Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,16,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, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
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: | \(4.28080515300\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −234.000 | −1.29268 | −0.646340 | − | 0.763050i | \(-0.723701\pi\) | ||||
−0.646340 | + | 0.763050i | \(0.723701\pi\) | |||||||
\(3\) | −2187.00 | −0.577350 | ||||||||
\(4\) | 21988.0 | 0.671021 | ||||||||
\(5\) | 280710. | 1.60688 | 0.803439 | − | 0.595387i | \(-0.203001\pi\) | ||||
0.803439 | + | 0.595387i | \(0.203001\pi\) | |||||||
\(6\) | 511758. | 0.746329 | ||||||||
\(7\) | −1.37334e6 | −0.630295 | −0.315148 | − | 0.949043i | \(-0.602054\pi\) | ||||
−0.315148 | + | 0.949043i | \(0.602054\pi\) | |||||||
\(8\) | 2.52252e6 | 0.425265 | ||||||||
\(9\) | 4.78297e6 | 0.333333 | ||||||||
\(10\) | −6.56861e7 | −2.07718 | ||||||||
\(11\) | 3.40311e7 | 0.526539 | 0.263269 | − | 0.964722i | \(-0.415199\pi\) | ||||
0.263269 | + | 0.964722i | \(0.415199\pi\) | |||||||
\(12\) | −4.80878e7 | −0.387414 | ||||||||
\(13\) | 3.84022e8 | 1.69739 | 0.848694 | − | 0.528884i | \(-0.177389\pi\) | ||||
0.848694 | + | 0.528884i | \(0.177389\pi\) | |||||||
\(14\) | 3.21362e8 | 0.814770 | ||||||||
\(15\) | −6.13913e8 | −0.927731 | ||||||||
\(16\) | −1.31077e9 | −1.22075 | ||||||||
\(17\) | 1.25921e9 | 0.744270 | 0.372135 | − | 0.928179i | \(-0.378626\pi\) | ||||
0.372135 | + | 0.928179i | \(0.378626\pi\) | |||||||
\(18\) | −1.11921e9 | −0.430893 | ||||||||
\(19\) | −2.49907e9 | −0.641397 | −0.320698 | − | 0.947181i | \(-0.603918\pi\) | ||||
−0.320698 | + | 0.947181i | \(0.603918\pi\) | |||||||
\(20\) | 6.17225e9 | 1.07825 | ||||||||
\(21\) | 3.00350e9 | 0.363901 | ||||||||
\(22\) | −7.96327e9 | −0.680646 | ||||||||
\(23\) | 1.12848e10 | 0.691093 | 0.345546 | − | 0.938402i | \(-0.387694\pi\) | ||||
0.345546 | + | 0.938402i | \(0.387694\pi\) | |||||||
\(24\) | −5.51675e9 | −0.245527 | ||||||||
\(25\) | 4.82805e10 | 1.58206 | ||||||||
\(26\) | −8.98612e10 | −2.19418 | ||||||||
\(27\) | −1.04604e10 | −0.192450 | ||||||||
\(28\) | −3.01971e10 | −0.422941 | ||||||||
\(29\) | −4.84135e10 | −0.521172 | −0.260586 | − | 0.965451i | \(-0.583916\pi\) | ||||
−0.260586 | + | 0.965451i | \(0.583916\pi\) | |||||||
\(30\) | 1.43656e11 | 1.19926 | ||||||||
\(31\) | 1.30547e11 | 0.852227 | 0.426113 | − | 0.904670i | \(-0.359882\pi\) | ||||
0.426113 | + | 0.904670i | \(0.359882\pi\) | |||||||
\(32\) | 2.24063e11 | 1.15278 | ||||||||
\(33\) | −7.44259e10 | −0.303997 | ||||||||
\(34\) | −2.94655e11 | −0.962102 | ||||||||
\(35\) | −3.85511e11 | −1.01281 | ||||||||
\(36\) | 1.05168e11 | 0.223674 | ||||||||
\(37\) | −2.00223e11 | −0.346738 | −0.173369 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173369 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(38\) | 5.84783e11 | 0.829120 | ||||||||
\(39\) | −8.39857e11 | −0.979988 | ||||||||
\(40\) | 7.08097e11 | 0.683349 | ||||||||
\(41\) | 6.79142e11 | 0.544605 | 0.272302 | − | 0.962212i | \(-0.412215\pi\) | ||||
0.272302 | + | 0.962212i | \(0.412215\pi\) | |||||||
\(42\) | −7.02820e11 | −0.470408 | ||||||||
\(43\) | 2.79482e11 | 0.156798 | 0.0783990 | − | 0.996922i | \(-0.475019\pi\) | ||||
0.0783990 | + | 0.996922i | \(0.475019\pi\) | |||||||
\(44\) | 7.48275e11 | 0.353318 | ||||||||
\(45\) | 1.34263e12 | 0.535626 | ||||||||
\(46\) | −2.64065e12 | −0.893362 | ||||||||
\(47\) | 1.52067e12 | 0.437826 | 0.218913 | − | 0.975744i | \(-0.429749\pi\) | ||||
0.218913 | + | 0.975744i | \(0.429749\pi\) | |||||||
\(48\) | 2.86666e12 | 0.704801 | ||||||||
\(49\) | −2.86149e12 | −0.602728 | ||||||||
\(50\) | −1.12976e13 | −2.04509 | ||||||||
\(51\) | −2.75389e12 | −0.429704 | ||||||||
\(52\) | 8.44388e12 | 1.13898 | ||||||||
\(53\) | 2.64605e12 | 0.309407 | 0.154703 | − | 0.987961i | \(-0.450558\pi\) | ||||
0.154703 | + | 0.987961i | \(0.450558\pi\) | |||||||
\(54\) | 2.44772e12 | 0.248776 | ||||||||
\(55\) | 9.55286e12 | 0.846083 | ||||||||
\(56\) | −3.46429e12 | −0.268043 | ||||||||
\(57\) | 5.46547e12 | 0.370310 | ||||||||
\(58\) | 1.13287e13 | 0.673708 | ||||||||
\(59\) | 7.39937e12 | 0.387084 | 0.193542 | − | 0.981092i | \(-0.438002\pi\) | ||||
0.193542 | + | 0.981092i | \(0.438002\pi\) | |||||||
\(60\) | −1.34987e13 | −0.622527 | ||||||||
\(61\) | −4.26596e13 | −1.73797 | −0.868987 | − | 0.494835i | \(-0.835228\pi\) | ||||
−0.868987 | + | 0.494835i | \(0.835228\pi\) | |||||||
\(62\) | −3.05481e13 | −1.10166 | ||||||||
\(63\) | −6.56866e12 | −0.210098 | ||||||||
\(64\) | −9.47931e12 | −0.269418 | ||||||||
\(65\) | 1.07799e14 | 2.72750 | ||||||||
\(66\) | 1.74157e13 | 0.392971 | ||||||||
\(67\) | −5.64080e13 | −1.13705 | −0.568525 | − | 0.822666i | \(-0.692486\pi\) | ||||
−0.568525 | + | 0.822666i | \(0.692486\pi\) | |||||||
\(68\) | 2.76875e13 | 0.499420 | ||||||||
\(69\) | −2.46799e13 | −0.399003 | ||||||||
\(70\) | 9.02097e13 | 1.30924 | ||||||||
\(71\) | −1.33150e14 | −1.73741 | −0.868705 | − | 0.495329i | \(-0.835047\pi\) | ||||
−0.868705 | + | 0.495329i | \(0.835047\pi\) | |||||||
\(72\) | 1.20651e13 | 0.141755 | ||||||||
\(73\) | 1.05603e14 | 1.11881 | 0.559405 | − | 0.828895i | \(-0.311030\pi\) | ||||
0.559405 | + | 0.828895i | \(0.311030\pi\) | |||||||
\(74\) | 4.68523e13 | 0.448221 | ||||||||
\(75\) | −1.05590e14 | −0.913401 | ||||||||
\(76\) | −5.49496e13 | −0.430390 | ||||||||
\(77\) | −4.67363e13 | −0.331875 | ||||||||
\(78\) | 1.96526e14 | 1.26681 | ||||||||
\(79\) | −5.56657e13 | −0.326125 | −0.163063 | − | 0.986616i | \(-0.552137\pi\) | ||||
−0.163063 | + | 0.986616i | \(0.552137\pi\) | |||||||
\(80\) | −3.67947e14 | −1.96160 | ||||||||
\(81\) | 2.28768e13 | 0.111111 | ||||||||
\(82\) | −1.58919e14 | −0.704000 | ||||||||
\(83\) | 3.78077e14 | 1.52931 | 0.764654 | − | 0.644441i | \(-0.222910\pi\) | ||||
0.764654 | + | 0.644441i | \(0.222910\pi\) | |||||||
\(84\) | 6.60410e13 | 0.244185 | ||||||||
\(85\) | 3.53472e14 | 1.19595 | ||||||||
\(86\) | −6.53988e13 | −0.202690 | ||||||||
\(87\) | 1.05880e14 | 0.300899 | ||||||||
\(88\) | 8.58440e13 | 0.223918 | ||||||||
\(89\) | 2.19315e14 | 0.525586 | 0.262793 | − | 0.964852i | \(-0.415356\pi\) | ||||
0.262793 | + | 0.964852i | \(0.415356\pi\) | |||||||
\(90\) | −3.14175e14 | −0.692393 | ||||||||
\(91\) | −5.27395e14 | −1.06986 | ||||||||
\(92\) | 2.48131e14 | 0.463737 | ||||||||
\(93\) | −2.85507e14 | −0.492033 | ||||||||
\(94\) | −3.55837e14 | −0.565969 | ||||||||
\(95\) | −7.01514e14 | −1.03065 | ||||||||
\(96\) | −4.90025e14 | −0.665556 | ||||||||
\(97\) | 7.03323e14 | 0.883826 | 0.441913 | − | 0.897058i | \(-0.354300\pi\) | ||||
0.441913 | + | 0.897058i | \(0.354300\pi\) | |||||||
\(98\) | 6.69588e14 | 0.779134 | ||||||||
\(99\) | 1.62769e14 | 0.175513 | ||||||||
\(100\) | 1.06159e15 | 1.06159 | ||||||||
\(101\) | 5.60434e14 | 0.520132 | 0.260066 | − | 0.965591i | \(-0.416256\pi\) | ||||
0.260066 | + | 0.965591i | \(0.416256\pi\) | |||||||
\(102\) | 6.44410e14 | 0.555470 | ||||||||
\(103\) | −2.24049e15 | −1.79499 | −0.897497 | − | 0.441021i | \(-0.854616\pi\) | ||||
−0.897497 | + | 0.441021i | \(0.854616\pi\) | |||||||
\(104\) | 9.68704e14 | 0.721840 | ||||||||
\(105\) | 8.43113e14 | 0.584745 | ||||||||
\(106\) | −6.19177e14 | −0.399964 | ||||||||
\(107\) | −1.23611e15 | −0.744184 | −0.372092 | − | 0.928196i | \(-0.621359\pi\) | ||||
−0.372092 | + | 0.928196i | \(0.621359\pi\) | |||||||
\(108\) | −2.30002e14 | −0.129138 | ||||||||
\(109\) | 9.13052e14 | 0.478406 | 0.239203 | − | 0.970970i | \(-0.423114\pi\) | ||||
0.239203 | + | 0.970970i | \(0.423114\pi\) | |||||||
