Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,82,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 82, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 82);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 82 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(41.5501285538\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3 x^{5} + \cdots - 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{58}\cdot 3^{26}\cdot 5^{7}\cdot 7^{3}\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.85696e10\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.75084e12 | −1.76909 | −0.884546 | − | 0.466452i | \(-0.845532\pi\) | ||||
−0.884546 | + | 0.466452i | \(0.845532\pi\) | |||||||
\(3\) | −2.21125e19 | −1.05009 | −0.525045 | − | 0.851075i | \(-0.675951\pi\) | ||||
−0.525045 | + | 0.851075i | \(0.675951\pi\) | |||||||
\(4\) | 5.14927e24 | 2.12969 | ||||||||
\(5\) | 2.52982e28 | 1.24395 | 0.621976 | − | 0.783036i | \(-0.286330\pi\) | ||||
0.621976 | + | 0.783036i | \(0.286330\pi\) | |||||||
\(6\) | 6.08279e31 | 1.85771 | ||||||||
\(7\) | −2.62798e34 | −1.56009 | −0.780047 | − | 0.625721i | \(-0.784805\pi\) | ||||
−0.780047 | + | 0.625721i | \(0.784805\pi\) | |||||||
\(8\) | −7.51371e36 | −1.99853 | ||||||||
\(9\) | 4.55346e37 | 0.102688 | ||||||||
\(10\) | −6.95912e40 | −2.20067 | ||||||||
\(11\) | −6.46669e41 | −0.430802 | −0.215401 | − | 0.976526i | \(-0.569106\pi\) | ||||
−0.215401 | + | 0.976526i | \(0.569106\pi\) | |||||||
\(12\) | −1.13863e44 | −2.23637 | ||||||||
\(13\) | 1.64391e45 | 1.26233 | 0.631165 | − | 0.775648i | \(-0.282577\pi\) | ||||
0.631165 | + | 0.775648i | \(0.282577\pi\) | |||||||
\(14\) | 7.22914e46 | 2.75995 | ||||||||
\(15\) | −5.59405e47 | −1.30626 | ||||||||
\(16\) | 8.21884e48 | 1.40589 | ||||||||
\(17\) | 1.28166e49 | 0.188188 | 0.0940941 | − | 0.995563i | \(-0.470005\pi\) | ||||
0.0940941 | + | 0.995563i | \(0.470005\pi\) | |||||||
\(18\) | −1.25259e50 | −0.181665 | ||||||||
\(19\) | −8.42462e51 | −1.36782 | −0.683911 | − | 0.729566i | \(-0.739722\pi\) | ||||
−0.683911 | + | 0.729566i | \(0.739722\pi\) | |||||||
\(20\) | 1.30267e53 | 2.64923 | ||||||||
\(21\) | 5.81110e53 | 1.63824 | ||||||||
\(22\) | 1.77888e54 | 0.762129 | ||||||||
\(23\) | 1.57219e55 | 1.11309 | 0.556543 | − | 0.830819i | \(-0.312127\pi\) | ||||
0.556543 | + | 0.830819i | \(0.312127\pi\) | |||||||
\(24\) | 1.66147e56 | 2.09863 | ||||||||
\(25\) | 2.26406e56 | 0.547417 | ||||||||
\(26\) | −4.52214e57 | −2.23318 | ||||||||
\(27\) | 8.79837e57 | 0.942258 | ||||||||
\(28\) | −1.35322e59 | −3.32252 | ||||||||
\(29\) | 1.02296e59 | 0.606375 | 0.303187 | − | 0.952931i | \(-0.401949\pi\) | ||||
0.303187 | + | 0.952931i | \(0.401949\pi\) | |||||||
\(30\) | 1.53883e60 | 2.31090 | ||||||||
\(31\) | 3.33151e59 | 0.132585 | 0.0662923 | − | 0.997800i | \(-0.478883\pi\) | ||||
0.0662923 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(32\) | −4.44168e60 | −0.488622 | ||||||||
\(33\) | 1.42994e61 | 0.452381 | ||||||||
\(34\) | −3.52565e61 | −0.332923 | ||||||||
\(35\) | −6.64829e62 | −1.94068 | ||||||||
\(36\) | 2.34470e62 | 0.218694 | ||||||||
\(37\) | 8.95735e62 | 0.275429 | 0.137715 | − | 0.990472i | \(-0.456024\pi\) | ||||
0.137715 | + | 0.990472i | \(0.456024\pi\) | |||||||
\(38\) | 2.31748e64 | 2.41980 | ||||||||
\(39\) | −3.63510e64 | −1.32556 | ||||||||
\(40\) | −1.90083e65 | −2.48607 | ||||||||
\(41\) | 1.61632e65 | 0.777647 | 0.388823 | − | 0.921312i | \(-0.372882\pi\) | ||||
0.388823 | + | 0.921312i | \(0.372882\pi\) | |||||||
\(42\) | −1.59854e66 | −2.89820 | ||||||||
\(43\) | 1.76087e66 | 1.23099 | 0.615496 | − | 0.788140i | \(-0.288956\pi\) | ||||
0.615496 | + | 0.788140i | \(0.288956\pi\) | |||||||
\(44\) | −3.32987e66 | −0.917475 | ||||||||
\(45\) | 1.15194e66 | 0.127739 | ||||||||
\(46\) | −4.32486e67 | −1.96915 | ||||||||
\(47\) | −8.77094e67 | −1.67141 | −0.835704 | − | 0.549179i | \(-0.814940\pi\) | ||||
−0.835704 | + | 0.549179i | \(0.814940\pi\) | |||||||
\(48\) | −1.81739e68 | −1.47631 | ||||||||
\(49\) | 4.06872e68 | 1.43389 | ||||||||
\(50\) | −6.22808e68 | −0.968432 | ||||||||
\(51\) | −2.83407e68 | −0.197615 | ||||||||
\(52\) | 8.46496e69 | 2.68837 | ||||||||
\(53\) | 2.20440e69 | 0.323681 | 0.161841 | − | 0.986817i | \(-0.448257\pi\) | ||||
0.161841 | + | 0.986817i | \(0.448257\pi\) | |||||||
\(54\) | −2.42029e70 | −1.66694 | ||||||||
\(55\) | −1.63595e70 | −0.535897 | ||||||||
\(56\) | 1.97458e71 | 3.11789 | ||||||||
\(57\) | 1.86289e71 | 1.43634 | ||||||||
\(58\) | −2.81401e71 | −1.07273 | ||||||||
\(59\) | 3.92989e71 | 0.749676 | 0.374838 | − | 0.927090i | \(-0.377698\pi\) | ||||
0.374838 | + | 0.927090i | \(0.377698\pi\) | |||||||
\(60\) | −2.88053e72 | −2.78193 | ||||||||
\(61\) | −7.29227e71 | −0.360582 | −0.180291 | − | 0.983613i | \(-0.557704\pi\) | ||||
−0.180291 | + | 0.983613i | \(0.557704\pi\) | |||||||
\(62\) | −9.16446e71 | −0.234554 | ||||||||
\(63\) | −1.19664e72 | −0.160203 | ||||||||
\(64\) | −7.65357e72 | −0.541471 | ||||||||
\(65\) | 4.15880e73 | 1.57028 | ||||||||
\(66\) | −3.93355e73 | −0.800304 | ||||||||
\(67\) | 1.78309e73 | 0.197308 | 0.0986538 | − | 0.995122i | \(-0.468546\pi\) | ||||
0.0986538 | + | 0.995122i | \(0.468546\pi\) | |||||||
\(68\) | 6.59963e73 | 0.400783 | ||||||||
\(69\) | −3.47651e74 | −1.16884 | ||||||||
\(70\) | 1.82884e75 | 3.43325 | ||||||||
\(71\) | −3.78476e74 | −0.400014 | −0.200007 | − | 0.979794i | \(-0.564097\pi\) | ||||
−0.200007 | + | 0.979794i | \(0.564097\pi\) | |||||||
\(72\) | −3.42134e74 | −0.205225 | ||||||||
\(73\) | −1.18691e75 | −0.407234 | −0.203617 | − | 0.979051i | \(-0.565270\pi\) | ||||
−0.203617 | + | 0.979051i | \(0.565270\pi\) | |||||||
\(74\) | −2.46402e75 | −0.487260 | ||||||||
\(75\) | −5.00640e75 | −0.574837 | ||||||||
\(76\) | −4.33807e76 | −2.91304 | ||||||||
\(77\) | 1.69943e76 | 0.672092 | ||||||||
\(78\) | 9.99958e76 | 2.34504 | ||||||||
\(79\) | −3.54946e76 | −0.496895 | −0.248448 | − | 0.968645i | \(-0.579920\pi\) | ||||
−0.248448 | + | 0.968645i | \(0.579920\pi\) | |||||||
\(80\) | 2.07921e77 | 1.74886 | ||||||||
\(81\) | −2.14745e77 | −1.09214 | ||||||||
\(82\) | −4.44625e77 | −1.37573 | ||||||||
\(83\) | −5.45755e76 | −0.103356 | −0.0516779 | − | 0.998664i | \(-0.516457\pi\) | ||||
−0.0516779 | + | 0.998664i | \(0.516457\pi\) | |||||||
\(84\) | 2.99230e78 | 3.48894 | ||||||||
\(85\) | 3.24237e77 | 0.234097 | ||||||||
\(86\) | −4.84388e78 | −2.17774 | ||||||||
\(87\) | −2.26202e78 | −0.636748 | ||||||||
\(88\) | 4.85888e78 | 0.860970 | ||||||||
\(89\) | −1.21164e79 | −1.35856 | −0.679278 | − | 0.733881i | \(-0.737707\pi\) | ||||
−0.679278 | + | 0.733881i | \(0.737707\pi\) | |||||||
\(90\) | −3.16881e78 | −0.225982 | ||||||||
\(91\) | −4.32017e79 | −1.96935 | ||||||||
\(92\) | 8.09566e79 | 2.37053 | ||||||||
\(93\) | −7.36680e78 | −0.139226 | ||||||||
\(94\) | 2.41274e80 | 2.95688 | ||||||||
\(95\) | −2.13127e80 | −1.70150 | ||||||||
\(96\) | 9.82165e79 | 0.513097 | ||||||||
\(97\) | 2.69780e80 | 0.926305 | 0.463153 | − | 0.886279i | \(-0.346718\pi\) | ||||
0.463153 | + | 0.886279i | \(0.346718\pi\) | |||||||
\(98\) | −1.11924e81 | −2.53669 | ||||||||
\(99\) | −2.94458e79 | −0.0442383 | ||||||||
\(100\) | 1.16583e81 | 1.16583 | ||||||||
\(101\) | −1.21458e81 | −0.811726 | −0.405863 | − | 0.913934i | \(-0.633029\pi\) | ||||
−0.405863 | + | 0.913934i | \(0.633029\pi\) | |||||||
\(102\) | 7.79608e80 | 0.349598 | ||||||||
\(103\) | 1.20510e81 | 0.364011 | 0.182006 | − | 0.983298i | \(-0.441741\pi\) | ||||
0.182006 | + | 0.983298i | \(0.441741\pi\) | |||||||
\(104\) | −1.23519e82 | −2.52280 | ||||||||
\(105\) | 1.47010e82 | 2.03789 | ||||||||
\(106\) | −6.06395e81 | −0.572622 | ||||||||
