Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,40,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, 40, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 40);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 40 \) |
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: | \(9.63395513897\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 175630027x - 142249227846 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{5}\cdot 5\cdot 13 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-812.996\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 241488. | 0.325694 | 0.162847 | − | 0.986651i | \(-0.447932\pi\) | ||||
0.162847 | + | 0.986651i | \(0.447932\pi\) | |||||||
\(3\) | −3.14962e9 | −1.56457 | −0.782283 | − | 0.622923i | \(-0.785945\pi\) | ||||
−0.782283 | + | 0.622923i | \(0.785945\pi\) | |||||||
\(4\) | −4.91439e11 | −0.893923 | ||||||||
\(5\) | 5.36221e13 | 1.25727 | 0.628636 | − | 0.777700i | \(-0.283614\pi\) | ||||
0.628636 | + | 0.777700i | \(0.283614\pi\) | |||||||
\(6\) | −7.60595e14 | −0.509571 | ||||||||
\(7\) | 1.82084e16 | 0.603752 | 0.301876 | − | 0.953347i | \(-0.402387\pi\) | ||||
0.301876 | + | 0.953347i | \(0.402387\pi\) | |||||||
\(8\) | −2.51436e17 | −0.616840 | ||||||||
\(9\) | 5.86757e18 | 1.44787 | ||||||||
\(10\) | 1.29491e19 | 0.409486 | ||||||||
\(11\) | 2.56889e20 | 1.26645 | 0.633225 | − | 0.773968i | \(-0.281731\pi\) | ||||
0.633225 | + | 0.773968i | \(0.281731\pi\) | |||||||
\(12\) | 1.54785e21 | 1.39860 | ||||||||
\(13\) | −2.93238e21 | −0.556319 | −0.278160 | − | 0.960535i | \(-0.589724\pi\) | ||||
−0.278160 | + | 0.960535i | \(0.589724\pi\) | |||||||
\(14\) | 4.39709e21 | 0.196639 | ||||||||
\(15\) | −1.68890e23 | −1.96709 | ||||||||
\(16\) | 2.09453e23 | 0.693022 | ||||||||
\(17\) | −9.89190e22 | −0.100352 | −0.0501759 | − | 0.998740i | \(-0.515978\pi\) | ||||
−0.0501759 | + | 0.998740i | \(0.515978\pi\) | |||||||
\(18\) | 1.41695e24 | 0.471563 | ||||||||
\(19\) | 1.24548e25 | 1.44425 | 0.722125 | − | 0.691763i | \(-0.243166\pi\) | ||||
0.722125 | + | 0.691763i | \(0.243166\pi\) | |||||||
\(20\) | −2.63520e25 | −1.12390 | ||||||||
\(21\) | −5.73494e25 | −0.944611 | ||||||||
\(22\) | 6.20355e25 | 0.412476 | ||||||||
\(23\) | −1.86286e26 | −0.520580 | −0.260290 | − | 0.965531i | \(-0.583818\pi\) | ||||
−0.260290 | + | 0.965531i | \(0.583818\pi\) | |||||||
\(24\) | 7.91928e26 | 0.965087 | ||||||||
\(25\) | 1.05635e27 | 0.580732 | ||||||||
\(26\) | −7.08133e26 | −0.181190 | ||||||||
\(27\) | −5.71661e27 | −0.700721 | ||||||||
\(28\) | −8.94830e27 | −0.539708 | ||||||||
\(29\) | 1.31775e28 | 0.400932 | 0.200466 | − | 0.979701i | \(-0.435754\pi\) | ||||
0.200466 | + | 0.979701i | \(0.435754\pi\) | |||||||
\(30\) | −4.07848e28 | −0.640669 | ||||||||
\(31\) | 1.89026e29 | 1.56663 | 0.783317 | − | 0.621623i | \(-0.213526\pi\) | ||||
0.783317 | + | 0.621623i | \(0.213526\pi\) | |||||||
\(32\) | 1.88809e29 | 0.842553 | ||||||||
\(33\) | −8.09103e29 | −1.98145 | ||||||||
\(34\) | −2.38877e28 | −0.0326840 | ||||||||
\(35\) | 9.76371e29 | 0.759081 | ||||||||
\(36\) | −2.88356e30 | −1.29428 | ||||||||
\(37\) | 3.22957e30 | 0.849593 | 0.424797 | − | 0.905289i | \(-0.360346\pi\) | ||||
0.424797 | + | 0.905289i | \(0.360346\pi\) | |||||||
\(38\) | 3.00769e30 | 0.470384 | ||||||||
\(39\) | 9.23588e30 | 0.870399 | ||||||||
\(40\) | −1.34825e31 | −0.775536 | ||||||||
\(41\) | −2.27011e31 | −0.806793 | −0.403397 | − | 0.915025i | \(-0.632171\pi\) | ||||
−0.403397 | + | 0.915025i | \(0.632171\pi\) | |||||||
\(42\) | −1.38492e31 | −0.307654 | ||||||||
\(43\) | 5.36582e31 | 0.753357 | 0.376679 | − | 0.926344i | \(-0.377066\pi\) | ||||
0.376679 | + | 0.926344i | \(0.377066\pi\) | |||||||
\(44\) | −1.26245e32 | −1.13211 | ||||||||
\(45\) | 3.14632e32 | 1.82036 | ||||||||
\(46\) | −4.49858e31 | −0.169550 | ||||||||
\(47\) | 1.87430e32 | 0.464442 | 0.232221 | − | 0.972663i | \(-0.425401\pi\) | ||||
0.232221 | + | 0.972663i | \(0.425401\pi\) | |||||||
\(48\) | −6.59698e32 | −1.08428 | ||||||||
\(49\) | −5.78000e32 | −0.635483 | ||||||||
\(50\) | 2.55095e32 | 0.189141 | ||||||||
\(51\) | 3.11557e32 | 0.157007 | ||||||||
\(52\) | 1.44109e33 | 0.497307 | ||||||||
\(53\) | −3.22443e32 | −0.0767490 | −0.0383745 | − | 0.999263i | \(-0.512218\pi\) | ||||
−0.0383745 | + | 0.999263i | \(0.512218\pi\) | |||||||
\(54\) | −1.38049e33 | −0.228221 | ||||||||
\(55\) | 1.37749e34 | 1.59227 | ||||||||
\(56\) | −4.57823e33 | −0.372419 | ||||||||
\(57\) | −3.92280e34 | −2.25962 | ||||||||
\(58\) | 3.18220e33 | 0.130581 | ||||||||
\(59\) | 1.01307e34 | 0.297870 | 0.148935 | − | 0.988847i | \(-0.452415\pi\) | ||||
0.148935 | + | 0.988847i | \(0.452415\pi\) | |||||||
\(60\) | 8.29990e34 | 1.75842 | ||||||||
\(61\) | −8.66378e34 | −1.32977 | −0.664884 | − | 0.746947i | \(-0.731519\pi\) | ||||
−0.664884 | + | 0.746947i | \(0.731519\pi\) | |||||||
\(62\) | 4.56473e34 | 0.510244 | ||||||||
\(63\) | 1.06839e35 | 0.874155 | ||||||||
\(64\) | −6.95530e34 | −0.418607 | ||||||||
\(65\) | −1.57240e35 | −0.699445 | ||||||||
\(66\) | −1.95389e35 | −0.645345 | ||||||||
\(67\) | −5.98696e33 | −0.0147485 | −0.00737424 | − | 0.999973i | \(-0.502347\pi\) | ||||
−0.00737424 | + | 0.999973i | \(0.502347\pi\) | |||||||
\(68\) | 4.86127e34 | 0.0897069 | ||||||||
\(69\) | 5.86730e35 | 0.814482 | ||||||||
\(70\) | 2.35782e35 | 0.247228 | ||||||||
\(71\) | 5.02476e35 | 0.399556 | 0.199778 | − | 0.979841i | \(-0.435978\pi\) | ||||
0.199778 | + | 0.979841i | \(0.435978\pi\) | |||||||
\(72\) | −1.47532e36 | −0.893104 | ||||||||
\(73\) | 1.14062e36 | 0.527651 | 0.263826 | − | 0.964570i | \(-0.415016\pi\) | ||||
0.263826 | + | 0.964570i | \(0.415016\pi\) | |||||||
\(74\) | 7.79901e35 | 0.276708 | ||||||||
\(75\) | −3.32709e36 | −0.908594 | ||||||||
\(76\) | −6.12079e36 | −1.29105 | ||||||||
\(77\) | 4.67752e36 | 0.764622 | ||||||||
\(78\) | 2.23035e36 | 0.283484 | ||||||||
\(79\) | 7.78268e36 | 0.771615 | 0.385808 | − | 0.922579i | \(-0.373923\pi\) | ||||
0.385808 | + | 0.922579i | \(0.373923\pi\) | |||||||
\(80\) | 1.12313e37 | 0.871317 | ||||||||
\(81\) | −5.77348e36 | −0.351544 | ||||||||
\(82\) | −5.48205e36 | −0.262768 | ||||||||
\(83\) | −4.09909e37 | −1.55119 | −0.775594 | − | 0.631232i | \(-0.782550\pi\) | ||||
−0.775594 | + | 0.631232i | \(0.782550\pi\) | |||||||
\(84\) | 2.81838e37 | 0.844410 | ||||||||
\(85\) | −5.30425e36 | −0.126170 | ||||||||
\(86\) | 1.29578e37 | 0.245364 | ||||||||
\(87\) | −4.15041e37 | −0.627286 | ||||||||
\(88\) | −6.45911e37 | −0.781197 | ||||||||
\(89\) | 2.04808e38 | 1.98720 | 0.993600 | − | 0.112954i | \(-0.0360312\pi\) | ||||
0.993600 | + | 0.112954i | \(0.0360312\pi\) | |||||||
\(90\) | 7.59797e37 | 0.592883 | ||||||||
\(91\) | −5.33937e37 | −0.335879 | ||||||||
\(92\) | 9.15483e37 | 0.465358 | ||||||||
\(93\) | −5.95359e38 | −2.45110 | ||||||||
\(94\) | 4.52621e37 | 0.151266 | ||||||||
\(95\) | 6.67854e38 | 1.81581 | ||||||||
\(96\) | −5.94676e38 | −1.31823 | ||||||||
\(97\) | −2.29267e38 | −0.415234 | −0.207617 | − | 0.978210i | \(-0.566571\pi\) | ||||
−0.207617 | + | 0.978210i | \(0.566571\pi\) | |||||||
\(98\) | −1.39580e38 | −0.206973 | ||||||||
\(99\) | 1.50731e39 | 1.83365 | ||||||||
\(100\) | −5.19130e38 | −0.519130 | ||||||||
\(101\) | 1.29569e39 | 1.06717 | 0.533587 | − | 0.845745i | \(-0.320844\pi\) | ||||
0.533587 | + | 0.845745i | \(0.320844\pi\) | |||||||
\(102\) | 7.52373e37 | 0.0511364 | ||||||||
\(103\) | −2.69807e39 | −1.51610 | −0.758049 | − | 0.652198i | \(-0.773847\pi\) | ||||
−0.758049 | + | 0.652198i | \(0.773847\pi\) | |||||||
\(104\) | 7.37304e38 | 0.343160 | ||||||||
\(105\) | −3.07520e39 | −1.18763 | ||||||||
\(106\) | −7.78659e37 | −0.0249967 | ||||||||
