Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,22,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(27.9477344287\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{157921}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 39480 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(199.196\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1024.00 | −0.707107 | ||||||||
\(3\) | −174616. | −1.70730 | −0.853652 | − | 0.520844i | \(-0.825617\pi\) | ||||
−0.853652 | + | 0.520844i | \(0.825617\pi\) | |||||||
\(4\) | 1.04858e6 | 0.500000 | ||||||||
\(5\) | −9.76562e6 | −0.447214 | ||||||||
\(6\) | 1.78807e8 | 1.20725 | ||||||||
\(7\) | −9.60462e8 | −1.28514 | −0.642570 | − | 0.766227i | \(-0.722132\pi\) | ||||
−0.642570 | + | 0.766227i | \(0.722132\pi\) | |||||||
\(8\) | −1.07374e9 | −0.353553 | ||||||||
\(9\) | 2.00304e10 | 1.91489 | ||||||||
\(10\) | 1.00000e10 | 0.316228 | ||||||||
\(11\) | 8.54661e10 | 0.993507 | 0.496753 | − | 0.867892i | \(-0.334525\pi\) | ||||
0.496753 | + | 0.867892i | \(0.334525\pi\) | |||||||
\(12\) | −1.83098e11 | −0.853652 | ||||||||
\(13\) | 9.74302e11 | 1.96015 | 0.980073 | − | 0.198640i | \(-0.0636523\pi\) | ||||
0.980073 | + | 0.198640i | \(0.0636523\pi\) | |||||||
\(14\) | 9.83513e11 | 0.908732 | ||||||||
\(15\) | 1.70523e12 | 0.763529 | ||||||||
\(16\) | 1.09951e12 | 0.250000 | ||||||||
\(17\) | −1.17045e13 | −1.40812 | −0.704058 | − | 0.710143i | \(-0.748630\pi\) | ||||
−0.704058 | + | 0.710143i | \(0.748630\pi\) | |||||||
\(18\) | −2.05111e13 | −1.35403 | ||||||||
\(19\) | 1.41128e13 | 0.528081 | 0.264041 | − | 0.964512i | \(-0.414945\pi\) | ||||
0.264041 | + | 0.964512i | \(0.414945\pi\) | |||||||
\(20\) | −1.02400e13 | −0.223607 | ||||||||
\(21\) | 1.67712e14 | 2.19413 | ||||||||
\(22\) | −8.75173e13 | −0.702515 | ||||||||
\(23\) | −2.65862e13 | −0.133818 | −0.0669090 | − | 0.997759i | \(-0.521314\pi\) | ||||
−0.0669090 | + | 0.997759i | \(0.521314\pi\) | |||||||
\(24\) | 1.87492e14 | 0.603623 | ||||||||
\(25\) | 9.53674e13 | 0.200000 | ||||||||
\(26\) | −9.97685e14 | −1.38603 | ||||||||
\(27\) | −1.67108e15 | −1.56199 | ||||||||
\(28\) | −1.00712e15 | −0.642570 | ||||||||
\(29\) | 1.45075e15 | 0.640346 | 0.320173 | − | 0.947359i | \(-0.396259\pi\) | ||||
0.320173 | + | 0.947359i | \(0.396259\pi\) | |||||||
\(30\) | −1.74616e15 | −0.539897 | ||||||||
\(31\) | −7.63253e15 | −1.67252 | −0.836259 | − | 0.548335i | \(-0.815262\pi\) | ||||
−0.836259 | + | 0.548335i | \(0.815262\pi\) | |||||||
\(32\) | −1.12590e15 | −0.176777 | ||||||||
\(33\) | −1.49237e16 | −1.69622 | ||||||||
\(34\) | 1.19854e16 | 0.995688 | ||||||||
\(35\) | 9.37951e15 | 0.574732 | ||||||||
\(36\) | 2.10034e16 | 0.957443 | ||||||||
\(37\) | 1.09912e16 | 0.375773 | 0.187886 | − | 0.982191i | \(-0.439836\pi\) | ||||
0.187886 | + | 0.982191i | \(0.439836\pi\) | |||||||
\(38\) | −1.44515e16 | −0.373410 | ||||||||
\(39\) | −1.70129e17 | −3.34656 | ||||||||
\(40\) | 1.04858e16 | 0.158114 | ||||||||
\(41\) | 7.93639e16 | 0.923406 | 0.461703 | − | 0.887035i | \(-0.347239\pi\) | ||||
0.461703 | + | 0.887035i | \(0.347239\pi\) | |||||||
\(42\) | −1.71737e17 | −1.55148 | ||||||||
\(43\) | −8.36751e16 | −0.590442 | −0.295221 | − | 0.955429i | \(-0.595393\pi\) | ||||
−0.295221 | + | 0.955429i | \(0.595393\pi\) | |||||||
\(44\) | 8.96177e16 | 0.496753 | ||||||||
\(45\) | −1.95609e17 | −0.856363 | ||||||||
\(46\) | 2.72243e16 | 0.0946236 | ||||||||
\(47\) | 3.57127e17 | 0.990365 | 0.495183 | − | 0.868789i | \(-0.335101\pi\) | ||||
0.495183 | + | 0.868789i | \(0.335101\pi\) | |||||||
\(48\) | −1.91992e17 | −0.426826 | ||||||||
\(49\) | 3.63941e17 | 0.651586 | ||||||||
\(50\) | −9.76562e16 | −0.141421 | ||||||||
\(51\) | 2.04379e18 | 2.40408 | ||||||||
\(52\) | 1.02163e18 | 0.980073 | ||||||||
\(53\) | −8.17016e17 | −0.641702 | −0.320851 | − | 0.947130i | \(-0.603969\pi\) | ||||
−0.320851 | + | 0.947130i | \(0.603969\pi\) | |||||||
\(54\) | 1.71119e18 | 1.10449 | ||||||||
\(55\) | −8.34630e17 | −0.444310 | ||||||||
\(56\) | 1.03129e18 | 0.454366 | ||||||||
\(57\) | −2.46432e18 | −0.901595 | ||||||||
\(58\) | −1.48557e18 | −0.452793 | ||||||||
\(59\) | 8.21011e17 | 0.209124 | 0.104562 | − | 0.994518i | \(-0.466656\pi\) | ||||
0.104562 | + | 0.994518i | \(0.466656\pi\) | |||||||
\(60\) | 1.78807e18 | 0.381765 | ||||||||
\(61\) | 4.53683e18 | 0.814310 | 0.407155 | − | 0.913359i | \(-0.366521\pi\) | ||||
0.407155 | + | 0.913359i | \(0.366521\pi\) | |||||||
\(62\) | 7.81571e18 | 1.18265 | ||||||||
\(63\) | −1.92384e19 | −2.46090 | ||||||||
\(64\) | 1.15292e18 | 0.125000 | ||||||||
\(65\) | −9.51466e18 | −0.876604 | ||||||||
\(66\) | 1.52819e19 | 1.19941 | ||||||||
\(67\) | 8.02826e18 | 0.538066 | 0.269033 | − | 0.963131i | \(-0.413296\pi\) | ||||
0.269033 | + | 0.963131i | \(0.413296\pi\) | |||||||
\(68\) | −1.22730e19 | −0.704058 | ||||||||
\(69\) | 4.64238e18 | 0.228468 | ||||||||
\(70\) | −9.60462e18 | −0.406397 | ||||||||
\(71\) | −5.25728e19 | −1.91668 | −0.958338 | − | 0.285638i | \(-0.907794\pi\) | ||||
−0.958338 | + | 0.285638i | \(0.907794\pi\) | |||||||
\(72\) | −2.15075e19 | −0.677014 | ||||||||
\(73\) | 9.28698e18 | 0.252921 | 0.126460 | − | 0.991972i | \(-0.459638\pi\) | ||||
0.126460 | + | 0.991972i | \(0.459638\pi\) | |||||||
\(74\) | −1.12549e19 | −0.265711 | ||||||||
\(75\) | −1.66527e19 | −0.341461 | ||||||||
\(76\) | 1.47984e19 | 0.264041 | ||||||||
\(77\) | −8.20869e19 | −1.27680 | ||||||||
\(78\) | 1.74212e20 | 2.36638 | ||||||||
\(79\) | 1.08861e19 | 0.129356 | 0.0646781 | − | 0.997906i | \(-0.479398\pi\) | ||||
0.0646781 | + | 0.997906i | \(0.479398\pi\) | |||||||
\(80\) | −1.07374e19 | −0.111803 | ||||||||
\(81\) | 8.22724e19 | 0.751902 | ||||||||
\(82\) | −8.12687e19 | −0.652947 | ||||||||
\(83\) | −4.79994e19 | −0.339560 | −0.169780 | − | 0.985482i | \(-0.554306\pi\) | ||||
−0.169780 | + | 0.985482i | \(0.554306\pi\) | |||||||
\(84\) | 1.75859e20 | 1.09706 | ||||||||
\(85\) | 1.14302e20 | 0.629728 | ||||||||
\(86\) | 8.56833e19 | 0.417506 | ||||||||
\(87\) | −2.53325e20 | −1.09327 | ||||||||
\(88\) | −9.17685e19 | −0.351258 | ||||||||
\(89\) | 2.35270e20 | 0.799783 | 0.399891 | − | 0.916563i | \(-0.369048\pi\) | ||||
0.399891 | + | 0.916563i | \(0.369048\pi\) | |||||||
\(90\) | 2.00304e20 | 0.605540 | ||||||||
\(91\) | −9.35779e20 | −2.51906 | ||||||||
\(92\) | −2.78777e19 | −0.0669090 | ||||||||
\(93\) | 1.33276e21 | 2.85549 | ||||||||
\(94\) | −3.65698e20 | −0.700294 | ||||||||
\(95\) | −1.37820e20 | −0.236165 | ||||||||
\(96\) | 1.96600e20 | 0.301812 | ||||||||
\(97\) | 7.25967e20 | 0.999571 | 0.499786 | − | 0.866149i | \(-0.333412\pi\) | ||||
0.499786 | + | 0.866149i | \(0.333412\pi\) | |||||||
\(98\) | −3.72675e20 | −0.460741 | ||||||||
\(99\) | 1.71192e21 | 1.90245 | ||||||||
\(100\) | 1.00000e20 | 0.100000 | ||||||||
\(101\) | 3.23940e20 | 0.291803 | 0.145902 | − | 0.989299i | \(-0.453392\pi\) | ||||
0.145902 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(102\) | −2.09284e21 | −1.69994 | ||||||||
\(103\) | 5.76074e20 | 0.422364 | 0.211182 | − | 0.977447i | \(-0.432269\pi\) | ||||
0.211182 | + | 0.977447i | \(0.432269\pi\) | |||||||
\(104\) | −1.04615e21 | −0.693016 | ||||||||
\(105\) | −1.63781e21 | −0.981243 | ||||||||
\(106\) | 8.36624e20 | 0.453752 | ||||||||
\(107\) | −3.09648e21 | −1.52174 | −0.760868 | − | 0.648907i | \(-0.775226\pi\) | ||||
−0.760868 | + | 0.648907i | \(0.775226\pi\) | |||||||
\(108\) | −1.75225e21 | −0.780994 | ||||||||
\(109\) | −2.84500e21 | −1.15108 | −0.575539 | − | 0.817775i | \(-0.695208\pi\) | ||||
−0.575539 | + | 0.817775i | \(0.695208\pi\) | |||||||
