Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [162,7,Mod(161,162)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(162, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("162.161");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 162 = 2 \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 162.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: | \(37.2687615464\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 1382x^{6} - 288x^{5} + 716245x^{4} + 201312x^{3} - 164876604x^{2} - 33576768x + 14252103396 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{16} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.3 | ||
Root | \(16.6034 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 162.161 |
Dual form | 162.7.b.b.161.6 |
$q$-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 \(\left(\mathbb{Z}/162\mathbb{Z}\right)^\times\).
\(n\) | \(83\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 5.65685i | − 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −32.0000 | −0.500000 | ||||||||
\(5\) | 85.6833i | 0.685467i | 0.939433 | + | 0.342733i | \(0.111353\pi\) | ||||
−0.939433 | + | 0.342733i | \(0.888647\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −564.058 | −1.64448 | −0.822242 | − | 0.569138i | \(-0.807277\pi\) | ||||
−0.822242 | + | 0.569138i | \(0.807277\pi\) | |||||||
\(8\) | 181.019i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 484.698 | 0.484698 | ||||||||
\(11\) | 1453.72i | 1.09220i | 0.837718 | + | 0.546102i | \(0.183889\pi\) | ||||
−0.837718 | + | 0.546102i | \(0.816111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 840.623 | 0.382623 | 0.191312 | − | 0.981529i | \(-0.438726\pi\) | ||||
0.191312 | + | 0.981529i | \(0.438726\pi\) | |||||||
\(14\) | 3190.79i | 1.16283i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1024.00 | 0.250000 | ||||||||
\(17\) | − 5090.31i | − 1.03609i | −0.855353 | − | 0.518045i | \(-0.826660\pi\) | ||||
0.855353 | − | 0.518045i | \(-0.173340\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6688.88 | −0.975198 | −0.487599 | − | 0.873068i | \(-0.662127\pi\) | ||||
−0.487599 | + | 0.873068i | \(0.662127\pi\) | |||||||
\(20\) | − 2741.87i | − 0.342733i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 8223.51 | 0.772305 | ||||||||
\(23\) | − 11850.8i | − 0.974012i | −0.873399 | − | 0.487006i | \(-0.838089\pi\) | ||||
0.873399 | − | 0.487006i | \(-0.161911\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8283.37 | 0.530136 | ||||||||
\(26\) | − 4755.28i | − 0.270555i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 18049.9 | 0.822242 | ||||||||
\(29\) | 15431.8i | 0.632735i | 0.948637 | + | 0.316367i | \(0.102463\pi\) | ||||
−0.948637 | + | 0.316367i | \(0.897537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33082.2 | 1.11048 | 0.555239 | − | 0.831691i | \(-0.312627\pi\) | ||||
0.555239 | + | 0.831691i | \(0.312627\pi\) | |||||||
\(32\) | − 5792.62i | − 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −28795.1 | −0.732626 | ||||||||
\(35\) | − 48330.3i | − 1.12724i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 84382.4 | 1.66589 | 0.832945 | − | 0.553355i | \(-0.186653\pi\) | ||||
0.832945 | + | 0.553355i | \(0.186653\pi\) | |||||||
\(38\) | 37838.0i | 0.689569i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −15510.3 | −0.242349 | ||||||||
\(41\) | − 16156.3i | − 0.234418i | −0.993107 | − | 0.117209i | \(-0.962605\pi\) | ||||
0.993107 | − | 0.117209i | \(-0.0373948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −66110.9 | −0.831510 | −0.415755 | − | 0.909477i | \(-0.636483\pi\) | ||||
−0.415755 | + | 0.909477i | \(0.636483\pi\) | |||||||
\(44\) | − 46519.2i | − 0.546102i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −67038.2 | −0.688730 | ||||||||
\(47\) | − 159085.i | − 1.53227i | −0.642681 | − | 0.766134i | \(-0.722178\pi\) | ||||
0.642681 | − | 0.766134i | \(-0.277822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 200512. | 1.70433 | ||||||||
\(50\) | − 46857.8i | − 0.374862i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −26899.9 | −0.191312 | ||||||||
\(53\) | − 150118.i | − 1.00834i | −0.863606 | − | 0.504168i | \(-0.831799\pi\) | ||||
0.863606 | − | 0.504168i | \(-0.168201\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −124560. | −0.748670 | ||||||||
\(56\) | − 102105.i | − 0.581413i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 87295.3 | 0.447411 | ||||||||
\(59\) | − 192083.i | − 0.935263i | −0.883924 | − | 0.467631i | \(-0.845108\pi\) | ||||
0.883924 | − | 0.467631i | \(-0.154892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −382488. | −1.68511 | −0.842554 | − | 0.538611i | \(-0.818949\pi\) | ||||
−0.842554 | + | 0.538611i | \(0.818949\pi\) | |||||||
\(62\) | − 187141.i | − 0.785226i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −32768.0 | −0.125000 | ||||||||
\(65\) | 72027.4i | 0.262275i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 237549. | 0.789820 | 0.394910 | − | 0.918720i | \(-0.370776\pi\) | ||||
0.394910 | + | 0.918720i | \(0.370776\pi\) | |||||||
\(68\) | 162890.i | 0.518045i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −273398. | −0.797078 | ||||||||
\(71\) | 688359.i | 1.92327i | 0.274334 | + | 0.961635i | \(0.411543\pi\) | ||||
−0.274334 | + | 0.961635i | \(0.588457\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 379634. | 0.975880 | 0.487940 | − | 0.872877i | \(-0.337749\pi\) | ||||
0.487940 | + | 0.872877i | \(0.337749\pi\) | |||||||
\(74\) | − 477339.i | − 1.17796i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 214044. | 0.487599 | ||||||||
\(77\) | − 819985.i | − 1.79611i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −770991. | −1.56375 | −0.781877 | − | 0.623433i | \(-0.785737\pi\) | ||||
−0.781877 | + | 0.623433i | \(0.785737\pi\) | |||||||
\(80\) | 87739.7i | 0.171367i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −91394.1 | −0.165759 | ||||||||
\(83\) | − 755560.i | − 1.32140i | −0.750649 | − | 0.660701i | \(-0.770259\pi\) | ||||
0.750649 | − | 0.660701i | \(-0.229741\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 436155. | 0.710205 | ||||||||
\(86\) | 373980.i | 0.587967i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −263152. | −0.386153 | ||||||||
\(89\) | − 871169.i | − 1.23575i | −0.786274 | − | 0.617877i | \(-0.787993\pi\) | ||||
0.786274 | − | 0.617877i | \(-0.212007\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −474160. | −0.629217 | ||||||||
\(92\) | 379226.i | 0.487006i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −899918. | −1.08348 | ||||||||
\(95\) | − 573125.i | − 0.668465i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.21326e6 | 1.32935 | 0.664675 | − | 0.747133i | \(-0.268570\pi\) | ||||
0.664675 | + | 0.747133i | \(0.268570\pi\) | |||||||
\(98\) | − 1.13427e6i | − 1.20514i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −265068. | −0.265068 | ||||||||
\(101\) | − 798017.i | − 0.774547i | −0.921965 | − | 0.387274i | \(-0.873417\pi\) | ||||
0.921965 | − | 0.387274i | \(-0.126583\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 743896. | 0.680770 | 0.340385 | − | 0.940286i | \(-0.389443\pi\) | ||||