\(107\) | 1.69252e39 | 0.452430 | 0.226215 | − | 0.974077i | \(-0.427365\pi\) | ||||
0.226215 | + | 0.974077i | \(0.427365\pi\) | |||||||
\(108\) | 2.80937e39 | 0.626391 | ||||||||
\(109\) | 1.65572e39 | 0.308439 | 0.154220 | − | 0.988037i | \(-0.450714\pi\) | ||||
0.154220 | + | 0.988037i | \(0.450714\pi\) | |||||||
\(110\) | 3.32648e39 | 0.518594 | ||||||||
\(111\) | −1.01719e40 | −1.32924 | ||||||||
\(112\) | 3.81379e39 | 0.418414 | ||||||||
\(113\) | 1.65677e40 | 1.52839 | 0.764193 | − | 0.644988i | \(-0.223137\pi\) | ||||
0.764193 | + | 0.644988i | \(0.223137\pi\) | |||||||
\(114\) | −9.47308e39 | −0.735947 | ||||||||
\(115\) | −9.98905e39 | −0.654510 | ||||||||
\(116\) | −6.47593e39 | −0.358403 | ||||||||
\(117\) | −1.72059e40 | −0.805478 | ||||||||
\(118\) | 2.44645e39 | 0.0970145 | ||||||||
\(119\) | −1.80115e39 | −0.0605877 | ||||||||
\(120\) | 4.24649e40 | 1.21338 | ||||||||
\(121\) | 2.48471e40 | 0.603895 | ||||||||
\(122\) | −2.09220e40 | −0.433098 | ||||||||
\(123\) | 7.15000e40 | 1.26228 | ||||||||
\(124\) | −9.28946e40 | −1.40045 | ||||||||
\(125\) | −4.08946e40 | −0.527134 | ||||||||
\(126\) | 2.58003e40 | 0.284707 | ||||||||
\(127\) | 1.00910e41 | 0.954473 | 0.477236 | − | 0.878775i | \(-0.341639\pi\) | ||||
0.477236 | + | 0.878775i | \(0.341639\pi\) | |||||||
\(128\) | −1.20595e41 | −0.978891 | ||||||||
\(129\) | −1.69003e41 | −1.17868 | ||||||||
\(130\) | −3.79716e40 | −0.227805 | ||||||||
\(131\) | 3.37684e40 | 0.174470 | 0.0872348 | − | 0.996188i | \(-0.472197\pi\) | ||||
0.0872348 | + | 0.996188i | \(0.472197\pi\) | |||||||
\(132\) | 3.97625e41 | 1.77126 | ||||||||
\(133\) | 2.26782e41 | 0.871969 | ||||||||
\(134\) | −1.44578e39 | −0.00480350 | ||||||||
\(135\) | −3.06537e41 | −0.880997 | ||||||||
\(136\) | 2.48718e40 | 0.0619011 | ||||||||
\(137\) | −5.27644e41 | −1.13839 | −0.569193 | − | 0.822204i | \(-0.692744\pi\) | ||||
−0.569193 | + | 0.822204i | \(0.692744\pi\) | |||||||
\(138\) | 1.41688e41 | 0.265272 | ||||||||
\(139\) | 6.43985e41 | 1.04734 | 0.523669 | − | 0.851922i | \(-0.324563\pi\) | ||||
0.523669 | + | 0.851922i | \(0.324563\pi\) | |||||||
\(140\) | −4.79827e41 | −0.678560 | ||||||||
\(141\) | −5.90335e41 | −0.726650 | ||||||||
\(142\) | 1.21342e41 | 0.130133 | ||||||||
\(143\) | −7.53295e41 | −0.704551 | ||||||||
\(144\) | 1.22898e42 | 1.00341 | ||||||||
\(145\) | 7.06604e41 | 0.504081 | ||||||||
\(146\) | 2.75447e41 | 0.171853 | ||||||||
\(147\) | 1.82048e42 | 0.994256 | ||||||||
\(148\) | −1.58714e42 | −0.759471 | ||||||||
\(149\) | 1.12323e42 | 0.471341 | 0.235671 | − | 0.971833i | \(-0.424271\pi\) | ||||
0.235671 | + | 0.971833i | \(0.424271\pi\) | |||||||
\(150\) | −8.03452e41 | −0.295924 | ||||||||
\(151\) | −3.59308e42 | −1.16256 | −0.581281 | − | 0.813703i | \(-0.697448\pi\) | ||||
−0.581281 | + | 0.813703i | \(0.697448\pi\) | |||||||
\(152\) | −3.13159e42 | −0.890871 | ||||||||
\(153\) | −5.80414e41 | −0.145296 | ||||||||
\(154\) | 1.12956e42 | 0.249033 | ||||||||
\(155\) | 1.01360e43 | 1.96968 | ||||||||
\(156\) | −4.53887e42 | −0.778070 | ||||||||
\(157\) | −2.11217e42 | −0.319659 | −0.159829 | − | 0.987145i | \(-0.551094\pi\) | ||||
−0.159829 | + | 0.987145i | \(0.551094\pi\) | |||||||
\(158\) | 1.87942e42 | 0.251311 | ||||||||
\(159\) | 1.01557e42 | 0.120079 | ||||||||
\(160\) | 1.01243e43 | 1.05932 | ||||||||
\(161\) | −3.39196e42 | −0.314301 | ||||||||
\(162\) | −1.39422e42 | −0.114496 | ||||||||
\(163\) | −5.72434e42 | −0.416934 | −0.208467 | − | 0.978029i | \(-0.566847\pi\) | ||||
−0.208467 | + | 0.978029i | \(0.566847\pi\) | |||||||
\(164\) | 1.11562e43 | 0.721211 | ||||||||
\(165\) | −4.33859e43 | −2.49122 | ||||||||
\(166\) | −9.89879e42 | −0.505213 | ||||||||
\(167\) | 3.34941e43 | 1.52054 | 0.760268 | − | 0.649610i | \(-0.225068\pi\) | ||||
0.760268 | + | 0.649610i | \(0.225068\pi\) | |||||||
\(168\) | 1.44197e43 | 0.582674 | ||||||||
\(169\) | −1.91849e43 | −0.690509 | ||||||||
\(170\) | −1.28091e42 | −0.0410927 | ||||||||
\(171\) | 7.30795e43 | 2.09108 | ||||||||
\(172\) | −2.63697e43 | −0.673444 | ||||||||
\(173\) | −3.41377e43 | −0.778636 | −0.389318 | − | 0.921103i | \(-0.627289\pi\) | ||||
−0.389318 | + | 0.921103i | \(0.627289\pi\) | |||||||
\(174\) | −1.00227e43 | −0.204303 | ||||||||
\(175\) | 1.92343e43 | 0.350618 | ||||||||
\(176\) | 5.38062e43 | 0.877678 | ||||||||
\(177\) | −3.19080e43 | −0.466037 | ||||||||
\(178\) | 4.94586e43 | 0.647220 | ||||||||
\(179\) | −1.44182e44 | −1.69151 | −0.845757 | − | 0.533569i | \(-0.820851\pi\) | ||||
−0.845757 | + | 0.533569i | \(0.820851\pi\) | |||||||
\(180\) | −1.54622e44 | −1.62727 | ||||||||
\(181\) | 3.88244e43 | 0.366752 | 0.183376 | − | 0.983043i | \(-0.441297\pi\) | ||||
0.183376 | + | 0.983043i | \(0.441297\pi\) | |||||||
\(182\) | −1.28939e43 | −0.109394 | ||||||||
\(183\) | 2.72877e44 | 2.08051 | ||||||||
\(184\) | 4.68390e43 | 0.321114 | ||||||||
\(185\) | 1.73176e44 | 1.06817 | ||||||||
\(186\) | −1.43772e44 | −0.798310 | ||||||||
\(187\) | −2.54112e43 | −0.127091 | ||||||||
\(188\) | −9.21106e43 | −0.415175 | ||||||||
\(189\) | −1.04090e44 | −0.423062 | ||||||||
\(190\) | 1.61279e44 | 0.591400 | ||||||||
\(191\) | −1.72164e44 | −0.569889 | −0.284945 | − | 0.958544i | \(-0.591975\pi\) | ||||
−0.284945 | + | 0.958544i | \(0.591975\pi\) | |||||||
\(192\) | 2.19066e44 | 0.654939 | ||||||||
\(193\) | −6.30991e44 | −1.70473 | −0.852365 | − | 0.522947i | \(-0.824832\pi\) | ||||
−0.852365 | + | 0.522947i | \(0.824832\pi\) | |||||||
\(194\) | −5.53651e43 | −0.135239 | ||||||||
\(195\) | 4.95248e44 | 1.09433 | ||||||||
\(196\) | 2.84052e44 | 0.568073 | ||||||||
\(197\) | −1.00595e45 | −1.82173 | −0.910865 | − | 0.412705i | \(-0.864584\pi\) | ||||
−0.910865 | + | 0.412705i | \(0.864584\pi\) | |||||||
\(198\) | 3.63998e44 | 0.597211 | ||||||||
\(199\) | 1.18780e45 | 1.76648 | 0.883242 | − | 0.468918i | \(-0.155356\pi\) | ||||
0.883242 | + | 0.468918i | \(0.155356\pi\) | |||||||
\(200\) | −2.65603e44 | −0.358219 | ||||||||
\(201\) | 1.88567e43 | 0.0230750 | ||||||||
\(202\) | 3.12894e44 | 0.347572 | ||||||||
\(203\) | 2.39940e44 | 0.242064 | ||||||||
\(204\) | −1.53112e44 | −0.140352 | ||||||||
\(205\) | −1.21728e45 | −1.01436 | ||||||||
\(206\) | −6.51551e44 | −0.493784 | ||||||||
\(207\) | −1.09305e45 | −0.753731 | ||||||||
\(208\) | −6.14195e44 | −0.385542 | ||||||||
\(209\) | 3.19950e45 | 1.82907 | ||||||||
\(210\) | −7.42623e44 | −0.386805 | ||||||||
\(211\) | −3.02479e43 | −0.0143611 | −0.00718054 | − | 0.999974i | \(-0.502286\pi\) | ||||
−0.00718054 | + | 0.999974i | \(0.502286\pi\) | |||||||
\(212\) | 1.58461e44 | 0.0686078 | ||||||||
\(213\) | −1.58261e45 | −0.625132 | ||||||||
\(214\) | 4.08724e44 | 0.147354 | ||||||||
\(215\) | 2.87727e45 | 0.947175 | ||||||||
\(216\) | 1.43736e45 | 0.432233 | ||||||||
\(217\) | 3.44184e45 | 0.945859 | ||||||||
\(218\) | 3.99836e44 | 0.100457 | ||||||||
\(219\) | −3.59254e45 | −0.825545 | ||||||||
\(220\) | −6.76955e45 | −1.42337 | ||||||||
\(221\) | 2.90068e44 | 0.0558277 | ||||||||
\(222\) | −2.45640e45 | −0.432928 | ||||||||
\(223\) | −6.62720e45 | −1.07000 | −0.535002 | − | 0.844851i | \(-0.679689\pi\) | ||||
−0.535002 | + | 0.844851i | \(0.679689\pi\) | |||||||
\(224\) | 3.43790e45 | 0.508694 | ||||||||
\(225\) | 6.19818e45 | 0.840824 | ||||||||
\(226\) | 4.00090e45 | 0.497787 | ||||||||
\(227\) | −5.09742e45 | −0.581897 | −0.290948 | − | 0.956739i | \(-0.593971\pi\) | ||||
−0.290948 | + | 0.956739i | \(0.593971\pi\) | |||||||
\(228\) | 1.92782e46 | 2.01993 | ||||||||
\(229\) | −5.09087e45 | −0.489778 | −0.244889 | − | 0.969551i | \(-0.578752\pi\) | ||||
−0.244889 | + | 0.969551i | \(0.578752\pi\) | |||||||
