Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
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, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(135.996742959\) |
Analytic rank: | \(1\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −42.1259 | −0.930861 | −0.465430 | − | 0.885084i | \(-0.654100\pi\) | ||||
−0.465430 | + | 0.885084i | \(0.654100\pi\) | |||||||
\(3\) | −243.000 | −0.577350 | ||||||||
\(4\) | −273.404 | −0.133498 | ||||||||
\(5\) | −6338.85 | −0.907142 | −0.453571 | − | 0.891220i | \(-0.649850\pi\) | ||||
−0.453571 | + | 0.891220i | \(0.649850\pi\) | |||||||
\(6\) | 10236.6 | 0.537433 | ||||||||
\(7\) | −22948.3 | −0.516074 | −0.258037 | − | 0.966135i | \(-0.583076\pi\) | ||||
−0.258037 | + | 0.966135i | \(0.583076\pi\) | |||||||
\(8\) | 97791.4 | 1.05513 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 267030. | 0.844423 | ||||||||
\(11\) | −43451.8 | −0.0813481 | −0.0406741 | − | 0.999172i | \(-0.512951\pi\) | ||||
−0.0406741 | + | 0.999172i | \(0.512951\pi\) | |||||||
\(12\) | 66437.3 | 0.0770752 | ||||||||
\(13\) | −820123. | −0.612619 | −0.306310 | − | 0.951932i | \(-0.599094\pi\) | ||||
−0.306310 | + | 0.951932i | \(0.599094\pi\) | |||||||
\(14\) | 966721. | 0.480393 | ||||||||
\(15\) | 1.54034e6 | 0.523739 | ||||||||
\(16\) | −3.55962e6 | −0.848680 | ||||||||
\(17\) | −5.29095e6 | −0.903784 | −0.451892 | − | 0.892073i | \(-0.649251\pi\) | ||||
−0.451892 | + | 0.892073i | \(0.649251\pi\) | |||||||
\(18\) | −2.48750e6 | −0.310287 | ||||||||
\(19\) | −9.56089e6 | −0.885836 | −0.442918 | − | 0.896562i | \(-0.646057\pi\) | ||||
−0.442918 | + | 0.896562i | \(0.646057\pi\) | |||||||
\(20\) | 1.73307e6 | 0.121102 | ||||||||
\(21\) | 5.57645e6 | 0.297956 | ||||||||
\(22\) | 1.83045e6 | 0.0757238 | ||||||||
\(23\) | −1.56497e7 | −0.506994 | −0.253497 | − | 0.967336i | \(-0.581581\pi\) | ||||
−0.253497 | + | 0.967336i | \(0.581581\pi\) | |||||||
\(24\) | −2.37633e7 | −0.609179 | ||||||||
\(25\) | −8.64713e6 | −0.177093 | ||||||||
\(26\) | 3.45485e7 | 0.570263 | ||||||||
\(27\) | −1.43489e7 | −0.192450 | ||||||||
\(28\) | 6.27418e6 | 0.0688950 | ||||||||
\(29\) | −4.39579e7 | −0.397968 | −0.198984 | − | 0.980003i | \(-0.563764\pi\) | ||||
−0.198984 | + | 0.980003i | \(0.563764\pi\) | |||||||
\(30\) | −6.48883e7 | −0.487528 | ||||||||
\(31\) | 2.36187e8 | 1.48172 | 0.740861 | − | 0.671658i | \(-0.234418\pi\) | ||||
0.740861 | + | 0.671658i | \(0.234418\pi\) | |||||||
\(32\) | −5.03243e7 | −0.265126 | ||||||||
\(33\) | 1.05588e7 | 0.0469664 | ||||||||
\(34\) | 2.22886e8 | 0.841297 | ||||||||
\(35\) | 1.45466e8 | 0.468153 | ||||||||
\(36\) | −1.61443e7 | −0.0444994 | ||||||||
\(37\) | 4.01725e8 | 0.952399 | 0.476199 | − | 0.879337i | \(-0.342014\pi\) | ||||
0.476199 | + | 0.879337i | \(0.342014\pi\) | |||||||
\(38\) | 4.02761e8 | 0.824590 | ||||||||
\(39\) | 1.99290e8 | 0.353696 | ||||||||
\(40\) | −6.19885e8 | −0.957152 | ||||||||
\(41\) | −8.87829e8 | −1.19679 | −0.598395 | − | 0.801201i | \(-0.704195\pi\) | ||||
−0.598395 | + | 0.801201i | \(0.704195\pi\) | |||||||
\(42\) | −2.34913e8 | −0.277355 | ||||||||
\(43\) | 1.42442e9 | 1.47761 | 0.738806 | − | 0.673918i | \(-0.235390\pi\) | ||||
0.738806 | + | 0.673918i | \(0.235390\pi\) | |||||||
\(44\) | 1.18799e7 | 0.0108598 | ||||||||
\(45\) | −3.74303e8 | −0.302381 | ||||||||
\(46\) | 6.59259e8 | 0.471941 | ||||||||
\(47\) | 3.01297e9 | 1.91627 | 0.958133 | − | 0.286322i | \(-0.0924329\pi\) | ||||
0.958133 | + | 0.286322i | \(0.0924329\pi\) | |||||||
\(48\) | 8.64988e8 | 0.489986 | ||||||||
\(49\) | −1.45070e9 | −0.733667 | ||||||||
\(50\) | 3.64269e8 | 0.164849 | ||||||||
\(51\) | 1.28570e9 | 0.521800 | ||||||||
\(52\) | 2.24225e8 | 0.0817836 | ||||||||
\(53\) | −1.28336e8 | −0.0421534 | −0.0210767 | − | 0.999778i | \(-0.506709\pi\) | ||||
−0.0210767 | + | 0.999778i | \(0.506709\pi\) | |||||||
\(54\) | 6.04461e8 | 0.179144 | ||||||||
\(55\) | 2.75434e8 | 0.0737943 | ||||||||
\(56\) | −2.24415e9 | −0.544525 | ||||||||
\(57\) | 2.32330e9 | 0.511438 | ||||||||
\(58\) | 1.85177e9 | 0.370453 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | −4.21136e8 | −0.0699182 | ||||||||
\(61\) | −9.01975e8 | −0.136735 | −0.0683676 | − | 0.997660i | \(-0.521779\pi\) | ||||
−0.0683676 | + | 0.997660i | \(0.521779\pi\) | |||||||
\(62\) | −9.94960e9 | −1.37928 | ||||||||
\(63\) | −1.35508e9 | −0.172025 | ||||||||
\(64\) | 9.41006e9 | 1.09548 | ||||||||
\(65\) | 5.19864e9 | 0.555733 | ||||||||
\(66\) | −4.44799e8 | −0.0437191 | ||||||||
\(67\) | −4.70084e9 | −0.425367 | −0.212684 | − | 0.977121i | \(-0.568220\pi\) | ||||
−0.212684 | + | 0.977121i | \(0.568220\pi\) | |||||||
\(68\) | 1.44657e9 | 0.120654 | ||||||||
\(69\) | 3.80288e9 | 0.292713 | ||||||||
\(70\) | −6.12790e9 | −0.435785 | ||||||||
\(71\) | 2.04793e10 | 1.34708 | 0.673541 | − | 0.739150i | \(-0.264773\pi\) | ||||
0.673541 | + | 0.739150i | \(0.264773\pi\) | |||||||
\(72\) | 5.77448e9 | 0.351710 | ||||||||
\(73\) | −1.87288e10 | −1.05739 | −0.528695 | − | 0.848812i | \(-0.677318\pi\) | ||||
−0.528695 | + | 0.848812i | \(0.677318\pi\) | |||||||
\(74\) | −1.69230e10 | −0.886551 | ||||||||
\(75\) | 2.10125e9 | 0.102245 | ||||||||
\(76\) | 2.61399e9 | 0.118258 | ||||||||
\(77\) | 9.97146e8 | 0.0419817 | ||||||||
\(78\) | −8.39528e9 | −0.329242 | ||||||||
\(79\) | 4.04588e10 | 1.47933 | 0.739664 | − | 0.672977i | \(-0.234985\pi\) | ||||
0.739664 | + | 0.672977i | \(0.234985\pi\) | |||||||
\(80\) | 2.25639e10 | 0.769873 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 3.74006e10 | 1.11405 | ||||||||
\(83\) | 5.18160e10 | 1.44389 | 0.721945 | − | 0.691950i | \(-0.243248\pi\) | ||||
0.721945 | + | 0.691950i | \(0.243248\pi\) | |||||||
\(84\) | −1.52463e9 | −0.0397765 | ||||||||
\(85\) | 3.35385e10 | 0.819860 | ||||||||
\(86\) | −6.00049e10 | −1.37545 | ||||||||
\(87\) | 1.06818e10 | 0.229767 | ||||||||
\(88\) | −4.24921e9 | −0.0858328 | ||||||||
\(89\) | −2.60402e10 | −0.494309 | −0.247155 | − | 0.968976i | \(-0.579496\pi\) | ||||
−0.247155 | + | 0.968976i | \(0.579496\pi\) | |||||||
\(90\) | 1.57679e10 | 0.281474 | ||||||||
\(91\) | 1.88205e10 | 0.316157 | ||||||||
\(92\) | 4.27870e9 | 0.0676828 | ||||||||
\(93\) | −5.73935e10 | −0.855473 | ||||||||
\(94\) | −1.26924e11 | −1.78378 | ||||||||
\(95\) | 6.06050e10 | 0.803579 | ||||||||
\(96\) | 1.22288e10 | 0.153071 | ||||||||
\(97\) | −1.89722e10 | −0.224323 | −0.112161 | − | 0.993690i | \(-0.535777\pi\) | ||||
−0.112161 | + | 0.993690i | \(0.535777\pi\) | |||||||
\(98\) | 6.11121e10 | 0.682942 | ||||||||
\(99\) | −2.56578e9 | −0.0271160 | ||||||||
\(100\) | 2.36416e9 | 0.0236416 | ||||||||
\(101\) | 5.38175e10 | 0.509514 | 0.254757 | − | 0.967005i | \(-0.418004\pi\) | ||||
0.254757 | + | 0.967005i | \(0.418004\pi\) | |||||||
\(102\) | −5.41614e10 | −0.485723 | ||||||||
\(103\) | 8.25502e10 | 0.701638 | 0.350819 | − | 0.936443i | \(-0.385903\pi\) | ||||
0.350819 | + | 0.936443i | \(0.385903\pi\) | |||||||
\(104\) | −8.02010e10 | −0.646393 | ||||||||
\(105\) | −3.53483e10 | −0.270288 | ||||||||
\(106\) | 5.40630e9 | 0.0392390 | ||||||||
\(107\) | −5.51260e10 | −0.379967 | −0.189983 | − | 0.981787i | \(-0.560843\pi\) | ||||
−0.189983 | + | 0.981787i | \(0.560843\pi\) | |||||||
\(108\) | 3.92305e9 | 0.0256917 | ||||||||
\(109\) | 3.01295e11 | 1.87563 | 0.937813 | − | 0.347140i | \(-0.112847\pi\) | ||||
0.937813 | + | 0.347140i | \(0.112847\pi\) | |||||||
\(110\) | −1.16029e10 | −0.0686922 | ||||||||
\(111\) | −9.76191e10 | −0.549868 | ||||||||
\(112\) | 8.16874e10 | 0.437982 | ||||||||