\(110\) | 8.54661e20 | 0.314174 | ||||||||
\(111\) | −1.91923e21 | −0.641558 | ||||||||
\(112\) | −1.05604e21 | −0.321285 | ||||||||
\(113\) | −5.61097e21 | −1.55494 | −0.777471 | − | 0.628919i | \(-0.783498\pi\) | ||||
−0.777471 | + | 0.628919i | \(0.783498\pi\) | |||||||
\(114\) | 2.52347e21 | 0.637524 | ||||||||
\(115\) | 2.59631e20 | 0.0598452 | ||||||||
\(116\) | 1.52123e21 | 0.320173 | ||||||||
\(117\) | 1.95156e22 | 3.75345 | ||||||||
\(118\) | −8.40715e20 | −0.147873 | ||||||||
\(119\) | 1.12417e22 | 1.80963 | ||||||||
\(120\) | −1.83098e21 | −0.269948 | ||||||||
\(121\) | −9.57949e19 | −0.0129448 | ||||||||
\(122\) | −4.64572e21 | −0.575804 | ||||||||
\(123\) | −1.38582e22 | −1.57653 | ||||||||
\(124\) | −8.00329e21 | −0.836259 | ||||||||
\(125\) | −9.31323e20 | −0.0894427 | ||||||||
\(126\) | 1.97001e22 | 1.74012 | ||||||||
\(127\) | 1.60366e22 | 1.30368 | 0.651842 | − | 0.758355i | \(-0.273997\pi\) | ||||
0.651842 | + | 0.758355i | \(0.273997\pi\) | |||||||
\(128\) | −1.18059e21 | −0.0883883 | ||||||||
\(129\) | 1.46110e22 | 1.00806 | ||||||||
\(130\) | 9.74302e21 | 0.619852 | ||||||||
\(131\) | −1.39854e22 | −0.820969 | −0.410485 | − | 0.911868i | \(-0.634640\pi\) | ||||
−0.410485 | + | 0.911868i | \(0.634640\pi\) | |||||||
\(132\) | −1.56487e22 | −0.848109 | ||||||||
\(133\) | −1.35548e22 | −0.678659 | ||||||||
\(134\) | −8.22093e21 | −0.380470 | ||||||||
\(135\) | 1.63191e22 | 0.698542 | ||||||||
\(136\) | 1.25676e22 | 0.497844 | ||||||||
\(137\) | −3.49305e22 | −1.28127 | −0.640633 | − | 0.767847i | \(-0.721328\pi\) | ||||
−0.640633 | + | 0.767847i | \(0.721328\pi\) | |||||||
\(138\) | −4.75380e21 | −0.161551 | ||||||||
\(139\) | −1.16733e22 | −0.367737 | −0.183868 | − | 0.982951i | \(-0.558862\pi\) | ||||
−0.183868 | + | 0.982951i | \(0.558862\pi\) | |||||||
\(140\) | 9.83513e21 | 0.287366 | ||||||||
\(141\) | −6.23601e22 | −1.69085 | ||||||||
\(142\) | 5.38346e22 | 1.35529 | ||||||||
\(143\) | 8.32698e22 | 1.94742 | ||||||||
\(144\) | 2.20236e22 | 0.478722 | ||||||||
\(145\) | −1.41675e22 | −0.286371 | ||||||||
\(146\) | −9.50986e21 | −0.178842 | ||||||||
\(147\) | −6.35499e22 | −1.11246 | ||||||||
\(148\) | 1.15251e22 | 0.187886 | ||||||||
\(149\) | −2.99897e22 | −0.455530 | −0.227765 | − | 0.973716i | \(-0.573142\pi\) | ||||
−0.227765 | + | 0.973716i | \(0.573142\pi\) | |||||||
\(150\) | 1.70523e22 | 0.241449 | ||||||||
\(151\) | −8.80845e22 | −1.16317 | −0.581583 | − | 0.813487i | \(-0.697566\pi\) | ||||
−0.581583 | + | 0.813487i | \(0.697566\pi\) | |||||||
\(152\) | −1.51535e22 | −0.186705 | ||||||||
\(153\) | −2.34445e23 | −2.69638 | ||||||||
\(154\) | 8.40570e22 | 0.902831 | ||||||||
\(155\) | 7.45364e22 | 0.747972 | ||||||||
\(156\) | −1.78393e23 | −1.67328 | ||||||||
\(157\) | 1.76504e23 | 1.54813 | 0.774067 | − | 0.633104i | \(-0.218219\pi\) | ||||
0.774067 | + | 0.633104i | \(0.218219\pi\) | |||||||
\(158\) | −1.11473e22 | −0.0914686 | ||||||||
\(159\) | 1.42664e23 | 1.09558 | ||||||||
\(160\) | 1.09951e22 | 0.0790569 | ||||||||
\(161\) | 2.55351e22 | 0.171975 | ||||||||
\(162\) | −8.42469e22 | −0.531675 | ||||||||
\(163\) | 9.36633e22 | 0.554115 | 0.277057 | − | 0.960853i | \(-0.410641\pi\) | ||||
0.277057 | + | 0.960853i | \(0.410641\pi\) | |||||||
\(164\) | 8.32191e22 | 0.461703 | ||||||||
\(165\) | 1.45740e23 | 0.758571 | ||||||||
\(166\) | 4.91514e22 | 0.240105 | ||||||||
\(167\) | −2.77263e23 | −1.27166 | −0.635828 | − | 0.771831i | \(-0.719341\pi\) | ||||
−0.635828 | + | 0.771831i | \(0.719341\pi\) | |||||||
\(168\) | −1.80079e23 | −0.775740 | ||||||||
\(169\) | 7.02199e23 | 2.84217 | ||||||||
\(170\) | −1.17045e23 | −0.445285 | ||||||||
\(171\) | 2.82685e23 | 1.01122 | ||||||||
\(172\) | −8.77397e22 | −0.295221 | ||||||||
\(173\) | −3.84494e23 | −1.21732 | −0.608661 | − | 0.793431i | \(-0.708293\pi\) | ||||
−0.608661 | + | 0.793431i | \(0.708293\pi\) | |||||||
\(174\) | 2.59405e23 | 0.773055 | ||||||||
\(175\) | −9.15968e22 | −0.257028 | ||||||||
\(176\) | 9.39710e22 | 0.248377 | ||||||||
\(177\) | −1.43362e23 | −0.357037 | ||||||||
\(178\) | −2.40917e23 | −0.565532 | ||||||||
\(179\) | 4.54367e22 | 0.100566 | 0.0502828 | − | 0.998735i | \(-0.483988\pi\) | ||||
0.0502828 | + | 0.998735i | \(0.483988\pi\) | |||||||
\(180\) | −2.05111e23 | −0.428182 | ||||||||
\(181\) | 8.61960e23 | 1.69770 | 0.848852 | − | 0.528630i | \(-0.177294\pi\) | ||||
0.848852 | + | 0.528630i | \(0.177294\pi\) | |||||||
\(182\) | 9.58238e23 | 1.78125 | ||||||||
\(183\) | −7.92204e23 | −1.39027 | ||||||||
\(184\) | 2.85467e22 | 0.0473118 | ||||||||
\(185\) | −1.07336e23 | −0.168051 | ||||||||
\(186\) | −1.36475e24 | −2.01914 | ||||||||
\(187\) | −1.00034e24 | −1.39897 | ||||||||
\(188\) | 3.74475e23 | 0.495183 | ||||||||
\(189\) | 1.60501e24 | 2.00737 | ||||||||
\(190\) | 1.41128e23 | 0.166994 | ||||||||
\(191\) | −2.31575e23 | −0.259323 | −0.129661 | − | 0.991558i | \(-0.541389\pi\) | ||||
−0.129661 | + | 0.991558i | \(0.541389\pi\) | |||||||
\(192\) | −2.01319e23 | −0.213413 | ||||||||
\(193\) | −1.13487e24 | −1.13919 | −0.569595 | − | 0.821926i | \(-0.692900\pi\) | ||||
−0.569595 | + | 0.821926i | \(0.692900\pi\) | |||||||
\(194\) | −7.43390e23 | −0.706804 | ||||||||
\(195\) | 1.66141e24 | 1.49663 | ||||||||
\(196\) | 3.81620e23 | 0.325793 | ||||||||
\(197\) | −6.29771e23 | −0.509668 | −0.254834 | − | 0.966985i | \(-0.582021\pi\) | ||||
−0.254834 | + | 0.966985i | \(0.582021\pi\) | |||||||
\(198\) | −1.75300e24 | −1.34524 | ||||||||
\(199\) | −7.13426e23 | −0.519268 | −0.259634 | − | 0.965707i | \(-0.583602\pi\) | ||||
−0.259634 | + | 0.965707i | \(0.583602\pi\) | |||||||
\(200\) | −1.02400e23 | −0.0707107 | ||||||||
\(201\) | −1.40186e24 | −0.918642 | ||||||||
\(202\) | −3.31715e23 | −0.206336 | ||||||||
\(203\) | −1.39339e24 | −0.822935 | ||||||||
\(204\) | 2.14307e24 | 1.20204 | ||||||||
\(205\) | −7.75039e23 | −0.412960 | ||||||||
\(206\) | −5.89899e23 | −0.298657 | ||||||||
\(207\) | −5.32532e23 | −0.256246 | ||||||||
\(208\) | 1.07126e24 | 0.490036 | ||||||||
\(209\) | 1.20617e24 | 0.524652 | ||||||||
\(210\) | 1.67712e24 | 0.693843 | ||||||||
\(211\) | −2.57567e24 | −1.01374 | −0.506868 | − | 0.862024i | \(-0.669197\pi\) | ||||
−0.506868 | + | 0.862024i | \(0.669197\pi\) | |||||||
\(212\) | −8.56703e23 | −0.320851 | ||||||||
\(213\) | 9.18005e24 | 3.27235 | ||||||||
\(214\) | 3.17080e24 | 1.07603 | ||||||||
\(215\) | 8.17140e23 | 0.264054 | ||||||||
\(216\) | 1.79431e24 | 0.552246 | ||||||||
\(217\) | 7.33075e24 | 2.14942 | ||||||||
\(218\) | 2.91328e24 | 0.813934 | ||||||||
\(219\) | −1.62165e24 | −0.431812 | ||||||||
\(220\) | −8.75173e23 | −0.222155 | ||||||||
\(221\) | −1.14037e25 | −2.76011 | ||||||||
\(222\) | 1.96529e24 | 0.453650 | ||||||||
\(223\) | −7.24650e24 | −1.59561 | −0.797806 | − | 0.602914i | \(-0.794006\pi\) | ||||
−0.797806 | + | 0.602914i | \(0.794006\pi\) | |||||||
\(224\) | 1.08138e24 | 0.227183 | ||||||||
\(225\) | 1.91025e24 | 0.382977 | ||||||||
\(226\) | 5.74563e24 | 1.09951 | ||||||||
\(227\) | −1.55126e24 | −0.283409 | −0.141704 | − | 0.989909i | \(-0.545258\pi\) | ||||
−0.141704 | + | 0.989909i | \(0.545258\pi\) | |||||||
\(228\) | −2.58403e24 | −0.450798 | ||||||||
\(229\) | −9.95437e24 | −1.65860 | −0.829299 | − | 0.558805i | \(-0.811260\pi\) | ||||
−0.829299 | + | 0.558805i | \(0.811260\pi\) | |||||||
\(230\) | −2.65862e23 | −0.0423170 | ||||||||
\(231\) | 1.43337e25 | 2.17988 | ||||||||
\(232\) | −1.55773e24 | −0.226396 | ||||||||
\(233\) | −4.62738e23 | −0.0642833 | −0.0321417 | − | 0.999483i | \(-0.510233\pi\) | ||||
