Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,18,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(1.83222087345\) |
Analytic rank: | \(1\) |
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 | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −528.000 | −1.45841 | −0.729204 | − | 0.684297i | \(-0.760109\pi\) | ||||
−0.729204 | + | 0.684297i | \(0.760109\pi\) | |||||||
\(3\) | −4284.00 | −0.376980 | −0.188490 | − | 0.982075i | \(-0.560359\pi\) | ||||
−0.188490 | + | 0.982075i | \(0.560359\pi\) | |||||||
\(4\) | 147712. | 1.12695 | ||||||||
\(5\) | −1.02585e6 | −1.17446 | −0.587231 | − | 0.809420i | \(-0.699782\pi\) | ||||
−0.587231 | + | 0.809420i | \(0.699782\pi\) | |||||||
\(6\) | 2.26195e6 | 0.549791 | ||||||||
\(7\) | 3.22599e6 | 0.211510 | 0.105755 | − | 0.994392i | \(-0.466274\pi\) | ||||
0.105755 | + | 0.994392i | \(0.466274\pi\) | |||||||
\(8\) | −8.78592e6 | −0.185149 | ||||||||
\(9\) | −1.10788e8 | −0.857886 | ||||||||
\(10\) | 5.41649e8 | 1.71284 | ||||||||
\(11\) | −7.53618e8 | −1.06002 | −0.530009 | − | 0.847992i | \(-0.677812\pi\) | ||||
−0.530009 | + | 0.847992i | \(0.677812\pi\) | |||||||
\(12\) | −6.32798e8 | −0.424839 | ||||||||
\(13\) | 2.54106e9 | 0.863967 | 0.431984 | − | 0.901881i | \(-0.357814\pi\) | ||||
0.431984 | + | 0.901881i | \(0.357814\pi\) | |||||||
\(14\) | −1.70332e9 | −0.308467 | ||||||||
\(15\) | 4.39474e9 | 0.442749 | ||||||||
\(16\) | −1.47219e10 | −0.856930 | ||||||||
\(17\) | −5.42974e9 | −0.188783 | −0.0943916 | − | 0.995535i | \(-0.530091\pi\) | ||||
−0.0943916 | + | 0.995535i | \(0.530091\pi\) | |||||||
\(18\) | 5.84958e10 | 1.25115 | ||||||||
\(19\) | 1.48750e9 | 0.0200933 | 0.0100467 | − | 0.999950i | \(-0.496802\pi\) | ||||
0.0100467 | + | 0.999950i | \(0.496802\pi\) | |||||||
\(20\) | −1.51530e11 | −1.32356 | ||||||||
\(21\) | −1.38201e10 | −0.0797350 | ||||||||
\(22\) | 3.97910e11 | 1.54594 | ||||||||
\(23\) | −3.17092e11 | −0.844303 | −0.422152 | − | 0.906525i | \(-0.638725\pi\) | ||||
−0.422152 | + | 0.906525i | \(0.638725\pi\) | |||||||
\(24\) | 3.76389e10 | 0.0697977 | ||||||||
\(25\) | 2.89429e11 | 0.379360 | ||||||||
\(26\) | −1.34168e12 | −1.26002 | ||||||||
\(27\) | 1.02785e12 | 0.700387 | ||||||||
\(28\) | 4.76518e11 | 0.238361 | ||||||||
\(29\) | 2.43341e12 | 0.903301 | 0.451650 | − | 0.892195i | \(-0.350835\pi\) | ||||
0.451650 | + | 0.892195i | \(0.350835\pi\) | |||||||
\(30\) | −2.32042e12 | −0.645709 | ||||||||
\(31\) | −8.84972e12 | −1.86361 | −0.931805 | − | 0.362958i | \(-0.881767\pi\) | ||||
−0.931805 | + | 0.362958i | \(0.881767\pi\) | |||||||
\(32\) | 8.92477e12 | 1.43490 | ||||||||
\(33\) | 3.22850e12 | 0.399606 | ||||||||
\(34\) | 2.86690e12 | 0.275323 | ||||||||
\(35\) | −3.30938e12 | −0.248410 | ||||||||
\(36\) | −1.63646e13 | −0.966797 | ||||||||
\(37\) | 1.26917e13 | 0.594023 | 0.297012 | − | 0.954874i | \(-0.404010\pi\) | ||||
0.297012 | + | 0.954874i | \(0.404010\pi\) | |||||||
\(38\) | −7.85400e11 | −0.0293042 | ||||||||
\(39\) | −1.08859e13 | −0.325699 | ||||||||
\(40\) | 9.01304e12 | 0.217451 | ||||||||
\(41\) | 4.88642e13 | 0.955713 | 0.477857 | − | 0.878438i | \(-0.341414\pi\) | ||||
0.477857 | + | 0.878438i | \(0.341414\pi\) | |||||||
\(42\) | 7.29704e12 | 0.116286 | ||||||||
\(43\) | −9.10200e13 | −1.18756 | −0.593779 | − | 0.804628i | \(-0.702365\pi\) | ||||
−0.593779 | + | 0.804628i | \(0.702365\pi\) | |||||||
\(44\) | −1.11318e14 | −1.19459 | ||||||||
\(45\) | 1.13651e14 | 1.00755 | ||||||||
\(46\) | 1.67424e14 | 1.23134 | ||||||||
\(47\) | −4.93050e13 | −0.302036 | −0.151018 | − | 0.988531i | \(-0.548255\pi\) | ||||
−0.151018 | + | 0.988531i | \(0.548255\pi\) | |||||||
\(48\) | 6.30688e13 | 0.323046 | ||||||||
\(49\) | −2.22223e14 | −0.955264 | ||||||||
\(50\) | −1.52818e14 | −0.553262 | ||||||||
\(51\) | 2.32610e13 | 0.0711676 | ||||||||
\(52\) | 3.75346e14 | 0.973650 | ||||||||
\(53\) | 2.29405e13 | 0.0506124 | 0.0253062 | − | 0.999680i | \(-0.491944\pi\) | ||||
0.0253062 | + | 0.999680i | \(0.491944\pi\) | |||||||
\(54\) | −5.42705e14 | −1.02145 | ||||||||
\(55\) | 7.73099e14 | 1.24495 | ||||||||
\(56\) | −2.83433e13 | −0.0391609 | ||||||||
\(57\) | −6.37245e12 | −0.00757478 | ||||||||
\(58\) | −1.28484e15 | −1.31738 | ||||||||
\(59\) | 3.26951e13 | 0.0289895 | 0.0144947 | − | 0.999895i | \(-0.495386\pi\) | ||||
0.0144947 | + | 0.999895i | \(0.495386\pi\) | |||||||
\(60\) | 6.49156e14 | 0.498957 | ||||||||
\(61\) | −1.30829e15 | −0.873774 | −0.436887 | − | 0.899516i | \(-0.643919\pi\) | ||||
−0.436887 | + | 0.899516i | \(0.643919\pi\) | |||||||
\(62\) | 4.67265e15 | 2.71790 | ||||||||
\(63\) | −3.57400e14 | −0.181451 | ||||||||
\(64\) | −2.78265e15 | −1.23574 | ||||||||
\(65\) | −2.60675e15 | −1.01470 | ||||||||
\(66\) | −1.70465e15 | −0.582789 | ||||||||
\(67\) | 5.19614e15 | 1.56331 | 0.781655 | − | 0.623711i | \(-0.214376\pi\) | ||||
0.781655 | + | 0.623711i | \(0.214376\pi\) | |||||||
\(68\) | −8.02038e14 | −0.212750 | ||||||||
\(69\) | 1.35842e15 | 0.318286 | ||||||||
\(70\) | 1.74735e15 | 0.362283 | ||||||||
\(71\) | −3.70949e15 | −0.681739 | −0.340870 | − | 0.940111i | \(-0.610721\pi\) | ||||
−0.340870 | + | 0.940111i | \(0.610721\pi\) | |||||||
\(72\) | 9.73370e14 | 0.158837 | ||||||||
\(73\) | 3.40237e15 | 0.493785 | 0.246892 | − | 0.969043i | \(-0.420591\pi\) | ||||
0.246892 | + | 0.969043i | \(0.420591\pi\) | |||||||
\(74\) | −6.70119e15 | −0.866328 | ||||||||
\(75\) | −1.23991e15 | −0.143011 | ||||||||
\(76\) | 2.19722e14 | 0.0226442 | ||||||||
\(77\) | −2.43117e15 | −0.224204 | ||||||||
\(78\) | 5.74777e15 | 0.475001 | ||||||||
\(79\) | 2.36653e15 | 0.175502 | 0.0877511 | − | 0.996142i | \(-0.472032\pi\) | ||||
0.0877511 | + | 0.996142i | \(0.472032\pi\) | |||||||
\(80\) | 1.51025e16 | 1.00643 | ||||||||
\(81\) | 9.90381e15 | 0.593854 | ||||||||
\(82\) | −2.58003e16 | −1.39382 | ||||||||
\(83\) | −2.97668e16 | −1.45067 | −0.725333 | − | 0.688398i | \(-0.758314\pi\) | ||||
−0.725333 | + | 0.688398i | \(0.758314\pi\) | |||||||
\(84\) | −2.04140e15 | −0.0898576 | ||||||||
\(85\) | 5.57010e15 | 0.221719 | ||||||||
\(86\) | 4.80585e16 | 1.73194 | ||||||||
\(87\) | −1.04247e16 | −0.340527 | ||||||||
\(88\) | 6.62123e15 | 0.196262 | ||||||||
\(89\) | 2.91672e16 | 0.785379 | 0.392690 | − | 0.919671i | \(-0.371545\pi\) | ||||
0.392690 | + | 0.919671i | \(0.371545\pi\) | |||||||
\(90\) | −6.00079e16 | −1.46942 | ||||||||
\(91\) | 8.19745e15 | 0.182737 | ||||||||
\(92\) | −4.68383e16 | −0.951490 | ||||||||
\(93\) | 3.79122e16 | 0.702545 | ||||||||
\(94\) | 2.60330e16 | 0.440492 | ||||||||
\(95\) | −1.52595e15 | −0.0235988 | ||||||||
\(96\) | −3.82337e16 | −0.540930 | ||||||||
\(97\) | −6.37699e16 | −0.826144 | −0.413072 | − | 0.910698i | \(-0.635544\pi\) | ||||
−0.413072 | + | 0.910698i | \(0.635544\pi\) | |||||||
\(98\) | 1.17334e17 | 1.39316 | ||||||||
\(99\) | 8.34915e16 | 0.909375 | ||||||||
\(100\) | 4.27521e16 | 0.427521 | ||||||||
\(101\) | −1.60611e17 | −1.47586 | −0.737929 | − | 0.674878i | \(-0.764196\pi\) | ||||
−0.737929 | + | 0.674878i | \(0.764196\pi\) | |||||||
\(102\) | −1.22818e16 | −0.103791 | ||||||||
\(103\) | −9.07136e16 | −0.705596 | −0.352798 | − | 0.935700i | \(-0.614770\pi\) | ||||
−0.352798 | + | 0.935700i | \(0.614770\pi\) | |||||||
\(104\) | −2.23256e16 | −0.159963 | ||||||||
\(105\) | 1.41774e16 | 0.0936456 | ||||||||
\(106\) | −1.21126e16 | −0.0738135 | ||||||||
\(107\) | 1.95549e17 | 1.10026 | 0.550129 | − | 0.835080i | \(-0.314579\pi\) | ||||
0.550129 | + | 0.835080i | \(0.314579\pi\) | |||||||
\(108\) | 1.51826e17 | 0.789303 | ||||||||
\(109\) | 2.13756e17 | 1.02753 | 0.513763 | − | 0.857932i | \(-0.328251\pi\) | ||||
0.513763 | + | 0.857932i | \(0.328251\pi\) | |||||||
