Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6,12,Mod(1,6)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6 = 2 \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 6.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: | \(4.61005908336\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 6.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 32.0000 | 0.707107 | ||||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | 1024.00 | 0.500000 | ||||||||
\(5\) | 3630.00 | 0.519483 | 0.259742 | − | 0.965678i | \(-0.416363\pi\) | ||||
0.259742 | + | 0.965678i | \(0.416363\pi\) | |||||||
\(6\) | 7776.00 | 0.408248 | ||||||||
\(7\) | 32936.0 | 0.740682 | 0.370341 | − | 0.928896i | \(-0.379241\pi\) | ||||
0.370341 | + | 0.928896i | \(0.379241\pi\) | |||||||
\(8\) | 32768.0 | 0.353553 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 116160. | 0.367330 | ||||||||
\(11\) | −758748. | −1.42049 | −0.710244 | − | 0.703955i | \(-0.751416\pi\) | ||||
−0.710244 | + | 0.703955i | \(0.751416\pi\) | |||||||
\(12\) | 248832. | 0.288675 | ||||||||
\(13\) | −2.48286e6 | −1.85466 | −0.927328 | − | 0.374249i | \(-0.877900\pi\) | ||||
−0.927328 | + | 0.374249i | \(0.877900\pi\) | |||||||
\(14\) | 1.05395e6 | 0.523741 | ||||||||
\(15\) | 882090. | 0.299924 | ||||||||
\(16\) | 1.04858e6 | 0.250000 | ||||||||
\(17\) | 8.29039e6 | 1.41614 | 0.708069 | − | 0.706143i | \(-0.249566\pi\) | ||||
0.708069 | + | 0.706143i | \(0.249566\pi\) | |||||||
\(18\) | 1.88957e6 | 0.235702 | ||||||||
\(19\) | −1.08673e7 | −1.00688 | −0.503439 | − | 0.864031i | \(-0.667932\pi\) | ||||
−0.503439 | + | 0.864031i | \(0.667932\pi\) | |||||||
\(20\) | 3.71712e6 | 0.259742 | ||||||||
\(21\) | 8.00345e6 | 0.427633 | ||||||||
\(22\) | −2.42799e7 | −1.00444 | ||||||||
\(23\) | 2.05393e7 | 0.665399 | 0.332699 | − | 0.943033i | \(-0.392041\pi\) | ||||
0.332699 | + | 0.943033i | \(0.392041\pi\) | |||||||
\(24\) | 7.96262e6 | 0.204124 | ||||||||
\(25\) | −3.56512e7 | −0.730137 | ||||||||
\(26\) | −7.94515e7 | −1.31144 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | 3.37265e7 | 0.370341 | ||||||||
\(29\) | 2.88146e7 | 0.260869 | 0.130435 | − | 0.991457i | \(-0.458363\pi\) | ||||
0.130435 | + | 0.991457i | \(0.458363\pi\) | |||||||
\(30\) | 2.82269e7 | 0.212078 | ||||||||
\(31\) | 1.50501e8 | 0.944172 | 0.472086 | − | 0.881552i | \(-0.343501\pi\) | ||||
0.472086 | + | 0.881552i | \(0.343501\pi\) | |||||||
\(32\) | 3.35544e7 | 0.176777 | ||||||||
\(33\) | −1.84376e8 | −0.820120 | ||||||||
\(34\) | 2.65292e8 | 1.00136 | ||||||||
\(35\) | 1.19558e8 | 0.384772 | ||||||||
\(36\) | 6.04662e7 | 0.166667 | ||||||||
\(37\) | −3.19892e8 | −0.758392 | −0.379196 | − | 0.925316i | \(-0.623799\pi\) | ||||
−0.379196 | + | 0.925316i | \(0.623799\pi\) | |||||||
\(38\) | −3.47754e8 | −0.711970 | ||||||||
\(39\) | −6.03334e8 | −1.07079 | ||||||||
\(40\) | 1.18948e8 | 0.183665 | ||||||||
\(41\) | −3.68009e8 | −0.496075 | −0.248037 | − | 0.968750i | \(-0.579786\pi\) | ||||
−0.248037 | + | 0.968750i | \(0.579786\pi\) | |||||||
\(42\) | 2.56110e8 | 0.302382 | ||||||||
\(43\) | 6.20470e8 | 0.643641 | 0.321821 | − | 0.946801i | \(-0.395705\pi\) | ||||
0.321821 | + | 0.946801i | \(0.395705\pi\) | |||||||
\(44\) | −7.76958e8 | −0.710244 | ||||||||
\(45\) | 2.14348e8 | 0.173161 | ||||||||
\(46\) | 6.57257e8 | 0.470508 | ||||||||
\(47\) | 2.76311e9 | 1.75736 | 0.878679 | − | 0.477414i | \(-0.158426\pi\) | ||||
0.878679 | + | 0.477414i | \(0.158426\pi\) | |||||||
\(48\) | 2.54804e8 | 0.144338 | ||||||||
\(49\) | −8.92547e8 | −0.451391 | ||||||||
\(50\) | −1.14084e9 | −0.516285 | ||||||||
\(51\) | 2.01456e9 | 0.817608 | ||||||||
\(52\) | −2.54245e9 | −0.927328 | ||||||||
\(53\) | −2.68284e8 | −0.0881207 | −0.0440603 | − | 0.999029i | \(-0.514029\pi\) | ||||
−0.0440603 | + | 0.999029i | \(0.514029\pi\) | |||||||
\(54\) | 4.59165e8 | 0.136083 | ||||||||
\(55\) | −2.75426e9 | −0.737920 | ||||||||
\(56\) | 1.07925e9 | 0.261871 | ||||||||
\(57\) | −2.64075e9 | −0.581321 | ||||||||
\(58\) | 9.22066e8 | 0.184462 | ||||||||
\(59\) | 1.67289e9 | 0.304637 | 0.152318 | − | 0.988331i | \(-0.451326\pi\) | ||||
0.152318 | + | 0.988331i | \(0.451326\pi\) | |||||||
\(60\) | 9.03260e8 | 0.149962 | ||||||||
\(61\) | −7.78720e9 | −1.18050 | −0.590252 | − | 0.807219i | \(-0.700971\pi\) | ||||
−0.590252 | + | 0.807219i | \(0.700971\pi\) | |||||||
\(62\) | 4.81604e9 | 0.667631 | ||||||||
\(63\) | 1.94484e9 | 0.246894 | ||||||||
\(64\) | 1.07374e9 | 0.125000 | ||||||||
\(65\) | −9.01277e9 | −0.963463 | ||||||||
\(66\) | −5.90002e9 | −0.579912 | ||||||||
\(67\) | 1.87067e10 | 1.69272 | 0.846361 | − | 0.532610i | \(-0.178789\pi\) | ||||
0.846361 | + | 0.532610i | \(0.178789\pi\) | |||||||
\(68\) | 8.48936e9 | 0.708069 | ||||||||
\(69\) | 4.99104e9 | 0.384168 | ||||||||
\(70\) | 3.82585e9 | 0.272075 | ||||||||
\(71\) | −8.34699e9 | −0.549046 | −0.274523 | − | 0.961580i | \(-0.588520\pi\) | ||||
−0.274523 | + | 0.961580i | \(0.588520\pi\) | |||||||
\(72\) | 1.93492e9 | 0.117851 | ||||||||
\(73\) | 1.96417e10 | 1.10893 | 0.554465 | − | 0.832207i | \(-0.312923\pi\) | ||||
0.554465 | + | 0.832207i | \(0.312923\pi\) | |||||||
\(74\) | −1.02365e10 | −0.536264 | ||||||||
\(75\) | −8.66325e9 | −0.421545 | ||||||||
\(76\) | −1.11281e10 | −0.503439 | ||||||||
\(77\) | −2.49901e10 | −1.05213 | ||||||||
\(78\) | −1.93067e10 | −0.757160 | ||||||||
\(79\) | −5.87381e9 | −0.214769 | −0.107384 | − | 0.994218i | \(-0.534248\pi\) | ||||
−0.107384 | + | 0.994218i | \(0.534248\pi\) | |||||||
\(80\) | 3.80633e9 | 0.129871 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | −1.17763e10 | −0.350778 | ||||||||
\(83\) | 8.49256e9 | 0.236651 | 0.118326 | − | 0.992975i | \(-0.462247\pi\) | ||||
0.118326 | + | 0.992975i | \(0.462247\pi\) | |||||||
\(84\) | 8.19553e9 | 0.213816 | ||||||||
\(85\) | 3.00941e10 | 0.735660 | ||||||||
\(86\) | 1.98550e10 | 0.455123 | ||||||||
\(87\) | 7.00194e9 | 0.150613 | ||||||||
\(88\) | −2.48627e10 | −0.502219 | ||||||||
\(89\) | 7.55279e10 | 1.43371 | 0.716856 | − | 0.697221i | \(-0.245580\pi\) | ||||
0.716856 | + | 0.697221i | \(0.245580\pi\) | |||||||
\(90\) | 6.85913e9 | 0.122443 | ||||||||
\(91\) | −8.17754e10 | −1.37371 | ||||||||
\(92\) | 2.10322e10 | 0.332699 | ||||||||
\(93\) | 3.65718e10 | 0.545118 | ||||||||
\(94\) | 8.84195e10 | 1.24264 | ||||||||
\(95\) | −3.94483e10 | −0.523056 | ||||||||
\(96\) | 8.15373e9 | 0.102062 | ||||||||
\(97\) | −8.23568e10 | −0.973767 | −0.486883 | − | 0.873467i | \(-0.661866\pi\) | ||||
−0.486883 | + | 0.873467i | \(0.661866\pi\) | |||||||
\(98\) | −2.85615e10 | −0.319181 | ||||||||
\(99\) | −4.48033e10 | −0.473496 | ||||||||
\(100\) | −3.65069e10 | −0.365069 | ||||||||
\(101\) | −4.13141e10 | −0.391138 | −0.195569 | − | 0.980690i | \(-0.562655\pi\) | ||||
−0.195569 | + | 0.980690i | \(0.562655\pi\) | |||||||
\(102\) | 6.44660e10 | 0.578136 | ||||||||
\(103\) | −6.45183e10 | −0.548376 | −0.274188 | − | 0.961676i | \(-0.588409\pi\) | ||||
−0.274188 | + | 0.961676i | \(0.588409\pi\) | |||||||
\(104\) | −8.13583e10 | −0.655720 | ||||||||
\(105\) | 2.90525e10 | 0.222148 | ||||||||
\(106\) | −8.58510e9 | −0.0623107 | ||||||||
\(107\) | 1.10219e11 | 0.759706 | 0.379853 | − | 0.925047i | \(-0.375975\pi\) | ||||
0.379853 | + | 0.925047i | \(0.375975\pi\) | |||||||
\(108\) | 1.46933e10 | 0.0962250 | ||||||||
\(109\) | 1.77778e11 | 1.10671 | 0.553353 | − | 0.832947i | \(-0.313348\pi\) | ||||
0.553353 | + | 0.832947i | \(0.313348\pi\) | |||||||
\(110\) | −8.81362e10 | −0.521788 | ||||||||
\(111\) | −7.77337e10 | −0.437858 | ||||||||
\(112\) | 3.45359e10 | 0.185170 | ||||||||
\(113\) | 7.89206e10 | 0.402957 | 0.201479 | − | 0.979493i | \(-0.435425\pi\) | ||||
