Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,28,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 28, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 28);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 28 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(13.8556672451\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{30001}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 7500 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-86.1040\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 21703.1 | 1.87334 | 0.936671 | − | 0.350212i | \(-0.113890\pi\) | ||||
0.936671 | + | 0.350212i | \(0.113890\pi\) | |||||||
\(3\) | −1.59432e6 | −0.577350 | ||||||||
\(4\) | 3.36807e8 | 2.50941 | ||||||||
\(5\) | −6.93920e8 | −0.254223 | −0.127111 | − | 0.991888i | \(-0.540571\pi\) | ||||
−0.127111 | + | 0.991888i | \(0.540571\pi\) | |||||||
\(6\) | −3.46018e10 | −1.08157 | ||||||||
\(7\) | 3.81056e11 | 1.48650 | 0.743250 | − | 0.669014i | \(-0.233283\pi\) | ||||
0.743250 | + | 0.669014i | \(0.233283\pi\) | |||||||
\(8\) | 4.39681e12 | 2.82763 | ||||||||
\(9\) | 2.54187e12 | 0.333333 | ||||||||
\(10\) | −1.50602e13 | −0.476246 | ||||||||
\(11\) | 1.26337e14 | 1.10339 | 0.551697 | − | 0.834045i | \(-0.313981\pi\) | ||||
0.551697 | + | 0.834045i | \(0.313981\pi\) | |||||||
\(12\) | −5.36979e14 | −1.44881 | ||||||||
\(13\) | −1.31606e15 | −1.20515 | −0.602574 | − | 0.798063i | \(-0.705858\pi\) | ||||
−0.602574 | + | 0.798063i | \(0.705858\pi\) | |||||||
\(14\) | 8.27009e15 | 2.78472 | ||||||||
\(15\) | 1.10633e15 | 0.146776 | ||||||||
\(16\) | 5.02190e16 | 2.78772 | ||||||||
\(17\) | −3.53536e16 | −0.865711 | −0.432855 | − | 0.901463i | \(-0.642494\pi\) | ||||
−0.432855 | + | 0.901463i | \(0.642494\pi\) | |||||||
\(18\) | 5.51664e16 | 0.624447 | ||||||||
\(19\) | 8.65178e16 | 0.471989 | 0.235994 | − | 0.971754i | \(-0.424165\pi\) | ||||
0.235994 | + | 0.971754i | \(0.424165\pi\) | |||||||
\(20\) | −2.33717e17 | −0.637948 | ||||||||
\(21\) | −6.07526e17 | −0.858231 | ||||||||
\(22\) | 2.74191e18 | 2.06703 | ||||||||
\(23\) | 5.10955e17 | 0.211376 | 0.105688 | − | 0.994399i | \(-0.466295\pi\) | ||||
0.105688 | + | 0.994399i | \(0.466295\pi\) | |||||||
\(24\) | −7.00994e18 | −1.63254 | ||||||||
\(25\) | −6.96906e18 | −0.935371 | ||||||||
\(26\) | −2.85626e19 | −2.25765 | ||||||||
\(27\) | −4.05256e18 | −0.192450 | ||||||||
\(28\) | 1.28342e20 | 3.73023 | ||||||||
\(29\) | −2.74961e19 | −0.497620 | −0.248810 | − | 0.968552i | \(-0.580039\pi\) | ||||
−0.248810 | + | 0.968552i | \(0.580039\pi\) | |||||||
\(30\) | 2.40109e19 | 0.274961 | ||||||||
\(31\) | −9.77996e19 | −0.719373 | −0.359687 | − | 0.933073i | \(-0.617116\pi\) | ||||
−0.359687 | + | 0.933073i | \(0.617116\pi\) | |||||||
\(32\) | 4.99779e20 | 2.39471 | ||||||||
\(33\) | −2.01422e20 | −0.637044 | ||||||||
\(34\) | −7.67282e20 | −1.62177 | ||||||||
\(35\) | −2.64422e20 | −0.377902 | ||||||||
\(36\) | 8.56118e20 | 0.836469 | ||||||||
\(37\) | −1.80293e21 | −1.21690 | −0.608450 | − | 0.793592i | \(-0.708208\pi\) | ||||
−0.608450 | + | 0.793592i | \(0.708208\pi\) | |||||||
\(38\) | 1.87770e21 | 0.884196 | ||||||||
\(39\) | 2.09822e21 | 0.695793 | ||||||||
\(40\) | −3.05104e21 | −0.718849 | ||||||||
\(41\) | −5.17966e21 | −0.874419 | −0.437209 | − | 0.899360i | \(-0.644033\pi\) | ||||
−0.437209 | + | 0.899360i | \(0.644033\pi\) | |||||||
\(42\) | −1.31852e22 | −1.60776 | ||||||||
\(43\) | 8.74613e21 | 0.776233 | 0.388116 | − | 0.921610i | \(-0.373126\pi\) | ||||
0.388116 | + | 0.921610i | \(0.373126\pi\) | |||||||
\(44\) | 4.25513e22 | 2.76886 | ||||||||
\(45\) | −1.76385e21 | −0.0847409 | ||||||||
\(46\) | 1.10893e22 | 0.395980 | ||||||||
\(47\) | 2.51817e22 | 0.672611 | 0.336306 | − | 0.941753i | \(-0.390823\pi\) | ||||
0.336306 | + | 0.941753i | \(0.390823\pi\) | |||||||
\(48\) | −8.00654e22 | −1.60949 | ||||||||
\(49\) | 7.94910e22 | 1.20968 | ||||||||
\(50\) | −1.51250e23 | −1.75227 | ||||||||
\(51\) | 5.63650e22 | 0.499818 | ||||||||
\(52\) | −4.43258e23 | −3.02421 | ||||||||
\(53\) | 2.11957e23 | 1.11821 | 0.559106 | − | 0.829096i | \(-0.311144\pi\) | ||||
0.559106 | + | 0.829096i | \(0.311144\pi\) | |||||||
\(54\) | −8.79530e22 | −0.360525 | ||||||||
\(55\) | −8.76680e22 | −0.280508 | ||||||||
\(56\) | 1.67543e24 | 4.20328 | ||||||||
\(57\) | −1.37937e23 | −0.272503 | ||||||||
\(58\) | −5.96750e23 | −0.932212 | ||||||||
\(59\) | −7.00844e23 | −0.869199 | −0.434600 | − | 0.900624i | \(-0.643110\pi\) | ||||
−0.434600 | + | 0.900624i | \(0.643110\pi\) | |||||||
\(60\) | 3.72620e23 | 0.368320 | ||||||||
\(61\) | 1.08505e23 | 0.0858020 | 0.0429010 | − | 0.999079i | \(-0.486340\pi\) | ||||
0.0429010 | + | 0.999079i | \(0.486340\pi\) | |||||||
\(62\) | −2.12256e24 | −1.34763 | ||||||||
\(63\) | 9.68592e23 | 0.495500 | ||||||||
\(64\) | 4.10646e24 | 1.69839 | ||||||||
\(65\) | 9.13240e23 | 0.306376 | ||||||||
\(66\) | −4.37149e24 | −1.19340 | ||||||||
\(67\) | 2.46540e24 | 0.549387 | 0.274693 | − | 0.961532i | \(-0.411424\pi\) | ||||
0.274693 | + | 0.961532i | \(0.411424\pi\) | |||||||
\(68\) | −1.19073e25 | −2.17242 | ||||||||
\(69\) | −8.14627e23 | −0.122038 | ||||||||
\(70\) | −5.73878e24 | −0.707939 | ||||||||
\(71\) | 1.29459e25 | 1.31870 | 0.659349 | − | 0.751837i | \(-0.270832\pi\) | ||||
0.659349 | + | 0.751837i | \(0.270832\pi\) | |||||||
\(72\) | 1.11761e25 | 0.942545 | ||||||||
\(73\) | 7.46465e24 | 0.522577 | 0.261289 | − | 0.965261i | \(-0.415853\pi\) | ||||
0.261289 | + | 0.965261i | \(0.415853\pi\) | |||||||
\(74\) | −3.91291e25 | −2.27967 | ||||||||
\(75\) | 1.11109e25 | 0.540037 | ||||||||
\(76\) | 2.91398e25 | 1.18441 | ||||||||
\(77\) | 4.81415e25 | 1.64019 | ||||||||
\(78\) | 4.55380e25 | 1.30346 | ||||||||
\(79\) | −4.94644e25 | −1.19214 | −0.596070 | − | 0.802933i | \(-0.703272\pi\) | ||||
−0.596070 | + | 0.802933i | \(0.703272\pi\) | |||||||
\(80\) | −3.48480e25 | −0.708701 | ||||||||
\(81\) | 6.46108e24 | 0.111111 | ||||||||
\(82\) | −1.12415e26 | −1.63808 | ||||||||
\(83\) | −5.54332e25 | −0.685828 | −0.342914 | − | 0.939367i | \(-0.611414\pi\) | ||||
−0.342914 | + | 0.939367i | \(0.611414\pi\) | |||||||
\(84\) | −2.04619e26 | −2.15365 | ||||||||
\(85\) | 2.45325e25 | 0.220083 | ||||||||
\(86\) | 1.89818e26 | 1.45415 | ||||||||
\(87\) | 4.38376e25 | 0.287301 | ||||||||
\(88\) | 5.55481e26 | 3.11999 | ||||||||
\(89\) | −1.32973e26 | −0.641206 | −0.320603 | − | 0.947214i | \(-0.603886\pi\) | ||||
−0.320603 | + | 0.947214i | \(0.603886\pi\) | |||||||
\(90\) | −3.82811e25 | −0.158749 | ||||||||
\(91\) | −5.01492e26 | −1.79145 | ||||||||
\(92\) | 1.72093e26 | 0.530430 | ||||||||
\(93\) | 1.55924e26 | 0.415330 | ||||||||
\(94\) | 5.46521e26 | 1.26003 | ||||||||
\(95\) | −6.00364e25 | −0.119990 | ||||||||
\(96\) | −7.96808e26 | −1.38259 | ||||||||
\(97\) | −1.06222e27 | −1.60249 | −0.801243 | − | 0.598339i | \(-0.795827\pi\) | ||||
−0.801243 | + | 0.598339i | \(0.795827\pi\) | |||||||
\(98\) | 1.72520e27 | 2.26615 | ||||||||
\(99\) | 3.21132e26 | 0.367798 | ||||||||
\(100\) | −2.34723e27 | −2.34723 | ||||||||
\(101\) | 1.74011e27 | 1.52138 | 0.760691 | − | 0.649114i | \(-0.224860\pi\) | ||||
0.760691 | + | 0.649114i | \(0.224860\pi\) | |||||||
\(102\) | 1.22330e27 | 0.936330 | ||||||||
\(103\) | 4.99563e26 | 0.335187 | 0.167594 | − | 0.985856i | \(-0.446400\pi\) | ||||
0.167594 | + | 0.985856i | \(0.446400\pi\) | |||||||
\(104\) | −5.78647e27 | −3.40772 | ||||||||
\(105\) | 4.21574e26 | 0.218182 | ||||||||
\(106\) | 4.60013e27 | 2.09479 | ||||||||
\(107\) | −1.30395e27 | −0.523096 | −0.261548 | − | 0.965190i | \(-0.584233\pi\) | ||||
