Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 31.6204 | 0.698718 | 0.349359 | − | 0.936989i | \(-0.386399\pi\) | ||||
0.349359 | + | 0.936989i | \(0.386399\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −1048.15 | −0.511793 | ||||||||
\(5\) | −7920.33 | −1.13347 | −0.566733 | − | 0.823902i | \(-0.691793\pi\) | ||||
−0.566733 | + | 0.823902i | \(0.691793\pi\) | |||||||
\(6\) | 7683.75 | 0.403405 | ||||||||
\(7\) | 55386.7 | 1.24556 | 0.622782 | − | 0.782395i | \(-0.286002\pi\) | ||||
0.622782 | + | 0.782395i | \(0.286002\pi\) | |||||||
\(8\) | −97901.5 | −1.05632 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | −250444. | −0.791973 | ||||||||
\(11\) | 749288. | 1.40278 | 0.701389 | − | 0.712779i | \(-0.252564\pi\) | ||||
0.701389 | + | 0.712779i | \(0.252564\pi\) | |||||||
\(12\) | −254701. | −0.295484 | ||||||||
\(13\) | −855073. | −0.638726 | −0.319363 | − | 0.947632i | \(-0.603469\pi\) | ||||
−0.319363 | + | 0.947632i | \(0.603469\pi\) | |||||||
\(14\) | 1.75135e6 | 0.870298 | ||||||||
\(15\) | −1.92464e6 | −0.654407 | ||||||||
\(16\) | −949065. | −0.226275 | ||||||||
\(17\) | −8.42911e6 | −1.43983 | −0.719917 | − | 0.694060i | \(-0.755820\pi\) | ||||
−0.719917 | + | 0.694060i | \(0.755820\pi\) | |||||||
\(18\) | 1.86715e6 | 0.232906 | ||||||||
\(19\) | −235588. | −0.0218277 | −0.0109139 | − | 0.999940i | \(-0.503474\pi\) | ||||
−0.0109139 | + | 0.999940i | \(0.503474\pi\) | |||||||
\(20\) | 8.30172e6 | 0.580100 | ||||||||
\(21\) | 1.34590e7 | 0.719127 | ||||||||
\(22\) | 2.36928e7 | 0.980146 | ||||||||
\(23\) | 1.10354e7 | 0.357506 | 0.178753 | − | 0.983894i | \(-0.442794\pi\) | ||||
0.178753 | + | 0.983894i | \(0.442794\pi\) | |||||||
\(24\) | −2.37901e7 | −0.609865 | ||||||||
\(25\) | 1.39036e7 | 0.284745 | ||||||||
\(26\) | −2.70377e7 | −0.446289 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −5.80537e7 | −0.637471 | ||||||||
\(29\) | −3.07296e7 | −0.278207 | −0.139103 | − | 0.990278i | \(-0.544422\pi\) | ||||
−0.139103 | + | 0.990278i | \(0.544422\pi\) | |||||||
\(30\) | −6.08579e7 | −0.457246 | ||||||||
\(31\) | 9.66575e7 | 0.606382 | 0.303191 | − | 0.952930i | \(-0.401948\pi\) | ||||
0.303191 | + | 0.952930i | \(0.401948\pi\) | |||||||
\(32\) | 1.70492e8 | 0.898215 | ||||||||
\(33\) | 1.82077e8 | 0.809894 | ||||||||
\(34\) | −2.66531e8 | −1.00604 | ||||||||
\(35\) | −4.38681e8 | −1.41180 | ||||||||
\(36\) | −6.18923e7 | −0.170598 | ||||||||
\(37\) | −7.15175e8 | −1.69552 | −0.847759 | − | 0.530381i | \(-0.822049\pi\) | ||||
−0.847759 | + | 0.530381i | \(0.822049\pi\) | |||||||
\(38\) | −7.44938e6 | −0.0152514 | ||||||||
\(39\) | −2.07783e8 | −0.368769 | ||||||||
\(40\) | 7.75412e8 | 1.19730 | ||||||||
\(41\) | 1.96874e8 | 0.265386 | 0.132693 | − | 0.991157i | \(-0.457638\pi\) | ||||
0.132693 | + | 0.991157i | \(0.457638\pi\) | |||||||
\(42\) | 4.25578e8 | 0.502467 | ||||||||
\(43\) | 1.69435e9 | 1.75763 | 0.878813 | − | 0.477166i | \(-0.158336\pi\) | ||||
0.878813 | + | 0.477166i | \(0.158336\pi\) | |||||||
\(44\) | −7.85368e8 | −0.717932 | ||||||||
\(45\) | −4.67688e8 | −0.377822 | ||||||||
\(46\) | 3.48942e8 | 0.249796 | ||||||||
\(47\) | −3.75191e8 | −0.238624 | −0.119312 | − | 0.992857i | \(-0.538069\pi\) | ||||
−0.119312 | + | 0.992857i | \(0.538069\pi\) | |||||||
\(48\) | −2.30623e8 | −0.130640 | ||||||||
\(49\) | 1.09036e9 | 0.551431 | ||||||||
\(50\) | 4.39636e8 | 0.198956 | ||||||||
\(51\) | −2.04827e9 | −0.831289 | ||||||||
\(52\) | 8.96246e8 | 0.326896 | ||||||||
\(53\) | −2.44790e9 | −0.804038 | −0.402019 | − | 0.915631i | \(-0.631691\pi\) | ||||
−0.402019 | + | 0.915631i | \(0.631691\pi\) | |||||||
\(54\) | 4.53718e8 | 0.134468 | ||||||||
\(55\) | −5.93461e9 | −1.59000 | ||||||||
\(56\) | −5.42244e9 | −1.31571 | ||||||||
\(57\) | −5.72479e7 | −0.0126022 | ||||||||
\(58\) | −9.71681e8 | −0.194388 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 2.01732e9 | 0.334921 | ||||||||
\(61\) | 1.16084e9 | 0.175978 | 0.0879892 | − | 0.996121i | \(-0.471956\pi\) | ||||
0.0879892 | + | 0.996121i | \(0.471956\pi\) | |||||||
\(62\) | 3.05635e9 | 0.423690 | ||||||||
\(63\) | 3.27053e9 | 0.415188 | ||||||||
\(64\) | 7.33472e9 | 0.853874 | ||||||||
\(65\) | 6.77246e9 | 0.723974 | ||||||||
\(66\) | 5.75734e9 | 0.565888 | ||||||||
\(67\) | 3.45178e9 | 0.312343 | 0.156172 | − | 0.987730i | \(-0.450085\pi\) | ||||
0.156172 | + | 0.987730i | \(0.450085\pi\) | |||||||
\(68\) | 8.83499e9 | 0.736897 | ||||||||
\(69\) | 2.68159e9 | 0.206406 | ||||||||
\(70\) | −1.38713e10 | −0.986454 | ||||||||
\(71\) | 2.89581e10 | 1.90480 | 0.952401 | − | 0.304848i | \(-0.0986057\pi\) | ||||
0.952401 | + | 0.304848i | \(0.0986057\pi\) | |||||||
\(72\) | −5.78098e9 | −0.352106 | ||||||||
\(73\) | −3.54355e9 | −0.200061 | −0.100031 | − | 0.994984i | \(-0.531894\pi\) | ||||
−0.100031 | + | 0.994984i | \(0.531894\pi\) | |||||||
\(74\) | −2.26141e10 | −1.18469 | ||||||||
\(75\) | 3.37857e9 | 0.164398 | ||||||||
\(76\) | 2.46932e8 | 0.0111713 | ||||||||
\(77\) | 4.15006e10 | 1.74725 | ||||||||
\(78\) | −6.57016e9 | −0.257665 | ||||||||
\(79\) | 3.21817e10 | 1.17668 | 0.588342 | − | 0.808612i | \(-0.299781\pi\) | ||||
0.588342 | + | 0.808612i | \(0.299781\pi\) | |||||||
\(80\) | 7.51691e9 | 0.256475 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 6.22523e9 | 0.185430 | ||||||||
\(83\) | 5.97408e10 | 1.66472 | 0.832360 | − | 0.554235i | \(-0.186989\pi\) | ||||
0.832360 | + | 0.554235i | \(0.186989\pi\) | |||||||
\(84\) | −1.41070e10 | −0.368044 | ||||||||
\(85\) | 6.67613e10 | 1.63200 | ||||||||
\(86\) | 5.35760e10 | 1.22809 | ||||||||
\(87\) | −7.46729e9 | −0.160623 | ||||||||
\(88\) | −7.33564e10 | −1.48178 | ||||||||
\(89\) | 8.65853e10 | 1.64361 | 0.821806 | − | 0.569768i | \(-0.192967\pi\) | ||||
0.821806 | + | 0.569768i | \(0.192967\pi\) | |||||||
\(90\) | −1.47885e10 | −0.263991 | ||||||||
\(91\) | −4.73596e10 | −0.795574 | ||||||||
\(92\) | −1.15667e10 | −0.182969 | ||||||||
\(93\) | 2.34878e10 | 0.350095 | ||||||||
\(94\) | −1.18637e10 | −0.166731 | ||||||||
\(95\) | 1.86594e9 | 0.0247410 | ||||||||
\(96\) | 4.14297e10 | 0.518585 | ||||||||
\(97\) | −1.01633e11 | −1.20168 | −0.600841 | − | 0.799369i | \(-0.705167\pi\) | ||||
−0.600841 | + | 0.799369i | \(0.705167\pi\) | |||||||
\(98\) | 3.44776e10 | 0.385295 | ||||||||
\(99\) | 4.42447e10 | 0.467592 | ||||||||
\(100\) | −1.45730e10 | −0.145730 | ||||||||
\(101\) | 1.49093e11 | 1.41153 | 0.705763 | − | 0.708448i | \(-0.250604\pi\) | ||||
0.705763 | + | 0.708448i | \(0.250604\pi\) | |||||||
\(102\) | −6.47671e10 | −0.580836 | ||||||||
\(103\) | 2.23141e10 | 0.189659 | 0.0948296 | − | 0.995494i | \(-0.469769\pi\) | ||||
0.0948296 | + | 0.995494i | \(0.469769\pi\) | |||||||
\(104\) | 8.37129e10 | 0.674697 | ||||||||
\(105\) | −1.06600e11 | −0.815106 | ||||||||
\(106\) | −7.74035e10 | −0.561796 | ||||||||
\(107\) | 2.06906e11 | 1.42614 | 0.713071 | − | 0.701091i | \(-0.247304\pi\) | ||||
0.713071 | + | 0.701091i | \(0.247304\pi\) | |||||||
\(108\) | −1.50398e10 | −0.0984946 | ||||||||
\(109\) | −1.32255e8 | −0.000823314 0 | −0.000411657 | − | 1.00000i | \(-0.500131\pi\) | ||||
−0.000411657 | 1.00000i | \(0.500131\pi\) | ||||||||
\(110\) | −1.87654e11 | −1.11096 | ||||||||
\(111\) | −1.73787e11 | −0.978908 | ||||||||
\(112\) | −5.25656e10 | −0.281840 | ||||||||
\(113\) | −2.69080e11 | −1.37388 | −0.686942 | − | 0.726712i | \(-0.741047\pi\) | ||||
−0.686942 | + | 0.726712i | \(0.741047\pi\) | |||||||
\(114\) | −1.81020e9 | −0.00880541 | ||||||||
\(115\) | −8.74038e10 | −0.405221 | ||||||||