\(107\) | −2.32176e82 | −1.49891 | −0.749453 | − | 0.662058i | \(-0.769683\pi\) | ||||
−0.749453 | + | 0.662058i | \(0.769683\pi\) | |||||||
\(108\) | 4.53052e82 | 2.00672 | ||||||||
\(109\) | 6.16704e82 | 1.88063 | 0.940315 | − | 0.340304i | \(-0.110530\pi\) | ||||
0.940315 | + | 0.340304i | \(0.110530\pi\) | |||||||
\(110\) | 4.50024e82 | 0.948052 | ||||||||
\(111\) | −1.98069e82 | −0.289225 | ||||||||
\(112\) | −2.15989e83 | −2.19332 | ||||||||
\(113\) | −3.91748e82 | −0.277543 | −0.138771 | − | 0.990324i | \(-0.544315\pi\) | ||||
−0.138771 | + | 0.990324i | \(0.544315\pi\) | |||||||
\(114\) | −5.12452e83 | −2.54101 | ||||||||
\(115\) | 3.97736e83 | 1.38463 | ||||||||
\(116\) | 5.26752e83 | 1.29139 | ||||||||
\(117\) | 7.48550e82 | 0.129626 | ||||||||
\(118\) | −1.08105e84 | −1.32625 | ||||||||
\(119\) | −3.36818e83 | −0.293591 | ||||||||
\(120\) | 4.20320e84 | 2.61060 | ||||||||
\(121\) | −1.83506e84 | −0.814409 | ||||||||
\(122\) | 2.00599e84 | 0.637903 | ||||||||
\(123\) | −3.57409e84 | −0.816598 | ||||||||
\(124\) | 1.71549e84 | 0.282364 | ||||||||
\(125\) | −4.73541e84 | −0.562992 | ||||||||
\(126\) | 3.29176e84 | 0.283414 | ||||||||
\(127\) | 3.92700e84 | 0.245477 | 0.122738 | − | 0.992439i | \(-0.460832\pi\) | ||||
0.122738 | + | 0.992439i | \(0.460832\pi\) | |||||||
\(128\) | 3.17931e85 | 1.44653 | ||||||||
\(129\) | −3.89372e85 | −1.29265 | ||||||||
\(130\) | −1.14402e86 | −2.77797 | ||||||||
\(131\) | −3.67830e85 | −0.654877 | −0.327439 | − | 0.944872i | \(-0.606185\pi\) | ||||
−0.327439 | + | 0.944872i | \(0.606185\pi\) | |||||||
\(132\) | 7.36317e85 | 0.963431 | ||||||||
\(133\) | 2.21397e86 | 2.13393 | ||||||||
\(134\) | −4.90500e85 | −0.349055 | ||||||||
\(135\) | 2.22583e86 | 1.17212 | ||||||||
\(136\) | −9.63004e85 | −0.376099 | ||||||||
\(137\) | 1.69752e86 | 0.492755 | 0.246378 | − | 0.969174i | \(-0.420760\pi\) | ||||
0.246378 | + | 0.969174i | \(0.420760\pi\) | |||||||
\(138\) | 9.56332e86 | 2.06779 | ||||||||
\(139\) | −1.16624e87 | −1.88229 | −0.941146 | − | 0.337999i | \(-0.890250\pi\) | ||||
−0.941146 | + | 0.337999i | \(0.890250\pi\) | |||||||
\(140\) | −3.42339e87 | −4.13305 | ||||||||
\(141\) | 1.93947e87 | 1.75513 | ||||||||
\(142\) | 1.04113e87 | 0.707662 | ||||||||
\(143\) | −1.06307e87 | −0.543815 | ||||||||
\(144\) | 3.74242e86 | 0.144368 | ||||||||
\(145\) | 2.58791e87 | 0.754301 | ||||||||
\(146\) | 3.26501e87 | 0.720434 | ||||||||
\(147\) | −8.99695e87 | −1.50572 | ||||||||
\(148\) | 4.61239e87 | 0.586579 | ||||||||
\(149\) | −8.60592e87 | −0.833208 | −0.416604 | − | 0.909088i | \(-0.636780\pi\) | ||||
−0.416604 | + | 0.909088i | \(0.636780\pi\) | |||||||
\(150\) | 1.37718e88 | 1.01694 | ||||||||
\(151\) | −1.22694e88 | −0.692243 | −0.346121 | − | 0.938190i | \(-0.612501\pi\) | ||||
−0.346121 | + | 0.938190i | \(0.612501\pi\) | |||||||
\(152\) | 6.33002e88 | 2.73363 | ||||||||
\(153\) | 5.83601e86 | 0.0193247 | ||||||||
\(154\) | −4.67486e88 | −1.18899 | ||||||||
\(155\) | 8.42811e87 | 0.164929 | ||||||||
\(156\) | −1.87181e89 | −2.82303 | ||||||||
\(157\) | 6.39779e88 | 0.744893 | 0.372447 | − | 0.928054i | \(-0.378519\pi\) | ||||
0.372447 | + | 0.928054i | \(0.378519\pi\) | |||||||
\(158\) | 9.76399e88 | 0.879054 | ||||||||
\(159\) | −4.87447e88 | −0.339894 | ||||||||
\(160\) | −1.12366e89 | −0.607823 | ||||||||
\(161\) | −4.13169e89 | −1.73652 | ||||||||
\(162\) | 5.90729e89 | 1.93210 | ||||||||
\(163\) | 3.48502e89 | 0.888398 | 0.444199 | − | 0.895928i | \(-0.353488\pi\) | ||||
0.444199 | + | 0.895928i | \(0.353488\pi\) | |||||||
\(164\) | 8.32290e89 | 1.65615 | ||||||||
\(165\) | 3.61749e89 | 0.562740 | ||||||||
\(166\) | 1.50128e89 | 0.182846 | ||||||||
\(167\) | −6.12121e89 | −0.584548 | −0.292274 | − | 0.956335i | \(-0.594412\pi\) | ||||
−0.292274 | + | 0.956335i | \(0.594412\pi\) | |||||||
\(168\) | −4.36629e90 | −3.27406 | ||||||||
\(169\) | 1.00651e90 | 0.593479 | ||||||||
\(170\) | −8.91925e89 | −0.414140 | ||||||||
\(171\) | −3.83612e89 | −0.140459 | ||||||||
\(172\) | 9.06722e90 | 2.62163 | ||||||||
\(173\) | −7.84695e90 | −1.79405 | −0.897023 | − | 0.441984i | \(-0.854275\pi\) | ||||
−0.897023 | + | 0.441984i | \(0.854275\pi\) | |||||||
\(174\) | 6.22247e90 | 1.12647 | ||||||||
\(175\) | −5.94990e90 | −0.854022 | ||||||||
\(176\) | −5.31486e90 | −0.605660 | ||||||||
\(177\) | −8.68995e90 | −0.787227 | ||||||||
\(178\) | 3.33302e91 | 2.40341 | ||||||||
\(179\) | −1.27646e91 | −0.733599 | −0.366800 | − | 0.930300i | \(-0.619547\pi\) | ||||
−0.366800 | + | 0.930300i | \(0.619547\pi\) | |||||||
\(180\) | 5.93167e90 | 0.272045 | ||||||||
\(181\) | −4.31048e91 | −1.57959 | −0.789794 | − | 0.613372i | \(-0.789813\pi\) | ||||
−0.789794 | + | 0.613372i | \(0.789813\pi\) | |||||||
\(182\) | 1.18841e92 | 3.48397 | ||||||||
\(183\) | 1.61250e91 | 0.378644 | ||||||||
\(184\) | −1.18130e92 | −2.22453 | ||||||||
\(185\) | 2.26604e91 | 0.342621 | ||||||||
\(186\) | 2.02649e91 | 0.246303 | ||||||||
\(187\) | −8.28811e90 | −0.0810719 | ||||||||
\(188\) | −4.51640e92 | −3.55958 | ||||||||
\(189\) | −2.31219e92 | −1.47001 | ||||||||
\(190\) | 5.86280e92 | 3.01012 | ||||||||
\(191\) | 1.96408e92 | 0.815280 | 0.407640 | − | 0.913143i | \(-0.366352\pi\) | ||||
0.407640 | + | 0.913143i | \(0.366352\pi\) | |||||||
\(192\) | 1.69239e92 | 0.568593 | ||||||||
\(193\) | 7.05705e92 | 1.92111 | 0.960555 | − | 0.278090i | \(-0.0897013\pi\) | ||||
0.960555 | + | 0.278090i | \(0.0897013\pi\) | |||||||
\(194\) | −7.42121e92 | −1.63872 | ||||||||
\(195\) | −9.19613e92 | −1.64893 | ||||||||
\(196\) | 2.09510e93 | 3.05375 | ||||||||
\(197\) | −3.03690e92 | −0.360204 | −0.180102 | − | 0.983648i | \(-0.557643\pi\) | ||||
−0.180102 | + | 0.983648i | \(0.557643\pi\) | |||||||
\(198\) | 8.10008e91 | 0.0782616 | ||||||||
\(199\) | −1.81756e93 | −1.43199 | −0.715995 | − | 0.698105i | \(-0.754027\pi\) | ||||
−0.715995 | + | 0.698105i | \(0.754027\pi\) | |||||||
\(200\) | −1.70115e93 | −1.09403 | ||||||||
\(201\) | −3.94285e92 | −0.207191 | ||||||||
\(202\) | 3.34111e93 | 1.43602 | ||||||||
\(203\) | −2.68832e93 | −0.946002 | ||||||||
\(204\) | −1.45934e93 | −0.420858 | ||||||||
\(205\) | 4.08900e93 | 0.967355 | ||||||||
\(206\) | −3.31503e93 | −0.643969 | ||||||||
\(207\) | 7.15893e92 | 0.114301 | ||||||||
\(208\) | 1.35111e94 | 1.77470 | ||||||||
\(209\) | 5.44794e93 | 0.589261 | ||||||||
\(210\) | −4.04402e94 | −3.60522 | ||||||||
\(211\) | 4.77860e93 | 0.351448 | 0.175724 | − | 0.984439i | \(-0.443773\pi\) | ||||
0.175724 | + | 0.984439i | \(0.443773\pi\) | |||||||
\(212\) | 1.13511e94 | 0.689340 | ||||||||
\(213\) | 8.36904e93 | 0.420051 | ||||||||
\(214\) | 6.38679e94 | 2.65170 | ||||||||
\(215\) | 4.45468e94 | 1.53130 | ||||||||
\(216\) | −6.61084e94 | −1.88313 | ||||||||
\(217\) | −8.75513e93 | −0.206844 | ||||||||
\(218\) | −1.69645e95 | −3.32701 | ||||||||
\(219\) | 2.62456e94 | 0.427632 | ||||||||
\(220\) | −8.42397e94 | −1.14130 | ||||||||
\(221\) | 2.10694e94 | 0.237556 | ||||||||
\(222\) | 5.44857e94 | 0.511666 | ||||||||
\(223\) | 1.37268e95 | 1.07454 | 0.537268 | − | 0.843412i | \(-0.319456\pi\) | ||||
0.537268 | + | 0.843412i | \(0.319456\pi\) | |||||||
\(224\) | 1.16726e95 | 0.762296 | ||||||||
\(225\) | 1.03093e94 | 0.0562132 | ||||||||
\(226\) | 1.07764e95 | 0.490999 | ||||||||
\(227\) | −4.29567e95 | −1.63676 | −0.818378 | − | 0.574680i | \(-0.805127\pi\) | ||||
−0.818378 | + | 0.574680i | \(0.805127\pi\) | |||||||
\(228\) | 9.59254e95 | 3.05895 | ||||||||
\(229\) | 3.49520e95 | 0.933545 | 0.466773 | − | 0.884377i | \(-0.345417\pi\) | ||||
0.466773 | + | 0.884377i | \(0.345417\pi\) | |||||||
\(230\) | −1.09411e96 | −2.44953 | ||||||||
\(231\) | −3.75786e95 | −0.705757 | ||||||||
