Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,18,Mod(1,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 18, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.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: | \(38.4766383424\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 542084x^{3} + 28429210x^{2} + 53238758035x - 7826067153800 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{5}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-658.650\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −709.650 | −1.96015 | −0.980074 | − | 0.198631i | \(-0.936350\pi\) | ||||
−0.980074 | + | 0.198631i | \(0.936350\pi\) | |||||||
\(3\) | 6561.00 | 0.577350 | ||||||||
\(4\) | 372531. | 2.84218 | ||||||||
\(5\) | −1.31505e6 | −1.50556 | −0.752778 | − | 0.658275i | \(-0.771287\pi\) | ||||
−0.752778 | + | 0.658275i | \(0.771287\pi\) | |||||||
\(6\) | −4.65601e6 | −1.13169 | ||||||||
\(7\) | −5.76480e6 | −0.377964 | ||||||||
\(8\) | −1.71351e8 | −3.61095 | ||||||||
\(9\) | 4.30467e7 | 0.333333 | ||||||||
\(10\) | 9.33224e8 | 2.95111 | ||||||||
\(11\) | 7.09802e8 | 0.998389 | 0.499194 | − | 0.866490i | \(-0.333629\pi\) | ||||
0.499194 | + | 0.866490i | \(0.333629\pi\) | |||||||
\(12\) | 2.44417e9 | 1.64093 | ||||||||
\(13\) | −3.34343e9 | −1.13677 | −0.568386 | − | 0.822762i | \(-0.692432\pi\) | ||||
−0.568386 | + | 0.822762i | \(0.692432\pi\) | |||||||
\(14\) | 4.09099e9 | 0.740867 | ||||||||
\(15\) | −8.62804e9 | −0.869233 | ||||||||
\(16\) | 7.27708e10 | 4.23582 | ||||||||
\(17\) | −3.89845e10 | −1.35543 | −0.677714 | − | 0.735326i | \(-0.737029\pi\) | ||||
−0.677714 | + | 0.735326i | \(0.737029\pi\) | |||||||
\(18\) | −3.05481e10 | −0.653383 | ||||||||
\(19\) | 5.37884e10 | 0.726579 | 0.363290 | − | 0.931676i | \(-0.381654\pi\) | ||||
0.363290 | + | 0.931676i | \(0.381654\pi\) | |||||||
\(20\) | −4.89896e11 | −4.27906 | ||||||||
\(21\) | −3.78229e10 | −0.218218 | ||||||||
\(22\) | −5.03711e11 | −1.95699 | ||||||||
\(23\) | −4.45041e11 | −1.18499 | −0.592493 | − | 0.805576i | \(-0.701856\pi\) | ||||
−0.592493 | + | 0.805576i | \(0.701856\pi\) | |||||||
\(24\) | −1.12423e12 | −2.08478 | ||||||||
\(25\) | 9.66414e11 | 1.26670 | ||||||||
\(26\) | 2.37266e12 | 2.22824 | ||||||||
\(27\) | 2.82430e11 | 0.192450 | ||||||||
\(28\) | −2.14756e12 | −1.07424 | ||||||||
\(29\) | −3.25985e12 | −1.21008 | −0.605041 | − | 0.796194i | \(-0.706843\pi\) | ||||
−0.605041 | + | 0.796194i | \(0.706843\pi\) | |||||||
\(30\) | 6.12288e12 | 1.70383 | ||||||||
\(31\) | −9.89984e10 | −0.0208475 | −0.0104238 | − | 0.999946i | \(-0.503318\pi\) | ||||
