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 | 22.7 | ||
Root | \(1052.17 + 197.039i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 23.22 |
Dual form | 23.13.b.c.22.8 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −43.1697 | −0.674527 | −0.337263 | − | 0.941410i | \(-0.609501\pi\) | ||||
−0.337263 | + | 0.941410i | \(0.609501\pi\) | |||||||
\(3\) | −1083.34 | −1.48606 | −0.743031 | − | 0.669257i | \(-0.766612\pi\) | ||||
−0.743031 | + | 0.669257i | \(0.766612\pi\) | |||||||
\(4\) | −2232.38 | −0.545014 | ||||||||
\(5\) | − | 197.039i | − | 0.0126105i | −0.999980 | − | 0.00630526i | \(-0.997993\pi\) | ||
0.999980 | − | 0.00630526i | \(-0.00200704\pi\) | |||||||
\(6\) | 46767.4 | 1.00239 | ||||||||
\(7\) | − | 138687.i | − | 1.17882i | −0.807834 | − | 0.589410i | \(-0.799360\pi\) | ||
0.807834 | − | 0.589410i | \(-0.200640\pi\) | |||||||
\(8\) | 273194. | 1.04215 | ||||||||
\(9\) | 642183. | 1.20838 | ||||||||
\(10\) | 8506.13i | 0.00850613i | ||||||||
\(11\) | − | 3.09310e6i | − | 1.74597i | −0.487745 | − | 0.872986i | \(-0.662180\pi\) | ||
0.487745 | − | 0.872986i | \(-0.337820\pi\) | |||||||
\(12\) | 2.41842e6 | 0.809924 | ||||||||
\(13\) | −782061. | −0.162024 | −0.0810122 | − | 0.996713i | \(-0.525815\pi\) | ||||
−0.0810122 | + | 0.996713i | \(0.525815\pi\) | |||||||
\(14\) | 5.98707e6i | 0.795145i | ||||||||
\(15\) | 213460.i | 0.0187400i | ||||||||
\(16\) | −2.64989e6 | −0.157946 | ||||||||
\(17\) | 1.68131e7i | 0.696555i | 0.937391 | + | 0.348278i | \(0.113233\pi\) | ||||
−0.937391 | + | 0.348278i | \(0.886767\pi\) | |||||||
\(18\) | −2.77228e7 | −0.815084 | ||||||||
\(19\) | − | 8.31755e7i | − | 1.76797i | −0.467519 | − | 0.883983i | \(-0.654852\pi\) | ||
0.467519 | − | 0.883983i | \(-0.345148\pi\) | |||||||
\(20\) | 439866.i | 0.00687291i | ||||||||
\(21\) | 1.50245e8i | 1.75180i | ||||||||
\(22\) | 1.33528e8i | 1.17770i | ||||||||
\(23\) | −1.21849e8 | − | 8.40675e7i | −0.823107 | − | 0.567886i | ||||
\(24\) | −2.95962e8 | −1.54870 | ||||||||
\(25\) | 2.44102e8 | 0.999841 | ||||||||
\(26\) | 3.37613e7 | 0.109290 | ||||||||
\(27\) | −1.19971e8 | −0.309666 | ||||||||
\(28\) | 3.09601e8i | 0.642473i | ||||||||
\(29\) | −4.26269e8 | −0.716631 | −0.358315 | − | 0.933601i | \(-0.616649\pi\) | ||||
−0.358315 | + | 0.933601i | \(0.616649\pi\) | |||||||
\(30\) | − | 9.21502e6i | − | 0.0126406i | ||||||
\(31\) | −1.02830e9 | −1.15864 | −0.579321 | − | 0.815099i | \(-0.696682\pi\) | ||||
−0.579321 | + | 0.815099i | \(0.696682\pi\) | |||||||
\(32\) | −1.00461e9 | −0.935614 | ||||||||
\(33\) | 3.35087e9i | 2.59462i | ||||||||
\(34\) | − | 7.25819e8i | − | 0.469845i | ||||||
\(35\) | −2.73268e7 | −0.0148655 | ||||||||
\(36\) | −1.43359e9 | −0.658584 | ||||||||
\(37\) | − | 3.34404e9i | − | 1.30335i | −0.758499 | − | 0.651674i | \(-0.774067\pi\) | ||
0.758499 | − | 0.651674i | \(-0.225933\pi\) | |||||||
\(38\) | 3.59066e9i | 1.19254i | ||||||||
\(39\) | 8.47237e8 | 0.240778 | ||||||||
\(40\) | − | 5.38300e7i | − | 0.0131421i | ||||||
\(41\) | 3.61362e9 | 0.760746 | 0.380373 | − | 0.924833i | \(-0.375796\pi\) | ||||
0.380373 | + | 0.924833i | \(0.375796\pi\) | |||||||
\(42\) | − | 6.48603e9i | − | 1.18163i | ||||||
\(43\) | − | 7.08764e9i | − | 1.12122i | −0.828080 | − | 0.560610i | \(-0.810567\pi\) | ||
0.828080 | − | 0.560610i | \(-0.189433\pi\) | |||||||
\(44\) | 6.90496e9i | 0.951579i | ||||||||
\(45\) | − | 1.26535e8i | − | 0.0152383i | ||||||
\(46\) | 5.26020e9 | + | 3.62917e9i | 0.555208 | + | 0.383054i | ||||
\(47\) | 1.41856e10 | 1.31602 | 0.658009 | − | 0.753010i | \(-0.271399\pi\) | ||||
0.658009 | + | 0.753010i | \(0.271399\pi\) | |||||||
\(48\) | 2.87073e9 | 0.234717 | ||||||||
\(49\) | −5.39277e9 | −0.389615 | ||||||||
\(50\) | −1.05378e10 | −0.674419 | ||||||||
\(51\) | − | 1.82143e10i | − | 1.03512i | ||||||
\(52\) | 1.74586e9 | 0.0883056 | ||||||||
\(53\) | − | 7.07215e9i | − | 0.319077i | −0.987192 | − | 0.159539i | \(-0.948999\pi\) | ||
0.987192 | − | 0.159539i | \(-0.0510007\pi\) | |||||||
\(54\) | 5.17910e9 | 0.208878 | ||||||||
\(55\) | −6.09461e8 | −0.0220176 | ||||||||
\(56\) | − | 3.78884e10i | − | 1.22851i | ||||||
\(57\) | 9.01073e10i | 2.62731i | ||||||||
\(58\) | 1.84019e10 | 0.483387 | ||||||||
\(59\) | −3.08437e10 | −0.731231 | −0.365615 | − | 0.930766i | \(-0.619141\pi\) | ||||
−0.365615 | + | 0.930766i | \(0.619141\pi\) | |||||||
\(60\) | − | 4.76524e8i | − | 0.0102136i | ||||||
\(61\) | − | 1.27252e9i | − | 0.0246994i | −0.999924 | − | 0.0123497i | \(-0.996069\pi\) | ||
0.999924 | − | 0.0123497i | \(-0.00393114\pi\) | |||||||
\(62\) | 4.43914e10 | 0.781535 | ||||||||
\(63\) | − | 8.90623e10i | − | 1.42446i | ||||||
\(64\) | 5.42226e10 | 0.789042 | ||||||||
\(65\) | 1.54097e8i | 0.00204321i | ||||||||
\(66\) | − | 1.44656e11i | − | 1.75014i | ||||||
\(67\) | 5.88741e10i | 0.650842i | 0.945569 | + | 0.325421i | \(0.105506\pi\) | ||||
−0.945569 | + | 0.325421i | \(0.894494\pi\) | |||||||
\(68\) | − | 3.75333e10i | − | 0.379632i | ||||||
\(69\) | 1.32004e11 | + | 9.10737e10i | 1.22319 | + | 0.843914i | ||||
\(70\) | 1.17969e9 | 0.0100272 | ||||||||
\(71\) | −7.96554e10 | −0.621821 | −0.310910 | − | 0.950439i | \(-0.600634\pi\) | ||||
−0.310910 | + | 0.950439i | \(0.600634\pi\) | |||||||
\(72\) | 1.75441e11 | 1.25932 | ||||||||
\(73\) | −2.01818e11 | −1.33359 | −0.666796 | − | 0.745240i | \(-0.732335\pi\) | ||||
−0.666796 | + | 0.745240i | \(0.732335\pi\) | |||||||
\(74\) | 1.44361e11i | 0.879143i | ||||||||
\(75\) | −2.64445e11 | −1.48583 | ||||||||
\(76\) | 1.85679e11i | 0.963566i | ||||||||
\(77\) | −4.28972e11 | −2.05819 | ||||||||
\(78\) | −3.65750e10 | −0.162411 | ||||||||
\(79\) | 2.84935e11i | 1.17215i | 0.810256 | + | 0.586076i | \(0.199328\pi\) | ||||
−0.810256 | + | 0.586076i | \(0.800672\pi\) | |||||||
\(80\) | 5.22133e8i | 0.00199178i | ||||||||
\(81\) | −2.11313e11 | −0.748198 | ||||||||
\(82\) | −1.55999e11 | −0.513143 | ||||||||
\(83\) | 3.50338e11i | 1.07156i | 0.844356 | + | 0.535782i | \(0.179983\pi\) | ||||
−0.844356 | + | 0.535782i | \(0.820017\pi\) | |||||||
\(84\) | − | 3.35403e11i | − | 0.954755i | ||||||
\(85\) | 3.31285e9 | 0.00878392 | ||||||||
\(86\) | 3.05971e11i | 0.756292i | ||||||||
\(87\) | 4.61794e11 | 1.06496 | ||||||||
\(88\) | − | 8.45016e11i | − | 1.81957i | ||||||
\(89\) | − | 1.59579e11i | − | 0.321097i | −0.987028 | − | 0.160549i | \(-0.948674\pi\) | ||
0.987028 | − | 0.160549i | \(-0.0513263\pi\) | |||||||
\(90\) | 5.46249e9i | 0.0102786i | ||||||||
\(91\) | 1.08462e11i | 0.190998i | ||||||||
\(92\) | 2.72014e11 | + | 1.87670e11i | 0.448605 | + | 0.309506i | ||||
\(93\) | 1.11400e12 | 1.72182 | ||||||||
\(94\) | −6.12390e11 | −0.887689 | ||||||||
\(95\) | −1.63888e10 | −0.0222950 | ||||||||
\(96\) | 1.08833e12 | 1.39038 | ||||||||
\(97\) | − | 1.07543e11i | − | 0.129108i | −0.997914 | − | 0.0645540i | \(-0.979438\pi\) | ||
0.997914 | − | 0.0645540i | \(-0.0205625\pi\) | |||||||
\(98\) | 2.32804e11 | 0.262806 | ||||||||
\(99\) | − | 1.98633e12i | − | 2.10980i | ||||||
\(100\) | −5.44927e11 | −0.544927 | ||||||||
\(101\) | 4.11180e11 | 0.387350 | 0.193675 | − | 0.981066i | \(-0.437959\pi\) | ||||
0.193675 | + | 0.981066i | \(0.437959\pi\) | |||||||
\(102\) | 7.86308e11i | 0.698219i | ||||||||
\(103\) | − | 3.73778e11i | − | 0.313033i | −0.987675 | − | 0.156516i | \(-0.949974\pi\) | ||
0.987675 | − | 0.156516i | \(-0.0500264\pi\) | |||||||
\(104\) | −2.13654e11 | −0.168854 | ||||||||
\(105\) | 2.96042e10 | 0.0220911 | ||||||||
\(106\) | 3.05302e11i | 0.215226i | ||||||||
\(107\) | − | 1.61213e12i | − | 1.07423i | −0.843510 | − | 0.537114i | \(-0.819515\pi\) | ||
0.843510 | − | 0.537114i | \(-0.180485\pi\) | |||||||
\(108\) | 2.67820e11 | 0.168772 | ||||||||
\(109\) | 2.83913e12i | 1.69288i | 0.532482 | + | 0.846441i | \(0.321259\pi\) | ||||
−0.532482 | + | 0.846441i | \(0.678741\pi\) | |||||||
\(110\) | 2.63103e10 | 0.0148515 | ||||||||
\(111\) | 3.62273e12i | 1.93686i | ||||||||
\(112\) | 3.67505e11i | 0.186190i | ||||||||