0.340385 | + | 0.940286i | \(0.389443\pi\) | |||||||
\(104\) | 152169.i | 0.135278i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −849196. | −0.713001 | ||||||||
\(107\) | 1.02594e6i | 0.837474i | 0.908108 | + | 0.418737i | \(0.137527\pi\) | ||||
−0.908108 | + | 0.418737i | \(0.862473\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.09355e6 | 0.844421 | 0.422210 | − | 0.906498i | \(-0.361254\pi\) | ||||
0.422210 | + | 0.906498i | \(0.361254\pi\) | |||||||
\(110\) | 704617.i | 0.529389i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −577595. | −0.411121 | ||||||||
\(113\) | 364476.i | 0.252600i | 0.991992 | + | 0.126300i | \(0.0403102\pi\) | ||||
−0.991992 | + | 0.126300i | \(0.959690\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.01542e6 | 0.667652 | ||||||||
\(116\) | − 493817.i | − 0.316367i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.08659e6 | −0.661330 | ||||||||
\(119\) | 2.87123e6i | 1.70383i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −341754. | −0.192911 | ||||||||
\(122\) | 2.16368e6i | 1.19155i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.05863e6 | −0.555239 | ||||||||
\(125\) | 2.04855e6i | 1.04886i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.27969e6 | 1.11292 | 0.556461 | − | 0.830874i | \(-0.312159\pi\) | ||||
0.556461 | + | 0.830874i | \(0.312159\pi\) | |||||||
\(128\) | 185364.i | 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 407448. | 0.185457 | ||||||||
\(131\) | − 152500.i | − 0.0678351i | −0.999425 | − | 0.0339176i | \(-0.989202\pi\) | ||||
0.999425 | − | 0.0339176i | \(-0.0107984\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.77292e6 | 1.60370 | ||||||||
\(134\) | − 1.34378e6i | − 0.558487i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 921444. | 0.366313 | ||||||||
\(137\) | 3.05911e6i | 1.18969i | 0.803841 | + | 0.594844i | \(0.202786\pi\) | ||||
−0.803841 | + | 0.594844i | \(0.797214\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 622018. | 0.231611 | 0.115805 | − | 0.993272i | \(-0.463055\pi\) | ||||
0.115805 | + | 0.993272i | \(0.463055\pi\) | |||||||
\(140\) | 1.54657e6i | 0.563619i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.89395e6 | 1.35996 | ||||||||
\(143\) | 1.22203e6i | 0.417903i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.32225e6 | −0.433719 | ||||||||
\(146\) | − 2.14753e6i | − 0.690051i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.70024e6 | −0.832945 | ||||||||
\(149\) | − 3.82058e6i | − 1.15497i | −0.816402 | − | 0.577484i | \(-0.804034\pi\) | ||||
0.816402 | − | 0.577484i | \(-0.195966\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.85930e6 | 1.41138 | 0.705688 | − | 0.708522i | \(-0.250638\pi\) | ||||
0.705688 | + | 0.708522i | \(0.250638\pi\) | |||||||
\(152\) | − 1.21082e6i | − 0.344784i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.63853e6 | −1.27004 | ||||||||
\(155\) | 2.83459e6i | 0.761195i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.39974e6 | −1.39532 | −0.697660 | − | 0.716429i | \(-0.745775\pi\) | ||||
−0.697660 | + | 0.716429i | \(0.745775\pi\) | |||||||
\(158\) | 4.36139e6i | 1.10574i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 496331. | 0.121175 | ||||||||
\(161\) | 6.68454e6i | 1.60175i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.13788e6 | −0.262744 | −0.131372 | − | 0.991333i | \(-0.541938\pi\) | ||||
−0.131372 | + | 0.991333i | \(0.541938\pi\) | |||||||
\(164\) | 517003.i | 0.117209i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.27409e6 | −0.934372 | ||||||||
\(167\) | 1.53256e6i | 0.329055i | 0.986373 | + | 0.164527i | \(0.0526099\pi\) | ||||
−0.986373 | + | 0.164527i | \(0.947390\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.12016e6 | −0.853600 | ||||||||
\(170\) | − 2.46726e6i | − 0.502191i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.11555e6 | 0.415755 | ||||||||
\(173\) | − 6.37589e6i | − 1.23141i | −0.787977 | − | 0.615704i | \(-0.788872\pi\) | ||||
0.787977 | − | 0.615704i | \(-0.211128\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.67230e6 | −0.871799 | ||||||||
\(176\) | 1.48861e6i | 0.273051i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.92808e6 | −0.873811 | ||||||||
\(179\) | − 719446.i | − 0.125441i | −0.998031 | − | 0.0627204i | \(-0.980022\pi\) | ||||
0.998031 | − | 0.0627204i | \(-0.0199776\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.41982e6 | 1.25129 | 0.625645 | − | 0.780108i | \(-0.284836\pi\) | ||||
0.625645 | + | 0.780108i | \(0.284836\pi\) | |||||||
\(182\) | 2.68225e6i | 0.444924i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.14522e6 | 0.344365 | ||||||||
\(185\) | 7.23016e6i | 1.14191i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.39991e6 | 1.13162 | ||||||||
\(188\) | 5.09071e6i | 0.766134i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.24209e6 | −0.472676 | ||||||||
\(191\) | 2.04203e6i | 0.293063i | 0.989206 | + | 0.146532i | \(0.0468110\pi\) | ||||
−0.989206 | + | 0.146532i | \(0.953189\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.20898e6 | 0.585471 | 0.292735 | − | 0.956194i | \(-0.405435\pi\) | ||||
0.292735 | + | 0.956194i | \(0.405435\pi\) | |||||||
\(194\) | − 6.86325e6i | − 0.939992i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.41639e6 | −0.852163 | ||||||||
\(197\) | 1.06745e7i | 1.39621i | 0.715995 | + | 0.698105i | \(0.245973\pi\) | ||||
−0.715995 | + | 0.698105i | \(0.754027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.53584e6 | −0.448676 | −0.224338 | − | 0.974511i | \(-0.572022\pi\) | ||||
−0.224338 | + | 0.974511i | \(0.572022\pi\) | |||||||
\(200\) | 1.49945e6i | 0.187431i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.51427e6 | −0.547688 | ||||||||
\(203\) | − 8.70441e6i | − 1.04052i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.38433e6 | 0.160686 | ||||||||
\(206\) | − 4.20811e6i | − 0.481377i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 860798. | 0.0956558 | ||||||||
\(209\) | − 9.72379e6i | − 1.06512i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.20482e6 | 0.766965 | 0.383483 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383483 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(212\) | 4.80378e6i | 0.504168i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.80360e6 | 0.592184 | ||||||||
\(215\) | − 5.66460e6i | − 0.569973i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.86603e7 | −1.82616 | ||||||||
\(218\) | − 6.18605e6i | − 0.597096i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.98592e6 | 0.374335 | ||||||||
\(221\) | − 4.27903e6i | − 0.396432i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.30991e7 | −1.18121 | −0.590603 | − | 0.806962i | \(-0.701110\pi\) | ||||
−0.590603 | + | 0.806962i | \(0.701110\pi\) | |||||||
\(224\) | 3.26737e6i | 0.290706i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.06179e6 | 0.178615 | ||||||||
\(227\) | − 3.62456e6i | − 0.309869i | −0.987925 | − | 0.154934i | \(-0.950483\pi\) | ||||
