Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (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: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.85 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.16 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 47.5424i | 1.48570i | 0.669457 | + | 0.742850i | \(0.266527\pi\) | ||||
−0.669457 | + | 0.742850i | \(0.733473\pi\) | |||||||
\(3\) | 140.296 | 0.577350 | ||||||||
\(4\) | −1236.28 | −1.20731 | ||||||||
\(5\) | −4974.64 | −1.59189 | −0.795943 | − | 0.605371i | \(-0.793025\pi\) | ||||
−0.795943 | + | 0.605371i | \(0.793025\pi\) | |||||||
\(6\) | 6670.02i | 0.857770i | ||||||||
\(7\) | 12474.7 | 0.742233 | 0.371117 | − | 0.928586i | \(-0.378975\pi\) | ||||
0.371117 | + | 0.928586i | \(0.378975\pi\) | |||||||
\(8\) | − | 10092.4i | − | 0.307996i | ||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | − | 236507.i | − | 2.36507i | ||||||
\(11\) | − | 91525.3i | − | 0.568300i | −0.958780 | − | 0.284150i | \(-0.908289\pi\) | ||
0.958780 | − | 0.284150i | \(-0.0917114\pi\) | |||||||
\(12\) | −173446. | −0.697039 | ||||||||
\(13\) | 581654.i | 1.56656i | 0.621668 | + | 0.783281i | \(0.286455\pi\) | ||||
−0.621668 | + | 0.783281i | \(0.713545\pi\) | |||||||
\(14\) | 593078.i | 1.10274i | ||||||||
\(15\) | −697923. | −0.919076 | ||||||||
\(16\) | −786135. | −0.749717 | ||||||||
\(17\) | 253586. | 0.178600 | 0.0892999 | − | 0.996005i | \(-0.471537\pi\) | ||||
0.0892999 | + | 0.996005i | \(0.471537\pi\) | |||||||
\(18\) | 935778.i | 0.495234i | ||||||||
\(19\) | −3.54734e6 | −1.43263 | −0.716316 | − | 0.697776i | \(-0.754173\pi\) | ||||
−0.716316 | + | 0.697776i | \(0.754173\pi\) | |||||||
\(20\) | 6.15006e6 | 1.92189 | ||||||||
\(21\) | 1.75015e6 | 0.428529 | ||||||||
\(22\) | 4.35134e6 | 0.844324 | ||||||||
\(23\) | 7.87195e6i | 1.22305i | 0.791226 | + | 0.611523i | \(0.209443\pi\) | ||||
−0.791226 | + | 0.611523i | \(0.790557\pi\) | |||||||
\(24\) | − | 1.41593e6i | − | 0.177821i | ||||||
\(25\) | 1.49815e7 | 1.53410 | ||||||||
\(26\) | −2.76532e7 | −2.32744 | ||||||||
\(27\) | 2.76145e6 | 0.192450 | ||||||||
\(28\) | −1.54223e7 | −0.896103 | ||||||||
\(29\) | −3.50297e7 | −1.70784 | −0.853919 | − | 0.520406i | \(-0.825781\pi\) | ||||
−0.853919 | + | 0.520406i | \(0.825781\pi\) | |||||||
\(30\) | − | 3.31810e7i | − | 1.36547i | ||||||
\(31\) | − | 4.69488e7i | − | 1.63990i | −0.572438 | − | 0.819948i | \(-0.694002\pi\) | ||
0.572438 | − | 0.819948i | \(-0.305998\pi\) | |||||||
\(32\) | − | 4.77094e7i | − | 1.42185i | ||||||
\(33\) | − | 1.28406e7i | − | 0.328108i | ||||||
\(34\) | 1.20561e7i | 0.265346i | ||||||||
\(35\) | −6.20573e7 | −1.18155 | ||||||||
\(36\) | −2.43337e7 | −0.402436 | ||||||||
\(37\) | − | 7.93633e7i | − | 1.14449i | −0.820084 | − | 0.572244i | \(-0.806073\pi\) | ||
0.820084 | − | 0.572244i | \(-0.193927\pi\) | |||||||
\(38\) | − | 1.68649e8i | − | 2.12846i | ||||||
\(39\) | 8.16037e7i | 0.904455i | ||||||||
\(40\) | 5.02061e7i | 0.490294i | ||||||||
\(41\) | 9.67573e6 | 0.0835150 | 0.0417575 | − | 0.999128i | \(-0.486704\pi\) | ||||
0.0417575 | + | 0.999128i | \(0.486704\pi\) | |||||||
\(42\) | 8.32066e7i | 0.636665i | ||||||||
\(43\) | 7.78354e7i | 0.529462i | 0.964322 | + | 0.264731i | \(0.0852832\pi\) | ||||
−0.964322 | + | 0.264731i | \(0.914717\pi\) | |||||||
\(44\) | 1.13151e8i | 0.686113i | ||||||||
\(45\) | −9.79159e7 | −0.530629 | ||||||||
\(46\) | −3.74251e8 | −1.81708 | ||||||||
\(47\) | 4.77102e7i | 0.208028i | 0.994576 | + | 0.104014i | \(0.0331687\pi\) | ||||
−0.994576 | + | 0.104014i | \(0.966831\pi\) | |||||||
\(48\) | −1.10292e8 | −0.432849 | ||||||||
\(49\) | −1.26857e8 | −0.449090 | ||||||||
\(50\) | 7.12255e8i | 2.27922i | ||||||||
\(51\) | 3.55772e7 | 0.103115 | ||||||||
\(52\) | − | 7.19088e8i | − | 1.89132i | ||||||
\(53\) | 6.70282e8 | 1.60280 | 0.801398 | − | 0.598131i | \(-0.204090\pi\) | ||||
0.801398 | + | 0.598131i | \(0.204090\pi\) | |||||||
\(54\) | 1.31286e8i | 0.285923i | ||||||||
\(55\) | 4.55306e8i | 0.904669i | ||||||||
\(56\) | − | 1.25900e8i | − | 0.228605i | ||||||
\(57\) | −4.97678e8 | −0.827131 | ||||||||
\(58\) | − | 1.66540e9i | − | 2.53734i | ||||||
\(59\) | 7.02192e8 | − | 1.34322e8i | 0.982191 | − | 0.187883i | ||||
\(60\) | 8.62830e8 | 1.10961 | ||||||||
\(61\) | 1.29266e9i | 1.53051i | 0.643727 | + | 0.765255i | \(0.277387\pi\) | ||||
−0.643727 | + | 0.765255i | \(0.722613\pi\) | |||||||
\(62\) | 2.23206e9 | 2.43639 | ||||||||
\(63\) | 2.45540e8 | 0.247411 | ||||||||
\(64\) | 1.46322e9 | 1.36273 | ||||||||
\(65\) | − | 2.89352e9i | − | 2.49379i | ||||||
\(66\) | 6.10475e8 | 0.487471 | ||||||||
\(67\) | − | 1.73077e9i | − | 1.28193i | −0.767569 | − | 0.640966i | \(-0.778534\pi\) | ||
0.767569 | − | 0.640966i | \(-0.221466\pi\) | |||||||
\(68\) | −3.13504e8 | −0.215625 | ||||||||
\(69\) | 1.10440e9i | 0.706126i | ||||||||
\(70\) | − | 2.95035e9i | − | 1.75543i | ||||||
\(71\) | −3.39938e9 | −1.88412 | −0.942058 | − | 0.335451i | \(-0.891111\pi\) | ||||
−0.942058 | + | 0.335451i | \(0.891111\pi\) | |||||||
\(72\) | − | 1.98649e8i | − | 0.102665i | ||||||
\(73\) | − | 1.89958e7i | − | 0.00916311i | −0.999990 | − | 0.00458155i | \(-0.998542\pi\) | ||
0.999990 | − | 0.00458155i | \(-0.00145836\pi\) | |||||||
\(74\) | 3.77312e9 | 1.70037 | ||||||||
\(75\) | 2.10184e9 | 0.885714 | ||||||||
\(76\) | 4.38551e9 | 1.72963 | ||||||||
\(77\) | − | 1.14175e9i | − | 0.421811i | ||||||
\(78\) | −3.87964e9 | −1.34375 | ||||||||
\(79\) | 2.81385e9 | 0.914460 | 0.457230 | − | 0.889348i | \(-0.348842\pi\) | ||||
0.457230 | + | 0.889348i | \(0.348842\pi\) | |||||||
\(80\) | 3.91074e9 | 1.19346 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | 4.60008e8i | 0.124078i | ||||||||
\(83\) | 3.49802e9i | 0.888038i | 0.896017 | + | 0.444019i | \(0.146448\pi\) | ||||
−0.896017 | + | 0.444019i | \(0.853552\pi\) | |||||||
\(84\) | −2.16368e9 | −0.517365 | ||||||||
\(85\) | −1.26150e9 | −0.284311 | ||||||||
\(86\) | −3.70048e9 | −0.786622 | ||||||||
\(87\) | −4.91453e9 | −0.986021 | ||||||||
\(88\) | −9.23711e8 | −0.175034 | ||||||||
\(89\) | − | 2.25318e9i | − | 0.403503i | −0.979437 | − | 0.201751i | \(-0.935337\pi\) | ||
0.979437 | − | 0.201751i | \(-0.0646633\pi\) | |||||||
\(90\) | − | 4.65516e9i | − | 0.788356i | ||||||
\(91\) | 7.25596e9i | 1.16275i | ||||||||
\(92\) | − | 9.73195e9i | − | 1.47659i | ||||||
\(93\) | − | 6.58674e9i | − | 0.946794i | ||||||
\(94\) | −2.26826e9 | −0.309067 | ||||||||
\(95\) | 1.76468e10 | 2.28059 | ||||||||
\(96\) | − | 6.69344e9i | − | 0.820906i | ||||||
\(97\) | − | 1.06360e10i | − | 1.23857i | −0.785167 | − | 0.619284i | \(-0.787423\pi\) | ||
0.785167 | − | 0.619284i | \(-0.212577\pi\) | |||||||
\(98\) | − | 6.03108e9i | − | 0.667213i | ||||||
\(99\) | − | 1.80149e9i | − | 0.189433i | ||||||
\(100\) | −1.85213e10 | −1.85213 | ||||||||
\(101\) | 1.46879e9i | 0.139750i | 0.997556 | + | 0.0698752i | \(0.0222601\pi\) | ||||
−0.997556 | + | 0.0698752i | \(0.977740\pi\) | |||||||
\(102\) | 1.69142e9i | 0.153198i | ||||||||
\(103\) | − | 1.96079e10i | − | 1.69139i | −0.533666 | − | 0.845695i | \(-0.679186\pi\) | ||
0.533666 | − | 0.845695i | \(-0.320814\pi\) | |||||||
\(104\) | 5.87028e9 | 0.482495 | ||||||||
\(105\) | −8.70639e9 | −0.682169 | ||||||||
\(106\) | 3.18668e10i | 2.38128i | ||||||||
\(107\) | 1.03987e10 | 0.741416 | 0.370708 | − | 0.928749i | \(-0.379115\pi\) | ||||
0.370708 | + | 0.928749i | \(0.379115\pi\) | |||||||
\(108\) | −3.41393e9 | −0.232346 | ||||||||
\(109\) | − | 6.75429e9i | − | 0.438983i | −0.975614 | − | 0.219491i | \(-0.929560\pi\) | ||
0.975614 | − | 0.219491i | \(-0.0704397\pi\) | |||||||
\(110\) | −2.16463e10 | −1.34407 | ||||||||
\(111\) | − | 1.11344e10i | − | 0.660770i | ||||||
\(112\) | −9.80682e9 | −0.556465 | ||||||||
\(113\) | 1.66808e10i | 0.905367i | 0.891671 | + | 0.452683i | \(0.149533\pi\) | ||||
