Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −112.878 | −1.24714 | −0.623570 | − | 0.781768i | \(-0.714318\pi\) | ||||
−0.623570 | + | 0.781768i | \(0.714318\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | 4549.48 | 0.555357 | ||||||||
\(5\) | 37606.3 | 1.07635 | 0.538177 | − | 0.842832i | \(-0.319113\pi\) | ||||
0.538177 | + | 0.842832i | \(0.319113\pi\) | |||||||
\(6\) | −82288.2 | −0.720036 | ||||||||
\(7\) | −60488.5 | −0.194328 | −0.0971641 | − | 0.995268i | \(-0.530977\pi\) | ||||
−0.0971641 | + | 0.995268i | \(0.530977\pi\) | |||||||
\(8\) | 411161. | 0.554532 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | −4.24493e6 | −1.34236 | ||||||||
\(11\) | −5.38497e6 | −0.916497 | −0.458248 | − | 0.888824i | \(-0.651523\pi\) | ||||
−0.458248 | + | 0.888824i | \(0.651523\pi\) | |||||||
\(12\) | 3.31657e6 | 0.320635 | ||||||||
\(13\) | 1.78547e7 | 1.02594 | 0.512969 | − | 0.858407i | \(-0.328546\pi\) | ||||
0.512969 | + | 0.858407i | \(0.328546\pi\) | |||||||
\(14\) | 6.82784e6 | 0.242354 | ||||||||
\(15\) | 2.74150e7 | 0.621434 | ||||||||
\(16\) | −8.36804e7 | −1.24694 | ||||||||
\(17\) | −7.26826e7 | −0.730318 | −0.365159 | − | 0.930945i | \(-0.618985\pi\) | ||||
−0.365159 | + | 0.930945i | \(0.618985\pi\) | |||||||
\(18\) | −5.99881e7 | −0.415713 | ||||||||
\(19\) | 2.05937e8 | 1.00424 | 0.502119 | − | 0.864799i | \(-0.332554\pi\) | ||||
0.502119 | + | 0.864799i | \(0.332554\pi\) | |||||||
\(20\) | 1.71089e8 | 0.597761 | ||||||||
\(21\) | −4.40961e7 | −0.112195 | ||||||||
\(22\) | 6.07846e8 | 1.14300 | ||||||||
\(23\) | −2.11582e8 | −0.298021 | −0.149011 | − | 0.988836i | \(-0.547609\pi\) | ||||
−0.149011 | + | 0.988836i | \(0.547609\pi\) | |||||||
\(24\) | 2.99736e8 | 0.320159 | ||||||||
\(25\) | 1.93529e8 | 0.158539 | ||||||||
\(26\) | −2.01541e9 | −1.27949 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −2.75192e8 | −0.107921 | ||||||||
\(29\) | 4.90852e9 | 1.53237 | 0.766185 | − | 0.642620i | \(-0.222152\pi\) | ||||
0.766185 | + | 0.642620i | \(0.222152\pi\) | |||||||
\(30\) | −3.09455e9 | −0.775014 | ||||||||
\(31\) | −5.76225e9 | −1.16611 | −0.583057 | − | 0.812431i | \(-0.698144\pi\) | ||||
−0.583057 | + | 0.812431i | \(0.698144\pi\) | |||||||
\(32\) | 6.07747e9 | 1.00057 | ||||||||
\(33\) | −3.92564e9 | −0.529140 | ||||||||
\(34\) | 8.20427e9 | 0.910809 | ||||||||
\(35\) | −2.27475e9 | −0.209166 | ||||||||
\(36\) | 2.41778e9 | 0.185119 | ||||||||
\(37\) | 5.09808e8 | 0.0326659 | 0.0163330 | − | 0.999867i | \(-0.494801\pi\) | ||||
0.0163330 | + | 0.999867i | \(0.494801\pi\) | |||||||
\(38\) | −2.32458e10 | −1.25242 | ||||||||
\(39\) | 1.30161e10 | 0.592326 | ||||||||
\(40\) | 1.54622e10 | 0.596873 | ||||||||
\(41\) | −4.36319e9 | −0.143453 | −0.0717264 | − | 0.997424i | \(-0.522851\pi\) | ||||
−0.0717264 | + | 0.997424i | \(0.522851\pi\) | |||||||
\(42\) | 4.97749e9 | 0.139923 | ||||||||
\(43\) | −1.35776e9 | −0.0327550 | −0.0163775 | − | 0.999866i | \(-0.505213\pi\) | ||||
−0.0163775 | + | 0.999866i | \(0.505213\pi\) | |||||||
\(44\) | −2.44988e10 | −0.508982 | ||||||||
\(45\) | 1.99855e10 | 0.358785 | ||||||||
\(46\) | 2.38830e10 | 0.371674 | ||||||||
\(47\) | −1.26930e11 | −1.71762 | −0.858812 | − | 0.512291i | \(-0.828797\pi\) | ||||
−0.858812 | + | 0.512291i | \(0.828797\pi\) | |||||||
\(48\) | −6.10030e10 | −0.719919 | ||||||||
\(49\) | −9.32301e10 | −0.962237 | ||||||||
\(50\) | −2.18452e10 | −0.197720 | ||||||||
\(51\) | −5.29856e10 | −0.421649 | ||||||||
\(52\) | 8.12297e10 | 0.569761 | ||||||||
\(53\) | −2.89318e10 | −0.179301 | −0.0896504 | − | 0.995973i | \(-0.528575\pi\) | ||||
−0.0896504 | + | 0.995973i | \(0.528575\pi\) | |||||||
\(54\) | −4.37313e10 | −0.240012 | ||||||||
\(55\) | −2.02509e11 | −0.986475 | ||||||||
\(56\) | −2.48705e10 | −0.107761 | ||||||||
\(57\) | 1.50128e11 | 0.579797 | ||||||||
\(58\) | −5.54065e11 | −1.91108 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | 1.24724e11 | 0.345117 | ||||||||
\(61\) | 2.30201e11 | 0.572088 | 0.286044 | − | 0.958216i | \(-0.407660\pi\) | ||||
0.286044 | + | 0.958216i | \(0.407660\pi\) | |||||||
\(62\) | 6.50432e11 | 1.45431 | ||||||||
\(63\) | −3.21461e10 | −0.0647761 | ||||||||
\(64\) | −5.03064e8 | −0.000915069 0 | ||||||||
\(65\) | 6.71449e11 | 1.10427 | ||||||||
\(66\) | 4.43119e11 | 0.659911 | ||||||||
\(67\) | −1.70285e11 | −0.229980 | −0.114990 | − | 0.993367i | \(-0.536684\pi\) | ||||
−0.114990 | + | 0.993367i | \(0.536684\pi\) | |||||||
\(68\) | −3.30668e11 | −0.405587 | ||||||||
\(69\) | −1.54243e11 | −0.172063 | ||||||||
\(70\) | 2.56769e11 | 0.260859 | ||||||||
\(71\) | −1.48653e12 | −1.37719 | −0.688594 | − | 0.725147i | \(-0.741772\pi\) | ||||
−0.688594 | + | 0.725147i | \(0.741772\pi\) | |||||||
\(72\) | 2.18508e11 | 0.184844 | ||||||||
\(73\) | −1.87627e12 | −1.45110 | −0.725550 | − | 0.688170i | \(-0.758414\pi\) | ||||
−0.725550 | + | 0.688170i | \(0.758414\pi\) | |||||||
\(74\) | −5.75462e10 | −0.0407390 | ||||||||
\(75\) | 1.41083e11 | 0.0915325 | ||||||||
\(76\) | 9.36907e11 | 0.557710 | ||||||||
\(77\) | 3.25729e11 | 0.178101 | ||||||||
\(78\) | −1.46923e12 | −0.738713 | ||||||||
\(79\) | −2.52869e12 | −1.17036 | −0.585180 | − | 0.810904i | \(-0.698976\pi\) | ||||
−0.585180 | + | 0.810904i | \(0.698976\pi\) | |||||||
\(80\) | −3.14691e12 | −1.34214 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | 4.92509e11 | 0.178906 | ||||||||
\(83\) | −1.34332e12 | −0.450995 | −0.225498 | − | 0.974244i | \(-0.572401\pi\) | ||||
−0.225498 | + | 0.974244i | \(0.572401\pi\) | |||||||
\(84\) | −2.00615e11 | −0.0623085 | ||||||||
\(85\) | −2.73332e12 | −0.786081 | ||||||||
\(86\) | 1.53261e11 | 0.0408500 | ||||||||
\(87\) | 3.57831e12 | 0.884715 | ||||||||
\(88\) | −2.21409e12 | −0.508227 | ||||||||
\(89\) | −1.41898e12 | −0.302650 | −0.151325 | − | 0.988484i | \(-0.548354\pi\) | ||||
−0.151325 | + | 0.988484i | \(0.548354\pi\) | |||||||
\(90\) | −2.25593e12 | −0.447455 | ||||||||
\(91\) | −1.08001e12 | −0.199369 | ||||||||
\(92\) | −9.62587e11 | −0.165508 | ||||||||
\(93\) | −4.20068e12 | −0.673256 | ||||||||
\(94\) | 1.43276e13 | 2.14212 | ||||||||
\(95\) | 7.74453e12 | 1.08092 | ||||||||
\(96\) | 4.43047e12 | 0.577680 | ||||||||
\(97\) | 1.48907e13 | 1.81509 | 0.907543 | − | 0.419958i | \(-0.137955\pi\) | ||||
0.907543 | + | 0.419958i | \(0.137955\pi\) | |||||||
\(98\) | 1.05236e13 | 1.20004 | ||||||||
\(99\) | −2.86179e12 | −0.305499 | ||||||||
\(100\) | 8.80457e11 | 0.0880457 | ||||||||
\(101\) | 2.00384e13 | 1.87834 | 0.939169 | − | 0.343456i | \(-0.111597\pi\) | ||||
0.939169 | + | 0.343456i | \(0.111597\pi\) | |||||||
\(102\) | 5.98092e12 | 0.525856 | ||||||||
\(103\) | −1.87483e13 | −1.54710 | −0.773551 | − | 0.633734i | \(-0.781521\pi\) | ||||
−0.773551 | + | 0.633734i | \(0.781521\pi\) | |||||||
\(104\) | 7.34116e12 | 0.568916 | ||||||||
\(105\) | −1.65829e12 | −0.120762 | ||||||||
\(106\) | 3.26577e12 | 0.223613 | ||||||||
\(107\) | 7.48333e11 | 0.0482059 | 0.0241030 | − | 0.999709i | \(-0.492327\pi\) | ||||
0.0241030 | + | 0.999709i | \(0.492327\pi\) | |||||||
\(108\) | 1.76256e12 | 0.106878 | ||||||||
\(109\) | −5.69983e12 | −0.325529 | −0.162765 | − | 0.986665i | \(-0.552041\pi\) | ||||
−0.162765 | + | 0.986665i | \(0.552041\pi\) | |||||||
\(110\) | 2.28588e13 | 1.23027 | ||||||||
\(111\) | 3.71650e11 | 0.0188597 | ||||||||
\(112\) | 5.06171e12 | 0.242315 | ||||||||
\(113\) | 3.56191e13 | 1.60944 | 0.804718 | − | 0.593658i | \(-0.202317\pi\) | ||||
0.804718 | + | 0.593658i | \(0.202317\pi\) | |||||||