0.201479 | + | 0.979493i | \(0.435425\pi\) | |||||||
\(114\) | −8.45041e10 | −0.411056 | ||||||||
\(115\) | 7.45576e10 | 0.345664 | ||||||||
\(116\) | 2.95061e10 | 0.130435 | ||||||||
\(117\) | −1.46610e11 | −0.618219 | ||||||||
\(118\) | 5.35326e10 | 0.215411 | ||||||||
\(119\) | 2.73052e11 | 1.04891 | ||||||||
\(120\) | 2.89043e10 | 0.106039 | ||||||||
\(121\) | 2.90387e11 | 1.01779 | ||||||||
\(122\) | −2.49190e11 | −0.834742 | ||||||||
\(123\) | −8.94262e10 | −0.286409 | ||||||||
\(124\) | 1.54113e11 | 0.472086 | ||||||||
\(125\) | −3.06660e11 | −0.898777 | ||||||||
\(126\) | 6.22348e10 | 0.174580 | ||||||||
\(127\) | −2.76649e11 | −0.743035 | −0.371518 | − | 0.928426i | \(-0.621162\pi\) | ||||
−0.371518 | + | 0.928426i | \(0.621162\pi\) | |||||||
\(128\) | 3.43597e10 | 0.0883883 | ||||||||
\(129\) | 1.50774e11 | 0.371607 | ||||||||
\(130\) | −2.88409e11 | −0.681271 | ||||||||
\(131\) | −3.40872e11 | −0.771968 | −0.385984 | − | 0.922505i | \(-0.626138\pi\) | ||||
−0.385984 | + | 0.922505i | \(0.626138\pi\) | |||||||
\(132\) | −1.88801e11 | −0.410060 | ||||||||
\(133\) | −3.57925e11 | −0.745776 | ||||||||
\(134\) | 5.98614e11 | 1.19694 | ||||||||
\(135\) | 5.20865e10 | 0.0999746 | ||||||||
\(136\) | 2.71659e11 | 0.500681 | ||||||||
\(137\) | −9.44784e11 | −1.67251 | −0.836256 | − | 0.548339i | \(-0.815260\pi\) | ||||
−0.836256 | + | 0.548339i | \(0.815260\pi\) | |||||||
\(138\) | 1.59713e11 | 0.271648 | ||||||||
\(139\) | 1.03770e11 | 0.169626 | 0.0848128 | − | 0.996397i | \(-0.472971\pi\) | ||||
0.0848128 | + | 0.996397i | \(0.472971\pi\) | |||||||
\(140\) | 1.22427e11 | 0.192386 | ||||||||
\(141\) | 6.71436e11 | 1.01461 | ||||||||
\(142\) | −2.67104e11 | −0.388234 | ||||||||
\(143\) | 1.88386e12 | 2.63452 | ||||||||
\(144\) | 6.19174e10 | 0.0833333 | ||||||||
\(145\) | 1.04597e11 | 0.135517 | ||||||||
\(146\) | 6.28536e11 | 0.784132 | ||||||||
\(147\) | −2.16889e11 | −0.260610 | ||||||||
\(148\) | −3.27569e11 | −0.379196 | ||||||||
\(149\) | −1.22852e12 | −1.37043 | −0.685216 | − | 0.728340i | \(-0.740292\pi\) | ||||
−0.685216 | + | 0.728340i | \(0.740292\pi\) | |||||||
\(150\) | −2.77224e11 | −0.298077 | ||||||||
\(151\) | 2.12466e11 | 0.220250 | 0.110125 | − | 0.993918i | \(-0.464875\pi\) | ||||
0.110125 | + | 0.993918i | \(0.464875\pi\) | |||||||
\(152\) | −3.56100e11 | −0.355985 | ||||||||
\(153\) | 4.89539e11 | 0.472046 | ||||||||
\(154\) | −7.99684e11 | −0.743968 | ||||||||
\(155\) | 5.46320e11 | 0.490482 | ||||||||
\(156\) | −6.17815e11 | −0.535393 | ||||||||
\(157\) | −1.58632e12 | −1.32722 | −0.663612 | − | 0.748077i | \(-0.730977\pi\) | ||||
−0.663612 | + | 0.748077i | \(0.730977\pi\) | |||||||
\(158\) | −1.87962e11 | −0.151864 | ||||||||
\(159\) | −6.51931e10 | −0.0508765 | ||||||||
\(160\) | 1.21803e11 | 0.0918325 | ||||||||
\(161\) | 6.76481e11 | 0.492849 | ||||||||
\(162\) | 1.11577e11 | 0.0785674 | ||||||||
\(163\) | 8.65020e11 | 0.588836 | 0.294418 | − | 0.955677i | \(-0.404874\pi\) | ||||
0.294418 | + | 0.955677i | \(0.404874\pi\) | |||||||
\(164\) | −3.76841e11 | −0.248037 | ||||||||
\(165\) | −6.69284e11 | −0.426038 | ||||||||
\(166\) | 2.71762e11 | 0.167338 | ||||||||
\(167\) | −2.25802e12 | −1.34520 | −0.672600 | − | 0.740006i | \(-0.734823\pi\) | ||||
−0.672600 | + | 0.740006i | \(0.734823\pi\) | |||||||
\(168\) | 2.62257e11 | 0.151191 | ||||||||
\(169\) | 4.37242e12 | 2.43975 | ||||||||
\(170\) | 9.63011e11 | 0.520190 | ||||||||
\(171\) | −6.41703e11 | −0.335626 | ||||||||
\(172\) | 6.35361e11 | 0.321821 | ||||||||
\(173\) | −2.15960e12 | −1.05955 | −0.529773 | − | 0.848139i | \(-0.677723\pi\) | ||||
−0.529773 | + | 0.848139i | \(0.677723\pi\) | |||||||
\(174\) | 2.24062e11 | 0.106499 | ||||||||
\(175\) | −1.17421e12 | −0.540799 | ||||||||
\(176\) | −7.95605e11 | −0.355122 | ||||||||
\(177\) | 4.06513e11 | 0.175882 | ||||||||
\(178\) | 2.41689e12 | 1.01379 | ||||||||
\(179\) | 4.50786e12 | 1.83349 | 0.916745 | − | 0.399472i | \(-0.130807\pi\) | ||||
0.916745 | + | 0.399472i | \(0.130807\pi\) | |||||||
\(180\) | 2.19492e11 | 0.0865806 | ||||||||
\(181\) | 4.34053e11 | 0.166077 | 0.0830387 | − | 0.996546i | \(-0.473537\pi\) | ||||
0.0830387 | + | 0.996546i | \(0.473537\pi\) | |||||||
\(182\) | −2.61681e12 | −0.971360 | ||||||||
\(183\) | −1.89229e12 | −0.681564 | ||||||||
\(184\) | 6.73031e11 | 0.235254 | ||||||||
\(185\) | −1.16121e12 | −0.393972 | ||||||||
\(186\) | 1.17030e12 | 0.385457 | ||||||||
\(187\) | −6.29031e12 | −2.01161 | ||||||||
\(188\) | 2.82942e12 | 0.878679 | ||||||||
\(189\) | 4.72596e11 | 0.142544 | ||||||||
\(190\) | −1.26235e12 | −0.369857 | ||||||||
\(191\) | 8.67702e11 | 0.246994 | 0.123497 | − | 0.992345i | \(-0.460589\pi\) | ||||
0.123497 | + | 0.992345i | \(0.460589\pi\) | |||||||
\(192\) | 2.60919e11 | 0.0721688 | ||||||||
\(193\) | 1.86946e11 | 0.0502516 | 0.0251258 | − | 0.999684i | \(-0.492001\pi\) | ||||
0.0251258 | + | 0.999684i | \(0.492001\pi\) | |||||||
\(194\) | −2.63542e12 | −0.688557 | ||||||||
\(195\) | −2.19010e12 | −0.556256 | ||||||||
\(196\) | −9.13968e11 | −0.225695 | ||||||||
\(197\) | 3.32798e12 | 0.799129 | 0.399565 | − | 0.916705i | \(-0.369161\pi\) | ||||
0.399565 | + | 0.916705i | \(0.369161\pi\) | |||||||
\(198\) | −1.43371e12 | −0.334812 | ||||||||
\(199\) | −1.58581e12 | −0.360212 | −0.180106 | − | 0.983647i | \(-0.557644\pi\) | ||||
−0.180106 | + | 0.983647i | \(0.557644\pi\) | |||||||
\(200\) | −1.16822e12 | −0.258142 | ||||||||
\(201\) | 4.54573e12 | 0.977293 | ||||||||
\(202\) | −1.32205e12 | −0.276577 | ||||||||
\(203\) | 9.49036e11 | 0.193221 | ||||||||
\(204\) | 2.06291e12 | 0.408804 | ||||||||
\(205\) | −1.33587e12 | −0.257703 | ||||||||
\(206\) | −2.06459e12 | −0.387760 | ||||||||
\(207\) | 1.21282e12 | 0.221800 | ||||||||
\(208\) | −2.60347e12 | −0.463664 | ||||||||
\(209\) | 8.24554e12 | 1.43026 | ||||||||
\(210\) | 9.29681e11 | 0.157082 | ||||||||
\(211\) | 3.54958e12 | 0.584283 | 0.292142 | − | 0.956375i | \(-0.405632\pi\) | ||||
0.292142 | + | 0.956375i | \(0.405632\pi\) | |||||||
\(212\) | −2.74723e11 | −0.0440603 | ||||||||
\(213\) | −2.02832e12 | −0.316992 | ||||||||
\(214\) | 3.52701e12 | 0.537193 | ||||||||
\(215\) | 2.25230e12 | 0.334361 | ||||||||
\(216\) | 4.70185e11 | 0.0680414 | ||||||||
\(217\) | 4.95691e12 | 0.699331 | ||||||||
\(218\) | 5.68890e12 | 0.782560 | ||||||||
\(219\) | 4.77294e12 | 0.640241 | ||||||||
\(220\) | −2.82036e12 | −0.368960 | ||||||||
\(221\) | −2.05839e13 | −2.62645 | ||||||||
\(222\) | −2.48748e12 | −0.309612 | ||||||||
\(223\) | −5.18022e12 | −0.629030 | −0.314515 | − | 0.949252i | \(-0.601842\pi\) | ||||
−0.314515 | + | 0.949252i | \(0.601842\pi\) | |||||||
\(224\) | 1.10515e12 | 0.130935 | ||||||||
\(225\) | −2.10517e12 | −0.243379 | ||||||||
\(226\) | 2.52546e12 | 0.284934 | ||||||||
\(227\) | −1.33665e13 | −1.47189 | −0.735943 | − | 0.677044i | \(-0.763261\pi\) | ||||
−0.735943 | + | 0.677044i | \(0.763261\pi\) | |||||||
\(228\) | −2.70413e12 | −0.290661 | ||||||||
\(229\) | −2.03080e12 | −0.213095 | −0.106547 | − | 0.994308i | \(-0.533980\pi\) | ||||
−0.106547 | + | 0.994308i | \(0.533980\pi\) | |||||||
\(230\) | 2.38584e12 | 0.244421 | ||||||||
\(231\) | −6.07260e12 | −0.607448 | ||||||||
\(232\) | 9.44195e11 | 0.0922312 | ||||||||
\(233\) | 7.13322e12 | 0.680500 | 0.340250 | − | 0.940335i | \(-0.389488\pi\) | ||||
0.340250 | + | 0.940335i | \(0.389488\pi\) | |||||||
\(234\) | −4.69153e12 | −0.437147 | ||||||||
\(235\) | 1.00301e13 | 0.912918 | ||||||||
\(236\) | 1.71304e12 | 0.152318 | ||||||||
\(237\) | −1.42734e12 | −0.123997 | ||||||||
\(238\) | 8.73767e12 | 0.741690 | ||||||||
\(239\) | 3.30363e12 | 0.274033 | 0.137016 | − | 0.990569i | \(-0.456249\pi\) | ||||