\(110\) | −2.23537e15 | −1.09371 | ||||||||
\(111\) | 4.37888e14 | 0.200189 | ||||||||
\(112\) | 1.80014e15 | 0.769434 | ||||||||
\(113\) | −1.99316e15 | −0.796990 | −0.398495 | − | 0.917170i | \(-0.630467\pi\) | ||||
−0.398495 | + | 0.917170i | \(0.630467\pi\) | |||||||
\(114\) | −1.27892e15 | −0.478693 | ||||||||
\(115\) | 3.16777e15 | 1.11050 | ||||||||
\(116\) | −1.06452e15 | −0.349717 | ||||||||
\(117\) | 1.83677e15 | 0.565796 | ||||||||
\(118\) | −1.73145e15 | −0.500375 | ||||||||
\(119\) | −1.72933e15 | −0.469110 | ||||||||
\(120\) | −1.54861e15 | −0.394532 | ||||||||
\(121\) | −3.01914e15 | −0.722757 | ||||||||
\(122\) | 9.98235e15 | 2.24664 | ||||||||
\(123\) | −1.48528e15 | −0.314428 | ||||||||
\(124\) | 2.87047e15 | 0.571862 | ||||||||
\(125\) | 4.98624e15 | 0.935293 | ||||||||
\(126\) | 1.53707e15 | 0.271590 | ||||||||
\(127\) | 4.90777e15 | 0.817252 | 0.408626 | − | 0.912702i | \(-0.366008\pi\) | ||||
0.408626 | + | 0.912702i | \(0.366008\pi\) | |||||||
\(128\) | −5.12393e15 | −0.804505 | ||||||||
\(129\) | −6.11228e14 | −0.0905274 | ||||||||
\(130\) | −2.52249e16 | −3.52578 | ||||||||
\(131\) | −3.51036e15 | −0.463252 | −0.231626 | − | 0.972805i | \(-0.574405\pi\) | ||||
−0.231626 | + | 0.972805i | \(0.574405\pi\) | |||||||
\(132\) | −1.63648e15 | −0.203988 | ||||||||
\(133\) | 3.43208e15 | 0.404269 | ||||||||
\(134\) | 1.31995e16 | 1.46984 | ||||||||
\(135\) | −2.93633e15 | −0.309244 | ||||||||
\(136\) | 3.17638e15 | 0.316512 | ||||||||
\(137\) | −7.53799e15 | −0.710970 | −0.355485 | − | 0.934682i | \(-0.615684\pi\) | ||||
−0.355485 | + | 0.934682i | \(0.615684\pi\) | |||||||
\(138\) | 5.77510e15 | 0.515783 | ||||||||
\(139\) | 1.28475e16 | 1.08695 | 0.543474 | − | 0.839426i | \(-0.317109\pi\) | ||||
0.543474 | + | 0.839426i | \(0.317109\pi\) | |||||||
\(140\) | −8.47662e15 | −0.679615 | ||||||||
\(141\) | −3.32571e15 | −0.252779 | ||||||||
\(142\) | 3.11570e16 | 2.24592 | ||||||||
\(143\) | 1.30687e16 | 0.893741 | ||||||||
\(144\) | −6.26938e15 | −0.406917 | ||||||||
\(145\) | −1.35901e16 | −0.837460 | ||||||||
\(146\) | −2.47112e16 | −1.44626 | ||||||||
\(147\) | 6.25807e15 | 0.347985 | ||||||||
\(148\) | −4.40251e15 | −0.232668 | ||||||||
\(149\) | −1.88397e16 | −0.946620 | −0.473310 | − | 0.880896i | \(-0.656941\pi\) | ||||
−0.473310 | + | 0.880896i | \(0.656941\pi\) | |||||||
\(150\) | 2.47079e16 | 1.18073 | ||||||||
\(151\) | −2.86423e16 | −1.30221 | −0.651105 | − | 0.758988i | \(-0.725694\pi\) | ||||
−0.651105 | + | 0.758988i | \(0.725694\pi\) | |||||||
\(152\) | −6.30396e15 | −0.272764 | ||||||||
\(153\) | 6.02275e15 | 0.248090 | ||||||||
\(154\) | 1.09363e16 | 0.429008 | ||||||||
\(155\) | 3.66459e16 | 1.36942 | ||||||||
\(156\) | −1.84668e16 | −0.657592 | ||||||||
\(157\) | −4.28834e16 | −1.45560 | −0.727799 | − | 0.685790i | \(-0.759457\pi\) | ||||
−0.727799 | + | 0.685790i | \(0.759457\pi\) | |||||||
\(158\) | 1.30258e16 | 0.421575 | ||||||||
\(159\) | −5.78692e15 | −0.178636 | ||||||||
\(160\) | 6.28967e16 | 1.85237 | ||||||||
\(161\) | −1.54980e16 | −0.435593 | ||||||||
\(162\) | −5.35317e15 | −0.143631 | ||||||||
\(163\) | 1.55067e16 | 0.397294 | 0.198647 | − | 0.980071i | \(-0.436345\pi\) | ||||
0.198647 | + | 0.980071i | \(0.436345\pi\) | |||||||
\(164\) | 1.49330e16 | 0.365441 | ||||||||
\(165\) | −2.08921e16 | −0.488486 | ||||||||
\(166\) | −8.84701e16 | −1.97691 | ||||||||
\(167\) | 8.14637e16 | 1.74017 | 0.870083 | − | 0.492906i | \(-0.164065\pi\) | ||||
0.870083 | + | 0.492906i | \(0.164065\pi\) | |||||||
\(168\) | 7.57640e15 | 0.154754 | ||||||||
\(169\) | 9.62872e16 | 1.88113 | ||||||||
\(170\) | −8.27125e16 | −1.54598 | ||||||||
\(171\) | −1.19530e16 | −0.213799 | ||||||||
\(172\) | 6.14525e15 | 0.105215 | ||||||||
\(173\) | 4.87723e16 | 0.799517 | 0.399758 | − | 0.916621i | \(-0.369094\pi\) | ||||
0.399758 | + | 0.916621i | \(0.369094\pi\) | |||||||
\(174\) | −2.47760e16 | −0.388966 | ||||||||
\(175\) | −6.63058e16 | −0.997163 | ||||||||
\(176\) | −4.46070e16 | −0.642773 | ||||||||
\(177\) | −1.61824e16 | −0.223483 | ||||||||
\(178\) | −5.13197e16 | −0.679414 | ||||||||
\(179\) | −7.76361e16 | −0.985521 | −0.492760 | − | 0.870165i | \(-0.664012\pi\) | ||||
−0.492760 | + | 0.870165i | \(0.664012\pi\) | |||||||
\(180\) | 2.95217e16 | 0.359416 | ||||||||
\(181\) | −1.26205e16 | −0.147397 | −0.0736985 | − | 0.997281i | \(-0.523480\pi\) | ||||
−0.0736985 | + | 0.997281i | \(0.523480\pi\) | |||||||
\(182\) | 1.23410e17 | 1.38298 | ||||||||
\(183\) | 9.32966e16 | 1.00342 | ||||||||
\(184\) | 2.84662e16 | 0.293898 | ||||||||
\(185\) | −5.62047e16 | −0.557166 | ||||||||
\(186\) | 6.68086e16 | 0.636041 | ||||||||
\(187\) | 4.28522e16 | 0.391887 | ||||||||
\(188\) | 3.34366e16 | 0.293790 | ||||||||
\(189\) | 1.43657e16 | 0.121300 | ||||||||
\(190\) | 1.64154e17 | 1.33229 | ||||||||
\(191\) | −6.26505e16 | −0.488849 | −0.244424 | − | 0.969668i | \(-0.578599\pi\) | ||||
−0.244424 | + | 0.969668i | \(0.578599\pi\) | |||||||
\(192\) | 2.07312e16 | 0.155549 | ||||||||
\(193\) | −2.21474e16 | −0.159824 | −0.0799122 | − | 0.996802i | \(-0.525464\pi\) | ||||
−0.0799122 | + | 0.996802i | \(0.525464\pi\) | |||||||
\(194\) | −1.64578e17 | −1.14250 | ||||||||
\(195\) | −2.35756e17 | −1.57472 | ||||||||
\(196\) | −6.29184e16 | −0.404443 | ||||||||
\(197\) | −1.63106e17 | −1.00919 | −0.504594 | − | 0.863357i | \(-0.668358\pi\) | ||||
−0.504594 | + | 0.863357i | \(0.668358\pi\) | |||||||
\(198\) | −3.80881e16 | −0.226882 | ||||||||
\(199\) | 7.34283e16 | 0.421178 | 0.210589 | − | 0.977575i | \(-0.432462\pi\) | ||||
0.210589 | + | 0.977575i | \(0.432462\pi\) | |||||||
\(200\) | 1.21789e17 | 0.672793 | ||||||||
\(201\) | 1.23364e17 | 0.656477 | ||||||||
\(202\) | −1.31141e17 | −0.672364 | ||||||||
\(203\) | 6.64883e16 | 0.328492 | ||||||||
\(204\) | −6.05525e16 | −0.288340 | ||||||||
\(205\) | 1.90642e17 | 0.875113 | ||||||||
\(206\) | 5.24274e17 | 2.32035 | ||||||||
\(207\) | 5.39750e16 | 0.230364 | ||||||||
\(208\) | −5.03366e17 | −2.07209 | ||||||||
\(209\) | −8.50460e16 | −0.337720 | ||||||||
\(210\) | −1.97289e17 | −0.755887 | ||||||||
\(211\) | −1.22953e15 | −0.00454589 | −0.00227295 | − | 0.999997i | \(-0.500724\pi\) | ||||
−0.00227295 | + | 0.999997i | \(0.500724\pi\) | |||||||
\(212\) | 5.81814e16 | 0.207618 | ||||||||
\(213\) | 2.91198e17 | 1.00309 | ||||||||
\(214\) | 2.89251e17 | 0.961991 | ||||||||
\(215\) | 7.84534e16 | 0.251955 | ||||||||
\(216\) | −2.63865e16 | −0.0818423 | ||||||||
\(217\) | −1.79286e17 | −0.537154 | ||||||||
\(218\) | −2.13654e17 | −0.618426 | ||||||||
\(219\) | −2.30955e17 | −0.645945 | ||||||||
\(220\) | 2.10048e17 | 0.567739 | ||||||||
\(221\) | 4.83564e17 | 1.26332 | ||||||||
\(222\) | −1.02466e17 | −0.258781 | ||||||||
\(223\) | −8.18320e17 | −1.99819 | −0.999095 | − | 0.0425326i | \(-0.986457\pi\) | ||||
−0.999095 | + | 0.0425326i | \(0.986457\pi\) | |||||||
\(224\) | −3.07715e17 | −0.726589 | ||||||||
\(225\) | 2.30924e17 | 0.527352 | ||||||||
\(226\) | 4.66399e17 | 1.03025 | ||||||||
\(227\) | −5.79062e17 | −1.23746 | −0.618730 | − | 0.785604i | \(-0.712353\pi\) | ||||
−0.618730 | + | 0.785604i | \(0.712353\pi\) | |||||||
\(228\) | 1.20175e17 | 0.248486 | ||||||||
\(229\) | 9.00391e17 | 1.80163 | 0.900813 | − | 0.434207i | \(-0.142971\pi\) | ||||
0.900813 | + | 0.434207i | \(0.142971\pi\) | |||||||
\(230\) | −7.41257e17 | −1.43552 | ||||||||
\(231\) | 1.02212e17 | 0.191608 | ||||||||
\(232\) | −1.22124e17 | −0.221636 | ||||||||
\(233\) | −3.97437e17 | −0.698391 | −0.349196 | − | 0.937050i | \(-0.613545\pi\) | ||||
−0.349196 | + | 0.937050i | \(0.613545\pi\) | |||||||
\(234\) | −4.29803e17 | −0.731393 | ||||||||