\(114\) | −1.69462e13 | −0.723087 | ||||||||
\(115\) | −7.95680e12 | −0.320777 | ||||||||
\(116\) | 2.23312e13 | 0.851012 | ||||||||
\(117\) | 9.48873e12 | 0.341979 | ||||||||
\(118\) | −4.76126e12 | −0.162364 | ||||||||
\(119\) | 4.39646e12 | 0.141921 | ||||||||
\(120\) | 1.12720e13 | 0.344605 | ||||||||
\(121\) | −5.52481e12 | −0.160034 | ||||||||
\(122\) | −2.59847e13 | −0.713474 | ||||||||
\(123\) | −3.18077e12 | −0.0828226 | ||||||||
\(124\) | −2.62152e13 | −0.647609 | ||||||||
\(125\) | −3.86282e13 | −0.905710 | ||||||||
\(126\) | 3.62859e12 | 0.0807848 | ||||||||
\(127\) | 7.89356e13 | 1.66936 | 0.834678 | − | 0.550738i | \(-0.185654\pi\) | ||||
0.834678 | + | 0.550738i | \(0.185654\pi\) | |||||||
\(128\) | −4.97298e13 | −0.999429 | ||||||||
\(129\) | −9.89806e11 | −0.0189111 | ||||||||
\(130\) | −7.57920e13 | −1.37718 | ||||||||
\(131\) | 1.09063e14 | 1.88545 | 0.942724 | − | 0.333575i | \(-0.108255\pi\) | ||||
0.942724 | + | 0.333575i | \(0.108255\pi\) | |||||||
\(132\) | −1.78596e13 | −0.293861 | ||||||||
\(133\) | −1.24568e13 | −0.195152 | ||||||||
\(134\) | 1.92214e13 | 0.286817 | ||||||||
\(135\) | 1.45694e13 | 0.207145 | ||||||||
\(136\) | −2.98842e13 | −0.404985 | ||||||||
\(137\) | −1.02328e14 | −1.32224 | −0.661118 | − | 0.750282i | \(-0.729918\pi\) | ||||
−0.661118 | + | 0.750282i | \(0.729918\pi\) | |||||||
\(138\) | 1.74107e13 | 0.214586 | ||||||||
\(139\) | 9.41040e13 | 1.10665 | 0.553327 | − | 0.832964i | \(-0.313358\pi\) | ||||
0.553327 | + | 0.832964i | \(0.313358\pi\) | |||||||
\(140\) | −1.03489e13 | −0.116162 | ||||||||
\(141\) | −9.25319e13 | −0.991670 | ||||||||
\(142\) | 1.67796e14 | 1.71754 | ||||||||
\(143\) | −9.61471e13 | −0.940269 | ||||||||
\(144\) | −4.44712e13 | −0.415645 | ||||||||
\(145\) | 1.84591e14 | 1.64937 | ||||||||
\(146\) | 2.11790e14 | 1.80972 | ||||||||
\(147\) | −6.79648e13 | −0.555548 | ||||||||
\(148\) | 2.31936e12 | 0.0181412 | ||||||||
\(149\) | 1.84740e14 | 1.38309 | 0.691544 | − | 0.722334i | \(-0.256931\pi\) | ||||
0.691544 | + | 0.722334i | \(0.256931\pi\) | |||||||
\(150\) | −1.59252e13 | −0.114154 | ||||||||
\(151\) | −1.90572e14 | −1.30831 | −0.654153 | − | 0.756363i | \(-0.726975\pi\) | ||||
−0.654153 | + | 0.756363i | \(0.726975\pi\) | |||||||
\(152\) | 8.46733e13 | 0.556882 | ||||||||
\(153\) | −3.86265e13 | −0.243439 | ||||||||
\(154\) | −3.67677e13 | −0.222117 | ||||||||
\(155\) | −2.16697e14 | −1.25515 | ||||||||
\(156\) | 5.92164e13 | 0.328952 | ||||||||
\(157\) | 1.24248e13 | 0.0662125 | 0.0331063 | − | 0.999452i | \(-0.489460\pi\) | ||||
0.0331063 | + | 0.999452i | \(0.489460\pi\) | |||||||
\(158\) | 2.85434e14 | 1.45960 | ||||||||
\(159\) | −2.10913e13 | −0.103519 | ||||||||
\(160\) | 2.28551e14 | 1.07697 | ||||||||
\(161\) | 1.27983e13 | 0.0579139 | ||||||||
\(162\) | −3.18801e13 | −0.138571 | ||||||||
\(163\) | 5.65179e13 | 0.236030 | 0.118015 | − | 0.993012i | \(-0.462347\pi\) | ||||
0.118015 | + | 0.993012i | \(0.462347\pi\) | |||||||
\(164\) | −1.98503e13 | −0.0796675 | ||||||||
\(165\) | −1.47629e14 | −0.569542 | ||||||||
\(166\) | 1.51632e14 | 0.562454 | ||||||||
\(167\) | −2.93952e14 | −1.04862 | −0.524311 | − | 0.851527i | \(-0.675677\pi\) | ||||
−0.524311 | + | 0.851527i | \(0.675677\pi\) | |||||||
\(168\) | −1.81306e13 | −0.0622160 | ||||||||
\(169\) | 1.59157e13 | 0.0525487 | ||||||||
\(170\) | 3.08532e14 | 0.980353 | ||||||||
\(171\) | 1.09443e14 | 0.334746 | ||||||||
\(172\) | −6.17710e12 | −0.0181907 | ||||||||
\(173\) | 1.71073e14 | 0.485158 | 0.242579 | − | 0.970132i | \(-0.422007\pi\) | ||||
0.242579 | + | 0.970132i | \(0.422007\pi\) | |||||||
\(174\) | −4.03914e14 | −1.10336 | ||||||||
\(175\) | −1.17063e13 | −0.0308086 | ||||||||
\(176\) | 4.50617e14 | 1.14281 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | 1.60171e14 | 0.377446 | ||||||||
\(179\) | −5.94981e14 | −1.35194 | −0.675971 | − | 0.736928i | \(-0.736276\pi\) | ||||
−0.675971 | + | 0.736928i | \(0.736276\pi\) | |||||||
\(180\) | 9.09238e13 | 0.199254 | ||||||||
\(181\) | 5.40767e14 | 1.14314 | 0.571570 | − | 0.820553i | \(-0.306334\pi\) | ||||
0.571570 | + | 0.820553i | \(0.306334\pi\) | |||||||
\(182\) | 1.21909e14 | 0.248641 | ||||||||
\(183\) | 1.67816e14 | 0.330295 | ||||||||
\(184\) | −8.69941e13 | −0.165262 | ||||||||
\(185\) | 1.91720e13 | 0.0351601 | ||||||||
\(186\) | 4.74165e14 | 0.839644 | ||||||||
\(187\) | 3.91393e14 | 0.669334 | ||||||||
\(188\) | −5.77465e14 | −0.953894 | ||||||||
\(189\) | −2.34345e13 | −0.0373985 | ||||||||
\(190\) | −8.74188e14 | −1.34805 | ||||||||
\(191\) | −4.12874e14 | −0.615319 | −0.307660 | − | 0.951496i | \(-0.599546\pi\) | ||||
−0.307660 | + | 0.951496i | \(0.599546\pi\) | |||||||
\(192\) | −3.66734e11 | −0.000528315 0 | ||||||||
\(193\) | −1.00065e15 | −1.39366 | −0.696831 | − | 0.717235i | \(-0.745407\pi\) | ||||
−0.696831 | + | 0.717235i | \(0.745407\pi\) | |||||||
\(194\) | −1.68083e15 | −2.26367 | ||||||||
\(195\) | 4.89487e14 | 0.637552 | ||||||||
\(196\) | −4.24149e14 | −0.534384 | ||||||||
\(197\) | −1.03802e15 | −1.26524 | −0.632622 | − | 0.774460i | \(-0.718021\pi\) | ||||
−0.632622 | + | 0.774460i | \(0.718021\pi\) | |||||||
\(198\) | 3.23034e14 | 0.381000 | ||||||||
\(199\) | 3.01937e14 | 0.344645 | 0.172322 | − | 0.985041i | \(-0.444873\pi\) | ||||
0.172322 | + | 0.985041i | \(0.444873\pi\) | |||||||
\(200\) | 7.95715e13 | 0.0879150 | ||||||||
\(201\) | −1.24137e14 | −0.132779 | ||||||||
\(202\) | −2.26190e15 | −2.34255 | ||||||||
\(203\) | −2.96909e14 | −0.297783 | ||||||||
\(204\) | −2.41057e14 | −0.234166 | ||||||||
\(205\) | −1.64083e14 | −0.154406 | ||||||||
\(206\) | 2.11627e15 | 1.92945 | ||||||||
\(207\) | −1.12443e14 | −0.0993404 | ||||||||
\(208\) | −1.49409e15 | −1.27928 | ||||||||
\(209\) | −1.10897e15 | −0.920380 | ||||||||
\(210\) | 1.87185e14 | 0.150607 | ||||||||
\(211\) | 1.70594e15 | 1.33085 | 0.665424 | − | 0.746466i | \(-0.268251\pi\) | ||||
0.665424 | + | 0.746466i | \(0.268251\pi\) | |||||||
\(212\) | −1.31625e14 | −0.0995759 | ||||||||
\(213\) | −1.08368e15 | −0.795120 | ||||||||
\(214\) | −8.44705e13 | −0.0601195 | ||||||||
\(215\) | −5.10602e13 | −0.0352560 | ||||||||
\(216\) | 1.59292e14 | 0.106720 | ||||||||
\(217\) | 3.48550e14 | 0.226609 | ||||||||
\(218\) | 6.43387e14 | 0.405980 | ||||||||
\(219\) | −1.36780e15 | −0.837792 | ||||||||
\(220\) | −9.21310e14 | −0.547846 | ||||||||
\(221\) | −1.29773e15 | −0.749261 | ||||||||
\(222\) | −4.19511e13 | −0.0235207 | ||||||||
\(223\) | 1.57255e14 | 0.0856294 | 0.0428147 | − | 0.999083i | \(-0.486367\pi\) | ||||
0.0428147 | + | 0.999083i | \(0.486367\pi\) | |||||||
\(224\) | −3.67617e14 | −0.194439 | ||||||||
\(225\) | 1.02849e14 | 0.0528463 | ||||||||
\(226\) | −4.02062e15 | −2.00719 | ||||||||
\(227\) | −1.32918e15 | −0.644784 | −0.322392 | − | 0.946606i | \(-0.604487\pi\) | ||||
−0.322392 | + | 0.946606i | \(0.604487\pi\) | |||||||
\(228\) | 6.83005e14 | 0.321994 | ||||||||
\(229\) | −3.49747e15 | −1.60259 | −0.801296 | − | 0.598268i | \(-0.795856\pi\) | ||||
−0.801296 | + | 0.598268i | \(0.795856\pi\) | |||||||
\(230\) | 8.98149e14 | 0.400053 | ||||||||
\(231\) | 2.37456e14 | 0.102827 | ||||||||
\(232\) | 2.01819e15 | 0.849749 | ||||||||
\(233\) | −7.41920e14 | −0.303769 | −0.151884 | − | 0.988398i | \(-0.548534\pi\) | ||||
−0.151884 | + | 0.988398i | \(0.548534\pi\) | |||||||
\(234\) | −1.07107e15 | −0.426496 | ||||||||
\(235\) | −4.77336e15 | −1.84877 | ||||||||
\(236\) | 1.91900e14 | 0.0723013 | ||||||||
\(237\) | −1.84341e15 | −0.675707 | ||||||||
\(238\) | −4.96265e14 | −0.176996 | ||||||||