−0.891671 | + | 0.452683i | \(0.850467\pi\) | |||||||
\(114\) | − | 2.36608e10i | − | 1.22887i | ||||||
\(115\) | − | 3.91601e10i | − | 1.94695i | ||||||
\(116\) | 4.33066e10 | 2.06188 | ||||||||
\(117\) | 1.14487e10i | 0.522187i | ||||||||
\(118\) | 6.38601e9 | + | 3.33839e10i | 0.279138 | + | 1.45924i | ||||
\(119\) | 3.16342e9 | 0.132563 | ||||||||
\(120\) | 7.04372e9i | 0.283072i | ||||||||
\(121\) | 1.75605e10 | 0.677035 | ||||||||
\(122\) | −6.14563e10 | −2.27388 | ||||||||
\(123\) | 1.35747e9 | 0.0482174 | ||||||||
\(124\) | 5.80420e10i | 1.97986i | ||||||||
\(125\) | −2.59469e10 | −0.850229 | ||||||||
\(126\) | 1.16736e10i | 0.367579i | ||||||||
\(127\) | 4.88844e10 | 1.47962 | 0.739812 | − | 0.672814i | \(-0.234915\pi\) | ||||
0.739812 | + | 0.672814i | \(0.234915\pi\) | |||||||
\(128\) | 2.07105e10i | 0.602755i | ||||||||
\(129\) | 1.09200e10i | 0.305685i | ||||||||
\(130\) | 1.37565e11 | 3.70502 | ||||||||
\(131\) | 3.48703e10i | 0.903857i | 0.892054 | + | 0.451928i | \(0.149264\pi\) | ||||
−0.892054 | + | 0.451928i | \(0.850736\pi\) | |||||||
\(132\) | 1.58747e10i | 0.396127i | ||||||||
\(133\) | −4.42520e10 | −1.06335 | ||||||||
\(134\) | 8.22849e10 | 1.90457 | ||||||||
\(135\) | −1.37372e10 | −0.306359 | ||||||||
\(136\) | − | 2.55929e9i | − | 0.0550080i | ||||||
\(137\) | −6.88870e10 | −1.42736 | −0.713681 | − | 0.700471i | \(-0.752974\pi\) | ||||
−0.713681 | + | 0.700471i | \(0.752974\pi\) | |||||||
\(138\) | −5.25060e10 | −1.04909 | ||||||||
\(139\) | 1.14551e10 | 0.220763 | 0.110381 | − | 0.993889i | \(-0.464793\pi\) | ||||
0.110381 | + | 0.993889i | \(0.464793\pi\) | |||||||
\(140\) | 7.67203e10 | 1.42649 | ||||||||
\(141\) | 6.69355e9i | 0.120105i | ||||||||
\(142\) | − | 1.61615e11i | − | 2.79923i | ||||||
\(143\) | 5.32360e10 | 0.890278 | ||||||||
\(144\) | −1.54735e10 | −0.249906 | ||||||||
\(145\) | 1.74260e11 | 2.71868 | ||||||||
\(146\) | 9.03105e8 | 0.0136136 | ||||||||
\(147\) | −1.77975e10 | −0.259282 | ||||||||
\(148\) | 9.81154e10i | 1.38175i | ||||||||
\(149\) | − | 1.15357e11i | − | 1.57076i | −0.619011 | − | 0.785382i | \(-0.712466\pi\) | ||
0.619011 | − | 0.785382i | \(-0.287534\pi\) | |||||||
\(150\) | 9.99266e10i | 1.31591i | ||||||||
\(151\) | − | 1.05286e11i | − | 1.34118i | −0.741830 | − | 0.670588i | \(-0.766042\pi\) | ||
0.741830 | − | 0.670588i | \(-0.233958\pi\) | |||||||
\(152\) | 3.58012e10i | 0.441245i | ||||||||
\(153\) | 4.99134e9 | 0.0595333 | ||||||||
\(154\) | 5.42817e10 | 0.626685 | ||||||||
\(155\) | 2.33554e11i | 2.61053i | ||||||||
\(156\) | − | 1.00885e11i | − | 1.09195i | ||||||
\(157\) | − | 1.54569e10i | − | 0.162041i | −0.996712 | − | 0.0810204i | \(-0.974182\pi\) | ||
0.996712 | − | 0.0810204i | \(-0.0258179\pi\) | |||||||
\(158\) | 1.33777e11i | 1.35861i | ||||||||
\(159\) | 9.40380e10 | 0.925375 | ||||||||
\(160\) | 2.37337e11i | 2.26343i | ||||||||
\(161\) | 9.82003e10i | 0.907786i | ||||||||
\(162\) | 1.84189e10i | 0.165078i | ||||||||
\(163\) | 1.75392e11 | 1.52431 | 0.762153 | − | 0.647397i | \(-0.224142\pi\) | ||||
0.762153 | + | 0.647397i | \(0.224142\pi\) | |||||||
\(164\) | −1.19619e10 | −0.100828 | ||||||||
\(165\) | 6.38776e10i | 0.522311i | ||||||||
\(166\) | −1.66304e11 | −1.31936 | ||||||||
\(167\) | 5.47488e10 | 0.421494 | 0.210747 | − | 0.977541i | \(-0.432410\pi\) | ||||
0.210747 | + | 0.977541i | \(0.432410\pi\) | |||||||
\(168\) | − | 1.76633e10i | − | 0.131985i | ||||||
\(169\) | −2.00462e11 | −1.45412 | ||||||||
\(170\) | − | 5.99748e10i | − | 0.422400i | ||||||
\(171\) | −6.98223e10 | −0.477544 | ||||||||
\(172\) | − | 9.62265e10i | − | 0.639223i | ||||||
\(173\) | 1.16508e11i | 0.751841i | 0.926652 | + | 0.375920i | \(0.122673\pi\) | ||||
−0.926652 | + | 0.375920i | \(0.877327\pi\) | |||||||
\(174\) | − | 2.33649e11i | − | 1.46493i | ||||||
\(175\) | 1.86889e11 | 1.13866 | ||||||||
\(176\) | 7.19513e10i | 0.426064i | ||||||||
\(177\) | 9.85149e10 | − | 1.88449e10i | 0.567068 | − | 0.108474i | ||||
\(178\) | 1.07122e11 | 0.599485 | ||||||||
\(179\) | 2.34414e11i | 1.27561i | 0.770198 | + | 0.637805i | \(0.220157\pi\) | ||||
−0.770198 | + | 0.637805i | \(0.779843\pi\) | |||||||
\(180\) | 1.21052e11 | 0.640632 | ||||||||
\(181\) | 1.22529e11 | 0.630736 | 0.315368 | − | 0.948969i | \(-0.397872\pi\) | ||||
0.315368 | + | 0.948969i | \(0.397872\pi\) | |||||||
\(182\) | −3.44966e11 | −1.72751 | ||||||||
\(183\) | 1.81356e11i | 0.883640i | ||||||||
\(184\) | 7.94469e10 | 0.376693 | ||||||||
\(185\) | 3.94804e11i | 1.82189i | ||||||||
\(186\) | 3.13149e11 | 1.40665 | ||||||||
\(187\) | − | 2.32096e10i | − | 0.101498i | ||||||
\(188\) | − | 5.89833e10i | − | 0.251154i | ||||||
\(189\) | 3.44483e10 | 0.142843 | ||||||||
\(190\) | 8.38969e11i | 3.38827i | ||||||||
\(191\) | − | 4.02313e11i | − | 1.58269i | −0.611368 | − | 0.791347i | \(-0.709380\pi\) | ||
0.611368 | − | 0.791347i | \(-0.290620\pi\) | |||||||
\(192\) | 2.05284e11 | 0.786771 | ||||||||
\(193\) | −1.97970e11 | −0.739288 | −0.369644 | − | 0.929173i | \(-0.620520\pi\) | ||||
−0.369644 | + | 0.929173i | \(0.620520\pi\) | |||||||
\(194\) | 5.05662e11 | 1.84014 | ||||||||
\(195\) | − | 4.05950e11i | − | 1.43979i | ||||||
\(196\) | 1.56831e11 | 0.542189 | ||||||||
\(197\) | −3.75407e11 | −1.26523 | −0.632617 | − | 0.774465i | \(-0.718019\pi\) | ||||
−0.632617 | + | 0.774465i | \(0.718019\pi\) | |||||||
\(198\) | 8.56473e10 | 0.281441 | ||||||||
\(199\) | 2.97679e11 | 0.953856 | 0.476928 | − | 0.878942i | \(-0.341750\pi\) | ||||
0.476928 | + | 0.878942i | \(0.341750\pi\) | |||||||
\(200\) | − | 1.51199e11i | − | 0.472497i | ||||||
\(201\) | − | 2.42820e11i | − | 0.740124i | ||||||
\(202\) | −6.98299e10 | −0.207627 | ||||||||
\(203\) | −4.36986e11 | −1.26761 | ||||||||
\(204\) | −4.39834e10 | −0.124491 | ||||||||
\(205\) | −4.81333e10 | −0.132946 | ||||||||
\(206\) | 9.32205e11 | 2.51290 | ||||||||
\(207\) | 1.54944e11i | 0.407682i | ||||||||
\(208\) | − | 4.57259e11i | − | 1.17448i | ||||||
\(209\) | 3.24671e11i | 0.814165i | ||||||||
\(210\) | − | 4.13923e11i | − | 1.01350i | ||||||
\(211\) | − | 3.79905e11i | − | 0.908370i | −0.890907 | − | 0.454185i | \(-0.849931\pi\) | ||
0.890907 | − | 0.454185i | \(-0.150069\pi\) | |||||||
\(212\) | −8.28658e11 | −1.93507 | ||||||||
\(213\) | −4.76919e11 | −1.08779 | ||||||||
\(214\) | 4.94382e11i | 1.10152i | ||||||||
\(215\) | − | 3.87203e11i | − | 0.842843i | ||||||
\(216\) | − | 2.78697e10i | − | 0.0592738i | ||||||
\(217\) | − | 5.85673e11i | − | 1.21719i | ||||||
\(218\) | 3.21115e11 | 0.652197 | ||||||||
\(219\) | − | 2.66503e9i | − | 0.00529032i | ||||||
\(220\) | − | 5.62886e11i | − | 1.09221i | ||||||
\(221\) | 1.47499e11i | 0.279788i | ||||||||
\(222\) | 5.29354e11 | 0.981707 | ||||||||
\(223\) | −9.15378e11 | −1.65988 | −0.829939 | − | 0.557854i | \(-0.811625\pi\) | ||||
−0.829939 | + | 0.557854i | \(0.811625\pi\) | |||||||
\(224\) | − | 5.95161e11i | − | 1.05535i | ||||||
\(225\) | 2.94880e11 | 0.511367 | ||||||||
\(226\) | −7.93045e11 | −1.34510 | ||||||||
\(227\) | − | 3.00794e11i | − | 0.499045i | −0.968369 | − | 0.249523i | \(-0.919726\pi\) | ||
0.968369 | − | 0.249523i | \(-0.0802737\pi\) | |||||||
\(228\) | 6.15270e11 | 0.998600 | ||||||||
\(229\) | − | 5.50473e11i | − | 0.874094i | −0.899439 | − | 0.437047i | \(-0.856024\pi\) | ||
0.899439 | − | 0.437047i | \(-0.143976\pi\) | |||||||
\(230\) | 1.86177e12 | 2.89259 | ||||||||
\(231\) | − | 1.60183e11i | − | 0.243533i | ||||||
\(232\) | 3.53534e11i | 0.526007i | ||||||||
\(233\) | 8.38036e11i | 1.22035i | 0.792268 | + | 0.610173i | \(0.208900\pi\) | ||||
−0.792268 | + | 0.610173i | \(0.791100\pi\) | |||||||
\(234\) | −5.44298e11 | −0.775814 | ||||||||
\(235\) | − | 2.37341e11i | − | 0.331157i | ||||||
\(236\) | −8.68108e11 | + | 1.66060e11i | −1.18581 | + | 0.226833i | ||||
\(237\) | 3.94772e11 | 0.527964 | ||||||||
