Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,50,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 50, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 50);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 50 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(30.4132410198\) |
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: | \( x^{3} - x^{2} - 104434803447206332x + 4289992005756109702361620 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{22}\cdot 3^{5}\cdot 5^{2}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(3.00244e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67772e7 | 0.707107 | ||||||||
\(3\) | −6.77152e11 | −1.38425 | −0.692126 | − | 0.721777i | \(-0.743326\pi\) | ||||
−0.692126 | + | 0.721777i | \(0.743326\pi\) | |||||||
\(4\) | 2.81475e14 | 0.500000 | ||||||||
\(5\) | −2.33026e17 | −1.74839 | −0.874196 | − | 0.485573i | \(-0.838611\pi\) | ||||
−0.874196 | + | 0.485573i | \(0.838611\pi\) | |||||||
\(6\) | −1.13607e19 | −0.978814 | ||||||||
\(7\) | −5.15430e20 | −1.01688 | −0.508438 | − | 0.861099i | \(-0.669777\pi\) | ||||
−0.508438 | + | 0.861099i | \(0.669777\pi\) | |||||||
\(8\) | 4.72237e21 | 0.353553 | ||||||||
\(9\) | 2.19235e23 | 0.916153 | ||||||||
\(10\) | −3.90952e24 | −1.23630 | ||||||||
\(11\) | −5.21317e25 | −1.59581 | −0.797905 | − | 0.602783i | \(-0.794058\pi\) | ||||
−0.797905 | + | 0.602783i | \(0.794058\pi\) | |||||||
\(12\) | −1.90601e26 | −0.692126 | ||||||||
\(13\) | 1.37568e27 | 0.702920 | 0.351460 | − | 0.936203i | \(-0.385685\pi\) | ||||
0.351460 | + | 0.936203i | \(0.385685\pi\) | |||||||
\(14\) | −8.64748e27 | −0.719040 | ||||||||
\(15\) | 1.57794e29 | 2.42021 | ||||||||
\(16\) | 7.92282e28 | 0.250000 | ||||||||
\(17\) | −9.93263e29 | −0.709685 | −0.354843 | − | 0.934926i | \(-0.615466\pi\) | ||||
−0.354843 | + | 0.934926i | \(0.615466\pi\) | |||||||
\(18\) | 3.67815e30 | 0.647818 | ||||||||
\(19\) | 1.85532e31 | 0.868871 | 0.434436 | − | 0.900703i | \(-0.356948\pi\) | ||||
0.434436 | + | 0.900703i | \(0.356948\pi\) | |||||||
\(20\) | −6.55909e31 | −0.874196 | ||||||||
\(21\) | 3.49024e32 | 1.40761 | ||||||||
\(22\) | −8.74625e32 | −1.12841 | ||||||||
\(23\) | −2.69345e33 | −1.16944 | −0.584718 | − | 0.811236i | \(-0.698795\pi\) | ||||
−0.584718 | + | 0.811236i | \(0.698795\pi\) | |||||||
\(24\) | −3.19776e33 | −0.489407 | ||||||||
\(25\) | 3.65374e34 | 2.05687 | ||||||||
\(26\) | 2.30801e34 | 0.497039 | ||||||||
\(27\) | 1.35867e34 | 0.116065 | ||||||||
\(28\) | −1.45081e35 | −0.508438 | ||||||||
\(29\) | −3.88028e34 | −0.0575588 | −0.0287794 | − | 0.999586i | \(-0.509162\pi\) | ||||
−0.0287794 | + | 0.999586i | \(0.509162\pi\) | |||||||
\(30\) | 2.64734e36 | 1.71135 | ||||||||
\(31\) | −8.58347e35 | −0.248486 | −0.124243 | − | 0.992252i | \(-0.539650\pi\) | ||||
−0.124243 | + | 0.992252i | \(0.539650\pi\) | |||||||
\(32\) | 1.32923e36 | 0.176777 | ||||||||
\(33\) | 3.53011e37 | 2.20900 | ||||||||
\(34\) | −1.66642e37 | −0.501823 | ||||||||
\(35\) | 1.20108e38 | 1.77790 | ||||||||
\(36\) | 6.17091e37 | 0.458077 | ||||||||
\(37\) | 2.50854e38 | 0.951652 | 0.475826 | − | 0.879539i | \(-0.342149\pi\) | ||||
0.475826 | + | 0.879539i | \(0.342149\pi\) | |||||||
\(38\) | 3.11271e38 | 0.614385 | ||||||||
\(39\) | −9.31545e38 | −0.973018 | ||||||||
\(40\) | −1.10043e39 | −0.618150 | ||||||||
\(41\) | 2.12382e38 | 0.0651498 | 0.0325749 | − | 0.999469i | \(-0.489629\pi\) | ||||
0.0325749 | + | 0.999469i | \(0.489629\pi\) | |||||||
\(42\) | 5.85566e39 | 0.995332 | ||||||||
\(43\) | −3.48149e39 | −0.332497 | −0.166249 | − | 0.986084i | \(-0.553165\pi\) | ||||
−0.166249 | + | 0.986084i | \(0.553165\pi\) | |||||||
\(44\) | −1.46738e40 | −0.797905 | ||||||||
\(45\) | −5.10874e40 | −1.60179 | ||||||||
\(46\) | −4.51886e40 | −0.826916 | ||||||||
\(47\) | 2.11562e40 | 0.228581 | 0.114290 | − | 0.993447i | \(-0.463541\pi\) | ||||
0.114290 | + | 0.993447i | \(0.463541\pi\) | |||||||
\(48\) | −5.36495e40 | −0.346063 | ||||||||
\(49\) | 8.74461e39 | 0.0340358 | ||||||||
\(50\) | 6.12996e41 | 1.45443 | ||||||||
\(51\) | 6.72589e41 | 0.982383 | ||||||||
\(52\) | 3.87220e41 | 0.351460 | ||||||||
\(53\) | −2.52544e42 | −1.43740 | −0.718701 | − | 0.695319i | \(-0.755263\pi\) | ||||
−0.718701 | + | 0.695319i | \(0.755263\pi\) | |||||||
\(54\) | 2.27947e41 | 0.0820703 | ||||||||
\(55\) | 1.21480e43 | 2.79010 | ||||||||
\(56\) | −2.43405e42 | −0.359520 | ||||||||
\(57\) | −1.25633e43 | −1.20274 | ||||||||
\(58\) | −6.51003e41 | −0.0407002 | ||||||||
\(59\) | −4.29058e43 | −1.76458 | −0.882290 | − | 0.470707i | \(-0.843999\pi\) | ||||
−0.882290 | + | 0.470707i | \(0.843999\pi\) | |||||||
\(60\) | 4.44150e43 | 1.21011 | ||||||||
\(61\) | −1.42312e43 | −0.258619 | −0.129309 | − | 0.991604i | \(-0.541276\pi\) | ||||
−0.129309 | + | 0.991604i | \(0.541276\pi\) | |||||||
\(62\) | −1.44007e43 | −0.175706 | ||||||||
\(63\) | −1.13000e44 | −0.931614 | ||||||||
\(64\) | 2.23007e43 | 0.125000 | ||||||||
\(65\) | −3.20569e44 | −1.22898 | ||||||||
\(66\) | 5.92254e44 | 1.56200 | ||||||||
\(67\) | 2.95546e44 | 0.539254 | 0.269627 | − | 0.962965i | \(-0.413100\pi\) | ||||
0.269627 | + | 0.962965i | \(0.413100\pi\) | |||||||
\(68\) | −2.79579e44 | −0.354843 | ||||||||
\(69\) | 1.82387e45 | 1.61879 | ||||||||
\(70\) | 2.01509e45 | 1.25716 | ||||||||
\(71\) | −2.56483e45 | −1.13039 | −0.565197 | − | 0.824956i | \(-0.691200\pi\) | ||||
−0.565197 | + | 0.824956i | \(0.691200\pi\) | |||||||
\(72\) | 1.03531e45 | 0.323909 | ||||||||
\(73\) | −5.17938e45 | −1.15576 | −0.577880 | − | 0.816122i | \(-0.696120\pi\) | ||||
−0.577880 | + | 0.816122i | \(0.696120\pi\) | |||||||
\(74\) | 4.20863e45 | 0.672920 | ||||||||
\(75\) | −2.47414e46 | −2.84723 | ||||||||
\(76\) | 5.22226e45 | 0.434436 | ||||||||
\(77\) | 2.68703e46 | 1.62274 | ||||||||
\(78\) | −1.56287e46 | −0.688027 | ||||||||
\(79\) | 1.28546e46 | 0.414185 | 0.207092 | − | 0.978321i | \(-0.433600\pi\) | ||||
0.207092 | + | 0.978321i | \(0.433600\pi\) | |||||||
\(80\) | −1.84622e46 | −0.437098 | ||||||||
\(81\) | −6.16630e46 | −1.07682 | ||||||||
\(82\) | 3.56318e45 | 0.0460679 | ||||||||
\(83\) | 8.58374e46 | 0.824638 | 0.412319 | − | 0.911040i | \(-0.364719\pi\) | ||||
0.412319 | + | 0.911040i | \(0.364719\pi\) | |||||||
\(84\) | 9.82416e46 | 0.703806 | ||||||||
\(85\) | 2.31456e47 | 1.24081 | ||||||||
\(86\) | −5.84097e46 | −0.235111 | ||||||||
\(87\) | 2.62754e46 | 0.0796759 | ||||||||
\(88\) | −2.46185e47 | −0.564204 | ||||||||
\(89\) | 6.95931e47 | 1.20924 | 0.604618 | − | 0.796516i | \(-0.293326\pi\) | ||||
0.604618 | + | 0.796516i | \(0.293326\pi\) | |||||||
\(90\) | −8.57104e47 | −1.13264 | ||||||||
\(91\) | −7.09067e47 | −0.714782 | ||||||||
\(92\) | −7.58138e47 | −0.584718 | ||||||||
\(93\) | 5.81231e47 | 0.343967 | ||||||||
\(94\) | 3.54942e47 | 0.161631 | ||||||||
\(95\) | −4.32337e48 | −1.51913 | ||||||||
\(96\) | −9.00089e47 | −0.244703 | ||||||||
\(97\) | 7.53593e48 | 1.58939 | 0.794693 | − | 0.607011i | \(-0.207632\pi\) | ||||
0.794693 | + | 0.607011i | \(0.207632\pi\) | |||||||
\(98\) | 1.46710e47 | 0.0240670 | ||||||||
\(99\) | −1.14291e49 | −1.46201 | ||||||||
\(100\) | 1.02844e49 | 1.02844 | ||||||||
\(101\) | 2.43523e49 | 1.90839 | 0.954195 | − | 0.299185i | \(-0.0967147\pi\) | ||||
0.954195 | + | 0.299185i | \(0.0967147\pi\) | |||||||
\(102\) | 1.12842e49 | 0.694650 | ||||||||
\(103\) | 4.35062e48 | 0.210882 | 0.105441 | − | 0.994426i | \(-0.466375\pi\) | ||||
0.105441 | + | 0.994426i | \(0.466375\pi\) | |||||||
\(104\) | 6.49647e48 | 0.248520 | ||||||||
\(105\) | −8.13316e49 | −2.46106 | ||||||||