\(230\) | −2.41223e45 | −0.213170 | ||||||||
\(231\) | −1.47324e46 | −1.19630 | ||||||||
\(232\) | −3.31329e45 | −0.247311 | ||||||||
\(233\) | 2.36093e46 | 1.62048 | 0.810239 | − | 0.586100i | \(-0.199337\pi\) | ||||
0.810239 | + | 0.586100i | \(0.199337\pi\) | |||||||
\(234\) | −4.15502e45 | −0.262340 | ||||||||
\(235\) | 1.00504e46 | 0.583930 | ||||||||
\(236\) | −4.97864e45 | −0.266273 | ||||||||
\(237\) | −2.45125e46 | −1.20724 | ||||||||
\(238\) | −4.34956e44 | −0.0197331 | ||||||||
\(239\) | −1.68674e46 | −0.705162 | −0.352581 | − | 0.935781i | \(-0.614696\pi\) | ||||
−0.352581 | + | 0.935781i | \(0.614696\pi\) | |||||||
\(240\) | −3.53744e46 | −1.36323 | ||||||||
\(241\) | 3.12678e46 | 1.11113 | 0.555565 | − | 0.831473i | \(-0.312502\pi\) | ||||
0.555565 | + | 0.831473i | \(0.312502\pi\) | |||||||
\(242\) | 6.00028e45 | 0.196685 | ||||||||
\(243\) | 4.13512e46 | 1.25074 | ||||||||
\(244\) | 4.25773e46 | 1.18871 | ||||||||
\(245\) | −3.09936e46 | −0.798975 | ||||||||
\(246\) | 1.72664e46 | 0.411118 | ||||||||
\(247\) | −3.65222e46 | −0.803464 | ||||||||
\(248\) | −4.75278e46 | −0.966362 | ||||||||
\(249\) | 1.29106e47 | 2.42694 | ||||||||
\(250\) | −9.87555e45 | −0.171684 | ||||||||
\(251\) | −6.69718e46 | −1.07710 | −0.538548 | − | 0.842595i | \(-0.681027\pi\) | ||||
−0.538548 | + | 0.842595i | \(0.681027\pi\) | |||||||
\(252\) | −5.25048e46 | −0.781427 | ||||||||
\(253\) | −4.78548e46 | −0.659288 | ||||||||
\(254\) | 2.43686e46 | 0.310866 | ||||||||
\(255\) | 1.67064e46 | 0.197401 | ||||||||
\(256\) | 9.11500e45 | 0.0997878 | ||||||||
\(257\) | −3.87410e46 | −0.393074 | −0.196537 | − | 0.980496i | \(-0.562970\pi\) | ||||
−0.196537 | + | 0.980496i | \(0.562970\pi\) | |||||||
\(258\) | −4.08122e46 | −0.383889 | ||||||||
\(259\) | 5.88051e46 | 0.512944 | ||||||||
\(260\) | 7.72741e46 | 0.625250 | ||||||||
\(261\) | 7.73197e46 | 0.580498 | ||||||||
\(262\) | 8.15465e45 | 0.0568238 | ||||||||
\(263\) | −5.89846e45 | −0.0381594 | −0.0190797 | − | 0.999818i | \(-0.506074\pi\) | ||||
−0.0190797 | + | 0.999818i | \(0.506074\pi\) | |||||||
\(264\) | 2.03438e47 | 1.22223 | ||||||||
\(265\) | −1.72901e46 | −0.0964944 | ||||||||
\(266\) | 5.47650e46 | 0.283995 | ||||||||
\(267\) | −6.45068e47 | −3.10911 | ||||||||
\(268\) | 2.94223e45 | 0.0131840 | ||||||||
\(269\) | 8.99725e46 | 0.374921 | 0.187461 | − | 0.982272i | \(-0.439974\pi\) | ||||
0.187461 | + | 0.982272i | \(0.439974\pi\) | |||||||
\(270\) | −7.40249e46 | −0.286936 | ||||||||
\(271\) | 1.93454e47 | 0.697711 | 0.348855 | − | 0.937177i | \(-0.386570\pi\) | ||||
0.348855 | + | 0.937177i | \(0.386570\pi\) | |||||||
\(272\) | −2.07189e46 | −0.0695461 | ||||||||
\(273\) | 1.68170e47 | 0.525505 | ||||||||
\(274\) | −1.27420e47 | −0.370766 | ||||||||
\(275\) | 2.71363e47 | 0.735468 | ||||||||
\(276\) | −2.88342e47 | −0.728084 | ||||||||
\(277\) | −5.39283e47 | −1.26900 | −0.634500 | − | 0.772923i | \(-0.718794\pi\) | ||||
−0.634500 | + | 0.772923i | \(0.718794\pi\) | |||||||
\(278\) | 1.55514e47 | 0.341112 | ||||||||
\(279\) | 1.10912e48 | 2.26828 | ||||||||
\(280\) | −2.45495e47 | −0.468231 | ||||||||
\(281\) | 3.42772e47 | 0.609862 | 0.304931 | − | 0.952374i | \(-0.401367\pi\) | ||||
0.304931 | + | 0.952374i | \(0.401367\pi\) | |||||||
\(282\) | −1.42559e47 | −0.236666 | ||||||||
\(283\) | 8.61731e47 | 1.33517 | 0.667584 | − | 0.744534i | \(-0.267328\pi\) | ||||
0.667584 | + | 0.744534i | \(0.267328\pi\) | |||||||
\(284\) | −2.46937e47 | −0.357172 | ||||||||
\(285\) | −2.10349e48 | −2.84096 | ||||||||
\(286\) | −1.81911e47 | −0.229468 | ||||||||
\(287\) | −4.13350e47 | −0.487104 | ||||||||
\(288\) | 1.10785e48 | 1.21991 | ||||||||
\(289\) | −9.61861e47 | −0.989929 | ||||||||
\(290\) | 1.70636e47 | 0.164176 | ||||||||
\(291\) | 7.22104e47 | 0.649661 | ||||||||
\(292\) | −5.60548e47 | −0.471679 | ||||||||
\(293\) | 1.93492e48 | 1.52316 | 0.761578 | − | 0.648073i | \(-0.224425\pi\) | ||||
0.761578 | + | 0.648073i | \(0.224425\pi\) | |||||||
\(294\) | 4.39624e47 | 0.323823 | ||||||||
\(295\) | 5.43232e47 | 0.374503 | ||||||||
\(296\) | −8.12030e47 | −0.524063 | ||||||||
\(297\) | −1.46853e48 | −0.887428 | ||||||||
\(298\) | 2.71246e47 | 0.153513 | ||||||||
\(299\) | 5.46260e47 | 0.289609 | ||||||||
\(300\) | 1.63506e48 | 0.812213 | ||||||||
\(301\) | 9.77027e47 | 0.454841 | ||||||||
\(302\) | −8.67684e47 | −0.378640 | ||||||||
\(303\) | −4.08094e48 | −1.66966 | ||||||||
\(304\) | 2.60870e48 | 1.00090 | ||||||||
\(305\) | −4.64571e48 | −1.67188 | ||||||||
\(306\) | −1.40163e47 | −0.0473222 | ||||||||
\(307\) | −1.51569e48 | −0.480188 | −0.240094 | − | 0.970750i | \(-0.577178\pi\) | ||||
−0.240094 | + | 0.970750i | \(0.577178\pi\) | |||||||
\(308\) | −2.29872e48 | −0.683514 | ||||||||
\(309\) | 8.49790e48 | 2.37204 | ||||||||
\(310\) | 2.44771e48 | 0.641515 | ||||||||
\(311\) | 1.19146e48 | 0.293260 | 0.146630 | − | 0.989191i | \(-0.453157\pi\) | ||||
0.146630 | + | 0.989191i | \(0.453157\pi\) | |||||||
\(312\) | −2.32223e48 | −0.536897 | ||||||||
\(313\) | −4.44520e47 | −0.0965555 | −0.0482778 | − | 0.998834i | \(-0.515373\pi\) | ||||
−0.0482778 | + | 0.998834i | \(0.515373\pi\) | |||||||
\(314\) | −5.10064e47 | −0.104111 | ||||||||
\(315\) | 5.72893e48 | 1.09905 | ||||||||
\(316\) | −3.82472e48 | −0.689765 | ||||||||
\(317\) | −1.03382e48 | −0.175303 | −0.0876516 | − | 0.996151i | \(-0.527936\pi\) | ||||
−0.0876516 | + | 0.996151i | \(0.527936\pi\) | |||||||
\(318\) | 2.45248e47 | 0.0391091 | ||||||||
\(319\) | 3.38515e48 | 0.507761 | ||||||||
\(320\) | −3.72958e48 | −0.526303 | ||||||||
\(321\) | −5.33082e48 | −0.707857 | ||||||||
\(322\) | −8.19117e47 | −0.102366 | ||||||||
\(323\) | −1.23202e48 | −0.144933 | ||||||||
\(324\) | 2.83732e48 | 0.314253 | ||||||||
\(325\) | −3.09760e48 | −0.323073 | ||||||||
\(326\) | −1.38236e48 | −0.135793 | ||||||||
\(327\) | −5.21489e48 | −0.482574 | ||||||||
\(328\) | 5.70788e48 | 0.497663 | ||||||||
\(329\) | 3.41280e48 | 0.280408 | ||||||||
\(330\) | −1.04772e49 | −0.811375 | ||||||||
\(331\) | 6.53650e48 | 0.477199 | 0.238599 | − | 0.971118i | \(-0.423312\pi\) | ||||
0.238599 | + | 0.971118i | \(0.423312\pi\) | |||||||
\(332\) | 2.01445e49 | 1.38664 | ||||||||
\(333\) | 1.89497e49 | 1.23010 | ||||||||
\(334\) | 8.08841e48 | 0.495230 | ||||||||
\(335\) | −3.21033e47 | −0.0185429 | ||||||||
\(336\) | −1.20120e49 | −0.654636 | ||||||||
\(337\) | −2.75713e49 | −1.41799 | −0.708996 | − | 0.705213i | \(-0.750852\pi\) | ||||
−0.708996 | + | 0.705213i | \(0.750852\pi\) | |||||||
\(338\) | −4.63292e48 | −0.224895 | ||||||||
\(339\) | −5.21821e49 | −2.39126 | ||||||||
\(340\) | 2.60672e48 | 0.112786 | ||||||||
\(341\) | 4.85586e49 | 1.98406 | ||||||||
\(342\) | 1.76478e49 | 0.681054 | ||||||||
\(343\) | −2.70857e49 | −0.987427 | ||||||||
\(344\) | −1.34916e49 | −0.464701 | ||||||||
\(345\) | 3.14617e49 | 1.02402 | ||||||||
\(346\) | −8.24383e48 | −0.253597 | ||||||||
\(347\) | 1.59040e48 | 0.0462468 | 0.0231234 | − | 0.999733i | \(-0.492639\pi\) | ||||
0.0231234 | + | 0.999733i | \(0.492639\pi\) | |||||||
\(348\) | 2.03967e49 | 0.560745 | ||||||||
\(349\) | −4.30840e49 | −1.12001 | −0.560003 | − | 0.828491i | \(-0.689200\pi\) | ||||
−0.560003 | + | 0.828491i | \(0.689200\pi\) | |||||||
\(350\) | 4.64485e48 | 0.114194 | ||||||||
\(351\) | 1.67633e49 | 0.389825 | ||||||||
\(352\) | 4.85029e49 | 1.06705 | ||||||||
\(353\) | 4.31576e49 | 0.898361 | 0.449181 | − | 0.893441i | \(-0.351716\pi\) | ||||
0.449181 | + | 0.893441i | \(0.351716\pi\) | |||||||
\(354\) | −7.70539e48 | −0.151786 | ||||||||
\(355\) | 2.69439e49 | 0.502350 | ||||||||
\(356\) | −1.00651e50 | −1.77640 | ||||||||
\(357\) | 5.67295e48 | 0.0947935 | ||||||||