\(238\) | 1.50396e11i | 0.196949i | ||||||||
\(239\) | −9.21230e11 | −1.18135 | −0.590675 | − | 0.806909i | \(-0.701138\pi\) | ||||
−0.590675 | + | 0.806909i | \(0.701138\pi\) | |||||||
\(240\) | 5.48662e11 | 0.689047 | ||||||||
\(241\) | 2.06797e11 | 0.254366 | 0.127183 | − | 0.991879i | \(-0.459406\pi\) | ||||
0.127183 | + | 0.991879i | \(0.459406\pi\) | |||||||
\(242\) | 8.34871e11i | 1.00587i | ||||||||
\(243\) | 5.43536e10 | 0.0641500 | ||||||||
\(244\) | − | 1.59810e12i | − | 1.84779i | ||||||
\(245\) | 6.31067e11 | 0.714900 | ||||||||
\(246\) | 6.45373e10i | 0.0716366i | ||||||||
\(247\) | − | 2.06332e12i | − | 2.24431i | ||||||
\(248\) | −4.73827e11 | −0.505081 | ||||||||
\(249\) | 4.90758e11i | 0.512709i | ||||||||
\(250\) | − | 1.23358e12i | − | 1.26319i | ||||||
\(251\) | 7.95542e11 | 0.798536 | 0.399268 | − | 0.916834i | \(-0.369264\pi\) | ||||
0.399268 | + | 0.916834i | \(0.369264\pi\) | |||||||
\(252\) | −3.03556e11 | −0.298701 | ||||||||
\(253\) | 7.20482e11 | 0.695058 | ||||||||
\(254\) | 2.32408e12i | 2.19828i | ||||||||
\(255\) | −1.76984e11 | −0.164147 | ||||||||
\(256\) | 5.13708e11 | 0.467214 | ||||||||
\(257\) | 1.25101e12 | 1.11583 | 0.557913 | − | 0.829900i | \(-0.311602\pi\) | ||||
0.557913 | + | 0.829900i | \(0.311602\pi\) | |||||||
\(258\) | −5.19163e11 | −0.454157 | ||||||||
\(259\) | − | 9.90034e11i | − | 0.849477i | ||||||
\(260\) | 3.57721e12i | 3.01077i | ||||||||
\(261\) | −6.89490e11 | −0.569279 | ||||||||
\(262\) | −1.65782e12 | −1.34286 | ||||||||
\(263\) | −2.17127e12 | −1.72558 | −0.862790 | − | 0.505562i | \(-0.831285\pi\) | ||||
−0.862790 | + | 0.505562i | \(0.831285\pi\) | |||||||
\(264\) | −1.29593e11 | −0.101056 | ||||||||
\(265\) | −3.33442e12 | −2.55147 | ||||||||
\(266\) | − | 2.10385e12i | − | 1.57982i | ||||||
\(267\) | − | 3.16113e11i | − | 0.232963i | ||||||
\(268\) | 2.13972e12i | 1.54768i | ||||||||
\(269\) | − | 6.00038e10i | − | 0.0426007i | −0.999773 | − | 0.0213004i | \(-0.993219\pi\) | ||
0.999773 | − | 0.0213004i | \(-0.00678063\pi\) | |||||||
\(270\) | − | 6.53101e11i | − | 0.455157i | ||||||
\(271\) | 1.84863e12 | 1.26475 | 0.632374 | − | 0.774663i | \(-0.282081\pi\) | ||||
0.632374 | + | 0.774663i | \(0.282081\pi\) | |||||||
\(272\) | −1.99353e11 | −0.133899 | ||||||||
\(273\) | 1.01798e12i | 0.671317i | ||||||||
\(274\) | − | 3.27505e12i | − | 2.12063i | ||||||
\(275\) | − | 1.37118e12i | − | 0.871830i | ||||||
\(276\) | − | 1.36535e12i | − | 0.852511i | ||||||
\(277\) | 1.48046e12 | 0.907815 | 0.453908 | − | 0.891049i | \(-0.350030\pi\) | ||||
0.453908 | + | 0.891049i | \(0.350030\pi\) | |||||||
\(278\) | 5.44605e11i | 0.327988i | ||||||||
\(279\) | − | 9.24094e11i | − | 0.546632i | ||||||
\(280\) | 6.26307e11i | 0.363913i | ||||||||
\(281\) | −1.16588e11 | −0.0665463 | −0.0332731 | − | 0.999446i | \(-0.510593\pi\) | ||||
−0.0332731 | + | 0.999446i | \(0.510593\pi\) | |||||||
\(282\) | −3.18228e11 | −0.178440 | ||||||||
\(283\) | − | 2.02531e12i | − | 1.11573i | −0.829932 | − | 0.557865i | \(-0.811621\pi\) | ||
0.829932 | − | 0.557865i | \(-0.188379\pi\) | |||||||
\(284\) | 4.20259e12 | 2.27471 | ||||||||
\(285\) | 2.47577e12 | 1.31670 | ||||||||
\(286\) | 2.53097e12i | 1.32269i | ||||||||
\(287\) | 1.20702e11 | 0.0619876 | ||||||||
\(288\) | − | 9.39064e11i | − | 0.473950i | ||||||
\(289\) | −1.95169e12 | −0.968102 | ||||||||
\(290\) | 8.28476e12i | 4.03915i | ||||||||
\(291\) | − | 1.49219e12i | − | 0.715088i | ||||||
\(292\) | 2.34841e10i | 0.0110627i | ||||||||
\(293\) | 4.07698e11 | 0.188799 | 0.0943997 | − | 0.995534i | \(-0.469907\pi\) | ||||
0.0943997 | + | 0.995534i | \(0.469907\pi\) | |||||||
\(294\) | − | 8.46137e11i | − | 0.385216i | ||||||
\(295\) | −3.49316e12 | + | 6.68206e11i | −1.56354 | + | 0.299089i | ||||
\(296\) | −8.00966e11 | −0.352497 | ||||||||
\(297\) | − | 2.52742e11i | − | 0.109369i | ||||||
\(298\) | 5.48433e12 | 2.33369 | ||||||||
\(299\) | −4.57875e12 | −1.91598 | ||||||||
\(300\) | −2.59847e12 | −1.06933 | ||||||||
\(301\) | 9.70974e11i | 0.392984i | ||||||||
\(302\) | 5.00555e12 | 1.99259 | ||||||||
\(303\) | 2.06066e11i | 0.0806849i | ||||||||
\(304\) | 2.78869e12 | 1.07407 | ||||||||
\(305\) | − | 6.43054e12i | − | 2.43640i | ||||||
\(306\) | 2.37300e11i | 0.0884486i | ||||||||
\(307\) | 3.87561e11 | 0.142118 | 0.0710589 | − | 0.997472i | \(-0.477362\pi\) | ||||
0.0710589 | + | 0.997472i | \(0.477362\pi\) | |||||||
\(308\) | 1.41153e12i | 0.509256i | ||||||||
\(309\) | − | 2.75091e12i | − | 0.976525i | ||||||
\(310\) | −1.11037e13 | −3.87846 | ||||||||
\(311\) | −2.53610e12 | −0.871696 | −0.435848 | − | 0.900020i | \(-0.643551\pi\) | ||||
−0.435848 | + | 0.900020i | \(0.643551\pi\) | |||||||
\(312\) | 8.23578e11 | 0.278568 | ||||||||
\(313\) | − | 1.19694e12i | − | 0.398427i | −0.979956 | − | 0.199214i | \(-0.936161\pi\) | ||
0.979956 | − | 0.199214i | \(-0.0638388\pi\) | |||||||
\(314\) | 7.34859e11 | 0.240744 | ||||||||
\(315\) | −1.22147e12 | −0.393850 | ||||||||
\(316\) | −3.47871e12 | −1.10403 | ||||||||
\(317\) | 3.26824e12 | 1.02098 | 0.510490 | − | 0.859884i | \(-0.329464\pi\) | ||||
0.510490 | + | 0.859884i | \(0.329464\pi\) | |||||||
\(318\) | 4.47079e12i | 1.37483i | ||||||||
\(319\) | 3.20611e12i | 0.970564i | ||||||||
\(320\) | −7.27899e12 | −2.16931 | ||||||||
\(321\) | 1.45890e12 | 0.428057 | ||||||||
\(322\) | −4.66868e12 | −1.34870 | ||||||||
\(323\) | −8.99556e11 | −0.255868 | ||||||||
\(324\) | −4.78961e11 | −0.134145 | ||||||||
\(325\) | 8.71402e12i | 2.40327i | ||||||||
\(326\) | 8.33857e12i | 2.26466i | ||||||||
\(327\) | − | 9.47601e11i | − | 0.253447i | ||||||
\(328\) | − | 9.76514e10i | − | 0.0257223i | ||||||
\(329\) | 5.95171e11i | 0.154405i | ||||||||
\(330\) | −3.03690e12 | −0.775998 | ||||||||
\(331\) | 3.09341e12 | 0.778571 | 0.389285 | − | 0.921117i | \(-0.372722\pi\) | ||||
0.389285 | + | 0.921117i | \(0.372722\pi\) | |||||||
\(332\) | − | 4.32454e12i | − | 1.07213i | ||||||
\(333\) | − | 1.56211e12i | − | 0.381496i | ||||||
\(334\) | 2.60289e12i | 0.626215i | ||||||||
\(335\) | 8.60996e12i | 2.04069i | ||||||||
\(336\) | −1.37586e12 | −0.321275 | ||||||||
\(337\) | − | 7.64173e11i | − | 0.175809i | −0.996129 | − | 0.0879047i | \(-0.971983\pi\) | ||
0.996129 | − | 0.0879047i | \(-0.0280171\pi\) | |||||||
\(338\) | − | 9.53047e12i | − | 2.16038i | ||||||
\(339\) | 2.34025e12i | 0.522714i | ||||||||
\(340\) | 1.55957e12 | 0.343250 | ||||||||
\(341\) | −4.29701e12 | −0.931953 | ||||||||
\(342\) | − | 3.31952e12i | − | 0.709488i | ||||||
\(343\) | −5.10630e12 | −1.07556 | ||||||||
\(344\) | 7.85546e11 | 0.163072 | ||||||||
\(345\) | − | 5.49402e12i | − | 1.12407i | ||||||
\(346\) | −5.53908e12 | −1.11701 | ||||||||
\(347\) | 3.69950e11i | 0.0735353i | 0.999324 | + | 0.0367677i | \(0.0117061\pi\) | ||||
−0.999324 | + | 0.0367677i | \(0.988294\pi\) | |||||||
\(348\) | 6.07575e12 | 1.19043 | ||||||||
\(349\) | − | 8.71421e11i | − | 0.168306i | −0.996453 | − | 0.0841532i | \(-0.973181\pi\) | ||
0.996453 | − | 0.0841532i | \(-0.0268185\pi\) | |||||||
\(350\) | 8.88518e12i | 1.69171i | ||||||||
\(351\) | 1.60621e12i | 0.301485i | ||||||||
\(352\) | −4.36662e12 | −0.808038 | ||||||||
\(353\) | − | 5.40604e12i | − | 0.986292i | −0.869947 | − | 0.493146i | \(-0.835847\pi\) | ||
0.869947 | − | 0.493146i | \(-0.164153\pi\) | |||||||
\(354\) | 8.95932e11 | + | 4.68364e12i | 0.161161 | + | 0.842494i | ||||
\(355\) | 1.69107e13 | 2.99930 | ||||||||
\(356\) | 2.78557e12i | 0.487152i | ||||||||
\(357\) | 4.43815e11 | 0.0765351 | ||||||||
\(358\) | −1.11446e13 | −1.89517 | ||||||||
\(359\) | −1.06964e13 | −1.79377 | −0.896885 | − | 0.442264i | \(-0.854176\pi\) | ||||
−0.896885 | + | 0.442264i | \(0.854176\pi\) | |||||||
\(360\) | 9.88207e11i | 0.163431i | ||||||||
\(361\) | 6.45255e12 | 1.05243 | ||||||||
\(362\) | 5.82535e12i | 0.937085i | ||||||||