\(113\) | − | 2.73172e12i | − | 1.31210i | −0.754718 | − | 0.656049i | \(-0.772227\pi\) | ||
0.754718 | − | 0.656049i | \(-0.227773\pi\) | |||||||
\(114\) | − | 3.88990e12i | − | 1.77219i | ||||||
\(115\) | −1.65646e10 | + | 2.40091e10i | −0.00716134 | + | 0.0103798i | ||||
\(116\) | 9.51593e11 | 0.390574 | ||||||||
\(117\) | −5.02226e11 | −0.195787 | ||||||||
\(118\) | 1.33151e12 | 0.493235 | ||||||||
\(119\) | 2.33176e12 | 0.821113 | ||||||||
\(120\) | 5.83161e10i | 0.0195299i | ||||||||
\(121\) | −6.42882e12 | −2.04842 | ||||||||
\(122\) | 5.49345e10i | 0.0166604i | ||||||||
\(123\) | −3.91478e12 | −1.13052 | ||||||||
\(124\) | 2.29555e12 | 0.631477 | ||||||||
\(125\) | − | 9.62029e10i | − | 0.0252190i | ||||||
\(126\) | 3.84479e12i | 0.960837i | ||||||||
\(127\) | 1.65478e12 | 0.394383 | 0.197192 | − | 0.980365i | \(-0.436818\pi\) | ||||
0.197192 | + | 0.980365i | \(0.436818\pi\) | |||||||
\(128\) | 1.77410e12 | 0.403384 | ||||||||
\(129\) | 7.67831e12i | 1.66620i | ||||||||
\(130\) | − | 6.65231e9i | − | 0.00137820i | ||||||
\(131\) | 2.38314e12 | 0.471543 | 0.235772 | − | 0.971808i | \(-0.424238\pi\) | ||||
0.235772 | + | 0.971808i | \(0.424238\pi\) | |||||||
\(132\) | − | 7.48041e12i | − | 1.41411i | ||||||
\(133\) | −1.15354e13 | −2.08411 | ||||||||
\(134\) | − | 2.54158e12i | − | 0.439010i | ||||||
\(135\) | 2.36390e10i | 0.00390504i | ||||||||
\(136\) | 4.59325e12i | 0.725917i | ||||||||
\(137\) | 8.82608e12i | 1.33489i | 0.744661 | + | 0.667443i | \(0.232611\pi\) | ||||
−0.744661 | + | 0.667443i | \(0.767389\pi\) | |||||||
\(138\) | −5.69858e12 | − | 3.93162e12i | −0.825073 | − | 0.569242i | ||||
\(139\) | 3.10954e12 | 0.431129 | 0.215564 | − | 0.976490i | \(-0.430841\pi\) | ||||
0.215564 | + | 0.976490i | \(0.430841\pi\) | |||||||
\(140\) | 6.10037e10 | 0.00810191 | ||||||||
\(141\) | −1.53679e13 | −1.95568 | ||||||||
\(142\) | 3.43870e12 | 0.419435 | ||||||||
\(143\) | 2.41899e12i | 0.282890i | ||||||||
\(144\) | −1.70171e12 | −0.190859 | ||||||||
\(145\) | 8.39917e10i | 0.00903708i | ||||||||
\(146\) | 8.71243e12 | 0.899543 | ||||||||
\(147\) | 5.84220e12 | 0.578992 | ||||||||
\(148\) | 7.46515e12i | 0.710343i | ||||||||
\(149\) | − | 1.17065e13i | − | 1.06982i | −0.844910 | − | 0.534908i | \(-0.820346\pi\) | ||
0.844910 | − | 0.534908i | \(-0.179654\pi\) | |||||||
\(150\) | 1.14160e13 | 1.00223 | ||||||||
\(151\) | 4.11075e12 | 0.346785 | 0.173392 | − | 0.984853i | \(-0.444527\pi\) | ||||
0.173392 | + | 0.984853i | \(0.444527\pi\) | |||||||
\(152\) | − | 2.27231e13i | − | 1.84249i | ||||||
\(153\) | 1.07971e13i | 0.841703i | ||||||||
\(154\) | 1.85186e13 | 1.38830 | ||||||||
\(155\) | 2.02615e11i | 0.0146111i | ||||||||
\(156\) | −1.89135e12 | −0.131228 | ||||||||
\(157\) | − | 1.21477e13i | − | 0.811141i | −0.914064 | − | 0.405570i | \(-0.867073\pi\) | ||
0.914064 | − | 0.405570i | \(-0.132927\pi\) | |||||||
\(158\) | − | 1.23006e13i | − | 0.790648i | ||||||
\(159\) | 7.66153e12i | 0.474169i | ||||||||
\(160\) | 1.97947e11i | 0.0117986i | ||||||||
\(161\) | −1.16591e13 | + | 1.68989e13i | −0.669435 | + | 0.970294i | ||||
\(162\) | 9.12233e12 | 0.504679 | ||||||||
\(163\) | −1.82565e13 | −0.973399 | −0.486699 | − | 0.873569i | \(-0.661799\pi\) | ||||
−0.486699 | + | 0.873569i | \(0.661799\pi\) | |||||||
\(164\) | −8.06697e12 | −0.414617 | ||||||||
\(165\) | 6.60253e11 | 0.0327195 | ||||||||
\(166\) | − | 1.51240e13i | − | 0.722798i | ||||||
\(167\) | 2.51714e13 | 1.16040 | 0.580200 | − | 0.814474i | \(-0.302974\pi\) | ||||
0.580200 | + | 0.814474i | \(0.302974\pi\) | |||||||
\(168\) | 4.10460e13i | 1.82564i | ||||||||
\(169\) | −2.26865e13 | −0.973748 | ||||||||
\(170\) | −1.43015e11 | −0.00592499 | ||||||||
\(171\) | − | 5.34139e13i | − | 2.13637i | ||||||
\(172\) | 1.58223e13i | 0.611080i | ||||||||
\(173\) | 4.22256e13 | 1.57507 | 0.787533 | − | 0.616272i | \(-0.211358\pi\) | ||||
0.787533 | + | 0.616272i | \(0.211358\pi\) | |||||||
\(174\) | −1.99355e13 | −0.718342 | ||||||||
\(175\) | − | 3.38537e13i | − | 1.17863i | ||||||
\(176\) | 8.19637e12i | 0.275769i | ||||||||
\(177\) | 3.34142e13 | 1.08665 | ||||||||
\(178\) | 6.88899e12i | 0.216589i | ||||||||
\(179\) | 2.19570e13 | 0.667507 | 0.333753 | − | 0.942660i | \(-0.391685\pi\) | ||||
0.333753 | + | 0.942660i | \(0.391685\pi\) | |||||||
\(180\) | 2.82474e11i | 0.00830508i | ||||||||
\(181\) | 4.45881e13i | 1.26808i | 0.773300 | + | 0.634041i | \(0.218605\pi\) | ||||
−0.773300 | + | 0.634041i | \(0.781395\pi\) | |||||||
\(182\) | − | 4.68226e12i | − | 0.128833i | ||||||
\(183\) | 1.37858e12i | 0.0367049i | ||||||||
\(184\) | −3.32885e13 | − | 2.29668e13i | −0.857803 | − | 0.591824i | ||||
\(185\) | −6.58907e11 | −0.0164359 | ||||||||
\(186\) | −4.80909e13 | −1.16141 | ||||||||
\(187\) | 5.20047e13 | 1.21617 | ||||||||
\(188\) | −3.16677e13 | −0.717248 | ||||||||
\(189\) | 1.66384e13i | 0.365040i | ||||||||
\(190\) | 7.07501e11 | 0.0150385 | ||||||||
\(191\) | − | 5.08450e13i | − | 1.04724i | −0.851951 | − | 0.523622i | \(-0.824580\pi\) | ||
0.851951 | − | 0.523622i | \(-0.175420\pi\) | |||||||
\(192\) | −5.87414e13 | −1.17257 | ||||||||
\(193\) | −3.49289e13 | −0.675836 | −0.337918 | − | 0.941176i | \(-0.609723\pi\) | ||||
−0.337918 | + | 0.941176i | \(0.609723\pi\) | |||||||
\(194\) | 4.64261e12i | 0.0870868i | ||||||||
\(195\) | − | 1.66939e11i | − | 0.00303634i | ||||||
\(196\) | 1.20387e13 | 0.212346 | ||||||||
\(197\) | 6.41407e13 | 1.09733 | 0.548664 | − | 0.836043i | \(-0.315137\pi\) | ||||
0.548664 | + | 0.836043i | \(0.315137\pi\) | |||||||
\(198\) | 8.57494e13i | 1.42311i | ||||||||
\(199\) | 4.57253e13i | 0.736272i | 0.929772 | + | 0.368136i | \(0.120004\pi\) | ||||
−0.929772 | + | 0.368136i | \(0.879996\pi\) | |||||||
\(200\) | 6.66872e13 | 1.04199 | ||||||||
\(201\) | − | 6.37807e13i | − | 0.967192i | ||||||
\(202\) | −1.77505e13 | −0.261278 | ||||||||
\(203\) | 5.91179e13i | 0.844778i | ||||||||
\(204\) | 4.06613e13i | 0.564157i | ||||||||
\(205\) | − | 7.12025e11i | − | 0.00959340i | ||||||
\(206\) | 1.61359e13i | 0.211149i | ||||||||
\(207\) | −7.82496e13 | − | 5.39867e13i | −0.994626 | − | 0.686222i | ||||
\(208\) | 2.07238e12 | 0.0255911 | ||||||||
\(209\) | −2.57270e14 | −3.08682 | ||||||||
\(210\) | −1.27800e12 | −0.0149010 | ||||||||
\(211\) | −1.42466e14 | −1.61442 | −0.807211 | − | 0.590263i | \(-0.799024\pi\) | ||||
−0.807211 | + | 0.590263i | \(0.799024\pi\) | |||||||
\(212\) | 1.57877e13i | 0.173902i | ||||||||
\(213\) | 8.62938e13 | 0.924064 | ||||||||
\(214\) | 6.95950e13i | 0.724595i | ||||||||
\(215\) | −1.39654e12 | −0.0141392 | ||||||||
\(216\) | −3.27753e13 | −0.322719 | ||||||||
\(217\) | 1.42612e14i | 1.36583i | ||||||||
\(218\) | − | 1.22565e14i | − | 1.14189i | ||||||
\(219\) | 2.18637e14 | 1.98180 | ||||||||
\(220\) | 1.36055e12 | 0.0119999 | ||||||||
\(221\) | − | 1.31489e13i | − | 0.112859i | ||||||
\(222\) | − | 1.56392e14i | − | 1.30646i | ||||||
\(223\) | 8.84136e12 | 0.0718936 | 0.0359468 | − | 0.999354i | \(-0.488555\pi\) | ||||
0.0359468 | + | 0.999354i | \(0.488555\pi\) | |||||||
\(224\) | 1.39326e14i | 1.10292i | ||||||||
\(225\) | 1.56758e14 | 1.20819 | ||||||||
\(226\) | 1.17928e14i | 0.885045i | ||||||||
\(227\) | − | 1.27980e14i | − | 0.935378i | −0.883893 | − | 0.467689i | \(-0.845087\pi\) | ||
0.883893 | − | 0.467689i | \(-0.154913\pi\) | |||||||
\(228\) | − | 2.01153e14i | − | 1.43192i | ||||||
\(229\) | − | 8.38302e13i | − | 0.581283i | −0.956832 | − | 0.290641i | \(-0.906131\pi\) | ||
0.956832 | − | 0.290641i | \(-0.0938687\pi\) | |||||||
\(230\) | 7.15089e11 | − | 1.03647e12i | 0.00483051 | − | 0.00700145i | ||||
\(231\) | 4.64722e14 | 3.05859 | ||||||||
\(232\) | −1.16454e14 | −0.746839 | ||||||||
\(233\) | 4.36679e13 | 0.272915 | 0.136457 | − | 0.990646i | \(-0.456428\pi\) | ||||
0.136457 | + | 0.990646i | \(0.456428\pi\) | |||||||
\(234\) | 2.16809e13 | 0.132064 | ||||||||
\(235\) | − | 2.79513e12i | − | 0.0165957i | ||||||
\(236\) | 6.88548e13 | 0.398531 | ||||||||