\(358\) | −3.48181e49 | −0.550916 | ||||||||
\(359\) | −2.80608e49 | −0.420492 | −0.210246 | − | 0.977648i | \(-0.567427\pi\) | ||||
−0.210246 | + | 0.977648i | \(0.567427\pi\) | |||||||
\(360\) | −7.91097e49 | −1.12287 | ||||||||
\(361\) | 8.07537e49 | 1.08586 | ||||||||
\(362\) | 9.37562e48 | 0.119449 | ||||||||
\(363\) | −7.82591e49 | −0.944834 | ||||||||
\(364\) | 2.62398e49 | 0.300250 | ||||||||
\(365\) | 6.11627e49 | 0.663401 | ||||||||
\(366\) | 6.58963e49 | 0.677610 | ||||||||
\(367\) | 8.06624e49 | 0.786472 | 0.393236 | − | 0.919438i | \(-0.371356\pi\) | ||||
0.393236 | + | 0.919438i | \(0.371356\pi\) | |||||||
\(368\) | −3.90181e49 | −0.360773 | ||||||||
\(369\) | −1.33200e50 | −1.16813 | ||||||||
\(370\) | 4.18200e49 | 0.347897 | ||||||||
\(371\) | −5.87115e48 | −0.0463374 | ||||||||
\(372\) | 2.92583e50 | 2.19110 | ||||||||
\(373\) | −2.09254e50 | −1.48714 | −0.743571 | − | 0.668657i | \(-0.766870\pi\) | ||||
−0.743571 | + | 0.668657i | \(0.766870\pi\) | |||||||
\(374\) | −6.13649e48 | −0.0413927 | ||||||||
\(375\) | 1.28803e50 | 0.824736 | ||||||||
\(376\) | −4.71267e49 | −0.286486 | ||||||||
\(377\) | −3.86413e49 | −0.223046 | ||||||||
\(378\) | −2.51365e49 | −0.137789 | ||||||||
\(379\) | 3.48223e49 | 0.181298 | 0.0906489 | − | 0.995883i | \(-0.471106\pi\) | ||||
0.0906489 | + | 0.995883i | \(0.471106\pi\) | |||||||
\(380\) | −3.28210e50 | −1.62320 | ||||||||
\(381\) | −3.17830e50 | −1.49334 | ||||||||
\(382\) | −4.15754e49 | −0.185610 | ||||||||
\(383\) | 6.27597e49 | 0.266259 | 0.133130 | − | 0.991099i | \(-0.457497\pi\) | ||||
0.133130 | + | 0.991099i | \(0.457497\pi\) | |||||||
\(384\) | 3.79828e50 | 1.53154 | ||||||||
\(385\) | 2.50819e50 | 0.961338 | ||||||||
\(386\) | −1.52377e50 | −0.555221 | ||||||||
\(387\) | 3.14843e50 | 1.09076 | ||||||||
\(388\) | 1.12671e50 | 0.371187 | ||||||||
\(389\) | −2.37857e50 | −0.745245 | −0.372623 | − | 0.927983i | \(-0.621541\pi\) | ||||
−0.372623 | + | 0.927983i | \(0.621541\pi\) | |||||||
\(390\) | 1.19596e50 | 0.356416 | ||||||||
\(391\) | 1.84272e49 | 0.0522412 | ||||||||
\(392\) | 1.45330e50 | 0.391991 | ||||||||
\(393\) | −1.06358e50 | −0.272969 | ||||||||
\(394\) | −2.42924e50 | −0.593327 | ||||||||
\(395\) | 4.17324e50 | 0.970130 | ||||||||
\(396\) | −7.40753e50 | −1.63915 | ||||||||
\(397\) | −1.69815e50 | −0.357734 | −0.178867 | − | 0.983873i | \(-0.557243\pi\) | ||||
−0.178867 | + | 0.983873i | \(0.557243\pi\) | |||||||
\(398\) | 2.86840e50 | 0.575334 | ||||||||
\(399\) | −7.14277e50 | −1.36425 | ||||||||
\(400\) | 2.21255e50 | 0.402460 | ||||||||
\(401\) | 1.06858e51 | 1.85136 | 0.925681 | − | 0.378306i | \(-0.123493\pi\) | ||||
0.925681 | + | 0.378306i | \(0.123493\pi\) | |||||||
\(402\) | 4.55365e48 | 0.00751539 | ||||||||
\(403\) | −5.54294e50 | −0.871549 | ||||||||
\(404\) | −6.36754e50 | −0.953971 | ||||||||
\(405\) | −3.09586e50 | −0.441986 | ||||||||
\(406\) | 5.79426e49 | 0.0788388 | ||||||||
\(407\) | 8.29640e50 | 1.07597 | ||||||||
\(408\) | −7.83367e49 | −0.0968483 | ||||||||
\(409\) | 1.58478e50 | 0.186794 | 0.0933972 | − | 0.995629i | \(-0.470227\pi\) | ||||
0.0933972 | + | 0.995629i | \(0.470227\pi\) | |||||||
\(410\) | −2.93959e50 | −0.330371 | ||||||||
\(411\) | 1.66188e51 | 1.78108 | ||||||||
\(412\) | 1.32594e51 | 1.35528 | ||||||||
\(413\) | 1.84464e50 | 0.179840 | ||||||||
\(414\) | −2.63957e50 | −0.245486 | ||||||||
\(415\) | −2.19802e51 | −1.95026 | ||||||||
\(416\) | −5.53658e50 | −0.468729 | ||||||||
\(417\) | −2.02831e51 | −1.63863 | ||||||||
\(418\) | 7.72641e50 | 0.595717 | ||||||||
\(419\) | −2.13326e50 | −0.156989 | −0.0784947 | − | 0.996915i | \(-0.525011\pi\) | ||||
−0.0784947 | + | 0.996915i | \(0.525011\pi\) | |||||||
\(420\) | 1.51128e51 | 1.06165 | ||||||||
\(421\) | −1.07542e51 | −0.721232 | −0.360616 | − | 0.932714i | \(-0.617434\pi\) | ||||
−0.360616 | + | 0.932714i | \(0.617434\pi\) | |||||||
\(422\) | −7.30450e48 | −0.00467732 | ||||||||
\(423\) | 1.09976e51 | 0.672451 | ||||||||
\(424\) | 8.10737e49 | 0.0473419 | ||||||||
\(425\) | −1.04493e50 | −0.0582776 | ||||||||
\(426\) | −3.82181e50 | −0.203602 | ||||||||
\(427\) | −1.57753e51 | −0.802851 | ||||||||
\(428\) | −8.31774e50 | −0.404438 | ||||||||
\(429\) | 2.37259e51 | 1.10232 | ||||||||
\(430\) | 6.94825e50 | 0.308489 | ||||||||
\(431\) | 3.49435e51 | 1.48272 | 0.741360 | − | 0.671108i | \(-0.234181\pi\) | ||||
0.741360 | + | 0.671108i | \(0.234181\pi\) | |||||||
\(432\) | −1.19736e51 | −0.485615 | ||||||||
\(433\) | 2.34196e51 | 0.907956 | 0.453978 | − | 0.891013i | \(-0.350005\pi\) | ||||
0.453978 | + | 0.891013i | \(0.350005\pi\) | |||||||
\(434\) | 8.31163e50 | 0.308061 | ||||||||
\(435\) | −2.22554e51 | −0.788668 | ||||||||
\(436\) | −8.13685e50 | −0.275721 | ||||||||
\(437\) | −2.32016e51 | −0.751847 | ||||||||
\(438\) | −8.67553e50 | −0.268875 | ||||||||
\(439\) | 1.54147e51 | 0.456960 | 0.228480 | − | 0.973549i | \(-0.426624\pi\) | ||||
0.228480 | + | 0.973549i | \(0.426624\pi\) | |||||||
\(440\) | −3.46351e51 | −0.982177 | ||||||||
\(441\) | −3.39145e51 | −0.920096 | ||||||||
\(442\) | 7.00477e49 | 0.0181828 | ||||||||
\(443\) | −6.02650e51 | −1.49690 | −0.748449 | − | 0.663192i | \(-0.769201\pi\) | ||||
−0.748449 | + | 0.663192i | \(0.769201\pi\) | |||||||
\(444\) | 4.99889e51 | 1.18824 | ||||||||
\(445\) | 1.09822e52 | 2.49845 | ||||||||
\(446\) | −1.60039e51 | −0.348494 | ||||||||
\(447\) | −3.53774e51 | −0.737445 | ||||||||
\(448\) | −1.26645e51 | −0.252735 | ||||||||
\(449\) | 8.31046e51 | 1.58789 | 0.793947 | − | 0.607987i | \(-0.208023\pi\) | ||||
0.793947 | + | 0.607987i | \(0.208023\pi\) | |||||||
\(450\) | 1.49678e51 | 0.273852 | ||||||||
\(451\) | −5.83167e51 | −1.02176 | ||||||||
\(452\) | −8.14203e51 | −1.36626 | ||||||||
\(453\) | 1.13168e52 | 1.81891 | ||||||||
\(454\) | −1.23096e51 | −0.189520 | ||||||||
\(455\) | −2.86309e51 | −0.422291 | ||||||||
\(456\) | 9.86332e51 | 1.39383 | ||||||||
\(457\) | −7.27855e51 | −0.985551 | −0.492776 | − | 0.870156i | \(-0.664018\pi\) | ||||
−0.492776 | + | 0.870156i | \(0.664018\pi\) | |||||||
\(458\) | −1.22938e51 | −0.159518 | ||||||||
\(459\) | 5.65481e50 | 0.0703187 | ||||||||
\(460\) | 4.90901e51 | 0.585082 | ||||||||
\(461\) | −1.09767e51 | −0.125402 | −0.0627008 | − | 0.998032i | \(-0.519971\pi\) | ||||
−0.0627008 | + | 0.998032i | \(0.519971\pi\) | |||||||
\(462\) | −3.55770e51 | −0.389629 | ||||||||
\(463\) | −8.46883e51 | −0.889189 | −0.444595 | − | 0.895732i | \(-0.646652\pi\) | ||||
−0.444595 | + | 0.895732i | \(0.646652\pi\) | |||||||
\(464\) | 2.76006e51 | 0.277855 | ||||||||
\(465\) | −3.19244e52 | −3.08170 | ||||||||
\(466\) | 5.70136e51 | 0.527780 | ||||||||
\(467\) | 1.69800e52 | 1.50751 | 0.753753 | − | 0.657158i | \(-0.228242\pi\) | ||||
0.753753 | + | 0.657158i | \(0.228242\pi\) | |||||||
\(468\) | 8.45567e51 | 0.720035 | ||||||||
\(469\) | −1.09013e50 | −0.00890443 | ||||||||
\(470\) | 2.42705e51 | 0.190183 | ||||||||
\(471\) | 6.65255e51 | 0.500127 | ||||||||
\(472\) | −2.54723e51 | −0.183738 | ||||||||
\(473\) | 1.37842e52 | 0.954089 | ||||||||
\(474\) | −5.91947e51 | −0.393192 | ||||||||
\(475\) | 1.31566e52 | 0.838722 | ||||||||
\(476\) | 8.85157e50 | 0.0541608 | ||||||||
\(477\) | −1.89195e51 | −0.111123 | ||||||||
\(478\) | −4.07327e51 | −0.229667 | ||||||||
\(479\) | 2.99013e51 | 0.161863 | 0.0809314 | − | 0.996720i | \(-0.474211\pi\) | ||||
0.0809314 | + | 0.996720i | \(0.474211\pi\) | |||||||
\(480\) | −3.18878e52 | −1.65737 | ||||||||
\(481\) | −9.47031e51 | −0.472645 | ||||||||
\(482\) | 7.55078e51 | 0.361889 | ||||||||
\(483\) | 1.06834e52 | 0.491745 | ||||||||
\(484\) | −1.22109e52 | −0.539836 | ||||||||