\(363\) | 2.46368e12 | 0.390886 | ||||||||
\(364\) | − | 8.97042e12i | − | 1.40380i | ||||||
\(365\) | 9.44972e10i | 0.0145866i | ||||||||
\(366\) | −8.62209e12 | −1.31283 | ||||||||
\(367\) | − | 8.00075e12i | − | 1.20171i | −0.799358 | − | 0.600856i | \(-0.794827\pi\) | ||
0.799358 | − | 0.600856i | \(-0.205173\pi\) | |||||||
\(368\) | − | 6.18842e12i | − | 0.916939i | ||||||
\(369\) | 1.90447e11 | 0.0278383 | ||||||||
\(370\) | −1.87699e13 | −2.70679 | ||||||||
\(371\) | 8.36158e12 | 1.18965 | ||||||||
\(372\) | 8.14307e12i | 1.14307i | ||||||||
\(373\) | −1.08064e12 | −0.149670 | −0.0748351 | − | 0.997196i | \(-0.523843\pi\) | ||||
−0.0748351 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(374\) | 1.10344e12 | 0.150796 | ||||||||
\(375\) | −3.64025e12 | −0.490880 | ||||||||
\(376\) | 4.81511e11 | 0.0640718 | ||||||||
\(377\) | − | 2.03752e13i | − | 2.67543i | ||||||
\(378\) | 1.63775e12i | 0.212222i | ||||||||
\(379\) | −4.13823e12 | −0.529198 | −0.264599 | − | 0.964359i | \(-0.585240\pi\) | ||||
−0.264599 | + | 0.964359i | \(0.585240\pi\) | |||||||
\(380\) | −2.18164e13 | −2.75337 | ||||||||
\(381\) | 6.85828e12 | 0.854261 | ||||||||
\(382\) | 1.91269e13 | 2.35141 | ||||||||
\(383\) | −2.76676e12 | −0.335720 | −0.167860 | − | 0.985811i | \(-0.553686\pi\) | ||||
−0.167860 | + | 0.985811i | \(0.553686\pi\) | |||||||
\(384\) | 2.90560e12i | 0.348001i | ||||||||
\(385\) | 5.67981e12i | 0.671476i | ||||||||
\(386\) | − | 9.41200e12i | − | 1.09836i | ||||||
\(387\) | 1.53203e12i | 0.176487i | ||||||||
\(388\) | 1.31491e13i | 1.49533i | ||||||||
\(389\) | 1.31884e13 | 1.48062 | 0.740311 | − | 0.672265i | \(-0.234678\pi\) | ||||
0.740311 | + | 0.672265i | \(0.234678\pi\) | |||||||
\(390\) | 1.92998e13 | 2.13910 | ||||||||
\(391\) | 1.99622e12i | 0.218436i | ||||||||
\(392\) | 1.28029e12i | 0.138318i | ||||||||
\(393\) | 4.89217e12i | 0.521842i | ||||||||
\(394\) | − | 1.78477e13i | − | 1.87976i | ||||||
\(395\) | −1.39979e13 | −1.45572 | ||||||||
\(396\) | 2.22715e12i | 0.228704i | ||||||||
\(397\) | − | 6.53060e12i | − | 0.662218i | −0.943593 | − | 0.331109i | \(-0.892577\pi\) | ||
0.943593 | − | 0.331109i | \(-0.107423\pi\) | |||||||
\(398\) | 1.41524e13i | 1.41714i | ||||||||
\(399\) | −6.20839e12 | −0.613924 | ||||||||
\(400\) | −1.17775e13 | −1.15014 | ||||||||
\(401\) | 1.79410e13i | 1.73032i | 0.501500 | + | 0.865158i | \(0.332782\pi\) | ||||
−0.501500 | + | 0.865158i | \(0.667218\pi\) | |||||||
\(402\) | 1.15443e13 | 1.09960 | ||||||||
\(403\) | 2.73080e13 | 2.56900 | ||||||||
\(404\) | − | 1.81584e12i | − | 0.168722i | ||||||
\(405\) | −1.92728e12 | −0.176876 | ||||||||
\(406\) | − | 2.07754e13i | − | 1.88330i | ||||||
\(407\) | −7.26375e12 | −0.650412 | ||||||||
\(408\) | − | 3.59059e11i | − | 0.0317589i | ||||||
\(409\) | − | 1.13865e13i | − | 0.994889i | −0.867496 | − | 0.497445i | \(-0.834272\pi\) | ||
0.867496 | − | 0.497445i | \(-0.165728\pi\) | |||||||
\(410\) | − | 2.28837e12i | − | 0.197519i | ||||||
\(411\) | −9.66458e12 | −0.824088 | ||||||||
\(412\) | 2.42408e13i | 2.04203i | ||||||||
\(413\) | 8.75965e12 | − | 1.67563e12i | 0.729015 | − | 0.139453i | ||||
\(414\) | −7.36639e12 | −0.605694 | ||||||||
\(415\) | − | 1.74014e13i | − | 1.41366i | ||||||
\(416\) | 2.77504e13 | 2.22742 | ||||||||
\(417\) | 1.60711e12 | 0.127458 | ||||||||
\(418\) | −1.54357e13 | −1.20961 | ||||||||
\(419\) | − | 1.39833e12i | − | 0.108278i | −0.998533 | − | 0.0541390i | \(-0.982759\pi\) | ||
0.998533 | − | 0.0541390i | \(-0.0172414\pi\) | |||||||
\(420\) | 1.07636e13 | 0.823587 | ||||||||
\(421\) | − | 7.96565e12i | − | 0.602297i | −0.953577 | − | 0.301149i | \(-0.902630\pi\) | ||
0.953577 | − | 0.301149i | \(-0.0973700\pi\) | |||||||
\(422\) | 1.80616e13 | 1.34957 | ||||||||
\(423\) | 9.39080e11i | 0.0693427i | ||||||||
\(424\) | − | 6.76476e12i | − | 0.493654i | ||||||
\(425\) | 3.79909e12 | 0.273990 | ||||||||
\(426\) | − | 2.26739e13i | − | 1.61614i | ||||||
\(427\) | 1.61256e13i | 1.13600i | ||||||||
\(428\) | −1.28558e13 | −0.895117 | ||||||||
\(429\) | 7.46881e12 | 0.514002 | ||||||||
\(430\) | 1.84086e13 | 1.25221 | ||||||||
\(431\) | − | 5.37574e12i | − | 0.361453i | −0.983533 | − | 0.180726i | \(-0.942155\pi\) | ||
0.983533 | − | 0.180726i | \(-0.0578448\pi\) | |||||||
\(432\) | −2.17087e12 | −0.144283 | ||||||||
\(433\) | −1.42980e13 | −0.939369 | −0.469685 | − | 0.882834i | \(-0.655632\pi\) | ||||
−0.469685 | + | 0.882834i | \(0.655632\pi\) | |||||||
\(434\) | 2.78443e13 | 1.80837 | ||||||||
\(435\) | 2.44481e13 | 1.56963 | ||||||||
\(436\) | 8.35021e12i | 0.529987i | ||||||||
\(437\) | − | 2.79245e13i | − | 1.75218i | ||||||
\(438\) | 1.26702e11 | 0.00785983 | ||||||||
\(439\) | −9.94179e12 | −0.609736 | −0.304868 | − | 0.952395i | \(-0.598612\pi\) | ||||
−0.304868 | + | 0.952395i | \(0.598612\pi\) | |||||||
\(440\) | 4.59513e12 | 0.278634 | ||||||||
\(441\) | −2.49692e12 | −0.149697 | ||||||||
\(442\) | −7.01248e12 | −0.415681 | ||||||||
\(443\) | 1.00600e13i | 0.589630i | 0.955554 | + | 0.294815i | \(0.0952581\pi\) | ||||
−0.955554 | + | 0.294815i | \(0.904742\pi\) | |||||||
\(444\) | 1.37652e13i | 0.797752i | ||||||||
\(445\) | 1.12088e13i | 0.642331i | ||||||||
\(446\) | − | 4.35193e13i | − | 2.46608i | ||||||
\(447\) | − | 1.61841e13i | − | 0.906881i | ||||||
\(448\) | 1.82532e13 | 1.01146 | ||||||||
\(449\) | 3.03874e13 | 1.66518 | 0.832592 | − | 0.553886i | \(-0.186856\pi\) | ||||
0.832592 | + | 0.553886i | \(0.186856\pi\) | |||||||
\(450\) | 1.40193e13i | 0.759739i | ||||||||
\(451\) | − | 8.85574e11i | − | 0.0474616i | ||||||
\(452\) | − | 2.06222e13i | − | 1.09306i | ||||||
\(453\) | − | 1.47712e13i | − | 0.774329i | ||||||
\(454\) | 1.43005e13 | 0.741432 | ||||||||
\(455\) | − | 3.60958e13i | − | 1.85097i | ||||||
\(456\) | 5.02277e12i | 0.254753i | ||||||||
\(457\) | 2.85028e13i | 1.42990i | 0.699173 | + | 0.714952i | \(0.253552\pi\) | ||||
−0.699173 | + | 0.714952i | \(0.746448\pi\) | |||||||
\(458\) | 2.61708e13 | 1.29864 | ||||||||
\(459\) | 7.00265e11 | 0.0343715 | ||||||||
\(460\) | 4.84130e13i | 2.35057i | ||||||||
\(461\) | −7.52318e12 | −0.361324 | −0.180662 | − | 0.983545i | \(-0.557824\pi\) | ||||
−0.180662 | + | 0.983545i | \(0.557824\pi\) | |||||||
\(462\) | 7.61551e12 | 0.361817 | ||||||||
\(463\) | 3.38232e12i | 0.158968i | 0.996836 | + | 0.0794841i | \(0.0253273\pi\) | ||||
−0.996836 | + | 0.0794841i | \(0.974673\pi\) | |||||||
\(464\) | 2.75381e13 | 1.28040 | ||||||||
\(465\) | 3.27667e13i | 1.50719i | ||||||||
\(466\) | −3.98423e13 | −1.81307 | ||||||||
\(467\) | − | 3.58012e13i | − | 1.61181i | −0.592046 | − | 0.805904i | \(-0.701680\pi\) | ||
0.592046 | − | 0.805904i | \(-0.298320\pi\) | |||||||
\(468\) | − | 1.41538e13i | − | 0.630440i | ||||||
\(469\) | − | 2.15908e13i | − | 0.951492i | ||||||
\(470\) | 1.12838e13 | 0.492000 | ||||||||
\(471\) | − | 2.16854e12i | − | 0.0935543i | ||||||
\(472\) | −1.35564e12 | − | 7.08681e12i | −0.0578672 | − | 0.302511i | ||||
\(473\) | 7.12391e12 | 0.300893 | ||||||||
\(474\) | 1.87684e13i | 0.784396i | ||||||||
\(475\) | −5.31443e13 | −2.19780 | ||||||||
\(476\) | −3.91087e12 | −0.160044 | ||||||||
\(477\) | 1.31932e13 | 0.534265 | ||||||||
\(478\) | − | 4.37975e13i | − | 1.75513i | ||||||
\(479\) | −3.00548e13 | −1.19189 | −0.595945 | − | 0.803025i | \(-0.703223\pi\) | ||||
−0.595945 | + | 0.803025i | \(0.703223\pi\) | |||||||
\(480\) | 3.32975e13i | 1.30679i | ||||||||
\(481\) | 4.61619e13 | 1.79291 | ||||||||
\(482\) | 9.83163e12i | 0.377912i | ||||||||
\(483\) | 1.37771e13i | 0.524110i | ||||||||
\(484\) | −2.17098e13 | −0.817389 | ||||||||
\(485\) | 5.29104e13i | 1.97166i | ||||||||
\(486\) | 2.58410e12i | 0.0953077i | ||||||||
\(487\) | −4.04542e13 | −1.47679 | −0.738396 | − | 0.674368i | \(-0.764416\pi\) | ||||
−0.738396 | + | 0.674368i | \(0.764416\pi\) | |||||||
