | − | 0.993697i | ||||||
\(729\) | 1.14057e17 | 0.759900 | ||||||||
\(730\) | − | 1.88091e17i | − | 1.24289i | ||||||
\(731\) | −2.16953e17 | −1.42188 | ||||||||
\(732\) | − | 4.73411e17i | − | 3.07732i | ||||||
\(733\) | 2.01711e17i | 1.30049i | 0.759726 | + | 0.650243i | \(0.225333\pi\) | ||||
−0.759726 | + | 0.650243i | \(0.774667\pi\) | |||||||
\(734\) | − | 3.86618e17i | − | 2.47232i | ||||||
\(735\) | 2.39597e17i | 1.51970i | ||||||||
\(736\) | 1.80065e16 | + | 1.99807e16i | 0.113282 | + | 0.125702i | ||||
\(737\) | 1.07891e17 | 0.673257 | ||||||||
\(738\) | −5.72995e15 | −0.0354660 | ||||||||
\(739\) | 1.04830e16 | 0.0643605 | 0.0321802 | − | 0.999482i | \(-0.489755\pi\) | ||||
0.0321802 | + | 0.999482i | \(0.489755\pi\) | |||||||
\(740\) | 1.34183e17 | 0.817163 | ||||||||
\(741\) | 1.84153e15i | 0.0111242i | ||||||||
\(742\) | 1.01875e18 | 6.10445 | ||||||||
\(743\) | 1.08652e17i | 0.645812i | 0.946431 | + | 0.322906i | \(0.104660\pi\) | ||||
−0.946431 | + | 0.322906i | \(0.895340\pi\) | |||||||
\(744\) | 4.21665e17 | 2.48616 | ||||||||
\(745\) | −7.03568e16 | −0.411499 | ||||||||
\(746\) | − | 3.21533e17i | − | 1.86549i | ||||||
\(747\) | 1.22495e16i | 0.0705010i | ||||||||
\(748\) | 1.64246e17 | 0.937745 | ||||||||
\(749\) | 4.04037e16 | 0.228839 | ||||||||
\(750\) | 2.88681e17i | 1.62200i | ||||||||
\(751\) | − | 5.37097e16i | − | 0.299373i | −0.988733 | − | 0.149687i | \(-0.952174\pi\) | ||
0.988733 | − | 0.149687i | \(-0.0478265\pi\) | |||||||
\(752\) | 3.96321e15 | 0.0219149 | ||||||||
\(753\) | 3.79674e16i | 0.208277i | ||||||||
\(754\) | 7.61679e16 | 0.414519 | ||||||||
\(755\) | − | 4.40305e16i | − | 0.237724i | ||||||
\(756\) | − | 6.70911e17i | − | 3.59364i | ||||||
\(757\) | 7.69491e16i | 0.408911i | 0.978876 | + | 0.204455i | \(0.0655423\pi\) | ||||
−0.978876 | + | 0.204455i | \(0.934458\pi\) | |||||||
\(758\) | − | 5.49521e17i | − | 2.89714i | ||||||
\(759\) | −8.33301e16 | + | 7.50968e16i | −0.435864 | + | 0.392800i | ||||
\(760\) | −6.33784e15 | −0.0328897 | ||||||||
\(761\) | 1.18624e17 | 0.610753 | 0.305377 | − | 0.952232i | \(-0.401218\pi\) | ||||
0.305377 | + | 0.952232i | \(0.401218\pi\) | |||||||
\(762\) | −7.61935e16 | −0.389214 | ||||||||
\(763\) | −5.72096e17 | −2.89949 | ||||||||
\(764\) | 5.24509e17i | 2.63750i | ||||||||
\(765\) | 1.48804e16 | 0.0742416 | ||||||||
\(766\) | 1.50370e17i | 0.744370i | ||||||||
\(767\) | −3.64880e16 | −0.179216 | ||||||||
\(768\) | −4.53368e17 | −2.20945 | ||||||||
\(769\) | 1.49752e17i | 0.724126i | 0.932154 | + | 0.362063i | \(0.117928\pi\) | ||||
−0.932154 | + | 0.362063i | \(0.882072\pi\) | |||||||
\(770\) | 1.87627e17i | 0.900226i | ||||||||
\(771\) | −2.65822e17 | −1.26551 | ||||||||
\(772\) | 4.85311e17 | 2.29253 | ||||||||
\(773\) | 4.89890e16i | 0.229626i | 0.993387 | + | 0.114813i | \(0.0366270\pi\) | ||||