\(232\) | −7.68625e95 | −1.21186 | ||||||||
\(233\) | 1.12210e96 | 1.48634 | 0.743169 | − | 0.669104i | \(-0.233322\pi\) | ||||
0.743169 | + | 0.669104i | \(0.233322\pi\) | |||||||
\(234\) | −2.05914e95 | −0.229321 | ||||||||
\(235\) | −2.21889e96 | −2.07915 | ||||||||
\(236\) | 2.02361e96 | 1.59658 | ||||||||
\(237\) | 7.84873e95 | 0.521784 | ||||||||
\(238\) | 9.26533e95 | 0.519390 | ||||||||
\(239\) | 5.57365e95 | 0.263648 | 0.131824 | − | 0.991273i | \(-0.457917\pi\) | ||||
0.131824 | + | 0.991273i | \(0.457917\pi\) | |||||||
\(240\) | −4.59766e96 | −1.83646 | ||||||||
\(241\) | −2.44469e96 | −0.825150 | −0.412575 | − | 0.910924i | \(-0.635370\pi\) | ||||
−0.412575 | + | 0.910924i | \(0.635370\pi\) | |||||||
\(242\) | 5.04796e96 | 1.44077 | ||||||||
\(243\) | 8.47109e95 | 0.204590 | ||||||||
\(244\) | −3.75499e96 | −0.767928 | ||||||||
\(245\) | 1.02931e97 | 1.78369 | ||||||||
\(246\) | 9.83176e96 | 1.44464 | ||||||||
\(247\) | −1.38493e97 | −1.72664 | ||||||||
\(248\) | −2.50320e96 | −0.264974 | ||||||||
\(249\) | 1.20680e96 | 0.108533 | ||||||||
\(250\) | 1.30264e97 | 0.995985 | ||||||||
\(251\) | −1.07328e97 | −0.698114 | −0.349057 | − | 0.937101i | \(-0.613498\pi\) | ||||
−0.349057 | + | 0.937101i | \(0.613498\pi\) | |||||||
\(252\) | −6.16182e96 | −0.341183 | ||||||||
\(253\) | −1.01669e97 | −0.479520 | ||||||||
\(254\) | −1.08026e97 | −0.434271 | ||||||||
\(255\) | −7.16968e96 | −0.245823 | ||||||||
\(256\) | −6.89525e97 | −2.01758 | ||||||||
\(257\) | −2.29731e97 | −0.574021 | −0.287010 | − | 0.957928i | \(-0.592661\pi\) | ||||
−0.287010 | + | 0.957928i | \(0.592661\pi\) | |||||||
\(258\) | 1.07110e98 | 2.28682 | ||||||||
\(259\) | −2.35397e97 | −0.429695 | ||||||||
\(260\) | 2.14148e98 | 3.34421 | ||||||||
\(261\) | 4.65803e96 | 0.0622675 | ||||||||
\(262\) | 1.01184e98 | 1.15854 | ||||||||
\(263\) | −1.00706e98 | −0.988205 | −0.494102 | − | 0.869404i | \(-0.664503\pi\) | ||||
−0.494102 | + | 0.869404i | \(0.664503\pi\) | |||||||
\(264\) | −1.07442e98 | −0.904095 | ||||||||
\(265\) | 5.57672e97 | 0.402644 | ||||||||
\(266\) | −6.09028e98 | −3.77512 | ||||||||
\(267\) | 2.67923e98 | 1.42660 | ||||||||
\(268\) | 9.18162e97 | 0.420204 | ||||||||
\(269\) | 1.53194e98 | 0.602941 | 0.301471 | − | 0.953475i | \(-0.402522\pi\) | ||||
0.301471 | + | 0.953475i | \(0.402522\pi\) | |||||||
\(270\) | −6.12289e98 | −2.07360 | ||||||||
\(271\) | 4.06678e98 | 1.18575 | 0.592877 | − | 0.805293i | \(-0.297992\pi\) | ||||
0.592877 | + | 0.805293i | \(0.297992\pi\) | |||||||
\(272\) | 1.05338e98 | 0.264572 | ||||||||
\(273\) | 9.55295e98 | 2.06800 | ||||||||
\(274\) | −4.66960e98 | −0.871730 | ||||||||
\(275\) | −1.46410e98 | −0.235829 | ||||||||
\(276\) | −1.79015e99 | −2.48927 | ||||||||
\(277\) | −1.40686e99 | −1.68974 | −0.844868 | − | 0.534974i | \(-0.820321\pi\) | ||||
−0.844868 | + | 0.534974i | \(0.820321\pi\) | |||||||
\(278\) | 3.20813e99 | 3.32995 | ||||||||
\(279\) | 1.51699e97 | 0.0136149 | ||||||||
\(280\) | 4.99533e99 | 3.87850 | ||||||||
\(281\) | −2.51972e99 | −1.69335 | −0.846674 | − | 0.532112i | \(-0.821398\pi\) | ||||
−0.846674 | + | 0.532112i | \(0.821398\pi\) | |||||||
\(282\) | −5.33517e99 | −3.10499 | ||||||||
\(283\) | 2.91238e99 | 1.46858 | 0.734289 | − | 0.678837i | \(-0.237516\pi\) | ||||
0.734289 | + | 0.678837i | \(0.237516\pi\) | |||||||
\(284\) | −1.94888e99 | −0.851906 | ||||||||
\(285\) | 4.71277e99 | 1.78673 | ||||||||
\(286\) | 2.92433e99 | 0.962059 | ||||||||
\(287\) | −4.24766e99 | −1.21320 | ||||||||
\(288\) | −2.02250e98 | −0.0501757 | ||||||||
\(289\) | −4.47407e99 | −0.964585 | ||||||||
\(290\) | −7.11893e99 | −1.33443 | ||||||||
\(291\) | −5.96550e99 | −0.972703 | ||||||||
\(292\) | −6.11175e99 | −0.867282 | ||||||||
\(293\) | 4.29360e99 | 0.530497 | 0.265249 | − | 0.964180i | \(-0.414546\pi\) | ||||
0.265249 | + | 0.964180i | \(0.414546\pi\) | |||||||
\(294\) | 2.47492e100 | 2.66375 | ||||||||
\(295\) | 9.94189e99 | 0.932561 | ||||||||
\(296\) | −6.73029e99 | −0.550452 | ||||||||
\(297\) | −5.68963e99 | −0.405927 | ||||||||
\(298\) | 2.36735e100 | 1.47402 | ||||||||
\(299\) | 2.58455e100 | 1.40508 | ||||||||
\(300\) | −2.57793e100 | −1.22422 | ||||||||
\(301\) | −4.62753e100 | −1.92046 | ||||||||
\(302\) | 3.37513e100 | 1.22464 | ||||||||
\(303\) | 2.68573e100 | 0.852385 | ||||||||
\(304\) | −6.92406e100 | −1.92301 | ||||||||
\(305\) | −1.84481e100 | −0.448547 | ||||||||
\(306\) | −1.60539e99 | −0.0341872 | ||||||||
\(307\) | −8.74192e100 | −1.63118 | −0.815592 | − | 0.578628i | \(-0.803588\pi\) | ||||
−0.815592 | + | 0.578628i | \(0.803588\pi\) | |||||||
\(308\) | 8.75083e100 | 1.43135 | ||||||||
\(309\) | −2.66477e100 | −0.382244 | ||||||||
\(310\) | −2.31844e100 | −0.291774 | ||||||||
\(311\) | 7.37638e100 | 0.814793 | 0.407397 | − | 0.913251i | \(-0.366437\pi\) | ||||
0.407397 | + | 0.913251i | \(0.366437\pi\) | |||||||
\(312\) | 2.73131e101 | 2.64917 | ||||||||
\(313\) | −2.41414e100 | −0.205692 | −0.102846 | − | 0.994697i | \(-0.532795\pi\) | ||||
−0.102846 | + | 0.994697i | \(0.532795\pi\) | |||||||
\(314\) | −1.75993e101 | −1.31779 | ||||||||
\(315\) | −3.02728e100 | −0.199285 | ||||||||
\(316\) | −1.82771e101 | −1.05823 | ||||||||
\(317\) | −3.79837e99 | −0.0193507 | −0.00967536 | − | 0.999953i | \(-0.503080\pi\) | ||||
−0.00967536 | + | 0.999953i | \(0.503080\pi\) | |||||||
\(318\) | 1.34089e101 | 0.601304 | ||||||||
\(319\) | −6.61518e100 | −0.261228 | ||||||||
\(320\) | −1.93621e101 | −0.673564 | ||||||||
\(321\) | 5.13398e101 | 1.57398 | ||||||||
\(322\) | 1.13656e102 | 3.07206 | ||||||||
\(323\) | −1.07975e101 | −0.257408 | ||||||||
\(324\) | −1.10578e102 | −2.32593 | ||||||||
\(325\) | 3.72193e101 | 0.691021 | ||||||||
\(326\) | −9.58674e101 | −1.57166 | ||||||||
\(327\) | −1.36368e102 | −1.97483 | ||||||||
\(328\) | −1.21446e102 | −1.55415 | ||||||||
\(329\) | 2.30498e102 | 2.60755 | ||||||||
\(330\) | −9.95115e101 | −0.995540 | ||||||||
\(331\) | 1.31632e102 | 1.16501 | 0.582503 | − | 0.812829i | \(-0.302074\pi\) | ||||
0.582503 | + | 0.812829i | \(0.302074\pi\) | |||||||
\(332\) | −2.81024e101 | −0.220116 | ||||||||
\(333\) | 4.07870e100 | 0.0282833 | ||||||||
\(334\) | 1.68385e102 | 1.03412 | ||||||||
\(335\) | 4.51089e101 | 0.245441 | ||||||||
\(336\) | 4.77605e102 | 2.30318 | ||||||||
\(337\) | −2.45788e102 | −1.05087 | −0.525435 | − | 0.850834i | \(-0.676097\pi\) | ||||
−0.525435 | + | 0.850834i | \(0.676097\pi\) | |||||||
\(338\) | −2.76874e102 | −1.04992 | ||||||||
\(339\) | 8.66252e101 | 0.291445 | ||||||||
\(340\) | 1.66959e102 | 0.498554 | ||||||||
\(341\) | −2.15438e101 | −0.0571177 | ||||||||
\(342\) | 1.05526e102 | 0.248485 | ||||||||
\(343\) | −3.23553e102 | −0.676914 | ||||||||
\(344\) | −1.32307e103 | −2.46017 | ||||||||
\(345\) | −8.79493e102 | −1.45398 | ||||||||
\(346\) | 2.15857e103 | 3.17383 | ||||||||
\(347\) | −4.49961e102 | −0.588615 | −0.294308 | − | 0.955711i | \(-0.595089\pi\) | ||||
−0.294308 | + | 0.955711i | \(0.595089\pi\) | |||||||
\(348\) | −1.16478e103 | −1.35608 | ||||||||
\(349\) | −2.66970e102 | −0.276715 | −0.138357 | − | 0.990382i | \(-0.544182\pi\) | ||||
−0.138357 | + | 0.990382i | \(0.544182\pi\) | |||||||
\(350\) | 1.63672e103 | 1.51084 | ||||||||
\(351\) | 1.44638e103 | 1.18944 | ||||||||
\(352\) | 2.87230e102 | 0.210500 | ||||||||
\(353\) | −2.24963e102 | −0.146972 | −0.0734861 | − | 0.997296i | \(-0.523412\pi\) | ||||
−0.0734861 | + | 0.997296i | \(0.523412\pi\) | |||||||
\(354\) | 2.39047e103 | 1.39268 | ||||||||
\(355\) | −9.57475e102 | −0.497598 | ||||||||
\(356\) | −6.23905e103 | −2.89330 | ||||||||
\(357\) | 7.44787e102 | 0.308297 | ||||||||
\(358\) | 3.51133e103 | 1.29781 | ||||||||