\(239\) | −5.56819e15 | −1.93254 | −0.966268 | − | 0.257539i | \(-0.917089\pi\) | ||||
−0.966268 | + | 0.257539i | \(0.917089\pi\) | |||||||
\(240\) | −2.29410e15 | −0.774888 | ||||||||
\(241\) | 1.25296e15 | 0.411933 | 0.205967 | − | 0.978559i | \(-0.433966\pi\) | ||||
0.205967 | + | 0.978559i | \(0.433966\pi\) | |||||||
\(242\) | 6.23631e14 | 0.199585 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | 1.04729e15 | 0.317713 | ||||||||
\(245\) | −3.50604e15 | −1.03571 | ||||||||
\(246\) | 3.59039e14 | 0.103291 | ||||||||
\(247\) | 3.67695e15 | 1.03029 | ||||||||
\(248\) | −2.36921e15 | −0.646648 | ||||||||
\(249\) | −9.79281e14 | −0.260382 | ||||||||
\(250\) | 4.36028e15 | 1.12955 | ||||||||
\(251\) | −5.16714e15 | −1.30428 | −0.652140 | − | 0.758099i | \(-0.726128\pi\) | ||||
−0.652140 | + | 0.758099i | \(0.726128\pi\) | |||||||
\(252\) | −1.46248e14 | −0.0359738 | ||||||||
\(253\) | 1.13936e15 | 0.273135 | ||||||||
\(254\) | −8.91011e15 | −2.08192 | ||||||||
\(255\) | −1.99259e15 | −0.453844 | ||||||||
\(256\) | 5.61753e15 | 1.24734 | ||||||||
\(257\) | −2.18653e15 | −0.473359 | −0.236679 | − | 0.971588i | \(-0.576059\pi\) | ||||
−0.236679 | + | 0.971588i | \(0.576059\pi\) | |||||||
\(258\) | 1.11727e14 | 0.0235848 | ||||||||
\(259\) | −3.08375e13 | −0.00634791 | ||||||||
\(260\) | 3.05475e15 | 0.613265 | ||||||||
\(261\) | 2.60859e15 | 0.510790 | ||||||||
\(262\) | −1.23108e16 | −2.35142 | ||||||||
\(263\) | 4.80148e15 | 0.894670 | 0.447335 | − | 0.894366i | \(-0.352373\pi\) | ||||
0.447335 | + | 0.894366i | \(0.352373\pi\) | |||||||
\(264\) | −1.61407e15 | −0.293425 | ||||||||
\(265\) | −1.08802e15 | −0.192991 | ||||||||
\(266\) | 1.40610e15 | 0.243381 | ||||||||
\(267\) | −1.03443e15 | −0.174735 | ||||||||
\(268\) | −7.74707e14 | −0.127721 | ||||||||
\(269\) | −1.07930e16 | −1.73681 | −0.868404 | − | 0.495858i | \(-0.834854\pi\) | ||||
−0.868404 | + | 0.495858i | \(0.834854\pi\) | |||||||
\(270\) | −1.64457e15 | −0.258338 | ||||||||
\(271\) | 7.90679e15 | 1.21255 | 0.606275 | − | 0.795255i | \(-0.292663\pi\) | ||||
0.606275 | + | 0.795255i | \(0.292663\pi\) | |||||||
\(272\) | 6.08211e15 | 0.910660 | ||||||||
\(273\) | −7.87324e14 | −0.115106 | ||||||||
\(274\) | 1.15506e16 | 1.64901 | ||||||||
\(275\) | −1.04215e15 | −0.145300 | ||||||||
\(276\) | −7.01726e14 | −0.0955561 | ||||||||
\(277\) | −4.13424e15 | −0.549892 | −0.274946 | − | 0.961460i | \(-0.588660\pi\) | ||||
−0.274946 | + | 0.961460i | \(0.588660\pi\) | |||||||
\(278\) | −1.06223e16 | −1.38015 | ||||||||
\(279\) | −3.06229e15 | −0.388705 | ||||||||
\(280\) | −9.35288e14 | −0.115989 | ||||||||
\(281\) | 2.12797e15 | 0.257854 | 0.128927 | − | 0.991654i | \(-0.458847\pi\) | ||||
0.128927 | + | 0.991654i | \(0.458847\pi\) | |||||||
\(282\) | 1.04448e16 | 1.23675 | ||||||||
\(283\) | 8.05949e15 | 0.932601 | 0.466300 | − | 0.884626i | \(-0.345587\pi\) | ||||
0.466300 | + | 0.884626i | \(0.345587\pi\) | |||||||
\(284\) | −6.76292e15 | −0.764830 | ||||||||
\(285\) | 5.64576e15 | 0.624067 | ||||||||
\(286\) | 1.08529e16 | 1.17265 | ||||||||
\(287\) | 2.63923e14 | 0.0278769 | ||||||||
\(288\) | 3.22981e15 | 0.333523 | ||||||||
\(289\) | −4.62182e15 | −0.466635 | ||||||||
\(290\) | −2.08363e16 | −2.05700 | ||||||||
\(291\) | 1.08553e16 | 1.04794 | ||||||||
\(292\) | −8.53606e15 | −0.805878 | ||||||||
\(293\) | −5.20186e15 | −0.480307 | −0.240153 | − | 0.970735i | \(-0.577198\pi\) | ||||
−0.240153 | + | 0.970735i | \(0.577198\pi\) | |||||||
\(294\) | 7.67174e15 | 0.692845 | ||||||||
\(295\) | 1.58625e15 | 0.140129 | ||||||||
\(296\) | 2.09613e14 | 0.0181143 | ||||||||
\(297\) | −2.08625e15 | −0.176380 | ||||||||
\(298\) | −2.08531e16 | −1.72490 | ||||||||
\(299\) | −3.77773e15 | −0.305751 | ||||||||
\(300\) | 6.41853e14 | 0.0508332 | ||||||||
\(301\) | 8.21288e13 | 0.00636522 | ||||||||
\(302\) | 2.15114e16 | 1.63164 | ||||||||
\(303\) | 1.46080e16 | 1.08446 | ||||||||
\(304\) | −1.72329e16 | −1.25222 | ||||||||
\(305\) | 8.65700e15 | 0.615770 | ||||||||
\(306\) | 4.36009e15 | 0.303603 | ||||||||
\(307\) | −9.62580e15 | −0.656202 | −0.328101 | − | 0.944643i | \(-0.606409\pi\) | ||||
−0.328101 | + | 0.944643i | \(0.606409\pi\) | |||||||
\(308\) | 1.48190e15 | 0.0989096 | ||||||||
\(309\) | −1.36675e16 | −0.893220 | ||||||||
\(310\) | 2.44603e16 | 1.56535 | ||||||||
\(311\) | −2.75576e16 | −1.72703 | −0.863514 | − | 0.504325i | \(-0.831741\pi\) | ||||
−0.863514 | + | 0.504325i | \(0.831741\pi\) | |||||||
\(312\) | 5.35170e15 | 0.328464 | ||||||||
\(313\) | 2.39181e16 | 1.43777 | 0.718883 | − | 0.695131i | \(-0.244654\pi\) | ||||
0.718883 | + | 0.695131i | \(0.244654\pi\) | |||||||
\(314\) | −1.40248e15 | −0.0825763 | ||||||||
\(315\) | −1.20889e15 | −0.0697220 | ||||||||
\(316\) | −1.15042e16 | −0.649967 | ||||||||
\(317\) | −4.59540e15 | −0.254354 | −0.127177 | − | 0.991880i | \(-0.540592\pi\) | ||||
−0.127177 | + | 0.991880i | \(0.540592\pi\) | |||||||
\(318\) | 2.38075e15 | 0.129103 | ||||||||
\(319\) | −2.64323e16 | −1.40441 | ||||||||
\(320\) | −1.89184e13 | −0.000984938 0 | ||||||||
\(321\) | 5.45535e14 | 0.0278317 | ||||||||
\(322\) | −1.44465e15 | −0.0722267 | ||||||||
\(323\) | −1.49680e16 | −0.733413 | ||||||||
\(324\) | 1.28491e15 | 0.0617063 | ||||||||
\(325\) | 3.45541e15 | 0.162651 | ||||||||
\(326\) | −6.37964e15 | −0.294362 | ||||||||
\(327\) | −4.15518e15 | −0.187944 | ||||||||
\(328\) | −1.79397e15 | −0.0795492 | ||||||||
\(329\) | 7.67781e15 | 0.333783 | ||||||||
\(330\) | 1.66641e16 | 0.710298 | ||||||||
\(331\) | −2.20324e16 | −0.920831 | −0.460415 | − | 0.887704i | \(-0.652300\pi\) | ||||
−0.460415 | + | 0.887704i | \(0.652300\pi\) | |||||||
\(332\) | −6.11141e15 | −0.250463 | ||||||||
\(333\) | 2.70933e14 | 0.0108886 | ||||||||
\(334\) | 3.31807e16 | 1.30778 | ||||||||
\(335\) | −6.40377e15 | −0.247539 | ||||||||
\(336\) | 3.68998e15 | 0.139900 | ||||||||
\(337\) | 3.26438e16 | 1.21397 | 0.606983 | − | 0.794715i | \(-0.292380\pi\) | ||||
0.606983 | + | 0.794715i | \(0.292380\pi\) | |||||||
\(338\) | −1.79653e15 | −0.0655356 | ||||||||
\(339\) | 2.59664e16 | 0.929208 | ||||||||
\(340\) | −1.24352e16 | −0.436556 | ||||||||
\(341\) | 3.10295e16 | 1.06874 | ||||||||
\(342\) | −1.23538e16 | −0.417475 | ||||||||
\(343\) | 1.15000e16 | 0.381318 | ||||||||
\(344\) | −5.58257e14 | −0.0181637 | ||||||||
\(345\) | −5.80051e15 | −0.185200 | ||||||||
\(346\) | −1.93105e16 | −0.605059 | ||||||||
\(347\) | −2.58464e16 | −0.794801 | −0.397400 | − | 0.917645i | \(-0.630088\pi\) | ||||
−0.397400 | + | 0.917645i | \(0.630088\pi\) | |||||||
\(348\) | 1.62795e16 | 0.491332 | ||||||||
\(349\) | 1.49249e16 | 0.442127 | 0.221063 | − | 0.975259i | \(-0.429047\pi\) | ||||
0.221063 | + | 0.975259i | \(0.429047\pi\) | |||||||
\(350\) | 1.32138e15 | 0.0384226 | ||||||||
\(351\) | 6.91728e15 | 0.197442 | ||||||||
\(352\) | −3.27270e16 | −0.917019 | ||||||||
\(353\) | 3.75129e16 | 1.03192 | 0.515958 | − | 0.856614i | \(-0.327436\pi\) | ||||
0.515958 | + | 0.856614i | \(0.327436\pi\) | |||||||
\(354\) | −3.47096e15 | −0.0937407 | ||||||||
\(355\) | −5.59027e16 | −1.48234 | ||||||||
\(356\) | −6.45561e15 | −0.168079 | ||||||||
\(357\) | 3.20502e15 | 0.0819384 | ||||||||
\(358\) | 6.71603e16 | 1.68606 | ||||||||
\(359\) | 3.72336e16 | 0.917953 | 0.458977 | − | 0.888448i | \(-0.348216\pi\) | ||||
0.458977 | + | 0.888448i | \(0.348216\pi\) | |||||||
\(360\) | 8.21726e15 | 0.198958 | ||||||||
\(361\) | 3.57124e14 | 0.00849224 | ||||||||
\(362\) | −6.10408e16 | −1.42566 | ||||||||