\(237\) | − | 3.08682e14i | − | 1.74189i | ||||||
\(238\) | −1.00662e14 | −0.553862 | ||||||||
\(239\) | −2.02270e14 | −1.08528 | −0.542642 | − | 0.839964i | \(-0.682576\pi\) | ||||
−0.542642 | + | 0.839964i | \(0.682576\pi\) | |||||||
\(240\) | − | 5.65647e11i | − | 0.00295991i | ||||||
\(241\) | − | 5.60211e13i | − | 0.285923i | −0.989728 | − | 0.142961i | \(-0.954337\pi\) | ||
0.989728 | − | 0.142961i | \(-0.0456625\pi\) | |||||||
\(242\) | 2.77530e14 | 1.38171 | ||||||||
\(243\) | 2.92681e14 | 1.42153 | ||||||||
\(244\) | 2.84075e12i | 0.0134615i | ||||||||
\(245\) | 1.06259e12i | 0.00491324i | ||||||||
\(246\) | 1.69000e14 | 0.762563 | ||||||||
\(247\) | 6.50483e13i | 0.286454i | ||||||||
\(248\) | −2.80925e14 | −1.20748 | ||||||||
\(249\) | − | 3.79534e14i | − | 1.59241i | ||||||
\(250\) | 4.15305e12i | 0.0170109i | ||||||||
\(251\) | 4.73764e14i | 1.89461i | 0.320333 | + | 0.947305i | \(0.396205\pi\) | ||||
−0.320333 | + | 0.947305i | \(0.603795\pi\) | |||||||
\(252\) | 1.98821e14i | 0.776351i | ||||||||
\(253\) | −2.60029e14 | + | 3.76892e14i | −0.991514 | + | 1.43712i | ||||
\(254\) | −7.14364e13 | −0.266022 | ||||||||
\(255\) | −3.58894e12 | −0.0130534 | ||||||||
\(256\) | −2.98683e14 | −1.06114 | ||||||||
\(257\) | −3.96953e12 | −0.0137765 | −0.00688827 | − | 0.999976i | \(-0.502193\pi\) | ||||
−0.00688827 | + | 0.999976i | \(0.502193\pi\) | |||||||
\(258\) | − | 3.31471e14i | − | 1.12390i | ||||||
\(259\) | −4.63774e14 | −1.53641 | ||||||||
\(260\) | − | 3.44002e11i | − | 0.00111358i | ||||||
\(261\) | −2.73742e14 | −0.865962 | ||||||||
\(262\) | −1.02879e14 | −0.318068 | ||||||||
\(263\) | − | 8.48743e13i | − | 0.256473i | −0.991744 | − | 0.128237i | \(-0.959068\pi\) | ||
0.991744 | − | 0.128237i | \(-0.0409317\pi\) | |||||||
\(264\) | 9.15439e14i | 2.70399i | ||||||||
\(265\) | −1.39349e12 | −0.00402373 | ||||||||
\(266\) | 4.97978e14 | 1.40579 | ||||||||
\(267\) | 1.72878e14i | 0.477170i | ||||||||
\(268\) | − | 1.31429e14i | − | 0.354718i | ||||||
\(269\) | 2.77036e14 | 0.731178 | 0.365589 | − | 0.930776i | \(-0.380868\pi\) | ||||
0.365589 | + | 0.930776i | \(0.380868\pi\) | |||||||
\(270\) | − | 1.02049e12i | − | 0.00263405i | ||||||
\(271\) | −5.60984e14 | −1.41623 | −0.708117 | − | 0.706095i | \(-0.750455\pi\) | ||||
−0.708117 | + | 0.706095i | \(0.750455\pi\) | |||||||
\(272\) | − | 4.45530e13i | − | 0.110018i | ||||||
\(273\) | − | 1.17501e14i | − | 0.283834i | ||||||
\(274\) | − | 3.81019e14i | − | 0.900417i | ||||||
\(275\) | − | 7.55030e14i | − | 1.74569i | ||||||
\(276\) | −2.94683e14 | − | 2.03311e14i | −0.666655 | − | 0.459945i | ||||
\(277\) | 8.52398e14 | 1.88697 | 0.943483 | − | 0.331421i | \(-0.107528\pi\) | ||||
0.943483 | + | 0.331421i | \(0.107528\pi\) | |||||||
\(278\) | −1.34238e14 | −0.290808 | ||||||||
\(279\) | −6.60356e14 | −1.40008 | ||||||||
\(280\) | −7.46551e12 | −0.0154921 | ||||||||
\(281\) | 9.27542e14i | 1.88406i | 0.335524 | + | 0.942032i | \(0.391087\pi\) | ||||
−0.335524 | + | 0.942032i | \(0.608913\pi\) | |||||||
\(282\) | 6.63426e14 | 1.31916 | ||||||||
\(283\) | 9.58382e14i | 1.86561i | 0.360386 | + | 0.932803i | \(0.382645\pi\) | ||||
−0.360386 | + | 0.932803i | \(0.617355\pi\) | |||||||
\(284\) | 1.77821e14 | 0.338901 | ||||||||
\(285\) | 1.77547e13 | 0.0331317 | ||||||||
\(286\) | − | 1.04427e14i | − | 0.190817i | ||||||
\(287\) | − | 5.01162e14i | − | 0.896782i | ||||||
\(288\) | −6.45142e14 | −1.13058 | ||||||||
\(289\) | 2.99940e14 | 0.514811 | ||||||||
\(290\) | − | 3.62590e12i | − | 0.00609575i | ||||||
\(291\) | 1.16506e14i | 0.191862i | ||||||||
\(292\) | 4.50534e14 | 0.726826 | ||||||||
\(293\) | − | 5.49275e14i | − | 0.868129i | −0.900882 | − | 0.434065i | \(-0.857079\pi\) | ||
0.900882 | − | 0.434065i | \(-0.142921\pi\) | |||||||
\(294\) | −2.52206e14 | −0.390545 | ||||||||
\(295\) | 6.07742e12i | 0.00922120i | ||||||||
\(296\) | − | 9.13571e14i | − | 1.35829i | ||||||
\(297\) | 3.71081e14i | 0.540667i | ||||||||
\(298\) | 5.05366e14i | 0.721619i | ||||||||
\(299\) | 9.52937e13 | + | 6.57459e13i | 0.133363 | + | 0.0920114i | ||||
\(300\) | 5.90341e14 | 0.809796 | ||||||||
\(301\) | −9.82962e14 | −1.32172 | ||||||||
\(302\) | −1.77460e14 | −0.233915 | ||||||||
\(303\) | −4.45447e14 | −0.575626 | ||||||||
\(304\) | 2.20406e14i | 0.279243i | ||||||||
\(305\) | −2.50737e11 | −0.000311473 | ||||||||
\(306\) | − | 4.66108e14i | − | 0.567751i | ||||||
\(307\) | −1.73028e13 | −0.0206674 | −0.0103337 | − | 0.999947i | \(-0.503289\pi\) | ||||
−0.0103337 | + | 0.999947i | \(0.503289\pi\) | |||||||
\(308\) | 9.57627e14 | 1.12174 | ||||||||
\(309\) | 4.04928e14i | 0.465186i | ||||||||
\(310\) | − | 8.74685e12i | − | 0.00985556i | ||||||
\(311\) | −1.19719e15 | −1.32313 | −0.661564 | − | 0.749889i | \(-0.730107\pi\) | ||||
−0.661564 | + | 0.749889i | \(0.730107\pi\) | |||||||
\(312\) | 2.31460e14 | 0.250928 | ||||||||
\(313\) | − | 4.06703e14i | − | 0.432525i | −0.976335 | − | 0.216262i | \(-0.930613\pi\) | ||
0.976335 | − | 0.216262i | \(-0.0693867\pi\) | |||||||
\(314\) | 5.24413e14i | 0.547136i | ||||||||
\(315\) | −1.75488e13 | −0.0179632 | ||||||||
\(316\) | − | 6.36083e14i | − | 0.638839i | ||||||
\(317\) | 7.39236e14 | 0.728496 | 0.364248 | − | 0.931302i | \(-0.381326\pi\) | ||||
0.364248 | + | 0.931302i | \(0.381326\pi\) | |||||||
\(318\) | − | 3.30746e14i | − | 0.319839i | ||||||
\(319\) | 1.31849e15i | 1.25122i | ||||||||
\(320\) | − | 1.06840e13i | − | 0.00995023i | ||||||
\(321\) | 1.74648e15i | 1.59637i | ||||||||
\(322\) | 5.03318e14 | − | 7.29521e14i | 0.451552 | − | 0.654489i | ||||
\(323\) | 1.39844e15 | 1.23149 | ||||||||
\(324\) | 4.71731e14 | 0.407778 | ||||||||
\(325\) | −1.90903e14 | −0.161999 | ||||||||
\(326\) | 7.88126e14 | 0.656583 | ||||||||
\(327\) | − | 3.07575e15i | − | 2.51573i | ||||||
\(328\) | 9.87220e14 | 0.792813 | ||||||||
\(329\) | − | 1.96736e15i | − | 1.55135i | ||||||
\(330\) | −2.85029e13 | −0.0220702 | ||||||||
\(331\) | 4.84433e14 | 0.368354 | 0.184177 | − | 0.982893i | \(-0.441038\pi\) | ||||
0.184177 | + | 0.982893i | \(0.441038\pi\) | |||||||
\(332\) | − | 7.82086e14i | − | 0.584017i | ||||||
\(333\) | − | 2.14748e15i | − | 1.57494i | ||||||
\(334\) | −1.08664e15 | −0.782721 | ||||||||
\(335\) | 1.16005e13 | 0.00820746 | ||||||||
\(336\) | − | 3.98133e14i | − | 0.276689i | ||||||
\(337\) | 1.35339e14i | 0.0923937i | 0.998932 | + | 0.0461968i | \(0.0147101\pi\) | ||||
−0.998932 | + | 0.0461968i | \(0.985290\pi\) | |||||||
\(338\) | 9.79368e14 | 0.656819 | ||||||||
\(339\) | 2.95938e15i | 1.94986i | ||||||||
\(340\) | −7.39553e12 | −0.00478736 | ||||||||
\(341\) | 3.18063e15i | 2.02296i | ||||||||
\(342\) | 2.30586e15i | 1.44104i | ||||||||
\(343\) | − | 1.17170e15i | − | 0.719534i | ||||||
\(344\) | − | 1.93630e15i | − | 1.16848i | ||||||
\(345\) | 1.79451e13 | − | 2.60100e13i | 0.0106422 | − | 0.0154250i | ||||
\(346\) | −1.82287e15 | −1.06242 | ||||||||
\(347\) | 9.68253e14 | 0.554641 | 0.277321 | − | 0.960777i | \(-0.410554\pi\) | ||||
0.277321 | + | 0.960777i | \(0.410554\pi\) | |||||||
\(348\) | −1.03090e15 | −0.580417 | ||||||||
\(349\) | −2.67043e15 | −1.47785 | −0.738923 | − | 0.673790i | \(-0.764665\pi\) | ||||
−0.738923 | + | 0.673790i | \(0.764665\pi\) | |||||||
\(350\) | 1.46146e15i | 0.795018i | ||||||||
\(351\) | 9.38245e13 | 0.0501734 | ||||||||
\(352\) | 3.10735e15i | 1.63356i | ||||||||
\(353\) | 6.07180e14 | 0.313812 | 0.156906 | − | 0.987614i | \(-0.449848\pi\) | ||||
0.156906 | + | 0.987614i | \(0.449848\pi\) | |||||||
\(354\) | −1.44248e15 | −0.732977 | ||||||||
\(355\) | 1.56952e13i | 0.00784148i | ||||||||
\(356\) | 3.56241e14i | 0.175002i | ||||||||
\(357\) | −2.52609e15 | −1.22022 | ||||||||
\(358\) | −9.47879e14 | −0.450251 | ||||||||
\(359\) | − | 1.09407e15i | − | 0.511067i | −0.966800 | − | 0.255534i | \(-0.917749\pi\) | ||
0.966800 | − | 0.255534i | \(-0.0822512\pi\) | |||||||
\(360\) | − | 3.45687e13i | − | 0.0158806i | ||||||
\(361\) | −4.70485e15 | −2.12570 | ||||||||