−0.261548 | + | 0.965190i | \(0.584233\pi\) | |||||||
\(108\) | −1.36493e27 | −0.482936 | ||||||||
\(109\) | −5.74920e27 | −1.79618 | −0.898089 | − | 0.439814i | \(-0.855044\pi\) | ||||
−0.898089 | + | 0.439814i | \(0.855044\pi\) | |||||||
\(110\) | −1.90267e27 | −0.525486 | ||||||||
\(111\) | 2.87445e27 | 0.702578 | ||||||||
\(112\) | 1.91362e28 | 4.14394 | ||||||||
\(113\) | 8.29240e27 | 1.59265 | 0.796326 | − | 0.604867i | \(-0.206774\pi\) | ||||
0.796326 | + | 0.604867i | \(0.206774\pi\) | |||||||
\(114\) | −2.99367e27 | −0.510491 | ||||||||
\(115\) | −3.54562e26 | −0.0537367 | ||||||||
\(116\) | −9.26087e27 | −1.24873 | ||||||||
\(117\) | −3.34525e27 | −0.401716 | ||||||||
\(118\) | −1.52105e28 | −1.62831 | ||||||||
\(119\) | −1.34717e28 | −1.28688 | ||||||||
\(120\) | 4.86434e27 | 0.415028 | ||||||||
\(121\) | 2.85111e27 | 0.217476 | ||||||||
\(122\) | 2.35490e27 | 0.160736 | ||||||||
\(123\) | 8.25805e27 | 0.504846 | ||||||||
\(124\) | −3.29396e28 | −1.80520 | ||||||||
\(125\) | 1.00061e28 | 0.492015 | ||||||||
\(126\) | 2.10215e28 | 0.928240 | ||||||||
\(127\) | 2.16098e27 | 0.0857631 | 0.0428815 | − | 0.999080i | \(-0.486346\pi\) | ||||
0.0428815 | + | 0.999080i | \(0.486346\pi\) | |||||||
\(128\) | 2.20438e28 | 0.786957 | ||||||||
\(129\) | −1.39442e28 | −0.448158 | ||||||||
\(130\) | 1.98202e28 | 0.573947 | ||||||||
\(131\) | 7.19824e28 | 1.87959 | 0.939797 | − | 0.341734i | \(-0.111014\pi\) | ||||
0.939797 | + | 0.341734i | \(0.111014\pi\) | |||||||
\(132\) | −6.78405e28 | −1.59860 | ||||||||
\(133\) | 3.29681e28 | 0.701611 | ||||||||
\(134\) | 5.35069e28 | 1.02919 | ||||||||
\(135\) | 2.81215e27 | 0.0489252 | ||||||||
\(136\) | −1.55443e29 | −2.44791 | ||||||||
\(137\) | −8.23477e28 | −1.17469 | −0.587346 | − | 0.809336i | \(-0.699827\pi\) | ||||
−0.587346 | + | 0.809336i | \(0.699827\pi\) | |||||||
\(138\) | −1.76799e28 | −0.228619 | ||||||||
\(139\) | 1.17233e29 | 1.37515 | 0.687574 | − | 0.726114i | \(-0.258676\pi\) | ||||
0.687574 | + | 0.726114i | \(0.258676\pi\) | |||||||
\(140\) | −8.90592e28 | −0.948310 | ||||||||
\(141\) | −4.01478e28 | −0.388332 | ||||||||
\(142\) | 2.80967e29 | 2.47037 | ||||||||
\(143\) | −1.66267e29 | −1.32975 | ||||||||
\(144\) | 1.27650e29 | 0.929239 | ||||||||
\(145\) | 1.90801e28 | 0.126506 | ||||||||
\(146\) | 1.62006e29 | 0.978966 | ||||||||
\(147\) | −1.26734e29 | −0.698410 | ||||||||
\(148\) | −6.07239e29 | −3.05370 | ||||||||
\(149\) | −2.66795e28 | −0.122508 | −0.0612538 | − | 0.998122i | \(-0.519510\pi\) | ||||
−0.0612538 | + | 0.998122i | \(0.519510\pi\) | |||||||
\(150\) | 2.41142e29 | 1.01167 | ||||||||
\(151\) | −4.49422e29 | −1.72372 | −0.861859 | − | 0.507149i | \(-0.830699\pi\) | ||||
−0.861859 | + | 0.507149i | \(0.830699\pi\) | |||||||
\(152\) | 3.80403e29 | 1.33461 | ||||||||
\(153\) | −8.98640e28 | −0.288570 | ||||||||
\(154\) | 1.04482e30 | 3.07264 | ||||||||
\(155\) | 6.78651e28 | 0.182881 | ||||||||
\(156\) | 7.06697e29 | 1.74603 | ||||||||
\(157\) | 2.00427e29 | 0.454268 | 0.227134 | − | 0.973864i | \(-0.427065\pi\) | ||||
0.227134 | + | 0.973864i | \(0.427065\pi\) | |||||||
\(158\) | −1.07353e30 | −2.23328 | ||||||||
\(159\) | −3.37928e29 | −0.645600 | ||||||||
\(160\) | −3.46806e29 | −0.608790 | ||||||||
\(161\) | 1.94702e29 | 0.314211 | ||||||||
\(162\) | 1.40226e29 | 0.208149 | ||||||||
\(163\) | 6.62774e29 | 0.905384 | 0.452692 | − | 0.891667i | \(-0.350464\pi\) | ||||
0.452692 | + | 0.891667i | \(0.350464\pi\) | |||||||
\(164\) | −1.74455e30 | −2.19427 | ||||||||
\(165\) | 1.39771e29 | 0.161951 | ||||||||
\(166\) | −1.20307e30 | −1.28479 | ||||||||
\(167\) | 1.07500e30 | 1.05861 | 0.529307 | − | 0.848431i | \(-0.322452\pi\) | ||||
0.529307 | + | 0.848431i | \(0.322452\pi\) | |||||||
\(168\) | −2.67118e30 | −2.42676 | ||||||||
\(169\) | 5.39481e29 | 0.452382 | ||||||||
\(170\) | 5.32432e29 | 0.412291 | ||||||||
\(171\) | 2.19917e29 | 0.157330 | ||||||||
\(172\) | 2.94576e30 | 1.94788 | ||||||||
\(173\) | 8.13189e29 | 0.497244 | 0.248622 | − | 0.968601i | \(-0.420022\pi\) | ||||
0.248622 | + | 0.968601i | \(0.420022\pi\) | |||||||
\(174\) | 9.51413e29 | 0.538213 | ||||||||
\(175\) | −2.65560e30 | −1.39043 | ||||||||
\(176\) | 6.34454e30 | 3.07595 | ||||||||
\(177\) | 1.11737e30 | 0.501832 | ||||||||
\(178\) | −2.88592e30 | −1.20120 | ||||||||
\(179\) | 1.37936e30 | 0.532305 | 0.266152 | − | 0.963931i | \(-0.414248\pi\) | ||||
0.266152 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(180\) | −5.94077e29 | −0.212649 | ||||||||
\(181\) | −1.97778e30 | −0.656927 | −0.328464 | − | 0.944517i | \(-0.606531\pi\) | ||||
−0.328464 | + | 0.944517i | \(0.606531\pi\) | |||||||
\(182\) | −1.08839e31 | −3.35600 | ||||||||
\(183\) | −1.72992e29 | −0.0495378 | ||||||||
\(184\) | 2.24657e30 | 0.597695 | ||||||||
\(185\) | 1.25109e30 | 0.309364 | ||||||||
\(186\) | 3.38404e30 | 0.778056 | ||||||||
\(187\) | −4.46647e30 | −0.955219 | ||||||||
\(188\) | 8.48137e30 | 1.68785 | ||||||||
\(189\) | −1.54425e30 | −0.286077 | ||||||||
\(190\) | −1.30298e30 | −0.224783 | ||||||||
\(191\) | 8.23146e30 | 1.32290 | 0.661449 | − | 0.749990i | \(-0.269942\pi\) | ||||
0.661449 | + | 0.749990i | \(0.269942\pi\) | |||||||
\(192\) | −6.54702e30 | −0.980567 | ||||||||
\(193\) | −2.63632e30 | −0.368107 | −0.184054 | − | 0.982916i | \(-0.558922\pi\) | ||||
−0.184054 | + | 0.982916i | \(0.558922\pi\) | |||||||
\(194\) | −2.30534e31 | −3.00200 | ||||||||
\(195\) | −1.45600e30 | −0.176886 | ||||||||
\(196\) | 2.67731e31 | 3.03558 | ||||||||
\(197\) | 9.66937e30 | 1.02354 | 0.511769 | − | 0.859123i | \(-0.328990\pi\) | ||||
0.511769 | + | 0.859123i | \(0.328990\pi\) | |||||||
\(198\) | 6.96957e30 | 0.689011 | ||||||||
\(199\) | −8.33709e30 | −0.770012 | −0.385006 | − | 0.922914i | \(-0.625801\pi\) | ||||
−0.385006 | + | 0.922914i | \(0.625801\pi\) | |||||||
\(200\) | −3.06416e31 | −2.64489 | ||||||||
\(201\) | −3.93065e30 | −0.317189 | ||||||||
\(202\) | 3.77658e31 | 2.85007 | ||||||||
\(203\) | −1.04775e31 | −0.739712 | ||||||||
\(204\) | 1.89841e31 | 1.25425 | ||||||||
\(205\) | 3.59427e30 | 0.222297 | ||||||||
\(206\) | 1.08421e31 | 0.627920 | ||||||||
\(207\) | 1.29878e30 | 0.0704588 | ||||||||
\(208\) | −6.60913e31 | −3.35961 | ||||||||
\(209\) | 1.09304e31 | 0.520789 | ||||||||
\(210\) | 9.14947e30 | 0.408729 | ||||||||
\(211\) | 1.34579e31 | 0.563850 | 0.281925 | − | 0.959437i | \(-0.409027\pi\) | ||||
0.281925 | + | 0.959437i | \(0.409027\pi\) | |||||||
\(212\) | 7.13887e31 | 2.80605 | ||||||||
\(213\) | −2.06400e31 | −0.761351 | ||||||||
\(214\) | −2.82998e31 | −0.979937 | ||||||||
\(215\) | −6.06912e30 | −0.197336 | ||||||||
\(216\) | −1.78183e31 | −0.544178 | ||||||||
\(217\) | −3.72671e31 | −1.06935 | ||||||||
\(218\) | −1.24775e32 | −3.36485 | ||||||||
\(219\) | −1.19011e31 | −0.301710 | ||||||||
\(220\) | −2.95272e31 | −0.703908 | ||||||||
\(221\) | 4.65274e31 | 1.04331 | ||||||||
\(222\) | 6.23845e31 | 1.31617 | ||||||||
\(223\) | 7.20166e30 | 0.142994 | 0.0714969 | − | 0.997441i | \(-0.477222\pi\) | ||||
0.0714969 | + | 0.997441i | \(0.477222\pi\) | |||||||
\(224\) | 1.90443e32 | 3.55974 | ||||||||
\(225\) | −1.77144e31 | −0.311790 | ||||||||
\(226\) | 1.79971e32 | 2.98358 | ||||||||
\(227\) | −1.24397e32 | −1.94294 | −0.971472 | − | 0.237153i | \(-0.923786\pi\) | ||||
−0.971472 | + | 0.237153i | \(0.923786\pi\) | |||||||
\(228\) | −4.64582e31 | −0.683821 | ||||||||
\(229\) | 1.14944e32 | 1.59481 | 0.797403 | − | 0.603447i | \(-0.206206\pi\) | ||||
0.797403 | + | 0.603447i | \(0.206206\pi\) | |||||||
\(230\) | −7.69509e30 | −0.100667 | ||||||||
