Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [197,14,Mod(1,197)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(197, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("197.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 197 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 197.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: | \(211.244930035\) |
Analytic rank: | \(1\) |
Dimension: | \(104\) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 197.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −140.225 | −1.54928 | −0.774639 | − | 0.632404i | \(-0.782068\pi\) | ||||
−0.774639 | + | 0.632404i | \(0.782068\pi\) | |||||||
\(3\) | −1671.46 | −1.32375 | −0.661877 | − | 0.749613i | \(-0.730240\pi\) | ||||
−0.661877 | + | 0.749613i | \(0.730240\pi\) | |||||||
\(4\) | 11470.9 | 1.40026 | ||||||||
\(5\) | 31759.0 | 0.908995 | 0.454498 | − | 0.890748i | \(-0.349819\pi\) | ||||
0.454498 | + | 0.890748i | \(0.349819\pi\) | |||||||
\(6\) | 234379. | 2.05086 | ||||||||
\(7\) | −135007. | −0.433729 | −0.216865 | − | 0.976202i | \(-0.569583\pi\) | ||||
−0.216865 | + | 0.976202i | \(0.569583\pi\) | |||||||
\(8\) | −459789. | −0.620117 | ||||||||
\(9\) | 1.19945e6 | 0.752323 | ||||||||
\(10\) | −4.45339e6 | −1.40829 | ||||||||
\(11\) | 6.61641e6 | 1.12608 | 0.563041 | − | 0.826429i | \(-0.309631\pi\) | ||||
0.563041 | + | 0.826429i | \(0.309631\pi\) | |||||||
\(12\) | −1.91732e7 | −1.85360 | ||||||||
\(13\) | 4.45473e6 | 0.255971 | 0.127985 | − | 0.991776i | \(-0.459149\pi\) | ||||
0.127985 | + | 0.991776i | \(0.459149\pi\) | |||||||
\(14\) | 1.89313e7 | 0.671967 | ||||||||
\(15\) | −5.30838e7 | −1.20329 | ||||||||
\(16\) | −2.94963e7 | −0.439529 | ||||||||
\(17\) | 1.10551e8 | 1.11082 | 0.555409 | − | 0.831577i | \(-0.312562\pi\) | ||||
0.555409 | + | 0.831577i | \(0.312562\pi\) | |||||||
\(18\) | −1.68192e8 | −1.16556 | ||||||||
\(19\) | 2.92939e8 | 1.42850 | 0.714249 | − | 0.699892i | \(-0.246769\pi\) | ||||
0.714249 | + | 0.699892i | \(0.246769\pi\) | |||||||
\(20\) | 3.64306e8 | 1.27283 | ||||||||
\(21\) | 2.25658e8 | 0.574151 | ||||||||
\(22\) | −9.27784e8 | −1.74461 | ||||||||
\(23\) | 5.09095e8 | 0.717080 | 0.358540 | − | 0.933514i | \(-0.383275\pi\) | ||||
0.358540 | + | 0.933514i | \(0.383275\pi\) | |||||||
\(24\) | 7.68517e8 | 0.820881 | ||||||||
\(25\) | −2.12070e8 | −0.173728 | ||||||||
\(26\) | −6.24663e8 | −0.396570 | ||||||||
\(27\) | 6.60019e8 | 0.327863 | ||||||||
\(28\) | −1.54866e9 | −0.607334 | ||||||||
\(29\) | −1.71152e9 | −0.534314 | −0.267157 | − | 0.963653i | \(-0.586084\pi\) | ||||
−0.267157 | + | 0.963653i | \(0.586084\pi\) | |||||||
\(30\) | 7.44365e9 | 1.86422 | ||||||||
\(31\) | 3.16666e9 | 0.640840 | 0.320420 | − | 0.947276i | \(-0.396176\pi\) | ||||
0.320420 | + | 0.947276i | \(0.396176\pi\) | |||||||
\(32\) | 7.90269e9 | 1.30107 | ||||||||
\(33\) | −1.10591e10 | −1.49066 | ||||||||
\(34\) | −1.55019e10 | −1.72097 | ||||||||
\(35\) | −4.28768e9 | −0.394258 | ||||||||
\(36\) | 1.37588e10 | 1.05345 | ||||||||
\(37\) | 8.61199e9 | 0.551814 | 0.275907 | − | 0.961184i | \(-0.411022\pi\) | ||||
0.275907 | + | 0.961184i | \(0.411022\pi\) | |||||||
\(38\) | −4.10773e10 | −2.21314 | ||||||||
\(39\) | −7.44590e9 | −0.338842 | ||||||||
\(40\) | −1.46024e10 | −0.563683 | ||||||||
\(41\) | −3.93198e10 | −1.29276 | −0.646378 | − | 0.763017i | \(-0.723717\pi\) | ||||
−0.646378 | + | 0.763017i | \(0.723717\pi\) | |||||||
\(42\) | −3.16428e10 | −0.889519 | ||||||||
\(43\) | −2.13346e10 | −0.514682 | −0.257341 | − | 0.966321i | \(-0.582846\pi\) | ||||
−0.257341 | + | 0.966321i | \(0.582846\pi\) | |||||||
\(44\) | 7.58965e10 | 1.57681 | ||||||||
\(45\) | 3.80932e10 | 0.683858 | ||||||||
\(46\) | −7.13876e10 | −1.11096 | ||||||||
\(47\) | −3.20059e10 | −0.433106 | −0.216553 | − | 0.976271i | \(-0.569481\pi\) | ||||
−0.216553 | + | 0.976271i | \(0.569481\pi\) | |||||||
\(48\) | 4.93018e10 | 0.581828 | ||||||||
\(49\) | −7.86621e10 | −0.811879 | ||||||||
\(50\) | 2.97374e10 | 0.269152 | ||||||||
\(51\) | −1.84780e11 | −1.47045 | ||||||||
\(52\) | 5.11000e10 | 0.358426 | ||||||||
\(53\) | −1.62511e11 | −1.00714 | −0.503570 | − | 0.863955i | \(-0.667980\pi\) | ||||
−0.503570 | + | 0.863955i | \(0.667980\pi\) | |||||||
\(54\) | −9.25510e10 | −0.507951 | ||||||||
\(55\) | 2.10131e11 | 1.02360 | ||||||||
\(56\) | 6.20746e10 | 0.268963 | ||||||||
\(57\) | −4.89636e11 | −1.89098 | ||||||||
\(58\) | 2.39998e11 | 0.827800 | ||||||||
\(59\) | −3.08362e11 | −0.951749 | −0.475875 | − | 0.879513i | \(-0.657868\pi\) | ||||
−0.475875 | + | 0.879513i | \(0.657868\pi\) | |||||||
\(60\) | −6.08921e11 | −1.68491 | ||||||||
\(61\) | −1.33000e11 | −0.330528 | −0.165264 | − | 0.986249i | \(-0.552848\pi\) | ||||
−0.165264 | + | 0.986249i | \(0.552848\pi\) | |||||||
\(62\) | −4.44043e11 | −0.992840 | ||||||||
\(63\) | −1.61934e11 | −0.326305 | ||||||||
\(64\) | −8.66519e11 | −1.57619 | ||||||||
\(65\) | 1.41478e11 | 0.232676 | ||||||||
\(66\) | 1.55075e12 | 2.30944 | ||||||||
\(67\) | −5.24160e11 | −0.707909 | −0.353955 | − | 0.935263i | \(-0.615163\pi\) | ||||
−0.353955 | + | 0.935263i | \(0.615163\pi\) | |||||||
\(68\) | 1.26812e12 | 1.55544 | ||||||||
\(69\) | −8.50930e11 | −0.949237 | ||||||||
\(70\) | 6.01239e11 | 0.610815 | ||||||||
\(71\) | −2.72013e11 | −0.252005 | −0.126003 | − | 0.992030i | \(-0.540215\pi\) | ||||
−0.126003 | + | 0.992030i | \(0.540215\pi\) | |||||||
\(72\) | −5.51492e11 | −0.466528 | ||||||||
\(73\) | −1.27492e12 | −0.986020 | −0.493010 | − | 0.870024i | \(-0.664103\pi\) | ||||
−0.493010 | + | 0.870024i | \(0.664103\pi\) | |||||||
\(74\) | −1.20761e12 | −0.854913 | ||||||||
\(75\) | 3.54466e11 | 0.229973 | ||||||||
\(76\) | 3.36029e12 | 2.00027 | ||||||||
\(77\) | −8.93261e11 | −0.488415 | ||||||||
\(78\) | 1.04410e12 | 0.524960 | ||||||||
\(79\) | 1.40738e12 | 0.651383 | 0.325692 | − | 0.945476i | \(-0.394403\pi\) | ||||
0.325692 | + | 0.945476i | \(0.394403\pi\) | |||||||
\(80\) | −9.36772e11 | −0.399530 | ||||||||
\(81\) | −3.01550e12 | −1.18633 | ||||||||
\(82\) | 5.51361e12 | 2.00284 | ||||||||
\(83\) | −1.20424e12 | −0.404303 | −0.202151 | − | 0.979354i | \(-0.564793\pi\) | ||||
−0.202151 | + | 0.979354i | \(0.564793\pi\) | |||||||
\(84\) | 2.58851e12 | 0.803961 | ||||||||
\(85\) | 3.51097e12 | 1.00973 | ||||||||
\(86\) | 2.99163e12 | 0.797386 | ||||||||
\(87\) | 2.86074e12 | 0.707300 | ||||||||
\(88\) | −3.04215e12 | −0.698302 | ||||||||
\(89\) | 3.94850e12 | 0.842165 | 0.421082 | − | 0.907022i | \(-0.361650\pi\) | ||||
0.421082 | + | 0.907022i | \(0.361650\pi\) | |||||||
\(90\) | −5.34160e12 | −1.05949 | ||||||||
\(91\) | −6.01420e11 | −0.111022 | ||||||||
\(92\) | 5.83980e12 | 1.00410 | ||||||||
\(93\) | −5.29293e12 | −0.848314 | ||||||||
\(94\) | 4.48801e12 | 0.671001 | ||||||||
\(95\) | 9.30346e12 | 1.29850 | ||||||||
\(96\) | −1.32090e13 | −1.72229 | ||||||||
\(97\) | 1.10967e13 | 1.35262 | 0.676311 | − | 0.736616i | \(-0.263578\pi\) | ||||
0.676311 | + | 0.736616i | \(0.263578\pi\) | |||||||
\(98\) | 1.10304e13 | 1.25783 | ||||||||
\(99\) | 7.93603e12 | 0.847178 | ||||||||
\(100\) | −2.43264e12 | −0.243264 | ||||||||
\(101\) | 6.50973e12 | 0.610202 | 0.305101 | − | 0.952320i | \(-0.401310\pi\) | ||||
0.305101 | + | 0.952320i | \(0.401310\pi\) | |||||||
\(102\) | 2.59108e13 | 2.27813 | ||||||||
\(103\) | −3.57787e12 | −0.295245 | −0.147623 | − | 0.989044i | \(-0.547162\pi\) | ||||
−0.147623 | + | 0.989044i | \(0.547162\pi\) | |||||||
\(104\) | −2.04824e12 | −0.158732 | ||||||||
\(105\) | 7.16668e12 | 0.521900 | ||||||||