\(363\) | −4.02759e15 | −0.0923958 | ||||||||
\(364\) | −4.91347e15 | −0.110721 | ||||||||
\(365\) | −7.05596e16 | −1.56190 | ||||||||
\(366\) | −1.89428e16 | −0.411924 | ||||||||
\(367\) | 3.69154e16 | 0.788639 | 0.394319 | − | 0.918973i | \(-0.370980\pi\) | ||||
0.394319 | + | 0.918973i | \(0.370980\pi\) | |||||||
\(368\) | 1.77053e16 | 0.371613 | ||||||||
\(369\) | −2.31878e15 | −0.0478176 | ||||||||
\(370\) | −2.16410e15 | −0.0438496 | ||||||||
\(371\) | 1.75004e15 | 0.0348432 | ||||||||
\(372\) | −1.91109e16 | −0.373897 | ||||||||
\(373\) | 5.13533e16 | 0.987328 | 0.493664 | − | 0.869653i | \(-0.335657\pi\) | ||||
0.493664 | + | 0.869653i | \(0.335657\pi\) | |||||||
\(374\) | −4.41798e16 | −0.834753 | ||||||||
\(375\) | −2.81600e16 | −0.522912 | ||||||||
\(376\) | −5.21886e16 | −0.952478 | ||||||||
\(377\) | 8.76403e16 | 1.57212 | ||||||||
\(378\) | 2.64524e15 | 0.0466411 | ||||||||
\(379\) | 3.45756e16 | 0.599260 | 0.299630 | − | 0.954056i | \(-0.403137\pi\) | ||||
0.299630 | + | 0.954056i | \(0.403137\pi\) | |||||||
\(380\) | 3.52336e16 | 0.600293 | ||||||||
\(381\) | 5.75441e16 | 0.963803 | ||||||||
\(382\) | 4.66045e16 | 0.767389 | ||||||||
\(383\) | −7.39616e16 | −1.19733 | −0.598666 | − | 0.800999i | \(-0.704302\pi\) | ||||
−0.598666 | + | 0.800999i | \(0.704302\pi\) | |||||||
\(384\) | −3.62530e16 | −0.577021 | ||||||||
\(385\) | 1.22495e16 | 0.191700 | ||||||||
\(386\) | 1.12951e17 | 1.73809 | ||||||||
\(387\) | −7.21568e14 | −0.0109183 | ||||||||
\(388\) | 6.77448e16 | 1.00802 | ||||||||
\(389\) | 3.29116e16 | 0.481589 | 0.240795 | − | 0.970576i | \(-0.422592\pi\) | ||||
0.240795 | + | 0.970576i | \(0.422592\pi\) | |||||||
\(390\) | −5.52523e16 | −0.795117 | ||||||||
\(391\) | 1.53783e16 | 0.217650 | ||||||||
\(392\) | −3.83326e16 | −0.533591 | ||||||||
\(393\) | 7.95070e16 | 1.08856 | ||||||||
\(394\) | 1.17170e17 | 1.57794 | ||||||||
\(395\) | −9.50945e16 | −1.25972 | ||||||||
\(396\) | −1.30197e16 | −0.169661 | ||||||||
\(397\) | −4.79591e15 | −0.0614798 | −0.0307399 | − | 0.999527i | \(-0.509786\pi\) | ||||
−0.0307399 | + | 0.999527i | \(0.509786\pi\) | |||||||
\(398\) | −3.40821e16 | −0.429820 | ||||||||
\(399\) | −9.08103e15 | −0.112671 | ||||||||
\(400\) | −1.61946e16 | −0.197688 | ||||||||
\(401\) | −1.13071e17 | −1.35804 | −0.679020 | − | 0.734119i | \(-0.737595\pi\) | ||||
−0.679020 | + | 0.734119i | \(0.737595\pi\) | |||||||
\(402\) | 1.40124e16 | 0.165594 | ||||||||
\(403\) | −1.02883e17 | −1.19636 | ||||||||
\(404\) | 9.11643e16 | 1.04315 | ||||||||
\(405\) | 1.06211e16 | 0.119595 | ||||||||
\(406\) | 3.35146e16 | 0.371377 | ||||||||
\(407\) | −2.74530e15 | −0.0299382 | ||||||||
\(408\) | −2.17856e16 | −0.233818 | ||||||||
\(409\) | −1.02879e17 | −1.08674 | −0.543369 | − | 0.839494i | \(-0.682852\pi\) | ||||
−0.543369 | + | 0.839494i | \(0.682852\pi\) | |||||||
\(410\) | 1.85214e16 | 0.192566 | ||||||||
\(411\) | −7.45968e16 | −0.763394 | ||||||||
\(412\) | −8.52949e16 | −0.859193 | ||||||||
\(413\) | −2.55144e15 | −0.0252994 | ||||||||
\(414\) | 1.26924e16 | 0.123891 | ||||||||
\(415\) | −5.05173e16 | −0.485431 | ||||||||
\(416\) | 1.08511e17 | 1.02652 | ||||||||
\(417\) | 6.86018e16 | 0.638927 | ||||||||
\(418\) | 1.25178e17 | 1.14784 | ||||||||
\(419\) | −1.30846e17 | −1.18132 | −0.590661 | − | 0.806920i | \(-0.701133\pi\) | ||||
−0.590661 | + | 0.806920i | \(0.701133\pi\) | |||||||
\(420\) | −7.54437e15 | −0.0670660 | ||||||||
\(421\) | 1.95222e17 | 1.70881 | 0.854407 | − | 0.519605i | \(-0.173921\pi\) | ||||
0.854407 | + | 0.519605i | \(0.173921\pi\) | |||||||
\(422\) | −1.92564e17 | −1.65975 | ||||||||
\(423\) | −6.74558e16 | −0.572541 | ||||||||
\(424\) | −1.18956e16 | −0.0994281 | ||||||||
\(425\) | −1.40662e16 | −0.115784 | ||||||||
\(426\) | 1.22323e17 | 0.991625 | ||||||||
\(427\) | −1.39245e16 | −0.111173 | ||||||||
\(428\) | 3.40453e15 | 0.0267715 | ||||||||
\(429\) | −7.00912e16 | −0.542864 | ||||||||
\(430\) | 5.76358e15 | 0.0439691 | ||||||||
\(431\) | −6.29681e16 | −0.473171 | −0.236586 | − | 0.971611i | \(-0.576028\pi\) | ||||
−0.236586 | + | 0.971611i | \(0.576028\pi\) | |||||||
\(432\) | −3.24195e16 | −0.239973 | ||||||||
\(433\) | −7.19886e16 | −0.524919 | −0.262460 | − | 0.964943i | \(-0.584534\pi\) | ||||
−0.262460 | + | 0.964943i | \(0.584534\pi\) | |||||||
\(434\) | −3.93437e16 | −0.282613 | ||||||||
\(435\) | 1.34567e17 | 0.952267 | ||||||||
\(436\) | −2.59313e16 | −0.180785 | ||||||||
\(437\) | −4.35725e16 | −0.299284 | ||||||||
\(438\) | 1.54395e17 | 1.04484 | ||||||||
\(439\) | 2.01569e16 | 0.134402 | 0.0672008 | − | 0.997739i | \(-0.478593\pi\) | ||||
0.0672008 | + | 0.997739i | \(0.478593\pi\) | |||||||
\(440\) | −8.32636e16 | −0.547032 | ||||||||
\(441\) | −4.95463e16 | −0.320746 | ||||||||
\(442\) | 1.46485e17 | 0.934433 | ||||||||
\(443\) | −1.48799e17 | −0.935351 | −0.467676 | − | 0.883900i | \(-0.654908\pi\) | ||||
−0.467676 | + | 0.883900i | \(0.654908\pi\) | |||||||
\(444\) | 1.69081e15 | 0.0104739 | ||||||||
\(445\) | −5.33624e16 | −0.325758 | ||||||||
\(446\) | −1.77507e16 | −0.106792 | ||||||||
\(447\) | 1.34675e17 | 0.798526 | ||||||||
\(448\) | 3.04296e13 | 0.000177824 0 | ||||||||
\(449\) | 1.70580e17 | 0.982485 | 0.491242 | − | 0.871023i | \(-0.336543\pi\) | ||||
0.491242 | + | 0.871023i | \(0.336543\pi\) | |||||||
\(450\) | −1.16094e16 | −0.0659067 | ||||||||
\(451\) | 2.34957e16 | 0.131474 | ||||||||
\(452\) | 1.62049e17 | 0.893811 | ||||||||
\(453\) | −1.38927e17 | −0.755350 | ||||||||
\(454\) | 1.50035e17 | 0.804135 | ||||||||
\(455\) | −4.06150e16 | −0.214591 | ||||||||
\(456\) | 6.17268e16 | 0.321516 | ||||||||
\(457\) | −1.64203e17 | −0.843190 | −0.421595 | − | 0.906784i | \(-0.638530\pi\) | ||||
−0.421595 | + | 0.906784i | \(0.638530\pi\) | |||||||
\(458\) | 3.94788e17 | 1.99866 | ||||||||
\(459\) | −2.81587e16 | −0.140550 | ||||||||
\(460\) | −3.61993e16 | −0.178145 | ||||||||
\(461\) | −2.46285e17 | −1.19504 | −0.597519 | − | 0.801855i | \(-0.703847\pi\) | ||||
−0.597519 | + | 0.801855i | \(0.703847\pi\) | |||||||
\(462\) | −2.68036e16 | −0.128239 | ||||||||
\(463\) | −1.89854e17 | −0.895659 | −0.447829 | − | 0.894119i | \(-0.647803\pi\) | ||||
−0.447829 | + | 0.894119i | \(0.647803\pi\) | |||||||
\(464\) | −4.10747e17 | −1.91077 | ||||||||
\(465\) | −1.57972e17 | −0.724662 | ||||||||
\(466\) | 8.37465e16 | 0.378842 | ||||||||
\(467\) | −3.77881e17 | −1.68576 | −0.842880 | − | 0.538102i | \(-0.819141\pi\) | ||||
−0.842880 | + | 0.538102i | \(0.819141\pi\) | |||||||
\(468\) | 4.31688e16 | 0.189920 | ||||||||
\(469\) | 1.03003e16 | 0.0446915 | ||||||||
\(470\) | 5.38808e17 | 2.30568 | ||||||||
\(471\) | 9.05765e15 | 0.0382278 | ||||||||
\(472\) | 1.73430e16 | 0.0721939 | ||||||||
\(473\) | 7.31149e15 | 0.0300198 | ||||||||
\(474\) | 2.08081e17 | 0.842701 | ||||||||
\(475\) | 3.98548e16 | 0.159211 | ||||||||
\(476\) | 2.00016e16 | 0.0788170 | ||||||||
\(477\) | −1.53755e16 | −0.0597669 | ||||||||
\(478\) | 6.28527e17 | 2.41014 | ||||||||
\(479\) | −2.06918e17 | −0.782738 | −0.391369 | − | 0.920234i | \(-0.627998\pi\) | ||||
−0.391369 | + | 0.920234i | \(0.627998\pi\) | |||||||
\(480\) | 1.66614e17 | 0.621788 | ||||||||
\(481\) | 9.10247e15 | 0.0335132 | ||||||||
\(482\) | −1.41432e17 | −0.513738 | ||||||||
\(483\) | 9.32994e15 | 0.0334366 | ||||||||
\(484\) | −2.51350e16 | −0.0888760 | ||||||||
\(485\) | 5.59982e17 | 1.95368 | ||||||||
\(486\) | −2.32406e16 | −0.0800040 | ||||||||
\(487\) | 2.82990e17 | 0.961241 | 0.480620 | − | 0.876929i | \(-0.340412\pi\) | ||||