\(235\) | 4.26868e17 | 0.703533 | ||||||||
\(236\) | 1.62697e17 | 0.259741 | ||||||||
\(237\) | 1.21741e17 | 0.188288 | ||||||||
\(238\) | 4.04662e17 | 0.606409 | ||||||||
\(239\) | 1.06770e18 | 1.55047 | 0.775236 | − | 0.631672i | \(-0.217631\pi\) | ||||
0.775236 | + | 0.631672i | \(0.217631\pi\) | |||||||
\(240\) | 8.04700e17 | 1.13253 | ||||||||
\(241\) | −2.98003e17 | −0.406530 | −0.203265 | − | 0.979124i | \(-0.565155\pi\) | ||||
−0.203265 | + | 0.979124i | \(0.565155\pi\) | |||||||
\(242\) | 7.06478e17 | 0.934293 | ||||||||
\(243\) | −5.00315e16 | −0.0641500 | ||||||||
\(244\) | −9.38000e17 | −1.16622 | ||||||||
\(245\) | −8.03248e17 | −0.968510 | ||||||||
\(246\) | 3.47556e17 | 0.406454 | ||||||||
\(247\) | −9.59699e17 | −1.08870 | ||||||||
\(248\) | 3.29308e17 | 0.362422 | ||||||||
\(249\) | −8.26855e17 | −0.882947 | ||||||||
\(250\) | −1.16678e18 | −1.20903 | ||||||||
\(251\) | 8.01026e17 | 0.805552 | 0.402776 | − | 0.915299i | \(-0.368045\pi\) | ||||
0.402776 | + | 0.915299i | \(0.368045\pi\) | |||||||
\(252\) | −1.44432e17 | −0.140980 | ||||||||
\(253\) | 3.84035e17 | 0.363887 | ||||||||
\(254\) | −1.14842e18 | −1.05644 | ||||||||
\(255\) | −7.73044e17 | −0.690482 | ||||||||
\(256\) | 1.50962e18 | 1.30939 | ||||||||
\(257\) | −1.35952e18 | −1.14522 | −0.572608 | − | 0.819829i | \(-0.694068\pi\) | ||||
−0.572608 | + | 0.819829i | \(0.694068\pi\) | |||||||
\(258\) | 1.43027e17 | 0.117023 | ||||||||
\(259\) | 2.74975e17 | 0.218547 | ||||||||
\(260\) | 2.37028e18 | 1.83021 | ||||||||
\(261\) | −2.31560e17 | −0.173724 | ||||||||
\(262\) | 8.21424e17 | 0.598836 | ||||||||
\(263\) | 2.74388e18 | 1.94401 | 0.972003 | − | 0.234967i | \(-0.0754983\pi\) | ||||
0.972003 | + | 0.234967i | \(0.0754983\pi\) | |||||||
\(264\) | −1.87741e17 | −0.129279 | ||||||||
\(265\) | 7.42774e17 | 0.497179 | ||||||||
\(266\) | −8.03108e17 | −0.522591 | ||||||||
\(267\) | −4.79642e17 | −0.303447 | ||||||||
\(268\) | −1.24030e18 | −0.762984 | ||||||||
\(269\) | −1.71195e18 | −1.02412 | −0.512058 | − | 0.858951i | \(-0.671117\pi\) | ||||
−0.512058 | + | 0.858951i | \(0.671117\pi\) | |||||||
\(270\) | 6.87100e17 | 0.399753 | ||||||||
\(271\) | −1.67001e18 | −0.945036 | −0.472518 | − | 0.881321i | \(-0.656655\pi\) | ||||
−0.472518 | + | 0.881321i | \(0.656655\pi\) | |||||||
\(272\) | −1.65053e18 | −0.908569 | ||||||||
\(273\) | 1.15341e18 | 0.617682 | ||||||||
\(274\) | 1.76389e18 | 0.919057 | ||||||||
\(275\) | 1.64304e18 | 0.833014 | ||||||||
\(276\) | −5.42662e17 | −0.267739 | ||||||||
\(277\) | −6.50407e17 | −0.312311 | −0.156155 | − | 0.987733i | \(-0.549910\pi\) | ||||
−0.156155 | + | 0.987733i | \(0.549910\pi\) | |||||||
\(278\) | −3.00632e18 | −1.40507 | ||||||||
\(279\) | 6.24404e17 | 0.284076 | ||||||||
\(280\) | −9.72460e17 | −0.430712 | ||||||||
\(281\) | 1.43557e18 | 0.619052 | 0.309526 | − | 0.950891i | \(-0.399830\pi\) | ||||
0.309526 | + | 0.950891i | \(0.399830\pi\) | |||||||
\(282\) | 7.78216e17 | 0.326762 | ||||||||
\(283\) | 2.60218e18 | 1.06399 | 0.531996 | − | 0.846747i | \(-0.321442\pi\) | ||||
0.531996 | + | 0.846747i | \(0.321442\pi\) | |||||||
\(284\) | −2.92770e18 | −1.16584 | ||||||||
\(285\) | 1.53421e18 | 0.595044 | ||||||||
\(286\) | −3.05807e18 | −1.15532 | ||||||||
\(287\) | −9.32695e17 | −0.343262 | ||||||||
\(288\) | 1.07169e18 | 0.384259 | ||||||||
\(289\) | −1.27682e18 | −0.446062 | ||||||||
\(290\) | 3.18009e18 | 1.08257 | ||||||||
\(291\) | −1.53817e18 | −0.510277 | ||||||||
\(292\) | 2.32201e18 | 0.750744 | ||||||||
\(293\) | −1.14850e18 | −0.361931 | −0.180965 | − | 0.983489i | \(-0.557922\pi\) | ||||
−0.180965 | + | 0.983489i | \(0.557922\pi\) | |||||||
\(294\) | −1.46439e18 | −0.449833 | ||||||||
\(295\) | 2.07708e18 | 0.621996 | ||||||||
\(296\) | −5.05067e17 | −0.147456 | ||||||||
\(297\) | −3.55977e17 | −0.101332 | ||||||||
\(298\) | 4.40848e18 | 1.22368 | ||||||||
\(299\) | 4.33363e18 | 1.17305 | ||||||||
\(300\) | −2.32170e18 | −0.612911 | ||||||||
\(301\) | −3.83825e17 | −0.0988291 | ||||||||
\(302\) | 6.70230e18 | 1.68334 | ||||||||
\(303\) | −1.22567e18 | −0.300299 | ||||||||
\(304\) | 3.27571e18 | 0.782986 | ||||||||
\(305\) | −1.19750e19 | −2.79271 | ||||||||
\(306\) | −1.40932e18 | −0.320701 | ||||||||
\(307\) | −5.53368e18 | −1.22879 | −0.614393 | − | 0.789000i | \(-0.710599\pi\) | ||||
−0.614393 | + | 0.789000i | \(0.710599\pi\) | |||||||
\(308\) | −1.02764e18 | −0.222695 | ||||||||
\(309\) | 4.89994e18 | 1.03634 | ||||||||
\(310\) | −8.57515e18 | −1.77023 | ||||||||
\(311\) | 2.57410e18 | 0.518708 | 0.259354 | − | 0.965782i | \(-0.416490\pi\) | ||||
0.259354 | + | 0.965782i | \(0.416490\pi\) | |||||||
\(312\) | −2.11856e18 | −0.416755 | ||||||||
\(313\) | −5.90030e18 | −1.13316 | −0.566581 | − | 0.824006i | \(-0.691734\pi\) | ||||
−0.566581 | + | 0.824006i | \(0.691734\pi\) | |||||||
\(314\) | 1.00347e19 | 1.88162 | ||||||||
\(315\) | −1.84389e18 | −0.337602 | ||||||||
\(316\) | −1.22398e18 | −0.218837 | ||||||||
\(317\) | 5.15806e18 | 0.900621 | 0.450310 | − | 0.892872i | \(-0.351313\pi\) | ||||
0.450310 | + | 0.892872i | \(0.351313\pi\) | |||||||
\(318\) | 1.35414e18 | 0.230919 | ||||||||
\(319\) | −1.64756e18 | −0.274417 | ||||||||
\(320\) | −2.66094e18 | −0.432922 | ||||||||
\(321\) | 2.70338e18 | 0.429655 | ||||||||
\(322\) | 3.62652e18 | 0.563082 | ||||||||
\(323\) | −3.14685e18 | −0.477372 | ||||||||
\(324\) | 5.03015e17 | 0.0745578 | ||||||||
\(325\) | 1.85408e19 | 2.68536 | ||||||||
\(326\) | −3.62857e18 | −0.513574 | ||||||||
\(327\) | −1.99684e18 | −0.276208 | ||||||||
\(328\) | 1.71315e18 | 0.231601 | ||||||||
\(329\) | −2.08841e18 | −0.275960 | ||||||||
\(330\) | 4.88875e18 | 0.631456 | ||||||||
\(331\) | 4.14841e18 | 0.523807 | 0.261903 | − | 0.965094i | \(-0.415650\pi\) | ||||
0.261903 | + | 0.965094i | \(0.415650\pi\) | |||||||
\(332\) | 8.31317e18 | 1.02620 | ||||||||
\(333\) | −9.57662e17 | −0.115579 | ||||||||
\(334\) | −1.90625e19 | −2.24948 | ||||||||
\(335\) | −1.58343e19 | −1.82710 | ||||||||
\(336\) | −3.93691e18 | −0.444233 | ||||||||
\(337\) | 3.83002e18 | 0.422646 | 0.211323 | − | 0.977416i | \(-0.432223\pi\) | ||||
0.211323 | + | 0.977416i | \(0.432223\pi\) | |||||||
\(338\) | −2.25312e19 | −2.43170 | ||||||||
\(339\) | 4.35903e18 | 0.460143 | ||||||||
\(340\) | 7.77215e18 | 0.802507 | ||||||||
\(341\) | 4.44266e18 | 0.448730 | ||||||||
\(342\) | 2.79700e18 | 0.276373 | ||||||||
\(343\) | 1.04498e19 | 1.01019 | ||||||||
\(344\) | 7.04999e17 | 0.0666807 | ||||||||
\(345\) | −6.92790e18 | −0.641148 | ||||||||
\(346\) | −1.14127e19 | −1.03352 | ||||||||
\(347\) | 1.29300e19 | 1.14585 | 0.572926 | − | 0.819607i | \(-0.305808\pi\) | ||||
0.572926 | + | 0.819607i | \(0.305808\pi\) | |||||||
\(348\) | 2.32809e18 | 0.201909 | ||||||||
\(349\) | 4.28556e18 | 0.363762 | 0.181881 | − | 0.983321i | \(-0.441781\pi\) | ||||
0.181881 | + | 0.983321i | \(0.441781\pi\) | |||||||
\(350\) | 1.55156e19 | 1.28901 | ||||||||
\(351\) | −4.01701e18 | −0.326663 | ||||||||
\(352\) | 7.62509e18 | 0.606981 | ||||||||
\(353\) | −1.23957e19 | −0.965967 | −0.482984 | − | 0.875629i | \(-0.660447\pi\) | ||||
−0.482984 | + | 0.875629i | \(0.660447\pi\) | |||||||
\(354\) | 3.78669e18 | 0.288892 | ||||||||
\(355\) | −3.73764e19 | −2.79181 | ||||||||
\(356\) | 4.82230e18 | 0.352679 | ||||||||
\(357\) | 3.78203e18 | 0.270841 | ||||||||
\(358\) | 1.81668e19 | 1.27396 | ||||||||
\(359\) | 1.32770e19 | 0.911784 | 0.455892 | − | 0.890035i | \(-0.349320\pi\) | ||||
0.455892 | + | 0.890035i | \(0.349320\pi\) | |||||||
\(360\) | 3.38680e18 | 0.227783 | ||||||||
\(361\) | −8.93577e18 | −0.588611 | ||||||||