\(359\) | −2.07238e103 | −0.684140 | −0.342070 | − | 0.939674i | \(-0.611128\pi\) | ||||
−0.342070 | + | 0.939674i | \(0.611128\pi\) | |||||||
\(360\) | −8.65536e102 | −0.255290 | ||||||||
\(361\) | 3.30391e103 | 0.870937 | ||||||||
\(362\) | 1.18575e104 | 2.79444 | ||||||||
\(363\) | 4.05777e103 | 0.855203 | ||||||||
\(364\) | −2.22457e104 | −4.19412 | ||||||||
\(365\) | −3.00268e103 | −0.506579 | ||||||||
\(366\) | −4.43573e103 | −0.669856 | ||||||||
\(367\) | 1.73601e103 | 0.234734 | 0.117367 | − | 0.993089i | \(-0.462555\pi\) | ||||
0.117367 | + | 0.993089i | \(0.462555\pi\) | |||||||
\(368\) | 1.29216e104 | 1.56488 | ||||||||
\(369\) | 7.35987e102 | 0.0798551 | ||||||||
\(370\) | −6.23353e103 | −0.606128 | ||||||||
\(371\) | −5.79311e103 | −0.504973 | ||||||||
\(372\) | −3.79337e103 | −0.296507 | ||||||||
\(373\) | −2.70244e104 | −1.89473 | −0.947366 | − | 0.320152i | \(-0.896266\pi\) | ||||
−0.947366 | + | 0.320152i | \(0.896266\pi\) | |||||||
\(374\) | 2.27993e103 | 0.143424 | ||||||||
\(375\) | 1.04712e104 | 0.591192 | ||||||||
\(376\) | 6.59023e104 | 3.34035 | ||||||||
\(377\) | 1.68166e104 | 0.765446 | ||||||||
\(378\) | 6.36047e104 | 2.60059 | ||||||||
\(379\) | 1.10245e104 | 0.405016 | 0.202508 | − | 0.979281i | \(-0.435091\pi\) | ||||
0.202508 | + | 0.979281i | \(0.435091\pi\) | |||||||
\(380\) | −1.09745e105 | −3.62368 | ||||||||
\(381\) | −8.68357e103 | −0.257773 | ||||||||
\(382\) | −5.40286e104 | −1.44231 | ||||||||
\(383\) | 4.67521e104 | 1.12267 | 0.561333 | − | 0.827590i | \(-0.310289\pi\) | ||||
0.561333 | + | 0.827590i | \(0.310289\pi\) | |||||||
\(384\) | −7.03024e104 | −1.51899 | ||||||||
\(385\) | 4.29924e104 | 0.836050 | ||||||||
\(386\) | −1.94128e105 | −3.39862 | ||||||||
\(387\) | 8.01807e103 | 0.126408 | ||||||||
\(388\) | 1.38917e105 | 1.97274 | ||||||||
\(389\) | 3.56223e103 | 0.0455788 | 0.0227894 | − | 0.999740i | \(-0.492745\pi\) | ||||
0.0227894 | + | 0.999740i | \(0.492745\pi\) | |||||||
\(390\) | 2.52971e105 | 2.91712 | ||||||||
\(391\) | 2.01502e104 | 0.209470 | ||||||||
\(392\) | −3.05712e105 | −2.86567 | ||||||||
\(393\) | 8.13363e104 | 0.687680 | ||||||||
\(394\) | 8.35403e104 | 0.637234 | ||||||||
\(395\) | −8.97947e104 | −0.618114 | ||||||||
\(396\) | −1.51625e104 | −0.0942138 | ||||||||
\(397\) | 1.81315e104 | 0.101723 | 0.0508615 | − | 0.998706i | \(-0.483803\pi\) | ||||
0.0508615 | + | 0.998706i | \(0.483803\pi\) | |||||||
\(398\) | 4.99983e105 | 2.53332 | ||||||||
\(399\) | −4.89563e105 | −2.24082 | ||||||||
\(400\) | 1.86080e105 | 0.769608 | ||||||||
\(401\) | −3.21134e103 | −0.0120044 | −0.00600218 | − | 0.999982i | \(-0.501911\pi\) | ||||
−0.00600218 | + | 0.999982i | \(0.501911\pi\) | |||||||
\(402\) | 1.08462e105 | 0.366539 | ||||||||
\(403\) | 5.47672e104 | 0.167366 | ||||||||
\(404\) | −6.25419e105 | −1.72872 | ||||||||
\(405\) | −5.43265e105 | −1.35857 | ||||||||
\(406\) | 7.39515e105 | 1.67357 | ||||||||
\(407\) | −5.79244e104 | −0.118655 | ||||||||
\(408\) | 2.12944e105 | 0.394938 | ||||||||
\(409\) | 7.61995e105 | 1.27985 | 0.639923 | − | 0.768439i | \(-0.278966\pi\) | ||||
0.639923 | + | 0.768439i | \(0.278966\pi\) | |||||||
\(410\) | −1.12482e106 | −1.71134 | ||||||||
\(411\) | −3.75363e105 | −0.517437 | ||||||||
\(412\) | 6.20538e105 | 0.775231 | ||||||||
\(413\) | −1.03276e106 | −1.16956 | ||||||||
\(414\) | −1.96931e105 | −0.202209 | ||||||||
\(415\) | −1.38066e105 | −0.128570 | ||||||||
\(416\) | −7.30174e105 | −0.616803 | ||||||||
\(417\) | 2.57884e106 | 1.97658 | ||||||||
\(418\) | −1.49864e106 | −1.04246 | ||||||||
\(419\) | 5.20228e105 | 0.328493 | 0.164246 | − | 0.986419i | \(-0.447481\pi\) | ||||
0.164246 | + | 0.986419i | \(0.447481\pi\) | |||||||
\(420\) | 7.56996e106 | 4.34007 | ||||||||
\(421\) | −1.35551e106 | −0.705792 | −0.352896 | − | 0.935663i | \(-0.614803\pi\) | ||||
−0.352896 | + | 0.935663i | \(0.614803\pi\) | |||||||
\(422\) | −1.31452e106 | −0.621745 | ||||||||
\(423\) | −3.99381e105 | −0.171634 | ||||||||
\(424\) | −1.65632e106 | −0.646885 | ||||||||
\(425\) | 2.90177e105 | 0.103017 | ||||||||
\(426\) | −2.30219e106 | −0.743109 | ||||||||
\(427\) | 1.91639e106 | 0.562542 | ||||||||
\(428\) | −1.19554e107 | −3.19220 | ||||||||
\(429\) | 2.35070e106 | 0.571055 | ||||||||
\(430\) | −1.22541e107 | −2.70901 | ||||||||
\(431\) | 9.80300e106 | 1.97256 | 0.986278 | − | 0.165091i | \(-0.0527917\pi\) | ||||
0.986278 | + | 0.165091i | \(0.0527917\pi\) | |||||||
\(432\) | 7.23124e106 | 1.32471 | ||||||||
\(433\) | −2.54698e106 | −0.424879 | −0.212439 | − | 0.977174i | \(-0.568141\pi\) | ||||
−0.212439 | + | 0.977174i | \(0.568141\pi\) | |||||||
\(434\) | 2.40840e106 | 0.365927 | ||||||||
\(435\) | −5.72251e106 | −0.792084 | ||||||||
\(436\) | 3.17558e107 | 4.00516 | ||||||||
\(437\) | −1.32451e107 | −1.52250 | ||||||||
\(438\) | −7.21975e106 | −0.756521 | ||||||||
\(439\) | 2.15473e106 | 0.205864 | 0.102932 | − | 0.994688i | \(-0.467178\pi\) | ||||
0.102932 | + | 0.994688i | \(0.467178\pi\) | |||||||
\(440\) | 1.22921e107 | 1.07101 | ||||||||
\(441\) | 1.85268e106 | 0.147244 | ||||||||
\(442\) | −5.79587e106 | −0.420258 | ||||||||
\(443\) | 1.17940e107 | 0.780391 | 0.390195 | − | 0.920732i | \(-0.372407\pi\) | ||||
0.390195 | + | 0.920732i | \(0.372407\pi\) | |||||||
\(444\) | −1.01991e107 | −0.615960 | ||||||||
\(445\) | −3.06522e107 | −1.68998 | ||||||||
\(446\) | −3.77601e107 | −1.90095 | ||||||||
\(447\) | 1.90298e107 | 0.874943 | ||||||||
\(448\) | 2.01134e107 | 0.844746 | ||||||||
\(449\) | 3.36157e107 | 1.28993 | 0.644964 | − | 0.764213i | \(-0.276872\pi\) | ||||
0.644964 | + | 0.764213i | \(0.276872\pi\) | |||||||
\(450\) | −2.83593e106 | −0.0994464 | ||||||||
\(451\) | −1.04523e107 | −0.335012 | ||||||||
\(452\) | −2.01722e107 | −0.591081 | ||||||||
\(453\) | 2.71308e107 | 0.726917 | ||||||||
\(454\) | 1.18167e108 | 2.89558 | ||||||||
\(455\) | −1.09292e108 | −2.44978 | ||||||||
\(456\) | −1.39972e108 | −2.87055 | ||||||||
\(457\) | −7.65904e106 | −0.143737 | −0.0718685 | − | 0.997414i | \(-0.522896\pi\) | ||||
−0.0718685 | + | 0.997414i | \(0.522896\pi\) | |||||||
\(458\) | −9.61475e107 | −1.65153 | ||||||||
\(459\) | 1.12765e107 | 0.177322 | ||||||||
\(460\) | 2.04805e108 | 2.94882 | ||||||||
\(461\) | 7.66641e107 | 1.01089 | 0.505446 | − | 0.862858i | \(-0.331328\pi\) | ||||
0.505446 | + | 0.862858i | \(0.331328\pi\) | |||||||
\(462\) | 1.03373e108 | 1.24855 | ||||||||
\(463\) | 4.28640e107 | 0.474310 | 0.237155 | − | 0.971472i | \(-0.423785\pi\) | ||||
0.237155 | + | 0.971472i | \(0.423785\pi\) | |||||||
\(464\) | 8.40757e107 | 0.852496 | ||||||||
\(465\) | −1.86366e107 | −0.173190 | ||||||||
\(466\) | −3.08672e108 | −2.62947 | ||||||||
\(467\) | −9.14459e107 | −0.714218 | −0.357109 | − | 0.934063i | \(-0.616237\pi\) | ||||
−0.357109 | + | 0.934063i | \(0.616237\pi\) | |||||||
\(468\) | 3.85449e107 | 0.276064 | ||||||||
\(469\) | −4.68592e107 | −0.307818 | ||||||||
\(470\) | 6.10380e108 | 3.67821 | ||||||||
\(471\) | −1.41471e108 | −0.782205 | ||||||||
\(472\) | −2.95280e108 | −1.49825 | ||||||||
\(473\) | −1.13870e108 | −0.530315 | ||||||||
\(474\) | −2.15906e108 | −0.923085 | ||||||||
\(475\) | −1.90739e108 | −0.748769 | ||||||||
\(476\) | −1.73437e108 | −0.625259 | ||||||||
\(477\) | 1.00376e107 | 0.0332382 | ||||||||
\(478\) | −1.53322e108 | −0.466418 | ||||||||
\(479\) | 1.30765e108 | 0.365514 | 0.182757 | − | 0.983158i | \(-0.441498\pi\) | ||||
0.182757 | + | 0.983158i | \(0.441498\pi\) | |||||||
\(480\) | 2.48470e108 | 0.638268 | ||||||||
\(481\) | 1.47251e108 | 0.347683 | ||||||||
\(482\) | 6.72494e108 | 1.45977 | ||||||||
\(483\) | 9.13618e108 | 1.82350 | ||||||||
\(484\) | −9.44923e108 | −1.73444 | ||||||||