0.480620 | + | 0.876929i | \(0.340412\pi\) | |||||||
\(488\) | 9.46496e16 | 0.317241 | ||||||||
\(489\) | 4.12015e16 | 0.136272 | ||||||||
\(490\) | 3.95755e17 | 1.29167 | ||||||||
\(491\) | 5.16102e17 | 1.66229 | 0.831144 | − | 0.556057i | \(-0.187687\pi\) | ||||
0.831144 | + | 0.556057i | \(0.187687\pi\) | |||||||
\(492\) | −1.44708e16 | −0.0459961 | ||||||||
\(493\) | −3.56764e17 | −1.11912 | ||||||||
\(494\) | −4.15047e17 | −1.28491 | ||||||||
\(495\) | −1.07621e17 | −0.328825 | ||||||||
\(496\) | 4.82187e17 | 1.45407 | ||||||||
\(497\) | 8.99177e16 | 0.267626 | ||||||||
\(498\) | 1.10539e17 | 0.324733 | ||||||||
\(499\) | −4.45068e17 | −1.29054 | −0.645272 | − | 0.763953i | \(-0.723256\pi\) | ||||
−0.645272 | + | 0.763953i | \(0.723256\pi\) | |||||||
\(500\) | −1.75738e17 | −0.502992 | ||||||||
\(501\) | −2.14291e17 | −0.605422 | ||||||||
\(502\) | 5.83257e17 | 1.62662 | ||||||||
\(503\) | −5.08695e16 | −0.140044 | −0.0700221 | − | 0.997545i | \(-0.522307\pi\) | ||||
−0.0700221 | + | 0.997545i | \(0.522307\pi\) | |||||||
\(504\) | −1.32172e16 | −0.0359204 | ||||||||
\(505\) | 7.53569e17 | 2.02176 | ||||||||
\(506\) | −1.28609e17 | −0.340638 | ||||||||
\(507\) | 1.16025e16 | 0.0303390 | ||||||||
\(508\) | 3.59116e17 | 0.927088 | ||||||||
\(509\) | −5.39326e17 | −1.37463 | −0.687315 | − | 0.726359i | \(-0.741211\pi\) | ||||
−0.687315 | + | 0.726359i | \(0.741211\pi\) | |||||||
\(510\) | 2.24920e17 | 0.566007 | ||||||||
\(511\) | 1.13493e17 | 0.281989 | ||||||||
\(512\) | −2.26710e17 | −0.556181 | ||||||||
\(513\) | 7.97843e16 | 0.193266 | ||||||||
\(514\) | 2.46812e17 | 0.590345 | ||||||||
\(515\) | −7.05052e17 | −1.66523 | ||||||||
\(516\) | −4.50310e15 | −0.0105024 | ||||||||
\(517\) | 6.83514e17 | 1.57420 | ||||||||
\(518\) | 3.48088e15 | 0.00791673 | ||||||||
\(519\) | 1.24713e17 | 0.280106 | ||||||||
\(520\) | 2.76074e17 | 0.612355 | ||||||||
\(521\) | −1.85031e17 | −0.405321 | −0.202660 | − | 0.979249i | \(-0.564959\pi\) | ||||
−0.202660 | + | 0.979249i | \(0.564959\pi\) | |||||||
\(522\) | −2.94453e17 | −0.637027 | ||||||||
\(523\) | 5.78358e16 | 0.123577 | 0.0617883 | − | 0.998089i | \(-0.480320\pi\) | ||||
0.0617883 | + | 0.998089i | \(0.480320\pi\) | |||||||
\(524\) | 4.96181e17 | 1.04710 | ||||||||
\(525\) | −8.53388e15 | −0.0177873 | ||||||||
\(526\) | −5.41983e17 | −1.11578 | ||||||||
\(527\) | 4.18815e17 | 0.851634 | ||||||||
\(528\) | 3.28500e17 | 0.659803 | ||||||||
\(529\) | −4.59270e17 | −0.911183 | ||||||||
\(530\) | 1.22813e17 | 0.240687 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | −5.66722e16 | −0.108379 | ||||||||
\(533\) | −7.79036e16 | −0.147174 | ||||||||
\(534\) | 1.16765e17 | 0.217919 | ||||||||
\(535\) | 2.81420e16 | 0.0518867 | ||||||||
\(536\) | −7.00144e16 | −0.127531 | ||||||||
\(537\) | −4.33741e17 | −0.780544 | ||||||||
\(538\) | 1.21829e18 | 2.16604 | ||||||||
\(539\) | 5.02042e17 | 0.881886 | ||||||||
\(540\) | 6.62834e16 | 0.115039 | ||||||||
\(541\) | −9.84842e17 | −1.68882 | −0.844412 | − | 0.535695i | \(-0.820050\pi\) | ||||
−0.844412 | + | 0.535695i | \(0.820050\pi\) | |||||||
\(542\) | −8.92504e17 | −1.51222 | ||||||||
\(543\) | 3.94219e17 | 0.659992 | ||||||||
\(544\) | −4.41726e17 | −0.730735 | ||||||||
\(545\) | −2.14349e17 | −0.350385 | ||||||||
\(546\) | 8.88717e16 | 0.143553 | ||||||||
\(547\) | −5.30697e17 | −0.847089 | −0.423545 | − | 0.905875i | \(-0.639214\pi\) | ||||
−0.423545 | + | 0.905875i | \(0.639214\pi\) | |||||||
\(548\) | −4.65538e17 | −0.734313 | ||||||||
\(549\) | 1.22338e17 | 0.190696 | ||||||||
\(550\) | 1.17636e17 | 0.181210 | ||||||||
\(551\) | 1.01085e18 | 1.53886 | ||||||||
\(552\) | −6.34187e16 | −0.0954143 | ||||||||
\(553\) | 1.52957e17 | 0.227434 | ||||||||
\(554\) | 4.66666e17 | 0.685792 | ||||||||
\(555\) | 1.39764e16 | 0.0202997 | ||||||||
\(556\) | 4.28124e17 | 0.614587 | ||||||||
\(557\) | 2.55005e17 | 0.361818 | 0.180909 | − | 0.983500i | \(-0.442096\pi\) | ||||
0.180909 | + | 0.983500i | \(0.442096\pi\) | |||||||
\(558\) | 3.45666e17 | 0.484769 | ||||||||
\(559\) | −2.42424e16 | −0.0336046 | ||||||||
\(560\) | 1.90352e17 | 0.260817 | ||||||||
\(561\) | 2.85326e17 | 0.386440 | ||||||||
\(562\) | −2.40201e17 | −0.321580 | ||||||||
\(563\) | 2.29203e17 | 0.303331 | 0.151665 | − | 0.988432i | \(-0.451536\pi\) | ||||
0.151665 | + | 0.988432i | \(0.451536\pi\) | |||||||
\(564\) | −4.20972e17 | −0.550731 | ||||||||
\(565\) | 1.33950e18 | 1.73232 | ||||||||
\(566\) | −9.09740e17 | −1.16308 | ||||||||
\(567\) | −1.70837e16 | −0.0215920 | ||||||||
\(568\) | −6.11201e17 | −0.763695 | ||||||||
\(569\) | 3.00295e17 | 0.370953 | 0.185477 | − | 0.982649i | \(-0.440617\pi\) | ||||
0.185477 | + | 0.982649i | \(0.440617\pi\) | |||||||
\(570\) | −6.37283e17 | −0.778298 | ||||||||
\(571\) | −2.35916e17 | −0.284854 | −0.142427 | − | 0.989805i | \(-0.545491\pi\) | ||||
−0.142427 | + | 0.989805i | \(0.545491\pi\) | |||||||
\(572\) | −4.37419e17 | −0.522184 | ||||||||
\(573\) | −3.00985e17 | −0.355255 | ||||||||
\(574\) | −2.97912e16 | −0.0347664 | ||||||||
\(575\) | −4.09472e16 | −0.0472480 | ||||||||
\(576\) | −2.67349e14 | −0.000305023 0 | ||||||||
\(577\) | 4.01859e17 | 0.453348 | 0.226674 | − | 0.973971i | \(-0.427215\pi\) | ||||
0.226674 | + | 0.973971i | \(0.427215\pi\) | |||||||
\(578\) | 5.21703e17 | 0.581959 | ||||||||
\(579\) | −7.29470e17 | −0.804631 | ||||||||
\(580\) | 8.39795e17 | 0.915991 | ||||||||
\(581\) | 8.12555e16 | 0.0876411 | ||||||||
\(582\) | −1.22532e18 | −1.30693 | ||||||||
\(583\) | 1.55797e17 | 0.164329 | ||||||||
\(584\) | −7.71449e17 | −0.804681 | ||||||||
\(585\) | 3.56836e17 | 0.368091 | ||||||||
\(586\) | 5.87176e17 | 0.599010 | ||||||||
\(587\) | −3.28742e17 | −0.331671 | −0.165836 | − | 0.986153i | \(-0.553032\pi\) | ||||
−0.165836 | + | 0.986153i | \(0.553032\pi\) | |||||||
\(588\) | −3.09205e17 | −0.308527 | ||||||||
\(589\) | −1.18666e18 | −1.17105 | ||||||||
\(590\) | −1.79053e17 | −0.174761 | ||||||||
\(591\) | −7.56715e17 | −0.730489 | ||||||||
\(592\) | −4.26609e16 | −0.0407323 | ||||||||
\(593\) | −3.60972e17 | −0.340893 | −0.170447 | − | 0.985367i | \(-0.554521\pi\) | ||||
−0.170447 | + | 0.985367i | \(0.554521\pi\) | |||||||
\(594\) | 2.35492e17 | 0.219970 | ||||||||
\(595\) | 1.65335e17 | 0.152758 | ||||||||
\(596\) | 8.40471e17 | 0.768107 | ||||||||
\(597\) | 2.20112e17 | 0.198981 | ||||||||
\(598\) | 4.26423e17 | 0.381315 | ||||||||
\(599\) | −5.53752e17 | −0.489825 | −0.244912 | − | 0.969545i | \(-0.578759\pi\) | ||||
−0.244912 | + | 0.969545i | \(0.578759\pi\) | |||||||
\(600\) | 5.80077e16 | 0.0507577 | ||||||||
\(601\) | 3.16392e17 | 0.273868 | 0.136934 | − | 0.990580i | \(-0.456275\pi\) | ||||
0.136934 | + | 0.990580i | \(0.456275\pi\) | |||||||
\(602\) | −9.27055e15 | −0.00793831 | ||||||||
\(603\) | −9.04962e16 | −0.0766598 | ||||||||
\(604\) | −8.67004e17 | −0.726576 | ||||||||
\(605\) | −2.07768e17 | −0.172253 | ||||||||
\(606\) | −1.64892e18 | −1.35247 | ||||||||
\(607\) | −1.18964e18 | −0.965360 | −0.482680 | − | 0.875797i | \(-0.660337\pi\) | ||||
−0.482680 | + | 0.875797i | \(0.660337\pi\) | |||||||
\(608\) | 1.25158e18 | 1.00481 | ||||||||
\(609\) | −2.16447e17 | −0.171925 | ||||||||
\(610\) | −9.77186e17 | −0.767951 | ||||||||
\(611\) | −2.26630e18 | −1.76218 | ||||||||
\(612\) | −1.75731e17 | −0.135196 | ||||||||
\(613\) | 5.22634e17 | 0.397836 | 0.198918 | − | 0.980016i | \(-0.436257\pi\) | ||||
0.198918 | + | 0.980016i | \(0.436257\pi\) | |||||||
\(614\) | 1.08654e18 | 0.818375 | ||||||||
\(615\) | −1.19617e17 | −0.0891464 | ||||||||