−0.0321417 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(234\) | −1.99840e25 | −2.65409 | ||||||||
\(235\) | −3.48757e24 | −0.442905 | ||||||||
\(236\) | 8.60892e23 | 0.104562 | ||||||||
\(237\) | −1.90088e24 | −0.220850 | ||||||||
\(238\) | −1.15115e25 | −1.27960 | ||||||||
\(239\) | 1.06208e25 | 1.12975 | 0.564873 | − | 0.825178i | \(-0.308925\pi\) | ||||
0.564873 | + | 0.825178i | \(0.308925\pi\) | |||||||
\(240\) | 1.87492e24 | 0.190882 | ||||||||
\(241\) | 1.67701e24 | 0.163439 | 0.0817195 | − | 0.996655i | \(-0.473959\pi\) | ||||
0.0817195 | + | 0.996655i | \(0.473959\pi\) | |||||||
\(242\) | 9.80940e22 | 0.00915337 | ||||||||
\(243\) | 3.11401e24 | 0.278262 | ||||||||
\(244\) | 4.75722e24 | 0.407155 | ||||||||
\(245\) | −3.55411e24 | −0.291398 | ||||||||
\(246\) | 1.41908e25 | 1.11478 | ||||||||
\(247\) | 1.37501e25 | 1.03512 | ||||||||
\(248\) | 8.19536e24 | 0.591324 | ||||||||
\(249\) | 8.38147e24 | 0.579732 | ||||||||
\(250\) | 9.53674e23 | 0.0632456 | ||||||||
\(251\) | −2.15807e25 | −1.37243 | −0.686216 | − | 0.727398i | \(-0.740730\pi\) | ||||
−0.686216 | + | 0.727398i | \(0.740730\pi\) | |||||||
\(252\) | −2.01729e25 | −1.23045 | ||||||||
\(253\) | −2.27222e24 | −0.132949 | ||||||||
\(254\) | −1.64214e25 | −0.921843 | ||||||||
\(255\) | −1.99589e25 | −1.07514 | ||||||||
\(256\) | 1.20893e24 | 0.0625000 | ||||||||
\(257\) | 7.72467e24 | 0.383338 | 0.191669 | − | 0.981460i | \(-0.438610\pi\) | ||||
0.191669 | + | 0.981460i | \(0.438610\pi\) | |||||||
\(258\) | −1.49617e25 | −0.712809 | ||||||||
\(259\) | −1.05566e25 | −0.482921 | ||||||||
\(260\) | −9.97685e24 | −0.438302 | ||||||||
\(261\) | 2.90592e25 | 1.22619 | ||||||||
\(262\) | 1.43211e25 | 0.580513 | ||||||||
\(263\) | 1.35616e25 | 0.528174 | 0.264087 | − | 0.964499i | \(-0.414929\pi\) | ||||
0.264087 | + | 0.964499i | \(0.414929\pi\) | |||||||
\(264\) | 1.60243e25 | 0.599703 | ||||||||
\(265\) | 7.97867e24 | 0.286978 | ||||||||
\(266\) | 1.38801e25 | 0.479884 | ||||||||
\(267\) | −4.10819e25 | −1.36547 | ||||||||
\(268\) | 8.41824e24 | 0.269033 | ||||||||
\(269\) | −2.23157e25 | −0.685822 | −0.342911 | − | 0.939368i | \(-0.611413\pi\) | ||||
−0.342911 | + | 0.939368i | \(0.611413\pi\) | |||||||
\(270\) | −1.67108e25 | −0.493944 | ||||||||
\(271\) | 8.79105e24 | 0.249956 | 0.124978 | − | 0.992160i | \(-0.460114\pi\) | ||||
0.124978 | + | 0.992160i | \(0.460114\pi\) | |||||||
\(272\) | −1.28692e25 | −0.352029 | ||||||||
\(273\) | 1.63402e26 | 4.30080 | ||||||||
\(274\) | 3.57689e25 | 0.905992 | ||||||||
\(275\) | 8.15068e24 | 0.198701 | ||||||||
\(276\) | 4.86789e24 | 0.114234 | ||||||||
\(277\) | 3.23947e25 | 0.731874 | 0.365937 | − | 0.930640i | \(-0.380749\pi\) | ||||
0.365937 | + | 0.930640i | \(0.380749\pi\) | |||||||
\(278\) | 1.19534e25 | 0.260029 | ||||||||
\(279\) | −1.52882e26 | −3.20268 | ||||||||
\(280\) | −1.00712e25 | −0.203199 | ||||||||
\(281\) | 1.62934e25 | 0.316662 | 0.158331 | − | 0.987386i | \(-0.449389\pi\) | ||||
0.158331 | + | 0.987386i | \(0.449389\pi\) | |||||||
\(282\) | 6.38568e25 | 1.19561 | ||||||||
\(283\) | 7.24900e25 | 1.30774 | 0.653869 | − | 0.756608i | \(-0.273145\pi\) | ||||
0.653869 | + | 0.756608i | \(0.273145\pi\) | |||||||
\(284\) | −5.51266e25 | −0.958338 | ||||||||
\(285\) | 2.40656e25 | 0.403206 | ||||||||
\(286\) | −8.52682e25 | −1.37703 | ||||||||
\(287\) | −7.62260e25 | −1.18671 | ||||||||
\(288\) | −2.25522e25 | −0.338507 | ||||||||
\(289\) | 6.79028e25 | 0.982790 | ||||||||
\(290\) | 1.45075e25 | 0.202495 | ||||||||
\(291\) | −1.26765e26 | −1.70657 | ||||||||
\(292\) | 9.73810e24 | 0.126460 | ||||||||
\(293\) | −7.90881e25 | −0.990835 | −0.495418 | − | 0.868655i | \(-0.664985\pi\) | ||||
−0.495418 | + | 0.868655i | \(0.664985\pi\) | |||||||
\(294\) | 6.50751e25 | 0.786625 | ||||||||
\(295\) | −8.01769e24 | −0.0935229 | ||||||||
\(296\) | −1.18017e25 | −0.132856 | ||||||||
\(297\) | −1.42821e26 | −1.55185 | ||||||||
\(298\) | 3.07095e25 | 0.322108 | ||||||||
\(299\) | −2.59030e25 | −0.262303 | ||||||||
\(300\) | −1.74616e25 | −0.170730 | ||||||||
\(301\) | 8.03667e25 | 0.758801 | ||||||||
\(302\) | 9.01985e25 | 0.822482 | ||||||||
\(303\) | −5.65651e25 | −0.498197 | ||||||||
\(304\) | 1.55172e25 | 0.132020 | ||||||||
\(305\) | −4.43050e25 | −0.364170 | ||||||||
\(306\) | 2.40072e26 | 1.90663 | ||||||||
\(307\) | −1.19014e26 | −0.913363 | −0.456682 | − | 0.889630i | \(-0.650962\pi\) | ||||
−0.456682 | + | 0.889630i | \(0.650962\pi\) | |||||||
\(308\) | −8.60744e25 | −0.638398 | ||||||||
\(309\) | −1.00592e26 | −0.721104 | ||||||||
\(310\) | −7.63253e25 | −0.528896 | ||||||||
\(311\) | −1.66399e26 | −1.11472 | −0.557360 | − | 0.830271i | \(-0.688186\pi\) | ||||
−0.557360 | + | 0.830271i | \(0.688186\pi\) | |||||||
\(312\) | 1.82674e26 | 1.18319 | ||||||||
\(313\) | 2.24533e25 | 0.140626 | 0.0703128 | − | 0.997525i | \(-0.477600\pi\) | ||||
0.0703128 | + | 0.997525i | \(0.477600\pi\) | |||||||
\(314\) | −1.80740e26 | −1.09470 | ||||||||
\(315\) | 1.87875e26 | 1.10055 | ||||||||
\(316\) | 1.14149e25 | 0.0646781 | ||||||||
\(317\) | 1.10755e26 | 0.607076 | 0.303538 | − | 0.952819i | \(-0.401832\pi\) | ||||
0.303538 | + | 0.952819i | \(0.401832\pi\) | |||||||
\(318\) | −1.46088e26 | −0.774693 | ||||||||
\(319\) | 1.23990e26 | 0.636188 | ||||||||
\(320\) | −1.12590e25 | −0.0559017 | ||||||||
\(321\) | 5.40695e26 | 2.59806 | ||||||||
\(322\) | −2.61479e25 | −0.121605 | ||||||||
\(323\) | −1.65183e26 | −0.743599 | ||||||||
\(324\) | 8.62689e25 | 0.375951 | ||||||||
\(325\) | 9.29166e25 | 0.392029 | ||||||||
\(326\) | −9.59112e25 | −0.391818 | ||||||||
\(327\) | 4.96783e26 | 1.96524 | ||||||||
\(328\) | −8.52164e25 | −0.326473 | ||||||||
\(329\) | −3.43007e26 | −1.27276 | ||||||||
\(330\) | −1.49237e26 | −0.536391 | ||||||||
\(331\) | −2.18220e26 | −0.759803 | −0.379901 | − | 0.925027i | \(-0.624042\pi\) | ||||
−0.379901 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(332\) | −5.03311e25 | −0.169780 | ||||||||
\(333\) | 2.20157e26 | 0.719562 | ||||||||
\(334\) | 2.83918e26 | 0.899196 | ||||||||
\(335\) | −7.84009e25 | −0.240631 | ||||||||
\(336\) | 1.84401e26 | 0.548531 | ||||||||
\(337\) | 5.33804e26 | 1.53910 | 0.769551 | − | 0.638585i | \(-0.220480\pi\) | ||||
0.769551 | + | 0.638585i | \(0.220480\pi\) | |||||||
\(338\) | −7.19052e26 | −2.00972 | ||||||||
\(339\) | 9.79765e26 | 2.65476 | ||||||||
\(340\) | 1.19854e26 | 0.314864 | ||||||||
\(341\) | −6.52322e26 | −1.66166 | ||||||||
\(342\) | −2.89469e26 | −0.715037 | ||||||||
\(343\) | 1.86911e26 | 0.447761 | ||||||||
\(344\) | 8.98455e25 | 0.208753 | ||||||||
\(345\) | −4.53357e25 | −0.102174 | ||||||||
\(346\) | 3.93722e26 | 0.860776 | ||||||||
\(347\) | −4.09971e26 | −0.869548 | −0.434774 | − | 0.900540i | \(-0.643172\pi\) | ||||
−0.434774 | + | 0.900540i | \(0.643172\pi\) | |||||||
\(348\) | −2.65630e26 | −0.546633 | ||||||||
\(349\) | 2.06527e26 | 0.412392 | 0.206196 | − | 0.978511i | \(-0.433892\pi\) | ||||
0.206196 | + | 0.978511i | \(0.433892\pi\) | |||||||
\(350\) | 9.37951e25 | 0.181746 | ||||||||
\(351\) | −1.62814e27 | −3.06172 | ||||||||
\(352\) | −9.62263e25 | −0.175629 | ||||||||
\(353\) | 2.63582e26 | 0.466961 | 0.233481 | − | 0.972361i | \(-0.424988\pi\) | ||||
0.233481 | + | 0.972361i | \(0.424988\pi\) | |||||||
\(354\) | 1.46802e26 | 0.252464 | ||||||||
\(355\) | 5.13406e26 | 0.857163 | ||||||||
\(356\) | 2.46699e26 | 0.399891 | ||||||||
\(357\) | −1.96298e27 | −3.08958 | ||||||||
\(358\) | −4.65272e25 | −0.0711107 | ||||||||
\(359\) | 2.72697e26 | 0.404751 | 0.202376 | − | 0.979308i | \(-0.435134\pi\) | ||||
0.202376 | + | 0.979308i | \(0.435134\pi\) | |||||||