\(362\) | 2.95320e18 | 0.190537 | ||||||||
\(363\) | 6.60285e18 | 0.417284 | ||||||||
\(364\) | −1.15964e19 | −0.717895 | ||||||||
\(365\) | 2.96439e19 | 1.79779 | ||||||||
\(366\) | −2.18314e19 | −1.29710 | ||||||||
\(367\) | −4.37416e18 | −0.254624 | −0.127312 | − | 0.991863i | \(-0.540635\pi\) | ||||
−0.127312 | + | 0.991863i | \(0.540635\pi\) | |||||||
\(368\) | −1.47918e19 | −0.843653 | ||||||||
\(369\) | 3.24831e18 | 0.181535 | ||||||||
\(370\) | 1.31519e19 | 0.720237 | ||||||||
\(371\) | −3.63394e18 | −0.195018 | ||||||||
\(372\) | −6.27773e18 | −0.330164 | ||||||||
\(373\) | 2.25672e19 | 1.16322 | 0.581608 | − | 0.813469i | \(-0.302424\pi\) | ||||
0.581608 | + | 0.813469i | \(0.302424\pi\) | |||||||
\(374\) | −1.00274e19 | −0.506584 | ||||||||
\(375\) | −1.09049e19 | −0.539992 | ||||||||
\(376\) | 3.83593e18 | 0.186192 | ||||||||
\(377\) | −1.85918e19 | −0.884631 | ||||||||
\(378\) | −3.36157e18 | −0.156803 | ||||||||
\(379\) | −2.49747e19 | −1.14211 | −0.571053 | − | 0.820913i | \(-0.693465\pi\) | ||||
−0.571053 | + | 0.820913i | \(0.693465\pi\) | |||||||
\(380\) | −1.54249e19 | −0.691584 | ||||||||
\(381\) | −1.07333e19 | −0.471841 | ||||||||
\(382\) | 1.46602e19 | 0.631925 | ||||||||
\(383\) | 5.61575e18 | 0.237365 | 0.118683 | − | 0.992932i | \(-0.462133\pi\) | ||||
0.118683 | + | 0.992932i | \(0.462133\pi\) | |||||||
\(384\) | 1.12060e19 | 0.464481 | ||||||||
\(385\) | −1.31194e19 | −0.533282 | ||||||||
\(386\) | 5.18250e18 | 0.206602 | ||||||||
\(387\) | 1.33675e18 | 0.0522660 | ||||||||
\(388\) | 1.54647e19 | 0.593065 | ||||||||
\(389\) | 2.11288e19 | 0.794792 | 0.397396 | − | 0.917647i | \(-0.369914\pi\) | ||||
0.397396 | + | 0.917647i | \(0.369914\pi\) | |||||||
\(390\) | 5.51669e19 | 2.03561 | ||||||||
\(391\) | 1.42099e19 | 0.514360 | ||||||||
\(392\) | −7.21816e18 | −0.256319 | ||||||||
\(393\) | 7.67716e18 | 0.267458 | ||||||||
\(394\) | 3.81667e19 | 1.30456 | ||||||||
\(395\) | −1.56259e19 | −0.524043 | ||||||||
\(396\) | 3.57898e18 | 0.117773 | ||||||||
\(397\) | −2.47105e19 | −0.797909 | −0.398955 | − | 0.916971i | \(-0.630627\pi\) | ||||
−0.398955 | + | 0.916971i | \(0.630627\pi\) | |||||||
\(398\) | −1.71822e19 | −0.544448 | ||||||||
\(399\) | −7.50597e18 | −0.233405 | ||||||||
\(400\) | −6.32848e19 | −1.93130 | ||||||||
\(401\) | 1.37114e18 | 0.0410675 | 0.0205338 | − | 0.999789i | \(-0.493463\pi\) | ||||
0.0205338 | + | 0.999789i | \(0.493463\pi\) | |||||||
\(402\) | −2.88673e19 | −0.848614 | ||||||||
\(403\) | 5.01331e19 | 1.44656 | ||||||||
\(404\) | 1.23228e19 | 0.349019 | ||||||||
\(405\) | 6.42174e18 | 0.178542 | ||||||||
\(406\) | −1.55583e19 | −0.424635 | ||||||||
\(407\) | −6.81381e18 | −0.182571 | ||||||||
\(408\) | −6.94674e18 | −0.182738 | ||||||||
\(409\) | −4.55723e19 | −1.17700 | −0.588500 | − | 0.808497i | \(-0.700281\pi\) | ||||
−0.588500 | + | 0.808497i | \(0.700281\pi\) | |||||||
\(410\) | −4.46102e19 | −1.13124 | ||||||||
\(411\) | 1.64856e19 | 0.410479 | ||||||||
\(412\) | −4.92638e19 | −1.20448 | ||||||||
\(413\) | −1.01619e19 | −0.243977 | ||||||||
\(414\) | −1.26302e19 | −0.297787 | ||||||||
\(415\) | 1.06130e20 | 2.45741 | ||||||||
\(416\) | 8.60451e19 | 1.95671 | ||||||||
\(417\) | −2.80975e19 | −0.627549 | ||||||||
\(418\) | 1.99008e19 | 0.436564 | ||||||||
\(419\) | −5.38156e18 | −0.115959 | −0.0579793 | − | 0.998318i | \(-0.518466\pi\) | ||||
−0.0579793 | + | 0.998318i | \(0.518466\pi\) | |||||||
\(420\) | 1.85384e19 | 0.392376 | ||||||||
\(421\) | −2.32562e19 | −0.483530 | −0.241765 | − | 0.970335i | \(-0.577726\pi\) | ||||
−0.241765 | + | 0.970335i | \(0.577726\pi\) | |||||||
\(422\) | 2.87709e17 | 0.00587638 | ||||||||
\(423\) | 7.27333e18 | 0.145942 | ||||||||
\(424\) | 6.67472e18 | 0.131580 | ||||||||
\(425\) | 6.07952e19 | 1.17748 | ||||||||
\(426\) | −6.81404e19 | −1.29668 | ||||||||
\(427\) | 5.85863e19 | 1.09544 | ||||||||
\(428\) | −2.71797e19 | −0.499363 | ||||||||
\(429\) | −2.85812e19 | −0.516001 | ||||||||
\(430\) | −1.83581e19 | −0.325698 | ||||||||
\(431\) | 9.18432e18 | 0.160128 | 0.0800640 | − | 0.996790i | \(-0.474488\pi\) | ||||
0.0800640 | + | 0.996790i | \(0.474488\pi\) | |||||||
\(432\) | 1.37111e19 | 0.234934 | ||||||||
\(433\) | −4.10991e19 | −0.692107 | −0.346053 | − | 0.938215i | \(-0.612478\pi\) | ||||
−0.346053 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(434\) | 4.19530e19 | 0.694368 | ||||||||
\(435\) | 2.97216e19 | 0.483508 | ||||||||
\(436\) | 2.00762e19 | 0.321020 | ||||||||
\(437\) | −2.82016e19 | −0.443265 | ||||||||
\(438\) | 5.40434e19 | 0.835000 | ||||||||
\(439\) | −1.19914e20 | −1.82132 | −0.910661 | − | 0.413154i | \(-0.864427\pi\) | ||||
−0.910661 | + | 0.413154i | \(0.864427\pi\) | |||||||
\(440\) | 2.40973e19 | 0.359810 | ||||||||
\(441\) | −1.36864e19 | −0.200909 | ||||||||
\(442\) | −1.13154e20 | −1.63306 | ||||||||
\(443\) | −8.85273e19 | −1.25617 | −0.628086 | − | 0.778144i | \(-0.716162\pi\) | ||||
−0.628086 | + | 0.778144i | \(0.716162\pi\) | |||||||
\(444\) | 9.62829e18 | 0.134331 | ||||||||
\(445\) | 6.15639e19 | 0.844552 | ||||||||
\(446\) | 1.91487e20 | 2.58302 | ||||||||
\(447\) | 4.12023e19 | 0.546532 | ||||||||
\(448\) | 1.30184e19 | 0.169813 | ||||||||
\(449\) | −1.33463e20 | −1.71203 | −0.856016 | − | 0.516949i | \(-0.827068\pi\) | ||||
−0.856016 | + | 0.516949i | \(0.827068\pi\) | |||||||
\(450\) | −5.40363e19 | −0.681697 | ||||||||
\(451\) | 2.31119e19 | 0.286755 | ||||||||
\(452\) | −4.38255e19 | −0.534797 | ||||||||
\(453\) | 6.26407e19 | 0.751831 | ||||||||
\(454\) | 1.35501e20 | 1.59964 | ||||||||
\(455\) | −1.48045e20 | −1.71913 | ||||||||
\(456\) | 1.37868e19 | 0.157480 | ||||||||
\(457\) | −1.02907e19 | −0.115631 | −0.0578154 | − | 0.998327i | \(-0.518413\pi\) | ||||
−0.0578154 | + | 0.998327i | \(0.518413\pi\) | |||||||
\(458\) | −2.10691e20 | −2.32893 | ||||||||
\(459\) | −1.31718e19 | −0.143235 | ||||||||
\(460\) | 6.96528e19 | 0.745169 | ||||||||
\(461\) | 1.62617e20 | 1.71163 | 0.855815 | − | 0.517282i | \(-0.173056\pi\) | ||||
0.855815 | + | 0.517282i | \(0.173056\pi\) | |||||||
\(462\) | −2.39177e19 | −0.247688 | ||||||||
\(463\) | 7.89872e18 | 0.0804821 | 0.0402410 | − | 0.999190i | \(-0.487187\pi\) | ||||
0.0402410 | + | 0.999190i | \(0.487187\pi\) | |||||||
\(464\) | 6.34590e19 | 0.636222 | ||||||||
\(465\) | −8.01446e19 | −0.790637 | ||||||||
\(466\) | 9.30002e19 | 0.902796 | ||||||||
\(467\) | 1.94989e20 | 1.86266 | 0.931328 | − | 0.364182i | \(-0.118651\pi\) | ||||
0.931328 | + | 0.364182i | \(0.118651\pi\) | |||||||
\(468\) | 4.03868e19 | 0.379661 | ||||||||
\(469\) | 7.74676e19 | 0.716678 | ||||||||
\(470\) | −9.98871e19 | −0.909443 | ||||||||
\(471\) | 9.37859e19 | 0.840390 | ||||||||
\(472\) | 1.86651e19 | 0.164613 | ||||||||
\(473\) | 9.51107e18 | 0.0825602 | ||||||||
\(474\) | −2.84874e19 | −0.243397 | ||||||||
\(475\) | −1.20656e20 | −1.01473 | ||||||||
\(476\) | −3.80244e19 | −0.314782 | ||||||||
\(477\) | 1.26560e19 | 0.103136 | ||||||||
\(478\) | −2.49841e20 | −2.00426 | ||||||||
\(479\) | −1.29233e20 | −1.02061 | −0.510303 | − | 0.859995i | \(-0.670467\pi\) | ||||
−0.510303 | + | 0.859995i | \(0.670467\pi\) | |||||||
\(480\) | −1.37555e20 | −1.06947 | ||||||||
\(481\) | −7.68902e19 | −0.588549 | ||||||||
\(482\) | 6.97326e19 | 0.525513 | ||||||||
\(483\) | 3.38940e19 | 0.251489 | ||||||||
\(484\) | −6.63848e19 | −0.484985 | ||||||||
\(485\) | 1.97430e20 | 1.42020 | ||||||||
\(486\) | 1.17074e19 | 0.0829254 | ||||||||
\(487\) | −1.65971e19 | −0.115762 | −0.0578808 | − | 0.998323i | \(-0.518434\pi\) | ||||
−0.0578808 | + | 0.998323i | \(0.518434\pi\) | |||||||
\(488\) | −1.07610e20 | −0.739100 | ||||||||