−0.993387 | + | 0.114813i | \(0.963373\pi\) | |||||||
\(774\) | − | 1.13686e17i | − | 0.528763i | ||||||
\(775\) | −2.07538e17 | −0.957827 | ||||||||
\(776\) | 4.63741e17i | 2.12376i | ||||||||
\(777\) | −3.88473e17 | −1.76536 | ||||||||
\(778\) | − | 1.97426e17i | − | 0.890281i | ||||||
\(779\) | 9.33151e14i | 0.00417568i | ||||||||
\(780\) | − | 6.68934e16i | − | 0.297041i | ||||||
\(781\) | − | 1.64300e17i | − | 0.723988i | ||||||
\(782\) | −2.51546e17 | + | 2.26693e17i | −1.09996 | + | 0.991281i | ||||
\(783\) | 1.76723e17 | 0.766872 | ||||||||
\(784\) | −7.67246e17 | −3.30399 | ||||||||
\(785\) | 1.19804e17 | 0.511979 | ||||||||
\(786\) | 3.41168e17 | 1.44688 | ||||||||
\(787\) | 2.81296e17i | 1.18390i | 0.805974 | + | 0.591951i | \(0.201642\pi\) | ||||
−0.805974 | + | 0.591951i | \(0.798358\pi\) | |||||||
\(788\) | 8.08154e17 | 3.37549 | ||||||||
\(789\) | 1.78886e17i | 0.741506i | ||||||||
\(790\) | −2.45558e17 | −1.01016 | ||||||||
\(791\) | 4.22704e17 | 1.72575 | ||||||||
\(792\) | 4.40285e16i | 0.178395i | ||||||||
\(793\) | − | 9.48253e16i | − | 0.381316i | ||||||
\(794\) | −2.75962e17 | −1.10135 | ||||||||
\(795\) | 2.35673e17 | 0.933484 | ||||||||
\(796\) | − | 1.29161e17i | − | 0.507753i | ||||||
\(797\) | − | 4.20209e17i | − | 1.63952i | −0.572709 | − | 0.819758i | \(-0.694108\pi\) | ||
0.572709 | − | 0.819758i | \(-0.305892\pi\) | |||||||
\(798\) | 3.58677e16 | 0.138895 | ||||||||
\(799\) | 4.22670e15i | 0.0162450i | ||||||||
\(800\) | −3.39514e16 | −0.129514 | ||||||||
\(801\) | 1.83647e16i | 0.0695325i | ||||||||
\(802\) | − | 1.03376e17i | − | 0.388484i | ||||||
\(803\) | 2.12795e17i | 0.793722i | ||||||||
\(804\) | 7.49200e17i | 2.77371i | ||||||||
\(805\) | −1.73983e17 | − | 1.93058e17i | −0.639341 | − | 0.709436i | ||||
\(806\) | 1.65103e17 | 0.602204 | ||||||||
\(807\) | −5.57556e16 | −0.201859 | ||||||||
\(808\) | −3.33996e17 | −1.20025 | ||||||||
\(809\) | −2.85070e17 | −1.01686 | −0.508429 | − | 0.861104i | \(-0.669773\pi\) | ||||
−0.508429 | + | 0.861104i | \(0.669773\pi\) | |||||||
\(810\) | − | 2.74165e17i | − | 0.970737i | ||||||
\(811\) | 3.03956e17 | 1.06828 | 0.534141 | − | 0.845396i | \(-0.320635\pi\) | ||||
0.534141 | + | 0.845396i | \(0.320635\pi\) | |||||||
\(812\) | − | 9.96704e17i | − | 3.47720i | ||||||
\(813\) | 4.68304e17 | 1.62175 | ||||||||
\(814\) | −2.25955e17 | −0.776741 | ||||||||
\(815\) | − | 5.56454e16i | − | 0.189882i | ||||||
\(816\) | 3.11356e17i | 1.05467i | ||||||||
\(817\) | −1.85143e16 | −0.0622551 | ||||||||
\(818\) | 2.17052e17 | 0.724510 | ||||||||
\(819\) | 2.96386e16i | 0.0982098i | ||||||||
\(820\) | − | 3.38966e16i | − | 0.111500i | ||||||
\(821\) | −3.93145e16 | −0.128379 | −0.0641895 | − | 0.997938i | \(-0.520446\pi\) | ||||