\(616\) | 1.33927e17 | 0.0987628 | ||||||||
\(617\) | 4.74752e16 | 0.0346428 | 0.0173214 | − | 0.999850i | \(-0.494486\pi\) | ||||
0.0173214 | + | 0.999850i | \(0.494486\pi\) | |||||||
\(618\) | 1.54276e18 | 1.11397 | ||||||||
\(619\) | −2.02115e18 | −1.44414 | −0.722070 | − | 0.691820i | \(-0.756809\pi\) | ||||
−0.722070 | + | 0.691820i | \(0.756809\pi\) | |||||||
\(620\) | −9.85858e17 | −0.697057 | ||||||||
\(621\) | −8.19711e16 | −0.0573542 | ||||||||
\(622\) | 3.11065e18 | 2.15384 | ||||||||
\(623\) | 8.58318e16 | 0.0588134 | ||||||||
\(624\) | −1.08919e18 | −0.738592 | ||||||||
\(625\) | −1.68890e18 | −1.13340 | ||||||||
\(626\) | −2.69983e18 | −1.79309 | ||||||||
\(627\) | −8.08436e17 | −0.531382 | ||||||||
\(628\) | 5.65262e16 | 0.0367716 | ||||||||
\(629\) | −3.70541e16 | −0.0238565 | ||||||||
\(630\) | 1.36458e17 | 0.0869531 | ||||||||
\(631\) | 3.30428e17 | 0.208394 | 0.104197 | − | 0.994557i | \(-0.466773\pi\) | ||||
0.104197 | + | 0.994557i | \(0.466773\pi\) | |||||||
\(632\) | −1.03970e18 | −0.649002 | ||||||||
\(633\) | 1.24363e18 | 0.768365 | ||||||||
\(634\) | 5.18721e17 | 0.317215 | ||||||||
\(635\) | 2.96848e18 | 1.79682 | ||||||||
\(636\) | −9.59544e16 | −0.0574902 | ||||||||
\(637\) | −1.66460e18 | −0.987195 | ||||||||
\(638\) | 2.98362e18 | 1.75150 | ||||||||
\(639\) | −7.90001e17 | −0.459062 | ||||||||
\(640\) | −1.87015e18 | −1.07574 | ||||||||
\(641\) | 1.91323e18 | 1.08941 | 0.544704 | − | 0.838629i | \(-0.316642\pi\) | ||||
0.544704 | + | 0.838629i | \(0.316642\pi\) | |||||||
\(642\) | −6.15790e16 | −0.0347100 | ||||||||
\(643\) | 2.29819e18 | 1.28237 | 0.641186 | − | 0.767386i | \(-0.278443\pi\) | ||||
0.641186 | + | 0.767386i | \(0.278443\pi\) | |||||||
\(644\) | 5.82255e16 | 0.0321629 | ||||||||
\(645\) | −3.72229e16 | −0.0203550 | ||||||||
\(646\) | 1.68956e18 | 0.914668 | ||||||||
\(647\) | 1.04365e18 | 0.559344 | 0.279672 | − | 0.960096i | \(-0.409774\pi\) | ||||
0.279672 | + | 0.960096i | \(0.409774\pi\) | |||||||
\(648\) | 1.16124e17 | 0.0616147 | ||||||||
\(649\) | −2.27141e17 | −0.119318 | ||||||||
\(650\) | −3.90040e17 | −0.202849 | ||||||||
\(651\) | 2.54093e17 | 0.130833 | ||||||||
\(652\) | 2.57127e17 | 0.131081 | ||||||||
\(653\) | −2.93783e18 | −1.48283 | −0.741413 | − | 0.671049i | \(-0.765844\pi\) | ||||
−0.741413 | + | 0.671049i | \(0.765844\pi\) | |||||||
\(654\) | 4.69029e17 | 0.234393 | ||||||||
\(655\) | 4.10146e18 | 2.02941 | ||||||||
\(656\) | 3.65114e17 | 0.178877 | ||||||||
\(657\) | −9.97128e17 | −0.483700 | ||||||||
\(658\) | −8.66657e17 | −0.416274 | ||||||||
\(659\) | 3.86883e18 | 1.84003 | 0.920014 | − | 0.391886i | \(-0.128177\pi\) | ||||
0.920014 | + | 0.391886i | \(0.128177\pi\) | |||||||
\(660\) | −6.71635e17 | −0.316299 | ||||||||
\(661\) | −3.25119e18 | −1.51612 | −0.758059 | − | 0.652186i | \(-0.773852\pi\) | ||||
−0.758059 | + | 0.652186i | \(0.773852\pi\) | |||||||
\(662\) | 2.48698e18 | 1.14840 | ||||||||
\(663\) | −9.46042e17 | −0.432586 | ||||||||
\(664\) | −5.52321e17 | −0.250091 | ||||||||
\(665\) | −4.68455e17 | −0.210052 | ||||||||
\(666\) | −3.05824e16 | −0.0135797 | ||||||||
\(667\) | −1.03855e18 | −0.456679 | ||||||||
\(668\) | −1.33733e18 | −0.582359 | ||||||||
\(669\) | 1.14639e17 | 0.0494382 | ||||||||
\(670\) | 7.22846e17 | 0.308716 | ||||||||
\(671\) | −1.23962e18 | −0.524317 | ||||||||
\(672\) | −2.67993e17 | −0.112259 | ||||||||
\(673\) | −1.43947e18 | −0.597179 | −0.298590 | − | 0.954382i | \(-0.596516\pi\) | ||||
−0.298590 | + | 0.954382i | \(0.596516\pi\) | |||||||
\(674\) | −3.68477e18 | −1.51398 | ||||||||
\(675\) | 7.49771e16 | 0.0305108 | ||||||||
\(676\) | 7.24082e16 | 0.0291833 | ||||||||
\(677\) | 4.50455e18 | 1.79815 | 0.899073 | − | 0.437799i | \(-0.144242\pi\) | ||||
0.899073 | + | 0.437799i | \(0.144242\pi\) | |||||||
\(678\) | −2.93103e18 | −1.15885 | ||||||||
\(679\) | −9.00714e17 | −0.352723 | ||||||||
\(680\) | −1.12383e18 | −0.435907 | ||||||||
\(681\) | −9.68969e17 | −0.372266 | ||||||||
\(682\) | −3.50256e18 | −1.33287 | ||||||||
\(683\) | −3.11602e18 | −1.17453 | −0.587267 | − | 0.809393i | \(-0.699796\pi\) | ||||
−0.587267 | + | 0.809393i | \(0.699796\pi\) | |||||||
\(684\) | 4.97911e17 | 0.185903 | ||||||||
\(685\) | −3.84816e18 | −1.42320 | ||||||||
\(686\) | −1.29810e18 | −0.475557 | ||||||||
\(687\) | −2.54965e18 | −0.925257 | ||||||||
\(688\) | 1.13618e17 | 0.0408434 | ||||||||
\(689\) | −5.16569e17 | −0.183952 | ||||||||
\(690\) | 6.54751e17 | 0.230971 | ||||||||
\(691\) | −2.28134e18 | −0.797227 | −0.398613 | − | 0.917119i | \(-0.630508\pi\) | ||||
−0.398613 | + | 0.917119i | \(0.630508\pi\) | |||||||
\(692\) | 7.78295e17 | 0.269436 | ||||||||
\(693\) | 1.73106e17 | 0.0593670 | ||||||||
\(694\) | 2.91749e18 | 0.991228 | ||||||||
\(695\) | 3.53890e18 | 1.19115 | ||||||||
\(696\) | 1.47126e18 | 0.490603 | ||||||||
\(697\) | 3.17128e17 | 0.104766 | ||||||||
\(698\) | −1.68470e18 | −0.551394 | ||||||||
\(699\) | −5.40859e17 | −0.175381 | ||||||||
\(700\) | −5.32575e16 | −0.0171098 | ||||||||
\(701\) | 2.07987e18 | 0.662016 | 0.331008 | − | 0.943628i | \(-0.392611\pi\) | ||||
0.331008 | + | 0.943628i | \(0.392611\pi\) | |||||||
\(702\) | −7.80810e17 | −0.246238 | ||||||||
\(703\) | 1.04988e17 | 0.0328043 | ||||||||
\(704\) | 2.70899e15 | 0.000838657 0 | ||||||||
\(705\) | −3.47978e18 | −1.06739 | ||||||||
\(706\) | −4.23438e18 | −1.28694 | ||||||||
\(707\) | −1.21209e18 | −0.365014 | ||||||||
\(708\) | 1.39895e17 | 0.0417432 | ||||||||
\(709\) | −4.44743e18 | −1.31495 | −0.657474 | − | 0.753477i | \(-0.728375\pi\) | ||||
−0.657474 | + | 0.753477i | \(0.728375\pi\) | |||||||
\(710\) | 6.31019e18 | 1.84869 | ||||||||
\(711\) | −1.34385e18 | −0.390120 | ||||||||
\(712\) | −5.83428e17 | −0.167829 | ||||||||
\(713\) | 1.21919e18 | 0.347527 | ||||||||
\(714\) | −3.61777e17 | −0.102189 | ||||||||
\(715\) | −3.61573e18 | −1.01206 | ||||||||
\(716\) | −2.70685e18 | −0.750810 | ||||||||
\(717\) | −4.05921e18 | −1.11575 | ||||||||
\(718\) | −4.20286e18 | −1.14482 | ||||||||
\(719\) | −4.13508e18 | −1.11621 | −0.558105 | − | 0.829770i | \(-0.688471\pi\) | ||||
−0.558105 | + | 0.829770i | \(0.688471\pi\) | |||||||
\(720\) | −1.67240e18 | −0.447382 | ||||||||
\(721\) | 1.13405e18 | 0.300646 | ||||||||
\(722\) | −4.03115e16 | −0.0105910 | ||||||||
\(723\) | 9.13409e17 | 0.237830 | ||||||||
\(724\) | 2.46021e18 | 0.634851 | ||||||||
\(725\) | 9.49942e17 | 0.242940 | ||||||||
\(726\) | 4.54627e17 | 0.115230 | ||||||||
\(727\) | 2.82326e18 | 0.709214 | 0.354607 | − | 0.935016i | \(-0.384615\pi\) | ||||
0.354607 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(728\) | −4.44056e17 | −0.110556 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | 7.96464e18 | 1.94790 | ||||||||
\(731\) | 9.86853e16 | 0.0239216 | ||||||||
\(732\) | 7.63478e17 | 0.183432 | ||||||||
\(733\) | −1.09963e18 | −0.261862 | −0.130931 | − | 0.991391i | \(-0.541797\pi\) | ||||
−0.130931 | + | 0.991391i | \(0.541797\pi\) | |||||||
\(734\) | −4.16694e18 | −0.983543 | ||||||||
\(735\) | −2.55590e18 | −0.597966 | ||||||||
\(736\) | −1.28588e18 | −0.298191 | ||||||||
\(737\) | 9.16977e17 | 0.210775 | ||||||||
\(738\) | 2.61740e17 | 0.0596352 | ||||||||
\(739\) | −3.16812e18 | −0.715506 | −0.357753 | − | 0.933816i | \(-0.616457\pi\) | ||||
−0.357753 | + | 0.933816i | \(0.616457\pi\) | |||||||
\(740\) | 8.72225e16 | 0.0195264 | ||||||||
\(741\) | 2.68050e18 | 0.594835 | ||||||||
\(742\) | −1.97542e17 | −0.0434543 | ||||||||
\(743\) | −6.30790e18 | −1.37549 | −0.687745 | − | 0.725952i | \(-0.741399\pi\) | ||||