\(489\) | −3.39132e19 | −0.229378 | ||||||||
\(490\) | 1.87960e20 | 1.25197 | ||||||||
\(491\) | −5.60231e19 | −0.367499 | −0.183749 | − | 0.982973i | \(-0.558823\pi\) | ||||
−0.183749 | + | 0.982973i | \(0.558823\pi\) | |||||||
\(492\) | −3.26584e19 | −0.210987 | ||||||||
\(493\) | −6.09626e19 | −0.387893 | ||||||||
\(494\) | 2.24570e20 | 1.40734 | ||||||||
\(495\) | 4.56910e19 | 0.282028 | ||||||||
\(496\) | −1.71118e20 | −1.04036 | ||||||||
\(497\) | 1.82860e20 | 1.09508 | ||||||||
\(498\) | 1.93484e20 | 1.14137 | ||||||||
\(499\) | 2.21529e20 | 1.28729 | 0.643646 | − | 0.765324i | \(-0.277421\pi\) | ||||
0.643646 | + | 0.765324i | \(0.277421\pi\) | |||||||
\(500\) | 1.09637e20 | 0.627601 | ||||||||
\(501\) | −1.78161e20 | −1.00469 | ||||||||
\(502\) | −1.87440e20 | −1.04132 | ||||||||
\(503\) | 1.93755e20 | 1.06046 | 0.530229 | − | 0.847855i | \(-0.322106\pi\) | ||||
0.530229 | + | 0.847855i | \(0.322106\pi\) | |||||||
\(504\) | −1.65696e19 | −0.0893475 | ||||||||
\(505\) | 1.57319e20 | 0.835789 | ||||||||
\(506\) | −8.98641e19 | −0.470389 | ||||||||
\(507\) | −2.10580e20 | −1.08607 | ||||||||
\(508\) | 1.07912e20 | 0.548393 | ||||||||
\(509\) | −2.73407e20 | −1.36907 | −0.684536 | − | 0.728979i | \(-0.739995\pi\) | ||||
−0.684536 | + | 0.728979i | \(0.739995\pi\) | |||||||
\(510\) | 1.80892e20 | 0.892573 | ||||||||
\(511\) | −1.45030e20 | −0.705180 | ||||||||
\(512\) | −1.85350e20 | −0.888111 | ||||||||
\(513\) | 2.61412e19 | 0.123437 | ||||||||
\(514\) | 3.18128e20 | 1.48040 | ||||||||
\(515\) | −6.28927e20 | −2.88434 | ||||||||
\(516\) | −1.34397e19 | −0.0607457 | ||||||||
\(517\) | 5.17501e19 | 0.230532 | ||||||||
\(518\) | −6.43443e19 | −0.282512 | ||||||||
\(519\) | −1.06665e20 | −0.461601 | ||||||||
\(520\) | 2.71925e20 | 1.15991 | ||||||||
\(521\) | 3.07240e20 | 1.29180 | 0.645900 | − | 0.763422i | \(-0.276482\pi\) | ||||
0.645900 | + | 0.763422i | \(0.276482\pi\) | |||||||
\(522\) | 5.41851e19 | 0.224569 | ||||||||
\(523\) | 1.31068e20 | 0.535470 | 0.267735 | − | 0.963493i | \(-0.413725\pi\) | ||||
0.267735 | + | 0.963493i | \(0.413725\pi\) | |||||||
\(524\) | −7.71858e19 | −0.310851 | ||||||||
\(525\) | 1.45011e20 | 0.575712 | ||||||||
\(526\) | −6.42069e20 | −2.51298 | ||||||||
\(527\) | 1.64386e20 | 0.634287 | ||||||||
\(528\) | 9.75554e19 | 0.371105 | ||||||||
\(529\) | −1.39288e20 | −0.522391 | ||||||||
\(530\) | −1.73809e20 | −0.642693 | ||||||||
\(531\) | 3.53910e19 | 0.129028 | ||||||||
\(532\) | 7.54647e19 | 0.271273 | ||||||||
\(533\) | 2.60806e20 | 0.924406 | ||||||||
\(534\) | 1.12236e20 | 0.392260 | ||||||||
\(535\) | −3.46990e20 | −1.19581 | ||||||||
\(536\) | −1.42290e20 | −0.483548 | ||||||||
\(537\) | 1.69790e20 | 0.568991 | ||||||||
\(538\) | 4.00597e20 | 1.32385 | ||||||||
\(539\) | −9.73794e19 | −0.317360 | ||||||||
\(540\) | −6.45639e19 | −0.207509 | ||||||||
\(541\) | −2.52109e20 | −0.799114 | −0.399557 | − | 0.916708i | \(-0.630836\pi\) | ||||
−0.399557 | + | 0.916708i | \(0.630836\pi\) | |||||||
\(542\) | 3.90781e20 | 1.22163 | ||||||||
\(543\) | 2.76011e19 | 0.0850996 | ||||||||
\(544\) | 2.82142e20 | 0.857976 | ||||||||
\(545\) | 2.56303e20 | 0.768740 | ||||||||
\(546\) | −2.69898e20 | −0.798464 | ||||||||
\(547\) | 3.05687e20 | 0.892014 | 0.446007 | − | 0.895029i | \(-0.352846\pi\) | ||||
0.446007 | + | 0.895029i | \(0.352846\pi\) | |||||||
\(548\) | −1.65745e20 | −0.477076 | ||||||||
\(549\) | −2.04040e20 | −0.579325 | ||||||||
\(550\) | −3.84471e20 | −1.07682 | ||||||||
\(551\) | 1.20989e20 | 0.334278 | ||||||||
\(552\) | −6.22556e19 | −0.169682 | ||||||||
\(553\) | 7.64481e19 | 0.205555 | ||||||||
\(554\) | 1.52195e20 | 0.403718 | ||||||||
\(555\) | 1.22920e20 | 0.321680 | ||||||||
\(556\) | 2.82491e20 | 0.729364 | ||||||||
\(557\) | −6.09048e20 | −1.55145 | −0.775725 | − | 0.631071i | \(-0.782616\pi\) | ||||
−0.775725 | + | 0.631071i | \(0.782616\pi\) | |||||||
\(558\) | −1.46110e20 | −0.367219 | ||||||||
\(559\) | 1.07327e20 | 0.266147 | ||||||||
\(560\) | 5.05318e20 | 1.23639 | ||||||||
\(561\) | −9.37177e19 | −0.226256 | ||||||||
\(562\) | −3.35923e20 | −0.800236 | ||||||||
\(563\) | 8.90973e19 | 0.209436 | 0.104718 | − | 0.994502i | \(-0.466606\pi\) | ||||
0.104718 | + | 0.994502i | \(0.466606\pi\) | |||||||
\(564\) | −7.31257e19 | −0.169620 | ||||||||
\(565\) | −5.59499e20 | −1.28067 | ||||||||
\(566\) | −6.08909e20 | −1.37540 | ||||||||
\(567\) | −3.14177e19 | −0.0700328 | ||||||||
\(568\) | −3.35873e20 | −0.738860 | ||||||||
\(569\) | 5.02180e19 | 0.109023 | 0.0545114 | − | 0.998513i | \(-0.482640\pi\) | ||||
0.0545114 | + | 0.998513i | \(0.482640\pi\) | |||||||
\(570\) | −3.59006e20 | −0.769201 | ||||||||
\(571\) | 1.61396e20 | 0.341289 | 0.170645 | − | 0.985333i | \(-0.445415\pi\) | ||||
0.170645 | + | 0.985333i | \(0.445415\pi\) | |||||||
\(572\) | 2.87354e20 | 0.599718 | ||||||||
\(573\) | 1.37017e20 | 0.282237 | ||||||||
\(574\) | 2.18251e20 | 0.443728 | ||||||||
\(575\) | 5.44838e20 | 1.09335 | ||||||||
\(576\) | −4.53392e19 | −0.0898060 | ||||||||
\(577\) | 8.65106e20 | 1.69142 | 0.845709 | − | 0.533644i | \(-0.179178\pi\) | ||||
0.845709 | + | 0.533644i | \(0.179178\pi\) | |||||||
\(578\) | 2.98776e20 | 0.576616 | ||||||||
\(579\) | 4.84364e19 | 0.0922747 | ||||||||
\(580\) | −2.98820e20 | −0.561953 | ||||||||
\(581\) | −5.19230e20 | −0.963916 | ||||||||
\(582\) | 3.59931e20 | 0.659625 | ||||||||
\(583\) | 9.00480e19 | 0.162915 | ||||||||
\(584\) | 2.66387e20 | 0.475791 | ||||||||
\(585\) | 5.15599e20 | 0.909165 | ||||||||
\(586\) | 2.68750e20 | 0.467860 | ||||||||
\(587\) | 2.88926e20 | 0.496593 | 0.248296 | − | 0.968684i | \(-0.420129\pi\) | ||||
0.248296 | + | 0.968684i | \(0.420129\pi\) | |||||||
\(588\) | 1.37603e20 | 0.233505 | ||||||||
\(589\) | −3.26247e20 | −0.546615 | ||||||||
\(590\) | −4.86036e20 | −0.804042 | ||||||||
\(591\) | 3.56712e20 | 0.582655 | ||||||||
\(592\) | 2.62447e20 | 0.423281 | ||||||||
\(593\) | −8.44010e20 | −1.34412 | −0.672059 | − | 0.740498i | \(-0.734590\pi\) | ||||
−0.672059 | + | 0.740498i | \(0.734590\pi\) | |||||||
\(594\) | 8.32986e19 | 0.130990 | ||||||||
\(595\) | −4.85439e20 | −0.753802 | ||||||||
\(596\) | −4.14246e20 | −0.635202 | ||||||||
\(597\) | −1.60588e20 | −0.243167 | ||||||||
\(598\) | −1.01407e21 | −1.51638 | ||||||||
\(599\) | 8.76702e19 | 0.129465 | 0.0647323 | − | 0.997903i | \(-0.479381\pi\) | ||||
0.0647323 | + | 0.997903i | \(0.479381\pi\) | |||||||
\(600\) | −2.66352e20 | −0.388437 | ||||||||
\(601\) | 3.17659e20 | 0.457512 | 0.228756 | − | 0.973484i | \(-0.426534\pi\) | ||||
0.228756 | + | 0.973484i | \(0.426534\pi\) | |||||||
\(602\) | 8.98151e19 | 0.127754 | ||||||||
\(603\) | −2.69798e20 | −0.379017 | ||||||||
\(604\) | −6.29787e20 | −0.873809 | ||||||||
\(605\) | −8.47502e20 | −1.16138 | ||||||||
\(606\) | 2.86806e20 | 0.388190 | ||||||||
\(607\) | 4.16004e19 | 0.0556138 | 0.0278069 | − | 0.999613i | \(-0.491148\pi\) | ||||
0.0278069 | + | 0.999613i | \(0.491148\pi\) | |||||||
\(608\) | −5.59949e20 | −0.739387 | ||||||||
\(609\) | −1.45410e20 | −0.189655 | ||||||||
\(610\) | 2.80215e21 | 3.61008 | ||||||||
\(611\) | 5.83972e20 | 0.743161 | ||||||||
\(612\) | 1.32428e20 | 0.166473 | ||||||||
\(613\) | 1.14258e21 | 1.41883 | 0.709417 | − | 0.704789i | \(-0.248958\pi\) | ||||
0.709417 | + | 0.704789i | \(0.248958\pi\) | |||||||
\(614\) | 1.29488e21 | 1.58843 | ||||||||
\(615\) | −4.16934e20 | −0.505247 | ||||||||
\(616\) | −1.17893e20 | −0.141135 | ||||||||
\(617\) | −1.25983e21 | −1.48996 | −0.744979 | − | 0.667088i | \(-0.767541\pi\) | ||||
−0.744979 | + | 0.667088i | \(0.767541\pi\) | |||||||