\(106\) | 2.27880e13 | 1.56034 | ||||||||
\(107\) | 3.88532e12 | 0.250284 | 0.125142 | − | 0.992139i | \(-0.460061\pi\) | ||||
0.125142 | + | 0.992139i | \(0.460061\pi\) | |||||||
\(108\) | 7.57105e12 | 0.459094 | ||||||||
\(109\) | 1.78459e13 | 1.01922 | 0.509609 | − | 0.860406i | \(-0.329790\pi\) | ||||
0.509609 | + | 0.860406i | \(0.329790\pi\) | |||||||
\(110\) | −2.94655e13 | −1.58585 | ||||||||
\(111\) | −1.43946e13 | −0.730465 | ||||||||
\(112\) | 3.98220e12 | 0.190637 | ||||||||
\(113\) | −3.60185e13 | −1.62748 | −0.813740 | − | 0.581228i | \(-0.802572\pi\) | ||||
−0.813740 | + | 0.581228i | \(0.802572\pi\) | |||||||
\(114\) | 6.86590e13 | 2.92965 | ||||||||
\(115\) | 1.61683e13 | 0.651822 | ||||||||
\(116\) | −1.96328e13 | −0.748179 | ||||||||
\(117\) | 5.34322e12 | 0.192573 | ||||||||
\(118\) | 4.32399e13 | 1.47452 | ||||||||
\(119\) | −1.49251e13 | −0.481794 | ||||||||
\(120\) | 2.44073e13 | 0.746177 | ||||||||
\(121\) | 9.25421e12 | 0.268061 | ||||||||
\(122\) | 1.86499e13 | 0.512079 | ||||||||
\(123\) | 6.57214e13 | 1.71129 | ||||||||
\(124\) | 3.63245e13 | 0.897344 | ||||||||
\(125\) | −4.55034e13 | −1.06691 | ||||||||
\(126\) | 2.27071e13 | 0.505537 | ||||||||
\(127\) | −4.42550e13 | −0.935919 | −0.467959 | − | 0.883750i | \(-0.655011\pi\) | ||||
−0.467959 | + | 0.883750i | \(0.655011\pi\) | |||||||
\(128\) | 5.67684e13 | 1.14088 | ||||||||
\(129\) | 3.56599e13 | 0.681313 | ||||||||
\(130\) | −1.98387e13 | −0.360480 | ||||||||
\(131\) | −7.50175e13 | −1.29688 | −0.648439 | − | 0.761267i | \(-0.724578\pi\) | ||||
−0.648439 | + | 0.761267i | \(0.724578\pi\) | |||||||
\(132\) | −1.26858e14 | −2.08731 | ||||||||
\(133\) | −3.95489e13 | −0.619581 | ||||||||
\(134\) | 7.35001e13 | 1.09675 | ||||||||
\(135\) | 2.09615e13 | 0.298026 | ||||||||
\(136\) | −5.08299e13 | −0.688836 | ||||||||
\(137\) | −1.03816e14 | −1.34147 | −0.670737 | − | 0.741695i | \(-0.734022\pi\) | ||||
−0.670737 | + | 0.741695i | \(0.734022\pi\) | |||||||
\(138\) | 1.19321e14 | 1.47063 | ||||||||
\(139\) | −1.04040e13 | −0.122351 | −0.0611753 | − | 0.998127i | \(-0.519485\pi\) | ||||
−0.0611753 | + | 0.998127i | \(0.519485\pi\) | |||||||
\(140\) | −4.91838e13 | −0.552064 | ||||||||
\(141\) | 5.34965e13 | 0.573325 | ||||||||
\(142\) | 3.81429e13 | 0.390426 | ||||||||
\(143\) | 2.94744e13 | 0.288244 | ||||||||
\(144\) | −3.53792e13 | −0.330668 | ||||||||
\(145\) | −5.43563e13 | −0.485689 | ||||||||
\(146\) | 1.78776e14 | 1.52762 | ||||||||
\(147\) | 1.31480e14 | 1.07473 | ||||||||
\(148\) | 9.87877e13 | 0.772684 | ||||||||
\(149\) | 1.12802e14 | 0.844513 | 0.422257 | − | 0.906476i | \(-0.361238\pi\) | ||||
0.422257 | + | 0.906476i | \(0.361238\pi\) | |||||||
\(150\) | −4.97048e13 | −0.356292 | ||||||||
\(151\) | 1.03365e14 | 0.709619 | 0.354809 | − | 0.934939i | \(-0.384546\pi\) | ||||
0.354809 | + | 0.934939i | \(0.384546\pi\) | |||||||
\(152\) | −1.34690e14 | −0.885835 | ||||||||
\(153\) | 1.32599e14 | 0.835694 | ||||||||
\(154\) | 1.25257e14 | 0.756690 | ||||||||
\(155\) | 1.00570e14 | 0.582521 | ||||||||
\(156\) | −8.54115e13 | −0.474467 | ||||||||
\(157\) | 1.87835e14 | 1.00099 | 0.500493 | − | 0.865740i | \(-0.333152\pi\) | ||||
0.500493 | + | 0.865740i | \(0.333152\pi\) | |||||||
\(158\) | −1.97350e14 | −1.00917 | ||||||||
\(159\) | 2.71630e14 | 1.33320 | ||||||||
\(160\) | 2.50982e14 | 1.18267 | ||||||||
\(161\) | −6.87313e13 | −0.311019 | ||||||||
\(162\) | 4.22847e14 | 1.83796 | ||||||||
\(163\) | −3.78993e13 | −0.158275 | −0.0791375 | − | 0.996864i | \(-0.525217\pi\) | ||||
−0.0791375 | + | 0.996864i | \(0.525217\pi\) | |||||||
\(164\) | −4.51036e14 | −1.81020 | ||||||||
\(165\) | −3.51224e14 | −1.35500 | ||||||||
\(166\) | 1.68865e14 | 0.626377 | ||||||||
\(167\) | −1.24321e14 | −0.443493 | −0.221746 | − | 0.975104i | \(-0.571176\pi\) | ||||
−0.221746 | + | 0.975104i | \(0.571176\pi\) | |||||||
\(168\) | −1.03755e14 | −0.356040 | ||||||||
\(169\) | −2.83030e14 | −0.934479 | ||||||||
\(170\) | −4.92325e14 | −1.56435 | ||||||||
\(171\) | 3.51365e14 | 1.07469 | ||||||||
\(172\) | −2.44728e14 | −0.720690 | ||||||||
\(173\) | −1.99199e14 | −0.564920 | −0.282460 | − | 0.959279i | \(-0.591150\pi\) | ||||
−0.282460 | + | 0.959279i | \(0.591150\pi\) | |||||||
\(174\) | −4.01146e14 | −1.09580 | ||||||||
\(175\) | 2.86309e13 | 0.0753508 | ||||||||
\(176\) | −1.95160e14 | −0.494946 | ||||||||
\(177\) | 5.15414e14 | 1.25988 | ||||||||
\(178\) | −5.53677e14 | −1.30475 | ||||||||
\(179\) | −2.31982e14 | −0.527119 | −0.263560 | − | 0.964643i | \(-0.584897\pi\) | ||||
−0.263560 | + | 0.964643i | \(0.584897\pi\) | |||||||
\(180\) | 4.36965e14 | 0.957581 | ||||||||
\(181\) | 6.65129e14 | 1.40603 | 0.703016 | − | 0.711174i | \(-0.251836\pi\) | ||||
0.703016 | + | 0.711174i | \(0.251836\pi\) | |||||||
\(182\) | 8.43339e13 | 0.172004 | ||||||||
\(183\) | 2.22304e14 | 0.437537 | ||||||||
\(184\) | −2.34076e14 | −0.444673 | ||||||||
\(185\) | 2.73508e14 | 0.501596 | ||||||||
\(186\) | 7.42199e14 | 1.31427 | ||||||||
\(187\) | 7.31448e14 | 1.25087 | ||||||||
\(188\) | −3.67138e14 | −0.606461 | ||||||||
\(189\) | −8.91072e13 | −0.142204 | ||||||||
\(190\) | −1.30457e15 | −2.01173 | ||||||||
\(191\) | 5.58080e14 | 0.831725 | 0.415862 | − | 0.909428i | \(-0.363480\pi\) | ||||
0.415862 | + | 0.909428i | \(0.363480\pi\) | |||||||
\(192\) | 1.44835e15 | 2.08648 | ||||||||
\(193\) | −1.11274e15 | −1.54979 | −0.774893 | − | 0.632092i | \(-0.782196\pi\) | ||||
−0.774893 | + | 0.632092i | \(0.782196\pi\) | |||||||
\(194\) | −1.55603e15 | −2.09559 | ||||||||
\(195\) | −2.36474e14 | −0.308006 | ||||||||
\(196\) | −9.02329e14 | −1.13684 | ||||||||
\(197\) | −5.84517e13 | −0.0712470 | ||||||||
\(198\) | −1.11283e15 | −1.31251 | ||||||||
\(199\) | −3.09044e14 | −0.352757 | −0.176378 | − | 0.984322i | \(-0.556438\pi\) | ||||
−0.176378 | + | 0.984322i | \(0.556438\pi\) | |||||||
\(200\) | 9.75074e13 | 0.107731 | ||||||||
\(201\) | 8.76111e14 | 0.937097 | ||||||||
\(202\) | −9.12824e14 | −0.945373 | ||||||||
\(203\) | 2.31068e14 | 0.231747 | ||||||||
\(204\) | −2.11961e15 | −2.05901 | ||||||||
\(205\) | −1.24876e15 | −1.17511 | ||||||||
\(206\) | 5.01706e14 | 0.457417 | ||||||||
\(207\) | 6.10632e14 | 0.539476 | ||||||||
\(208\) | −1.31398e14 | −0.112506 | ||||||||
\(209\) | 1.93821e15 | 1.60861 | ||||||||
\(210\) | −1.00494e15 | −0.808568 | ||||||||
\(211\) | −1.10742e15 | −0.863929 | −0.431965 | − | 0.901891i | \(-0.642179\pi\) | ||||
−0.431965 | + | 0.901891i | \(0.642179\pi\) | |||||||
\(212\) | −1.86415e15 | −1.41026 | ||||||||
\(213\) | 4.54657e14 | 0.333593 | ||||||||
\(214\) | −5.44818e14 | −0.387759 | ||||||||
\(215\) | −6.77565e14 | −0.467844 | ||||||||
\(216\) | −3.03469e14 | −0.203313 | ||||||||
\(217\) | −4.27520e14 | −0.277951 | ||||||||
\(218\) | −2.50244e15 | −1.57905 | ||||||||
\(219\) | 2.13098e15 | 1.30525 | ||||||||
\(220\) | 2.41040e15 | 1.43331 | ||||||||
\(221\) | 4.92473e14 | 0.284337 | ||||||||
\(222\) | 2.01847e15 | 1.13169 | ||||||||
\(223\) | −3.14593e14 | −0.171304 | −0.0856520 | − | 0.996325i | \(-0.527297\pi\) | ||||
−0.0856520 | + | 0.996325i | \(0.527297\pi\) | |||||||
\(224\) | −1.06692e15 | −0.564312 | ||||||||
\(225\) | −2.54367e14 | −0.130699 | ||||||||
\(226\) | 5.05068e15 | 2.52142 | ||||||||
\(227\) | 3.77257e14 | 0.183007 | 0.0915037 | − | 0.995805i | \(-0.470833\pi\) | ||||
0.0915037 | + | 0.995805i | \(0.470833\pi\) | |||||||
\(228\) | −5.61658e15 | −2.64786 | ||||||||
\(229\) | 1.98983e15 | 0.911770 | 0.455885 | − | 0.890039i | \(-0.349323\pi\) | ||||
0.455885 | + | 0.890039i | \(0.349323\pi\) | |||||||
