Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,36,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 36, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 36);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 36 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(23.2785391901\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{2196841}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 549210 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{4}\cdot 3\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(741.587\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −279461. | −1.50764 | −0.753818 | − | 0.657083i | \(-0.771790\pi\) | ||||
−0.753818 | + | 0.657083i | \(0.771790\pi\) | |||||||
\(3\) | 1.29140e8 | 0.577350 | ||||||||
\(4\) | 4.37389e10 | 1.27297 | ||||||||
\(5\) | −3.65354e11 | −0.214160 | −0.107080 | − | 0.994250i | \(-0.534150\pi\) | ||||
−0.107080 | + | 0.994250i | \(0.534150\pi\) | |||||||
\(6\) | −3.60897e13 | −0.870435 | ||||||||
\(7\) | −6.36148e14 | −1.03358 | −0.516788 | − | 0.856113i | \(-0.672872\pi\) | ||||
−0.516788 | + | 0.856113i | \(0.672872\pi\) | |||||||
\(8\) | −2.62111e15 | −0.411538 | ||||||||
\(9\) | 1.66772e16 | 0.333333 | ||||||||
\(10\) | 1.02102e17 | 0.322876 | ||||||||
\(11\) | 1.49276e17 | 0.0890467 | 0.0445234 | − | 0.999008i | \(-0.485823\pi\) | ||||
0.0445234 | + | 0.999008i | \(0.485823\pi\) | |||||||
\(12\) | 5.64845e18 | 0.734949 | ||||||||
\(13\) | 5.52590e19 | 1.77172 | 0.885858 | − | 0.463956i | \(-0.153570\pi\) | ||||
0.885858 | + | 0.463956i | \(0.153570\pi\) | |||||||
\(14\) | 1.77779e20 | 1.55826 | ||||||||
\(15\) | −4.71819e19 | −0.123646 | ||||||||
\(16\) | −7.70358e20 | −0.652519 | ||||||||
\(17\) | 1.81211e21 | 0.531285 | 0.265643 | − | 0.964072i | \(-0.414416\pi\) | ||||
0.265643 | + | 0.964072i | \(0.414416\pi\) | |||||||
\(18\) | −4.66063e21 | −0.502546 | ||||||||
\(19\) | −3.32454e22 | −1.39169 | −0.695846 | − | 0.718191i | \(-0.744970\pi\) | ||||
−0.695846 | + | 0.718191i | \(0.744970\pi\) | |||||||
\(20\) | −1.59802e22 | −0.272620 | ||||||||
\(21\) | −8.21522e22 | −0.596735 | ||||||||
\(22\) | −4.17169e22 | −0.134250 | ||||||||
\(23\) | 1.00717e24 | 1.48890 | 0.744451 | − | 0.667677i | \(-0.232711\pi\) | ||||
0.744451 | + | 0.667677i | \(0.232711\pi\) | |||||||
\(24\) | −3.38490e23 | −0.237602 | ||||||||
\(25\) | −2.77690e24 | −0.954135 | ||||||||
\(26\) | −1.54428e25 | −2.67111 | ||||||||
\(27\) | 2.15369e24 | 0.192450 | ||||||||
\(28\) | −2.78244e25 | −1.31571 | ||||||||
\(29\) | −4.49573e25 | −1.15036 | −0.575182 | − | 0.818026i | \(-0.695069\pi\) | ||||
−0.575182 | + | 0.818026i | \(0.695069\pi\) | |||||||
\(30\) | 1.31855e25 | 0.186413 | ||||||||
\(31\) | −2.23850e25 | −0.178291 | −0.0891453 | − | 0.996019i | \(-0.528414\pi\) | ||||
−0.0891453 | + | 0.996019i | \(0.528414\pi\) | |||||||
\(32\) | 3.05346e26 | 1.39530 | ||||||||
\(33\) | 1.92775e25 | 0.0514112 | ||||||||
\(34\) | −5.06414e26 | −0.800985 | ||||||||
\(35\) | 2.32419e26 | 0.221351 | ||||||||
\(36\) | 7.29441e26 | 0.424323 | ||||||||
\(37\) | −2.91588e27 | −1.05012 | −0.525060 | − | 0.851065i | \(-0.675957\pi\) | ||||
−0.525060 | + | 0.851065i | \(0.675957\pi\) | |||||||
\(38\) | 9.29079e27 | 2.09817 | ||||||||
\(39\) | 7.13616e27 | 1.02290 | ||||||||
\(40\) | 9.57633e26 | 0.0881352 | ||||||||
\(41\) | −4.18186e27 | −0.249834 | −0.124917 | − | 0.992167i | \(-0.539866\pi\) | ||||
−0.124917 | + | 0.992167i | \(0.539866\pi\) | |||||||
\(42\) | 2.29584e28 | 0.899660 | ||||||||
\(43\) | −5.84123e28 | −1.51638 | −0.758188 | − | 0.652037i | \(-0.773915\pi\) | ||||
−0.758188 | + | 0.652037i | \(0.773915\pi\) | |||||||
\(44\) | 6.52916e27 | 0.113354 | ||||||||
\(45\) | −6.09308e27 | −0.0713868 | ||||||||
\(46\) | −2.81465e29 | −2.24472 | ||||||||
\(47\) | −5.23894e28 | −0.286768 | −0.143384 | − | 0.989667i | \(-0.545798\pi\) | ||||
−0.143384 | + | 0.989667i | \(0.545798\pi\) | |||||||
\(48\) | −9.94842e28 | −0.376732 | ||||||||
\(49\) | 2.58653e28 | 0.0682788 | ||||||||
\(50\) | 7.76036e29 | 1.43849 | ||||||||
\(51\) | 2.34016e29 | 0.306738 | ||||||||
\(52\) | 2.41697e30 | 2.25534 | ||||||||
\(53\) | −2.64063e30 | −1.76555 | −0.882775 | − | 0.469796i | \(-0.844327\pi\) | ||||
−0.882775 | + | 0.469796i | \(0.844327\pi\) | |||||||
\(54\) | −6.01874e29 | −0.290145 | ||||||||
\(55\) | −5.45386e28 | −0.0190703 | ||||||||
\(56\) | 1.66741e30 | 0.425356 | ||||||||
\(57\) | −4.29331e30 | −0.803493 | ||||||||
\(58\) | 1.25638e31 | 1.73433 | ||||||||
\(59\) | 2.44829e30 | 0.250584 | 0.125292 | − | 0.992120i | \(-0.460013\pi\) | ||||
0.125292 | + | 0.992120i | \(0.460013\pi\) | |||||||
\(60\) | −2.06368e30 | −0.157397 | ||||||||
\(61\) | −1.37521e31 | −0.785412 | −0.392706 | − | 0.919664i | \(-0.628461\pi\) | ||||
−0.392706 | + | 0.919664i | \(0.628461\pi\) | |||||||
\(62\) | 6.25575e30 | 0.268797 | ||||||||
\(63\) | −1.06092e31 | −0.344525 | ||||||||
\(64\) | −5.88631e31 | −1.45109 | ||||||||
\(65\) | −2.01891e31 | −0.379432 | ||||||||
\(66\) | −5.38732e30 | −0.0775093 | ||||||||
\(67\) | −6.70306e31 | −0.741249 | −0.370625 | − | 0.928783i | \(-0.620856\pi\) | ||||
−0.370625 | + | 0.928783i | \(0.620856\pi\) | |||||||
\(68\) | 7.92595e31 | 0.676310 | ||||||||
\(69\) | 1.30066e32 | 0.859618 | ||||||||
\(70\) | −6.49522e31 | −0.333717 | ||||||||
\(71\) | 4.91498e32 | 1.97015 | 0.985077 | − | 0.172113i | \(-0.0550595\pi\) | ||||
0.985077 | + | 0.172113i | \(0.0550595\pi\) | |||||||
\(72\) | −4.37127e31 | −0.137179 | ||||||||
\(73\) | 1.37337e32 | 0.338561 | 0.169280 | − | 0.985568i | \(-0.445856\pi\) | ||||
0.169280 | + | 0.985568i | \(0.445856\pi\) | |||||||
\(74\) | 8.14875e32 | 1.58320 | ||||||||
\(75\) | −3.58609e32 | −0.550870 | ||||||||
\(76\) | −1.45411e33 | −1.77158 | ||||||||
\(77\) | −9.49616e31 | −0.0920365 | ||||||||
\(78\) | −1.99428e33 | −1.54216 | ||||||||
\(79\) | 1.07453e33 | 0.664879 | 0.332440 | − | 0.943125i | \(-0.392128\pi\) | ||||
0.332440 | + | 0.943125i | \(0.392128\pi\) | |||||||
\(80\) | 2.81454e32 | 0.139744 | ||||||||
\(81\) | 2.78128e32 | 0.111111 | ||||||||
\(82\) | 1.16867e33 | 0.376659 | ||||||||
\(83\) | −3.27927e33 | −0.854890 | −0.427445 | − | 0.904041i | \(-0.640586\pi\) | ||||
−0.427445 | + | 0.904041i | \(0.640586\pi\) | |||||||
\(84\) | −3.59325e33 | −0.759625 | ||||||||
\(85\) | −6.62061e32 | −0.113780 | ||||||||
\(86\) | 1.63240e34 | 2.28614 | ||||||||
\(87\) | −5.80579e33 | −0.664163 | ||||||||
\(88\) | −3.91268e32 | −0.0366461 | ||||||||
\(89\) | 3.27218e33 | 0.251485 | 0.125743 | − | 0.992063i | \(-0.459869\pi\) | ||||
0.125743 | + | 0.992063i | \(0.459869\pi\) | |||||||
\(90\) | 1.70278e33 | 0.107625 | ||||||||
\(91\) | −3.51529e34 | −1.83120 | ||||||||
\(92\) | 4.40526e34 | 1.89533 | ||||||||
\(93\) | −2.89081e33 | −0.102936 | ||||||||
\(94\) | 1.46408e34 | 0.432343 | ||||||||
\(95\) | 1.21463e34 | 0.298045 | ||||||||
\(96\) | 3.94324e34 | 0.805577 | ||||||||
\(97\) | −1.46799e34 | −0.250160 | −0.125080 | − | 0.992147i | \(-0.539919\pi\) | ||||
−0.125080 | + | 0.992147i | \(0.539919\pi\) | |||||||
\(98\) | −7.22835e33 | −0.102940 | ||||||||
\(99\) | 2.48950e33 | 0.0296822 | ||||||||
\(100\) | −1.21458e35 | −1.21458 | ||||||||
\(101\) | −2.12591e35 | −1.78617 | −0.893083 | − | 0.449893i | \(-0.851462\pi\) | ||||
−0.893083 | + | 0.449893i | \(0.851462\pi\) | |||||||
\(102\) | −6.53984e34 | −0.462449 | ||||||||
\(103\) | −5.17494e34 | −0.308499 | −0.154250 | − | 0.988032i | \(-0.549296\pi\) | ||||
−0.154250 | + | 0.988032i | \(0.549296\pi\) | |||||||
\(104\) | −1.44840e35 | −0.729129 | ||||||||
\(105\) | 3.00147e34 | 0.127797 | ||||||||
\(106\) | 7.37954e35 | 2.66181 | ||||||||