\(618\) | −1.14659e21 | −1.33966 | ||||||||
\(619\) | −1.25354e21 | −1.44696 | −0.723482 | − | 0.690343i | \(-0.757459\pi\) | ||||
−0.723482 | + | 0.690343i | \(0.757459\pi\) | |||||||
\(620\) | 8.05771e20 | 0.918912 | ||||||||
\(621\) | −1.18043e20 | −0.133001 | ||||||||
\(622\) | −6.02340e20 | −0.670523 | ||||||||
\(623\) | −3.01195e20 | −0.331274 | ||||||||
\(624\) | 1.10086e21 | 1.19632 | ||||||||
\(625\) | −7.37181e19 | −0.0791542 | ||||||||
\(626\) | 1.38067e21 | 1.46481 | ||||||||
\(627\) | 1.85996e20 | 0.194983 | ||||||||
\(628\) | −9.42919e20 | −0.976736 | ||||||||
\(629\) | −2.52123e20 | −0.258067 | ||||||||
\(630\) | 4.31470e20 | 0.436412 | ||||||||
\(631\) | 1.47433e21 | 1.47359 | 0.736794 | − | 0.676118i | \(-0.236339\pi\) | ||||
0.736794 | + | 0.676118i | \(0.236339\pi\) | |||||||
\(632\) | −1.40418e20 | −0.138690 | ||||||||
\(633\) | 2.68897e18 | 0.00262457 | ||||||||
\(634\) | −1.20699e21 | −1.16421 | ||||||||
\(635\) | 1.37766e21 | 1.31322 | ||||||||
\(636\) | −1.27243e20 | −0.119868 | ||||||||
\(637\) | −1.09888e21 | −1.02306 | ||||||||
\(638\) | 3.85529e20 | 0.354734 | ||||||||
\(639\) | −6.36851e20 | −0.579137 | ||||||||
\(640\) | −1.43834e21 | −1.29274 | ||||||||
\(641\) | 1.46302e21 | 1.29962 | 0.649808 | − | 0.760098i | \(-0.274849\pi\) | ||||
0.649808 | + | 0.760098i | \(0.274849\pi\) | |||||||
\(642\) | −6.32591e20 | −0.555406 | ||||||||
\(643\) | 4.28205e20 | 0.371595 | 0.185798 | − | 0.982588i | \(-0.440513\pi\) | ||||
0.185798 | + | 0.982588i | \(0.440513\pi\) | |||||||
\(644\) | −3.40769e20 | −0.292292 | ||||||||
\(645\) | −1.71578e20 | −0.145466 | ||||||||
\(646\) | 7.36363e20 | 0.617089 | ||||||||
\(647\) | 3.19295e20 | 0.264491 | 0.132245 | − | 0.991217i | \(-0.457781\pi\) | ||||
0.132245 | + | 0.991217i | \(0.457781\pi\) | |||||||
\(648\) | 5.77072e19 | 0.0472517 | ||||||||
\(649\) | 2.51808e20 | 0.203814 | ||||||||
\(650\) | −4.33855e21 | −3.47132 | ||||||||
\(651\) | 3.92099e20 | 0.310126 | ||||||||
\(652\) | 3.40961e20 | 0.266593 | ||||||||
\(653\) | 2.05259e21 | 1.58655 | 0.793276 | − | 0.608863i | \(-0.208374\pi\) | ||||
0.793276 | + | 0.608863i | \(0.208374\pi\) | |||||||
\(654\) | 4.67262e20 | 0.357048 | ||||||||
\(655\) | −9.85393e20 | −0.744389 | ||||||||
\(656\) | −8.90200e20 | −0.664827 | ||||||||
\(657\) | 5.05098e20 | 0.372937 | ||||||||
\(658\) | 4.88687e20 | 0.356728 | ||||||||
\(659\) | −6.54661e20 | −0.472472 | −0.236236 | − | 0.971696i | \(-0.575914\pi\) | ||||
−0.236236 | + | 0.971696i | \(0.575914\pi\) | |||||||
\(660\) | −4.59375e20 | −0.327784 | ||||||||
\(661\) | −1.05234e19 | −0.00742415 | −0.00371207 | − | 0.999993i | \(-0.501182\pi\) | ||||
−0.00371207 | + | 0.999993i | \(0.501182\pi\) | |||||||
\(662\) | −9.70727e20 | −0.677115 | ||||||||
\(663\) | −1.05755e21 | −0.729375 | ||||||||
\(664\) | 9.53708e20 | 0.650361 | ||||||||
\(665\) | 9.63420e20 | 0.649611 | ||||||||
\(666\) | 2.24093e20 | 0.149407 | ||||||||
\(667\) | −5.46338e20 | −0.360178 | ||||||||
\(668\) | 1.79122e21 | 1.16769 | ||||||||
\(669\) | 1.78967e21 | 1.15366 | ||||||||
\(670\) | 3.70523e21 | 2.36186 | ||||||||
\(671\) | −1.45175e21 | −0.915110 | ||||||||
\(672\) | 6.72973e20 | 0.419497 | ||||||||
\(673\) | 1.38475e21 | 0.853606 | 0.426803 | − | 0.904345i | \(-0.359640\pi\) | ||||
0.426803 | + | 0.904345i | \(0.359640\pi\) | |||||||
\(674\) | −8.96225e20 | −0.546346 | ||||||||
\(675\) | −5.05031e20 | −0.304467 | ||||||||
\(676\) | 2.11716e21 | 1.26228 | ||||||||
\(677\) | −2.38617e21 | −1.40697 | −0.703487 | − | 0.710708i | \(-0.748375\pi\) | ||||
−0.703487 | + | 0.710708i | \(0.748375\pi\) | |||||||
\(678\) | −1.02001e21 | −0.594817 | ||||||||
\(679\) | −9.65904e20 | −0.557071 | ||||||||
\(680\) | 8.91641e20 | 0.508596 | ||||||||
\(681\) | 1.26641e21 | 0.714448 | ||||||||
\(682\) | −1.03958e21 | −0.580064 | ||||||||
\(683\) | 7.22891e20 | 0.398949 | 0.199475 | − | 0.979903i | \(-0.436076\pi\) | ||||
0.199475 | + | 0.979903i | \(0.436076\pi\) | |||||||
\(684\) | −2.62822e20 | −0.143463 | ||||||||
\(685\) | −2.11599e21 | −1.14244 | ||||||||
\(686\) | −2.44526e21 | −1.30585 | ||||||||
\(687\) | −1.96915e21 | −1.04017 | ||||||||
\(688\) | −3.66338e20 | −0.191412 | ||||||||
\(689\) | 1.01614e21 | 0.525183 | ||||||||
\(690\) | 1.62113e21 | 0.828800 | ||||||||
\(691\) | −3.35500e21 | −1.69671 | −0.848355 | − | 0.529428i | \(-0.822407\pi\) | ||||
−0.848355 | + | 0.529428i | \(0.822407\pi\) | |||||||
\(692\) | 1.07241e21 | 0.536492 | ||||||||
\(693\) | −2.23538e20 | −0.110625 | ||||||||
\(694\) | −3.02563e21 | −1.48122 | ||||||||
\(695\) | 3.60643e21 | 1.74659 | ||||||||
\(696\) | 2.67085e20 | 0.127962 | ||||||||
\(697\) | 8.55180e20 | 0.405333 | ||||||||
\(698\) | −1.00282e21 | −0.470227 | ||||||||
\(699\) | 8.69194e20 | 0.403216 | ||||||||
\(700\) | −1.45793e21 | −0.669117 | ||||||||
\(701\) | −2.23696e21 | −1.01572 | −0.507859 | − | 0.861440i | \(-0.669563\pi\) | ||||
−0.507859 | + | 0.861440i | \(0.669563\pi\) | |||||||
\(702\) | 9.39980e20 | 0.422270 | ||||||||
\(703\) | 5.00372e20 | 0.222397 | ||||||||
\(704\) | −3.22591e20 | −0.141859 | ||||||||
\(705\) | −9.33560e20 | −0.406185 | ||||||||
\(706\) | 2.90060e21 | 1.24869 | ||||||||
\(707\) | −7.69668e20 | −0.327837 | ||||||||
\(708\) | −3.55819e20 | −0.149962 | ||||||||
\(709\) | 9.51303e20 | 0.396709 | 0.198355 | − | 0.980130i | \(-0.436440\pi\) | ||||
0.198355 | + | 0.980130i | \(0.436440\pi\) | |||||||
\(710\) | 8.74609e21 | 3.60891 | ||||||||
\(711\) | −2.66247e20 | −0.108708 | ||||||||
\(712\) | 5.53227e20 | 0.223513 | ||||||||
\(713\) | 1.47320e21 | 0.588968 | ||||||||
\(714\) | −8.84996e20 | −0.350110 | ||||||||
\(715\) | 3.66851e21 | 1.43613 | ||||||||
\(716\) | −1.70706e21 | −0.661305 | ||||||||
\(717\) | −2.33505e21 | −0.895165 | ||||||||
\(718\) | −3.10682e21 | −1.17864 | ||||||||
\(719\) | −2.88492e21 | −1.08310 | −0.541549 | − | 0.840669i | \(-0.682162\pi\) | ||||
−0.541549 | + | 0.840669i | \(0.682162\pi\) | |||||||
\(720\) | −1.75988e21 | −0.653866 | ||||||||
\(721\) | 3.07696e21 | 1.13138 | ||||||||
\(722\) | 2.09097e21 | 0.760885 | ||||||||
\(723\) | 6.51732e20 | 0.234710 | ||||||||
\(724\) | −2.77500e20 | −0.0989064 | ||||||||
\(725\) | −2.33743e21 | −0.824524 | ||||||||
\(726\) | −1.54507e21 | −0.539414 | ||||||||
\(727\) | −5.91622e20 | −0.204426 | −0.102213 | − | 0.994763i | \(-0.532592\pi\) | ||||
−0.102213 | + | 0.994763i | \(0.532592\pi\) | |||||||
\(728\) | −1.33036e21 | −0.454972 | ||||||||
\(729\) | 1.09419e20 | 0.0370370 | ||||||||
\(730\) | −6.93668e21 | −2.32397 | ||||||||
\(731\) | 3.51926e20 | 0.116700 | ||||||||
\(732\) | 2.05141e21 | 0.673315 | ||||||||
\(733\) | 2.12276e21 | 0.689639 | 0.344819 | − | 0.938669i | \(-0.387940\pi\) | ||||
0.344819 | + | 0.938669i | \(0.387940\pi\) | |||||||
\(734\) | 1.02355e21 | 0.329147 | ||||||||
\(735\) | 1.75670e21 | 0.559170 | ||||||||
\(736\) | 2.52851e21 | 0.796675 | ||||||||
\(737\) | −1.91962e21 | −0.598701 | ||||||||
\(738\) | −7.60105e20 | −0.234667 | ||||||||
\(739\) | 1.37093e21 | 0.418970 | 0.209485 | − | 0.977812i | \(-0.432821\pi\) | ||||
0.209485 | + | 0.977812i | \(0.432821\pi\) | |||||||
\(740\) | −1.23583e21 | −0.373870 | ||||||||
\(741\) | 2.09886e21 | 0.628561 | ||||||||
\(742\) | 8.50342e20 | 0.252095 | ||||||||
\(743\) | 3.08860e21 | 0.906452 | 0.453226 | − | 0.891396i | \(-0.350273\pi\) | ||||
0.453226 | + | 0.891396i | \(0.350273\pi\) | |||||||
\(744\) | −7.20197e20 | −0.209245 | ||||||||
\(745\) | −5.28848e21 | −1.52110 | ||||||||
\(746\) | −5.28071e21 | −1.50367 | ||||||||
\(747\) | 1.80833e21 | 0.509769 | ||||||||
\(748\) | 9.42233e20 | 0.262964 | ||||||||
\(749\) | 1.69761e21 | 0.469056 | ||||||||