\(113\) | 1.06462e11 | 0.543578 | 0.271789 | − | 0.962357i | \(-0.412385\pi\) | ||||
0.271789 | + | 0.962357i | \(0.412385\pi\) | |||||||
\(114\) | −9.78710e10 | −0.476077 | ||||||||
\(115\) | 9.92011e10 | 0.459916 | ||||||||
\(116\) | 1.20183e10 | 0.0531280 | ||||||||
\(117\) | −4.84275e10 | −0.204206 | ||||||||
\(118\) | −3.01169e10 | −0.121188 | ||||||||
\(119\) | 1.21419e11 | 0.466420 | ||||||||
\(120\) | 1.50632e11 | 0.552612 | ||||||||
\(121\) | −2.83424e11 | −0.993382 | ||||||||
\(122\) | 3.79965e10 | 0.127281 | ||||||||
\(123\) | 2.15742e11 | 0.690967 | ||||||||
\(124\) | −6.45746e10 | −0.197807 | ||||||||
\(125\) | 3.64327e11 | 1.06779 | ||||||||
\(126\) | 5.70839e10 | 0.160131 | ||||||||
\(127\) | −8.13135e10 | −0.218395 | −0.109197 | − | 0.994020i | \(-0.534828\pi\) | ||||
−0.109197 | + | 0.994020i | \(0.534828\pi\) | |||||||
\(128\) | −2.93344e11 | −0.754609 | ||||||||
\(129\) | −3.46133e11 | −0.853100 | ||||||||
\(130\) | −2.18998e11 | −0.517310 | ||||||||
\(131\) | −6.71116e11 | −1.51987 | −0.759934 | − | 0.650001i | \(-0.774769\pi\) | ||||
−0.759934 | + | 0.650001i | \(0.774769\pi\) | |||||||
\(132\) | −2.88682e9 | −0.00626993 | ||||||||
\(133\) | 2.19407e11 | 0.457157 | ||||||||
\(134\) | 1.98027e11 | 0.395958 | ||||||||
\(135\) | 9.09555e10 | 0.174580 | ||||||||
\(136\) | −5.17409e11 | −0.953609 | ||||||||
\(137\) | 9.04544e11 | 1.60128 | 0.800639 | − | 0.599147i | \(-0.204493\pi\) | ||||
0.800639 | + | 0.599147i | \(0.204493\pi\) | |||||||
\(138\) | −1.60200e11 | −0.272475 | ||||||||
\(139\) | −1.05942e12 | −1.73176 | −0.865881 | − | 0.500250i | \(-0.833241\pi\) | ||||
−0.865881 | + | 0.500250i | \(0.833241\pi\) | |||||||
\(140\) | −3.97711e10 | −0.0624975 | ||||||||
\(141\) | −7.32151e11 | −1.10636 | ||||||||
\(142\) | −8.62709e11 | −1.25395 | ||||||||
\(143\) | 3.56358e10 | 0.0498354 | ||||||||
\(144\) | −2.10192e11 | −0.282893 | ||||||||
\(145\) | 2.78643e11 | 0.361014 | ||||||||
\(146\) | 7.88970e11 | 0.984282 | ||||||||
\(147\) | 3.52520e11 | 0.423583 | ||||||||
\(148\) | −1.09833e11 | −0.127144 | ||||||||
\(149\) | 1.19574e12 | 1.33386 | 0.666932 | − | 0.745118i | \(-0.267607\pi\) | ||||
0.666932 | + | 0.745118i | \(0.267607\pi\) | |||||||
\(150\) | −8.85173e10 | −0.0951757 | ||||||||
\(151\) | 1.93531e11 | 0.200621 | 0.100310 | − | 0.994956i | \(-0.468016\pi\) | ||||
0.100310 | + | 0.994956i | \(0.468016\pi\) | |||||||
\(152\) | −9.34972e11 | −0.934672 | ||||||||
\(153\) | −3.12425e11 | −0.301261 | ||||||||
\(154\) | −4.20057e10 | −0.0390791 | ||||||||
\(155\) | −1.49715e12 | −1.34413 | ||||||||
\(156\) | −5.44867e10 | −0.0472178 | ||||||||
\(157\) | −5.92815e11 | −0.495988 | −0.247994 | − | 0.968762i | \(-0.579771\pi\) | ||||
−0.247994 | + | 0.968762i | \(0.579771\pi\) | |||||||
\(158\) | −1.70437e12 | −1.37705 | ||||||||
\(159\) | 3.11858e10 | 0.0243373 | ||||||||
\(160\) | 3.18998e11 | 0.240507 | ||||||||
\(161\) | 3.59135e11 | 0.261647 | ||||||||
\(162\) | −1.46884e11 | −0.103429 | ||||||||
\(163\) | −1.24681e12 | −0.848731 | −0.424366 | − | 0.905491i | \(-0.639503\pi\) | ||||
−0.424366 | + | 0.905491i | \(0.639503\pi\) | |||||||
\(164\) | 2.42736e11 | 0.159769 | ||||||||
\(165\) | −6.69305e10 | −0.0426052 | ||||||||
\(166\) | −2.18280e12 | −1.34406 | ||||||||
\(167\) | 1.26546e12 | 0.753891 | 0.376946 | − | 0.926235i | \(-0.376974\pi\) | ||||
0.376946 | + | 0.926235i | \(0.376974\pi\) | |||||||
\(168\) | 5.45328e11 | 0.314382 | ||||||||
\(169\) | −1.11956e12 | −0.624697 | ||||||||
\(170\) | −1.41284e12 | −0.763176 | ||||||||
\(171\) | −5.64561e11 | −0.295279 | ||||||||
\(172\) | −3.89442e11 | −0.197259 | ||||||||
\(173\) | −3.14569e12 | −1.54334 | −0.771672 | − | 0.636020i | \(-0.780579\pi\) | ||||
−0.771672 | + | 0.636020i | \(0.780579\pi\) | |||||||
\(174\) | −4.49980e11 | −0.213881 | ||||||||
\(175\) | 1.98437e11 | 0.0913932 | ||||||||
\(176\) | 1.54672e11 | 0.0690385 | ||||||||
\(177\) | −1.73727e11 | −0.0751646 | ||||||||
\(178\) | 1.09697e12 | 0.460133 | ||||||||
\(179\) | 4.17961e12 | 1.69998 | 0.849991 | − | 0.526797i | \(-0.176607\pi\) | ||||
0.849991 | + | 0.526797i | \(0.176607\pi\) | |||||||
\(180\) | 1.02336e11 | 0.0403673 | ||||||||
\(181\) | −1.62172e12 | −0.620504 | −0.310252 | − | 0.950654i | \(-0.600413\pi\) | ||||
−0.310252 | + | 0.950654i | \(0.600413\pi\) | |||||||
\(182\) | −7.92830e11 | −0.294298 | ||||||||
\(183\) | 2.19180e11 | 0.0789441 | ||||||||
\(184\) | −1.53041e12 | −0.534944 | ||||||||
\(185\) | −2.54647e12 | −0.863961 | ||||||||
\(186\) | 2.41775e12 | 0.796326 | ||||||||
\(187\) | 2.29901e11 | 0.0735211 | ||||||||
\(188\) | −8.23758e11 | −0.255818 | ||||||||
\(189\) | 3.29284e11 | 0.0993185 | ||||||||
\(190\) | −2.55304e12 | −0.748020 | ||||||||
\(191\) | −1.51844e12 | −0.432229 | −0.216115 | − | 0.976368i | \(-0.569338\pi\) | ||||
−0.216115 | + | 0.976368i | \(0.569338\pi\) | |||||||
\(192\) | −2.28665e12 | −0.632473 | ||||||||
\(193\) | −2.43837e12 | −0.655441 | −0.327720 | − | 0.944775i | \(-0.606280\pi\) | ||||
−0.327720 | + | 0.944775i | \(0.606280\pi\) | |||||||
\(194\) | 7.99223e11 | 0.208813 | ||||||||
\(195\) | −1.26327e12 | −0.320853 | ||||||||
\(196\) | 3.96628e11 | 0.0979433 | ||||||||
\(197\) | −3.16608e12 | −0.760252 | −0.380126 | − | 0.924935i | \(-0.624119\pi\) | ||||
−0.380126 | + | 0.924935i | \(0.624119\pi\) | |||||||
\(198\) | 1.08086e11 | 0.0252413 | ||||||||
\(199\) | −7.69861e11 | −0.174872 | −0.0874360 | − | 0.996170i | \(-0.527867\pi\) | ||||
−0.0874360 | + | 0.996170i | \(0.527867\pi\) | |||||||
\(200\) | −8.45615e11 | −0.186856 | ||||||||
\(201\) | 1.14230e12 | 0.245586 | ||||||||
\(202\) | −2.26711e12 | −0.474287 | ||||||||
\(203\) | 1.00876e12 | 0.205381 | ||||||||
\(204\) | −3.51516e11 | −0.0696594 | ||||||||
\(205\) | 5.62781e12 | 1.08566 | ||||||||
\(206\) | −3.47750e12 | −0.653127 | ||||||||
\(207\) | −9.24099e11 | −0.168998 | ||||||||
\(208\) | 2.91933e12 | 0.519918 | ||||||||
\(209\) | 4.15437e11 | 0.0720611 | ||||||||
\(210\) | 1.48908e12 | 0.251601 | ||||||||
\(211\) | 1.12202e13 | 1.84692 | 0.923459 | − | 0.383696i | \(-0.125349\pi\) | ||||
0.923459 | + | 0.383696i | \(0.125349\pi\) | |||||||
\(212\) | 3.50878e10 | 0.00562741 | ||||||||
\(213\) | −4.97647e12 | −0.777738 | ||||||||
\(214\) | 2.32224e12 | 0.353696 | ||||||||
\(215\) | −9.02916e12 | −1.34040 | ||||||||
\(216\) | −1.40320e12 | −0.203060 | ||||||||
\(217\) | −5.42010e12 | −0.764679 | ||||||||
\(218\) | −1.26923e13 | −1.74595 | ||||||||
\(219\) | 4.55111e12 | 0.610484 | ||||||||
\(220\) | −7.53049e10 | −0.00985141 | ||||||||
\(221\) | 4.33923e12 | 0.553676 | ||||||||
\(222\) | 4.11230e12 | 0.511850 | ||||||||
\(223\) | −6.37305e12 | −0.773874 | −0.386937 | − | 0.922106i | \(-0.626467\pi\) | ||||
−0.386937 | + | 0.922106i | \(0.626467\pi\) | |||||||
\(224\) | 1.15486e12 | 0.136825 | ||||||||
\(225\) | −5.10604e11 | −0.0590311 | ||||||||
\(226\) | −4.48480e12 | −0.505995 | ||||||||
\(227\) | −1.20818e13 | −1.33043 | −0.665213 | − | 0.746654i | \(-0.731659\pi\) | ||||
−0.665213 | + | 0.746654i | \(0.731659\pi\) | |||||||
\(228\) | −6.35199e11 | −0.0682760 | ||||||||
\(229\) | 1.24786e13 | 1.30939 | 0.654696 | − | 0.755893i | \(-0.272797\pi\) | ||||
0.654696 | + | 0.755893i | \(0.272797\pi\) | |||||||
\(230\) | −4.17894e12 | −0.428118 | ||||||||
\(231\) | −2.42306e11 | −0.0242381 | ||||||||
\(232\) | −4.29871e12 | −0.419908 | ||||||||
\(233\) | −1.29692e13 | −1.23724 | −0.618622 | − | 0.785688i | \(-0.712309\pi\) | ||||
−0.618622 | + | 0.785688i | \(0.712309\pi\) | |||||||
\(234\) | 2.04005e12 | 0.190088 | ||||||||