\(360\) | 2.10034e26 | 0.302770 | ||||||||
\(361\) | −5.15038e26 | −0.721130 | ||||||||
\(362\) | −8.82647e26 | −1.20046 | ||||||||
\(363\) | 1.67273e25 | 0.0221007 | ||||||||
\(364\) | −9.81236e26 | −1.25953 | ||||||||
\(365\) | −9.06931e25 | −0.113110 | ||||||||
\(366\) | 8.11217e26 | 0.983072 | ||||||||
\(367\) | −1.67539e26 | −0.197297 | −0.0986487 | − | 0.995122i | \(-0.531452\pi\) | ||||
−0.0986487 | + | 0.995122i | \(0.531452\pi\) | |||||||
\(368\) | −2.92319e25 | −0.0334545 | ||||||||
\(369\) | 1.58969e27 | 1.76822 | ||||||||
\(370\) | 1.09912e26 | 0.118830 | ||||||||
\(371\) | 7.84712e26 | 0.824678 | ||||||||
\(372\) | 1.39750e27 | 1.42775 | ||||||||
\(373\) | 9.92406e26 | 0.985704 | 0.492852 | − | 0.870113i | \(-0.335954\pi\) | ||||
0.492852 | + | 0.870113i | \(0.335954\pi\) | |||||||
\(374\) | 1.02434e27 | 0.989223 | ||||||||
\(375\) | 1.62624e26 | 0.152706 | ||||||||
\(376\) | −3.83462e26 | −0.350147 | ||||||||
\(377\) | 1.41347e27 | 1.25517 | ||||||||
\(378\) | −1.64353e27 | −1.41943 | ||||||||
\(379\) | 1.41427e25 | 0.0118801 | 0.00594007 | − | 0.999982i | \(-0.498109\pi\) | ||||
0.00594007 | + | 0.999982i | \(0.498109\pi\) | |||||||
\(380\) | −1.44515e26 | −0.118083 | ||||||||
\(381\) | −2.80024e27 | −2.22578 | ||||||||
\(382\) | 2.37132e26 | 0.183369 | ||||||||
\(383\) | 2.51013e26 | 0.188847 | 0.0944234 | − | 0.995532i | \(-0.469899\pi\) | ||||
0.0944234 | + | 0.995532i | \(0.469899\pi\) | |||||||
\(384\) | 2.06150e26 | 0.150906 | ||||||||
\(385\) | 8.01630e26 | 0.571000 | ||||||||
\(386\) | 1.16211e27 | 0.805529 | ||||||||
\(387\) | −1.67604e27 | −1.13063 | ||||||||
\(388\) | 7.61232e26 | 0.499786 | ||||||||
\(389\) | −2.50259e27 | −1.59926 | −0.799629 | − | 0.600495i | \(-0.794970\pi\) | ||||
−0.799629 | + | 0.600495i | \(0.794970\pi\) | |||||||
\(390\) | −1.70129e27 | −1.05828 | ||||||||
\(391\) | 3.11178e26 | 0.188431 | ||||||||
\(392\) | −3.90779e26 | −0.230371 | ||||||||
\(393\) | 2.44208e27 | 1.40164 | ||||||||
\(394\) | 6.44886e26 | 0.360390 | ||||||||
\(395\) | −1.06309e26 | −0.0578498 | ||||||||
\(396\) | 1.79508e27 | 0.951226 | ||||||||
\(397\) | 3.29042e26 | 0.169805 | 0.0849027 | − | 0.996389i | \(-0.472942\pi\) | ||||
0.0849027 | + | 0.996389i | \(0.472942\pi\) | |||||||
\(398\) | 7.30548e26 | 0.367178 | ||||||||
\(399\) | 2.36689e27 | 1.15868 | ||||||||
\(400\) | 1.04858e26 | 0.0500000 | ||||||||
\(401\) | 8.45309e26 | 0.392645 | 0.196322 | − | 0.980539i | \(-0.437100\pi\) | ||||
0.196322 | + | 0.980539i | \(0.437100\pi\) | |||||||
\(402\) | 1.43551e27 | 0.649578 | ||||||||
\(403\) | −7.43638e27 | −3.27838 | ||||||||
\(404\) | 3.39676e26 | 0.145902 | ||||||||
\(405\) | −8.03441e26 | −0.336261 | ||||||||
\(406\) | 1.42683e27 | 0.581903 | ||||||||
\(407\) | 9.39371e26 | 0.373333 | ||||||||
\(408\) | −2.19450e27 | −0.849971 | ||||||||
\(409\) | −1.58724e27 | −0.599167 | −0.299583 | − | 0.954070i | \(-0.596848\pi\) | ||||
−0.299583 | + | 0.954070i | \(0.596848\pi\) | |||||||
\(410\) | 7.93639e26 | 0.292007 | ||||||||
\(411\) | 6.09943e27 | 2.18751 | ||||||||
\(412\) | 6.04057e26 | 0.211182 | ||||||||
\(413\) | −7.88550e26 | −0.268753 | ||||||||
\(414\) | 5.45313e26 | 0.181193 | ||||||||
\(415\) | 4.68745e26 | 0.151856 | ||||||||
\(416\) | −1.09697e27 | −0.346508 | ||||||||
\(417\) | 2.03834e27 | 0.627839 | ||||||||
\(418\) | −1.23512e27 | −0.370985 | ||||||||
\(419\) | −1.46560e25 | −0.00429308 | −0.00214654 | − | 0.999998i | \(-0.500683\pi\) | ||||
−0.00214654 | + | 0.999998i | \(0.500683\pi\) | |||||||
\(420\) | −1.71737e27 | −0.490621 | ||||||||
\(421\) | −2.07639e27 | −0.578559 | −0.289280 | − | 0.957245i | \(-0.593416\pi\) | ||||
−0.289280 | + | 0.957245i | \(0.593416\pi\) | |||||||
\(422\) | 2.63749e27 | 0.716819 | ||||||||
\(423\) | 7.15340e27 | 1.89644 | ||||||||
\(424\) | 8.77264e26 | 0.226876 | ||||||||
\(425\) | −1.11623e27 | −0.281623 | ||||||||
\(426\) | −9.40037e27 | −2.31390 | ||||||||
\(427\) | −4.35746e27 | −1.04650 | ||||||||
\(428\) | −3.24690e27 | −0.760868 | ||||||||
\(429\) | −1.45402e28 | −3.32483 | ||||||||
\(430\) | −8.36751e26 | −0.186714 | ||||||||
\(431\) | −2.88896e27 | −0.629115 | −0.314558 | − | 0.949238i | \(-0.601856\pi\) | ||||
−0.314558 | + | 0.949238i | \(0.601856\pi\) | |||||||
\(432\) | −1.83737e27 | −0.390497 | ||||||||
\(433\) | 6.58569e27 | 1.36609 | 0.683044 | − | 0.730377i | \(-0.260656\pi\) | ||||
0.683044 | + | 0.730377i | \(0.260656\pi\) | |||||||
\(434\) | −7.50669e27 | −1.51987 | ||||||||
\(435\) | 2.47387e27 | 0.488923 | ||||||||
\(436\) | −2.98320e27 | −0.575539 | ||||||||
\(437\) | −3.75206e26 | −0.0706668 | ||||||||
\(438\) | 1.66057e27 | 0.305337 | ||||||||
\(439\) | −9.33293e26 | −0.167548 | −0.0837742 | − | 0.996485i | \(-0.526697\pi\) | ||||
−0.0837742 | + | 0.996485i | \(0.526697\pi\) | |||||||
\(440\) | 8.96177e26 | 0.157087 | ||||||||
\(441\) | 7.28987e27 | 1.24771 | ||||||||
\(442\) | 1.16774e28 | 1.95169 | ||||||||
\(443\) | 9.69019e27 | 1.58159 | 0.790793 | − | 0.612083i | \(-0.209668\pi\) | ||||
0.790793 | + | 0.612083i | \(0.209668\pi\) | |||||||
\(444\) | −2.01246e27 | −0.320779 | ||||||||
\(445\) | −2.29756e27 | −0.357674 | ||||||||
\(446\) | 7.42042e27 | 1.12827 | ||||||||
\(447\) | 5.23669e27 | 0.777728 | ||||||||
\(448\) | −1.10734e27 | −0.160643 | ||||||||
\(449\) | −9.90883e27 | −1.40422 | −0.702111 | − | 0.712067i | \(-0.747759\pi\) | ||||
−0.702111 | + | 0.712067i | \(0.747759\pi\) | |||||||
\(450\) | −1.95609e27 | −0.270806 | ||||||||
\(451\) | 6.78293e27 | 0.917410 | ||||||||
\(452\) | −5.88353e27 | −0.777471 | ||||||||
\(453\) | 1.53810e28 | 1.98588 | ||||||||
\(454\) | 1.58849e27 | 0.200400 | ||||||||
\(455\) | 9.13847e27 | 1.12656 | ||||||||
\(456\) | 2.64605e27 | 0.318762 | ||||||||
\(457\) | −1.41062e28 | −1.66069 | −0.830346 | − | 0.557248i | \(-0.811857\pi\) | ||||
−0.830346 | + | 0.557248i | \(0.811857\pi\) | |||||||
\(458\) | 1.01933e28 | 1.17281 | ||||||||
\(459\) | 1.95591e28 | 2.19946 | ||||||||
\(460\) | 2.72243e26 | 0.0299226 | ||||||||
\(461\) | 1.40343e26 | 0.0150776 | 0.00753880 | − | 0.999972i | \(-0.497600\pi\) | ||||
0.00753880 | + | 0.999972i | \(0.497600\pi\) | |||||||
\(462\) | −1.46777e28 | −1.54141 | ||||||||
\(463\) | −1.54202e28 | −1.58303 | −0.791514 | − | 0.611150i | \(-0.790707\pi\) | ||||
−0.791514 | + | 0.611150i | \(0.790707\pi\) | |||||||
\(464\) | 1.59512e27 | 0.160086 | ||||||||
\(465\) | −1.30152e28 | −1.27702 | ||||||||
\(466\) | 4.73844e26 | 0.0454552 | ||||||||
\(467\) | 1.42166e28 | 1.33343 | 0.666713 | − | 0.745314i | \(-0.267701\pi\) | ||||
0.666713 | + | 0.745314i | \(0.267701\pi\) | |||||||
\(468\) | 2.04636e28 | 1.87673 | ||||||||
\(469\) | −7.71083e27 | −0.691491 | ||||||||
\(470\) | 3.57127e27 | 0.313181 | ||||||||
\(471\) | −3.08204e28 | −2.64313 | ||||||||
\(472\) | −8.81554e26 | −0.0739363 | ||||||||
\(473\) | −7.15138e27 | −0.586608 | ||||||||
\(474\) | 1.94650e27 | 0.156165 | ||||||||
\(475\) | 1.34590e27 | 0.105616 | ||||||||
\(476\) | 1.17878e28 | 0.904813 | ||||||||
\(477\) | −1.63651e28 | −1.22879 | ||||||||
\(478\) | −1.08757e28 | −0.798851 | ||||||||
\(479\) | 1.82659e28 | 1.31256 | 0.656280 | − | 0.754518i | \(-0.272129\pi\) | ||||
0.656280 | + | 0.754518i | \(0.272129\pi\) | |||||||
\(480\) | −1.91992e27 | −0.134974 | ||||||||
\(481\) | 1.07087e28 | 0.736569 | ||||||||
\(482\) | −1.71725e27 | −0.115569 | ||||||||
\(483\) | −4.45883e27 | −0.293613 | ||||||||
\(484\) | −1.00448e26 | −0.00647241 | ||||||||
\(485\) | −7.08952e27 | −0.447022 | ||||||||
\(486\) | −3.18875e27 | −0.196761 | ||||||||
\(487\) | 3.19696e28 | 1.93056 | 0.965280 | − | 0.261218i | \(-0.0841243\pi\) | ||||