\(750\) | 2.55175e21 | 0.698036 | ||||||||
\(751\) | −3.91840e21 | −1.06123 | −0.530615 | − | 0.847613i | \(-0.678039\pi\) | ||||
−0.530615 | + | 0.847613i | \(0.678039\pi\) | |||||||
\(752\) | −1.99326e21 | −0.534477 | ||||||||
\(753\) | −1.75184e21 | −0.465086 | ||||||||
\(754\) | 4.35049e21 | 1.14355 | ||||||||
\(755\) | −8.04018e21 | −2.09249 | ||||||||
\(756\) | 3.15872e20 | 0.0813950 | ||||||||
\(757\) | 5.36424e21 | 1.36864 | 0.684319 | − | 0.729182i | \(-0.260099\pi\) | ||||
0.684319 | + | 0.729182i | \(0.260099\pi\) | |||||||
\(758\) | 5.84409e21 | 1.47638 | ||||||||
\(759\) | −8.39884e20 | −0.210090 | ||||||||
\(760\) | −1.76958e21 | −0.438298 | ||||||||
\(761\) | 2.53746e21 | 0.622320 | 0.311160 | − | 0.950358i | \(-0.399283\pi\) | ||||
0.311160 | + | 0.950358i | \(0.399283\pi\) | |||||||
\(762\) | 2.51159e21 | 0.609939 | ||||||||
\(763\) | −1.25393e21 | −0.301537 | ||||||||
\(764\) | −1.37756e21 | −0.328027 | ||||||||
\(765\) | 1.69065e21 | 0.398650 | ||||||||
\(766\) | −1.31409e21 | −0.306837 | ||||||||
\(767\) | 2.84152e21 | 0.657031 | ||||||||
\(768\) | −3.30153e21 | −0.755974 | ||||||||
\(769\) | 2.55340e21 | 0.578990 | 0.289495 | − | 0.957180i | \(-0.406513\pi\) | ||||
0.289495 | + | 0.957180i | \(0.406513\pi\) | |||||||
\(770\) | 3.06993e21 | 0.689363 | ||||||||
\(771\) | 2.97327e21 | 0.661191 | ||||||||
\(772\) | −4.86977e20 | −0.107246 | ||||||||
\(773\) | 1.21187e21 | 0.264307 | 0.132154 | − | 0.991229i | \(-0.457811\pi\) | ||||
0.132154 | + | 0.991229i | \(0.457811\pi\) | |||||||
\(774\) | −3.12801e20 | −0.0675632 | ||||||||
\(775\) | 6.30289e21 | 1.34827 | ||||||||
\(776\) | 1.77415e21 | 0.375860 | ||||||||
\(777\) | −6.01371e20 | −0.126178 | ||||||||
\(778\) | −4.94415e21 | −1.02741 | ||||||||
\(779\) | −1.69722e21 | −0.349308 | ||||||||
\(780\) | −5.18381e21 | −1.05667 | ||||||||
\(781\) | −4.53122e21 | −0.914814 | ||||||||
\(782\) | −3.32513e21 | −0.664902 | ||||||||
\(783\) | 5.06422e20 | 0.100300 | ||||||||
\(784\) | 3.75076e21 | 0.735781 | ||||||||
\(785\) | −1.20378e22 | −2.33897 | ||||||||
\(786\) | −1.79646e21 | −0.345738 | ||||||||
\(787\) | 5.53051e21 | 1.05428 | 0.527139 | − | 0.849779i | \(-0.323265\pi\) | ||||
0.527139 | + | 0.849779i | \(0.323265\pi\) | |||||||
\(788\) | −3.58636e21 | −0.677186 | ||||||||
\(789\) | −6.00088e21 | −1.12237 | ||||||||
\(790\) | 3.65646e21 | 0.677420 | ||||||||
\(791\) | 2.73729e21 | 0.502339 | ||||||||
\(792\) | 4.10589e20 | 0.0746395 | ||||||||
\(793\) | −1.63822e22 | −2.95002 | ||||||||
\(794\) | 5.78227e21 | 1.03144 | ||||||||
\(795\) | −1.62445e21 | −0.287046 | ||||||||
\(796\) | 1.61454e21 | 0.282619 | ||||||||
\(797\) | 9.38793e21 | 1.62792 | 0.813959 | − | 0.580922i | \(-0.197308\pi\) | ||||
0.813959 | + | 0.580922i | \(0.197308\pi\) | |||||||
\(798\) | 1.75640e21 | 0.301718 | ||||||||
\(799\) | 1.91484e21 | 0.325861 | ||||||||
\(800\) | 1.08179e22 | 1.82376 | ||||||||
\(801\) | 1.04898e21 | 0.175195 | ||||||||
\(802\) | −3.20846e20 | −0.0530871 | ||||||||
\(803\) | 3.59379e21 | 0.589097 | ||||||||
\(804\) | 2.71254e21 | 0.440509 | ||||||||
\(805\) | −4.35043e21 | −0.699944 | ||||||||
\(806\) | −1.17311e22 | −1.86994 | ||||||||
\(807\) | 3.74404e21 | 0.591274 | ||||||||
\(808\) | 1.41370e21 | 0.221194 | ||||||||
\(809\) | 6.04998e21 | 0.937864 | 0.468932 | − | 0.883234i | \(-0.344639\pi\) | ||||
0.468932 | + | 0.883234i | \(0.344639\pi\) | |||||||
\(810\) | −1.50269e21 | −0.230798 | ||||||||
\(811\) | −3.97224e21 | −0.604475 | −0.302238 | − | 0.953233i | \(-0.597734\pi\) | ||||
−0.302238 | + | 0.953233i | \(0.597734\pi\) | |||||||
\(812\) | 1.46195e21 | 0.220425 | ||||||||
\(813\) | 3.65230e21 | 0.545617 | ||||||||
\(814\) | 1.59443e21 | 0.236006 | ||||||||
\(815\) | 4.35289e21 | 0.638404 | ||||||||
\(816\) | 3.60972e21 | 0.524562 | ||||||||
\(817\) | −6.98446e20 | −0.100570 | ||||||||
\(818\) | 1.06639e22 | 1.52148 | ||||||||
\(819\) | −2.52251e21 | −0.356619 | ||||||||
\(820\) | 4.19183e21 | 0.587219 | ||||||||
\(821\) | −1.22139e21 | −0.169543 | −0.0847717 | − | 0.996400i | \(-0.527016\pi\) | ||||
−0.0847717 | + | 0.996400i | \(0.527016\pi\) | |||||||
\(822\) | −3.85763e21 | −0.530618 | ||||||||
\(823\) | −7.21274e21 | −0.983109 | −0.491554 | − | 0.870847i | \(-0.663571\pi\) | ||||
−0.491554 | + | 0.870847i | \(0.663571\pi\) | |||||||
\(824\) | −5.65167e21 | −0.763348 | ||||||||
\(825\) | −3.59332e21 | −0.480941 | ||||||||
\(826\) | 2.37788e21 | 0.315384 | ||||||||
\(827\) | −1.42305e22 | −1.87038 | −0.935189 | − | 0.354150i | \(-0.884770\pi\) | ||||
−0.935189 | + | 0.354150i | \(0.884770\pi\) | |||||||
\(828\) | 1.18680e21 | 0.154579 | ||||||||
\(829\) | 3.26530e21 | 0.421468 | 0.210734 | − | 0.977543i | \(-0.432415\pi\) | ||||
0.210734 | + | 0.977543i | \(0.432415\pi\) | |||||||
\(830\) | −2.48344e22 | −3.17665 | ||||||||
\(831\) | 1.42244e21 | 0.180313 | ||||||||
\(832\) | −3.64027e21 | −0.457307 | ||||||||
\(833\) | −3.60321e21 | −0.448592 | ||||||||
\(834\) | 6.57482e21 | 0.811220 | ||||||||
\(835\) | 2.28677e22 | 2.79623 | ||||||||
\(836\) | −1.86999e21 | −0.226617 | ||||||||
\(837\) | −1.36557e21 | −0.164011 | ||||||||
\(838\) | 1.25928e21 | 0.149897 | ||||||||
\(839\) | −6.61493e21 | −0.780388 | −0.390194 | − | 0.920733i | \(-0.627592\pi\) | ||||
−0.390194 | + | 0.920733i | \(0.627592\pi\) | |||||||
\(840\) | 2.12677e21 | 0.248671 | ||||||||
\(841\) | −6.28533e21 | −0.728380 | ||||||||
\(842\) | 5.44195e21 | 0.625049 | ||||||||
\(843\) | −3.13959e21 | −0.357410 | ||||||||
\(844\) | −2.70348e19 | −0.00305039 | ||||||||
\(845\) | 2.70288e22 | 3.02274 | ||||||||
\(846\) | −1.70196e21 | −0.188656 | ||||||||
\(847\) | 4.14631e21 | 0.455550 | ||||||||
\(848\) | −3.46837e21 | −0.377709 | ||||||||
\(849\) | −5.69096e21 | −0.614296 | ||||||||
\(850\) | −1.42261e22 | −1.52210 | ||||||||
\(851\) | −2.25949e21 | −0.239628 | ||||||||
\(852\) | 6.40287e21 | 0.673097 | ||||||||
\(853\) | 1.18003e22 | 1.22963 | 0.614815 | − | 0.788672i | \(-0.289231\pi\) | ||||
0.614815 | + | 0.788672i | \(0.289231\pi\) | |||||||
\(854\) | −1.37092e22 | −1.41605 | ||||||||
\(855\) | −3.35532e21 | −0.343549 | ||||||||
\(856\) | −3.11812e21 | −0.316475 | ||||||||
\(857\) | 2.98481e21 | 0.300304 | 0.150152 | − | 0.988663i | \(-0.452024\pi\) | ||||
0.150152 | + | 0.988663i | \(0.452024\pi\) | |||||||
\(858\) | 6.68800e21 | 0.667024 | ||||||||
\(859\) | 2.59672e21 | 0.256730 | 0.128365 | − | 0.991727i | \(-0.459027\pi\) | ||||
0.128365 | + | 0.991727i | \(0.459027\pi\) | |||||||
\(860\) | 1.72503e21 | 0.169067 | ||||||||
\(861\) | 2.03980e21 | 0.198182 | ||||||||
\(862\) | −2.14913e21 | −0.206994 | ||||||||
\(863\) | 2.37732e21 | 0.226990 | 0.113495 | − | 0.993539i | \(-0.463795\pi\) | ||||
0.113495 | + | 0.993539i | \(0.463795\pi\) | |||||||
\(864\) | −2.34378e21 | −0.221852 | ||||||||
\(865\) | 1.36909e22 | 1.28473 | ||||||||
\(866\) | 9.61719e21 | 0.894672 | ||||||||
\(867\) | 2.79240e21 | 0.257534 | ||||||||
\(868\) | −3.94215e21 | −0.360442 | ||||||||
\(869\) | −1.89436e21 | −0.171717 | ||||||||
\(870\) | −6.95486e21 | −0.625020 | ||||||||
\(871\) | −2.16619e22 | −1.93002 | ||||||||
\(872\) | 2.30319e21 | 0.203449 | ||||||||
\(873\) | 3.36397e21 | 0.294609 | ||||||||
\(874\) | 6.59917e21 | 0.572999 | ||||||||
\(875\) | −6.84782e21 | −0.589511 | ||||||||
\(876\) | −5.07823e21 | −0.433442 | ||||||||
\(877\) | −6.08094e21 | −0.514605 | −0.257302 | − | 0.966331i | \(-0.582834\pi\) | ||||
−0.257302 | + | 0.966331i | \(0.582834\pi\) | |||||||
\(878\) | 2.80599e22 | 2.35439 | ||||||||
\(879\) | 2.51178e21 | 0.208961 | ||||||||
\(880\) | −1.25216e22 | −1.03286 | ||||||||