\(110\) | −4.08196e17 | −1.81565 | ||||||||
\(111\) | −5.43710e16 | −0.223935 | ||||||||
\(112\) | −4.74929e16 | −0.181249 | ||||||||
\(113\) | −2.81383e17 | −0.995706 | −0.497853 | − | 0.867262i | \(-0.665878\pi\) | ||||
−0.497853 | + | 0.867262i | \(0.665878\pi\) | |||||||
\(114\) | 3.36465e15 | 0.0110471 | ||||||||
\(115\) | 3.25289e17 | 0.991602 | ||||||||
\(116\) | 3.59444e17 | 1.01798 | ||||||||
\(117\) | −2.81518e17 | −0.741185 | ||||||||
\(118\) | −1.72630e16 | −0.0422785 | ||||||||
\(119\) | −1.75163e16 | −0.0399295 | ||||||||
\(120\) | −3.86118e16 | −0.0819747 | ||||||||
\(121\) | 6.24934e16 | 0.123640 | ||||||||
\(122\) | 6.90775e17 | 1.27432 | ||||||||
\(123\) | −2.09334e17 | −0.360285 | ||||||||
\(124\) | −1.30721e18 | −2.10020 | ||||||||
\(125\) | 4.85751e17 | 0.728918 | ||||||||
\(126\) | 1.88707e17 | 0.264630 | ||||||||
\(127\) | −8.70305e17 | −1.14114 | −0.570571 | − | 0.821248i | \(-0.693278\pi\) | ||||
−0.570571 | + | 0.821248i | \(0.693278\pi\) | |||||||
\(128\) | 2.99449e17 | 0.367315 | ||||||||
\(129\) | 3.89930e17 | 0.447686 | ||||||||
\(130\) | 1.37636e18 | 1.47984 | ||||||||
\(131\) | 1.31783e17 | 0.132756 | 0.0663781 | − | 0.997795i | \(-0.478856\pi\) | ||||
0.0663781 | + | 0.997795i | \(0.478856\pi\) | |||||||
\(132\) | 4.76888e17 | 0.450338 | ||||||||
\(133\) | 4.79866e15 | 0.00424993 | ||||||||
\(134\) | −2.74356e18 | −2.27994 | ||||||||
\(135\) | −1.05442e18 | −0.822577 | ||||||||
\(136\) | 4.77053e16 | 0.0349531 | ||||||||
\(137\) | 1.87128e18 | 1.28829 | 0.644147 | − | 0.764902i | \(-0.277213\pi\) | ||||
0.644147 | + | 0.764902i | \(0.277213\pi\) | |||||||
\(138\) | −7.17246e17 | −0.464190 | ||||||||
\(139\) | 1.58706e18 | 0.965980 | 0.482990 | − | 0.875626i | \(-0.339551\pi\) | ||||
0.482990 | + | 0.875626i | \(0.339551\pi\) | |||||||
\(140\) | −4.88836e17 | −0.279946 | ||||||||
\(141\) | 2.11223e17 | 0.113862 | ||||||||
\(142\) | 1.95861e18 | 0.994254 | ||||||||
\(143\) | −1.91499e18 | −0.915821 | ||||||||
\(144\) | 1.63101e18 | 0.735148 | ||||||||
\(145\) | −2.49631e18 | −1.06089 | ||||||||
\(146\) | −1.79645e18 | −0.720139 | ||||||||
\(147\) | 9.52005e17 | 0.360116 | ||||||||
\(148\) | 1.87471e18 | 0.669436 | ||||||||
\(149\) | −4.77240e17 | −0.160936 | −0.0804680 | − | 0.996757i | \(-0.525641\pi\) | ||||
−0.0804680 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(150\) | 6.54674e17 | 0.208569 | ||||||||
\(151\) | −3.92964e18 | −1.18317 | −0.591587 | − | 0.806241i | \(-0.701499\pi\) | ||||
−0.591587 | + | 0.806241i | \(0.701499\pi\) | |||||||
\(152\) | −1.30691e16 | −0.00372026 | ||||||||
\(153\) | 6.01548e17 | 0.161954 | ||||||||
\(154\) | 1.28366e18 | 0.326981 | ||||||||
\(155\) | 9.07849e18 | 2.18874 | ||||||||
\(156\) | −1.60798e18 | −0.367047 | ||||||||
\(157\) | −2.29453e18 | −0.496075 | −0.248038 | − | 0.968750i | \(-0.579786\pi\) | ||||
−0.248038 | + | 0.968750i | \(0.579786\pi\) | |||||||
\(158\) | −1.24953e18 | −0.255954 | ||||||||
\(159\) | −9.82769e16 | −0.0190799 | ||||||||
\(160\) | −9.15548e18 | −1.68524 | ||||||||
\(161\) | −1.02294e18 | −0.178578 | ||||||||
\(162\) | −5.22921e18 | −0.866081 | ||||||||
\(163\) | 8.01044e18 | 1.25910 | 0.629552 | − | 0.776958i | \(-0.283238\pi\) | ||||
0.629552 | + | 0.776958i | \(0.283238\pi\) | |||||||
\(164\) | 7.21782e18 | 1.07704 | ||||||||
\(165\) | −3.31196e18 | −0.469322 | ||||||||
\(166\) | 1.57168e19 | 2.11566 | ||||||||
\(167\) | −8.61477e18 | −1.10193 | −0.550965 | − | 0.834528i | \(-0.685740\pi\) | ||||
−0.550965 | + | 0.834528i | \(0.685740\pi\) | |||||||
\(168\) | 1.21423e17 | 0.0147629 | ||||||||
\(169\) | −2.19341e18 | −0.253561 | ||||||||
\(170\) | −2.94101e18 | −0.323356 | ||||||||
\(171\) | −1.64796e17 | −0.0172378 | ||||||||
\(172\) | −1.34447e19 | −1.33832 | ||||||||
\(173\) | 2.31430e18 | 0.219294 | 0.109647 | − | 0.993971i | \(-0.465028\pi\) | ||||
0.109647 | + | 0.993971i | \(0.465028\pi\) | |||||||
\(174\) | 5.50426e18 | 0.496627 | ||||||||
\(175\) | 9.33695e17 | 0.0802383 | ||||||||
\(176\) | 1.10947e19 | 0.908362 | ||||||||
\(177\) | −1.40066e17 | −0.0109285 | ||||||||
\(178\) | −1.54003e19 | −1.14540 | ||||||||
\(179\) | −7.90307e18 | −0.560461 | −0.280230 | − | 0.959933i | \(-0.590411\pi\) | ||||
−0.280230 | + | 0.959933i | \(0.590411\pi\) | |||||||
\(180\) | 1.67877e19 | 1.13547 | ||||||||
\(181\) | 1.40729e19 | 0.908060 | 0.454030 | − | 0.890986i | \(-0.349986\pi\) | ||||
0.454030 | + | 0.890986i | \(0.349986\pi\) | |||||||
\(182\) | −4.32826e18 | −0.266505 | ||||||||
\(183\) | 5.60470e18 | 0.329396 | ||||||||
\(184\) | 2.78594e18 | 0.156322 | ||||||||
\(185\) | −1.30197e19 | −0.697658 | ||||||||
\(186\) | −2.00176e19 | −1.02460 | ||||||||
\(187\) | 4.09195e18 | 0.200114 | ||||||||
\(188\) | −7.28294e18 | −0.340381 | ||||||||
\(189\) | 3.31584e18 | 0.148138 | ||||||||
\(190\) | 8.05703e17 | 0.0344167 | ||||||||
\(191\) | −2.82501e19 | −1.15408 | −0.577040 | − | 0.816716i | \(-0.695792\pi\) | ||||
−0.577040 | + | 0.816716i | \(0.695792\pi\) | |||||||
\(192\) | 1.19209e19 | 0.465851 | ||||||||
\(193\) | 4.91755e19 | 1.83870 | 0.919351 | − | 0.393437i | \(-0.128714\pi\) | ||||
0.919351 | + | 0.393437i | \(0.128714\pi\) | |||||||
\(194\) | 3.36705e19 | 1.20486 | ||||||||
\(195\) | 1.11673e19 | 0.382521 | ||||||||
\(196\) | −3.28251e19 | −1.07654 | ||||||||
\(197\) | 1.29458e19 | 0.406598 | 0.203299 | − | 0.979117i | \(-0.434834\pi\) | ||||
0.203299 | + | 0.979117i | \(0.434834\pi\) | |||||||
\(198\) | −4.40835e19 | −1.32624 | ||||||||
\(199\) | −5.51755e19 | −1.59036 | −0.795179 | − | 0.606375i | \(-0.792623\pi\) | ||||
−0.795179 | + | 0.606375i | \(0.792623\pi\) | |||||||
\(200\) | −2.54290e18 | −0.0702383 | ||||||||
\(201\) | −2.22603e19 | −0.589338 | ||||||||
\(202\) | 8.48028e19 | 2.15240 | ||||||||
\(203\) | 7.85016e18 | 0.191057 | ||||||||
\(204\) | 3.43593e18 | 0.0802025 | ||||||||
\(205\) | −5.01273e19 | −1.12245 | ||||||||
\(206\) | 4.78968e19 | 1.02905 | ||||||||
\(207\) | 3.51298e19 | 0.724316 | ||||||||
\(208\) | −3.74094e19 | −0.740359 | ||||||||
\(209\) | −1.12101e18 | −0.0212993 | ||||||||
\(210\) | −7.48567e18 | −0.136574 | ||||||||
\(211\) | 1.73510e19 | 0.304035 | 0.152017 | − | 0.988378i | \(-0.451423\pi\) | ||||
0.152017 | + | 0.988378i | \(0.451423\pi\) | |||||||
\(212\) | 3.38858e18 | 0.0570378 | ||||||||
\(213\) | 1.58915e19 | 0.257002 | ||||||||
\(214\) | −1.03250e20 | −1.60462 | ||||||||
\(215\) | 9.33728e19 | 1.39474 | ||||||||
\(216\) | −9.03061e18 | −0.129676 | ||||||||
\(217\) | −2.85491e19 | −0.394171 | ||||||||
\(218\) | −1.12863e20 | −1.49855 | ||||||||
\(219\) | −1.45758e19 | −0.186147 | ||||||||
\(220\) | 1.14196e20 | 1.40300 | ||||||||
\(221\) | −1.37973e19 | −0.163102 | ||||||||
\(222\) | 2.87079e19 | 0.326589 | ||||||||
\(223\) | 9.48415e19 | 1.03850 | 0.519251 | − | 0.854622i | \(-0.326211\pi\) | ||||
0.519251 | + | 0.854622i | \(0.326211\pi\) | |||||||
\(224\) | 2.87912e19 | 0.303496 | ||||||||
\(225\) | −3.20651e19 | −0.325448 | ||||||||
\(226\) | 1.48570e20 | 1.45214 | ||||||||
\(227\) | −1.83782e20 | −1.73015 | −0.865073 | − | 0.501647i | \(-0.832728\pi\) | ||||
−0.865073 | + | 0.501647i | \(0.832728\pi\) | |||||||
\(228\) | −9.41287e17 | −0.00853642 | ||||||||
\(229\) | −9.14908e19 | −0.799422 | −0.399711 | − | 0.916641i | \(-0.630889\pi\) | ||||
−0.399711 | + | 0.916641i | \(0.630889\pi\) | |||||||
\(230\) | −1.71752e20 | −1.44616 | ||||||||
\(231\) | 1.04151e19 | 0.0845205 | ||||||||
\(232\) | −2.13798e19 | −0.167246 | ||||||||
\(233\) | 9.87497e19 | 0.744750 | 0.372375 | − | 0.928082i | \(-0.378544\pi\) | ||||
0.372375 | + | 0.928082i | \(0.378544\pi\) | |||||||
\(234\) | 1.48642e20 | 1.08095 | ||||||||