\(116\) | 3.22093e10 | 0.142384 | ||||||||
\(117\) | −5.04912e10 | −0.212909 | ||||||||
\(118\) | 2.26062e10 | 0.0909653 | ||||||||
\(119\) | −4.66860e11 | −1.79341 | ||||||||
\(120\) | 1.88425e11 | 0.691261 | ||||||||
\(121\) | 2.76120e11 | 0.967785 | ||||||||
\(122\) | 3.67063e10 | 0.122959 | ||||||||
\(123\) | 4.78404e10 | 0.153220 | ||||||||
\(124\) | −1.01312e11 | −0.310342 | ||||||||
\(125\) | 2.76614e11 | 0.810717 | ||||||||
\(126\) | 1.03415e11 | 0.290099 | ||||||||
\(127\) | 2.62532e11 | 0.705119 | 0.352559 | − | 0.935789i | \(-0.385311\pi\) | ||||
0.352559 | + | 0.935789i | \(0.385311\pi\) | |||||||
\(128\) | −1.17242e11 | −0.301598 | ||||||||
\(129\) | 4.11727e11 | 1.01477 | ||||||||
\(130\) | 2.14148e11 | 0.505854 | ||||||||
\(131\) | 5.48081e11 | 1.24123 | 0.620615 | − | 0.784115i | \(-0.286883\pi\) | ||||
0.620615 | + | 0.784115i | \(0.286883\pi\) | |||||||
\(132\) | −1.90844e11 | −0.414498 | ||||||||
\(133\) | −1.30484e10 | −0.0271878 | ||||||||
\(134\) | 1.09147e11 | 0.218240 | ||||||||
\(135\) | −1.13648e11 | −0.218136 | ||||||||
\(136\) | 8.25222e11 | 1.52092 | ||||||||
\(137\) | −3.83305e11 | −0.678550 | −0.339275 | − | 0.940687i | \(-0.610182\pi\) | ||||
−0.339275 | + | 0.940687i | \(0.610182\pi\) | |||||||
\(138\) | 8.47930e10 | 0.144220 | ||||||||
\(139\) | −8.99134e10 | −0.146975 | −0.0734874 | − | 0.997296i | \(-0.523413\pi\) | ||||
−0.0734874 | + | 0.997296i | \(0.523413\pi\) | |||||||
\(140\) | 4.59805e11 | 0.722552 | ||||||||
\(141\) | −9.11714e10 | −0.137770 | ||||||||
\(142\) | 9.15667e11 | 1.33092 | ||||||||
\(143\) | −6.40695e11 | −0.895990 | ||||||||
\(144\) | −5.60413e10 | −0.0754249 | ||||||||
\(145\) | 2.43389e11 | 0.315338 | ||||||||
\(146\) | −1.12048e11 | −0.139786 | ||||||||
\(147\) | 2.64957e11 | 0.318369 | ||||||||
\(148\) | 7.49612e11 | 0.867755 | ||||||||
\(149\) | −9.17759e10 | −0.102377 | −0.0511887 | − | 0.998689i | \(-0.516301\pi\) | ||||
−0.0511887 | + | 0.998689i | \(0.516301\pi\) | |||||||
\(150\) | 1.06831e11 | 0.114868 | ||||||||
\(151\) | −4.78141e11 | −0.495658 | −0.247829 | − | 0.968804i | \(-0.579717\pi\) | ||||
−0.247829 | + | 0.968804i | \(0.579717\pi\) | |||||||
\(152\) | 2.30644e10 | 0.0230570 | ||||||||
\(153\) | −4.97730e11 | −0.479945 | ||||||||
\(154\) | 1.31226e12 | 1.22084 | ||||||||
\(155\) | −7.65560e11 | −0.687313 | ||||||||
\(156\) | 2.17788e11 | 0.188733 | ||||||||
\(157\) | 2.26002e11 | 0.189088 | 0.0945440 | − | 0.995521i | \(-0.469861\pi\) | ||||
0.0945440 | + | 0.995521i | \(0.469861\pi\) | |||||||
\(158\) | 1.01760e12 | 0.822171 | ||||||||
\(159\) | −5.94840e11 | −0.464211 | ||||||||
\(160\) | −1.35036e12 | −1.01810 | ||||||||
\(161\) | 6.11213e11 | 0.445297 | ||||||||
\(162\) | 1.10253e11 | 0.0776353 | ||||||||
\(163\) | 2.24541e12 | 1.52849 | 0.764247 | − | 0.644924i | \(-0.223111\pi\) | ||||
0.764247 | + | 0.644924i | \(0.223111\pi\) | |||||||
\(164\) | −2.06354e11 | −0.135823 | ||||||||
\(165\) | −1.44211e12 | −0.917987 | ||||||||
\(166\) | 1.88902e12 | 1.16317 | ||||||||
\(167\) | 8.48590e11 | 0.505542 | 0.252771 | − | 0.967526i | \(-0.418658\pi\) | ||||
0.252771 | + | 0.967526i | \(0.418658\pi\) | |||||||
\(168\) | −1.31765e12 | −0.759626 | ||||||||
\(169\) | −1.06101e12 | −0.592029 | ||||||||
\(170\) | 2.11102e12 | 1.14031 | ||||||||
\(171\) | −1.39112e10 | −0.00727590 | ||||||||
\(172\) | −1.77594e12 | −0.899541 | ||||||||
\(173\) | −2.23867e12 | −1.09834 | −0.549170 | − | 0.835711i | \(-0.685056\pi\) | ||||
−0.549170 | + | 0.835711i | \(0.685056\pi\) | |||||||
\(174\) | −2.36118e11 | −0.112230 | ||||||||
\(175\) | 7.70072e11 | 0.354668 | ||||||||
\(176\) | −7.11123e11 | −0.317413 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 2.73786e12 | 1.14842 | ||||||||
\(179\) | −1.28996e12 | −0.524669 | −0.262335 | − | 0.964977i | \(-0.584492\pi\) | ||||
−0.262335 | + | 0.964977i | \(0.584492\pi\) | |||||||
\(180\) | 4.90208e11 | 0.193367 | ||||||||
\(181\) | 3.31228e12 | 1.26735 | 0.633673 | − | 0.773601i | \(-0.281546\pi\) | ||||
0.633673 | + | 0.773601i | \(0.281546\pi\) | |||||||
\(182\) | −1.49753e12 | −0.555882 | ||||||||
\(183\) | 2.82085e11 | 0.101601 | ||||||||
\(184\) | −1.08038e12 | −0.377640 | ||||||||
\(185\) | 5.66442e12 | 1.92181 | ||||||||
\(186\) | 7.42692e11 | 0.244618 | ||||||||
\(187\) | −6.31583e12 | −2.01977 | ||||||||
\(188\) | 3.93257e11 | 0.122126 | ||||||||
\(189\) | 7.94739e11 | 0.239709 | ||||||||
\(190\) | 5.90016e10 | 0.0172870 | ||||||||
\(191\) | 5.17579e12 | 1.47331 | 0.736654 | − | 0.676270i | \(-0.236405\pi\) | ||||
0.736654 | + | 0.676270i | \(0.236405\pi\) | |||||||
\(192\) | 1.78234e12 | 0.492984 | ||||||||
\(193\) | 4.26973e12 | 1.14772 | 0.573859 | − | 0.818954i | \(-0.305446\pi\) | ||||
0.573859 | + | 0.818954i | \(0.305446\pi\) | |||||||
\(194\) | −3.21367e12 | −0.839637 | ||||||||
\(195\) | 1.64571e12 | 0.417987 | ||||||||
\(196\) | −1.14286e12 | −0.282219 | ||||||||
\(197\) | −1.76272e12 | −0.423273 | −0.211636 | − | 0.977349i | \(-0.567879\pi\) | ||||
−0.211636 | + | 0.977349i | \(0.567879\pi\) | |||||||
\(198\) | 1.39903e12 | 0.326715 | ||||||||
\(199\) | −1.04809e12 | −0.238071 | −0.119035 | − | 0.992890i | \(-0.537980\pi\) | ||||
−0.119035 | + | 0.992890i | \(0.537980\pi\) | |||||||
\(200\) | −1.36118e12 | −0.300781 | ||||||||
\(201\) | 8.38783e11 | 0.180331 | ||||||||
\(202\) | 4.71437e12 | 0.986259 | ||||||||
\(203\) | −1.70201e12 | −0.346524 | ||||||||
\(204\) | 2.14690e12 | 0.425448 | ||||||||
\(205\) | −1.55931e12 | −0.300806 | ||||||||
\(206\) | 7.05579e11 | 0.132518 | ||||||||
\(207\) | 6.51627e11 | 0.119169 | ||||||||
\(208\) | 8.11520e11 | 0.144528 | ||||||||
\(209\) | −1.76523e11 | −0.0306194 | ||||||||
\(210\) | −3.37072e12 | −0.569529 | ||||||||
\(211\) | −9.21253e12 | −1.51644 | −0.758220 | − | 0.651999i | \(-0.773931\pi\) | ||||
−0.758220 | + | 0.651999i | \(0.773931\pi\) | |||||||
\(212\) | 2.56577e12 | 0.411501 | ||||||||
\(213\) | 7.03683e12 | 1.09974 | ||||||||
\(214\) | 6.54245e12 | 0.996472 | ||||||||
\(215\) | −1.34198e13 | −1.99221 | ||||||||
\(216\) | −1.40478e12 | −0.203288 | ||||||||
\(217\) | 5.35354e12 | 0.755288 | ||||||||
\(218\) | −4.18194e9 | −0.000575264 0 | ||||||||
\(219\) | −8.61082e11 | −0.115505 | ||||||||
\(220\) | 6.22037e12 | 0.813751 | ||||||||
\(221\) | 7.20750e12 | 0.919659 | ||||||||
\(222\) | −5.49522e12 | −0.683981 | ||||||||
\(223\) | 7.77435e12 | 0.944034 | 0.472017 | − | 0.881590i | \(-0.343526\pi\) | ||||
0.472017 | + | 0.881590i | \(0.343526\pi\) | |||||||
\(224\) | 9.44301e12 | 1.11878 | ||||||||
\(225\) | 8.20991e11 | 0.0949150 | ||||||||
\(226\) | −8.50841e12 | −0.959958 | ||||||||
\(227\) | 5.30903e12 | 0.584620 | 0.292310 | − | 0.956324i | \(-0.405576\pi\) | ||||
0.292310 | + | 0.956324i | \(0.405576\pi\) | |||||||
\(228\) | 6.00045e10 | 0.00644974 | ||||||||
\(229\) | 1.30474e13 | 1.36908 | 0.684540 | − | 0.728976i | \(-0.260003\pi\) | ||||
0.684540 | + | 0.728976i | \(0.260003\pi\) | |||||||
\(230\) | −2.76374e12 | −0.283135 | ||||||||
\(231\) | 1.00846e13 | 1.00878 | ||||||||
\(232\) | 3.00847e12 | 0.293875 | ||||||||
\(233\) | 7.49739e12 | 0.715242 | 0.357621 | − | 0.933867i | \(-0.383588\pi\) | ||||
0.357621 | + | 0.933867i | \(0.383588\pi\) | |||||||
\(234\) | −1.59655e12 | −0.148763 | ||||||||
\(235\) | 2.97164e12 | 0.270472 | ||||||||
\(236\) | −7.49350e11 | −0.0666298 | ||||||||
\(237\) | 7.82016e12 | 0.679359 | ||||||||
\(238\) | −1.47623e13 | −1.25309 | ||||||||
\(239\) | 1.12891e13 | 0.936424 | 0.468212 | − | 0.883616i | \(-0.344898\pi\) | ||||