0.965280 | + | 0.261218i | \(0.0841243\pi\) | |||||||
\(488\) | −4.87139e27 | −0.287902 | ||||||||
\(489\) | −1.63551e28 | −0.946042 | ||||||||
\(490\) | 3.63941e27 | 0.206050 | ||||||||
\(491\) | −1.06661e28 | −0.591086 | −0.295543 | − | 0.955329i | \(-0.595501\pi\) | ||||
−0.295543 | + | 0.955329i | \(0.595501\pi\) | |||||||
\(492\) | −1.45314e28 | −0.788267 | ||||||||
\(493\) | −1.69803e28 | −0.901681 | ||||||||
\(494\) | −1.40801e28 | −0.731937 | ||||||||
\(495\) | −1.67180e28 | −0.850802 | ||||||||
\(496\) | −8.39205e27 | −0.418129 | ||||||||
\(497\) | 5.04942e28 | 2.46320 | ||||||||
\(498\) | −8.58262e27 | −0.409932 | ||||||||
\(499\) | −1.19664e28 | −0.559638 | −0.279819 | − | 0.960053i | \(-0.590275\pi\) | ||||
−0.279819 | + | 0.960053i | \(0.590275\pi\) | |||||||
\(500\) | −9.76563e26 | −0.0447214 | ||||||||
\(501\) | 4.84146e28 | 2.17110 | ||||||||
\(502\) | 2.20986e28 | 0.970456 | ||||||||
\(503\) | −3.75074e28 | −1.61307 | −0.806534 | − | 0.591188i | \(-0.798659\pi\) | ||||
−0.806534 | + | 0.591188i | \(0.798659\pi\) | |||||||
\(504\) | 2.06571e28 | 0.870059 | ||||||||
\(505\) | −3.16348e27 | −0.130498 | ||||||||
\(506\) | 2.32675e27 | 0.0940092 | ||||||||
\(507\) | −1.22615e29 | −4.85245 | ||||||||
\(508\) | 1.68156e28 | 0.651842 | ||||||||
\(509\) | 3.27640e28 | 1.24411 | 0.622057 | − | 0.782972i | \(-0.286297\pi\) | ||||
0.622057 | + | 0.782972i | \(0.286297\pi\) | |||||||
\(510\) | 2.04379e28 | 0.760237 | ||||||||
\(511\) | −8.91979e27 | −0.325039 | ||||||||
\(512\) | −1.23794e27 | −0.0441942 | ||||||||
\(513\) | −2.35836e28 | −0.824857 | ||||||||
\(514\) | −7.91006e27 | −0.271061 | ||||||||
\(515\) | −5.62572e27 | −0.188887 | ||||||||
\(516\) | 1.53208e28 | 0.504032 | ||||||||
\(517\) | 3.05223e28 | 0.983934 | ||||||||
\(518\) | 1.08099e28 | 0.341477 | ||||||||
\(519\) | 6.71388e28 | 2.07834 | ||||||||
\(520\) | 1.02163e28 | 0.309926 | ||||||||
\(521\) | −5.49377e27 | −0.163333 | −0.0816667 | − | 0.996660i | \(-0.526024\pi\) | ||||
−0.0816667 | + | 0.996660i | \(0.526024\pi\) | |||||||
\(522\) | −2.97566e28 | −0.867047 | ||||||||
\(523\) | 9.60628e27 | 0.274339 | 0.137170 | − | 0.990548i | \(-0.456199\pi\) | ||||
0.137170 | + | 0.990548i | \(0.456199\pi\) | |||||||
\(524\) | −1.46648e28 | −0.410485 | ||||||||
\(525\) | 1.59943e28 | 0.438825 | ||||||||
\(526\) | −1.38871e28 | −0.373475 | ||||||||
\(527\) | 8.93347e28 | 2.35510 | ||||||||
\(528\) | −1.64088e28 | −0.424054 | ||||||||
\(529\) | −3.87648e28 | −0.982093 | ||||||||
\(530\) | −8.17016e27 | −0.202924 | ||||||||
\(531\) | 1.64452e28 | 0.400448 | ||||||||
\(532\) | −1.42133e28 | −0.339329 | ||||||||
\(533\) | 7.73244e28 | 1.81001 | ||||||||
\(534\) | 4.20679e28 | 0.965534 | ||||||||
\(535\) | 3.02391e28 | 0.680541 | ||||||||
\(536\) | −8.62027e27 | −0.190235 | ||||||||
\(537\) | −7.93397e27 | −0.171696 | ||||||||
\(538\) | 2.28513e28 | 0.484949 | ||||||||
\(539\) | 3.11046e28 | 0.647355 | ||||||||
\(540\) | 1.71119e28 | 0.349271 | ||||||||
\(541\) | −7.34453e28 | −1.47026 | −0.735128 | − | 0.677929i | \(-0.762878\pi\) | ||||
−0.735128 | + | 0.677929i | \(0.762878\pi\) | |||||||
\(542\) | −9.00204e27 | −0.176745 | ||||||||
\(543\) | −1.50512e29 | −2.89850 | ||||||||
\(544\) | 1.31781e28 | 0.248922 | ||||||||
\(545\) | 2.77832e28 | 0.514777 | ||||||||
\(546\) | −1.67324e29 | −3.04113 | ||||||||
\(547\) | 4.12363e28 | 0.735212 | 0.367606 | − | 0.929982i | \(-0.380178\pi\) | ||||
0.367606 | + | 0.929982i | \(0.380178\pi\) | |||||||
\(548\) | −3.66273e28 | −0.640633 | ||||||||
\(549\) | 9.08745e28 | 1.55931 | ||||||||
\(550\) | −8.34630e27 | −0.140503 | ||||||||
\(551\) | 2.04742e28 | 0.338155 | ||||||||
\(552\) | −4.98472e27 | −0.0807756 | ||||||||
\(553\) | −1.04557e28 | −0.166241 | ||||||||
\(554\) | −3.31722e28 | −0.517513 | ||||||||
\(555\) | 1.87425e28 | 0.286914 | ||||||||
\(556\) | −1.22403e28 | −0.183868 | ||||||||
\(557\) | −8.83426e27 | −0.130224 | −0.0651119 | − | 0.997878i | \(-0.520740\pi\) | ||||
−0.0651119 | + | 0.997878i | \(0.520740\pi\) | |||||||
\(558\) | 1.56552e29 | 2.26464 | ||||||||
\(559\) | −8.15248e28 | −1.15735 | ||||||||
\(560\) | 1.03129e28 | 0.143683 | ||||||||
\(561\) | 1.74675e29 | 2.38847 | ||||||||
\(562\) | −1.66845e28 | −0.223914 | ||||||||
\(563\) | −1.06900e29 | −1.40811 | −0.704057 | − | 0.710143i | \(-0.748630\pi\) | ||||
−0.704057 | + | 0.710143i | \(0.748630\pi\) | |||||||
\(564\) | −6.53893e28 | −0.845427 | ||||||||
\(565\) | 5.47946e28 | 0.695391 | ||||||||
\(566\) | −7.42298e28 | −0.924711 | ||||||||
\(567\) | −7.90195e28 | −0.966300 | ||||||||
\(568\) | 5.64496e28 | 0.677647 | ||||||||
\(569\) | −1.27688e29 | −1.50477 | −0.752386 | − | 0.658723i | \(-0.771097\pi\) | ||||
−0.752386 | + | 0.658723i | \(0.771097\pi\) | |||||||
\(570\) | −2.46432e28 | −0.285109 | ||||||||
\(571\) | −8.59333e28 | −0.976073 | −0.488037 | − | 0.872823i | \(-0.662287\pi\) | ||||
−0.488037 | + | 0.872823i | \(0.662287\pi\) | |||||||
\(572\) | 8.73147e28 | 0.973709 | ||||||||
\(573\) | 4.04366e28 | 0.442743 | ||||||||
\(574\) | 7.80555e28 | 0.839128 | ||||||||
\(575\) | −2.53546e27 | −0.0267636 | ||||||||
\(576\) | 2.30935e28 | 0.239361 | ||||||||
\(577\) | −1.28637e29 | −1.30925 | −0.654623 | − | 0.755956i | \(-0.727172\pi\) | ||||
−0.654623 | + | 0.755956i | \(0.727172\pi\) | |||||||
\(578\) | −6.95325e28 | −0.694937 | ||||||||
\(579\) | 1.98167e29 | 1.94494 | ||||||||
\(580\) | −1.48557e28 | −0.143186 | ||||||||
\(581\) | 4.61016e28 | 0.436382 | ||||||||
\(582\) | 1.29808e29 | 1.20673 | ||||||||
\(583\) | −6.98271e28 | −0.637536 | ||||||||
\(584\) | −9.97182e27 | −0.0894210 | ||||||||
\(585\) | −1.90582e29 | −1.67860 | ||||||||
\(586\) | 8.09863e28 | 0.700626 | ||||||||
\(587\) | −3.48294e28 | −0.295969 | −0.147985 | − | 0.988990i | \(-0.547279\pi\) | ||||
−0.147985 | + | 0.988990i | \(0.547279\pi\) | |||||||
\(588\) | −6.66369e28 | −0.556228 | ||||||||
\(589\) | −1.07716e29 | −0.883225 | ||||||||
\(590\) | 8.21011e27 | 0.0661307 | ||||||||
\(591\) | 1.09968e29 | 0.870158 | ||||||||
\(592\) | 1.20849e28 | 0.0939432 | ||||||||
\(593\) | −8.77330e28 | −0.670021 | −0.335011 | − | 0.942214i | \(-0.608740\pi\) | ||||
−0.335011 | + | 0.942214i | \(0.608740\pi\) | |||||||
\(594\) | 1.46248e29 | 1.09732 | ||||||||
\(595\) | −1.09782e29 | −0.809290 | ||||||||
\(596\) | −3.14465e28 | −0.227765 | ||||||||
\(597\) | 1.24576e29 | 0.886548 | ||||||||
\(598\) | 2.65247e28 | 0.185476 | ||||||||
\(599\) | −1.00705e29 | −0.691944 | −0.345972 | − | 0.938245i | \(-0.612451\pi\) | ||||
−0.345972 | + | 0.938245i | \(0.612451\pi\) | |||||||
\(600\) | 1.78807e28 | 0.120725 | ||||||||
\(601\) | −1.06089e29 | −0.703861 | −0.351930 | − | 0.936026i | \(-0.614475\pi\) | ||||
−0.351930 | + | 0.936026i | \(0.614475\pi\) | |||||||
\(602\) | −8.22955e28 | −0.536554 | ||||||||
\(603\) | 1.60809e29 | 1.03034 | ||||||||
\(604\) | −9.23633e28 | −0.581583 | ||||||||
\(605\) | 9.35497e26 | 0.00578910 | ||||||||
\(606\) | 5.79227e28 | 0.352278 | ||||||||
\(607\) | 5.05632e28 | 0.302241 | 0.151120 | − | 0.988515i | \(-0.451712\pi\) | ||||
0.151120 | + | 0.988515i | \(0.451712\pi\) | |||||||
\(608\) | −1.58896e28 | −0.0933525 | ||||||||
\(609\) | 2.43309e29 | 1.40500 | ||||||||
\(610\) | 4.53683e28 | 0.257507 | ||||||||
\(611\) | 3.47950e29 | 1.94126 | ||||||||
\(612\) | −2.45834e29 | −1.34819 | ||||||||
\(613\) | 1.21126e29 | 0.652985 | 0.326493 | − | 0.945200i | \(-0.394133\pi\) | ||||
0.326493 | + | 0.945200i | \(0.394133\pi\) | |||||||
\(614\) | 1.21870e29 | 0.645845 | ||||||||
\(615\) | 1.35334e29 | 0.705048 | ||||||||
\(616\) | 8.81402e28 | 0.451415 | ||||||||