−0.0104238 | + | 0.999946i | \(0.503318\pi\) | |||||||
\(32\) | −2.91825e13 | −4.69188 | ||||||||
\(33\) | 4.65701e12 | 0.576420 | ||||||||
\(34\) | 2.76653e13 | 2.65684 | ||||||||
\(35\) | 7.58100e12 | 0.569047 | ||||||||
\(36\) | 1.60362e13 | 0.947394 | ||||||||
\(37\) | −1.33773e13 | −0.626113 | −0.313056 | − | 0.949735i | \(-0.601353\pi\) | ||||
−0.313056 | + | 0.949735i | \(0.601353\pi\) | |||||||
\(38\) | −3.81709e13 | −1.42420 | ||||||||
\(39\) | −2.19362e13 | −0.656316 | ||||||||
\(40\) | 2.25335e14 | 5.43649 | ||||||||
\(41\) | 2.18414e13 | 0.427187 | 0.213593 | − | 0.976923i | \(-0.431483\pi\) | ||||
0.213593 | + | 0.976923i | \(0.431483\pi\) | |||||||
\(42\) | 2.68410e13 | 0.427739 | ||||||||
\(43\) | −4.29370e13 | −0.560208 | −0.280104 | − | 0.959970i | \(-0.590369\pi\) | ||||
−0.280104 | + | 0.959970i | \(0.590369\pi\) | |||||||
\(44\) | 2.64423e14 | 2.83760 | ||||||||
\(45\) | −5.66085e13 | −0.501852 | ||||||||
\(46\) | 3.15823e14 | 2.32275 | ||||||||
\(47\) | −9.94703e13 | −0.609343 | −0.304671 | − | 0.952458i | \(-0.598547\pi\) | ||||
−0.304671 | + | 0.952458i | \(0.598547\pi\) | |||||||
\(48\) | 4.77449e14 | 2.44555 | ||||||||
\(49\) | 3.32329e13 | 0.142857 | ||||||||
\(50\) | −6.85815e14 | −2.48292 | ||||||||
\(51\) | −2.55777e14 | −0.782556 | ||||||||
\(52\) | −1.24553e15 | −3.23092 | ||||||||
\(53\) | 4.58643e14 | 1.01188 | 0.505941 | − | 0.862568i | \(-0.331145\pi\) | ||||
0.505941 | + | 0.862568i | \(0.331145\pi\) | |||||||
\(54\) | −2.00426e14 | −0.377231 | ||||||||
\(55\) | −9.33425e14 | −1.50313 | ||||||||
\(56\) | 9.87804e14 | 1.36481 | ||||||||
\(57\) | 3.52906e14 | 0.419491 | ||||||||
\(58\) | 2.31335e15 | 2.37194 | ||||||||
\(59\) | 1.36981e15 | 1.21456 | 0.607281 | − | 0.794487i | \(-0.292260\pi\) | ||||
0.607281 | + | 0.794487i | \(0.292260\pi\) | |||||||
\(60\) | −3.21421e15 | −2.47052 | ||||||||
\(61\) | 2.32347e14 | 0.155179 | 0.0775896 | − | 0.996985i | \(-0.475278\pi\) | ||||
0.0775896 | + | 0.996985i | \(0.475278\pi\) | |||||||
\(62\) | 7.02542e13 | 0.0408642 | ||||||||
\(63\) | −2.48156e14 | −0.125988 | ||||||||
\(64\) | 1.11711e16 | 4.96097 | ||||||||
\(65\) | 4.39677e15 | 1.71147 | ||||||||
\(66\) | −3.30485e15 | −1.12987 | ||||||||
\(67\) | 4.61272e14 | 0.138778 | 0.0693891 | − | 0.997590i | \(-0.477895\pi\) | ||||
0.0693891 | + | 0.997590i | \(0.477895\pi\) | |||||||
\(68\) | −1.45229e16 | −3.85237 | ||||||||
\(69\) | −2.91991e15 | −0.684152 | ||||||||
\(70\) | −5.37985e15 | −1.11542 | ||||||||
\(71\) | 3.27411e15 | 0.601724 | 0.300862 | − | 0.953668i | \(-0.402726\pi\) | ||||