0.468212 | + | 0.883616i | \(0.344898\pi\) | |||||||
\(240\) | 1.82661e12 | 0.148076 | ||||||||
\(241\) | −9.51986e12 | −0.754287 | −0.377144 | − | 0.926155i | \(-0.623094\pi\) | ||||
−0.377144 | + | 0.926155i | \(0.623094\pi\) | |||||||
\(242\) | 8.73102e12 | 0.676209 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −1.21674e12 | −0.0900646 | ||||||||
\(245\) | −8.63601e12 | −0.625028 | ||||||||
\(246\) | 1.51273e12 | 0.107058 | ||||||||
\(247\) | 2.01445e11 | 0.0139419 | ||||||||
\(248\) | −9.46291e12 | −0.640532 | ||||||||
\(249\) | 1.45170e13 | 0.961127 | ||||||||
\(250\) | 8.74664e12 | 0.566463 | ||||||||
\(251\) | −2.05017e13 | −1.29892 | −0.649462 | − | 0.760394i | \(-0.725006\pi\) | ||||
−0.649462 | + | 0.760394i | \(0.725006\pi\) | |||||||
\(252\) | −3.42801e12 | −0.212490 | ||||||||
\(253\) | 8.26866e12 | 0.501502 | ||||||||
\(254\) | 8.30137e12 | 0.492679 | ||||||||
\(255\) | 1.62230e13 | 0.942237 | ||||||||
\(256\) | −1.87287e13 | −1.06461 | ||||||||
\(257\) | −2.52685e13 | −1.40588 | −0.702940 | − | 0.711250i | \(-0.748130\pi\) | ||||
−0.702940 | + | 0.711250i | \(0.748130\pi\) | |||||||
\(258\) | 1.30190e13 | 0.709035 | ||||||||
\(259\) | −3.96112e13 | −2.11188 | ||||||||
\(260\) | −7.09857e12 | −0.370525 | ||||||||
\(261\) | −1.81455e12 | −0.0927356 | ||||||||
\(262\) | 1.73305e13 | 0.867270 | ||||||||
\(263\) | 6.25225e12 | 0.306394 | 0.153197 | − | 0.988196i | \(-0.451043\pi\) | ||||
0.153197 | + | 0.988196i | \(0.451043\pi\) | |||||||
\(264\) | −1.78256e13 | −0.855505 | ||||||||
\(265\) | 1.93882e13 | 0.911349 | ||||||||
\(266\) | −4.12596e11 | −0.0189966 | ||||||||
\(267\) | 2.10402e13 | 0.948940 | ||||||||
\(268\) | −3.61799e12 | −0.159855 | ||||||||
\(269\) | −1.23070e13 | −0.532740 | −0.266370 | − | 0.963871i | \(-0.585824\pi\) | ||||
−0.266370 | + | 0.963871i | \(0.585824\pi\) | |||||||
\(270\) | −3.59360e12 | −0.152415 | ||||||||
\(271\) | 1.97816e13 | 0.822110 | 0.411055 | − | 0.911611i | \(-0.365160\pi\) | ||||
0.411055 | + | 0.911611i | \(0.365160\pi\) | |||||||
\(272\) | 7.99977e12 | 0.325798 | ||||||||
\(273\) | −1.15084e13 | −0.459325 | ||||||||
\(274\) | −1.21203e13 | −0.474115 | ||||||||
\(275\) | 1.04178e13 | 0.399434 | ||||||||
\(276\) | −2.81072e12 | −0.105637 | ||||||||
\(277\) | 1.10910e13 | 0.408633 | 0.204316 | − | 0.978905i | \(-0.434503\pi\) | ||||
0.204316 | + | 0.978905i | \(0.434503\pi\) | |||||||
\(278\) | −2.84310e12 | −0.102694 | ||||||||
\(279\) | 5.70753e12 | 0.202127 | ||||||||
\(280\) | 4.29475e13 | 1.49131 | ||||||||
\(281\) | −3.82184e13 | −1.30133 | −0.650666 | − | 0.759364i | \(-0.725510\pi\) | ||||
−0.650666 | + | 0.759364i | \(0.725510\pi\) | |||||||
\(282\) | −2.88287e12 | −0.0962621 | ||||||||
\(283\) | −6.07773e12 | −0.199029 | −0.0995144 | − | 0.995036i | \(-0.531729\pi\) | ||||
−0.0995144 | + | 0.995036i | \(0.531729\pi\) | |||||||
\(284\) | −3.03525e13 | −0.974864 | ||||||||
\(285\) | 4.53422e11 | 0.0142842 | ||||||||
\(286\) | −2.02590e13 | −0.626045 | ||||||||
\(287\) | 1.09042e13 | 0.330555 | ||||||||
\(288\) | 1.00674e13 | 0.299405 | ||||||||
\(289\) | 3.67779e13 | 1.07312 | ||||||||
\(290\) | 7.69604e12 | 0.220332 | ||||||||
\(291\) | −2.46968e13 | −0.693791 | ||||||||
\(292\) | 3.71418e12 | 0.102390 | ||||||||
\(293\) | 5.19893e13 | 1.40651 | 0.703254 | − | 0.710938i | \(-0.251730\pi\) | ||||
0.703254 | + | 0.710938i | \(0.251730\pi\) | |||||||
\(294\) | 8.37805e12 | 0.222450 | ||||||||
\(295\) | −5.66244e12 | −0.147565 | ||||||||
\(296\) | 7.00167e13 | 1.79101 | ||||||||
\(297\) | 1.07515e13 | 0.269965 | ||||||||
\(298\) | −2.90199e12 | −0.0715329 | ||||||||
\(299\) | −9.43604e12 | −0.228349 | ||||||||
\(300\) | −3.54125e12 | −0.0841375 | ||||||||
\(301\) | 9.38444e13 | 2.18924 | ||||||||
\(302\) | −1.51190e13 | −0.346326 | ||||||||
\(303\) | 3.62295e13 | 0.814945 | ||||||||
\(304\) | 2.23588e11 | 0.00493906 | ||||||||
\(305\) | −9.19427e12 | −0.199466 | ||||||||
\(306\) | −1.57384e13 | −0.335346 | ||||||||
\(307\) | −1.89550e13 | −0.396700 | −0.198350 | − | 0.980131i | \(-0.563558\pi\) | ||||
−0.198350 | + | 0.980131i | \(0.563558\pi\) | |||||||
\(308\) | −4.34989e13 | −0.894230 | ||||||||
\(309\) | 5.42232e12 | 0.109500 | ||||||||
\(310\) | −2.42073e13 | −0.480238 | ||||||||
\(311\) | −2.99384e13 | −0.583507 | −0.291754 | − | 0.956494i | \(-0.594239\pi\) | ||||
−0.291754 | + | 0.956494i | \(0.594239\pi\) | |||||||
\(312\) | 2.03422e13 | 0.389537 | ||||||||
\(313\) | 4.90106e12 | 0.0922139 | 0.0461069 | − | 0.998937i | \(-0.485319\pi\) | ||||
0.0461069 | + | 0.998937i | \(0.485319\pi\) | |||||||
\(314\) | 7.14626e12 | 0.132119 | ||||||||
\(315\) | −2.59037e13 | −0.470602 | ||||||||
\(316\) | −3.37313e13 | −0.602219 | ||||||||
\(317\) | 2.55905e13 | 0.449007 | 0.224504 | − | 0.974473i | \(-0.427924\pi\) | ||||
0.224504 | + | 0.974473i | \(0.427924\pi\) | |||||||
\(318\) | −1.88091e13 | −0.324353 | ||||||||
\(319\) | −2.30253e13 | −0.390262 | ||||||||
\(320\) | −5.80934e13 | −0.967837 | ||||||||
\(321\) | 5.02782e13 | 0.823384 | ||||||||
\(322\) | 1.93268e13 | 0.311137 | ||||||||
\(323\) | 1.98580e12 | 0.0314283 | ||||||||
\(324\) | −3.65468e12 | −0.0568659 | ||||||||
\(325\) | −1.18886e13 | −0.181874 | ||||||||
\(326\) | 7.10007e13 | 1.06799 | ||||||||
\(327\) | −3.21379e10 | −0.000475340 0 | ||||||||
\(328\) | −1.92743e13 | −0.280331 | ||||||||
\(329\) | −2.07806e13 | −0.297222 | ||||||||
\(330\) | −4.56000e13 | −0.641414 | ||||||||
\(331\) | −1.07132e14 | −1.48205 | −0.741027 | − | 0.671475i | \(-0.765661\pi\) | ||||
−0.741027 | + | 0.671475i | \(0.765661\pi\) | |||||||
\(332\) | −6.26174e13 | −0.851992 | ||||||||
\(333\) | −4.22303e13 | −0.565173 | ||||||||
\(334\) | 2.68327e13 | 0.353231 | ||||||||
\(335\) | −2.73393e13 | −0.354030 | ||||||||
\(336\) | −1.27734e13 | −0.162720 | ||||||||
\(337\) | 8.98851e12 | 0.112648 | 0.0563240 | − | 0.998413i | \(-0.482062\pi\) | ||||
0.0563240 | + | 0.998413i | \(0.482062\pi\) | |||||||
\(338\) | −3.35496e13 | −0.413661 | ||||||||
\(339\) | −6.53865e13 | −0.793212 | ||||||||
\(340\) | −6.99760e13 | −0.835248 | ||||||||
\(341\) | 7.24243e13 | 0.850619 | ||||||||
\(342\) | −4.39878e11 | −0.00508381 | ||||||||
\(343\) | −4.91262e13 | −0.558722 | ||||||||
\(344\) | −1.65879e14 | −1.85661 | ||||||||
\(345\) | −2.12391e13 | −0.233955 | ||||||||
\(346\) | −7.07876e13 | −0.767430 | ||||||||
\(347\) | 1.31761e14 | 1.40597 | 0.702984 | − | 0.711205i | \(-0.251850\pi\) | ||||
0.702984 | + | 0.711205i | \(0.251850\pi\) | |||||||
\(348\) | 7.82686e12 | 0.0822056 | ||||||||
\(349\) | −1.70214e14 | −1.75977 | −0.879886 | − | 0.475184i | \(-0.842381\pi\) | ||||
−0.879886 | + | 0.475184i | \(0.842381\pi\) | |||||||
\(350\) | 2.43500e13 | 0.247813 | ||||||||
\(351\) | −1.22694e13 | −0.122923 | ||||||||
\(352\) | 1.27748e14 | 1.26000 | ||||||||
\(353\) | 1.79417e14 | 1.74222 | 0.871111 | − | 0.491086i | \(-0.163400\pi\) | ||||
0.871111 | + | 0.491086i | \(0.163400\pi\) | |||||||
\(354\) | 5.49330e12 | 0.0525189 | ||||||||
\(355\) | −2.29358e14 | −2.15903 | ||||||||
\(356\) | −9.07546e13 | −0.841189 | ||||||||
\(357\) | −1.13447e14 | −1.03542 | ||||||||
\(358\) | −4.07891e13 | −0.366596 | ||||||||
\(359\) | −9.61034e13 | −0.850588 | −0.425294 | − | 0.905055i | \(-0.639829\pi\) | ||||
−0.425294 | + | 0.905055i | \(0.639829\pi\) | |||||||
\(360\) | 4.57873e13 | 0.399100 | ||||||||
\(361\) | −1.16435e14 | −0.999524 | ||||||||
\(362\) | 1.04736e14 | 0.885518 | ||||||||
\(363\) | 6.70972e13 | 0.558751 | ||||||||