\(231\) | −7.67531e31 | −0.946966 | ||||||||
\(232\) | −1.20895e32 | −1.40709 | ||||||||
\(233\) | 1.39267e32 | 1.52948 | 0.764741 | − | 0.644337i | \(-0.222867\pi\) | ||||
0.764741 | + | 0.644337i | \(0.222867\pi\) | |||||||
\(234\) | −7.26023e31 | −0.752551 | ||||||||
\(235\) | −1.74741e31 | −0.170993 | ||||||||
\(236\) | −2.36049e32 | −2.18117 | ||||||||
\(237\) | 7.88622e31 | 0.688282 | ||||||||
\(238\) | −2.92377e32 | −2.41076 | ||||||||
\(239\) | 1.18142e32 | 0.920517 | 0.460259 | − | 0.887785i | \(-0.347757\pi\) | ||||
0.460259 | + | 0.887785i | \(0.347757\pi\) | |||||||
\(240\) | 5.55590e31 | 0.409169 | ||||||||
\(241\) | 1.39602e32 | 0.971991 | 0.485996 | − | 0.873961i | \(-0.338457\pi\) | ||||
0.485996 | + | 0.873961i | \(0.338457\pi\) | |||||||
\(242\) | 6.18779e31 | 0.407407 | ||||||||
\(243\) | −1.03011e31 | −0.0641500 | ||||||||
\(244\) | 3.65453e31 | 0.215312 | ||||||||
\(245\) | −5.51604e31 | −0.307528 | ||||||||
\(246\) | 1.79225e32 | 0.945748 | ||||||||
\(247\) | −1.13863e32 | −0.568817 | ||||||||
\(248\) | −4.30007e32 | −2.03412 | ||||||||
\(249\) | 8.83784e31 | 0.395963 | ||||||||
\(250\) | 2.17163e32 | 0.921712 | ||||||||
\(251\) | 9.88006e31 | 0.397342 | 0.198671 | − | 0.980066i | \(-0.436338\pi\) | ||||
0.198671 | + | 0.980066i | \(0.436338\pi\) | |||||||
\(252\) | 3.26229e32 | 1.24341 | ||||||||
\(253\) | 6.45526e31 | 0.233231 | ||||||||
\(254\) | 4.69000e31 | 0.160664 | ||||||||
\(255\) | −3.91128e31 | −0.127065 | ||||||||
\(256\) | −7.27415e31 | −0.224152 | ||||||||
\(257\) | −8.60649e31 | −0.251611 | −0.125805 | − | 0.992055i | \(-0.540151\pi\) | ||||
−0.125805 | + | 0.992055i | \(0.540151\pi\) | |||||||
\(258\) | −3.02631e32 | −0.839553 | ||||||||
\(259\) | −6.87016e32 | −1.80892 | ||||||||
\(260\) | 3.07586e32 | 0.768822 | ||||||||
\(261\) | −6.98913e31 | −0.165873 | ||||||||
\(262\) | 1.56224e33 | 3.52112 | ||||||||
\(263\) | −2.80912e32 | −0.601405 | −0.300703 | − | 0.953718i | \(-0.597221\pi\) | ||||
−0.300703 | + | 0.953718i | \(0.597221\pi\) | |||||||
\(264\) | −8.85617e32 | −1.80133 | ||||||||
\(265\) | −1.47081e32 | −0.284275 | ||||||||
\(266\) | 7.15510e32 | 1.31436 | ||||||||
\(267\) | 2.12002e32 | 0.370200 | ||||||||
\(268\) | 8.30365e32 | 1.37864 | ||||||||
\(269\) | −1.02703e32 | −0.162153 | −0.0810767 | − | 0.996708i | \(-0.525836\pi\) | ||||
−0.0810767 | + | 0.996708i | \(0.525836\pi\) | |||||||
\(270\) | 6.10324e31 | 0.0916536 | ||||||||
\(271\) | −1.27505e33 | −1.82155 | −0.910775 | − | 0.412903i | \(-0.864515\pi\) | ||||
−0.910775 | + | 0.412903i | \(0.864515\pi\) | |||||||
\(272\) | −1.77542e33 | −2.41336 | ||||||||
\(273\) | 7.99540e32 | 1.03430 | ||||||||
\(274\) | −1.78720e33 | −2.20060 | ||||||||
\(275\) | −8.80451e32 | −1.03208 | ||||||||
\(276\) | −2.74372e32 | −0.306244 | ||||||||
\(277\) | 1.09712e33 | 1.16621 | 0.583107 | − | 0.812396i | \(-0.301837\pi\) | ||||
0.583107 | + | 0.812396i | \(0.301837\pi\) | |||||||
\(278\) | 2.54432e33 | 2.57612 | ||||||||
\(279\) | −2.48594e32 | −0.239791 | ||||||||
\(280\) | −1.16261e33 | −1.06857 | ||||||||
\(281\) | 1.35684e33 | 1.18849 | 0.594244 | − | 0.804285i | \(-0.297451\pi\) | ||||
0.594244 | + | 0.804285i | \(0.297451\pi\) | |||||||
\(282\) | −8.71331e32 | −0.727479 | ||||||||
\(283\) | 2.13864e33 | 1.70224 | 0.851120 | − | 0.524972i | \(-0.175924\pi\) | ||||
0.851120 | + | 0.524972i | \(0.175924\pi\) | |||||||
\(284\) | 4.36028e33 | 3.30915 | ||||||||
\(285\) | 9.57174e31 | 0.0692764 | ||||||||
\(286\) | −3.60852e33 | −2.49108 | ||||||||
\(287\) | −1.97374e33 | −1.29982 | ||||||||
\(288\) | 1.27037e33 | 0.798237 | ||||||||
\(289\) | −4.17837e32 | −0.250545 | ||||||||
\(290\) | 4.14097e32 | 0.236989 | ||||||||
\(291\) | 1.69351e33 | 0.925195 | ||||||||
\(292\) | 2.51414e33 | 1.31136 | ||||||||
\(293\) | 4.30088e32 | 0.214212 | 0.107106 | − | 0.994248i | \(-0.465842\pi\) | ||||
0.107106 | + | 0.994248i | \(0.465842\pi\) | |||||||
\(294\) | −2.75053e33 | −1.30836 | ||||||||
\(295\) | 4.86330e32 | 0.220970 | ||||||||
\(296\) | −7.92714e33 | −3.44095 | ||||||||
\(297\) | −5.11989e32 | −0.212348 | ||||||||
\(298\) | −5.79028e32 | −0.229499 | ||||||||
\(299\) | −6.72447e32 | −0.254740 | ||||||||
\(300\) | 3.74224e33 | 1.35517 | ||||||||
\(301\) | 3.33276e33 | 1.15387 | ||||||||
\(302\) | −9.75386e33 | −3.22911 | ||||||||
\(303\) | −2.77430e33 | −0.878370 | ||||||||
\(304\) | 4.34484e33 | 1.31577 | ||||||||
\(305\) | −7.52938e31 | −0.0218128 | ||||||||
\(306\) | −1.95033e33 | −0.540591 | ||||||||
\(307\) | −5.70033e32 | −0.151193 | −0.0755966 | − | 0.997138i | \(-0.524086\pi\) | ||||
−0.0755966 | + | 0.997138i | \(0.524086\pi\) | |||||||
\(308\) | 1.62144e34 | 4.11591 | ||||||||
\(309\) | −7.96464e32 | −0.193520 | ||||||||
\(310\) | 1.47288e33 | 0.342599 | ||||||||
\(311\) | −4.65284e33 | −1.03622 | −0.518111 | − | 0.855313i | \(-0.673365\pi\) | ||||
−0.518111 | + | 0.855313i | \(0.673365\pi\) | |||||||
\(312\) | 9.22550e33 | 1.96745 | ||||||||
\(313\) | 4.33109e33 | 0.884604 | 0.442302 | − | 0.896866i | \(-0.354162\pi\) | ||||
0.442302 | + | 0.896866i | \(0.354162\pi\) | |||||||
\(314\) | 4.34990e33 | 0.850998 | ||||||||
\(315\) | −6.72126e32 | −0.125967 | ||||||||
\(316\) | −1.66600e34 | −2.99156 | ||||||||
\(317\) | −2.47386e33 | −0.425671 | −0.212836 | − | 0.977088i | \(-0.568270\pi\) | ||||
−0.212836 | + | 0.977088i | \(0.568270\pi\) | |||||||
\(318\) | −7.33410e33 | −1.20943 | ||||||||
\(319\) | −3.47378e33 | −0.549070 | ||||||||
\(320\) | −2.84955e33 | −0.431770 | ||||||||
\(321\) | 2.07892e33 | 0.302010 | ||||||||
\(322\) | 4.22564e33 | 0.588624 | ||||||||
\(323\) | −3.05871e33 | −0.408606 | ||||||||
\(324\) | 2.17614e33 | 0.278823 | ||||||||
\(325\) | 9.17170e33 | 1.12726 | ||||||||
\(326\) | 1.43842e34 | 1.69609 | ||||||||
\(327\) | 9.16607e33 | 1.03702 | ||||||||
\(328\) | −2.27740e34 | −2.47254 | ||||||||
\(329\) | 9.59563e33 | 0.999836 | ||||||||
\(330\) | 3.03347e33 | 0.303390 | ||||||||
\(331\) | −2.93911e33 | −0.282188 | −0.141094 | − | 0.989996i | \(-0.545062\pi\) | ||||
−0.141094 | + | 0.989996i | \(0.545062\pi\) | |||||||
\(332\) | −1.86703e34 | −1.72102 | ||||||||
\(333\) | −4.58280e33 | −0.405633 | ||||||||
\(334\) | 2.33309e34 | 1.98314 | ||||||||
\(335\) | −1.71079e33 | −0.139667 | ||||||||
\(336\) | −3.05094e34 | −2.39250 | ||||||||
\(337\) | −1.57199e34 | −1.18426 | −0.592128 | − | 0.805844i | \(-0.701712\pi\) | ||||
−0.592128 | + | 0.805844i | \(0.701712\pi\) | |||||||
\(338\) | 1.17084e34 | 0.847466 | ||||||||
\(339\) | −1.32208e34 | −0.919518 | ||||||||
\(340\) | 8.26273e33 | 0.552279 | ||||||||
\(341\) | −1.23557e34 | −0.793752 | ||||||||
\(342\) | 4.77287e33 | 0.294732 | ||||||||
\(343\) | 5.25043e33 | 0.311691 | ||||||||
\(344\) | 3.84551e34 | 2.19490 | ||||||||
\(345\) | 5.65286e32 | 0.0310249 | ||||||||
\(346\) | 1.76487e34 | 0.931507 | ||||||||
\(347\) | 2.55505e34 | 1.29703 | 0.648516 | − | 0.761201i | \(-0.275390\pi\) | ||||
0.648516 | + | 0.761201i | \(0.275390\pi\) | |||||||
\(348\) | 1.47648e34 | 0.720955 | ||||||||
\(349\) | −3.50116e34 | −1.64463 | −0.822316 | − | 0.569031i | \(-0.807319\pi\) | ||||
−0.822316 | + | 0.569031i | \(0.807319\pi\) | |||||||
\(350\) | −5.76347e34 | −2.60475 | ||||||||
\(351\) | 5.33341e33 | 0.231931 | ||||||||
\(352\) | 6.31407e34 | 2.64231 | ||||||||
\(353\) | −6.64200e33 | −0.267510 | −0.133755 | − | 0.991014i | \(-0.542704\pi\) | ||||
−0.133755 | + | 0.991014i | \(0.542704\pi\) | |||||||
\(354\) | 2.42504e34 | 0.940103 | ||||||||
\(355\) | −8.98343e33 | −0.335243 | ||||||||
\(356\) | −4.47861e34 | −1.60905 | ||||||||
\(357\) | 2.14782e34 | 0.742980 | ||||||||