0.300862 | + | 0.953668i | \(0.402726\pi\) | |||||||
\(72\) | −7.37610e15 | −1.20365 | ||||||||
\(73\) | 3.54172e15 | 0.514008 | 0.257004 | − | 0.966410i | \(-0.417265\pi\) | ||||
0.257004 | + | 0.966410i | \(0.417265\pi\) | |||||||
\(74\) | 9.49317e15 | 1.22727 | ||||||||
\(75\) | 6.34064e15 | 0.731329 | ||||||||
\(76\) | 2.00378e16 | 2.06507 | ||||||||
\(77\) | −4.09187e15 | −0.377355 | ||||||||
\(78\) | 1.55670e16 | 1.28648 | ||||||||
\(79\) | 1.17172e16 | 0.868947 | 0.434473 | − | 0.900685i | \(-0.356934\pi\) | ||||
0.434473 | + | 0.900685i | \(0.356934\pi\) | |||||||
\(80\) | −9.56972e16 | −6.37726 | ||||||||
\(81\) | 1.85302e15 | 0.111111 | ||||||||
\(82\) | −1.54997e16 | −0.837350 | ||||||||
\(83\) | 1.42944e16 | 0.696629 | 0.348315 | − | 0.937378i | \(-0.386754\pi\) | ||||
0.348315 | + | 0.937378i | \(0.386754\pi\) | |||||||
\(84\) | −1.40902e16 | −0.620215 | ||||||||
\(85\) | 5.12665e16 | 2.04067 | ||||||||
\(86\) | 3.04702e16 | 1.09809 | ||||||||
\(87\) | −2.13879e16 | −0.698641 | ||||||||
\(88\) | −1.21625e17 | −3.60513 | ||||||||
\(89\) | 1.04458e16 | 0.281271 | 0.140635 | − | 0.990061i | \(-0.455085\pi\) | ||||
0.140635 | + | 0.990061i | \(0.455085\pi\) | |||||||
\(90\) | 4.01722e16 | 0.983704 | ||||||||
\(91\) | 1.92742e16 | 0.429660 | ||||||||
\(92\) | −1.65791e17 | −3.36795 | ||||||||
\(93\) | −6.49529e14 | −0.0120363 | ||||||||
\(94\) | 7.05891e16 | 1.19440 | ||||||||
\(95\) | −7.07344e16 | −1.09391 | ||||||||
\(96\) | −1.91466e17 | −2.70886 | ||||||||
\(97\) | 3.23350e16 | 0.418903 | 0.209452 | − | 0.977819i | \(-0.432832\pi\) | ||||
0.209452 | + | 0.977819i | \(0.432832\pi\) | |||||||
\(98\) | −2.35837e16 | −0.280021 | ||||||||
\(99\) | 3.05547e16 | 0.332796 | ||||||||
\(100\) | 3.60019e17 | 3.60019 | ||||||||
\(101\) | −1.04483e17 | −0.960097 | −0.480048 | − | 0.877242i | \(-0.659381\pi\) | ||||
−0.480048 | + | 0.877242i | \(0.659381\pi\) | |||||||
\(102\) | 1.81512e17 | 1.53393 | ||||||||
\(103\) | −4.70064e16 | −0.365629 | −0.182815 | − | 0.983147i | \(-0.558521\pi\) | ||||
−0.182815 | + | 0.983147i | \(0.558521\pi\) | |||||||
\(104\) | 5.72900e17 | 4.10483 | ||||||||
\(105\) | 4.97389e16 | 0.328539 | ||||||||
\(106\) | −3.25476e17 | −1.98344 | ||||||||
\(107\) | 3.11125e17 | 1.75054 | 0.875271 | − | 0.483633i | \(-0.160683\pi\) | ||||
0.875271 | + | 0.483633i | \(0.160683\pi\) | |||||||
\(108\) | 1.05214e17 | 0.546978 | ||||||||
\(109\) | 4.34709e16 | 0.208965 | 0.104483 | − | 0.994527i | \(-0.466681\pi\) | ||||
0.104483 | + | 0.994527i | \(0.466681\pi\) | |||||||
\(110\) | 6.62405e17 | 2.94636 | ||||||||