\(364\) | 4.96401e13 | 0.407170 | ||||||||
\(365\) | 2.80661e13 | 0.226762 | ||||||||
\(366\) | 8.91963e12 | 0.0709906 | ||||||||
\(367\) | 7.60650e13 | 0.596378 | 0.298189 | − | 0.954507i | \(-0.403617\pi\) | ||||
0.298189 | + | 0.954507i | \(0.403617\pi\) | |||||||
\(368\) | −1.04733e13 | −0.0808946 | ||||||||
\(369\) | 1.16252e13 | 0.0884619 | ||||||||
\(370\) | 1.79111e14 | 1.34281 | ||||||||
\(371\) | −1.35581e14 | −1.00148 | ||||||||
\(372\) | −2.46188e13 | −0.179176 | ||||||||
\(373\) | −2.23217e14 | −1.60077 | −0.800385 | − | 0.599486i | \(-0.795372\pi\) | ||||
−0.800385 | + | 0.599486i | \(0.795372\pi\) | |||||||
\(374\) | −1.99709e14 | −1.41125 | ||||||||
\(375\) | 6.72172e13 | 0.468068 | ||||||||
\(376\) | 3.67317e13 | 0.252063 | ||||||||
\(377\) | 2.62760e13 | 0.177698 | ||||||||
\(378\) | 2.51299e13 | 0.167489 | ||||||||
\(379\) | −8.76788e13 | −0.575942 | −0.287971 | − | 0.957639i | \(-0.592981\pi\) | ||||
−0.287971 | + | 0.957639i | \(0.592981\pi\) | |||||||
\(380\) | −1.95578e12 | −0.0126623 | ||||||||
\(381\) | 6.37953e13 | 0.407100 | ||||||||
\(382\) | 1.63660e14 | 1.02943 | ||||||||
\(383\) | 1.10103e14 | 0.682665 | 0.341333 | − | 0.939943i | \(-0.389122\pi\) | ||||
0.341333 | + | 0.939943i | \(0.389122\pi\) | |||||||
\(384\) | −2.84898e13 | −0.174128 | ||||||||
\(385\) | −3.28698e14 | −1.98045 | ||||||||
\(386\) | 1.35011e14 | 0.801932 | ||||||||
\(387\) | 1.00050e14 | 0.585876 | ||||||||
\(388\) | 1.06527e14 | 0.615012 | ||||||||
\(389\) | 1.01968e14 | 0.580419 | 0.290209 | − | 0.956963i | \(-0.406275\pi\) | ||||
0.290209 | + | 0.956963i | \(0.406275\pi\) | |||||||
\(390\) | 5.20379e13 | 0.292055 | ||||||||
\(391\) | −9.30183e13 | −0.514750 | ||||||||
\(392\) | −1.06748e14 | −0.582486 | ||||||||
\(393\) | 1.33184e14 | 0.716625 | ||||||||
\(394\) | −5.57380e13 | −0.295748 | ||||||||
\(395\) | −2.54890e14 | −1.33373 | ||||||||
\(396\) | −4.63752e13 | −0.239311 | ||||||||
\(397\) | 2.02693e14 | 1.03155 | 0.515777 | − | 0.856723i | \(-0.327503\pi\) | ||||
0.515777 | + | 0.856723i | \(0.327503\pi\) | |||||||
\(398\) | −3.31410e13 | −0.166344 | ||||||||
\(399\) | −3.17077e12 | −0.0156969 | ||||||||
\(400\) | −1.31954e13 | −0.0644306 | ||||||||
\(401\) | −2.31232e14 | −1.11367 | −0.556833 | − | 0.830625i | \(-0.687984\pi\) | ||||
−0.556833 | + | 0.830625i | \(0.687984\pi\) | |||||||
\(402\) | 2.65226e13 | 0.126001 | ||||||||
\(403\) | −8.26492e13 | −0.387312 | ||||||||
\(404\) | −1.56272e14 | −0.722409 | ||||||||
\(405\) | −2.76165e13 | −0.125941 | ||||||||
\(406\) | −5.38182e13 | −0.242123 | ||||||||
\(407\) | −5.35872e14 | −2.37844 | ||||||||
\(408\) | 2.00529e14 | 0.878104 | ||||||||
\(409\) | 8.97745e13 | 0.387860 | 0.193930 | − | 0.981015i | \(-0.437877\pi\) | ||||
0.193930 | + | 0.981015i | \(0.437877\pi\) | |||||||
\(410\) | −4.93059e13 | −0.210178 | ||||||||
\(411\) | −9.31432e13 | −0.391761 | ||||||||
\(412\) | −2.33885e13 | −0.0970662 | ||||||||
\(413\) | 3.95973e13 | 0.162159 | ||||||||
\(414\) | 2.06047e13 | 0.0832654 | ||||||||
\(415\) | −4.73167e14 | −1.88690 | ||||||||
\(416\) | −1.45783e14 | −0.573713 | ||||||||
\(417\) | −2.18490e13 | −0.0848560 | ||||||||
\(418\) | −5.58173e12 | −0.0213943 | ||||||||
\(419\) | 6.50052e13 | 0.245907 | 0.122953 | − | 0.992412i | \(-0.460763\pi\) | ||||
0.122953 | + | 0.992412i | \(0.460763\pi\) | |||||||
\(420\) | 1.11733e14 | 0.417166 | ||||||||
\(421\) | −2.99663e14 | −1.10429 | −0.552144 | − | 0.833749i | \(-0.686190\pi\) | ||||
−0.552144 | + | 0.833749i | \(0.686190\pi\) | |||||||
\(422\) | −2.91303e14 | −1.05956 | ||||||||
\(423\) | −2.21546e13 | −0.0795413 | ||||||||
\(424\) | 2.39653e14 | 0.849319 | ||||||||
\(425\) | −1.17195e14 | −0.409986 | ||||||||
\(426\) | 2.22507e14 | 0.768407 | ||||||||
\(427\) | 6.42953e13 | 0.219193 | ||||||||
\(428\) | −2.16869e14 | −0.729890 | ||||||||
\(429\) | −1.55689e14 | −0.517300 | ||||||||
\(430\) | −4.24340e14 | −1.39199 | ||||||||
\(431\) | −3.95410e14 | −1.28063 | −0.640313 | − | 0.768114i | \(-0.721195\pi\) | ||||
−0.640313 | + | 0.768114i | \(0.721195\pi\) | |||||||
\(432\) | −1.36180e13 | −0.0435466 | ||||||||
\(433\) | 3.39133e14 | 1.07075 | 0.535373 | − | 0.844616i | \(-0.320171\pi\) | ||||
0.535373 | + | 0.844616i | \(0.320171\pi\) | |||||||
\(434\) | 1.69281e14 | 0.527733 | ||||||||
\(435\) | 5.91434e13 | 0.182060 | ||||||||
\(436\) | 1.38623e11 | 0.000421366 0 | ||||||||
\(437\) | −2.59980e12 | −0.00780355 | ||||||||
\(438\) | −2.72277e13 | −0.0807056 | ||||||||
\(439\) | 4.69140e14 | 1.37324 | 0.686622 | − | 0.727015i | \(-0.259093\pi\) | ||||
0.686622 | + | 0.727015i | \(0.259093\pi\) | |||||||
\(440\) | 5.81007e14 | 1.67954 | ||||||||
\(441\) | 6.43846e13 | 0.183810 | ||||||||
\(442\) | 2.27904e14 | 0.642583 | ||||||||
\(443\) | 2.89324e14 | 0.805682 | 0.402841 | − | 0.915270i | \(-0.368023\pi\) | ||||
0.402841 | + | 0.915270i | \(0.368023\pi\) | |||||||
\(444\) | 1.82156e14 | 0.500999 | ||||||||
\(445\) | −6.85785e14 | −1.86298 | ||||||||
\(446\) | 2.45828e14 | 0.659613 | ||||||||
\(447\) | −2.23015e13 | −0.0591076 | ||||||||
\(448\) | 4.06246e14 | 1.06355 | ||||||||
\(449\) | 4.27685e14 | 1.10604 | 0.553018 | − | 0.833169i | \(-0.313476\pi\) | ||||
0.553018 | + | 0.833169i | \(0.313476\pi\) | |||||||
\(450\) | 2.59601e13 | 0.0663188 | ||||||||
\(451\) | 1.47515e14 | 0.372277 | ||||||||
\(452\) | 2.82037e14 | 0.703144 | ||||||||
\(453\) | −1.16188e14 | −0.286169 | ||||||||
\(454\) | 1.67874e14 | 0.408484 | ||||||||
\(455\) | 3.75104e14 | 0.901756 | ||||||||
\(456\) | 5.60465e12 | 0.0133120 | ||||||||
\(457\) | −5.39035e14 | −1.26496 | −0.632482 | − | 0.774575i | \(-0.717964\pi\) | ||||
−0.632482 | + | 0.774575i | \(0.717964\pi\) | |||||||
\(458\) | 4.12563e14 | 0.956600 | ||||||||
\(459\) | −1.20948e14 | −0.277096 | ||||||||
\(460\) | 9.16125e13 | 0.207389 | ||||||||
\(461\) | −2.58635e14 | −0.578538 | −0.289269 | − | 0.957248i | \(-0.593412\pi\) | ||||
−0.289269 | + | 0.957248i | \(0.593412\pi\) | |||||||
\(462\) | 3.18880e14 | 0.704849 | ||||||||
\(463\) | 8.68735e14 | 1.89754 | 0.948772 | − | 0.315961i | \(-0.102327\pi\) | ||||
0.948772 | + | 0.315961i | \(0.102327\pi\) | |||||||
\(464\) | 2.91644e13 | 0.0629512 | ||||||||
\(465\) | −1.86031e14 | −0.396821 | ||||||||
\(466\) | 2.37070e14 | 0.499752 | ||||||||
\(467\) | 1.04128e14 | 0.216934 | 0.108467 | − | 0.994100i | \(-0.465406\pi\) | ||||
0.108467 | + | 0.994100i | \(0.465406\pi\) | |||||||
\(468\) | 5.29224e13 | 0.108965 | ||||||||
\(469\) | 1.91183e14 | 0.389044 | ||||||||
\(470\) | 9.39642e13 | 0.188984 | ||||||||
\(471\) | 5.49185e13 | 0.109170 | ||||||||
\(472\) | −6.99921e13 | −0.137521 | ||||||||
\(473\) | 1.26956e15 | 2.46556 | ||||||||
\(474\) | 2.47276e14 | 0.474681 | ||||||||
\(475\) | −3.27551e12 | −0.00621533 | ||||||||
\(476\) | 4.89341e14 | 0.917853 | ||||||||
\(477\) | −1.44546e14 | −0.268013 | ||||||||
\(478\) | 3.56967e14 | 0.654297 | ||||||||
\(479\) | 9.78913e13 | 0.177378 | 0.0886888 | − | 0.996059i | \(-0.471732\pi\) | ||||
0.0886888 | + | 0.996059i | \(0.471732\pi\) | |||||||
\(480\) | −3.28137e14 | −0.587798 | ||||||||
\(481\) | 6.11526e14 | 1.08297 | ||||||||
\(482\) | −3.01021e14 | −0.527034 | ||||||||
\(483\) | 1.48525e14 | 0.257092 | ||||||||
\(484\) | −2.89416e14 | −0.495306 | ||||||||
\(485\) | 8.04966e14 | 1.36207 | ||||||||
\(486\) | 2.67916e13 | 0.0448228 | ||||||||
\(487\) | −1.79576e14 | −0.297057 | −0.148528 | − | 0.988908i | \(-0.547454\pi\) | ||||
−0.148528 | + | 0.988908i | \(0.547454\pi\) | |||||||