\(617\) | 7.11151e28 | 0.358070 | 0.179035 | − | 0.983843i | \(-0.442702\pi\) | ||||
0.179035 | + | 0.983843i | \(0.442702\pi\) | |||||||
\(618\) | 1.03006e29 | 0.509898 | ||||||||
\(619\) | −1.87344e28 | −0.0911774 | −0.0455887 | − | 0.998960i | \(-0.514516\pi\) | ||||
−0.0455887 | + | 0.998960i | \(0.514516\pi\) | |||||||
\(620\) | 7.81571e28 | 0.373986 | ||||||||
\(621\) | 4.44277e28 | 0.209022 | ||||||||
\(622\) | 1.70392e29 | 0.788225 | ||||||||
\(623\) | −2.25968e29 | −1.02783 | ||||||||
\(624\) | −1.87058e29 | −0.836641 | ||||||||
\(625\) | 9.09495e27 | 0.0400000 | ||||||||
\(626\) | −2.29922e28 | −0.0994374 | ||||||||
\(627\) | −2.10616e29 | −0.895741 | ||||||||
\(628\) | 1.85078e29 | 0.774067 | ||||||||
\(629\) | −1.28646e29 | −0.529131 | ||||||||
\(630\) | −1.92384e29 | −0.778204 | ||||||||
\(631\) | 1.18886e29 | 0.472956 | 0.236478 | − | 0.971637i | \(-0.424007\pi\) | ||||
0.236478 | + | 0.971637i | \(0.424007\pi\) | |||||||
\(632\) | −1.16888e28 | −0.0457343 | ||||||||
\(633\) | 4.49753e29 | 1.73075 | ||||||||
\(634\) | −1.13414e29 | −0.429267 | ||||||||
\(635\) | −1.56607e29 | −0.583025 | ||||||||
\(636\) | 1.49594e29 | 0.547790 | ||||||||
\(637\) | 3.54588e29 | 1.27720 | ||||||||
\(638\) | −1.26966e29 | −0.449853 | ||||||||
\(639\) | −1.05305e30 | −3.67021 | ||||||||
\(640\) | 1.15292e28 | 0.0395285 | ||||||||
\(641\) | −4.05009e29 | −1.36602 | −0.683008 | − | 0.730411i | \(-0.739329\pi\) | ||||
−0.683008 | + | 0.730411i | \(0.739329\pi\) | |||||||
\(642\) | −5.53672e29 | −1.83711 | ||||||||
\(643\) | 2.92040e29 | 0.953296 | 0.476648 | − | 0.879094i | \(-0.341852\pi\) | ||||
0.476648 | + | 0.879094i | \(0.341852\pi\) | |||||||
\(644\) | 2.67754e28 | 0.0859875 | ||||||||
\(645\) | −1.42686e29 | −0.450820 | ||||||||
\(646\) | 1.69147e29 | 0.525804 | ||||||||
\(647\) | −1.30263e29 | −0.398407 | −0.199203 | − | 0.979958i | \(-0.563835\pi\) | ||||
−0.199203 | + | 0.979958i | \(0.563835\pi\) | |||||||
\(648\) | −8.83393e28 | −0.265838 | ||||||||
\(649\) | 7.01686e28 | 0.207766 | ||||||||
\(650\) | −9.51466e28 | −0.277206 | ||||||||
\(651\) | −1.28007e30 | −3.66971 | ||||||||
\(652\) | 9.82131e28 | 0.277057 | ||||||||
\(653\) | −1.49980e29 | −0.416337 | −0.208169 | − | 0.978093i | \(-0.566750\pi\) | ||||
−0.208169 | + | 0.978093i | \(0.566750\pi\) | |||||||
\(654\) | −5.08706e29 | −1.38963 | ||||||||
\(655\) | 1.36576e29 | 0.367149 | ||||||||
\(656\) | 8.72616e28 | 0.230852 | ||||||||
\(657\) | 1.86022e29 | 0.484314 | ||||||||
\(658\) | 3.51239e29 | 0.899976 | ||||||||
\(659\) | 3.09551e29 | 0.780613 | 0.390307 | − | 0.920685i | \(-0.372369\pi\) | ||||
0.390307 | + | 0.920685i | \(0.372369\pi\) | |||||||
\(660\) | 1.52819e29 | 0.379286 | ||||||||
\(661\) | −1.06593e29 | −0.260383 | −0.130191 | − | 0.991489i | \(-0.541559\pi\) | ||||
−0.130191 | + | 0.991489i | \(0.541559\pi\) | |||||||
\(662\) | 2.23457e29 | 0.537262 | ||||||||
\(663\) | 1.99127e30 | 4.71235 | ||||||||
\(664\) | 5.15390e28 | 0.120053 | ||||||||
\(665\) | 1.32371e29 | 0.303505 | ||||||||
\(666\) | −2.25441e29 | −0.508807 | ||||||||
\(667\) | −3.85701e28 | −0.0856898 | ||||||||
\(668\) | −2.90732e29 | −0.635828 | ||||||||
\(669\) | 1.26535e30 | 2.72419 | ||||||||
\(670\) | 8.02826e28 | 0.170151 | ||||||||
\(671\) | 3.87746e29 | 0.809022 | ||||||||
\(672\) | −1.88827e29 | −0.387870 | ||||||||
\(673\) | −7.90406e29 | −1.59842 | −0.799212 | − | 0.601049i | \(-0.794750\pi\) | ||||
−0.799212 | + | 0.601049i | \(0.794750\pi\) | |||||||
\(674\) | −5.46615e29 | −1.08831 | ||||||||
\(675\) | −1.59367e29 | −0.312398 | ||||||||
\(676\) | 7.36309e29 | 1.42108 | ||||||||
\(677\) | −3.48611e29 | −0.662461 | −0.331230 | − | 0.943550i | \(-0.607464\pi\) | ||||
−0.331230 | + | 0.943550i | \(0.607464\pi\) | |||||||
\(678\) | −1.00328e30 | −1.87720 | ||||||||
\(679\) | −6.97264e29 | −1.28459 | ||||||||
\(680\) | −1.22730e29 | −0.222643 | ||||||||
\(681\) | 2.70875e29 | 0.483865 | ||||||||
\(682\) | 6.67978e29 | 1.17497 | ||||||||
\(683\) | 3.87738e28 | 0.0671617 | 0.0335808 | − | 0.999436i | \(-0.489309\pi\) | ||||
0.0335808 | + | 0.999436i | \(0.489309\pi\) | |||||||
\(684\) | 2.96417e29 | 0.505608 | ||||||||
\(685\) | 3.41118e29 | 0.572999 | ||||||||
\(686\) | −1.91397e29 | −0.316615 | ||||||||
\(687\) | 1.73819e30 | 2.83173 | ||||||||
\(688\) | −9.20017e28 | −0.147611 | ||||||||
\(689\) | −7.96020e29 | −1.25783 | ||||||||
\(690\) | 4.64238e28 | 0.0722479 | ||||||||
\(691\) | 7.13503e29 | 1.09364 | 0.546822 | − | 0.837249i | \(-0.315837\pi\) | ||||
0.546822 | + | 0.837249i | \(0.315837\pi\) | |||||||
\(692\) | −4.03171e29 | −0.608661 | ||||||||
\(693\) | −1.64423e30 | −2.44492 | ||||||||
\(694\) | 4.19810e29 | 0.614863 | ||||||||
\(695\) | 1.13997e29 | 0.164457 | ||||||||
\(696\) | 2.72005e29 | 0.386528 | ||||||||
\(697\) | −9.28913e29 | −1.30026 | ||||||||
\(698\) | −2.11484e29 | −0.291605 | ||||||||
\(699\) | 8.08015e28 | 0.109751 | ||||||||
\(700\) | −9.60462e28 | −0.128514 | ||||||||
\(701\) | −8.08128e28 | −0.106522 | −0.0532612 | − | 0.998581i | \(-0.516962\pi\) | ||||
−0.0532612 | + | 0.998581i | \(0.516962\pi\) | |||||||
\(702\) | 1.66721e30 | 2.16497 | ||||||||
\(703\) | 1.55116e29 | 0.198439 | ||||||||
\(704\) | 9.85357e28 | 0.124188 | ||||||||
\(705\) | 6.08986e29 | 0.756173 | ||||||||
\(706\) | −2.69908e29 | −0.330191 | ||||||||
\(707\) | −3.11132e29 | −0.375008 | ||||||||
\(708\) | −1.50326e29 | −0.178519 | ||||||||
\(709\) | 7.67692e28 | 0.0898259 | 0.0449129 | − | 0.998991i | \(-0.485699\pi\) | ||||
0.0449129 | + | 0.998991i | \(0.485699\pi\) | |||||||
\(710\) | −5.25728e29 | −0.606106 | ||||||||
\(711\) | 2.18052e29 | 0.247702 | ||||||||
\(712\) | −2.52620e29 | −0.282766 | ||||||||
\(713\) | 2.02920e29 | 0.223813 | ||||||||
\(714\) | 2.01009e30 | 2.18466 | ||||||||
\(715\) | −8.13181e29 | −0.870911 | ||||||||
\(716\) | 4.76438e28 | 0.0502828 | ||||||||
\(717\) | −1.85457e30 | −1.92882 | ||||||||
\(718\) | −2.79241e29 | −0.286202 | ||||||||
\(719\) | 4.77523e29 | 0.482326 | 0.241163 | − | 0.970485i | \(-0.422471\pi\) | ||||
0.241163 | + | 0.970485i | \(0.422471\pi\) | |||||||
\(720\) | −2.15075e29 | −0.214091 | ||||||||
\(721\) | −5.53297e29 | −0.542797 | ||||||||
\(722\) | 5.27399e29 | 0.509916 | ||||||||
\(723\) | −2.92832e29 | −0.279040 | ||||||||
\(724\) | 9.03830e29 | 0.848852 | ||||||||
\(725\) | 1.38355e29 | 0.128069 | ||||||||
\(726\) | −1.71288e28 | −0.0156276 | ||||||||
\(727\) | −8.17519e29 | −0.735168 | −0.367584 | − | 0.929990i | \(-0.619815\pi\) | ||||
−0.367584 | + | 0.929990i | \(0.619815\pi\) | |||||||
\(728\) | 1.00479e30 | 0.890623 | ||||||||
\(729\) | −1.40435e30 | −1.22698 | ||||||||
\(730\) | 9.28698e28 | 0.0799805 | ||||||||
\(731\) | 9.79373e29 | 0.831411 | ||||||||
\(732\) | −8.30686e29 | −0.695137 | ||||||||
\(733\) | −1.25004e30 | −1.03118 | −0.515588 | − | 0.856837i | \(-0.672426\pi\) | ||||
−0.515588 | + | 0.856837i | \(0.672426\pi\) | |||||||
\(734\) | 1.71560e29 | 0.139510 | ||||||||
\(735\) | 6.20604e29 | 0.497505 | ||||||||
\(736\) | 2.99334e28 | 0.0236559 | ||||||||
\(737\) | 6.86144e29 | 0.534572 | ||||||||
\(738\) | −1.62784e30 | −1.25032 | ||||||||
\(739\) | 1.41926e30 | 1.07472 | 0.537359 | − | 0.843354i | \(-0.319422\pi\) | ||||
0.537359 | + | 0.843354i | \(0.319422\pi\) | |||||||
\(740\) | −1.12549e29 | −0.0840253 | ||||||||
\(741\) | −2.40099e30 | −1.76726 | ||||||||
\(742\) | −8.03545e29 | −0.583135 | ||||||||
\(743\) | −4.94344e29 | −0.353709 | −0.176855 | − | 0.984237i | \(-0.556592\pi\) | ||||
−0.176855 | + | 0.984237i | \(0.556592\pi\) | |||||||
\(744\) | −1.43104e30 | −1.00957 | ||||||||