\(485\) | 6.82493e108 | 1.15228 | ||||||||
\(486\) | −2.33026e108 | −0.361939 | ||||||||
\(487\) | 1.34851e109 | 1.92722 | 0.963612 | − | 0.267303i | \(-0.0861326\pi\) | ||||
0.963612 | + | 0.267303i | \(0.0861326\pi\) | |||||||
\(488\) | 5.47920e108 | 0.720633 | ||||||||
\(489\) | −7.70624e108 | −0.932898 | ||||||||
\(490\) | −2.83147e109 | −3.15552 | ||||||||
\(491\) | −1.05930e109 | −1.08698 | −0.543488 | − | 0.839417i | \(-0.682897\pi\) | ||||
−0.543488 | + | 0.839417i | \(0.682897\pi\) | |||||||
\(492\) | −1.84040e109 | −1.73910 | ||||||||
\(493\) | 1.31109e108 | 0.114113 | ||||||||
\(494\) | 3.80974e109 | 3.05459 | ||||||||
\(495\) | −7.44925e107 | −0.0550303 | ||||||||
\(496\) | 2.73812e108 | 0.186399 | ||||||||
\(497\) | 9.94626e108 | 0.624060 | ||||||||
\(498\) | −3.31971e108 | −0.192005 | ||||||||
\(499\) | −1.24975e109 | −0.666427 | −0.333213 | − | 0.942851i | \(-0.608133\pi\) | ||||
−0.333213 | + | 0.942851i | \(0.608133\pi\) | |||||||
\(500\) | −2.43839e109 | −1.19900 | ||||||||
\(501\) | 1.35355e109 | 0.613828 | ||||||||
\(502\) | 2.95242e109 | 1.23503 | ||||||||
\(503\) | −2.57395e109 | −0.993337 | −0.496669 | − | 0.867940i | \(-0.665444\pi\) | ||||
−0.496669 | + | 0.867940i | \(0.665444\pi\) | |||||||
\(504\) | 8.99120e108 | 0.320170 | ||||||||
\(505\) | −3.07266e109 | −1.00975 | ||||||||
\(506\) | 2.79675e109 | 0.848316 | ||||||||
\(507\) | −2.22564e109 | −0.623207 | ||||||||
\(508\) | 2.02212e109 | 0.522790 | ||||||||
\(509\) | −2.29496e109 | −0.547905 | −0.273953 | − | 0.961743i | \(-0.588331\pi\) | ||||
−0.273953 | + | 0.961743i | \(0.588331\pi\) | |||||||
\(510\) | 1.97227e109 | 0.434884 | ||||||||
\(511\) | 3.11918e109 | 0.635323 | ||||||||
\(512\) | 1.12806e110 | 2.12276 | ||||||||
\(513\) | −7.41229e109 | −1.28884 | ||||||||
\(514\) | 6.31952e109 | 1.01550 | ||||||||
\(515\) | 3.04867e109 | 0.452812 | ||||||||
\(516\) | −2.00499e110 | −2.75295 | ||||||||
\(517\) | 5.67189e109 | 0.720047 | ||||||||
\(518\) | 6.47540e109 | 0.760171 | ||||||||
\(519\) | 1.73515e110 | 1.88391 | ||||||||
\(520\) | −3.12480e110 | −3.13824 | ||||||||
\(521\) | −1.75441e110 | −1.63006 | −0.815030 | − | 0.579418i | \(-0.803280\pi\) | ||||
−0.815030 | + | 0.579418i | \(0.803280\pi\) | |||||||
\(522\) | −1.28135e109 | −0.110157 | ||||||||
\(523\) | −5.76234e109 | −0.458438 | −0.229219 | − | 0.973375i | \(-0.573617\pi\) | ||||
−0.229219 | + | 0.973375i | \(0.573617\pi\) | |||||||
\(524\) | −1.89406e110 | −1.39469 | ||||||||
\(525\) | 1.31567e110 | 0.896800 | ||||||||
\(526\) | 2.77026e110 | 1.74823 | ||||||||
\(527\) | 4.26988e108 | 0.0249509 | ||||||||
\(528\) | 1.17525e110 | 0.635998 | ||||||||
\(529\) | 4.76740e109 | 0.238961 | ||||||||
\(530\) | −1.53407e110 | −0.712314 | ||||||||
\(531\) | 1.78946e109 | 0.0769828 | ||||||||
\(532\) | 1.14003e111 | 4.54461 | ||||||||
\(533\) | 2.65710e110 | 0.981647 | ||||||||
\(534\) | −7.37013e110 | −2.52380 | ||||||||
\(535\) | −5.87362e110 | −1.86457 | ||||||||
\(536\) | −1.33976e110 | −0.394324 | ||||||||
\(537\) | 2.82256e110 | 0.770345 | ||||||||
\(538\) | −4.21413e110 | −1.06666 | ||||||||
\(539\) | −2.63111e110 | −0.617724 | ||||||||
\(540\) | 1.14614e111 | 2.49626 | ||||||||
\(541\) | −7.18664e110 | −1.45223 | −0.726117 | − | 0.687571i | \(-0.758677\pi\) | ||||
−0.726117 | + | 0.687571i | \(0.758677\pi\) | |||||||
\(542\) | −1.11871e111 | −2.09771 | ||||||||
\(543\) | 9.53154e110 | 1.65871 | ||||||||
\(544\) | −5.69274e109 | −0.0919530 | ||||||||
\(545\) | 1.56015e111 | 2.33941 | ||||||||
\(546\) | −2.62786e111 | −3.65848 | ||||||||
\(547\) | −6.52155e110 | −0.843070 | −0.421535 | − | 0.906812i | \(-0.638509\pi\) | ||||
−0.421535 | + | 0.906812i | \(0.638509\pi\) | |||||||
\(548\) | 8.74098e110 | 1.04942 | ||||||||
\(549\) | −3.32051e109 | −0.0370275 | ||||||||
\(550\) | 4.02750e110 | 0.417203 | ||||||||
\(551\) | −8.61808e110 | −0.829413 | ||||||||
\(552\) | 2.61215e111 | 2.33596 | ||||||||
\(553\) | 9.32789e110 | 0.775203 | ||||||||
\(554\) | 3.87004e111 | 2.98930 | ||||||||
\(555\) | −5.01078e110 | −0.359782 | ||||||||
\(556\) | −6.00527e111 | −4.00870 | ||||||||
\(557\) | −1.59621e111 | −0.990731 | −0.495366 | − | 0.868685i | \(-0.664966\pi\) | ||||
−0.495366 | + | 0.868685i | \(0.664966\pi\) | |||||||
\(558\) | −4.17300e109 | −0.0240859 | ||||||||
\(559\) | 2.89472e111 | 1.55392 | ||||||||
\(560\) | −5.46412e111 | −2.72838 | ||||||||
\(561\) | 1.83271e110 | 0.0851328 | ||||||||
\(562\) | 6.93135e111 | 2.99569 | ||||||||
\(563\) | −2.62548e111 | −1.05589 | −0.527945 | − | 0.849278i | \(-0.677037\pi\) | ||||
−0.527945 | + | 0.849278i | \(0.677037\pi\) | |||||||
\(564\) | 9.98686e111 | 3.73788 | ||||||||
\(565\) | −9.91051e110 | −0.345250 | ||||||||
\(566\) | −8.01148e111 | −2.59805 | ||||||||
\(567\) | 5.64344e111 | 1.70385 | ||||||||
\(568\) | 2.84376e111 | 0.799439 | ||||||||
\(569\) | −4.82520e111 | −1.26319 | −0.631594 | − | 0.775299i | \(-0.717599\pi\) | ||||
−0.631594 | + | 0.775299i | \(0.717599\pi\) | |||||||
\(570\) | −1.29641e112 | −3.16090 | ||||||||
\(571\) | −2.19654e111 | −0.498858 | −0.249429 | − | 0.968393i | \(-0.580243\pi\) | ||||
−0.249429 | + | 0.968393i | \(0.580243\pi\) | |||||||
\(572\) | −5.47403e111 | −1.15816 | ||||||||
\(573\) | −4.34306e111 | −0.856117 | ||||||||
\(574\) | 1.16846e112 | 2.14627 | ||||||||
\(575\) | 3.55955e111 | 0.609322 | ||||||||
\(576\) | −3.48503e110 | −0.0556026 | ||||||||
\(577\) | 1.35541e111 | 0.201581 | 0.100790 | − | 0.994908i | \(-0.467863\pi\) | ||||
0.100790 | + | 0.994908i | \(0.467863\pi\) | |||||||
\(578\) | 1.23075e112 | 1.70644 | ||||||||
\(579\) | −1.56049e112 | −2.01734 | ||||||||
\(580\) | 1.33259e112 | 1.60643 | ||||||||
\(581\) | 1.43423e111 | 0.161245 | ||||||||
\(582\) | 1.64101e112 | 1.72080 | ||||||||
\(583\) | −1.42552e111 | −0.139443 | ||||||||
\(584\) | 8.91813e111 | 0.813867 | ||||||||
\(585\) | 1.89369e111 | 0.161249 | ||||||||
\(586\) | −1.18110e112 | −0.938499 | ||||||||
\(587\) | 1.67568e112 | 1.24265 | 0.621325 | − | 0.783553i | \(-0.286595\pi\) | ||||
0.621325 | + | 0.783553i | \(0.286595\pi\) | |||||||
\(588\) | −4.63277e112 | −3.20671 | ||||||||
\(589\) | −2.80667e111 | −0.181352 | ||||||||
\(590\) | −2.73485e112 | −1.64979 | ||||||||
\(591\) | 6.71534e111 | 0.378247 | ||||||||
\(592\) | 7.36190e111 | 0.387223 | ||||||||
\(593\) | 7.97650e111 | 0.391830 | 0.195915 | − | 0.980621i | \(-0.437232\pi\) | ||||
0.195915 | + | 0.980621i | \(0.437232\pi\) | |||||||
\(594\) | 1.56513e112 | 0.718122 | ||||||||
\(595\) | −8.52087e111 | −0.365214 | ||||||||
\(596\) | −4.43142e112 | −1.77447 | ||||||||
\(597\) | 4.01908e112 | 1.50372 | ||||||||
\(598\) | −7.10969e112 | −2.48572 | ||||||||
\(599\) | 2.32037e112 | 0.758178 | 0.379089 | − | 0.925360i | \(-0.376237\pi\) | ||||
0.379089 | + | 0.925360i | \(0.376237\pi\) | |||||||
\(600\) | 3.76167e112 | 1.14883 | ||||||||
\(601\) | 3.08514e112 | 0.880762 | 0.440381 | − | 0.897811i | \(-0.354843\pi\) | ||||
0.440381 | + | 0.897811i | \(0.354843\pi\) | |||||||
\(602\) | 1.27296e113 | 3.39748 | ||||||||
\(603\) | 8.11923e110 | 0.0202611 | ||||||||
\(604\) | −6.31787e112 | −1.47426 | ||||||||
\(605\) | −4.64236e112 | −1.01309 | ||||||||
\(606\) | −7.38801e112 | −1.50795 | ||||||||
\(607\) | −1.27038e112 | −0.242544 | −0.121272 | − | 0.992619i | \(-0.538697\pi\) | ||||
−0.121272 | + | 0.992619i | \(0.538697\pi\) | |||||||
\(608\) | 3.74195e112 | 0.668348 | ||||||||
\(609\) | 5.94455e112 | 0.993387 | ||||||||
\(610\) | 5.07478e112 | 0.793521 | ||||||||
\(611\) | −1.44187e113 | −2.10987 | ||||||||
\(612\) | 3.00512e111 | 0.0411556 | ||||||||
\(613\) | 5.88625e112 | 0.754553 | 0.377276 | − | 0.926101i | \(-0.376861\pi\) | ||||