\(488\) | −1.13648e14 | −0.185889 | ||||||||
\(489\) | 5.45635e14 | 0.882476 | ||||||||
\(490\) | −2.73074e14 | −0.436719 | ||||||||
\(491\) | −9.44720e14 | −1.49401 | −0.747007 | − | 0.664816i | \(-0.768510\pi\) | ||||
−0.747007 | + | 0.664816i | \(0.768510\pi\) | |||||||
\(492\) | −5.01440e13 | −0.0784172 | ||||||||
\(493\) | 2.59023e14 | 0.400572 | ||||||||
\(494\) | 6.36976e12 | 0.00974148 | ||||||||
\(495\) | −3.50433e14 | −0.530000 | ||||||||
\(496\) | −9.17343e13 | −0.137209 | ||||||||
\(497\) | 1.60390e15 | 2.37255 | ||||||||
\(498\) | 4.59033e14 | 0.671556 | ||||||||
\(499\) | −5.43255e14 | −0.786051 | −0.393026 | − | 0.919528i | \(-0.628572\pi\) | ||||
−0.393026 | + | 0.919528i | \(0.628572\pi\) | |||||||
\(500\) | −2.89934e14 | −0.414919 | ||||||||
\(501\) | 2.06207e14 | 0.291875 | ||||||||
\(502\) | −6.48270e14 | −0.907582 | ||||||||
\(503\) | 5.41766e14 | 0.750219 | 0.375109 | − | 0.926981i | \(-0.377605\pi\) | ||||
0.375109 | + | 0.926981i | \(0.377605\pi\) | |||||||
\(504\) | −3.20190e14 | −0.438570 | ||||||||
\(505\) | −1.18086e15 | −1.59992 | ||||||||
\(506\) | 2.61458e14 | 0.350408 | ||||||||
\(507\) | −2.57826e14 | −0.341808 | ||||||||
\(508\) | −2.75174e14 | −0.360875 | ||||||||
\(509\) | 8.67796e14 | 1.12582 | 0.562911 | − | 0.826518i | \(-0.309681\pi\) | ||||
0.562911 | + | 0.826518i | \(0.309681\pi\) | |||||||
\(510\) | 5.12977e14 | 0.658358 | ||||||||
\(511\) | −1.96265e14 | −0.249189 | ||||||||
\(512\) | −3.52098e14 | −0.442261 | ||||||||
\(513\) | −3.38043e12 | −0.00420075 | ||||||||
\(514\) | −7.99001e14 | −0.982313 | ||||||||
\(515\) | −1.76735e14 | −0.214972 | ||||||||
\(516\) | −4.31553e14 | −0.519350 | ||||||||
\(517\) | −2.81126e14 | −0.334736 | ||||||||
\(518\) | −1.25252e15 | −1.47561 | ||||||||
\(519\) | −5.43997e14 | −0.634127 | ||||||||
\(520\) | −6.63034e14 | −0.764746 | ||||||||
\(521\) | 1.74053e15 | 1.98644 | 0.993219 | − | 0.116259i | \(-0.0370904\pi\) | ||||
0.993219 | + | 0.116259i | \(0.0370904\pi\) | |||||||
\(522\) | −5.73768e13 | −0.0647960 | ||||||||
\(523\) | 1.55814e15 | 1.74119 | 0.870596 | − | 0.491998i | \(-0.163733\pi\) | ||||
0.870596 | + | 0.491998i | \(0.163733\pi\) | |||||||
\(524\) | −5.74472e14 | −0.635253 | ||||||||
\(525\) | 1.87128e14 | 0.204768 | ||||||||
\(526\) | 1.97698e14 | 0.214083 | ||||||||
\(527\) | −8.14737e14 | −0.873090 | ||||||||
\(528\) | −1.72803e14 | −0.183259 | ||||||||
\(529\) | −8.31030e14 | −0.872189 | ||||||||
\(530\) | 6.13062e14 | 0.636776 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | 1.36768e13 | 0.0139145 | ||||||||
\(533\) | −1.68342e14 | −0.169509 | ||||||||
\(534\) | 6.65300e14 | 0.663041 | ||||||||
\(535\) | −1.63877e15 | −1.61648 | ||||||||
\(536\) | −3.37935e14 | −0.329933 | ||||||||
\(537\) | −3.13461e14 | −0.302918 | ||||||||
\(538\) | −3.89152e14 | −0.372235 | ||||||||
\(539\) | 8.16993e14 | 0.773535 | ||||||||
\(540\) | 1.19121e14 | 0.111640 | ||||||||
\(541\) | 4.54369e14 | 0.421526 | 0.210763 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210763 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(542\) | 6.25501e14 | 0.574423 | ||||||||
\(543\) | 8.04885e14 | 0.731703 | ||||||||
\(544\) | −1.43710e15 | −1.29328 | ||||||||
\(545\) | 1.04750e12 | 0.000933198 0 | ||||||||
\(546\) | −3.63900e14 | −0.320939 | ||||||||
\(547\) | 2.80242e14 | 0.244683 | 0.122341 | − | 0.992488i | \(-0.460960\pi\) | ||||
0.122341 | + | 0.992488i | \(0.460960\pi\) | |||||||
\(548\) | 4.01762e14 | 0.347277 | ||||||||
\(549\) | 6.85466e13 | 0.0586595 | ||||||||
\(550\) | 3.29414e14 | 0.279092 | ||||||||
\(551\) | 7.23952e12 | 0.00607262 | ||||||||
\(552\) | −2.62532e14 | −0.218031 | ||||||||
\(553\) | 1.78244e15 | 1.46564 | ||||||||
\(554\) | 3.50702e14 | 0.285519 | ||||||||
\(555\) | 1.37645e15 | 1.10956 | ||||||||
\(556\) | 9.42430e13 | 0.0752207 | ||||||||
\(557\) | −9.57487e14 | −0.756710 | −0.378355 | − | 0.925661i | \(-0.623510\pi\) | ||||
−0.378355 | + | 0.925661i | \(0.623510\pi\) | |||||||
\(558\) | 1.80474e14 | 0.141230 | ||||||||
\(559\) | −1.44879e15 | −1.12264 | ||||||||
\(560\) | 4.16337e14 | 0.319456 | ||||||||
\(561\) | −1.53475e15 | −1.16611 | ||||||||
\(562\) | −1.20848e15 | −0.909264 | ||||||||
\(563\) | 3.47122e14 | 0.258634 | 0.129317 | − | 0.991603i | \(-0.458721\pi\) | ||||
0.129317 | + | 0.991603i | \(0.458721\pi\) | |||||||
\(564\) | 9.55615e13 | 0.0705095 | ||||||||
\(565\) | 2.13120e15 | 1.55725 | ||||||||
\(566\) | −1.92180e14 | −0.139065 | ||||||||
\(567\) | 1.93121e14 | 0.138396 | ||||||||
\(568\) | −2.83505e15 | −2.01207 | ||||||||
\(569\) | 1.78084e15 | 1.25172 | 0.625860 | − | 0.779936i | \(-0.284748\pi\) | ||||
0.625860 | + | 0.779936i | \(0.284748\pi\) | |||||||
\(570\) | 1.43374e13 | 0.00998063 | ||||||||
\(571\) | −1.77494e15 | −1.22373 | −0.611866 | − | 0.790962i | \(-0.709581\pi\) | ||||
−0.611866 | + | 0.790962i | \(0.709581\pi\) | |||||||
\(572\) | 6.71546e14 | 0.458562 | ||||||||
\(573\) | 1.25772e15 | 0.850614 | ||||||||
\(574\) | 3.44795e14 | 0.230965 | ||||||||
\(575\) | 1.53431e14 | 0.101798 | ||||||||
\(576\) | 4.33108e14 | 0.284625 | ||||||||
\(577\) | −1.72513e15 | −1.12293 | −0.561467 | − | 0.827499i | \(-0.689763\pi\) | ||||
−0.561467 | + | 0.827499i | \(0.689763\pi\) | |||||||
\(578\) | 1.16293e15 | 0.749810 | ||||||||
\(579\) | 1.03755e15 | 0.662636 | ||||||||
\(580\) | −2.55108e14 | −0.161388 | ||||||||
\(581\) | 3.30884e15 | 2.07352 | ||||||||
\(582\) | −7.80921e14 | −0.484764 | ||||||||
\(583\) | −1.83418e15 | −1.12789 | ||||||||
\(584\) | 3.46919e14 | 0.211328 | ||||||||
\(585\) | 3.99907e14 | 0.241325 | ||||||||
\(586\) | 1.64392e15 | 0.982753 | ||||||||
\(587\) | −4.62864e14 | −0.274122 | −0.137061 | − | 0.990563i | \(-0.543766\pi\) | ||||
−0.137061 | + | 0.990563i | \(0.543766\pi\) | |||||||
\(588\) | −2.77716e14 | −0.162939 | ||||||||
\(589\) | −2.27713e13 | −0.0132359 | ||||||||
\(590\) | −1.79048e14 | −0.103106 | ||||||||
\(591\) | −4.28342e14 | −0.244377 | ||||||||
\(592\) | 6.78747e14 | 0.383653 | ||||||||
\(593\) | 1.66652e15 | 0.933276 | 0.466638 | − | 0.884448i | \(-0.345465\pi\) | ||||
0.466638 | + | 0.884448i | \(0.345465\pi\) | |||||||
\(594\) | 3.39965e14 | 0.188629 | ||||||||
\(595\) | 3.69769e15 | 2.03277 | ||||||||
\(596\) | 9.61951e13 | 0.0523961 | ||||||||
\(597\) | −2.54686e14 | −0.137450 | ||||||||
\(598\) | −2.98371e14 | −0.159551 | ||||||||
\(599\) | 1.04977e15 | 0.556222 | 0.278111 | − | 0.960549i | \(-0.410292\pi\) | ||||
0.278111 | + | 0.960549i | \(0.410292\pi\) | |||||||
\(600\) | −3.30767e14 | −0.173656 | ||||||||
\(601\) | 9.21075e14 | 0.479166 | 0.239583 | − | 0.970876i | \(-0.422989\pi\) | ||||
0.239583 | + | 0.970876i | \(0.422989\pi\) | |||||||
\(602\) | 2.96740e15 | 1.52966 | ||||||||
\(603\) | 2.03824e14 | 0.104114 | ||||||||
\(604\) | 5.01164e14 | 0.253675 | ||||||||
\(605\) | −2.18696e15 | −1.09695 | ||||||||
\(606\) | 1.14559e15 | 0.569417 | ||||||||
\(607\) | −3.46584e15 | −1.70715 | −0.853574 | − | 0.520972i | \(-0.825569\pi\) | ||||
−0.853574 | + | 0.520972i | \(0.825569\pi\) | |||||||
\(608\) | −4.01660e13 | −0.0196060 | ||||||||
\(609\) | −4.13588e14 | −0.200066 | ||||||||
\(610\) | −2.90726e14 | −0.139370 | ||||||||
\(611\) | 3.20815e14 | 0.152415 | ||||||||
\(612\) | 5.21697e14 | 0.245632 | ||||||||
\(613\) | 6.47040e13 | 0.0301925 | 0.0150962 | − | 0.999886i | \(-0.495195\pi\) | ||||
0.0150962 | + | 0.999886i | \(0.495195\pi\) | |||||||
\(614\) | −5.99363e14 | −0.277181 | ||||||||
\(615\) | −3.78912e14 | −0.173670 | ||||||||
\(616\) | −4.06297e15 | −1.84565 | ||||||||