\(235\) | −1.90987e13 | −1.73833 | ||||||||
\(236\) | −1.95463e11 | −0.0173800 | ||||||||
\(237\) | −9.83150e12 | −0.854090 | ||||||||
\(238\) | −5.11487e12 | −0.434172 | ||||||||
\(239\) | 7.24829e12 | 0.601239 | 0.300619 | − | 0.953744i | \(-0.402807\pi\) | ||||
0.300619 | + | 0.953744i | \(0.402807\pi\) | |||||||
\(240\) | −5.48303e12 | −0.444487 | ||||||||
\(241\) | −2.18446e13 | −1.73082 | −0.865408 | − | 0.501069i | \(-0.832940\pi\) | ||||
−0.865408 | + | 0.501069i | \(0.832940\pi\) | |||||||
\(242\) | 1.19395e13 | 0.924701 | ||||||||
\(243\) | −8.47289e11 | −0.0641500 | ||||||||
\(244\) | 2.46604e11 | 0.0182539 | ||||||||
\(245\) | 9.19577e12 | 0.665541 | ||||||||
\(246\) | −9.08836e12 | −0.643194 | ||||||||
\(247\) | 7.84111e12 | 0.542680 | ||||||||
\(248\) | 2.30971e13 | 1.56341 | ||||||||
\(249\) | −1.25913e13 | −0.833630 | ||||||||
\(250\) | −1.53476e13 | −0.993965 | ||||||||
\(251\) | −8.06503e12 | −0.510976 | −0.255488 | − | 0.966812i | \(-0.582236\pi\) | ||||
−0.255488 | + | 0.966812i | \(0.582236\pi\) | |||||||
\(252\) | 3.70484e11 | 0.0229650 | ||||||||
\(253\) | 6.80007e11 | 0.0412430 | ||||||||
\(254\) | 3.42541e12 | 0.203295 | ||||||||
\(255\) | −8.14986e12 | −0.473347 | ||||||||
\(256\) | −6.91442e12 | −0.393040 | ||||||||
\(257\) | 2.01417e13 | 1.12064 | 0.560318 | − | 0.828278i | \(-0.310679\pi\) | ||||
0.560318 | + | 0.828278i | \(0.310679\pi\) | |||||||
\(258\) | 1.45812e13 | 0.794117 | ||||||||
\(259\) | −9.21891e12 | −0.491508 | ||||||||
\(260\) | −1.42133e12 | −0.0741893 | ||||||||
\(261\) | −2.59567e12 | −0.132656 | ||||||||
\(262\) | 2.82714e13 | 1.41478 | ||||||||
\(263\) | 1.65928e13 | 0.813135 | 0.406568 | − | 0.913621i | \(-0.366726\pi\) | ||||
0.406568 | + | 0.913621i | \(0.366726\pi\) | |||||||
\(264\) | 1.03256e12 | 0.0495556 | ||||||||
\(265\) | 8.13505e11 | 0.0382391 | ||||||||
\(266\) | −9.24271e12 | −0.425550 | ||||||||
\(267\) | 6.32776e12 | 0.285390 | ||||||||
\(268\) | 1.28523e12 | 0.0567858 | ||||||||
\(269\) | −6.97094e12 | −0.301754 | −0.150877 | − | 0.988553i | \(-0.548210\pi\) | ||||
−0.150877 | + | 0.988553i | \(0.548210\pi\) | |||||||
\(270\) | −3.83159e12 | −0.162509 | ||||||||
\(271\) | 1.91165e13 | 0.794471 | 0.397236 | − | 0.917717i | \(-0.369970\pi\) | ||||
0.397236 | + | 0.917717i | \(0.369970\pi\) | |||||||
\(272\) | 1.88338e13 | 0.767023 | ||||||||
\(273\) | −4.57337e12 | −0.182533 | ||||||||
\(274\) | −3.81048e13 | −1.49057 | ||||||||
\(275\) | 3.75733e11 | 0.0144062 | ||||||||
\(276\) | −1.03972e12 | −0.0390767 | ||||||||
\(277\) | −1.82569e13 | −0.672647 | −0.336324 | − | 0.941746i | \(-0.609184\pi\) | ||||
−0.336324 | + | 0.941746i | \(0.609184\pi\) | |||||||
\(278\) | 4.46292e13 | 1.61203 | ||||||||
\(279\) | 1.39466e13 | 0.493907 | ||||||||
\(280\) | 1.42253e13 | 0.493961 | ||||||||
\(281\) | 5.49608e13 | 1.87141 | 0.935704 | − | 0.352786i | \(-0.114766\pi\) | ||||
0.935704 | + | 0.352786i | \(0.114766\pi\) | |||||||
\(282\) | 3.08425e13 | 1.02986 | ||||||||
\(283\) | −3.20931e12 | −0.105096 | −0.0525479 | − | 0.998618i | \(-0.516734\pi\) | ||||
−0.0525479 | + | 0.998618i | \(0.516734\pi\) | |||||||
\(284\) | −5.59913e12 | −0.179833 | ||||||||
\(285\) | −1.47270e13 | −0.463947 | ||||||||
\(286\) | −1.50119e12 | −0.0463899 | ||||||||
\(287\) | 2.03742e13 | 0.617633 | ||||||||
\(288\) | −2.97160e12 | −0.0883754 | ||||||||
\(289\) | −6.27774e12 | −0.183175 | ||||||||
\(290\) | −1.17381e13 | −0.336053 | ||||||||
\(291\) | 4.61025e12 | 0.129513 | ||||||||
\(292\) | 5.12054e12 | 0.141160 | ||||||||
\(293\) | 4.15063e13 | 1.12290 | 0.561451 | − | 0.827510i | \(-0.310243\pi\) | ||||
0.561451 | + | 0.827510i | \(0.310243\pi\) | |||||||
\(294\) | −1.48502e13 | −0.394297 | ||||||||
\(295\) | −4.53180e12 | −0.118100 | ||||||||
\(296\) | 3.92852e13 | 1.00490 | ||||||||
\(297\) | 6.23485e11 | 0.0156555 | ||||||||
\(298\) | −5.03716e13 | −1.24164 | ||||||||
\(299\) | 1.28347e13 | 0.310595 | ||||||||
\(300\) | −5.74492e11 | −0.0136495 | ||||||||
\(301\) | −3.26880e13 | −0.762557 | ||||||||
\(302\) | −8.15266e12 | −0.186750 | ||||||||
\(303\) | −1.30777e13 | −0.294168 | ||||||||
\(304\) | 3.40331e13 | 0.751791 | ||||||||
\(305\) | 5.71748e12 | 0.124038 | ||||||||
\(306\) | 1.31612e13 | 0.280432 | ||||||||
\(307\) | 4.41029e13 | 0.923009 | 0.461505 | − | 0.887138i | \(-0.347310\pi\) | ||||
0.461505 | + | 0.887138i | \(0.347310\pi\) | |||||||
\(308\) | −2.72624e11 | −0.00560448 | ||||||||
\(309\) | −2.00597e13 | −0.405091 | ||||||||
\(310\) | 6.30690e13 | 1.25120 | ||||||||
\(311\) | 6.84662e13 | 1.33442 | 0.667212 | − | 0.744868i | \(-0.267488\pi\) | ||||
0.667212 | + | 0.744868i | \(0.267488\pi\) | |||||||
\(312\) | 1.94888e13 | 0.373195 | ||||||||
\(313\) | 6.28941e13 | 1.18336 | 0.591679 | − | 0.806173i | \(-0.298465\pi\) | ||||
0.591679 | + | 0.806173i | \(0.298465\pi\) | |||||||
\(314\) | 2.49729e13 | 0.461696 | ||||||||
\(315\) | 8.58963e12 | 0.156051 | ||||||||
\(316\) | −1.10616e13 | −0.197488 | ||||||||
\(317\) | −5.13678e13 | −0.901290 | −0.450645 | − | 0.892703i | \(-0.648806\pi\) | ||||
−0.450645 | + | 0.892703i | \(0.648806\pi\) | |||||||
\(318\) | −1.31373e12 | −0.0226546 | ||||||||
\(319\) | 1.91005e12 | 0.0323740 | ||||||||
\(320\) | −5.96490e13 | −0.993752 | ||||||||
\(321\) | 1.33956e13 | 0.219374 | ||||||||
\(322\) | −1.51289e13 | −0.243557 | ||||||||
\(323\) | 5.05862e13 | 0.800605 | ||||||||
\(324\) | −9.53302e11 | −0.0148331 | ||||||||
\(325\) | 7.09171e12 | 0.108491 | ||||||||
\(326\) | 5.25233e13 | 0.790050 | ||||||||
\(327\) | −7.32147e13 | −1.08289 | ||||||||
\(328\) | −8.68220e13 | −1.26277 | ||||||||
\(329\) | −6.91426e13 | −0.988936 | ||||||||
\(330\) | 2.81951e12 | 0.0396595 | ||||||||
\(331\) | −1.07656e14 | −1.48930 | −0.744652 | − | 0.667453i | \(-0.767384\pi\) | ||||
−0.744652 | + | 0.667453i | \(0.767384\pi\) | |||||||
\(332\) | −1.41667e13 | −0.192757 | ||||||||
\(333\) | 2.37214e13 | 0.317466 | ||||||||
\(334\) | −5.33088e13 | −0.701768 | ||||||||
\(335\) | 2.97979e13 | 0.385868 | ||||||||
\(336\) | −1.98500e13 | −0.252869 | ||||||||
\(337\) | −8.93066e13 | −1.11923 | −0.559615 | − | 0.828753i | \(-0.689051\pi\) | ||||
−0.559615 | + | 0.828753i | \(0.689051\pi\) | |||||||
\(338\) | 4.71624e13 | 0.581506 | ||||||||
\(339\) | −2.58702e13 | −0.313835 | ||||||||
\(340\) | −9.16958e12 | −0.109450 | ||||||||
\(341\) | −1.02627e13 | −0.120535 | ||||||||
\(342\) | 2.37827e13 | 0.274863 | ||||||||
\(343\) | 7.86675e13 | 0.894701 | ||||||||
\(344\) | 1.39296e14 | 1.55907 | ||||||||
\(345\) | −2.41059e13 | −0.265533 | ||||||||
\(346\) | 1.32515e14 | 1.43664 | ||||||||
\(347\) | −1.03776e14 | −1.10735 | −0.553677 | − | 0.832732i | \(-0.686776\pi\) | ||||
−0.553677 | + | 0.832732i | \(0.686776\pi\) | |||||||
\(348\) | −2.92044e12 | −0.0306735 | ||||||||
\(349\) | 7.86088e12 | 0.0812701 | 0.0406351 | − | 0.999174i | \(-0.487062\pi\) | ||||
0.0406351 | + | 0.999174i | \(0.487062\pi\) | |||||||
\(350\) | −8.35936e12 | −0.0850744 | ||||||||
\(351\) | 1.17679e13 | 0.117899 | ||||||||
\(352\) | 2.18668e12 | 0.0215675 | ||||||||
\(353\) | 3.58529e13 | 0.348148 | 0.174074 | − | 0.984733i | \(-0.444307\pi\) | ||||
0.174074 | + | 0.984733i | \(0.444307\pi\) | |||||||
\(354\) | 7.31840e12 | 0.0699678 | ||||||||
\(355\) | −1.29815e14 | −1.22199 | ||||||||
\(356\) | 7.11950e12 | 0.0659894 | ||||||||
\(357\) | −2.95047e13 | −0.269287 | ||||||||
\(358\) | −1.76070e14 | −1.58245 | ||||||||
\(359\) | −5.98494e13 | −0.529713 | −0.264856 | − | 0.964288i | \(-0.585325\pi\) | ||||
−0.264856 | + | 0.964288i | \(0.585325\pi\) | |||||||