0.377276 | + | 0.926101i | \(0.376861\pi\) | |||||||
\(614\) | 2.40476e113 | 2.88571 | ||||||||
\(615\) | −9.04179e112 | −1.01581 | ||||||||
\(616\) | −1.27690e113 | −1.34319 | ||||||||
\(617\) | −1.09249e113 | −1.07614 | −0.538071 | − | 0.842900i | \(-0.680847\pi\) | ||||
−0.538071 | + | 0.842900i | \(0.680847\pi\) | |||||||
\(618\) | 7.33035e112 | 0.676225 | ||||||||
\(619\) | −1.28134e113 | −1.10711 | −0.553556 | − | 0.832812i | \(-0.686730\pi\) | ||||
−0.553556 | + | 0.832812i | \(0.686730\pi\) | |||||||
\(620\) | 4.33987e112 | 0.351247 | ||||||||
\(621\) | 1.38327e113 | 1.04881 | ||||||||
\(622\) | −2.02912e113 | −1.44144 | ||||||||
\(623\) | 3.18415e113 | 2.11947 | ||||||||
\(624\) | −2.98763e113 | −1.86359 | ||||||||
\(625\) | −2.13437e113 | −1.24775 | ||||||||
\(626\) | 6.64092e112 | 0.363888 | ||||||||
\(627\) | −1.20467e113 | −0.618777 | ||||||||
\(628\) | 3.29440e113 | 1.58639 | ||||||||
\(629\) | 1.14803e112 | 0.0518325 | ||||||||
\(630\) | 8.32756e112 | 0.352554 | ||||||||
\(631\) | −3.06535e112 | −0.121700 | −0.0608500 | − | 0.998147i | \(-0.519381\pi\) | ||||
−0.0608500 | + | 0.998147i | \(0.519381\pi\) | |||||||
\(632\) | 2.66696e113 | 0.993058 | ||||||||
\(633\) | −1.05667e113 | −0.369052 | ||||||||
\(634\) | 1.04487e112 | 0.0342332 | ||||||||
\(635\) | 9.93459e112 | 0.305361 | ||||||||
\(636\) | −2.51000e113 | −0.723869 | ||||||||
\(637\) | 6.68863e113 | 1.81005 | ||||||||
\(638\) | 1.81973e113 | 0.462136 | ||||||||
\(639\) | −1.72338e112 | −0.0410767 | ||||||||
\(640\) | 8.04306e113 | 1.79942 | ||||||||
\(641\) | 1.95149e113 | 0.409841 | 0.204920 | − | 0.978779i | \(-0.434306\pi\) | ||||
0.204920 | + | 0.978779i | \(0.434306\pi\) | |||||||
\(642\) | −1.41228e114 | −2.78453 | ||||||||
\(643\) | 2.08964e112 | 0.0386837 | 0.0193418 | − | 0.999813i | \(-0.493843\pi\) | ||||
0.0193418 | + | 0.999813i | \(0.493843\pi\) | |||||||
\(644\) | −2.12752e114 | −3.69825 | ||||||||
\(645\) | −9.85040e113 | −1.60800 | ||||||||
\(646\) | 2.97023e113 | 0.455379 | ||||||||
\(647\) | −3.65213e113 | −0.525924 | −0.262962 | − | 0.964806i | \(-0.584699\pi\) | ||||
−0.262962 | + | 0.964806i | \(0.584699\pi\) | |||||||
\(648\) | 1.61353e114 | 2.18268 | ||||||||
\(649\) | −2.54133e113 | −0.322962 | ||||||||
\(650\) | −1.02384e114 | −1.22248 | ||||||||
\(651\) | 1.93598e113 | 0.217205 | ||||||||
\(652\) | 1.79453e114 | 1.89201 | ||||||||
\(653\) | 1.17868e114 | 1.16792 | 0.583958 | − | 0.811784i | \(-0.301503\pi\) | ||||
0.583958 | + | 0.811784i | \(0.301503\pi\) | |||||||
\(654\) | 3.75128e114 | 3.49366 | ||||||||
\(655\) | −9.30542e113 | −0.814636 | ||||||||
\(656\) | 1.32843e114 | 1.09328 | ||||||||
\(657\) | −5.40457e112 | −0.0418181 | ||||||||
\(658\) | −6.34064e114 | −4.61301 | ||||||||
\(659\) | −1.22498e114 | −0.838047 | −0.419023 | − | 0.907975i | \(-0.637627\pi\) | ||||
−0.419023 | + | 0.907975i | \(0.637627\pi\) | |||||||
\(660\) | 1.86275e114 | 1.19846 | ||||||||
\(661\) | 2.44914e114 | 1.48202 | 0.741011 | − | 0.671492i | \(-0.234346\pi\) | ||||
0.741011 | + | 0.671492i | \(0.234346\pi\) | |||||||
\(662\) | −3.62099e114 | −2.06100 | ||||||||
\(663\) | −4.65897e113 | −0.249455 | ||||||||
\(664\) | 4.10064e113 | 0.206559 | ||||||||
\(665\) | 5.60094e114 | 2.65451 | ||||||||
\(666\) | −1.12198e113 | −0.0500358 | ||||||||
\(667\) | 1.60830e114 | 0.674948 | ||||||||
\(668\) | −3.15198e114 | −1.24491 | ||||||||
\(669\) | −3.03532e114 | −1.12836 | ||||||||
\(670\) | −1.24087e114 | −0.434208 | ||||||||
\(671\) | 4.71568e113 | 0.155340 | ||||||||
\(672\) | −2.58111e114 | −0.800480 | ||||||||
\(673\) | −3.94004e114 | −1.15051 | −0.575256 | − | 0.817974i | \(-0.695098\pi\) | ||||
−0.575256 | + | 0.817974i | \(0.695098\pi\) | |||||||
\(674\) | 6.76122e114 | 1.85909 | ||||||||
\(675\) | 1.99201e114 | 0.515808 | ||||||||
\(676\) | 5.18279e114 | 1.26393 | ||||||||
\(677\) | −3.10016e114 | −0.712104 | −0.356052 | − | 0.934466i | \(-0.615877\pi\) | ||||
−0.356052 | + | 0.934466i | \(0.615877\pi\) | |||||||
\(678\) | −2.38292e114 | −0.515593 | ||||||||
\(679\) | −7.08975e114 | −1.44512 | ||||||||
\(680\) | −2.43622e114 | −0.467849 | ||||||||
\(681\) | 9.49880e114 | 1.71874 | ||||||||
\(682\) | 5.92637e113 | 0.101047 | ||||||||
\(683\) | −8.16946e114 | −1.31267 | −0.656334 | − | 0.754470i | \(-0.727894\pi\) | ||||
−0.656334 | + | 0.754470i | \(0.727894\pi\) | |||||||
\(684\) | −1.97532e114 | −0.299134 | ||||||||
\(685\) | 4.29441e114 | 0.612964 | ||||||||
\(686\) | 8.90043e114 | 1.19752 | ||||||||
\(687\) | −7.72875e114 | −0.980306 | ||||||||
\(688\) | 1.44723e115 | 1.73064 | ||||||||
\(689\) | 3.62384e114 | 0.408593 | ||||||||
\(690\) | 2.41934e115 | 2.57223 | ||||||||
\(691\) | 5.12579e114 | 0.513925 | 0.256963 | − | 0.966421i | \(-0.417278\pi\) | ||||
0.256963 | + | 0.966421i | \(0.417278\pi\) | |||||||
\(692\) | −4.04061e115 | −3.82076 | ||||||||
\(693\) | 7.73829e113 | 0.0690159 | ||||||||
\(694\) | 1.23777e115 | 1.04131 | ||||||||
\(695\) | −2.95036e115 | −2.34148 | ||||||||
\(696\) | 1.69962e115 | 1.27256 | ||||||||
\(697\) | 2.07158e114 | 0.146344 | ||||||||
\(698\) | 7.34391e114 | 0.489534 | ||||||||
\(699\) | −2.48124e115 | −1.56079 | ||||||||
\(700\) | −3.06377e115 | −1.81880 | ||||||||
\(701\) | 2.06857e115 | 1.15902 | 0.579509 | − | 0.814966i | \(-0.303244\pi\) | ||||
0.579509 | + | 0.814966i | \(0.303244\pi\) | |||||||
\(702\) | −3.97875e115 | −2.10423 | ||||||||
\(703\) | −7.54623e114 | −0.376738 | ||||||||
\(704\) | 4.94933e114 | 0.233267 | ||||||||
\(705\) | 4.90650e115 | 2.18330 | ||||||||
\(706\) | 6.18837e114 | 0.260007 | ||||||||
\(707\) | 3.19188e115 | 1.26637 | ||||||||
\(708\) | −4.47469e115 | −1.67655 | ||||||||
\(709\) | 1.30065e115 | 0.460243 | 0.230121 | − | 0.973162i | \(-0.426088\pi\) | ||||
0.230121 | + | 0.973162i | \(0.426088\pi\) | |||||||
\(710\) | 2.63386e115 | 0.880298 | ||||||||
\(711\) | −1.61623e114 | −0.0510252 | ||||||||
\(712\) | 9.10389e115 | 2.71511 | ||||||||
\(713\) | 5.23778e114 | 0.147578 | ||||||||
\(714\) | −2.04879e115 | −0.545406 | ||||||||
\(715\) | −2.68936e115 | −0.676480 | ||||||||
\(716\) | −6.57284e115 | −1.56234 | ||||||||
\(717\) | −1.23247e115 | −0.276854 | ||||||||
\(718\) | 5.70080e115 | 1.21031 | ||||||||
\(719\) | 2.80859e115 | 0.563596 | 0.281798 | − | 0.959474i | \(-0.409069\pi\) | ||||
0.281798 | + | 0.959474i | \(0.409069\pi\) | |||||||
\(720\) | 9.46763e114 | 0.179587 | ||||||||
\(721\) | −3.16697e115 | −0.567891 | ||||||||
\(722\) | −9.08853e115 | −1.54077 | ||||||||
\(723\) | 5.40580e115 | 0.866481 | ||||||||
\(724\) | −2.21959e116 | −3.36403 | ||||||||
\(725\) | 2.31605e115 | 0.331940 | ||||||||
\(726\) | −1.11623e116 | −1.51293 | ||||||||
\(727\) | −3.89805e115 | −0.499694 | −0.249847 | − | 0.968285i | \(-0.580380\pi\) | ||||
−0.249847 | + | 0.968285i | \(0.580380\pi\) | |||||||
\(728\) | 3.24605e116 | 3.93581 | ||||||||
\(729\) | 7.64919e115 | 0.877305 | ||||||||
\(730\) | 8.25988e115 | 0.896186 | ||||||||
\(731\) | 2.25685e115 | 0.231658 | ||||||||
\(732\) | 8.30320e115 | 0.806393 | ||||||||
\(733\) | −6.67683e115 | −0.613563 | −0.306782 | − | 0.951780i | \(-0.599252\pi\) | ||||
−0.306782 | + | 0.951780i | \(0.599252\pi\) | |||||||
\(734\) | −4.77547e115 | −0.415266 | ||||||||
\(735\) | −2.27606e116 | −1.87304 | ||||||||
\(736\) | −6.98318e115 | −0.543879 | ||||||||
\(737\) | −1.15307e115 | −0.0850005 | ||||||||
\(738\) | −2.02458e115 | −0.141271 | ||||||||
\(739\) | −1.41381e116 | −0.933883 | −0.466941 | − | 0.884288i | \(-0.654644\pi\) | ||||
−0.466941 | + | 0.884288i | \(0.654644\pi\) | |||||||
\(740\) | 1.16685e116 | 0.729676 | ||||||||
\(741\) | 3.06243e116 | 1.81313 | ||||||||
\(742\) | 1.59359e116 | 0.893344 | ||||||||