\(358\) | 2.99363e34 | 0.997188 | ||||||||
\(359\) | 4.11061e34 | 1.31865 | 0.659327 | − | 0.751856i | \(-0.270841\pi\) | ||||
0.659327 | + | 0.751856i | \(0.270841\pi\) | |||||||
\(360\) | −7.75533e33 | −0.239616 | ||||||||
\(361\) | −2.61153e34 | −0.777227 | ||||||||
\(362\) | −4.29240e34 | −1.23065 | ||||||||
\(363\) | −4.54559e33 | −0.125560 | ||||||||
\(364\) | −1.68906e35 | −4.49548 | ||||||||
\(365\) | −5.17987e33 | −0.132851 | ||||||||
\(366\) | −3.75447e33 | −0.0928012 | ||||||||
\(367\) | −3.04370e33 | −0.0725121 | −0.0362560 | − | 0.999343i | \(-0.511543\pi\) | ||||
−0.0362560 | + | 0.999343i | \(0.511543\pi\) | |||||||
\(368\) | 2.56597e34 | 0.589258 | ||||||||
\(369\) | −1.31660e34 | −0.291473 | ||||||||
\(370\) | 2.71525e34 | 0.579544 | ||||||||
\(371\) | 8.07675e34 | 1.66222 | ||||||||
\(372\) | 5.25164e34 | 1.04223 | ||||||||
\(373\) | 4.11966e34 | 0.788483 | 0.394242 | − | 0.919007i | \(-0.371007\pi\) | ||||
0.394242 | + | 0.919007i | \(0.371007\pi\) | |||||||
\(374\) | −9.69363e34 | −1.78945 | ||||||||
\(375\) | −1.59529e34 | −0.284065 | ||||||||
\(376\) | 1.10719e35 | 1.90190 | ||||||||
\(377\) | 3.61865e34 | 0.599706 | ||||||||
\(378\) | −3.35150e34 | −0.535920 | ||||||||
\(379\) | 8.35010e34 | 1.28843 | 0.644217 | − | 0.764842i | \(-0.277183\pi\) | ||||
0.644217 | + | 0.764842i | \(0.277183\pi\) | |||||||
\(380\) | −2.02207e34 | −0.301104 | ||||||||
\(381\) | −3.44530e33 | −0.0495153 | ||||||||
\(382\) | 1.78648e35 | 2.47824 | ||||||||
\(383\) | −5.20579e34 | −0.697113 | −0.348557 | − | 0.937288i | \(-0.613328\pi\) | ||||
−0.348557 | + | 0.937288i | \(0.613328\pi\) | |||||||
\(384\) | −3.51449e34 | −0.454350 | ||||||||
\(385\) | −3.34064e34 | −0.416974 | ||||||||
\(386\) | −5.72163e34 | −0.689591 | ||||||||
\(387\) | 2.22315e34 | 0.258744 | ||||||||
\(388\) | −3.57761e35 | −4.02129 | ||||||||
\(389\) | −3.57703e34 | −0.388332 | −0.194166 | − | 0.980969i | \(-0.562200\pi\) | ||||
−0.194166 | + | 0.980969i | \(0.562200\pi\) | |||||||
\(390\) | −3.15997e34 | −0.331368 | ||||||||
\(391\) | −1.80641e34 | −0.182991 | ||||||||
\(392\) | 3.49507e35 | 3.42054 | ||||||||
\(393\) | −1.14763e35 | −1.08518 | ||||||||
\(394\) | 2.09855e35 | 1.91744 | ||||||||
\(395\) | 3.43243e34 | 0.303069 | ||||||||
\(396\) | 1.08160e35 | 0.922954 | ||||||||
\(397\) | −7.79828e34 | −0.643172 | −0.321586 | − | 0.946880i | \(-0.604216\pi\) | ||||
−0.321586 | + | 0.946880i | \(0.604216\pi\) | |||||||
\(398\) | −1.80941e35 | −1.44250 | ||||||||
\(399\) | −5.25618e34 | −0.405075 | ||||||||
\(400\) | −3.49979e35 | −2.60755 | ||||||||
\(401\) | −2.28761e34 | −0.164791 | −0.0823955 | − | 0.996600i | \(-0.526257\pi\) | ||||
−0.0823955 | + | 0.996600i | \(0.526257\pi\) | |||||||
\(402\) | −8.53073e34 | −0.594203 | ||||||||
\(403\) | 1.28710e35 | 0.866952 | ||||||||
\(404\) | 5.86081e35 | 3.81777 | ||||||||
\(405\) | −4.48347e33 | −0.0282470 | ||||||||
\(406\) | −2.27395e35 | −1.38573 | ||||||||
\(407\) | −2.27777e35 | −1.34272 | ||||||||
\(408\) | 2.47826e35 | 1.41330 | ||||||||
\(409\) | −1.15859e34 | −0.0639243 | −0.0319621 | − | 0.999489i | \(-0.510176\pi\) | ||||
−0.0319621 | + | 0.999489i | \(0.510176\pi\) | |||||||
\(410\) | 7.80068e34 | 0.416438 | ||||||||
\(411\) | 1.31289e35 | 0.678209 | ||||||||
\(412\) | 1.68256e35 | 0.841121 | ||||||||
\(413\) | −2.67061e35 | −1.29206 | ||||||||
\(414\) | 2.81875e34 | 0.131993 | ||||||||
\(415\) | 3.84662e34 | 0.174353 | ||||||||
\(416\) | −6.57739e35 | −2.88598 | ||||||||
\(417\) | −1.86907e35 | −0.793942 | ||||||||
\(418\) | 2.37224e35 | 0.975616 | ||||||||
\(419\) | 6.19060e34 | 0.246515 | 0.123258 | − | 0.992375i | \(-0.460666\pi\) | ||||
0.123258 | + | 0.992375i | \(0.460666\pi\) | |||||||
\(420\) | 1.41989e35 | 0.547507 | ||||||||
\(421\) | −8.53227e33 | −0.0318608 | −0.0159304 | − | 0.999873i | \(-0.505071\pi\) | ||||
−0.0159304 | + | 0.999873i | \(0.505071\pi\) | |||||||
\(422\) | 2.92078e35 | 1.05628 | ||||||||
\(423\) | 6.40085e34 | 0.224204 | ||||||||
\(424\) | 9.31937e35 | 3.16190 | ||||||||
\(425\) | 2.46381e35 | 0.809761 | ||||||||
\(426\) | −4.47952e35 | −1.42627 | ||||||||
\(427\) | 4.13465e34 | 0.127545 | ||||||||
\(428\) | −4.39181e35 | −1.31266 | ||||||||
\(429\) | 2.65084e35 | 0.767733 | ||||||||
\(430\) | −1.31719e35 | −0.369678 | ||||||||
\(431\) | 4.08719e35 | 1.11169 | 0.555843 | − | 0.831288i | \(-0.312396\pi\) | ||||
0.555843 | + | 0.831288i | \(0.312396\pi\) | |||||||
\(432\) | −2.03515e35 | −0.536496 | ||||||||
\(433\) | 1.44666e35 | 0.369642 | 0.184821 | − | 0.982772i | \(-0.440830\pi\) | ||||
0.184821 | + | 0.982772i | \(0.440830\pi\) | |||||||
\(434\) | −8.08812e35 | −2.00325 | ||||||||
\(435\) | −3.04198e34 | −0.0730385 | ||||||||
\(436\) | −1.93637e36 | −4.50734 | ||||||||
\(437\) | 4.42067e34 | 0.0997673 | ||||||||
\(438\) | −2.58290e35 | −0.565206 | ||||||||
\(439\) | 2.97115e34 | 0.0630454 | 0.0315227 | − | 0.999503i | \(-0.489964\pi\) | ||||
0.0315227 | + | 0.999503i | \(0.489964\pi\) | |||||||
\(440\) | −3.85460e35 | −0.793173 | ||||||||
\(441\) | 2.02055e35 | 0.403227 | ||||||||
\(442\) | 1.00979e36 | 1.95448 | ||||||||
\(443\) | −1.94735e35 | −0.365589 | −0.182795 | − | 0.983151i | \(-0.558514\pi\) | ||||
−0.182795 | + | 0.983151i | \(0.558514\pi\) | |||||||
\(444\) | 9.68134e35 | 1.76305 | ||||||||
\(445\) | 9.22725e34 | 0.163009 | ||||||||
\(446\) | 1.56298e35 | 0.267876 | ||||||||
\(447\) | 4.25357e34 | 0.0707298 | ||||||||
\(448\) | 1.56479e36 | 2.52466 | ||||||||
\(449\) | −3.89051e35 | −0.609089 | −0.304544 | − | 0.952498i | \(-0.598504\pi\) | ||||
−0.304544 | + | 0.952498i | \(0.598504\pi\) | |||||||
\(450\) | −3.84458e35 | −0.584090 | ||||||||
\(451\) | −6.54384e35 | −0.964827 | ||||||||
\(452\) | 2.79294e36 | 3.99661 | ||||||||
\(453\) | 7.16525e35 | 0.995188 | ||||||||
\(454\) | −2.69980e36 | −3.63980 | ||||||||
\(455\) | 3.47995e35 | 0.455428 | ||||||||
\(456\) | −6.06485e35 | −0.770538 | ||||||||
\(457\) | −7.79952e35 | −0.962053 | −0.481027 | − | 0.876706i | \(-0.659736\pi\) | ||||
−0.481027 | + | 0.876706i | \(0.659736\pi\) | |||||||
\(458\) | 2.49465e36 | 2.98762 | ||||||||
\(459\) | 1.43272e35 | 0.166606 | ||||||||
\(460\) | −1.19419e35 | −0.134847 | ||||||||
\(461\) | −1.33828e36 | −1.46752 | −0.733760 | − | 0.679408i | \(-0.762236\pi\) | ||||
−0.733760 | + | 0.679408i | \(0.762236\pi\) | |||||||
\(462\) | −1.66578e36 | −1.77399 | ||||||||
\(463\) | 3.79932e35 | 0.392973 | 0.196486 | − | 0.980507i | \(-0.437047\pi\) | ||||
0.196486 | + | 0.980507i | \(0.437047\pi\) | |||||||
\(464\) | −1.38083e36 | −1.38722 | ||||||||
\(465\) | −1.08199e35 | −0.105586 | ||||||||
\(466\) | 3.02253e36 | 2.86524 | ||||||||
\(467\) | −7.20473e35 | −0.663499 | −0.331749 | − | 0.943368i | \(-0.607639\pi\) | ||||
−0.331749 | + | 0.943368i | \(0.607639\pi\) | |||||||
\(468\) | −1.12670e36 | −1.00807 | ||||||||
\(469\) | 9.39456e35 | 0.816664 | ||||||||
\(470\) | −3.79242e35 | −0.320328 | ||||||||
\(471\) | −3.19546e35 | −0.262271 | ||||||||
\(472\) | −3.08148e36 | −2.45778 | ||||||||
\(473\) | 1.10496e36 | 0.856490 | ||||||||
\(474\) | 1.71156e36 | 1.28939 | ||||||||
\(475\) | −6.02947e35 | −0.441485 | ||||||||
\(476\) | −4.53735e36 | −3.22930 | ||||||||
\(477\) | 5.38767e35 | 0.372737 | ||||||||
\(478\) | 2.56404e36 | 1.72444 | ||||||||
\(479\) | −4.56900e34 | −0.0298739 | −0.0149370 | − | 0.999888i | \(-0.504755\pi\) | ||||
−0.0149370 | + | 0.999888i | \(0.504755\pi\) | |||||||
\(480\) | 5.52921e35 | 0.351485 | ||||||||
\(481\) | 2.37276e36 | 1.46655 | ||||||||
\(482\) | 3.02980e36 | 1.82087 | ||||||||
\(483\) | −3.10418e35 | −0.181410 | ||||||||