0.987925 | − | 0.154934i | \(-0.0495166\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.32984e7 | 1.10737 | 0.553683 | − | 0.832727i | \(-0.313222\pi\) | ||||
0.553683 | + | 0.832727i | \(0.313222\pi\) | |||||||
\(230\) | − 5.74406e6i | − 0.472102i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.79345e6 | −0.223706 | ||||||||
\(233\) | − 2.32921e7i | − 1.84137i | −0.390308 | − | 0.920684i | \(-0.627631\pi\) | ||||
0.390308 | − | 0.920684i | \(-0.372369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.36309e7 | 1.05032 | ||||||||
\(236\) | 6.14666e6i | 0.467631i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.62421e7 | 1.20479 | ||||||||
\(239\) | − 1.61394e7i | − 1.18220i | −0.806597 | − | 0.591102i | \(-0.798693\pi\) | ||||
0.806597 | − | 0.591102i | \(-0.201307\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.11953e7 | −0.799809 | −0.399904 | − | 0.916557i | \(-0.630957\pi\) | ||||
−0.399904 | + | 0.916557i | \(0.630957\pi\) | |||||||
\(242\) | 1.93325e6i | 0.136409i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.22396e7 | 0.842554 | ||||||||
\(245\) | 1.71806e7i | 1.16826i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.62283e6 | −0.373133 | ||||||||
\(248\) | 5.98852e6i | 0.392613i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.15883e7 | 0.741654 | ||||||||
\(251\) | − 1.76943e7i | − 1.11896i | −0.828845 | − | 0.559478i | \(-0.811002\pi\) | ||||
0.828845 | − | 0.559478i | \(-0.188998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.72278e7 | 1.06382 | ||||||||
\(254\) | − 1.28959e7i | − 0.786954i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.04858e6 | 0.0625000 | ||||||||
\(257\) | 2.81347e7i | 1.65746i | 0.559648 | + | 0.828730i | \(0.310936\pi\) | ||||
−0.559648 | + | 0.828730i | \(0.689064\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.75965e7 | −2.73953 | ||||||||
\(260\) | − 2.30488e6i | − 0.131138i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −862668. | −0.0479667 | ||||||||
\(263\) | − 2.71927e6i | − 0.149480i | −0.997203 | − | 0.0747402i | \(-0.976187\pi\) | ||||
0.997203 | − | 0.0747402i | \(-0.0238128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.28626e7 | 0.691180 | ||||||||
\(266\) | − 2.13428e7i | − 1.13398i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.60156e6 | −0.394910 | ||||||||
\(269\) | − 2.04116e7i | − 1.04863i | −0.851525 | − | 0.524314i | \(-0.824322\pi\) | ||||
0.851525 | − | 0.524314i | \(-0.175678\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.14647e7 | −0.576044 | −0.288022 | − | 0.957624i | \(-0.592998\pi\) | ||||
−0.288022 | + | 0.957624i | \(0.592998\pi\) | |||||||
\(272\) | − 5.21248e6i | − 0.259022i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.73049e7 | 0.841237 | ||||||||
\(275\) | 1.20417e7i | 0.579017i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.12684e7 | 1.00068 | 0.500340 | − | 0.865829i | \(-0.333208\pi\) | ||||
0.500340 | + | 0.865829i | \(0.333208\pi\) | |||||||
\(278\) | − 3.51866e6i | − 0.163773i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 8.74873e6 | 0.398539 | ||||||||
\(281\) | − 1.50482e7i | − 0.678213i | −0.940748 | − | 0.339107i | \(-0.889875\pi\) | ||||
0.940748 | − | 0.339107i | \(-0.110125\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.70775e7 | −0.753470 | −0.376735 | − | 0.926321i | \(-0.622953\pi\) | ||||
−0.376735 | + | 0.926321i | \(0.622953\pi\) | |||||||
\(284\) | − 2.20275e7i | − 0.961635i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.91287e6 | 0.295502 | ||||||||
\(287\) | 9.11311e6i | 0.385497i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.77368e6 | −0.0734822 | ||||||||
\(290\) | 7.47975e6i | 0.306685i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.21483e7 | −0.487940 | ||||||||
\(293\) | − 2.81002e7i | − 1.11714i | −0.829458 | − | 0.558569i | \(-0.811351\pi\) | ||||
0.829458 | − | 0.558569i | \(-0.188649\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.64583e7 | 0.641091 | ||||||||
\(296\) | 1.52748e7i | 0.588981i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.16125e7 | −0.816686 | ||||||||
\(299\) | − 9.96205e6i | − 0.372679i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.72904e7 | 1.36740 | ||||||||
\(302\) | − 2.74884e7i | − 0.997994i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.84941e6 | −0.243799 | ||||||||
\(305\) | − 3.27728e7i | − 1.15509i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.48453e7 | −0.858676 | −0.429338 | − | 0.903144i | \(-0.641253\pi\) | ||||
−0.429338 | + | 0.903144i | \(0.641253\pi\) | |||||||
\(308\) | 2.62395e7i | 0.898056i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.60349e7 | 0.538246 | ||||||||
\(311\) | 2.54535e7i | 0.846188i | 0.906086 | + | 0.423094i | \(0.139056\pi\) | ||||
−0.906086 | + | 0.423094i | \(0.860944\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.80377e7 | −0.588233 | −0.294116 | − | 0.955770i | \(-0.595025\pi\) | ||||
−0.294116 | + | 0.955770i | \(0.595025\pi\) | |||||||
\(314\) | 3.05455e7i | 0.986641i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.46717e7 | 0.781877 | ||||||||
\(317\) | − 2.48387e7i | − 0.779744i | −0.920869 | − | 0.389872i | \(-0.872519\pi\) | ||||
0.920869 | − | 0.389872i | \(-0.127481\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.24335e7 | −0.691076 | ||||||||
\(320\) | − 2.80767e6i | − 0.0856833i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.78134e7 | 1.13261 | ||||||||
\(323\) | 3.40485e7i | 1.01039i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.96319e6 | 0.202842 | ||||||||
\(326\) | 6.43680e6i | 0.185788i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.92461e6 | 0.0828794 | ||||||||
\(329\) | 8.97329e7i | 2.51979i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.19747e7 | −0.881702 | −0.440851 | − | 0.897580i | \(-0.645323\pi\) | ||||
−0.440851 | + | 0.897580i | \(0.645323\pi\) | |||||||
\(332\) | 2.41779e7i | 0.660701i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 8.66947e6 | 0.232677 | ||||||||
\(335\) | 2.03540e7i | 0.541395i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.03435e7 | −1.83795 | −0.918977 | − | 0.394312i | \(-0.870983\pi\) | ||||
−0.918977 | + | 0.394312i | \(0.870983\pi\) | |||||||
\(338\) | 2.33072e7i | 0.603586i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.39569e7 | −0.355102 | ||||||||
\(341\) | 4.80924e7i | 1.21287i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.67397e7 | −1.15825 | ||||||||
\(344\) | − 1.19673e7i | − 0.293983i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.60675e7 | −0.870737 | ||||||||
\(347\) | − 4.91231e7i | − 1.17570i | −0.808969 | − | 0.587851i | \(-0.799974\pi\) | ||||
0.808969 | − | 0.587851i | \(-0.200026\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.49390e7 | 0.821928 | 0.410964 | − | 0.911652i | \(-0.365192\pi\) | ||||
0.410964 | + | 0.911652i | \(0.365192\pi\) | |||||||
\(350\) | 2.64305e7i | 0.616455i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.42087e6 | 0.193076 | ||||||||
\(353\) | 7.49168e6i | 0.170316i | 0.996367 | + | 0.0851579i | \(0.0271395\pi\) | ||||