0.137016 | + | 0.990569i | \(0.456249\pi\) | |||||||
\(240\) | 9.24938e11 | 0.0749810 | ||||||||
\(241\) | 4.16938e11 | 0.0330353 | 0.0165176 | − | 0.999864i | \(-0.494742\pi\) | ||||
0.0165176 | + | 0.999864i | \(0.494742\pi\) | |||||||
\(242\) | 9.29238e12 | 0.719685 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −7.97409e12 | −0.590252 | ||||||||
\(245\) | −3.23994e12 | −0.234490 | ||||||||
\(246\) | −2.86164e12 | −0.202522 | ||||||||
\(247\) | 2.69820e13 | 1.86741 | ||||||||
\(248\) | 4.93163e12 | 0.333815 | ||||||||
\(249\) | 2.06369e12 | 0.136631 | ||||||||
\(250\) | −9.81312e12 | −0.635532 | ||||||||
\(251\) | −1.91970e12 | −0.121626 | −0.0608131 | − | 0.998149i | \(-0.519369\pi\) | ||||
−0.0608131 | + | 0.998149i | \(0.519369\pi\) | |||||||
\(252\) | 1.99151e12 | 0.123447 | ||||||||
\(253\) | −1.55841e13 | −0.945191 | ||||||||
\(254\) | −8.85278e12 | −0.525405 | ||||||||
\(255\) | 7.31287e12 | 0.424734 | ||||||||
\(256\) | 1.09951e12 | 0.0625000 | ||||||||
\(257\) | 9.76031e12 | 0.543040 | 0.271520 | − | 0.962433i | \(-0.412474\pi\) | ||||
0.271520 | + | 0.962433i | \(0.412474\pi\) | |||||||
\(258\) | 4.82477e12 | 0.262766 | ||||||||
\(259\) | −1.05360e13 | −0.561727 | ||||||||
\(260\) | −9.22908e12 | −0.481732 | ||||||||
\(261\) | 1.70147e12 | 0.0869564 | ||||||||
\(262\) | −1.09079e13 | −0.545864 | ||||||||
\(263\) | −4.04845e12 | −0.198396 | −0.0991980 | − | 0.995068i | \(-0.531628\pi\) | ||||
−0.0991980 | + | 0.995068i | \(0.531628\pi\) | |||||||
\(264\) | −6.04163e12 | −0.289956 | ||||||||
\(265\) | −9.73872e11 | −0.0457772 | ||||||||
\(266\) | −1.14536e13 | −0.527343 | ||||||||
\(267\) | 1.83533e13 | 0.827754 | ||||||||
\(268\) | 1.91557e13 | 0.846361 | ||||||||
\(269\) | −1.13455e13 | −0.491118 | −0.245559 | − | 0.969382i | \(-0.578972\pi\) | ||||
−0.245559 | + | 0.969382i | \(0.578972\pi\) | |||||||
\(270\) | 1.66677e12 | 0.0706927 | ||||||||
\(271\) | −2.35252e12 | −0.0977691 | −0.0488846 | − | 0.998804i | \(-0.515567\pi\) | ||||
−0.0488846 | + | 0.998804i | \(0.515567\pi\) | |||||||
\(272\) | 8.69310e12 | 0.354035 | ||||||||
\(273\) | −1.98714e13 | −0.793112 | ||||||||
\(274\) | −3.02331e13 | −1.18264 | ||||||||
\(275\) | 2.70503e13 | 1.03715 | ||||||||
\(276\) | 5.11083e12 | 0.192084 | ||||||||
\(277\) | −4.36327e13 | −1.60758 | −0.803791 | − | 0.594912i | \(-0.797187\pi\) | ||||
−0.803791 | + | 0.594912i | \(0.797187\pi\) | |||||||
\(278\) | 3.32065e12 | 0.119943 | ||||||||
\(279\) | 8.88696e12 | 0.314724 | ||||||||
\(280\) | 3.91767e12 | 0.136037 | ||||||||
\(281\) | 2.75099e13 | 0.936707 | 0.468353 | − | 0.883541i | \(-0.344847\pi\) | ||||
0.468353 | + | 0.883541i | \(0.344847\pi\) | |||||||
\(282\) | 2.14859e13 | 0.717438 | ||||||||
\(283\) | −2.57815e13 | −0.844273 | −0.422136 | − | 0.906532i | \(-0.638720\pi\) | ||||
−0.422136 | + | 0.906532i | \(0.638720\pi\) | |||||||
\(284\) | −8.54732e12 | −0.274523 | ||||||||
\(285\) | −9.58594e12 | −0.301987 | ||||||||
\(286\) | 6.02836e13 | 1.86289 | ||||||||
\(287\) | −1.21207e13 | −0.367434 | ||||||||
\(288\) | 1.98136e12 | 0.0589256 | ||||||||
\(289\) | 3.44586e13 | 1.00545 | ||||||||
\(290\) | 3.34710e12 | 0.0958251 | ||||||||
\(291\) | −2.00127e13 | −0.562204 | ||||||||
\(292\) | 2.01131e13 | 0.554465 | ||||||||
\(293\) | 5.59324e13 | 1.51318 | 0.756591 | − | 0.653888i | \(-0.226863\pi\) | ||||
0.756591 | + | 0.653888i | \(0.226863\pi\) | |||||||
\(294\) | −6.94044e12 | −0.184279 | ||||||||
\(295\) | 6.07261e12 | 0.158254 | ||||||||
\(296\) | −1.04822e13 | −0.268132 | ||||||||
\(297\) | −1.08872e13 | −0.273373 | ||||||||
\(298\) | −3.93126e13 | −0.969041 | ||||||||
\(299\) | −5.09961e13 | −1.23409 | ||||||||
\(300\) | −8.87117e12 | −0.210772 | ||||||||
\(301\) | 2.04358e13 | 0.476733 | ||||||||
\(302\) | 6.79890e12 | 0.155740 | ||||||||
\(303\) | −1.00393e13 | −0.225824 | ||||||||
\(304\) | −1.13952e13 | −0.251719 | ||||||||
\(305\) | −2.82675e13 | −0.613252 | ||||||||
\(306\) | 1.56652e13 | 0.333787 | ||||||||
\(307\) | 5.68056e13 | 1.18886 | 0.594429 | − | 0.804148i | \(-0.297378\pi\) | ||||
0.594429 | + | 0.804148i | \(0.297378\pi\) | |||||||
\(308\) | −2.55899e13 | −0.526065 | ||||||||
\(309\) | −1.56779e13 | −0.316605 | ||||||||
\(310\) | 1.74822e13 | 0.346823 | ||||||||
\(311\) | −6.71193e13 | −1.30817 | −0.654087 | − | 0.756419i | \(-0.726947\pi\) | ||||
−0.654087 | + | 0.756419i | \(0.726947\pi\) | |||||||
\(312\) | −1.97701e13 | −0.378580 | ||||||||
\(313\) | −3.66685e13 | −0.689920 | −0.344960 | − | 0.938617i | \(-0.612108\pi\) | ||||
−0.344960 | + | 0.938617i | \(0.612108\pi\) | |||||||
\(314\) | −5.07624e13 | −0.938488 | ||||||||
\(315\) | 7.05976e12 | 0.128257 | ||||||||
\(316\) | −6.01478e12 | −0.107384 | ||||||||
\(317\) | 1.01210e14 | 1.77581 | 0.887905 | − | 0.460027i | \(-0.152160\pi\) | ||||
0.887905 | + | 0.460027i | \(0.152160\pi\) | |||||||
\(318\) | −2.08618e12 | −0.0359751 | ||||||||
\(319\) | −2.18630e13 | −0.370562 | ||||||||
\(320\) | 3.89768e12 | 0.0649354 | ||||||||
\(321\) | 2.67832e13 | 0.438616 | ||||||||
\(322\) | 2.16474e13 | 0.348497 | ||||||||
\(323\) | −9.00941e13 | −1.42588 | ||||||||
\(324\) | 3.57047e12 | 0.0555556 | ||||||||
\(325\) | 8.85169e13 | 1.35415 | ||||||||
\(326\) | 2.76806e13 | 0.416370 | ||||||||
\(327\) | 4.32001e13 | 0.638957 | ||||||||
\(328\) | −1.20589e13 | −0.175389 | ||||||||
\(329\) | 9.10058e13 | 1.30164 | ||||||||
\(330\) | −2.14171e13 | −0.301255 | ||||||||
\(331\) | 4.96614e13 | 0.687013 | 0.343506 | − | 0.939150i | \(-0.388385\pi\) | ||||
0.343506 | + | 0.939150i | \(0.388385\pi\) | |||||||
\(332\) | 8.69638e12 | 0.118326 | ||||||||
\(333\) | −1.88893e13 | −0.252797 | ||||||||
\(334\) | −7.22566e13 | −0.951200 | ||||||||
\(335\) | 6.79053e13 | 0.879341 | ||||||||
\(336\) | 8.39222e12 | 0.106908 | ||||||||
\(337\) | −8.40508e13 | −1.05336 | −0.526681 | − | 0.850063i | \(-0.676564\pi\) | ||||
−0.526681 | + | 0.850063i | \(0.676564\pi\) | |||||||
\(338\) | 1.39918e14 | 1.72516 | ||||||||
\(339\) | 1.91777e13 | 0.232647 | ||||||||
\(340\) | 3.08164e13 | 0.367830 | ||||||||
\(341\) | −1.14193e14 | −1.34119 | ||||||||
\(342\) | −2.05345e13 | −0.237323 | ||||||||
\(343\) | −9.45221e13 | −1.07502 | ||||||||
\(344\) | 2.03315e13 | 0.227562 | ||||||||
\(345\) | 1.81175e13 | 0.199569 | ||||||||
\(346\) | −6.91072e13 | −0.749212 | ||||||||
\(347\) | 1.74097e13 | 0.185772 | 0.0928858 | − | 0.995677i | \(-0.470391\pi\) | ||||
0.0928858 | + | 0.995677i | \(0.470391\pi\) | |||||||
\(348\) | 7.16998e12 | 0.0753065 | ||||||||
\(349\) | −6.60920e13 | −0.683296 | −0.341648 | − | 0.939828i | \(-0.610985\pi\) | ||||
−0.341648 | + | 0.939828i | \(0.610985\pi\) | |||||||
\(350\) | −3.75747e13 | −0.382403 | ||||||||
\(351\) | −3.56263e13 | −0.356929 | ||||||||
\(352\) | −2.54594e13 | −0.251109 | ||||||||
\(353\) | −1.74556e14 | −1.69502 | −0.847508 | − | 0.530783i | \(-0.821898\pi\) | ||||
−0.847508 | + | 0.530783i | \(0.821898\pi\) | |||||||
\(354\) | 1.30084e13 | 0.124368 | ||||||||
\(355\) | −3.02996e13 | −0.285220 | ||||||||
\(356\) | 7.73405e13 | 0.716856 | ||||||||
\(357\) | 6.63517e13 | 0.605587 | ||||||||
\(358\) | 1.44251e14 | 1.29647 | ||||||||
\(359\) | 3.60488e13 | 0.319059 | 0.159530 | − | 0.987193i | \(-0.449002\pi\) | ||||
0.159530 | + | 0.987193i | \(0.449002\pi\) | |||||||
\(360\) | 7.02375e12 | 0.0612217 | ||||||||
\(361\) | 1.60795e12 | 0.0138033 | ||||||||
\(362\) | 1.38897e13 | 0.117434 | ||||||||
\(363\) | 7.05640e13 | 0.587620 | ||||||||
\(364\) | −8.37380e13 | −0.686855 | ||||||||
\(365\) | 7.12995e13 | 0.576071 | ||||||||
\(366\) | −6.05532e13 | −0.481938 | ||||||||
\(367\) | −5.04151e13 | −0.395273 | −0.197636 | − | 0.980275i | \(-0.563327\pi\) | ||||