\(111\) | −8.77682e16 | −0.361486 | ||||||||
\(112\) | −4.19509e17 | −1.60099 | ||||||||
\(113\) | 4.21097e17 | 1.49010 | 0.745051 | − | 0.667008i | \(-0.232425\pi\) | ||||
0.745051 | + | 0.667008i | \(0.232425\pi\) | |||||||
\(114\) | −2.50439e17 | −0.822264 | ||||||||
\(115\) | 5.85250e17 | 1.78406 | ||||||||
\(116\) | −1.21439e18 | −3.43927 | ||||||||
\(117\) | −1.43924e17 | −0.378924 | ||||||||
\(118\) | −9.72088e17 | −2.38072 | ||||||||
\(119\) | 2.24738e17 | 0.512303 | ||||||||
\(120\) | 1.47842e18 | 3.13876 | ||||||||
\(121\) | −1.62753e15 | −0.00321998 | ||||||||
\(122\) | −1.64885e17 | −0.304174 | ||||||||
\(123\) | 1.43301e17 | 0.246636 | ||||||||
\(124\) | −3.68799e16 | −0.0592524 | ||||||||
\(125\) | −2.67579e17 | −0.401529 | ||||||||
\(126\) | 1.76104e17 | 0.246956 | ||||||||
\(127\) | 7.57737e17 | 0.993544 | 0.496772 | − | 0.867881i | \(-0.334519\pi\) | ||||
0.496772 | + | 0.867881i | \(0.334519\pi\) | |||||||
\(128\) | −4.10257e18 | −5.03235 | ||||||||
\(129\) | −2.81709e17 | −0.323436 | ||||||||
\(130\) | −3.12017e18 | −3.35474 | ||||||||
\(131\) | −8.90186e17 | −0.896757 | −0.448378 | − | 0.893844i | \(-0.647998\pi\) | ||||
−0.448378 | + | 0.893844i | \(0.647998\pi\) | |||||||
\(132\) | 1.73488e18 | 1.63829 | ||||||||
\(133\) | −3.10079e17 | −0.274621 | ||||||||
\(134\) | −3.27341e17 | −0.272026 | ||||||||
\(135\) | −3.71409e17 | −0.289744 | ||||||||
\(136\) | 6.68003e18 | 4.89438 | ||||||||
\(137\) | 2.11172e18 | 1.45382 | 0.726912 | − | 0.686730i | \(-0.240955\pi\) | ||||
0.726912 | + | 0.686730i | \(0.240955\pi\) | |||||||
\(138\) | 2.07211e18 | 1.34104 | ||||||||
\(139\) | −3.04391e18 | −1.85270 | −0.926352 | − | 0.376660i | \(-0.877073\pi\) | ||||
−0.926352 | + | 0.376660i | \(0.877073\pi\) | |||||||
\(140\) | 2.82415e18 | 1.61733 | ||||||||
\(141\) | −6.52625e17 | −0.351804 | ||||||||
\(142\) | −2.32347e18 | −1.17947 | ||||||||
\(143\) | −2.37317e18 | −1.13494 | ||||||||
\(144\) | 3.13254e18 | 1.41194 | ||||||||
\(145\) | 4.28687e18 | 1.82185 | ||||||||
\(146\) | −2.51338e18 | −1.00753 | ||||||||
\(147\) | 2.18041e17 | 0.0824786 | ||||||||
\(148\) | −4.98344e18 | −1.77953 | ||||||||
\(149\) | 3.84925e18 | 1.29805 | 0.649027 | − | 0.760766i | \(-0.275176\pi\) | ||||
0.649027 | + | 0.760766i | \(0.275176\pi\) | |||||||
\(150\) | −4.49963e18 | −1.43351 | ||||||||
\(151\) | −4.46007e18 | −1.34288 | −0.671441 | − | 0.741058i | \(-0.734324\pi\) | ||||
−0.671441 | + | 0.741058i | \(0.734324\pi\) | |||||||
\(152\) | −9.21669e18 | −2.62364 | ||||||||
\(153\) | −1.67816e18 | −0.451809 | ||||||||