\(107\) | 1.53325e35 | 0.469242 | 0.234621 | − | 0.972087i | \(-0.424615\pi\) | ||||
0.234621 | + | 0.972087i | \(0.424615\pi\) | |||||||
\(108\) | 9.42002e34 | 0.244983 | ||||||||
\(109\) | 4.10693e35 | 0.908979 | 0.454489 | − | 0.890752i | \(-0.349822\pi\) | ||||
0.454489 | + | 0.890752i | \(0.349822\pi\) | |||||||
\(110\) | 1.52414e34 | 0.0287511 | ||||||||
\(111\) | −3.76557e35 | −0.606288 | ||||||||
\(112\) | 4.90062e35 | 0.674428 | ||||||||
\(113\) | −1.00388e36 | −1.18253 | −0.591263 | − | 0.806479i | \(-0.701371\pi\) | ||||
−0.591263 | + | 0.806479i | \(0.701371\pi\) | |||||||
\(114\) | 1.19981e36 | 1.21138 | ||||||||
\(115\) | −3.67974e35 | −0.318864 | ||||||||
\(116\) | −1.96638e36 | −1.46438 | ||||||||
\(117\) | 9.21564e35 | 0.590572 | ||||||||
\(118\) | −6.84203e35 | −0.377790 | ||||||||
\(119\) | −1.15277e36 | −0.549124 | ||||||||
\(120\) | 1.23669e35 | 0.0508849 | ||||||||
\(121\) | −2.78796e36 | −0.992071 | ||||||||
\(122\) | 3.84318e36 | 1.18412 | ||||||||
\(123\) | −5.40046e35 | −0.144242 | ||||||||
\(124\) | −9.79097e35 | −0.226958 | ||||||||
\(125\) | 2.07787e36 | 0.418498 | ||||||||
\(126\) | 2.96485e36 | 0.519419 | ||||||||
\(127\) | −4.93177e36 | −0.752381 | −0.376191 | − | 0.926542i | \(-0.622766\pi\) | ||||
−0.376191 | + | 0.926542i | \(0.622766\pi\) | |||||||
\(128\) | 5.95834e36 | 0.792412 | ||||||||
\(129\) | −7.54338e36 | −0.875480 | ||||||||
\(130\) | 5.64208e36 | 0.572045 | ||||||||
\(131\) | −1.37663e37 | −1.22059 | −0.610294 | − | 0.792175i | \(-0.708949\pi\) | ||||
−0.610294 | + | 0.792175i | \(0.708949\pi\) | |||||||
\(132\) | 8.43177e35 | 0.0654448 | ||||||||
\(133\) | 2.11490e37 | 1.43842 | ||||||||
\(134\) | 1.87325e37 | 1.11753 | ||||||||
\(135\) | −7.86861e35 | −0.0412152 | ||||||||
\(136\) | −4.74973e36 | −0.218644 | ||||||||
\(137\) | 1.40102e37 | 0.567328 | 0.283664 | − | 0.958924i | \(-0.408450\pi\) | ||||
0.283664 | + | 0.958924i | \(0.408450\pi\) | |||||||
\(138\) | −3.63485e37 | −1.29599 | ||||||||
\(139\) | 4.03059e37 | 1.26651 | 0.633256 | − | 0.773942i | \(-0.281718\pi\) | ||||
0.633256 | + | 0.773942i | \(0.281718\pi\) | |||||||
\(140\) | 1.01658e37 | 0.281773 | ||||||||
\(141\) | −6.76558e36 | −0.165566 | ||||||||
\(142\) | −1.37355e38 | −2.97028 | ||||||||
\(143\) | 8.24884e36 | 0.157766 | ||||||||
\(144\) | −1.28474e37 | −0.217506 | ||||||||
\(145\) | 1.64253e37 | 0.246362 | ||||||||
\(146\) | −3.83803e37 | −0.510427 | ||||||||
\(147\) | 3.34025e36 | 0.0394208 | ||||||||
\(148\) | −1.27537e38 | −1.33677 | ||||||||
\(149\) | 1.09713e38 | 1.02211 | 0.511054 | − | 0.859548i | \(-0.329255\pi\) | ||||
0.511054 | + | 0.859548i | \(0.329255\pi\) | |||||||
\(150\) | 1.00217e38 | 0.830512 | ||||||||
\(151\) | 1.08195e38 | 0.798199 | 0.399099 | − | 0.916908i | \(-0.369323\pi\) | ||||
0.399099 | + | 0.916908i | \(0.369323\pi\) | |||||||
\(152\) | 8.71396e37 | 0.572734 | ||||||||
\(153\) | 3.02208e37 | 0.177095 | ||||||||
\(154\) | 2.65381e37 | 0.138758 | ||||||||
\(155\) | 8.17847e36 | 0.0381828 | ||||||||
\(156\) | 3.12127e38 | 1.30212 | ||||||||
\(157\) | 3.80493e38 | 1.41939 | 0.709697 | − | 0.704507i | \(-0.248832\pi\) | ||||
0.709697 | + | 0.704507i | \(0.248832\pi\) | |||||||
\(158\) | −3.00288e38 | −1.00240 | ||||||||
\(159\) | −3.41012e38 | −1.01934 | ||||||||
\(160\) | −1.11559e38 | −0.298818 | ||||||||
\(161\) | −6.40710e38 | −1.53889 | ||||||||
\(162\) | −7.77261e37 | −0.167515 | ||||||||
\(163\) | −5.15630e38 | −0.997826 | −0.498913 | − | 0.866652i | \(-0.666267\pi\) | ||||
−0.498913 | + | 0.866652i | \(0.666267\pi\) | |||||||
\(164\) | −1.82910e38 | −0.318031 | ||||||||
\(165\) | −7.04313e36 | −0.0110102 | ||||||||
\(166\) | 9.16428e38 | 1.28886 | ||||||||
\(167\) | −2.92786e38 | −0.370691 | −0.185346 | − | 0.982673i | \(-0.559340\pi\) | ||||
−0.185346 | + | 0.982673i | \(0.559340\pi\) | |||||||
\(168\) | 2.15330e38 | 0.245579 | ||||||||
\(169\) | 2.08077e39 | 2.13898 | ||||||||
\(170\) | 1.85020e38 | 0.171539 | ||||||||
\(171\) | −5.54439e38 | −0.463897 | ||||||||
\(172\) | −2.55489e39 | −1.93030 | ||||||||
\(173\) | −2.25696e39 | −1.54070 | −0.770349 | − | 0.637623i | \(-0.779918\pi\) | ||||
−0.770349 | + | 0.637623i | \(0.779918\pi\) | |||||||
\(174\) | 1.62249e39 | 1.00132 | ||||||||
\(175\) | 1.76652e39 | 0.986171 | ||||||||
\(176\) | −1.14996e38 | −0.0581047 | ||||||||
\(177\) | 3.16173e38 | 0.144675 | ||||||||
\(178\) | −9.14448e38 | −0.379148 | ||||||||
\(179\) | 3.55925e39 | 1.33792 | 0.668961 | − | 0.743298i | \(-0.266739\pi\) | ||||
0.668961 | + | 0.743298i | \(0.266739\pi\) | |||||||
\(180\) | −2.66504e38 | −0.0908732 | ||||||||
\(181\) | −4.44114e39 | −1.37442 | −0.687211 | − | 0.726458i | \(-0.741165\pi\) | ||||
−0.687211 | + | 0.726458i | \(0.741165\pi\) | |||||||
\(182\) | 9.82387e39 | 2.76079 | ||||||||
\(183\) | −1.77595e39 | −0.453458 | ||||||||
\(184\) | −2.63990e39 | −0.612740 | ||||||||
\(185\) | 1.06533e39 | 0.224894 | ||||||||
\(186\) | 8.07869e38 | 0.155190 | ||||||||
\(187\) | 2.70504e38 | 0.0473092 | ||||||||
\(188\) | −2.29146e39 | −0.365047 | ||||||||
\(189\) | −1.37007e39 | −0.198912 | ||||||||
\(190\) | −3.39443e39 | −0.449344 | ||||||||
\(191\) | −8.19302e39 | −0.989373 | −0.494686 | − | 0.869072i | \(-0.664717\pi\) | ||||
−0.494686 | + | 0.869072i | \(0.664717\pi\) | |||||||
\(192\) | −7.60158e39 | −0.837785 | ||||||||
\(193\) | 3.38085e39 | 0.340230 | 0.170115 | − | 0.985424i | \(-0.445586\pi\) | ||||
0.170115 | + | 0.985424i | \(0.445586\pi\) | |||||||
\(194\) | 4.10246e39 | 0.377150 | ||||||||
\(195\) | −2.60722e39 | −0.219065 | ||||||||
\(196\) | 1.13132e39 | 0.0869168 | ||||||||
\(197\) | −1.27322e40 | −0.894836 | −0.447418 | − | 0.894325i | \(-0.647656\pi\) | ||||
−0.447418 | + | 0.894325i | \(0.647656\pi\) | |||||||
\(198\) | −6.95720e38 | −0.0447500 | ||||||||
\(199\) | −7.27758e39 | −0.428606 | −0.214303 | − | 0.976767i | \(-0.568748\pi\) | ||||
−0.214303 | + | 0.976767i | \(0.568748\pi\) | |||||||
\(200\) | 7.27855e39 | 0.392663 | ||||||||
\(201\) | −8.65635e39 | −0.427960 | ||||||||
\(202\) | 5.94111e40 | 2.69289 | ||||||||
\(203\) | 2.85995e40 | 1.18899 | ||||||||
\(204\) | 1.02356e40 | 0.390468 | ||||||||
\(205\) | 1.52786e39 | 0.0535046 | ||||||||
\(206\) | 1.44620e40 | 0.465105 | ||||||||
\(207\) | 1.67968e40 | 0.496301 | ||||||||
\(208\) | −4.25692e40 | −1.15608 | ||||||||
\(209\) | −4.96273e39 | −0.123926 | ||||||||
\(210\) | −8.38794e39 | −0.192672 | ||||||||
\(211\) | −2.76616e40 | −0.584701 | −0.292351 | − | 0.956311i | \(-0.594437\pi\) | ||||
−0.292351 | + | 0.956311i | \(0.594437\pi\) | |||||||
\(212\) | −1.15498e41 | −2.24749 | ||||||||
\(213\) | 6.34721e40 | 1.13747 | ||||||||
\(214\) | −4.28484e40 | −0.707446 | ||||||||
\(215\) | 2.13412e40 | 0.324747 | ||||||||
\(216\) | −5.64506e39 | −0.0792005 | ||||||||
\(217\) | 1.42402e40 | 0.184277 | ||||||||
\(218\) | −1.14773e41 | −1.37041 | ||||||||
\(219\) | 1.77357e40 | 0.195468 | ||||||||
\(220\) | −2.38546e39 | −0.0242759 | ||||||||
\(221\) | 1.00135e41 | 0.941287 | ||||||||
\(222\) | 1.05233e41 | 0.914062 | ||||||||
\(223\) | 3.35919e40 | 0.269712 | 0.134856 | − | 0.990865i | \(-0.456943\pi\) | ||||
0.134856 | + | 0.990865i | \(0.456943\pi\) | |||||||
\(224\) | −1.94245e41 | −1.44215 | ||||||||
\(225\) | −4.63109e40 | −0.318045 | ||||||||
\(226\) | 2.80547e41 | 1.78282 | ||||||||
\(227\) | 1.89749e41 | 1.11616 | 0.558081 | − | 0.829787i | \(-0.311538\pi\) | ||||
0.558081 | + | 0.829787i | \(0.311538\pi\) | |||||||
\(228\) | −1.87785e41 | −1.02282 | ||||||||
\(229\) | −1.77014e41 | −0.893071 | −0.446536 | − | 0.894766i | \(-0.647342\pi\) | ||||