−0.0641895 | + | 0.997938i | \(0.520446\pi\) | |||||||
\(822\) | 1.62576e17i | 0.527019i | ||||||||
\(823\) | 1.85166e17 | 0.595886 | 0.297943 | − | 0.954584i | \(-0.403700\pi\) | ||||
0.297943 | + | 0.954584i | \(0.403700\pi\) | |||||||
\(824\) | 5.12174e17i | 1.63627i | ||||||||
\(825\) | − | 1.41596e17i | − | 0.449083i | ||||||
\(826\) | 7.10680e17i | 2.23766i | ||||||||
\(827\) | − | 2.07427e17i | − | 0.648385i | −0.945991 | − | 0.324192i | \(-0.894908\pi\) | ||
0.945991 | − | 0.324192i | \(-0.105092\pi\) | |||||||
\(828\) | −7.98081e16 | − | 8.85579e16i | −0.247665 | − | 0.274818i | ||||
\(829\) | 1.15761e17 | 0.356645 | 0.178323 | − | 0.983972i | \(-0.442933\pi\) | ||||
0.178323 | + | 0.983972i | \(0.442933\pi\) | |||||||
\(830\) | −1.07859e17 | −0.329903 | ||||||||
\(831\) | −3.78449e17 | −1.14922 | ||||||||
\(832\) | −7.76182e16 | −0.234004 | ||||||||
\(833\) | − | 8.18257e17i | − | 2.44917i | ||||||
\(834\) | −4.39948e17 | −1.30739 | ||||||||
\(835\) | − | 6.10996e16i | − | 0.180268i | ||||||
\(836\) | 1.40164e16 | 0.0410580 | ||||||||
\(837\) | 3.83068e17 | 1.11410 | ||||||||
\(838\) | 1.64913e17i | 0.476202i | ||||||||
\(839\) | − | 4.61990e17i | − | 1.32453i | −0.749271 | − | 0.662264i | \(-0.769596\pi\) | ||
0.749271 | − | 0.662264i | \(-0.230404\pi\) | |||||||
\(840\) | −6.66511e17 | −1.89728 | ||||||||
\(841\) | −9.12752e16 | −0.257975 | ||||||||
\(842\) | 2.46280e17i | 0.691125i | ||||||||
\(843\) | 6.48577e17i | 1.80716i | ||||||||
\(844\) | 3.90280e17 | 1.07975 | ||||||||
\(845\) | 1.62929e17i | 0.447568i | ||||||||
\(846\) | −2.21484e15 | −0.00604115 | ||||||||
\(847\) | 5.15727e17i | 1.39675i | ||||||||
\(848\) | 7.54682e17i | 2.02950i | ||||||||
\(849\) | − | 1.49687e17i | − | 0.399703i | ||||||
\(850\) | − | 4.27431e17i | − | 1.13332i | ||||||
\(851\) | 2.32496e17 | − | 2.09525e17i | 0.612122 | − | 0.551643i | ||||
\(852\) | 1.14091e18 | 2.98272 | ||||||||
\(853\) | −1.88602e17 | −0.489612 | −0.244806 | − | 0.969572i | \(-0.578724\pi\) | ||||
−0.244806 | + | 0.969572i | \(0.578724\pi\) | |||||||
\(854\) | −1.84692e18 | −4.76104 | ||||||||
\(855\) | 1.26986e15 | 0.00325058 | ||||||||
\(856\) | 8.34823e16i | 0.212203i | ||||||||
\(857\) | −2.33141e17 | −0.588484 | −0.294242 | − | 0.955731i | \(-0.595067\pi\) | ||||
−0.294242 | + | 0.955731i | \(0.595067\pi\) | |||||||
\(858\) | 1.12644e17i | 0.282347i | ||||||||
\(859\) | −6.31515e16 | −0.157190 | −0.0785949 | − | 0.996907i | \(-0.525043\pi\) | ||||
−0.0785949 | + | 0.996907i | \(0.525043\pi\) | |||||||
\(860\) | 6.72530e17 | 1.66234 | ||||||||
\(861\) | 9.81335e16i | 0.240879i | ||||||||
\(862\) | 8.43539e17i | 2.05618i | ||||||||
\(863\) | 5.13360e17 | 1.24267 | 0.621337 | − | 0.783543i | \(-0.286590\pi\) | ||||
0.621337 | + | 0.783543i | \(0.286590\pi\) | |||||||