−0.996367 | + | 0.0851579i | \(0.972861\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.89809e7 | −1.31834 | ||||||||
\(356\) | 2.78774e7i | 0.617877i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.06980e6 | −0.0887001 | ||||||||
\(359\) | − 3.14246e7i | − 0.679183i | −0.940573 | − | 0.339592i | \(-0.889711\pi\) | ||||
0.940573 | − | 0.339592i | \(-0.110289\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.30477e6 | −0.0489898 | ||||||||
\(362\) | − 4.19729e7i | − 0.884795i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.51731e7 | 0.314609 | ||||||||
\(365\) | 3.25283e7i | 0.668933i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.63284e7 | 0.937237 | 0.468618 | − | 0.883401i | \(-0.344752\pi\) | ||||
0.468618 | + | 0.883401i | \(0.344752\pi\) | |||||||
\(368\) | − 1.21352e7i | − 0.243503i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.09000e7 | 0.807454 | ||||||||
\(371\) | 8.46752e7i | 1.65819i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.28264e6 | −0.140334 | −0.0701669 | − | 0.997535i | \(-0.522353\pi\) | ||||
−0.0701669 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(374\) | − 4.18602e7i | − 0.800178i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.87974e7 | 0.541738 | ||||||||
\(377\) | 1.29723e7i | 0.242099i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.01546e7 | −1.10497 | −0.552486 | − | 0.833522i | \(-0.686321\pi\) | ||||
−0.552486 | + | 0.833522i | \(0.686321\pi\) | |||||||
\(380\) | 1.83400e7i | 0.334233i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.15515e7 | 0.207227 | ||||||||
\(383\) | − 8.58659e6i | − 0.152836i | −0.997076 | − | 0.0764178i | \(-0.975652\pi\) | ||||
0.997076 | − | 0.0764178i | \(-0.0243483\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.02590e7 | 1.23118 | ||||||||
\(386\) | − 2.38096e7i | − 0.413990i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.88244e7 | −0.664675 | ||||||||
\(389\) | − 7.66723e7i | − 1.30254i | −0.758848 | − | 0.651268i | \(-0.774237\pi\) | ||||
0.758848 | − | 0.651268i | \(-0.225763\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.03242e7 | −1.00916 | ||||||||
\(392\) | 3.62966e7i | 0.602570i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.03844e7 | 0.987270 | ||||||||
\(395\) | − 6.60611e7i | − 1.07190i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.57190e7 | 1.05031 | 0.525157 | − | 0.851005i | \(-0.324006\pi\) | ||||
0.525157 | + | 0.851005i | \(0.324006\pi\) | |||||||
\(398\) | 2.00017e7i | 0.317262i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.48217e6 | 0.132534 | ||||||||
\(401\) | 1.62827e7i | 0.252519i | 0.991997 | + | 0.126260i | \(0.0402972\pi\) | ||||
−0.991997 | + | 0.126260i | \(0.959703\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.78097e7 | 0.424894 | ||||||||
\(404\) | 2.55365e7i | 0.387274i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.92396e7 | −0.735760 | ||||||||
\(407\) | 1.22669e8i | 1.81949i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −4.61848e7 | −0.675039 | −0.337519 | − | 0.941319i | \(-0.609588\pi\) | ||||
−0.337519 | + | 0.941319i | \(0.609588\pi\) | |||||||
\(410\) | − 7.83095e6i | − 0.113622i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.38047e7 | −0.340385 | ||||||||
\(413\) | 1.08346e8i | 1.53802i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.47389e7 | 0.905777 | ||||||||
\(416\) | − 4.86941e6i | − 0.0676389i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.50061e7 | −0.753150 | ||||||||
\(419\) | − 2.23089e7i | − 0.303274i | −0.988436 | − | 0.151637i | \(-0.951545\pi\) | ||||
0.988436 | − | 0.151637i | \(-0.0484545\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.79778e6 | −0.0642974 | −0.0321487 | − | 0.999483i | \(-0.510235\pi\) | ||||
−0.0321487 | + | 0.999483i | \(0.510235\pi\) | |||||||
\(422\) | − 4.07566e7i | − 0.542326i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.71743e7 | 0.356501 | ||||||||
\(425\) | − 4.21649e7i | − 0.549268i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.15745e8 | 2.77113 | ||||||||
\(428\) | − 3.28301e7i | − 0.418737i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.20438e7 | −0.403031 | ||||||||
\(431\) | 1.04853e8i | 1.30963i | 0.755791 | + | 0.654813i | \(0.227253\pi\) | ||||
−0.755791 | + | 0.654813i | \(0.772747\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.10290e8 | 1.35854 | 0.679270 | − | 0.733889i | \(-0.262297\pi\) | ||||
0.679270 | + | 0.733889i | \(0.262297\pi\) | |||||||
\(434\) | 1.05559e8i | 1.29129i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.49936e7 | −0.422210 | ||||||||
\(437\) | 7.92686e7i | 0.949854i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.35146e6 | −0.110531 | −0.0552657 | − | 0.998472i | \(-0.517601\pi\) | ||||
−0.0552657 | + | 0.998472i | \(0.517601\pi\) | |||||||
\(440\) | − 2.25478e7i | − 0.264695i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.42059e7 | −0.280320 | ||||||||
\(443\) | 1.94364e7i | 0.223566i | 0.993733 | + | 0.111783i | \(0.0356561\pi\) | ||||
−0.993733 | + | 0.111783i | \(0.964344\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.46446e7 | 0.847069 | ||||||||
\(446\) | 7.40995e7i | 0.835239i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.84830e7 | 0.205560 | ||||||||
\(449\) | − 1.24211e8i | − 1.37221i | −0.727503 | − | 0.686105i | \(-0.759319\pi\) | ||||
0.727503 | − | 0.686105i | \(-0.240681\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.34869e7 | 0.256033 | ||||||||
\(452\) | − 1.16632e7i | − 0.126300i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.05036e7 | −0.219110 | ||||||||
\(455\) | − 4.06276e7i | − 0.431307i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.75216e7 | −0.183580 | −0.0917902 | − | 0.995778i | \(-0.529259\pi\) | ||||
−0.0917902 | + | 0.995778i | \(0.529259\pi\) | |||||||
\(458\) | − 7.52268e7i | − 0.783026i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.24933e7 | −0.333826 | ||||||||
\(461\) | − 3.53923e7i | − 0.361249i | −0.983552 | − | 0.180624i | \(-0.942188\pi\) | ||||
0.983552 | − | 0.180624i | \(-0.0578118\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.08613e6 | −0.0310936 | −0.0155468 | − | 0.999879i | \(-0.504949\pi\) | ||||
−0.0155468 | + | 0.999879i | \(0.504949\pi\) | |||||||
\(464\) | 1.58021e7i | 0.158184i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.31760e8 | −1.30204 | ||||||||
\(467\) | − 1.08045e8i | − 1.06085i | −0.847731 | − | 0.530427i | \(-0.822032\pi\) | ||||
0.847731 | − | 0.530427i | \(-0.177968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.33991e8 | −1.29885 | ||||||||
\(470\) | − 7.71080e7i | − 0.742687i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.47708e7 | 0.330665 | ||||||||
\(473\) | − 9.61070e7i | − 0.908179i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.54065e7 | −0.516987 | ||||||||
\(476\) | − 9.18793e7i | − 0.851916i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −9.12980e7 | −0.835944 | ||||||||
\(479\) | 1.31304e8i | 1.19474i | 0.801967 | + | 0.597368i | \(0.203787\pi\) | ||||
−0.801967 | + | 0.597368i | \(0.796213\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.09338e7 | 0.637408 | ||||||||