\(484\) | 9.60274e35 | 0.545736 | ||||||||
\(485\) | 7.37092e35 | 0.407388 | ||||||||
\(486\) | −2.23565e35 | −0.120175 | ||||||||
\(487\) | −2.25055e36 | −1.17665 | −0.588326 | − | 0.808624i | \(-0.700213\pi\) | ||||
−0.588326 | + | 0.808624i | \(0.700213\pi\) | |||||||
\(488\) | 4.77077e35 | 0.242617 | ||||||||
\(489\) | −1.05668e36 | −0.522723 | ||||||||
\(490\) | −1.19715e36 | −0.576106 | ||||||||
\(491\) | −3.36099e36 | −1.57350 | −0.786751 | − | 0.617271i | \(-0.788238\pi\) | ||||
−0.786751 | + | 0.617271i | \(0.788238\pi\) | |||||||
\(492\) | 2.78137e36 | 1.26686 | ||||||||
\(493\) | 9.72085e35 | 0.430795 | ||||||||
\(494\) | −2.47117e36 | −1.06559 | ||||||||
\(495\) | −2.22840e35 | −0.0935025 | ||||||||
\(496\) | −4.91140e36 | −2.00541 | ||||||||
\(497\) | 4.93312e36 | 1.96024 | ||||||||
\(498\) | 1.91808e36 | 0.741774 | ||||||||
\(499\) | 1.11121e35 | 0.0418253 | 0.0209127 | − | 0.999781i | \(-0.493343\pi\) | ||||
0.0209127 | + | 0.999781i | \(0.493343\pi\) | |||||||
\(500\) | 3.37012e36 | 1.23467 | ||||||||
\(501\) | −1.71390e36 | −0.611191 | ||||||||
\(502\) | 2.14428e36 | 0.744357 | ||||||||
\(503\) | −1.49384e36 | −0.504818 | −0.252409 | − | 0.967621i | \(-0.581223\pi\) | ||||
−0.252409 | + | 0.967621i | \(0.581223\pi\) | |||||||
\(504\) | 4.25872e36 | 1.40109 | ||||||||
\(505\) | −1.20750e36 | −0.386770 | ||||||||
\(506\) | 1.40099e36 | 0.436922 | ||||||||
\(507\) | −8.60107e35 | −0.261183 | ||||||||
\(508\) | 7.27833e35 | 0.215215 | ||||||||
\(509\) | −5.00593e36 | −1.44143 | −0.720717 | − | 0.693230i | \(-0.756187\pi\) | ||||
−0.720717 | + | 0.693230i | \(0.756187\pi\) | |||||||
\(510\) | −8.48869e35 | −0.238036 | ||||||||
\(511\) | 2.84445e36 | 0.776811 | ||||||||
\(512\) | −4.53738e36 | −1.20687 | ||||||||
\(513\) | −3.50618e35 | −0.0908343 | ||||||||
\(514\) | −1.86788e36 | −0.471352 | ||||||||
\(515\) | −3.46657e35 | −0.0852122 | ||||||||
\(516\) | −4.69649e36 | −1.12461 | ||||||||
\(517\) | 3.18139e36 | 0.742154 | ||||||||
\(518\) | −1.49104e37 | −3.38873 | ||||||||
\(519\) | −1.29649e36 | −0.287084 | ||||||||
\(520\) | 4.01535e36 | 0.866319 | ||||||||
\(521\) | 3.77205e36 | 0.792990 | 0.396495 | − | 0.918037i | \(-0.370226\pi\) | ||||
0.396495 | + | 0.918037i | \(0.370226\pi\) | |||||||
\(522\) | −1.51686e36 | −0.310737 | ||||||||
\(523\) | −7.85298e35 | −0.156770 | −0.0783848 | − | 0.996923i | \(-0.524976\pi\) | ||||
−0.0783848 | + | 0.996923i | \(0.524976\pi\) | |||||||
\(524\) | 2.42442e37 | 4.71666 | ||||||||
\(525\) | 4.23388e36 | 0.802764 | ||||||||
\(526\) | −6.09666e36 | −1.12664 | ||||||||
\(527\) | 3.45757e36 | 0.622769 | ||||||||
\(528\) | −1.01152e37 | −1.77590 | ||||||||
\(529\) | −5.58214e36 | −0.955320 | ||||||||
\(530\) | −3.19212e36 | −0.532544 | ||||||||
\(531\) | −1.78145e36 | −0.289733 | ||||||||
\(532\) | 1.11039e37 | 1.76063 | ||||||||
\(533\) | 6.81675e36 | 1.05380 | ||||||||
\(534\) | 4.60109e36 | 0.693512 | ||||||||
\(535\) | 9.04840e35 | 0.132983 | ||||||||
\(536\) | 1.08399e37 | 1.55347 | ||||||||
\(537\) | −2.19914e36 | −0.307326 | ||||||||
\(538\) | −2.22897e36 | −0.303769 | ||||||||
\(539\) | 1.00427e37 | 1.33475 | ||||||||
\(540\) | 9.47151e35 | 0.122773 | ||||||||
\(541\) | 6.90432e36 | 0.872887 | 0.436444 | − | 0.899732i | \(-0.356238\pi\) | ||||
0.436444 | + | 0.899732i | \(0.356238\pi\) | |||||||
\(542\) | −2.76725e37 | −3.41238 | ||||||||
\(543\) | 3.15322e36 | 0.379277 | ||||||||
\(544\) | −1.76690e37 | −2.07313 | ||||||||
\(545\) | 3.98948e36 | 0.456629 | ||||||||
\(546\) | 1.73525e37 | 1.93759 | ||||||||
\(547\) | −4.90777e36 | −0.534632 | −0.267316 | − | 0.963609i | \(-0.586137\pi\) | ||||
−0.267316 | + | 0.963609i | \(0.586137\pi\) | |||||||
\(548\) | −2.77353e37 | −2.94778 | ||||||||
\(549\) | 2.75805e35 | 0.0286007 | ||||||||
\(550\) | −1.91085e37 | −1.93344 | ||||||||
\(551\) | −2.37890e36 | −0.234871 | ||||||||
\(552\) | −3.58176e36 | −0.345080 | ||||||||
\(553\) | −1.88487e37 | −1.77211 | ||||||||
\(554\) | 2.38109e37 | 2.18471 | ||||||||
\(555\) | −1.99464e36 | −0.178611 | ||||||||
\(556\) | 3.94848e37 | 3.45081 | ||||||||
\(557\) | −8.37169e36 | −0.714115 | −0.357058 | − | 0.934082i | \(-0.616220\pi\) | ||||
−0.357058 | + | 0.934082i | \(0.616220\pi\) | |||||||
\(558\) | −5.39525e36 | −0.449211 | ||||||||
\(559\) | −1.15104e37 | −0.935475 | ||||||||
\(560\) | −1.32790e37 | −1.05348 | ||||||||
\(561\) | 7.12100e36 | 0.551496 | ||||||||
\(562\) | 2.94477e37 | 2.22644 | ||||||||
\(563\) | 1.53607e37 | 1.13383 | 0.566913 | − | 0.823778i | \(-0.308138\pi\) | ||||
0.566913 | + | 0.823778i | \(0.308138\pi\) | |||||||
\(564\) | −1.35220e37 | −0.974484 | ||||||||
\(565\) | −5.75426e36 | −0.404889 | ||||||||
\(566\) | 4.64151e37 | 3.18887 | ||||||||
\(567\) | 2.46203e36 | 0.165167 | ||||||||
\(568\) | 5.69208e37 | 3.72879 | ||||||||
\(569\) | −2.56048e37 | −1.63797 | −0.818986 | − | 0.573814i | \(-0.805463\pi\) | ||||
−0.818986 | + | 0.573814i | \(0.805463\pi\) | |||||||
\(570\) | 2.07737e36 | 0.129778 | ||||||||
\(571\) | −1.84375e37 | −1.12490 | −0.562450 | − | 0.826831i | \(-0.690141\pi\) | ||||
−0.562450 | + | 0.826831i | \(0.690141\pi\) | |||||||
\(572\) | −5.60000e37 | −3.33689 | ||||||||
\(573\) | −1.31236e37 | −0.763775 | ||||||||
\(574\) | −4.28363e37 | −2.43501 | ||||||||
\(575\) | −3.56087e36 | −0.197715 | ||||||||
\(576\) | 1.04381e37 | 0.566131 | ||||||||
\(577\) | 2.60648e37 | 1.38096 | 0.690479 | − | 0.723352i | \(-0.257400\pi\) | ||||
0.690479 | + | 0.723352i | \(0.257400\pi\) | |||||||
\(578\) | −9.06835e36 | −0.469356 | ||||||||
\(579\) | 4.20315e36 | 0.212527 | ||||||||
\(580\) | 6.42630e36 | 0.317456 | ||||||||
\(581\) | −2.11231e37 | −1.01948 | ||||||||
\(582\) | 3.67545e37 | 1.73321 | ||||||||
\(583\) | 2.67781e37 | 1.23383 | ||||||||
\(584\) | 3.28207e37 | 1.47766 | ||||||||
\(585\) | 2.32133e36 | 0.102125 | ||||||||
\(586\) | 9.33423e36 | 0.401292 | ||||||||
\(587\) | 1.64116e37 | 0.689505 | 0.344752 | − | 0.938694i | \(-0.387963\pi\) | ||||
0.344752 | + | 0.938694i | \(0.387963\pi\) | |||||||
\(588\) | −4.26850e37 | −1.75259 | ||||||||
\(589\) | −8.46141e36 | −0.339536 | ||||||||
\(590\) | 1.05549e37 | 0.413953 | ||||||||
\(591\) | −1.54161e37 | −0.590940 | ||||||||
\(592\) | −9.05413e37 | −3.39237 | ||||||||
\(593\) | 6.39232e35 | 0.0234110 | 0.0117055 | − | 0.999931i | \(-0.496274\pi\) | ||||
0.0117055 | + | 0.999931i | \(0.496274\pi\) | |||||||
\(594\) | −1.11117e37 | −0.397800 | ||||||||
\(595\) | 9.34827e36 | 0.327154 | ||||||||
\(596\) | −8.98584e36 | −0.307421 | ||||||||
\(597\) | 1.32920e37 | 0.444567 | ||||||||
\(598\) | −1.45942e37 | −0.477215 | ||||||||
\(599\) | 3.67500e37 | 1.17488 | 0.587442 | − | 0.809266i | \(-0.300135\pi\) | ||||
0.587442 | + | 0.809266i | \(0.300135\pi\) | |||||||
\(600\) | 4.88527e37 | 1.52703 | ||||||||
\(601\) | 4.35901e36 | 0.133224 | 0.0666120 | − | 0.997779i | \(-0.478781\pi\) | ||||
0.0666120 | + | 0.997779i | \(0.478781\pi\) | |||||||
\(602\) | 7.23313e37 | 2.16159 | ||||||||
\(603\) | 6.26673e36 | 0.183129 | ||||||||
\(604\) | −1.51369e38 | −4.32551 | ||||||||
\(605\) | −1.97844e36 | −0.0552874 | ||||||||
\(606\) | −6.02109e37 | −1.64549 | ||||||||
\(607\) | 4.98438e37 | 1.33218 | 0.666092 | − | 0.745870i | \(-0.267966\pi\) | ||||
0.666092 | + | 0.745870i | \(0.267966\pi\) | |||||||
\(608\) | 4.32397e37 | 1.13028 | ||||||||
\(609\) | 1.67046e37 | 0.427073 | ||||||||
\(610\) | −1.63411e36 | −0.0408628 | ||||||||
\(611\) | −3.31406e37 | −0.810596 | ||||||||
\(612\) | −3.02668e37 | −0.724140 | ||||||||
\(613\) | 2.09778e37 | 0.490958 | 0.245479 | − | 0.969402i | \(-0.421055\pi\) | ||||