−0.197636 | + | 0.980275i | \(0.563327\pi\) | |||||||
\(368\) | 2.15370e13 | 0.166350 | ||||||||
\(369\) | −2.17306e13 | −0.165358 | ||||||||
\(370\) | −3.71586e13 | −0.278580 | ||||||||
\(371\) | −8.83621e12 | −0.0652694 | ||||||||
\(372\) | 3.74496e13 | 0.272559 | ||||||||
\(373\) | 2.09367e14 | 1.50144 | 0.750722 | − | 0.660619i | \(-0.229706\pi\) | ||||
0.750722 | + | 0.660619i | \(0.229706\pi\) | |||||||
\(374\) | −2.01290e14 | −1.42242 | ||||||||
\(375\) | −7.45184e13 | −0.518909 | ||||||||
\(376\) | 9.05416e13 | 0.621320 | ||||||||
\(377\) | −7.15424e13 | −0.483823 | ||||||||
\(378\) | 1.51231e13 | 0.100794 | ||||||||
\(379\) | 2.95197e14 | 1.93908 | 0.969540 | − | 0.244931i | \(-0.0787655\pi\) | ||||
0.969540 | + | 0.244931i | \(0.0787655\pi\) | |||||||
\(380\) | −4.03951e13 | −0.261528 | ||||||||
\(381\) | −6.72258e13 | −0.428992 | ||||||||
\(382\) | 2.77664e13 | 0.174651 | ||||||||
\(383\) | 1.28924e14 | 0.799356 | 0.399678 | − | 0.916656i | \(-0.369122\pi\) | ||||
0.399678 | + | 0.916656i | \(0.369122\pi\) | |||||||
\(384\) | 8.34942e12 | 0.0510310 | ||||||||
\(385\) | −9.07142e13 | −0.546564 | ||||||||
\(386\) | 5.98226e12 | 0.0355333 | ||||||||
\(387\) | 3.66381e13 | 0.214547 | ||||||||
\(388\) | −8.43333e13 | −0.486883 | ||||||||
\(389\) | 1.04145e14 | 0.592810 | 0.296405 | − | 0.955062i | \(-0.404212\pi\) | ||||
0.296405 | + | 0.955062i | \(0.404212\pi\) | |||||||
\(390\) | −7.00833e13 | −0.393332 | ||||||||
\(391\) | 1.70278e14 | 0.942297 | ||||||||
\(392\) | −2.92470e13 | −0.159591 | ||||||||
\(393\) | −8.28319e13 | −0.445696 | ||||||||
\(394\) | 1.06496e14 | 0.565070 | ||||||||
\(395\) | −2.13219e13 | −0.111569 | ||||||||
\(396\) | −4.58786e13 | −0.236748 | ||||||||
\(397\) | −1.15408e14 | −0.587338 | −0.293669 | − | 0.955907i | \(-0.594876\pi\) | ||||
−0.293669 | + | 0.955907i | \(0.594876\pi\) | |||||||
\(398\) | −5.07458e13 | −0.254709 | ||||||||
\(399\) | −8.69759e13 | −0.430574 | ||||||||
\(400\) | −3.73830e13 | −0.182534 | ||||||||
\(401\) | −2.20847e14 | −1.06365 | −0.531824 | − | 0.846855i | \(-0.678493\pi\) | ||||
−0.531824 | + | 0.846855i | \(0.678493\pi\) | |||||||
\(402\) | 1.45463e14 | 0.691051 | ||||||||
\(403\) | −3.73674e14 | −1.75111 | ||||||||
\(404\) | −4.23056e13 | −0.195569 | ||||||||
\(405\) | 1.26570e13 | 0.0577204 | ||||||||
\(406\) | 3.03692e13 | 0.136628 | ||||||||
\(407\) | 2.42717e14 | 1.07729 | ||||||||
\(408\) | 6.60132e13 | 0.289068 | ||||||||
\(409\) | −8.56852e13 | −0.370193 | −0.185096 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185096 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(410\) | −4.27479e13 | −0.182223 | ||||||||
\(411\) | −2.29582e14 | −0.965626 | ||||||||
\(412\) | −6.60667e13 | −0.274188 | ||||||||
\(413\) | 5.50985e13 | 0.225639 | ||||||||
\(414\) | 3.88104e13 | 0.156836 | ||||||||
\(415\) | 3.08280e13 | 0.122936 | ||||||||
\(416\) | −8.33109e13 | −0.327860 | ||||||||
\(417\) | 2.52162e13 | 0.0979334 | ||||||||
\(418\) | 2.63857e14 | 1.01135 | ||||||||
\(419\) | 2.58945e14 | 0.979560 | 0.489780 | − | 0.871846i | \(-0.337077\pi\) | ||||
0.489780 | + | 0.871846i | \(0.337077\pi\) | |||||||
\(420\) | 2.97498e13 | 0.111074 | ||||||||
\(421\) | 1.09351e14 | 0.402968 | 0.201484 | − | 0.979492i | \(-0.435424\pi\) | ||||
0.201484 | + | 0.979492i | \(0.435424\pi\) | |||||||
\(422\) | 1.13587e14 | 0.413151 | ||||||||
\(423\) | 1.63159e14 | 0.585786 | ||||||||
\(424\) | −8.79114e12 | −0.0311554 | ||||||||
\(425\) | −2.95562e14 | −1.03398 | ||||||||
\(426\) | −6.49062e13 | −0.224147 | ||||||||
\(427\) | −2.56479e14 | −0.874377 | ||||||||
\(428\) | 1.12864e14 | 0.379853 | ||||||||
\(429\) | 4.57779e14 | 1.52104 | ||||||||
\(430\) | 7.20737e13 | 0.236429 | ||||||||
\(431\) | 2.92180e14 | 0.946292 | 0.473146 | − | 0.880984i | \(-0.343118\pi\) | ||||
0.473146 | + | 0.880984i | \(0.343118\pi\) | |||||||
\(432\) | 1.50459e13 | 0.0481125 | ||||||||
\(433\) | 9.53988e13 | 0.301203 | 0.150602 | − | 0.988595i | \(-0.451879\pi\) | ||||
0.150602 | + | 0.988595i | \(0.451879\pi\) | |||||||
\(434\) | 1.58621e14 | 0.494502 | ||||||||
\(435\) | 2.54170e13 | 0.0782409 | ||||||||
\(436\) | 1.82045e14 | 0.553353 | ||||||||
\(437\) | −2.23206e14 | −0.669975 | ||||||||
\(438\) | 1.52734e14 | 0.452719 | ||||||||
\(439\) | −4.80574e14 | −1.40671 | −0.703357 | − | 0.710837i | \(-0.748316\pi\) | ||||
−0.703357 | + | 0.710837i | \(0.748316\pi\) | |||||||
\(440\) | −9.02514e13 | −0.260894 | ||||||||
\(441\) | −5.27040e13 | −0.150464 | ||||||||
\(442\) | −6.58683e14 | −1.85718 | ||||||||
\(443\) | −3.15148e14 | −0.877596 | −0.438798 | − | 0.898586i | \(-0.644596\pi\) | ||||
−0.438798 | + | 0.898586i | \(0.644596\pi\) | |||||||
\(444\) | −7.95993e13 | −0.218929 | ||||||||
\(445\) | 2.74166e14 | 0.744790 | ||||||||
\(446\) | −1.65767e14 | −0.444792 | ||||||||
\(447\) | −2.98530e14 | −0.791219 | ||||||||
\(448\) | 3.53648e13 | 0.0925852 | ||||||||
\(449\) | 5.03692e14 | 1.30260 | 0.651299 | − | 0.758821i | \(-0.274224\pi\) | ||||
0.651299 | + | 0.758821i | \(0.274224\pi\) | |||||||
\(450\) | −6.73654e13 | −0.172095 | ||||||||
\(451\) | 2.79226e14 | 0.704669 | ||||||||
\(452\) | 8.08147e13 | 0.201479 | ||||||||
\(453\) | 5.16292e13 | 0.127161 | ||||||||
\(454\) | −4.27726e14 | −1.04078 | ||||||||
\(455\) | −2.96845e14 | −0.713619 | ||||||||
\(456\) | −8.65322e13 | −0.205528 | ||||||||
\(457\) | −2.96302e14 | −0.695338 | −0.347669 | − | 0.937617i | \(-0.613027\pi\) | ||||
−0.347669 | + | 0.937617i | \(0.613027\pi\) | |||||||
\(458\) | −6.49857e13 | −0.150681 | ||||||||
\(459\) | 1.18958e14 | 0.272536 | ||||||||
\(460\) | 7.63469e13 | 0.172832 | ||||||||
\(461\) | 1.00284e14 | 0.224325 | 0.112163 | − | 0.993690i | \(-0.464222\pi\) | ||||
0.112163 | + | 0.993690i | \(0.464222\pi\) | |||||||
\(462\) | −1.94323e14 | −0.429530 | ||||||||
\(463\) | 2.49998e14 | 0.546061 | 0.273030 | − | 0.962005i | \(-0.411974\pi\) | ||||
0.273030 | + | 0.962005i | \(0.411974\pi\) | |||||||
\(464\) | 3.02142e13 | 0.0652173 | ||||||||
\(465\) | 1.32756e14 | 0.283180 | ||||||||
\(466\) | 2.28263e14 | 0.481186 | ||||||||
\(467\) | −7.16272e13 | −0.149223 | −0.0746114 | − | 0.997213i | \(-0.523772\pi\) | ||||
−0.0746114 | + | 0.997213i | \(0.523772\pi\) | |||||||
\(468\) | −1.50129e14 | −0.309109 | ||||||||
\(469\) | 6.16124e14 | 1.25377 | ||||||||
\(470\) | 3.20963e14 | 0.645530 | ||||||||
\(471\) | −3.85477e14 | −0.766273 | ||||||||
\(472\) | 5.48174e13 | 0.107705 | ||||||||
\(473\) | −4.70780e14 | −0.914285 | ||||||||
\(474\) | −4.56747e13 | −0.0876789 | ||||||||
\(475\) | 3.87433e14 | 0.735159 | ||||||||
\(476\) | 2.79605e14 | 0.524454 | ||||||||
\(477\) | −1.58419e13 | −0.0293736 | ||||||||
\(478\) | 1.05716e14 | 0.193771 | ||||||||
\(479\) | 2.34866e14 | 0.425574 | 0.212787 | − | 0.977099i | \(-0.431746\pi\) | ||||
0.212787 | + | 0.977099i | \(0.431746\pi\) | |||||||
\(480\) | 2.95980e13 | 0.0530195 | ||||||||
\(481\) | 7.94246e14 | 1.40656 | ||||||||
\(482\) | 1.33420e13 | 0.0233595 | ||||||||
\(483\) | 1.64385e14 | 0.284546 | ||||||||
\(484\) | 2.97356e14 | 0.508894 | ||||||||
\(485\) | −2.98955e14 | −0.505855 | ||||||||
\(486\) | 2.71132e13 | 0.0453609 | ||||||||
\(487\) | −9.89828e14 | −1.63738 | −0.818692 | − | 0.574233i | \(-0.805300\pi\) | ||||
−0.818692 | + | 0.574233i | \(0.805300\pi\) | |||||||
\(488\) | −2.55171e14 | −0.417371 | ||||||||
\(489\) | 2.10200e14 | 0.339965 | ||||||||
\(490\) | −1.03678e14 | −0.165809 | ||||||||
\(491\) | −8.70345e14 | −1.37639 | −0.688197 | − | 0.725523i | \(-0.741598\pi\) | ||||
−0.688197 | + | 0.725523i | \(0.741598\pi\) | |||||||
\(492\) | −9.15724e13 | −0.143204 | ||||||||
\(493\) | 2.38884e14 | 0.369427 | ||||||||