\(864\) | 6.26667e16 | 0.150645 | ||||||||
\(865\) | 2.50490e17i | 0.597990i | ||||||||
\(866\) | 5.05997e17i | 1.19961i | ||||||||
\(867\) | 1.29457e17 | 0.304797 | ||||||||
\(868\) | − | 2.16047e18i | − | 5.05161i | ||||||
\(869\) | 2.77809e17 | 0.645102 | ||||||||
\(870\) | − | 3.43192e17i | − | 0.791446i | ||||||
\(871\) | 1.50066e17i | 0.343696i | ||||||||
\(872\) | − | 1.18207e18i | − | 2.68871i | ||||||
\(873\) | − | 9.29161e16i | − | 0.209897i | ||||||
\(874\) | −2.14664e16 | + | 1.93454e16i | −0.0481604 | + | 0.0434020i | ||||
\(875\) | 7.56654e17 | 1.68597 | ||||||||
\(876\) | −1.47766e18 | −3.27001 | ||||||||
\(877\) | 9.02951e16 | 0.198457 | 0.0992286 | − | 0.995065i | \(-0.468362\pi\) | ||||
0.0992286 | + | 0.995065i | \(0.468362\pi\) | |||||||
\(878\) | 1.69297e17 | 0.369557 | ||||||||
\(879\) | − | 5.40010e17i | − | 1.17076i | ||||||
\(880\) | −1.38992e17 | −0.299291 | ||||||||
\(881\) | 3.39144e17i | 0.725319i | 0.931922 | + | 0.362660i | \(0.118131\pi\) | ||||
−0.931922 | + | 0.362660i | \(0.881869\pi\) | |||||||
\(882\) | 4.28775e17 | 0.910790 | ||||||||
\(883\) | −3.53331e17 | −0.745449 | −0.372724 | − | 0.927942i | \(-0.621576\pi\) | ||||
−0.372724 | + | 0.927942i | \(0.621576\pi\) | |||||||
\(884\) | 2.28451e17i | 0.478717i | ||||||||
\(885\) | 1.64405e17i | 0.342180i | ||||||||
\(886\) | 4.56781e17 | 0.944290 | ||||||||
\(887\) | −6.67281e17 | −1.37015 | −0.685073 | − | 0.728474i | \(-0.740230\pi\) | ||||
−0.685073 | + | 0.728474i | \(0.740230\pi\) | |||||||
\(888\) | − | 8.02665e17i | − | 1.63703i | ||||||
\(889\) | 1.99709e17i | 0.404564i | ||||||||
\(890\) | −1.61703e17 | −0.325371 | ||||||||
\(891\) | 3.10174e17i | 0.619925i | ||||||||
\(892\) | 1.40788e18 | 2.79498 | ||||||||
\(893\) | 3.60697e14i | 0.000711269i | ||||||||
\(894\) | 8.22701e17i | 1.61145i | ||||||||
\(895\) | 1.50415e17i | 0.292653i | ||||||||
\(896\) | 1.68441e18i | 3.25536i | ||||||||
\(897\) | −1.04453e17 | − | 1.15904e17i | −0.200523 | − | 0.222508i | ||||
\(898\) | 1.02315e18 | 1.95110 | ||||||||
\(899\) | 5.69085e17 | 1.07800 | ||||||||
\(900\) | 1.50479e17 | 0.283153 | ||||||||
\(901\) | −8.04857e17 | −1.50442 | ||||||||
\(902\) | 5.70795e16i | 0.105984i | ||||||||
\(903\) | −1.94703e18 | −3.59126 | ||||||||
\(904\) | 8.73395e17i | 1.60030i | ||||||||
\(905\) | −1.71687e17 | −0.312496 | ||||||||
\(906\) | −5.14861e17 | −0.930939 | ||||||||
\(907\) | − | 4.75850e17i | − | 0.854724i | −0.904081 | − | 0.427362i | \(-0.859443\pi\) | ||
0.904081 | − | 0.427362i | \(-0.140557\pi\) | |||||||
\(908\) | − | 2.05341e18i | − | 3.66404i | ||||||
\(909\) | 6.69201e16 | 0.118624 | ||||||||
\(910\) | −2.60972e17 | −0.459563 | ||||||||
\(911\) | 2.13503e17i | 0.373502i | 0.982407 | + | 0.186751i | \(0.0597958\pi\) | ||||
−0.982407 | + | 0.186751i | \(0.940204\pi\) | |||||||