\(485\) | −1.22938e52 | −0.522061 | ||||||||
\(486\) | 9.98580e51 | 0.407357 | ||||||||
\(487\) | −1.46011e52 | −0.572232 | −0.286116 | − | 0.958195i | \(-0.592364\pi\) | ||||
−0.286116 | + | 0.958195i | \(0.592364\pi\) | |||||||
\(488\) | 2.17839e52 | 0.820254 | ||||||||
\(489\) | 1.80295e52 | 0.652321 | ||||||||
\(490\) | −7.48457e51 | −0.260222 | ||||||||
\(491\) | −1.53063e52 | −0.511426 | −0.255713 | − | 0.966753i | \(-0.582310\pi\) | ||||
−0.255713 | + | 0.966753i | \(0.582310\pi\) | |||||||
\(492\) | −3.51379e52 | −1.12838 | ||||||||
\(493\) | −1.30350e51 | −0.0402343 | ||||||||
\(494\) | −8.81966e51 | −0.261684 | ||||||||
\(495\) | 8.08254e52 | 2.30540 | ||||||||
\(496\) | 3.95920e52 | 1.08571 | ||||||||
\(497\) | 9.14926e51 | 0.241233 | ||||||||
\(498\) | 3.11775e52 | 0.790440 | ||||||||
\(499\) | −4.30786e51 | −0.105027 | −0.0525135 | − | 0.998620i | \(-0.516723\pi\) | ||||
−0.0525135 | + | 0.998620i | \(0.516723\pi\) | |||||||
\(500\) | 2.00972e52 | 0.471217 | ||||||||
\(501\) | −1.05494e53 | −2.37898 | ||||||||
\(502\) | −1.61729e52 | −0.350804 | ||||||||
\(503\) | −7.62462e52 | −1.59090 | −0.795449 | − | 0.606020i | \(-0.792765\pi\) | ||||
−0.795449 | + | 0.606020i | \(0.792765\pi\) | |||||||
\(504\) | −2.68631e52 | −0.539214 | ||||||||
\(505\) | 6.94778e52 | 1.34173 | ||||||||
\(506\) | −1.15563e52 | −0.214726 | ||||||||
\(507\) | 6.04253e52 | 1.08035 | ||||||||
\(508\) | −4.95914e52 | −0.853225 | ||||||||
\(509\) | 4.36698e51 | 0.0723078 | 0.0361539 | − | 0.999346i | \(-0.488489\pi\) | ||||
0.0361539 | + | 0.999346i | \(0.488489\pi\) | |||||||
\(510\) | 4.03439e51 | 0.0642923 | ||||||||
\(511\) | 2.07689e52 | 0.318571 | ||||||||
\(512\) | 6.84989e52 | 1.01139 | ||||||||
\(513\) | −7.11993e52 | −1.01202 | ||||||||
\(514\) | −9.35547e51 | −0.128022 | ||||||||
\(515\) | −1.44676e53 | −1.90615 | ||||||||
\(516\) | 8.30548e52 | 1.05365 | ||||||||
\(517\) | 4.81487e52 | 0.588192 | ||||||||
\(518\) | 1.42007e52 | 0.167063 | ||||||||
\(519\) | 1.07521e53 | 1.21823 | ||||||||
\(520\) | 3.95358e52 | 0.431445 | ||||||||
\(521\) | −2.72686e51 | −0.0286634 | −0.0143317 | − | 0.999897i | \(-0.504562\pi\) | ||||
−0.0143317 | + | 0.999897i | \(0.504562\pi\) | |||||||
\(522\) | 1.86718e52 | 0.189065 | ||||||||
\(523\) | 3.45861e52 | 0.337379 | 0.168690 | − | 0.985669i | \(-0.446046\pi\) | ||||
0.168690 | + | 0.985669i | \(0.446046\pi\) | |||||||
\(524\) | −1.65951e52 | −0.155962 | ||||||||
\(525\) | −6.05808e52 | −0.548566 | ||||||||
\(526\) | −1.42441e51 | −0.0124283 | ||||||||
\(527\) | −1.86982e52 | −0.157215 | ||||||||
\(528\) | −1.69469e53 | −1.37319 | ||||||||
\(529\) | −9.33493e52 | −0.728997 | ||||||||
\(530\) | −4.17534e51 | −0.0314277 | ||||||||
\(531\) | 5.94428e52 | 0.431277 | ||||||||
\(532\) | −1.11449e53 | −0.779473 | ||||||||
\(533\) | 6.65682e52 | 0.448835 | ||||||||
\(534\) | −1.55776e53 | −1.01262 | ||||||||
\(535\) | 9.07568e52 | 0.568827 | ||||||||
\(536\) | 1.50534e51 | 0.00909746 | ||||||||
\(537\) | 4.54117e53 | 2.64649 | ||||||||
\(538\) | 2.17273e52 | 0.122110 | ||||||||
\(539\) | −1.48482e53 | −0.804807 | ||||||||
\(540\) | 1.50644e53 | 0.787544 | ||||||||
\(541\) | −1.10485e53 | −0.557129 | −0.278565 | − | 0.960417i | \(-0.589859\pi\) | ||||
−0.278565 | + | 0.960417i | \(0.589859\pi\) | |||||||
\(542\) | 4.67167e52 | 0.227240 | ||||||||
\(543\) | −1.22282e53 | −0.573809 | ||||||||
\(544\) | −1.86768e52 | −0.0845518 | ||||||||
\(545\) | 8.87832e52 | 0.387792 | ||||||||
\(546\) | 4.06110e52 | 0.171154 | ||||||||
\(547\) | −1.77885e52 | −0.0723413 | −0.0361706 | − | 0.999346i | \(-0.511516\pi\) | ||||
−0.0361706 | + | 0.999346i | \(0.511516\pi\) | |||||||
\(548\) | 2.59305e53 | 1.01763 | ||||||||
\(549\) | −5.08354e53 | −1.92533 | ||||||||
\(550\) | 6.55310e52 | 0.239538 | ||||||||
\(551\) | 1.64123e53 | 0.579046 | ||||||||
\(552\) | −1.47525e53 | −0.502405 | ||||||||
\(553\) | 1.41710e53 | 0.465865 | ||||||||
\(554\) | −1.30230e53 | −0.413306 | ||||||||
\(555\) | −5.45440e53 | −1.67122 | ||||||||
\(556\) | −3.16480e53 | −0.936240 | ||||||||
\(557\) | 3.89141e53 | 1.11155 | 0.555777 | − | 0.831332i | \(-0.312421\pi\) | ||||
0.555777 | + | 0.831332i | \(0.312421\pi\) | |||||||
\(558\) | 2.67839e53 | 0.738766 | ||||||||
\(559\) | −1.57346e53 | −0.419107 | ||||||||
\(560\) | 2.04504e53 | 0.526060 | ||||||||
\(561\) | 8.00356e52 | 0.198842 | ||||||||
\(562\) | 8.27752e52 | 0.198629 | ||||||||
\(563\) | −4.03186e53 | −0.934528 | −0.467264 | − | 0.884118i | \(-0.654760\pi\) | ||||
−0.467264 | + | 0.884118i | \(0.654760\pi\) | |||||||
\(564\) | 2.90114e53 | 0.649570 | ||||||||
\(565\) | 8.88397e53 | 1.92160 | ||||||||
\(566\) | 2.08097e53 | 0.434857 | ||||||||
\(567\) | −1.05126e53 | −0.212246 | ||||||||
\(568\) | −1.26341e53 | −0.246462 | ||||||||
\(569\) | −6.36680e52 | −0.120014 | −0.0600070 | − | 0.998198i | \(-0.519112\pi\) | ||||
−0.0600070 | + | 0.998198i | \(0.519112\pi\) | |||||||
\(570\) | −5.07967e53 | −0.925285 | ||||||||
\(571\) | −6.36424e53 | −1.12032 | −0.560160 | − | 0.828384i | \(-0.689260\pi\) | ||||
−0.560160 | + | 0.828384i | \(0.689260\pi\) | |||||||
\(572\) | 3.70199e53 | 0.629814 | ||||||||
\(573\) | 5.42250e53 | 0.891630 | ||||||||
\(574\) | −9.98190e52 | −0.158647 | ||||||||
\(575\) | −1.96782e53 | −0.302317 | ||||||||
\(576\) | −4.08107e53 | −0.606088 | ||||||||
\(577\) | −9.29606e53 | −1.33466 | −0.667330 | − | 0.744762i | \(-0.732563\pi\) | ||||
−0.667330 | + | 0.744762i | \(0.732563\pi\) | |||||||
\(578\) | −2.32278e53 | −0.322414 | ||||||||
\(579\) | 1.98738e54 | 2.66716 | ||||||||
\(580\) | −3.47253e53 | −0.450610 | ||||||||
\(581\) | −7.46376e53 | −0.936533 | ||||||||
\(582\) | 1.74379e53 | 0.211591 | ||||||||
\(583\) | −8.28319e52 | −0.0971988 | ||||||||
\(584\) | −2.86794e53 | −0.325476 | ||||||||
\(585\) | −9.22618e53 | −1.01270 | ||||||||
\(586\) | 4.67260e53 | 0.496083 | ||||||||
\(587\) | 6.03454e52 | 0.0619728 | 0.0309864 | − | 0.999520i | \(-0.490135\pi\) | ||||
0.0309864 | + | 0.999520i | \(0.490135\pi\) | |||||||
\(588\) | −8.94656e53 | −0.888788 | ||||||||
\(589\) | 2.35428e54 | 2.26261 | ||||||||
\(590\) | 1.31184e53 | 0.121974 | ||||||||
\(591\) | 3.16835e54 | 2.85022 | ||||||||
\(592\) | 6.76443e53 | 0.588787 | ||||||||
\(593\) | −1.41264e54 | −1.18977 | −0.594886 | − | 0.803810i | \(-0.702803\pi\) | ||||
−0.594886 | + | 0.803810i | \(0.702803\pi\) | |||||||
\(594\) | −3.54633e53 | −0.289030 | ||||||||
\(595\) | −9.65816e52 | −0.0761752 | ||||||||
\(596\) | −5.51998e53 | −0.421343 | ||||||||
\(597\) | −3.74113e54 | −2.76378 | ||||||||
\(598\) | 1.31915e53 | 0.0943239 | ||||||||
\(599\) | −1.17608e54 | −0.813979 | −0.406990 | − | 0.913433i | \(-0.633421\pi\) | ||||
−0.406990 | + | 0.913433i | \(0.633421\pi\) | |||||||
\(600\) | 8.36550e53 | 0.560457 | ||||||||
\(601\) | −1.78335e53 | −0.115660 | −0.0578300 | − | 0.998326i | \(-0.518418\pi\) | ||||
−0.0578300 | + | 0.998326i | \(0.518418\pi\) | |||||||
\(602\) | 2.35940e53 | 0.148139 | ||||||||
\(603\) | −3.51289e52 | −0.0213539 | ||||||||
\(604\) | 1.76578e54 | 1.03924 | ||||||||
\(605\) | 1.33236e54 | 0.759260 | ||||||||
\(606\) | −9.85497e53 | −0.543800 | ||||||||
\(607\) | −1.82763e54 | −0.976582 | −0.488291 | − | 0.872681i | \(-0.662380\pi\) | ||||
−0.488291 | + | 0.872681i | \(0.662380\pi\) | |||||||
\(608\) | 2.35158e54 | 1.21686 | ||||||||
\(609\) | −7.55721e53 | −0.378725 | ||||||||
\(610\) | −1.12188e54 | −0.544522 | ||||||||
\(611\) | −5.49616e53 | −0.258378 | ||||||||
\(612\) | 2.85238e53 | 0.129884 | ||||||||
\(613\) | 1.27061e54 | 0.560446 | 0.280223 | − | 0.959935i | \(-0.409592\pi\) | ||||
0.280223 | + | 0.959935i | \(0.409592\pi\) | |||||||
\(614\) | −3.66020e53 | −0.156395 | ||||||||