\(494\) | 8.63423e14 | 1.32046 | ||||||||
\(495\) | −1.62636e14 | −0.245973 | ||||||||
\(496\) | 1.57812e14 | 0.236043 | ||||||||
\(497\) | −2.74916e14 | −0.406669 | ||||||||
\(498\) | 6.60381e13 | 0.0966125 | ||||||||
\(499\) | −5.38314e14 | −0.778902 | −0.389451 | − | 0.921047i | \(-0.627335\pi\) | ||||
−0.389451 | + | 0.921047i | \(0.627335\pi\) | |||||||
\(500\) | −3.14020e14 | −0.449389 | ||||||||
\(501\) | −5.48698e14 | −0.776652 | ||||||||
\(502\) | −6.14303e13 | −0.0860027 | ||||||||
\(503\) | 8.38818e14 | 1.16157 | 0.580783 | − | 0.814059i | \(-0.302747\pi\) | ||||
0.580783 | + | 0.814059i | \(0.302747\pi\) | |||||||
\(504\) | 6.37284e13 | 0.0872902 | ||||||||
\(505\) | −1.49970e14 | −0.203190 | ||||||||
\(506\) | −4.98692e14 | −0.668351 | ||||||||
\(507\) | 1.06250e15 | 1.40859 | ||||||||
\(508\) | −2.83289e14 | −0.371518 | ||||||||
\(509\) | −5.97231e14 | −0.774809 | −0.387404 | − | 0.921910i | \(-0.626628\pi\) | ||||
−0.387404 | + | 0.921910i | \(0.626628\pi\) | |||||||
\(510\) | 2.34012e14 | 0.300332 | ||||||||
\(511\) | 6.46921e14 | 0.821365 | ||||||||
\(512\) | 3.51844e13 | 0.0441942 | ||||||||
\(513\) | −1.55934e14 | −0.193774 | ||||||||
\(514\) | 3.12330e14 | 0.383987 | ||||||||
\(515\) | −2.34201e14 | −0.284872 | ||||||||
\(516\) | 1.54393e14 | 0.185803 | ||||||||
\(517\) | −2.09650e15 | −2.49631 | ||||||||
\(518\) | −3.37151e14 | −0.397201 | ||||||||
\(519\) | −5.24783e14 | −0.611729 | ||||||||
\(520\) | −2.95331e14 | −0.340636 | ||||||||
\(521\) | 1.36712e15 | 1.56027 | 0.780133 | − | 0.625613i | \(-0.215151\pi\) | ||||
0.780133 | + | 0.625613i | \(0.215151\pi\) | |||||||
\(522\) | 5.44471e13 | 0.0614875 | ||||||||
\(523\) | 6.90497e14 | 0.771619 | 0.385809 | − | 0.922579i | \(-0.373922\pi\) | ||||
0.385809 | + | 0.922579i | \(0.373922\pi\) | |||||||
\(524\) | −3.49053e14 | −0.385984 | ||||||||
\(525\) | −2.85333e14 | −0.312231 | ||||||||
\(526\) | −1.29551e14 | −0.140287 | ||||||||
\(527\) | 1.24771e15 | 1.33708 | ||||||||
\(528\) | −1.93332e14 | −0.205030 | ||||||||
\(529\) | −5.30948e14 | −0.557245 | ||||||||
\(530\) | −3.11639e13 | −0.0323694 | ||||||||
\(531\) | 9.87828e13 | 0.101546 | ||||||||
\(532\) | −3.66516e14 | −0.372888 | ||||||||
\(533\) | 9.13714e14 | 0.920048 | ||||||||
\(534\) | 5.87305e14 | 0.585311 | ||||||||
\(535\) | 4.00095e14 | 0.394655 | ||||||||
\(536\) | 6.12981e14 | 0.598468 | ||||||||
\(537\) | 1.09541e15 | 1.05857 | ||||||||
\(538\) | −3.63056e14 | −0.347273 | ||||||||
\(539\) | 6.77218e14 | 0.641195 | ||||||||
\(540\) | 5.33366e13 | 0.0499873 | ||||||||
\(541\) | −4.48077e14 | −0.415688 | −0.207844 | − | 0.978162i | \(-0.566645\pi\) | ||||
−0.207844 | + | 0.978162i | \(0.566645\pi\) | |||||||
\(542\) | −7.52806e13 | −0.0691332 | ||||||||
\(543\) | 1.05475e14 | 0.0958848 | ||||||||
\(544\) | 2.78179e14 | 0.250340 | ||||||||
\(545\) | 6.45334e14 | 0.574915 | ||||||||
\(546\) | −6.35886e14 | −0.560815 | ||||||||
\(547\) | 8.45293e14 | 0.738035 | 0.369017 | − | 0.929423i | \(-0.379694\pi\) | ||||
0.369017 | + | 0.929423i | \(0.379694\pi\) | |||||||
\(548\) | −9.67459e14 | −0.836256 | ||||||||
\(549\) | −4.59826e14 | −0.393501 | ||||||||
\(550\) | 8.65609e14 | 0.733377 | ||||||||
\(551\) | −3.13136e14 | −0.262663 | ||||||||
\(552\) | 1.63547e14 | 0.135824 | ||||||||
\(553\) | −1.93460e14 | −0.159075 | ||||||||
\(554\) | −1.39625e15 | −1.13673 | ||||||||
\(555\) | −2.82173e14 | −0.227460 | ||||||||
\(556\) | 1.06261e14 | 0.0848128 | ||||||||
\(557\) | −6.21109e14 | −0.490868 | −0.245434 | − | 0.969413i | \(-0.578930\pi\) | ||||
−0.245434 | + | 0.969413i | \(0.578930\pi\) | |||||||
\(558\) | 2.84383e14 | 0.222544 | ||||||||
\(559\) | −1.54054e15 | −1.19373 | ||||||||
\(560\) | 1.25365e14 | 0.0961930 | ||||||||
\(561\) | −1.52855e15 | −1.16140 | ||||||||
\(562\) | 8.80316e14 | 0.662352 | ||||||||
\(563\) | −2.31809e15 | −1.72717 | −0.863585 | − | 0.504203i | \(-0.831786\pi\) | ||||
−0.863585 | + | 0.504203i | \(0.831786\pi\) | |||||||
\(564\) | 6.87550e14 | 0.507305 | ||||||||
\(565\) | 2.86482e14 | 0.209330 | ||||||||
\(566\) | −8.25008e14 | −0.596991 | ||||||||
\(567\) | 1.14841e14 | 0.0822980 | ||||||||
\(568\) | −2.73514e14 | −0.194117 | ||||||||
\(569\) | −1.54963e15 | −1.08921 | −0.544605 | − | 0.838693i | \(-0.683320\pi\) | ||||
−0.544605 | + | 0.838693i | \(0.683320\pi\) | |||||||
\(570\) | −3.06750e14 | −0.213537 | ||||||||
\(571\) | 1.59408e15 | 1.09903 | 0.549516 | − | 0.835483i | \(-0.314812\pi\) | ||||
0.549516 | + | 0.835483i | \(0.314812\pi\) | |||||||
\(572\) | 1.92908e15 | 1.31726 | ||||||||
\(573\) | 2.10851e14 | 0.142602 | ||||||||
\(574\) | −3.87864e14 | −0.259815 | ||||||||
\(575\) | −7.32250e14 | −0.485832 | ||||||||
\(576\) | 6.34034e13 | 0.0416667 | ||||||||
\(577\) | 1.77831e15 | 1.15755 | 0.578777 | − | 0.815486i | \(-0.303530\pi\) | ||||
0.578777 | + | 0.815486i | \(0.303530\pi\) | |||||||
\(578\) | 1.10268e15 | 0.710959 | ||||||||
\(579\) | 4.54278e13 | 0.0290128 | ||||||||
\(580\) | 1.07107e14 | 0.0677586 | ||||||||
\(581\) | 2.79711e14 | 0.175283 | ||||||||
\(582\) | −6.40406e14 | −0.397539 | ||||||||
\(583\) | 2.03560e14 | 0.125174 | ||||||||
\(584\) | 6.43621e14 | 0.392066 | ||||||||
\(585\) | −5.32195e14 | −0.321154 | ||||||||
\(586\) | 1.78984e15 | 1.06998 | ||||||||
\(587\) | 2.98810e14 | 0.176964 | 0.0884821 | − | 0.996078i | \(-0.471798\pi\) | ||||
0.0884821 | + | 0.996078i | \(0.471798\pi\) | |||||||
\(588\) | −2.22094e14 | −0.130305 | ||||||||
\(589\) | −1.63554e15 | −0.950666 | ||||||||
\(590\) | 1.94323e14 | 0.111902 | ||||||||
\(591\) | 8.08700e14 | 0.461378 | ||||||||
\(592\) | −3.35431e14 | −0.189598 | ||||||||
\(593\) | 2.13060e15 | 1.19317 | 0.596585 | − | 0.802550i | \(-0.296524\pi\) | ||||
0.596585 | + | 0.802550i | \(0.296524\pi\) | |||||||
\(594\) | −3.48391e14 | −0.193304 | ||||||||
\(595\) | 9.91179e14 | 0.544890 | ||||||||
\(596\) | −1.25800e15 | −0.685216 | ||||||||
\(597\) | −3.85351e14 | −0.207969 | ||||||||
\(598\) | −1.63188e15 | −0.872631 | ||||||||
\(599\) | 6.91981e14 | 0.366646 | 0.183323 | − | 0.983053i | \(-0.441315\pi\) | ||||
0.183323 | + | 0.983053i | \(0.441315\pi\) | |||||||
\(600\) | −2.83877e14 | −0.149039 | ||||||||
\(601\) | 1.90167e15 | 0.989296 | 0.494648 | − | 0.869094i | \(-0.335297\pi\) | ||||
0.494648 | + | 0.869094i | \(0.335297\pi\) | |||||||
\(602\) | 6.53945e14 | 0.337101 | ||||||||
\(603\) | 1.10461e15 | 0.564241 | ||||||||
\(604\) | 2.17565e14 | 0.110125 | ||||||||
\(605\) | 1.05410e15 | 0.528724 | ||||||||
\(606\) | −3.21258e14 | −0.159682 | ||||||||
\(607\) | 2.60368e14 | 0.128248 | 0.0641238 | − | 0.997942i | \(-0.479575\pi\) | ||||
0.0641238 | + | 0.997942i | \(0.479575\pi\) | |||||||
\(608\) | −3.64646e14 | −0.177993 | ||||||||
\(609\) | 2.30616e14 | 0.111556 | ||||||||
\(610\) | −9.04561e14 | −0.433634 | ||||||||
\(611\) | −6.86041e15 | −3.25929 | ||||||||
\(612\) | 5.01288e14 | 0.236023 | ||||||||
\(613\) | −3.20683e15 | −1.49638 | −0.748192 | − | 0.663482i | \(-0.769078\pi\) | ||||
−0.748192 | + | 0.663482i | \(0.769078\pi\) | |||||||
\(614\) | 1.81778e15 | 0.840649 | ||||||||
\(615\) | −3.24617e14 | −0.148785 | ||||||||
\(616\) | −8.18876e14 | −0.371984 | ||||||||
\(617\) | 3.99520e15 | 1.79875 | 0.899374 | − | 0.437180i | \(-0.144023\pi\) | ||||
0.899374 | + | 0.437180i | \(0.144023\pi\) | |||||||
\(618\) | −5.01694e14 | −0.223873 | ||||||||
\(619\) | −1.00277e15 | −0.443508 | −0.221754 | − | 0.975103i | \(-0.571178\pi\) | ||||
−0.221754 | + | 0.975103i | \(0.571178\pi\) | |||||||
\(620\) | 5.59432e14 | 0.245241 | ||||||||
\(621\) | 2.94716e14 | 0.128056 | ||||||||
\(622\) | −2.14782e15 | −0.925019 | ||||||||
\(623\) | 2.48759e15 | 1.06192 | ||||||||
\(624\) | −6.32642e14 | −0.267697 | ||||||||