\(488\) | 1.30461e13 | 0.471391 | ||||||||
\(489\) | 2.46068e13 | 0.880059 | ||||||||
\(490\) | 3.00025e13i | 1.06213i | ||||||||
\(491\) | −4.42270e13 | −1.54982 | −0.774908 | − | 0.632074i | \(-0.782204\pi\) | ||||
−0.774908 | + | 0.632074i | \(0.782204\pi\) | |||||||
\(492\) | −1.67821e12 | −0.0582132 | ||||||||
\(493\) | −8.88305e12 | −0.305019 | ||||||||
\(494\) | 9.80954e13 | 3.33437 | ||||||||
\(495\) | 8.96179e12i | 0.301556i | ||||||||
\(496\) | 3.69081e13i | 1.22946i | ||||||||
\(497\) | −4.24062e13 | −1.39845 | ||||||||
\(498\) | −2.33318e13 | −0.761732 | ||||||||
\(499\) | −5.35177e13 | −1.72980 | −0.864898 | − | 0.501947i | \(-0.832617\pi\) | ||||
−0.864898 | + | 0.501947i | \(0.832617\pi\) | |||||||
\(500\) | 3.20777e13 | 1.02649 | ||||||||
\(501\) | 7.68104e12 | 0.243350 | ||||||||
\(502\) | 3.78220e13i | 1.18638i | ||||||||
\(503\) | − | 4.96500e13i | − | 1.54198i | −0.636846 | − | 0.770991i | \(-0.719761\pi\) | ||
0.636846 | − | 0.770991i | \(-0.280239\pi\) | |||||||
\(504\) | − | 2.47809e12i | − | 0.0762016i | ||||||
\(505\) | − | 7.30671e12i | − | 0.222467i | ||||||
\(506\) | 3.42535e13i | 1.03265i | ||||||||
\(507\) | −2.81241e13 | −0.839535 | ||||||||
\(508\) | −6.04348e13 | −1.78636 | ||||||||
\(509\) | − | 2.10201e13i | − | 0.615240i | −0.951509 | − | 0.307620i | \(-0.900467\pi\) | ||
0.951509 | − | 0.307620i | \(-0.0995326\pi\) | |||||||
\(510\) | − | 8.41423e12i | − | 0.243873i | ||||||
\(511\) | − | 2.36967e11i | − | 0.00680116i | ||||||
\(512\) | 4.56305e13i | 1.29690i | ||||||||
\(513\) | −9.79579e12 | −0.275710 | ||||||||
\(514\) | 5.94762e13i | 1.65778i | ||||||||
\(515\) | 9.75421e13i | 2.69250i | ||||||||
\(516\) | − | 1.35002e13i | − | 0.369056i | ||||||
\(517\) | 4.36669e12 | 0.118222 | ||||||||
\(518\) | 4.70686e13 | 1.26207 | ||||||||
\(519\) | 1.63456e13i | 0.434075i | ||||||||
\(520\) | −2.92026e13 | −0.768077 | ||||||||
\(521\) | 9.13680e12 | 0.238016 | 0.119008 | − | 0.992893i | \(-0.462029\pi\) | ||||
0.119008 | + | 0.992893i | \(0.462029\pi\) | |||||||
\(522\) | − | 3.27800e13i | − | 0.845779i | ||||||
\(523\) | 3.04103e12 | 0.0777164 | 0.0388582 | − | 0.999245i | \(-0.487628\pi\) | ||||
0.0388582 | + | 0.999245i | \(0.487628\pi\) | |||||||
\(524\) | − | 4.31096e13i | − | 1.09123i | ||||||
\(525\) | 2.62199e13 | 0.657406 | ||||||||
\(526\) | − | 1.03227e14i | − | 2.56370i | ||||||
\(527\) | − | 1.19056e13i | − | 0.292885i | ||||||
\(528\) | 1.00945e13i | 0.245988i | ||||||||
\(529\) | −2.05410e13 | −0.495843 | ||||||||
\(530\) | − | 1.58526e14i | − | 3.79072i | ||||||
\(531\) | 1.38213e13 | − | 2.64387e12i | 0.327397 | − | 0.0626277i | ||||
\(532\) | 5.47080e13 | 1.28379 | ||||||||
\(533\) | 5.62792e12i | 0.130831i | ||||||||
\(534\) | 1.50288e13 | 0.346113 | ||||||||
\(535\) | −5.17301e13 | −1.18025 | ||||||||
\(536\) | −1.74676e13 | −0.394830 | ||||||||
\(537\) | 3.28873e13i | 0.736473i | ||||||||
\(538\) | 2.85272e12 | 0.0632919 | ||||||||
\(539\) | 1.16106e13i | 0.255218i | ||||||||
\(540\) | 1.69831e13 | 0.369869 | ||||||||
\(541\) | 1.97545e12i | 0.0426266i | 0.999773 | + | 0.0213133i | \(0.00678474\pi\) | ||||
−0.999773 | + | 0.0213133i | \(0.993215\pi\) | |||||||
\(542\) | 8.78884e13i | 1.87904i | ||||||||
\(543\) | 1.71904e13 | 0.364155 | ||||||||
\(544\) | − | 1.20984e13i | − | 0.253942i | ||||||
\(545\) | 3.36002e13i | 0.698810i | ||||||||
\(546\) | −4.83974e13 | −0.997376 | ||||||||
\(547\) | −1.58960e13 | −0.324601 | −0.162301 | − | 0.986741i | \(-0.551891\pi\) | ||||
−0.162301 | + | 0.986741i | \(0.551891\pi\) | |||||||
\(548\) | 8.51637e13 | 1.72326 | ||||||||
\(549\) | 2.54435e13i | 0.510170i | ||||||||
\(550\) | 6.51894e13 | 1.29528 | ||||||||
\(551\) | 1.24262e14 | 2.44670 | ||||||||
\(552\) | 1.11461e13 | 0.217484 | ||||||||
\(553\) | 3.51019e13 | 0.678743 | ||||||||
\(554\) | 7.03846e13i | 1.34874i | ||||||||
\(555\) | 5.53895e13i | 1.05187i | ||||||||
\(556\) | −1.41618e13 | −0.266529 | ||||||||
\(557\) | −8.16098e12 | −0.152218 | −0.0761091 | − | 0.997099i | \(-0.524250\pi\) | ||||
−0.0761091 | + | 0.997099i | \(0.524250\pi\) | |||||||
\(558\) | 4.39337e13 | 0.812132 | ||||||||
\(559\) | −4.52732e13 | −0.829435 | ||||||||
\(560\) | 4.87854e13 | 0.885829 | ||||||||
\(561\) | − | 3.25621e12i | − | 0.0586001i | ||||||
\(562\) | − | 5.54289e12i | − | 0.0988678i | ||||||
\(563\) | − | 2.87343e12i | − | 0.0507995i | −0.999677 | − | 0.0253997i | \(-0.991914\pi\) | ||
0.999677 | − | 0.0253997i | \(-0.00808585\pi\) | |||||||
\(564\) | − | 8.27512e12i | − | 0.145004i | ||||||
\(565\) | − | 8.29810e13i | − | 1.44124i | ||||||
\(566\) | 9.62881e13 | 1.65764 | ||||||||
\(567\) | 4.83296e12 | 0.0824704 | ||||||||
\(568\) | 3.43079e13i | 0.580300i | ||||||||
\(569\) | − | 8.08683e12i | − | 0.135587i | −0.997699 | − | 0.0677933i | \(-0.978404\pi\) | ||
0.997699 | − | 0.0677933i | \(-0.0215958\pi\) | |||||||
\(570\) | 1.17704e14i | 1.95622i | ||||||||
\(571\) | − | 2.30233e13i | − | 0.379304i | −0.981851 | − | 0.189652i | \(-0.939264\pi\) | ||
0.981851 | − | 0.189652i | \(-0.0607360\pi\) | |||||||
\(572\) | −6.58148e13 | −1.07484 | ||||||||
\(573\) | − | 5.64429e13i | − | 0.913768i | ||||||
\(574\) | 5.73846e12i | 0.0920950i | ||||||||
\(575\) | 1.17933e14i | 1.87628i | ||||||||
\(576\) | 2.88005e13 | 0.454243 | ||||||||
\(577\) | −7.83551e13 | −1.22515 | −0.612573 | − | 0.790414i | \(-0.709866\pi\) | ||||
−0.612573 | + | 0.790414i | \(0.709866\pi\) | |||||||
\(578\) | − | 9.27880e13i | − | 1.43831i | ||||||
\(579\) | −2.77745e13 | −0.426828 | ||||||||
\(580\) | −2.15435e14 | −3.28228 | ||||||||
\(581\) | 4.36368e13i | 0.659132i | ||||||||
\(582\) | 7.09424e13 | 1.06241 | ||||||||
\(583\) | − | 6.13478e13i | − | 0.910869i | ||||||
\(584\) | −1.91713e11 | −0.00282220 | ||||||||
\(585\) | − | 5.69532e13i | − | 0.831263i | ||||||
\(586\) | 1.93830e13i | 0.280499i | ||||||||
\(587\) | 1.36868e13i | 0.196386i | 0.995167 | + | 0.0981929i | \(0.0313062\pi\) | ||||
−0.995167 | + | 0.0981929i | \(0.968694\pi\) | |||||||
\(588\) | 2.20027e13 | 0.313033 | ||||||||
\(589\) | 1.66543e14i | 2.34937i | ||||||||
\(590\) | −3.17681e13 | − | 1.66073e14i | −0.444356 | − | 2.32295i | ||||
\(591\) | −5.26681e13 | −0.730483 | ||||||||
\(592\) | 6.23903e13i | 0.858042i | ||||||||
\(593\) | −1.74570e13 | −0.238066 | −0.119033 | − | 0.992890i | \(-0.537979\pi\) | ||||
−0.119033 | + | 0.992890i | \(0.537979\pi\) | |||||||
\(594\) | 1.20160e13 | 0.162490 | ||||||||
\(595\) | −1.57369e13 | −0.211025 | ||||||||
\(596\) | 1.42613e14i | 1.89639i | ||||||||
\(597\) | 4.17632e13 | 0.550709 | ||||||||
\(598\) | − | 2.17685e14i | − | 2.84657i | ||||||
\(599\) | −7.08734e13 | −0.919071 | −0.459536 | − | 0.888159i | \(-0.651984\pi\) | ||||
−0.459536 | + | 0.888159i | \(0.651984\pi\) | |||||||
\(600\) | − | 2.12126e13i | − | 0.272796i | ||||||
\(601\) | 1.17177e14i | 1.49442i | 0.664590 | + | 0.747208i | \(0.268606\pi\) | ||||
−0.664590 | + | 0.747208i | \(0.731394\pi\) | |||||||
\(602\) | −4.61625e13 | −0.583857 | ||||||||
\(603\) | − | 3.40667e13i | − | 0.427311i | ||||||
\(604\) | 1.30163e14i | 1.61921i | ||||||||
\(605\) | −8.73575e13 | −1.07776 | ||||||||
\(606\) | −9.79686e12 | −0.119874 | ||||||||
\(607\) | −1.78667e11 | −0.00216821 | −0.00108411 | − | 0.999999i | \(-0.500345\pi\) | ||||
−0.00108411 | + | 0.999999i | \(0.500345\pi\) | |||||||
\(608\) | 1.69241e14i | 2.03699i | ||||||||
\(609\) | −6.13074e13 | −0.731857 | ||||||||
\(610\) | 3.05723e14 | 3.61976 | ||||||||
\(611\) | −2.77508e13 | −0.325889 | ||||||||
\(612\) | −6.17070e12 | −0.0718749 | ||||||||
\(613\) | − | 3.48149e13i | − | 0.402219i | −0.979569 | − | 0.201109i | \(-0.935545\pi\) | ||
0.979569 | − | 0.201109i | \(-0.0644547\pi\) | |||||||
\(614\) | 1.84256e13i | 0.211144i | ||||||||
\(615\) | −6.75292e12 | −0.0767566 | ||||||||
\(616\) | −1.15230e13 | −0.129916 | ||||||||