\(615\) | 3.83398e54 | 1.58703 | ||||||||
\(616\) | −1.17610e54 | −0.471650 | ||||||||
\(617\) | 1.76693e54 | 0.686530 | 0.343265 | − | 0.939239i | \(-0.388467\pi\) | ||||
0.343265 | + | 0.939239i | \(0.388467\pi\) | |||||||
\(618\) | 2.05214e54 | 0.772559 | ||||||||
\(619\) | −2.12154e54 | −0.773897 | −0.386948 | − | 0.922101i | \(-0.626471\pi\) | ||||
−0.386948 | + | 0.922101i | \(0.626471\pi\) | |||||||
\(620\) | −4.98121e54 | −1.76075 | ||||||||
\(621\) | 1.06492e54 | 0.364781 | ||||||||
\(622\) | 2.87723e53 | 0.0955130 | ||||||||
\(623\) | 3.72922e54 | 1.19978 | ||||||||
\(624\) | 1.93448e54 | 0.603205 | ||||||||
\(625\) | −4.11434e54 | −1.24348 | ||||||||
\(626\) | −1.07346e53 | −0.0314476 | ||||||||
\(627\) | −1.00772e55 | −2.86170 | ||||||||
\(628\) | 1.03801e54 | 0.285750 | ||||||||
\(629\) | −3.19466e53 | −0.0852583 | ||||||||
\(630\) | 1.38347e54 | 0.357954 | ||||||||
\(631\) | 4.38932e54 | 1.10109 | 0.550547 | − | 0.834804i | \(-0.314419\pi\) | ||||
0.550547 | + | 0.834804i | \(0.314419\pi\) | |||||||
\(632\) | −1.95684e54 | −0.475963 | ||||||||
\(633\) | 9.52695e52 | 0.0224689 | ||||||||
\(634\) | −2.49655e53 | −0.0570953 | ||||||||
\(635\) | 5.41103e54 | 1.20003 | ||||||||
\(636\) | −4.99093e53 | −0.107341 | ||||||||
\(637\) | 1.69491e54 | 0.353532 | ||||||||
\(638\) | 8.17471e53 | 0.165375 | ||||||||
\(639\) | 2.94831e54 | 0.578505 | ||||||||
\(640\) | −6.46656e54 | −1.23073 | ||||||||
\(641\) | 8.28753e54 | 1.53001 | 0.765004 | − | 0.644025i | \(-0.222737\pi\) | ||||
0.765004 | + | 0.644025i | \(0.222737\pi\) | |||||||
\(642\) | −1.28733e54 | −0.230545 | ||||||||
\(643\) | −1.96493e54 | −0.341376 | −0.170688 | − | 0.985325i | \(-0.554599\pi\) | ||||
−0.170688 | + | 0.985325i | \(0.554599\pi\) | |||||||
\(644\) | 1.66694e54 | 0.280961 | ||||||||
\(645\) | −9.06230e54 | −1.48192 | ||||||||
\(646\) | −2.97517e53 | −0.0472039 | ||||||||
\(647\) | 8.12153e54 | 1.25027 | 0.625136 | − | 0.780516i | \(-0.285044\pi\) | ||||
0.625136 | + | 0.780516i | \(0.285044\pi\) | |||||||
\(648\) | 1.45166e54 | 0.216846 | ||||||||
\(649\) | 2.60247e54 | 0.377237 | ||||||||
\(650\) | −7.48033e53 | −0.105223 | ||||||||
\(651\) | −1.08405e55 | −1.47986 | ||||||||
\(652\) | 2.81317e54 | 0.372707 | ||||||||
\(653\) | −1.31229e55 | −1.68741 | −0.843707 | − | 0.536804i | \(-0.819632\pi\) | ||||
−0.843707 | + | 0.536804i | \(0.819632\pi\) | |||||||
\(654\) | −1.25933e54 | −0.157172 | ||||||||
\(655\) | 1.81073e54 | 0.219356 | ||||||||
\(656\) | −4.75482e54 | −0.559126 | ||||||||
\(657\) | 6.69269e54 | 0.763970 | ||||||||
\(658\) | 8.24148e53 | 0.0913273 | ||||||||
\(659\) | −1.11571e55 | −1.20029 | −0.600146 | − | 0.799890i | \(-0.704891\pi\) | ||||
−0.600146 | + | 0.799890i | \(0.704891\pi\) | |||||||
\(660\) | 2.13215e55 | 2.22696 | ||||||||
\(661\) | −3.62687e54 | −0.367793 | −0.183897 | − | 0.982946i | \(-0.558871\pi\) | ||||
−0.183897 | + | 0.982946i | \(0.558871\pi\) | |||||||
\(662\) | 1.57848e54 | 0.155421 | ||||||||
\(663\) | −9.13603e53 | −0.0873462 | ||||||||
\(664\) | 1.03066e55 | 0.956835 | ||||||||
\(665\) | 1.21605e55 | 1.09630 | ||||||||
\(666\) | 4.57613e54 | 0.400636 | ||||||||
\(667\) | −2.45478e54 | −0.208717 | ||||||||
\(668\) | −1.64603e55 | −1.35924 | ||||||||
\(669\) | 2.08732e55 | 1.67409 | ||||||||
\(670\) | −7.75256e52 | −0.00603930 | ||||||||
\(671\) | −2.22563e55 | −1.68408 | ||||||||
\(672\) | −1.08281e55 | −0.795885 | ||||||||
\(673\) | −1.86876e54 | −0.133432 | −0.0667159 | − | 0.997772i | \(-0.521252\pi\) | ||||
−0.0667159 | + | 0.997772i | \(0.521252\pi\) | |||||||
\(674\) | −6.65812e54 | −0.461832 | ||||||||
\(675\) | −6.03872e54 | −0.406931 | ||||||||
\(676\) | 9.42823e54 | 0.617262 | ||||||||
\(677\) | 1.48956e55 | 0.947498 | 0.473749 | − | 0.880660i | \(-0.342900\pi\) | ||||
0.473749 | + | 0.880660i | \(0.342900\pi\) | |||||||
\(678\) | −1.26013e55 | −0.778821 | ||||||||
\(679\) | −4.17457e54 | −0.250698 | ||||||||
\(680\) | 1.33368e54 | 0.0778265 | ||||||||
\(681\) | 1.60549e55 | 0.910416 | ||||||||
\(682\) | 1.17263e55 | 0.646198 | ||||||||
\(683\) | 9.58075e54 | 0.513093 | 0.256546 | − | 0.966532i | \(-0.417415\pi\) | ||||
0.256546 | + | 0.966532i | \(0.417415\pi\) | |||||||
\(684\) | −3.59142e55 | −1.86927 | ||||||||
\(685\) | −2.82934e55 | −1.43126 | ||||||||
\(686\) | −6.54087e54 | −0.321599 | ||||||||
\(687\) | 1.60343e55 | 0.766291 | ||||||||
\(688\) | 1.12389e55 | 0.522093 | ||||||||
\(689\) | 9.45523e53 | 0.0426970 | ||||||||
\(690\) | 7.59763e54 | 0.333519 | ||||||||
\(691\) | 1.23084e54 | 0.0525267 | 0.0262634 | − | 0.999655i | \(-0.491639\pi\) | ||||
0.0262634 | + | 0.999655i | \(0.491639\pi\) | |||||||
\(692\) | 1.67766e55 | 0.696041 | ||||||||
\(693\) | 2.74457e55 | 1.10707 | ||||||||
\(694\) | 3.84062e53 | 0.0150623 | ||||||||
\(695\) | 3.45319e55 | 1.31679 | ||||||||
\(696\) | 1.04356e55 | 0.386935 | ||||||||
\(697\) | 2.24557e54 | 0.0809633 | ||||||||
\(698\) | −1.04043e55 | −0.364779 | ||||||||
\(699\) | −7.43605e55 | −2.53535 | ||||||||
\(700\) | −9.45250e54 | −0.313426 | ||||||||
\(701\) | −4.60890e55 | −1.48627 | −0.743133 | − | 0.669144i | \(-0.766661\pi\) | ||||
−0.743133 | + | 0.669144i | \(0.766661\pi\) | |||||||
\(702\) | 4.04812e54 | 0.126964 | ||||||||
\(703\) | 4.02237e55 | 1.22702 | ||||||||
\(704\) | −1.78674e55 | −0.530145 | ||||||||
\(705\) | −3.16550e55 | −0.913597 | ||||||||
\(706\) | 1.04220e55 | 0.292591 | ||||||||
\(707\) | 2.35924e55 | 0.644308 | ||||||||
\(708\) | 1.56808e55 | 0.416602 | ||||||||
\(709\) | −4.42017e54 | −0.114245 | −0.0571226 | − | 0.998367i | \(-0.518193\pi\) | ||||
−0.0571226 | + | 0.998367i | \(0.518193\pi\) | |||||||
\(710\) | 6.50661e54 | 0.163613 | ||||||||
\(711\) | 4.56654e55 | 1.11720 | ||||||||
\(712\) | −5.14961e55 | −1.22578 | ||||||||
\(713\) | −3.52128e55 | −0.815558 | ||||||||
\(714\) | 1.36995e54 | 0.0308737 | ||||||||
\(715\) | −4.03933e55 | −0.885812 | ||||||||
\(716\) | 7.08565e55 | 1.51208 | ||||||||
\(717\) | 5.31259e55 | 1.10327 | ||||||||
\(718\) | −6.77634e54 | −0.136952 | ||||||||
\(719\) | 4.79691e55 | 0.943514 | 0.471757 | − | 0.881729i | \(-0.343620\pi\) | ||||
0.471757 | + | 0.881729i | \(0.343620\pi\) | |||||||
\(720\) | 6.59006e55 | 1.26155 | ||||||||
\(721\) | −4.91274e55 | −0.915348 | ||||||||
\(722\) | 1.95010e55 | 0.353657 | ||||||||
\(723\) | −9.84817e55 | −1.73844 | ||||||||
\(724\) | −1.90799e55 | −0.327848 | ||||||||
\(725\) | 1.39200e55 | 0.232834 | ||||||||
\(726\) | −1.88986e55 | −0.307727 | ||||||||
\(727\) | 1.02822e56 | 1.62991 | 0.814956 | − | 0.579523i | \(-0.196761\pi\) | ||||
0.814956 | + | 0.579523i | \(0.196761\pi\) | |||||||
\(728\) | 1.34251e55 | 0.207184 | ||||||||
\(729\) | −1.06843e56 | −1.60531 | ||||||||
\(730\) | 1.47700e55 | 0.216066 | ||||||||
\(731\) | −5.30781e54 | −0.0756008 | ||||||||
\(732\) | −1.34102e56 | −1.85982 | ||||||||
\(733\) | −5.77006e55 | −0.779207 | −0.389603 | − | 0.920983i | \(-0.627388\pi\) | ||||
−0.389603 | + | 0.920983i | \(0.627388\pi\) | |||||||
\(734\) | 1.94790e55 | 0.256149 | ||||||||
\(735\) | 9.76181e55 | 1.25005 | ||||||||
\(736\) | −3.51724e55 | −0.438616 | ||||||||
\(737\) | −1.53798e54 | −0.0186782 | ||||||||
\(738\) | −3.21663e55 | −0.380454 | ||||||||
\(739\) | 1.40056e56 | 1.61337 | 0.806686 | − | 0.590980i | \(-0.201259\pi\) | ||||
0.806686 | + | 0.590980i | \(0.201259\pi\) | |||||||
\(740\) | −8.51057e55 | −0.954861 | ||||||||
\(741\) | 1.15031e56 | 1.25707 | ||||||||
\(742\) | −1.41781e54 | −0.0150918 | ||||||||
\(743\) | 7.96262e54 | 0.0825609 | 0.0412804 | − | 0.999148i | \(-0.486856\pi\) | ||||
0.0412804 | + | 0.999148i | \(0.486856\pi\) | |||||||
\(744\) | 1.49695e56 | 1.51194 | ||||||||