\(625\) | 6.27607e14 | 0.263237 | ||||||||
\(626\) | −1.17339e15 | −0.487847 | ||||||||
\(627\) | 2.00367e15 | 0.825760 | ||||||||
\(628\) | −1.62440e15 | −0.663612 | ||||||||
\(629\) | −2.65203e15 | −1.07399 | ||||||||
\(630\) | 2.25912e14 | 0.0906916 | ||||||||
\(631\) | −2.06951e15 | −0.823579 | −0.411790 | − | 0.911279i | \(-0.635096\pi\) | ||||
−0.411790 | + | 0.911279i | \(0.635096\pi\) | |||||||
\(632\) | −1.92473e14 | −0.0759321 | ||||||||
\(633\) | 8.62548e14 | 0.337336 | ||||||||
\(634\) | 3.23871e15 | 1.25569 | ||||||||
\(635\) | −1.00424e15 | −0.385994 | ||||||||
\(636\) | −6.67577e13 | −0.0254383 | ||||||||
\(637\) | 2.21607e15 | 0.837174 | ||||||||
\(638\) | −6.99615e14 | −0.262027 | ||||||||
\(639\) | −4.92881e14 | −0.183015 | ||||||||
\(640\) | 1.24726e14 | 0.0459163 | ||||||||
\(641\) | −1.00036e14 | −0.0365122 | −0.0182561 | − | 0.999833i | \(-0.505811\pi\) | ||||
−0.0182561 | + | 0.999833i | \(0.505811\pi\) | |||||||
\(642\) | 8.57063e14 | 0.310149 | ||||||||
\(643\) | −3.03786e14 | −0.108995 | −0.0544976 | − | 0.998514i | \(-0.517356\pi\) | ||||
−0.0544976 | + | 0.998514i | \(0.517356\pi\) | |||||||
\(644\) | 6.92717e14 | 0.246424 | ||||||||
\(645\) | 5.47310e14 | 0.193043 | ||||||||
\(646\) | −2.88301e15 | −1.00825 | ||||||||
\(647\) | 1.90746e14 | 0.0661426 | 0.0330713 | − | 0.999453i | \(-0.489471\pi\) | ||||
0.0330713 | + | 0.999453i | \(0.489471\pi\) | |||||||
\(648\) | 1.14255e14 | 0.0392837 | ||||||||
\(649\) | −1.26931e15 | −0.432733 | ||||||||
\(650\) | 2.83254e15 | 0.957531 | ||||||||
\(651\) | 1.20453e15 | 0.403759 | ||||||||
\(652\) | 8.85780e14 | 0.294418 | ||||||||
\(653\) | 1.64793e15 | 0.543145 | 0.271573 | − | 0.962418i | \(-0.412456\pi\) | ||||
0.271573 | + | 0.962418i | \(0.412456\pi\) | |||||||
\(654\) | 1.38240e15 | 0.451811 | ||||||||
\(655\) | −1.23737e15 | −0.401025 | ||||||||
\(656\) | −3.85885e14 | −0.124019 | ||||||||
\(657\) | 1.15983e15 | 0.369644 | ||||||||
\(658\) | 2.91219e15 | 0.920400 | ||||||||
\(659\) | −2.62861e15 | −0.823866 | −0.411933 | − | 0.911214i | \(-0.635146\pi\) | ||||
−0.411933 | + | 0.911214i | \(0.635146\pi\) | |||||||
\(660\) | −6.85347e14 | −0.213019 | ||||||||
\(661\) | 4.80241e15 | 1.48031 | 0.740153 | − | 0.672439i | \(-0.234753\pi\) | ||||
0.740153 | + | 0.672439i | \(0.234753\pi\) | |||||||
\(662\) | 1.58916e15 | 0.485791 | ||||||||
\(663\) | −5.00188e15 | −1.51638 | ||||||||
\(664\) | 2.78284e14 | 0.0836689 | ||||||||
\(665\) | −1.29927e15 | −0.387418 | ||||||||
\(666\) | −6.04457e14 | −0.178755 | ||||||||
\(667\) | 5.91830e14 | 0.173582 | ||||||||
\(668\) | −2.31221e15 | −0.672600 | ||||||||
\(669\) | −1.25879e15 | −0.363171 | ||||||||
\(670\) | 2.17297e15 | 0.621788 | ||||||||
\(671\) | 5.90852e15 | 1.67689 | ||||||||
\(672\) | 2.68551e14 | 0.0755955 | ||||||||
\(673\) | −1.25325e15 | −0.349909 | −0.174954 | − | 0.984577i | \(-0.555978\pi\) | ||||
−0.174954 | + | 0.984577i | \(0.555978\pi\) | |||||||
\(674\) | −2.68963e15 | −0.744839 | ||||||||
\(675\) | −5.11556e14 | −0.140515 | ||||||||
\(676\) | 4.47736e15 | 1.21988 | ||||||||
\(677\) | −1.92035e15 | −0.518969 | −0.259485 | − | 0.965747i | \(-0.583553\pi\) | ||||
−0.259485 | + | 0.965747i | \(0.583553\pi\) | |||||||
\(678\) | 6.13686e14 | 0.164507 | ||||||||
\(679\) | −2.71250e15 | −0.721251 | ||||||||
\(680\) | 9.86124e14 | 0.260095 | ||||||||
\(681\) | −3.24805e15 | −0.849793 | ||||||||
\(682\) | −3.65416e15 | −0.948362 | ||||||||
\(683\) | 6.12548e14 | 0.157698 | 0.0788490 | − | 0.996887i | \(-0.474875\pi\) | ||||
0.0788490 | + | 0.996887i | \(0.474875\pi\) | |||||||
\(684\) | −6.57104e14 | −0.167813 | ||||||||
\(685\) | −3.42957e15 | −0.868842 | ||||||||
\(686\) | −3.02471e15 | −0.760153 | ||||||||
\(687\) | −4.93485e14 | −0.123030 | ||||||||
\(688\) | 6.50610e14 | 0.160910 | ||||||||
\(689\) | 6.66112e14 | 0.163434 | ||||||||
\(690\) | 5.79760e14 | 0.141117 | ||||||||
\(691\) | 5.08990e15 | 1.22908 | 0.614539 | − | 0.788886i | \(-0.289342\pi\) | ||||
0.614539 | + | 0.788886i | \(0.289342\pi\) | |||||||
\(692\) | −2.21143e15 | −0.529773 | ||||||||
\(693\) | −1.47564e15 | −0.350710 | ||||||||
\(694\) | 5.57111e14 | 0.131360 | ||||||||
\(695\) | 3.76686e14 | 0.0881177 | ||||||||
\(696\) | 2.29439e14 | 0.0532497 | ||||||||
\(697\) | −3.05094e15 | −0.702511 | ||||||||
\(698\) | −2.11494e15 | −0.483163 | ||||||||
\(699\) | 1.73337e15 | 0.392887 | ||||||||
\(700\) | −1.20239e15 | −0.270400 | ||||||||
\(701\) | −1.78664e15 | −0.398647 | −0.199323 | − | 0.979934i | \(-0.563874\pi\) | ||||
−0.199323 | + | 0.979934i | \(0.563874\pi\) | |||||||
\(702\) | −1.14004e15 | −0.252387 | ||||||||
\(703\) | 3.47636e15 | 0.763608 | ||||||||
\(704\) | −8.14699e14 | −0.177561 | ||||||||
\(705\) | 2.43731e15 | 0.527073 | ||||||||
\(706\) | −5.58579e15 | −1.19856 | ||||||||
\(707\) | −1.36072e15 | −0.289709 | ||||||||
\(708\) | 4.16270e14 | 0.0879411 | ||||||||
\(709\) | 4.18187e15 | 0.876631 | 0.438315 | − | 0.898821i | \(-0.355575\pi\) | ||||
0.438315 | + | 0.898821i | \(0.355575\pi\) | |||||||
\(710\) | −9.69586e14 | −0.201681 | ||||||||
\(711\) | −3.46842e14 | −0.0715895 | ||||||||
\(712\) | 2.47490e15 | 0.506894 | ||||||||
\(713\) | 3.09119e15 | 0.628251 | ||||||||
\(714\) | 2.12325e15 | 0.428215 | ||||||||
\(715\) | 6.83842e15 | 1.36859 | ||||||||
\(716\) | 4.61605e15 | 0.916745 | ||||||||
\(717\) | 8.02782e14 | 0.158213 | ||||||||
\(718\) | 1.15356e15 | 0.225609 | ||||||||
\(719\) | 8.02554e15 | 1.55763 | 0.778817 | − | 0.627251i | \(-0.215820\pi\) | ||||
0.778817 | + | 0.627251i | \(0.215820\pi\) | |||||||
\(720\) | 2.24760e14 | 0.0432903 | ||||||||
\(721\) | −2.12497e15 | −0.406172 | ||||||||
\(722\) | 5.14544e13 | 0.00976041 | ||||||||
\(723\) | 1.01316e14 | 0.0190729 | ||||||||
\(724\) | 4.44470e14 | 0.0830387 | ||||||||
\(725\) | −1.02727e15 | −0.190470 | ||||||||
\(726\) | 2.25805e15 | 0.415510 | ||||||||
\(727\) | −2.93804e15 | −0.536560 | −0.268280 | − | 0.963341i | \(-0.586455\pi\) | ||||
−0.268280 | + | 0.963341i | \(0.586455\pi\) | |||||||
\(728\) | −2.67962e15 | −0.485680 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 2.28159e15 | 0.407344 | ||||||||
\(731\) | 5.14393e15 | 0.911485 | ||||||||
\(732\) | −1.93770e15 | −0.340782 | ||||||||
\(733\) | −4.42319e15 | −0.772083 | −0.386042 | − | 0.922481i | \(-0.626158\pi\) | ||||
−0.386042 | + | 0.922481i | \(0.626158\pi\) | |||||||
\(734\) | −1.61328e15 | −0.279500 | ||||||||
\(735\) | −7.87306e14 | −0.135383 | ||||||||
\(736\) | 6.89184e14 | 0.117627 | ||||||||
\(737\) | −1.41937e16 | −2.40449 | ||||||||
\(738\) | −6.95378e14 | −0.116926 | ||||||||
\(739\) | −1.11732e16 | −1.86481 | −0.932405 | − | 0.361416i | \(-0.882293\pi\) | ||||
−0.932405 | + | 0.361416i | \(0.882293\pi\) | |||||||
\(740\) | −1.18908e15 | −0.196986 | ||||||||
\(741\) | 6.55662e15 | 1.07815 | ||||||||
\(742\) | −2.82759e14 | −0.0461524 | ||||||||
\(743\) | 1.98624e15 | 0.321805 | 0.160903 | − | 0.986970i | \(-0.448559\pi\) | ||||
0.160903 | + | 0.986970i | \(0.448559\pi\) | |||||||
\(744\) | 1.19839e15 | 0.192728 | ||||||||
\(745\) | −4.45952e15 | −0.711916 | ||||||||
\(746\) | 6.69973e15 | 1.06168 | ||||||||
\(747\) | 5.01477e14 | 0.0788838 | ||||||||
\(748\) | −6.44128e15 | −1.00580 | ||||||||
\(749\) | 3.63017e15 | 0.562700 | ||||||||
\(750\) | −2.38459e15 | −0.366924 | ||||||||
\(751\) | −7.63503e15 | −1.16625 | −0.583125 | − | 0.812383i | \(-0.698170\pi\) | ||||
−0.583125 | + | 0.812383i | \(0.698170\pi\) | |||||||
\(752\) | 2.89733e15 | 0.439339 | ||||||||
\(753\) | −4.66486e14 | −0.0702209 | ||||||||
\(754\) | −2.28936e15 | −0.342114 | ||||||||
\(755\) | 7.71251e14 | 0.114416 | ||||||||
\(756\) | 4.83938e14 | 0.0712721 | ||||||||