\(881\) | 4.02742e20 | 0.0329387 | 0.0164694 | − | 0.999864i | \(-0.494757\pi\) | ||||
0.0164694 | + | 0.999864i | \(0.494757\pi\) | |||||||
\(882\) | 3.20262e21 | 0.259711 | ||||||||
\(883\) | −1.25847e22 | −1.01190 | −0.505951 | − | 0.862562i | \(-0.668858\pi\) | ||||
−0.505951 | + | 0.862562i | \(0.668858\pi\) | |||||||
\(884\) | 1.06326e22 | 0.847710 | ||||||||
\(885\) | −4.54257e21 | −0.359110 | ||||||||
\(886\) | 2.07154e22 | 1.62383 | ||||||||
\(887\) | −3.44552e21 | −0.267811 | −0.133905 | − | 0.990994i | \(-0.542752\pi\) | ||||
−0.133905 | + | 0.990994i | \(0.542752\pi\) | |||||||
\(888\) | 1.10458e21 | 0.0851336 | ||||||||
\(889\) | −6.74005e21 | −0.515110 | ||||||||
\(890\) | −1.44060e22 | −1.09173 | ||||||||
\(891\) | 7.78521e20 | 0.0585043 | ||||||||
\(892\) | −1.79932e22 | −1.34083 | ||||||||
\(893\) | −3.80027e21 | −0.280820 | ||||||||
\(894\) | −9.64134e21 | −0.706490 | ||||||||
\(895\) | −2.17932e22 | −1.58361 | ||||||||
\(896\) | 7.03692e21 | 0.507076 | ||||||||
\(897\) | −9.47764e21 | −0.677262 | ||||||||
\(898\) | 3.12303e22 | 2.21311 | ||||||||
\(899\) | −6.32024e21 | −0.444157 | ||||||||
\(900\) | 5.07756e21 | 0.353864 | ||||||||
\(901\) | 3.33193e21 | 0.230282 | ||||||||
\(902\) | −5.40819e21 | −0.370683 | ||||||||
\(903\) | 8.39426e20 | 0.0570590 | ||||||||
\(904\) | −5.02778e21 | −0.338932 | ||||||||
\(905\) | −3.54271e21 | −0.236849 | ||||||||
\(906\) | −1.46579e22 | −0.971876 | ||||||||
\(907\) | 2.23611e22 | 1.47041 | 0.735204 | − | 0.677846i | \(-0.237086\pi\) | ||||
0.735204 | + | 0.677846i | \(0.237086\pi\) | |||||||
\(908\) | −1.27324e22 | −0.830361 | ||||||||
\(909\) | 2.68054e21 | 0.173377 | ||||||||
\(910\) | 3.46425e22 | 2.22228 | ||||||||
\(911\) | 2.26193e22 | 1.43910 | 0.719550 | − | 0.694441i | \(-0.244348\pi\) | ||||
0.719550 | + | 0.694441i | \(0.244348\pi\) | |||||||
\(912\) | −7.16399e21 | −0.452057 | ||||||||
\(913\) | 1.28664e22 | 0.805240 | ||||||||
\(914\) | 2.40802e21 | 0.149474 | ||||||||
\(915\) | 2.61893e22 | 1.61237 | ||||||||
\(916\) | 1.97978e22 | 1.20893 | ||||||||
\(917\) | 4.82093e21 | 0.291985 | ||||||||
\(918\) | 3.08219e21 | 0.185157 | ||||||||
\(919\) | −2.65500e21 | −0.158197 | −0.0790986 | − | 0.996867i | \(-0.525204\pi\) | ||||
−0.0790986 | + | 0.996867i | \(0.525204\pi\) | |||||||
\(920\) | 7.99075e21 | 0.472258 | ||||||||
\(921\) | 1.21022e22 | 0.709440 | ||||||||
\(922\) | −3.80525e22 | −2.21259 | ||||||||
\(923\) | −5.11324e22 | −2.94906 | ||||||||
\(924\) | 2.24745e21 | 0.128573 | ||||||||
\(925\) | −9.66689e21 | −0.548559 | ||||||||
\(926\) | −1.84830e21 | −0.104038 | ||||||||
\(927\) | −1.07162e22 | −0.598331 | ||||||||
\(928\) | −1.08477e22 | −0.600795 | ||||||||
\(929\) | 1.28056e22 | 0.703532 | 0.351766 | − | 0.936088i | \(-0.385581\pi\) | ||||
0.351766 | + | 0.936088i | \(0.385581\pi\) | |||||||
\(930\) | 1.87538e22 | 1.02204 | ||||||||
\(931\) | 7.15106e21 | 0.386588 | ||||||||
\(932\) | −8.73884e21 | −0.468635 | ||||||||
\(933\) | −5.62956e21 | −0.299476 | ||||||||
\(934\) | −4.56273e22 | −2.40782 | ||||||||
\(935\) | 1.20290e22 | 0.629714 | ||||||||
\(936\) | 4.63328e21 | 0.240613 | ||||||||
\(937\) | −6.63077e21 | −0.341599 | −0.170800 | − | 0.985306i | \(-0.554635\pi\) | ||||
−0.170800 | + | 0.985306i | \(0.554635\pi\) | |||||||
\(938\) | −1.81274e22 | −0.926435 | ||||||||
\(939\) | 1.29040e22 | 0.654231 | ||||||||
\(940\) | 9.38598e21 | 0.472085 | ||||||||
\(941\) | −3.64056e21 | −0.181654 | −0.0908272 | − | 0.995867i | \(-0.528951\pi\) | ||||
−0.0908272 | + | 0.995867i | \(0.528951\pi\) | |||||||
\(942\) | −2.19459e22 | −1.08635 | ||||||||
\(943\) | 7.66400e21 | 0.376372 | ||||||||
\(944\) | −9.69889e21 | −0.472533 | ||||||||
\(945\) | 4.03259e21 | 0.194915 | ||||||||
\(946\) | −2.22559e21 | −0.106724 | ||||||||
\(947\) | 3.77681e21 | 0.179680 | 0.0898401 | − | 0.995956i | \(-0.471364\pi\) | ||||
0.0898401 | + | 0.995956i | \(0.471364\pi\) | |||||||
\(948\) | 2.67684e21 | 0.126345 | ||||||||
\(949\) | 4.05540e22 | 1.89905 | ||||||||
\(950\) | 2.82336e22 | 1.31171 | ||||||||
\(951\) | −1.12807e22 | −0.519974 | ||||||||
\(952\) | −4.36226e21 | −0.199496 | ||||||||
\(953\) | −2.57524e22 | −1.16848 | −0.584238 | − | 0.811582i | \(-0.698607\pi\) | ||||
−0.584238 | + | 0.811582i | \(0.698607\pi\) | |||||||
\(954\) | −2.96150e21 | −0.133321 | ||||||||
\(955\) | −1.75866e22 | −0.785520 | ||||||||
\(956\) | 2.34765e22 | 1.04040 | ||||||||
\(957\) | 3.60322e21 | 0.158435 | ||||||||
\(958\) | 3.02406e22 | 1.31932 | ||||||||
\(959\) | 1.03523e22 | 0.448121 | ||||||||
\(960\) | 5.81947e21 | 0.249948 | ||||||||
\(961\) | −6.42267e21 | −0.273710 | ||||||||
\(962\) | 1.79923e22 | 0.760806 | ||||||||
\(963\) | −5.91230e21 | −0.248061 | ||||||||
\(964\) | −6.55248e21 | −0.272790 | ||||||||
\(965\) | −6.21700e21 | −0.256818 | ||||||||
\(966\) | −7.93120e21 | −0.325095 | ||||||||
\(967\) | 2.79126e22 | 1.13528 | 0.567639 | − | 0.823277i | \(-0.307857\pi\) | ||||
0.567639 | + | 0.823277i | \(0.307857\pi\) | |||||||
\(968\) | −7.61583e21 | −0.307363 | ||||||||
\(969\) | 6.88216e21 | 0.275611 | ||||||||
\(970\) | −4.61986e22 | −1.83586 | ||||||||
\(971\) | 2.84337e22 | 1.12122 | 0.560608 | − | 0.828081i | \(-0.310568\pi\) | ||||
0.560608 | + | 0.828081i | \(0.310568\pi\) | |||||||
\(972\) | −1.10009e21 | −0.0430460 | ||||||||
\(973\) | −1.76441e22 | −0.685098 | ||||||||
\(974\) | 3.88372e21 | 0.149643 | ||||||||
\(975\) | −4.05487e22 | −1.55040 | ||||||||
\(976\) | 5.59171e22 | 2.12163 | ||||||||
\(977\) | −2.39578e22 | −0.902064 | −0.451032 | − | 0.892508i | \(-0.648944\pi\) | ||||
−0.451032 | + | 0.892508i | \(0.648944\pi\) | |||||||
\(978\) | 7.93568e21 | 0.296512 | ||||||||
\(979\) | 7.46352e21 | 0.276741 | ||||||||
\(980\) | −1.76618e22 | −0.649890 | ||||||||
\(981\) | 4.36710e21 | 0.159469 | ||||||||
\(982\) | 1.31094e22 | 0.475058 | ||||||||
\(983\) | 2.01688e22 | 0.725319 | 0.362660 | − | 0.931922i | \(-0.381869\pi\) | ||||
0.362660 | + | 0.931922i | \(0.381869\pi\) | |||||||
\(984\) | −3.74666e21 | −0.133715 | ||||||||
\(985\) | −4.57853e22 | −1.62164 | ||||||||
\(986\) | 1.42652e22 | 0.501421 | ||||||||
\(987\) | 4.56735e21 | 0.159325 | ||||||||
\(988\) | −2.11019e22 | −0.730539 | ||||||||
\(989\) | 3.15391e21 | 0.108362 | ||||||||
\(990\) | −1.06917e22 | −0.364572 | ||||||||
\(991\) | 6.46390e21 | 0.218747 | 0.109374 | − | 0.994001i | \(-0.465116\pi\) | ||||
0.109374 | + | 0.994001i | \(0.465116\pi\) | |||||||
\(992\) | 2.92508e22 | 0.982426 | ||||||||
\(993\) | −9.07256e21 | −0.302420 | ||||||||
\(994\) | −4.27893e22 | −1.41559 | ||||||||
\(995\) | 2.06121e22 | 0.676781 | ||||||||
\(996\) | −1.81809e22 | −0.592475 | ||||||||
\(997\) | 2.36491e22 | 0.764895 | 0.382447 | − | 0.923977i | \(-0.375081\pi\) | ||||
0.382447 | + | 0.923977i | \(0.375081\pi\) | |||||||
\(998\) | −5.18378e22 | −1.66406 | ||||||||
\(999\) | 2.09441e21 | 0.0667298 |
(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 | 3.16.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 9.16.a.d.1.1 | 1 | |||
4.3 | odd | 2 | 48.16.a.g.1.1 | 1 | |||
5.2 | odd | 4 | 75.16.b.a.49.1 | 2 | |||
5.3 | odd | 4 | 75.16.b.a.49.2 | 2 | |||
5.4 | even | 2 | 75.16.a.b.1.1 | 1 | |||
7.6 | odd | 2 | 147.16.a.a.1.1 | 1 | |||
12.11 | even | 2 | 144.16.a.b.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.16.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
9.16.a.d.1.1 | 1 | 3.2 | odd | 2 | |||
48.16.a.g.1.1 | 1 | 4.3 | odd | 2 | |||
75.16.a.b.1.1 | 1 | 5.4 | even | 2 | |||
75.16.b.a.49.1 | 2 | 5.2 | odd | 4 | |||
75.16.b.a.49.2 | 2 | 5.3 | odd | 4 | |||
144.16.a.b.1.1 | 1 | 12.11 | even | 2 | |||
147.16.a.a.1.1 | 1 | 7.6 | odd | 2 |