0.245479 | + | 0.969402i | \(0.421055\pi\) | |||||||
\(614\) | −1.23715e37 | −0.283236 | ||||||||
\(615\) | −5.73043e36 | −0.128343 | ||||||||
\(616\) | 2.11669e38 | 4.63787 | ||||||||
\(617\) | −9.28596e37 | −1.99057 | −0.995284 | − | 0.0970039i | \(-0.969074\pi\) | ||||
−0.995284 | + | 0.0970039i | \(0.969074\pi\) | |||||||
\(618\) | −1.72857e37 | −0.362530 | ||||||||
\(619\) | 4.21148e37 | 0.864194 | 0.432097 | − | 0.901827i | \(-0.357774\pi\) | ||||
0.432097 | + | 0.901827i | \(0.357774\pi\) | |||||||
\(620\) | 2.28574e37 | 0.458923 | ||||||||
\(621\) | −2.07067e36 | −0.0406794 | ||||||||
\(622\) | −1.00981e38 | −1.94120 | ||||||||
\(623\) | −5.06700e37 | −0.953153 | ||||||||
\(624\) | 1.05371e38 | 1.93967 | ||||||||
\(625\) | 4.49801e37 | 0.810289 | ||||||||
\(626\) | 9.39981e37 | 1.65716 | ||||||||
\(627\) | −1.74266e37 | −0.300678 | ||||||||
\(628\) | 6.75053e37 | 1.13994 | ||||||||
\(629\) | 6.37399e37 | 1.05348 | ||||||||
\(630\) | −1.45872e37 | −0.235980 | ||||||||
\(631\) | −1.60405e37 | −0.253993 | −0.126997 | − | 0.991903i | \(-0.540534\pi\) | ||||
−0.126997 | + | 0.991903i | \(0.540534\pi\) | |||||||
\(632\) | −2.17486e38 | −3.37093 | ||||||||
\(633\) | −2.14562e37 | −0.325539 | ||||||||
\(634\) | −5.36903e37 | −0.797427 | ||||||||
\(635\) | −1.49955e36 | −0.0218029 | ||||||||
\(636\) | −1.13817e38 | −1.62007 | ||||||||
\(637\) | −1.04615e38 | −1.45784 | ||||||||
\(638\) | −7.53918e37 | −1.02860 | ||||||||
\(639\) | 3.29068e37 | 0.439566 | ||||||||
\(640\) | −1.52966e37 | −0.200062 | ||||||||
\(641\) | −4.27881e37 | −0.547948 | −0.273974 | − | 0.961737i | \(-0.588338\pi\) | ||||
−0.273974 | + | 0.961737i | \(0.588338\pi\) | |||||||
\(642\) | 4.51191e37 | 0.565767 | ||||||||
\(643\) | 6.44875e36 | 0.0791821 | 0.0395911 | − | 0.999216i | \(-0.487394\pi\) | ||||
0.0395911 | + | 0.999216i | \(0.487394\pi\) | |||||||
\(644\) | 6.55770e37 | 0.788483 | ||||||||
\(645\) | 9.67613e36 | 0.113932 | ||||||||
\(646\) | −6.63835e37 | −0.765458 | ||||||||
\(647\) | 1.16912e38 | 1.32024 | 0.660118 | − | 0.751162i | \(-0.270506\pi\) | ||||
0.660118 | + | 0.751162i | \(0.270506\pi\) | |||||||
\(648\) | 2.84082e37 | 0.314182 | ||||||||
\(649\) | −8.85427e37 | −0.959068 | ||||||||
\(650\) | 1.99054e38 | 2.11174 | ||||||||
\(651\) | 5.94158e37 | 0.617389 | ||||||||
\(652\) | 2.23227e38 | 2.27198 | ||||||||
\(653\) | −7.34409e37 | −0.732167 | −0.366083 | − | 0.930582i | \(-0.619301\pi\) | ||||
−0.366083 | + | 0.930582i | \(0.619301\pi\) | |||||||
\(654\) | 1.98932e38 | 1.94270 | ||||||||
\(655\) | −4.99500e37 | −0.477835 | ||||||||
\(656\) | −2.60118e38 | −2.43763 | ||||||||
\(657\) | 1.89741e37 | 0.174192 | ||||||||
\(658\) | 2.08255e38 | 1.87303 | ||||||||
\(659\) | 3.42254e37 | 0.301575 | 0.150788 | − | 0.988566i | \(-0.451819\pi\) | ||||
0.150788 | + | 0.988566i | \(0.451819\pi\) | |||||||
\(660\) | 4.70759e37 | 0.406401 | ||||||||
\(661\) | −1.89312e37 | −0.160125 | −0.0800625 | − | 0.996790i | \(-0.525512\pi\) | ||||
−0.0800625 | + | 0.996790i | \(0.525512\pi\) | |||||||
\(662\) | −6.37878e37 | −0.528634 | ||||||||
\(663\) | −7.41797e37 | −0.602355 | ||||||||
\(664\) | −2.43729e38 | −1.93927 | ||||||||
\(665\) | −2.28772e37 | −0.178366 | ||||||||
\(666\) | −9.94610e37 | −0.759890 | ||||||||
\(667\) | −1.40493e37 | −0.105185 | ||||||||
\(668\) | 3.62068e38 | 2.65649 | ||||||||
\(669\) | −1.14818e37 | −0.0825575 | ||||||||
\(670\) | −3.71295e37 | −0.261643 | ||||||||
\(671\) | 1.37082e37 | 0.0946733 | ||||||||
\(672\) | −3.03628e38 | −2.05521 | ||||||||
\(673\) | 2.43532e38 | 1.61567 | 0.807835 | − | 0.589409i | \(-0.200639\pi\) | ||||
0.807835 | + | 0.589409i | \(0.200639\pi\) | |||||||
\(674\) | −3.41170e38 | −2.21852 | ||||||||
\(675\) | 2.82425e37 | 0.180012 | ||||||||
\(676\) | 1.81701e38 | 1.13521 | ||||||||
\(677\) | 2.58654e38 | 1.58406 | 0.792032 | − | 0.610479i | \(-0.209023\pi\) | ||||
0.792032 | + | 0.610479i | \(0.209023\pi\) | |||||||
\(678\) | −2.86931e38 | −1.72257 | ||||||||
\(679\) | −4.04763e38 | −2.38209 | ||||||||
\(680\) | 1.07865e38 | 0.622315 | ||||||||
\(681\) | 1.98329e38 | 1.12176 | ||||||||
\(682\) | −2.68158e38 | −1.48697 | ||||||||
\(683\) | 5.72592e37 | 0.311290 | 0.155645 | − | 0.987813i | \(-0.450254\pi\) | ||||
0.155645 | + | 0.987813i | \(0.450254\pi\) | |||||||
\(684\) | 7.40694e37 | 0.394804 | ||||||||
\(685\) | 5.71427e37 | 0.298633 | ||||||||
\(686\) | 1.13951e38 | 0.583903 | ||||||||
\(687\) | −1.83258e38 | −0.920762 | ||||||||
\(688\) | 4.39222e38 | 2.16392 | ||||||||
\(689\) | −2.78949e38 | −1.34761 | ||||||||
\(690\) | 1.22685e37 | 0.0581202 | ||||||||
\(691\) | −1.45765e38 | −0.677175 | −0.338588 | − | 0.940935i | \(-0.609949\pi\) | ||||
−0.338588 | + | 0.940935i | \(0.609949\pi\) | |||||||
\(692\) | 2.73888e38 | 1.24779 | ||||||||
\(693\) | 1.22369e38 | 0.546731 | ||||||||
\(694\) | 5.54524e38 | 2.42978 | ||||||||
\(695\) | −8.13502e37 | −0.349594 | ||||||||
\(696\) | 1.92746e38 | 0.812382 | ||||||||
\(697\) | 1.83120e38 | 0.756994 | ||||||||
\(698\) | −7.59861e38 | −3.08096 | ||||||||
\(699\) | −2.22037e38 | −0.883047 | ||||||||
\(700\) | −8.94424e38 | −3.48915 | ||||||||
\(701\) | −5.69328e37 | −0.217856 | −0.108928 | − | 0.994050i | \(-0.534742\pi\) | ||||
−0.108928 | + | 0.994050i | \(0.534742\pi\) | |||||||
\(702\) | 1.15751e38 | 0.434486 | ||||||||
\(703\) | −1.55985e38 | −0.574363 | ||||||||
\(704\) | 5.18799e38 | 1.87399 | ||||||||
\(705\) | 2.78593e37 | 0.0987229 | ||||||||
\(706\) | −1.44152e38 | −0.501138 | ||||||||
\(707\) | 6.63079e38 | 2.26153 | ||||||||
\(708\) | 3.76339e38 | 1.25930 | ||||||||
\(709\) | 2.15586e38 | 0.707776 | 0.353888 | − | 0.935288i | \(-0.384859\pi\) | ||||
0.353888 | + | 0.935288i | \(0.384859\pi\) | |||||||
\(710\) | −1.94968e38 | −0.628024 | ||||||||
\(711\) | −1.25732e38 | −0.397380 | ||||||||
\(712\) | −5.84656e38 | −1.81310 | ||||||||
\(713\) | −4.99712e37 | −0.152059 | ||||||||
\(714\) | 4.66144e38 | 1.39185 | ||||||||
\(715\) | 1.15376e38 | 0.338053 | ||||||||
\(716\) | 4.64577e38 | 1.33577 | ||||||||
\(717\) | −1.88356e38 | −0.531461 | ||||||||
\(718\) | 8.92129e38 | 2.47029 | ||||||||
\(719\) | 2.25632e38 | 0.613141 | 0.306571 | − | 0.951848i | \(-0.400818\pi\) | ||||
0.306571 | + | 0.951848i | \(0.400818\pi\) | |||||||
\(720\) | −8.85789e37 | −0.236234 | ||||||||
\(721\) | 1.90361e38 | 0.498256 | ||||||||
\(722\) | −5.66783e38 | −1.45601 | ||||||||
\(723\) | −2.22571e38 | −0.561179 | ||||||||
\(724\) | −6.66130e38 | −1.64850 | ||||||||
\(725\) | 1.91622e38 | 0.465459 | ||||||||
\(726\) | −9.86534e37 | −0.235217 | ||||||||
\(727\) | 3.26448e38 | 0.764010 | 0.382005 | − | 0.924160i | \(-0.375234\pi\) | ||||
0.382005 | + | 0.924160i | \(0.375234\pi\) | |||||||
\(728\) | −2.20497e39 | −5.06557 | ||||||||
\(729\) | 1.64232e37 | 0.0370370 | ||||||||
\(730\) | −1.12419e38 | −0.248875 | ||||||||
\(731\) | −3.09207e38 | −0.671993 | ||||||||
\(732\) | −5.82649e37 | −0.124310 | ||||||||
\(733\) | 3.51091e38 | 0.735387 | 0.367694 | − | 0.929947i | \(-0.380147\pi\) | ||||
0.367694 | + | 0.929947i | \(0.380147\pi\) | |||||||
\(734\) | −6.60578e37 | −0.135840 | ||||||||
\(735\) | 8.79435e37 | 0.177552 | ||||||||
\(736\) | 2.55364e38 | 0.506185 | ||||||||
\(737\) | 3.11472e38 | 0.606190 | ||||||||
\(738\) | −2.85743e38 | −0.546028 | ||||||||
\(739\) | −5.12467e38 | −0.961537 | −0.480768 | − | 0.876848i | \(-0.659642\pi\) | ||||
−0.480768 | + | 0.876848i | \(0.659642\pi\) | |||||||
\(740\) | 4.21375e38 | 0.776320 | ||||||||
\(741\) | 1.81534e38 | 0.328406 | ||||||||
\(742\) | 1.75291e39 | 3.11391 | ||||||||