−0.446536 | + | 0.894766i | \(0.647342\pi\) | |||||||
\(230\) | 1.02835e41 | 0.480731 | ||||||||
\(231\) | −1.22634e40 | −0.0531373 | ||||||||
\(232\) | 1.17838e41 | 0.473419 | ||||||||
\(233\) | −1.57002e40 | −0.0585026 | −0.0292513 | − | 0.999572i | \(-0.509312\pi\) | ||||
−0.0292513 | + | 0.999572i | \(0.509312\pi\) | |||||||
\(234\) | −2.57542e41 | −0.890369 | ||||||||
\(235\) | 1.91407e40 | 0.0614144 | ||||||||
\(236\) | 1.07086e41 | 0.318986 | ||||||||
\(237\) | 1.38764e41 | 0.383868 | ||||||||
\(238\) | 3.22154e41 | 0.827879 | ||||||||
\(239\) | −2.98699e41 | −0.713297 | −0.356648 | − | 0.934239i | \(-0.616081\pi\) | ||||
−0.356648 | + | 0.934239i | \(0.616081\pi\) | |||||||
\(240\) | 3.63470e40 | 0.0806811 | ||||||||
\(241\) | −6.82984e40 | −0.140965 | −0.0704827 | − | 0.997513i | \(-0.522454\pi\) | ||||
−0.0704827 | + | 0.997513i | \(0.522454\pi\) | |||||||
\(242\) | 7.79127e41 | 1.49568 | ||||||||
\(243\) | 3.59175e40 | 0.0641500 | ||||||||
\(244\) | −6.01502e41 | −0.999805 | ||||||||
\(245\) | −9.45000e39 | −0.0146226 | ||||||||
\(246\) | 1.50922e41 | 0.217464 | ||||||||
\(247\) | −1.83710e42 | −2.46568 | ||||||||
\(248\) | 5.86736e40 | 0.0733734 | ||||||||
\(249\) | −4.23485e41 | −0.493571 | ||||||||
\(250\) | −5.80685e41 | −0.630944 | ||||||||
\(251\) | −8.56382e40 | −0.0867715 | −0.0433858 | − | 0.999058i | \(-0.513814\pi\) | ||||
−0.0433858 | + | 0.999058i | \(0.513814\pi\) | |||||||
\(252\) | −4.64032e41 | −0.438570 | ||||||||
\(253\) | 1.50347e41 | 0.132582 | ||||||||
\(254\) | 1.37824e42 | 1.13432 | ||||||||
\(255\) | −8.54987e40 | −0.0656911 | ||||||||
\(256\) | 3.57394e41 | 0.256417 | ||||||||
\(257\) | 1.59187e42 | 1.06679 | 0.533393 | − | 0.845868i | \(-0.320917\pi\) | ||||
0.533393 | + | 0.845868i | \(0.320917\pi\) | |||||||
\(258\) | 2.10808e42 | 1.31991 | ||||||||
\(259\) | 1.85493e42 | 1.08538 | ||||||||
\(260\) | −8.83049e41 | −0.483005 | ||||||||
\(261\) | −7.49761e41 | −0.383455 | ||||||||
\(262\) | 3.84715e42 | 1.84020 | ||||||||
\(263\) | −1.67624e42 | −0.750085 | −0.375043 | − | 0.927008i | \(-0.622372\pi\) | ||||
−0.375043 | + | 0.927008i | \(0.622372\pi\) | |||||||
\(264\) | −5.05285e40 | −0.0211576 | ||||||||
\(265\) | 9.64766e41 | 0.378111 | ||||||||
\(266\) | −5.91032e42 | −2.16861 | ||||||||
\(267\) | 4.22570e41 | 0.145195 | ||||||||
\(268\) | −2.93184e42 | −0.943587 | ||||||||
\(269\) | −8.26329e41 | −0.249166 | −0.124583 | − | 0.992209i | \(-0.539759\pi\) | ||||
−0.124583 | + | 0.992209i | \(0.539759\pi\) | |||||||
\(270\) | 2.19897e41 | 0.0621375 | ||||||||
\(271\) | 5.20129e42 | 1.37768 | 0.688840 | − | 0.724914i | \(-0.258120\pi\) | ||||
0.688840 | + | 0.724914i | \(0.258120\pi\) | |||||||
\(272\) | −1.39597e42 | −0.346674 | ||||||||
\(273\) | −4.53965e42 | −1.05725 | ||||||||
\(274\) | −3.91531e42 | −0.855325 | ||||||||
\(275\) | −4.14524e41 | −0.0849626 | ||||||||
\(276\) | 5.68895e42 | 1.09427 | ||||||||
\(277\) | −8.57159e41 | −0.154762 | −0.0773812 | − | 0.997002i | \(-0.524656\pi\) | ||||
−0.0773812 | + | 0.997002i | \(0.524656\pi\) | |||||||
\(278\) | −1.12639e43 | −1.90944 | ||||||||
\(279\) | −3.73319e41 | −0.0594302 | ||||||||
\(280\) | −6.09196e41 | −0.0910944 | ||||||||
\(281\) | 7.78049e42 | 1.09307 | 0.546533 | − | 0.837438i | \(-0.315947\pi\) | ||||
0.546533 | + | 0.837438i | \(0.315947\pi\) | |||||||
\(282\) | 1.89072e42 | 0.249613 | ||||||||
\(283\) | −5.95094e41 | −0.0738454 | −0.0369227 | − | 0.999318i | \(-0.511756\pi\) | ||||
−0.0369227 | + | 0.999318i | \(0.511756\pi\) | |||||||
\(284\) | 2.14976e43 | 2.50795 | ||||||||
\(285\) | 1.56858e42 | 0.172076 | ||||||||
\(286\) | −2.30523e42 | −0.237853 | ||||||||
\(287\) | 2.66028e42 | 0.258222 | ||||||||
\(288\) | 5.09231e42 | 0.465100 | ||||||||
\(289\) | −8.34982e42 | −0.717736 | ||||||||
\(290\) | −4.59025e42 | −0.371425 | ||||||||
\(291\) | −1.89576e42 | −0.144430 | ||||||||
\(292\) | 6.00696e42 | 0.430977 | ||||||||
\(293\) | −1.97041e43 | −1.33160 | −0.665800 | − | 0.746130i | \(-0.731910\pi\) | ||||
−0.665800 | + | 0.746130i | \(0.731910\pi\) | |||||||
\(294\) | −9.33470e41 | −0.0594322 | ||||||||
\(295\) | −8.94495e41 | −0.0536652 | ||||||||
\(296\) | 7.64283e42 | 0.432165 | ||||||||
\(297\) | 3.21495e41 | 0.0171371 | ||||||||
\(298\) | −3.06605e43 | −1.54097 | ||||||||
\(299\) | 5.56553e43 | 2.63791 | ||||||||
\(300\) | −1.56852e43 | −0.701241 | ||||||||
\(301\) | 3.71589e43 | 1.56729 | ||||||||
\(302\) | −3.02363e43 | −1.20339 | ||||||||
\(303\) | −2.74541e43 | −1.03124 | ||||||||
\(304\) | 2.56108e43 | 0.908105 | ||||||||
\(305\) | 5.02439e42 | 0.168204 | ||||||||
\(306\) | −8.44556e42 | −0.266995 | ||||||||
\(307\) | −3.56177e43 | −1.06352 | −0.531759 | − | 0.846896i | \(-0.678469\pi\) | ||||
−0.531759 | + | 0.846896i | \(0.678469\pi\) | |||||||
\(308\) | −4.15351e42 | −0.117160 | ||||||||
\(309\) | −6.68293e42 | −0.178112 | ||||||||
\(310\) | −2.28557e42 | −0.0575658 | ||||||||
\(311\) | 3.70185e43 | 0.881276 | 0.440638 | − | 0.897685i | \(-0.354752\pi\) | ||||
0.440638 | + | 0.897685i | \(0.354752\pi\) | |||||||
\(312\) | −1.87046e43 | −0.420963 | ||||||||
\(313\) | −4.19837e43 | −0.893419 | −0.446709 | − | 0.894679i | \(-0.647404\pi\) | ||||
−0.446709 | + | 0.894679i | \(0.647404\pi\) | |||||||
\(314\) | −1.06333e44 | −2.13993 | ||||||||
\(315\) | 3.87610e42 | 0.0737837 | ||||||||
\(316\) | 4.69986e43 | 0.846371 | ||||||||
\(317\) | 3.62720e43 | 0.618066 | 0.309033 | − | 0.951051i | \(-0.399995\pi\) | ||||
0.309033 | + | 0.951051i | \(0.399995\pi\) | |||||||
\(318\) | 9.52995e43 | 1.53680 | ||||||||
\(319\) | −6.71104e42 | −0.102436 | ||||||||
\(320\) | 2.15059e43 | 0.310765 | ||||||||
\(321\) | 1.98004e43 | 0.270917 | ||||||||
\(322\) | 1.79054e44 | 2.32009 | ||||||||
\(323\) | −6.02441e43 | −0.739385 | ||||||||
\(324\) | 1.21650e43 | 0.141441 | ||||||||
\(325\) | −1.53449e44 | −1.69046 | ||||||||
\(326\) | 1.44099e44 | 1.50436 | ||||||||
\(327\) | 5.30370e43 | 0.524799 | ||||||||
\(328\) | 1.09611e43 | 0.102816 | ||||||||
\(329\) | 3.33274e43 | 0.296397 | ||||||||
\(330\) | 1.96828e42 | 0.0165994 | ||||||||
\(331\) | −1.52756e44 | −1.22182 | −0.610911 | − | 0.791700i | \(-0.709197\pi\) | ||||
−0.610911 | + | 0.791700i | \(0.709197\pi\) | |||||||
\(332\) | −1.43432e44 | −1.08825 | ||||||||
\(333\) | −4.86286e43 | −0.350040 | ||||||||
\(334\) | 8.18224e43 | 0.558868 | ||||||||
\(335\) | 2.44899e43 | 0.158746 | ||||||||
\(336\) | 6.32867e43 | 0.389381 | ||||||||
\(337\) | −1.48437e44 | −0.867002 | −0.433501 | − | 0.901153i | \(-0.642722\pi\) | ||||
−0.433501 | + | 0.901153i | \(0.642722\pi\) | |||||||
\(338\) | −5.81495e44 | −3.22481 | ||||||||
\(339\) | −1.29642e44 | −0.682732 | ||||||||
\(340\) | −2.89578e43 | −0.144839 | ||||||||
\(341\) | −3.34155e42 | −0.0158762 | ||||||||
\(342\) | 1.54944e44 | 0.699388 | ||||||||
\(343\) | 2.24531e44 | 0.963004 | ||||||||
\(344\) | 1.53105e44 | 0.624046 | ||||||||
\(345\) | −4.75203e43 | −0.184096 | ||||||||
\(346\) | 6.30734e44 | 2.32281 | ||||||||
\(347\) | 4.00770e44 | 1.40323 | 0.701616 | − | 0.712555i | \(-0.252462\pi\) | ||||
0.701616 | + | 0.712555i | \(0.252462\pi\) | |||||||
\(348\) | −2.53939e44 | −0.845459 | ||||||||
\(349\) | 9.71517e43 | 0.307614 | 0.153807 | − | 0.988101i | \(-0.450847\pi\) | ||||
0.153807 | + | 0.988101i | \(0.450847\pi\) | |||||||
\(350\) | −4.93674e44 | −1.48679 | ||||||||
\(351\) | 1.19011e44 | 0.340967 | ||||||||
\(352\) | 4.55808e43 | 0.124247 | ||||||||
\(353\) | 5.81527e44 | 1.50839 | 0.754193 | − | 0.656653i | \(-0.228028\pi\) | ||||
0.754193 | + | 0.656653i | \(0.228028\pi\) | |||||||
\(354\) | −8.83581e43 | −0.218117 | ||||||||
\(355\) | −1.79571e44 | −0.421929 | ||||||||