\(360\) | −3.66036e13 | −0.319051 | ||||||||
\(361\) | −2.50797e13 | −0.215294 | ||||||||
\(362\) | 6.83166e13 | 0.577602 | ||||||||
\(363\) | 6.88719e13 | 0.573530 | ||||||||
\(364\) | −5.14560e12 | −0.0422064 | ||||||||
\(365\) | 1.18719e14 | 0.959202 | ||||||||
\(366\) | −9.23316e12 | −0.0734860 | ||||||||
\(367\) | −1.42760e14 | −1.11929 | −0.559646 | − | 0.828732i | \(-0.689063\pi\) | ||||
−0.559646 | + | 0.828732i | \(0.689063\pi\) | |||||||
\(368\) | 5.57070e13 | 0.430276 | ||||||||
\(369\) | −5.24254e13 | −0.398930 | ||||||||
\(370\) | 1.07273e14 | 0.804228 | ||||||||
\(371\) | 2.94511e12 | 0.0217543 | ||||||||
\(372\) | 1.56916e13 | 0.114204 | ||||||||
\(373\) | 1.71705e14 | 1.23136 | 0.615680 | − | 0.787996i | \(-0.288881\pi\) | ||||
0.615680 | + | 0.787996i | \(0.288881\pi\) | |||||||
\(374\) | −9.68480e12 | −0.0684379 | ||||||||
\(375\) | −8.85314e13 | −0.616489 | ||||||||
\(376\) | 2.94642e14 | 2.02191 | ||||||||
\(377\) | 3.60509e13 | 0.243803 | ||||||||
\(378\) | −1.38714e13 | −0.0924517 | ||||||||
\(379\) | −5.75920e13 | −0.378309 | −0.189155 | − | 0.981947i | \(-0.560575\pi\) | ||||
−0.189155 | + | 0.981947i | \(0.560575\pi\) | |||||||
\(380\) | −1.65697e13 | −0.107276 | ||||||||
\(381\) | 1.97592e13 | 0.126090 | ||||||||
\(382\) | 6.39657e13 | 0.402345 | ||||||||
\(383\) | 1.08461e14 | 0.672481 | 0.336241 | − | 0.941776i | \(-0.390844\pi\) | ||||
0.336241 | + | 0.941776i | \(0.390844\pi\) | |||||||
\(384\) | 7.12825e13 | 0.435674 | ||||||||
\(385\) | −6.32076e12 | −0.0380833 | ||||||||
\(386\) | 1.02718e14 | 0.610124 | ||||||||
\(387\) | 8.41104e13 | 0.492537 | ||||||||
\(388\) | 5.18709e12 | 0.0299467 | ||||||||
\(389\) | 2.10424e14 | 1.19777 | 0.598883 | − | 0.800837i | \(-0.295612\pi\) | ||||
0.598883 | + | 0.800837i | \(0.295612\pi\) | |||||||
\(390\) | 5.32164e13 | 0.298669 | ||||||||
\(391\) | 8.28018e13 | 0.458213 | ||||||||
\(392\) | −1.41866e14 | −0.774114 | ||||||||
\(393\) | 1.63081e14 | 0.877496 | ||||||||
\(394\) | 1.33374e14 | 0.707688 | ||||||||
\(395\) | −2.56462e14 | −1.34196 | ||||||||
\(396\) | 7.01496e11 | 0.00361994 | ||||||||
\(397\) | 2.01577e14 | 1.02587 | 0.512936 | − | 0.858427i | \(-0.328558\pi\) | ||||
0.512936 | + | 0.858427i | \(0.328558\pi\) | |||||||
\(398\) | 3.24311e13 | 0.162781 | ||||||||
\(399\) | −5.33158e13 | −0.263940 | ||||||||
\(400\) | 3.07805e13 | 0.150295 | ||||||||
\(401\) | 1.92815e14 | 0.928639 | 0.464319 | − | 0.885668i | \(-0.346299\pi\) | ||||
0.464319 | + | 0.885668i | \(0.346299\pi\) | |||||||
\(402\) | −4.81206e13 | −0.228606 | ||||||||
\(403\) | −1.93703e14 | −0.907732 | ||||||||
\(404\) | −1.47139e13 | −0.0680192 | ||||||||
\(405\) | −2.21022e13 | −0.100794 | ||||||||
\(406\) | −4.24950e13 | −0.191181 | ||||||||
\(407\) | −1.74556e13 | −0.0774759 | ||||||||
\(408\) | 1.25730e14 | 0.550566 | ||||||||
\(409\) | −2.88002e14 | −1.24428 | −0.622140 | − | 0.782906i | \(-0.713736\pi\) | ||||
−0.622140 | + | 0.782906i | \(0.713736\pi\) | |||||||
\(410\) | −2.37077e14 | −1.01060 | ||||||||
\(411\) | −2.19804e14 | −0.924498 | ||||||||
\(412\) | −2.25696e13 | −0.0936674 | ||||||||
\(413\) | −1.64063e13 | −0.0671871 | ||||||||
\(414\) | 3.89286e13 | 0.157314 | ||||||||
\(415\) | −3.28454e14 | −1.30981 | ||||||||
\(416\) | 4.12721e13 | 0.162421 | ||||||||
\(417\) | 2.57440e14 | 0.999833 | ||||||||
\(418\) | −1.75007e13 | −0.0670789 | ||||||||
\(419\) | 4.16674e12 | 0.0157623 | 0.00788114 | − | 0.999969i | \(-0.497491\pi\) | ||||
0.00788114 | + | 0.999969i | \(0.497491\pi\) | |||||||
\(420\) | 9.66437e12 | 0.0360830 | ||||||||
\(421\) | −1.19932e14 | −0.441960 | −0.220980 | − | 0.975278i | \(-0.570926\pi\) | ||||
−0.220980 | + | 0.975278i | \(0.570926\pi\) | |||||||
\(422\) | −4.72662e14 | −1.71922 | ||||||||
\(423\) | 1.77913e14 | 0.638756 | ||||||||
\(424\) | −1.25502e13 | −0.0444773 | ||||||||
\(425\) | 4.57515e13 | 0.160054 | ||||||||
\(426\) | 2.09638e14 | 0.723966 | ||||||||
\(427\) | 2.06988e13 | 0.0705655 | ||||||||
\(428\) | 1.50717e13 | 0.0507249 | ||||||||
\(429\) | −8.65950e12 | −0.0287725 | ||||||||
\(430\) | 3.80362e14 | 1.24773 | ||||||||
\(431\) | 3.51165e14 | 1.13733 | 0.568665 | − | 0.822569i | \(-0.307460\pi\) | ||||
0.568665 | + | 0.822569i | \(0.307460\pi\) | |||||||
\(432\) | 5.10767e13 | 0.163329 | ||||||||
\(433\) | −2.56097e14 | −0.808577 | −0.404289 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404289 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(434\) | 2.28327e14 | 0.711809 | ||||||||
\(435\) | −6.77102e13 | −0.208431 | ||||||||
\(436\) | −8.23754e13 | −0.250393 | ||||||||
\(437\) | 1.49625e14 | 0.449114 | ||||||||
\(438\) | −1.91720e14 | −0.568276 | ||||||||
\(439\) | −4.65884e14 | −1.36371 | −0.681856 | − | 0.731486i | \(-0.738827\pi\) | ||||
−0.681856 | + | 0.731486i | \(0.738827\pi\) | |||||||
\(440\) | 2.69351e13 | 0.0778625 | ||||||||
\(441\) | −8.56624e13 | −0.244556 | ||||||||
\(442\) | −1.82794e14 | −0.515395 | ||||||||
\(443\) | 2.81744e14 | 0.784574 | 0.392287 | − | 0.919843i | \(-0.371684\pi\) | ||||
0.392287 | + | 0.919843i | \(0.371684\pi\) | |||||||
\(444\) | 2.66895e13 | 0.0734064 | ||||||||
\(445\) | 1.65065e14 | 0.448409 | ||||||||
\(446\) | 2.68471e14 | 0.720369 | ||||||||
\(447\) | −2.90564e14 | −0.770107 | ||||||||
\(448\) | −2.15945e14 | −0.565347 | ||||||||
\(449\) | −5.79944e13 | −0.149979 | −0.0749897 | − | 0.997184i | \(-0.523892\pi\) | ||||
−0.0749897 | + | 0.997184i | \(0.523892\pi\) | |||||||
\(450\) | 2.15097e13 | 0.0549497 | ||||||||
\(451\) | 3.85777e13 | 0.0973567 | ||||||||
\(452\) | −2.91071e13 | −0.0725667 | ||||||||
\(453\) | −4.70279e13 | −0.115829 | ||||||||
\(454\) | 5.08959e14 | 1.23844 | ||||||||
\(455\) | −1.19300e14 | −0.286799 | ||||||||
\(456\) | 2.27198e14 | 0.539633 | ||||||||
\(457\) | −5.19449e14 | −1.21900 | −0.609500 | − | 0.792786i | \(-0.708630\pi\) | ||||
−0.609500 | + | 0.792786i | \(0.708630\pi\) | |||||||
\(458\) | −5.25671e14 | −1.21886 | ||||||||
\(459\) | 7.59194e13 | 0.173933 | ||||||||
\(460\) | −2.71220e13 | −0.0613979 | ||||||||
\(461\) | −8.64623e14 | −1.93407 | −0.967033 | − | 0.254650i | \(-0.918040\pi\) | ||||
−0.967033 | + | 0.254650i | \(0.918040\pi\) | |||||||
\(462\) | 1.02074e13 | 0.0225623 | ||||||||
\(463\) | 3.06029e14 | 0.668448 | 0.334224 | − | 0.942494i | \(-0.391526\pi\) | ||||
0.334224 | + | 0.942494i | \(0.391526\pi\) | |||||||
\(464\) | 1.56474e14 | 0.337748 | ||||||||
\(465\) | 3.63808e14 | 0.776035 | ||||||||
\(466\) | 5.46340e14 | 1.15170 | ||||||||
\(467\) | 3.41995e14 | 0.712487 | 0.356243 | − | 0.934393i | \(-0.384057\pi\) | ||||
0.356243 | + | 0.934393i | \(0.384057\pi\) | |||||||
\(468\) | 1.32403e13 | 0.0272612 | ||||||||
\(469\) | 1.07876e14 | 0.219521 | ||||||||
\(470\) | 8.04552e14 | 1.61814 | ||||||||
\(471\) | 1.44054e14 | 0.286359 | ||||||||
\(472\) | 6.99134e13 | 0.137366 | ||||||||
\(473\) | −6.18934e13 | −0.120201 | ||||||||
\(474\) | 4.14161e14 | 0.795039 | ||||||||
\(475\) | 8.26743e13 | 0.156876 | ||||||||
\(476\) | −3.31964e13 | −0.0622662 | ||||||||
\(477\) | −7.57814e12 | −0.0140511 | ||||||||
\(478\) | −3.05341e14 | −0.559670 | ||||||||
\(479\) | 3.83828e14 | 0.695490 | 0.347745 | − | 0.937589i | \(-0.386948\pi\) | ||||
0.347745 | + | 0.937589i | \(0.386948\pi\) | |||||||
\(480\) | −7.75165e13 | −0.138857 | ||||||||
\(481\) | −3.29464e14 | −0.583458 | ||||||||
\(482\) | 9.20225e14 | 1.61115 | ||||||||
\(483\) | −8.72698e13 | −0.151062 | ||||||||
\(484\) | 7.74892e13 | 0.132615 | ||||||||
\(485\) | 1.20262e14 | 0.203493 | ||||||||
\(486\) | 3.56928e13 | 0.0597147 | ||||||||