\(235\) | 5.05795e19 | 0.354730 | ||||||||
\(236\) | 4.82946e18 | 0.0326698 | ||||||||
\(237\) | −1.01382e19 | −0.0661609 | ||||||||
\(238\) | 9.24861e18 | 0.0582334 | ||||||||
\(239\) | 1.89337e20 | 1.15041 | 0.575206 | − | 0.818009i | \(-0.304922\pi\) | ||||
0.575206 | + | 0.818009i | \(0.304922\pi\) | |||||||
\(240\) | −6.46991e19 | −0.379405 | ||||||||
\(241\) | −1.38762e20 | −0.785463 | −0.392731 | − | 0.919653i | \(-0.628470\pi\) | ||||
−0.392731 | + | 0.919653i | \(0.628470\pi\) | |||||||
\(242\) | −3.29965e19 | −0.180317 | ||||||||
\(243\) | −1.75165e20 | −0.924258 | ||||||||
\(244\) | −1.93250e20 | −0.984702 | ||||||||
\(245\) | 2.27968e20 | 1.12192 | ||||||||
\(246\) | 1.10528e20 | 0.525443 | ||||||||
\(247\) | 3.77983e18 | 0.0173600 | ||||||||
\(248\) | 7.77529e19 | 0.345046 | ||||||||
\(249\) | 1.27521e20 | 0.546873 | ||||||||
\(250\) | −2.56476e20 | −1.06306 | ||||||||
\(251\) | −3.34508e20 | −1.34023 | −0.670115 | − | 0.742257i | \(-0.733755\pi\) | ||||
−0.670115 | + | 0.742257i | \(0.733755\pi\) | |||||||
\(252\) | −5.27922e19 | −0.204487 | ||||||||
\(253\) | 2.38966e20 | 0.894977 | ||||||||
\(254\) | 4.59521e20 | 1.66425 | ||||||||
\(255\) | −2.38623e19 | −0.0835836 | ||||||||
\(256\) | 2.06618e20 | 0.700048 | ||||||||
\(257\) | 4.91382e19 | 0.161060 | 0.0805300 | − | 0.996752i | \(-0.474339\pi\) | ||||
0.0805300 | + | 0.996752i | \(0.474339\pi\) | |||||||
\(258\) | −2.05883e20 | −0.652909 | ||||||||
\(259\) | 4.09432e19 | 0.125642 | ||||||||
\(260\) | −3.85048e20 | −1.14352 | ||||||||
\(261\) | −2.69591e20 | −0.774929 | ||||||||
\(262\) | −6.95816e19 | −0.193613 | ||||||||
\(263\) | 1.78845e19 | 0.0481784 | 0.0240892 | − | 0.999710i | \(-0.492331\pi\) | ||||
0.0240892 | + | 0.999710i | \(0.492331\pi\) | |||||||
\(264\) | −2.83653e19 | −0.0739869 | ||||||||
\(265\) | −2.35335e19 | −0.0594423 | ||||||||
\(266\) | −2.53369e18 | −0.00619812 | ||||||||
\(267\) | −1.24952e20 | −0.296073 | ||||||||
\(268\) | 7.67533e20 | 1.76178 | ||||||||
\(269\) | 1.15237e20 | 0.256270 | 0.128135 | − | 0.991757i | \(-0.459101\pi\) | ||||
0.128135 | + | 0.991757i | \(0.459101\pi\) | |||||||
\(270\) | 5.56734e20 | 1.19965 | ||||||||
\(271\) | −1.47067e20 | −0.307098 | −0.153549 | − | 0.988141i | \(-0.549070\pi\) | ||||
−0.153549 | + | 0.988141i | \(0.549070\pi\) | |||||||
\(272\) | 7.99363e19 | 0.161774 | ||||||||
\(273\) | −3.51179e19 | −0.0688884 | ||||||||
\(274\) | −9.88038e20 | −1.87886 | ||||||||
\(275\) | −2.18119e20 | −0.402129 | ||||||||
\(276\) | 2.00655e20 | 0.358693 | ||||||||
\(277\) | −1.78744e20 | −0.309852 | −0.154926 | − | 0.987926i | \(-0.549514\pi\) | ||||
−0.154926 | + | 0.987926i | \(0.549514\pi\) | |||||||
\(278\) | −8.37969e20 | −1.40879 | ||||||||
\(279\) | 9.80439e20 | 1.59877 | ||||||||
\(280\) | 2.90760e19 | 0.0459929 | ||||||||
\(281\) | 2.80546e20 | 0.430527 | 0.215263 | − | 0.976556i | \(-0.430939\pi\) | ||||
0.215263 | + | 0.976556i | \(0.430939\pi\) | |||||||
\(282\) | −1.11526e20 | −0.166057 | ||||||||
\(283\) | 3.39877e20 | 0.491062 | 0.245531 | − | 0.969389i | \(-0.421038\pi\) | ||||
0.245531 | + | 0.969389i | \(0.421038\pi\) | |||||||
\(284\) | −5.47936e20 | −0.768288 | ||||||||
\(285\) | 6.53718e18 | 0.00889629 | ||||||||
\(286\) | 1.01112e21 | 1.33564 | ||||||||
\(287\) | 1.57635e20 | 0.202142 | ||||||||
\(288\) | −9.88753e20 | −1.23098 | ||||||||
\(289\) | −7.97758e20 | −0.964361 | ||||||||
\(290\) | 1.31805e21 | 1.54721 | ||||||||
\(291\) | 2.73190e20 | 0.311440 | ||||||||
\(292\) | 5.02571e20 | 0.556472 | ||||||||
\(293\) | −7.64887e20 | −0.822664 | −0.411332 | − | 0.911486i | \(-0.634936\pi\) | ||||
−0.411332 | + | 0.911486i | \(0.634936\pi\) | |||||||
\(294\) | −5.02659e20 | −0.525196 | ||||||||
\(295\) | −3.35403e19 | −0.0340470 | ||||||||
\(296\) | −1.11508e20 | −0.109983 | ||||||||
\(297\) | −7.74607e20 | −0.742423 | ||||||||
\(298\) | 2.51983e20 | 0.234710 | ||||||||
\(299\) | −8.05751e20 | −0.729450 | ||||||||
\(300\) | −1.83150e20 | −0.161167 | ||||||||
\(301\) | −2.93630e20 | −0.251180 | ||||||||
\(302\) | 2.07485e21 | 1.72555 | ||||||||
\(303\) | 6.88059e20 | 0.556370 | ||||||||
\(304\) | −2.18989e19 | −0.0172185 | ||||||||
\(305\) | 1.34211e21 | 1.02621 | ||||||||
\(306\) | −3.17617e20 | −0.236196 | ||||||||
\(307\) | 1.38472e21 | 1.00158 | 0.500789 | − | 0.865569i | \(-0.333043\pi\) | ||||
0.500789 | + | 0.865569i | \(0.333043\pi\) | |||||||
\(308\) | −3.59112e20 | −0.252667 | ||||||||
\(309\) | 3.88617e20 | 0.265996 | ||||||||
\(310\) | −4.79344e21 | −3.19207 | ||||||||
\(311\) | −2.34733e21 | −1.52094 | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(312\) | 9.56428e19 | 0.0603029 | ||||||||
\(313\) | 1.58424e21 | 0.972065 | 0.486033 | − | 0.873941i | \(-0.338444\pi\) | ||||
0.486033 | + | 0.873941i | \(0.338444\pi\) | |||||||
\(314\) | 1.21151e21 | 0.723480 | ||||||||
\(315\) | 3.66638e20 | 0.213107 | ||||||||
\(316\) | 3.49565e20 | 0.197783 | ||||||||
\(317\) | 8.98378e20 | 0.494829 | 0.247415 | − | 0.968910i | \(-0.420419\pi\) | ||||
0.247415 | + | 0.968910i | \(0.420419\pi\) | |||||||
\(318\) | 5.18902e19 | 0.0278263 | ||||||||
\(319\) | −1.83386e21 | −0.957516 | ||||||||
\(320\) | 2.85458e21 | 1.45133 | ||||||||
\(321\) | −8.37734e20 | −0.414776 | ||||||||
\(322\) | 5.40110e20 | 0.260440 | ||||||||
\(323\) | −8.07674e18 | −0.00379328 | ||||||||
\(324\) | 1.46291e21 | 0.669245 | ||||||||
\(325\) | 7.35457e20 | 0.327755 | ||||||||
\(326\) | −4.22951e21 | −1.83629 | ||||||||
\(327\) | −9.15730e20 | −0.387357 | ||||||||
\(328\) | −4.29317e20 | −0.176950 | ||||||||
\(329\) | −1.59058e20 | −0.0638836 | ||||||||
\(330\) | 1.74871e21 | 0.684463 | ||||||||
\(331\) | 4.00469e21 | 1.52767 | 0.763837 | − | 0.645409i | \(-0.223313\pi\) | ||||
0.763837 | + | 0.645409i | \(0.223313\pi\) | |||||||
\(332\) | −4.39691e21 | −1.63483 | ||||||||
\(333\) | −1.40608e21 | −0.509604 | ||||||||
\(334\) | 4.54860e21 | 1.60706 | ||||||||
\(335\) | −5.33046e21 | −1.83605 | ||||||||
\(336\) | 2.03459e20 | 0.0683273 | ||||||||
\(337\) | −1.06753e21 | −0.349564 | −0.174782 | − | 0.984607i | \(-0.555922\pi\) | ||||
−0.174782 | + | 0.984607i | \(0.555922\pi\) | |||||||
\(338\) | 1.15812e21 | 0.369795 | ||||||||
\(339\) | 1.20544e21 | 0.375362 | ||||||||
\(340\) | 8.22771e20 | 0.249867 | ||||||||
\(341\) | 6.66931e21 | 1.97546 | ||||||||
\(342\) | 8.70125e19 | 0.0251397 | ||||||||
\(343\) | −1.46736e21 | −0.413557 | ||||||||
\(344\) | 7.99694e20 | 0.219876 | ||||||||
\(345\) | −1.39354e21 | −0.373814 | ||||||||
\(346\) | −1.22195e21 | −0.319821 | ||||||||
\(347\) | −1.61841e21 | −0.413321 | −0.206660 | − | 0.978413i | \(-0.566260\pi\) | ||||
−0.206660 | + | 0.978413i | \(0.566260\pi\) | |||||||
\(348\) | −1.53986e21 | −0.383758 | ||||||||
\(349\) | −5.60078e21 | −1.36217 | −0.681086 | − | 0.732203i | \(-0.738492\pi\) | ||||
−0.681086 | + | 0.732203i | \(0.738492\pi\) | |||||||
\(350\) | −4.92991e20 | −0.117020 | ||||||||
\(351\) | 2.61183e21 | 0.605111 | ||||||||
\(352\) | −6.72587e21 | −1.52102 | ||||||||
\(353\) | 5.10774e21 | 1.12757 | 0.563785 | − | 0.825921i | \(-0.309344\pi\) | ||||
0.563785 | + | 0.825921i | \(0.309344\pi\) | |||||||
\(354\) | 7.39547e19 | 0.0159382 | ||||||||
\(355\) | 3.80538e21 | 0.800676 | ||||||||
\(356\) | 4.30834e21 | 0.885086 | ||||||||
\(357\) | 7.50399e19 | 0.0150526 | ||||||||
\(358\) | 4.17282e21 | 0.817380 | ||||||||
\(359\) | 5.84965e21 | 1.11899 | 0.559496 | − | 0.828833i | \(-0.310995\pi\) | ||||
0.559496 | + | 0.828833i | \(0.310995\pi\) | |||||||
\(360\) | −9.98532e20 | −0.186548 | ||||||||
\(361\) | −5.47817e21 | −0.999596 | ||||||||
\(362\) | −7.43047e21 | −1.32432 | ||||||||
\(363\) | −2.67722e20 | −0.0466098 | ||||||||