\(743\) | −3.10050e116 | −1.64583 | −0.822915 | − | 0.568164i | \(-0.807654\pi\) | ||||
−0.822915 | + | 0.568164i | \(0.807654\pi\) | |||||||
\(744\) | 5.53520e115 | 0.278246 | ||||||||
\(745\) | −2.17714e116 | −1.03647 | ||||||||
\(746\) | 7.43397e116 | 3.35196 | ||||||||
\(747\) | −2.48507e114 | −0.0106134 | ||||||||
\(748\) | −4.26778e115 | −0.172658 | ||||||||
\(749\) | 6.10153e116 | 2.33843 | ||||||||
\(750\) | −2.88045e116 | −1.04587 | ||||||||
\(751\) | −2.35328e116 | −0.809573 | −0.404786 | − | 0.914411i | \(-0.632654\pi\) | ||||
−0.404786 | + | 0.914411i | \(0.632654\pi\) | |||||||
\(752\) | −7.20869e116 | −2.34982 | ||||||||
\(753\) | 2.37328e116 | 0.733083 | ||||||||
\(754\) | −4.62599e116 | −1.35414 | ||||||||
\(755\) | −3.10394e116 | −0.861117 | ||||||||
\(756\) | −1.19061e117 | −3.13067 | ||||||||
\(757\) | 7.10783e116 | 1.77155 | 0.885776 | − | 0.464113i | \(-0.153627\pi\) | ||||
0.885776 | + | 0.464113i | \(0.153627\pi\) | |||||||
\(758\) | −3.03267e116 | −0.716511 | ||||||||
\(759\) | 2.24815e116 | 0.503539 | ||||||||
\(760\) | 1.60138e117 | 3.40050 | ||||||||
\(761\) | 1.38307e116 | 0.278462 | 0.139231 | − | 0.990260i | \(-0.455537\pi\) | ||||
0.139231 | + | 0.990260i | \(0.455537\pi\) | |||||||
\(762\) | 2.38871e116 | 0.456024 | ||||||||
\(763\) | −1.62068e117 | −2.93396 | ||||||||
\(764\) | 1.01136e117 | 1.73629 | ||||||||
\(765\) | 1.47640e115 | 0.0240390 | ||||||||
\(766\) | −1.28608e117 | −1.98610 | ||||||||
\(767\) | 6.46039e116 | 0.946339 | ||||||||
\(768\) | 1.52471e117 | 2.11864 | ||||||||
\(769\) | 9.90906e115 | 0.130622 | 0.0653109 | − | 0.997865i | \(-0.479196\pi\) | ||||
0.0653109 | + | 0.997865i | \(0.479196\pi\) | |||||||
\(770\) | −1.18265e117 | −1.47905 | ||||||||
\(771\) | 5.07991e116 | 0.602773 | ||||||||
\(772\) | 3.63387e117 | 4.09137 | ||||||||
\(773\) | −1.27598e117 | −1.36325 | −0.681624 | − | 0.731703i | \(-0.738726\pi\) | ||||
−0.681624 | + | 0.731703i | \(0.738726\pi\) | |||||||
\(774\) | −2.20564e116 | −0.223628 | ||||||||
\(775\) | 7.54276e115 | 0.0725790 | ||||||||
\(776\) | −2.02705e117 | −1.85125 | ||||||||
\(777\) | 5.20521e116 | 0.451219 | ||||||||
\(778\) | −9.79912e115 | −0.0806331 | ||||||||
\(779\) | −1.36169e117 | −1.06368 | ||||||||
\(780\) | −4.73534e117 | −3.51172 | ||||||||
\(781\) | 2.44749e116 | 0.172327 | ||||||||
\(782\) | −5.54301e116 | −0.370571 | ||||||||
\(783\) | 9.00041e116 | 0.571362 | ||||||||
\(784\) | 3.34402e117 | 2.01589 | ||||||||
\(785\) | 1.61852e117 | 0.926612 | ||||||||
\(786\) | −2.23743e117 | −1.21657 | ||||||||
\(787\) | 9.41474e116 | 0.486219 | 0.243109 | − | 0.969999i | \(-0.421833\pi\) | ||||
0.243109 | + | 0.969999i | \(0.421833\pi\) | |||||||
\(788\) | −1.56378e117 | −0.767123 | ||||||||
\(789\) | 2.22686e117 | 1.03770 | ||||||||
\(790\) | 2.47011e117 | 1.09350 | ||||||||
\(791\) | 1.02951e117 | 0.432993 | ||||||||
\(792\) | 2.21247e116 | 0.0884114 | ||||||||
\(793\) | −1.19879e117 | −0.455174 | ||||||||
\(794\) | −4.98770e116 | −0.179957 | ||||||||
\(795\) | −1.23315e117 | −0.422812 | ||||||||
\(796\) | −9.35913e117 | −3.04969 | ||||||||
\(797\) | 2.29481e117 | 0.710696 | 0.355348 | − | 0.934734i | \(-0.384362\pi\) | ||||
0.355348 | + | 0.934734i | \(0.384362\pi\) | |||||||
\(798\) | 1.34671e118 | 3.96422 | ||||||||
\(799\) | −1.12414e117 | −0.314540 | ||||||||
\(800\) | −1.00562e117 | −0.267480 | ||||||||
\(801\) | −5.51714e116 | −0.139507 | ||||||||
\(802\) | 8.83388e115 | 0.0212368 | ||||||||
\(803\) | 7.67541e116 | 0.175437 | ||||||||
\(804\) | −2.03028e117 | −0.441252 | ||||||||
\(805\) | −1.04524e118 | −2.16015 | ||||||||
\(806\) | −1.50656e117 | −0.296085 | ||||||||
\(807\) | −3.38750e117 | −0.633142 | ||||||||
\(808\) | 9.12598e117 | 1.62226 | ||||||||
\(809\) | 1.11320e118 | 1.88217 | 0.941084 | − | 0.338174i | \(-0.109809\pi\) | ||||
0.941084 | + | 0.338174i | \(0.109809\pi\) | |||||||
\(810\) | 1.49444e118 | 2.40344 | ||||||||
\(811\) | −6.69075e117 | −1.02360 | −0.511800 | − | 0.859105i | \(-0.671021\pi\) | ||||
−0.511800 | + | 0.859105i | \(0.671021\pi\) | |||||||
\(812\) | −1.38429e118 | −2.01469 | ||||||||
\(813\) | −8.99266e117 | −1.24515 | ||||||||
\(814\) | 1.59341e117 | 0.209913 | ||||||||
\(815\) | 8.81646e117 | 1.10512 | ||||||||
\(816\) | −2.32928e117 | −0.277824 | ||||||||
\(817\) | −1.48347e118 | −1.68378 | ||||||||
\(818\) | −2.09613e118 | −2.26417 | ||||||||
\(819\) | −1.96717e117 | −0.202229 | ||||||||
\(820\) | 2.10554e118 | 2.06017 | ||||||||
\(821\) | 1.07493e117 | 0.100111 | 0.0500555 | − | 0.998746i | \(-0.484060\pi\) | ||||
0.0500555 | + | 0.998746i | \(0.484060\pi\) | |||||||
\(822\) | 1.03256e118 | 0.915394 | ||||||||
\(823\) | −8.97693e117 | −0.757591 | −0.378795 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378795 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(824\) | −9.05475e117 | −0.727486 | ||||||||
\(825\) | 3.23748e117 | 0.247641 | ||||||||
\(826\) | 2.84097e118 | 2.06907 | ||||||||
\(827\) | 4.59941e117 | 0.318955 | 0.159477 | − | 0.987202i | \(-0.449019\pi\) | ||||
0.159477 | + | 0.987202i | \(0.449019\pi\) | |||||||
\(828\) | 3.68633e117 | 0.243425 | ||||||||
\(829\) | 2.87941e118 | 1.81070 | 0.905348 | − | 0.424671i | \(-0.139610\pi\) | ||||
0.905348 | + | 0.424671i | \(0.139610\pi\) | |||||||
\(830\) | 3.79797e117 | 0.227452 | ||||||||
\(831\) | 3.11091e118 | 1.77437 | ||||||||
\(832\) | −1.25818e118 | −0.683516 | ||||||||
\(833\) | 5.21473e117 | 0.269842 | ||||||||
\(834\) | −7.09397e118 | −3.49675 | ||||||||
\(835\) | −1.54855e118 | −0.727150 | ||||||||
\(836\) | 2.80529e118 | 1.25494 | ||||||||
\(837\) | 2.93119e117 | 0.124929 | ||||||||
\(838\) | −1.43107e118 | −0.581135 | ||||||||
\(839\) | −2.90748e118 | −1.12501 | −0.562506 | − | 0.826793i | \(-0.690163\pi\) | ||||
−0.562506 | + | 0.826793i | \(0.690163\pi\) | |||||||
\(840\) | −1.10459e119 | −4.07278 | ||||||||
\(841\) | −1.79956e118 | −0.632309 | ||||||||
\(842\) | 3.72878e118 | 1.24861 | ||||||||
\(843\) | 5.57172e118 | 1.77817 | ||||||||
\(844\) | 2.46063e118 | 0.748476 | ||||||||
\(845\) | 2.54628e118 | 0.738260 | ||||||||
\(846\) | 1.09863e118 | 0.303636 | ||||||||
\(847\) | 4.82249e118 | 1.27056 | ||||||||
\(848\) | 1.81176e118 | 0.455060 | ||||||||
\(849\) | −6.43998e118 | −1.54214 | ||||||||
\(850\) | −7.98230e117 | −0.182247 | ||||||||
\(851\) | 1.40827e118 | 0.306576 | ||||||||
\(852\) | 4.30945e118 | 0.894578 | ||||||||
\(853\) | −6.52434e118 | −1.29152 | −0.645759 | − | 0.763541i | \(-0.723459\pi\) | ||||
−0.645759 | + | 0.763541i | \(0.723459\pi\) | |||||||
\(854\) | −5.27168e118 | −0.995189 | ||||||||
\(855\) | −9.70468e117 | −0.174724 | ||||||||
\(856\) | 1.74450e119 | 2.99560 | ||||||||
\(857\) | −1.76150e118 | −0.288508 | −0.144254 | − | 0.989541i | \(-0.546078\pi\) | ||||
−0.144254 | + | 0.989541i | \(0.546078\pi\) | |||||||
\(858\) | −6.46641e118 | −1.01025 | ||||||||
\(859\) | −1.96639e118 | −0.293053 | −0.146526 | − | 0.989207i | \(-0.546809\pi\) | ||||
−0.146526 | + | 0.989207i | \(0.546809\pi\) | |||||||
\(860\) | 2.29384e119 | 3.26119 | ||||||||
\(861\) | 9.39262e118 | 1.27397 | ||||||||
\(862\) | −2.69665e119 | −3.48964 | ||||||||
\(863\) | −1.80815e118 | −0.223253 | −0.111626 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111626 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(864\) | −3.90795e118 | −0.460408 | ||||||||
\(865\) | −1.98513e119 | −2.23171 | ||||||||
\(866\) | 7.00633e118 | 0.751650 | ||||||||
\(867\) | 9.89328e118 | 1.01290 | ||||||||
\(868\) | −4.50826e118 | −0.440514 | ||||||||
\(869\) | 2.29532e118 | 0.214064 | ||||||||
\(870\) | 1.57417e119 | 1.40127 | ||||||||
\(871\) | 2.93125e118 | 0.249067 | ||||||||
\(872\) | −4.63373e119 | −3.75849 | ||||||||