\(912\) | 2.65704e16i | 0.0461774i | ||||||||
\(913\) | 1.22025e17 | 0.210680 | ||||||||
\(914\) | 1.13221e18i | 1.94200i | ||||||||
\(915\) | −4.27257e17 | −0.728052 | ||||||||
\(916\) | − | 9.70734e17i | − | 1.64334i | ||||||
\(917\) | − | 8.94227e17i | − | 1.50394i | ||||||
\(918\) | 7.88941e17i | 1.31822i | ||||||||
\(919\) | − | 2.83161e16i | − | 0.0470046i | −0.999724 | − | 0.0235023i | \(-0.992518\pi\) | ||
0.999724 | − | 0.0235023i | \(-0.00748170\pi\) | |||||||
\(920\) | 3.98898e17 | − | 3.59486e17i | 0.657862 | − | 0.592864i | ||||
\(921\) | 5.90854e17 | 0.968105 | ||||||||
\(922\) | 4.58556e17 | 0.746461 | ||||||||
\(923\) | 2.28526e17 | 0.369594 | ||||||||
\(924\) | 1.47401e18 | 2.36848 | ||||||||
\(925\) | 3.95061e17i | 0.630686i | ||||||||
\(926\) | −1.24342e18 | −1.97220 | ||||||||
\(927\) | − | 1.02620e17i | − | 0.161717i | ||||||
\(928\) | 9.30975e16 | 0.145764 | ||||||||
\(929\) | 1.27279e18 | 1.97998 | 0.989991 | − | 0.141131i | \(-0.0450737\pi\) | ||||
0.989991 | + | 0.141131i | \(0.0450737\pi\) | |||||||
\(930\) | − | 7.43907e17i | − | 1.14980i | ||||||
\(931\) | − | 6.98282e16i | − | 0.107234i | ||||||
\(932\) | −1.68909e18 | −2.57725 | ||||||||
\(933\) | 3.65187e17 | 0.553637 | ||||||||
\(934\) | − | 1.81064e18i | − | 2.72742i | ||||||
\(935\) | − | 1.48233e17i | − | 0.221858i | ||||||
\(936\) | −6.12395e16 | −0.0910703 | ||||||||
\(937\) | 2.82721e17i | 0.417754i | 0.977942 | + | 0.208877i | \(0.0669808\pi\) | ||||
−0.977942 | + | 0.208877i | \(0.933019\pi\) | |||||||
\(938\) | 2.92286e18 | 4.29132 | ||||||||
\(939\) | 7.82551e17i | 1.14161i | ||||||||
\(940\) | − | 1.31023e16i | − | 0.0189924i | ||||||
\(941\) | − | 1.06068e18i | − | 1.52773i | −0.645378 | − | 0.763864i | \(-0.723300\pi\) | ||
0.645378 | − | 0.763864i | \(-0.276700\pi\) | |||||||
\(942\) | − | 1.40090e18i | − | 2.00494i | ||||||
\(943\) | −5.29288e16 | − | 5.87317e16i | −0.0752700 | − | 0.0835223i | ||||
\(944\) | −5.26464e17 | −0.743937 | ||||||||
\(945\) | −6.05502e17 | −0.850206 | ||||||||
\(946\) | −1.13249e18 | −1.58011 | ||||||||
\(947\) | −7.04354e17 | −0.976543 | −0.488271 | − | 0.872692i | \(-0.662372\pi\) | ||||
−0.488271 | + | 0.872692i | \(0.662372\pi\) | |||||||
\(948\) | 1.92912e18i | 2.65772i | ||||||||
\(949\) | −2.95978e17 | −0.405193 | ||||||||
\(950\) | − | 3.64760e16i | − | 0.0496210i | ||||||
\(951\) | 1.16285e18 | 1.57195 | ||||||||
\(952\) | 2.27623e18 | 3.05770 | ||||||||
\(953\) | 5.17590e16i | 0.0690921i | 0.999403 | + | 0.0345460i | \(0.0109985\pi\) | ||||
−0.999403 | + | 0.0345460i | \(0.989001\pi\) | |||||||
\(954\) | − | 4.21754e17i | − | 0.559460i | ||||||
\(955\) | 4.73373e17 | 0.623997 | ||||||||
\(956\) | −5.96788e17 | −0.781758 | ||||||||
\(957\) | 3.88267e17i | 0.505427i | ||||||||
\(958\) | − | 2.51146e17i | − | 0.324888i | ||||||