\(364\) | 1.21086e21 | 0.205936 | ||||||||
\(365\) | −3.49032e21 | −0.579931 | ||||||||
\(366\) | −2.95928e21 | −0.480393 | ||||||||
\(367\) | 4.29535e20 | 0.0681297 | 0.0340649 | − | 0.999420i | \(-0.489155\pi\) | ||||
0.0340649 | + | 0.999420i | \(0.489155\pi\) | |||||||
\(368\) | 4.66821e21 | 0.723509 | ||||||||
\(369\) | −5.41354e21 | −0.819893 | ||||||||
\(370\) | 6.87442e21 | 1.01747 | ||||||||
\(371\) | 7.40057e19 | 0.0107050 | ||||||||
\(372\) | 5.60009e21 | 0.791735 | ||||||||
\(373\) | −6.54734e21 | −0.904774 | −0.452387 | − | 0.891822i | \(-0.649427\pi\) | ||||
−0.452387 | + | 0.891822i | \(0.649427\pi\) | |||||||
\(374\) | −2.16055e21 | −0.291847 | ||||||||
\(375\) | −2.08096e21 | −0.274788 | ||||||||
\(376\) | 4.33190e20 | 0.0559218 | ||||||||
\(377\) | 6.18345e21 | 0.780422 | ||||||||
\(378\) | −1.75076e21 | −0.216046 | ||||||||
\(379\) | 1.51850e21 | 0.183223 | 0.0916117 | − | 0.995795i | \(-0.470798\pi\) | ||||
0.0916117 | + | 0.995795i | \(0.470798\pi\) | |||||||
\(380\) | −2.25401e20 | −0.0265948 | ||||||||
\(381\) | 3.72839e21 | 0.430188 | ||||||||
\(382\) | 1.49160e22 | 1.68312 | ||||||||
\(383\) | −8.04597e21 | −0.887951 | −0.443975 | − | 0.896039i | \(-0.646432\pi\) | ||||
−0.443975 | + | 0.896039i | \(0.646432\pi\) | |||||||
\(384\) | −1.28284e21 | −0.138470 | ||||||||
\(385\) | 2.49401e21 | 0.263319 | ||||||||
\(386\) | −2.59647e22 | −2.68158 | ||||||||
\(387\) | 1.00839e22 | 1.01879 | ||||||||
\(388\) | −9.41958e21 | −0.931026 | ||||||||
\(389\) | 6.84040e21 | 0.661470 | 0.330735 | − | 0.943724i | \(-0.392703\pi\) | ||||
0.330735 | + | 0.943724i | \(0.392703\pi\) | |||||||
\(390\) | −5.89635e21 | −0.557871 | ||||||||
\(391\) | 1.72173e21 | 0.159390 | ||||||||
\(392\) | 1.95244e21 | 0.176867 | ||||||||
\(393\) | −5.64560e20 | −0.0500465 | ||||||||
\(394\) | −6.83536e21 | −0.592985 | ||||||||
\(395\) | −2.42771e21 | −0.206121 | ||||||||
\(396\) | 1.23327e22 | 1.02482 | ||||||||
\(397\) | 6.23458e21 | 0.507093 | 0.253547 | − | 0.967323i | \(-0.418403\pi\) | ||||
0.253547 | + | 0.967323i | \(0.418403\pi\) | |||||||
\(398\) | 2.91327e22 | 2.31939 | ||||||||
\(399\) | −2.05575e19 | −0.00160214 | ||||||||
\(400\) | −4.26095e21 | −0.325085 | ||||||||
\(401\) | −2.32048e21 | −0.173320 | −0.0866602 | − | 0.996238i | \(-0.527619\pi\) | ||||
−0.0866602 | + | 0.996238i | \(0.527619\pi\) | |||||||
\(402\) | 1.17534e22 | 0.859494 | ||||||||
\(403\) | −2.24877e22 | −1.61010 | ||||||||
\(404\) | −2.37242e22 | −1.66322 | ||||||||
\(405\) | −1.01598e22 | −0.697458 | ||||||||
\(406\) | −4.14489e21 | −0.278639 | ||||||||
\(407\) | −9.56466e21 | −0.629676 | ||||||||
\(408\) | −2.04369e20 | −0.0131766 | ||||||||
\(409\) | 2.38590e22 | 1.50662 | 0.753312 | − | 0.657663i | \(-0.228455\pi\) | ||||
0.753312 | + | 0.657663i | \(0.228455\pi\) | |||||||
\(410\) | 2.64672e22 | 1.63699 | ||||||||
\(411\) | −8.01658e21 | −0.485661 | ||||||||
\(412\) | −1.33995e22 | −0.795173 | ||||||||
\(413\) | 1.05474e20 | 0.00613155 | ||||||||
\(414\) | −1.85485e22 | −1.05635 | ||||||||
\(415\) | 3.05362e22 | 1.70375 | ||||||||
\(416\) | 2.26784e22 | 1.23971 | ||||||||
\(417\) | −6.79898e21 | −0.364156 | ||||||||
\(418\) | 5.91892e20 | 0.0310630 | ||||||||
\(419\) | −2.61839e22 | −1.34653 | −0.673263 | − | 0.739403i | \(-0.735108\pi\) | ||||
−0.673263 | + | 0.739403i | \(0.735108\pi\) | |||||||
\(420\) | 2.09417e21 | 0.105534 | ||||||||
\(421\) | 1.11903e22 | 0.552642 | 0.276321 | − | 0.961065i | \(-0.410885\pi\) | ||||
0.276321 | + | 0.961065i | \(0.410885\pi\) | |||||||
\(422\) | −9.16132e21 | −0.443407 | ||||||||
\(423\) | 5.46238e21 | 0.259113 | ||||||||
\(424\) | −2.01553e20 | −0.00937086 | ||||||||
\(425\) | −1.57152e21 | −0.0716168 | ||||||||
\(426\) | −8.39069e21 | −0.374814 | ||||||||
\(427\) | −4.22052e21 | −0.184812 | ||||||||
\(428\) | 2.88850e22 | 1.23994 | ||||||||
\(429\) | 8.20383e21 | 0.345247 | ||||||||
\(430\) | −4.93009e22 | −2.03410 | ||||||||
\(431\) | 1.74296e22 | 0.705068 | 0.352534 | − | 0.935799i | \(-0.385320\pi\) | ||||
0.352534 | + | 0.935799i | \(0.385320\pi\) | |||||||
\(432\) | −1.51319e22 | −0.600182 | ||||||||
\(433\) | −4.51413e22 | −1.75560 | −0.877802 | − | 0.479024i | \(-0.840991\pi\) | ||||
−0.877802 | + | 0.479024i | \(0.840991\pi\) | |||||||
\(434\) | 1.50739e22 | 0.574863 | ||||||||
\(435\) | 1.06942e22 | 0.399936 | ||||||||
\(436\) | 3.15743e22 | 1.15797 | ||||||||
\(437\) | −4.71674e20 | −0.0169648 | ||||||||
\(438\) | 7.69600e21 | 0.271478 | ||||||||
\(439\) | 3.85266e22 | 1.33294 | 0.666472 | − | 0.745530i | \(-0.267804\pi\) | ||||
0.666472 | + | 0.745530i | \(0.267804\pi\) | |||||||
\(440\) | −6.79239e21 | −0.230502 | ||||||||
\(441\) | 2.46196e22 | 0.819507 | ||||||||
\(442\) | 7.28499e21 | 0.237870 | ||||||||
\(443\) | −3.84966e21 | −0.123308 | −0.0616539 | − | 0.998098i | \(-0.519637\pi\) | ||||
−0.0616539 | + | 0.998098i | \(0.519637\pi\) | |||||||
\(444\) | −8.03126e21 | −0.252364 | ||||||||
\(445\) | −2.99212e22 | −0.922398 | ||||||||
\(446\) | −5.00763e22 | −1.51456 | ||||||||
\(447\) | 2.04449e21 | 0.0606697 | ||||||||
\(448\) | −8.97679e21 | −0.261371 | ||||||||
\(449\) | −2.77614e21 | −0.0793136 | −0.0396568 | − | 0.999213i | \(-0.512626\pi\) | ||||
−0.0396568 | + | 0.999213i | \(0.512626\pi\) | |||||||
\(450\) | 1.69304e22 | 0.474635 | ||||||||
\(451\) | −3.68249e22 | −1.01307 | ||||||||
\(452\) | −4.15636e22 | −1.12211 | ||||||||
\(453\) | 1.68346e22 | 0.446034 | ||||||||
\(454\) | 9.70368e22 | 2.52326 | ||||||||
\(455\) | −8.40936e21 | −0.214618 | ||||||||
\(456\) | 5.59878e19 | 0.00140247 | ||||||||
\(457\) | −1.34139e22 | −0.329814 | −0.164907 | − | 0.986309i | \(-0.552732\pi\) | ||||
−0.164907 | + | 0.986309i | \(0.552732\pi\) | |||||||
\(458\) | 4.83071e22 | 1.16588 | ||||||||
\(459\) | −5.58096e21 | −0.132221 | ||||||||
\(460\) | 4.80490e22 | 1.11749 | ||||||||
\(461\) | −4.32728e22 | −0.988000 | −0.494000 | − | 0.869462i | \(-0.664466\pi\) | ||||
−0.494000 | + | 0.869462i | \(0.664466\pi\) | |||||||
\(462\) | −5.49918e21 | −0.123265 | ||||||||
\(463\) | 3.85721e22 | 0.848859 | 0.424429 | − | 0.905461i | \(-0.360475\pi\) | ||||
0.424429 | + | 0.905461i | \(0.360475\pi\) | |||||||
\(464\) | −3.58245e22 | −0.774065 | ||||||||
\(465\) | −3.88922e22 | −0.825112 | ||||||||
\(466\) | −5.21398e22 | −1.08615 | ||||||||
\(467\) | 4.96724e22 | 1.01607 | 0.508033 | − | 0.861338i | \(-0.330373\pi\) | ||||
0.508033 | + | 0.861338i | \(0.330373\pi\) | |||||||
\(468\) | −4.15836e22 | −0.835281 | ||||||||
\(469\) | 1.67627e22 | 0.330655 | ||||||||
\(470\) | −2.67060e22 | −0.517341 | ||||||||
\(471\) | 9.82978e21 | 0.187011 | ||||||||
\(472\) | −2.87256e20 | −0.00536739 | ||||||||
\(473\) | 6.85943e22 | 1.25883 | ||||||||
\(474\) | 5.35299e21 | 0.0964895 | ||||||||
\(475\) | 4.30525e20 | 0.00762260 | ||||||||
\(476\) | −2.58737e21 | −0.0449986 | ||||||||
\(477\) | −2.54152e21 | −0.0434197 | ||||||||
\(478\) | −9.99699e22 | −1.67777 | ||||||||
\(479\) | −4.26513e22 | −0.703202 | −0.351601 | − | 0.936150i | \(-0.614363\pi\) | ||||
−0.351601 | + | 0.936150i | \(0.614363\pi\) | |||||||
\(480\) | 3.92221e22 | 0.635302 | ||||||||
\(481\) | 3.22503e22 | 0.513217 | ||||||||
\(482\) | 7.32663e22 | 1.14553 | ||||||||
\(483\) | 4.38226e21 | 0.0673205 | ||||||||
\(484\) | 9.23103e21 | 0.139336 | ||||||||
\(485\) | 6.54183e22 | 0.970275 | ||||||||
\(486\) | 9.24869e22 | 1.34794 | ||||||||
\(487\) | −9.28126e22 | −1.32926 | −0.664631 | − | 0.747172i | \(-0.731411\pi\) | ||||
−0.664631 | + | 0.747172i | \(0.731411\pi\) | |||||||
\(488\) | 1.14945e22 | 0.161779 | ||||||||
\(489\) | −3.43167e22 | −0.474658 | ||||||||
\(490\) | −1.20367e23 | −1.63622 | ||||||||