\(230\) | −2.26720e15 | −1.00985 | ||||||||
\(231\) | 1.49305e15 | 0.646541 | ||||||||
\(232\) | 7.86940e14 | 0.331337 | ||||||||
\(233\) | −6.03475e14 | −0.247085 | −0.123542 | − | 0.992339i | \(-0.539425\pi\) | ||||
−0.123542 | + | 0.992339i | \(0.539425\pi\) | |||||||
\(234\) | −7.49250e14 | −0.298348 | ||||||||
\(235\) | −1.01647e15 | −0.393691 | ||||||||
\(236\) | −3.53720e15 | −1.33270 | ||||||||
\(237\) | −2.35238e15 | −0.862271 | ||||||||
\(238\) | 2.09286e15 | 0.746433 | ||||||||
\(239\) | 2.10461e14 | 0.0730441 | 0.0365220 | − | 0.999333i | \(-0.488372\pi\) | ||||
0.0365220 | + | 0.999333i | \(0.488372\pi\) | |||||||
\(240\) | 1.56577e15 | 0.528879 | ||||||||
\(241\) | 1.78464e15 | 0.586731 | 0.293365 | − | 0.956000i | \(-0.405225\pi\) | ||||
0.293365 | + | 0.956000i | \(0.405225\pi\) | |||||||
\(242\) | −1.29767e15 | −0.415302 | ||||||||
\(243\) | 3.98799e15 | 1.24255 | ||||||||
\(244\) | −1.52564e15 | −0.462826 | ||||||||
\(245\) | −2.49823e15 | −0.737994 | ||||||||
\(246\) | −9.21576e15 | −2.65126 | ||||||||
\(247\) | 1.30497e15 | 0.365653 | ||||||||
\(248\) | −1.45599e15 | −0.397396 | ||||||||
\(249\) | 2.01284e15 | 0.535197 | ||||||||
\(250\) | 6.38070e15 | 1.65294 | ||||||||
\(251\) | −5.13746e14 | −0.129679 | −0.0648395 | − | 0.997896i | \(-0.520654\pi\) | ||||
−0.0648395 | + | 0.997896i | \(0.520654\pi\) | |||||||
\(252\) | −1.85753e15 | −0.456912 | ||||||||
\(253\) | 3.36838e15 | 0.807491 | ||||||||
\(254\) | 6.20564e15 | 1.45000 | ||||||||
\(255\) | −5.86844e15 | −1.33663 | ||||||||
\(256\) | −8.61804e14 | −0.191359 | ||||||||
\(257\) | 6.08202e15 | 1.31669 | 0.658343 | − | 0.752718i | \(-0.271257\pi\) | ||||
0.658343 | + | 0.752718i | \(0.271257\pi\) | |||||||
\(258\) | −5.00039e15 | −1.05554 | ||||||||
\(259\) | −1.16268e15 | −0.239338 | ||||||||
\(260\) | 1.62288e15 | 0.325807 | ||||||||
\(261\) | −2.05288e15 | −0.401977 | ||||||||
\(262\) | 1.05193e16 | 2.00922 | ||||||||
\(263\) | −9.29108e15 | −1.73123 | −0.865613 | − | 0.500714i | \(-0.833071\pi\) | ||||
−0.865613 | + | 0.500714i | \(0.833071\pi\) | |||||||
\(264\) | 5.08483e15 | 0.924380 | ||||||||
\(265\) | −5.16118e15 | −0.915485 | ||||||||
\(266\) | 5.54572e15 | 0.959903 | ||||||||
\(267\) | −6.59975e15 | −1.11482 | ||||||||
\(268\) | −6.01261e15 | −0.991258 | ||||||||
\(269\) | −1.46786e15 | −0.236208 | −0.118104 | − | 0.993001i | \(-0.537682\pi\) | ||||
−0.118104 | + | 0.993001i | \(0.537682\pi\) | |||||||
\(270\) | −2.93932e15 | −0.461725 | ||||||||
\(271\) | −5.57160e15 | −0.854436 | −0.427218 | − | 0.904149i | \(-0.640506\pi\) | ||||
−0.427218 | + | 0.904149i | \(0.640506\pi\) | |||||||
\(272\) | −3.26083e15 | −0.488237 | ||||||||
\(273\) | 1.00525e15 | 0.146966 | ||||||||
\(274\) | 1.45576e16 | 2.07832 | ||||||||
\(275\) | −1.40314e15 | −0.195632 | ||||||||
\(276\) | −9.76097e15 | −1.32918 | ||||||||
\(277\) | −1.02135e16 | −1.35849 | −0.679243 | − | 0.733913i | \(-0.737692\pi\) | ||||
−0.679243 | + | 0.733913i | \(0.737692\pi\) | |||||||
\(278\) | 1.45890e15 | 0.189555 | ||||||||
\(279\) | 3.79823e15 | 0.482119 | ||||||||
\(280\) | 1.97143e15 | 0.244486 | ||||||||
\(281\) | 1.25359e16 | 1.51903 | 0.759513 | − | 0.650492i | \(-0.225437\pi\) | ||||
0.759513 | + | 0.650492i | \(0.225437\pi\) | |||||||
\(282\) | −7.50152e15 | −0.888240 | ||||||||
\(283\) | −1.06728e16 | −1.23500 | −0.617502 | − | 0.786569i | \(-0.711855\pi\) | ||||
−0.617502 | + | 0.786569i | \(0.711855\pi\) | |||||||
\(284\) | −3.12024e15 | −0.352873 | ||||||||
\(285\) | −1.55503e16 | −1.71889 | ||||||||
\(286\) | −4.13303e15 | −0.446570 | ||||||||
\(287\) | 5.30845e15 | 0.560706 | ||||||||
\(288\) | 9.47886e15 | 0.978824 | ||||||||
\(289\) | 2.31684e15 | 0.233916 | ||||||||
\(290\) | 7.62209e15 | 0.752466 | ||||||||
\(291\) | −1.85476e16 | −1.79054 | ||||||||
\(292\) | −1.46246e16 | −1.38069 | ||||||||
\(293\) | −1.20060e16 | −1.10856 | −0.554279 | − | 0.832331i | \(-0.687006\pi\) | ||||
−0.554279 | + | 0.832331i | \(0.687006\pi\) | |||||||
\(294\) | −1.84368e16 | −1.66505 | ||||||||
\(295\) | −9.79326e15 | −0.865136 | ||||||||
\(296\) | −3.95970e15 | −0.342189 | ||||||||
\(297\) | 4.36696e15 | 0.369201 | ||||||||
\(298\) | −1.58176e16 | −1.30839 | ||||||||
\(299\) | 2.26788e15 | 0.183551 | ||||||||
\(300\) | 4.06606e15 | 0.322022 | ||||||||
\(301\) | 2.88032e15 | 0.223233 | ||||||||
\(302\) | −1.44944e16 | −1.09940 | ||||||||
\(303\) | −1.08807e16 | −0.807757 | ||||||||
\(304\) | −8.64063e15 | −0.627866 | ||||||||
\(305\) | −4.22395e15 | −0.300448 | ||||||||
\(306\) | −1.85937e16 | −1.29472 | ||||||||
\(307\) | −1.38748e16 | −0.945862 | −0.472931 | − | 0.881100i | \(-0.656804\pi\) | ||||
−0.472931 | + | 0.881100i | \(0.656804\pi\) | |||||||
\(308\) | −1.02466e16 | −0.683909 | ||||||||
\(309\) | 5.98026e15 | 0.390832 | ||||||||
\(310\) | −1.41024e16 | −0.902486 | ||||||||
\(311\) | −2.02532e16 | −1.26926 | −0.634630 | − | 0.772816i | \(-0.718848\pi\) | ||||
−0.634630 | + | 0.772816i | \(0.718848\pi\) | |||||||
\(312\) | 3.42354e15 | 0.210121 | ||||||||
\(313\) | 2.26452e16 | 1.36125 | 0.680626 | − | 0.732631i | \(-0.261708\pi\) | ||||
0.680626 | + | 0.732631i | \(0.261708\pi\) | |||||||
\(314\) | −2.63391e16 | −1.55081 | ||||||||
\(315\) | −5.14285e15 | −0.296609 | ||||||||
\(316\) | 1.61440e16 | 0.912107 | ||||||||
\(317\) | −1.44965e16 | −0.802378 | −0.401189 | − | 0.915995i | \(-0.631403\pi\) | ||||
−0.401189 | + | 0.915995i | \(0.631403\pi\) | |||||||
\(318\) | −3.80892e16 | −2.06550 | ||||||||
\(319\) | −1.13242e16 | −0.601681 | ||||||||
\(320\) | −2.75198e16 | −1.43275 | ||||||||
\(321\) | −6.49415e15 | −0.331314 | ||||||||
\(322\) | 9.63782e15 | 0.481854 | ||||||||
\(323\) | 3.23846e16 | 1.58680 | ||||||||
\(324\) | −3.45906e16 | −1.66118 | ||||||||
\(325\) | −9.44715e14 | −0.0444692 | ||||||||
\(326\) | 5.31442e15 | 0.245212 | ||||||||
\(327\) | −2.98287e16 | −1.34919 | ||||||||
\(328\) | 1.80788e16 | 0.801660 | ||||||||
\(329\) | 4.32102e15 | 0.187851 | ||||||||
\(330\) | 4.92503e16 | 2.09927 | ||||||||
\(331\) | 2.35879e16 | 0.985844 | 0.492922 | − | 0.870074i | \(-0.335929\pi\) | ||||
0.492922 | + | 0.870074i | \(0.335929\pi\) | |||||||
\(332\) | −1.38138e16 | −0.566130 | ||||||||
\(333\) | 1.03296e16 | 0.415142 | ||||||||
\(334\) | 1.74328e16 | 0.687093 | ||||||||
\(335\) | −1.66468e16 | −0.643486 | ||||||||
\(336\) | −6.65608e15 | −0.252356 | ||||||||
\(337\) | 1.40141e16 | 0.521158 | 0.260579 | − | 0.965452i | \(-0.416086\pi\) | ||||
0.260579 | + | 0.965452i | \(0.416086\pi\) | |||||||
\(338\) | 3.96878e16 | 1.44777 | ||||||||
\(339\) | 6.02034e16 | 2.15438 | ||||||||
\(340\) | 4.02742e16 | 1.41388 | ||||||||
\(341\) | 2.09519e16 | 0.721639 | ||||||||
\(342\) | −4.92701e16 | −1.66500 | ||||||||
\(343\) | 2.37006e16 | 0.785865 | ||||||||
\(344\) | 9.80940e15 | 0.319163 | ||||||||
\(345\) | −2.70247e16 | −0.862852 | ||||||||
\(346\) | 2.79326e16 | 0.875218 | ||||||||
\(347\) | 4.89592e16 | 1.50554 | 0.752771 | − | 0.658283i | \(-0.228717\pi\) | ||||
0.752771 | + | 0.658283i | \(0.228717\pi\) | |||||||
\(348\) | 3.28154e16 | 0.990404 | ||||||||
\(349\) | 1.69796e16 | 0.502993 | 0.251497 | − | 0.967858i | \(-0.419077\pi\) | ||||
0.251497 | + | 0.967858i | \(0.419077\pi\) | |||||||
\(350\) | −4.01476e15 | −0.116739 | ||||||||
\(351\) | 2.94021e15 | 0.0839232 | ||||||||
\(352\) | 5.22875e16 | 1.46511 | ||||||||
\(353\) | 6.34394e15 | 0.174511 | 0.0872556 | − | 0.996186i | \(-0.472190\pi\) | ||||
0.0872556 | + | 0.996186i | \(0.472190\pi\) | |||||||
\(354\) | −7.22737e16 | −1.95191 | ||||||||
\(355\) | −8.63884e15 | −0.229072 | ||||||||