\(745\) | 2.92869e29 | 0.203719 | ||||||||
\(746\) | −1.01622e30 | −0.696998 | ||||||||
\(747\) | −9.61447e29 | −0.650218 | ||||||||
\(748\) | −1.04893e30 | −0.699486 | ||||||||
\(749\) | 2.97405e30 | 1.95564 | ||||||||
\(750\) | −1.66527e29 | −0.107979 | ||||||||
\(751\) | −1.81607e30 | −1.16121 | −0.580607 | − | 0.814184i | \(-0.697185\pi\) | ||||
−0.580607 | + | 0.814184i | \(0.697185\pi\) | |||||||
\(752\) | 3.92666e29 | 0.247591 | ||||||||
\(753\) | 3.76833e30 | 2.34316 | ||||||||
\(754\) | −1.44740e30 | −0.887540 | ||||||||
\(755\) | 8.60200e29 | 0.520183 | ||||||||
\(756\) | 1.68297e30 | 1.00369 | ||||||||
\(757\) | −3.23429e30 | −1.90227 | −0.951136 | − | 0.308772i | \(-0.900082\pi\) | ||||
−0.951136 | + | 0.308772i | \(0.900082\pi\) | |||||||
\(758\) | −1.44822e28 | −0.00840053 | ||||||||
\(759\) | 3.96766e29 | 0.226984 | ||||||||
\(760\) | 1.47984e29 | 0.0834970 | ||||||||
\(761\) | 5.91876e29 | 0.329376 | 0.164688 | − | 0.986346i | \(-0.447338\pi\) | ||||
0.164688 | + | 0.986346i | \(0.447338\pi\) | |||||||
\(762\) | 2.86745e30 | 1.57387 | ||||||||
\(763\) | 2.73252e30 | 1.47930 | ||||||||
\(764\) | −2.42824e29 | −0.129661 | ||||||||
\(765\) | 2.28950e30 | 1.20586 | ||||||||
\(766\) | −2.57038e29 | −0.133535 | ||||||||
\(767\) | 7.99912e29 | 0.409912 | ||||||||
\(768\) | −2.11098e29 | −0.106706 | ||||||||
\(769\) | 3.65919e30 | 1.82456 | 0.912281 | − | 0.409565i | \(-0.134320\pi\) | ||||
0.912281 | + | 0.409565i | \(0.134320\pi\) | |||||||
\(770\) | −8.20869e29 | −0.403758 | ||||||||
\(771\) | −1.34885e30 | −0.654475 | ||||||||
\(772\) | −1.19000e30 | −0.569595 | ||||||||
\(773\) | −3.12612e30 | −1.47612 | −0.738059 | − | 0.674736i | \(-0.764257\pi\) | ||||
−0.738059 | + | 0.674736i | \(0.764257\pi\) | |||||||
\(774\) | 1.71627e30 | 0.799476 | ||||||||
\(775\) | −7.27895e29 | −0.334503 | ||||||||
\(776\) | −7.79501e29 | −0.353402 | ||||||||
\(777\) | 1.84335e30 | 0.824492 | ||||||||
\(778\) | 2.56265e30 | 1.13085 | ||||||||
\(779\) | 1.12005e30 | 0.487633 | ||||||||
\(780\) | 1.74212e30 | 0.748314 | ||||||||
\(781\) | −4.49319e30 | −1.90423 | ||||||||
\(782\) | −3.18646e29 | −0.133241 | ||||||||
\(783\) | −2.42433e30 | −1.00021 | ||||||||
\(784\) | 4.00157e29 | 0.162897 | ||||||||
\(785\) | −1.72367e30 | −0.692346 | ||||||||
\(786\) | −2.50069e30 | −0.991112 | ||||||||
\(787\) | 1.94010e30 | 0.758735 | 0.379368 | − | 0.925246i | \(-0.376142\pi\) | ||||
0.379368 | + | 0.925246i | \(0.376142\pi\) | |||||||
\(788\) | −6.60363e29 | −0.254834 | ||||||||
\(789\) | −2.36808e30 | −0.901753 | ||||||||
\(790\) | 1.08861e29 | 0.0409060 | ||||||||
\(791\) | 5.38912e30 | 1.99832 | ||||||||
\(792\) | −1.83816e30 | −0.672618 | ||||||||
\(793\) | 4.42024e30 | 1.59617 | ||||||||
\(794\) | −3.36939e29 | −0.120071 | ||||||||
\(795\) | −1.39320e30 | −0.489959 | ||||||||
\(796\) | −7.48081e29 | −0.259634 | ||||||||
\(797\) | 1.87837e30 | 0.643383 | 0.321691 | − | 0.946845i | \(-0.395749\pi\) | ||||
0.321691 | + | 0.946845i | \(0.395749\pi\) | |||||||
\(798\) | −2.42369e30 | −0.819308 | ||||||||
\(799\) | −4.17999e30 | −1.39455 | ||||||||
\(800\) | −1.07374e29 | −0.0353553 | ||||||||
\(801\) | 4.71255e30 | 1.53149 | ||||||||
\(802\) | −8.65597e29 | −0.277642 | ||||||||
\(803\) | 7.93722e29 | 0.251278 | ||||||||
\(804\) | −1.46996e30 | −0.459321 | ||||||||
\(805\) | −2.49366e29 | −0.0769095 | ||||||||
\(806\) | 7.61486e30 | 2.31816 | ||||||||
\(807\) | 3.89668e30 | 1.17091 | ||||||||
\(808\) | −3.47828e29 | −0.103168 | ||||||||
\(809\) | 3.76184e30 | 1.10139 | 0.550694 | − | 0.834707i | \(-0.314363\pi\) | ||||
0.550694 | + | 0.834707i | \(0.314363\pi\) | |||||||
\(810\) | 8.22724e29 | 0.237772 | ||||||||
\(811\) | −1.39769e30 | −0.398741 | −0.199370 | − | 0.979924i | \(-0.563890\pi\) | ||||
−0.199370 | + | 0.979924i | \(0.563890\pi\) | |||||||
\(812\) | −1.46108e30 | −0.411467 | ||||||||
\(813\) | −1.53506e30 | −0.426751 | ||||||||
\(814\) | −9.61916e29 | −0.263986 | ||||||||
\(815\) | −9.14681e29 | −0.247808 | ||||||||
\(816\) | 2.24717e30 | 0.601020 | ||||||||
\(817\) | −1.18089e30 | −0.311801 | ||||||||
\(818\) | 1.62533e30 | 0.423675 | ||||||||
\(819\) | −1.87440e31 | −4.82372 | ||||||||
\(820\) | −8.12687e29 | −0.206480 | ||||||||
\(821\) | 3.06130e30 | 0.767897 | 0.383948 | − | 0.923355i | \(-0.374564\pi\) | ||||
0.383948 | + | 0.923355i | \(0.374564\pi\) | |||||||
\(822\) | −6.24581e30 | −1.54680 | ||||||||
\(823\) | −2.80656e30 | −0.686239 | −0.343120 | − | 0.939292i | \(-0.611484\pi\) | ||||
−0.343120 | + | 0.939292i | \(0.611484\pi\) | |||||||
\(824\) | −6.18554e29 | −0.149328 | ||||||||
\(825\) | −1.42324e30 | −0.339243 | ||||||||
\(826\) | 8.07475e29 | 0.190037 | ||||||||
\(827\) | −1.80807e30 | −0.420153 | −0.210077 | − | 0.977685i | \(-0.567371\pi\) | ||||
−0.210077 | + | 0.977685i | \(0.567371\pi\) | |||||||
\(828\) | −5.58401e29 | −0.128123 | ||||||||
\(829\) | 6.48512e30 | 1.46925 | 0.734625 | − | 0.678473i | \(-0.237358\pi\) | ||||
0.734625 | + | 0.678473i | \(0.237358\pi\) | |||||||
\(830\) | −4.79994e29 | −0.107378 | ||||||||
\(831\) | −5.65663e30 | −1.24953 | ||||||||
\(832\) | 1.12329e30 | 0.245018 | ||||||||
\(833\) | −4.25974e30 | −0.917509 | ||||||||
\(834\) | −2.08726e30 | −0.443949 | ||||||||
\(835\) | 2.70765e30 | 0.568702 | ||||||||
\(836\) | 1.26476e30 | 0.262326 | ||||||||
\(837\) | 1.27546e31 | 2.61245 | ||||||||
\(838\) | 1.50078e28 | 0.00303566 | ||||||||
\(839\) | 5.47358e30 | 1.09338 | 0.546690 | − | 0.837335i | \(-0.315888\pi\) | ||||
0.546690 | + | 0.837335i | \(0.315888\pi\) | |||||||
\(840\) | 1.75859e30 | 0.346922 | ||||||||
\(841\) | −3.02816e30 | −0.589957 | ||||||||
\(842\) | 2.12623e30 | 0.409103 | ||||||||
\(843\) | −2.84509e30 | −0.540639 | ||||||||
\(844\) | −2.70079e30 | −0.506868 | ||||||||
\(845\) | −6.85741e30 | −1.27106 | ||||||||
\(846\) | −7.32508e30 | −1.34098 | ||||||||
\(847\) | 9.20073e28 | 0.0166359 | ||||||||
\(848\) | −8.98318e29 | −0.160426 | ||||||||
\(849\) | −1.26579e31 | −2.23271 | ||||||||
\(850\) | 1.14302e30 | 0.199138 | ||||||||
\(851\) | −2.92213e29 | −0.0502851 | ||||||||
\(852\) | 9.62598e30 | 1.63617 | ||||||||
\(853\) | −7.71396e30 | −1.29513 | −0.647564 | − | 0.762011i | \(-0.724212\pi\) | ||||
−0.647564 | + | 0.762011i | \(0.724212\pi\) | |||||||
\(854\) | 4.46203e30 | 0.739989 | ||||||||
\(855\) | −2.76060e30 | −0.452229 | ||||||||
\(856\) | 3.32482e30 | 0.538015 | ||||||||
\(857\) | 1.69666e29 | 0.0271205 | 0.0135602 | − | 0.999908i | \(-0.495684\pi\) | ||||
0.0135602 | + | 0.999908i | \(0.495684\pi\) | |||||||
\(858\) | 1.48892e31 | 2.35101 | ||||||||
\(859\) | 4.91435e30 | 0.766545 | 0.383273 | − | 0.923635i | \(-0.374797\pi\) | ||||
0.383273 | + | 0.923635i | \(0.374797\pi\) | |||||||
\(860\) | 8.56833e29 | 0.132027 | ||||||||
\(861\) | 1.33103e31 | 2.02607 | ||||||||
\(862\) | 2.95829e30 | 0.444851 | ||||||||
\(863\) | 1.11211e31 | 1.65209 | 0.826047 | − | 0.563602i | \(-0.190585\pi\) | ||||
0.826047 | + | 0.563602i | \(0.190585\pi\) | |||||||
\(864\) | 1.88147e30 | 0.276123 | ||||||||
\(865\) | 3.75482e30 | 0.544403 | ||||||||
\(866\) | −6.74375e30 | −0.965970 | ||||||||
\(867\) | −1.18569e31 | −1.67792 | ||||||||
\(868\) | 7.68685e30 | 1.07471 | ||||||||
\(869\) | 9.30391e29 | 0.128516 | ||||||||
\(870\) | −2.53325e30 | −0.345721 | ||||||||
\(871\) | 7.82194e30 | 1.05469 | ||||||||
\(872\) | 3.05480e30 | 0.406967 | ||||||||
\(873\) | 1.45414e31 | 1.91406 | ||||||||
\(874\) | 3.84211e29 | 0.0499689 | ||||||||
\(875\) | 8.94500e29 | 0.114946 | ||||||||
\(876\) | −1.70043e30 | −0.215906 | ||||||||