−0.687745 | + | 0.725952i | \(0.741399\pi\) | |||||||
\(744\) | −1.72715e18 | −0.373342 | ||||||||
\(745\) | 6.94738e18 | 1.48869 | ||||||||
\(746\) | −5.79667e18 | −1.23134 | ||||||||
\(747\) | −7.13896e17 | −0.150332 | ||||||||
\(748\) | 1.78064e18 | 0.371719 | ||||||||
\(749\) | −4.52656e16 | −0.00936777 | ||||||||
\(750\) | 3.17864e18 | 0.652144 | ||||||||
\(751\) | 1.38416e18 | 0.281531 | 0.140765 | − | 0.990043i | \(-0.455044\pi\) | ||||
0.140765 | + | 0.990043i | \(0.455044\pi\) | |||||||
\(752\) | 1.06216e19 | 2.14177 | ||||||||
\(753\) | −3.76684e18 | −0.753026 | ||||||||
\(754\) | −9.89267e18 | −1.96065 | ||||||||
\(755\) | −7.16671e18 | −1.40820 | ||||||||
\(756\) | −1.06615e17 | −0.0207695 | ||||||||
\(757\) | 1.50601e18 | 0.290873 | 0.145436 | − | 0.989368i | \(-0.453541\pi\) | ||||
0.145436 | + | 0.989368i | \(0.453541\pi\) | |||||||
\(758\) | −3.90283e18 | −0.747360 | ||||||||
\(759\) | 8.30594e17 | 0.157695 | ||||||||
\(760\) | 3.18425e18 | 0.599402 | ||||||||
\(761\) | −5.30144e17 | −0.0989450 | −0.0494725 | − | 0.998775i | \(-0.515754\pi\) | ||||
−0.0494725 | + | 0.998775i | \(0.515754\pi\) | |||||||
\(762\) | −6.49547e18 | −1.20200 | ||||||||
\(763\) | 3.44775e17 | 0.0632595 | ||||||||
\(764\) | −1.87836e18 | −0.341722 | ||||||||
\(765\) | −1.45260e18 | −0.262027 | ||||||||
\(766\) | 8.34866e18 | 1.49324 | ||||||||
\(767\) | 7.53121e17 | 0.133566 | ||||||||
\(768\) | 4.09518e18 | 0.720154 | ||||||||
\(769\) | 8.41617e18 | 1.46755 | 0.733776 | − | 0.679391i | \(-0.237756\pi\) | ||||
0.733776 | + | 0.679391i | \(0.237756\pi\) | |||||||
\(770\) | −1.38270e18 | −0.239077 | ||||||||
\(771\) | −1.59398e18 | −0.273294 | ||||||||
\(772\) | −4.55242e18 | −0.773980 | ||||||||
\(773\) | −5.35077e18 | −0.902090 | −0.451045 | − | 0.892501i | \(-0.648949\pi\) | ||||
−0.451045 | + | 0.892501i | \(0.648949\pi\) | |||||||
\(774\) | 8.14493e16 | 0.0136167 | ||||||||
\(775\) | −1.11516e18 | −0.184874 | ||||||||
\(776\) | 6.12245e18 | 1.00652 | ||||||||
\(777\) | −2.24806e16 | −0.00366497 | ||||||||
\(778\) | −3.71500e18 | −0.600609 | ||||||||
\(779\) | −8.98543e17 | −0.144061 | ||||||||
\(780\) | 2.22691e18 | 0.354069 | ||||||||
\(781\) | 8.00489e18 | 1.26219 | ||||||||
\(782\) | −1.73587e18 | −0.271440 | ||||||||
\(783\) | 1.90166e18 | 0.294905 | ||||||||
\(784\) | 7.80154e18 | 1.19985 | ||||||||
\(785\) | 4.67249e17 | 0.0712682 | ||||||||
\(786\) | −8.97460e18 | −1.35759 | ||||||||
\(787\) | 1.03442e19 | 1.55189 | 0.775947 | − | 0.630798i | \(-0.217272\pi\) | ||||
0.775947 | + | 0.630798i | \(0.217272\pi\) | |||||||
\(788\) | −4.72245e18 | −0.702662 | ||||||||
\(789\) | 3.50028e18 | 0.516538 | ||||||||
\(790\) | 1.07341e19 | 1.57105 | ||||||||
\(791\) | −2.15455e18 | −0.312759 | ||||||||
\(792\) | −1.17666e18 | −0.169409 | ||||||||
\(793\) | 4.11017e18 | 0.586927 | ||||||||
\(794\) | 5.41353e17 | 0.0766739 | ||||||||
\(795\) | −7.93164e17 | −0.111424 | ||||||||
\(796\) | 1.37366e18 | 0.191401 | ||||||||
\(797\) | 2.65964e18 | 0.367573 | 0.183786 | − | 0.982966i | \(-0.441165\pi\) | ||||
0.183786 | + | 0.982966i | \(0.441165\pi\) | |||||||
\(798\) | 1.02505e18 | 0.140516 | ||||||||
\(799\) | 9.22559e18 | 1.25441 | ||||||||
\(800\) | 1.17617e18 | 0.158629 | ||||||||
\(801\) | −7.54102e17 | −0.100883 | ||||||||
\(802\) | 1.27632e19 | 1.69367 | ||||||||
\(803\) | 1.01037e19 | 1.32993 | ||||||||
\(804\) | −5.64761e17 | −0.0737396 | ||||||||
\(805\) | 4.81295e17 | 0.0623359 | ||||||||
\(806\) | 1.16133e19 | 1.49203 | ||||||||
\(807\) | −7.86808e18 | −1.00275 | ||||||||
\(808\) | 8.23900e18 | 1.04160 | ||||||||
\(809\) | −6.86795e18 | −0.861314 | −0.430657 | − | 0.902516i | \(-0.641718\pi\) | ||||
−0.430657 | + | 0.902516i | \(0.641718\pi\) | |||||||
\(810\) | −1.19889e18 | −0.149152 | ||||||||
\(811\) | 3.89506e18 | 0.480705 | 0.240352 | − | 0.970686i | \(-0.422737\pi\) | ||||
0.240352 | + | 0.970686i | \(0.422737\pi\) | |||||||
\(812\) | −1.35078e18 | −0.165376 | ||||||||
\(813\) | 5.76405e18 | 0.700067 | ||||||||
\(814\) | 3.09884e17 | 0.0373371 | ||||||||
\(815\) | 2.12543e18 | 0.254052 | ||||||||
\(816\) | 4.43386e18 | 0.525770 | ||||||||
\(817\) | −2.79613e17 | −0.0328938 | ||||||||
\(818\) | 1.16128e19 | 1.35531 | ||||||||
\(819\) | −5.73959e17 | −0.0664562 | ||||||||
\(820\) | −7.46495e17 | −0.0857505 | ||||||||
\(821\) | 3.11330e18 | 0.354806 | 0.177403 | − | 0.984138i | \(-0.443230\pi\) | ||||
0.177403 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(822\) | 8.42035e18 | 0.952058 | ||||||||
\(823\) | −1.17761e19 | −1.32100 | −0.660501 | − | 0.750825i | \(-0.729656\pi\) | ||||
−0.660501 | + | 0.750825i | \(0.729656\pi\) | |||||||
\(824\) | −7.70855e18 | −0.857918 | ||||||||
\(825\) | −7.59726e17 | −0.0838892 | ||||||||
\(826\) | 2.88002e17 | 0.0315518 | ||||||||
\(827\) | −6.06239e18 | −0.658958 | −0.329479 | − | 0.944163i | \(-0.606873\pi\) | ||||
−0.329479 | + | 0.944163i | \(0.606873\pi\) | |||||||
\(828\) | −5.11558e17 | −0.0551694 | ||||||||
\(829\) | 9.26464e18 | 0.991343 | 0.495672 | − | 0.868510i | \(-0.334922\pi\) | ||||
0.495672 | + | 0.868510i | \(0.334922\pi\) | |||||||
\(830\) | 5.70230e18 | 0.605400 | ||||||||
\(831\) | −3.01386e18 | −0.317480 | ||||||||
\(832\) | −8.98207e15 | −0.000938804 0 | ||||||||
\(833\) | 6.77621e18 | 0.702739 | ||||||||
\(834\) | −7.74364e18 | −0.796831 | ||||||||
\(835\) | −1.10544e19 | −1.12869 | ||||||||
\(836\) | −5.04522e18 | −0.511139 | ||||||||
\(837\) | −2.23241e18 | −0.224419 | ||||||||
\(838\) | 1.47696e19 | 1.47327 | ||||||||
\(839\) | 1.26271e19 | 1.24983 | 0.624917 | − | 0.780691i | \(-0.285133\pi\) | ||||
0.624917 | + | 0.780691i | \(0.285133\pi\) | |||||||
\(840\) | −6.81825e17 | −0.0669665 | ||||||||
\(841\) | 1.38330e19 | 1.34816 | ||||||||
\(842\) | −2.20363e19 | −2.13113 | ||||||||
\(843\) | 1.55129e18 | 0.148872 | ||||||||
\(844\) | 7.76115e18 | 0.739095 | ||||||||
\(845\) | 5.98530e17 | 0.0565610 | ||||||||
\(846\) | 7.61428e18 | 0.714039 | ||||||||
\(847\) | 3.34188e17 | 0.0310991 | ||||||||
\(848\) | 2.42103e18 | 0.223577 | ||||||||
\(849\) | 5.87537e18 | 0.538437 | ||||||||
\(850\) | 1.58777e18 | 0.144399 | ||||||||
\(851\) | −1.07866e17 | −0.00973514 | ||||||||
\(852\) | −4.93017e18 | −0.441575 | ||||||||
\(853\) | 1.35794e18 | 0.120702 | 0.0603508 | − | 0.998177i | \(-0.480778\pi\) | ||||
0.0603508 | + | 0.998177i | \(0.480778\pi\) | |||||||
\(854\) | 1.57177e18 | 0.138648 | ||||||||
\(855\) | 4.11576e18 | 0.360305 | ||||||||
\(856\) | 3.07685e17 | 0.0267317 | ||||||||
\(857\) | 1.32280e18 | 0.114056 | 0.0570280 | − | 0.998373i | \(-0.481838\pi\) | ||||
0.0570280 | + | 0.998373i | \(0.481838\pi\) | |||||||
\(858\) | 7.91177e18 | 0.677027 | ||||||||
\(859\) | 4.68816e18 | 0.398150 | 0.199075 | − | 0.979984i | \(-0.436206\pi\) | ||||
0.199075 | + | 0.979984i | \(0.436206\pi\) | |||||||
\(860\) | −2.32298e17 | −0.0195796 | ||||||||
\(861\) | 1.92400e17 | 0.0160948 | ||||||||
\(862\) | 7.10772e18 | 0.590111 | ||||||||
\(863\) | 1.90241e19 | 1.56759 | 0.783797 | − | 0.621017i | \(-0.213280\pi\) | ||||
0.783797 | + | 0.621017i | \(0.213280\pi\) | |||||||
\(864\) | 2.35453e18 | 0.192560 | ||||||||
\(865\) | 6.43343e18 | 0.522202 | ||||||||
\(866\) | 8.12595e18 | 0.654648 | ||||||||
\(867\) | −3.36931e18 | −0.269412 | ||||||||
\(868\) | 1.58572e18 | 0.125849 | ||||||||
\(869\) | 1.36169e19 | 1.07263 | ||||||||
\(870\) | −1.51897e19 | −1.18761 | ||||||||
\(871\) | −3.04038e18 | −0.235945 | ||||||||
\(872\) | −2.34355e18 | −0.180516 | ||||||||