\(362\) | − | 1.92485e15i | − | 0.855354i | ||||||
\(363\) | 6.96459e15 | 3.04408 | ||||||||
\(364\) | − | 2.42127e14i | − | 0.104096i | ||||||
\(365\) | 3.97661e13i | 0.0168173i | ||||||||
\(366\) | − | 5.95127e13i | − | 0.0247584i | ||||||
\(367\) | − | 2.80459e14i | − | 0.114782i | −0.998352 | − | 0.0573910i | \(-0.981722\pi\) | ||
0.998352 | − | 0.0573910i | \(-0.0182782\pi\) | |||||||
\(368\) | 3.22888e14 | + | 2.22770e14i | 0.130006 | + | 0.0896953i | ||||
\(369\) | 2.32061e15 | 0.919270 | ||||||||
\(370\) | 2.84448e13 | 0.0110864 | ||||||||
\(371\) | −9.80814e14 | −0.376135 | ||||||||
\(372\) | −2.48686e15 | −0.938413 | ||||||||
\(373\) | 1.71276e15i | 0.635981i | 0.948094 | + | 0.317991i | \(0.103008\pi\) | ||||
−0.948094 | + | 0.317991i | \(0.896992\pi\) | |||||||
\(374\) | −2.24503e15 | −0.820336 | ||||||||
\(375\) | 1.04220e14i | 0.0374770i | ||||||||
\(376\) | 3.87543e15 | 1.37149 | ||||||||
\(377\) | 3.33368e14 | 0.116112 | ||||||||
\(378\) | − | 7.18274e14i | − | 0.246229i | ||||||
\(379\) | 6.47468e14i | 0.218465i | 0.994016 | + | 0.109233i | \(0.0348394\pi\) | ||||
−0.994016 | + | 0.109233i | \(0.965161\pi\) | |||||||
\(380\) | 3.65861e13 | 0.0121511 | ||||||||
\(381\) | −1.79269e15 | −0.586078 | ||||||||
\(382\) | 2.19496e15i | 0.706394i | ||||||||
\(383\) | 1.26707e15i | 0.401428i | 0.979650 | + | 0.200714i | \(0.0643262\pi\) | ||||
−0.979650 | + | 0.200714i | \(0.935674\pi\) | |||||||
\(384\) | −1.92195e15 | −0.599454 | ||||||||
\(385\) | 8.45243e13i | 0.0259548i | ||||||||
\(386\) | 1.50787e15 | 0.455869 | ||||||||
\(387\) | − | 4.55156e15i | − | 1.35486i | ||||||
\(388\) | 2.40077e14i | 0.0703656i | ||||||||
\(389\) | 1.30007e15i | 0.375204i | 0.982245 | + | 0.187602i | \(0.0600716\pi\) | ||||
−0.982245 | + | 0.187602i | \(0.939928\pi\) | |||||||
\(390\) | 7.20671e12i | 0.00204809i | ||||||||
\(391\) | 1.41344e15 | − | 2.04867e15i | 0.395564 | − | 0.573339i | ||||
\(392\) | −1.47327e15 | −0.406038 | ||||||||
\(393\) | −2.58175e15 | −0.700742 | ||||||||
\(394\) | −2.76893e15 | −0.740177 | ||||||||
\(395\) | 5.61435e13 | 0.0147814 | ||||||||
\(396\) | 4.43424e15i | 1.14987i | ||||||||
\(397\) | −4.74502e14 | −0.121198 | −0.0605990 | − | 0.998162i | \(-0.519301\pi\) | ||||
−0.0605990 | + | 0.998162i | \(0.519301\pi\) | |||||||
\(398\) | − | 1.97395e15i | − | 0.496635i | ||||||
\(399\) | 1.24967e16 | 3.09712 | ||||||||
\(400\) | −6.46843e14 | −0.157921 | ||||||||
\(401\) | 3.07327e14i | 0.0739152i | 0.999317 | + | 0.0369576i | \(0.0117667\pi\) | ||||
−0.999317 | + | 0.0369576i | \(0.988233\pi\) | |||||||
\(402\) | 2.75339e15i | 0.652397i | ||||||||
\(403\) | 8.04193e14 | 0.187728 | ||||||||
\(404\) | −9.17908e14 | −0.211111 | ||||||||
\(405\) | 4.16370e13i | 0.00943516i | ||||||||
\(406\) | − | 2.55210e15i | − | 0.569825i | ||||||
\(407\) | −1.03434e16 | −2.27561 | ||||||||
\(408\) | − | 4.97605e15i | − | 1.07876i | ||||||
\(409\) | 3.89538e15 | 0.832165 | 0.416083 | − | 0.909327i | \(-0.363403\pi\) | ||||
0.416083 | + | 0.909327i | \(0.363403\pi\) | |||||||
\(410\) | 3.07379e13i | 0.00647100i | ||||||||
\(411\) | − | 9.56164e15i | − | 1.98372i | ||||||
\(412\) | 8.34413e14i | 0.170607i | ||||||||
\(413\) | 4.27762e15i | 0.861989i | ||||||||
\(414\) | 3.37801e15 | + | 2.33059e15i | 0.670902 | + | 0.462875i | ||||
\(415\) | 6.90303e13 | 0.0135130 | ||||||||
\(416\) | 7.85665e14 | 0.151592 | ||||||||
\(417\) | −3.36868e15 | −0.640684 | ||||||||
\(418\) | 1.11063e16 | 2.08214 | ||||||||
\(419\) | − | 8.83024e15i | − | 1.63188i | −0.578136 | − | 0.815940i | \(-0.696220\pi\) | ||
0.578136 | − | 0.815940i | \(-0.303780\pi\) | |||||||
\(420\) | −6.60876e13 | −0.0120399 | ||||||||
\(421\) | 4.47391e15i | 0.803516i | 0.915746 | + | 0.401758i | \(0.131601\pi\) | ||||
−0.915746 | + | 0.401758i | \(0.868399\pi\) | |||||||
\(422\) | 6.15022e15 | 1.08897 | ||||||||
\(423\) | 9.10977e15 | 1.59025 | ||||||||
\(424\) | − | 1.93207e15i | − | 0.332527i | ||||||
\(425\) | 4.10412e15i | 0.696444i | ||||||||
\(426\) | −3.72528e15 | −0.623306 | ||||||||
\(427\) | −1.76482e14 | −0.0291162 | ||||||||
\(428\) | 3.59887e15i | 0.585469i | ||||||||
\(429\) | − | 2.62059e15i | − | 0.420392i | ||||||
\(430\) | 6.02883e13 | 0.00953724 | ||||||||
\(431\) | 5.48668e15i | 0.855945i | 0.903792 | + | 0.427973i | \(0.140772\pi\) | ||||
−0.903792 | + | 0.427973i | \(0.859228\pi\) | |||||||
\(432\) | 3.17909e14 | 0.0489104 | ||||||||
\(433\) | − | 1.04265e16i | − | 1.58202i | −0.611806 | − | 0.791008i | \(-0.709557\pi\) | ||
0.611806 | − | 0.791008i | \(-0.290443\pi\) | |||||||
\(434\) | − | 6.15651e15i | − | 0.921289i | ||||||
\(435\) | − | 9.09915e13i | − | 0.0134297i | ||||||
\(436\) | − | 6.33802e15i | − | 0.922645i | ||||||
\(437\) | −6.99236e15 | + | 1.01349e16i | −1.00400 | + | 1.45523i | ||||
\(438\) | −9.43851e15 | −1.33678 | ||||||||
\(439\) | 1.26503e16 | 1.76732 | 0.883658 | − | 0.468133i | \(-0.155073\pi\) | ||||
0.883658 | + | 0.468133i | \(0.155073\pi\) | |||||||
\(440\) | −1.66501e14 | −0.0229457 | ||||||||
\(441\) | −3.46314e15 | −0.470803 | ||||||||
\(442\) | 5.67634e14i | 0.0761264i | ||||||||
\(443\) | 3.32307e15 | 0.439660 | 0.219830 | − | 0.975538i | \(-0.429450\pi\) | ||||
0.219830 | + | 0.975538i | \(0.429450\pi\) | |||||||
\(444\) | − | 8.08729e15i | − | 1.05561i | ||||||
\(445\) | −3.14434e13 | −0.00404920 | ||||||||
\(446\) | −3.81679e14 | −0.0484941 | ||||||||
\(447\) | 1.26821e16i | 1.58981i | ||||||||
\(448\) | − | 7.51996e15i | − | 0.930138i | ||||||
\(449\) | −5.72605e15 | −0.698839 | −0.349420 | − | 0.936966i | \(-0.613621\pi\) | ||||
−0.349420 | + | 0.936966i | \(0.613621\pi\) | |||||||
\(450\) | −6.76719e15 | −0.814955 | ||||||||
\(451\) | − | 1.11773e16i | − | 1.32824i | ||||||
\(452\) | 6.09824e15i | 0.715112i | ||||||||
\(453\) | −4.45334e15 | −0.515343 | ||||||||
\(454\) | 5.52486e15i | 0.630937i | ||||||||
\(455\) | 2.13712e13 | 0.00240858 | ||||||||
\(456\) | 2.46168e16i | 2.73806i | ||||||||
\(457\) | 1.38287e16i | 1.51804i | 0.651067 | + | 0.759020i | \(0.274322\pi\) | ||||
−0.651067 | + | 0.759020i | \(0.725678\pi\) | |||||||
\(458\) | 3.61892e15i | 0.392091i | ||||||||
\(459\) | − | 2.01709e15i | − | 0.215699i | ||||||
\(460\) | 3.69785e13 | − | 5.35974e13i | 0.00390303 | − | 0.00565714i | ||||
\(461\) | 1.68026e15 | 0.175053 | 0.0875267 | − | 0.996162i | \(-0.472104\pi\) | ||||
0.0875267 | + | 0.996162i | \(0.472104\pi\) | |||||||
\(462\) | −2.00619e16 | −2.06310 | ||||||||
\(463\) | −1.04060e16 | −1.05633 | −0.528163 | − | 0.849143i | \(-0.677119\pi\) | ||||
−0.528163 | + | 0.849143i | \(0.677119\pi\) | |||||||
\(464\) | 1.12957e15 | 0.113189 | ||||||||
\(465\) | − | 2.19501e14i | − | 0.0217130i | ||||||
\(466\) | −1.88513e15 | −0.184088 | ||||||||
\(467\) | − | 5.47474e15i | − | 0.527791i | −0.964551 | − | 0.263895i | \(-0.914993\pi\) | ||
0.964551 | − | 0.263895i | \(-0.0850074\pi\) | |||||||
\(468\) | 1.12116e15 | 0.106707 | ||||||||
\(469\) | 8.16507e15 | 0.767226 | ||||||||
\(470\) | 1.20665e14i | 0.0111942i | ||||||||
\(471\) | 1.31601e16i | 1.20541i | ||||||||
\(472\) | −8.42632e15 | −0.762054 | ||||||||
\(473\) | −2.19227e16 | −1.95762 | ||||||||
\(474\) | 1.33257e16i | 1.17495i | ||||||||
\(475\) | − | 2.03033e16i | − | 1.76768i | ||||||
\(476\) | −5.20538e15 | −0.447518 | ||||||||
\(477\) | − | 4.54161e15i | − | 0.385567i | ||||||
\(478\) | 8.73192e15 | 0.732053 | ||||||||
\(479\) | − | 5.52874e15i | − | 0.457734i | −0.973458 | − | 0.228867i | \(-0.926498\pi\) | ||
0.973458 | − | 0.228867i | \(-0.0735021\pi\) | |||||||
\(480\) | − | 2.14444e14i | − | 0.0175334i | ||||||
\(481\) | 2.61524e15i | 0.211174i | ||||||||
\(482\) | 2.41841e15i | 0.192863i | ||||||||
\(483\) | 1.26307e16 | − | 1.83073e16i | 0.994822 | − | 1.44192i | ||||
\(484\) | 1.43515e16 | 1.11642 | ||||||||
\(485\) | −2.11903e13 | −0.00162812 | ||||||||
\(486\) | −1.26350e16 | −0.958862 | ||||||||
\(487\) | 1.69381e16 | 1.26967 | 0.634833 | − | 0.772649i | \(-0.281069\pi\) | ||||