\(482\) | 6.33304e7i | 0.565550i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.09361e7 | 0.0964555 | ||||||||
\(485\) | 1.03956e8i | 0.911225i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.65915e7 | −0.403385 | −0.201692 | − | 0.979449i | \(-0.564644\pi\) | ||||
−0.201692 | + | 0.979449i | \(0.564644\pi\) | |||||||
\(488\) | − 6.92377e7i | − 0.595776i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.71879e7 | 0.826083 | ||||||||
\(491\) | − 2.19500e8i | − 1.85435i | −0.374632 | − | 0.927173i | \(-0.622231\pi\) | ||||
0.374632 | − | 0.927173i | \(-0.377769\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.85525e7 | 0.655570 | ||||||||
\(494\) | 3.18075e7i | 0.263845i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.38762e7 | 0.277619 | ||||||||
\(497\) | − 3.88274e8i | − 3.16278i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.33446e8 | −1.07400 | −0.537001 | − | 0.843581i | \(-0.680443\pi\) | ||||
−0.537001 | + | 0.843581i | \(0.680443\pi\) | |||||||
\(500\) | − 6.55535e7i | − 0.524428i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.00094e8 | −0.791221 | ||||||||
\(503\) | − 1.81087e7i | − 0.142293i | −0.997466 | − | 0.0711463i | \(-0.977334\pi\) | ||||
0.997466 | − | 0.0711463i | \(-0.0226657\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.83767e7 | 0.530926 | ||||||||
\(506\) | − 9.74551e7i | − 0.752234i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.29501e7 | −0.556461 | ||||||||
\(509\) | − 1.34559e8i | − 1.02037i | −0.860064 | − | 0.510187i | \(-0.829576\pi\) | ||||
0.860064 | − | 0.510187i | \(-0.170424\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.14135e8 | −1.60482 | ||||||||
\(512\) | − 5.93164e6i | − 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.59154e8 | 1.17200 | ||||||||
\(515\) | 6.37395e7i | 0.466645i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.31265e8 | 1.67355 | ||||||||
\(518\) | 2.69247e8i | 1.93714i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.30383e7 | −0.0927283 | ||||||||
\(521\) | 6.97595e7i | 0.493276i | 0.969108 | + | 0.246638i | \(0.0793259\pi\) | ||||
−0.969108 | + | 0.246638i | \(0.920674\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.49134e7 | −0.104249 | −0.0521245 | − | 0.998641i | \(-0.516599\pi\) | ||||
−0.0521245 | + | 0.998641i | \(0.516599\pi\) | |||||||
\(524\) | 4.87999e6i | 0.0339176i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.53825e7 | −0.105699 | ||||||||
\(527\) | − 1.68399e8i | − 1.15055i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.59444e6 | 0.0513013 | ||||||||
\(530\) | − 7.27619e7i | − 0.488738i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.20733e8 | −0.801848 | ||||||||
\(533\) | − 1.35814e7i | − 0.0896938i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −8.79061e7 | −0.574061 | ||||||||
\(536\) | 4.30009e7i | 0.279244i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.15466e8 | −0.741492 | ||||||||
\(539\) | 2.91490e8i | 1.86147i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00053e8 | 1.26344 | 0.631718 | − | 0.775198i | \(-0.282350\pi\) | ||||
0.631718 | + | 0.775198i | \(0.282350\pi\) | |||||||
\(542\) | 6.48542e7i | 0.407324i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.94862e7 | −0.183157 | ||||||||
\(545\) | 9.36989e7i | 0.578822i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.59236e8 | −1.58392 | −0.791962 | − | 0.610571i | \(-0.790940\pi\) | ||||
−0.791962 | + | 0.610571i | \(0.790940\pi\) | |||||||
\(548\) | − 9.78915e7i | − 0.594844i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 6.81183e7 | 0.409427 | ||||||||
\(551\) | − 1.03221e8i | − 0.617041i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.34884e8 | 2.57157 | ||||||||
\(554\) | − 1.20312e8i | − 0.707587i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.99046e7 | −0.115805 | ||||||||
\(557\) | − 2.08528e8i | − 1.20670i | −0.797477 | − | 0.603349i | \(-0.793833\pi\) | ||||
0.797477 | − | 0.603349i | \(-0.206167\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.55743e7 | −0.318155 | ||||||||
\(560\) | − 4.94903e7i | − 0.281810i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.51256e7 | −0.479569 | ||||||||
\(563\) | − 3.10432e8i | − 1.73957i | −0.493431 | − | 0.869785i | \(-0.664258\pi\) | ||||
0.493431 | − | 0.869785i | \(-0.335742\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.12295e7 | −0.173149 | ||||||||
\(566\) | 9.66051e7i | 0.532783i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −1.24606e8 | −0.679978 | ||||||||
\(569\) | 1.85571e8i | 1.00734i | 0.863897 | + | 0.503668i | \(0.168016\pi\) | ||||
−0.863897 | + | 0.503668i | \(0.831984\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.04718e7 | −0.432250 | −0.216125 | − | 0.976366i | \(-0.569342\pi\) | ||||
−0.216125 | + | 0.976366i | \(0.569342\pi\) | |||||||
\(572\) | − 3.91051e7i | − 0.208951i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.15515e7 | 0.272588 | ||||||||
\(575\) | − 9.81645e7i | − 0.516358i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8.84457e7 | 0.460415 | 0.230207 | − | 0.973142i | \(-0.426060\pi\) | ||||
0.230207 | + | 0.973142i | \(0.426060\pi\) | |||||||
\(578\) | 1.00335e7i | 0.0519597i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.23119e7 | 0.216859 | ||||||||
\(581\) | 4.26180e8i | 2.17302i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.18230e8 | 1.10131 | ||||||||
\(584\) | 6.87211e7i | 0.345026i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.58959e8 | −0.789936 | ||||||||
\(587\) | − 3.13917e8i | − 1.55203i | −0.630715 | − | 0.776015i | \(-0.717238\pi\) | ||||
0.630715 | − | 0.776015i | \(-0.282762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.21283e8 | −1.08293 | ||||||||
\(590\) | − 9.31024e7i | − 0.453320i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.64075e7 | 0.416473 | ||||||||
\(593\) | 3.05107e8i | 1.46315i | 0.681762 | + | 0.731574i | \(0.261214\pi\) | ||||
−0.681762 | + | 0.731574i | \(0.738786\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.46016e8 | −1.16792 | ||||||||
\(596\) | 1.22258e8i | 0.577484i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.63539e7 | −0.263524 | ||||||||
\(599\) | 6.17896e7i | 0.287498i | 0.989614 | + | 0.143749i | \(0.0459158\pi\) | ||||
−0.989614 | + | 0.143749i | \(0.954084\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.79901e8 | 1.75004 | 0.875019 | − | 0.484089i | \(-0.160849\pi\) | ||||
0.875019 | + | 0.484089i | \(0.160849\pi\) | |||||||
\(602\) | − 2.10946e8i | − 0.966901i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.55498e8 | −0.705688 | ||||||||
\(605\) | − 2.92826e7i | − 0.132234i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.41765e7 | 0.242239 | 0.121120 | − | 0.992638i | \(-0.461352\pi\) | ||||
0.121120 | + | 0.992638i | \(0.461352\pi\) | |||||||
\(608\) | 3.87461e7i | 0.172392i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.85391e8 | −0.816769 | ||||||||
\(611\) | − 1.33730e8i | − 0.586281i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.26874e7 | 0.185318 | 0.0926592 | − | 0.995698i | \(-0.470463\pi\) | ||||