\(491\) | 1.29877e21 | 0.0173516 | 0.00867579 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867579 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(492\) | −3.09211e22 | −0.406024 | ||||||||
\(493\) | −1.32128e22 | −0.170528 | ||||||||
\(494\) | −1.99575e21 | −0.0253179 | ||||||||
\(495\) | −8.56497e22 | −1.06803 | ||||||||
\(496\) | 1.30285e23 | 1.59698 | ||||||||
\(497\) | −1.19668e22 | −0.144194 | ||||||||
\(498\) | −6.73310e22 | −0.797564 | ||||||||
\(499\) | −7.66788e22 | −0.892937 | −0.446468 | − | 0.894799i | \(-0.647318\pi\) | ||||
−0.446468 | + | 0.894799i | \(0.647318\pi\) | |||||||
\(500\) | 7.17512e22 | 0.821456 | ||||||||
\(501\) | 3.69057e22 | 0.415406 | ||||||||
\(502\) | 1.76620e23 | 1.95460 | ||||||||
\(503\) | 6.67712e22 | 0.726543 | 0.363272 | − | 0.931683i | \(-0.381660\pi\) | ||||
0.363272 | + | 0.931683i | \(0.381660\pi\) | |||||||
\(504\) | 3.14008e21 | 0.0335956 | ||||||||
\(505\) | 1.64763e23 | 1.73334 | ||||||||
\(506\) | −1.26174e23 | −1.30524 | ||||||||
\(507\) | 9.39656e21 | 0.0955875 | ||||||||
\(508\) | −1.28555e23 | −1.28601 | ||||||||
\(509\) | −1.15659e23 | −1.13783 | −0.568916 | − | 0.822395i | \(-0.692637\pi\) | ||||
−0.568916 | + | 0.822395i | \(0.692637\pi\) | |||||||
\(510\) | 1.25993e22 | 0.121899 | ||||||||
\(511\) | 1.09760e22 | 0.104440 | ||||||||
\(512\) | −1.48344e23 | −1.38827 | ||||||||
\(513\) | 1.52893e21 | 0.0140731 | ||||||||
\(514\) | −2.59450e22 | −0.234891 | ||||||||
\(515\) | 9.30585e22 | 0.828695 | ||||||||
\(516\) | 5.75973e22 | 0.504521 | ||||||||
\(517\) | 3.71571e22 | 0.320164 | ||||||||
\(518\) | −2.16180e22 | −0.183237 | ||||||||
\(519\) | −9.91446e21 | −0.0826697 | ||||||||
\(520\) | 2.29027e22 | 0.187870 | ||||||||
\(521\) | −1.79855e23 | −1.45145 | −0.725725 | − | 0.687985i | \(-0.758496\pi\) | ||||
−0.725725 | + | 0.687985i | \(0.758496\pi\) | |||||||
\(522\) | 1.42344e23 | 1.13016 | ||||||||
\(523\) | 9.37211e22 | 0.732104 | 0.366052 | − | 0.930594i | \(-0.380709\pi\) | ||||
0.366052 | + | 0.930594i | \(0.380709\pi\) | |||||||
\(524\) | 1.94660e22 | 0.149610 | ||||||||
\(525\) | −3.99995e21 | −0.0302483 | ||||||||
\(526\) | −9.44299e21 | −0.0702637 | ||||||||
\(527\) | 4.80517e22 | 0.351818 | ||||||||
\(528\) | −4.75298e22 | −0.342435 | ||||||||
\(529\) | −4.05028e22 | −0.287152 | ||||||||
\(530\) | 1.24257e22 | 0.0866912 | ||||||||
\(531\) | −3.62221e21 | −0.0248697 | ||||||||
\(532\) | 7.08820e20 | 0.00478947 | ||||||||
\(533\) | 1.24167e23 | 0.825705 | ||||||||
\(534\) | 6.59748e22 | 0.431795 | ||||||||
\(535\) | −2.00604e23 | −1.29221 | ||||||||
\(536\) | −4.56529e22 | −0.289446 | ||||||||
\(537\) | 3.38568e22 | 0.211283 | ||||||||
\(538\) | −6.08452e22 | −0.373746 | ||||||||
\(539\) | 1.67472e23 | 1.01260 | ||||||||
\(540\) | −1.55750e23 | −0.927006 | ||||||||
\(541\) | −1.52396e23 | −0.892889 | −0.446444 | − | 0.894811i | \(-0.647310\pi\) | ||||
−0.446444 | + | 0.894811i | \(0.647310\pi\) | |||||||
\(542\) | 7.76514e22 | 0.447874 | ||||||||
\(543\) | −6.02881e22 | −0.342321 | ||||||||
\(544\) | −4.84592e22 | −0.270886 | ||||||||
\(545\) | −2.19281e23 | −1.20679 | ||||||||
\(546\) | 1.85422e22 | 0.100467 | ||||||||
\(547\) | 2.04979e23 | 1.09349 | 0.546747 | − | 0.837298i | \(-0.315866\pi\) | ||||
0.546747 | + | 0.837298i | \(0.315866\pi\) | |||||||
\(548\) | 2.76411e23 | 1.45185 | ||||||||
\(549\) | 1.44942e23 | 0.749598 | ||||||||
\(550\) | 1.15167e23 | 0.586468 | ||||||||
\(551\) | 3.61970e21 | 0.0181503 | ||||||||
\(552\) | −1.19350e22 | −0.0589304 | ||||||||
\(553\) | 7.63442e21 | 0.0371204 | ||||||||
\(554\) | 9.43770e22 | 0.451890 | ||||||||
\(555\) | 5.57765e22 | 0.263003 | ||||||||
\(556\) | 2.34428e23 | 1.08861 | ||||||||
\(557\) | −4.07359e23 | −1.86298 | −0.931490 | − | 0.363767i | \(-0.881491\pi\) | ||||
−0.931490 | + | 0.363767i | \(0.881491\pi\) | |||||||
\(558\) | −5.17672e23 | −2.33165 | ||||||||
\(559\) | −2.31288e23 | −1.02601 | ||||||||
\(560\) | 4.87206e22 | 0.212870 | ||||||||
\(561\) | −1.75299e22 | −0.0754390 | ||||||||
\(562\) | −1.48128e23 | −0.627884 | ||||||||
\(563\) | 2.21297e23 | 0.923962 | 0.461981 | − | 0.886890i | \(-0.347139\pi\) | ||||
0.461981 | + | 0.886890i | \(0.347139\pi\) | |||||||
\(564\) | 3.12001e22 | 0.128317 | ||||||||
\(565\) | 2.88657e23 | 1.16942 | ||||||||
\(566\) | −1.79455e23 | −0.716169 | ||||||||
\(567\) | 3.19496e22 | 0.125606 | ||||||||
\(568\) | 3.25913e22 | 0.126224 | ||||||||
\(569\) | 4.88686e23 | 1.86456 | 0.932278 | − | 0.361743i | \(-0.117818\pi\) | ||||
0.932278 | + | 0.361743i | \(0.117818\pi\) | |||||||
\(570\) | −3.45163e21 | −0.0129744 | ||||||||
\(571\) | 3.42218e20 | 0.00126735 | 0.000633673 | − | 1.00000i | \(-0.499798\pi\) | ||||
0.000633673 | 1.00000i | \(0.499798\pi\) | ||||||||
\(572\) | −2.82867e23 | −1.03209 | ||||||||
\(573\) | 1.21023e23 | 0.435065 | ||||||||
\(574\) | −8.32315e22 | −0.294806 | ||||||||
\(575\) | −9.17755e22 | −0.320295 | ||||||||
\(576\) | 3.08282e23 | 1.06013 | ||||||||
\(577\) | −1.95911e23 | −0.663840 | −0.331920 | − | 0.943308i | \(-0.607696\pi\) | ||||
−0.331920 | + | 0.943308i | \(0.607696\pi\) | |||||||
\(578\) | 4.21216e23 | 1.40643 | ||||||||
\(579\) | −2.10668e23 | −0.693155 | ||||||||
\(580\) | −3.68736e23 | −1.19558 | ||||||||
\(581\) | −9.60273e22 | −0.306830 | ||||||||
\(582\) | −1.44244e23 | −0.454207 | ||||||||
\(583\) | −1.72883e22 | −0.0536501 | ||||||||
\(584\) | −2.98930e22 | −0.0914239 | ||||||||
\(585\) | 2.88795e23 | 0.870493 | ||||||||
\(586\) | 4.03860e23 | 1.19978 | ||||||||
\(587\) | −4.80676e23 | −1.40744 | −0.703719 | − | 0.710479i | \(-0.748478\pi\) | ||||
−0.703719 | + | 0.710479i | \(0.748478\pi\) | |||||||
\(588\) | 1.40623e23 | 0.405834 | ||||||||
\(589\) | −1.31640e22 | −0.0374461 | ||||||||
\(590\) | 1.77093e22 | 0.0496545 | ||||||||
\(591\) | −5.54596e22 | −0.153279 | ||||||||
\(592\) | −1.86846e23 | −0.509036 | ||||||||
\(593\) | −6.40804e23 | −1.72092 | −0.860459 | − | 0.509519i | \(-0.829823\pi\) | ||||
−0.860459 | + | 0.509519i | \(0.829823\pi\) | |||||||
\(594\) | 4.08992e23 | 1.08276 | ||||||||
\(595\) | 1.79691e22 | 0.0468956 | ||||||||
\(596\) | −7.04940e22 | −0.181367 | ||||||||
\(597\) | 2.36372e23 | 0.599534 | ||||||||
\(598\) | 4.25436e23 | 1.06384 | ||||||||
\(599\) | 3.60950e23 | 0.889854 | 0.444927 | − | 0.895567i | \(-0.353230\pi\) | ||||
0.444927 | + | 0.895567i | \(0.353230\pi\) | |||||||
\(600\) | 1.08938e22 | 0.0264785 | ||||||||
\(601\) | 6.53955e23 | 1.56717 | 0.783583 | − | 0.621287i | \(-0.213390\pi\) | ||||
0.783583 | + | 0.621287i | \(0.213390\pi\) | |||||||
\(602\) | 1.55036e23 | 0.366323 | ||||||||
\(603\) | −5.75668e23 | −1.34114 | ||||||||
\(604\) | −5.80455e23 | −1.33338 | ||||||||
\(605\) | −6.41089e22 | −0.145210 | ||||||||
\(606\) | −3.63295e23 | −0.811414 | ||||||||
\(607\) | 4.08715e23 | 0.900154 | 0.450077 | − | 0.892990i | \(-0.351397\pi\) | ||||
0.450077 | + | 0.892990i | \(0.351397\pi\) | |||||||
\(608\) | 1.32756e22 | 0.0288319 | ||||||||
\(609\) | −3.36301e22 | −0.0720247 | ||||||||
\(610\) | −7.08631e23 | −1.49664 | ||||||||
\(611\) | −1.25287e23 | −0.260949 | ||||||||
\(612\) | 8.88558e22 | 0.182515 | ||||||||
\(613\) | 1.80349e23 | 0.365343 | 0.182671 | − | 0.983174i | \(-0.441526\pi\) | ||||
0.182671 | + | 0.983174i | \(0.441526\pi\) | |||||||
\(614\) | −7.31131e23 | −1.46071 | ||||||||
\(615\) | 2.14745e23 | 0.423141 | ||||||||
\(616\) | 2.13600e22 | 0.0415113 | ||||||||
\(617\) | 4.42851e23 | 0.848856 | 0.424428 | − | 0.905462i | \(-0.360475\pi\) | ||||
0.424428 | + | 0.905462i | \(0.360475\pi\) | |||||||
\(618\) | −2.05190e23 | −0.387930 | ||||||||
\(619\) | 1.71098e22 | 0.0319062 | 0.0159531 | − | 0.999873i | \(-0.494922\pi\) | ||||
0.0159531 | + | 0.999873i | \(0.494922\pi\) | |||||||