\(617\) | −1.03087e15 | −0.464127 | −0.232064 | − | 0.972701i | \(-0.574548\pi\) | ||||
−0.232064 | + | 0.972701i | \(0.574548\pi\) | |||||||
\(618\) | 1.71456e14 | 0.0765095 | ||||||||
\(619\) | −1.27656e15 | −0.564601 | −0.282300 | − | 0.959326i | \(-0.591097\pi\) | ||||
−0.282300 | + | 0.959326i | \(0.591097\pi\) | |||||||
\(620\) | 8.02423e14 | 0.351762 | ||||||||
\(621\) | 1.58345e14 | 0.0688021 | ||||||||
\(622\) | −9.46663e14 | −0.407707 | ||||||||
\(623\) | 4.79567e15 | 2.04722 | ||||||||
\(624\) | 1.97199e14 | 0.0834430 | ||||||||
\(625\) | −2.86976e15 | −1.20367 | ||||||||
\(626\) | 1.54973e14 | 0.0644315 | ||||||||
\(627\) | −4.28951e13 | −0.0176781 | ||||||||
\(628\) | −2.36884e14 | −0.0967739 | ||||||||
\(629\) | 6.02828e15 | 2.44127 | ||||||||
\(630\) | −8.19084e14 | −0.328818 | ||||||||
\(631\) | −7.49684e14 | −0.298343 | −0.149172 | − | 0.988811i | \(-0.547661\pi\) | ||||
−0.149172 | + | 0.988811i | \(0.547661\pi\) | |||||||
\(632\) | −3.15064e15 | −1.24295 | ||||||||
\(633\) | −2.23864e15 | −0.875517 | ||||||||
\(634\) | 8.09182e14 | 0.313729 | ||||||||
\(635\) | −2.07934e15 | −0.799228 | ||||||||
\(636\) | 6.23483e14 | 0.237580 | ||||||||
\(637\) | −9.32337e14 | −0.352213 | ||||||||
\(638\) | −7.28068e14 | −0.272683 | ||||||||
\(639\) | 1.70995e15 | 0.634934 | ||||||||
\(640\) | 9.28596e14 | 0.341851 | ||||||||
\(641\) | −2.94694e15 | −1.07560 | −0.537801 | − | 0.843072i | \(-0.680745\pi\) | ||||
−0.537801 | + | 0.843072i | \(0.680745\pi\) | |||||||
\(642\) | 1.58982e15 | 0.575313 | ||||||||
\(643\) | 2.62564e15 | 0.942053 | 0.471027 | − | 0.882119i | \(-0.343884\pi\) | ||||
0.471027 | + | 0.882119i | \(0.343884\pi\) | |||||||
\(644\) | −6.40644e14 | −0.227900 | ||||||||
\(645\) | −3.26102e15 | −1.15020 | ||||||||
\(646\) | 6.27916e13 | 0.0219595 | ||||||||
\(647\) | −3.82331e14 | −0.132576 | −0.0662882 | − | 0.997801i | \(-0.521116\pi\) | ||||
−0.0662882 | + | 0.997801i | \(0.521116\pi\) | |||||||
\(648\) | −3.41361e14 | −0.117369 | ||||||||
\(649\) | 5.35684e14 | 0.182626 | ||||||||
\(650\) | −3.75921e14 | −0.127079 | ||||||||
\(651\) | 1.30091e15 | 0.436066 | ||||||||
\(652\) | −2.35353e15 | −0.782273 | ||||||||
\(653\) | −5.99018e14 | −0.197432 | −0.0987160 | − | 0.995116i | \(-0.531474\pi\) | ||||
−0.0987160 | + | 0.995116i | \(0.531474\pi\) | |||||||
\(654\) | −1.01621e12 | −0.000332129 0 | ||||||||
\(655\) | −4.34098e15 | −1.40689 | ||||||||
\(656\) | −1.86846e14 | −0.0600501 | ||||||||
\(657\) | −2.09243e14 | −0.0666870 | ||||||||
\(658\) | −6.57090e14 | −0.207674 | ||||||||
\(659\) | −6.11779e15 | −1.91745 | −0.958727 | − | 0.284327i | \(-0.908230\pi\) | ||||
−0.958727 | + | 0.284327i | \(0.908230\pi\) | |||||||
\(660\) | 1.51155e15 | 0.469820 | ||||||||
\(661\) | 2.93249e15 | 0.903917 | 0.451959 | − | 0.892039i | \(-0.350725\pi\) | ||||
0.451959 | + | 0.892039i | \(0.350725\pi\) | |||||||
\(662\) | −3.38755e15 | −1.03554 | ||||||||
\(663\) | 1.75142e15 | 0.530966 | ||||||||
\(664\) | −5.84871e15 | −1.75847 | ||||||||
\(665\) | 1.03348e14 | 0.0308165 | ||||||||
\(666\) | −1.33534e15 | −0.394897 | ||||||||
\(667\) | −3.39112e14 | −0.0994607 | ||||||||
\(668\) | −8.89451e14 | −0.258733 | ||||||||
\(669\) | 1.88917e15 | 0.545038 | ||||||||
\(670\) | −8.64478e14 | −0.247367 | ||||||||
\(671\) | 8.69806e14 | 0.246859 | ||||||||
\(672\) | 2.29465e15 | 0.645931 | ||||||||
\(673\) | 4.96390e15 | 1.38593 | 0.692963 | − | 0.720973i | \(-0.256305\pi\) | ||||
0.692963 | + | 0.720973i | \(0.256305\pi\) | |||||||
\(674\) | 2.84220e14 | 0.0787091 | ||||||||
\(675\) | 1.99501e14 | 0.0547992 | ||||||||
\(676\) | 1.11210e15 | 0.302996 | ||||||||
\(677\) | −2.98893e15 | −0.807751 | −0.403875 | − | 0.914814i | \(-0.632337\pi\) | ||||
−0.403875 | + | 0.914814i | \(0.632337\pi\) | |||||||
\(678\) | −2.06754e15 | −0.554232 | ||||||||
\(679\) | −5.62911e15 | −1.49677 | ||||||||
\(680\) | −6.53603e15 | −1.72391 | ||||||||
\(681\) | 1.29010e15 | 0.337530 | ||||||||
\(682\) | 2.29008e15 | 0.594343 | ||||||||
\(683\) | 3.57204e15 | 0.919607 | 0.459804 | − | 0.888021i | \(-0.347920\pi\) | ||||
0.459804 | + | 0.888021i | \(0.347920\pi\) | |||||||
\(684\) | 1.45811e13 | 0.00372376 | ||||||||
\(685\) | 3.03591e15 | 0.769113 | ||||||||
\(686\) | −1.55339e15 | −0.390389 | ||||||||
\(687\) | 3.17052e15 | 0.790438 | ||||||||
\(688\) | −1.60805e15 | −0.397706 | ||||||||
\(689\) | 2.09313e15 | 0.513560 | ||||||||
\(690\) | −6.71589e14 | −0.163468 | ||||||||
\(691\) | 1.69191e15 | 0.408553 | 0.204276 | − | 0.978913i | \(-0.434516\pi\) | ||||
0.204276 | + | 0.978913i | \(0.434516\pi\) | |||||||
\(692\) | 2.34647e15 | 0.562123 | ||||||||
\(693\) | 2.45057e15 | 0.582417 | ||||||||
\(694\) | 4.16634e15 | 0.982376 | ||||||||
\(695\) | 7.12144e14 | 0.166591 | ||||||||
\(696\) | 7.31059e14 | 0.169669 | ||||||||
\(697\) | −1.65947e15 | −0.382111 | ||||||||
\(698\) | −5.38224e15 | −1.22958 | ||||||||
\(699\) | 1.82187e15 | 0.412945 | ||||||||
\(700\) | −8.07153e14 | −0.181517 | ||||||||
\(701\) | 1.49899e15 | 0.334465 | 0.167232 | − | 0.985918i | \(-0.446517\pi\) | ||||
0.167232 | + | 0.985918i | \(0.446517\pi\) | |||||||
\(702\) | −3.87962e14 | −0.0858884 | ||||||||
\(703\) | 1.68487e14 | 0.0370093 | ||||||||
\(704\) | 5.49581e15 | 1.19779 | ||||||||
\(705\) | 7.22108e14 | 0.156157 | ||||||||
\(706\) | 5.67324e15 | 1.21732 | ||||||||
\(707\) | 8.25775e15 | 1.75815 | ||||||||
\(708\) | −1.82092e14 | −0.0384687 | ||||||||
\(709\) | 1.36239e14 | 0.0285592 | 0.0142796 | − | 0.999898i | \(-0.495455\pi\) | ||||
0.0142796 | + | 0.999898i | \(0.495455\pi\) | |||||||
\(710\) | −7.25239e15 | −1.50855 | ||||||||
\(711\) | 1.90030e15 | 0.392228 | ||||||||
\(712\) | −8.47683e15 | −1.73618 | ||||||||
\(713\) | 1.06665e15 | 0.216785 | ||||||||
\(714\) | −3.58724e15 | −0.723469 | ||||||||
\(715\) | 5.07452e15 | 1.01557 | ||||||||
\(716\) | 1.35208e15 | 0.268522 | ||||||||
\(717\) | 2.74326e15 | 0.540645 | ||||||||
\(718\) | −3.03882e15 | −0.594321 | ||||||||
\(719\) | −4.57140e15 | −0.887239 | −0.443619 | − | 0.896215i | \(-0.646306\pi\) | ||||
−0.443619 | + | 0.896215i | \(0.646306\pi\) | |||||||
\(720\) | 4.43866e14 | 0.0854916 | ||||||||
\(721\) | 1.23590e15 | 0.236233 | ||||||||
\(722\) | −3.68171e15 | −0.698385 | ||||||||
\(723\) | −2.31333e15 | −0.435488 | ||||||||
\(724\) | −3.47178e15 | −0.648619 | ||||||||
\(725\) | −4.27251e14 | −0.0792180 | ||||||||
\(726\) | 2.12164e15 | 0.390409 | ||||||||
\(727\) | −9.31384e15 | −1.70094 | −0.850471 | − | 0.526021i | \(-0.823683\pi\) | ||||
−0.850471 | + | 0.526021i | \(0.823683\pi\) | |||||||
\(728\) | 4.63658e15 | 0.840379 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 8.87460e14 | 0.158443 | ||||||||
\(731\) | −1.42819e16 | −2.53069 | ||||||||
\(732\) | −2.95668e14 | −0.0519988 | ||||||||
\(733\) | −2.93431e15 | −0.512194 | −0.256097 | − | 0.966651i | \(-0.582437\pi\) | ||||
−0.256097 | + | 0.966651i | \(0.582437\pi\) | |||||||
\(734\) | 2.40520e15 | 0.416700 | ||||||||
\(735\) | −2.09855e15 | −0.360860 | ||||||||
\(736\) | 1.88145e15 | 0.321118 | ||||||||
\(737\) | 2.58638e15 | 0.438148 | ||||||||
\(738\) | 3.67594e14 | 0.0618099 | ||||||||
\(739\) | −5.80834e14 | −0.0969410 | −0.0484705 | − | 0.998825i | \(-0.515435\pi\) | ||||
−0.0484705 | + | 0.998825i | \(0.515435\pi\) | |||||||
\(740\) | −5.93718e15 | −0.983571 | ||||||||
\(741\) | 4.89511e13 | 0.00804938 | ||||||||
\(742\) | −4.28713e15 | −0.699753 | ||||||||
\(743\) | 9.69848e15 | 1.57132 | 0.785661 | − | 0.618657i | \(-0.212323\pi\) | ||||