\(356\) | 1.43122e44 | 0.320133 | ||||||||
\(357\) | −1.48869e44 | −0.317037 | ||||||||
\(358\) | −9.94673e44 | −2.01710 | ||||||||
\(359\) | −3.64874e43 | −0.0704676 | −0.0352338 | − | 0.999379i | \(-0.511218\pi\) | ||||
−0.0352338 | + | 0.999379i | \(0.511218\pi\) | |||||||
\(360\) | 1.59706e43 | 0.0293784 | ||||||||
\(361\) | 5.34595e44 | 0.936805 | ||||||||
\(362\) | 1.24113e45 | 2.07213 | ||||||||
\(363\) | −3.60038e44 | −0.572772 | ||||||||
\(364\) | −1.53755e45 | −2.33107 | ||||||||
\(365\) | −5.01766e43 | −0.0725063 | ||||||||
\(366\) | 4.96309e44 | 0.683650 | ||||||||
\(367\) | 6.94503e44 | 0.912049 | 0.456025 | − | 0.889967i | \(-0.349273\pi\) | ||||
0.456025 | + | 0.889967i | \(0.349273\pi\) | |||||||
\(368\) | −7.75883e44 | −0.971537 | ||||||||
\(369\) | −6.97416e43 | −0.0832780 | ||||||||
\(370\) | −2.97718e44 | −0.339059 | ||||||||
\(371\) | 1.67983e45 | 1.82483 | ||||||||
\(372\) | −1.26441e44 | −0.131034 | ||||||||
\(373\) | −1.97985e45 | −1.95762 | −0.978808 | − | 0.204781i | \(-0.934352\pi\) | ||||
−0.978808 | + | 0.204781i | \(0.934352\pi\) | |||||||
\(374\) | −7.55954e43 | −0.0713251 | ||||||||
\(375\) | 2.68337e44 | 0.241620 | ||||||||
\(376\) | 1.37318e44 | 0.118016 | ||||||||
\(377\) | −2.48429e45 | −2.03812 | ||||||||
\(378\) | 3.82881e44 | 0.299887 | ||||||||
\(379\) | 1.79049e45 | 1.33902 | 0.669508 | − | 0.742805i | \(-0.266505\pi\) | ||||
0.669508 | + | 0.742805i | \(0.266505\pi\) | |||||||
\(380\) | 5.31267e44 | 0.379402 | ||||||||
\(381\) | −6.36890e44 | −0.434387 | ||||||||
\(382\) | 2.28963e45 | 1.49162 | ||||||||
\(383\) | −1.49796e45 | −0.932225 | −0.466113 | − | 0.884725i | \(-0.654346\pi\) | ||||
−0.466113 | + | 0.884725i | \(0.654346\pi\) | |||||||
\(384\) | 7.69461e44 | 0.457499 | ||||||||
\(385\) | 3.46946e43 | 0.0197106 | ||||||||
\(386\) | −9.44816e44 | −0.512943 | ||||||||
\(387\) | −9.74153e44 | −0.505458 | ||||||||
\(388\) | −6.42082e44 | −0.318446 | ||||||||
\(389\) | 1.77359e45 | 0.840882 | 0.420441 | − | 0.907320i | \(-0.361875\pi\) | ||||
0.420441 | + | 0.907320i | \(0.361875\pi\) | |||||||
\(390\) | 7.28618e44 | 0.330270 | ||||||||
\(391\) | 1.82510e45 | 0.791032 | ||||||||
\(392\) | −6.77957e43 | −0.0280993 | ||||||||
\(393\) | −1.77778e45 | −0.704707 | ||||||||
\(394\) | 3.55815e45 | 1.34909 | ||||||||
\(395\) | −3.92583e44 | −0.142391 | ||||||||
\(396\) | 1.08888e44 | 0.0377846 | ||||||||
\(397\) | −2.45730e44 | −0.0815876 | −0.0407938 | − | 0.999168i | \(-0.512989\pi\) | ||||
−0.0407938 | + | 0.999168i | \(0.512989\pi\) | |||||||
\(398\) | 2.03380e45 | 0.646182 | ||||||||
\(399\) | 2.73118e45 | 0.830471 | ||||||||
\(400\) | 2.13921e45 | 0.622591 | ||||||||
\(401\) | −3.47243e45 | −0.967401 | −0.483701 | − | 0.875234i | \(-0.660708\pi\) | ||||
−0.483701 | + | 0.875234i | \(0.660708\pi\) | |||||||
\(402\) | 2.41911e45 | 0.645209 | ||||||||
\(403\) | −1.23698e45 | −0.315880 | ||||||||
\(404\) | −9.29851e45 | −2.27373 | ||||||||
\(405\) | −1.01615e44 | −0.0237956 | ||||||||
\(406\) | −7.99245e45 | −1.79256 | ||||||||
\(407\) | −4.35271e44 | −0.0935098 | ||||||||
\(408\) | −6.13381e44 | −0.126234 | ||||||||
\(409\) | −5.60182e45 | −1.10451 | −0.552257 | − | 0.833674i | \(-0.686233\pi\) | ||||
−0.552257 | + | 0.833674i | \(0.686233\pi\) | |||||||
\(410\) | −4.26978e44 | −0.0806655 | ||||||||
\(411\) | 1.80928e45 | 0.327547 | ||||||||
\(412\) | −2.26346e45 | −0.392710 | ||||||||
\(413\) | −1.55748e45 | −0.258998 | ||||||||
\(414\) | −4.69405e45 | −0.748242 | ||||||||
\(415\) | 1.19809e45 | 0.183084 | ||||||||
\(416\) | 1.68731e46 | 2.47208 | ||||||||
\(417\) | 5.20511e45 | 0.731221 | ||||||||
\(418\) | 1.38689e45 | 0.186835 | ||||||||
\(419\) | 1.30103e46 | 1.68090 | 0.840449 | − | 0.541891i | \(-0.182291\pi\) | ||||
0.840449 | + | 0.541891i | \(0.182291\pi\) | |||||||
\(420\) | 1.31281e45 | 0.162682 | ||||||||
\(421\) | −3.23759e45 | −0.384844 | −0.192422 | − | 0.981312i | \(-0.561634\pi\) | ||||
−0.192422 | + | 0.981312i | \(0.561634\pi\) | |||||||
\(422\) | 7.73034e45 | 0.881517 | ||||||||
\(423\) | −8.73708e44 | −0.0955894 | ||||||||
\(424\) | 6.92138e45 | 0.726591 | ||||||||
\(425\) | −5.03204e45 | −0.506918 | ||||||||
\(426\) | −1.77380e46 | −1.71489 | ||||||||
\(427\) | 8.74838e45 | 0.811783 | ||||||||
\(428\) | 6.70626e45 | 0.597330 | ||||||||
\(429\) | 1.06526e45 | 0.0910860 | ||||||||
\(430\) | −5.96404e45 | −0.489601 | ||||||||
\(431\) | −7.33523e45 | −0.578178 | −0.289089 | − | 0.957302i | \(-0.593352\pi\) | ||||
−0.289089 | + | 0.957302i | \(0.593352\pi\) | |||||||
\(432\) | −1.65912e45 | −0.125577 | ||||||||
\(433\) | −3.13432e44 | −0.0227827 | −0.0113913 | − | 0.999935i | \(-0.503626\pi\) | ||||
−0.0113913 | + | 0.999935i | \(0.503626\pi\) | |||||||
\(434\) | −3.97958e45 | −0.277823 | ||||||||
\(435\) | 2.12117e45 | 0.142237 | ||||||||
\(436\) | 1.79633e46 | 1.15710 | ||||||||
\(437\) | −3.34838e46 | −2.07209 | ||||||||
\(438\) | −4.95644e45 | −0.294695 | ||||||||
\(439\) | −4.96227e45 | −0.283499 | −0.141749 | − | 0.989903i | \(-0.545273\pi\) | ||||
−0.141749 | + | 0.989903i | \(0.545273\pi\) | |||||||
\(440\) | 1.42952e44 | 0.00784815 | ||||||||
\(441\) | 4.31360e44 | 0.0227596 | ||||||||
\(442\) | −2.79839e46 | −1.41912 | ||||||||
\(443\) | 3.90477e46 | 1.90340 | 0.951701 | − | 0.307026i | \(-0.0993340\pi\) | ||||
0.951701 | + | 0.307026i | \(0.0993340\pi\) | |||||||
\(444\) | −1.64702e46 | −0.771785 | ||||||||
\(445\) | −1.19551e45 | −0.0538581 | ||||||||
\(446\) | −9.38765e45 | −0.406627 | ||||||||
\(447\) | 1.41683e46 | 0.590115 | ||||||||
\(448\) | 3.74456e46 | 1.49981 | ||||||||
\(449\) | 9.78942e45 | 0.377091 | 0.188545 | − | 0.982064i | \(-0.439623\pi\) | ||||
0.188545 | + | 0.982064i | \(0.439623\pi\) | |||||||
\(450\) | 1.29421e46 | 0.479497 | ||||||||
\(451\) | −6.24251e44 | −0.0222469 | ||||||||
\(452\) | −4.39088e46 | −1.50532 | ||||||||
\(453\) | 1.39723e46 | 0.460840 | ||||||||
\(454\) | −5.30275e46 | −1.68277 | ||||||||
\(455\) | 1.28433e46 | 0.392171 | ||||||||
\(456\) | 1.12532e46 | 0.330668 | ||||||||
\(457\) | −7.87990e45 | −0.222837 | −0.111419 | − | 0.993774i | \(-0.535539\pi\) | ||||
−0.111419 | + | 0.993774i | \(0.535539\pi\) | |||||||
\(458\) | 4.94685e46 | 1.34643 | ||||||||
\(459\) | 3.90272e45 | 0.102246 | ||||||||
\(460\) | −1.60948e46 | −0.405904 | ||||||||
\(461\) | −6.50894e46 | −1.58032 | −0.790158 | − | 0.612903i | \(-0.790002\pi\) | ||||
−0.790158 | + | 0.612903i | \(0.790002\pi\) | |||||||
\(462\) | 3.42713e45 | 0.0801118 | ||||||||
\(463\) | 4.77272e46 | 1.07423 | 0.537117 | − | 0.843508i | \(-0.319513\pi\) | ||||
0.537117 | + | 0.843508i | \(0.319513\pi\) | |||||||
\(464\) | 3.46332e46 | 0.750634 | ||||||||
\(465\) | 1.05617e45 | 0.0220448 | ||||||||
\(466\) | 4.38759e45 | 0.0882008 | ||||||||
\(467\) | −3.34554e46 | −0.647769 | −0.323885 | − | 0.946097i | \(-0.604989\pi\) | ||||
−0.323885 | + | 0.946097i | \(0.604989\pi\) | |||||||
\(468\) | 4.03082e46 | 0.751780 | ||||||||
\(469\) | 4.26414e46 | 0.766137 | ||||||||
\(470\) | −5.34909e45 | −0.0925906 | ||||||||
\(471\) | 4.91369e46 | 0.819487 | ||||||||
\(472\) | −6.41724e45 | −0.103125 | ||||||||
\(473\) | −8.71956e45 | −0.135028 | ||||||||
\(474\) | −3.87793e46 | −0.578734 | ||||||||
\(475\) | 9.23190e46 | 1.32786 | ||||||||
\(476\) | −5.04208e46 | −0.699017 | ||||||||
\(477\) | −4.40383e46 | −0.588517 | ||||||||
\(478\) | 8.34748e46 | 1.07539 | ||||||||
\(479\) | −9.78794e46 | −1.21568 | −0.607841 | − | 0.794059i | \(-0.707964\pi\) | ||||
−0.607841 | + | 0.794059i | \(0.707964\pi\) | |||||||
\(480\) | −1.44068e46 | −0.172523 | ||||||||
\(481\) | −1.61129e47 | −1.86052 | ||||||||