0.0926592 | + | 0.995698i | \(0.470463\pi\) | |||||||
\(614\) | 1.40546e8i | 0.607176i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.48433e8 | 0.635022 | ||||||||
\(617\) | 5.20036e7i | 0.221400i | 0.993854 | + | 0.110700i | \(0.0353093\pi\) | ||||
−0.993854 | + | 0.110700i | \(0.964691\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.47486e7 | −0.272997 | −0.136499 | − | 0.990640i | \(-0.543585\pi\) | ||||
−0.136499 | + | 0.990640i | \(0.543585\pi\) | |||||||
\(620\) | − 9.07070e7i | − 0.380597i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.43987e8 | 0.598345 | ||||||||
\(623\) | 4.91390e8i | 2.03218i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −4.60988e7 | −0.188821 | ||||||||
\(626\) | 1.02037e8i | 0.415944i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.72792e8 | 0.697660 | ||||||||
\(629\) | − 4.29532e8i | − 1.72601i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.62024e7 | 0.183898 | 0.0919489 | − | 0.995764i | \(-0.470690\pi\) | ||||
0.0919489 | + | 0.995764i | \(0.470690\pi\) | |||||||
\(632\) | − 1.39564e8i | − 0.552870i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.40509e8 | −0.551362 | ||||||||
\(635\) | 1.95331e8i | 0.762871i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.68555e8 | 0.652114 | ||||||||
\(638\) | 1.26903e8i | 0.488665i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.58826e7 | −0.0605873 | ||||||||
\(641\) | 2.58548e8i | 0.981674i | 0.871251 | + | 0.490837i | \(0.163309\pi\) | ||||
−0.871251 | + | 0.490837i | \(0.836691\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.24134e8 | −0.843090 | −0.421545 | − | 0.906808i | \(-0.638512\pi\) | ||||
−0.421545 | + | 0.906808i | \(0.638512\pi\) | |||||||
\(644\) | − 2.13905e8i | − 0.800873i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.92607e8 | 0.714455 | ||||||||
\(647\) | 2.73001e8i | 1.00798i | 0.863709 | + | 0.503990i | \(0.168135\pi\) | ||||
−0.863709 | + | 0.503990i | \(0.831865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.79236e8 | 1.02150 | ||||||||
\(650\) | − 3.93898e7i | − 0.143431i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.64120e7 | 0.131372 | ||||||||
\(653\) | 4.93887e8i | 1.77373i | 0.462025 | + | 0.886867i | \(0.347123\pi\) | ||||
−0.462025 | + | 0.886867i | \(0.652877\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.30667e7 | 0.0464987 | ||||||||
\(656\) | − 1.65441e7i | − 0.0586046i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.07606e8 | 1.78176 | ||||||||
\(659\) | 3.51067e8i | 1.22669i | 0.789817 | + | 0.613343i | \(0.210176\pi\) | ||||
−0.789817 | + | 0.613343i | \(0.789824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.15905e7 | −0.0401326 | −0.0200663 | − | 0.999799i | \(-0.506388\pi\) | ||||
−0.0200663 | + | 0.999799i | \(0.506388\pi\) | |||||||
\(662\) | 1.80876e8i | 0.623458i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.36771e8 | 0.467186 | ||||||||
\(665\) | 3.23276e8i | 1.09928i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.82879e8 | 0.616291 | ||||||||
\(668\) | − 4.90419e7i | − 0.164527i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.15139e8 | 0.382824 | ||||||||
\(671\) | − 5.56032e8i | − 1.84048i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.25203e8 | −0.410742 | −0.205371 | − | 0.978684i | \(-0.565840\pi\) | ||||
−0.205371 | + | 0.978684i | \(0.565840\pi\) | |||||||
\(674\) | 3.97923e8i | 1.29963i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.31845e8 | 0.426800 | ||||||||
\(677\) | − 1.35196e8i | − 0.435709i | −0.975981 | − | 0.217854i | \(-0.930094\pi\) | ||||
0.975981 | − | 0.217854i | \(-0.0699058\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.84350e8 | −2.18609 | ||||||||
\(680\) | 7.89524e7i | 0.251095i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.72052e8 | 0.857627 | ||||||||
\(683\) | − 1.53606e8i | − 0.482110i | −0.970511 | − | 0.241055i | \(-0.922507\pi\) | ||||
0.970511 | − | 0.241055i | \(-0.0774935\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.62115e8 | −0.815492 | ||||||||
\(686\) | 2.64399e8i | 0.819008i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.76976e7 | −0.207878 | ||||||||
\(689\) | − 1.26193e8i | − 0.385813i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.17865e8 | 0.963404 | 0.481702 | − | 0.876335i | \(-0.340019\pi\) | ||||
0.481702 | + | 0.876335i | \(0.340019\pi\) | |||||||
\(692\) | 2.04028e8i | 0.615704i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.77882e8 | −0.831346 | ||||||||
\(695\) | 5.32966e7i | 0.158761i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.22408e7 | −0.242878 | ||||||||
\(698\) | − 1.97645e8i | − 0.581191i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.49514e8 | 0.435900 | ||||||||
\(701\) | − 1.74451e8i | − 0.506431i | −0.967410 | − | 0.253215i | \(-0.918512\pi\) | ||||
0.967410 | − | 0.253215i | \(-0.0814881\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.64424e8 | −1.62457 | ||||||||
\(704\) | − 4.76356e7i | − 0.136526i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.23793e7 | 0.120432 | ||||||||
\(707\) | 4.50128e8i | 1.27373i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.84585e7 | 0.220141 | 0.110071 | − | 0.993924i | \(-0.464892\pi\) | ||||
0.110071 | + | 0.993924i | \(0.464892\pi\) | |||||||
\(710\) | 3.33646e8i | 0.932205i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.57698e8 | 0.436905 | ||||||||
\(713\) | − 3.92051e8i | − 1.08162i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.04708e8 | −0.286458 | ||||||||
\(716\) | 2.30223e7i | 0.0627204i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.77765e8 | −0.480255 | ||||||||
\(719\) | − 6.02172e8i | − 1.62007i | −0.586382 | − | 0.810035i | \(-0.699448\pi\) | ||||
0.586382 | − | 0.810035i | \(-0.300552\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.19600e8 | −1.11952 | ||||||||
\(722\) | 1.30377e7i | 0.0346410i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.37434e8 | −0.625645 | ||||||||
\(725\) | 1.27827e8i | 0.335435i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.88838e8 | 0.491459 | 0.245729 | − | 0.969338i | \(-0.420973\pi\) | ||||
0.245729 | + | 0.969338i | \(0.420973\pi\) | |||||||
\(728\) | − 8.58321e7i | − 0.222462i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.84008e8 | 0.473007 | ||||||||
\(731\) | 3.36525e8i | 0.861519i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.66823e8 | −0.677503 | −0.338752 | − | 0.940876i | \(-0.610005\pi\) | ||||
−0.338752 | + | 0.940876i | \(0.610005\pi\) | |||||||
\(734\) | − 2.62073e8i | − 0.662726i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.86472e7 | −0.172183 | ||||||||
\(737\) | 3.45330e8i | 0.862645i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.75150e7 | −0.167289 | −0.0836444 | − | 0.996496i | \(-0.526656\pi\) | ||||
−0.0836444 | + | 0.996496i | \(0.526656\pi\) | |||||||
\(740\) | − 2.31365e8i | − 0.570956i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4.78995e8 | 1.17252 | ||||||||
\(743\) | 4.38858e8i | 1.06994i | 0.844872 | + | 0.534968i | \(0.179676\pi\) | ||||