\(106\) | −4.23699e49 | −1.01640 | ||||||||
\(107\) | 4.63551e49 | 0.883477 | 0.441739 | − | 0.897144i | \(-0.354362\pi\) | ||||
0.441739 | + | 0.897144i | \(0.354362\pi\) | |||||||
\(108\) | 3.82431e48 | 0.0580325 | ||||||||
\(109\) | −3.16577e49 | −0.383293 | −0.191646 | − | 0.981464i | \(-0.561383\pi\) | ||||
−0.191646 | + | 0.981464i | \(0.561383\pi\) | |||||||
\(110\) | 2.03810e50 | 1.97290 | ||||||||
\(111\) | −1.69866e50 | −1.31733 | ||||||||
\(112\) | −4.08366e49 | −0.254219 | ||||||||
\(113\) | −2.77559e50 | −1.38974 | −0.694869 | − | 0.719136i | \(-0.744538\pi\) | ||||
−0.694869 | + | 0.719136i | \(0.744538\pi\) | |||||||
\(114\) | −2.10778e50 | −0.850463 | ||||||||
\(115\) | 6.27643e50 | 2.04463 | ||||||||
\(116\) | −1.09220e49 | −0.0287794 | ||||||||
\(117\) | 3.01597e50 | 0.643982 | ||||||||
\(118\) | −7.19839e50 | −1.24775 | ||||||||
\(119\) | 5.11958e50 | 0.721661 | ||||||||
\(120\) | 7.45160e50 | 0.855675 | ||||||||
\(121\) | 1.65053e51 | 1.54661 | ||||||||
\(122\) | −2.38760e50 | −0.182871 | ||||||||
\(123\) | −1.43815e50 | −0.0901837 | ||||||||
\(124\) | −2.41603e50 | −0.124243 | ||||||||
\(125\) | −4.37479e51 | −1.84783 | ||||||||
\(126\) | −1.89583e51 | −0.658750 | ||||||||
\(127\) | −1.11605e51 | −0.319516 | −0.159758 | − | 0.987156i | \(-0.551071\pi\) | ||||
−0.159758 | + | 0.987156i | \(0.551071\pi\) | |||||||
\(128\) | 3.74144e50 | 0.0883883 | ||||||||
\(129\) | 2.35750e51 | 0.460260 | ||||||||
\(130\) | −5.37826e51 | −0.869019 | ||||||||
\(131\) | 3.32081e51 | 0.444730 | 0.222365 | − | 0.974963i | \(-0.428622\pi\) | ||||
0.222365 | + | 0.974963i | \(0.428622\pi\) | |||||||
\(132\) | 9.93637e51 | 1.10450 | ||||||||
\(133\) | −9.56287e51 | −0.883534 | ||||||||
\(134\) | 4.95845e51 | 0.381310 | ||||||||
\(135\) | −3.16605e51 | −0.202927 | ||||||||
\(136\) | −4.69055e51 | −0.250912 | ||||||||
\(137\) | 2.87128e52 | 1.28358 | 0.641788 | − | 0.766882i | \(-0.278193\pi\) | ||||
0.641788 | + | 0.766882i | \(0.278193\pi\) | |||||||
\(138\) | 3.05995e52 | 1.14466 | ||||||||
\(139\) | −2.07847e52 | −0.651450 | −0.325725 | − | 0.945465i | \(-0.605608\pi\) | ||||
−0.325725 | + | 0.945465i | \(0.605608\pi\) | |||||||
\(140\) | 3.38075e52 | 0.888948 | ||||||||
\(141\) | −1.43260e52 | −0.316414 | ||||||||
\(142\) | −4.30308e52 | −0.799309 | ||||||||
\(143\) | −7.17166e52 | −1.12173 | ||||||||
\(144\) | 1.73696e52 | 0.229038 | ||||||||
\(145\) | 9.04205e51 | 0.100635 | ||||||||
\(146\) | −8.68956e52 | −0.817246 | ||||||||
\(147\) | −5.92142e51 | −0.0471142 | ||||||||
\(148\) | 7.06090e52 | 0.475826 | ||||||||
\(149\) | 2.65487e53 | 1.51698 | 0.758489 | − | 0.651686i | \(-0.225938\pi\) | ||||
0.758489 | + | 0.651686i | \(0.225938\pi\) | |||||||
\(150\) | −4.15091e53 | −2.01330 | ||||||||
\(151\) | −2.97824e52 | −0.122751 | −0.0613754 | − | 0.998115i | \(-0.519549\pi\) | ||||
−0.0613754 | + | 0.998115i | \(0.519549\pi\) | |||||||
\(152\) | 8.76150e52 | 0.307192 | ||||||||
\(153\) | −2.17758e53 | −0.650180 | ||||||||
\(154\) | 4.50808e53 | 1.14745 | ||||||||
\(155\) | 2.00017e53 | 0.434450 | ||||||||
\(156\) | −2.62206e53 | −0.486509 | ||||||||
\(157\) | −7.16451e52 | −0.113670 | −0.0568349 | − | 0.998384i | \(-0.518101\pi\) | ||||
−0.0568349 | + | 0.998384i | \(0.518101\pi\) | |||||||
\(158\) | 2.15664e53 | 0.292873 | ||||||||
\(159\) | 1.71011e54 | 1.98973 | ||||||||
\(160\) | −3.09744e53 | −0.309075 | ||||||||
\(161\) | 1.38828e54 | 1.18917 | ||||||||
\(162\) | −1.03453e54 | −0.761424 | ||||||||
\(163\) | −8.62792e53 | −0.546147 | −0.273074 | − | 0.961993i | \(-0.588040\pi\) | ||||
−0.273074 | + | 0.961993i | \(0.588040\pi\) | |||||||
\(164\) | 5.97802e52 | 0.0325749 | ||||||||
\(165\) | −8.22606e54 | −3.86220 | ||||||||
\(166\) | 1.44011e54 | 0.583107 | ||||||||
\(167\) | 1.80874e53 | 0.0632154 | 0.0316077 | − | 0.999500i | \(-0.489937\pi\) | ||||
0.0316077 | + | 0.999500i | \(0.489937\pi\) | |||||||
\(168\) | 1.64822e54 | 0.497666 | ||||||||
\(169\) | −1.93773e54 | −0.505904 | ||||||||
\(170\) | 3.88318e54 | 0.877383 | ||||||||
\(171\) | 4.06751e54 | 0.796019 | ||||||||
\(172\) | −9.79953e53 | −0.166249 | ||||||||
\(173\) | 8.09453e54 | 1.19141 | 0.595706 | − | 0.803202i | \(-0.296872\pi\) | ||||
0.595706 | + | 0.803202i | \(0.296872\pi\) | |||||||
\(174\) | 4.40827e53 | 0.0563394 | ||||||||
\(175\) | −1.88325e55 | −2.09158 | ||||||||
\(176\) | −4.13030e54 | −0.398953 | ||||||||
\(177\) | 2.90537e55 | 2.44262 | ||||||||
\(178\) | 1.16758e55 | 0.855058 | ||||||||
\(179\) | −9.52961e54 | −0.608381 | −0.304191 | − | 0.952611i | \(-0.598386\pi\) | ||||
−0.304191 | + | 0.952611i | \(0.598386\pi\) | |||||||
\(180\) | −1.43798e55 | −0.800897 | ||||||||
\(181\) | 1.57599e55 | 0.766354 | 0.383177 | − | 0.923675i | \(-0.374830\pi\) | ||||
0.383177 | + | 0.923675i | \(0.374830\pi\) | |||||||
\(182\) | −1.18962e55 | −0.505427 | ||||||||
\(183\) | 9.63667e54 | 0.357993 | ||||||||
\(184\) | −1.27194e55 | −0.413458 | ||||||||
\(185\) | −5.84553e55 | −1.66386 | ||||||||
\(186\) | 9.75143e54 | 0.243221 | ||||||||
\(187\) | 5.17805e55 | 1.13252 | ||||||||
\(188\) | 5.95494e54 | 0.114290 | ||||||||
\(189\) | −7.00298e54 | −0.118024 | ||||||||
\(190\) | −7.25341e55 | −1.07419 | ||||||||
\(191\) | −1.13259e56 | −1.47487 | −0.737435 | − | 0.675419i | \(-0.763963\pi\) | ||||
−0.737435 | + | 0.675419i | \(0.763963\pi\) | |||||||
\(192\) | −1.51010e55 | −0.173031 | ||||||||
\(193\) | 5.85668e55 | 0.590878 | 0.295439 | − | 0.955362i | \(-0.404534\pi\) | ||||
0.295439 | + | 0.955362i | \(0.404534\pi\) | |||||||
\(194\) | 1.26432e56 | 1.12387 | ||||||||
\(195\) | 2.17074e56 | 1.70122 | ||||||||
\(196\) | 2.46139e54 | 0.0170179 | ||||||||
\(197\) | 6.36238e55 | 0.388327 | 0.194163 | − | 0.980969i | \(-0.437801\pi\) | ||||
0.194163 | + | 0.980969i | \(0.437801\pi\) | |||||||
\(198\) | −1.91748e56 | −1.03379 | ||||||||
\(199\) | −1.38808e56 | −0.661475 | −0.330738 | − | 0.943723i | \(-0.607298\pi\) | ||||
−0.330738 | + | 0.943723i | \(0.607298\pi\) | |||||||
\(200\) | 1.72543e56 | 0.727215 | ||||||||
\(201\) | −2.00130e56 | −0.746463 | ||||||||
\(202\) | 4.08565e56 | 1.34944 | ||||||||
\(203\) | 2.00001e55 | 0.0585302 | ||||||||
\(204\) | 1.89317e56 | 0.491191 | ||||||||
\(205\) | −4.94905e55 | −0.113907 | ||||||||
\(206\) | 7.29914e55 | 0.149116 | ||||||||
\(207\) | −5.90498e56 | −1.07138 | ||||||||
\(208\) | 1.08993e56 | 0.175730 | ||||||||
\(209\) | −9.67210e56 | −1.38655 | ||||||||
\(210\) | −1.36452e57 | −1.74023 | ||||||||
\(211\) | 5.64284e55 | 0.0640586 | 0.0320293 | − | 0.999487i | \(-0.489803\pi\) | ||||
0.0320293 | + | 0.999487i | \(0.489803\pi\) | |||||||
\(212\) | −7.10849e56 | −0.718701 | ||||||||
\(213\) | 1.73678e57 | 1.56475 | ||||||||
\(214\) | 7.77710e56 | 0.624713 | ||||||||
\(215\) | 8.11277e56 | 0.581336 | ||||||||
\(216\) | 6.41613e55 | 0.0410352 | ||||||||
\(217\) | 4.42418e56 | 0.252679 | ||||||||
\(218\) | −5.31129e56 | −0.271029 | ||||||||
\(219\) | 3.50722e57 | 1.59986 | ||||||||
\(220\) | 3.41937e57 | 1.39505 | ||||||||
\(221\) | −1.36641e57 | −0.498852 | ||||||||
\(222\) | −2.84988e57 | −0.931490 | ||||||||
\(223\) | −6.70689e57 | −1.96360 | −0.981798 | − | 0.189928i | \(-0.939174\pi\) | ||||
−0.981798 | + | 0.189928i | \(0.939174\pi\) | |||||||
\(224\) | −6.85124e56 | −0.179760 | ||||||||
\(225\) | 8.01028e57 | 1.88441 | ||||||||
\(226\) | −4.65666e57 | −0.982694 | ||||||||
\(227\) | 1.77430e57 | 0.336042 | 0.168021 | − | 0.985783i | \(-0.446262\pi\) | ||||
0.168021 | + | 0.985783i | \(0.446262\pi\) | |||||||
\(228\) | −3.53626e57 | −0.601368 | ||||||||
\(229\) | 1.42321e57 | 0.217420 | 0.108710 | − | 0.994074i | \(-0.465328\pi\) | ||||