\(743\) | −6.94450e38 | −1.21141 | −0.605706 | − | 0.795688i | \(-0.707109\pi\) | ||||
−0.605706 | + | 0.795688i | \(0.707109\pi\) | |||||||
\(744\) | 6.85570e38 | 1.17440 | ||||||||
\(745\) | 1.85134e37 | 0.0311442 | ||||||||
\(746\) | 8.94095e38 | 1.47710 | ||||||||
\(747\) | −1.40904e38 | −0.228609 | ||||||||
\(748\) | −1.50434e39 | −2.39703 | ||||||||
\(749\) | −4.96879e38 | −0.777582 | ||||||||
\(750\) | −3.46228e38 | −0.532151 | ||||||||
\(751\) | 5.87337e38 | 0.886642 | 0.443321 | − | 0.896363i | \(-0.353800\pi\) | ||||
0.443321 | + | 0.896363i | \(0.353800\pi\) | |||||||
\(752\) | 1.26460e39 | 1.87505 | ||||||||
\(753\) | −1.57520e38 | −0.229405 | ||||||||
\(754\) | 7.85359e38 | 1.12345 | ||||||||
\(755\) | 3.11863e38 | 0.438208 | ||||||||
\(756\) | −5.20114e38 | −0.717884 | ||||||||
\(757\) | 1.01202e38 | 0.137212 | 0.0686062 | − | 0.997644i | \(-0.478145\pi\) | ||||
0.0686062 | + | 0.997644i | \(0.478145\pi\) | |||||||
\(758\) | 1.81223e39 | 2.41368 | ||||||||
\(759\) | −1.02918e38 | −0.134656 | ||||||||
\(760\) | −2.63969e38 | −0.339289 | ||||||||
\(761\) | −1.48838e39 | −1.87941 | −0.939705 | − | 0.341987i | \(-0.888900\pi\) | ||||
−0.939705 | + | 0.341987i | \(0.888900\pi\) | |||||||
\(762\) | −7.47737e37 | −0.0927591 | ||||||||
\(763\) | −2.19076e39 | −2.67002 | ||||||||
\(764\) | 2.77241e39 | 3.31969 | ||||||||
\(765\) | 6.23585e37 | 0.0733611 | ||||||||
\(766\) | −1.12982e39 | −1.30593 | ||||||||
\(767\) | 9.22353e38 | 1.04751 | ||||||||
\(768\) | 1.15973e38 | 0.129414 | ||||||||
\(769\) | −1.63286e39 | −1.79037 | −0.895186 | − | 0.445692i | \(-0.852958\pi\) | ||||
−0.895186 | + | 0.445692i | \(0.852958\pi\) | |||||||
\(770\) | −7.25022e38 | −0.781135 | ||||||||
\(771\) | 1.37215e38 | 0.145267 | ||||||||
\(772\) | −8.87931e38 | −0.923731 | ||||||||
\(773\) | 9.47969e36 | 0.00969105 | 0.00484552 | − | 0.999988i | \(-0.498458\pi\) | ||||
0.00484552 | + | 0.999988i | \(0.498458\pi\) | |||||||
\(774\) | 4.82492e38 | 0.484716 | ||||||||
\(775\) | 6.81571e38 | 0.672881 | ||||||||
\(776\) | −4.67036e39 | −4.53124 | ||||||||
\(777\) | 1.09532e39 | 1.04438 | ||||||||
\(778\) | −7.76327e38 | −0.727479 | ||||||||
\(779\) | −4.48133e38 | −0.412716 | ||||||||
\(780\) | −4.90391e38 | −0.443880 | ||||||||
\(781\) | 1.63555e39 | 1.45504 | ||||||||
\(782\) | −3.92046e38 | −0.342804 | ||||||||
\(783\) | 1.11429e38 | 0.0957670 | ||||||||
\(784\) | 3.99196e39 | 3.37225 | ||||||||
\(785\) | −1.39081e38 | −0.115485 | ||||||||
\(786\) | −2.49072e39 | −2.03292 | ||||||||
\(787\) | 1.01258e39 | 0.812401 | 0.406201 | − | 0.913784i | \(-0.366853\pi\) | ||||
0.406201 | + | 0.913784i | \(0.366853\pi\) | |||||||
\(788\) | 3.25671e39 | 2.56847 | ||||||||
\(789\) | 4.47864e38 | 0.347222 | ||||||||
\(790\) | 7.44945e38 | 0.567752 | ||||||||
\(791\) | 3.15986e39 | 2.36748 | ||||||||
\(792\) | 1.41196e39 | 1.04000 | ||||||||
\(793\) | −1.42799e38 | −0.103404 | ||||||||
\(794\) | −1.69247e39 | −1.20488 | ||||||||
\(795\) | 2.34495e38 | 0.164126 | ||||||||
\(796\) | −2.80799e39 | −1.93227 | ||||||||
\(797\) | −1.64542e39 | −1.11324 | −0.556620 | − | 0.830767i | \(-0.687902\pi\) | ||||
−0.556620 | + | 0.830767i | \(0.687902\pi\) | |||||||
\(798\) | −1.14075e39 | −0.758844 | ||||||||
\(799\) | −8.90263e38 | −0.582287 | ||||||||
\(800\) | −3.48298e39 | −2.23994 | ||||||||
\(801\) | −3.37999e38 | −0.213735 | ||||||||
\(802\) | −4.96483e38 | −0.308710 | ||||||||
\(803\) | 9.43063e38 | 0.576608 | ||||||||
\(804\) | −1.32387e39 | −0.795956 | ||||||||
\(805\) | −1.35108e38 | −0.0798796 | ||||||||
\(806\) | 2.79341e39 | 1.62410 | ||||||||
\(807\) | 1.63741e38 | 0.0936193 | ||||||||
\(808\) | 7.65094e39 | 4.30191 | ||||||||
\(809\) | −3.76453e38 | −0.208164 | −0.104082 | − | 0.994569i | \(-0.533190\pi\) | ||||
−0.104082 | + | 0.994569i | \(0.533190\pi\) | |||||||
\(810\) | −9.73053e37 | −0.0529162 | ||||||||
\(811\) | 1.84807e39 | 0.988408 | 0.494204 | − | 0.869346i | \(-0.335460\pi\) | ||||
0.494204 | + | 0.869346i | \(0.335460\pi\) | |||||||
\(812\) | −3.52891e39 | −1.85624 | ||||||||
\(813\) | 2.03284e39 | 1.05167 | ||||||||
\(814\) | −4.94347e39 | −2.51537 | ||||||||
\(815\) | −4.59912e38 | −0.230169 | ||||||||
\(816\) | 2.83060e39 | 1.39335 | ||||||||
\(817\) | 7.56696e38 | 0.366373 | ||||||||
\(818\) | −2.51450e38 | −0.119752 | ||||||||
\(819\) | −1.27473e39 | −0.597151 | ||||||||
\(820\) | 1.21058e39 | 0.557834 | ||||||||
\(821\) | −4.29041e39 | −1.94476 | −0.972380 | − | 0.233401i | \(-0.925014\pi\) | ||||
−0.972380 | + | 0.233401i | \(0.925014\pi\) | |||||||
\(822\) | 2.84938e39 | 1.27052 | ||||||||
\(823\) | −1.74258e39 | −0.764355 | −0.382177 | − | 0.924089i | \(-0.624826\pi\) | ||||
−0.382177 | + | 0.924089i | \(0.624826\pi\) | |||||||
\(824\) | 2.19648e39 | 0.947787 | ||||||||
\(825\) | 1.40372e39 | 0.595873 | ||||||||
\(826\) | −5.79604e39 | −2.42048 | ||||||||
\(827\) | 3.90760e39 | 1.60541 | 0.802704 | − | 0.596378i | \(-0.203394\pi\) | ||||
0.802704 | + | 0.596378i | \(0.203394\pi\) | |||||||
\(828\) | 4.37438e38 | 0.176810 | ||||||||
\(829\) | 1.05175e39 | 0.418243 | 0.209121 | − | 0.977890i | \(-0.432940\pi\) | ||||
0.209121 | + | 0.977890i | \(0.432940\pi\) | |||||||
\(830\) | 8.34836e38 | 0.326623 | ||||||||
\(831\) | −1.74917e39 | −0.673313 | ||||||||
\(832\) | −5.40435e39 | −2.04681 | ||||||||
\(833\) | −2.81029e39 | −1.04723 | ||||||||
\(834\) | −4.05646e39 | −1.48732 | ||||||||
\(835\) | −7.45966e38 | −0.269124 | ||||||||
\(836\) | 3.68144e39 | 1.30687 | ||||||||
\(837\) | 3.96338e38 | 0.138443 | ||||||||
\(838\) | 1.34355e39 | 0.461807 | ||||||||
\(839\) | −9.84534e38 | −0.333000 | −0.166500 | − | 0.986041i | \(-0.553247\pi\) | ||||
−0.166500 | + | 0.986041i | \(0.553247\pi\) | |||||||
\(840\) | 1.85358e39 | 0.616938 | ||||||||
\(841\) | −2.29710e39 | −0.752374 | ||||||||
\(842\) | −1.85177e38 | −0.0596861 | ||||||||
\(843\) | −2.16325e39 | −0.686173 | ||||||||
\(844\) | 4.53270e39 | 1.41493 | ||||||||
\(845\) | −3.74357e38 | −0.115006 | ||||||||
\(846\) | 1.38918e39 | 0.420010 | ||||||||
\(847\) | 1.08643e39 | 0.323278 | ||||||||
\(848\) | 1.06443e40 | 3.11726 | ||||||||
\(849\) | −3.40968e39 | −0.982788 | ||||||||
\(850\) | 5.34723e39 | 1.51696 | ||||||||
\(851\) | −9.21214e38 | −0.257224 | ||||||||
\(852\) | −6.95169e39 | −1.91054 | ||||||||
\(853\) | 2.30350e39 | 0.623125 | 0.311563 | − | 0.950226i | \(-0.399148\pi\) | ||||
0.311563 | + | 0.950226i | \(0.399148\pi\) | |||||||
\(854\) | 8.97347e38 | 0.238935 | ||||||||
\(855\) | −1.52605e38 | −0.0399968 | ||||||||
\(856\) | −5.73324e39 | −1.47912 | ||||||||
\(857\) | −1.77038e39 | −0.449600 | −0.224800 | − | 0.974405i | \(-0.572173\pi\) | ||||
−0.224800 | + | 0.974405i | \(0.572173\pi\) | |||||||
\(858\) | 5.75314e39 | 1.43823 | ||||||||
\(859\) | 5.46881e39 | 1.34581 | 0.672907 | − | 0.739727i | \(-0.265046\pi\) | ||||
0.672907 | + | 0.739727i | \(0.265046\pi\) | |||||||
\(860\) | −2.04412e39 | −0.495196 | ||||||||
\(861\) | 3.14678e39 | 0.750453 | ||||||||
\(862\) | 8.87047e39 | 2.08257 | ||||||||
\(863\) | 5.53394e39 | 1.27905 | 0.639526 | − | 0.768769i | \(-0.279130\pi\) | ||||
0.639526 | + | 0.768769i | \(0.279130\pi\) | |||||||
\(864\) | −2.02538e39 | −0.460862 | ||||||||
\(865\) | −5.64288e38 | −0.126411 | ||||||||
\(866\) | 3.13971e39 | 0.692465 | ||||||||
\(867\) | 6.66166e38 | 0.144652 | ||||||||
\(868\) | −1.25518e40 | −2.68343 | ||||||||
\(869\) | −6.24920e39 | −1.31540 | ||||||||
\(870\) | −6.60204e38 | −0.136826 | ||||||||
\(871\) | −3.24462e39 | −0.662093 | ||||||||
\(872\) | −2.52781e40 | −5.07893 | ||||||||
\(873\) | −2.70001e39 | −0.534162 | ||||||||
\(874\) | 9.59422e38 | 0.186898 | ||||||||