\(620\) | 1.34100e24 | 2.46661 | ||||||||
\(621\) | −3.25923e23 | −0.591339 | ||||||||
\(622\) | 1.23939e24 | 2.21815 | ||||||||
\(623\) | 9.40931e22 | 0.166115 | ||||||||
\(624\) | 1.60262e23 | 0.279101 | ||||||||
\(625\) | −7.19124e23 | −1.23545 | ||||||||
\(626\) | −8.36481e23 | −1.41767 | ||||||||
\(627\) | 4.80239e21 | 0.00802941 | ||||||||
\(628\) | −3.38930e23 | −0.559053 | ||||||||
\(629\) | −6.89124e22 | −0.112142 | ||||||||
\(630\) | −1.93585e23 | −0.310797 | ||||||||
\(631\) | −2.82293e23 | −0.447147 | −0.223574 | − | 0.974687i | \(-0.571772\pi\) | ||||
−0.223574 | + | 0.974687i | \(0.571772\pi\) | |||||||
\(632\) | −2.07922e22 | −0.0324941 | ||||||||
\(633\) | −7.43316e22 | −0.114615 | ||||||||
\(634\) | −4.74344e23 | −0.721663 | ||||||||
\(635\) | 8.92802e23 | 1.34023 | ||||||||
\(636\) | −1.45167e22 | −0.0215021 | ||||||||
\(637\) | −5.64684e23 | −0.825316 | ||||||||
\(638\) | 9.68279e23 | 1.39645 | ||||||||
\(639\) | 4.10965e23 | 0.584854 | ||||||||
\(640\) | −3.07190e23 | −0.431397 | ||||||||
\(641\) | −3.77613e23 | −0.523304 | −0.261652 | − | 0.965162i | \(-0.584267\pi\) | ||||
−0.261652 | + | 0.965162i | \(0.584267\pi\) | |||||||
\(642\) | 4.42323e23 | 0.604912 | ||||||||
\(643\) | −4.65536e23 | −0.628289 | −0.314145 | − | 0.949375i | \(-0.601718\pi\) | ||||
−0.314145 | + | 0.949375i | \(0.601718\pi\) | |||||||
\(644\) | −1.51100e23 | −0.201249 | ||||||||
\(645\) | −4.00009e23 | −0.525790 | ||||||||
\(646\) | 4.26452e21 | 0.00553215 | ||||||||
\(647\) | 1.00412e24 | 1.28558 | 0.642788 | − | 0.766045i | \(-0.277778\pi\) | ||||
0.642788 | + | 0.766045i | \(0.277778\pi\) | |||||||
\(648\) | −8.70141e22 | −0.109952 | ||||||||
\(649\) | −2.46396e22 | −0.0307294 | ||||||||
\(650\) | −3.88321e23 | −0.478000 | ||||||||
\(651\) | 1.22304e23 | 0.148595 | ||||||||
\(652\) | 1.18324e24 | 1.41895 | ||||||||
\(653\) | 1.26098e23 | 0.149261 | 0.0746304 | − | 0.997211i | \(-0.476222\pi\) | ||||
0.0746304 | + | 0.997211i | \(0.476222\pi\) | |||||||
\(654\) | 4.83505e23 | 0.564924 | ||||||||
\(655\) | −1.35190e23 | −0.155917 | ||||||||
\(656\) | −7.19375e23 | −0.818979 | ||||||||
\(657\) | −3.76940e23 | −0.423611 | ||||||||
\(658\) | 8.39824e22 | 0.0931683 | ||||||||
\(659\) | −1.06105e24 | −1.16201 | −0.581005 | − | 0.813900i | \(-0.697340\pi\) | ||||
−0.581005 | + | 0.813900i | \(0.697340\pi\) | |||||||
\(660\) | −4.89216e23 | −0.528904 | ||||||||
\(661\) | 1.57511e24 | 1.68112 | 0.840560 | − | 0.541719i | \(-0.182226\pi\) | ||||
0.840560 | + | 0.541719i | \(0.182226\pi\) | |||||||
\(662\) | −2.11448e24 | −2.22797 | ||||||||
\(663\) | 5.91077e22 | 0.0614864 | ||||||||
\(664\) | 2.61528e23 | 0.268590 | ||||||||
\(665\) | −4.92271e21 | −0.00499137 | ||||||||
\(666\) | 7.42408e23 | 0.743211 | ||||||||
\(667\) | −7.71615e23 | −0.762660 | ||||||||
\(668\) | −1.27251e24 | −1.24182 | ||||||||
\(669\) | −4.06301e23 | −0.391495 | ||||||||
\(670\) | 2.81449e24 | 2.67771 | ||||||||
\(671\) | 9.85948e23 | 0.926217 | ||||||||
\(672\) | −1.23342e23 | −0.114412 | ||||||||
\(673\) | 2.91330e23 | 0.266844 | 0.133422 | − | 0.991059i | \(-0.457403\pi\) | ||||
0.133422 | + | 0.991059i | \(0.457403\pi\) | |||||||
\(674\) | 5.63657e23 | 0.509807 | ||||||||
\(675\) | 2.97489e23 | 0.265699 | ||||||||
\(676\) | −3.23993e23 | −0.285751 | ||||||||
\(677\) | 1.33861e24 | 1.16587 | 0.582937 | − | 0.812517i | \(-0.301903\pi\) | ||||
0.582937 | + | 0.812517i | \(0.301903\pi\) | |||||||
\(678\) | −6.36475e23 | −0.547430 | ||||||||
\(679\) | −2.05721e23 | −0.174737 | ||||||||
\(680\) | −4.89385e22 | −0.0410511 | ||||||||
\(681\) | 7.87321e23 | 0.652231 | ||||||||
\(682\) | −3.52140e24 | −2.88103 | ||||||||
\(683\) | −1.05295e24 | −0.850812 | −0.425406 | − | 0.905003i | \(-0.639869\pi\) | ||||
−0.425406 | + | 0.905003i | \(0.639869\pi\) | |||||||
\(684\) | −2.43424e22 | −0.0194261 | ||||||||
\(685\) | −1.91966e24 | −1.51305 | ||||||||
\(686\) | 7.74764e23 | 0.603135 | ||||||||
\(687\) | 3.91947e23 | 0.301366 | ||||||||
\(688\) | 1.33999e24 | 1.01765 | ||||||||
\(689\) | 5.82932e22 | 0.0437275 | ||||||||
\(690\) | 7.35787e23 | 0.545174 | ||||||||
\(691\) | −5.71311e22 | −0.0418128 | −0.0209064 | − | 0.999781i | \(-0.506655\pi\) | ||||
−0.0209064 | + | 0.999781i | \(0.506655\pi\) | |||||||
\(692\) | 3.41850e23 | 0.247134 | ||||||||
\(693\) | 2.69343e23 | 0.192341 | ||||||||
\(694\) | 8.54519e23 | 0.602790 | ||||||||
\(695\) | −1.62809e24 | −1.13451 | ||||||||
\(696\) | 9.15909e22 | 0.0630483 | ||||||||
\(697\) | −2.65320e23 | −0.180423 | ||||||||
\(698\) | 2.95721e24 | 1.98660 | ||||||||
\(699\) | −4.23044e23 | −0.280756 | ||||||||
\(700\) | 1.37918e23 | 0.0904248 | ||||||||
\(701\) | −3.18403e23 | −0.206241 | −0.103120 | − | 0.994669i | \(-0.532883\pi\) | ||||
−0.103120 | + | 0.994669i | \(0.532883\pi\) | |||||||
\(702\) | −1.37905e24 | −0.882498 | ||||||||
\(703\) | 1.88788e22 | 0.0119359 | ||||||||
\(704\) | 2.09705e24 | 1.30991 | ||||||||
\(705\) | −2.16683e23 | −0.133726 | ||||||||
\(706\) | −2.69689e24 | −1.64446 | ||||||||
\(707\) | −5.18131e23 | −0.312158 | ||||||||
\(708\) | −2.06894e22 | −0.0123159 | ||||||||
\(709\) | 2.12997e24 | 1.25279 | 0.626397 | − | 0.779504i | \(-0.284529\pi\) | ||||
0.626397 | + | 0.779504i | \(0.284529\pi\) | |||||||
\(710\) | −2.00924e24 | −1.16771 | ||||||||
\(711\) | −2.62182e23 | −0.150561 | ||||||||
\(712\) | −2.56261e23 | −0.145413 | ||||||||
\(713\) | 2.80617e24 | 1.57345 | ||||||||
\(714\) | −3.96210e22 | −0.0219529 | ||||||||
\(715\) | 1.96450e24 | 1.07560 | ||||||||
\(716\) | −1.16738e24 | −0.631613 | ||||||||
\(717\) | −8.11119e23 | −0.433683 | ||||||||
\(718\) | −3.08861e24 | −1.63195 | ||||||||
\(719\) | −2.34234e24 | −1.22308 | −0.611540 | − | 0.791213i | \(-0.709450\pi\) | ||||
−0.611540 | + | 0.791213i | \(0.709450\pi\) | |||||||
\(720\) | −1.67317e24 | −0.863403 | ||||||||
\(721\) | −2.92641e23 | −0.149240 | ||||||||
\(722\) | 2.89248e24 | 1.45782 | ||||||||
\(723\) | 5.94456e23 | 0.296104 | ||||||||
\(724\) | 2.07873e24 | 1.02334 | ||||||||
\(725\) | 7.04299e23 | 0.342676 | ||||||||
\(726\) | 1.41357e23 | 0.0679761 | ||||||||
\(727\) | 3.58185e24 | 1.70241 | 0.851207 | − | 0.524830i | \(-0.175871\pi\) | ||||
0.851207 | + | 0.524830i | \(0.175871\pi\) | |||||||
\(728\) | −7.20222e22 | −0.0338337 | ||||||||
\(729\) | −5.28574e23 | −0.245427 | ||||||||
\(730\) | 1.84289e24 | 0.845776 | ||||||||
\(731\) | 4.94215e23 | 0.224191 | ||||||||
\(732\) | 8.27881e23 | 0.371213 | ||||||||
\(733\) | −3.29013e24 | −1.45824 | −0.729119 | − | 0.684387i | \(-0.760070\pi\) | ||||
−0.729119 | + | 0.684387i | \(0.760070\pi\) | |||||||
\(734\) | −2.26794e23 | −0.0993609 | ||||||||
\(735\) | −9.76615e23 | −0.422942 | ||||||||
\(736\) | −2.82997e24 | −1.21149 | ||||||||
\(737\) | −3.91591e24 | −1.65714 | ||||||||
\(738\) | 2.85835e24 | 1.19574 | ||||||||
\(739\) | 1.74130e24 | 0.720103 | 0.360052 | − | 0.932932i | \(-0.382759\pi\) | ||||
0.360052 | + | 0.932932i | \(0.382759\pi\) | |||||||
\(740\) | −1.92317e24 | −0.786227 | ||||||||
\(741\) | −1.61928e22 | −0.00654436 | ||||||||
\(742\) | −3.90750e22 | −0.0156123 | ||||||||
\(743\) | −4.61544e24 | −1.82309 | −0.911545 | − | 0.411199i | \(-0.865110\pi\) | ||||
−0.911545 | + | 0.411199i | \(0.865110\pi\) | |||||||
\(744\) | −3.33094e23 | −0.130076 | ||||||||
\(745\) | 4.89576e23 | 0.189013 | ||||||||
\(746\) | 3.45700e24 | 1.31953 | ||||||||
\(747\) | 3.29778e24 | 1.24451 | ||||||||
\(748\) | 6.04431e23 | 0.225519 | ||||||||
\(749\) | 6.30841e23 | 0.232715 | ||||||||
\(750\) | 1.09875e24 | 0.400753 | ||||||||
\(751\) | −8.19607e22 | −0.0295574 | −0.0147787 | − | 0.999891i | \(-0.504704\pi\) | ||||
−0.0147787 | + | 0.999891i | \(0.504704\pi\) | |||||||