\(959\) | 4.26124e17 | 0.547804 | ||||||||
\(960\) | 3.49726e17i | 0.446787i | ||||||||
\(961\) | 4.45893e17 | 0.566097 | ||||||||
\(962\) | − | 3.14283e17i | − | 0.396525i | ||||||
\(963\) | − | 1.67267e16i | − | 0.0209726i | ||||||
\(964\) | 1.42283e17i | 0.177292i | ||||||||
\(965\) | − | 4.37996e17i | − | 0.542383i | ||||||
\(966\) | −2.25748e18 | + | 2.03444e18i | −2.77819 | + | 2.50369i | ||||
\(967\) | −9.80540e17 | −1.19924 | −0.599620 | − | 0.800285i | \(-0.704682\pi\) | ||||
−0.599620 | + | 0.800285i | \(0.704682\pi\) | |||||||
\(968\) | −1.06560e18 | −1.29521 | ||||||||
\(969\) | −2.83369e16 | −0.0342303 | ||||||||
\(970\) | 8.18139e17 | 0.982192 | ||||||||
\(971\) | 1.25448e18i | 1.49675i | 0.663274 | + | 0.748376i | \(0.269166\pi\) | ||||
−0.663274 | + | 0.748376i | \(0.730834\pi\) | |||||||
\(972\) | −6.16758e17 | −0.731337 | ||||||||
\(973\) | 1.15314e18i | 1.35895i | ||||||||
\(974\) | −1.00461e18 | −1.17664 | ||||||||
\(975\) | 1.96947e17 | 0.229256 | ||||||||
\(976\) | − | 1.36818e18i | − | 1.58287i | ||||||
\(977\) | 1.09837e18i | 1.26294i | 0.775402 | + | 0.631468i | \(0.217547\pi\) | ||||
−0.775402 | + | 0.631468i | \(0.782453\pi\) | |||||||
\(978\) | −6.50677e17 | −0.743588 | ||||||||
\(979\) | 1.82941e17 | 0.207786 | ||||||||
\(980\) | 2.53650e18i | 2.86338i | ||||||||
\(981\) | 2.36842e17i | 0.265732i | ||||||||
\(982\) | −1.47427e18 | −1.64402 | ||||||||
\(983\) | − | 8.99943e17i | − | 0.997456i | −0.866759 | − | 0.498728i | \(-0.833801\pi\) | ||
0.866759 | − | 0.498728i | \(-0.166199\pi\) | |||||||
\(984\) | −2.02764e17 | −0.223368 | ||||||||
\(985\) | − | 7.29364e17i | − | 0.798595i | ||||||
\(986\) | 1.17205e18i | 1.27551i | ||||||||
\(987\) | 3.79322e16i | 0.0410304i | ||||||||
\(988\) | 1.94955e16i | 0.0209600i | ||||||||
\(989\) | 1.16527e18 | − | 1.05014e18i | 1.24523 | − | 1.12220i | ||||
\(990\) | 7.76757e16 | 0.0825038 | ||||||||
\(991\) | −1.40137e18 | −1.47949 | −0.739743 | − | 0.672889i | \(-0.765053\pi\) | ||||
−0.739743 | + | 0.672889i | \(0.765053\pi\) | |||||||
\(992\) | 2.01799e17 | 0.211763 | ||||||||
\(993\) | 1.25612e15 | 0.00131019 | ||||||||
\(994\) | − | 4.45102e18i | − | 4.61468i | ||||||
\(995\) | −1.16569e17 | −0.120128 | ||||||||
\(996\) | 8.47345e17i | 0.867969i | ||||||||
\(997\) | 2.18779e17 | 0.222759 | 0.111379 | − | 0.993778i | \(-0.464473\pi\) | ||||
0.111379 | + | 0.993778i | \(0.464473\pi\) | |||||||
\(998\) | −3.82434e15 | −0.00387056 | ||||||||
\(999\) | − | 7.29193e17i | − | 0.733583i |
(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 | 23.13.b.c.22.1 | ✓ | 20 | |
23.22 | odd | 2 | inner | 23.13.b.c.22.2 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.13.b.c.22.1 | ✓ | 20 | 1.1 | even | 1 | trivial | |
23.13.b.c.22.2 | yes | 20 | 23.22 | odd | 2 | inner |