−0.844872 | + | 0.534968i | \(0.820324\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.27360e8 | 0.791692 | ||||||||
\(746\) | 4.11968e7i | 0.0992310i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.36797e8 | −0.565811 | ||||||||
\(749\) | − 5.78691e8i | − 1.37721i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.42114e8 | 0.807701 | 0.403851 | − | 0.914825i | \(-0.367672\pi\) | ||||
0.403851 | + | 0.914825i | \(0.367672\pi\) | |||||||
\(752\) | − 1.62903e8i | − 0.383067i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.33824e7 | 0.171190 | ||||||||
\(755\) | 4.16361e8i | 0.967452i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.84203e7 | 0.203828 | 0.101914 | − | 0.994793i | \(-0.467503\pi\) | ||||
0.101914 | + | 0.994793i | \(0.467503\pi\) | |||||||
\(758\) | 3.40286e8i | 0.781333i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.03747e8 | 0.236338 | ||||||||
\(761\) | 3.90287e8i | 0.885584i | 0.896624 | + | 0.442792i | \(0.146012\pi\) | ||||
−0.896624 | + | 0.442792i | \(0.853988\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.16825e8 | −1.38864 | ||||||||
\(764\) | − 6.53449e7i | − 0.146532i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.85731e7 | −0.108071 | ||||||||
\(767\) | − 1.61470e8i | − 0.357853i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.37049e8 | 0.301368 | 0.150684 | − | 0.988582i | \(-0.451852\pi\) | ||||
0.150684 | + | 0.988582i | \(0.451852\pi\) | |||||||
\(770\) | − 3.97445e8i | − 0.870572i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.34687e8 | −0.292735 | ||||||||
\(773\) | − 1.98181e6i | − 0.00429065i | −0.999998 | − | 0.00214533i | \(-0.999317\pi\) | ||||
0.999998 | − | 0.00214533i | \(-0.000682879\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.74032e8 | 0.588703 | ||||||||
\(776\) | 2.19624e8i | 0.469996i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.33724e8 | −0.921032 | ||||||||
\(779\) | 1.08068e8i | 0.228604i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.00068e9 | −2.10060 | ||||||||
\(782\) | 3.41245e8i | 0.713586i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.05325e8 | 0.426081 | ||||||||
\(785\) | − 4.62668e8i | − 0.956446i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.21733e8 | −0.249738 | −0.124869 | − | 0.992173i | \(-0.539851\pi\) | ||||
−0.124869 | + | 0.992173i | \(0.539851\pi\) | |||||||
\(788\) | − 3.41586e8i | − 0.698105i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.73698e8 | −0.757948 | ||||||||
\(791\) | − 2.05585e8i | − 0.415396i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.21528e8 | −0.644762 | ||||||||
\(794\) | − 3.71763e8i | − 0.742685i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.13147e8 | 0.224338 | ||||||||
\(797\) | 3.61504e8i | 0.714065i | 0.934092 | + | 0.357033i | \(0.116211\pi\) | ||||
−0.934092 | + | 0.357033i | \(0.883789\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.09790e8 | −1.58757 | ||||||||
\(800\) | − 4.79824e7i | − 0.0937156i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.21090e7 | 0.178558 | ||||||||
\(803\) | 5.51883e8i | 1.06586i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.72753e8 | −1.09794 | ||||||||
\(806\) | − 1.57315e8i | − 0.300446i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.44457e8 | 0.273844 | ||||||||
\(809\) | − 2.16174e8i | − 0.408279i | −0.978942 | − | 0.204140i | \(-0.934560\pi\) | ||||
0.978942 | − | 0.204140i | \(-0.0654396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.81616e6 | −0.00902897 | −0.00451449 | − | 0.999990i | \(-0.501437\pi\) | ||||
−0.00451449 | + | 0.999990i | \(0.501437\pi\) | |||||||
\(812\) | 2.78541e8i | 0.520261i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.93919e8 | 1.28658 | ||||||||
\(815\) | − 9.74970e7i | − 0.180102i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.42208e8 | 0.810887 | ||||||||
\(818\) | 2.61260e8i | 0.477325i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −4.42985e7 | −0.0803429 | ||||||||
\(821\) | − 6.91066e8i | − 1.24879i | −0.781108 | − | 0.624396i | \(-0.785345\pi\) | ||||
0.781108 | − | 0.624396i | \(-0.214655\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.01432e9 | 1.81959 | 0.909795 | − | 0.415058i | \(-0.136239\pi\) | ||||
0.909795 | + | 0.415058i | \(0.136239\pi\) | |||||||
\(824\) | 1.34660e8i | 0.240689i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.12898e8 | 1.08755 | ||||||||
\(827\) | − 3.47789e8i | − 0.614892i | −0.951566 | − | 0.307446i | \(-0.900526\pi\) | ||||
0.951566 | − | 0.307446i | \(-0.0994743\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.07108e8 | 0.890096 | 0.445048 | − | 0.895507i | \(-0.353187\pi\) | ||||
0.445048 | + | 0.895507i | \(0.353187\pi\) | |||||||
\(830\) | − 3.66219e8i | − 0.640481i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.75455e7 | −0.0478279 | ||||||||
\(833\) | − 1.02067e9i | − 1.76583i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.31315e8 | −0.225556 | ||||||||
\(836\) | 3.11161e8i | 0.532558i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.26198e8 | −0.214447 | ||||||||
\(839\) | 1.74329e8i | 0.295178i | 0.989049 | + | 0.147589i | \(0.0471513\pi\) | ||||
−0.989049 | + | 0.147589i | \(0.952849\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.56684e8 | 0.599647 | ||||||||
\(842\) | 2.71403e7i | 0.0454651i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −2.30554e8 | −0.383483 | ||||||||
\(845\) | − 3.53029e8i | − 0.585114i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.92769e8 | 0.317239 | ||||||||
\(848\) | − 1.53721e8i | − 0.252084i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.38521e8 | −0.388391 | ||||||||
\(851\) | − 9.99999e8i | − 1.62260i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.14584e8 | −0.506862 | −0.253431 | − | 0.967354i | \(-0.581559\pi\) | ||||
−0.253431 | + | 0.967354i | \(0.581559\pi\) | |||||||
\(854\) | − 1.22044e9i | − 1.95949i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.85715e8 | −0.296092 | ||||||||
\(857\) | 6.87822e8i | 1.09278i | 0.837530 | + | 0.546391i | \(0.183999\pi\) | ||||
−0.837530 | + | 0.546391i | \(0.816001\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.88341e8 | 1.24375 | 0.621877 | − | 0.783115i | \(-0.286370\pi\) | ||||
0.621877 | + | 0.783115i | \(0.286370\pi\) | |||||||
\(860\) | 1.81267e8i | 0.284986i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.93136e8 | 0.926045 | ||||||||
\(863\) | − 9.95858e8i | − 1.54941i | −0.632326 | − | 0.774703i | \(-0.717899\pi\) | ||||
0.632326 | − | 0.774703i | \(-0.282101\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.46307e8 | 0.844089 | ||||||||
\(866\) | − 6.23894e8i | − 0.960632i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.97129e8 | 0.913081 | ||||||||
\(869\) | − 1.12081e9i | − 1.70794i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.99689e8 | 0.302204 | ||||||||
\(872\) | 1.97954e8i | 0.298548i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.48411e8 | 0.671648 | ||||||||
\(875\) | − 1.15550e9i | − 1.72483i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.19092e8 | −0.324808 | −0.162404 | − | 0.986724i | \(-0.551925\pi\) | ||||