\(487\) | 3.12675e14 | 0.517230 | 0.258615 | − | 0.965981i | \(-0.416734\pi\) | ||||
0.258615 | + | 0.965981i | \(0.416734\pi\) | |||||||
\(488\) | −8.82054e13 | −0.144273 | ||||||||
\(489\) | 3.02976e14 | 0.490015 | ||||||||
\(490\) | −3.87380e14 | −0.619526 | ||||||||
\(491\) | −5.31503e14 | −0.840538 | −0.420269 | − | 0.907399i | \(-0.638064\pi\) | ||||
−0.420269 | + | 0.907399i | \(0.638064\pi\) | |||||||
\(492\) | −5.89849e13 | −0.0922429 | ||||||||
\(493\) | 2.32579e14 | 0.359677 | ||||||||
\(494\) | −3.30314e14 | −0.505160 | ||||||||
\(495\) | 1.62641e13 | 0.0245981 | ||||||||
\(496\) | −8.40737e14 | −1.25751 | ||||||||
\(497\) | −4.69966e14 | −0.695194 | ||||||||
\(498\) | 5.30420e14 | 0.775994 | ||||||||
\(499\) | −2.07233e14 | −0.299852 | −0.149926 | − | 0.988697i | \(-0.547904\pi\) | ||||
−0.149926 | + | 0.988697i | \(0.547904\pi\) | |||||||
\(500\) | −9.96086e13 | −0.142548 | ||||||||
\(501\) | −3.07507e14 | −0.435259 | ||||||||
\(502\) | 3.39747e14 | 0.475647 | ||||||||
\(503\) | −1.27957e15 | −1.77190 | −0.885952 | − | 0.463776i | \(-0.846494\pi\) | ||||
−0.885952 | + | 0.463776i | \(0.846494\pi\) | |||||||
\(504\) | −1.32515e14 | −0.181508 | ||||||||
\(505\) | −3.41141e14 | −0.462202 | ||||||||
\(506\) | −2.86460e13 | −0.0383915 | ||||||||
\(507\) | 2.72053e14 | 0.360669 | ||||||||
\(508\) | 2.22315e13 | 0.0291553 | ||||||||
\(509\) | 4.87736e14 | 0.632757 | 0.316379 | − | 0.948633i | \(-0.397533\pi\) | ||||
0.316379 | + | 0.948633i | \(0.397533\pi\) | |||||||
\(510\) | 3.43321e14 | 0.440620 | ||||||||
\(511\) | 4.29796e14 | 0.545691 | ||||||||
\(512\) | 8.92045e14 | 1.12047 | ||||||||
\(513\) | 1.37188e14 | 0.170479 | ||||||||
\(514\) | −8.48489e14 | −1.04316 | ||||||||
\(515\) | −5.23273e14 | −0.636485 | ||||||||
\(516\) | 9.46343e13 | 0.113887 | ||||||||
\(517\) | −1.30919e14 | −0.155885 | ||||||||
\(518\) | 3.88355e14 | 0.457526 | ||||||||
\(519\) | 7.64404e14 | 0.891050 | ||||||||
\(520\) | 5.08382e14 | 0.586370 | ||||||||
\(521\) | −6.24714e14 | −0.712974 | −0.356487 | − | 0.934300i | \(-0.616026\pi\) | ||||
−0.356487 | + | 0.934300i | \(0.616026\pi\) | |||||||
\(522\) | 1.09345e14 | 0.123484 | ||||||||
\(523\) | −6.72168e14 | −0.751136 | −0.375568 | − | 0.926795i | \(-0.622552\pi\) | ||||
−0.375568 | + | 0.926795i | \(0.622552\pi\) | |||||||
\(524\) | 1.83486e14 | 0.202900 | ||||||||
\(525\) | −4.82203e13 | −0.0527659 | ||||||||
\(526\) | −6.98987e14 | −0.756916 | ||||||||
\(527\) | −1.24965e15 | −1.33916 | ||||||||
\(528\) | −3.75853e13 | −0.0398594 | ||||||||
\(529\) | −7.07896e14 | −0.742957 | ||||||||
\(530\) | −3.42697e13 | −0.0355953 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −5.99867e13 | −0.0610297 | ||||||||
\(533\) | 7.28129e14 | 0.733177 | ||||||||
\(534\) | −2.66563e14 | −0.265658 | ||||||||
\(535\) | 3.49435e14 | 0.344684 | ||||||||
\(536\) | −4.59701e14 | −0.448817 | ||||||||
\(537\) | −1.01565e15 | −0.981485 | ||||||||
\(538\) | 2.93657e14 | 0.280891 | ||||||||
\(539\) | 6.30355e13 | 0.0596825 | ||||||||
\(540\) | −2.48676e13 | −0.0233061 | ||||||||
\(541\) | −1.89209e15 | −1.75532 | −0.877660 | − | 0.479284i | \(-0.840896\pi\) | ||||
−0.877660 | + | 0.479284i | \(0.840896\pi\) | |||||||
\(542\) | −8.05302e14 | −0.739542 | ||||||||
\(543\) | 3.94078e14 | 0.358248 | ||||||||
\(544\) | 2.66263e14 | 0.239617 | ||||||||
\(545\) | −1.90986e15 | −1.70146 | ||||||||
\(546\) | 1.92658e14 | 0.169913 | ||||||||
\(547\) | 4.47659e14 | 0.390856 | 0.195428 | − | 0.980718i | \(-0.437390\pi\) | ||||
0.195428 | + | 0.980718i | \(0.437390\pi\) | |||||||
\(548\) | −2.47306e14 | −0.213768 | ||||||||
\(549\) | −5.32607e13 | −0.0455784 | ||||||||
\(550\) | −1.58281e13 | −0.0134102 | ||||||||
\(551\) | 4.20277e14 | 0.352535 | ||||||||
\(552\) | 3.71889e14 | 0.308850 | ||||||||
\(553\) | −9.28463e14 | −0.763443 | ||||||||
\(554\) | 7.69088e14 | 0.626141 | ||||||||
\(555\) | 6.18792e14 | 0.498808 | ||||||||
\(556\) | 2.89651e14 | 0.231187 | ||||||||
\(557\) | −1.13843e15 | −0.899708 | −0.449854 | − | 0.893102i | \(-0.648524\pi\) | ||||
−0.449854 | + | 0.893102i | \(0.648524\pi\) | |||||||
\(558\) | −5.87514e14 | −0.459759 | ||||||||
\(559\) | −1.16820e15 | −0.905214 | ||||||||
\(560\) | −5.17804e14 | −0.397312 | ||||||||
\(561\) | −5.58660e13 | −0.0424474 | ||||||||
\(562\) | −2.31528e15 | −1.74202 | ||||||||
\(563\) | −7.36979e14 | −0.549110 | −0.274555 | − | 0.961571i | \(-0.588530\pi\) | ||||
−0.274555 | + | 0.961571i | \(0.588530\pi\) | |||||||
\(564\) | 2.00173e14 | 0.147697 | ||||||||
\(565\) | −6.74844e14 | −0.493102 | ||||||||
\(566\) | 1.35195e14 | 0.0978296 | ||||||||
\(567\) | −8.00159e13 | −0.0573416 | ||||||||
\(568\) | 2.00270e15 | 1.42135 | ||||||||
\(569\) | 5.76359e14 | 0.405112 | 0.202556 | − | 0.979271i | \(-0.435075\pi\) | ||||
0.202556 | + | 0.979271i | \(0.435075\pi\) | |||||||
\(570\) | 6.20390e14 | 0.431870 | ||||||||
\(571\) | −3.57344e14 | −0.246370 | −0.123185 | − | 0.992384i | \(-0.539311\pi\) | ||||
−0.123185 | + | 0.992384i | \(0.539311\pi\) | |||||||
\(572\) | −9.74298e12 | −0.00665294 | ||||||||
\(573\) | 3.68981e14 | 0.249548 | ||||||||
\(574\) | −8.58283e14 | −0.574930 | ||||||||
\(575\) | 1.35325e14 | 0.0897853 | ||||||||
\(576\) | 5.55655e14 | 0.365158 | ||||||||
\(577\) | −2.37673e15 | −1.54708 | −0.773542 | − | 0.633746i | \(-0.781517\pi\) | ||||
−0.773542 | + | 0.633746i | \(0.781517\pi\) | |||||||
\(578\) | 2.64456e14 | 0.170510 | ||||||||
\(579\) | 5.92523e14 | 0.378419 | ||||||||
\(580\) | −7.61821e13 | −0.0481947 | ||||||||
\(581\) | −1.18909e15 | −0.745154 | ||||||||
\(582\) | −1.94211e14 | −0.120558 | ||||||||
\(583\) | 5.57645e12 | 0.00342910 | ||||||||
\(584\) | −1.83152e15 | −1.11568 | ||||||||
\(585\) | 3.06974e14 | 0.185244 | ||||||||
\(586\) | −1.74849e15 | −1.04527 | ||||||||
\(587\) | 2.70630e15 | 1.60275 | 0.801376 | − | 0.598161i | \(-0.204102\pi\) | ||||
0.801376 | + | 0.598161i | \(0.204102\pi\) | |||||||
\(588\) | −9.63805e13 | −0.0565476 | ||||||||
\(589\) | −2.25816e15 | −1.31256 | ||||||||
\(590\) | 1.90906e14 | 0.109935 | ||||||||
\(591\) | 7.69357e14 | 0.438931 | ||||||||
\(592\) | −1.42999e15 | −0.808282 | ||||||||
\(593\) | 1.40696e15 | 0.787919 | 0.393959 | − | 0.919128i | \(-0.371105\pi\) | ||||
0.393959 | + | 0.919128i | \(0.371105\pi\) | |||||||
\(594\) | −2.62649e13 | −0.0145730 | ||||||||
\(595\) | −7.69654e14 | −0.423109 | ||||||||
\(596\) | −3.26920e14 | −0.178069 | ||||||||
\(597\) | 1.87076e14 | 0.100962 | ||||||||
\(598\) | −5.40673e14 | −0.289120 | ||||||||
\(599\) | −1.52686e15 | −0.809005 | −0.404503 | − | 0.914537i | \(-0.632555\pi\) | ||||
−0.404503 | + | 0.914537i | \(0.632555\pi\) | |||||||
\(600\) | 2.05484e14 | 0.107881 | ||||||||
\(601\) | 2.89353e15 | 1.50529 | 0.752643 | − | 0.658429i | \(-0.228779\pi\) | ||||
0.752643 | + | 0.658429i | \(0.228779\pi\) | |||||||
\(602\) | 1.37701e15 | 0.709835 | ||||||||
\(603\) | −2.77580e14 | −0.141789 | ||||||||
\(604\) | −5.29121e13 | −0.0267825 | ||||||||
\(605\) | 1.79658e15 | 0.901139 | ||||||||
\(606\) | 5.50909e14 | 0.273830 | ||||||||
\(607\) | −3.95001e15 | −1.94563 | −0.972815 | − | 0.231583i | \(-0.925610\pi\) | ||||
−0.972815 | + | 0.231583i | \(0.925610\pi\) | |||||||
\(608\) | 4.81145e14 | 0.234858 | ||||||||
\(609\) | −2.45129e14 | −0.118577 | ||||||||
\(610\) | −2.40854e14 | −0.115462 | ||||||||
\(611\) | −2.47100e15 | −1.17394 | ||||||||
\(612\) | 8.54184e13 | 0.0402178 | ||||||||
\(613\) | 2.65826e15 | 1.24041 | 0.620204 | − | 0.784441i | \(-0.287050\pi\) | ||||
0.620204 | + | 0.784441i | \(0.287050\pi\) | |||||||