\(752\) | 7.25865e23 | 0.258824 | ||||||||
\(753\) | 1.43303e24 | 0.505241 | ||||||||
\(754\) | −3.26486e24 | −1.13817 | ||||||||
\(755\) | 4.03122e24 | 1.38959 | ||||||||
\(756\) | 4.89789e23 | 0.166945 | ||||||||
\(757\) | −2.51608e24 | −0.848025 | −0.424013 | − | 0.905656i | \(-0.639379\pi\) | ||||
−0.424013 | + | 0.905656i | \(0.639379\pi\) | |||||||
\(758\) | −8.01767e23 | −0.267215 | ||||||||
\(759\) | −1.02373e24 | −0.337389 | ||||||||
\(760\) | 1.34069e22 | 0.00436931 | ||||||||
\(761\) | −5.27745e23 | −0.170081 | −0.0850403 | − | 0.996378i | \(-0.527102\pi\) | ||||
−0.0850403 | + | 0.996378i | \(0.527102\pi\) | |||||||
\(762\) | −1.96859e24 | −0.627390 | ||||||||
\(763\) | 6.89574e23 | 0.217331 | ||||||||
\(764\) | −4.17287e24 | −1.30059 | ||||||||
\(765\) | −6.17098e23 | −0.190209 | ||||||||
\(766\) | 4.24827e24 | 1.29499 | ||||||||
\(767\) | 8.30803e22 | 0.0250460 | ||||||||
\(768\) | −8.85151e23 | −0.263905 | ||||||||
\(769\) | −7.51719e23 | −0.221657 | −0.110828 | − | 0.993840i | \(-0.535350\pi\) | ||||
−0.110828 | + | 0.993840i | \(0.535350\pi\) | |||||||
\(770\) | −1.31684e24 | −0.384027 | ||||||||
\(771\) | −2.10508e23 | −0.0607165 | ||||||||
\(772\) | 7.26381e24 | 2.07213 | ||||||||
\(773\) | 2.81914e24 | 0.795409 | 0.397704 | − | 0.917514i | \(-0.369807\pi\) | ||||
0.397704 | + | 0.917514i | \(0.369807\pi\) | |||||||
\(774\) | −5.32429e24 | −1.48581 | ||||||||
\(775\) | −2.56136e24 | −0.706980 | ||||||||
\(776\) | 5.60277e23 | 0.152960 | ||||||||
\(777\) | −1.75401e23 | −0.0473644 | ||||||||
\(778\) | −3.61173e24 | −0.964693 | ||||||||
\(779\) | 7.26854e22 | 0.0192034 | ||||||||
\(780\) | 1.64955e24 | 0.431083 | ||||||||
\(781\) | 2.79554e24 | 0.722656 | ||||||||
\(782\) | −9.09072e23 | −0.232456 | ||||||||
\(783\) | 2.50118e24 | 0.632660 | ||||||||
\(784\) | 3.27156e24 | 0.818594 | ||||||||
\(785\) | 2.35385e24 | 0.582621 | ||||||||
\(786\) | 2.98088e23 | 0.0729882 | ||||||||
\(787\) | −3.20732e24 | −0.776887 | −0.388443 | − | 0.921473i | \(-0.626987\pi\) | ||||
−0.388443 | + | 0.921473i | \(0.626987\pi\) | |||||||
\(788\) | 1.91224e24 | 0.458216 | ||||||||
\(789\) | −7.66170e22 | −0.0181623 | ||||||||
\(790\) | 1.28183e24 | 0.300608 | ||||||||
\(791\) | −9.07739e23 | −0.210601 | ||||||||
\(792\) | −7.33550e23 | −0.168370 | ||||||||
\(793\) | −3.32444e24 | −0.754912 | ||||||||
\(794\) | −3.29186e24 | −0.739549 | ||||||||
\(795\) | 1.00817e23 | 0.0224086 | ||||||||
\(796\) | −8.15008e24 | −1.79226 | ||||||||
\(797\) | 2.36328e24 | 0.514186 | 0.257093 | − | 0.966387i | \(-0.417235\pi\) | ||||
0.257093 | + | 0.966387i | \(0.417235\pi\) | |||||||
\(798\) | 1.08543e22 | 0.00233657 | ||||||||
\(799\) | 2.67713e23 | 0.0570194 | ||||||||
\(800\) | 2.58309e24 | 0.544345 | ||||||||
\(801\) | −3.23136e24 | −0.673766 | ||||||||
\(802\) | 1.22521e24 | 0.252772 | ||||||||
\(803\) | −2.56409e24 | −0.523421 | ||||||||
\(804\) | −3.28811e24 | −0.664156 | ||||||||
\(805\) | 1.04938e24 | 0.209733 | ||||||||
\(806\) | 1.18735e25 | 2.34818 | ||||||||
\(807\) | −4.93676e23 | −0.0966088 | ||||||||
\(808\) | 1.41112e24 | 0.273254 | ||||||||
\(809\) | 9.60721e24 | 1.84092 | 0.920460 | − | 0.390836i | \(-0.127814\pi\) | ||||
0.920460 | + | 0.390836i | \(0.127814\pi\) | |||||||
\(810\) | 5.36439e24 | 1.01718 | ||||||||
\(811\) | −6.64616e24 | −1.24708 | −0.623539 | − | 0.781792i | \(-0.714306\pi\) | ||||
−0.623539 | + | 0.781792i | \(0.714306\pi\) | |||||||
\(812\) | 1.15956e24 | 0.215312 | ||||||||
\(813\) | 6.30035e23 | 0.115770 | ||||||||
\(814\) | 5.05014e24 | 0.918324 | ||||||||
\(815\) | −8.21751e24 | −1.47877 | ||||||||
\(816\) | −3.42447e23 | −0.0609856 | ||||||||
\(817\) | −1.35392e23 | −0.0238620 | ||||||||
\(818\) | −1.25976e25 | −2.19727 | ||||||||
\(819\) | −9.08175e23 | −0.156768 | ||||||||
\(820\) | −7.40440e24 | −1.26495 | ||||||||
\(821\) | −5.09458e24 | −0.861373 | −0.430687 | − | 0.902502i | \(-0.641729\pi\) | ||||
−0.430687 | + | 0.902502i | \(0.641729\pi\) | |||||||
\(822\) | 4.23275e24 | 0.708292 | ||||||||
\(823\) | 5.78198e24 | 0.957586 | 0.478793 | − | 0.877928i | \(-0.341074\pi\) | ||||
0.478793 | + | 0.877928i | \(0.341074\pi\) | |||||||
\(824\) | 7.97002e23 | 0.130641 | ||||||||
\(825\) | 9.34421e23 | 0.151595 | ||||||||
\(826\) | −5.56903e22 | −0.00894230 | ||||||||
\(827\) | 8.38907e24 | 1.33327 | 0.666633 | − | 0.745386i | \(-0.267735\pi\) | ||||
0.666633 | + | 0.745386i | \(0.267735\pi\) | |||||||
\(828\) | 5.18909e24 | 0.816270 | ||||||||
\(829\) | 5.02769e24 | 0.782808 | 0.391404 | − | 0.920219i | \(-0.371989\pi\) | ||||
0.391404 | + | 0.920219i | \(0.371989\pi\) | |||||||
\(830\) | −1.61231e25 | −2.48477 | ||||||||
\(831\) | 7.65741e23 | 0.116808 | ||||||||
\(832\) | −7.07088e24 | −1.06764 | ||||||||
\(833\) | 1.20662e24 | 0.180338 | ||||||||
\(834\) | 3.58986e24 | 0.531087 | ||||||||
\(835\) | 8.83747e24 | 1.29417 | ||||||||
\(836\) | −1.65586e23 | −0.0240033 | ||||||||
\(837\) | −9.09619e24 | −1.30525 | ||||||||
\(838\) | 1.38251e25 | 1.96378 | ||||||||
\(839\) | 9.38328e23 | 0.131940 | 0.0659702 | − | 0.997822i | \(-0.478986\pi\) | ||||
0.0659702 | + | 0.997822i | \(0.478986\pi\) | |||||||
\(840\) | −1.24562e23 | −0.0173384 | ||||||||
\(841\) | −1.33566e24 | −0.184048 | ||||||||
\(842\) | −5.90847e24 | −0.805977 | ||||||||
\(843\) | −1.20186e24 | −0.162300 | ||||||||
\(844\) | 2.56295e24 | 0.342633 | ||||||||
\(845\) | 2.25011e24 | 0.297798 | ||||||||
\(846\) | −2.88414e24 | −0.377892 | ||||||||
\(847\) | 2.01603e23 | 0.0261510 | ||||||||
\(848\) | −3.37728e23 | −0.0433713 | ||||||||
\(849\) | −1.45603e24 | −0.185121 | ||||||||
\(850\) | 8.29764e23 | 0.104447 | ||||||||
\(851\) | −4.02442e24 | −0.501536 | ||||||||
\(852\) | 2.34736e24 | 0.289630 | ||||||||
\(853\) | 2.33188e24 | 0.284865 | 0.142433 | − | 0.989805i | \(-0.454508\pi\) | ||||
0.142433 | + | 0.989805i | \(0.454508\pi\) | |||||||
\(854\) | 2.22843e24 | 0.269531 | ||||||||
\(855\) | 1.69056e23 | 0.0202451 | ||||||||
\(856\) | −1.71808e24 | −0.203712 | ||||||||
\(857\) | −1.09008e25 | −1.27974 | −0.639872 | − | 0.768482i | \(-0.721012\pi\) | ||||
−0.639872 | + | 0.768482i | \(0.721012\pi\) | |||||||
\(858\) | −4.33162e24 | −0.503510 | ||||||||
\(859\) | −1.47838e25 | −1.70155 | −0.850773 | − | 0.525533i | \(-0.823866\pi\) | ||||
−0.850773 | + | 0.525533i | \(0.823866\pi\) | |||||||
\(860\) | 1.37923e25 | 1.57181 | ||||||||
\(861\) | −6.75310e23 | −0.0762037 | ||||||||
\(862\) | −9.20284e24 | −1.02828 | ||||||||
\(863\) | 5.86087e24 | 0.648441 | 0.324220 | − | 0.945982i | \(-0.394898\pi\) | ||||
0.324220 | + | 0.945982i | \(0.394898\pi\) | |||||||
\(864\) | 9.17333e24 | 1.00499 | ||||||||
\(865\) | −2.37412e24 | −0.257553 | ||||||||
\(866\) | 2.38346e25 | 2.56039 | ||||||||
\(867\) | 3.41760e24 | 0.363545 | ||||||||
\(868\) | −4.21705e24 | −0.444213 | ||||||||
\(869\) | −1.78346e24 | −0.186036 | ||||||||
\(870\) | −5.64654e24 | −0.583269 | ||||||||
\(871\) | 1.32037e25 | 1.35065 | ||||||||
\(872\) | −1.87804e24 | −0.190246 | ||||||||
\(873\) | 7.06491e24 | 0.708737 | ||||||||
\(874\) | 2.49044e23 | 0.0247417 | ||||||||
\(875\) | 1.56703e24 | 0.154173 | ||||||||
\(876\) | −2.15302e24 | −0.209779 | ||||||||
\(877\) | −1.08364e25 | −1.04565 | −0.522827 | − | 0.852439i | \(-0.675122\pi\) | ||||
−0.522827 | + | 0.852439i | \(0.675122\pi\) | |||||||
\(878\) | −2.03420e25 | −1.94398 | ||||||||
\(879\) | 3.27678e24 | 0.310128 | ||||||||
\(880\) | −1.13815e25 | −1.06684 | ||||||||
\(881\) | 5.00054e24 | 0.464217 | 0.232109 | − | 0.972690i | \(-0.425437\pi\) | ||||
0.232109 | + | 0.972690i | \(0.425437\pi\) | |||||||
\(882\) | −1.29991e25 | −1.19518 | ||||||||