\(745\) | 6.02299e55 | 0.592604 | ||||||||
\(746\) | −5.05324e55 | −0.484354 | ||||||||
\(747\) | −2.40517e56 | −2.24592 | ||||||||
\(748\) | 1.24881e55 | 0.113609 | ||||||||
\(749\) | 3.08181e55 | 0.273156 | ||||||||
\(750\) | 3.11042e55 | 0.268612 | ||||||||
\(751\) | −8.79022e55 | −0.739641 | −0.369821 | − | 0.929103i | \(-0.620581\pi\) | ||||
−0.369821 | + | 0.929103i | \(0.620581\pi\) | |||||||
\(752\) | 3.92578e55 | 0.321868 | ||||||||
\(753\) | 2.10936e56 | 1.68519 | ||||||||
\(754\) | −9.33140e54 | −0.0726450 | ||||||||
\(755\) | −1.92669e56 | −1.46166 | ||||||||
\(756\) | 5.11540e55 | 0.378185 | ||||||||
\(757\) | −6.05512e54 | −0.0436268 | −0.0218134 | − | 0.999762i | \(-0.506944\pi\) | ||||
−0.0218134 | + | 0.999762i | \(0.506944\pi\) | |||||||
\(758\) | 8.40915e54 | 0.0590477 | ||||||||
\(759\) | 1.50725e56 | 1.03150 | ||||||||
\(760\) | −1.67922e56 | −1.12007 | ||||||||
\(761\) | −2.67473e56 | −1.73892 | −0.869458 | − | 0.494008i | \(-0.835532\pi\) | ||||
−0.869458 | + | 0.494008i | \(0.835532\pi\) | |||||||
\(762\) | −7.67520e55 | −0.486371 | ||||||||
\(763\) | 3.01479e55 | 0.186221 | ||||||||
\(764\) | 8.46080e55 | 0.509437 | ||||||||
\(765\) | −3.11230e55 | −0.182677 | ||||||||
\(766\) | 1.51557e55 | 0.0867191 | ||||||||
\(767\) | −2.97071e55 | −0.165711 | ||||||||
\(768\) | −2.87088e55 | −0.156125 | ||||||||
\(769\) | 3.07792e55 | 0.163190 | 0.0815951 | − | 0.996666i | \(-0.473999\pi\) | ||||
0.0815951 | + | 0.996666i | \(0.473999\pi\) | |||||||
\(770\) | 6.05697e55 | 0.313102 | ||||||||
\(771\) | 1.22019e56 | 0.614991 | ||||||||
\(772\) | 3.10094e56 | 1.52390 | ||||||||
\(773\) | 7.39678e55 | 0.354440 | 0.177220 | − | 0.984171i | \(-0.443290\pi\) | ||||
0.177220 | + | 0.984171i | \(0.443290\pi\) | |||||||
\(774\) | 7.60307e55 | 0.355255 | ||||||||
\(775\) | 1.99676e56 | 0.909794 | ||||||||
\(776\) | 5.76459e55 | 0.256133 | ||||||||
\(777\) | −1.85214e56 | −0.802535 | ||||||||
\(778\) | −5.74396e55 | −0.242722 | ||||||||
\(779\) | −2.82738e56 | −1.16521 | ||||||||
\(780\) | −2.43384e56 | −0.978245 | ||||||||
\(781\) | 1.29081e56 | 0.506018 | ||||||||
\(782\) | 4.44995e54 | 0.0170146 | ||||||||
\(783\) | −7.53305e55 | −0.280942 | ||||||||
\(784\) | −1.21064e56 | −0.440404 | ||||||||
\(785\) | −1.13259e56 | −0.401898 | ||||||||
\(786\) | −2.56841e55 | −0.0889046 | ||||||||
\(787\) | −3.95231e56 | −1.33458 | −0.667289 | − | 0.744799i | \(-0.732545\pi\) | ||||
−0.667289 | + | 0.744799i | \(0.732545\pi\) | |||||||
\(788\) | 4.94362e56 | 1.62849 | ||||||||
\(789\) | 1.85779e55 | 0.0597030 | ||||||||
\(790\) | 1.00779e56 | 0.315966 | ||||||||
\(791\) | 3.01671e56 | 0.922767 | ||||||||
\(792\) | −3.78993e56 | −1.13107 | ||||||||
\(793\) | 2.54055e56 | 0.739776 | ||||||||
\(794\) | −4.10082e55 | −0.116512 | ||||||||
\(795\) | 5.44572e55 | 0.150972 | ||||||||
\(796\) | −5.83734e56 | −1.57910 | ||||||||
\(797\) | −1.36161e56 | −0.359432 | −0.179716 | − | 0.983719i | \(-0.557518\pi\) | ||||
−0.179716 | + | 0.983719i | \(0.557518\pi\) | |||||||
\(798\) | −1.72489e56 | −0.444330 | ||||||||
\(799\) | −1.85404e55 | −0.0466076 | ||||||||
\(800\) | 1.99447e56 | 0.489298 | ||||||||
\(801\) | 1.20172e57 | 2.87721 | ||||||||
\(802\) | 2.58049e56 | 0.602978 | ||||||||
\(803\) | 2.93014e56 | 0.668244 | ||||||||
\(804\) | −9.26690e54 | −0.0206273 | ||||||||
\(805\) | −1.81884e56 | −0.395162 | ||||||||
\(806\) | −1.33855e56 | −0.283858 | ||||||||
\(807\) | −2.83379e56 | −0.586590 | ||||||||
\(808\) | −3.25783e56 | −0.658275 | ||||||||
\(809\) | 5.42801e56 | 1.07064 | 0.535321 | − | 0.844649i | \(-0.320191\pi\) | ||||
0.535321 | + | 0.844649i | \(0.320191\pi\) | |||||||
\(810\) | −7.47613e55 | −0.143952 | ||||||||
\(811\) | −8.54286e56 | −1.60582 | −0.802910 | − | 0.596100i | \(-0.796716\pi\) | ||||
−0.802910 | + | 0.596100i | \(0.796716\pi\) | |||||||
\(812\) | −1.17916e56 | −0.216387 | ||||||||
\(813\) | −6.09306e56 | −1.09162 | ||||||||
\(814\) | 2.00348e56 | 0.350436 | ||||||||
\(815\) | −3.06952e56 | −0.524199 | ||||||||
\(816\) | 6.52566e55 | 0.108809 | ||||||||
\(817\) | 6.68303e56 | 1.08804 | ||||||||
\(818\) | 3.82704e55 | 0.0608379 | ||||||||
\(819\) | −3.13291e56 | −0.486309 | ||||||||
\(820\) | 5.98221e56 | 0.906759 | ||||||||
\(821\) | −2.83593e56 | −0.419763 | −0.209882 | − | 0.977727i | \(-0.567308\pi\) | ||||
−0.209882 | + | 0.977727i | \(0.567308\pi\) | |||||||
\(822\) | 4.01323e56 | 0.580088 | ||||||||
\(823\) | −7.79009e56 | −1.09963 | −0.549814 | − | 0.835287i | \(-0.685301\pi\) | ||||
−0.549814 | + | 0.835287i | \(0.685301\pi\) | |||||||
\(824\) | 6.78392e56 | 0.935190 | ||||||||
\(825\) | −8.54693e56 | −1.15069 | ||||||||
\(826\) | 4.45458e55 | 0.0585728 | ||||||||
\(827\) | 2.44580e56 | 0.314097 | 0.157049 | − | 0.987591i | \(-0.449802\pi\) | ||||
0.157049 | + | 0.987591i | \(0.449802\pi\) | |||||||
\(828\) | 5.37166e56 | 0.673778 | ||||||||
\(829\) | −1.26495e56 | −0.154974 | −0.0774871 | − | 0.996993i | \(-0.524690\pi\) | ||||
−0.0774871 | + | 0.996993i | \(0.524690\pi\) | |||||||
\(830\) | −5.30795e56 | −0.635190 | ||||||||
\(831\) | 1.69854e57 | 1.98543 | ||||||||
\(832\) | 2.03956e56 | 0.232879 | ||||||||
\(833\) | 5.71751e55 | 0.0637719 | ||||||||
\(834\) | −4.89812e56 | −0.533693 | ||||||||
\(835\) | 1.79602e57 | 1.91173 | ||||||||
\(836\) | −1.57236e57 | −1.63505 | ||||||||
\(837\) | −1.08059e57 | −1.09777 | ||||||||
\(838\) | −5.15156e55 | −0.0511305 | ||||||||
\(839\) | 1.05147e57 | 1.01962 | 0.509809 | − | 0.860287i | \(-0.329716\pi\) | ||||
0.509809 | + | 0.860287i | \(0.329716\pi\) | |||||||
\(840\) | 7.73216e56 | 0.732579 | ||||||||
\(841\) | −9.06598e56 | −0.839253 | ||||||||
\(842\) | −2.59700e56 | −0.234901 | ||||||||
\(843\) | −1.07960e57 | −0.954170 | ||||||||
\(844\) | 1.48650e55 | 0.0128377 | ||||||||
\(845\) | −1.02874e57 | −0.868157 | ||||||||
\(846\) | 2.65579e56 | 0.219013 | ||||||||
\(847\) | 4.52425e56 | 0.364603 | ||||||||
\(848\) | −6.75366e55 | −0.0531888 | ||||||||
\(849\) | −2.71413e57 | −2.08896 | ||||||||
\(850\) | −2.52337e55 | −0.0189807 | ||||||||
\(851\) | −6.01623e56 | −0.442281 | ||||||||
\(852\) | 7.77757e56 | 0.558820 | ||||||||
\(853\) | 2.14388e57 | 1.50555 | 0.752775 | − | 0.658278i | \(-0.228715\pi\) | ||||
0.752775 | + | 0.658278i | \(0.228715\pi\) | |||||||
\(854\) | −3.80955e56 | −0.261484 | ||||||||
\(855\) | 3.91868e57 | 2.62906 | ||||||||
\(856\) | −4.25562e56 | −0.279077 | ||||||||
\(857\) | 1.76630e57 | 1.13224 | 0.566119 | − | 0.824323i | \(-0.308444\pi\) | ||||
0.566119 | + | 0.824323i | \(0.308444\pi\) | |||||||
\(858\) | 5.72952e56 | 0.359018 | ||||||||
\(859\) | −1.41212e57 | −0.864978 | −0.432489 | − | 0.901639i | \(-0.642365\pi\) | ||||
−0.432489 | + | 0.901639i | \(0.642365\pi\) | |||||||
\(860\) | −1.41400e57 | −0.846702 | ||||||||
\(861\) | 1.30190e57 | 0.762106 | ||||||||
\(862\) | 8.43842e56 | 0.482913 | ||||||||
\(863\) | −2.76506e57 | −1.54702 | −0.773508 | − | 0.633787i | \(-0.781500\pi\) | ||||
−0.773508 | + | 0.633787i | \(0.781500\pi\) | |||||||
\(864\) | −1.07935e57 | −0.590395 | ||||||||
\(865\) | −1.83053e57 | −0.978958 | ||||||||
\(866\) | 5.65553e56 | 0.295716 | ||||||||
\(867\) | 3.02950e57 | 1.54881 | ||||||||
\(868\) | −1.69146e57 | −0.845525 | ||||||||
\(869\) | 1.99928e57 | 0.977212 | ||||||||
\(870\) | −5.37440e56 | −0.256865 | ||||||||
\(871\) | 1.75560e55 | 0.00820487 | ||||||||
\(872\) | −4.16307e56 | −0.190258 | ||||||||
\(873\) | −1.34524e57 | −0.601204 | ||||||||
\(874\) | −5.60289e56 | −0.244872 | ||||||||
\(875\) | −7.44623e56 | −0.318258 | ||||||||
\(876\) | 1.76551e57 | 0.737974 | ||||||||
\(877\) | −7.42378e56 | −0.303482 | −0.151741 | − | 0.988420i | \(-0.548488\pi\) | ||||