\(356\) | 4.52930e16 | 1.17925 | ||||||||
\(357\) | 2.49466e16 | 0.637777 | ||||||||
\(358\) | 3.25295e16 | 0.816654 | ||||||||
\(359\) | 6.16263e16 | 1.51933 | 0.759665 | − | 0.650314i | \(-0.225363\pi\) | ||||
0.759665 | + | 0.650314i | \(0.225363\pi\) | |||||||
\(360\) | −1.75148e16 | −0.424072 | ||||||||
\(361\) | 4.37606e16 | 1.04061 | ||||||||
\(362\) | −9.32675e16 | −2.17834 | ||||||||
\(363\) | −1.54680e16 | −0.354847 | ||||||||
\(364\) | −6.89885e15 | −0.155460 | ||||||||
\(365\) | −4.04903e16 | −0.896287 | ||||||||
\(366\) | −3.11725e16 | −0.677867 | ||||||||
\(367\) | −9.13912e16 | −1.95243 | −0.976214 | − | 0.216808i | \(-0.930435\pi\) | ||||
−0.976214 | + | 0.216808i | \(0.930435\pi\) | |||||||
\(368\) | −1.50164e16 | −0.315177 | ||||||||
\(369\) | −4.71620e16 | −0.972571 | ||||||||
\(370\) | −3.83526e16 | −0.777111 | ||||||||
\(371\) | 2.19401e16 | 0.436826 | ||||||||
\(372\) | −6.07149e16 | −1.18786 | ||||||||
\(373\) | −4.21386e16 | −0.810163 | −0.405082 | − | 0.914280i | \(-0.632757\pi\) | ||||
−0.405082 | + | 0.914280i | \(0.632757\pi\) | |||||||
\(374\) | −1.02567e17 | −1.93795 | ||||||||
\(375\) | 7.60570e16 | 1.41233 | ||||||||
\(376\) | 1.47159e16 | 0.268576 | ||||||||
\(377\) | −7.62439e15 | −0.136769 | ||||||||
\(378\) | 1.24950e16 | 0.220313 | ||||||||
\(379\) | −4.93938e16 | −0.856087 | −0.428043 | − | 0.903758i | \(-0.640797\pi\) | ||||
−0.428043 | + | 0.903758i | \(0.640797\pi\) | |||||||
\(380\) | 1.06719e17 | 1.81824 | ||||||||
\(381\) | 7.39703e16 | 1.23893 | ||||||||
\(382\) | −7.82566e16 | −1.28857 | ||||||||
\(383\) | −9.22544e16 | −1.49347 | −0.746733 | − | 0.665124i | \(-0.768379\pi\) | ||||
−0.746733 | + | 0.665124i | \(0.768379\pi\) | |||||||
\(384\) | −9.48859e16 | −1.51025 | ||||||||
\(385\) | −2.83691e16 | −0.443967 | ||||||||
\(386\) | 1.56034e17 | 2.40105 | ||||||||
\(387\) | −2.55897e16 | −0.387208 | ||||||||
\(388\) | 1.27289e17 | 1.89402 | ||||||||
\(389\) | 9.87570e16 | 1.44509 | 0.722546 | − | 0.691323i | \(-0.242972\pi\) | ||||
0.722546 | + | 0.691323i | \(0.242972\pi\) | |||||||
\(390\) | 3.31595e16 | 0.477186 | ||||||||
\(391\) | 5.62807e16 | 0.796545 | ||||||||
\(392\) | 3.61680e16 | 0.503460 | ||||||||
\(393\) | 1.25389e17 | 1.71675 | ||||||||
\(394\) | 8.19637e15 | 0.110381 | ||||||||
\(395\) | 4.46971e16 | 0.592104 | ||||||||
\(396\) | 9.10338e16 | 1.18627 | ||||||||
\(397\) | −3.96288e16 | −0.508011 | −0.254005 | − | 0.967203i | \(-0.581748\pi\) | ||||
−0.254005 | + | 0.967203i | \(0.581748\pi\) | |||||||
\(398\) | 4.33356e16 | 0.546519 | ||||||||
\(399\) | 6.61042e16 | 0.820173 | ||||||||
\(400\) | 6.25528e15 | 0.0763584 | ||||||||
\(401\) | −2.02446e14 | −0.00243148 | −0.00121574 | − | 0.999999i | \(-0.500387\pi\) | ||||
−0.00121574 | + | 0.999999i | \(0.500387\pi\) | |||||||
\(402\) | −1.22852e17 | −1.45182 | ||||||||
\(403\) | 1.41066e16 | 0.164036 | ||||||||
\(404\) | 7.46727e16 | 0.854443 | ||||||||
\(405\) | −9.57692e16 | −1.07837 | ||||||||
\(406\) | −3.24014e16 | −0.359041 | ||||||||
\(407\) | 5.69805e16 | 0.621388 | ||||||||
\(408\) | 8.49600e16 | 0.911850 | ||||||||
\(409\) | 8.76083e16 | 0.925430 | 0.462715 | − | 0.886507i | \(-0.346875\pi\) | ||||
0.462715 | + | 0.886507i | \(0.346875\pi\) | |||||||
\(410\) | 1.75107e17 | 1.82057 | ||||||||
\(411\) | 1.73525e17 | 1.77578 | ||||||||
\(412\) | −4.10416e16 | −0.413421 | ||||||||
\(413\) | 4.16310e16 | 0.412802 | ||||||||
\(414\) | −8.56256e16 | −0.835798 | ||||||||
\(415\) | −3.82456e16 | −0.367509 | ||||||||
\(416\) | 3.52044e16 | 0.333035 | ||||||||
\(417\) | 1.73899e16 | 0.161962 | ||||||||
\(418\) | −2.71785e17 | −2.49218 | ||||||||
\(419\) | −3.36606e16 | −0.303900 | −0.151950 | − | 0.988388i | \(-0.548555\pi\) | ||||
−0.151950 | + | 0.988388i | \(0.548555\pi\) | |||||||
\(420\) | 8.22086e16 | 0.730797 | ||||||||
\(421\) | −1.23424e17 | −1.08036 | −0.540178 | − | 0.841551i | \(-0.681643\pi\) | ||||
−0.540178 | + | 0.841551i | \(0.681643\pi\) | |||||||
\(422\) | 1.55288e17 | 1.33847 | ||||||||
\(423\) | −3.83893e16 | −0.325835 | ||||||||
\(424\) | 7.47207e16 | 0.624544 | ||||||||
\(425\) | −2.34444e16 | −0.192980 | ||||||||
\(426\) | −6.37542e16 | −0.516828 | ||||||||
\(427\) | 1.79559e16 | 0.143360 | ||||||||
\(428\) | 4.45683e16 | 0.350463 | ||||||||
\(429\) | −4.92651e16 | −0.381564 | ||||||||
\(430\) | 9.50113e16 | 0.724820 | ||||||||
\(431\) | −9.22113e16 | −0.692918 | −0.346459 | − | 0.938065i | \(-0.612616\pi\) | ||||
−0.346459 | + | 0.938065i | \(0.612616\pi\) | |||||||
\(432\) | −1.94681e16 | −0.144105 | ||||||||
\(433\) | 1.75215e17 | 1.27762 | 0.638808 | − | 0.769366i | \(-0.279428\pi\) | ||||
0.638808 | + | 0.769366i | \(0.279428\pi\) | |||||||
\(434\) | 5.99489e16 | 0.430624 | ||||||||
\(435\) | 9.08542e16 | 0.642932 | ||||||||
\(436\) | 2.04710e17 | 1.42717 | ||||||||
\(437\) | 1.49134e17 | 1.02435 | ||||||||
\(438\) | −2.98816e17 | −2.02219 | ||||||||
\(439\) | 7.21607e15 | 0.0481151 | 0.0240576 | − | 0.999711i | \(-0.492342\pi\) | ||||
0.0240576 | + | 0.999711i | \(0.492342\pi\) | |||||||
\(440\) | −9.66156e16 | −0.634753 | ||||||||
\(441\) | −9.43510e16 | −0.610795 | ||||||||
\(442\) | −6.90569e16 | −0.440516 | ||||||||
\(443\) | 5.08150e16 | 0.319424 | 0.159712 | − | 0.987164i | \(-0.448943\pi\) | ||||
0.159712 | + | 0.987164i | \(0.448943\pi\) | |||||||
\(444\) | −1.65119e17 | −1.02284 | ||||||||
\(445\) | 1.25400e17 | 0.765524 | ||||||||
\(446\) | 4.41137e16 | 0.265397 | ||||||||
\(447\) | −1.88544e17 | −1.11793 | ||||||||
\(448\) | 1.16986e17 | 0.683639 | ||||||||
\(449\) | −5.14420e15 | −0.0296290 | −0.0148145 | − | 0.999890i | \(-0.504716\pi\) | ||||
−0.0148145 | + | 0.999890i | \(0.504716\pi\) | |||||||
\(450\) | 3.56685e16 | 0.202490 | ||||||||
\(451\) | −2.60156e17 | −1.45575 | ||||||||
\(452\) | −4.13166e17 | −2.27890 | ||||||||
\(453\) | −1.72771e17 | −0.939360 | ||||||||
\(454\) | −5.29007e16 | −0.283529 | ||||||||
\(455\) | −1.91005e16 | −0.100918 | ||||||||
\(456\) | 2.25129e17 | 1.17263 | ||||||||
\(457\) | −1.83536e17 | −0.942465 | −0.471232 | − | 0.882009i | \(-0.656191\pi\) | ||||
−0.471232 | + | 0.882009i | \(0.656191\pi\) | |||||||
\(458\) | −2.79023e17 | −1.41259 | ||||||||
\(459\) | 7.29655e16 | 0.364196 | ||||||||
\(460\) | 1.85466e17 | 0.912722 | ||||||||
\(461\) | 1.48249e17 | 0.719341 | 0.359670 | − | 0.933079i | \(-0.382889\pi\) | ||||
0.359670 | + | 0.933079i | \(0.382889\pi\) | |||||||
\(462\) | −2.09362e17 | −1.00167 | ||||||||
\(463\) | −3.08487e17 | −1.45533 | −0.727664 | − | 0.685933i | \(-0.759394\pi\) | ||||
−0.727664 | + | 0.685933i | \(0.759394\pi\) | |||||||
\(464\) | 5.04836e16 | 0.234846 | ||||||||
\(465\) | −1.68098e17 | −0.771114 | ||||||||
\(466\) | 8.46221e16 | 0.382803 | ||||||||
\(467\) | −9.63205e16 | −0.429694 | −0.214847 | − | 0.976648i | \(-0.568925\pi\) | ||||
−0.214847 | + | 0.976648i | \(0.568925\pi\) | |||||||
\(468\) | 6.12917e16 | 0.269652 | ||||||||
\(469\) | 7.07652e16 | 0.307041 | ||||||||
\(470\) | 1.42535e17 | 0.609937 | ||||||||
\(471\) | −3.13958e17 | −1.32506 | ||||||||
\(472\) | 1.41781e17 | 0.590196 | ||||||||
\(473\) | −1.41158e17 | −0.579575 | ||||||||
\(474\) | 3.29862e17 | 1.33590 | ||||||||
\(475\) | −6.21237e16 | −0.248170 | ||||||||
\(476\) | −1.71205e17 | −0.674638 | ||||||||
\(477\) | −1.94923e17 | −0.757695 | ||||||||
\(478\) | −2.95118e16 | −0.113166 | ||||||||
\(479\) | 1.71642e17 | 0.649297 | 0.324649 | − | 0.945835i | \(-0.394754\pi\) | ||||
0.324649 | + | 0.945835i | \(0.394754\pi\) | |||||||
\(480\) | −4.19505e17 | −1.56556 | ||||||||
\(481\) | 3.83641e16 | 0.141248 | ||||||||