\(482\) | 1.90868e46 | 0.212525 | ||||||||
\(483\) | −8.27414e46 | −0.888481 | ||||||||
\(484\) | −1.21942e47 | −1.26288 | ||||||||
\(485\) | 5.36336e45 | 0.0535743 | ||||||||
\(486\) | −1.00376e46 | −0.0967150 | ||||||||
\(487\) | 1.03689e47 | 0.963777 | 0.481889 | − | 0.876232i | \(-0.339951\pi\) | ||||
0.481889 | + | 0.876232i | \(0.339951\pi\) | |||||||
\(488\) | 3.60458e46 | 0.323227 | ||||||||
\(489\) | −6.65885e46 | −0.576095 | ||||||||
\(490\) | 2.64091e45 | 0.0220456 | ||||||||
\(491\) | 1.30638e46 | 0.105231 | 0.0526155 | − | 0.998615i | \(-0.483244\pi\) | ||||
0.0526155 | + | 0.998615i | \(0.483244\pi\) | |||||||
\(492\) | −2.36210e46 | −0.183615 | ||||||||
\(493\) | −8.14674e46 | −0.611171 | ||||||||
\(494\) | 5.13400e47 | 3.71735 | ||||||||
\(495\) | −9.09551e44 | −0.00635676 | ||||||||
\(496\) | 1.72445e46 | 0.116338 | ||||||||
\(497\) | −3.12665e47 | −2.03630 | ||||||||
\(498\) | 1.18348e47 | 0.744126 | ||||||||
\(499\) | 1.66085e46 | 0.100826 | 0.0504129 | − | 0.998728i | \(-0.483946\pi\) | ||||
0.0504129 | + | 0.998728i | \(0.483946\pi\) | |||||||
\(500\) | 9.08838e46 | 0.532735 | ||||||||
\(501\) | −3.78105e46 | −0.214019 | ||||||||
\(502\) | 2.39326e46 | 0.130820 | ||||||||
\(503\) | 2.15922e47 | 1.13987 | 0.569937 | − | 0.821689i | \(-0.306968\pi\) | ||||
0.569937 | + | 0.821689i | \(0.306968\pi\) | |||||||
\(504\) | 2.78077e46 | 0.141785 | ||||||||
\(505\) | 7.76712e46 | 0.382526 | ||||||||
\(506\) | −4.20160e46 | −0.199885 | ||||||||
\(507\) | 2.68711e47 | 1.23494 | ||||||||
\(508\) | −2.15710e47 | −0.957758 | ||||||||
\(509\) | 3.50805e47 | 1.50489 | 0.752444 | − | 0.658656i | \(-0.228875\pi\) | ||||
0.752444 | + | 0.658656i | \(0.228875\pi\) | |||||||
\(510\) | 2.38936e46 | 0.0990383 | ||||||||
\(511\) | −8.73665e46 | −0.349928 | ||||||||
\(512\) | −3.04605e47 | −1.17900 | ||||||||
\(513\) | −7.16003e46 | −0.267831 | ||||||||
\(514\) | −4.44865e47 | −1.60832 | ||||||||
\(515\) | 1.89069e46 | 0.0660683 | ||||||||
\(516\) | −3.29939e47 | −1.11446 | ||||||||
\(517\) | −7.82048e45 | −0.0255358 | ||||||||
\(518\) | −5.18381e47 | −1.63636 | ||||||||
\(519\) | −2.91464e47 | −0.889522 | ||||||||
\(520\) | 5.29178e46 | 0.156151 | ||||||||
\(521\) | 4.99886e47 | 1.42630 | 0.713149 | − | 0.701012i | \(-0.247268\pi\) | ||||
0.713149 | + | 0.701012i | \(0.247268\pi\) | |||||||
\(522\) | 2.09529e47 | 0.578110 | ||||||||
\(523\) | −2.90357e46 | −0.0774733 | −0.0387367 | − | 0.999249i | \(-0.512333\pi\) | ||||
−0.0387367 | + | 0.999249i | \(0.512333\pi\) | |||||||
\(524\) | −6.02122e47 | −1.55377 | ||||||||
\(525\) | 2.28128e47 | 0.569366 | ||||||||
\(526\) | 4.68444e47 | 1.13086 | ||||||||
\(527\) | −4.05641e46 | −0.0947231 | ||||||||
\(528\) | −1.48506e46 | −0.0335468 | ||||||||
\(529\) | 5.56807e47 | 1.21683 | ||||||||
\(530\) | −2.69615e47 | −0.570054 | ||||||||
\(531\) | 4.08306e46 | 0.0835280 | ||||||||
\(532\) | 9.25032e47 | 1.83106 | ||||||||
\(533\) | −2.31085e47 | −0.442635 | ||||||||
\(534\) | −1.18092e47 | −0.218901 | ||||||||
\(535\) | −5.60179e46 | −0.100493 | ||||||||
\(536\) | 1.75694e47 | 0.305052 | ||||||||
\(537\) | 4.59642e47 | 0.772449 | ||||||||
\(538\) | 2.30927e47 | 0.375651 | ||||||||
\(539\) | 3.86107e45 | 0.00608001 | ||||||||
\(540\) | −3.44164e46 | −0.0524657 | ||||||||
\(541\) | −7.56060e47 | −1.11585 | −0.557923 | − | 0.829893i | \(-0.688402\pi\) | ||||
−0.557923 | + | 0.829893i | \(0.688402\pi\) | |||||||
\(542\) | −1.45356e48 | −2.07704 | ||||||||
\(543\) | −5.73530e47 | −0.793522 | ||||||||
\(544\) | 5.53320e47 | 0.741302 | ||||||||
\(545\) | −1.50048e47 | −0.194667 | ||||||||
\(546\) | 1.26866e48 | 1.59394 | ||||||||
\(547\) | −5.49459e47 | −0.668586 | −0.334293 | − | 0.942469i | \(-0.608497\pi\) | ||||
−0.334293 | + | 0.942469i | \(0.608497\pi\) | |||||||
\(548\) | 6.12790e47 | 0.722191 | ||||||||
\(549\) | −2.29347e47 | −0.261804 | ||||||||
\(550\) | 1.15844e47 | 0.128093 | ||||||||
\(551\) | 1.49462e48 | 1.60095 | ||||||||
\(552\) | −3.40918e47 | −0.353766 | ||||||||
\(553\) | −6.83557e47 | −0.687203 | ||||||||
\(554\) | 2.39543e47 | 0.233325 | ||||||||
\(555\) | 1.37577e47 | 0.129843 | ||||||||
\(556\) | 1.76293e48 | 1.61223 | ||||||||
\(557\) | 1.06798e48 | 0.946449 | 0.473225 | − | 0.880942i | \(-0.343090\pi\) | ||||
0.473225 | + | 0.880942i | \(0.343090\pi\) | |||||||
\(558\) | 1.04328e47 | 0.0895991 | ||||||||
\(559\) | −3.22781e48 | −2.68659 | ||||||||
\(560\) | −1.79046e47 | −0.144436 | ||||||||
\(561\) | 3.49329e46 | 0.0273140 | ||||||||
\(562\) | −2.17435e48 | −1.64795 | ||||||||
\(563\) | −2.95577e47 | −0.217157 | −0.108578 | − | 0.994088i | \(-0.534630\pi\) | ||||
−0.108578 | + | 0.994088i | \(0.534630\pi\) | |||||||
\(564\) | −2.95919e47 | −0.210760 | ||||||||
\(565\) | 3.66773e47 | 0.253250 | ||||||||
\(566\) | 1.66306e47 | 0.111332 | ||||||||
\(567\) | −1.76931e47 | −0.114842 | ||||||||
\(568\) | −1.28827e48 | −0.810794 | ||||||||
\(569\) | 1.55924e47 | 0.0951587 | 0.0475794 | − | 0.998867i | \(-0.484849\pi\) | ||||
0.0475794 | + | 0.998867i | \(0.484849\pi\) | |||||||
\(570\) | −4.38357e47 | −0.259429 | ||||||||
\(571\) | 2.44889e48 | 1.40552 | 0.702761 | − | 0.711426i | \(-0.251950\pi\) | ||||
0.702761 | + | 0.711426i | \(0.251950\pi\) | |||||||
\(572\) | 3.60795e47 | 0.200831 | ||||||||
\(573\) | −1.05805e48 | −0.571215 | ||||||||
\(574\) | −7.43445e47 | −0.389306 | ||||||||
\(575\) | −2.79681e48 | −1.42061 | ||||||||
\(576\) | −9.81670e47 | −0.483695 | ||||||||
\(577\) | 2.16685e48 | 1.03575 | 0.517873 | − | 0.855458i | \(-0.326724\pi\) | ||||
0.517873 | + | 0.855458i | \(0.326724\pi\) | |||||||
\(578\) | 2.33345e48 | 1.08209 | ||||||||
\(579\) | 4.36603e47 | 0.196432 | ||||||||
\(580\) | 7.18426e47 | 0.313612 | ||||||||
\(581\) | 2.08610e48 | 0.883594 | ||||||||
\(582\) | 5.29792e47 | 0.217748 | ||||||||
\(583\) | −3.94183e47 | −0.157216 | ||||||||
\(584\) | −3.59974e47 | −0.139331 | ||||||||
\(585\) | −3.36697e47 | −0.126477 | ||||||||
\(586\) | 5.50654e48 | 2.00757 | ||||||||
\(587\) | 3.51258e47 | 0.124296 | 0.0621482 | − | 0.998067i | \(-0.480205\pi\) | ||||
0.0621482 | + | 0.998067i | \(0.480205\pi\) | |||||||
\(588\) | 1.46099e47 | 0.0501814 | ||||||||
\(589\) | 7.44199e47 | 0.248125 | ||||||||
\(590\) | 2.49977e47 | 0.0809076 | ||||||||
\(591\) | −1.64423e48 | −0.516634 | ||||||||
\(592\) | 2.24627e48 | 0.685224 | ||||||||
\(593\) | 3.58906e47 | 0.106298 | 0.0531489 | − | 0.998587i | \(-0.483074\pi\) | ||||
0.0531489 | + | 0.998587i | \(0.483074\pi\) | |||||||
\(594\) | −8.98454e46 | −0.0258364 | ||||||||
\(595\) | 4.21169e47 | 0.117601 | ||||||||
\(596\) | 4.79871e48 | 1.30111 | ||||||||
\(597\) | −9.39828e47 | −0.247456 | ||||||||
\(598\) | −1.55535e49 | −3.97702 | ||||||||
\(599\) | −2.08154e48 | −0.516911 | −0.258456 | − | 0.966023i | \(-0.583214\pi\) | ||||
−0.258456 | + | 0.966023i | \(0.583214\pi\) | |||||||
\(600\) | 9.39953e47 | 0.226704 | ||||||||
\(601\) | −1.00213e48 | −0.234758 | −0.117379 | − | 0.993087i | \(-0.537449\pi\) | ||||
−0.117379 | + | 0.993087i | \(0.537449\pi\) | |||||||
\(602\) | −1.03845e49 | −2.36290 | ||||||||
\(603\) | −1.11788e48 | −0.247083 | ||||||||
\(604\) | 4.73233e48 | 1.01608 | ||||||||
\(605\) | 1.01859e48 | 0.212462 | ||||||||
\(606\) | 7.67235e48 | 1.55474 | ||||||||
\(607\) | −4.36540e48 | −0.859453 | −0.429726 | − | 0.902959i | \(-0.641390\pi\) | ||||
−0.429726 | + | 0.902959i | \(0.641390\pi\) | |||||||
\(608\) | −1.01513e49 | −1.94183 | ||||||||
\(609\) | 3.69334e48 | 0.686463 | ||||||||
\(610\) | −1.40412e48 | −0.253591 | ||||||||
\(611\) | −2.89499e48 | −0.508072 | ||||||||
\(612\) | 1.32183e48 | 0.225437 | ||||||||