0.634833 | + | 0.772649i | \(0.281069\pi\) | |||||||
\(488\) | − | 3.47646e14i | − | 0.0257406i | ||||||
\(489\) | 1.97779e16 | 1.44653 | ||||||||
\(490\) | − | 4.58716e13i | − | 0.00331411i | ||||||
\(491\) | −4.59682e14 | −0.0328071 | −0.0164036 | − | 0.999865i | \(-0.505222\pi\) | ||||
−0.0164036 | + | 0.999865i | \(0.505222\pi\) | |||||||
\(492\) | 8.73926e15 | 0.616147 | ||||||||
\(493\) | − | 7.16692e15i | − | 0.499173i | ||||||
\(494\) | − | 2.80812e15i | − | 0.193221i | ||||||
\(495\) | −3.91386e14 | −0.0266056 | ||||||||
\(496\) | 2.72488e15 | 0.183003 | ||||||||
\(497\) | 1.10472e16i | 0.733014i | ||||||||
\(498\) | 1.63844e16i | 1.07412i | ||||||||
\(499\) | 2.02798e16 | 1.31359 | 0.656794 | − | 0.754070i | \(-0.271912\pi\) | ||||
0.656794 | + | 0.754070i | \(0.271912\pi\) | |||||||
\(500\) | 2.14761e14i | 0.0137447i | ||||||||
\(501\) | −2.72691e16 | −1.72443 | ||||||||
\(502\) | − | 2.04523e16i | − | 1.27796i | ||||||
\(503\) | 8.92318e15i | 0.550950i | 0.961308 | + | 0.275475i | \(0.0888351\pi\) | ||||
−0.961308 | + | 0.275475i | \(0.911165\pi\) | |||||||
\(504\) | − | 2.43313e16i | − | 1.48451i | ||||||
\(505\) | − | 8.10185e13i | − | 0.00488468i | ||||||
\(506\) | 1.12254e16 | − | 1.62703e16i | 0.668802 | − | 0.969377i | ||||
\(507\) | 2.45771e16 | 1.44705 | ||||||||
\(508\) | −3.69410e15 | −0.214944 | ||||||||
\(509\) | −1.11310e16 | −0.640073 | −0.320036 | − | 0.947405i | \(-0.603695\pi\) | ||||
−0.320036 | + | 0.947405i | \(0.603695\pi\) | |||||||
\(510\) | 1.54933e14 | 0.00880490 | ||||||||
\(511\) | 2.79895e16i | 1.57206i | ||||||||
\(512\) | 5.62734e15 | 0.312380 | ||||||||
\(513\) | 9.97863e15i | 0.547478i | ||||||||
\(514\) | 1.71363e14 | 0.00929264 | ||||||||
\(515\) | −7.36489e13 | −0.00394751 | ||||||||
\(516\) | − | 1.71409e16i | − | 0.908103i | ||||||
\(517\) | − | 4.38776e16i | − | 2.29773i | ||||||
\(518\) | 2.00210e16 | 1.03635 | ||||||||
\(519\) | −4.57446e16 | −2.34065 | ||||||||
\(520\) | 4.20983e13i | 0.00212934i | ||||||||
\(521\) | 1.60810e16i | 0.804057i | 0.915627 | + | 0.402029i | \(0.131695\pi\) | ||||
−0.915627 | + | 0.402029i | \(0.868305\pi\) | |||||||
\(522\) | 1.18174e16 | 0.584115 | ||||||||
\(523\) | 2.43390e15i | 0.118930i | 0.998230 | + | 0.0594652i | \(0.0189395\pi\) | ||||
−0.998230 | + | 0.0594652i | \(0.981060\pi\) | |||||||
\(524\) | −5.32006e15 | −0.256998 | ||||||||
\(525\) | 3.66751e16i | 1.75152i | ||||||||
\(526\) | 3.66400e15i | 0.172998i | ||||||||
\(527\) | − | 1.72890e16i | − | 0.807059i | ||||||
\(528\) | − | 8.87945e15i | − | 0.409810i | ||||||
\(529\) | 7.77992e15 | + | 2.04872e16i | 0.355010 | + | 0.934862i | ||||
\(530\) | 6.01566e13 | 0.00271411 | ||||||||
\(531\) | −1.98073e16 | −0.883605 | ||||||||
\(532\) | 2.57513e16 | 1.13587 | ||||||||
\(533\) | −2.82607e15 | −0.123259 | ||||||||
\(534\) | − | 7.46311e15i | − | 0.321864i | ||||||
\(535\) | −3.17652e14 | −0.0135466 | ||||||||
\(536\) | 1.60841e16i | 0.678277i | ||||||||
\(537\) | −2.37869e16 | −0.991957 | ||||||||
\(538\) | −1.19596e16 | −0.493199 | ||||||||
\(539\) | 1.66804e16i | 0.680257i | ||||||||
\(540\) | − | 5.27711e13i | − | 0.00212830i | ||||||
\(541\) | 1.80900e16 | 0.721532 | 0.360766 | − | 0.932656i | \(-0.382515\pi\) | ||||
0.360766 | + | 0.932656i | \(0.382515\pi\) | |||||||
\(542\) | 2.42175e16 | 0.955287 | ||||||||
\(543\) | − | 4.83040e16i | − | 1.88445i | ||||||
\(544\) | − | 1.68906e16i | − | 0.651707i | ||||||
\(545\) | 5.59421e14 | 0.0213481 | ||||||||
\(546\) | 5.07247e15i | 0.191454i | ||||||||
\(547\) | −4.12296e16 | −1.53917 | −0.769583 | − | 0.638547i | \(-0.779536\pi\) | ||||
−0.769583 | + | 0.638547i | \(0.779536\pi\) | |||||||
\(548\) | − | 1.97031e16i | − | 0.727532i | ||||||
\(549\) | − | 8.17193e14i | − | 0.0298463i | ||||||
\(550\) | 3.25944e16i | 1.17752i | ||||||||
\(551\) | 3.54551e16i | 1.26698i | ||||||||
\(552\) | 3.60628e16 | + | 2.48808e16i | 1.27475 | + | 0.879487i | ||||
\(553\) | 3.95168e16 | 1.38176 | ||||||||
\(554\) | −3.67978e16 | −1.27281 | ||||||||
\(555\) | 7.13819e14 | 0.0244248 | ||||||||
\(556\) | −6.94166e15 | −0.234971 | ||||||||
\(557\) | − | 5.55098e16i | − | 1.85882i | −0.369043 | − | 0.929412i | \(-0.620315\pi\) | ||
0.369043 | − | 0.929412i | \(-0.379685\pi\) | |||||||
\(558\) | 2.85074e16 | 0.944392 | ||||||||
\(559\) | 5.54296e15i | 0.181665i | ||||||||
\(560\) | 7.24130e13 | 0.00234795 | ||||||||
\(561\) | −5.63387e16 | −1.80730 | ||||||||
\(562\) | − | 4.00417e16i | − | 1.27085i | ||||||
\(563\) | 5.10025e16i | 1.60155i | 0.598964 | + | 0.800776i | \(0.295579\pi\) | ||||
−0.598964 | + | 0.800776i | \(0.704421\pi\) | |||||||
\(564\) | 3.43069e16 | 1.06588 | ||||||||
\(565\) | −5.38257e14 | −0.0165462 | ||||||||
\(566\) | − | 4.13731e16i | − | 1.25840i | ||||||
\(567\) | 2.93064e16i | 0.881990i | ||||||||
\(568\) | −2.17614e16 | −0.648032 | ||||||||
\(569\) | − | 3.79289e16i | − | 1.11763i | −0.829293 | − | 0.558814i | \(-0.811257\pi\) | ||
0.829293 | − | 0.558814i | \(-0.188743\pi\) | |||||||
\(570\) | −7.66464e14 | −0.0223482 | ||||||||
\(571\) | − | 7.91017e15i | − | 0.228228i | −0.993468 | − | 0.114114i | \(-0.963597\pi\) | ||
0.993468 | − | 0.114114i | \(-0.0364029\pi\) | |||||||
\(572\) | − | 5.40010e15i | − | 0.154179i | ||||||
\(573\) | 5.50823e16i | 1.55627i | ||||||||
\(574\) | 2.16350e16i | 0.604903i | ||||||||
\(575\) | −2.97437e16 | − | 2.05210e16i | −0.822976 | − | 0.567796i | ||||
\(576\) | 3.48208e16 | 0.953463 | ||||||||
\(577\) | −4.17872e16 | −1.13237 | −0.566186 | − | 0.824278i | \(-0.691581\pi\) | ||||
−0.566186 | + | 0.824278i | \(0.691581\pi\) | |||||||
\(578\) | −1.29483e16 | −0.347254 | ||||||||
\(579\) | 3.78399e16 | 1.00433 | ||||||||
\(580\) | − | 1.87501e14i | − | 0.00492534i | ||||||
\(581\) | 4.85872e16 | 1.26318 | ||||||||
\(582\) | − | 5.02952e15i | − | 0.129416i | ||||||
\(583\) | −2.18748e16 | −0.557100 | ||||||||
\(584\) | −5.51355e16 | −1.38981 | ||||||||
\(585\) | 9.89583e13i | 0.00246898i | ||||||||
\(586\) | 2.37121e16i | 0.585576i | ||||||||
\(587\) | 7.23158e16 | 1.76768 | 0.883842 | − | 0.467785i | \(-0.154948\pi\) | ||||
0.883842 | + | 0.467785i | \(0.154948\pi\) | |||||||
\(588\) | −1.30420e16 | −0.315559 | ||||||||
\(589\) | 8.55294e16i | 2.04844i | ||||||||
\(590\) | − | 2.62360e14i | − | 0.00621994i | ||||||
\(591\) | −6.94861e16 | −1.63070 | ||||||||
\(592\) | 8.86133e15i | 0.205859i | ||||||||
\(593\) | −4.60776e16 | −1.05965 | −0.529824 | − | 0.848107i | \(-0.677742\pi\) | ||||
−0.529824 | + | 0.848107i | \(0.677742\pi\) | |||||||
\(594\) | − | 1.60195e16i | − | 0.364694i | ||||||
\(595\) | − | 4.59449e14i | − | 0.0103547i | ||||||
\(596\) | 2.61333e16i | 0.583065i | ||||||||
\(597\) | − | 4.95360e16i | − | 1.09415i | ||||||
\(598\) | −4.11380e15 | − | 2.83823e15i | −0.0899572 | − | 0.0620642i | ||||
\(599\) | 2.79755e16 | 0.605643 | 0.302822 | − | 0.953047i | \(-0.402071\pi\) | ||||
0.302822 | + | 0.953047i | \(0.402071\pi\) | |||||||
\(600\) | −7.22448e16 | −1.54846 | ||||||||
\(601\) | −3.14835e16 | −0.668092 | −0.334046 | − | 0.942557i | \(-0.608414\pi\) | ||||
−0.334046 | + | 0.942557i | \(0.608414\pi\) | |||||||
\(602\) | 4.24342e16 | 0.891532 | ||||||||
\(603\) | 3.78080e16i | 0.786465i | ||||||||
\(604\) | −9.17675e15 | −0.189002 | ||||||||
\(605\) | 1.26673e15i | 0.0258316i | ||||||||
\(606\) | 1.92298e16 | 0.388275 | ||||||||
\(607\) | −1.94987e16 | −0.389828 | −0.194914 | − | 0.980820i | \(-0.562443\pi\) | ||||
−0.194914 | + | 0.980820i | \(0.562443\pi\) | |||||||
\(608\) | 8.35588e16i | 1.65413i | ||||||||
\(609\) | − | 6.40447e16i | − | 1.25539i | ||||||
\(610\) | 1.08243e13 | 0.000210097 | ||||||||
\(611\) | −1.10940e16 | −0.213227 | ||||||||
\(612\) | − | 2.41032e16i | − | 0.458740i | ||||||
\(613\) | − | 1.00393e16i | − | 0.189209i | −0.995515 | − | 0.0946043i | \(-0.969841\pi\) | ||
0.995515 | − | 0.0946043i | \(-0.0301586\pi\) | |||||||
\(614\) | 7.46957e14 | 0.0139407 | ||||||||
\(615\) | 7.71365e14i | 0.0142564i | ||||||||