0.108710 | + | 0.994074i | \(0.465328\pi\) | |||||||
\(230\) | 1.05301e58 | 1.44577 | ||||||||
\(231\) | −1.81952e58 | −2.24628 | ||||||||
\(232\) | −1.83241e56 | −0.0203501 | ||||||||
\(233\) | 6.14657e57 | 0.614346 | 0.307173 | − | 0.951654i | \(-0.400617\pi\) | ||||
0.307173 | + | 0.951654i | \(0.400617\pi\) | |||||||
\(234\) | 5.05996e57 | 0.455364 | ||||||||
\(235\) | −4.92994e57 | −0.399649 | ||||||||
\(236\) | −1.20769e58 | −0.882290 | ||||||||
\(237\) | −8.70449e57 | −0.573336 | ||||||||
\(238\) | 8.58922e57 | 0.510292 | ||||||||
\(239\) | −1.87389e58 | −1.00460 | −0.502301 | − | 0.864693i | \(-0.667513\pi\) | ||||
−0.502301 | + | 0.864693i | \(0.667513\pi\) | |||||||
\(240\) | 1.25017e58 | 0.605054 | ||||||||
\(241\) | 1.41041e58 | 0.616491 | 0.308245 | − | 0.951307i | \(-0.400258\pi\) | ||||
0.308245 | + | 0.951307i | \(0.400258\pi\) | |||||||
\(242\) | 2.76912e58 | 1.09362 | ||||||||
\(243\) | 3.85039e58 | 1.37452 | ||||||||
\(244\) | −4.00572e57 | −0.129309 | ||||||||
\(245\) | −2.03772e57 | −0.0595080 | ||||||||
\(246\) | −2.41281e57 | −0.0637695 | ||||||||
\(247\) | 2.55233e58 | 0.610747 | ||||||||
\(248\) | −4.05343e57 | −0.0878529 | ||||||||
\(249\) | −5.81249e58 | −1.14151 | ||||||||
\(250\) | −7.33968e58 | −1.30661 | ||||||||
\(251\) | 2.19883e58 | 0.354965 | 0.177482 | − | 0.984124i | \(-0.443205\pi\) | ||||
0.177482 | + | 0.984124i | \(0.443205\pi\) | |||||||
\(252\) | −3.18067e58 | −0.465807 | ||||||||
\(253\) | 1.40414e59 | 1.86620 | ||||||||
\(254\) | −1.87242e58 | −0.225932 | ||||||||
\(255\) | −1.56731e59 | −1.71759 | ||||||||
\(256\) | 6.27710e57 | 0.0625000 | ||||||||
\(257\) | −1.39270e58 | −0.126036 | −0.0630180 | − | 0.998012i | \(-0.520073\pi\) | ||||
−0.0630180 | + | 0.998012i | \(0.520073\pi\) | |||||||
\(258\) | 3.95522e58 | 0.325453 | ||||||||
\(259\) | −1.29298e59 | −0.967712 | ||||||||
\(260\) | −9.02322e58 | −0.614489 | ||||||||
\(261\) | −8.50692e57 | −0.0527327 | ||||||||
\(262\) | 5.57139e58 | 0.314472 | ||||||||
\(263\) | 1.50291e59 | 0.772710 | 0.386355 | − | 0.922350i | \(-0.373734\pi\) | ||||
0.386355 | + | 0.922350i | \(0.373734\pi\) | |||||||
\(264\) | 1.66705e59 | 0.781001 | ||||||||
\(265\) | 5.88493e59 | 2.51314 | ||||||||
\(266\) | −1.60438e59 | −0.624753 | ||||||||
\(267\) | −4.71250e59 | −1.67389 | ||||||||
\(268\) | 8.31889e58 | 0.269627 | ||||||||
\(269\) | 4.46165e59 | 1.31997 | 0.659986 | − | 0.751278i | \(-0.270562\pi\) | ||||
0.659986 | + | 0.751278i | \(0.270562\pi\) | |||||||
\(270\) | −5.31174e58 | −0.143491 | ||||||||
\(271\) | −1.87553e59 | −0.462782 | −0.231391 | − | 0.972861i | \(-0.574328\pi\) | ||||
−0.231391 | + | 0.972861i | \(0.574328\pi\) | |||||||
\(272\) | −7.86944e58 | −0.177421 | ||||||||
\(273\) | 4.80146e59 | 0.989438 | ||||||||
\(274\) | 4.81721e59 | 0.907626 | ||||||||
\(275\) | −1.90476e60 | −3.28238 | ||||||||
\(276\) | 5.13374e59 | 0.809397 | ||||||||
\(277\) | −5.17979e59 | −0.747408 | −0.373704 | − | 0.927548i | \(-0.621912\pi\) | ||||
−0.373704 | + | 0.927548i | \(0.621912\pi\) | |||||||
\(278\) | −3.48709e59 | −0.460645 | ||||||||
\(279\) | −1.88180e59 | −0.227651 | ||||||||
\(280\) | 5.67196e59 | 0.628581 | ||||||||
\(281\) | −1.19166e60 | −1.21017 | −0.605085 | − | 0.796161i | \(-0.706861\pi\) | ||||
−0.605085 | + | 0.796161i | \(0.706861\pi\) | |||||||
\(282\) | −2.40350e59 | −0.223738 | ||||||||
\(283\) | 2.07435e60 | 1.77058 | 0.885288 | − | 0.465044i | \(-0.153961\pi\) | ||||
0.885288 | + | 0.465044i | \(0.153961\pi\) | |||||||
\(284\) | −7.21936e59 | −0.565197 | ||||||||
\(285\) | 2.92758e60 | 2.10285 | ||||||||
\(286\) | −1.20321e60 | −0.793180 | ||||||||
\(287\) | −1.09468e59 | −0.0662492 | ||||||||
\(288\) | 2.91413e59 | 0.161955 | ||||||||
\(289\) | −9.72261e59 | −0.496347 | ||||||||
\(290\) | 1.51700e59 | 0.0711599 | ||||||||
\(291\) | −5.10297e60 | −2.20011 | ||||||||
\(292\) | −1.45787e60 | −0.577880 | ||||||||
\(293\) | 4.37111e60 | 1.59344 | 0.796719 | − | 0.604350i | \(-0.206567\pi\) | ||||
0.796719 | + | 0.604350i | \(0.206567\pi\) | |||||||
\(294\) | −9.93450e58 | −0.0333147 | ||||||||
\(295\) | 9.99814e60 | 3.08518 | ||||||||
\(296\) | 1.18462e60 | 0.336460 | ||||||||
\(297\) | −7.08297e59 | −0.185218 | ||||||||
\(298\) | 4.45413e60 | 1.07267 | ||||||||
\(299\) | −3.70533e60 | −0.822020 | ||||||||
\(300\) | −6.96408e60 | −1.42362 | ||||||||
\(301\) | 1.79447e60 | 0.338108 | ||||||||
\(302\) | −4.99666e59 | −0.0867979 | ||||||||
\(303\) | −1.64902e61 | −2.64169 | ||||||||
\(304\) | 1.46994e60 | 0.217218 | ||||||||
\(305\) | 3.31623e60 | 0.452167 | ||||||||
\(306\) | −3.65337e60 | −0.459747 | ||||||||
\(307\) | −4.69486e60 | −0.545421 | −0.272711 | − | 0.962096i | \(-0.587920\pi\) | ||||
−0.272711 | + | 0.962096i | \(0.587920\pi\) | |||||||
\(308\) | 7.56330e60 | 0.811370 | ||||||||
\(309\) | −2.94603e60 | −0.291914 | ||||||||
\(310\) | 3.35573e60 | 0.307203 | ||||||||
\(311\) | −1.13490e61 | −0.960127 | −0.480063 | − | 0.877234i | \(-0.659386\pi\) | ||||
−0.480063 | + | 0.877234i | \(0.659386\pi\) | |||||||
\(312\) | −4.39910e60 | −0.344014 | ||||||||
\(313\) | 2.24105e61 | 1.62037 | 0.810186 | − | 0.586173i | \(-0.199366\pi\) | ||||
0.810186 | + | 0.586173i | \(0.199366\pi\) | |||||||
\(314\) | −1.20201e60 | −0.0803767 | ||||||||
\(315\) | 2.63320e61 | 1.62883 | ||||||||
\(316\) | 3.61824e60 | 0.207092 | ||||||||
\(317\) | −1.97282e61 | −1.04505 | −0.522523 | − | 0.852625i | \(-0.675009\pi\) | ||||
−0.522523 | + | 0.852625i | \(0.675009\pi\) | |||||||
\(318\) | 2.86908e61 | 1.40695 | ||||||||
\(319\) | 2.02286e60 | 0.0918530 | ||||||||
\(320\) | −5.19665e60 | −0.218549 | ||||||||
\(321\) | −3.13895e61 | −1.22296 | ||||||||
\(322\) | 2.32915e61 | 0.840871 | ||||||||
\(323\) | −1.84282e61 | −0.616625 | ||||||||
\(324\) | −1.73566e61 | −0.538408 | ||||||||
\(325\) | 5.02638e61 | 1.44582 | ||||||||
\(326\) | −1.44752e61 | −0.386184 | ||||||||
\(327\) | 2.14371e61 | 0.530574 | ||||||||
\(328\) | 1.00295e60 | 0.0230339 | ||||||||
\(329\) | −1.09045e61 | −0.232438 | ||||||||
\(330\) | −1.38010e62 | −2.73099 | ||||||||
\(331\) | −8.48788e60 | −0.155960 | −0.0779801 | − | 0.996955i | \(-0.524847\pi\) | ||||
−0.0779801 | + | 0.996955i | \(0.524847\pi\) | |||||||
\(332\) | 2.41611e61 | 0.412319 | ||||||||
\(333\) | 5.49959e61 | 0.871859 | ||||||||
\(334\) | 3.03456e60 | 0.0447000 | ||||||||
\(335\) | −6.88699e61 | −0.942826 | ||||||||
\(336\) | 2.76526e61 | 0.351903 | ||||||||
\(337\) | −1.13716e62 | −1.34552 | −0.672760 | − | 0.739861i | \(-0.734891\pi\) | ||||
−0.672760 | + | 0.739861i | \(0.734891\pi\) | |||||||
\(338\) | −3.25097e61 | −0.357728 | ||||||||
\(339\) | 1.87949e62 | 1.92375 | ||||||||
\(340\) | 6.51490e61 | 0.620404 | ||||||||
\(341\) | 4.47471e61 | 0.396536 | ||||||||
\(342\) | 6.82414e61 | 0.562871 | ||||||||
\(343\) | 1.27919e62 | 0.982265 | ||||||||
\(344\) | −1.64409e61 | −0.117556 | ||||||||
\(345\) | −4.25009e62 | −2.83029 | ||||||||
\(346\) | 1.35804e62 | 0.842456 | ||||||||
\(347\) | 1.85460e62 | 1.07196 | 0.535979 | − | 0.844231i | \(-0.319943\pi\) | ||||
0.535979 | + | 0.844231i | \(0.319943\pi\) | |||||||
\(348\) | 7.39586e60 | 0.0398380 | ||||||||
\(349\) | 1.74990e62 | 0.878598 | 0.439299 | − | 0.898341i | \(-0.355227\pi\) | ||||
0.439299 | + | 0.898341i | \(0.355227\pi\) | |||||||
\(350\) | −3.15957e62 | −1.47897 | ||||||||
\(351\) | 1.86909e61 | 0.0815843 | ||||||||
\(352\) | −6.92949e61 | −0.282102 | ||||||||
\(353\) | −4.46780e62 | −1.69673 | −0.848367 | − | 0.529409i | \(-0.822414\pi\) | ||||
−0.848367 | + | 0.529409i | \(0.822414\pi\) | |||||||
\(354\) | 4.87440e62 | 1.72720 | ||||||||