\(482\) | −2.50250e17 | −0.909009 | ||||||||
\(483\) | 1.14881e17 | 0.411712 | ||||||||
\(484\) | 1.06154e17 | 0.375356 | ||||||||
\(485\) | 3.52419e17 | 1.22953 | ||||||||
\(486\) | −5.59215e17 | −1.92505 | ||||||||
\(487\) | −2.36270e17 | −0.802548 | −0.401274 | − | 0.915958i | \(-0.631432\pi\) | ||||
−0.401274 | + | 0.915958i | \(0.631432\pi\) | |||||||
\(488\) | 6.11519e16 | 0.204966 | ||||||||
\(489\) | 6.33471e16 | 0.209517 | ||||||||
\(490\) | 3.50313e17 | 1.14336 | ||||||||
\(491\) | 4.32643e17 | 1.39348 | 0.696738 | − | 0.717325i | \(-0.254634\pi\) | ||||
0.696738 | + | 0.717325i | \(0.254634\pi\) | |||||||
\(492\) | 7.53887e17 | 2.39625 | ||||||||
\(493\) | −1.89210e17 | −0.593525 | ||||||||
\(494\) | −1.82989e17 | −0.566499 | ||||||||
\(495\) | 2.52040e17 | 0.770081 | ||||||||
\(496\) | −9.34046e16 | −0.281668 | ||||||||
\(497\) | 3.67236e16 | 0.109302 | ||||||||
\(498\) | −2.82250e17 | −0.829169 | ||||||||
\(499\) | 2.78328e17 | 0.807056 | 0.403528 | − | 0.914967i | \(-0.367784\pi\) | ||||
0.403528 | + | 0.914967i | \(0.367784\pi\) | |||||||
\(500\) | −5.21967e17 | −1.49396 | ||||||||
\(501\) | 2.07797e17 | 0.587075 | ||||||||
\(502\) | 7.20399e16 | 0.200909 | ||||||||
\(503\) | −1.59643e17 | −0.439499 | −0.219749 | − | 0.975556i | \(-0.570524\pi\) | ||||
−0.219749 | + | 0.975556i | \(0.570524\pi\) | |||||||
\(504\) | 7.44552e16 | 0.202347 | ||||||||
\(505\) | 2.06742e17 | 0.554671 | ||||||||
\(506\) | −4.72330e17 | −1.25103 | ||||||||
\(507\) | 4.73073e17 | 1.23702 | ||||||||
\(508\) | −5.07646e17 | −1.31053 | ||||||||
\(509\) | −3.21473e17 | −0.819369 | −0.409684 | − | 0.912227i | \(-0.634361\pi\) | ||||
−0.409684 | + | 0.912227i | \(0.634361\pi\) | |||||||
\(510\) | 8.22900e17 | 2.07081 | ||||||||
\(511\) | 1.72124e17 | 0.427666 | ||||||||
\(512\) | −3.44200e17 | −0.844417 | ||||||||
\(513\) | 1.93346e17 | 0.468351 | ||||||||
\(514\) | −8.52849e17 | −2.03991 | ||||||||
\(515\) | −1.13630e17 | −0.268377 | ||||||||
\(516\) | 4.09052e17 | 0.954016 | ||||||||
\(517\) | −2.11764e17 | −0.487713 | ||||||||
\(518\) | 1.63036e17 | 0.370801 | ||||||||
\(519\) | 3.32952e17 | 0.747815 | ||||||||
\(520\) | −6.50499e16 | −0.144286 | ||||||||
\(521\) | −1.35189e17 | −0.296140 | −0.148070 | − | 0.988977i | \(-0.547306\pi\) | ||||
−0.148070 | + | 0.988977i | \(0.547306\pi\) | |||||||
\(522\) | 2.87865e17 | 0.622773 | ||||||||
\(523\) | 3.80866e17 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(524\) | −8.60522e17 | −1.81597 | ||||||||
\(525\) | −4.78553e16 | −0.0997459 | ||||||||
\(526\) | 1.30284e18 | 2.68215 | ||||||||
\(527\) | 3.50075e17 | 0.711857 | ||||||||
\(528\) | 3.26201e17 | 0.655186 | ||||||||
\(529\) | −2.44859e17 | −0.485796 | ||||||||
\(530\) | 7.23725e17 | 1.41834 | ||||||||
\(531\) | −3.69864e17 | −0.716023 | ||||||||
\(532\) | −4.53663e17 | −0.867576 | ||||||||
\(533\) | −1.75159e17 | −0.330908 | ||||||||
\(534\) | 9.25447e17 | 1.72716 | ||||||||
\(535\) | 1.23394e17 | 0.227507 | ||||||||
\(536\) | 2.41003e17 | 0.438986 | ||||||||
\(537\) | 3.87748e17 | 0.697776 | ||||||||
\(538\) | 2.05830e17 | 0.365953 | ||||||||
\(539\) | −5.20461e17 | −0.914242 | ||||||||
\(540\) | 2.40449e17 | 0.417314 | ||||||||
\(541\) | −5.22071e17 | −0.895256 | −0.447628 | − | 0.894220i | \(-0.647731\pi\) | ||||
−0.447628 | + | 0.894220i | \(0.647731\pi\) | |||||||
\(542\) | 7.81276e17 | 1.32376 | ||||||||
\(543\) | −1.11174e18 | −1.86124 | ||||||||
\(544\) | 8.73647e17 | 1.44525 | ||||||||
\(545\) | 5.66769e17 | 0.926464 | ||||||||
\(546\) | −1.40960e17 | −0.227691 | ||||||||
\(547\) | −1.46225e17 | −0.233401 | −0.116701 | − | 0.993167i | \(-0.537232\pi\) | ||||
−0.116701 | + | 0.993167i | \(0.537232\pi\) | |||||||
\(548\) | −1.19087e18 | −1.87841 | ||||||||
\(549\) | −1.59527e17 | −0.248664 | ||||||||
\(550\) | 1.96755e17 | 0.303088 | ||||||||
\(551\) | −5.01373e17 | −0.763266 | ||||||||
\(552\) | 3.91248e17 | 0.588638 | ||||||||
\(553\) | −1.90007e17 | −0.282524 | ||||||||
\(554\) | 1.43218e18 | 2.10467 | ||||||||
\(555\) | −4.57157e17 | −0.663989 | ||||||||
\(556\) | −1.19344e17 | −0.171323 | ||||||||
\(557\) | −4.99226e17 | −0.708334 | −0.354167 | − | 0.935182i | \(-0.615236\pi\) | ||||
−0.354167 | + | 0.935182i | \(0.615236\pi\) | |||||||
\(558\) | −5.32606e17 | −0.746936 | ||||||||
\(559\) | −9.50399e16 | −0.131744 | ||||||||
\(560\) | 1.26471e17 | 0.173288 | ||||||||
\(561\) | −1.22258e18 | −1.65585 | ||||||||
\(562\) | −1.75785e18 | −2.35339 | ||||||||
\(563\) | −2.77688e17 | −0.367496 | −0.183748 | − | 0.982973i | \(-0.558823\pi\) | ||||
−0.183748 | + | 0.982973i | \(0.558823\pi\) | |||||||
\(564\) | 6.13655e17 | 0.802805 | ||||||||
\(565\) | −1.14391e18 | −1.47937 | ||||||||
\(566\) | 1.49660e18 | 1.91336 | ||||||||
\(567\) | 4.07113e17 | 0.514547 | ||||||||
\(568\) | 1.25068e17 | 0.156273 | ||||||||
\(569\) | −6.91353e17 | −0.854024 | −0.427012 | − | 0.904246i | \(-0.640434\pi\) | ||||
−0.427012 | + | 0.904246i | \(0.640434\pi\) | |||||||
\(570\) | 2.18054e18 | 2.66304 | ||||||||
\(571\) | 1.30435e16 | 0.0157492 | 0.00787461 | − | 0.999969i | \(-0.497493\pi\) | ||||
0.00787461 | + | 0.999969i | \(0.497493\pi\) | |||||||
\(572\) | 3.38099e17 | 0.403617 | ||||||||
\(573\) | −9.32807e17 | −1.10100 | ||||||||
\(574\) | −7.44375e17 | −0.868690 | ||||||||
\(575\) | −1.07964e17 | −0.124577 | ||||||||
\(576\) | −1.03934e18 | −1.18580 | ||||||||
\(577\) | 1.28416e18 | 1.44869 | 0.724345 | − | 0.689438i | \(-0.242142\pi\) | ||||
0.724345 | + | 0.689438i | \(0.242142\pi\) | |||||||
\(578\) | −3.24878e17 | −0.362401 | ||||||||
\(579\) | 1.85990e18 | 2.05154 | ||||||||
\(580\) | −6.23518e17 | −0.680091 | ||||||||
\(581\) | 1.62581e17 | 0.175358 | ||||||||
\(582\) | 2.60083e18 | 2.77404 | ||||||||
\(583\) | −1.07524e18 | −1.13412 | ||||||||
\(584\) | 5.86195e17 | 0.611447 | ||||||||
\(585\) | 1.69695e17 | 0.175048 | ||||||||
\(586\) | 1.68354e18 | 1.71747 | ||||||||
\(587\) | 1.70835e17 | 0.172357 | 0.0861786 | − | 0.996280i | \(-0.472534\pi\) | ||||
0.0861786 | + | 0.996280i | \(0.472534\pi\) | |||||||
\(588\) | 1.50820e18 | 1.50490 | ||||||||
\(589\) | 9.27638e17 | 0.915439 | ||||||||
\(590\) | 1.37326e18 | 1.34034 | ||||||||
\(591\) | 9.76996e16 | 0.0943135 | ||||||||
\(592\) | −2.54022e17 | −0.242538 | ||||||||
\(593\) | 5.64393e17 | 0.532999 | 0.266499 | − | 0.963835i | \(-0.414133\pi\) | ||||
0.266499 | + | 0.963835i | \(0.414133\pi\) | |||||||
\(594\) | −6.12355e17 | −0.571994 | ||||||||
\(595\) | −4.74006e17 | −0.437949 | ||||||||
\(596\) | 1.29395e18 | 1.18254 | ||||||||
\(597\) | 5.16554e17 | 0.466963 | ||||||||
\(598\) | −3.18013e17 | −0.284372 | ||||||||
\(599\) | −9.10814e17 | −0.805667 | −0.402833 | − | 0.915273i | \(-0.631975\pi\) | ||||
−0.402833 | + | 0.915273i | \(0.631975\pi\) | |||||||
\(600\) | −1.62979e17 | −0.142610 | ||||||||
\(601\) | −1.48131e18 | −1.28222 | −0.641109 | − | 0.767450i | \(-0.721525\pi\) | ||||
−0.641109 | + | 0.767450i | \(0.721525\pi\) | |||||||
\(602\) | −4.03891e17 | −0.345850 | ||||||||
\(603\) | −6.28702e17 | −0.532577 | ||||||||
\(604\) | 1.18570e18 | 0.993652 | ||||||||
\(605\) | 2.93904e17 | 0.243667 | ||||||||
\(606\) | 1.52575e18 | 1.25144 | ||||||||
\(607\) | −1.87906e18 | −1.52481 | −0.762403 | − | 0.647102i | \(-0.775981\pi\) | ||||
−0.762403 | + | 0.647102i | \(0.775981\pi\) | |||||||
\(608\) | 2.31501e18 | 1.85857 | ||||||||
\(609\) | −3.86220e17 | −0.306777 | ||||||||
\(610\) | 5.92302e17 | 0.465478 | ||||||||
\(611\) | −1.42578e17 | −0.110862 | ||||||||
\(612\) | 1.52104e18 | 1.17019 | ||||||||