\(616\) | −1.17193e17 | −2.14494 | ||||||||
\(617\) | 1.08743e16i | 0.197101i | 0.995132 | + | 0.0985507i | \(0.0314207\pi\) | ||||
−0.995132 | + | 0.0985507i | \(0.968579\pi\) | |||||||
\(618\) | − | 1.74806e16i | − | 0.313780i | ||||||
\(619\) | − | 9.07446e16i | − | 1.61316i | −0.591126 | − | 0.806579i | \(-0.701316\pi\) | ||
0.591126 | − | 0.806579i | \(-0.298684\pi\) | |||||||
\(620\) | − | 4.52314e14i | − | 0.00796324i | ||||||
\(621\) | 1.46184e16 | + | 1.00856e16i | 0.254888 | + | 0.175855i | ||||
\(622\) | 5.16824e16 | 0.892485 | ||||||||
\(623\) | −2.21316e16 | −0.378516 | ||||||||
\(624\) | −2.24509e15 | −0.0380299 | ||||||||
\(625\) | 5.95762e16 | 0.999523 | ||||||||
\(626\) | 1.75572e16i | 0.291750i | ||||||||
\(627\) | 2.78710e17 | 4.58720 | ||||||||
\(628\) | 2.71183e16i | 0.442083i | ||||||||
\(629\) | 5.62238e16 | 0.907854 | ||||||||
\(630\) | 7.57575e14 | 0.0121166 | ||||||||
\(631\) | − | 6.54578e16i | − | 1.03702i | −0.855073 | − | 0.518508i | \(-0.826488\pi\) | ||
0.855073 | − | 0.518508i | \(-0.173512\pi\) | |||||||
\(632\) | 7.78427e16i | 1.22156i | ||||||||
\(633\) | 1.54339e17 | 2.39913 | ||||||||
\(634\) | −3.19126e16 | −0.491390 | ||||||||
\(635\) | − | 3.26057e14i | − | 0.00497338i | ||||||
\(636\) | − | 1.71034e16i | − | 0.258429i | ||||||
\(637\) | 4.21748e15 | 0.0631271 | ||||||||
\(638\) | − | 5.69188e16i | − | 0.843980i | ||||||
\(639\) | −5.11533e16 | −0.751396 | ||||||||
\(640\) | − | 3.49568e14i | − | 0.00508688i | ||||||
\(641\) | − | 1.02117e17i | − | 1.47214i | −0.676905 | − | 0.736070i | \(-0.736679\pi\) | ||
0.676905 | − | 0.736070i | \(-0.263321\pi\) | |||||||
\(642\) | − | 7.53950e16i | − | 1.07679i | ||||||
\(643\) | − | 8.63624e16i | − | 1.22197i | −0.791644 | − | 0.610983i | \(-0.790774\pi\) | ||
0.791644 | − | 0.610983i | \(-0.209226\pi\) | |||||||
\(644\) | 2.60274e16 | − | 3.77248e16i | 0.364852 | − | 0.528824i | ||||
\(645\) | 1.51293e15 | 0.0210117 | ||||||||
\(646\) | −6.03703e16 | −0.830670 | ||||||||
\(647\) | 5.86706e16 | 0.799825 | 0.399912 | − | 0.916553i | \(-0.369041\pi\) | ||||
0.399912 | + | 0.916553i | \(0.369041\pi\) | |||||||
\(648\) | −5.77295e16 | −0.779737 | ||||||||
\(649\) | 9.54026e16i | 1.27671i | ||||||||
\(650\) | 8.24120e15 | 0.109272 | ||||||||
\(651\) | − | 1.54497e17i | − | 2.02971i | ||||||
\(652\) | 4.07553e16 | 0.530516 | ||||||||
\(653\) | −5.01181e16 | −0.646422 | −0.323211 | − | 0.946327i | \(-0.604762\pi\) | ||||
−0.323211 | + | 0.946327i | \(0.604762\pi\) | |||||||
\(654\) | 1.32779e17i | 1.69693i | ||||||||
\(655\) | − | 4.69572e14i | − | 0.00594640i | ||||||
\(656\) | −9.57570e15 | −0.120157 | ||||||||
\(657\) | −1.29604e17 | −1.61149 | ||||||||
\(658\) | 8.49305e16i | 1.04643i | ||||||||
\(659\) | − | 1.84832e16i | − | 0.225665i | −0.993614 | − | 0.112833i | \(-0.964008\pi\) | ||
0.993614 | − | 0.112833i | \(-0.0359924\pi\) | |||||||
\(660\) | −1.47393e15 | −0.0178326 | ||||||||
\(661\) | 1.47351e17i | 1.76663i | 0.468784 | + | 0.883313i | \(0.344692\pi\) | ||||
−0.468784 | + | 0.883313i | \(0.655308\pi\) | |||||||
\(662\) | −2.09128e16 | −0.248465 | ||||||||
\(663\) | 1.42447e16i | 0.167715i | ||||||||
\(664\) | 9.57102e16i | 1.11673i | ||||||||
\(665\) | 2.27292e15i | 0.0262817i | ||||||||
\(666\) | 9.27062e16i | 1.06234i | ||||||||
\(667\) | 5.19406e16 | + | 3.58354e16i | 0.589864 | + | 0.406965i | ||||
\(668\) | −5.61920e16 | −0.632434 | ||||||||
\(669\) | −9.57819e15 | −0.106838 | ||||||||
\(670\) | −5.00791e14 | −0.00553615 | ||||||||
\(671\) | −3.93604e15 | −0.0431245 | ||||||||
\(672\) | − | 1.50937e17i | − | 1.63901i | ||||||
\(673\) | −3.84688e15 | −0.0414018 | −0.0207009 | − | 0.999786i | \(-0.506590\pi\) | ||||
−0.0207009 | + | 0.999786i | \(0.506590\pi\) | |||||||
\(674\) | − | 5.84253e15i | − | 0.0623220i | ||||||
\(675\) | −2.92851e16 | −0.309616 | ||||||||
\(676\) | 5.06447e16 | 0.530706 | ||||||||
\(677\) | − | 1.50179e17i | − | 1.55983i | −0.625885 | − | 0.779916i | \(-0.715262\pi\) | ||
0.625885 | − | 0.779916i | \(-0.284738\pi\) | |||||||
\(678\) | − | 1.27756e17i | − | 1.31523i | ||||||
\(679\) | −1.49149e16 | −0.152195 | ||||||||
\(680\) | 9.05051e14 | 0.00915419 | ||||||||
\(681\) | 1.38646e17i | 1.39003i | ||||||||
\(682\) | − | 1.37307e17i | − | 1.36454i | ||||||
\(683\) | 7.47720e16 | 0.736572 | 0.368286 | − | 0.929713i | \(-0.379945\pi\) | ||||
0.368286 | + | 0.929713i | \(0.379945\pi\) | |||||||
\(684\) | 1.19240e17i | 1.16435i | ||||||||
\(685\) | 1.73908e15 | 0.0168336 | ||||||||
\(686\) | 5.05819e16i | 0.485345i | ||||||||
\(687\) | 9.08165e16i | 0.863823i | ||||||||
\(688\) | 1.87815e16i | 0.177092i | ||||||||
\(689\) | 5.53085e15i | 0.0516983i | ||||||||
\(690\) | −7.74684e14 | + | 1.12284e15i | −0.00717844 | + | 0.0104046i | ||||
\(691\) | 2.57585e16 | 0.236620 | 0.118310 | − | 0.992977i | \(-0.462252\pi\) | ||||
0.118310 | + | 0.992977i | \(0.462252\pi\) | |||||||
\(692\) | −9.42634e16 | −0.858433 | ||||||||
\(693\) | −2.75478e17 | −2.48707 | ||||||||
\(694\) | −4.17992e16 | −0.374120 | ||||||||
\(695\) | − | 6.12701e14i | − | 0.00543676i | ||||||
\(696\) | 1.26159e17 | 1.10985 | ||||||||
\(697\) | 6.07564e16i | 0.529901i | ||||||||
\(698\) | 1.15282e17 | 0.996846 | ||||||||
\(699\) | −4.73072e16 | −0.405568 | ||||||||
\(700\) | 7.55743e16i | 0.642371i | ||||||||
\(701\) | 5.23286e16i | 0.440992i | 0.975388 | + | 0.220496i | \(0.0707676\pi\) | ||||
−0.975388 | + | 0.220496i | \(0.929232\pi\) | |||||||
\(702\) | −4.05037e15 | −0.0338433 | ||||||||
\(703\) | −2.78142e17 | −2.30428 | ||||||||
\(704\) | − | 1.67716e17i | − | 1.37765i | ||||||
\(705\) | 3.02807e15i | 0.0246622i | ||||||||
\(706\) | −2.62118e16 | −0.211674 | ||||||||
\(707\) | − | 5.70252e16i | − | 0.456615i | ||||||
\(708\) | −7.45931e16 | −0.592242 | ||||||||
\(709\) | − | 5.12273e16i | − | 0.403296i | −0.979458 | − | 0.201648i | \(-0.935370\pi\) | ||
0.979458 | − | 0.201648i | \(-0.0646298\pi\) | |||||||
\(710\) | − | 6.77559e14i | − | 0.00528929i | ||||||
\(711\) | 1.82981e17i | 1.41640i | ||||||||
\(712\) | − | 4.35961e16i | − | 0.334632i | ||||||
\(713\) | 1.25298e17 | + | 8.64466e16i | 0.953687 | + | 0.657977i | ||||
\(714\) | 1.09051e17 | 0.823074 | ||||||||
\(715\) | 4.76636e14 | 0.00356739 | ||||||||
\(716\) | −4.90164e16 | −0.363801 | ||||||||
\(717\) | 2.19127e17 | 1.61280 | ||||||||
\(718\) | 4.72306e16i | 0.344728i | ||||||||
\(719\) | 3.98857e16 | 0.288698 | 0.144349 | − | 0.989527i | \(-0.453891\pi\) | ||||
0.144349 | + | 0.989527i | \(0.453891\pi\) | |||||||
\(720\) | 3.35305e14i | 0.00240682i | ||||||||
\(721\) | −5.18381e16 | −0.369009 | ||||||||
\(722\) | 2.03107e17 | 1.43384 | ||||||||
\(723\) | 6.06898e16i | 0.424899i | ||||||||
\(724\) | − | 9.95374e16i | − | 0.691122i | ||||||
\(725\) | −1.04053e17 | −0.716517 | ||||||||
\(726\) | −3.00659e17 | −2.05331 | ||||||||
\(727\) | − | 1.33841e17i | − | 0.906530i | −0.891376 | − | 0.453265i | \(-0.850259\pi\) | ||
0.891376 | − | 0.453265i | \(-0.149741\pi\) | |||||||
\(728\) | 2.96311e16i | 0.199049i | ||||||||
\(729\) | −2.04773e17 | −1.36429 | ||||||||
\(730\) | − | 1.71669e15i | − | 0.0113437i | ||||||
\(731\) | 1.19165e17 | 0.780991 | ||||||||
\(732\) | − | 3.07750e15i | − | 0.0200047i | ||||||
\(733\) | − | 3.53101e16i | − | 0.227654i | −0.993501 | − | 0.113827i | \(-0.963689\pi\) | ||
0.993501 | − | 0.113827i | \(-0.0363109\pi\) | |||||||
\(734\) | 1.21073e16i | 0.0774235i | ||||||||
\(735\) | − | 1.15114e15i | − | 0.00730138i | ||||||
\(736\) | 1.22411e17 | + | 8.44549e16i | 0.770111 | + | 0.531322i | ||||
\(737\) | 1.82103e17 | 1.13635 | ||||||||
\(738\) | −1.00180e17 | −0.620072 | ||||||||
\(739\) | −2.12756e17 | −1.30622 | −0.653109 | − | 0.757264i | \(-0.726536\pi\) | ||||
−0.653109 | + | 0.757264i | \(0.726536\pi\) | |||||||
\(740\) | 1.47093e15 | 0.00895779 | ||||||||
\(741\) | − | 7.04694e16i | − | 0.425688i | ||||||
\(742\) | 4.23414e16 | 0.253713 | ||||||||
\(743\) | 2.09986e17i | 1.24812i | 0.781375 | + | 0.624062i | \(0.214519\pi\) | ||||