\(355\) | 5.97672e62 | 1.97637 | ||||||||
\(356\) | 1.95887e62 | 0.604618 | ||||||||
\(357\) | −3.46673e62 | −0.998961 | ||||||||
\(358\) | −1.59880e62 | −0.430190 | ||||||||
\(359\) | −6.15371e62 | −1.54640 | −0.773202 | − | 0.634160i | \(-0.781346\pi\) | ||||
−0.773202 | + | 0.634160i | \(0.781346\pi\) | |||||||
\(360\) | −2.41253e62 | −0.566320 | ||||||||
\(361\) | −1.11739e62 | −0.245063 | ||||||||
\(362\) | 2.64408e62 | 0.541894 | ||||||||
\(363\) | −1.11766e63 | −2.14090 | ||||||||
\(364\) | −1.99585e62 | −0.357391 | ||||||||
\(365\) | 1.20693e63 | 2.02072 | ||||||||
\(366\) | 1.61676e62 | 0.253140 | ||||||||
\(367\) | 1.78399e62 | 0.261261 | 0.130631 | − | 0.991431i | \(-0.458300\pi\) | ||||
0.130631 | + | 0.991431i | \(0.458300\pi\) | |||||||
\(368\) | −2.13397e62 | −0.292359 | ||||||||
\(369\) | 4.65615e61 | 0.0596872 | ||||||||
\(370\) | −9.80718e62 | −1.17653 | ||||||||
\(371\) | 1.30169e63 | 1.46166 | ||||||||
\(372\) | 1.63602e62 | 0.171983 | ||||||||
\(373\) | −6.15312e61 | −0.0605661 | −0.0302830 | − | 0.999541i | \(-0.509641\pi\) | ||||
−0.0302830 | + | 0.999541i | \(0.509641\pi\) | |||||||
\(374\) | 8.68733e62 | 0.800814 | ||||||||
\(375\) | 2.96240e63 | 2.55786 | ||||||||
\(376\) | 9.99073e61 | 0.0808156 | ||||||||
\(377\) | −5.33802e61 | −0.0404592 | ||||||||
\(378\) | −1.17491e62 | −0.0834553 | ||||||||
\(379\) | −1.93924e63 | −1.29113 | −0.645567 | − | 0.763704i | \(-0.723379\pi\) | ||||
−0.645567 | + | 0.763704i | \(0.723379\pi\) | |||||||
\(380\) | −1.21692e63 | −0.759564 | ||||||||
\(381\) | 7.55736e62 | 0.442291 | ||||||||
\(382\) | −1.90016e63 | −1.04289 | ||||||||
\(383\) | 4.92299e61 | 0.0253430 | 0.0126715 | − | 0.999920i | \(-0.495966\pi\) | ||||
0.0126715 | + | 0.999920i | \(0.495966\pi\) | |||||||
\(384\) | −2.53352e62 | −0.122352 | ||||||||
\(385\) | −6.26146e63 | −2.83719 | ||||||||
\(386\) | 9.82589e62 | 0.417814 | ||||||||
\(387\) | −7.63264e62 | −0.304619 | ||||||||
\(388\) | 2.12118e63 | 0.794693 | ||||||||
\(389\) | 1.52402e63 | 0.536075 | 0.268038 | − | 0.963408i | \(-0.413625\pi\) | ||||
0.268038 | + | 0.963408i | \(0.413625\pi\) | |||||||
\(390\) | 3.64189e63 | 1.20294 | ||||||||
\(391\) | 2.67530e63 | 0.829931 | ||||||||
\(392\) | 4.12952e61 | 0.0120335 | ||||||||
\(393\) | −2.24869e63 | −0.615619 | ||||||||
\(394\) | 1.06743e63 | 0.274588 | ||||||||
\(395\) | −2.99545e63 | −0.724157 | ||||||||
\(396\) | −3.21700e63 | −0.731003 | ||||||||
\(397\) | −4.22139e63 | −0.901753 | −0.450877 | − | 0.892586i | \(-0.648889\pi\) | ||||
−0.450877 | + | 0.892586i | \(0.648889\pi\) | |||||||
\(398\) | −2.32881e63 | −0.467734 | ||||||||
\(399\) | 6.47551e63 | 1.22303 | ||||||||
\(400\) | 2.89479e63 | 0.514218 | ||||||||
\(401\) | 7.10002e63 | 1.18638 | 0.593188 | − | 0.805064i | \(-0.297869\pi\) | ||||
0.593188 | + | 0.805064i | \(0.297869\pi\) | |||||||
\(402\) | −3.35762e63 | −0.527829 | ||||||||
\(403\) | −1.18081e63 | −0.174665 | ||||||||
\(404\) | 6.85458e63 | 0.954195 | ||||||||
\(405\) | 1.43691e64 | 1.88270 | ||||||||
\(406\) | 3.35546e62 | 0.0413871 | ||||||||
\(407\) | −1.30774e64 | −1.51866 | ||||||||
\(408\) | 3.17621e63 | 0.347325 | ||||||||
\(409\) | −4.19928e63 | −0.432468 | −0.216234 | − | 0.976342i | \(-0.569377\pi\) | ||||
−0.216234 | + | 0.976342i | \(0.569377\pi\) | |||||||
\(410\) | −8.30312e62 | −0.0805447 | ||||||||
\(411\) | −1.94429e64 | −1.77679 | ||||||||
\(412\) | 1.22459e63 | 0.105441 | ||||||||
\(413\) | 2.21149e64 | 1.79436 | ||||||||
\(414\) | −9.90691e63 | −0.757582 | ||||||||
\(415\) | −2.00023e64 | −1.44179 | ||||||||
\(416\) | 1.82859e63 | 0.124260 | ||||||||
\(417\) | 1.40744e64 | 0.901771 | ||||||||
\(418\) | −1.62271e64 | −0.980442 | ||||||||
\(419\) | 2.50397e64 | 1.42687 | 0.713436 | − | 0.700720i | \(-0.247138\pi\) | ||||
0.713436 | + | 0.700720i | \(0.247138\pi\) | |||||||
\(420\) | −2.28928e64 | −1.23053 | ||||||||
\(421\) | −2.02007e63 | −0.102437 | −0.0512184 | − | 0.998687i | \(-0.516310\pi\) | ||||
−0.0512184 | + | 0.998687i | \(0.516310\pi\) | |||||||
\(422\) | 9.46712e62 | 0.0452963 | ||||||||
\(423\) | 4.63818e63 | 0.209415 | ||||||||
\(424\) | −1.19261e64 | −0.508199 | ||||||||
\(425\) | −3.62913e64 | −1.45973 | ||||||||
\(426\) | 2.91383e64 | 1.10644 | ||||||||
\(427\) | 7.33518e63 | 0.262983 | ||||||||
\(428\) | 1.30478e64 | 0.441739 | ||||||||
\(429\) | 4.85630e64 | 1.55275 | ||||||||
\(430\) | 1.36110e64 | 0.411066 | ||||||||
\(431\) | −6.45676e64 | −1.84213 | −0.921067 | − | 0.389403i | \(-0.872681\pi\) | ||||
−0.921067 | + | 0.389403i | \(0.872681\pi\) | |||||||
\(432\) | 1.07645e63 | 0.0290162 | ||||||||
\(433\) | 5.64458e64 | 1.43773 | 0.718867 | − | 0.695148i | \(-0.244661\pi\) | ||||
0.718867 | + | 0.695148i | \(0.244661\pi\) | |||||||
\(434\) | 7.42254e63 | 0.178671 | ||||||||
\(435\) | −6.12283e63 | −0.139305 | ||||||||
\(436\) | −8.91086e63 | −0.191646 | ||||||||
\(437\) | −4.99721e64 | −1.01609 | ||||||||
\(438\) | 5.88415e64 | 1.13127 | ||||||||
\(439\) | 4.39799e64 | 0.799602 | 0.399801 | − | 0.916602i | \(-0.369079\pi\) | ||||
0.399801 | + | 0.916602i | \(0.369079\pi\) | |||||||
\(440\) | 5.73675e64 | 0.986450 | ||||||||
\(441\) | 1.91712e63 | 0.0311820 | ||||||||
\(442\) | −2.29246e64 | −0.352741 | ||||||||
\(443\) | 5.44392e64 | 0.792538 | 0.396269 | − | 0.918134i | \(-0.370305\pi\) | ||||
0.396269 | + | 0.918134i | \(0.370305\pi\) | |||||||
\(444\) | −4.78130e64 | −0.658663 | ||||||||
\(445\) | −1.62170e65 | −2.11422 | ||||||||
\(446\) | −1.12523e65 | −1.38847 | ||||||||
\(447\) | −1.79775e65 | −2.09988 | ||||||||
\(448\) | −1.14945e64 | −0.127109 | ||||||||
\(449\) | 6.51981e64 | 0.682652 | 0.341326 | − | 0.939945i | \(-0.389124\pi\) | ||||
0.341326 | + | 0.939945i | \(0.389124\pi\) | |||||||
\(450\) | 1.34390e65 | 1.33248 | ||||||||
\(451\) | −1.10718e64 | −0.103967 | ||||||||
\(452\) | −7.81258e64 | −0.694869 | ||||||||
\(453\) | 2.01672e64 | 0.169918 | ||||||||
\(454\) | 2.97678e64 | 0.237617 | ||||||||
\(455\) | 1.65231e65 | 1.24972 | ||||||||
\(456\) | −5.93286e64 | −0.425232 | ||||||||
\(457\) | 1.64423e65 | 1.11691 | 0.558453 | − | 0.829536i | \(-0.311395\pi\) | ||||
0.558453 | + | 0.829536i | \(0.311395\pi\) | |||||||
\(458\) | 2.38775e64 | 0.153739 | ||||||||
\(459\) | −1.34951e64 | −0.0823696 | ||||||||
\(460\) | 1.76666e65 | 1.02232 | ||||||||
\(461\) | 7.21325e64 | 0.395784 | 0.197892 | − | 0.980224i | \(-0.436590\pi\) | ||||
0.197892 | + | 0.980224i | \(0.436590\pi\) | |||||||
\(462\) | −3.05265e65 | −1.58836 | ||||||||
\(463\) | 1.94522e65 | 0.959916 | 0.479958 | − | 0.877291i | \(-0.340652\pi\) | ||||
0.479958 | + | 0.877291i | \(0.340652\pi\) | |||||||
\(464\) | −3.07427e63 | −0.0143897 | ||||||||
\(465\) | −1.35442e65 | −0.601388 | ||||||||
\(466\) | 1.03122e65 | 0.434408 | ||||||||
\(467\) | −7.84448e64 | −0.313545 | −0.156773 | − | 0.987635i | \(-0.550109\pi\) | ||||
−0.156773 | + | 0.987635i | \(0.550109\pi\) | |||||||
\(468\) | 8.48921e64 | 0.321991 | ||||||||
\(469\) | −1.52334e65 | −0.548354 | ||||||||
\(470\) | −8.27106e64 | −0.282595 | ||||||||
\(471\) | 4.85146e64 | 0.157348 | ||||||||
\(472\) | −2.02617e65 | −0.623873 | ||||||||
\(473\) | 1.81496e65 | 0.530603 | ||||||||
\(474\) | −1.46037e65 | −0.405410 | ||||||||
\(475\) | 6.77886e65 | 1.78716 | ||||||||
\(476\) | 1.44103e65 | 0.360831 | ||||||||
\(477\) | −5.53665e65 | −1.31688 | ||||||||
\(478\) | −3.14386e65 | −0.710362 | ||||||||
\(479\) | −3.87609e65 | −0.832097 | −0.416048 | − | 0.909342i | \(-0.636585\pi\) | ||||
−0.416048 | + | 0.909342i | \(0.636585\pi\) | |||||||
\(480\) | 2.09744e65 | 0.427838 | ||||||||
\(481\) | 3.45095e65 | 0.668935 | ||||||||