\(873\) | 7.91350e18 | 0.605029 | ||||||||
\(874\) | 4.91839e18 | 0.373249 | ||||||||
\(875\) | 2.33656e18 | 0.176005 | ||||||||
\(876\) | −6.22279e18 | −0.465274 | ||||||||
\(877\) | 1.15848e19 | 0.859785 | 0.429893 | − | 0.902880i | \(-0.358551\pi\) | ||||
0.429893 | + | 0.902880i | \(0.358551\pi\) | |||||||
\(878\) | −2.27527e18 | −0.167617 | ||||||||
\(879\) | −3.79215e18 | −0.277305 | ||||||||
\(880\) | 1.69460e19 | 1.23007 | ||||||||
\(881\) | −2.59103e19 | −1.86693 | −0.933465 | − | 0.358667i | \(-0.883231\pi\) | ||||
−0.933465 | + | 0.358667i | \(0.883231\pi\) | |||||||
\(882\) | 5.59270e18 | 0.400014 | ||||||||
\(883\) | −3.41825e18 | −0.242694 | −0.121347 | − | 0.992610i | \(-0.538721\pi\) | ||||
−0.121347 | + | 0.992610i | \(0.538721\pi\) | |||||||
\(884\) | −5.90398e18 | −0.416107 | ||||||||
\(885\) | 1.15638e18 | 0.0809038 | ||||||||
\(886\) | 1.67961e19 | 1.16651 | ||||||||
\(887\) | −5.83477e18 | −0.402272 | −0.201136 | − | 0.979563i | \(-0.564463\pi\) | ||||
−0.201136 | + | 0.979563i | \(0.564463\pi\) | |||||||
\(888\) | 1.52808e17 | 0.0104583 | ||||||||
\(889\) | −4.77470e18 | −0.324403 | ||||||||
\(890\) | 6.02345e18 | 0.406266 | ||||||||
\(891\) | −1.52087e18 | −0.101833 | ||||||||
\(892\) | 7.15429e17 | 0.0475549 | ||||||||
\(893\) | −2.61396e19 | −1.72490 | ||||||||
\(894\) | −1.52019e19 | −0.995874 | ||||||||
\(895\) | −2.23750e19 | −1.45517 | ||||||||
\(896\) | 3.00808e18 | 0.194217 | ||||||||
\(897\) | −2.75397e18 | −0.176526 | ||||||||
\(898\) | −1.92547e19 | −1.22530 | ||||||||
\(899\) | −2.82841e19 | −1.78692 | ||||||||
\(900\) | 4.67911e17 | 0.0293486 | ||||||||
\(901\) | 2.10284e18 | 0.130947 | ||||||||
\(902\) | −2.65215e18 | −0.163966 | ||||||||
\(903\) | 5.98719e16 | 0.00367496 | ||||||||
\(904\) | 1.46452e19 | 0.892484 | ||||||||
\(905\) | 2.03362e19 | 1.23042 | ||||||||
\(906\) | 1.56818e19 | 0.942027 | ||||||||
\(907\) | 8.30355e18 | 0.495241 | 0.247620 | − | 0.968857i | \(-0.420351\pi\) | ||||
0.247620 | + | 0.968857i | \(0.420351\pi\) | |||||||
\(908\) | −6.04706e18 | −0.358085 | ||||||||
\(909\) | 1.06492e19 | 0.626113 | ||||||||
\(910\) | 4.58455e18 | 0.267625 | ||||||||
\(911\) | 4.71643e18 | 0.273366 | 0.136683 | − | 0.990615i | \(-0.456356\pi\) | ||||
0.136683 | + | 0.990615i | \(0.456356\pi\) | |||||||
\(912\) | −1.25628e19 | −0.722969 | ||||||||
\(913\) | 7.23374e18 | 0.413336 | ||||||||
\(914\) | 1.85349e19 | 1.05158 | ||||||||
\(915\) | 6.31095e18 | 0.355515 | ||||||||
\(916\) | −1.59117e19 | −0.890010 | ||||||||
\(917\) | −6.59707e18 | −0.366396 | ||||||||
\(918\) | 3.17850e18 | 0.175285 | ||||||||
\(919\) | −1.67823e19 | −0.918968 | −0.459484 | − | 0.888186i | \(-0.651966\pi\) | ||||
−0.459484 | + | 0.888186i | \(0.651966\pi\) | |||||||
\(920\) | −3.27152e18 | −0.177881 | ||||||||
\(921\) | −7.01721e18 | −0.378858 | ||||||||
\(922\) | 2.78002e19 | 1.49038 | ||||||||
\(923\) | −2.65415e19 | −1.41291 | ||||||||
\(924\) | 1.08030e18 | 0.0571055 | ||||||||
\(925\) | 9.86626e16 | 0.00517882 | ||||||||
\(926\) | 2.14303e19 | 1.11701 | ||||||||
\(927\) | −9.96359e18 | −0.515701 | ||||||||
\(928\) | 2.98314e19 | 1.53324 | ||||||||
\(929\) | −4.47502e18 | −0.228398 | −0.114199 | − | 0.993458i | \(-0.536430\pi\) | ||||
−0.114199 | + | 0.993458i | \(0.536430\pi\) | |||||||
\(930\) | 1.78316e19 | 0.903755 | ||||||||
\(931\) | −1.91996e19 | −0.966314 | ||||||||
\(932\) | −3.37535e18 | −0.168700 | ||||||||
\(933\) | −2.00895e19 | −0.997100 | ||||||||
\(934\) | 4.26545e19 | 2.10238 | ||||||||
\(935\) | 1.47188e19 | 0.720441 | ||||||||
\(936\) | 3.90139e18 | 0.189639 | ||||||||
\(937\) | 2.18745e19 | 1.05592 | 0.527959 | − | 0.849270i | \(-0.322957\pi\) | ||||
0.527959 | + | 0.849270i | \(0.322957\pi\) | |||||||
\(938\) | −1.16268e18 | −0.0557365 | ||||||||
\(939\) | 1.74363e19 | 0.830095 | ||||||||
\(940\) | −2.17163e19 | −1.02673 | ||||||||
\(941\) | 3.27197e19 | 1.53630 | 0.768151 | − | 0.640269i | \(-0.221177\pi\) | ||||
0.768151 | + | 0.640269i | \(0.221177\pi\) | |||||||
\(942\) | −1.02241e18 | −0.0476754 | ||||||||
\(943\) | 9.23172e17 | 0.0427520 | ||||||||
\(944\) | −3.52969e18 | −0.162337 | ||||||||
\(945\) | −8.81284e17 | −0.0402540 | ||||||||
\(946\) | −8.25307e17 | −0.0374389 | ||||||||
\(947\) | −3.33673e19 | −1.50330 | −0.751652 | − | 0.659560i | \(-0.770743\pi\) | ||||
−0.751652 | + | 0.659560i | \(0.770743\pi\) | |||||||
\(948\) | −8.38658e18 | −0.375259 | ||||||||
\(949\) | −3.35003e19 | −1.48874 | ||||||||
\(950\) | −4.49874e18 | −0.198558 | ||||||||
\(951\) | −3.35005e18 | −0.146851 | ||||||||
\(952\) | 1.80765e18 | 0.0787000 | ||||||||
\(953\) | 1.58341e18 | 0.0684682 | 0.0342341 | − | 0.999414i | \(-0.489101\pi\) | ||||
0.0342341 | + | 0.999414i | \(0.489101\pi\) | |||||||
\(954\) | 1.73556e18 | 0.0745377 | ||||||||
\(955\) | −1.55267e19 | −0.662302 | ||||||||
\(956\) | −2.53324e19 | −1.07325 | ||||||||
\(957\) | −1.92691e19 | −0.810838 | ||||||||
\(958\) | 2.33565e19 | 0.976183 | ||||||||
\(959\) | 6.18965e18 | 0.256948 | ||||||||
\(960\) | −1.37915e16 | −0.000568654 0 | ||||||||
\(961\) | 8.78595e18 | 0.359821 | ||||||||
\(962\) | −1.02747e18 | −0.0417957 | ||||||||
\(963\) | 3.97695e17 | 0.0160686 | ||||||||
\(964\) | 5.70033e18 | 0.228770 | ||||||||
\(965\) | −3.76305e19 | −1.50008 | ||||||||
\(966\) | −1.05315e18 | −0.0417001 | ||||||||
\(967\) | 1.74059e19 | 0.684579 | 0.342290 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342290 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(968\) | −2.27159e18 | −0.0887441 | ||||||||
\(969\) | −1.09117e19 | −0.423436 | ||||||||
\(970\) | −6.32097e19 | −2.43651 | ||||||||
\(971\) | 4.41500e18 | 0.169046 | 0.0845231 | − | 0.996422i | \(-0.473063\pi\) | ||||
0.0845231 | + | 0.996422i | \(0.473063\pi\) | |||||||
\(972\) | 9.36698e17 | 0.0356261 | ||||||||
\(973\) | −5.69221e18 | −0.215054 | ||||||||
\(974\) | −3.19433e19 | −1.19880 | ||||||||
\(975\) | 2.51899e18 | 0.0939067 | ||||||||
\(976\) | −1.92633e19 | −0.713357 | ||||||||
\(977\) | −3.40810e19 | −1.25371 | −0.626856 | − | 0.779135i | \(-0.715658\pi\) | ||||
−0.626856 | + | 0.779135i | \(0.715658\pi\) | |||||||
\(978\) | −4.65075e18 | −0.169950 | ||||||||
\(979\) | 7.64115e18 | 0.277377 | ||||||||
\(980\) | −1.59507e19 | −0.575187 | ||||||||
\(981\) | −3.02912e18 | −0.108510 | ||||||||
\(982\) | −5.82567e19 | −2.07310 | ||||||||
\(983\) | −1.48223e19 | −0.523983 | −0.261992 | − | 0.965070i | \(-0.584379\pi\) | ||||
−0.261992 | + | 0.965070i | \(0.584379\pi\) | |||||||
\(984\) | −1.30781e18 | −0.0459278 | ||||||||
\(985\) | −3.90360e19 | −1.36185 | ||||||||
\(986\) | 4.02709e19 | 1.39570 | ||||||||
\(987\) | 5.59712e18 | 0.192710 | ||||||||
\(988\) | 1.67282e19 | 0.572176 | ||||||||
\(989\) | 2.87277e17 | 0.00976168 | ||||||||
\(990\) | 1.21481e19 | 0.410091 | ||||||||
\(991\) | 3.49904e18 | 0.117347 | 0.0586733 | − | 0.998277i | \(-0.481313\pi\) | ||||
0.0586733 | + | 0.998277i | \(0.481313\pi\) | |||||||
\(992\) | −3.50199e19 | −1.16678 | ||||||||
\(993\) | −1.60616e19 | −0.531642 | ||||||||
\(994\) | −1.01498e19 | −0.333767 | ||||||||
\(995\) | 1.13547e19 | 0.370960 | ||||||||
\(996\) | −4.45522e18 | −0.144605 | ||||||||
\(997\) | 8.94587e18 | 0.288472 | 0.144236 | − | 0.989543i | \(-0.453928\pi\) | ||||
0.144236 | + | 0.989543i | \(0.453928\pi\) | |||||||
\(998\) | 5.02385e19 | 1.60949 | ||||||||
\(999\) | 1.97510e17 | 0.00628656 |
(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 | 177.14.a.a.1.7 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.7 | ✓ | 30 | 1.1 | even | 1 | trivial |