\(154\) | 2.90379e18 | 0.739673 | ||||||||
\(155\) | 1.30188e17 | 0.0313871 | ||||||||
\(156\) | −8.17192e18 | −1.86537 | ||||||||
\(157\) | 4.88978e18 | 1.05716 | 0.528582 | − | 0.848882i | \(-0.322724\pi\) | ||||
0.528582 | + | 0.848882i | \(0.322724\pi\) | |||||||
\(158\) | −8.31510e18 | −1.70327 | ||||||||
\(159\) | 3.00916e18 | 0.584210 | ||||||||
\(160\) | 3.83764e19 | 7.06389 | ||||||||
\(161\) | 2.56557e18 | 0.447882 | ||||||||
\(162\) | −1.31499e18 | −0.217794 | ||||||||
\(163\) | −1.44995e18 | −0.227908 | −0.113954 | − | 0.993486i | \(-0.536352\pi\) | ||||
−0.113954 | + | 0.993486i | \(0.536352\pi\) | |||||||
\(164\) | 8.13659e18 | 1.21414 | ||||||||
\(165\) | −6.12420e18 | −0.867832 | ||||||||
\(166\) | −1.01440e19 | −1.36550 | ||||||||
\(167\) | −3.94593e18 | −0.504731 | −0.252365 | − | 0.967632i | \(-0.581208\pi\) | ||||
−0.252365 | + | 0.967632i | \(0.581208\pi\) | |||||||
\(168\) | 6.48098e18 | 0.787974 | ||||||||
\(169\) | 2.52810e18 | 0.292252 | ||||||||
\(170\) | −3.63813e19 | −4.00002 | ||||||||
\(171\) | 2.31541e18 | 0.242193 | ||||||||
\(172\) | −1.59953e19 | −1.59221 | ||||||||
\(173\) | −2.66187e18 | −0.252229 | −0.126115 | − | 0.992016i | \(-0.540251\pi\) | ||||
−0.126115 | + | 0.992016i | \(0.540251\pi\) | |||||||
\(174\) | 1.51779e19 | 1.36944 | ||||||||
\(175\) | −5.57119e18 | −0.478767 | ||||||||
\(176\) | 5.16529e19 | 4.22899 | ||||||||
\(177\) | 8.98735e18 | 0.701228 | ||||||||
\(178\) | −7.41283e18 | −0.551333 | ||||||||
\(179\) | −1.91064e19 | −1.35496 | −0.677481 | − | 0.735540i | \(-0.736929\pi\) | ||||
−0.677481 | + | 0.735540i | \(0.736929\pi\) | |||||||
\(180\) | −2.10884e19 | −1.42635 | ||||||||
\(181\) | −9.51107e18 | −0.613707 | −0.306854 | − | 0.951757i | \(-0.599276\pi\) | ||||
−0.306854 | + | 0.951757i | \(0.599276\pi\) | |||||||
\(182\) | −1.36779e19 | −0.842197 | ||||||||
\(183\) | 1.52443e18 | 0.0895927 | ||||||||
\(184\) | 7.62581e19 | 4.27893 | ||||||||
\(185\) | 1.75918e19 | 0.942648 | ||||||||
\(186\) | 4.60938e17 | 0.0235930 | ||||||||
\(187\) | −2.76713e19 | −1.35324 | ||||||||
\(188\) | −3.70557e19 | −1.73186 | ||||||||
\(189\) | −1.62815e18 | −0.0727393 | ||||||||
\(190\) | 5.01966e19 | 2.14422 | ||||||||
\(191\) | 4.26691e19 | 1.74313 | 0.871566 | − | 0.490278i | \(-0.163105\pi\) | ||||
0.871566 | + | 0.490278i | \(0.163105\pi\) | |||||||
\(192\) | 7.32936e19 | 2.86422 | ||||||||
\(193\) | 3.25397e19 | 1.21668 | 0.608339 | − | 0.793677i | \(-0.291836\pi\) | ||||
0.608339 | + | 0.793677i | \(0.291836\pi\) | |||||||
\(194\) | −2.29466e19 | −0.821113 | ||||||||
\(195\) | 2.88472e19 | 0.988120 | ||||||||