\(613\) | 9.45680e48 | 1.56742 | 0.783711 | − | 0.621126i | \(-0.213324\pi\) | ||||
0.783711 | + | 0.621126i | \(0.213324\pi\) | |||||||
\(614\) | 9.95378e48 | 1.60340 | ||||||||
\(615\) | 1.97308e47 | 0.0308909 | ||||||||
\(616\) | 2.48905e47 | 0.0378765 | ||||||||
\(617\) | −6.32292e47 | −0.0935249 | −0.0467625 | − | 0.998906i | \(-0.514890\pi\) | ||||
−0.0467625 | + | 0.998906i | \(0.514890\pi\) | |||||||
\(618\) | 1.86762e48 | 0.268528 | ||||||||
\(619\) | 2.65684e48 | 0.371346 | 0.185673 | − | 0.982612i | \(-0.440553\pi\) | ||||
0.185673 | + | 0.982612i | \(0.440553\pi\) | |||||||
\(620\) | 3.57717e47 | 0.0486055 | ||||||||
\(621\) | 2.16914e48 | 0.286539 | ||||||||
\(622\) | −1.03452e49 | −1.32864 | ||||||||
\(623\) | −2.08159e48 | −0.259929 | ||||||||
\(624\) | −5.49740e48 | −0.667462 | ||||||||
\(625\) | 7.32268e48 | 0.864510 | ||||||||
\(626\) | 1.17328e49 | 1.34695 | ||||||||
\(627\) | −6.40888e47 | −0.0715485 | ||||||||
\(628\) | 1.66423e49 | 1.80684 | ||||||||
\(629\) | −5.28389e48 | −0.557914 | ||||||||
\(630\) | −1.08322e48 | −0.111239 | ||||||||
\(631\) | 2.52797e47 | 0.0252498 | 0.0126249 | − | 0.999920i | \(-0.495981\pi\) | ||||
0.0126249 | + | 0.999920i | \(0.495981\pi\) | |||||||
\(632\) | −2.81645e48 | −0.273623 | ||||||||
\(633\) | −3.57222e48 | −0.337577 | ||||||||
\(634\) | −1.01366e49 | −0.931819 | ||||||||
\(635\) | 1.80184e48 | 0.161130 | ||||||||
\(636\) | −1.49155e49 | −1.29759 | ||||||||
\(637\) | 1.42929e48 | 0.120971 | ||||||||
\(638\) | 1.87548e48 | 0.154436 | ||||||||
\(639\) | 8.19679e48 | 0.656718 | ||||||||
\(640\) | −2.17691e48 | −0.169703 | ||||||||
\(641\) | 1.43723e49 | 1.09021 | 0.545105 | − | 0.838368i | \(-0.316490\pi\) | ||||
0.545105 | + | 0.838368i | \(0.316490\pi\) | |||||||
\(642\) | −5.53345e48 | −0.408444 | ||||||||
\(643\) | −3.98874e48 | −0.286513 | −0.143256 | − | 0.989686i | \(-0.545757\pi\) | ||||
−0.143256 | + | 0.989686i | \(0.545757\pi\) | |||||||
\(644\) | −2.80239e49 | −1.95896 | ||||||||
\(645\) | 2.75601e48 | 0.187493 | ||||||||
\(646\) | 1.68359e49 | 1.11472 | ||||||||
\(647\) | −2.33006e49 | −1.50156 | −0.750781 | − | 0.660552i | \(-0.770322\pi\) | ||||
−0.750781 | + | 0.660552i | \(0.770322\pi\) | |||||||
\(648\) | −7.29004e47 | −0.0457265 | ||||||||
\(649\) | 3.65471e47 | 0.0223137 | ||||||||
\(650\) | 4.28830e49 | 2.54860 | ||||||||
\(651\) | 1.83898e48 | 0.106392 | ||||||||
\(652\) | −2.25531e49 | −1.27020 | ||||||||
\(653\) | 1.17028e49 | 0.641666 | 0.320833 | − | 0.947136i | \(-0.396037\pi\) | ||||
0.320833 | + | 0.947136i | \(0.396037\pi\) | |||||||
\(654\) | −1.48218e49 | −0.791207 | ||||||||
\(655\) | 5.02957e48 | 0.261402 | ||||||||
\(656\) | 3.22153e48 | 0.163021 | ||||||||
\(657\) | 2.29039e48 | 0.112854 | ||||||||
\(658\) | −9.31372e48 | −0.446859 | ||||||||
\(659\) | −1.32090e49 | −0.617128 | −0.308564 | − | 0.951204i | \(-0.599848\pi\) | ||||
−0.308564 | + | 0.951204i | \(0.599848\pi\) | |||||||
\(660\) | −3.08058e47 | −0.0140157 | ||||||||
\(661\) | −3.80316e49 | −1.68508 | −0.842538 | − | 0.538637i | \(-0.818940\pi\) | ||||
−0.842538 | + | 0.538637i | \(0.818940\pi\) | |||||||
\(662\) | 4.26893e49 | 1.84206 | ||||||||
\(663\) | 1.29315e49 | 0.543452 | ||||||||
\(664\) | 8.59531e48 | 0.351820 | ||||||||
\(665\) | −7.72686e48 | −0.308052 | ||||||||
\(666\) | 1.35898e49 | 0.527734 | ||||||||
\(667\) | −4.52797e49 | −1.71278 | ||||||||
\(668\) | −1.28061e49 | −0.471879 | ||||||||
\(669\) | 4.33807e48 | 0.155718 | ||||||||
\(670\) | −6.84399e48 | −0.239332 | ||||||||
\(671\) | −2.05286e48 | −0.0699383 | ||||||||
\(672\) | −2.50848e49 | −0.832625 | ||||||||
\(673\) | 1.15552e49 | 0.373692 | 0.186846 | − | 0.982389i | \(-0.440173\pi\) | ||||
0.186846 | + | 0.982389i | \(0.440173\pi\) | |||||||
\(674\) | 4.14825e49 | 1.30712 | ||||||||
\(675\) | −5.98059e48 | −0.183623 | ||||||||
\(676\) | 9.10106e49 | 2.72286 | ||||||||
\(677\) | 5.18340e48 | 0.151117 | 0.0755585 | − | 0.997141i | \(-0.475926\pi\) | ||||
0.0755585 | + | 0.997141i | \(0.475926\pi\) | |||||||
\(678\) | 3.62298e49 | 1.02931 | ||||||||
\(679\) | 9.33858e48 | 0.258559 | ||||||||
\(680\) | 1.73533e48 | 0.0468249 | ||||||||
\(681\) | 2.45042e49 | 0.644416 | ||||||||
\(682\) | 9.33834e47 | 0.0239355 | ||||||||
\(683\) | 4.66690e49 | 1.16591 | 0.582957 | − | 0.812503i | \(-0.301896\pi\) | ||||
0.582957 | + | 0.812503i | \(0.301896\pi\) | |||||||
\(684\) | −2.42505e49 | −0.590527 | ||||||||
\(685\) | −5.11868e48 | −0.121499 | ||||||||
\(686\) | −6.27476e49 | −1.45186 | ||||||||
\(687\) | −2.28596e49 | −0.515615 | ||||||||
\(688\) | 4.49984e49 | 0.989463 | ||||||||
\(689\) | −1.45919e50 | −3.12805 | ||||||||
\(690\) | 1.32801e49 | 0.277550 | ||||||||
\(691\) | 5.17806e49 | 1.05512 | 0.527559 | − | 0.849519i | \(-0.323107\pi\) | ||||
0.527559 | + | 0.849519i | \(0.323107\pi\) | |||||||
\(692\) | −9.87170e49 | −1.96126 | ||||||||
\(693\) | −1.58369e48 | −0.0306788 | ||||||||
\(694\) | −1.12000e50 | −2.11557 | ||||||||
\(695\) | −1.47259e49 | −0.271237 | ||||||||
\(696\) | 1.52176e49 | 0.273328 | ||||||||
\(697\) | −7.57797e48 | −0.132733 | ||||||||
\(698\) | −2.71501e49 | −0.463770 | ||||||||
\(699\) | −2.02752e48 | −0.0337765 | ||||||||
\(700\) | 7.72655e49 | 1.25537 | ||||||||
\(701\) | 1.34782e49 | 0.213582 | 0.106791 | − | 0.994281i | \(-0.465942\pi\) | ||||
0.106791 | + | 0.994281i | \(0.465942\pi\) | |||||||
\(702\) | −3.32590e49 | −0.514055 | ||||||||
\(703\) | 9.69394e49 | 1.46144 | ||||||||
\(704\) | −8.78684e48 | −0.129214 | ||||||||
\(705\) | 2.47183e48 | 0.0354576 | ||||||||
\(706\) | −1.62514e50 | −2.27410 | ||||||||
\(707\) | 1.35240e50 | 1.84614 | ||||||||
\(708\) | 1.38291e49 | 0.184166 | ||||||||
\(709\) | 5.95415e49 | 0.773589 | 0.386795 | − | 0.922166i | \(-0.373582\pi\) | ||||
0.386795 | + | 0.922166i | \(0.373582\pi\) | |||||||
\(710\) | 5.01831e49 | 0.636116 | ||||||||
\(711\) | 1.79201e49 | 0.221626 | ||||||||
\(712\) | −8.57674e48 | −0.103496 | ||||||||
\(713\) | −2.25456e49 | −0.265457 | ||||||||
\(714\) | 4.16030e49 | 0.477976 | ||||||||
\(715\) | −3.01375e48 | −0.0337871 | ||||||||
\(716\) | 1.55678e50 | 1.70313 | ||||||||
\(717\) | −3.85740e49 | −0.411822 | ||||||||
\(718\) | 1.01968e49 | 0.106240 | ||||||||
\(719\) | 9.50970e49 | 0.966966 | 0.483483 | − | 0.875354i | \(-0.339371\pi\) | ||||
0.483483 | + | 0.875354i | \(0.339371\pi\) | |||||||
\(720\) | 4.69386e48 | 0.0465812 | ||||||||
\(721\) | 3.29203e49 | 0.318857 | ||||||||
\(722\) | −1.49399e50 | −1.41236 | ||||||||
\(723\) | −8.82007e48 | −0.0813864 | ||||||||
\(724\) | −1.94251e50 | −1.74960 | ||||||||
\(725\) | 1.24842e50 | 1.09760 | ||||||||
\(726\) | 1.00617e50 | 0.863533 | ||||||||
\(727\) | −7.28338e49 | −0.610212 | −0.305106 | − | 0.952318i | \(-0.598692\pi\) | ||||
−0.305106 | + | 0.952318i | \(0.598692\pi\) | |||||||
\(728\) | 9.21395e49 | 0.753610 | ||||||||
\(729\) | 4.63840e48 | 0.0370370 | ||||||||
\(730\) | 1.40224e49 | 0.109313 | ||||||||
\(731\) | −1.05849e50 | −0.805628 | ||||||||
\(732\) | −7.76781e49 | −0.577238 | ||||||||
\(733\) | −2.38824e50 | −1.73284 | −0.866421 | − | 0.499314i | \(-0.833585\pi\) | ||||
−0.866421 | + | 0.499314i | \(0.833585\pi\) | |||||||
\(734\) | −1.94087e50 | −1.37504 | ||||||||
\(735\) | −1.22037e48 | −0.00844237 | ||||||||
\(736\) | 3.07536e50 | 2.07747 | ||||||||
\(737\) | −1.00061e49 | −0.0660058 | ||||||||
\(738\) | 1.94901e49 | 0.125553 | ||||||||
\(739\) | 2.40229e50 | 1.51129 | 0.755646 | − | 0.654980i | \(-0.227323\pi\) | ||||
0.755646 | + | 0.654980i | \(0.227323\pi\) | |||||||
\(740\) | 4.65963e49 | 0.286283 | ||||||||
\(741\) | −2.37244e50 | −1.42356 | ||||||||