\(873\) | 1.22843e118 | 0.0951205 | ||||||||
\(874\) | 3.64353e119 | 2.69345 | ||||||||
\(875\) | 1.24445e119 | 0.878320 | ||||||||
\(876\) | 1.35146e119 | 0.910723 | ||||||||
\(877\) | −2.45811e119 | −1.58168 | −0.790838 | − | 0.612026i | \(-0.790355\pi\) | ||||
−0.790838 | + | 0.612026i | \(0.790355\pi\) | |||||||
\(878\) | −5.92733e118 | −0.364193 | ||||||||
\(879\) | −9.49421e118 | −0.557070 | ||||||||
\(880\) | −1.34456e119 | −0.753412 | ||||||||
\(881\) | −1.20622e119 | −0.645509 | −0.322754 | − | 0.946483i | \(-0.604609\pi\) | ||||
−0.322754 | + | 0.946483i | \(0.604609\pi\) | |||||||
\(882\) | −5.09642e118 | −0.260488 | ||||||||
\(883\) | 3.61723e119 | 1.76590 | 0.882952 | − | 0.469463i | \(-0.155552\pi\) | ||||
0.882952 | + | 0.469463i | \(0.155552\pi\) | |||||||
\(884\) | 1.08492e119 | 0.505920 | ||||||||
\(885\) | −2.19840e119 | −0.979272 | ||||||||
\(886\) | −3.24436e119 | −1.38058 | ||||||||
\(887\) | 9.24436e118 | 0.375812 | 0.187906 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187906 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(888\) | 1.48823e119 | 0.578024 | ||||||||
\(889\) | −1.03201e119 | −0.382967 | ||||||||
\(890\) | 8.43193e119 | 2.98973 | ||||||||
\(891\) | 1.38869e119 | 0.470498 | ||||||||
\(892\) | 7.06828e119 | 2.28843 | ||||||||
\(893\) | 7.38918e119 | 2.28619 | ||||||||
\(894\) | −5.23480e119 | −1.54785 | ||||||||
\(895\) | −3.22921e119 | −0.912563 | ||||||||
\(896\) | −8.35515e119 | −2.25673 | ||||||||
\(897\) | −5.71508e119 | −1.47546 | ||||||||
\(898\) | −9.24715e119 | −2.28200 | ||||||||
\(899\) | 3.40802e118 | 0.0803959 | ||||||||
\(900\) | 5.30856e118 | 0.119717 | ||||||||
\(901\) | 2.82530e118 | 0.0609130 | ||||||||
\(902\) | 2.87525e119 | 0.592667 | ||||||||
\(903\) | 1.02326e120 | 2.01666 | ||||||||
\(904\) | 2.94348e119 | 0.554677 | ||||||||
\(905\) | −1.09047e120 | −1.96493 | ||||||||
\(906\) | −7.46324e119 | −1.28598 | ||||||||
\(907\) | 3.32537e119 | 0.547954 | 0.273977 | − | 0.961736i | \(-0.411661\pi\) | ||||
0.273977 | + | 0.961736i | \(0.411661\pi\) | |||||||
\(908\) | −2.21196e120 | −3.48578 | ||||||||
\(909\) | −5.53053e118 | −0.0833546 | ||||||||
\(910\) | 3.00645e120 | 4.33389 | ||||||||
\(911\) | −1.17467e120 | −1.61966 | −0.809829 | − | 0.586666i | \(-0.800440\pi\) | ||||
−0.809829 | + | 0.586666i | \(0.800440\pi\) | |||||||
\(912\) | 1.53108e120 | 2.01933 | ||||||||
\(913\) | 3.52922e118 | 0.0445259 | ||||||||
\(914\) | 2.10688e119 | 0.254284 | ||||||||
\(915\) | 4.07933e119 | 0.471014 | ||||||||
\(916\) | 1.79978e120 | 1.98816 | ||||||||
\(917\) | 9.66649e119 | 1.02167 | ||||||||
\(918\) | −3.10200e119 | −0.313699 | ||||||||
\(919\) | 7.96795e119 | 0.771025 | 0.385512 | − | 0.922703i | \(-0.374025\pi\) | ||||
0.385512 | + | 0.922703i | \(0.374025\pi\) | |||||||
\(920\) | −2.98847e120 | −2.76721 | ||||||||
\(921\) | 1.93305e120 | 1.71289 | ||||||||
\(922\) | −2.10891e120 | −1.78836 | ||||||||
\(923\) | −6.22182e119 | −0.504950 | ||||||||
\(924\) | −1.93502e120 | −1.50304 | ||||||||
\(925\) | 2.02800e119 | 0.150775 | ||||||||
\(926\) | −1.17912e120 | −0.839098 | ||||||||
\(927\) | 5.48737e118 | 0.0373796 | ||||||||
\(928\) | −4.54368e119 | −0.296288 | ||||||||
\(929\) | 1.46480e120 | 0.914413 | 0.457207 | − | 0.889360i | \(-0.348850\pi\) | ||||
0.457207 | + | 0.889360i | \(0.348850\pi\) | |||||||
\(930\) | 5.12664e119 | 0.306389 | ||||||||
\(931\) | −3.42774e120 | −1.96131 | ||||||||
\(932\) | 5.77801e120 | 3.16544 | ||||||||
\(933\) | −1.63110e120 | −0.855606 | ||||||||
\(934\) | 2.51553e120 | 1.26352 | ||||||||
\(935\) | −2.09674e119 | −0.100850 | ||||||||
\(936\) | −5.62439e119 | −0.259062 | ||||||||
\(937\) | 1.21230e118 | 0.00534758 | 0.00267379 | − | 0.999996i | \(-0.499149\pi\) | ||||
0.00267379 | + | 0.999996i | \(0.499149\pi\) | |||||||
\(938\) | 1.28902e120 | 0.544559 | ||||||||
\(939\) | 5.33827e119 | 0.215995 | ||||||||
\(940\) | −1.14256e121 | −4.42795 | ||||||||
\(941\) | 1.76392e118 | 0.00654785 | 0.00327393 | − | 0.999995i | \(-0.498958\pi\) | ||||
0.00327393 | + | 0.999995i | \(0.498958\pi\) | |||||||
\(942\) | 3.89164e120 | 1.38379 | ||||||||
\(943\) | 2.54118e120 | 0.865588 | ||||||||
\(944\) | 3.22991e120 | 1.05396 | ||||||||
\(945\) | −5.84942e120 | −1.82862 | ||||||||
\(946\) | 3.13239e120 | 0.938176 | ||||||||
\(947\) | −1.62111e120 | −0.465200 | −0.232600 | − | 0.972573i | \(-0.574723\pi\) | ||||
−0.232600 | + | 0.972573i | \(0.574723\pi\) | |||||||
\(948\) | 4.04152e120 | 1.11124 | ||||||||
\(949\) | −1.95119e120 | −0.514064 | ||||||||
\(950\) | 5.24692e120 | 1.32464 | ||||||||
\(951\) | 8.39913e118 | 0.0203200 | ||||||||
\(952\) | 2.53075e120 | 0.586750 | ||||||||
\(953\) | −4.61855e120 | −1.02623 | −0.513113 | − | 0.858321i | \(-0.671508\pi\) | ||||
−0.513113 | + | 0.858321i | \(0.671508\pi\) | |||||||
\(954\) | −2.76120e119 | −0.0588015 | ||||||||
\(955\) | 4.96875e120 | 1.01417 | ||||||||
\(956\) | 2.87002e120 | 0.561489 | ||||||||
\(957\) | 1.46278e120 | 0.274313 | ||||||||
\(958\) | −3.59714e120 | −0.646628 | ||||||||
\(959\) | −4.46103e120 | −0.768744 | ||||||||
\(960\) | 4.28144e120 | 0.707303 | ||||||||
\(961\) | −6.20290e120 | −0.982421 | ||||||||
\(962\) | −4.05064e120 | −0.615083 | ||||||||
\(963\) | −1.05720e120 | −0.153920 | ||||||||
\(964\) | −1.25884e121 | −1.75731 | ||||||||
\(965\) | 1.78530e121 | 2.38977 | ||||||||
\(966\) | −2.51322e121 | −3.22594 | ||||||||
\(967\) | 1.32196e121 | 1.62722 | 0.813611 | − | 0.581410i | \(-0.197499\pi\) | ||||
0.813611 | + | 0.581410i | \(0.197499\pi\) | |||||||
\(968\) | 1.37881e121 | 1.62762 | ||||||||
\(969\) | 2.38760e120 | 0.270301 | ||||||||
\(970\) | −1.87743e121 | −2.03849 | ||||||||
\(971\) | −1.00799e121 | −1.04973 | −0.524867 | − | 0.851185i | \(-0.675885\pi\) | ||||
−0.524867 | + | 0.851185i | \(0.675885\pi\) | |||||||
\(972\) | 4.36200e120 | 0.435714 | ||||||||
\(973\) | 3.06484e121 | 2.93655 | ||||||||
\(974\) | −3.70955e121 | −3.40944 | ||||||||
\(975\) | −8.23009e120 | −0.725634 | ||||||||
\(976\) | −5.99339e120 | −0.506938 | ||||||||
\(977\) | 1.80749e120 | 0.146671 | 0.0733357 | − | 0.997307i | \(-0.476636\pi\) | ||||
0.0733357 | + | 0.997307i | \(0.476636\pi\) | |||||||
\(978\) | 2.11987e121 | 1.65038 | ||||||||
\(979\) | 7.83528e120 | 0.585269 | ||||||||
\(980\) | 5.30021e121 | 3.79872 | ||||||||
\(981\) | 2.80814e120 | 0.193118 | ||||||||
\(982\) | 2.91398e121 | 1.92296 | ||||||||
\(983\) | −2.03021e121 | −1.28566 | −0.642828 | − | 0.766011i | \(-0.722239\pi\) | ||||
−0.642828 | + | 0.766011i | \(0.722239\pi\) | |||||||
\(984\) | 2.68547e121 | 1.63199 | ||||||||
\(985\) | −7.68280e120 | −0.448077 | ||||||||
\(986\) | −3.60661e120 | −0.201876 | ||||||||
\(987\) | −5.09688e121 | −2.73817 | ||||||||
\(988\) | −7.13141e121 | −3.67722 | ||||||||
\(989\) | 2.76843e121 | 1.37020 | ||||||||
\(990\) | 2.04917e120 | 0.0973537 | ||||||||
\(991\) | 1.62263e121 | 0.740008 | 0.370004 | − | 0.929030i | \(-0.379356\pi\) | ||||
0.370004 | + | 0.929030i | \(0.379356\pi\) | |||||||
\(992\) | −1.47975e120 | −0.0647837 | ||||||||
\(993\) | −2.91071e121 | −1.22336 | ||||||||
\(994\) | −2.73606e121 | −1.10402 | ||||||||
\(995\) | −4.59810e121 | −1.78133 | ||||||||
\(996\) | 6.21413e120 | 0.231141 | ||||||||
\(997\) | 5.12490e121 | 1.83034 | 0.915170 | − | 0.403068i | \(-0.132056\pi\) | ||||
0.915170 | + | 0.403068i | \(0.132056\pi\) | |||||||
\(998\) | 3.43788e121 | 1.17897 | ||||||||
\(999\) | 7.88101e120 | 0.259525 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.82.a.a.1.1 | ✓ | 6 | |
3.2 | odd | 2 | 9.82.a.b.1.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.82.a.a.1.1 | ✓ | 6 | 1.1 | even | 1 | trivial | |
9.82.a.b.1.6 | 6 | 3.2 | odd | 2 |