\(614\) | −1.85788e15 | −0.859193 | ||||||||
\(615\) | −1.36756e15 | −0.626805 | ||||||||
\(616\) | 9.75123e13 | 0.0442961 | ||||||||
\(617\) | 1.38264e15 | 0.622502 | 0.311251 | − | 0.950328i | \(-0.399252\pi\) | ||||
0.311251 | + | 0.950328i | \(0.399252\pi\) | |||||||
\(618\) | 8.45033e14 | 0.377083 | ||||||||
\(619\) | −4.95786e14 | −0.219278 | −0.109639 | − | 0.993971i | \(-0.534969\pi\) | ||||
−0.109639 | + | 0.993971i | \(0.534969\pi\) | |||||||
\(620\) | 4.09328e14 | 0.179439 | ||||||||
\(621\) | 2.24556e14 | 0.0975711 | ||||||||
\(622\) | −2.88420e15 | −1.24216 | ||||||||
\(623\) | 5.97579e14 | 0.255100 | ||||||||
\(624\) | −7.09397e14 | −0.300175 | ||||||||
\(625\) | −1.88719e15 | −0.791545 | ||||||||
\(626\) | −2.64948e15 | −1.10154 | ||||||||
\(627\) | −1.00951e14 | −0.0416045 | ||||||||
\(628\) | 1.62078e14 | 0.0662135 | ||||||||
\(629\) | −2.12550e15 | −0.860763 | ||||||||
\(630\) | −3.61846e14 | −0.145262 | ||||||||
\(631\) | −4.17470e13 | −0.0166136 | −0.00830681 | − | 0.999965i | \(-0.502644\pi\) | ||||
−0.00830681 | + | 0.999965i | \(0.502644\pi\) | |||||||
\(632\) | 3.95652e15 | 1.56088 | ||||||||
\(633\) | −2.72651e15 | −1.06632 | ||||||||
\(634\) | 2.16392e15 | 0.838976 | ||||||||
\(635\) | 5.15434e14 | 0.198115 | ||||||||
\(636\) | −8.52632e12 | −0.00324898 | ||||||||
\(637\) | 1.18975e15 | 0.449459 | ||||||||
\(638\) | −8.04627e13 | −0.0301357 | ||||||||
\(639\) | 1.20928e15 | 0.449027 | ||||||||
\(640\) | 1.85946e15 | 0.684538 | ||||||||
\(641\) | 1.00484e15 | 0.366758 | 0.183379 | − | 0.983042i | \(-0.441296\pi\) | ||||
0.183379 | + | 0.983042i | \(0.441296\pi\) | |||||||
\(642\) | −5.64303e14 | −0.204207 | ||||||||
\(643\) | 2.31335e15 | 0.830004 | 0.415002 | − | 0.909820i | \(-0.363781\pi\) | ||||
0.415002 | + | 0.909820i | \(0.363781\pi\) | |||||||
\(644\) | −9.81890e13 | −0.0349294 | ||||||||
\(645\) | 2.19409e15 | 0.773883 | ||||||||
\(646\) | −2.13099e15 | −0.745251 | ||||||||
\(647\) | −1.17420e15 | −0.407162 | −0.203581 | − | 0.979058i | \(-0.565258\pi\) | ||||
−0.203581 | + | 0.979058i | \(0.565258\pi\) | |||||||
\(648\) | 3.40977e14 | 0.117237 | ||||||||
\(649\) | −3.10647e13 | −0.0105906 | ||||||||
\(650\) | −2.98745e14 | −0.100990 | ||||||||
\(651\) | 1.31708e15 | 0.441487 | ||||||||
\(652\) | 3.40885e14 | 0.113304 | ||||||||
\(653\) | 2.20085e15 | 0.725383 | 0.362692 | − | 0.931909i | \(-0.381858\pi\) | ||||
0.362692 | + | 0.931909i | \(0.381858\pi\) | |||||||
\(654\) | 3.08424e15 | 1.00802 | ||||||||
\(655\) | 4.25410e15 | 1.37874 | ||||||||
\(656\) | 3.16034e15 | 1.01569 | ||||||||
\(657\) | −1.10592e15 | −0.352463 | ||||||||
\(658\) | 2.91270e15 | 0.920561 | ||||||||
\(659\) | 7.28603e14 | 0.228361 | 0.114180 | − | 0.993460i | \(-0.463576\pi\) | ||||
0.114180 | + | 0.993460i | \(0.463576\pi\) | |||||||
\(660\) | 1.82991e13 | 0.00568771 | ||||||||
\(661\) | −3.22679e15 | −0.994634 | −0.497317 | − | 0.867569i | \(-0.665681\pi\) | ||||
−0.497317 | + | 0.867569i | \(0.665681\pi\) | |||||||
\(662\) | 4.53510e15 | 1.38633 | ||||||||
\(663\) | −1.05443e15 | −0.319665 | ||||||||
\(664\) | 5.06715e15 | 1.52349 | ||||||||
\(665\) | −1.39078e15 | −0.414707 | ||||||||
\(666\) | −9.99288e14 | −0.295517 | ||||||||
\(667\) | 6.87929e14 | 0.201768 | ||||||||
\(668\) | −3.45983e14 | −0.100643 | ||||||||
\(669\) | 1.54865e15 | 0.446796 | ||||||||
\(670\) | −1.25526e15 | −0.359190 | ||||||||
\(671\) | 3.91924e13 | 0.0111232 | ||||||||
\(672\) | −2.80631e14 | −0.0789958 | ||||||||
\(673\) | −3.32154e15 | −0.927376 | −0.463688 | − | 0.885998i | \(-0.653474\pi\) | ||||
−0.463688 | + | 0.885998i | \(0.653474\pi\) | |||||||
\(674\) | 3.76213e15 | 1.04185 | ||||||||
\(675\) | 1.24077e14 | 0.0340816 | ||||||||
\(676\) | 3.06092e14 | 0.0833960 | ||||||||
\(677\) | 9.35823e14 | 0.252904 | 0.126452 | − | 0.991973i | \(-0.459641\pi\) | ||||
0.126452 | + | 0.991973i | \(0.459641\pi\) | |||||||
\(678\) | 1.08981e15 | 0.292137 | ||||||||
\(679\) | 4.35381e14 | 0.115767 | ||||||||
\(680\) | 3.27978e15 | 0.865059 | ||||||||
\(681\) | 2.93589e15 | 0.768122 | ||||||||
\(682\) | 4.32328e14 | 0.112202 | ||||||||
\(683\) | −5.74313e14 | −0.147854 | −0.0739272 | − | 0.997264i | \(-0.523553\pi\) | ||||
−0.0739272 | + | 0.997264i | \(0.523553\pi\) | |||||||
\(684\) | 1.54353e14 | 0.0394192 | ||||||||
\(685\) | −5.73377e15 | −1.45259 | ||||||||
\(686\) | −3.31394e15 | −0.832842 | ||||||||
\(687\) | −3.03229e15 | −0.755978 | ||||||||
\(688\) | −5.07038e15 | −1.25402 | ||||||||
\(689\) | 1.05252e14 | 0.0258240 | ||||||||
\(690\) | 1.01548e15 | 0.247174 | ||||||||
\(691\) | 4.32175e15 | 1.04359 | 0.521796 | − | 0.853070i | \(-0.325262\pi\) | ||||
0.521796 | + | 0.853070i | \(0.325262\pi\) | |||||||
\(692\) | 8.60046e14 | 0.206034 | ||||||||
\(693\) | 5.88805e13 | 0.0139939 | ||||||||
\(694\) | 4.37168e15 | 1.03079 | ||||||||
\(695\) | 6.71552e15 | 1.57095 | ||||||||
\(696\) | 1.04459e15 | 0.242434 | ||||||||
\(697\) | 4.69746e15 | 1.08164 | ||||||||
\(698\) | −3.31147e14 | −0.0756512 | ||||||||
\(699\) | 3.15152e15 | 0.714324 | ||||||||
\(700\) | −5.42536e13 | −0.0122008 | ||||||||
\(701\) | 5.20866e14 | 0.116219 | 0.0581094 | − | 0.998310i | \(-0.481493\pi\) | ||||
0.0581094 | + | 0.998310i | \(0.481493\pi\) | |||||||
\(702\) | −4.95733e14 | −0.109747 | ||||||||
\(703\) | −3.84084e15 | −0.843669 | ||||||||
\(704\) | −4.08884e14 | −0.0891149 | ||||||||
\(705\) | 4.64099e15 | 1.00362 | ||||||||
\(706\) | −1.51034e15 | −0.324077 | ||||||||
\(707\) | −1.23502e15 | −0.262947 | ||||||||
\(708\) | 4.74976e13 | 0.0100343 | ||||||||
\(709\) | 7.72575e15 | 1.61952 | 0.809760 | − | 0.586762i | \(-0.199597\pi\) | ||||
0.809760 | + | 0.586762i | \(0.199597\pi\) | |||||||
\(710\) | 5.46858e15 | 1.13751 | ||||||||
\(711\) | 2.38905e15 | 0.493109 | ||||||||
\(712\) | −2.54650e15 | −0.521560 | ||||||||
\(713\) | −3.69626e15 | −0.751225 | ||||||||
\(714\) | 1.24291e15 | 0.250669 | ||||||||
\(715\) | −2.25890e14 | −0.0452078 | ||||||||
\(716\) | −1.14272e15 | −0.226945 | ||||||||
\(717\) | −1.76133e15 | −0.347125 | ||||||||
\(718\) | 2.52121e15 | 0.493089 | ||||||||
\(719\) | 5.14644e15 | 0.998844 | 0.499422 | − | 0.866359i | \(-0.333546\pi\) | ||||
0.499422 | + | 0.866359i | \(0.333546\pi\) | |||||||
\(720\) | 1.33238e15 | 0.256624 | ||||||||
\(721\) | −1.89439e15 | −0.362097 | ||||||||
\(722\) | 1.05651e15 | 0.200409 | ||||||||
\(723\) | 5.30824e15 | 0.999287 | ||||||||
\(724\) | 4.43386e14 | 0.0828361 | ||||||||
\(725\) | 3.80110e14 | 0.0704775 | ||||||||
\(726\) | −2.90130e15 | −0.533876 | ||||||||
\(727\) | 8.84127e15 | 1.61464 | 0.807320 | − | 0.590115i | \(-0.200917\pi\) | ||||
0.807320 | + | 0.590115i | \(0.200917\pi\) | |||||||
\(728\) | 1.84048e15 | 0.333586 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | −5.00116e15 | −0.892884 | ||||||||
\(731\) | −7.53652e15 | −1.33544 | ||||||||
\(732\) | −5.99247e13 | −0.0105389 | ||||||||
\(733\) | −4.36942e15 | −0.762698 | −0.381349 | − | 0.924431i | \(-0.624540\pi\) | ||||
−0.381349 | + | 0.924431i | \(0.624540\pi\) | |||||||
\(734\) | 6.01390e15 | 1.04190 | ||||||||
\(735\) | −2.23457e15 | −0.384250 | ||||||||
\(736\) | 7.87560e14 | 0.134417 | ||||||||
\(737\) | 2.04260e14 | 0.0346028 | ||||||||
\(738\) | 2.20847e15 | 0.371348 | ||||||||
\(739\) | −4.46605e15 | −0.745383 | −0.372691 | − | 0.927955i | \(-0.621565\pi\) | ||||
−0.372691 | + | 0.927955i | \(0.621565\pi\) | |||||||
\(740\) | 6.96216e14 | 0.115337 | ||||||||
\(741\) | −1.90539e15 | −0.313317 | ||||||||
\(742\) | −1.24066e14 | −0.0202502 | ||||||||