\(617\) | −8.79881e13 | −0.984006 | −0.492003 | − | 0.870593i | \(-0.663735\pi\) | ||||
−0.492003 | + | 0.870593i | \(0.663735\pi\) | |||||||
\(618\) | 1.30785e14 | 1.45082 | ||||||||
\(619\) | −8.43433e12 | −0.0928105 | −0.0464053 | − | 0.998923i | \(-0.514777\pi\) | ||||
−0.0464053 | + | 0.998923i | \(0.514777\pi\) | |||||||
\(620\) | − | 2.88738e14i | − | 3.15171i | ||||||
\(621\) | 2.17380e13i | 0.235375i | ||||||||
\(622\) | − | 1.20572e14i | − | 1.29508i | ||||||
\(623\) | − | 2.81078e13i | − | 0.299493i | ||||||
\(624\) | − | 6.41516e13i | − | 0.678086i | ||||||
\(625\) | −1.72266e13 | −0.180634 | ||||||||
\(626\) | 5.69052e13 | 0.591944 | ||||||||
\(627\) | 4.55501e13i | 0.470058i | ||||||||
\(628\) | 1.91091e13i | 0.195633i | ||||||||
\(629\) | − | 2.01254e13i | − | 0.204405i | ||||||
\(630\) | − | 5.80718e13i | − | 0.585144i | ||||||
\(631\) | 3.67916e13 | 0.367791 | 0.183896 | − | 0.982946i | \(-0.441129\pi\) | ||||
0.183896 | + | 0.982946i | \(0.441129\pi\) | |||||||
\(632\) | − | 2.83985e13i | − | 0.281650i | ||||||
\(633\) | − | 5.32992e13i | − | 0.524448i | ||||||
\(634\) | 1.55380e14i | 1.51687i | ||||||||
\(635\) | −2.43182e14 | −2.35539 | ||||||||
\(636\) | −1.16257e14 | −1.11721 | ||||||||
\(637\) | − | 7.37867e13i | − | 0.703527i | ||||||
\(638\) | −1.52426e14 | −1.44197 | ||||||||
\(639\) | −6.69099e13 | −0.628038 | ||||||||
\(640\) | − | 1.03027e14i | − | 0.959518i | ||||||
\(641\) | −1.03346e13 | −0.0955000 | −0.0477500 | − | 0.998859i | \(-0.515205\pi\) | ||||
−0.0477500 | + | 0.998859i | \(0.515205\pi\) | |||||||
\(642\) | 6.93598e13i | 0.635965i | ||||||||
\(643\) | −5.05738e13 | −0.460120 | −0.230060 | − | 0.973176i | \(-0.573892\pi\) | ||||
−0.230060 | + | 0.973176i | \(0.573892\pi\) | |||||||
\(644\) | − | 1.21403e14i | − | 1.09598i | ||||||
\(645\) | − | 5.43231e13i | − | 0.486616i | ||||||
\(646\) | − | 4.27671e13i | − | 0.380143i | ||||||
\(647\) | −1.17517e14 | −1.03652 | −0.518261 | − | 0.855222i | \(-0.673421\pi\) | ||||
−0.518261 | + | 0.855222i | \(0.673421\pi\) | |||||||
\(648\) | − | 3.91000e12i | − | 0.0342218i | ||||||
\(649\) | −1.22939e13 | − | 6.42684e13i | −0.106774 | − | 0.558180i | ||||
\(650\) | −4.14286e14 | −3.57053 | ||||||||
\(651\) | − | 8.21677e13i | − | 0.702742i | ||||||
\(652\) | −2.16834e14 | −1.84031 | ||||||||
\(653\) | 4.49008e13 | 0.378171 | 0.189086 | − | 0.981961i | \(-0.439448\pi\) | ||||
0.189086 | + | 0.981961i | \(0.439448\pi\) | |||||||
\(654\) | 4.50512e13 | 0.376546 | ||||||||
\(655\) | − | 1.73468e14i | − | 1.43884i | ||||||
\(656\) | −7.60643e12 | −0.0626126 | ||||||||
\(657\) | − | 3.73894e11i | − | 0.00305437i | ||||||
\(658\) | −2.82959e13 | −0.229400 | ||||||||
\(659\) | − | 1.77691e14i | − | 1.42968i | −0.699287 | − | 0.714841i | \(-0.746499\pi\) | ||
0.699287 | − | 0.714841i | \(-0.253501\pi\) | |||||||
\(660\) | − | 7.89708e13i | − | 0.630590i | ||||||
\(661\) | 1.37183e14 | 1.08716 | 0.543580 | − | 0.839358i | \(-0.317069\pi\) | ||||
0.543580 | + | 0.839358i | \(0.317069\pi\) | |||||||
\(662\) | 1.47068e14i | 1.15672i | ||||||||
\(663\) | 2.06936e13i | 0.161536i | ||||||||
\(664\) | 3.53034e13 | 0.273512 | ||||||||
\(665\) | 2.20138e14 | 1.69273 | ||||||||
\(666\) | 7.42664e13 | 0.566789 | ||||||||
\(667\) | − | 2.75752e14i | − | 2.08877i | ||||||
\(668\) | −6.76849e13 | −0.508873 | ||||||||
\(669\) | −1.28424e14 | −0.958331 | ||||||||
\(670\) | −4.09338e14 | −3.03185 | ||||||||
\(671\) | 1.18311e14 | 0.869789 | ||||||||
\(672\) | − | 8.34988e13i | − | 0.609304i | ||||||
\(673\) | 2.51484e14i | 1.82153i | 0.412929 | + | 0.910763i | \(0.364506\pi\) | ||||
−0.412929 | + | 0.910763i | \(0.635494\pi\) | |||||||
\(674\) | 3.63306e13 | 0.261200 | ||||||||
\(675\) | 4.13705e13 | 0.295238 | ||||||||
\(676\) | 2.47828e14 | 1.75557 | ||||||||
\(677\) | 1.43537e14 | 1.00930 | 0.504650 | − | 0.863324i | \(-0.331621\pi\) | ||||
0.504650 | + | 0.863324i | \(0.331621\pi\) | |||||||
\(678\) | −1.11261e14 | −0.776596 | ||||||||
\(679\) | − | 1.32681e14i | − | 0.919307i | ||||||
\(680\) | 1.27316e13i | 0.0875665i | ||||||||
\(681\) | − | 4.22002e13i | − | 0.288124i | ||||||
\(682\) | − | 2.04290e14i | − | 1.38460i | ||||||
\(683\) | − | 7.42403e13i | − | 0.499501i | −0.968310 | − | 0.249750i | \(-0.919651\pi\) | ||
0.968310 | − | 0.249750i | \(-0.0803486\pi\) | |||||||
\(684\) | 8.63200e13 | 0.576542 | ||||||||
\(685\) | 3.42688e14 | 2.27220 | ||||||||
\(686\) | − | 2.42766e14i | − | 1.59796i | ||||||
\(687\) | − | 7.72292e13i | − | 0.504659i | ||||||
\(688\) | − | 6.11892e13i | − | 0.396947i | ||||||
\(689\) | 3.89872e14i | 2.51088i | ||||||||
\(690\) | 2.61199e14 | 1.67004 | ||||||||
\(691\) | 1.72147e14i | 1.09272i | 0.837549 | + | 0.546362i | \(0.183988\pi\) | ||||
−0.837549 | + | 0.546362i | \(0.816012\pi\) | |||||||
\(692\) | − | 1.44037e14i | − | 0.907702i | ||||||
\(693\) | − | 2.24731e13i | − | 0.140604i | ||||||
\(694\) | −1.75883e13 | −0.109251 | ||||||||
\(695\) | −5.69852e13 | −0.351429 | ||||||||
\(696\) | 4.95995e13i | 0.303690i | ||||||||
\(697\) | 2.45363e12 | 0.0149158 | ||||||||
\(698\) | 4.14295e13 | 0.250053 | ||||||||
\(699\) | 1.17573e14i | 0.704568i | ||||||||
\(700\) | −2.31048e14 | −1.37471 | ||||||||
\(701\) | 2.95827e14i | 1.74762i | 0.486265 | + | 0.873811i | \(0.338359\pi\) | ||||
−0.486265 | + | 0.873811i | \(0.661641\pi\) | |||||||
\(702\) | −7.63630e13 | −0.447917 | ||||||||
\(703\) | 2.81528e14i | 1.63963i | ||||||||
\(704\) | − | 1.33921e14i | − | 0.774439i | ||||||
\(705\) | − | 3.32981e13i | − | 0.191194i | ||||||
\(706\) | 2.57016e14 | 1.46533 | ||||||||
\(707\) | 1.83227e13i | 0.103727i | ||||||||
\(708\) | −1.21792e14 | + | 2.32976e13i | −0.684626 | + | 0.130962i | ||||
\(709\) | −1.50979e13 | −0.0842723 | −0.0421361 | − | 0.999112i | \(-0.513416\pi\) | ||||
−0.0421361 | + | 0.999112i | \(0.513416\pi\) | |||||||
\(710\) | 8.03975e14i | 4.45606i | ||||||||
\(711\) | 5.53849e13 | 0.304820 | ||||||||
\(712\) | −2.27401e13 | −0.124277 | ||||||||
\(713\) | 3.69579e14 | 2.00567 | ||||||||
\(714\) | 2.11000e13i | 0.113708i | ||||||||
\(715\) | −2.64830e14 | −1.41722 | ||||||||
\(716\) | − | 2.89801e14i | − | 1.54005i | ||||||
\(717\) | −1.29245e14 | −0.682053 | ||||||||
\(718\) | − | 5.08534e14i | − | 2.66501i | ||||||
\(719\) | 8.37386e13i | 0.435794i | 0.975972 | + | 0.217897i | \(0.0699197\pi\) | ||||
−0.975972 | + | 0.217897i | \(0.930080\pi\) | |||||||
\(720\) | 7.69752e13 | 0.397821 | ||||||||
\(721\) | − | 2.44602e14i | − | 1.25541i | ||||||
\(722\) | 3.06770e14i | 1.56360i | ||||||||
\(723\) | 2.90128e13 | 0.146858 | ||||||||
\(724\) | −1.51481e14 | −0.761492 | ||||||||
\(725\) | −5.24796e14 | −2.62000 | ||||||||
\(726\) | 1.17129e14i | 0.580740i | ||||||||
\(727\) | −2.86584e14 | −1.41117 | −0.705586 | − | 0.708624i | \(-0.749316\pi\) | ||||
−0.705586 | + | 0.708624i | \(0.749316\pi\) | |||||||
\(728\) | 7.32301e13 | 0.358124 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | −4.49263e12 | −0.0216714 | ||||||||
\(731\) | 1.97380e13i | 0.0945618i | ||||||||
\(732\) | − | 2.24207e14i | − | 1.06682i | ||||||
\(733\) | −6.41426e13 | −0.303128 | −0.151564 | − | 0.988447i | \(-0.548431\pi\) | ||||
−0.151564 | + | 0.988447i | \(0.548431\pi\) | |||||||
\(734\) | 3.80375e14 | 1.78538 | ||||||||
\(735\) | 8.85363e13 | 0.412748 | ||||||||
\(736\) | 3.75566e14 | 1.73899 | ||||||||
\(737\) | −1.58409e14 | −0.728522 | ||||||||
\(738\) | 9.05433e12i | 0.0413594i | ||||||||
\(739\) | 4.93707e13i | 0.223999i | 0.993708 | + | 0.112000i | \(0.0357256\pi\) | ||||
−0.993708 | + | 0.112000i | \(0.964274\pi\) | |||||||
\(740\) | − | 4.88089e14i | − | 2.19958i | ||||||
\(741\) | − | 2.89476e14i | − | 1.29575i | ||||||
\(742\) | 3.97530e14i | 1.76746i | ||||||||
\(743\) | 3.80616e13 | 0.168090 | 0.0840451 | − | 0.996462i | \(-0.473216\pi\) | ||||
0.0840451 | + | 0.996462i | \(0.473216\pi\) | |||||||