\(613\) | 7.24602e17 | 0.551578 | 0.275789 | − | 0.961218i | \(-0.411061\pi\) | ||||
0.275789 | + | 0.961218i | \(0.411061\pi\) | |||||||
\(614\) | 1.94559e18 | 1.46540 | ||||||||
\(615\) | 2.08725e18 | 1.55555 | ||||||||
\(616\) | 4.10711e17 | 0.302874 | ||||||||
\(617\) | 2.58867e17 | 0.188896 | 0.0944481 | − | 0.995530i | \(-0.469891\pi\) | ||||
0.0944481 | + | 0.995530i | \(0.469891\pi\) | |||||||
\(618\) | −8.38580e17 | −0.605507 | ||||||||
\(619\) | −7.66455e17 | −0.547643 | −0.273822 | − | 0.961781i | \(-0.588288\pi\) | ||||
−0.273822 | + | 0.961781i | \(0.588288\pi\) | |||||||
\(620\) | 1.15363e18 | 0.815681 | ||||||||
\(621\) | 3.36012e17 | 0.235104 | ||||||||
\(622\) | 2.83999e18 | 1.96644 | ||||||||
\(623\) | −5.33075e17 | −0.365271 | ||||||||
\(624\) | 2.19626e17 | 0.148931 | ||||||||
\(625\) | −1.18627e18 | −0.796091 | ||||||||
\(626\) | −3.17542e18 | −2.10896 | ||||||||
\(627\) | −3.23963e18 | −2.12940 | ||||||||
\(628\) | 2.15464e18 | 1.40164 | ||||||||
\(629\) | 9.52060e17 | 0.612964 | ||||||||
\(630\) | 7.21154e17 | 0.459530 | ||||||||
\(631\) | −3.29066e17 | −0.207536 | −0.103768 | − | 0.994602i | \(-0.533090\pi\) | ||||
−0.103768 | + | 0.994602i | \(0.533090\pi\) | |||||||
\(632\) | −6.47099e17 | −0.403933 | ||||||||
\(633\) | 1.85101e18 | 1.14363 | ||||||||
\(634\) | 2.03277e18 | 1.24311 | ||||||||
\(635\) | −1.40549e18 | −0.850745 | ||||||||
\(636\) | 3.11585e18 | 1.86684 | ||||||||
\(637\) | −3.50419e17 | −0.207817 | ||||||||
\(638\) | 1.58793e18 | 0.932171 | ||||||||
\(639\) | −3.26264e17 | −0.189589 | ||||||||
\(640\) | 1.80291e18 | 1.03706 | ||||||||
\(641\) | −1.29971e18 | −0.740063 | −0.370032 | − | 0.929019i | \(-0.620653\pi\) | ||||
−0.370032 | + | 0.929019i | \(0.620653\pi\) | |||||||
\(642\) | 9.10639e17 | 0.513297 | ||||||||
\(643\) | 2.63085e18 | 1.46800 | 0.733998 | − | 0.679152i | \(-0.237652\pi\) | ||||
0.733998 | + | 0.679152i | \(0.237652\pi\) | |||||||
\(644\) | −7.88413e17 | −0.435508 | ||||||||
\(645\) | 1.13252e18 | 0.619310 | ||||||||
\(646\) | −4.54112e18 | −2.45839 | ||||||||
\(647\) | −5.10620e17 | −0.273666 | −0.136833 | − | 0.990594i | \(-0.543692\pi\) | ||||
−0.136833 | + | 0.990594i | \(0.543692\pi\) | |||||||
\(648\) | 1.38649e18 | 0.735665 | ||||||||
\(649\) | −2.04025e18 | −1.07175 | ||||||||
\(650\) | 1.32472e17 | 0.0688951 | ||||||||
\(651\) | 7.14582e17 | 0.367939 | ||||||||
\(652\) | −4.34741e17 | −0.221626 | ||||||||
\(653\) | 3.87962e18 | 1.95818 | 0.979091 | − | 0.203422i | \(-0.0652063\pi\) | ||||
0.979091 | + | 0.203422i | \(0.0652063\pi\) | |||||||
\(654\) | 4.18272e18 | 2.09027 | ||||||||
\(655\) | −2.38248e18 | −1.17886 | ||||||||
\(656\) | 1.15979e18 | 0.568204 | ||||||||
\(657\) | −1.52920e18 | −0.741806 | ||||||||
\(658\) | −6.05913e17 | −0.291033 | ||||||||
\(659\) | −3.20815e18 | −1.52581 | −0.762903 | − | 0.646513i | \(-0.776227\pi\) | ||||
−0.762903 | + | 0.646513i | \(0.776227\pi\) | |||||||
\(660\) | −4.02887e18 | −1.89735 | ||||||||
\(661\) | 4.53145e17 | 0.211314 | 0.105657 | − | 0.994403i | \(-0.466306\pi\) | ||||
0.105657 | + | 0.994403i | \(0.466306\pi\) | |||||||
\(662\) | −3.30761e18 | −1.52735 | ||||||||
\(663\) | −8.23148e17 | −0.376392 | ||||||||
\(664\) | 5.53698e17 | 0.250715 | ||||||||
\(665\) | −1.25603e18 | −0.563196 | ||||||||
\(666\) | −1.44847e18 | −0.643171 | ||||||||
\(667\) | −8.71328e17 | −0.383146 | ||||||||
\(668\) | −1.42608e18 | −0.621006 | ||||||||
\(669\) | 5.25829e17 | 0.226764 | ||||||||
\(670\) | 2.33429e18 | 0.996939 | ||||||||
\(671\) | −8.79984e17 | −0.372202 | ||||||||
\(672\) | 1.78331e18 | 0.747010 | ||||||||
\(673\) | −9.76762e17 | −0.405220 | −0.202610 | − | 0.979260i | \(-0.564942\pi\) | ||||
−0.202610 | + | 0.979260i | \(0.564942\pi\) | |||||||
\(674\) | −1.96512e18 | −0.807419 | ||||||||
\(675\) | −1.39970e17 | −0.0569589 | ||||||||
\(676\) | −3.24663e18 | −1.30852 | ||||||||
\(677\) | −2.03337e18 | −0.811692 | −0.405846 | − | 0.913942i | \(-0.633023\pi\) | ||||
−0.405846 | + | 0.913942i | \(0.633023\pi\) | |||||||
\(678\) | −8.44200e18 | −3.33774 | ||||||||
\(679\) | −1.49813e18 | −0.586672 | ||||||||
\(680\) | −1.61431e18 | −0.626149 | ||||||||
\(681\) | −6.30568e17 | −0.242257 | ||||||||
\(682\) | −2.93797e18 | −1.11802 | ||||||||
\(683\) | −4.56778e18 | −1.72175 | −0.860876 | − | 0.508816i | \(-0.830084\pi\) | ||||
−0.860876 | + | 0.508816i | \(0.830084\pi\) | |||||||
\(684\) | 4.03049e18 | 1.50485 | ||||||||
\(685\) | −3.29710e18 | −1.21939 | ||||||||
\(686\) | −3.32341e18 | −1.21752 | ||||||||
\(687\) | −3.32592e18 | −1.20696 | ||||||||
\(688\) | 6.29291e17 | 0.226218 | ||||||||
\(689\) | −7.23943e17 | −0.257798 | ||||||||
\(690\) | 3.78953e18 | 1.33680 | ||||||||
\(691\) | 5.08266e18 | 1.77617 | 0.888083 | − | 0.459683i | \(-0.152037\pi\) | ||||
0.888083 | + | 0.459683i | \(0.152037\pi\) | |||||||
\(692\) | −2.28500e18 | −0.791036 | ||||||||
\(693\) | −1.07142e18 | −0.367446 | ||||||||
\(694\) | −6.86528e18 | −2.33250 | ||||||||
\(695\) | −3.30422e17 | −0.111216 | ||||||||
\(696\) | −1.31534e18 | −0.438608 | ||||||||
\(697\) | −4.34683e18 | −1.43602 | ||||||||
\(698\) | −2.38096e18 | −0.779277 | ||||||||
\(699\) | 1.00868e18 | 0.327079 | ||||||||
\(700\) | 3.28424e17 | 0.105511 | ||||||||
\(701\) | 1.72071e18 | 0.547697 | 0.273848 | − | 0.961773i | \(-0.411703\pi\) | ||||
0.273848 | + | 0.961773i | \(0.411703\pi\) | |||||||
\(702\) | −4.12290e17 | −0.130020 | ||||||||
\(703\) | 2.52279e18 | 0.788264 | ||||||||
\(704\) | −5.73325e18 | −1.77492 | ||||||||
\(705\) | 1.69899e18 | 0.521150 | ||||||||
\(706\) | −8.89576e17 | −0.270366 | ||||||||
\(707\) | −8.78858e17 | −0.264663 | ||||||||
\(708\) | 5.91228e18 | 1.76416 | ||||||||
\(709\) | 1.83559e18 | 0.542720 | 0.271360 | − | 0.962478i | \(-0.412527\pi\) | ||||
0.271360 | + | 0.962478i | \(0.412527\pi\) | |||||||
\(710\) | 1.21138e18 | 0.354896 | ||||||||
\(711\) | 1.68808e18 | 0.490051 | ||||||||
\(712\) | −1.81547e18 | −0.522240 | ||||||||
\(713\) | 1.61213e18 | 0.459534 | ||||||||
\(714\) | −3.49813e18 | −0.988093 | ||||||||
\(715\) | 9.36076e17 | 0.262012 | ||||||||
\(716\) | −2.66105e18 | −0.738105 | ||||||||
\(717\) | −3.51776e17 | −0.0966924 | ||||||||
\(718\) | −8.64153e18 | −2.35387 | ||||||||
\(719\) | 6.61710e18 | 1.78620 | 0.893099 | − | 0.449859i | \(-0.148526\pi\) | ||||
0.893099 | + | 0.449859i | \(0.148526\pi\) | |||||||
\(720\) | −1.12361e18 | −0.300575 | ||||||||
\(721\) | 4.83038e17 | 0.128057 | ||||||||
\(722\) | −6.13631e18 | −1.61219 | ||||||||
\(723\) | −2.98294e18 | −0.776687 | ||||||||
\(724\) | 7.62966e18 | 1.96881 | ||||||||
\(725\) | 3.62963e17 | 0.0928251 | ||||||||
\(726\) | 2.16900e18 | 0.549757 | ||||||||
\(727\) | −7.10273e18 | −1.78423 | −0.892116 | − | 0.451806i | \(-0.850780\pi\) | ||||
−0.892116 | + | 0.451806i | \(0.850780\pi\) | |||||||
\(728\) | 2.76526e17 | 0.0688465 | ||||||||
\(729\) | −1.85808e18 | −0.458496 | ||||||||
\(730\) | 5.67774e18 | 1.38860 | ||||||||
\(731\) | −2.35855e18 | −0.571718 | ||||||||
\(732\) | 2.55004e18 | 0.612667 | ||||||||
\(733\) | −1.94777e18 | −0.463832 | −0.231916 | − | 0.972736i | \(-0.574499\pi\) | ||||
−0.231916 | + | 0.972736i | \(0.574499\pi\) | |||||||
\(734\) | 1.28153e19 | 3.02485 | ||||||||
\(735\) | 4.17568e18 | 0.976922 | ||||||||
\(736\) | 4.02322e18 | 0.932971 | ||||||||
\(737\) | −3.46806e18 | −0.797164 | ||||||||
\(738\) | 6.61328e18 | 1.50678 | ||||||||
\(739\) | −6.56867e18 | −1.48350 | −0.741752 | − | 0.670674i | \(-0.766005\pi\) | ||||
−0.741752 | + | 0.670674i | \(0.766005\pi\) | |||||||
\(740\) | 3.13740e18 | 0.702366 | ||||||||