−0.151741 | + | 0.988420i | \(0.548488\pi\) | |||||||
\(878\) | 3.72247e56 | 0.148829 | ||||||||
\(879\) | −6.09427e57 | −2.38308 | ||||||||
\(880\) | 2.88520e57 | 1.10348 | ||||||||
\(881\) | 6.13623e56 | 0.229547 | 0.114773 | − | 0.993392i | \(-0.463386\pi\) | ||||
0.114773 | + | 0.993392i | \(0.463386\pi\) | |||||||
\(882\) | −8.18994e56 | −0.299670 | ||||||||
\(883\) | 2.47374e57 | 0.885361 | 0.442681 | − | 0.896679i | \(-0.354028\pi\) | ||||
0.442681 | + | 0.896679i | \(0.354028\pi\) | |||||||
\(884\) | −1.42551e56 | −0.0499057 | ||||||||
\(885\) | −1.71097e57 | −0.585936 | ||||||||
\(886\) | −1.45533e57 | −0.487531 | ||||||||
\(887\) | 4.04554e57 | 1.32576 | 0.662882 | − | 0.748724i | \(-0.269333\pi\) | ||||
0.662882 | + | 0.748724i | \(0.269333\pi\) | |||||||
\(888\) | 2.55759e57 | 0.819932 | ||||||||
\(889\) | 1.83741e57 | 0.576265 | ||||||||
\(890\) | 2.65208e57 | 0.813731 | ||||||||
\(891\) | −1.48314e57 | −0.445213 | ||||||||
\(892\) | 3.25687e57 | 0.956501 | ||||||||
\(893\) | 2.33441e57 | 0.670770 | ||||||||
\(894\) | −8.54321e56 | −0.240182 | ||||||||
\(895\) | −7.73132e57 | −2.12669 | ||||||||
\(896\) | −2.19583e57 | −0.591008 | ||||||||
\(897\) | −1.72051e57 | −0.453112 | ||||||||
\(898\) | 2.00687e57 | 0.517168 | ||||||||
\(899\) | 2.49088e57 | 0.628114 | ||||||||
\(900\) | −3.04603e57 | −0.751632 | ||||||||
\(901\) | 3.18957e55 | 0.00770191 | ||||||||
\(902\) | −1.40828e57 | −0.332783 | ||||||||
\(903\) | −3.07727e57 | −0.711630 | ||||||||
\(904\) | −4.16572e57 | −0.942770 | ||||||||
\(905\) | 2.08185e57 | 0.461107 | ||||||||
\(906\) | 2.73288e57 | 0.592407 | ||||||||
\(907\) | 1.91109e57 | 0.405452 | 0.202726 | − | 0.979236i | \(-0.435020\pi\) | ||||
0.202726 | + | 0.979236i | \(0.435020\pi\) | |||||||
\(908\) | 2.50507e57 | 0.520171 | ||||||||
\(909\) | 7.60256e57 | 1.54513 | ||||||||
\(910\) | −6.91400e56 | −0.137538 | ||||||||
\(911\) | −6.02986e57 | −1.17408 | −0.587041 | − | 0.809557i | \(-0.699707\pi\) | ||||
−0.587041 | + | 0.809557i | \(0.699707\pi\) | |||||||
\(912\) | −8.21642e57 | −1.56597 | ||||||||
\(913\) | −1.05301e58 | −1.96450 | ||||||||
\(914\) | −1.75768e57 | −0.320988 | ||||||||
\(915\) | 1.46322e58 | 2.61577 | ||||||||
\(916\) | 2.50185e57 | 0.437824 | ||||||||
\(917\) | 6.14867e56 | 0.105336 | ||||||||
\(918\) | 1.36557e56 | 0.0229024 | ||||||||
\(919\) | 6.23642e57 | 1.02396 | 0.511980 | − | 0.858997i | \(-0.328912\pi\) | ||||
0.511980 | + | 0.858997i | \(0.328912\pi\) | |||||||
\(920\) | 2.51161e57 | 0.403728 | ||||||||
\(921\) | 4.77384e57 | 0.751286 | ||||||||
\(922\) | −2.65073e56 | −0.0408426 | ||||||||
\(923\) | −1.47345e57 | −0.222281 | ||||||||
\(924\) | 7.24010e57 | 1.06940 | ||||||||
\(925\) | 3.41154e57 | 0.493386 | ||||||||
\(926\) | −2.04512e57 | −0.289604 | ||||||||
\(927\) | −1.58311e58 | −2.19511 | ||||||||
\(928\) | 2.48802e57 | 0.337807 | ||||||||
\(929\) | 4.25561e57 | 0.565790 | 0.282895 | − | 0.959151i | \(-0.408705\pi\) | ||||
0.282895 | + | 0.959151i | \(0.408705\pi\) | |||||||
\(930\) | −7.70936e57 | −1.00369 | ||||||||
\(931\) | −7.19888e57 | −0.917796 | ||||||||
\(932\) | −1.16026e58 | −1.44858 | ||||||||
\(933\) | −3.75266e57 | −0.458825 | ||||||||
\(934\) | 4.10047e57 | 0.490986 | ||||||||
\(935\) | −1.36260e57 | −0.159787 | ||||||||
\(936\) | 4.32619e57 | 0.496851 | ||||||||
\(937\) | 1.14088e58 | 1.28327 | 0.641637 | − | 0.767008i | \(-0.278255\pi\) | ||||
0.641637 | + | 0.767008i | \(0.278255\pi\) | |||||||
\(938\) | −2.63252e55 | −0.00290012 | ||||||||
\(939\) | 1.40007e57 | 0.151068 | ||||||||
\(940\) | −4.93917e57 | −0.521988 | ||||||||
\(941\) | −2.33700e57 | −0.241914 | −0.120957 | − | 0.992658i | \(-0.538596\pi\) | ||||
−0.120957 | + | 0.992658i | \(0.538596\pi\) | |||||||
\(942\) | 1.60651e57 | 0.162889 | ||||||||
\(943\) | 4.22890e57 | 0.420000 | ||||||||
\(944\) | 2.12191e57 | 0.206430 | ||||||||
\(945\) | −5.58153e57 | −0.531904 | ||||||||
\(946\) | 3.32871e57 | 0.310741 | ||||||||
\(947\) | −4.94229e56 | −0.0451964 | −0.0225982 | − | 0.999745i | \(-0.507194\pi\) | ||||
−0.0225982 | + | 0.999745i | \(0.507194\pi\) | |||||||
\(948\) | 1.20464e58 | 1.07918 | ||||||||
\(949\) | −3.34474e57 | −0.293542 | ||||||||
\(950\) | 3.17716e57 | 0.273167 | ||||||||
\(951\) | 3.25615e57 | 0.274274 | ||||||||
\(952\) | 4.52874e56 | 0.0373729 | ||||||||
\(953\) | 1.48078e56 | 0.0119723 | 0.00598617 | − | 0.999982i | \(-0.498095\pi\) | ||||
0.00598617 | + | 0.999982i | \(0.498095\pi\) | |||||||
\(954\) | −4.56884e56 | −0.0361920 | ||||||||
\(955\) | −9.23178e57 | −0.716506 | ||||||||
\(956\) | 8.28930e57 | 0.630361 | ||||||||
\(957\) | −1.06619e58 | −0.794426 | ||||||||
\(958\) | 7.22079e56 | 0.0527178 | ||||||||
\(959\) | −9.60753e57 | −0.687304 | ||||||||
\(960\) | 1.17468e58 | 0.823436 | ||||||||
\(961\) | 2.11725e58 | 1.45434 | ||||||||
\(962\) | −2.28696e57 | −0.153938 | ||||||||
\(963\) | 9.93101e57 | 0.655059 | ||||||||
\(964\) | −1.53662e58 | −0.993264 | ||||||||
\(965\) | −3.38351e58 | −2.14331 | ||||||||
\(966\) | 2.57991e57 | 0.160159 | ||||||||
\(967\) | −6.58500e57 | −0.400627 | −0.200313 | − | 0.979732i | \(-0.564196\pi\) | ||||
−0.200313 | + | 0.979732i | \(0.564196\pi\) | |||||||
\(968\) | −6.24746e57 | −0.372507 | ||||||||
\(969\) | 3.88039e57 | 0.226758 | ||||||||
\(970\) | −2.96880e57 | −0.170032 | ||||||||
\(971\) | 4.39314e57 | 0.246604 | 0.123302 | − | 0.992369i | \(-0.460652\pi\) | ||||
0.123302 | + | 0.992369i | \(0.460652\pi\) | |||||||
\(972\) | −2.03216e58 | −1.11806 | ||||||||
\(973\) | 1.17259e58 | 0.632333 | ||||||||
\(974\) | −3.52600e57 | −0.186373 | ||||||||
\(975\) | 9.75628e57 | 0.505469 | ||||||||
\(976\) | −1.81466e58 | −0.921558 | ||||||||
\(977\) | 2.41520e58 | 1.20229 | 0.601144 | − | 0.799141i | \(-0.294712\pi\) | ||||
0.601144 | + | 0.799141i | \(0.294712\pi\) | |||||||
\(978\) | 4.35391e57 | 0.212457 | ||||||||
\(979\) | 5.26129e58 | 2.51669 | ||||||||
\(980\) | 1.52315e58 | 0.714222 | ||||||||
\(981\) | 9.71504e57 | 0.446580 | ||||||||
\(982\) | −3.69630e57 | −0.166568 | ||||||||
\(983\) | 7.73253e57 | 0.341608 | 0.170804 | − | 0.985305i | \(-0.445364\pi\) | ||||
0.170804 | + | 0.985305i | \(0.445364\pi\) | |||||||
\(984\) | −1.79777e58 | −0.778626 | ||||||||
\(985\) | −5.39411e58 | −2.29041 | ||||||||
\(986\) | −3.14780e56 | −0.0131041 | ||||||||
\(987\) | −1.07490e58 | −0.438717 | ||||||||
\(988\) | 1.79485e58 | 0.718235 | ||||||||
\(989\) | −9.99576e57 | −0.392183 | ||||||||
\(990\) | 1.95183e58 | 0.750856 | ||||||||
\(991\) | −2.62440e58 | −0.989904 | −0.494952 | − | 0.868920i | \(-0.664814\pi\) | ||||
−0.494952 | + | 0.868920i | \(0.664814\pi\) | |||||||
\(992\) | 3.56897e58 | 1.31997 | ||||||||
\(993\) | −2.05875e58 | −0.746609 | ||||||||
\(994\) | 2.20944e57 | 0.0785682 | ||||||||
\(995\) | 6.36926e58 | 2.22095 | ||||||||
\(996\) | −6.34477e58 | −2.16950 | ||||||||
\(997\) | −2.17628e58 | −0.729726 | −0.364863 | − | 0.931061i | \(-0.618884\pi\) | ||||
−0.364863 | + | 0.931061i | \(0.618884\pi\) | |||||||
\(998\) | −1.04029e57 | −0.0342067 | ||||||||
\(999\) | −1.84622e58 | −0.595328 |
(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 | 1.40.a.a.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 9.40.a.b.1.2 | 3 | |||
4.3 | odd | 2 | 16.40.a.c.1.3 | 3 | |||
5.2 | odd | 4 | 25.40.b.a.24.4 | 6 | |||
5.3 | odd | 4 | 25.40.b.a.24.3 | 6 | |||
5.4 | even | 2 | 25.40.a.a.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.40.a.a.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.40.a.b.1.2 | 3 | 3.2 | odd | 2 | |||
16.40.a.c.1.3 | 3 | 4.3 | odd | 2 | |||
25.40.a.a.1.2 | 3 | 5.4 | even | 2 | |||
25.40.b.a.24.3 | 6 | 5.3 | odd | 4 | |||
25.40.b.a.24.4 | 6 | 5.2 | odd | 4 |