\(744\) | −6.64760e13 | −0.291609 | ||||||||
\(745\) | 5.73858e14i | 2.50048i | ||||||||
\(746\) | − | 5.13761e13i | − | 0.222365i | ||||||
\(747\) | 6.88515e13i | 0.296013i | ||||||||
\(748\) | 2.86936e13i | 0.122540i | ||||||||
\(749\) | 1.29721e14 | 0.550304 | ||||||||
\(750\) | − | 1.73066e14i | − | 0.729301i | ||||||
\(751\) | 5.78775e13i | 0.242276i | 0.992636 | + | 0.121138i | \(0.0386543\pi\) | ||||
−0.992636 | + | 0.121138i | \(0.961346\pi\) | |||||||
\(752\) | − | 3.75067e13i | − | 0.155962i | ||||||
\(753\) | 1.11611e14 | 0.461035 | ||||||||
\(754\) | 9.68685e14 | 3.97490 | ||||||||
\(755\) | 5.23760e14i | 2.13500i | ||||||||
\(756\) | −4.25878e13 | −0.172455 | ||||||||
\(757\) | −1.62750e14 | −0.654700 | −0.327350 | − | 0.944903i | \(-0.606156\pi\) | ||||
−0.327350 | + | 0.944903i | \(0.606156\pi\) | |||||||
\(758\) | − | 1.96741e14i | − | 0.786230i | ||||||
\(759\) | 1.01081e14 | 0.401292 | ||||||||
\(760\) | − | 1.78098e14i | − | 0.702411i | ||||||
\(761\) | −3.92113e14 | −1.53634 | −0.768171 | − | 0.640245i | \(-0.778833\pi\) | ||||
−0.768171 | + | 0.640245i | \(0.778833\pi\) | |||||||
\(762\) | 3.26059e14i | 1.26918i | ||||||||
\(763\) | − | 8.42578e13i | − | 0.325827i | ||||||
\(764\) | 4.97372e14i | 1.91080i | ||||||||
\(765\) | −2.48301e13 | −0.0947702 | ||||||||
\(766\) | − | 1.31538e14i | − | 0.498780i | ||||||
\(767\) | 7.81291e13 | + | 4.08433e14i | 0.294331 | + | 1.53866i | ||||
\(768\) | 7.20712e13 | 0.269746 | ||||||||
\(769\) | − | 1.65204e14i | − | 0.614313i | −0.951659 | − | 0.307157i | \(-0.900622\pi\) | ||
0.951659 | − | 0.307157i | \(-0.0993775\pi\) | |||||||
\(770\) | −2.70032e14 | −0.997612 | ||||||||
\(771\) | 1.75512e14 | 0.644222 | ||||||||
\(772\) | 2.44747e14 | 0.892548 | ||||||||
\(773\) | − | 4.04252e14i | − | 1.46472i | −0.680918 | − | 0.732360i | \(-0.738419\pi\) | ||
0.680918 | − | 0.732360i | \(-0.261581\pi\) | |||||||
\(774\) | −7.28366e13 | −0.262207 | ||||||||
\(775\) | − | 7.03362e14i | − | 2.51577i | ||||||
\(776\) | −1.07343e14 | −0.381474 | ||||||||
\(777\) | − | 1.38898e14i | − | 0.490446i | ||||||
\(778\) | 6.27009e14i | 2.19976i | ||||||||
\(779\) | −3.43231e13 | −0.119646 | ||||||||
\(780\) | 5.01868e14i | 1.73827i | ||||||||
\(781\) | 3.11129e14i | 1.07074i | ||||||||
\(782\) | −9.49050e13 | −0.324530 | ||||||||
\(783\) | −9.67328e13 | −0.328674 | ||||||||
\(784\) | 9.97266e13 | 0.336690 | ||||||||
\(785\) | 7.68926e13i | 0.257950i | ||||||||
\(786\) | −2.32586e14 | −0.775301 | ||||||||
\(787\) | −2.01809e14 | −0.668447 | −0.334224 | − | 0.942494i | \(-0.608474\pi\) | ||||
−0.334224 | + | 0.942494i | \(0.608474\pi\) | |||||||
\(788\) | 4.64108e14 | 1.52753 | ||||||||
\(789\) | −3.04621e14 | −0.996265 | ||||||||
\(790\) | − | 6.65493e14i | − | 2.16276i | ||||||
\(791\) | 2.08088e14i | 0.671993i | ||||||||
\(792\) | −1.81814e13 | −0.0583447 | ||||||||
\(793\) | −7.51882e14 | −2.39764 | ||||||||
\(794\) | 3.10481e14 | 0.983857 | ||||||||
\(795\) | −4.67806e14 | −1.47309 | ||||||||
\(796\) | −3.68015e14 | −1.15160 | ||||||||
\(797\) | 6.11946e14i | 1.90292i | 0.307766 | + | 0.951462i | \(0.400418\pi\) | ||||
−0.307766 | + | 0.951462i | \(0.599582\pi\) | |||||||
\(798\) | − | 2.95162e14i | − | 0.912107i | ||||||
\(799\) | 1.20986e13i | 0.0371538i | ||||||||
\(800\) | − | 7.14757e14i | − | 2.18126i | ||||||
\(801\) | − | 4.43494e13i | − | 0.134501i | ||||||
\(802\) | −8.52960e14 | −2.57073 | ||||||||
\(803\) | −1.73859e12 | −0.00520739 | ||||||||
\(804\) | 3.00194e14i | 0.893556i | ||||||||
\(805\) | − | 4.88512e14i | − | 1.44509i | ||||||
\(806\) | 1.29829e15i | 3.81676i | ||||||||
\(807\) | − | 8.41829e12i | − | 0.0245955i | ||||||
\(808\) | 1.48236e13 | 0.0430425 | ||||||||
\(809\) | 3.26582e14i | 0.942431i | 0.882018 | + | 0.471216i | \(0.156185\pi\) | ||||
−0.882018 | + | 0.471216i | \(0.843815\pi\) | |||||||
\(810\) | − | 9.16275e13i | − | 0.262785i | ||||||
\(811\) | 5.83491e14i | 1.66314i | 0.555417 | + | 0.831572i | \(0.312559\pi\) | ||||
−0.555417 | + | 0.831572i | \(0.687441\pi\) | |||||||
\(812\) | 5.40238e14 | 1.53040 | ||||||||
\(813\) | 2.59356e14 | 0.730202 | ||||||||
\(814\) | − | 3.45336e14i | − | 0.966318i | ||||||
\(815\) | −8.72514e14 | −2.42652 | ||||||||
\(816\) | −2.79685e13 | −0.0773068 | ||||||||
\(817\) | − | 2.76109e14i | − | 0.758524i | ||||||
\(818\) | 5.41343e14 | 1.47811 | ||||||||
\(819\) | 1.42819e14i | 0.387585i | ||||||||
\(820\) | 5.95064e13 | 0.160507 | ||||||||
\(821\) | − | 1.57813e14i | − | 0.423085i | −0.977369 | − | 0.211542i | \(-0.932151\pi\) | ||
0.977369 | − | 0.211542i | \(-0.0678486\pi\) | |||||||
\(822\) | − | 4.59477e14i | − | 1.22435i | ||||||
\(823\) | 5.55993e13i | 0.147255i | 0.997286 | + | 0.0736275i | \(0.0234576\pi\) | ||||
−0.997286 | + | 0.0736275i | \(0.976542\pi\) | |||||||
\(824\) | −1.97890e14 | −0.520941 | ||||||||
\(825\) | − | 1.92372e14i | − | 0.503351i | ||||||
\(826\) | 7.96636e13 | + | 4.16455e14i | 0.207186 | + | 1.08310i | ||||
\(827\) | 6.21209e14 | 1.60587 | 0.802935 | − | 0.596067i | \(-0.203271\pi\) | ||||
0.802935 | + | 0.596067i | \(0.203271\pi\) | |||||||
\(828\) | − | 1.91554e14i | − | 0.492197i | ||||||
\(829\) | −4.72134e14 | −1.20585 | −0.602924 | − | 0.797799i | \(-0.705998\pi\) | ||||
−0.602924 | + | 0.797799i | \(0.705998\pi\) | |||||||
\(830\) | 8.27305e14 | 2.10027 | ||||||||
\(831\) | 2.07703e14 | 0.524128 | ||||||||
\(832\) | 8.51086e14i | 2.13480i | ||||||||
\(833\) | −3.21691e13 | −0.0802073 | ||||||||
\(834\) | 7.64059e13i | 0.189364i | ||||||||
\(835\) | −2.72356e14 | −0.670971 | ||||||||
\(836\) | − | 4.01385e14i | − | 0.982947i | ||||||
\(837\) | − | 1.29647e14i | − | 0.315598i | ||||||
\(838\) | 6.64801e13 | 0.160869 | ||||||||
\(839\) | − | 4.84153e13i | − | 0.116459i | −0.998303 | − | 0.0582295i | \(-0.981454\pi\) | ||
0.998303 | − | 0.0582295i | \(-0.0185455\pi\) | |||||||
\(840\) | 8.78685e13i | 0.210105i | ||||||||
\(841\) | 8.06374e14 | 1.91671 | ||||||||
\(842\) | 3.78707e14 | 0.894834 | ||||||||
\(843\) | −1.63569e13 | −0.0384205 | ||||||||
\(844\) | 4.69670e14i | 1.09668i | ||||||||
\(845\) | 9.97230e14 | 2.31479 | ||||||||
\(846\) | −4.46461e13 | −0.103022 | ||||||||
\(847\) | 2.19063e14 | 0.502518 | ||||||||
\(848\) | −5.26933e14 | −1.20164 | ||||||||
\(849\) | − | 2.84143e14i | − | 0.644167i | ||||||
\(850\) | 1.80618e14i | 0.407068i | ||||||||
\(851\) | 6.24744e14 | 1.39976 | ||||||||
\(852\) | 5.89607e14 | 1.31330 | ||||||||
\(853\) | −3.39041e14 | −0.750770 | −0.375385 | − | 0.926869i | \(-0.622489\pi\) | ||||
−0.375385 | + | 0.926869i | \(0.622489\pi\) | |||||||
\(854\) | −7.66650e14 | −1.68775 | ||||||||
\(855\) | 3.47341e14 | 0.760196 | ||||||||
\(856\) | − | 1.04948e14i | − | 0.228353i | ||||||
\(857\) | − | 3.69786e14i | − | 0.799919i | −0.916533 | − | 0.399960i | \(-0.869024\pi\) | ||
0.916533 | − | 0.399960i | \(-0.130976\pi\) | |||||||
\(858\) | 3.55085e14i | 0.763653i | ||||||||
\(859\) | 2.05420e14i | 0.439214i | 0.975588 | + | 0.219607i | \(0.0704775\pi\) | ||||
−0.975588 | + | 0.219607i | \(0.929523\pi\) | |||||||
\(860\) | 4.78693e14i | 1.01757i | ||||||||
\(861\) | 1.69340e13 | 0.0357886 | ||||||||
\(862\) | 2.55576e14 | 0.537011 | ||||||||
\(863\) | − | 3.55387e14i | − | 0.742416i | −0.928550 | − | 0.371208i | \(-0.878944\pi\) | ||
0.928550 | − | 0.371208i | \(-0.121056\pi\) | |||||||
\(864\) | − | 1.31747e14i | − | 0.273635i | ||||||
\(865\) | − | 5.79587e14i | − | 1.19684i | ||||||
\(866\) | − | 6.79762e14i | − | 1.39562i | ||||||
\(867\) | −2.73814e14 | −0.558934 | ||||||||
\(868\) | 7.24057e14i | 1.46952i | ||||||||
\(869\) | − | 2.57538e14i | − | 0.519688i | ||||||
\(870\) | 1.16232e15i | 2.33200i | ||||||||
\(871\) | 1.00671e15 | 2.00823 | ||||||||
\(872\) | −6.81670e13 | −0.135205 | ||||||||
\(873\) | − | 2.09349e14i | − | 0.412856i | ||||||
\(874\) | 1.32760e15 | 2.60321 | ||||||||