\(741\) | −2.18120e18 | −0.484035 | ||||||||
\(742\) | −3.07654e18 | −0.676765 | ||||||||
\(743\) | −3.26392e18 | −0.711726 | −0.355863 | − | 0.934538i | \(-0.615813\pi\) | ||||
−0.355863 | + | 0.934538i | \(0.615813\pi\) | |||||||
\(744\) | 2.43363e18 | 0.526054 | ||||||||
\(745\) | 3.58248e18 | 0.767658 | ||||||||
\(746\) | 5.90887e18 | 1.25517 | ||||||||
\(747\) | −1.44443e18 | −0.304166 | ||||||||
\(748\) | 8.39040e18 | 1.75155 | ||||||||
\(749\) | −5.24545e17 | −0.108555 | ||||||||
\(750\) | −1.06651e19 | −2.18809 | ||||||||
\(751\) | −8.54318e18 | −1.73764 | −0.868821 | − | 0.495127i | \(-0.835122\pi\) | ||||
−0.868821 | + | 0.495127i | \(0.835122\pi\) | |||||||
\(752\) | 9.44055e17 | 0.190362 | ||||||||
\(753\) | 8.58705e17 | 0.171663 | ||||||||
\(754\) | 1.06913e18 | 0.211892 | ||||||||
\(755\) | 3.28278e18 | 0.645040 | ||||||||
\(756\) | −1.02214e18 | −0.199122 | ||||||||
\(757\) | −3.28203e18 | −0.633898 | −0.316949 | − | 0.948443i | \(-0.602658\pi\) | ||||
−0.316949 | + | 0.948443i | \(0.602658\pi\) | |||||||
\(758\) | 6.92623e18 | 1.32632 | ||||||||
\(759\) | −5.63011e18 | −1.06892 | ||||||||
\(760\) | −4.27763e18 | −0.805220 | ||||||||
\(761\) | 7.20733e18 | 1.34516 | 0.672580 | − | 0.740024i | \(-0.265186\pi\) | ||||
0.672580 | + | 0.740024i | \(0.265186\pi\) | |||||||
\(762\) | −1.03725e19 | −1.91944 | ||||||||
\(763\) | −2.40932e18 | −0.442065 | ||||||||
\(764\) | 6.40171e18 | 1.16463 | ||||||||
\(765\) | 4.21122e18 | 0.759642 | ||||||||
\(766\) | 1.29363e19 | 2.31379 | ||||||||
\(767\) | −1.37367e18 | −0.243620 | ||||||||
\(768\) | 1.44047e18 | 0.253312 | ||||||||
\(769\) | 2.30431e18 | 0.401809 | 0.200904 | − | 0.979611i | \(-0.435612\pi\) | ||||
0.200904 | + | 0.979611i | \(0.435612\pi\) | |||||||
\(770\) | 3.97804e18 | 0.687828 | ||||||||
\(771\) | −1.01658e19 | −1.74297 | ||||||||
\(772\) | −1.27642e19 | −2.17011 | ||||||||
\(773\) | −7.52594e17 | −0.126880 | −0.0634401 | − | 0.997986i | \(-0.520207\pi\) | ||||
−0.0634401 | + | 0.997986i | \(0.520207\pi\) | |||||||
\(774\) | 3.58831e18 | 0.599892 | ||||||||
\(775\) | −6.71552e17 | −0.111332 | ||||||||
\(776\) | −5.10212e18 | −0.838783 | ||||||||
\(777\) | 1.94337e18 | 0.316824 | ||||||||
\(778\) | −1.38482e19 | −2.23885 | ||||||||
\(779\) | −1.15183e19 | −1.84670 | ||||||||
\(780\) | −2.71258e18 | −0.431289 | ||||||||
\(781\) | −1.79975e18 | −0.283779 | ||||||||
\(782\) | −7.89194e18 | −1.23407 | ||||||||
\(783\) | −1.12964e18 | −0.175182 | ||||||||
\(784\) | 2.32024e18 | 0.356844 | ||||||||
\(785\) | 5.96544e18 | 0.909892 | ||||||||
\(786\) | −1.75826e19 | −2.65972 | ||||||||
\(787\) | −6.55210e18 | −0.982980 | −0.491490 | − | 0.870883i | \(-0.663548\pi\) | ||||
−0.491490 | + | 0.870883i | \(0.663548\pi\) | |||||||
\(788\) | −6.70496e17 | −0.0997645 | ||||||||
\(789\) | 1.55296e19 | 2.29172 | ||||||||
\(790\) | −6.26763e18 | −0.917334 | ||||||||
\(791\) | 4.86275e18 | 0.705886 | ||||||||
\(792\) | −3.64890e18 | −0.525349 | ||||||||
\(793\) | −5.92480e17 | −0.0846054 | ||||||||
\(794\) | 5.55694e18 | 0.787050 | ||||||||
\(795\) | 8.62670e18 | 1.21188 | ||||||||
\(796\) | −3.54503e18 | −0.493952 | ||||||||
\(797\) | 7.85344e18 | 1.08538 | 0.542689 | − | 0.839934i | \(-0.317406\pi\) | ||||
0.542689 | + | 0.839934i | \(0.317406\pi\) | |||||||
\(798\) | −9.26944e18 | −1.27068 | ||||||||
\(799\) | −3.53827e18 | −0.481101 | ||||||||
\(800\) | −1.67592e18 | −0.226032 | ||||||||
\(801\) | 4.73601e18 | 0.633580 | ||||||||
\(802\) | 2.83879e16 | 0.00376704 | ||||||||
\(803\) | −8.43542e18 | −1.11034 | ||||||||
\(804\) | 1.00498e19 | 1.31218 | ||||||||
\(805\) | −2.18284e18 | −0.282714 | ||||||||
\(806\) | −1.97809e18 | −0.254138 | ||||||||
\(807\) | 2.45347e18 | 0.312682 | ||||||||
\(808\) | −2.99310e18 | −0.378397 | ||||||||
\(809\) | −1.88785e18 | −0.236757 | −0.118378 | − | 0.992969i | \(-0.537770\pi\) | ||||
−0.118378 | + | 0.992969i | \(0.537770\pi\) | |||||||
\(810\) | 1.34292e19 | 1.67070 | ||||||||
\(811\) | −6.01258e18 | −0.742037 | −0.371018 | − | 0.928625i | \(-0.620991\pi\) | ||||
−0.371018 | + | 0.928625i | \(0.620991\pi\) | |||||||
\(812\) | 2.65056e18 | 0.324507 | ||||||||
\(813\) | 9.31270e18 | 1.13106 | ||||||||
\(814\) | −7.99007e18 | −0.962702 | ||||||||
\(815\) | −1.20364e18 | −0.143871 | ||||||||
\(816\) | 5.45034e18 | 0.646305 | ||||||||
\(817\) | −6.24974e18 | −0.735223 | ||||||||
\(818\) | −1.22848e19 | −1.43375 | ||||||||
\(819\) | −7.21371e17 | −0.0835244 | ||||||||
\(820\) | −1.43244e19 | −1.64546 | ||||||||
\(821\) | −3.43222e18 | −0.391151 | −0.195575 | − | 0.980689i | \(-0.562657\pi\) | ||||
−0.195575 | + | 0.980689i | \(0.562657\pi\) | |||||||
\(822\) | −2.43324e19 | −2.75118 | ||||||||
\(823\) | −1.57612e19 | −1.76803 | −0.884014 | − | 0.467461i | \(-0.845169\pi\) | ||||
−0.884014 | + | 0.467461i | \(0.845169\pi\) | |||||||
\(824\) | 1.64507e18 | 0.183086 | ||||||||
\(825\) | 2.34529e18 | 0.258968 | ||||||||
\(826\) | −5.83769e18 | −0.639544 | ||||||||
\(827\) | 1.12764e19 | 1.22570 | 0.612851 | − | 0.790198i | \(-0.290023\pi\) | ||||
0.612851 | + | 0.790198i | \(0.290023\pi\) | |||||||
\(828\) | 7.00452e18 | 0.755408 | ||||||||
\(829\) | 7.10256e18 | 0.759994 | 0.379997 | − | 0.924988i | \(-0.375925\pi\) | ||||
0.379997 | + | 0.924988i | \(0.375925\pi\) | |||||||
\(830\) | 5.36297e18 | 0.569374 | ||||||||
\(831\) | 1.70714e19 | 1.79830 | ||||||||
\(832\) | −3.86011e18 | −0.403458 | ||||||||
\(833\) | −8.69614e18 | −0.901849 | ||||||||
\(834\) | −2.43849e18 | −0.250924 | ||||||||
\(835\) | −3.94830e18 | −0.403133 | ||||||||
\(836\) | 2.22331e19 | 2.25247 | ||||||||
\(837\) | 2.09005e18 | 0.210108 | ||||||||
\(838\) | 4.72005e18 | 0.470826 | ||||||||
\(839\) | 4.43372e18 | 0.438850 | 0.219425 | − | 0.975629i | \(-0.429582\pi\) | ||||
0.219425 | + | 0.975629i | \(0.429582\pi\) | |||||||
\(840\) | −3.29516e18 | −0.323639 | ||||||||
\(841\) | −7.33131e18 | −0.714509 | ||||||||
\(842\) | 1.73071e19 | 1.67377 | ||||||||
\(843\) | −2.09533e19 | −2.01082 | ||||||||
\(844\) | −1.27032e19 | −1.20973 | ||||||||
\(845\) | −8.98876e18 | −0.849437 | ||||||||
\(846\) | 5.38313e18 | 0.504810 | ||||||||
\(847\) | −1.24938e18 | −0.116266 | ||||||||
\(848\) | 4.79347e18 | 0.442667 | ||||||||
\(849\) | 1.78392e19 | 1.63484 | ||||||||
\(850\) | 3.28749e18 | 0.298979 | ||||||||
\(851\) | 4.38432e18 | 0.395695 | ||||||||
\(852\) | 5.21535e18 | 0.467117 | ||||||||
\(853\) | 9.43072e18 | 0.838255 | 0.419127 | − | 0.907927i | \(-0.362336\pi\) | ||||
0.419127 | + | 0.907927i | \(0.362336\pi\) | |||||||
\(854\) | −2.51786e18 | −0.222104 | ||||||||
\(855\) | 1.11590e19 | 0.976890 | ||||||||
\(856\) | −1.78643e18 | −0.155205 | ||||||||
\(857\) | 1.19757e19 | 1.03258 | 0.516292 | − | 0.856413i | \(-0.327312\pi\) | ||||
0.516292 | + | 0.856413i | \(0.327312\pi\) | |||||||
\(858\) | 6.90819e18 | 0.591148 | ||||||||
\(859\) | 1.78274e19 | 1.51403 | 0.757013 | − | 0.653400i | \(-0.226658\pi\) | ||||
0.757013 | + | 0.653400i | \(0.226658\pi\) | |||||||
\(860\) | −7.77231e18 | −0.655104 | ||||||||
\(861\) | −8.87285e18 | −0.742237 | ||||||||
\(862\) | 1.29303e19 | 1.07352 | ||||||||
\(863\) | −5.36874e17 | −0.0442387 | −0.0221193 | − | 0.999755i | \(-0.507041\pi\) | ||||
−0.0221193 | + | 0.999755i | \(0.507041\pi\) | |||||||
\(864\) | 5.21593e18 | 0.426572 | ||||||||
\(865\) | −6.32635e18 | −0.513510 | ||||||||
\(866\) | −2.45695e19 | −1.97938 | ||||||||
\(867\) | −3.87250e18 | −0.309647 | ||||||||
\(868\) | −4.90406e18 | −0.389204 | ||||||||
\(869\) | 9.31183e18 | 0.733511 | ||||||||
\(870\) | −1.27400e19 | −0.996080 | ||||||||