−0.162404 | + | 0.986724i | \(0.551925\pi\) | |||||||
\(878\) | 5.28999e7i | 0.0781576i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.27549e8 | −0.187167 | ||||||||
\(881\) | − 4.82715e8i | − 0.705932i | −0.935636 | − | 0.352966i | \(-0.885173\pi\) | ||||
0.935636 | − | 0.352966i | \(-0.114827\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.75993e8 | −1.12713 | −0.563567 | − | 0.826070i | \(-0.690571\pi\) | ||||
−0.563567 | + | 0.826070i | \(0.690571\pi\) | |||||||
\(884\) | 1.36929e8i | 0.198216i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.09949e8 | 0.158085 | ||||||||
\(887\) | 9.51645e8i | 1.36365i | 0.731514 | + | 0.681827i | \(0.238814\pi\) | ||||
−0.731514 | + | 0.681827i | \(0.761186\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.28588e9 | −1.83018 | ||||||||
\(890\) | − 4.22254e8i | − 0.598968i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.19170e8 | 0.590603 | ||||||||
\(893\) | 1.06410e9i | 1.49426i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.16445e7 | 0.0859855 | ||||||||
\(896\) | − 1.04556e8i | − 0.145353i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.02642e8 | −0.970298 | ||||||||
\(899\) | 5.10517e8i | 0.702638i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.64147e8 | −1.04473 | ||||||||
\(902\) | − 1.32862e8i | − 0.181042i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.59771e7 | −0.0893075 | ||||||||
\(905\) | 6.35755e8i | 0.857717i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.93579e8 | 0.661508 | 0.330754 | − | 0.943717i | \(-0.392697\pi\) | ||||
0.330754 | + | 0.943717i | \(0.392697\pi\) | |||||||
\(908\) | 1.15986e8i | 0.154934i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.29824e8 | −0.304980 | ||||||||
\(911\) | − 1.67733e8i | − 0.221851i | −0.993829 | − | 0.110926i | \(-0.964618\pi\) | ||||
0.993829 | − | 0.110926i | \(-0.0353816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.09838e9 | 1.44324 | ||||||||
\(914\) | 9.91174e7i | 0.129811i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4.25547e8 | −0.553683 | ||||||||
\(917\) | 8.60186e7i | 0.111554i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.11908e8 | 0.917227 | 0.458614 | − | 0.888636i | \(-0.348346\pi\) | ||||
0.458614 | + | 0.888636i | \(0.348346\pi\) | |||||||
\(920\) | 1.83810e8i | 0.236051i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.00209e8 | −0.255441 | ||||||||
\(923\) | 5.78651e8i | 0.735887i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.98970e8 | 0.883148 | ||||||||
\(926\) | 1.74578e7i | 0.0219865i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.93904e7 | 0.111853 | ||||||||
\(929\) | 5.56076e8i | 0.693565i | 0.937946 | + | 0.346783i | \(0.112726\pi\) | ||||
−0.937946 | + | 0.346783i | \(0.887274\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.34120e9 | −1.66205 | ||||||||
\(932\) | 7.45347e8i | 0.920684i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.11197e8 | −0.750137 | ||||||||
\(935\) | 6.34049e8i | 0.775689i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.14269e9 | 1.38902 | 0.694509 | − | 0.719484i | \(-0.255622\pi\) | ||||
0.694509 | + | 0.719484i | \(0.255622\pi\) | |||||||
\(938\) | 7.57969e8i | 0.918423i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −4.36189e8 | −0.525159 | ||||||||
\(941\) | 1.34486e8i | 0.161401i | 0.996738 | + | 0.0807006i | \(0.0257158\pi\) | ||||
−0.996738 | + | 0.0807006i | \(0.974284\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.91466e8 | −0.228326 | ||||||||
\(944\) | − 1.96693e8i | − 0.233816i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.43663e8 | −0.642180 | ||||||||
\(947\) | − 5.89972e8i | − 0.694674i | −0.937740 | − | 0.347337i | \(-0.887086\pi\) | ||||
0.937740 | − | 0.347337i | \(-0.112914\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.19129e8 | 0.373394 | ||||||||
\(950\) | 3.13426e8i | 0.365565i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.19748e8 | −0.602396 | ||||||||
\(953\) | − 4.97962e8i | − 0.575331i | −0.957731 | − | 0.287665i | \(-0.907121\pi\) | ||||
0.957731 | − | 0.287665i | \(-0.0928791\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.74968e8 | −0.200885 | ||||||||
\(956\) | 5.16459e8i | 0.591102i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7.42769e8 | 0.844806 | ||||||||
\(959\) | − 1.72551e9i | − 1.95642i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.06930e8 | 0.233159 | ||||||||
\(962\) | − 4.01262e8i | − 0.450716i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.58251e8 | 0.399904 | ||||||||
\(965\) | 3.60639e8i | 0.401320i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.65997e9 | 1.83579 | 0.917893 | − | 0.396828i | \(-0.129889\pi\) | ||||
0.917893 | + | 0.396828i | \(0.129889\pi\) | |||||||
\(968\) | − 6.18640e7i | − 0.0682044i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.88066e8 | 0.644333 | ||||||||
\(971\) | 1.02684e9i | 1.12162i | 0.827944 | + | 0.560810i | \(0.189510\pi\) | ||||
−0.827944 | + | 0.560810i | \(0.810490\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.50854e8 | −0.380880 | ||||||||
\(974\) | 2.63561e8i | 0.285236i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.91667e8 | −0.421277 | ||||||||
\(977\) | 2.80695e8i | 0.300990i | 0.988611 | + | 0.150495i | \(0.0480867\pi\) | ||||
−0.988611 | + | 0.150495i | \(0.951913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.26644e9 | 1.34970 | ||||||||
\(980\) | − 5.49778e8i | − 0.584129i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.24168e9 | −1.31122 | ||||||||
\(983\) | − 2.30006e8i | − 0.242147i | −0.992644 | − | 0.121073i | \(-0.961366\pi\) | ||||
0.992644 | − | 0.121073i | \(-0.0386337\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.14631e8 | −0.957055 | ||||||||
\(986\) | − 4.44360e8i | − 0.463558i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.79930e8 | 0.186567 | ||||||||
\(989\) | 7.83467e8i | 0.809901i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.95079e7 | 0.0919688 | 0.0459844 | − | 0.998942i | \(-0.485358\pi\) | ||||
0.0459844 | + | 0.998942i | \(0.485358\pi\) | |||||||
\(992\) | − 1.91633e8i | − 0.196306i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.19641e9 | −2.23643 | ||||||||
\(995\) | − 3.02962e8i | − 0.307553i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.24466e9 | 1.25593 | 0.627963 | − | 0.778243i | \(-0.283889\pi\) | ||||
0.627963 | + | 0.778243i | \(0.283889\pi\) | |||||||
\(998\) | 7.54887e8i | 0.759435i | ||||||||
\(999\) | 0 | 0 |
(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 | 162.7.b.b.161.3 | ✓ | 8 | |
3.2 | odd | 2 | inner | 162.7.b.b.161.6 | yes | 8 | |
9.2 | odd | 6 | 162.7.d.g.53.7 | 16 | |||
9.4 | even | 3 | 162.7.d.g.107.7 | 16 | |||
9.5 | odd | 6 | 162.7.d.g.107.2 | 16 | |||
9.7 | even | 3 | 162.7.d.g.53.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
162.7.b.b.161.3 | ✓ | 8 | 1.1 | even | 1 | trivial | |
162.7.b.b.161.6 | yes | 8 | 3.2 | odd | 2 | inner | |
162.7.d.g.53.2 | 16 | 9.7 | even | 3 | |||
162.7.d.g.53.7 | 16 | 9.2 | odd | 6 | |||
162.7.d.g.107.2 | 16 | 9.5 | odd | 6 | |||
162.7.d.g.107.7 | 16 | 9.4 | even | 3 |