\(482\) | 2.36627e65 | 0.435925 | ||||||||
\(483\) | −9.40079e65 | −1.64611 | ||||||||
\(484\) | 4.64582e65 | 0.773305 | ||||||||
\(485\) | −1.75607e66 | −2.77887 | ||||||||
\(486\) | 6.45988e65 | 0.971933 | ||||||||
\(487\) | 8.09553e65 | 1.15821 | 0.579103 | − | 0.815255i | \(-0.303403\pi\) | ||||
0.579103 | + | 0.815255i | \(0.303403\pi\) | |||||||
\(488\) | −6.72049e64 | −0.0914355 | ||||||||
\(489\) | 5.84241e65 | 0.756005 | ||||||||
\(490\) | −3.41872e64 | −0.0420785 | ||||||||
\(491\) | −1.15921e66 | −1.35727 | −0.678634 | − | 0.734477i | \(-0.737428\pi\) | ||||
−0.678634 | + | 0.734477i | \(0.737428\pi\) | |||||||
\(492\) | −4.04803e64 | −0.0450919 | ||||||||
\(493\) | 3.85414e64 | 0.0408486 | ||||||||
\(494\) | 4.28210e65 | 0.431863 | ||||||||
\(495\) | 2.66327e66 | 2.55616 | ||||||||
\(496\) | −6.80052e64 | −0.0621214 | ||||||||
\(497\) | 1.32199e66 | 1.14947 | ||||||||
\(498\) | −9.75175e65 | −0.807167 | ||||||||
\(499\) | 1.98775e66 | 1.56638 | 0.783191 | − | 0.621781i | \(-0.213591\pi\) | ||||
0.783191 | + | 0.621781i | \(0.213591\pi\) | |||||||
\(500\) | −1.23139e66 | −0.923915 | ||||||||
\(501\) | −1.22479e65 | −0.0875061 | ||||||||
\(502\) | 3.68902e65 | 0.250998 | ||||||||
\(503\) | −1.31100e66 | −0.849548 | −0.424774 | − | 0.905300i | \(-0.639646\pi\) | ||||
−0.424774 | + | 0.905300i | \(0.639646\pi\) | |||||||
\(504\) | −5.33629e65 | −0.329375 | ||||||||
\(505\) | −5.67472e66 | −3.33661 | ||||||||
\(506\) | 2.35576e66 | 1.31960 | ||||||||
\(507\) | 1.31213e66 | 0.700299 | ||||||||
\(508\) | −3.14141e65 | −0.159758 | ||||||||
\(509\) | 7.52616e65 | 0.364744 | 0.182372 | − | 0.983230i | \(-0.441623\pi\) | ||||
0.182372 | + | 0.983230i | \(0.441623\pi\) | |||||||
\(510\) | −2.62950e66 | −1.21452 | ||||||||
\(511\) | 2.66961e66 | 1.17526 | ||||||||
\(512\) | 1.05312e65 | 0.0441942 | ||||||||
\(513\) | 2.52076e65 | 0.100846 | ||||||||
\(514\) | −2.33656e65 | −0.0891210 | ||||||||
\(515\) | −1.01381e66 | −0.368704 | ||||||||
\(516\) | 6.63576e65 | 0.230130 | ||||||||
\(517\) | −1.10291e66 | −0.364772 | ||||||||
\(518\) | −2.16925e66 | −0.684275 | ||||||||
\(519\) | −5.48123e66 | −1.64922 | ||||||||
\(520\) | −1.51384e66 | −0.434510 | ||||||||
\(521\) | 2.28801e66 | 0.626519 | 0.313260 | − | 0.949667i | \(-0.398579\pi\) | ||||
0.313260 | + | 0.949667i | \(0.398579\pi\) | |||||||
\(522\) | −1.42722e65 | −0.0372877 | ||||||||
\(523\) | 3.63925e65 | 0.0907237 | 0.0453618 | − | 0.998971i | \(-0.485556\pi\) | ||||
0.0453618 | + | 0.998971i | \(0.485556\pi\) | |||||||
\(524\) | 9.34724e65 | 0.222365 | ||||||||
\(525\) | 1.27524e67 | 2.89528 | ||||||||
\(526\) | 2.52146e66 | 0.546389 | ||||||||
\(527\) | 8.52564e65 | 0.176347 | ||||||||
\(528\) | 2.79684e66 | 0.552251 | ||||||||
\(529\) | 1.94992e66 | 0.367581 | ||||||||
\(530\) | 9.87327e66 | 1.77706 | ||||||||
\(531\) | −9.40644e66 | −1.61663 | ||||||||
\(532\) | −2.69171e66 | −0.441767 | ||||||||
\(533\) | 2.92170e65 | 0.0457951 | ||||||||
\(534\) | −7.90627e66 | −1.18362 | ||||||||
\(535\) | −1.08019e67 | −1.54466 | ||||||||
\(536\) | 1.39568e66 | 0.190655 | ||||||||
\(537\) | 6.45299e66 | 0.842153 | ||||||||
\(538\) | 7.48541e66 | 0.933362 | ||||||||
\(539\) | −4.55871e65 | −0.0543147 | ||||||||
\(540\) | −8.91163e65 | −0.101464 | ||||||||
\(541\) | −1.63939e67 | −1.78382 | −0.891908 | − | 0.452218i | \(-0.850633\pi\) | ||||
−0.891908 | + | 0.452218i | \(0.850633\pi\) | |||||||
\(542\) | −3.14662e66 | −0.327236 | ||||||||
\(543\) | −1.06719e67 | −1.06083 | ||||||||
\(544\) | −1.32027e66 | −0.125456 | ||||||||
\(545\) | 7.37707e66 | 0.670146 | ||||||||
\(546\) | 8.05552e66 | 0.699638 | ||||||||
\(547\) | 1.43390e67 | 1.19078 | 0.595388 | − | 0.803439i | \(-0.296999\pi\) | ||||
0.595388 | + | 0.803439i | \(0.296999\pi\) | |||||||
\(548\) | 8.08194e66 | 0.641788 | ||||||||
\(549\) | −3.11997e66 | −0.236934 | ||||||||
\(550\) | −3.19565e67 | −2.32099 | ||||||||
\(551\) | −7.19915e65 | −0.0500112 | ||||||||
\(552\) | 8.61299e66 | 0.572330 | ||||||||
\(553\) | −6.62563e66 | −0.421174 | ||||||||
\(554\) | −8.69024e66 | −0.528497 | ||||||||
\(555\) | 3.95831e67 | 2.30320 | ||||||||
\(556\) | −5.85037e66 | −0.325725 | ||||||||
\(557\) | 1.82851e67 | 0.974193 | 0.487097 | − | 0.873348i | \(-0.338056\pi\) | ||||
0.487097 | + | 0.873348i | \(0.338056\pi\) | |||||||
\(558\) | −3.15713e66 | −0.160973 | ||||||||
\(559\) | −4.78942e66 | −0.233719 | ||||||||
\(560\) | 9.51597e66 | 0.444474 | ||||||||
\(561\) | −3.50632e67 | −1.56770 | ||||||||
\(562\) | −1.99927e67 | −0.855720 | ||||||||
\(563\) | −2.90085e67 | −1.18869 | −0.594346 | − | 0.804209i | \(-0.702589\pi\) | ||||
−0.594346 | + | 0.804209i | \(0.702589\pi\) | |||||||
\(564\) | −4.03240e66 | −0.158207 | ||||||||
\(565\) | 6.46783e67 | 2.42981 | ||||||||
\(566\) | 3.48018e67 | 1.25199 | ||||||||
\(567\) | 3.17830e67 | 1.09499 | ||||||||
\(568\) | −1.21121e67 | −0.399654 | ||||||||
\(569\) | −4.00130e66 | −0.126459 | −0.0632296 | − | 0.997999i | \(-0.520140\pi\) | ||||
−0.0632296 | + | 0.997999i | \(0.520140\pi\) | |||||||
\(570\) | 4.91166e67 | 1.48694 | ||||||||
\(571\) | −4.01640e67 | −1.16480 | −0.582401 | − | 0.812902i | \(-0.697887\pi\) | ||||
−0.582401 | + | 0.812902i | \(0.697887\pi\) | |||||||
\(572\) | −2.01864e67 | −0.560863 | ||||||||
\(573\) | 7.66932e67 | 2.04159 | ||||||||
\(574\) | −1.83657e66 | −0.0468453 | ||||||||
\(575\) | −9.84116e67 | −2.40538 | ||||||||
\(576\) | 4.88910e66 | 0.114519 | ||||||||
\(577\) | −4.66796e67 | −1.04790 | −0.523950 | − | 0.851749i | \(-0.675542\pi\) | ||||
−0.523950 | + | 0.851749i | \(0.675542\pi\) | |||||||
\(578\) | −1.63118e67 | −0.350970 | ||||||||
\(579\) | −3.96586e67 | −0.817924 | ||||||||
\(580\) | 2.54511e66 | 0.0503177 | ||||||||
\(581\) | −4.42432e67 | −0.838554 | ||||||||
\(582\) | −8.56136e67 | −1.55571 | ||||||||
\(583\) | 1.31656e68 | 2.29382 | ||||||||
\(584\) | −2.44589e67 | −0.408623 | ||||||||
\(585\) | −7.02799e67 | −1.12593 | ||||||||
\(586\) | 7.33351e67 | 1.12673 | ||||||||
\(587\) | 2.48745e67 | 0.366539 | 0.183270 | − | 0.983063i | \(-0.441332\pi\) | ||||
0.183270 | + | 0.983063i | \(0.441332\pi\) | |||||||
\(588\) | −1.66673e66 | −0.0235571 | ||||||||
\(589\) | −1.59251e67 | −0.215902 | ||||||||
\(590\) | 1.67741e68 | 2.18155 | ||||||||
\(591\) | −4.30830e67 | −0.537542 | ||||||||
\(592\) | 1.98747e67 | 0.237913 | ||||||||
\(593\) | 4.14071e66 | 0.0475592 | 0.0237796 | − | 0.999717i | \(-0.492430\pi\) | ||||
0.0237796 | + | 0.999717i | \(0.492430\pi\) | |||||||
\(594\) | −1.18833e67 | −0.130969 | ||||||||
\(595\) | −1.19299e68 | −1.26175 | ||||||||
\(596\) | 7.47279e67 | 0.758489 | ||||||||
\(597\) | 9.39940e67 | 0.915649 | ||||||||
\(598\) | −6.21650e67 | −0.581256 | ||||||||
\(599\) | 2.10487e68 | 1.88915 | 0.944577 | − | 0.328291i | \(-0.106473\pi\) | ||||
0.944577 | + | 0.328291i | \(0.106473\pi\) | |||||||
\(600\) | −1.16838e68 | −1.00665 | ||||||||
\(601\) | 1.59794e68 | 1.32171 | 0.660854 | − | 0.750514i | \(-0.270194\pi\) | ||||
0.660854 | + | 0.750514i | \(0.270194\pi\) | |||||||
\(602\) | 3.01061e67 | 0.239079 | ||||||||
\(603\) | 6.47941e67 | 0.494039 | ||||||||
\(604\) | −8.38300e66 | −0.0613754 | ||||||||
\(605\) | −3.84615e68 | −2.70408 | ||||||||
\(606\) | −2.76660e68 | −1.86796 | ||||||||
\(607\) | 2.59164e68 | 1.68055 | 0.840275 | − | 0.542160i | \(-0.182393\pi\) | ||||
0.840275 | + | 0.542160i | \(0.182393\pi\) | |||||||
\(608\) | 2.46614e67 | 0.153596 | ||||||||
\(609\) | −1.35431e67 | −0.0810205 | ||||||||
\(610\) | 5.56371e67 | 0.319730 | ||||||||
\(611\) | 2.91042e67 | 0.160674 | ||||||||
\(612\) | −6.12934e67 | −0.325090 | ||||||||