\(743\) | 1.09534e16 | 1.77464 | 0.887319 | − | 0.461157i | \(-0.152565\pi\) | ||||
0.887319 | + | 0.461157i | \(0.152565\pi\) | |||||||
\(744\) | −5.61258e15 | −0.902634 | ||||||||
\(745\) | −7.57960e15 | −1.21000 | ||||||||
\(746\) | −7.23325e15 | −1.14622 | ||||||||
\(747\) | 3.05968e15 | 0.481297 | ||||||||
\(748\) | −6.28560e13 | −0.00981494 | ||||||||
\(749\) | 1.26505e15 | 0.196091 | ||||||||
\(750\) | 3.72947e15 | 0.573866 | ||||||||
\(751\) | 6.98221e15 | 1.06653 | 0.533265 | − | 0.845948i | \(-0.320965\pi\) | ||||
0.533265 | + | 0.845948i | \(0.320965\pi\) | |||||||
\(752\) | −1.07250e16 | −1.62630 | ||||||||
\(753\) | 1.95980e15 | 0.295012 | ||||||||
\(754\) | −1.51868e15 | −0.226947 | ||||||||
\(755\) | −1.22676e15 | −0.181992 | ||||||||
\(756\) | −9.00276e13 | −0.0132588 | ||||||||
\(757\) | 8.12477e14 | 0.118791 | 0.0593955 | − | 0.998235i | \(-0.481083\pi\) | ||||
0.0593955 | + | 0.998235i | \(0.481083\pi\) | |||||||
\(758\) | 2.42612e15 | 0.352153 | ||||||||
\(759\) | −1.65242e14 | −0.0238117 | ||||||||
\(760\) | 5.92665e15 | 0.847880 | ||||||||
\(761\) | 9.50296e15 | 1.34972 | 0.674859 | − | 0.737946i | \(-0.264204\pi\) | ||||
0.674859 | + | 0.737946i | \(0.264204\pi\) | |||||||
\(762\) | −8.32374e14 | −0.117372 | ||||||||
\(763\) | −6.91422e15 | −0.967962 | ||||||||
\(764\) | 4.15148e14 | 0.0577018 | ||||||||
\(765\) | 1.98042e15 | 0.273287 | ||||||||
\(766\) | −4.56902e15 | −0.625986 | ||||||||
\(767\) | −5.86326e14 | −0.0797563 | ||||||||
\(768\) | 1.68021e15 | 0.226921 | ||||||||
\(769\) | 6.18404e15 | 0.829235 | 0.414617 | − | 0.909996i | \(-0.363915\pi\) | ||||
0.414617 | + | 0.909996i | \(0.363915\pi\) | |||||||
\(770\) | 2.66268e14 | 0.0354503 | ||||||||
\(771\) | −4.89444e15 | −0.646999 | ||||||||
\(772\) | 6.66660e14 | 0.0875002 | ||||||||
\(773\) | 1.21781e16 | 1.58705 | 0.793526 | − | 0.608537i | \(-0.208243\pi\) | ||||
0.793526 | + | 0.608537i | \(0.208243\pi\) | |||||||
\(774\) | −3.54323e15 | −0.458484 | ||||||||
\(775\) | −2.04234e15 | −0.262403 | ||||||||
\(776\) | −1.85532e15 | −0.236690 | ||||||||
\(777\) | 2.24020e15 | 0.283773 | ||||||||
\(778\) | −8.86430e15 | −1.11495 | ||||||||
\(779\) | 8.48843e15 | 1.06016 | ||||||||
\(780\) | 3.45383e14 | 0.0428332 | ||||||||
\(781\) | −8.89861e14 | −0.109583 | ||||||||
\(782\) | −3.48810e15 | −0.426533 | ||||||||
\(783\) | 6.30748e14 | 0.0765890 | ||||||||
\(784\) | 5.16394e15 | 0.622649 | ||||||||
\(785\) | 3.75777e15 | 0.449932 | ||||||||
\(786\) | −6.86995e15 | −0.816826 | ||||||||
\(787\) | −9.68489e15 | −1.14349 | −0.571747 | − | 0.820430i | \(-0.693734\pi\) | ||||
−0.571747 | + | 0.820430i | \(0.693734\pi\) | |||||||
\(788\) | 8.65619e14 | 0.101492 | ||||||||
\(789\) | −4.03205e15 | −0.469464 | ||||||||
\(790\) | 1.08037e16 | 1.24918 | ||||||||
\(791\) | −2.44312e15 | −0.280526 | ||||||||
\(792\) | −2.50911e14 | −0.0286109 | ||||||||
\(793\) | 7.39731e14 | 0.0837666 | ||||||||
\(794\) | −8.49162e15 | −0.954944 | ||||||||
\(795\) | −1.97682e14 | −0.0220774 | ||||||||
\(796\) | 2.10483e14 | 0.0233451 | ||||||||
\(797\) | −9.19553e15 | −1.01288 | −0.506438 | − | 0.862277i | \(-0.669038\pi\) | ||||
−0.506438 | + | 0.862277i | \(0.669038\pi\) | |||||||
\(798\) | 2.24598e15 | 0.245691 | ||||||||
\(799\) | −1.59415e16 | −1.73189 | ||||||||
\(800\) | 4.35160e14 | 0.0469520 | ||||||||
\(801\) | −1.53765e15 | −0.164770 | ||||||||
\(802\) | −8.12251e15 | −0.864433 | ||||||||
\(803\) | 8.13801e14 | 0.0860166 | ||||||||
\(804\) | −3.12311e14 | −0.0327853 | ||||||||
\(805\) | −2.27650e15 | −0.237351 | ||||||||
\(806\) | 8.15990e15 | 0.844972 | ||||||||
\(807\) | 1.69394e15 | 0.174218 | ||||||||
\(808\) | 5.26289e15 | 0.537603 | ||||||||
\(809\) | −1.38493e16 | −1.40511 | −0.702557 | − | 0.711628i | \(-0.747958\pi\) | ||||
−0.702557 | + | 0.711628i | \(0.747958\pi\) | |||||||
\(810\) | 9.31076e14 | 0.0938248 | ||||||||
\(811\) | 1.47735e16 | 1.47866 | 0.739332 | − | 0.673341i | \(-0.235141\pi\) | ||||
0.739332 | + | 0.673341i | \(0.235141\pi\) | |||||||
\(812\) | −2.75800e14 | −0.0274180 | ||||||||
\(813\) | −4.64532e15 | −0.458688 | ||||||||
\(814\) | 7.35335e14 | 0.0721193 | ||||||||
\(815\) | 7.90337e15 | 0.769920 | ||||||||
\(816\) | −4.57661e15 | −0.442841 | ||||||||
\(817\) | −1.36187e16 | −1.30892 | ||||||||
\(818\) | 1.21324e16 | 1.15825 | ||||||||
\(819\) | 1.11133e15 | 0.105386 | ||||||||
\(820\) | −1.53867e15 | −0.144934 | ||||||||
\(821\) | −6.05257e15 | −0.566307 | −0.283154 | − | 0.959075i | \(-0.591381\pi\) | ||||
−0.283154 | + | 0.959075i | \(0.591381\pi\) | |||||||
\(822\) | 9.25946e15 | 0.860579 | ||||||||
\(823\) | −1.42072e16 | −1.31163 | −0.655814 | − | 0.754923i | \(-0.727674\pi\) | ||||
−0.655814 | + | 0.754923i | \(0.727674\pi\) | |||||||
\(824\) | 8.07269e15 | 0.740319 | ||||||||
\(825\) | −9.13031e13 | −0.00831743 | ||||||||
\(826\) | 6.91132e14 | 0.0625419 | ||||||||
\(827\) | −1.76034e16 | −1.58240 | −0.791200 | − | 0.611558i | \(-0.790543\pi\) | ||||
−0.791200 | + | 0.611558i | \(0.790543\pi\) | |||||||
\(828\) | 2.52653e14 | 0.0225609 | ||||||||
\(829\) | 1.80575e16 | 1.60180 | 0.800900 | − | 0.598798i | \(-0.204355\pi\) | ||||
0.800900 | + | 0.598798i | \(0.204355\pi\) | |||||||
\(830\) | 1.38364e16 | 1.21925 | ||||||||
\(831\) | 4.43642e15 | 0.388353 | ||||||||
\(832\) | −7.71741e15 | −0.671110 | ||||||||
\(833\) | 7.67558e15 | 0.663077 | ||||||||
\(834\) | −1.08449e16 | −0.930706 | ||||||||
\(835\) | −8.02158e15 | −0.683887 | ||||||||
\(836\) | −1.13582e14 | −0.00962003 | ||||||||
\(837\) | −3.38903e15 | −0.285158 | ||||||||
\(838\) | −1.75528e14 | −0.0146725 | ||||||||
\(839\) | 1.10398e16 | 0.916793 | 0.458396 | − | 0.888748i | \(-0.348424\pi\) | ||||
0.458396 | + | 0.888748i | \(0.348424\pi\) | |||||||
\(840\) | −3.45675e15 | −0.285189 | ||||||||
\(841\) | −1.02682e16 | −0.841621 | ||||||||
\(842\) | 5.05224e15 | 0.411403 | ||||||||
\(843\) | −1.33555e16 | −1.08046 | ||||||||
\(844\) | −3.06766e15 | −0.246560 | ||||||||
\(845\) | 7.09671e15 | 0.566689 | ||||||||
\(846\) | −7.49474e15 | −0.594592 | ||||||||
\(847\) | 6.50410e15 | 0.512659 | ||||||||
\(848\) | 4.56829e14 | 0.0357748 | ||||||||
\(849\) | 7.79861e14 | 0.0606771 | ||||||||
\(850\) | −1.92733e15 | −0.148988 | ||||||||
\(851\) | −6.28687e15 | −0.482861 | ||||||||
\(852\) | 1.36059e15 | 0.103827 | ||||||||
\(853\) | 2.18701e16 | 1.65818 | 0.829089 | − | 0.559117i | \(-0.188860\pi\) | ||||
0.829089 | + | 0.559117i | \(0.188860\pi\) | |||||||
\(854\) | −8.71958e14 | −0.0656867 | ||||||||
\(855\) | 3.57867e15 | 0.267860 | ||||||||
\(856\) | −5.39085e15 | −0.400914 | ||||||||
\(857\) | −1.48496e16 | −1.09729 | −0.548645 | − | 0.836055i | \(-0.684856\pi\) | ||||
−0.548645 | + | 0.836055i | \(0.684856\pi\) | |||||||
\(858\) | 3.64790e14 | 0.0267832 | ||||||||
\(859\) | 8.24023e15 | 0.601142 | 0.300571 | − | 0.953760i | \(-0.402823\pi\) | ||||
0.300571 | + | 0.953760i | \(0.402823\pi\) | |||||||
\(860\) | 2.46861e15 | 0.178942 | ||||||||
\(861\) | −4.95093e15 | −0.356590 | ||||||||
\(862\) | −1.47932e16 | −1.05870 | ||||||||
\(863\) | −4.56565e15 | −0.324671 | −0.162336 | − | 0.986736i | \(-0.551903\pi\) | ||||
−0.162336 | + | 0.986736i | \(0.551903\pi\) | |||||||
\(864\) | 7.22098e14 | 0.0510235 | ||||||||
\(865\) | 1.99401e16 | 1.40003 | ||||||||
\(866\) | 1.07883e16 | 0.752673 | ||||||||
\(867\) | 1.52549e15 | 0.105756 | ||||||||
\(868\) | 1.48188e15 | 0.102083 | ||||||||
\(869\) | −1.75801e15 | −0.120341 | ||||||||
\(870\) | 2.85235e15 | 0.194021 | ||||||||
\(871\) | 3.85527e15 | 0.260588 | ||||||||
\(872\) | 2.94641e16 | 1.97903 | ||||||||