−0.781375 | + | 0.624062i | \(0.785481\pi\) | |||||||
\(744\) | 3.04338e17 | 1.79439 | ||||||||
\(745\) | −2.30664e15 | −0.0134909 | ||||||||
\(746\) | − | 7.39395e16i | − | 0.428986i | ||||||
\(747\) | 2.24981e17i | 1.29486i | ||||||||
\(748\) | −1.16094e17 | −0.662827 | ||||||||
\(749\) | −2.23581e17 | −1.26632 | ||||||||
\(750\) | − | 4.49916e15i | − | 0.0252792i | ||||||
\(751\) | 2.57245e17i | 1.43386i | 0.697144 | + | 0.716931i | \(0.254454\pi\) | ||||
−0.697144 | + | 0.716931i | \(0.745546\pi\) | |||||||
\(752\) | −3.75904e16 | −0.207860 | ||||||||
\(753\) | − | 5.13247e17i | − | 2.81551i | ||||||
\(754\) | −1.43914e16 | −0.0783204 | ||||||||
\(755\) | − | 8.09980e14i | − | 0.00437313i | ||||||
\(756\) | − | 3.71431e16i | − | 0.198952i | ||||||
\(757\) | − | 2.67529e17i | − | 1.42166i | −0.703365 | − | 0.710829i | \(-0.748320\pi\) | ||
0.703365 | − | 0.710829i | \(-0.251680\pi\) | |||||||
\(758\) | − | 2.79510e16i | − | 0.147361i | ||||||
\(759\) | 2.81700e17 | − | 4.08302e17i | 1.47345 | − | 2.13565i | ||||
\(760\) | −4.47734e15 | −0.0232348 | ||||||||
\(761\) | 4.34486e16 | 0.223701 | 0.111850 | − | 0.993725i | \(-0.464322\pi\) | ||||
0.111850 | + | 0.993725i | \(0.464322\pi\) | |||||||
\(762\) | 7.73899e16 | 0.395325 | ||||||||
\(763\) | 3.93751e17 | 1.99560 | ||||||||
\(764\) | 1.13505e17i | 0.570762i | ||||||||
\(765\) | 2.12746e15 | 0.0106143 | ||||||||
\(766\) | − | 5.46990e16i | − | 0.270774i | ||||||
\(767\) | 2.41217e16 | 0.118477 | ||||||||
\(768\) | 3.23575e17 | 1.57691 | ||||||||
\(769\) | 4.49253e16i | 0.217237i | 0.994084 | + | 0.108618i | \(0.0346427\pi\) | ||||
−0.994084 | + | 0.108618i | \(0.965357\pi\) | |||||||
\(770\) | − | 3.64889e15i | − | 0.0175072i | ||||||
\(771\) | 4.30035e15 | 0.0204728 | ||||||||
\(772\) | 7.79745e16 | 0.368340 | ||||||||
\(773\) | − | 2.47476e15i | − | 0.0115999i | −0.999983 | − | 0.00579996i | \(-0.998154\pi\) | ||
0.999983 | − | 0.00579996i | \(-0.00184620\pi\) | |||||||
\(774\) | 1.96489e17i | 0.913889i | ||||||||
\(775\) | −2.51010e17 | −1.15846 | ||||||||
\(776\) | − | 2.93802e16i | − | 0.134550i | ||||||
\(777\) | 5.02425e17 | 2.28320 | ||||||||
\(778\) | − | 5.61235e16i | − | 0.253085i | ||||||
\(779\) | − | 3.00565e17i | − | 1.34497i | ||||||
\(780\) | 3.72671e14i | 0.00165485i | ||||||||
\(781\) | 2.46382e17i | 1.08568i | ||||||||
\(782\) | −6.10178e16 | + | 8.84405e16i | −0.266818 | + | 0.386733i | ||||
\(783\) | 5.11398e16 | 0.221916 | ||||||||
\(784\) | 1.42903e16 | 0.0615380 | ||||||||
\(785\) | −2.39357e15 | −0.0102289 | ||||||||
\(786\) | 1.11453e17 | 0.472669 | ||||||||
\(787\) | − | 9.96355e15i | − | 0.0419339i | −0.999780 | − | 0.0209670i | \(-0.993326\pi\) | ||
0.999780 | − | 0.0209670i | \(-0.00667448\pi\) | |||||||
\(788\) | −1.43186e17 | −0.598059 | ||||||||
\(789\) | 9.19477e16i | 0.381135i | ||||||||
\(790\) | −2.42370e15 | −0.00997047 | ||||||||
\(791\) | −3.78854e17 | −1.54673 | ||||||||
\(792\) | − | 5.42654e17i | − | 2.19873i | ||||||
\(793\) | 9.95192e14i | 0.00400191i | ||||||||
\(794\) | 2.04841e16 | 0.0817512 | ||||||||
\(795\) | 1.50962e15 | 0.00597951 | ||||||||
\(796\) | − | 1.02076e17i | − | 0.401278i | ||||||
\(797\) | 1.11543e17i | 0.435203i | 0.976038 | + | 0.217602i | \(0.0698233\pi\) | ||||
−0.976038 | + | 0.217602i | \(0.930177\pi\) | |||||||
\(798\) | −5.39479e17 | −2.08909 | ||||||||
\(799\) | 2.38505e17i | 0.916679i | ||||||||
\(800\) | −2.45227e17 | −0.935465 | ||||||||
\(801\) | − | 1.02479e17i | − | 0.388007i | ||||||
\(802\) | − | 1.32672e16i | − | 0.0498578i | ||||||
\(803\) | 6.24243e17i | 2.32841i | ||||||||
\(804\) | 1.42383e17i | 0.527133i | ||||||||
\(805\) | 3.32975e15 | + | 2.29729e15i | 0.0122359 | + | 0.00844192i | ||||
\(806\) | −3.47168e16 | −0.126628 | ||||||||
\(807\) | −3.00124e17 | −1.08658 | ||||||||
\(808\) | 1.12332e17 | 0.403678 | ||||||||
\(809\) | 7.67640e16 | 0.273821 | 0.136910 | − | 0.990583i | \(-0.456283\pi\) | ||||
0.136910 | + | 0.990583i | \(0.456283\pi\) | |||||||
\(810\) | − | 1.79746e15i | − | 0.00636427i | ||||||
\(811\) | −5.07809e17 | −1.78474 | −0.892371 | − | 0.451303i | \(-0.850959\pi\) | ||||
−0.892371 | + | 0.451303i | \(0.850959\pi\) | |||||||
\(812\) | − | 1.31973e17i | − | 0.460416i | ||||||
\(813\) | 6.07736e17 | 2.10461 | ||||||||
\(814\) | 4.46523e17 | 1.53496 | ||||||||
\(815\) | 3.59724e15i | 0.0122751i | ||||||||
\(816\) | 4.82660e16i | 0.163494i | ||||||||
\(817\) | −5.89518e17 | −1.98228 | ||||||||
\(818\) | −1.68162e17 | −0.561318 | ||||||||
\(819\) | 6.96522e16i | 0.230798i | ||||||||
\(820\) | 1.58951e15i | 0.00522853i | ||||||||
\(821\) | −5.34524e17 | −1.74545 | −0.872726 | − | 0.488210i | \(-0.837650\pi\) | ||||
−0.872726 | + | 0.488210i | \(0.837650\pi\) | |||||||
\(822\) | 4.12773e17i | 1.33807i | ||||||||
\(823\) | 1.84477e17 | 0.593669 | 0.296834 | − | 0.954929i | \(-0.404069\pi\) | ||||
0.296834 | + | 0.954929i | \(0.404069\pi\) | |||||||
\(824\) | − | 1.02114e17i | − | 0.326228i | ||||||
\(825\) | 8.17954e17i | 2.59421i | ||||||||
\(826\) | − | 1.84664e17i | − | 0.581435i | ||||||
\(827\) | − | 2.43107e17i | − | 0.759915i | −0.925004 | − | 0.379957i | \(-0.875939\pi\) | ||
0.925004 | − | 0.379957i | \(-0.124061\pi\) | |||||||
\(828\) | 1.74683e17 | + | 1.20519e17i | 0.542085 | + | 0.374001i | ||||
\(829\) | 5.28902e17 | 1.62948 | 0.814739 | − | 0.579829i | \(-0.196880\pi\) | ||||
0.814739 | + | 0.579829i | \(0.196880\pi\) | |||||||
\(830\) | −2.98002e15 | −0.00911486 | ||||||||
\(831\) | −9.23437e17 | −2.80415 | ||||||||
\(832\) | −4.24054e16 | −0.127844 | ||||||||
\(833\) | − | 9.06695e16i | − | 0.271388i | ||||||
\(834\) | 1.45425e17 | 0.432158 | ||||||||
\(835\) | − | 4.95975e15i | − | 0.0146332i | ||||||
\(836\) | 5.74323e17 | 1.68236 | ||||||||
\(837\) | 1.23366e17 | 0.358792 | ||||||||
\(838\) | 3.81199e17i | 1.10075i | ||||||||
\(839\) | − | 3.72458e17i | − | 1.06784i | −0.845536 | − | 0.533919i | \(-0.820719\pi\) | ||
0.845536 | − | 0.533919i | \(-0.179281\pi\) | |||||||
\(840\) | 8.08768e15 | 0.0230223 | ||||||||
\(841\) | −1.72110e17 | −0.486440 | ||||||||
\(842\) | − | 1.93137e17i | − | 0.541993i | ||||||
\(843\) | − | 1.00484e18i | − | 2.79983i | ||||||
\(844\) | 3.18038e17 | 0.879882 | ||||||||
\(845\) | 4.47012e15i | 0.0122795i | ||||||||
\(846\) | −3.93266e17 | −1.07267 | ||||||||
\(847\) | 8.91593e17i | 2.41472i | ||||||||
\(848\) | 1.87404e16i | 0.0503969i | ||||||||
\(849\) | − | 1.03825e18i | − | 2.77241i | ||||||
\(850\) | − | 1.77174e17i | − | 0.469770i | ||||||
\(851\) | −2.81125e17 | + | 4.07469e17i | −0.740154 | + | 1.07280i | ||||
\(852\) | −1.92640e17 | −0.503628 | ||||||||
\(853\) | 1.71441e17 | 0.445062 | 0.222531 | − | 0.974926i | \(-0.428568\pi\) | ||||
0.222531 | + | 0.974926i | \(0.428568\pi\) | |||||||
\(854\) | 7.61869e15 | 0.0196396 | ||||||||
\(855\) | −1.05246e16 | −0.0269408 | ||||||||
\(856\) | − | 4.40423e17i | − | 1.11951i | ||||||
\(857\) | 7.39162e17 | 1.86576 | 0.932878 | − | 0.360194i | \(-0.117289\pi\) | ||||
0.932878 | + | 0.360194i | \(0.117289\pi\) | |||||||
\(858\) | 1.13130e17i | 0.283566i | ||||||||
\(859\) | 7.74483e16 | 0.192776 | 0.0963880 | − | 0.995344i | \(-0.469271\pi\) | ||||
0.0963880 | + | 0.995344i | \(0.469271\pi\) | |||||||
\(860\) | 3.11761e15 | 0.00770604 | ||||||||
\(861\) | 5.42928e17i | 1.33267i | ||||||||
\(862\) | − | 2.36858e17i | − | 0.577358i | ||||||
\(863\) | 9.60821e16 | 0.232583 | 0.116291 | − | 0.993215i | \(-0.462899\pi\) | ||||
0.116291 | + | 0.993215i | \(0.462899\pi\) | |||||||
\(864\) | 1.20524e17 | 0.289727 | ||||||||
\(865\) | − | 8.32010e15i | − | 0.0198624i | ||||||
\(866\) | 4.50108e17i | 1.06711i | ||||||||
\(867\) | −3.24937e17 | −0.765041 | ||||||||
\(868\) | − | 3.18363e17i | − | 0.744397i | ||||||
\(869\) | 8.81333e17 | 2.04654 | ||||||||
\(870\) | 3.92808e15i | 0.00905867i | ||||||||
\(871\) | − | 4.60432e16i | − | 0.105452i | ||||||
\(872\) | 7.75635e17i | 1.76424i | ||||||||
\(873\) | − | 6.90625e16i | − | 0.156011i | ||||||