\(613\) | −5.81382e67 | −0.296265 | −0.148132 | − | 0.988968i | \(-0.547326\pi\) | ||||
−0.148132 | + | 0.988968i | \(0.547326\pi\) | |||||||
\(614\) | −7.87666e67 | −0.385671 | ||||||||
\(615\) | 3.35125e67 | 0.157676 | ||||||||
\(616\) | 1.26891e68 | 0.573725 | ||||||||
\(617\) | −3.39743e68 | −1.47626 | −0.738131 | − | 0.674657i | \(-0.764291\pi\) | ||||
−0.738131 | + | 0.674657i | \(0.764291\pi\) | |||||||
\(618\) | −4.94262e67 | −0.206414 | ||||||||
\(619\) | 3.60992e67 | 0.144903 | 0.0724514 | − | 0.997372i | \(-0.476918\pi\) | ||||
0.0724514 | + | 0.997372i | \(0.476918\pi\) | |||||||
\(620\) | 5.62997e67 | 0.217225 | ||||||||
\(621\) | −3.65950e67 | −0.135731 | ||||||||
\(622\) | −1.90405e68 | −0.678912 | ||||||||
\(623\) | −3.58704e68 | −1.22964 | ||||||||
\(624\) | −7.38046e67 | −0.243254 | ||||||||
\(625\) | 3.70404e68 | 1.17386 | ||||||||
\(626\) | 3.75985e68 | 1.14578 | ||||||||
\(627\) | 6.54948e68 | 1.91934 | ||||||||
\(628\) | −2.01663e67 | −0.0568349 | ||||||||
\(629\) | −2.49164e68 | −0.675373 | ||||||||
\(630\) | 4.41777e68 | 1.15175 | ||||||||
\(631\) | −1.97407e68 | −0.495044 | −0.247522 | − | 0.968882i | \(-0.579616\pi\) | ||||
−0.247522 | + | 0.968882i | \(0.579616\pi\) | |||||||
\(632\) | 6.07040e67 | 0.146436 | ||||||||
\(633\) | −3.82106e67 | −0.0886733 | ||||||||
\(634\) | −3.30984e68 | −0.738959 | ||||||||
\(635\) | 2.60069e68 | 0.558640 | ||||||||
\(636\) | 4.81352e68 | 0.994864 | ||||||||
\(637\) | 1.20298e67 | 0.0239245 | ||||||||
\(638\) | 3.39379e67 | 0.0649498 | ||||||||
\(639\) | −5.62301e68 | −1.03561 | ||||||||
\(640\) | −8.71853e67 | −0.154537 | ||||||||
\(641\) | −8.01714e67 | −0.136772 | −0.0683861 | − | 0.997659i | \(-0.521785\pi\) | ||||
−0.0683861 | + | 0.997659i | \(0.521785\pi\) | |||||||
\(642\) | −5.26628e68 | −0.864760 | ||||||||
\(643\) | 1.38094e67 | 0.0218276 | 0.0109138 | − | 0.999940i | \(-0.496526\pi\) | ||||
0.0109138 | + | 0.999940i | \(0.496526\pi\) | |||||||
\(644\) | 3.90767e68 | 0.594586 | ||||||||
\(645\) | −5.49357e68 | −0.804715 | ||||||||
\(646\) | −3.09174e68 | −0.436020 | ||||||||
\(647\) | −3.29500e67 | −0.0447405 | −0.0223702 | − | 0.999750i | \(-0.507121\pi\) | ||||
−0.0223702 | + | 0.999750i | \(0.507121\pi\) | |||||||
\(648\) | −2.91195e68 | −0.380712 | ||||||||
\(649\) | 2.23675e69 | 2.81593 | ||||||||
\(650\) | 8.43287e68 | 1.02235 | ||||||||
\(651\) | −2.99584e68 | −0.349771 | ||||||||
\(652\) | −2.42854e68 | −0.273074 | ||||||||
\(653\) | −1.29443e69 | −1.40186 | −0.700929 | − | 0.713231i | \(-0.747231\pi\) | ||||
−0.700929 | + | 0.713231i | \(0.747231\pi\) | |||||||
\(654\) | 3.59655e68 | 0.375172 | ||||||||
\(655\) | −7.73833e68 | −0.777563 | ||||||||
\(656\) | 1.68266e67 | 0.0162874 | ||||||||
\(657\) | −1.13550e69 | −1.05885 | ||||||||
\(658\) | −1.82948e68 | −0.164359 | ||||||||
\(659\) | −1.29161e69 | −1.11799 | −0.558995 | − | 0.829171i | \(-0.688813\pi\) | ||||
−0.558995 | + | 0.829171i | \(0.688813\pi\) | |||||||
\(660\) | −2.31543e69 | −1.93110 | ||||||||
\(661\) | 9.63417e68 | 0.774245 | 0.387123 | − | 0.922028i | \(-0.373469\pi\) | ||||
0.387123 | + | 0.922028i | \(0.373469\pi\) | |||||||
\(662\) | −1.42403e68 | −0.110280 | ||||||||
\(663\) | 9.25269e68 | 0.690536 | ||||||||
\(664\) | 4.05356e68 | 0.291554 | ||||||||
\(665\) | 2.22840e69 | 1.54476 | ||||||||
\(666\) | 9.22677e68 | 0.616497 | ||||||||
\(667\) | 1.04513e68 | 0.0673114 | ||||||||
\(668\) | 5.09116e67 | 0.0316077 | ||||||||
\(669\) | 4.54158e69 | 2.71811 | ||||||||
\(670\) | −1.15545e69 | −0.666679 | ||||||||
\(671\) | 7.41896e68 | 0.412706 | ||||||||
\(672\) | 4.63933e68 | 0.248833 | ||||||||
\(673\) | 8.62520e68 | 0.446067 | 0.223034 | − | 0.974811i | \(-0.428404\pi\) | ||||
0.223034 | + | 0.974811i | \(0.428404\pi\) | |||||||
\(674\) | −1.90784e69 | −0.951426 | ||||||||
\(675\) | 4.96422e68 | 0.238731 | ||||||||
\(676\) | −5.45421e68 | −0.252952 | ||||||||
\(677\) | −2.63131e69 | −1.17693 | −0.588464 | − | 0.808524i | \(-0.700267\pi\) | ||||
−0.588464 | + | 0.808524i | \(0.700267\pi\) | |||||||
\(678\) | 3.15327e69 | 1.36030 | ||||||||
\(679\) | −3.88425e69 | −1.61621 | ||||||||
\(680\) | 1.09302e69 | 0.438692 | ||||||||
\(681\) | −1.20147e69 | −0.465167 | ||||||||
\(682\) | 7.50732e68 | 0.280393 | ||||||||
\(683\) | 1.91092e69 | 0.688551 | 0.344275 | − | 0.938869i | \(-0.388125\pi\) | ||||
0.344275 | + | 0.938869i | \(0.388125\pi\) | |||||||
\(684\) | 1.14490e69 | 0.398010 | ||||||||
\(685\) | −6.69082e69 | −2.24420 | ||||||||
\(686\) | 2.14612e69 | 0.694566 | ||||||||
\(687\) | −9.63727e68 | −0.300964 | ||||||||
\(688\) | −2.75832e68 | −0.0831243 | ||||||||
\(689\) | −3.47420e69 | −1.01038 | ||||||||
\(690\) | −7.13047e69 | −2.00132 | ||||||||
\(691\) | −3.63593e69 | −0.984926 | −0.492463 | − | 0.870333i | \(-0.663903\pi\) | ||||
−0.492463 | + | 0.870333i | \(0.663903\pi\) | |||||||
\(692\) | 2.27841e69 | 0.595706 | ||||||||
\(693\) | 5.89090e69 | 1.48668 | ||||||||
\(694\) | 3.11150e69 | 0.757989 | ||||||||
\(695\) | 4.84337e69 | 1.13899 | ||||||||
\(696\) | 1.24082e68 | 0.0281697 | ||||||||
\(697\) | −2.10951e68 | −0.0462358 | ||||||||
\(698\) | 2.93585e69 | 0.621263 | ||||||||
\(699\) | −4.16216e69 | −0.850409 | ||||||||
\(700\) | −5.30087e69 | −1.04579 | ||||||||
\(701\) | 8.99753e69 | 1.71408 | 0.857041 | − | 0.515248i | \(-0.172300\pi\) | ||||
0.857041 | + | 0.515248i | \(0.172300\pi\) | |||||||
\(702\) | 3.13582e68 | 0.0576888 | ||||||||
\(703\) | 4.65414e69 | 0.826863 | ||||||||
\(704\) | −1.16258e69 | −0.199476 | ||||||||
\(705\) | 3.33832e69 | 0.553215 | ||||||||
\(706\) | −7.49573e69 | −1.19977 | ||||||||
\(707\) | −1.25519e70 | −1.94060 | ||||||||
\(708\) | 8.17789e69 | 1.22131 | ||||||||
\(709\) | −7.36602e69 | −1.06267 | −0.531337 | − | 0.847160i | \(-0.678310\pi\) | ||||
−0.531337 | + | 0.847160i | \(0.678310\pi\) | |||||||
\(710\) | 1.00273e70 | 1.39751 | ||||||||
\(711\) | 2.81817e69 | 0.379457 | ||||||||
\(712\) | 3.28644e69 | 0.427529 | ||||||||
\(713\) | 2.31191e69 | 0.290588 | ||||||||
\(714\) | −5.81621e69 | −0.706372 | ||||||||
\(715\) | 1.67118e70 | 1.96122 | ||||||||
\(716\) | −2.68235e69 | −0.304191 | ||||||||
\(717\) | 1.26890e70 | 1.39062 | ||||||||
\(718\) | −1.03242e70 | −1.09347 | ||||||||
\(719\) | −7.15587e69 | −0.732495 | −0.366247 | − | 0.930518i | \(-0.619358\pi\) | ||||
−0.366247 | + | 0.930518i | \(0.619358\pi\) | |||||||
\(720\) | −4.04756e69 | −0.400449 | ||||||||
\(721\) | −2.24244e69 | −0.214441 | ||||||||
\(722\) | −1.87466e69 | −0.173285 | ||||||||
\(723\) | −9.55058e69 | −0.853378 | ||||||||
\(724\) | 4.43603e69 | 0.383177 | ||||||||
\(725\) | −1.41775e69 | −0.118391 | ||||||||
\(726\) | −1.87512e70 | −1.51384 | ||||||||
\(727\) | −1.60013e69 | −0.124900 | −0.0624501 | − | 0.998048i | \(-0.519891\pi\) | ||||
−0.0624501 | + | 0.998048i | \(0.519891\pi\) | |||||||
\(728\) | −3.34848e69 | −0.252714 | ||||||||
\(729\) | −1.13171e70 | −0.825866 | ||||||||
\(730\) | 2.02489e70 | 1.42887 | ||||||||
\(731\) | 3.45804e69 | 0.235968 | ||||||||
\(732\) | 2.71248e69 | 0.178997 | ||||||||
\(733\) | 2.09305e69 | 0.133577 | 0.0667887 | − | 0.997767i | \(-0.478725\pi\) | ||||
0.0667887 | + | 0.997767i | \(0.478725\pi\) | |||||||
\(734\) | 2.99304e69 | 0.184739 | ||||||||
\(735\) | 1.37984e69 | 0.0823740 | ||||||||
\(736\) | −3.58021e69 | −0.206729 | ||||||||
\(737\) | −1.54073e70 | −0.860546 | ||||||||
\(738\) | 7.81173e68 | 0.0422052 | ||||||||
\(739\) | 2.82972e70 | 1.47895 | 0.739477 | − | 0.673182i | \(-0.235073\pi\) | ||||
0.739477 | + | 0.673182i | \(0.235073\pi\) | |||||||
\(740\) | −1.64537e70 | −0.831930 | ||||||||