\(875\) | −3.23681e14 | −0.631068 | ||||||||
\(876\) | 3.29473e12i | 0.00638704i | ||||||||
\(877\) | 1.27466e14 | 0.245694 | 0.122847 | − | 0.992426i | \(-0.460797\pi\) | ||||
0.122847 | + | 0.992426i | \(0.460797\pi\) | |||||||
\(878\) | − | 4.72657e14i | − | 0.905886i | ||||||
\(879\) | 5.71985e13 | 0.109003 | ||||||||
\(880\) | − | 3.57932e14i | − | 0.678246i | ||||||
\(881\) | − | 6.92437e14i | − | 1.30467i | −0.757931 | − | 0.652335i | \(-0.773789\pi\) | ||
0.757931 | − | 0.652335i | \(-0.226211\pi\) | |||||||
\(882\) | − | 1.18710e14i | − | 0.222404i | ||||||
\(883\) | −1.09840e14 | −0.204625 | −0.102312 | − | 0.994752i | \(-0.532624\pi\) | ||||
−0.102312 | + | 0.994752i | \(0.532624\pi\) | |||||||
\(884\) | − | 1.82351e14i | − | 0.337790i | ||||||
\(885\) | −4.90076e14 | + | 9.37467e13i | −0.902708 | + | 0.172679i | ||||
\(886\) | −4.78277e14 | −0.876014 | ||||||||
\(887\) | − | 9.34334e14i | − | 1.70170i | −0.525406 | − | 0.850852i | \(-0.676086\pi\) | ||
0.525406 | − | 0.850852i | \(-0.323914\pi\) | |||||||
\(888\) | −1.12372e14 | −0.203514 | ||||||||
\(889\) | 6.09818e14 | 1.09823 | ||||||||
\(890\) | −5.32893e14 | −0.954311 | ||||||||
\(891\) | − | 3.54588e13i | − | 0.0631445i | ||||||
\(892\) | 1.13167e15 | 2.00398 | ||||||||
\(893\) | − | 1.69244e14i | − | 0.298028i | ||||||
\(894\) | 7.69430e14 | 1.34735 | ||||||||
\(895\) | − | 1.16612e15i | − | 2.03062i | ||||||
\(896\) | 2.58358e14i | 0.447385i | ||||||||
\(897\) | −6.42380e14 | −1.10619 | ||||||||
\(898\) | 1.44469e15i | 2.47397i | ||||||||
\(899\) | 1.64460e15i | 2.80068i | ||||||||
\(900\) | −3.64555e14 | −0.617377 | ||||||||
\(901\) | 1.69974e14 | 0.286259 | ||||||||
\(902\) | 4.21023e13 | 0.0705137 | ||||||||
\(903\) | 1.36224e14i | 0.226890i | ||||||||
\(904\) | 1.68349e14 | 0.278849 | ||||||||
\(905\) | −6.09540e14 | −1.00406 | ||||||||
\(906\) | 7.02260e14 | 1.15042 | ||||||||
\(907\) | 4.62853e14 | 0.754062 | 0.377031 | − | 0.926201i | \(-0.376945\pi\) | ||||
0.377031 | + | 0.926201i | \(0.376945\pi\) | |||||||
\(908\) | 3.71866e14i | 0.602500i | ||||||||
\(909\) | 2.89102e13i | 0.0465835i | ||||||||
\(910\) | 1.71608e15 | 2.74999 | ||||||||
\(911\) | 4.23336e14 | 0.674673 | 0.337337 | − | 0.941384i | \(-0.390474\pi\) | ||||
0.337337 | + | 0.941384i | \(0.390474\pi\) | |||||||
\(912\) | 3.91242e14 | 0.620114 | ||||||||
\(913\) | 3.20157e14 | 0.504672 | ||||||||
\(914\) | −1.35509e15 | −2.12441 | ||||||||
\(915\) | − | 9.02180e14i | − | 1.40665i | ||||||
\(916\) | 6.80540e14i | 1.05530i | ||||||||
\(917\) | 4.34998e14i | 0.670873i | ||||||||
\(918\) | 3.32923e13i | 0.0510658i | ||||||||
\(919\) | − | 4.78489e14i | − | 0.729952i | −0.931017 | − | 0.364976i | \(-0.881077\pi\) | ||
0.931017 | − | 0.364976i | \(-0.118923\pi\) | |||||||
\(920\) | −3.95220e14 | −0.599653 | ||||||||
\(921\) | 5.43733e13 | 0.0820517 | ||||||||
\(922\) | − | 3.57670e14i | − | 0.536820i | ||||||
\(923\) | − | 1.97726e15i | − | 2.95158i | ||||||
\(924\) | 1.98032e14i | 0.294019i | ||||||||
\(925\) | − | 1.18898e15i | − | 1.75576i | ||||||
\(926\) | −1.60804e14 | −0.236179 | ||||||||
\(927\) | − | 3.85941e14i | − | 0.563797i | ||||||
\(928\) | 1.67125e15i | 2.42829i | ||||||||
\(929\) | 3.29545e14i | 0.476252i | 0.971234 | + | 0.238126i | \(0.0765330\pi\) | ||||
−0.971234 | + | 0.238126i | \(0.923467\pi\) | |||||||
\(930\) | −1.55781e15 | −2.23923 | ||||||||
\(931\) | 4.50004e14 | 0.643380 | ||||||||
\(932\) | − | 1.03605e15i | − | 1.47333i | ||||||
\(933\) | −3.55805e14 | −0.503274 | ||||||||
\(934\) | 1.70208e15 | 2.39466 | ||||||||
\(935\) | 1.15459e14i | 0.161574i | ||||||||
\(936\) | 1.15545e14 | 0.160832 | ||||||||
\(937\) | 5.89156e14i | 0.815704i | 0.913048 | + | 0.407852i | \(0.133722\pi\) | ||||
−0.913048 | + | 0.407852i | \(0.866278\pi\) | |||||||
\(938\) | 1.02648e15 | 1.41363 | ||||||||
\(939\) | − | 1.67925e14i | − | 0.230032i | ||||||
\(940\) | 2.93421e14i | 0.399808i | ||||||||
\(941\) | − | 8.32873e14i | − | 1.12883i | −0.825489 | − | 0.564417i | \(-0.809101\pi\) | ||
0.825489 | − | 0.564417i | \(-0.190899\pi\) | |||||||
\(942\) | 1.03098e14 | 0.138994 | ||||||||
\(943\) | 7.61668e13i | 0.102143i | ||||||||
\(944\) | −5.52018e14 | + | 1.05596e14i | −0.736366 | + | 0.140859i | ||||
\(945\) | −1.71368e14 | −0.227390 | ||||||||
\(946\) | 3.38688e14i | 0.447038i | ||||||||
\(947\) | 2.84071e14 | 0.372972 | 0.186486 | − | 0.982458i | \(-0.440290\pi\) | ||||
0.186486 | + | 0.982458i | \(0.440290\pi\) | |||||||
\(948\) | −4.88049e14 | −0.637414 | ||||||||
\(949\) | 1.10490e13 | 0.0143546 | ||||||||
\(950\) | − | 2.52661e15i | − | 3.26528i | ||||||
\(951\) | 4.58521e14 | 0.589463 | ||||||||
\(952\) | − | 3.19265e13i | − | 0.0408288i | ||||||
\(953\) | −9.15181e14 | −1.16424 | −0.582120 | − | 0.813103i | \(-0.697777\pi\) | ||||
−0.582120 | + | 0.813103i | \(0.697777\pi\) | |||||||
\(954\) | 6.27235e14i | 0.793758i | ||||||||
\(955\) | 2.00136e15i | 2.51947i | ||||||||
\(956\) | 1.13890e15 | 1.42625 | ||||||||
\(957\) | 4.49804e14i | 0.560356i | ||||||||
\(958\) | − | 1.42888e15i | − | 1.77079i | ||||||
\(959\) | −8.59345e14 | −1.05944 | ||||||||
\(960\) | −1.02121e15 | −1.25245 | ||||||||
\(961\) | −1.38456e15 | −1.68926 | ||||||||
\(962\) | 2.19465e15i | 2.66373i | ||||||||
\(963\) | 2.04679e14 | 0.247139 | ||||||||
\(964\) | −2.55659e14 | −0.307098 | ||||||||
\(965\) | 9.84833e14 | 1.17686 | ||||||||
\(966\) | −6.54998e14 | −0.778671 | ||||||||
\(967\) | − | 1.12141e15i | − | 1.32627i | −0.748501 | − | 0.663133i | \(-0.769226\pi\) | ||
0.748501 | − | 0.663133i | \(-0.230774\pi\) | |||||||
\(968\) | − | 1.77228e14i | − | 0.208524i | ||||||
\(969\) | −1.26204e14 | −0.147725 | ||||||||
\(970\) | −2.51549e15 | −2.92930 | ||||||||
\(971\) | 3.73519e14 | 0.432729 | 0.216365 | − | 0.976313i | \(-0.430580\pi\) | ||||
0.216365 | + | 0.976313i | \(0.430580\pi\) | |||||||
\(972\) | −6.71964e13 | −0.0774488 | ||||||||
\(973\) | 1.42899e14 | 0.163858 | ||||||||
\(974\) | − | 1.92329e15i | − | 2.19407i | ||||||
\(975\) | 1.22254e15i | 1.38753i | ||||||||
\(976\) | − | 1.01621e15i | − | 1.14745i | ||||||
\(977\) | − | 1.25728e15i | − | 1.41241i | −0.708009 | − | 0.706203i | \(-0.750406\pi\) | ||
0.708009 | − | 0.706203i | \(-0.249594\pi\) | |||||||
\(978\) | 1.16987e15i | 1.30750i | ||||||||
\(979\) | −2.06223e14 | −0.229311 | ||||||||
\(980\) | −7.80177e14 | −0.863103 | ||||||||
\(981\) | − | 1.32945e14i | − | 0.146328i | ||||||
\(982\) | − | 2.10266e15i | − | 2.30256i | ||||||
\(983\) | 9.08229e14i | 0.989527i | 0.869028 | + | 0.494763i | \(0.164745\pi\) | ||||
−0.869028 | + | 0.494763i | \(0.835255\pi\) | |||||||
\(984\) | − | 1.37001e13i | − | 0.0148508i | ||||||
\(985\) | 1.86751e15 | 2.01411 | ||||||||
\(986\) | − | 4.22322e14i | − | 0.453168i | ||||||
\(987\) | 8.35002e13i | 0.0891460i | ||||||||
\(988\) | 2.55085e15i | 2.70957i | ||||||||
\(989\) | −6.12716e14 | −0.647557 | ||||||||
\(990\) | −4.26065e14 | −0.448023 | ||||||||
\(991\) | − | 1.06447e15i | − | 1.11369i | −0.830617 | − | 0.556844i | \(-0.812012\pi\) | ||
0.830617 | − | 0.556844i | \(-0.187988\pi\) | |||||||
\(992\) | −2.23990e15 | −2.33169 | ||||||||
\(993\) | 4.33994e14 | 0.449508 | ||||||||
\(994\) | − | 2.01610e15i | − | 2.07768i | ||||||
\(995\) | −1.48085e15 | −1.51843 | ||||||||
\(996\) | − | 6.06716e14i | − | 0.618997i | ||||||
\(997\) | 3.36798e14 | 0.341895 | 0.170948 | − | 0.985280i | \(-0.445317\pi\) | ||||
0.170948 | + | 0.985280i | \(0.445317\pi\) | |||||||
\(998\) | − | 2.54436e15i | − | 2.56996i | ||||||
\(999\) | − | 2.19158e14i | − | 0.220257i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.11.c.a.58.85 | yes | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.16 | ✓ | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.16 | ✓ | 100 | 59.58 | odd | 2 | inner | |
177.11.c.a.58.85 | yes | 100 | 1.1 | even | 1 | trivial |