\(883\) | −1.04108e24 | −0.0948025 | −0.0474012 | − | 0.998876i | \(-0.515094\pi\) | ||||
−0.0474012 | + | 0.998876i | \(0.515094\pi\) | |||||||
\(884\) | −2.03803e24 | −0.183809 | ||||||||
\(885\) | 1.43686e23 | 0.0128351 | ||||||||
\(886\) | 2.03262e24 | 0.179833 | ||||||||
\(887\) | 1.47651e25 | 1.29386 | 0.646929 | − | 0.762550i | \(-0.276053\pi\) | ||||
0.646929 | + | 0.762550i | \(0.276053\pi\) | |||||||
\(888\) | 4.77700e23 | 0.0414615 | ||||||||
\(889\) | −2.80760e24 | −0.241363 | ||||||||
\(890\) | 1.57984e25 | 1.34523 | ||||||||
\(891\) | −7.46369e24 | −0.629496 | ||||||||
\(892\) | 1.40092e25 | 1.17034 | ||||||||
\(893\) | −7.33412e22 | −0.00606891 | ||||||||
\(894\) | −1.07949e24 | −0.0884812 | ||||||||
\(895\) | 8.10737e24 | 0.658240 | ||||||||
\(896\) | 9.66021e23 | 0.0776906 | ||||||||
\(897\) | 3.45184e24 | 0.274988 | ||||||||
\(898\) | 1.46580e24 | 0.115672 | ||||||||
\(899\) | −2.15350e25 | −1.68340 | ||||||||
\(900\) | −4.73640e24 | −0.366764 | ||||||||
\(901\) | −1.24561e23 | −0.00955478 | ||||||||
\(902\) | 1.94436e25 | 1.47747 | ||||||||
\(903\) | 1.25791e24 | 0.0946899 | ||||||||
\(904\) | 2.47221e24 | 0.184354 | ||||||||
\(905\) | −1.44366e25 | −1.06648 | ||||||||
\(906\) | −8.88866e24 | −0.650499 | ||||||||
\(907\) | −2.99747e23 | −0.0217317 | −0.0108658 | − | 0.999941i | \(-0.503459\pi\) | ||||
−0.0108658 | + | 0.999941i | \(0.503459\pi\) | |||||||
\(908\) | −2.71468e25 | −1.94979 | ||||||||
\(909\) | 1.77937e25 | 1.26612 | ||||||||
\(910\) | 4.44014e24 | 0.313000 | ||||||||
\(911\) | −1.71431e24 | −0.119724 | −0.0598621 | − | 0.998207i | \(-0.519066\pi\) | ||||
−0.0598621 | + | 0.998207i | \(0.519066\pi\) | |||||||
\(912\) | 9.38148e22 | 0.00649106 | ||||||||
\(913\) | 2.24328e25 | 1.53773 | ||||||||
\(914\) | 7.08256e24 | 0.481003 | ||||||||
\(915\) | −5.74958e24 | −0.386863 | ||||||||
\(916\) | −1.35143e25 | −0.900911 | ||||||||
\(917\) | 4.25132e23 | 0.0280792 | ||||||||
\(918\) | 2.94675e24 | 0.192832 | ||||||||
\(919\) | −2.42539e25 | −1.57253 | −0.786265 | − | 0.617889i | \(-0.787988\pi\) | ||||
−0.786265 | + | 0.617889i | \(0.787988\pi\) | |||||||
\(920\) | −2.85796e24 | −0.183594 | ||||||||
\(921\) | −5.93213e24 | −0.377575 | ||||||||
\(922\) | 2.28480e25 | 1.44091 | ||||||||
\(923\) | −9.42605e24 | −0.589000 | ||||||||
\(924\) | 1.53844e24 | 0.0952507 | ||||||||
\(925\) | 3.67333e24 | 0.225349 | ||||||||
\(926\) | −2.03661e25 | −1.23798 | ||||||||
\(927\) | 1.00499e25 | 0.605320 | ||||||||
\(928\) | 2.17176e25 | 1.29615 | ||||||||
\(929\) | 1.40138e25 | 0.828745 | 0.414373 | − | 0.910107i | \(-0.364001\pi\) | ||||
0.414373 | + | 0.910107i | \(0.364001\pi\) | |||||||
\(930\) | 2.05351e25 | 1.20335 | ||||||||
\(931\) | −3.30557e23 | −0.0191944 | ||||||||
\(932\) | 1.45865e25 | 0.839298 | ||||||||
\(933\) | 1.00560e25 | 0.573364 | ||||||||
\(934\) | −2.62270e25 | −1.48184 | ||||||||
\(935\) | −4.19773e24 | −0.235026 | ||||||||
\(936\) | 2.47340e24 | 0.137230 | ||||||||
\(937\) | −2.43217e25 | −1.33724 | −0.668618 | − | 0.743606i | \(-0.733114\pi\) | ||||
−0.668618 | + | 0.743606i | \(0.733114\pi\) | |||||||
\(938\) | −8.85072e24 | −0.482230 | ||||||||
\(939\) | −6.78690e24 | −0.366449 | ||||||||
\(940\) | 7.47120e24 | 0.399764 | ||||||||
\(941\) | 5.98394e23 | 0.0317304 | 0.0158652 | − | 0.999874i | \(-0.494950\pi\) | ||||
0.0158652 | + | 0.999874i | \(0.494950\pi\) | |||||||
\(942\) | −5.19012e24 | −0.272738 | ||||||||
\(943\) | −1.54944e25 | −0.806912 | ||||||||
\(944\) | −4.81335e23 | −0.0248419 | ||||||||
\(945\) | −3.40155e24 | −0.173983 | ||||||||
\(946\) | −3.62178e25 | −1.83589 | ||||||||
\(947\) | 3.62477e25 | 1.82098 | 0.910491 | − | 0.413530i | \(-0.135704\pi\) | ||||
0.910491 | + | 0.413530i | \(0.135704\pi\) | |||||||
\(948\) | −1.49754e24 | −0.0745602 | ||||||||
\(949\) | 8.64565e24 | 0.426614 | ||||||||
\(950\) | −2.27317e23 | −0.0111169 | ||||||||
\(951\) | −3.84865e24 | −0.186541 | ||||||||
\(952\) | 1.53897e23 | 0.00739291 | ||||||||
\(953\) | −1.88157e25 | −0.895839 | −0.447919 | − | 0.894074i | \(-0.647835\pi\) | ||||
−0.447919 | + | 0.894074i | \(0.647835\pi\) | |||||||
\(954\) | 1.34192e24 | 0.0633236 | ||||||||
\(955\) | 2.89803e25 | 1.35542 | ||||||||
\(956\) | 2.79673e25 | 1.29646 | ||||||||
\(957\) | 7.85627e24 | 0.360965 | ||||||||
\(958\) | 2.25199e25 | 1.02556 | ||||||||
\(959\) | 6.03674e24 | 0.272486 | ||||||||
\(960\) | −1.22290e25 | −0.547124 | ||||||||
\(961\) | 5.57675e25 | 2.47305 | ||||||||
\(962\) | −1.70282e25 | −0.748479 | ||||||||
\(963\) | −2.16644e25 | −0.943896 | ||||||||
\(964\) | −2.04968e25 | −0.885180 | ||||||||
\(965\) | −5.04467e25 | −2.15949 | ||||||||
\(966\) | −2.31383e24 | −0.0981807 | ||||||||
\(967\) | −1.81212e24 | −0.0762186 | −0.0381093 | − | 0.999274i | \(-0.512134\pi\) | ||||
−0.0381093 | + | 0.999274i | \(0.512134\pi\) | |||||||
\(968\) | −5.49062e23 | −0.0228919 | ||||||||
\(969\) | 3.46008e22 | 0.00142999 | ||||||||
\(970\) | −3.45409e25 | −1.41506 | ||||||||
\(971\) | 2.03685e25 | 0.827170 | 0.413585 | − | 0.910465i | \(-0.364276\pi\) | ||||
0.413585 | + | 0.910465i | \(0.364276\pi\) | |||||||
\(972\) | −2.58739e25 | −1.04160 | ||||||||
\(973\) | 5.11985e24 | 0.204314 | ||||||||
\(974\) | 4.90050e25 | 1.93861 | ||||||||
\(975\) | −3.15070e24 | −0.123557 | ||||||||
\(976\) | 1.92605e25 | 0.748763 | ||||||||
\(977\) | −2.52590e25 | −0.973449 | −0.486724 | − | 0.873556i | \(-0.661808\pi\) | ||||
−0.486724 | + | 0.873556i | \(0.661808\pi\) | |||||||
\(978\) | 1.81192e25 | 0.692244 | ||||||||
\(979\) | −2.19809e25 | −0.832517 | ||||||||
\(980\) | 3.36736e25 | 1.26435 | ||||||||
\(981\) | −2.36815e25 | −0.881499 | ||||||||
\(982\) | −6.85750e23 | −0.0253057 | ||||||||
\(983\) | −1.51840e24 | −0.0555495 | −0.0277747 | − | 0.999614i | \(-0.508842\pi\) | ||||
−0.0277747 | + | 0.999614i | \(0.508842\pi\) | |||||||
\(984\) | 1.83919e24 | 0.0667066 | ||||||||
\(985\) | −1.32804e25 | −0.477533 | ||||||||
\(986\) | 6.97635e24 | 0.248699 | ||||||||
\(987\) | 6.81402e23 | 0.0240828 | ||||||||
\(988\) | 5.58327e23 | 0.0195639 | ||||||||
\(989\) | 2.88617e25 | 1.00266 | ||||||||
\(990\) | 4.52231e25 | 1.55762 | ||||||||
\(991\) | −6.69650e24 | −0.228677 | −0.114338 | − | 0.993442i | \(-0.536475\pi\) | ||||
−0.114338 | + | 0.993442i | \(0.536475\pi\) | |||||||
\(992\) | −7.89818e25 | −2.67410 | ||||||||
\(993\) | −1.71561e25 | −0.575903 | ||||||||
\(994\) | 6.31846e24 | 0.210294 | ||||||||
\(995\) | 5.66018e25 | 1.86781 | ||||||||
\(996\) | 1.88363e25 | 0.616300 | ||||||||
\(997\) | −3.45326e25 | −1.12026 | −0.560132 | − | 0.828404i | \(-0.689249\pi\) | ||||
−0.560132 | + | 0.828404i | \(0.689249\pi\) | |||||||
\(998\) | 4.04864e25 | 1.30227 | ||||||||
\(999\) | 1.30451e25 | 0.416046 |
(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 | 1.18.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.18.a.b.1.1 | 1 | |||
4.3 | odd | 2 | 16.18.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 25.18.b.a.24.1 | 2 | |||
5.3 | odd | 4 | 25.18.b.a.24.2 | 2 | |||
5.4 | even | 2 | 25.18.a.a.1.1 | 1 | |||
7.6 | odd | 2 | 49.18.a.a.1.1 | 1 | |||
8.3 | odd | 2 | 64.18.a.b.1.1 | 1 | |||
8.5 | even | 2 | 64.18.a.d.1.1 | 1 | |||
11.10 | odd | 2 | 121.18.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.18.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.18.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
16.18.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
25.18.a.a.1.1 | 1 | 5.4 | even | 2 | |||
25.18.b.a.24.1 | 2 | 5.2 | odd | 4 | |||
25.18.b.a.24.2 | 2 | 5.3 | odd | 4 | |||
49.18.a.a.1.1 | 1 | 7.6 | odd | 2 | |||
64.18.a.b.1.1 | 1 | 8.3 | odd | 2 | |||
64.18.a.d.1.1 | 1 | 8.5 | even | 2 | |||
121.18.a.b.1.1 | 1 | 11.10 | odd | 2 |