0.785661 | + | 0.618657i | \(0.212323\pi\) | |||||||
\(744\) | −2.29949e15 | −0.369811 | ||||||||
\(745\) | 7.26896e14 | 0.116041 | ||||||||
\(746\) | −7.05821e15 | −1.11849 | ||||||||
\(747\) | 3.52763e15 | 0.554907 | ||||||||
\(748\) | 6.61995e15 | 1.03370 | ||||||||
\(749\) | 1.14599e16 | 1.77635 | ||||||||
\(750\) | 2.12543e15 | 0.327047 | ||||||||
\(751\) | −2.36608e15 | −0.361418 | −0.180709 | − | 0.983537i | \(-0.557839\pi\) | ||||
−0.180709 | + | 0.983537i | \(0.557839\pi\) | |||||||
\(752\) | 3.56080e14 | 0.0539946 | ||||||||
\(753\) | −4.98191e15 | −0.749934 | ||||||||
\(754\) | 8.30858e14 | 0.124161 | ||||||||
\(755\) | 3.78703e15 | 0.561812 | ||||||||
\(756\) | −8.33007e14 | −0.122681 | ||||||||
\(757\) | 1.38403e15 | 0.202357 | 0.101179 | − | 0.994868i | \(-0.467739\pi\) | ||||
0.101179 | + | 0.994868i | \(0.467739\pi\) | |||||||
\(758\) | −2.77244e15 | −0.402421 | ||||||||
\(759\) | 2.00929e15 | 0.289542 | ||||||||
\(760\) | −1.82678e14 | −0.0261343 | ||||||||
\(761\) | −1.12056e16 | −1.59155 | −0.795776 | − | 0.605591i | \(-0.792937\pi\) | ||||
−0.795776 | + | 0.605591i | \(0.792937\pi\) | |||||||
\(762\) | 2.01723e15 | 0.284448 | ||||||||
\(763\) | −7.32515e12 | −0.00102549 | ||||||||
\(764\) | −5.42502e15 | −0.754029 | ||||||||
\(765\) | 3.94219e15 | 0.544001 | ||||||||
\(766\) | 3.48151e15 | 0.476991 | ||||||||
\(767\) | −6.11312e14 | −0.0831550 | ||||||||
\(768\) | −4.55108e15 | −0.614650 | ||||||||
\(769\) | 8.88072e15 | 1.19084 | 0.595420 | − | 0.803415i | \(-0.296986\pi\) | ||||
0.595420 | + | 0.803415i | \(0.296986\pi\) | |||||||
\(770\) | −1.03936e16 | −1.38377 | ||||||||
\(771\) | −6.14026e15 | −0.811685 | ||||||||
\(772\) | −4.47533e15 | −0.587395 | ||||||||
\(773\) | 4.81120e15 | 0.626997 | 0.313499 | − | 0.949589i | \(-0.398499\pi\) | ||||
0.313499 | + | 0.949589i | \(0.398499\pi\) | |||||||
\(774\) | 3.16361e15 | 0.409362 | ||||||||
\(775\) | 1.34388e15 | 0.172664 | ||||||||
\(776\) | 9.95000e15 | 1.26936 | ||||||||
\(777\) | −9.62551e15 | −1.21929 | ||||||||
\(778\) | 3.22427e15 | 0.405549 | ||||||||
\(779\) | −4.63812e13 | −0.00579276 | ||||||||
\(780\) | −1.72495e15 | −0.213923 | ||||||||
\(781\) | 2.16980e16 | 2.67201 | ||||||||
\(782\) | −2.94127e15 | −0.359665 | ||||||||
\(783\) | −4.40936e14 | −0.0535409 | ||||||||
\(784\) | −1.03482e15 | −0.124775 | ||||||||
\(785\) | −1.79001e15 | −0.214325 | ||||||||
\(786\) | 4.21132e15 | 0.500719 | ||||||||
\(787\) | 4.41430e15 | 0.521196 | 0.260598 | − | 0.965447i | \(-0.416080\pi\) | ||||
0.260598 | + | 0.965447i | \(0.416080\pi\) | |||||||
\(788\) | 1.84760e15 | 0.216628 | ||||||||
\(789\) | 1.51930e15 | 0.176896 | ||||||||
\(790\) | −8.05971e15 | −0.931903 | ||||||||
\(791\) | −1.49035e16 | −1.71126 | ||||||||
\(792\) | −4.33162e15 | −0.493926 | ||||||||
\(793\) | −9.92606e14 | −0.112402 | ||||||||
\(794\) | 6.40924e15 | 0.720765 | ||||||||
\(795\) | 4.71133e15 | 0.526168 | ||||||||
\(796\) | 1.09856e15 | 0.121843 | ||||||||
\(797\) | 1.28696e16 | 1.41757 | 0.708786 | − | 0.705424i | \(-0.249243\pi\) | ||||
0.708786 | + | 0.705424i | \(0.249243\pi\) | |||||||
\(798\) | −1.00261e14 | −0.0109677 | ||||||||
\(799\) | 3.16252e15 | 0.343579 | ||||||||
\(800\) | 2.37045e15 | 0.255762 | ||||||||
\(801\) | 5.11278e15 | 0.547871 | ||||||||
\(802\) | −7.31166e15 | −0.778138 | ||||||||
\(803\) | −2.65514e15 | −0.280641 | ||||||||
\(804\) | −8.79172e14 | −0.0922924 | ||||||||
\(805\) | −4.84101e15 | −0.504729 | ||||||||
\(806\) | −2.61340e15 | −0.270622 | ||||||||
\(807\) | −2.99060e15 | −0.307577 | ||||||||
\(808\) | −1.45964e16 | −1.49102 | ||||||||
\(809\) | −1.48045e15 | −0.150203 | −0.0751014 | − | 0.997176i | \(-0.523928\pi\) | ||||
−0.0751014 | + | 0.997176i | \(0.523928\pi\) | |||||||
\(810\) | −8.73244e14 | −0.0879970 | ||||||||
\(811\) | 7.61346e14 | 0.0762021 | 0.0381011 | − | 0.999274i | \(-0.487869\pi\) | ||||
0.0381011 | + | 0.999274i | \(0.487869\pi\) | |||||||
\(812\) | 1.78397e15 | 0.177349 | ||||||||
\(813\) | 4.80692e15 | 0.474645 | ||||||||
\(814\) | −1.69445e16 | −1.66186 | ||||||||
\(815\) | −1.77844e16 | −1.73250 | ||||||||
\(816\) | 1.94394e15 | 0.188100 | ||||||||
\(817\) | −3.99168e14 | −0.0383650 | ||||||||
\(818\) | 2.83870e15 | 0.271005 | ||||||||
\(819\) | −2.79654e15 | −0.265191 | ||||||||
\(820\) | 1.63439e15 | 0.153950 | ||||||||
\(821\) | −4.31889e15 | −0.404096 | −0.202048 | − | 0.979376i | \(-0.564760\pi\) | ||||
−0.202048 | + | 0.979376i | \(0.564760\pi\) | |||||||
\(822\) | −2.94522e15 | −0.273730 | ||||||||
\(823\) | −1.00319e16 | −0.926158 | −0.463079 | − | 0.886317i | \(-0.653255\pi\) | ||||
−0.463079 | + | 0.886317i | \(0.653255\pi\) | |||||||
\(824\) | −2.18458e15 | −0.200340 | ||||||||
\(825\) | 2.53152e15 | 0.230613 | ||||||||
\(826\) | 1.25208e15 | 0.113303 | ||||||||
\(827\) | 1.06302e16 | 0.955563 | 0.477782 | − | 0.878479i | \(-0.341441\pi\) | ||||
0.477782 | + | 0.878479i | \(0.341441\pi\) | |||||||
\(828\) | −6.83005e14 | −0.0609898 | ||||||||
\(829\) | −2.01838e16 | −1.79042 | −0.895208 | − | 0.445649i | \(-0.852973\pi\) | ||||
−0.895208 | + | 0.445649i | \(0.852973\pi\) | |||||||
\(830\) | −1.49617e16 | −1.31841 | ||||||||
\(831\) | 2.69512e15 | 0.235924 | ||||||||
\(832\) | −6.27172e15 | −0.545391 | ||||||||
\(833\) | −9.19076e15 | −0.793969 | ||||||||
\(834\) | −6.90872e14 | −0.0592904 | ||||||||
\(835\) | −6.72111e15 | −0.573014 | ||||||||
\(836\) | 1.85023e14 | 0.0156708 | ||||||||
\(837\) | 1.38693e15 | 0.116698 | ||||||||
\(838\) | 2.05549e15 | 0.171820 | ||||||||
\(839\) | 1.76431e16 | 1.46516 | 0.732578 | − | 0.680684i | \(-0.238317\pi\) | ||||
0.732578 | + | 0.680684i | \(0.238317\pi\) | |||||||
\(840\) | 1.04362e16 | 0.861010 | ||||||||
\(841\) | −1.12562e16 | −0.922601 | ||||||||
\(842\) | −9.47546e15 | −0.771585 | ||||||||
\(843\) | −9.28708e15 | −0.751325 | ||||||||
\(844\) | 9.65613e15 | 0.776104 | ||||||||
\(845\) | 8.40356e15 | 0.671045 | ||||||||
\(846\) | −7.00538e14 | −0.0555769 | ||||||||
\(847\) | 1.52934e16 | 1.20544 | ||||||||
\(848\) | 2.32322e15 | 0.181933 | ||||||||
\(849\) | −1.47689e15 | −0.114909 | ||||||||
\(850\) | −3.70574e15 | −0.286464 | ||||||||
\(851\) | −7.89222e15 | −0.606159 | ||||||||
\(852\) | −7.37567e15 | −0.562838 | ||||||||
\(853\) | −1.17114e16 | −0.887952 | −0.443976 | − | 0.896039i | \(-0.646432\pi\) | ||||
−0.443976 | + | 0.896039i | \(0.646432\pi\) | |||||||
\(854\) | 2.03304e15 | 0.153154 | ||||||||
\(855\) | 1.10182e14 | 0.00824699 | ||||||||
\(856\) | −2.02564e16 | −1.50646 | ||||||||
\(857\) | 1.71522e16 | 1.26743 | 0.633717 | − | 0.773565i | \(-0.281528\pi\) | ||||
0.633717 | + | 0.773565i | \(0.281528\pi\) | |||||||
\(858\) | −4.92294e15 | −0.361447 | ||||||||
\(859\) | 1.47994e16 | 1.07965 | 0.539824 | − | 0.841778i | \(-0.318491\pi\) | ||||
0.539824 | + | 0.841778i | \(0.318491\pi\) | |||||||
\(860\) | 1.40660e16 | 1.01960 | ||||||||
\(861\) | 2.64972e15 | 0.190846 | ||||||||
\(862\) | −1.25030e16 | −0.894796 | ||||||||
\(863\) | −1.22051e16 | −0.867924 | −0.433962 | − | 0.900931i | \(-0.642885\pi\) | ||||
−0.433962 | + | 0.900931i | \(0.642885\pi\) | |||||||
\(864\) | 2.44638e15 | 0.172862 | ||||||||
\(865\) | 1.77310e16 | 1.24493 | ||||||||
\(866\) | 1.07235e16 | 0.748149 | ||||||||
\(867\) | 8.93704e15 | 0.619568 | ||||||||
\(868\) | −5.61133e15 | −0.386551 | ||||||||
\(869\) | 2.41134e16 | 1.65063 | ||||||||
\(870\) | 1.87014e15 | 0.127209 | ||||||||
\(871\) | −2.95152e15 | −0.199502 | ||||||||
\(872\) | 1.29479e13 | 0.000869680 0 | ||||||||