\(875\) | 3.81287e39 | 0.731380 | ||||||||
\(876\) | −4.00836e39 | −0.757114 | ||||||||
\(877\) | 7.58578e39 | 1.41093 | 0.705466 | − | 0.708744i | \(-0.250738\pi\) | ||||
0.705466 | + | 0.708744i | \(0.250738\pi\) | |||||||
\(878\) | 6.44831e38 | 0.118106 | ||||||||
\(879\) | −6.85699e38 | −0.123675 | ||||||||
\(880\) | −4.40260e39 | −0.781976 | ||||||||
\(881\) | −5.97063e38 | −0.104435 | −0.0522174 | − | 0.998636i | \(-0.516629\pi\) | ||||
−0.0522174 | + | 0.998636i | \(0.516629\pi\) | |||||||
\(882\) | 4.38523e39 | 0.755382 | ||||||||
\(883\) | −7.85839e39 | −1.33310 | −0.666552 | − | 0.745459i | \(-0.732230\pi\) | ||||
−0.666552 | + | 0.745459i | \(0.732230\pi\) | |||||||
\(884\) | 1.56708e40 | 2.61809 | ||||||||
\(885\) | −7.75367e38 | −0.127577 | ||||||||
\(886\) | −4.22635e39 | −0.684874 | ||||||||
\(887\) | 5.04306e39 | 0.804869 | 0.402434 | − | 0.915449i | \(-0.368164\pi\) | ||||
0.402434 | + | 0.915449i | \(0.368164\pi\) | |||||||
\(888\) | 1.26384e40 | 1.98663 | ||||||||
\(889\) | 8.23453e38 | 0.127487 | ||||||||
\(890\) | 2.00260e39 | 0.305372 | ||||||||
\(891\) | 8.16275e38 | 0.122599 | ||||||||
\(892\) | 2.42557e39 | 0.358829 | ||||||||
\(893\) | 2.17866e39 | 0.317465 | ||||||||
\(894\) | 9.23157e38 | 0.132501 | ||||||||
\(895\) | −9.57163e38 | −0.135324 | ||||||||
\(896\) | 8.39990e39 | 1.16981 | ||||||||
\(897\) | 1.07210e39 | 0.147074 | ||||||||
\(898\) | −8.44360e39 | −1.14103 | ||||||||
\(899\) | 2.68911e39 | 0.357975 | ||||||||
\(900\) | −5.96633e39 | −0.782409 | ||||||||
\(901\) | −7.49345e39 | −0.968048 | ||||||||
\(902\) | −1.42022e40 | −1.80745 | ||||||||
\(903\) | −5.31350e39 | −0.666187 | ||||||||
\(904\) | 3.64601e40 | 4.50344 | ||||||||
\(905\) | 1.37242e39 | 0.167006 | ||||||||
\(906\) | 1.55508e40 | 1.86433 | ||||||||
\(907\) | −7.33863e39 | −0.866796 | −0.433398 | − | 0.901203i | \(-0.642686\pi\) | ||||
−0.433398 | + | 0.901203i | \(0.642686\pi\) | |||||||
\(908\) | −4.18977e40 | −4.87564 | ||||||||
\(909\) | 4.42313e39 | 0.507127 | ||||||||
\(910\) | 7.55258e39 | 0.853172 | ||||||||
\(911\) | 7.23054e39 | 0.804771 | 0.402386 | − | 0.915470i | \(-0.368181\pi\) | ||||
0.402386 | + | 0.915470i | \(0.368181\pi\) | |||||||
\(912\) | −6.92708e39 | −0.759661 | ||||||||
\(913\) | −7.00327e39 | −0.756738 | ||||||||
\(914\) | −1.69274e40 | −1.80225 | ||||||||
\(915\) | 1.20043e38 | 0.0125936 | ||||||||
\(916\) | 3.87140e40 | 4.00202 | ||||||||
\(917\) | 2.74293e40 | 2.79401 | ||||||||
\(918\) | 3.10945e39 | 0.312110 | ||||||||
\(919\) | −1.06263e40 | −1.05105 | −0.525523 | − | 0.850780i | \(-0.676130\pi\) | ||||
−0.525523 | + | 0.850780i | \(0.676130\pi\) | |||||||
\(920\) | −1.55894e39 | −0.151948 | ||||||||
\(921\) | 9.08817e38 | 0.0872914 | ||||||||
\(922\) | −2.90448e40 | −2.74917 | ||||||||
\(923\) | −1.70376e40 | −1.58923 | ||||||||
\(924\) | −2.58510e40 | −2.37632 | ||||||||
\(925\) | 1.25647e40 | 1.13825 | ||||||||
\(926\) | 8.24570e39 | 0.736172 | ||||||||
\(927\) | 1.26982e39 | 0.111729 | ||||||||
\(928\) | −1.37419e40 | −1.19166 | ||||||||
\(929\) | −9.62717e39 | −0.822785 | −0.411392 | − | 0.911458i | \(-0.634957\pi\) | ||||
−0.411392 | + | 0.911458i | \(0.634957\pi\) | |||||||
\(930\) | −2.34825e39 | −0.197799 | ||||||||
\(931\) | 6.87738e39 | 0.570956 | ||||||||
\(932\) | 4.69062e40 | 3.83809 | ||||||||
\(933\) | 7.41813e39 | 0.598263 | ||||||||
\(934\) | −1.56365e40 | −1.24296 | ||||||||
\(935\) | 3.09938e39 | 0.242838 | ||||||||
\(936\) | −1.47084e40 | −1.13591 | ||||||||
\(937\) | 1.21318e40 | 0.923509 | 0.461755 | − | 0.887008i | \(-0.347220\pi\) | ||||
0.461755 | + | 0.887008i | \(0.347220\pi\) | |||||||
\(938\) | 2.03891e40 | 1.52989 | ||||||||
\(939\) | −6.90516e39 | −0.510726 | ||||||||
\(940\) | −5.88539e39 | −0.429091 | ||||||||
\(941\) | −5.05393e38 | −0.0363219 | −0.0181610 | − | 0.999835i | \(-0.505781\pi\) | ||||
−0.0181610 | + | 0.999835i | \(0.505781\pi\) | |||||||
\(942\) | −6.93514e39 | −0.491324 | ||||||||
\(943\) | −2.64657e39 | −0.184831 | ||||||||
\(944\) | −3.51957e40 | −2.42308 | ||||||||
\(945\) | 1.07159e39 | 0.0727273 | ||||||||
\(946\) | 2.39811e40 | 1.60450 | ||||||||
\(947\) | 8.58094e39 | 0.565992 | 0.282996 | − | 0.959121i | \(-0.408672\pi\) | ||||
0.282996 | + | 0.959121i | \(0.408672\pi\) | |||||||
\(948\) | 2.65613e40 | 1.72718 | ||||||||
\(949\) | −9.82392e39 | −0.629783 | ||||||||
\(950\) | −1.30858e40 | −0.827051 | ||||||||
\(951\) | 3.94413e39 | 0.245761 | ||||||||
\(952\) | −5.92324e40 | −3.63882 | ||||||||
\(953\) | −2.53482e39 | −0.153530 | −0.0767649 | − | 0.997049i | \(-0.524459\pi\) | ||||
−0.0767649 | + | 0.997049i | \(0.524459\pi\) | |||||||
\(954\) | 1.16929e40 | 0.698264 | ||||||||
\(955\) | −5.71197e39 | −0.336311 | ||||||||
\(956\) | 3.97910e40 | 2.30995 | ||||||||
\(957\) | 5.53833e39 | 0.317006 | ||||||||
\(958\) | −9.91616e38 | −0.0559640 | ||||||||
\(959\) | −3.13791e40 | −1.74618 | ||||||||
\(960\) | 4.54311e39 | 0.249282 | ||||||||
\(961\) | −8.91794e39 | −0.482502 | ||||||||
\(962\) | 5.14963e40 | 2.74734 | ||||||||
\(963\) | −3.31448e39 | −0.174365 | ||||||||
\(964\) | 4.70190e40 | 2.43912 | ||||||||
\(965\) | 1.82940e39 | 0.0935813 | ||||||||
\(966\) | −6.73704e39 | −0.339842 | ||||||||
\(967\) | −2.17064e39 | −0.107977 | −0.0539884 | − | 0.998542i | \(-0.517193\pi\) | ||||
−0.0539884 | + | 0.998542i | \(0.517193\pi\) | |||||||
\(968\) | 1.25358e40 | 0.614943 | ||||||||
\(969\) | 4.87658e39 | 0.235909 | ||||||||
\(970\) | 1.59972e40 | 0.763177 | ||||||||
\(971\) | 2.71062e40 | 1.27529 | 0.637645 | − | 0.770330i | \(-0.279909\pi\) | ||||
0.637645 | + | 0.770330i | \(0.279909\pi\) | |||||||
\(972\) | −3.46947e39 | −0.160979 | ||||||||
\(973\) | 4.46722e40 | 2.04416 | ||||||||
\(974\) | −4.88440e40 | −2.20427 | ||||||||
\(975\) | −1.46226e40 | −0.650824 | ||||||||
\(976\) | 5.44902e39 | 0.239192 | ||||||||
\(977\) | −4.41710e40 | −1.91232 | −0.956161 | − | 0.292841i | \(-0.905399\pi\) | ||||
−0.956161 | + | 0.292841i | \(0.905399\pi\) | |||||||
\(978\) | −2.29331e40 | −0.979239 | ||||||||
\(979\) | −1.67994e40 | −0.707502 | ||||||||
\(980\) | −1.85784e40 | −0.771714 | ||||||||
\(981\) | −1.46137e40 | −0.598726 | ||||||||
\(982\) | −7.29439e40 | −2.94770 | ||||||||
\(983\) | −2.40915e40 | −0.960266 | −0.480133 | − | 0.877196i | \(-0.659412\pi\) | ||||
−0.480133 | + | 0.877196i | \(0.659412\pi\) | |||||||
\(984\) | 3.63091e40 | 1.42752 | ||||||||
\(985\) | −6.70977e39 | −0.260207 | ||||||||
\(986\) | 2.10972e40 | 0.807026 | ||||||||
\(987\) | −1.52985e40 | −0.577256 | ||||||||
\(988\) | −3.83497e40 | −1.42739 | ||||||||
\(989\) | 4.46888e39 | 0.164077 | ||||||||
\(990\) | −4.83632e39 | −0.175162 | ||||||||
\(991\) | −1.16541e39 | −0.0416376 | −0.0208188 | − | 0.999783i | \(-0.506627\pi\) | ||||
−0.0208188 | + | 0.999783i | \(0.506627\pi\) | |||||||
\(992\) | −4.88782e40 | −1.72269 | ||||||||
\(993\) | 4.68589e39 | 0.162921 | ||||||||
\(994\) | 1.07064e41 | 3.67221 | ||||||||
\(995\) | 5.78527e39 | 0.195755 | ||||||||
\(996\) | 2.97664e40 | 0.993633 | ||||||||
\(997\) | 5.76017e40 | 1.89693 | 0.948463 | − | 0.316888i | \(-0.102638\pi\) | ||||
0.948463 | + | 0.316888i | \(0.102638\pi\) | |||||||
\(998\) | 2.41167e39 | 0.0783531 | ||||||||
\(999\) | 7.30646e39 | 0.234193 |
(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 | 3.28.a.b.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9.28.a.b.1.1 | 2 | |||
4.3 | odd | 2 | 48.28.a.e.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.28.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.28.a.b.1.1 | 2 | 3.2 | odd | 2 | |||
48.28.a.e.1.2 | 2 | 4.3 | odd | 2 |