\(742\) | −4.69448e50 | −2.75118 | ||||||||
\(743\) | −3.09674e49 | −0.177256 | −0.0886279 | − | 0.996065i | \(-0.528248\pi\) | ||||
−0.0886279 | + | 0.996065i | \(0.528248\pi\) | |||||||
\(744\) | 7.57712e48 | 0.0423621 | ||||||||
\(745\) | −4.00840e49 | −0.218895 | ||||||||
\(746\) | 5.53291e50 | 2.95137 | ||||||||
\(747\) | −5.46889e49 | −0.284963 | ||||||||
\(748\) | 1.18315e49 | 0.0602232 | ||||||||
\(749\) | −9.75373e49 | −0.484997 | ||||||||
\(750\) | −7.49898e49 | −0.364275 | ||||||||
\(751\) | 4.66674e49 | 0.221470 | 0.110735 | − | 0.993850i | \(-0.464680\pi\) | ||||
0.110735 | + | 0.993850i | \(0.464680\pi\) | |||||||
\(752\) | 4.03586e49 | 0.187122 | ||||||||
\(753\) | −1.10593e49 | −0.0500976 | ||||||||
\(754\) | 6.94264e50 | 3.07274 | ||||||||
\(755\) | −3.95296e49 | −0.170943 | ||||||||
\(756\) | −5.99252e49 | −0.253208 | ||||||||
\(757\) | −1.36549e50 | −0.563780 | −0.281890 | − | 0.959447i | \(-0.590961\pi\) | ||||
−0.281890 | + | 0.959447i | \(0.590961\pi\) | |||||||
\(758\) | −5.00373e50 | −2.01875 | ||||||||
\(759\) | 1.94158e49 | 0.0765462 | ||||||||
\(760\) | −3.18368e49 | −0.122657 | ||||||||
\(761\) | 2.28332e48 | 0.00859677 | 0.00429839 | − | 0.999991i | \(-0.498632\pi\) | ||||
0.00429839 | + | 0.999991i | \(0.498632\pi\) | |||||||
\(762\) | 1.77986e50 | 0.654899 | ||||||||
\(763\) | −2.61262e50 | −0.939498 | ||||||||
\(764\) | −3.58353e50 | −1.25944 | ||||||||
\(765\) | −1.10413e49 | −0.0379267 | ||||||||
\(766\) | 4.18621e50 | 1.40546 | ||||||||
\(767\) | 1.35290e50 | 0.443964 | ||||||||
\(768\) | 4.61539e49 | 0.148043 | ||||||||
\(769\) | −5.95370e49 | −0.186671 | −0.0933354 | − | 0.995635i | \(-0.529753\pi\) | ||||
−0.0933354 | + | 0.995635i | \(0.529753\pi\) | |||||||
\(770\) | −9.69580e48 | −0.0297164 | ||||||||
\(771\) | 2.05574e50 | 0.615909 | ||||||||
\(772\) | 1.47874e50 | 0.433102 | ||||||||
\(773\) | 3.53372e50 | 1.01179 | 0.505895 | − | 0.862595i | \(-0.331162\pi\) | ||||
0.505895 | + | 0.862595i | \(0.331162\pi\) | |||||||
\(774\) | 2.72238e50 | 0.762048 | ||||||||
\(775\) | 6.21610e49 | 0.170113 | ||||||||
\(776\) | 3.84776e49 | 0.102950 | ||||||||
\(777\) | 2.39546e50 | 0.626644 | ||||||||
\(778\) | −4.95650e50 | −1.26774 | ||||||||
\(779\) | 1.39027e50 | 0.347692 | ||||||||
\(780\) | −1.14037e50 | −0.278863 | ||||||||
\(781\) | 7.33688e49 | 0.175436 | ||||||||
\(782\) | −5.10046e50 | −1.19259 | ||||||||
\(783\) | −9.68243e49 | −0.221388 | ||||||||
\(784\) | −1.99255e49 | −0.0445532 | ||||||||
\(785\) | −1.39015e50 | −0.303978 | ||||||||
\(786\) | 4.96821e50 | 1.06244 | ||||||||
\(787\) | −2.59047e50 | −0.541777 | −0.270888 | − | 0.962611i | \(-0.587317\pi\) | ||||
−0.270888 | + | 0.962611i | \(0.587317\pi\) | |||||||
\(788\) | −5.56891e50 | −1.13910 | ||||||||
\(789\) | −2.16470e50 | −0.433062 | ||||||||
\(790\) | 1.09712e50 | 0.214674 | ||||||||
\(791\) | 6.38619e50 | 1.22223 | ||||||||
\(792\) | −6.52525e48 | −0.0122154 | ||||||||
\(793\) | −7.59928e50 | −1.39153 | ||||||||
\(794\) | 6.86720e49 | 0.123004 | ||||||||
\(795\) | 1.24590e50 | 0.218302 | ||||||||
\(796\) | −3.18313e50 | −0.545602 | ||||||||
\(797\) | −2.98933e49 | −0.0501249 | −0.0250624 | − | 0.999686i | \(-0.507978\pi\) | ||||
−0.0250624 | + | 0.999686i | \(0.507978\pi\) | |||||||
\(798\) | −7.63259e50 | −1.25205 | ||||||||
\(799\) | −9.49353e49 | −0.152356 | ||||||||
\(800\) | −8.47915e50 | −1.33130 | ||||||||
\(801\) | 5.45708e49 | 0.0838284 | ||||||||
\(802\) | 9.70409e50 | 1.45849 | ||||||||
\(803\) | 2.05011e49 | 0.0301477 | ||||||||
\(804\) | −3.78619e50 | −0.544780 | ||||||||
\(805\) | 2.34086e50 | 0.329570 | ||||||||
\(806\) | 3.45687e50 | 0.476233 | ||||||||
\(807\) | −1.06712e50 | −0.143856 | ||||||||
\(808\) | 5.57225e50 | 0.735075 | ||||||||
\(809\) | −5.81772e50 | −0.751023 | −0.375512 | − | 0.926818i | \(-0.622533\pi\) | ||||
−0.375512 | + | 0.926818i | \(0.622533\pi\) | |||||||
\(810\) | 2.83976e49 | 0.0358751 | ||||||||
\(811\) | −2.08851e50 | −0.258209 | −0.129104 | − | 0.991631i | \(-0.541210\pi\) | ||||
−0.129104 | + | 0.991631i | \(0.541210\pi\) | |||||||
\(812\) | 1.25091e51 | 1.51355 | ||||||||
\(813\) | 6.71695e50 | 0.795404 | ||||||||
\(814\) | 1.21641e50 | 0.140979 | ||||||||
\(815\) | 1.88388e50 | 0.213695 | ||||||||
\(816\) | −1.80276e50 | −0.200152 | ||||||||
\(817\) | 1.94194e51 | 2.11033 | ||||||||
\(818\) | 1.56549e51 | 1.66521 | ||||||||
\(819\) | −5.86251e50 | −0.610401 | ||||||||
\(820\) | 6.68269e49 | 0.0681097 | ||||||||
\(821\) | 4.12142e50 | 0.411189 | 0.205595 | − | 0.978637i | \(-0.434087\pi\) | ||||
0.205595 | + | 0.978637i | \(0.434087\pi\) | |||||||
\(822\) | −5.05623e50 | −0.493822 | ||||||||
\(823\) | −1.26215e50 | −0.120674 | −0.0603371 | − | 0.998178i | \(-0.519218\pi\) | ||||
−0.0603371 | + | 0.998178i | \(0.519218\pi\) | |||||||
\(824\) | 1.35641e50 | 0.126959 | ||||||||
\(825\) | −5.35317e49 | −0.0490532 | ||||||||
\(826\) | 4.35254e50 | 0.390474 | ||||||||
\(827\) | −1.65632e51 | −1.45478 | −0.727390 | − | 0.686224i | \(-0.759267\pi\) | ||||
−0.727390 | + | 0.686224i | \(0.759267\pi\) | |||||||
\(828\) | 7.34672e50 | 0.631776 | ||||||||
\(829\) | −1.04352e51 | −0.878607 | −0.439303 | − | 0.898339i | \(-0.644775\pi\) | ||||
−0.439303 | + | 0.898339i | \(0.644775\pi\) | |||||||
\(830\) | −3.34821e50 | −0.276024 | ||||||||
\(831\) | −1.10694e50 | −0.0893521 | ||||||||
\(832\) | −3.25271e51 | −2.57091 | ||||||||
\(833\) | 4.68707e49 | 0.0362755 | ||||||||
\(834\) | −1.45463e51 | −1.10242 | ||||||||
\(835\) | 1.06971e50 | 0.0793874 | ||||||||
\(836\) | −2.17064e50 | −0.157753 | ||||||||
\(837\) | −4.82105e49 | −0.0343120 | ||||||||
\(838\) | −3.63587e51 | −2.53418 | ||||||||
\(839\) | 2.81406e51 | 1.92088 | 0.960438 | − | 0.278493i | \(-0.0898348\pi\) | ||||
0.960438 | + | 0.278493i | \(0.0898348\pi\) | |||||||
\(840\) | −7.86717e49 | −0.0525934 | ||||||||
\(841\) | 4.93839e50 | 0.323337 | ||||||||
\(842\) | 9.04780e50 | 0.580205 | ||||||||
\(843\) | 1.00477e51 | 0.631082 | ||||||||
\(844\) | −1.20989e51 | −0.744307 | ||||||||
\(845\) | −7.60218e50 | −0.458085 | ||||||||
\(846\) | 2.44168e50 | 0.144114 | ||||||||
\(847\) | 1.77355e51 | 1.02538 | ||||||||
\(848\) | 2.03423e51 | 1.15205 | ||||||||
\(849\) | −7.68506e49 | −0.0426346 | ||||||||
\(850\) | 1.40626e51 | 0.764248 | ||||||||
\(851\) | −2.93679e51 | −1.56353 | ||||||||
\(852\) | 2.77620e51 | 1.44796 | ||||||||
\(853\) | 2.01221e51 | 1.02817 | 0.514085 | − | 0.857739i | \(-0.328131\pi\) | ||||
0.514085 | + | 0.857739i | \(0.328131\pi\) | |||||||
\(854\) | −2.44483e51 | −1.22387 | ||||||||
\(855\) | 2.02567e50 | 0.0993484 | ||||||||
\(856\) | −4.01881e50 | −0.193111 | ||||||||
\(857\) | −2.58977e50 | −0.121926 | −0.0609630 | − | 0.998140i | \(-0.519417\pi\) | ||||
−0.0609630 | + | 0.998140i | \(0.519417\pi\) | |||||||
\(858\) | −2.97698e50 | −0.137325 | ||||||||
\(859\) | −3.01104e50 | −0.136093 | −0.0680465 | − | 0.997682i | \(-0.521677\pi\) | ||||
−0.0680465 | + | 0.997682i | \(0.521677\pi\) | |||||||
\(860\) | 9.33440e50 | 0.413393 | ||||||||
\(861\) | 3.43549e50 | 0.149085 | ||||||||
\(862\) | 2.04991e51 | 0.871682 | ||||||||
\(863\) | −3.72938e51 | −1.55399 | −0.776995 | − | 0.629507i | \(-0.783257\pi\) | ||||
−0.776995 | + | 0.629507i | \(0.783257\pi\) | |||||||
\(864\) | 6.57622e50 | 0.268526 | ||||||||
\(865\) | 8.24591e50 | 0.329956 | ||||||||
\(866\) | 8.75921e49 | 0.0343480 | ||||||||
\(867\) | −1.07830e51 | −0.414385 | ||||||||
\(868\) | 6.22850e50 | 0.234579 | ||||||||
\(869\) | 1.60401e50 | 0.0592053 | ||||||||
\(870\) | −5.92785e50 | −0.214442 | ||||||||
\(871\) | −3.70404e51 | −1.31328 | ||||||||
\(872\) | −1.07647e51 | −0.374079 | ||||||||