\(873\) | −6.00132e15 | −0.400561 | ||||||||
\(874\) | −8.22066e13 | −0.00545248 | ||||||||
\(875\) | 1.53207e16 | 1.00980 | ||||||||
\(876\) | 9.02545e14 | 0.0591148 | ||||||||
\(877\) | −2.11165e16 | −1.37444 | −0.687219 | − | 0.726450i | \(-0.741169\pi\) | ||||
−0.687219 | + | 0.726450i | \(0.741169\pi\) | |||||||
\(878\) | 1.48344e16 | 0.959510 | ||||||||
\(879\) | 1.26334e16 | 0.812048 | ||||||||
\(880\) | 5.63233e15 | 0.359777 | ||||||||
\(881\) | 1.99684e16 | 1.26758 | 0.633791 | − | 0.773505i | \(-0.281498\pi\) | ||||
0.633791 | + | 0.773505i | \(0.281498\pi\) | |||||||
\(882\) | 2.03587e15 | 0.128432 | ||||||||
\(883\) | 1.34077e16 | 0.840564 | 0.420282 | − | 0.907393i | \(-0.361931\pi\) | ||||
0.420282 | + | 0.907393i | \(0.361931\pi\) | |||||||
\(884\) | −7.55456e15 | −0.470675 | ||||||||
\(885\) | −1.37597e15 | −0.0851965 | ||||||||
\(886\) | 9.14852e15 | 0.562944 | ||||||||
\(887\) | −1.64730e16 | −1.00738 | −0.503689 | − | 0.863885i | \(-0.668024\pi\) | ||||
−0.503689 | + | 0.863885i | \(0.668024\pi\) | |||||||
\(888\) | 1.70140e16 | 1.03404 | ||||||||
\(889\) | 1.45408e16 | 0.878271 | ||||||||
\(890\) | −2.16848e16 | −1.30170 | ||||||||
\(891\) | 2.61260e15 | 0.155864 | ||||||||
\(892\) | −8.14871e15 | −0.483150 | ||||||||
\(893\) | 8.83904e13 | 0.00520861 | ||||||||
\(894\) | −7.05183e14 | −0.0412996 | ||||||||
\(895\) | 1.02169e16 | 0.594695 | ||||||||
\(896\) | −6.49365e15 | −0.375660 | ||||||||
\(897\) | −2.29296e15 | −0.131837 | ||||||||
\(898\) | 1.35236e16 | 0.772807 | ||||||||
\(899\) | −2.97025e15 | −0.168700 | ||||||||
\(900\) | −8.60524e14 | −0.0485768 | ||||||||
\(901\) | 2.06336e16 | 1.15768 | ||||||||
\(902\) | 4.66449e15 | 0.260117 | ||||||||
\(903\) | 2.28042e16 | 1.26396 | ||||||||
\(904\) | 2.63433e16 | 1.45126 | ||||||||
\(905\) | −2.62344e16 | −1.43649 | ||||||||
\(906\) | −3.67391e15 | −0.199951 | ||||||||
\(907\) | 5.02962e15 | 0.272079 | 0.136039 | − | 0.990703i | \(-0.456563\pi\) | ||||
0.136039 | + | 0.990703i | \(0.456563\pi\) | |||||||
\(908\) | −5.56468e15 | −0.299204 | ||||||||
\(909\) | 8.80377e15 | 0.470509 | ||||||||
\(910\) | 1.18609e16 | 0.630074 | ||||||||
\(911\) | 3.83505e15 | 0.202497 | 0.101249 | − | 0.994861i | \(-0.467716\pi\) | ||||
0.101249 | + | 0.994861i | \(0.467716\pi\) | |||||||
\(912\) | 5.43320e13 | 0.00285157 | ||||||||
\(913\) | 4.47630e16 | 2.33523 | ||||||||
\(914\) | −1.70445e16 | −0.883853 | ||||||||
\(915\) | −2.23421e15 | −0.115162 | ||||||||
\(916\) | −1.36757e16 | −0.700685 | ||||||||
\(917\) | 3.03564e16 | 1.54603 | ||||||||
\(918\) | −3.82444e15 | −0.193612 | ||||||||
\(919\) | 1.61837e14 | 0.00814409 | 0.00407204 | − | 0.999992i | \(-0.498704\pi\) | ||||
0.00407204 | + | 0.999992i | \(0.498704\pi\) | |||||||
\(920\) | 8.55696e15 | 0.428042 | ||||||||
\(921\) | −4.60606e15 | −0.229035 | ||||||||
\(922\) | −8.17813e15 | −0.404235 | ||||||||
\(923\) | −2.47613e16 | −1.21665 | ||||||||
\(924\) | −1.05702e16 | −0.516284 | ||||||||
\(925\) | −9.94348e15 | −0.482790 | ||||||||
\(926\) | 2.74697e16 | 1.32585 | ||||||||
\(927\) | 1.31762e15 | 0.0632197 | ||||||||
\(928\) | −5.23916e15 | −0.249889 | ||||||||
\(929\) | −1.72229e16 | −0.816620 | −0.408310 | − | 0.912843i | \(-0.633882\pi\) | ||||
−0.408310 | + | 0.912843i | \(0.633882\pi\) | |||||||
\(930\) | −5.88237e15 | −0.277266 | ||||||||
\(931\) | −2.56876e14 | −0.0120365 | ||||||||
\(932\) | −7.85841e15 | −0.366056 | ||||||||
\(933\) | −7.27503e15 | −0.336888 | ||||||||
\(934\) | 3.29258e15 | 0.151575 | ||||||||
\(935\) | 5.00234e16 | 2.28934 | ||||||||
\(936\) | 4.94316e15 | 0.224899 | ||||||||
\(937\) | −2.47773e16 | −1.12069 | −0.560345 | − | 0.828259i | \(-0.689331\pi\) | ||||
−0.560345 | + | 0.828259i | \(0.689331\pi\) | |||||||
\(938\) | 6.04527e15 | 0.271832 | ||||||||
\(939\) | 1.19096e15 | 0.0532397 | ||||||||
\(940\) | −3.11473e15 | −0.138426 | ||||||||
\(941\) | −2.69347e16 | −1.19006 | −0.595031 | − | 0.803703i | \(-0.702860\pi\) | ||||
−0.595031 | + | 0.803703i | \(0.702860\pi\) | |||||||
\(942\) | 1.73654e15 | 0.0762791 | ||||||||
\(943\) | 2.17258e15 | 0.0948771 | ||||||||
\(944\) | −6.78510e14 | −0.0294585 | ||||||||
\(945\) | −6.29459e15 | −0.271702 | ||||||||
\(946\) | 4.01438e16 | 1.72273 | ||||||||
\(947\) | 1.90161e16 | 0.811328 | 0.405664 | − | 0.914022i | \(-0.367040\pi\) | ||||
0.405664 | + | 0.914022i | \(0.367040\pi\) | |||||||
\(948\) | −8.19672e15 | −0.347691 | ||||||||
\(949\) | 3.02999e15 | 0.127784 | ||||||||
\(950\) | −1.03573e14 | −0.00434276 | ||||||||
\(951\) | 6.21850e15 | 0.259234 | ||||||||
\(952\) | 4.57063e16 | 1.89441 | ||||||||
\(953\) | −1.78696e15 | −0.0736382 | −0.0368191 | − | 0.999322i | \(-0.511723\pi\) | ||||
−0.0368191 | + | 0.999322i | \(0.511723\pi\) | |||||||
\(954\) | −4.57060e15 | −0.187265 | ||||||||
\(955\) | −4.09940e16 | −1.66994 | ||||||||
\(956\) | −1.18327e16 | −0.479256 | ||||||||
\(957\) | −5.59515e15 | −0.225318 | ||||||||
\(958\) | 3.09536e15 | 0.123937 | ||||||||
\(959\) | −2.12300e16 | −0.845178 | ||||||||
\(960\) | −1.41167e16 | −0.558781 | ||||||||
\(961\) | −1.60658e16 | −0.632301 | ||||||||
\(962\) | 1.93367e16 | 0.756692 | ||||||||
\(963\) | 1.22176e16 | 0.475381 | ||||||||
\(964\) | 9.97826e15 | 0.386039 | ||||||||
\(965\) | −3.38177e16 | −1.30090 | ||||||||
\(966\) | 4.69640e15 | 0.179635 | ||||||||
\(967\) | 5.39211e15 | 0.205075 | 0.102538 | − | 0.994729i | \(-0.467304\pi\) | ||||
0.102538 | + | 0.994729i | \(0.467304\pi\) | |||||||
\(968\) | −2.70326e16 | −1.02229 | ||||||||
\(969\) | 4.82548e14 | 0.0181451 | ||||||||
\(970\) | 2.54533e16 | 0.951700 | ||||||||
\(971\) | −9.33620e15 | −0.347108 | −0.173554 | − | 0.984824i | \(-0.555525\pi\) | ||||
−0.173554 | + | 0.984824i | \(0.555525\pi\) | |||||||
\(972\) | −8.88087e14 | −0.0328315 | ||||||||
\(973\) | −4.98001e15 | −0.183067 | ||||||||
\(974\) | −5.67827e15 | −0.207559 | ||||||||
\(975\) | −2.88892e15 | −0.105005 | ||||||||
\(976\) | −1.10172e15 | −0.0398195 | ||||||||
\(977\) | 4.82539e16 | 1.73425 | 0.867127 | − | 0.498087i | \(-0.165964\pi\) | ||||
0.867127 | + | 0.498087i | \(0.165964\pi\) | |||||||
\(978\) | 1.72532e16 | 0.616602 | ||||||||
\(979\) | 6.48773e16 | 2.30562 | ||||||||
\(980\) | 9.05185e15 | 0.319885 | ||||||||
\(981\) | −7.80951e12 | −0.000274438 0 | ||||||||
\(982\) | −2.98724e16 | −1.04390 | ||||||||
\(983\) | 4.12510e16 | 1.43347 | 0.716737 | − | 0.697343i | \(-0.245635\pi\) | ||||
0.716737 | + | 0.697343i | \(0.245635\pi\) | |||||||
\(984\) | −4.68365e15 | −0.161849 | ||||||||
\(985\) | 1.39614e16 | 0.479765 | ||||||||
\(986\) | 8.19040e15 | 0.279887 | ||||||||
\(987\) | −5.04968e15 | −0.171601 | ||||||||
\(988\) | −2.11145e14 | −0.00713538 | ||||||||
\(989\) | 1.86978e16 | 0.628363 | ||||||||
\(990\) | −1.10808e16 | −0.370321 | ||||||||
\(991\) | 7.84497e15 | 0.260727 | 0.130364 | − | 0.991466i | \(-0.458386\pi\) | ||||
0.130364 | + | 0.991466i | \(0.458386\pi\) | |||||||
\(992\) | 1.64794e16 | 0.544661 | ||||||||
\(993\) | −2.60330e16 | −0.855665 | ||||||||
\(994\) | 5.07158e16 | 1.65775 | ||||||||
\(995\) | 8.30122e15 | 0.269845 | ||||||||
\(996\) | −1.52160e16 | −0.491898 | ||||||||
\(997\) | 3.85622e16 | 1.23976 | 0.619881 | − | 0.784696i | \(-0.287181\pi\) | ||||
0.619881 | + | 0.784696i | \(0.287181\pi\) | |||||||
\(998\) | −1.71779e16 | −0.549228 | ||||||||
\(999\) | −1.02620e16 | −0.326303 |
(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 | 177.12.a.d.1.18 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.18 | ✓ | 28 | 1.1 | even | 1 | trivial |