\(873\) | −1.12029e15 | −0.0747743 | ||||||||
\(874\) | −6.30310e15 | −0.418063 | ||||||||
\(875\) | −8.36070e15 | −0.551059 | ||||||||
\(876\) | −1.24429e15 | −0.0814985 | ||||||||
\(877\) | −1.90914e16 | −1.24263 | −0.621314 | − | 0.783562i | \(-0.713401\pi\) | ||||
−0.621314 | + | 0.783562i | \(0.713401\pi\) | |||||||
\(878\) | 1.96258e16 | 1.26943 | ||||||||
\(879\) | −1.00860e16 | −0.648308 | ||||||||
\(880\) | −9.80441e14 | −0.0626278 | ||||||||
\(881\) | −4.49894e15 | −0.285590 | −0.142795 | − | 0.989752i | \(-0.545609\pi\) | ||||
−0.142795 | + | 0.989752i | \(0.545609\pi\) | |||||||
\(882\) | 3.60861e15 | 0.227647 | ||||||||
\(883\) | −2.15548e16 | −1.35133 | −0.675663 | − | 0.737211i | \(-0.736143\pi\) | ||||
−0.675663 | + | 0.737211i | \(0.736143\pi\) | |||||||
\(884\) | −1.18636e15 | −0.0739147 | ||||||||
\(885\) | 1.10123e15 | 0.0681850 | ||||||||
\(886\) | −1.18687e16 | −0.730330 | ||||||||
\(887\) | −2.49524e16 | −1.52592 | −0.762962 | − | 0.646443i | \(-0.776256\pi\) | ||||
−0.762962 | + | 0.646443i | \(0.776256\pi\) | |||||||
\(888\) | −9.54630e15 | −0.580181 | ||||||||
\(889\) | 1.86601e15 | 0.112708 | ||||||||
\(890\) | −6.95351e15 | −0.417406 | ||||||||
\(891\) | −1.51507e14 | −0.00903868 | ||||||||
\(892\) | 1.74242e15 | 0.103311 | ||||||||
\(893\) | −2.88066e16 | −1.69750 | ||||||||
\(894\) | 1.22403e16 | 0.716862 | ||||||||
\(895\) | −2.64939e16 | −1.54213 | ||||||||
\(896\) | 6.73175e15 | 0.389434 | ||||||||
\(897\) | −3.11883e15 | −0.179322 | ||||||||
\(898\) | 2.44307e15 | 0.139610 | ||||||||
\(899\) | −1.03823e16 | −0.589678 | ||||||||
\(900\) | 1.39601e14 | 0.00788054 | ||||||||
\(901\) | 6.79022e14 | 0.0380976 | ||||||||
\(902\) | −1.62512e15 | −0.0906255 | ||||||||
\(903\) | 7.94318e15 | 0.440263 | ||||||||
\(904\) | 1.04110e16 | 0.573545 | ||||||||
\(905\) | 1.02798e16 | 0.562885 | ||||||||
\(906\) | 1.98110e15 | 0.107820 | ||||||||
\(907\) | 1.55921e16 | 0.843462 | 0.421731 | − | 0.906721i | \(-0.361423\pi\) | ||||
0.421731 | + | 0.906721i | \(0.361423\pi\) | |||||||
\(908\) | 3.30323e15 | 0.177609 | ||||||||
\(909\) | 3.17787e15 | 0.169838 | ||||||||
\(910\) | 5.02563e15 | 0.266970 | ||||||||
\(911\) | 8.10417e15 | 0.427915 | 0.213957 | − | 0.976843i | \(-0.431365\pi\) | ||||
0.213957 | + | 0.976843i | \(0.431365\pi\) | |||||||
\(912\) | −8.27005e15 | −0.434047 | ||||||||
\(913\) | −2.25150e15 | −0.117458 | ||||||||
\(914\) | 2.18823e16 | 1.13472 | ||||||||
\(915\) | −1.38935e15 | −0.0716135 | ||||||||
\(916\) | −3.41169e15 | −0.174801 | ||||||||
\(917\) | 1.54010e16 | 0.784364 | ||||||||
\(918\) | −3.19817e15 | −0.161908 | ||||||||
\(919\) | −3.49537e16 | −1.75897 | −0.879484 | − | 0.475928i | \(-0.842112\pi\) | ||||
−0.879484 | + | 0.475928i | \(0.842112\pi\) | |||||||
\(920\) | 9.70101e15 | 0.485271 | ||||||||
\(921\) | −1.07170e16 | −0.532900 | ||||||||
\(922\) | 3.64230e16 | 1.80035 | ||||||||
\(923\) | −1.67955e16 | −0.825248 | ||||||||
\(924\) | 6.62476e13 | 0.00323575 | ||||||||
\(925\) | −3.47376e15 | −0.168663 | ||||||||
\(926\) | −1.28918e16 | −0.622232 | ||||||||
\(927\) | 4.87450e15 | 0.233879 | ||||||||
\(928\) | 2.21215e15 | 0.105512 | ||||||||
\(929\) | −2.60620e16 | −1.23572 | −0.617861 | − | 0.786287i | \(-0.712001\pi\) | ||||
−0.617861 | + | 0.786287i | \(0.712001\pi\) | |||||||
\(930\) | −1.53258e16 | −0.722381 | ||||||||
\(931\) | 1.38700e16 | 0.649909 | ||||||||
\(932\) | 3.54584e15 | 0.165170 | ||||||||
\(933\) | −1.66373e16 | −0.770430 | ||||||||
\(934\) | −1.44069e16 | −0.663226 | ||||||||
\(935\) | −1.45731e15 | −0.0666941 | ||||||||
\(936\) | −4.73579e15 | −0.215464 | ||||||||
\(937\) | −4.21844e16 | −1.90802 | −0.954012 | − | 0.299770i | \(-0.903090\pi\) | ||||
−0.954012 | + | 0.299770i | \(0.903090\pi\) | |||||||
\(938\) | −4.54440e15 | −0.204343 | ||||||||
\(939\) | −1.52833e16 | −0.683212 | ||||||||
\(940\) | 5.22168e15 | 0.232063 | ||||||||
\(941\) | −1.68830e16 | −0.745944 | −0.372972 | − | 0.927842i | \(-0.621661\pi\) | ||||
−0.372972 | + | 0.927842i | \(0.621661\pi\) | |||||||
\(942\) | −6.06842e15 | −0.266560 | ||||||||
\(943\) | 1.38943e16 | 0.606766 | ||||||||
\(944\) | −2.54486e15 | −0.110489 | ||||||||
\(945\) | −2.08728e15 | −0.0900960 | ||||||||
\(946\) | 2.60732e15 | 0.111890 | ||||||||
\(947\) | 1.02757e16 | 0.438416 | 0.219208 | − | 0.975678i | \(-0.429653\pi\) | ||||
0.219208 | + | 0.975678i | \(0.429653\pi\) | |||||||
\(948\) | 2.68797e15 | 0.114020 | ||||||||
\(949\) | 1.53600e16 | 0.647777 | ||||||||
\(950\) | −3.48273e15 | −0.146029 | ||||||||
\(951\) | 1.24824e16 | 0.520360 | ||||||||
\(952\) | 1.18737e16 | 0.492133 | ||||||||
\(953\) | −3.75513e16 | −1.54744 | −0.773719 | − | 0.633528i | \(-0.781606\pi\) | ||||
−0.773719 | + | 0.633528i | \(0.781606\pi\) | |||||||
\(954\) | 3.19236e14 | 0.0130797 | ||||||||
\(955\) | 9.62516e15 | 0.392093 | ||||||||
\(956\) | −1.98171e15 | −0.0802643 | ||||||||
\(957\) | −4.64142e14 | −0.0186911 | ||||||||
\(958\) | −1.61691e16 | −0.647404 | ||||||||
\(959\) | −2.07578e16 | −0.826378 | ||||||||
\(960\) | 1.44947e16 | 0.573743 | ||||||||
\(961\) | 3.03758e16 | 1.19550 | ||||||||
\(962\) | 1.38790e16 | 0.543118 | ||||||||
\(963\) | −3.25514e15 | −0.126656 | ||||||||
\(964\) | 5.97241e15 | 0.231061 | ||||||||
\(965\) | 1.54564e16 | 0.594578 | ||||||||
\(966\) | 3.67632e15 | 0.140617 | ||||||||
\(967\) | −7.88651e13 | −0.00299943 | −0.00149972 | − | 0.999999i | \(-0.500477\pi\) | ||||
−0.00149972 | + | 0.999999i | \(0.500477\pi\) | |||||||
\(968\) | −2.77164e16 | −1.04815 | ||||||||
\(969\) | −1.22924e16 | −0.462229 | ||||||||
\(970\) | −5.06615e15 | −0.189423 | ||||||||
\(971\) | −2.34143e16 | −0.870515 | −0.435257 | − | 0.900306i | \(-0.643343\pi\) | ||||
−0.435257 | + | 0.900306i | \(0.643343\pi\) | |||||||
\(972\) | 2.31652e14 | 0.00856391 | ||||||||
\(973\) | 2.43120e16 | 0.893718 | ||||||||
\(974\) | −1.31717e16 | −0.481469 | ||||||||
\(975\) | −1.72329e15 | −0.0626372 | ||||||||
\(976\) | 3.21069e15 | 0.116044 | ||||||||
\(977\) | −1.70904e16 | −0.614233 | −0.307117 | − | 0.951672i | \(-0.599364\pi\) | ||||
−0.307117 | + | 0.951672i | \(0.599364\pi\) | |||||||
\(978\) | −1.27632e16 | −0.456136 | ||||||||
\(979\) | 1.13149e15 | 0.0402112 | ||||||||
\(980\) | −2.51416e15 | −0.0888485 | ||||||||
\(981\) | 1.77912e16 | 0.625209 | ||||||||
\(982\) | 2.23901e16 | 0.782424 | ||||||||
\(983\) | −3.92844e16 | −1.36514 | −0.682568 | − | 0.730822i | \(-0.739137\pi\) | ||||
−0.682568 | + | 0.730822i | \(0.739137\pi\) | |||||||
\(984\) | 2.10977e16 | 0.729060 | ||||||||
\(985\) | 2.00693e16 | 0.689656 | ||||||||
\(986\) | −9.79762e15 | −0.334809 | ||||||||
\(987\) | 1.68016e16 | 0.570962 | ||||||||
\(988\) | −2.14379e15 | −0.0724469 | ||||||||
\(989\) | −2.22917e16 | −0.749141 | ||||||||
\(990\) | −6.85141e14 | −0.0228974 | ||||||||
\(991\) | −2.16313e16 | −0.718914 | −0.359457 | − | 0.933162i | \(-0.617038\pi\) | ||||
−0.359457 | + | 0.933162i | \(0.617038\pi\) | |||||||
\(992\) | −1.18859e16 | −0.392843 | ||||||||
\(993\) | 2.61603e16 | 0.859850 | ||||||||
\(994\) | 1.97978e16 | 0.647129 | ||||||||
\(995\) | 4.88003e15 | 0.158634 | ||||||||
\(996\) | 3.44251e15 | 0.111288 | ||||||||
\(997\) | −1.41029e16 | −0.453403 | −0.226702 | − | 0.973964i | \(-0.572794\pi\) | ||||
−0.226702 | + | 0.973964i | \(0.572794\pi\) | |||||||
\(998\) | 8.72991e15 | 0.279120 | ||||||||
\(999\) | −5.76431e15 | −0.183289 |
(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 | 177.12.a.a.1.9 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.a.1.9 | ✓ | 26 | 1.1 | even | 1 | trivial |