\(757\) | 7.89241e15 | 1.15394 | 0.576969 | − | 0.816766i | \(-0.304235\pi\) | ||||
0.576969 | + | 0.816766i | \(0.304235\pi\) | |||||||
\(758\) | 9.44630e15 | 1.37114 | ||||||||
\(759\) | −3.78694e15 | −0.545706 | ||||||||
\(760\) | −1.29264e15 | −0.184928 | ||||||||
\(761\) | −1.10602e16 | −1.57089 | −0.785446 | − | 0.618930i | \(-0.787566\pi\) | ||||
−0.785446 | + | 0.618930i | \(0.787566\pi\) | |||||||
\(762\) | −2.15123e15 | −0.303343 | ||||||||
\(763\) | 5.85530e15 | 0.819717 | ||||||||
\(764\) | 8.88526e14 | 0.123497 | ||||||||
\(765\) | 1.77703e15 | 0.245220 | ||||||||
\(766\) | 4.12557e15 | 0.565230 | ||||||||
\(767\) | −4.15356e15 | −0.564997 | ||||||||
\(768\) | 2.67181e14 | 0.0360844 | ||||||||
\(769\) | 1.66698e15 | 0.223529 | 0.111765 | − | 0.993735i | \(-0.464350\pi\) | ||||
0.111765 | + | 0.993735i | \(0.464350\pi\) | |||||||
\(770\) | −2.90285e15 | −0.386479 | ||||||||
\(771\) | 2.37176e15 | 0.313524 | ||||||||
\(772\) | 1.91432e14 | 0.0251258 | ||||||||
\(773\) | 6.92568e15 | 0.902558 | 0.451279 | − | 0.892383i | \(-0.350968\pi\) | ||||
0.451279 | + | 0.892383i | \(0.350968\pi\) | |||||||
\(774\) | 1.17242e15 | 0.151708 | ||||||||
\(775\) | −5.36556e15 | −0.689375 | ||||||||
\(776\) | −2.69867e15 | −0.344278 | ||||||||
\(777\) | −2.56024e15 | −0.324313 | ||||||||
\(778\) | 3.33264e15 | 0.419180 | ||||||||
\(779\) | 3.99926e15 | 0.499487 | ||||||||
\(780\) | −2.24267e15 | −0.278128 | ||||||||
\(781\) | 6.33326e15 | 0.779914 | ||||||||
\(782\) | 5.44891e15 | 0.666304 | ||||||||
\(783\) | 4.13457e14 | 0.0502043 | ||||||||
\(784\) | −9.35903e14 | −0.112848 | ||||||||
\(785\) | −5.75836e15 | −0.689470 | ||||||||
\(786\) | −2.65062e15 | −0.315155 | ||||||||
\(787\) | −2.99770e15 | −0.353939 | −0.176969 | − | 0.984216i | \(-0.556629\pi\) | ||||
−0.176969 | + | 0.984216i | \(0.556629\pi\) | |||||||
\(788\) | 3.40786e15 | 0.399565 | ||||||||
\(789\) | −9.83775e14 | −0.114544 | ||||||||
\(790\) | −6.82301e14 | −0.0788910 | ||||||||
\(791\) | 2.59933e15 | 0.298463 | ||||||||
\(792\) | −1.46811e15 | −0.167406 | ||||||||
\(793\) | 1.93345e16 | 2.18943 | ||||||||
\(794\) | −3.69306e15 | −0.415311 | ||||||||
\(795\) | −2.36651e14 | −0.0264295 | ||||||||
\(796\) | −1.62387e15 | −0.180106 | ||||||||
\(797\) | −5.67794e15 | −0.625417 | −0.312709 | − | 0.949849i | \(-0.601236\pi\) | ||||
−0.312709 | + | 0.949849i | \(0.601236\pi\) | |||||||
\(798\) | −2.78323e15 | −0.304462 | ||||||||
\(799\) | 2.29073e16 | 2.48866 | ||||||||
\(800\) | −1.19626e15 | −0.129071 | ||||||||
\(801\) | 4.45984e15 | 0.477904 | ||||||||
\(802\) | −7.06711e15 | −0.752113 | ||||||||
\(803\) | −1.49031e16 | −1.57522 | ||||||||
\(804\) | 4.65482e15 | 0.488647 | ||||||||
\(805\) | 2.45563e15 | 0.256027 | ||||||||
\(806\) | −1.19576e16 | −1.23823 | ||||||||
\(807\) | −2.75696e15 | −0.283547 | ||||||||
\(808\) | −1.35378e15 | −0.138288 | ||||||||
\(809\) | 4.43159e15 | 0.449617 | 0.224809 | − | 0.974403i | \(-0.427824\pi\) | ||||
0.224809 | + | 0.974403i | \(0.427824\pi\) | |||||||
\(810\) | 4.05025e14 | 0.0408145 | ||||||||
\(811\) | −8.99323e15 | −0.900121 | −0.450060 | − | 0.892998i | \(-0.648598\pi\) | ||||
−0.450060 | + | 0.892998i | \(0.648598\pi\) | |||||||
\(812\) | 9.71813e14 | 0.0966105 | ||||||||
\(813\) | −5.71662e14 | −0.0564470 | ||||||||
\(814\) | 7.76695e15 | 0.761757 | ||||||||
\(815\) | 3.14002e15 | 0.305890 | ||||||||
\(816\) | 2.11242e15 | 0.204402 | ||||||||
\(817\) | −6.74283e15 | −0.648068 | ||||||||
\(818\) | −2.74193e15 | −0.261766 | ||||||||
\(819\) | −4.82876e15 | −0.457903 | ||||||||
\(820\) | −1.36793e15 | −0.128851 | ||||||||
\(821\) | 9.08013e15 | 0.849581 | 0.424790 | − | 0.905292i | \(-0.360348\pi\) | ||||
0.424790 | + | 0.905292i | \(0.360348\pi\) | |||||||
\(822\) | −7.34664e15 | −0.682800 | ||||||||
\(823\) | −1.29654e16 | −1.19698 | −0.598488 | − | 0.801132i | \(-0.704232\pi\) | ||||
−0.598488 | + | 0.801132i | \(0.704232\pi\) | |||||||
\(824\) | −2.11414e15 | −0.193880 | ||||||||
\(825\) | 6.57322e15 | 0.598800 | ||||||||
\(826\) | 1.76315e15 | 0.159551 | ||||||||
\(827\) | −5.40262e15 | −0.485651 | −0.242826 | − | 0.970070i | \(-0.578074\pi\) | ||||
−0.242826 | + | 0.970070i | \(0.578074\pi\) | |||||||
\(828\) | 1.24193e15 | 0.110900 | ||||||||
\(829\) | −7.97388e14 | −0.0707326 | −0.0353663 | − | 0.999374i | \(-0.511260\pi\) | ||||
−0.0353663 | + | 0.999374i | \(0.511260\pi\) | |||||||
\(830\) | 9.86496e14 | 0.0869292 | ||||||||
\(831\) | −1.06027e16 | −0.928138 | ||||||||
\(832\) | −2.66595e15 | −0.231832 | ||||||||
\(833\) | −7.39956e15 | −0.639231 | ||||||||
\(834\) | 8.06918e14 | 0.0692494 | ||||||||
\(835\) | −8.19661e15 | −0.698809 | ||||||||
\(836\) | 8.44344e15 | 0.715129 | ||||||||
\(837\) | 2.15953e15 | 0.181706 | ||||||||
\(838\) | 8.28625e15 | 0.692653 | ||||||||
\(839\) | 1.02313e16 | 0.849646 | 0.424823 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424823 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(840\) | 9.51993e14 | 0.0785412 | ||||||||
\(841\) | −1.13702e16 | −0.931947 | ||||||||
\(842\) | 3.49922e15 | 0.284941 | ||||||||
\(843\) | 6.68490e15 | 0.540808 | ||||||||
\(844\) | 3.63477e15 | 0.292142 | ||||||||
\(845\) | 1.58719e16 | 1.26741 | ||||||||
\(846\) | 5.22108e15 | 0.414213 | ||||||||
\(847\) | 9.56418e15 | 0.753857 | ||||||||
\(848\) | −2.81316e14 | −0.0220302 | ||||||||
\(849\) | −6.26490e15 | −0.487441 | ||||||||
\(850\) | −9.45800e15 | −0.731131 | ||||||||
\(851\) | −6.57034e15 | −0.504633 | ||||||||
\(852\) | −2.07700e15 | −0.158496 | ||||||||
\(853\) | −1.33010e16 | −1.00847 | −0.504237 | − | 0.863565i | \(-0.668226\pi\) | ||||
−0.504237 | + | 0.863565i | \(0.668226\pi\) | |||||||
\(854\) | −8.20733e15 | −0.618278 | ||||||||
\(855\) | −2.32938e15 | −0.174352 | ||||||||
\(856\) | 3.61166e15 | 0.268597 | ||||||||
\(857\) | 3.38483e15 | 0.250116 | 0.125058 | − | 0.992149i | \(-0.460088\pi\) | ||||
0.125058 | + | 0.992149i | \(0.460088\pi\) | |||||||
\(858\) | 1.46489e16 | 1.07554 | ||||||||
\(859\) | 2.32376e16 | 1.69523 | 0.847615 | − | 0.530612i | \(-0.178038\pi\) | ||||
0.847615 | + | 0.530612i | \(0.178038\pi\) | |||||||
\(860\) | 2.30636e15 | 0.167180 | ||||||||
\(861\) | −2.94534e15 | −0.212138 | ||||||||
\(862\) | 9.34976e15 | 0.669130 | ||||||||
\(863\) | 2.44743e16 | 1.74041 | 0.870203 | − | 0.492693i | \(-0.163987\pi\) | ||||
0.870203 | + | 0.492693i | \(0.163987\pi\) | |||||||
\(864\) | 4.81469e14 | 0.0340207 | ||||||||
\(865\) | −7.83935e15 | −0.550417 | ||||||||
\(866\) | 3.05276e15 | 0.212983 | ||||||||
\(867\) | 8.37344e15 | 0.580496 | ||||||||
\(868\) | 5.07588e15 | 0.349666 | ||||||||
\(869\) | 4.45674e15 | 0.305076 | ||||||||
\(870\) | 8.13345e14 | 0.0553247 | ||||||||
\(871\) | −4.64461e16 | −3.13942 | ||||||||
\(872\) | 5.82543e15 | 0.391280 | ||||||||
\(873\) | −4.86309e15 | −0.324589 | ||||||||
\(874\) | −7.14261e15 | −0.473744 | ||||||||
\(875\) | −1.01002e16 | −0.665708 | ||||||||
\(876\) | 4.88750e15 | 0.320121 | ||||||||
\(877\) | 2.15305e16 | 1.40138 | 0.700689 | − | 0.713467i | \(-0.252876\pi\) | ||||
0.700689 | + | 0.713467i | \(0.252876\pi\) | |||||||
\(878\) | −1.53784e16 | −0.994697 | ||||||||
\(879\) | 1.35916e16 | 0.873636 | ||||||||
\(880\) | −2.88805e15 | −0.184480 | ||||||||
\(881\) | 2.77094e16 | 1.75898 | 0.879488 | − | 0.475922i | \(-0.157885\pi\) | ||||
0.879488 | + | 0.475922i | \(0.157885\pi\) | |||||||
\(882\) | −1.68653e15 | −0.106394 | ||||||||
\(883\) | −8.61677e15 | −0.540208 | −0.270104 | − | 0.962831i | \(-0.587058\pi\) | ||||
−0.270104 | + | 0.962831i | \(0.587058\pi\) | |||||||
\(884\) | −2.10779e16 | −1.31322 | ||||||||
\(885\) | 1.47564e15 | 0.0913679 | ||||||||
\(886\) | −1.00848e16 | −0.620554 | ||||||||