\(196\) | 1.23803e19 | 0.406026 | ||||||||
\(197\) | −6.46054e17 | −0.0202911 | −0.0101456 | − | 0.999949i | \(-0.503229\pi\) | ||||
−0.0101456 | + | 0.999949i | \(0.503229\pi\) | |||||||
\(198\) | −2.16831e19 | −0.652330 | ||||||||
\(199\) | −8.34990e18 | −0.240674 | −0.120337 | − | 0.992733i | \(-0.538398\pi\) | ||||
−0.120337 | + | 0.992733i | \(0.538398\pi\) | |||||||
\(200\) | −1.65596e20 | −4.57399 | ||||||||
\(201\) | 3.02640e18 | 0.0801236 | ||||||||
\(202\) | 7.41465e19 | 1.88193 | ||||||||
\(203\) | 1.87924e19 | 0.457368 | ||||||||
\(204\) | −9.52849e19 | −2.22417 | ||||||||
\(205\) | −2.87225e19 | −0.643154 | ||||||||
\(206\) | 3.33581e19 | 0.716688 | ||||||||
\(207\) | −1.91575e19 | −0.394995 | ||||||||
\(208\) | −2.43304e20 | −4.81516 | ||||||||
\(209\) | 3.81791e19 | 0.725408 | ||||||||
\(210\) | −3.52972e19 | −0.643986 | ||||||||
\(211\) | −6.36935e19 | −1.11608 | −0.558039 | − | 0.829815i | \(-0.688446\pi\) | ||||
−0.558039 | + | 0.829815i | \(0.688446\pi\) | |||||||
\(212\) | 1.70858e20 | 2.87595 | ||||||||
\(213\) | 2.14814e19 | 0.347405 | ||||||||
\(214\) | −2.20790e20 | −3.43132 | ||||||||
\(215\) | 5.64642e19 | 0.843425 | ||||||||
\(216\) | −4.83946e19 | −0.694928 | ||||||||
\(217\) | 5.70706e17 | 0.00787961 | ||||||||
\(218\) | −3.08491e19 | −0.409603 | ||||||||
\(219\) | 2.32372e19 | 0.296763 | ||||||||
\(220\) | −3.47729e20 | −4.27217 | ||||||||
\(221\) | 1.30342e20 | 1.54081 | ||||||||
\(222\) | 6.22847e19 | 0.708567 | ||||||||
\(223\) | 1.77854e20 | 1.94748 | 0.973741 | − | 0.227660i | \(-0.0731073\pi\) | ||||
0.973741 | + | 0.227660i | \(0.0731073\pi\) | |||||||
\(224\) | 1.68231e20 | 1.77336 | ||||||||
\(225\) | 4.16010e19 | 0.422233 | ||||||||
\(226\) | −2.98832e20 | −2.92082 | ||||||||
\(227\) | 1.53025e20 | 1.44059 | 0.720296 | − | 0.693666i | \(-0.244006\pi\) | ||||
0.720296 | + | 0.693666i | \(0.244006\pi\) | |||||||
\(228\) | 1.31468e20 | 1.19227 | ||||||||
\(229\) | 8.17318e19 | 0.714150 | 0.357075 | − | 0.934076i | \(-0.383774\pi\) | ||||
0.357075 | + | 0.934076i | \(0.383774\pi\) | |||||||
\(230\) | −4.15323e20 | −3.49703 | ||||||||
\(231\) | −2.68468e19 | −0.217866 | ||||||||
\(232\) | 5.58579e20 | 4.36955 | ||||||||
\(233\) | 1.15470e20 | 0.870851 | 0.435425 | − | 0.900225i | \(-0.356598\pi\) | ||||
0.435425 | + | 0.900225i | \(0.356598\pi\) | |||||||
\(234\) | 1.02135e20 | 0.742748 | ||||||||
\(235\) | 1.30808e20 | 0.917399 | ||||||||
\(236\) | 5.10298e20 | 3.45201 | ||||||||
\(237\) | 7.68765e19 | 0.501687 | ||||||||
\(238\) | −1.59485e20 | −1.00419 | ||||||||