\(873\) | −2.44819e50 | −0.0833866 | ||||||||
\(874\) | 9.35742e51 | 3.12396 | ||||||||
\(875\) | −1.32183e51 | −0.432550 | ||||||||
\(876\) | 7.75739e50 | 0.248825 | ||||||||
\(877\) | 1.47614e51 | 0.464124 | 0.232062 | − | 0.972701i | \(-0.425453\pi\) | ||||
0.232062 | + | 0.972701i | \(0.425453\pi\) | |||||||
\(878\) | 1.38676e51 | 0.427413 | ||||||||
\(879\) | −2.54460e51 | −0.768800 | ||||||||
\(880\) | 4.20143e49 | 0.0124437 | ||||||||
\(881\) | 5.35936e50 | 0.155609 | 0.0778045 | − | 0.996969i | \(-0.475209\pi\) | ||||
0.0778045 | + | 0.996969i | \(0.475209\pi\) | |||||||
\(882\) | −1.20548e50 | −0.0343132 | ||||||||
\(883\) | 2.24200e51 | 0.625638 | 0.312819 | − | 0.949813i | \(-0.398727\pi\) | ||||
0.312819 | + | 0.949813i | \(0.398727\pi\) | |||||||
\(884\) | 4.37980e51 | 1.19823 | ||||||||
\(885\) | −1.15515e50 | −0.0309836 | ||||||||
\(886\) | −1.09123e52 | −2.86964 | ||||||||
\(887\) | −7.00150e51 | −1.80521 | −0.902605 | − | 0.430470i | \(-0.858348\pi\) | ||||
−0.902605 | + | 0.430470i | \(0.858348\pi\) | |||||||
\(888\) | 9.86997e50 | 0.249510 | ||||||||
\(889\) | 3.13734e51 | 0.777643 | ||||||||
\(890\) | 3.34097e50 | 0.0811985 | ||||||||
\(891\) | 4.15179e49 | 0.00989408 | ||||||||
\(892\) | 1.46927e51 | 0.343335 | ||||||||
\(893\) | 1.74171e51 | 0.399093 | ||||||||
\(894\) | −3.95950e51 | −0.889679 | ||||||||
\(895\) | −1.30039e51 | −0.286530 | ||||||||
\(896\) | −3.79038e51 | −0.819017 | ||||||||
\(897\) | 7.18733e51 | 1.52300 | ||||||||
\(898\) | −2.73576e51 | −0.568516 | ||||||||
\(899\) | 1.00637e51 | 0.205099 | ||||||||
\(900\) | −2.02558e51 | −0.404862 | ||||||||
\(901\) | −4.78511e51 | −0.938011 | ||||||||
\(902\) | 1.74454e50 | 0.0335403 | ||||||||
\(903\) | 4.79870e51 | 0.904874 | ||||||||
\(904\) | 2.63129e51 | 0.486655 | ||||||||
\(905\) | 1.62259e51 | 0.294347 | ||||||||
\(906\) | −3.90473e51 | −0.694780 | ||||||||
\(907\) | −1.01982e52 | −1.77990 | −0.889951 | − | 0.456057i | \(-0.849261\pi\) | ||||
−0.889951 | + | 0.456057i | \(0.849261\pi\) | |||||||
\(908\) | 8.29941e51 | 1.42084 | ||||||||
\(909\) | −3.54542e51 | −0.595388 | ||||||||
\(910\) | −3.58919e51 | −0.591252 | ||||||||
\(911\) | −1.62989e51 | −0.263382 | −0.131691 | − | 0.991291i | \(-0.542041\pi\) | ||||
−0.131691 | + | 0.991291i | \(0.542041\pi\) | |||||||
\(912\) | 3.30739e51 | 0.524295 | ||||||||
\(913\) | −4.89516e50 | −0.0761252 | ||||||||
\(914\) | 2.20213e51 | 0.335957 | ||||||||
\(915\) | 6.48851e50 | 0.0971127 | ||||||||
\(916\) | −7.74238e51 | −1.13685 | ||||||||
\(917\) | 8.75740e51 | 1.26157 | ||||||||
\(918\) | −1.09066e51 | −0.154150 | ||||||||
\(919\) | 7.87901e51 | 1.09257 | 0.546286 | − | 0.837599i | \(-0.316041\pi\) | ||||
0.546286 | + | 0.837599i | \(0.316041\pi\) | |||||||
\(920\) | 9.64500e50 | 0.131225 | ||||||||
\(921\) | −4.59968e51 | −0.614022 | ||||||||
\(922\) | 1.81900e52 | 2.38254 | ||||||||
\(923\) | 2.71597e52 | 3.49056 | ||||||||
\(924\) | −5.36385e50 | −0.0676422 | ||||||||
\(925\) | 8.09710e51 | 1.00196 | ||||||||
\(926\) | −1.33379e52 | −1.61955 | ||||||||
\(927\) | −8.63034e50 | −0.102833 | ||||||||
\(928\) | −1.37275e52 | −1.60510 | ||||||||
\(929\) | −4.74316e51 | −0.544243 | −0.272122 | − | 0.962263i | \(-0.587725\pi\) | ||||
−0.272122 | + | 0.962263i | \(0.587725\pi\) | |||||||
\(930\) | −2.95158e50 | −0.0332356 | ||||||||
\(931\) | −8.59901e50 | −0.0950230 | ||||||||
\(932\) | −6.86708e50 | −0.0744721 | ||||||||
\(933\) | 4.78057e51 | 0.508805 | ||||||||
\(934\) | 9.34948e51 | 0.976601 | ||||||||
\(935\) | −9.88298e49 | −0.0101318 | ||||||||
\(936\) | −2.41552e51 | −0.243043 | ||||||||
\(937\) | −1.00541e52 | −0.992888 | −0.496444 | − | 0.868069i | \(-0.665361\pi\) | ||||
−0.496444 | + | 0.868069i | \(0.665361\pi\) | |||||||
\(938\) | −1.19166e52 | −1.15506 | ||||||||
\(939\) | −5.42179e51 | −0.515816 | ||||||||
\(940\) | 8.37193e50 | 0.0781786 | ||||||||
\(941\) | −6.43294e51 | −0.589646 | −0.294823 | − | 0.955552i | \(-0.595261\pi\) | ||||
−0.294823 | + | 0.955552i | \(0.595261\pi\) | |||||||
\(942\) | −1.37319e52 | −1.23549 | ||||||||
\(943\) | −4.21185e51 | −0.371979 | ||||||||
\(944\) | −1.88606e51 | −0.163511 | ||||||||
\(945\) | 5.00560e50 | 0.0425990 | ||||||||
\(946\) | 2.43678e51 | 0.203574 | ||||||||
\(947\) | −8.46249e51 | −0.694023 | −0.347011 | − | 0.937861i | \(-0.612803\pi\) | ||||
−0.347011 | + | 0.937861i | \(0.612803\pi\) | |||||||
\(948\) | 6.06940e51 | 0.488652 | ||||||||
\(949\) | 7.58909e51 | 0.599834 | ||||||||
\(950\) | −2.57996e52 | −2.00193 | ||||||||
\(951\) | 4.68418e51 | 0.356841 | ||||||||
\(952\) | 3.02153e51 | 0.225985 | ||||||||
\(953\) | −2.50917e51 | −0.184248 | −0.0921242 | − | 0.995748i | \(-0.529366\pi\) | ||||
−0.0921242 | + | 0.995748i | \(0.529366\pi\) | |||||||
\(954\) | 1.23070e52 | 0.887269 | ||||||||
\(955\) | 2.99335e51 | 0.211884 | ||||||||
\(956\) | −1.30648e52 | −0.908005 | ||||||||
\(957\) | −8.66665e50 | −0.0591415 | ||||||||
\(958\) | 2.73535e52 | 1.83281 | ||||||||
\(959\) | −8.91255e51 | −0.586376 | ||||||||
\(960\) | 2.77727e51 | 0.179420 | ||||||||
\(961\) | −1.52627e52 | −0.968212 | ||||||||
\(962\) | 4.50292e52 | 2.80498 | ||||||||
\(963\) | 2.55703e51 | 0.156414 | ||||||||
\(964\) | −2.98730e51 | −0.179445 | ||||||||
\(965\) | −1.23521e51 | −0.0728638 | ||||||||
\(966\) | 2.31230e52 | 1.33951 | ||||||||
\(967\) | 3.67568e50 | 0.0209110 | 0.0104555 | − | 0.999945i | \(-0.496672\pi\) | ||||
0.0104555 | + | 0.999945i | \(0.496672\pi\) | |||||||
\(968\) | 7.30754e51 | 0.408275 | ||||||||
\(969\) | −7.77994e51 | −0.426884 | ||||||||
\(970\) | −1.49885e51 | −0.0807706 | ||||||||
\(971\) | 2.67841e52 | 1.41756 | 0.708778 | − | 0.705431i | \(-0.249247\pi\) | ||||
0.708778 | + | 0.705431i | \(0.249247\pi\) | |||||||
\(972\) | 1.57099e51 | 0.0816610 | ||||||||
\(973\) | −2.56405e52 | −1.30904 | ||||||||
\(974\) | −2.89771e52 | −1.45303 | ||||||||
\(975\) | −1.98164e52 | −0.975986 | ||||||||
\(976\) | 1.05941e52 | 0.512496 | ||||||||
\(977\) | 1.70901e52 | 0.812062 | 0.406031 | − | 0.913859i | \(-0.366912\pi\) | ||||
0.406031 | + | 0.913859i | \(0.366912\pi\) | |||||||
\(978\) | 1.86089e52 | 0.868542 | ||||||||
\(979\) | 4.88458e50 | 0.0223939 | ||||||||
\(980\) | −4.13332e50 | −0.0186141 | ||||||||
\(981\) | 6.84920e51 | 0.302993 | ||||||||
\(982\) | −3.65083e51 | −0.158650 | ||||||||
\(983\) | 2.12016e50 | 0.00905069 | 0.00452535 | − | 0.999990i | \(-0.498560\pi\) | ||||
0.00452535 | + | 0.999990i | \(0.498560\pi\) | |||||||
\(984\) | 1.41552e51 | 0.0593610 | ||||||||
\(985\) | 4.65175e51 | 0.191638 | ||||||||
\(986\) | 2.27670e52 | 0.921424 | ||||||||
\(987\) | 4.30391e51 | 0.171125 | ||||||||
\(988\) | −8.03529e52 | −3.13874 | ||||||||
\(989\) | −5.88312e52 | −2.25773 | ||||||||
\(990\) | 2.54184e50 | 0.00958369 | ||||||||
\(991\) | 6.93693e50 | 0.0256968 | 0.0128484 | − | 0.999917i | \(-0.495910\pi\) | ||||
0.0128484 | + | 0.999917i | \(0.495910\pi\) | |||||||
\(992\) | −6.83518e51 | −0.248769 | ||||||||
\(993\) | −1.97269e52 | −0.705419 | ||||||||
\(994\) | 8.73778e52 | 3.07001 | ||||||||
\(995\) | 2.65889e51 | 0.0917904 | ||||||||
\(996\) | −1.85228e52 | −0.628301 | ||||||||
\(997\) | 2.96189e52 | 0.987196 | 0.493598 | − | 0.869690i | \(-0.335681\pi\) | ||||
0.493598 | + | 0.869690i | \(0.335681\pi\) | |||||||
\(998\) | −4.64144e51 | −0.152009 | ||||||||
\(999\) | −6.27991e51 | −0.202096 |
(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 | 3.36.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 9.36.a.a.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.36.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.36.a.a.1.2 | 2 | 3.2 | odd | 2 |