\(887\) | −3.22651e16 | −1.97312 | −0.986558 | − | 0.163409i | \(-0.947751\pi\) | ||||
−0.986558 | + | 0.163409i | \(0.947751\pi\) | |||||||
\(888\) | −2.54718e15 | −0.154806 | ||||||||
\(889\) | −9.11173e15 | −0.550353 | ||||||||
\(890\) | 8.77332e15 | 0.526646 | ||||||||
\(891\) | −2.64559e15 | −0.157832 | ||||||||
\(892\) | −5.30455e15 | −0.314515 | ||||||||
\(893\) | −3.00275e16 | −1.76944 | ||||||||
\(894\) | −9.55296e15 | −0.559476 | ||||||||
\(895\) | 1.63635e16 | 0.952468 | ||||||||
\(896\) | 1.13167e15 | 0.0654676 | ||||||||
\(897\) | −1.23921e16 | −0.712500 | ||||||||
\(898\) | 1.61181e16 | 0.921075 | ||||||||
\(899\) | 4.33663e15 | 0.246305 | ||||||||
\(900\) | −2.15569e15 | −0.121690 | ||||||||
\(901\) | −2.22418e15 | −0.124791 | ||||||||
\(902\) | 8.93523e15 | 0.498276 | ||||||||
\(903\) | 4.96590e15 | 0.275242 | ||||||||
\(904\) | 2.58607e15 | 0.142467 | ||||||||
\(905\) | 1.57561e15 | 0.0862744 | ||||||||
\(906\) | 1.65213e15 | 0.0899166 | ||||||||
\(907\) | 3.10436e16 | 1.67932 | 0.839658 | − | 0.543115i | \(-0.182755\pi\) | ||||
0.839658 | + | 0.543115i | \(0.182755\pi\) | |||||||
\(908\) | −1.36872e16 | −0.735943 | ||||||||
\(909\) | −2.43955e15 | −0.130379 | ||||||||
\(910\) | −9.49903e15 | −0.504605 | ||||||||
\(911\) | 1.78173e16 | 0.940786 | 0.470393 | − | 0.882457i | \(-0.344112\pi\) | ||||
0.470393 | + | 0.882457i | \(0.344112\pi\) | |||||||
\(912\) | −2.76903e15 | −0.145330 | ||||||||
\(913\) | −6.44371e15 | −0.336161 | ||||||||
\(914\) | −9.48167e15 | −0.491678 | ||||||||
\(915\) | −6.86901e15 | −0.354061 | ||||||||
\(916\) | −2.07954e15 | −0.106547 | ||||||||
\(917\) | −1.12270e16 | −0.571783 | ||||||||
\(918\) | 3.80666e15 | 0.192712 | ||||||||
\(919\) | 2.90046e16 | 1.45959 | 0.729797 | − | 0.683664i | \(-0.239615\pi\) | ||||
0.729797 | + | 0.683664i | \(0.239615\pi\) | |||||||
\(920\) | 2.44310e15 | 0.122211 | ||||||||
\(921\) | 1.38038e16 | 0.686387 | ||||||||
\(922\) | 3.20910e15 | 0.158622 | ||||||||
\(923\) | 2.07244e16 | 1.01829 | ||||||||
\(924\) | −6.21834e15 | −0.303724 | ||||||||
\(925\) | 1.14045e16 | 0.553730 | ||||||||
\(926\) | 7.99993e15 | 0.386123 | ||||||||
\(927\) | −3.80974e15 | −0.182792 | ||||||||
\(928\) | 9.66856e14 | 0.0461156 | ||||||||
\(929\) | 1.09610e16 | 0.519713 | 0.259856 | − | 0.965647i | \(-0.416325\pi\) | ||||
0.259856 | + | 0.965647i | \(0.416325\pi\) | |||||||
\(930\) | 4.24818e15 | 0.200238 | ||||||||
\(931\) | 9.69957e15 | 0.454495 | ||||||||
\(932\) | 7.30442e15 | 0.340250 | ||||||||
\(933\) | −1.63100e16 | −0.755274 | ||||||||
\(934\) | −2.29207e15 | −0.105516 | ||||||||
\(935\) | −2.28338e16 | −1.04500 | ||||||||
\(936\) | −4.80413e15 | −0.218573 | ||||||||
\(937\) | 9.13874e15 | 0.413351 | 0.206675 | − | 0.978410i | \(-0.433736\pi\) | ||||
0.206675 | + | 0.978410i | \(0.433736\pi\) | |||||||
\(938\) | 1.97160e16 | 0.886548 | ||||||||
\(939\) | −8.91043e15 | −0.398325 | ||||||||
\(940\) | 1.02708e16 | 0.456459 | ||||||||
\(941\) | 6.97287e14 | 0.0308083 | 0.0154042 | − | 0.999881i | \(-0.495097\pi\) | ||||
0.0154042 | + | 0.999881i | \(0.495097\pi\) | |||||||
\(942\) | −1.23353e16 | −0.541837 | ||||||||
\(943\) | −7.55864e15 | −0.330088 | ||||||||
\(944\) | 1.75416e15 | 0.0761592 | ||||||||
\(945\) | 1.71552e15 | 0.0740494 | ||||||||
\(946\) | −1.50650e16 | −0.646497 | ||||||||
\(947\) | −2.17555e15 | −0.0928205 | −0.0464103 | − | 0.998922i | \(-0.514778\pi\) | ||||
−0.0464103 | + | 0.998922i | \(0.514778\pi\) | |||||||
\(948\) | −1.46159e15 | −0.0619983 | ||||||||
\(949\) | −4.87677e16 | −2.05669 | ||||||||
\(950\) | 1.23978e16 | 0.519836 | ||||||||
\(951\) | 2.45940e16 | 1.02526 | ||||||||
\(952\) | 8.94737e15 | 0.370845 | ||||||||
\(953\) | −3.59675e16 | −1.48217 | −0.741087 | − | 0.671409i | \(-0.765690\pi\) | ||||
−0.741087 | + | 0.671409i | \(0.765690\pi\) | |||||||
\(954\) | −5.06941e14 | −0.0207702 | ||||||||
\(955\) | 3.14976e15 | 0.128309 | ||||||||
\(956\) | 3.38291e15 | 0.137016 | ||||||||
\(957\) | −5.31270e15 | −0.213944 | ||||||||
\(958\) | 7.51572e15 | 0.300926 | ||||||||
\(959\) | −3.11174e16 | −1.23880 | ||||||||
\(960\) | 9.47137e14 | 0.0374905 | ||||||||
\(961\) | −2.75781e15 | −0.108539 | ||||||||
\(962\) | 2.54159e16 | 0.994585 | ||||||||
\(963\) | 6.50832e15 | 0.253235 | ||||||||
\(964\) | 4.26945e14 | 0.0165176 | ||||||||
\(965\) | 6.78613e14 | 0.0261049 | ||||||||
\(966\) | 5.26032e15 | 0.201205 | ||||||||
\(967\) | 3.64625e16 | 1.38676 | 0.693379 | − | 0.720573i | \(-0.256121\pi\) | ||||
0.693379 | + | 0.720573i | \(0.256121\pi\) | |||||||
\(968\) | 9.51540e15 | 0.359842 | ||||||||
\(969\) | −2.18929e16 | −0.823231 | ||||||||
\(970\) | −9.56656e15 | −0.357694 | ||||||||
\(971\) | −1.01490e16 | −0.377328 | −0.188664 | − | 0.982042i | \(-0.560416\pi\) | ||||
−0.188664 | + | 0.982042i | \(0.560416\pi\) | |||||||
\(972\) | 8.67624e14 | 0.0320750 | ||||||||
\(973\) | 3.41778e15 | 0.125639 | ||||||||
\(974\) | −3.16745e16 | −1.15781 | ||||||||
\(975\) | 2.15096e16 | 0.781821 | ||||||||
\(976\) | −8.16547e15 | −0.295126 | ||||||||
\(977\) | 2.99278e16 | 1.07561 | 0.537804 | − | 0.843070i | \(-0.319254\pi\) | ||||
0.537804 | + | 0.843070i | \(0.319254\pi\) | |||||||
\(978\) | 6.72639e15 | 0.240391 | ||||||||
\(979\) | −5.73066e16 | −2.03657 | ||||||||
\(980\) | −3.31770e15 | −0.117245 | ||||||||
\(981\) | 1.04976e16 | 0.368902 | ||||||||
\(982\) | −2.78510e16 | −0.973258 | ||||||||
\(983\) | −3.23592e16 | −1.12448 | −0.562242 | − | 0.826973i | \(-0.690061\pi\) | ||||
−0.562242 | + | 0.826973i | \(0.690061\pi\) | |||||||
\(984\) | −2.93032e15 | −0.101261 | ||||||||
\(985\) | 1.20806e16 | 0.415134 | ||||||||
\(986\) | 7.64428e15 | 0.261224 | ||||||||
\(987\) | 2.21144e16 | 0.751503 | ||||||||
\(988\) | 2.76295e16 | 0.933706 | ||||||||
\(989\) | 1.27440e16 | 0.428278 | ||||||||
\(990\) | −5.20435e15 | −0.173929 | ||||||||
\(991\) | −2.28589e16 | −0.759716 | −0.379858 | − | 0.925045i | \(-0.624027\pi\) | ||||
−0.379858 | + | 0.925045i | \(0.624027\pi\) | |||||||
\(992\) | 5.04999e15 | 0.166908 | ||||||||
\(993\) | 1.20677e16 | 0.396647 | ||||||||
\(994\) | −8.79733e15 | −0.287558 | ||||||||
\(995\) | −5.75648e15 | −0.187124 | ||||||||
\(996\) | 2.11322e15 | 0.0683154 | ||||||||
\(997\) | −1.99784e16 | −0.642298 | −0.321149 | − | 0.947029i | \(-0.604069\pi\) | ||||
−0.321149 | + | 0.947029i | \(0.604069\pi\) | |||||||
\(998\) | −1.72260e16 | −0.550767 | ||||||||
\(999\) | −4.59010e15 | −0.145953 |
(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 | 6.12.a.c.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 18.12.a.a.1.1 | 1 | |||
4.3 | odd | 2 | 48.12.a.d.1.1 | 1 | |||
5.2 | odd | 4 | 150.12.c.e.49.2 | 2 | |||
5.3 | odd | 4 | 150.12.c.e.49.1 | 2 | |||
5.4 | even | 2 | 150.12.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 192.12.a.m.1.1 | 1 | |||
8.5 | even | 2 | 192.12.a.c.1.1 | 1 | |||
9.2 | odd | 6 | 162.12.c.i.109.1 | 2 | |||
9.4 | even | 3 | 162.12.c.b.55.1 | 2 | |||
9.5 | odd | 6 | 162.12.c.i.55.1 | 2 | |||
9.7 | even | 3 | 162.12.c.b.109.1 | 2 | |||
12.11 | even | 2 | 144.12.a.e.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6.12.a.c.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
18.12.a.a.1.1 | 1 | 3.2 | odd | 2 | |||
48.12.a.d.1.1 | 1 | 4.3 | odd | 2 | |||
144.12.a.e.1.1 | 1 | 12.11 | even | 2 | |||
150.12.a.a.1.1 | 1 | 5.4 | even | 2 | |||
150.12.c.e.49.1 | 2 | 5.3 | odd | 4 | |||
150.12.c.e.49.2 | 2 | 5.2 | odd | 4 | |||
162.12.c.b.55.1 | 2 | 9.4 | even | 3 | |||
162.12.c.b.109.1 | 2 | 9.7 | even | 3 | |||
162.12.c.i.55.1 | 2 | 9.5 | odd | 6 | |||
162.12.c.i.109.1 | 2 | 9.2 | odd | 6 | |||
192.12.a.c.1.1 | 1 | 8.5 | even | 2 | |||
192.12.a.m.1.1 | 1 | 8.3 | odd | 2 |