\(871\) | −2.33499e18 | −0.181204 | ||||||||
\(872\) | −8.20536e18 | −0.632034 | ||||||||
\(873\) | 1.33099e19 | 1.01761 | ||||||||
\(874\) | −2.09123e19 | −1.58700 | ||||||||
\(875\) | 6.14328e18 | 0.462751 | ||||||||
\(876\) | 2.44444e19 | 1.82769 | ||||||||
\(877\) | −2.07348e19 | −1.53887 | −0.769435 | − | 0.638725i | \(-0.779462\pi\) | ||||
−0.769435 | + | 0.638725i | \(0.779462\pi\) | |||||||
\(878\) | −1.01187e18 | −0.0745437 | ||||||||
\(879\) | 2.00675e19 | 1.46746 | ||||||||
\(880\) | −6.19807e18 | −0.449903 | ||||||||
\(881\) | 1.03039e19 | 0.742435 | 0.371217 | − | 0.928546i | \(-0.378940\pi\) | ||||
0.371217 | + | 0.928546i | \(0.378940\pi\) | |||||||
\(882\) | 1.32303e19 | 0.946292 | ||||||||
\(883\) | 1.57010e19 | 1.11476 | 0.557381 | − | 0.830257i | \(-0.311806\pi\) | ||||
0.557381 | + | 0.830257i | \(0.311806\pi\) | |||||||
\(884\) | 5.64913e18 | 0.398146 | ||||||||
\(885\) | 1.63690e19 | 1.14523 | ||||||||
\(886\) | −7.12551e18 | −0.494877 | ||||||||
\(887\) | −7.12346e18 | −0.491120 | −0.245560 | − | 0.969381i | \(-0.578972\pi\) | ||||
−0.245560 | + | 0.969381i | \(0.578972\pi\) | |||||||
\(888\) | 6.61846e18 | 0.452974 | ||||||||
\(889\) | 5.97473e18 | 0.405935 | ||||||||
\(890\) | −1.75842e19 | −1.18601 | ||||||||
\(891\) | −1.99518e19 | −1.33591 | ||||||||
\(892\) | −3.60868e18 | −0.239870 | ||||||||
\(893\) | −9.37579e18 | −0.618690 | ||||||||
\(894\) | 2.64385e19 | 1.73198 | ||||||||
\(895\) | −7.36750e18 | −0.479149 | ||||||||
\(896\) | −7.66412e18 | −0.494835 | ||||||||
\(897\) | −3.79067e18 | −0.242977 | ||||||||
\(898\) | 7.21344e17 | 0.0459036 | ||||||||
\(899\) | −5.41981e18 | −0.342410 | ||||||||
\(900\) | −2.91782e18 | −0.183013 | ||||||||
\(901\) | −1.79657e19 | −1.11875 | ||||||||
\(902\) | 3.64803e19 | 2.25536 | ||||||||
\(903\) | −4.81433e18 | −0.295505 | ||||||||
\(904\) | 1.65609e19 | 1.00923 | ||||||||
\(905\) | 2.11238e19 | 1.27808 | ||||||||
\(906\) | 2.42267e19 | 1.45533 | ||||||||
\(907\) | 1.29043e19 | 0.769641 | 0.384820 | − | 0.922991i | \(-0.374263\pi\) | ||||
0.384820 | + | 0.922991i | \(0.374263\pi\) | |||||||
\(908\) | 4.32749e18 | 0.256258 | ||||||||
\(909\) | 7.80807e18 | 0.459069 | ||||||||
\(910\) | 2.67836e18 | 0.156351 | ||||||||
\(911\) | 5.82587e18 | 0.337669 | 0.168834 | − | 0.985644i | \(-0.446000\pi\) | ||||
0.168834 | + | 0.985644i | \(0.446000\pi\) | |||||||
\(912\) | 1.44424e19 | 0.831140 | ||||||||
\(913\) | −7.96777e18 | −0.455278 | ||||||||
\(914\) | 2.57362e19 | 1.46014 | ||||||||
\(915\) | 7.06015e18 | 0.397719 | ||||||||
\(916\) | 2.28252e19 | 1.27672 | ||||||||
\(917\) | 1.01279e19 | 0.562494 | ||||||||
\(918\) | −1.02316e19 | −0.564241 | ||||||||
\(919\) | 2.39241e19 | 1.31004 | 0.655020 | − | 0.755612i | \(-0.272660\pi\) | ||||
0.655020 | + | 0.755612i | \(0.272660\pi\) | |||||||
\(920\) | −7.43402e18 | −0.404206 | ||||||||
\(921\) | 2.31912e19 | 1.25209 | ||||||||
\(922\) | −2.07881e19 | −1.11446 | ||||||||
\(923\) | −1.21174e18 | −0.0645059 | ||||||||
\(924\) | 1.71267e19 | 0.905326 | ||||||||
\(925\) | −1.82634e18 | −0.0958653 | ||||||||
\(926\) | 4.32575e19 | 2.25471 | ||||||||
\(927\) | −4.29147e18 | −0.222120 | ||||||||
\(928\) | −1.35257e19 | −0.695179 | ||||||||
\(929\) | −2.55828e19 | −1.30571 | −0.652853 | − | 0.757484i | \(-0.726428\pi\) | ||||
−0.652853 | + | 0.757484i | \(0.726428\pi\) | |||||||
\(930\) | 2.35715e19 | 1.19467 | ||||||||
\(931\) | −2.30432e19 | −1.15977 | ||||||||
\(932\) | −6.92243e18 | −0.345983 | ||||||||
\(933\) | 3.38523e19 | 1.68019 | ||||||||
\(934\) | 1.35065e19 | 0.665715 | ||||||||
\(935\) | 2.32300e19 | 1.13704 | ||||||||
\(936\) | −2.45675e18 | −0.119417 | ||||||||
\(937\) | −2.52399e18 | −0.121837 | −0.0609187 | − | 0.998143i | \(-0.519403\pi\) | ||||
−0.0609187 | + | 0.998143i | \(0.519403\pi\) | |||||||
\(938\) | −9.92302e18 | −0.475692 | ||||||||
\(939\) | −3.78505e19 | −1.80196 | ||||||||
\(940\) | −1.16599e19 | −0.551270 | ||||||||
\(941\) | −4.79789e18 | −0.225278 | −0.112639 | − | 0.993636i | \(-0.535930\pi\) | ||||
−0.112639 | + | 0.993636i | \(0.535930\pi\) | |||||||
\(942\) | 4.40246e19 | 2.05289 | ||||||||
\(943\) | −2.00175e19 | −0.927010 | ||||||||
\(944\) | 9.09553e18 | 0.418321 | ||||||||
\(945\) | −2.82995e18 | −0.129263 | ||||||||
\(946\) | 1.97939e19 | 0.897922 | ||||||||
\(947\) | 3.39201e19 | 1.52821 | 0.764103 | − | 0.645094i | \(-0.223182\pi\) | ||||
0.764103 | + | 0.645094i | \(0.223182\pi\) | |||||||
\(948\) | −2.69840e19 | −1.20740 | ||||||||
\(949\) | −5.67945e18 | −0.252392 | ||||||||
\(950\) | 8.71127e18 | 0.384484 | ||||||||
\(951\) | 2.42303e19 | 1.06215 | ||||||||
\(952\) | 6.86238e18 | 0.298769 | ||||||||
\(953\) | −2.25875e19 | −0.976709 | −0.488354 | − | 0.872645i | \(-0.662403\pi\) | ||||
−0.488354 | + | 0.872645i | \(0.662403\pi\) | |||||||
\(954\) | 2.73330e19 | 1.17388 | ||||||||
\(955\) | 1.77241e19 | 0.756034 | ||||||||
\(956\) | 2.41419e18 | 0.102281 | ||||||||
\(957\) | 1.89278e19 | 0.796477 | ||||||||
\(958\) | −2.40685e19 | −1.00594 | ||||||||
\(959\) | 1.40159e19 | 0.581836 | ||||||||
\(960\) | 4.59981e19 | 1.89660 | ||||||||
\(961\) | −1.43898e19 | −0.589324 | ||||||||
\(962\) | −5.37960e18 | −0.218832 | ||||||||
\(963\) | 4.66023e18 | 0.188294 | ||||||||
\(964\) | 2.04714e19 | 0.821576 | ||||||||
\(965\) | −3.53395e19 | −1.40875 | ||||||||
\(966\) | −1.61092e19 | −0.637856 | ||||||||
\(967\) | 2.54682e19 | 1.00167 | 0.500837 | − | 0.865542i | \(-0.333026\pi\) | ||||
0.500837 | + | 0.865542i | \(0.333026\pi\) | |||||||
\(968\) | −4.25498e18 | −0.166229 | ||||||||
\(969\) | −5.41295e19 | −2.10053 | ||||||||
\(970\) | −4.94178e19 | −1.90488 | ||||||||
\(971\) | 2.13048e19 | 0.815740 | 0.407870 | − | 0.913040i | \(-0.366272\pi\) | ||||
0.407870 | + | 0.913040i | \(0.366272\pi\) | |||||||
\(972\) | 4.57461e19 | 1.73989 | ||||||||
\(973\) | 1.40462e18 | 0.0530670 | ||||||||
\(974\) | 3.31309e19 | 1.24337 | ||||||||
\(975\) | 1.57905e18 | 0.0588662 | ||||||||
\(976\) | 3.92301e18 | 0.145277 | ||||||||
\(977\) | 1.69605e19 | 0.623912 | 0.311956 | − | 0.950097i | \(-0.399016\pi\) | ||||
0.311956 | + | 0.950097i | \(0.399016\pi\) | |||||||
\(978\) | −8.88283e18 | −0.324600 | ||||||||
\(979\) | 2.61249e19 | 0.948347 | ||||||||
\(980\) | −2.86571e19 | −1.03338 | ||||||||
\(981\) | 2.14052e19 | 0.766781 | ||||||||
\(982\) | −6.06672e19 | −2.15888 | ||||||||
\(983\) | −4.25684e18 | −0.150484 | −0.0752419 | − | 0.997165i | \(-0.523973\pi\) | ||||
−0.0752419 | + | 0.997165i | \(0.523973\pi\) | |||||||
\(984\) | −3.02180e19 | −1.06120 | ||||||||
\(985\) | −1.85637e18 | −0.0647632 | ||||||||
\(986\) | 2.65319e19 | 0.919535 | ||||||||
\(987\) | −7.22239e18 | −0.248668 | ||||||||
\(988\) | 1.49692e19 | 0.512010 | ||||||||
\(989\) | −1.08613e19 | −0.369069 | ||||||||
\(990\) | −3.53423e19 | −1.19307 | ||||||||
\(991\) | 4.55047e18 | 0.152608 | 0.0763041 | − | 0.997085i | \(-0.475688\pi\) | ||||
0.0763041 | + | 0.997085i | \(0.475688\pi\) | |||||||
\(992\) | 2.50251e19 | 0.833777 | ||||||||
\(993\) | −3.94262e19 | −1.30501 | ||||||||
\(994\) | −5.14955e18 | −0.169339 | ||||||||
\(995\) | −9.81493e18 | −0.320654 | ||||||||
\(996\) | 2.30892e19 | 0.749416 | ||||||||
\(997\) | 4.92378e19 | 1.58774 | 0.793872 | − | 0.608085i | \(-0.208062\pi\) | ||||
0.793872 | + | 0.608085i | \(0.208062\pi\) | |||||||
\(998\) | −3.90285e19 | −1.25035 | ||||||||
\(999\) | 5.68408e18 | 0.180919 |
(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 | 197.14.a.a.1.15 | ✓ | 104 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
197.14.a.a.1.15 | ✓ | 104 | 1.1 | even | 1 | trivial |