\(874\) | 3.01858e17 | − | 4.37520e17i | 0.677227 | − | 0.981588i | ||||
\(875\) | −1.33421e16 | −0.0297287 | ||||||||
\(876\) | −4.88081e17 | −1.08011 | ||||||||
\(877\) | −3.35782e17 | −0.738007 | −0.369003 | − | 0.929428i | \(-0.620301\pi\) | ||||
−0.369003 | + | 0.929428i | \(0.620301\pi\) | |||||||
\(878\) | −5.46110e17 | −1.19210 | ||||||||
\(879\) | 5.95051e17i | 1.29009i | ||||||||
\(880\) | 1.61501e15 | 0.00347759 | ||||||||
\(881\) | − | 8.78827e16i | − | 0.187952i | −0.995574 | − | 0.0939762i | \(-0.970042\pi\) | ||
0.995574 | − | 0.0939762i | \(-0.0299578\pi\) | |||||||
\(882\) | 1.49503e17 | 0.317569 | ||||||||
\(883\) | −7.17005e17 | −1.51272 | −0.756359 | − | 0.654156i | \(-0.773024\pi\) | ||||
−0.756359 | + | 0.654156i | \(0.773024\pi\) | |||||||
\(884\) | 2.93533e16i | 0.0615097i | ||||||||
\(885\) | − | 6.58391e15i | − | 0.0137033i | ||||||
\(886\) | −1.43456e17 | −0.296562 | ||||||||
\(887\) | −4.93950e17 | −1.01424 | −0.507121 | − | 0.861875i | \(-0.669290\pi\) | ||||
−0.507121 | + | 0.861875i | \(0.669290\pi\) | |||||||
\(888\) | 9.89707e17i | 2.01850i | ||||||||
\(889\) | − | 2.29497e17i | − | 0.464907i | ||||||
\(890\) | 1.35740e15 | 0.00273129 | ||||||||
\(891\) | 6.53612e17i | 1.30633i | ||||||||
\(892\) | −1.97373e16 | −0.0391830 | ||||||||
\(893\) | − | 1.17990e18i | − | 2.32668i | ||||||
\(894\) | − | 5.47483e17i | − | 1.07237i | ||||||
\(895\) | − | 4.32640e15i | − | 0.00841761i | ||||||
\(896\) | − | 2.46045e17i | − | 0.475517i | ||||||
\(897\) | −1.03235e17 | − | 7.12252e16i | −0.198186 | − | 0.136735i | ||||
\(898\) | 2.47192e17 | 0.471385 | ||||||||
\(899\) | 4.38332e17 | 0.830319 | ||||||||
\(900\) | −3.49943e17 | −0.658479 | ||||||||
\(901\) | 1.18905e17 | 0.222255 | ||||||||
\(902\) | 4.82520e17i | 0.895934i | ||||||||
\(903\) | 1.06488e18 | 1.96415 | ||||||||
\(904\) | − | 7.46291e17i | − | 1.36741i | ||||||
\(905\) | 8.78560e15 | 0.0159912 | ||||||||
\(906\) | 1.92249e17 | 0.347613 | ||||||||
\(907\) | − | 4.02229e17i | − | 0.722487i | −0.932471 | − | 0.361244i | \(-0.882352\pi\) | ||
0.932471 | − | 0.361244i | \(-0.117648\pi\) | |||||||
\(908\) | 2.85700e17i | 0.509794i | ||||||||
\(909\) | 2.64052e17 | 0.468066 | ||||||||
\(910\) | −9.22588e14 | −0.00162465 | ||||||||
\(911\) | 2.71856e17i | 0.475585i | 0.971316 | + | 0.237793i | \(0.0764238\pi\) | ||||
−0.971316 | + | 0.237793i | \(0.923576\pi\) | |||||||
\(912\) | − | 2.38774e17i | − | 0.414972i | ||||||
\(913\) | 1.08363e18 | 1.87092 | ||||||||
\(914\) | − | 5.96980e17i | − | 1.02396i | ||||||
\(915\) | 2.71633e14 | 0.000462868 | ||||||||
\(916\) | 1.87141e17i | 0.316807i | ||||||||
\(917\) | − | 3.30510e17i | − | 0.555864i | ||||||
\(918\) | 8.70770e16i | 0.145495i | ||||||||
\(919\) | 6.97302e17i | 1.15752i | 0.815499 | + | 0.578759i | \(0.196463\pi\) | ||||
−0.815499 | + | 0.578759i | \(0.803537\pi\) | |||||||
\(920\) | −4.52535e15 | + | 6.55915e15i | −0.00746321 | + | 0.0108173i | ||||
\(921\) | 1.87448e16 | 0.0307131 | ||||||||
\(922\) | −7.25363e16 | −0.118078 | ||||||||
\(923\) | 6.22954e16 | 0.100750 | ||||||||
\(924\) | −1.03744e18 | −1.66697 | ||||||||
\(925\) | − | 8.16285e17i | − | 1.30314i | ||||||
\(926\) | 4.49224e17 | 0.712520 | ||||||||
\(927\) | − | 2.40034e17i | − | 0.378263i | ||||||
\(928\) | 4.28233e17 | 0.670490 | ||||||||
\(929\) | −4.99060e17 | −0.776352 | −0.388176 | − | 0.921585i | \(-0.626895\pi\) | ||||
−0.388176 | + | 0.921585i | \(0.626895\pi\) | |||||||
\(930\) | 9.47580e15i | 0.0146460i | ||||||||
\(931\) | 4.48546e17i | 0.688826i | ||||||||
\(932\) | −9.74833e16 | −0.148742 | ||||||||
\(933\) | 1.29697e18 | 1.96625 | ||||||||
\(934\) | 2.36343e17i | 0.356009i | ||||||||
\(935\) | − | 1.02470e16i | − | 0.0153365i | ||||||
\(936\) | −1.37205e17 | −0.204040 | ||||||||
\(937\) | 2.02687e17i | 0.299495i | 0.988724 | + | 0.149747i | \(0.0478460\pi\) | ||||
−0.988724 | + | 0.149747i | \(0.952154\pi\) | |||||||
\(938\) | −3.52484e17 | −0.517514 | ||||||||
\(939\) | 4.40597e17i | 0.642759i | ||||||||
\(940\) | 6.23978e15i | 0.00904487i | ||||||||
\(941\) | − | 1.07140e18i | − | 1.54318i | −0.636123 | − | 0.771588i | \(-0.719463\pi\) | ||
0.636123 | − | 0.771588i | \(-0.280537\pi\) | |||||||
\(942\) | − | 5.68117e17i | − | 0.813078i | ||||||
\(943\) | −4.40318e17 | − | 3.03788e17i | −0.626175 | − | 0.432017i | ||||
\(944\) | 8.17325e16 | 0.115495 | ||||||||
\(945\) | 3.27841e15 | 0.00460334 | ||||||||
\(946\) | 9.46398e17 | 1.32047 | ||||||||
\(947\) | −4.67317e17 | −0.647906 | −0.323953 | − | 0.946073i | \(-0.605012\pi\) | ||||
−0.323953 | + | 0.946073i | \(0.605012\pi\) | |||||||
\(948\) | 6.89094e17i | 0.949354i | ||||||||
\(949\) | 1.57834e17 | 0.216075 | ||||||||
\(950\) | 8.76487e17i | 1.19235i | ||||||||
\(951\) | −8.00843e17 | −1.08259 | ||||||||
\(952\) | 6.37024e17 | 0.855725 | ||||||||
\(953\) | 1.45697e17i | 0.194489i | 0.995261 | + | 0.0972444i | \(0.0310029\pi\) | ||||
−0.995261 | + | 0.0972444i | \(0.968997\pi\) | |||||||
\(954\) | 1.96060e17i | 0.260075i | ||||||||
\(955\) | −1.00185e16 | −0.0132063 | ||||||||
\(956\) | 4.51542e17 | 0.591495 | ||||||||
\(957\) | − | 1.42837e18i | − | 1.85939i | ||||||
\(958\) | 2.38674e17i | 0.308754i | ||||||||
\(959\) | 1.22406e18 | 1.57359 | ||||||||
\(960\) | 1.15744e16i | 0.0147867i | ||||||||
\(961\) | 2.69738e17 | 0.342453 | ||||||||
\(962\) | − | 1.12899e17i | − | 0.142443i | ||||||
\(963\) | − | 1.03528e18i | − | 1.29808i | ||||||
\(964\) | 1.25060e17i | 0.155832i | ||||||||
\(965\) | 6.88237e15i | 0.00852264i | ||||||||
\(966\) | −5.45265e17 | + | 7.90319e17i | −0.671034 | + | 0.972612i | ||||
\(967\) | 5.00948e17 | 0.612680 | 0.306340 | − | 0.951922i | \(-0.400895\pi\) | ||||
0.306340 | + | 0.951922i | \(0.400895\pi\) | |||||||
\(968\) | −1.75631e18 | −2.13477 | ||||||||
\(969\) | −1.51499e18 | −1.83006 | ||||||||
\(970\) | 9.14777e14 | 0.00109821 | ||||||||
\(971\) | 8.15663e16i | 0.0973185i | 0.998815 | + | 0.0486593i | \(0.0154948\pi\) | ||||
−0.998815 | + | 0.0486593i | \(0.984505\pi\) | |||||||
\(972\) | −6.53375e17 | −0.774756 | ||||||||
\(973\) | − | 4.31252e17i | − | 0.508223i | ||||||
\(974\) | −7.31211e17 | −0.856424 | ||||||||
\(975\) | 2.06812e17 | 0.240740 | ||||||||
\(976\) | 3.37205e15i | 0.00390117i | ||||||||
\(977\) | 1.61924e18i | 1.86185i | 0.365210 | + | 0.930925i | \(0.380997\pi\) | ||||
−0.365210 | + | 0.930925i | \(0.619003\pi\) | |||||||
\(978\) | −8.53807e17 | −0.975724 | ||||||||
\(979\) | −4.93594e17 | −0.560627 | ||||||||
\(980\) | − | 2.37210e15i | − | 0.00267779i | ||||||
\(981\) | 1.82324e18i | 2.04565i | ||||||||
\(982\) | 1.98443e16 | 0.0221293 | ||||||||
\(983\) | − | 7.50585e17i | − | 0.831915i | −0.909384 | − | 0.415957i | \(-0.863447\pi\) | ||
0.909384 | − | 0.415957i | \(-0.136553\pi\) | |||||||
\(984\) | −1.06949e18 | −1.17817 | ||||||||
\(985\) | − | 1.26382e16i | − | 0.0138379i | ||||||
\(986\) | 3.09394e17i | 0.336705i | ||||||||
\(987\) | 2.13132e18i | 2.30540i | ||||||||
\(988\) | − | 1.45212e17i | − | 0.156121i | ||||||
\(989\) | −5.95840e17 | + | 8.63624e17i | −0.636725 | + | 0.922884i | ||||
\(990\) | 1.68960e16 | 0.0179462 | ||||||||
\(991\) | 9.73285e16 | 0.102754 | 0.0513769 | − | 0.998679i | \(-0.483639\pi\) | ||||
0.0513769 | + | 0.998679i | \(0.483639\pi\) | |||||||
\(992\) | 1.03304e18 | 1.08404 | ||||||||
\(993\) | −5.24805e17 | −0.547397 | ||||||||
\(994\) | − | 4.76903e17i | − | 0.494438i | ||||||
\(995\) | 9.00968e15 | 0.00928476 | ||||||||
\(996\) | 8.47264e17i | 0.867886i | ||||||||
\(997\) | −1.01590e18 | −1.03438 | −0.517191 | − | 0.855870i | \(-0.673022\pi\) | ||||
−0.517191 | + | 0.855870i | \(0.673022\pi\) | |||||||
\(998\) | −8.75471e17 | −0.886051 | ||||||||
\(999\) | 4.01187e17i | 0.403602i |
(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.22.7 | ✓ | 20 | |
23.22 | odd | 2 | inner | 23.13.b.c.22.8 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
23.13.b.c.22.7 | ✓ | 20 | 1.1 | even | 1 | trivial | |
23.13.b.c.22.8 | yes | 20 | 23.22 | odd | 2 | inner |