\(877\) | −1.05245e31 | −1.32041 | −0.660203 | − | 0.751088i | \(-0.729530\pi\) | ||||
−0.660203 | + | 0.751088i | \(0.729530\pi\) | |||||||
\(878\) | 9.55692e29 | 0.118475 | ||||||||
\(879\) | 1.38101e31 | 1.69166 | ||||||||
\(880\) | −9.17685e29 | −0.111077 | ||||||||
\(881\) | −8.70976e30 | −1.04174 | −0.520870 | − | 0.853636i | \(-0.674392\pi\) | ||||
−0.520870 | + | 0.853636i | \(0.674392\pi\) | |||||||
\(882\) | −7.46483e30 | −0.882267 | ||||||||
\(883\) | 7.95603e30 | 0.929199 | 0.464600 | − | 0.885521i | \(-0.346198\pi\) | ||||
0.464600 | + | 0.885521i | \(0.346198\pi\) | |||||||
\(884\) | −1.19576e31 | −1.38006 | ||||||||
\(885\) | 1.40002e30 | 0.159672 | ||||||||
\(886\) | −9.92275e30 | −1.11835 | ||||||||
\(887\) | −1.08949e31 | −1.21346 | −0.606729 | − | 0.794909i | \(-0.707519\pi\) | ||||
−0.606729 | + | 0.794909i | \(0.707519\pi\) | |||||||
\(888\) | 2.06076e30 | 0.226825 | ||||||||
\(889\) | −1.54025e31 | −1.67542 | ||||||||
\(890\) | 2.35270e30 | 0.252913 | ||||||||
\(891\) | 7.03150e30 | 0.747020 | ||||||||
\(892\) | −7.59851e30 | −0.797806 | ||||||||
\(893\) | 5.04007e30 | 0.522993 | ||||||||
\(894\) | −5.36237e30 | −0.549937 | ||||||||
\(895\) | −4.43718e29 | −0.0449743 | ||||||||
\(896\) | 1.13391e30 | 0.113591 | ||||||||
\(897\) | 4.52308e30 | 0.447830 | ||||||||
\(898\) | 1.01466e31 | 0.992935 | ||||||||
\(899\) | −1.10729e31 | −1.07099 | ||||||||
\(900\) | 2.00304e30 | 0.191489 | ||||||||
\(901\) | 9.56274e30 | 0.903591 | ||||||||
\(902\) | −6.94572e30 | −0.648707 | ||||||||
\(903\) | −1.40333e31 | −1.29550 | ||||||||
\(904\) | 6.02473e30 | 0.549755 | ||||||||
\(905\) | −8.41758e30 | −0.759236 | ||||||||
\(906\) | −1.57501e31 | −1.40423 | ||||||||
\(907\) | 7.14477e30 | 0.629668 | 0.314834 | − | 0.949147i | \(-0.398051\pi\) | ||||
0.314834 | + | 0.949147i | \(0.398051\pi\) | |||||||
\(908\) | −1.62661e30 | −0.141704 | ||||||||
\(909\) | 6.48864e30 | 0.558770 | ||||||||
\(910\) | −9.35779e30 | −0.796597 | ||||||||
\(911\) | −9.25953e30 | −0.779194 | −0.389597 | − | 0.920985i | \(-0.627386\pi\) | ||||
−0.389597 | + | 0.920985i | \(0.627386\pi\) | |||||||
\(912\) | −2.70955e30 | −0.225399 | ||||||||
\(913\) | −4.10233e30 | −0.337355 | ||||||||
\(914\) | 1.44447e31 | 1.17429 | ||||||||
\(915\) | 7.73636e30 | 0.621749 | ||||||||
\(916\) | −1.04379e31 | −0.829299 | ||||||||
\(917\) | 1.34325e31 | 1.05506 | ||||||||
\(918\) | −2.00285e31 | −1.55525 | ||||||||
\(919\) | 2.16799e31 | 1.66435 | 0.832174 | − | 0.554515i | \(-0.187096\pi\) | ||||
0.832174 | + | 0.554515i | \(0.187096\pi\) | |||||||
\(920\) | −2.78777e29 | −0.0211585 | ||||||||
\(921\) | 2.07817e31 | 1.55939 | ||||||||
\(922\) | −1.43712e29 | −0.0106615 | ||||||||
\(923\) | −5.12218e31 | −3.75696 | ||||||||
\(924\) | 1.50300e31 | 1.08994 | ||||||||
\(925\) | 1.04820e30 | 0.0751545 | ||||||||
\(926\) | 1.57903e31 | 1.11937 | ||||||||
\(927\) | 1.15390e31 | 0.808779 | ||||||||
\(928\) | −1.63340e30 | −0.113198 | ||||||||
\(929\) | −1.54089e31 | −1.05586 | −0.527929 | − | 0.849289i | \(-0.677031\pi\) | ||||
−0.527929 | + | 0.849289i | \(0.677031\pi\) | |||||||
\(930\) | 1.33276e31 | 0.902987 | ||||||||
\(931\) | 5.13623e30 | 0.344091 | ||||||||
\(932\) | −4.85216e29 | −0.0321417 | ||||||||
\(933\) | 2.90558e31 | 1.90316 | ||||||||
\(934\) | −1.45578e31 | −0.942875 | ||||||||
\(935\) | 9.76891e30 | 0.625639 | ||||||||
\(936\) | −2.09548e31 | −1.32705 | ||||||||
\(937\) | −2.18719e31 | −1.36969 | −0.684843 | − | 0.728691i | \(-0.740129\pi\) | ||||
−0.684843 | + | 0.728691i | \(0.740129\pi\) | |||||||
\(938\) | 7.89589e30 | 0.488958 | ||||||||
\(939\) | −3.92070e30 | −0.240091 | ||||||||
\(940\) | −3.65698e30 | −0.221452 | ||||||||
\(941\) | −5.71240e29 | −0.0342080 | −0.0171040 | − | 0.999854i | \(-0.505445\pi\) | ||||
−0.0171040 | + | 0.999854i | \(0.505445\pi\) | |||||||
\(942\) | 3.15601e31 | 1.86898 | ||||||||
\(943\) | −2.10999e30 | −0.123568 | ||||||||
\(944\) | 9.02711e29 | 0.0522809 | ||||||||
\(945\) | −1.56739e31 | −0.897725 | ||||||||
\(946\) | 7.32302e30 | 0.414795 | ||||||||
\(947\) | 6.38251e29 | 0.0357534 | 0.0178767 | − | 0.999840i | \(-0.494309\pi\) | ||||
0.0178767 | + | 0.999840i | \(0.494309\pi\) | |||||||
\(948\) | −1.99322e30 | −0.110425 | ||||||||
\(949\) | 9.04832e30 | 0.495761 | ||||||||
\(950\) | −1.37820e30 | −0.0746820 | ||||||||
\(951\) | −1.93397e31 | −1.03646 | ||||||||
\(952\) | −1.20707e31 | −0.639800 | ||||||||
\(953\) | −2.06863e31 | −1.08444 | −0.542222 | − | 0.840235i | \(-0.682417\pi\) | ||||
−0.542222 | + | 0.840235i | \(0.682417\pi\) | |||||||
\(954\) | 1.67579e31 | 0.868884 | ||||||||
\(955\) | 2.26147e30 | 0.115973 | ||||||||
\(956\) | 1.11368e31 | 0.564873 | ||||||||
\(957\) | −2.16507e31 | −1.08617 | ||||||||
\(958\) | −1.87043e31 | −0.928120 | ||||||||
\(959\) | 3.35494e31 | 1.64661 | ||||||||
\(960\) | 1.96600e30 | 0.0954412 | ||||||||
\(961\) | 3.74300e31 | 1.79731 | ||||||||
\(962\) | −1.09657e31 | −0.520833 | ||||||||
\(963\) | −6.20238e31 | −2.91395 | ||||||||
\(964\) | 1.75847e30 | 0.0817195 | ||||||||
\(965\) | 1.10828e31 | 0.509461 | ||||||||
\(966\) | 4.56584e30 | 0.207616 | ||||||||
\(967\) | 2.49286e31 | 1.12129 | 0.560647 | − | 0.828055i | \(-0.310552\pi\) | ||||
0.560647 | + | 0.828055i | \(0.310552\pi\) | |||||||
\(968\) | 1.02859e29 | 0.00457668 | ||||||||
\(969\) | 2.88436e31 | 1.26955 | ||||||||
\(970\) | 7.25967e30 | 0.316092 | ||||||||
\(971\) | 4.80972e30 | 0.207166 | 0.103583 | − | 0.994621i | \(-0.466969\pi\) | ||||
0.103583 | + | 0.994621i | \(0.466969\pi\) | |||||||
\(972\) | 3.26528e30 | 0.139131 | ||||||||
\(973\) | 1.12117e31 | 0.472594 | ||||||||
\(974\) | −3.27369e31 | −1.36511 | ||||||||
\(975\) | −1.62247e31 | −0.669313 | ||||||||
\(976\) | 4.98830e30 | 0.203577 | ||||||||
\(977\) | 1.25924e31 | 0.508411 | 0.254205 | − | 0.967150i | \(-0.418186\pi\) | ||||
0.254205 | + | 0.967150i | \(0.418186\pi\) | |||||||
\(978\) | 1.67476e31 | 0.668953 | ||||||||
\(979\) | 2.01076e31 | 0.794589 | ||||||||
\(980\) | −3.72675e30 | −0.145699 | ||||||||
\(981\) | −5.69865e31 | −2.20418 | ||||||||
\(982\) | 1.09221e31 | 0.417961 | ||||||||
\(983\) | 1.94974e31 | 0.738185 | 0.369093 | − | 0.929393i | \(-0.379669\pi\) | ||||
0.369093 | + | 0.929393i | \(0.379669\pi\) | |||||||
\(984\) | 1.48801e31 | 0.557389 | ||||||||
\(985\) | 6.15011e30 | 0.227930 | ||||||||
\(986\) | 1.73878e31 | 0.637585 | ||||||||
\(987\) | 5.98945e31 | 2.17299 | ||||||||
\(988\) | 1.44181e31 | 0.517558 | ||||||||
\(989\) | 2.22461e30 | 0.0790118 | ||||||||
\(990\) | 1.71192e31 | 0.601608 | ||||||||
\(991\) | −1.67935e31 | −0.583941 | −0.291971 | − | 0.956427i | \(-0.594311\pi\) | ||||
−0.291971 | + | 0.956427i | \(0.594311\pi\) | |||||||
\(992\) | 8.59346e30 | 0.295662 | ||||||||
\(993\) | 3.81047e31 | 1.29721 | ||||||||
\(994\) | −5.17060e31 | −1.74174 | ||||||||
\(995\) | 6.96705e30 | 0.232224 | ||||||||
\(996\) | 8.78861e30 | 0.289866 | ||||||||
\(997\) | 2.24576e31 | 0.732932 | 0.366466 | − | 0.930431i | \(-0.380568\pi\) | ||||
0.366466 | + | 0.930431i | \(0.380568\pi\) | |||||||
\(998\) | 1.22536e31 | 0.395724 | ||||||||
\(999\) | −1.83671e31 | −0.586953 |
(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 | 10.22.a.b.1.1 | ✓ | 2 | |
4.3 | odd | 2 | 80.22.a.d.1.2 | 2 | |||
5.2 | odd | 4 | 50.22.b.f.49.2 | 4 | |||
5.3 | odd | 4 | 50.22.b.f.49.3 | 4 | |||
5.4 | even | 2 | 50.22.a.f.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.22.a.b.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.22.a.f.1.2 | 2 | 5.4 | even | 2 | |||
50.22.b.f.49.2 | 4 | 5.2 | odd | 4 | |||
50.22.b.f.49.3 | 4 | 5.3 | odd | 4 | |||
80.22.a.d.1.2 | 2 | 4.3 | odd | 2 |