\(239\) | −2.82617e20 | −1.71718 | −0.858591 | − | 0.512661i | \(-0.828660\pi\) | ||||
−0.858591 | + | 0.512661i | \(0.828660\pi\) | |||||||
\(240\) | −6.27869e20 | −3.68191 | ||||||||
\(241\) | 1.75484e20 | 0.993326 | 0.496663 | − | 0.867943i | \(-0.334558\pi\) | ||||
0.496663 | + | 0.867943i | \(0.334558\pi\) | |||||||
\(242\) | 1.15497e18 | 0.00631163 | ||||||||
\(243\) | 1.21577e19 | 0.0641500 | ||||||||
\(244\) | 8.65563e19 | 0.441047 | ||||||||
\(245\) | −4.37029e19 | −0.215079 | ||||||||
\(246\) | −1.01694e20 | −0.483444 | ||||||||
\(247\) | −1.79838e20 | −0.825955 | ||||||||
\(248\) | 1.69635e19 | 0.0752793 | ||||||||
\(249\) | 9.37855e19 | 0.402199 | ||||||||
\(250\) | 1.89887e20 | 0.787057 | ||||||||
\(251\) | 2.12498e19 | 0.0851391 | 0.0425695 | − | 0.999094i | \(-0.486446\pi\) | ||||
0.0425695 | + | 0.999094i | \(0.486446\pi\) | |||||||
\(252\) | −9.24456e19 | −0.358081 | ||||||||
\(253\) | −3.15891e20 | −1.18308 | ||||||||
\(254\) | −5.37728e20 | −1.94749 | ||||||||
\(255\) | 3.36360e20 | 1.17818 | ||||||||
\(256\) | 1.44717e21 | 4.90319 | ||||||||
\(257\) | −5.46763e20 | −1.79212 | −0.896062 | − | 0.443929i | \(-0.853584\pi\) | ||||
−0.896062 | + | 0.443929i | \(0.853584\pi\) | |||||||
\(258\) | 1.99915e20 | 0.633983 | ||||||||
\(259\) | 7.71173e19 | 0.236648 | ||||||||
\(260\) | 1.63793e21 | 4.86432 | ||||||||
\(261\) | −1.40326e20 | −0.403361 | ||||||||
\(262\) | 6.31720e20 | 1.75778 | ||||||||
\(263\) | −2.38442e20 | −0.642330 | −0.321165 | − | 0.947023i | \(-0.604074\pi\) | ||||
−0.321165 | + | 0.947023i | \(0.604074\pi\) | |||||||
\(264\) | −7.97984e20 | −2.08142 | ||||||||
\(265\) | −6.03138e20 | −1.52344 | ||||||||
\(266\) | 2.20048e20 | 0.538298 | ||||||||
\(267\) | 6.85346e19 | 0.162392 | ||||||||
\(268\) | 1.71838e20 | 0.394433 | ||||||||
\(269\) | −4.55785e20 | −1.01360 | −0.506798 | − | 0.862065i | \(-0.669171\pi\) | ||||
−0.506798 | + | 0.862065i | \(0.669171\pi\) | |||||||
\(270\) | 2.63570e20 | 0.567942 | ||||||||
\(271\) | −4.90898e20 | −1.02507 | −0.512534 | − | 0.858667i | \(-0.671293\pi\) | ||||
−0.512534 | + | 0.858667i | \(0.671293\pi\) | |||||||
\(272\) | −2.83693e21 | −5.74134 | ||||||||
\(273\) | 1.26458e20 | 0.248064 | ||||||||
\(274\) | −1.49858e21 | −2.84971 | ||||||||
\(275\) | 6.85963e20 | 1.26466 | ||||||||
\(276\) | −1.08776e21 | −1.94448 | ||||||||
\(277\) | 7.90505e19 | 0.137033 | 0.0685167 | − | 0.997650i | \(-0.478173\pi\) | ||||
0.0685167 | + | 0.997650i | \(0.478173\pi\) | |||||||
\(278\) | 2.16011e21 | 3.63157 | ||||||||
\(279\) | −4.26156e18 | −0.00694917 | ||||||||