\(741\) | −1.72831e70 | −0.845427 | ||||||||
\(742\) | 2.18387e70 | 1.03355 | ||||||||
\(743\) | 3.69750e70 | 1.69310 | 0.846550 | − | 0.532310i | \(-0.178676\pi\) | ||||
0.846550 | + | 0.532310i | \(0.178676\pi\) | |||||||
\(744\) | 2.74478e69 | 0.121611 | ||||||||
\(745\) | −6.18653e70 | −2.65227 | ||||||||
\(746\) | −1.03232e69 | −0.0428267 | ||||||||
\(747\) | 1.88186e70 | 0.755495 | ||||||||
\(748\) | 1.45749e70 | 0.566261 | ||||||||
\(749\) | −2.38928e70 | −0.898386 | ||||||||
\(750\) | 4.97007e70 | 1.80868 | ||||||||
\(751\) | 3.61337e70 | 1.27272 | 0.636361 | − | 0.771391i | \(-0.280439\pi\) | ||||
0.636361 | + | 0.771391i | \(0.280439\pi\) | |||||||
\(752\) | 1.67617e69 | 0.0571452 | ||||||||
\(753\) | −1.48894e70 | −0.491361 | ||||||||
\(754\) | −8.95572e68 | −0.0286090 | ||||||||
\(755\) | 6.94006e69 | 0.214616 | ||||||||
\(756\) | −1.97116e69 | −0.0590118 | ||||||||
\(757\) | 3.99376e70 | 1.15753 | 0.578766 | − | 0.815493i | \(-0.303534\pi\) | ||||
0.578766 | + | 0.815493i | \(0.303534\pi\) | |||||||
\(758\) | −3.25351e70 | −0.912969 | ||||||||
\(759\) | −9.50816e70 | −2.58329 | ||||||||
\(760\) | −2.04165e70 | −0.537093 | ||||||||
\(761\) | 6.65810e70 | 1.69600 | 0.848000 | − | 0.529996i | \(-0.177807\pi\) | ||||
0.848000 | + | 0.529996i | \(0.177807\pi\) | |||||||
\(762\) | 1.26791e70 | 0.312747 | ||||||||
\(763\) | 1.63173e70 | 0.389761 | ||||||||
\(764\) | −3.18794e70 | −0.737435 | ||||||||
\(765\) | 5.07432e70 | 1.13677 | ||||||||
\(766\) | 8.25940e68 | 0.0179202 | ||||||||
\(767\) | −5.90246e70 | −1.24036 | ||||||||
\(768\) | −4.25055e69 | −0.0865157 | ||||||||
\(769\) | −5.73078e70 | −1.12984 | −0.564922 | − | 0.825144i | \(-0.691094\pi\) | ||||
−0.564922 | + | 0.825144i | \(0.691094\pi\) | |||||||
\(770\) | −1.05050e71 | −2.00619 | ||||||||
\(771\) | 9.43066e69 | 0.174466 | ||||||||
\(772\) | 1.64851e70 | 0.295439 | ||||||||
\(773\) | −6.58392e70 | −1.14311 | −0.571553 | − | 0.820565i | \(-0.693659\pi\) | ||||
−0.571553 | + | 0.820565i | \(0.693659\pi\) | |||||||
\(774\) | −1.28055e70 | −0.215398 | ||||||||
\(775\) | −3.13618e70 | −0.511104 | ||||||||
\(776\) | 3.55874e70 | 0.561933 | ||||||||
\(777\) | 8.75540e70 | 1.33956 | ||||||||
\(778\) | 2.55688e70 | 0.379062 | ||||||||
\(779\) | 3.94036e69 | 0.0566068 | ||||||||
\(780\) | 6.11009e70 | 0.850608 | ||||||||
\(781\) | 1.33709e71 | 1.80389 | ||||||||
\(782\) | 4.48841e70 | 0.586850 | ||||||||
\(783\) | −5.27201e68 | −0.00668056 | ||||||||
\(784\) | 6.92819e68 | 0.00850896 | ||||||||
\(785\) | 1.66952e70 | 0.198739 | ||||||||
\(786\) | −3.77267e70 | −0.435308 | ||||||||
\(787\) | 1.47428e71 | 1.64892 | 0.824460 | − | 0.565920i | \(-0.191479\pi\) | ||||
0.824460 | + | 0.565920i | \(0.191479\pi\) | |||||||
\(788\) | 1.79085e70 | 0.194163 | ||||||||
\(789\) | −1.01770e71 | −1.06963 | ||||||||
\(790\) | −5.02552e70 | −0.512056 | ||||||||
\(791\) | 1.43062e71 | 1.41319 | ||||||||
\(792\) | −5.39724e70 | −0.516897 | ||||||||
\(793\) | −1.95776e70 | −0.181788 | ||||||||
\(794\) | −7.08231e70 | −0.637636 | ||||||||
\(795\) | −3.98499e71 | −3.47882 | ||||||||
\(796\) | −3.90709e70 | −0.330738 | ||||||||
\(797\) | 3.58327e70 | 0.294138 | 0.147069 | − | 0.989126i | \(-0.453016\pi\) | ||||
0.147069 | + | 0.989126i | \(0.453016\pi\) | |||||||
\(798\) | 1.08641e71 | 0.864815 | ||||||||
\(799\) | −2.10137e70 | −0.162220 | ||||||||
\(800\) | 4.85666e70 | 0.363607 | ||||||||
\(801\) | 1.52572e71 | 1.10784 | ||||||||
\(802\) | 1.19119e71 | 0.838895 | ||||||||
\(803\) | 2.70010e71 | 1.84437 | ||||||||
\(804\) | −5.63315e70 | −0.373231 | ||||||||
\(805\) | −3.23506e71 | −2.07914 | ||||||||
\(806\) | −1.98107e70 | −0.123507 | ||||||||
\(807\) | −3.02122e71 | −1.82717 | ||||||||
\(808\) | 1.15001e71 | 0.674718 | ||||||||
\(809\) | 4.95238e70 | 0.281887 | 0.140943 | − | 0.990018i | \(-0.454986\pi\) | ||||
0.140943 | + | 0.990018i | \(0.454986\pi\) | |||||||
\(810\) | 2.41073e71 | 1.33127 | ||||||||
\(811\) | −3.54799e71 | −1.90095 | −0.950477 | − | 0.310796i | \(-0.899404\pi\) | ||||
−0.950477 | + | 0.310796i | \(0.899404\pi\) | |||||||
\(812\) | 5.62953e69 | 0.0292651 | ||||||||
\(813\) | 1.27002e71 | 0.640607 | ||||||||
\(814\) | −2.19403e71 | −1.07385 | ||||||||
\(815\) | 2.01053e71 | 0.954880 | ||||||||
\(816\) | 5.32880e70 | 0.245596 | ||||||||
\(817\) | −6.45928e70 | −0.288897 | ||||||||
\(818\) | −7.04522e70 | −0.305801 | ||||||||
\(819\) | −1.55452e71 | −0.654850 | ||||||||
\(820\) | −1.39303e70 | −0.0569537 | ||||||||
\(821\) | −1.95327e71 | −0.775095 | −0.387547 | − | 0.921850i | \(-0.626678\pi\) | ||||
−0.387547 | + | 0.921850i | \(0.626678\pi\) | |||||||
\(822\) | −3.26198e71 | −1.25638 | ||||||||
\(823\) | 2.05807e71 | 0.769421 | 0.384710 | − | 0.923037i | \(-0.374301\pi\) | ||||
0.384710 | + | 0.923037i | \(0.374301\pi\) | |||||||
\(824\) | 2.05452e70 | 0.0745581 | ||||||||
\(825\) | 1.28981e72 | 4.54364 | ||||||||
\(826\) | 3.71027e71 | 1.26880 | ||||||||
\(827\) | −8.99522e70 | −0.298625 | −0.149313 | − | 0.988790i | \(-0.547706\pi\) | ||||
−0.149313 | + | 0.988790i | \(0.547706\pi\) | |||||||
\(828\) | −1.66210e71 | −0.535691 | ||||||||
\(829\) | −4.10043e71 | −1.28305 | −0.641526 | − | 0.767102i | \(-0.721698\pi\) | ||||
−0.641526 | + | 0.767102i | \(0.721698\pi\) | |||||||
\(830\) | −3.35583e71 | −1.01950 | ||||||||
\(831\) | 3.50750e71 | 1.03460 | ||||||||
\(832\) | 3.06787e70 | 0.0878650 | ||||||||
\(833\) | −8.68569e69 | −0.0241547 | ||||||||
\(834\) | 2.36129e71 | 0.637648 | ||||||||
\(835\) | −4.21483e70 | −0.110525 | ||||||||
\(836\) | −2.72245e71 | −0.693277 | ||||||||
\(837\) | −1.16621e70 | −0.0288405 | ||||||||
\(838\) | 4.20096e71 | 1.00895 | ||||||||
\(839\) | −6.23847e69 | −0.0145516 | −0.00727579 | − | 0.999974i | \(-0.502316\pi\) | ||||
−0.00727579 | + | 0.999974i | \(0.502316\pi\) | |||||||
\(840\) | −3.84078e71 | −0.870115 | ||||||||
\(841\) | −4.52961e71 | −0.996687 | ||||||||
\(842\) | −3.38912e70 | −0.0724337 | ||||||||
\(843\) | 8.06932e71 | 1.67518 | ||||||||
\(844\) | 1.58832e70 | 0.0320293 | ||||||||
\(845\) | 4.51540e71 | 0.884518 | ||||||||
\(846\) | 7.78157e70 | 0.148079 | ||||||||
\(847\) | −8.50731e71 | −1.57271 | ||||||||
\(848\) | −2.00086e71 | −0.359351 | ||||||||
\(849\) | −1.40465e72 | −2.45092 | ||||||||
\(850\) | −6.08866e71 | −1.03219 | ||||||||
\(851\) | −6.75661e71 | −1.11290 | ||||||||
\(852\) | 4.88860e71 | 0.782375 | ||||||||
\(853\) | 1.20122e72 | 1.86798 | 0.933989 | − | 0.357301i | \(-0.116303\pi\) | ||||
0.933989 | + | 0.357301i | \(0.116303\pi\) | |||||||
\(854\) | 1.23064e71 | 0.185957 | ||||||||
\(855\) | −9.47834e71 | −1.39175 | ||||||||
\(856\) | 2.18906e71 | 0.312356 | ||||||||
\(857\) | 3.84535e71 | 0.533219 | 0.266610 | − | 0.963805i | \(-0.414097\pi\) | ||||
0.266610 | + | 0.963805i | \(0.414097\pi\) | |||||||
\(858\) | 8.14752e71 | 1.09796 | ||||||||
\(859\) | 4.56460e71 | 0.597820 | 0.298910 | − | 0.954281i | \(-0.403377\pi\) | ||||
0.298910 | + | 0.954281i | \(0.403377\pi\) | |||||||
\(860\) | 2.28354e71 | 0.290668 | ||||||||
\(861\) | 7.41264e70 | 0.0917056 | ||||||||
\(862\) | −1.08326e72 | −1.30259 | ||||||||
\(863\) | 9.22876e71 | 1.07865 | 0.539323 | − | 0.842099i | \(-0.318680\pi\) | ||||
0.539323 | + | 0.842099i | \(0.318680\pi\) | |||||||
\(864\) | 1.80598e70 | 0.0205176 | ||||||||
\(865\) | −1.88623e72 | −2.08306 | ||||||||
\(866\) | 9.47004e71 | 1.01663 | ||||||||
\(867\) | 6.58368e71 | 0.687070 | ||||||||
\(868\) | 1.24530e71 | 0.126339 | ||||||||
\(869\) | −6.70131e71 | −0.660960 | ||||||||
\(870\) | −1.02724e71 | −0.0985033 | ||||||||
\(871\) | 4.06578e71 | 0.379052 | ||||||||
\(872\) | −1.49499e71 | −0.135514 | ||||||||
\(873\) | 1.65214e72 | 1.45612 | ||||||||
\(874\) | −8.38392e71 | −0.718484 | ||||||||
\(875\) | 2.25490e72 | 1.87901 | ||||||||
\(876\) | 9.87196e71 | 0.799931 | ||||||||
\(877\) | 1.86935e72 | 1.47299 | 0.736496 | − | 0.676442i | \(-0.236479\pi\) | ||||
0.736496 | + | 0.676442i | \(0.236479\pi\) | |||||||
\(878\) | 7.37861e71 | 0.565404 | ||||||||
\(879\) | −2.95991e72 | −2.20572 | ||||||||
\(880\) | 9.62466e71 | 0.697525 | ||||||||
\(881\) | −2.06246e72 | −1.45370 | −0.726850 | − | 0.686796i | \(-0.759017\pi\) | ||||
−0.726850 | + | 0.686796i | \(0.759017\pi\) | |||||||
\(882\) | 3.21640e70 | 0.0220490 | ||||||||
\(883\) | 1.01095e72 | 0.674051 | 0.337026 | − | 0.941495i | \(-0.390579\pi\) | ||||
0.337026 | + | 0.941495i | \(0.390579\pi\) | |||||||
\(884\) | −3.84611e71 | −0.249426 | ||||||||
\(885\) | −6.77026e72 | −4.27066 | ||||||||
\(886\) | 9.13338e71 | 0.560409 | ||||||||
\(887\) | 3.84733e71 | 0.229631 | 0.114815 | − | 0.993387i | \(-0.463372\pi\) | ||||
0.114815 | + | 0.993387i | \(0.463372\pi\) | |||||||
\(888\) | −8.02169e71 | −0.465745 | ||||||||
\(889\) | 5.75247e71 | 0.324908 | ||||||||
\(890\) | −2.72076e72 | −1.49498 | ||||||||
\(891\) | 3.21460e72 | 1.71839 | ||||||||
\(892\) | −1.88782e72 | −0.981798 | ||||||||
\(893\) | 3.92515e71 | 0.198607 | ||||||||
\(894\) | −3.01612e72 | −1.48484 | ||||||||
\(895\) | 2.22064e72 | 1.06369 | ||||||||
\(896\) | −1.92845e71 | −0.0898799 | ||||||||
\(897\) | 2.50907e72 | 1.13788 | ||||||||
\(898\) | 1.09384e72 | 0.482708 | ||||||||
\(899\) | 3.33062e70 | 0.0143025 | ||||||||
\(900\) | 2.25469e72 | 0.942206 | ||||||||
\(901\) | 2.50843e72 | 1.02010 | ||||||||
\(902\) | −1.85755e71 | −0.0735156 | ||||||||
\(903\) | −1.21513e72 | −0.468027 | ||||||||
\(904\) | −1.31073e72 | −0.491347 | ||||||||
\(905\) | −3.67247e72 | −1.33989 | ||||||||
\(906\) | 3.38349e71 | 0.120150 | ||||||||
\(907\) | −1.65047e72 | −0.570465 | −0.285232 | − | 0.958458i | \(-0.592071\pi\) | ||||
−0.285232 | + | 0.958458i | \(0.592071\pi\) | |||||||
\(908\) | 4.99421e71 | 0.168021 | ||||||||
\(909\) | 5.33888e72 | 1.74838 | ||||||||
\(910\) | 2.77212e72 | 0.883684 | ||||||||
\(911\) | 1.74723e72 | 0.542188 | 0.271094 | − | 0.962553i | \(-0.412614\pi\) | ||||
0.271094 | + | 0.962553i | \(0.412614\pi\) | |||||||
\(912\) | −9.95369e71 | −0.300684 | ||||||||
\(913\) | −4.47485e72 | −1.31597 | ||||||||
\(914\) | 2.75856e72 | 0.789771 | ||||||||
\(915\) | −2.24559e72 | −0.625913 | ||||||||
\(916\) | 4.00597e71 | 0.108710 | ||||||||
\(917\) | −1.71164e72 | −0.452235 | ||||||||
\(918\) | −2.26411e71 | −0.0582441 | ||||||||
\(919\) | −2.26784e72 | −0.568044 | −0.284022 | − | 0.958818i | \(-0.591669\pi\) | ||||
−0.284022 | + | 0.958818i | \(0.591669\pi\) | |||||||
\(920\) | 2.96396e72 | 0.722887 | ||||||||
\(921\) | 3.17913e72 | 0.755000 | ||||||||
\(922\) | 1.21018e72 | 0.279861 | ||||||||
\(923\) | −3.52839e72 | −0.794576 | ||||||||
\(924\) | −5.12150e72 | −1.12314 | ||||||||
\(925\) | 9.16554e72 | 1.95743 | ||||||||
\(926\) | 3.26353e72 | 0.678763 | ||||||||
\(927\) | 9.53809e71 | 0.193200 | ||||||||
\(928\) | −5.15777e70 | −0.0101751 | ||||||||
\(929\) | −5.22436e72 | −1.00380 | −0.501901 | − | 0.864925i | \(-0.667366\pi\) | ||||
−0.501901 | + | 0.864925i | \(0.667366\pi\) | |||||||
\(930\) | −2.27233e72 | −0.425246 | ||||||||
\(931\) | 1.62240e71 | 0.0295728 | ||||||||
\(932\) | 1.73011e72 | 0.307173 | ||||||||
\(933\) | 7.68500e72 | 1.32906 | ||||||||
\(934\) | −1.31608e72 | −0.221710 | ||||||||
\(935\) | −1.20662e73 | −1.98009 | ||||||||
\(936\) | 1.42425e72 | 0.227682 | ||||||||
\(937\) | 2.17978e72 | 0.339464 | 0.169732 | − | 0.985490i | \(-0.445710\pi\) | ||||
0.169732 | + | 0.985490i | \(0.445710\pi\) | |||||||
\(938\) | −2.55573e72 | −0.387745 | ||||||||
\(939\) | −1.51753e73 | −2.24300 | ||||||||
\(940\) | −1.38765e72 | −0.199825 | ||||||||
\(941\) | −6.39953e72 | −0.897847 | −0.448924 | − | 0.893570i | \(-0.648192\pi\) | ||||
−0.448924 | + | 0.893570i | \(0.648192\pi\) | |||||||
\(942\) | 8.13940e71 | 0.111262 | ||||||||
\(943\) | −5.72040e71 | −0.0761885 | ||||||||
\(944\) | −3.39934e72 | −0.441145 | ||||||||
\(945\) | 1.63188e72 | 0.206352 | ||||||||
\(946\) | 3.04500e72 | 0.375193 | ||||||||
\(947\) | 8.32607e72 | 0.999691 | 0.499845 | − | 0.866115i | \(-0.333390\pi\) | ||||
0.499845 | + | 0.866115i | \(0.333390\pi\) | |||||||
\(948\) | −2.45010e72 | −0.286668 | ||||||||
\(949\) | −7.12517e72 | −0.812406 | ||||||||
\(950\) | 1.13730e73 | 1.26371 | ||||||||
\(951\) | 1.33590e73 | 1.44661 | ||||||||
\(952\) | 2.41765e72 | 0.255146 | ||||||||
\(953\) | 1.86907e73 | 1.92243 | 0.961214 | − | 0.275804i | \(-0.0889441\pi\) | ||||
0.961214 | + | 0.275804i | \(0.0889441\pi\) | |||||||
\(954\) | −9.28896e72 | −0.931176 | ||||||||
\(955\) | 2.63922e73 | 2.57865 | ||||||||
\(956\) | −5.27452e72 | −0.502301 | ||||||||
\(957\) | −1.36978e72 | −0.127148 | ||||||||
\(958\) | −6.50300e72 | −0.588381 | ||||||||
\(959\) | −1.47994e73 | −1.30524 | ||||||||
\(960\) | 3.51892e72 | 0.302527 | ||||||||
\(961\) | −1.11955e73 | −0.938255 | ||||||||
\(962\) | 5.78973e72 | 0.473008 | ||||||||
\(963\) | 1.01627e73 | 0.809401 | ||||||||
\(964\) | 3.96994e72 | 0.308245 | ||||||||
\(965\) | −1.36476e73 | −1.03309 | ||||||||
\(966\) | −1.57719e73 | −1.16398 | ||||||||
\(967\) | 7.70074e72 | 0.554095 | 0.277047 | − | 0.960856i | \(-0.410644\pi\) | ||||
0.277047 | + | 0.960856i | \(0.410644\pi\) | |||||||
\(968\) | 7.79439e72 | 0.546809 | ||||||||
\(969\) | 1.24787e73 | 0.853564 | ||||||||
\(970\) | −2.94619e73 | −1.96496 | ||||||||
\(971\) | 2.89962e72 | 0.188569 | 0.0942845 | − | 0.995545i | \(-0.469944\pi\) | ||||
0.0942845 | + | 0.995545i | \(0.469944\pi\) | |||||||
\(972\) | 1.08379e73 | 0.687260 | ||||||||
\(973\) | 1.07131e73 | 0.662444 | ||||||||
\(974\) | 1.35820e73 | 0.818975 | ||||||||
\(975\) | −3.40362e73 | −2.00137 | ||||||||
\(976\) | −1.12751e72 | −0.0646547 | ||||||||
\(977\) | 1.83564e73 | 1.02653 | 0.513263 | − | 0.858231i | \(-0.328437\pi\) | ||||
0.513263 | + | 0.858231i | \(0.328437\pi\) | |||||||
\(978\) | 9.80194e72 | 0.534577 | ||||||||
\(979\) | −3.62801e73 | −1.92971 | ||||||||
\(980\) | −5.73567e71 | −0.0297540 | ||||||||
\(981\) | −6.94048e72 | −0.351155 | ||||||||
\(982\) | −1.94483e73 | −0.959733 | ||||||||
\(983\) | −1.42481e73 | −0.685799 | −0.342900 | − | 0.939372i | \(-0.611409\pi\) | ||||
−0.342900 | + | 0.939372i | \(0.611409\pi\) | |||||||
\(984\) | −6.79146e71 | −0.0318848 | ||||||||
\(985\) | −1.48260e73 | −0.678947 | ||||||||
\(986\) | 6.46617e71 | 0.0288843 | ||||||||
\(987\) | 7.38403e72 | 0.321753 | ||||||||
\(988\) | 7.18416e72 | 0.305373 | ||||||||
\(989\) | 9.37722e72 | 0.388834 | ||||||||
\(990\) | 4.46823e73 | 1.80748 | ||||||||
\(991\) | −1.87344e73 | −0.739323 | −0.369662 | − | 0.929166i | \(-0.620526\pi\) | ||||
−0.369662 | + | 0.929166i | \(0.620526\pi\) | |||||||
\(992\) | −1.14094e72 | −0.0439265 | ||||||||
\(993\) | 5.74758e72 | 0.215888 | ||||||||
\(994\) | 2.21794e73 | 0.812798 | ||||||||
\(995\) | 3.23458e73 | 1.15652 | ||||||||
\(996\) | −1.63607e73 | −0.570753 | ||||||||
\(997\) | −4.87977e73 | −1.66099 | −0.830497 | − | 0.557023i | \(-0.811943\pi\) | ||||
−0.830497 | + | 0.557023i | \(0.811943\pi\) | |||||||
\(998\) | 3.33489e73 | 1.10760 | ||||||||
\(999\) | 3.40827e72 | 0.110453 |
(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 | 2.50.a.b.1.1 | ✓ | 3 | |
4.3 | odd | 2 | 16.50.a.b.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.50.a.b.1.1 | ✓ | 3 | 1.1 | even | 1 | trivial | |
16.50.a.b.1.3 | 3 | 4.3 | odd | 2 |