\(280\) | −1.29901e21 | −2.05480 | ||||||||
\(281\) | 7.88426e20 | 1.20992 | 0.604960 | − | 0.796255i | \(-0.293189\pi\) | ||||
0.604960 | + | 0.796255i | \(0.293189\pi\) | |||||||
\(282\) | 4.63135e20 | 0.689588 | ||||||||
\(283\) | −3.18868e20 | −0.460709 | −0.230354 | − | 0.973107i | \(-0.573989\pi\) | ||||
−0.230354 | + | 0.973107i | \(0.573989\pi\) | |||||||
\(284\) | 1.21971e21 | 1.71021 | ||||||||
\(285\) | −4.64088e20 | −0.631567 | ||||||||
\(286\) | 1.68412e21 | 2.22465 | ||||||||
\(287\) | −1.25911e20 | −0.161461 | ||||||||
\(288\) | −1.25621e21 | −1.56396 | ||||||||
\(289\) | 6.92551e20 | 0.837183 | ||||||||
\(290\) | −3.04217e21 | −3.57109 | ||||||||
\(291\) | 2.12150e20 | 0.241854 | ||||||||
\(292\) | 1.31940e21 | 1.46091 | ||||||||
\(293\) | −1.22458e21 | −1.31709 | −0.658543 | − | 0.752543i | \(-0.728827\pi\) | ||||
−0.658543 | + | 0.752543i | \(0.728827\pi\) | |||||||
\(294\) | −1.54733e20 | −0.161670 | ||||||||
\(295\) | −1.80137e21 | −1.82859 | ||||||||
\(296\) | 2.29221e21 | 2.26086 | ||||||||
\(297\) | 2.00469e20 | 0.192140 | ||||||||
\(298\) | −2.73162e21 | −2.54438 | ||||||||
\(299\) | 1.48796e21 | 1.34706 | ||||||||
\(300\) | 2.36208e21 | 2.07857 | ||||||||
\(301\) | 2.47523e20 | 0.211739 | ||||||||
\(302\) | 3.16509e21 | 2.63225 | ||||||||
\(303\) | −6.85514e20 | −0.554312 | ||||||||
\(304\) | 3.91422e21 | 3.07766 | ||||||||
\(305\) | −3.05548e20 | −0.233631 | ||||||||
\(306\) | 1.19090e21 | 0.885613 | ||||||||
\(307\) | −2.03078e21 | −1.46888 | −0.734440 | − | 0.678674i | \(-0.762555\pi\) | ||||
−0.734440 | + | 0.678674i | \(0.762555\pi\) | |||||||
\(308\) | −1.52435e21 | −1.07251 | ||||||||
\(309\) | −3.08409e20 | −0.211096 | ||||||||
\(310\) | −9.23877e19 | −0.0615233 | ||||||||
\(311\) | 6.75731e20 | 0.437835 | 0.218917 | − | 0.975743i | \(-0.429747\pi\) | ||||
0.218917 | + | 0.975743i | \(0.429747\pi\) | |||||||
\(312\) | 3.75879e21 | 2.36992 | ||||||||
\(313\) | −1.46148e21 | −0.896739 | −0.448369 | − | 0.893848i | \(-0.647995\pi\) | ||||
−0.448369 | + | 0.893848i | \(0.647995\pi\) | |||||||
\(314\) | −3.47003e21 | −2.07220 | ||||||||
\(315\) | 3.26337e20 | 0.189682 | ||||||||
\(316\) | 4.36501e21 | 2.46971 | ||||||||
\(317\) | 2.86207e21 | 1.57644 | 0.788219 | − | 0.615395i | \(-0.211003\pi\) | ||||
0.788219 | + | 0.615395i | \(0.211003\pi\) | |||||||
\(318\) | −2.13545e21 | −1.14514 | ||||||||
\(319\) | −2.31385e21 | −1.20813 | ||||||||
\(320\) | −1.46905e22 | −7.46901 | ||||||||
\(321\) | 2.04129e21 | 1.01068 | ||||||||
\(322\) | −1.82066e21 | −0.877916 | ||||||||
\(323\) | −2.09691e21 | −0.984825 | ||||||||
\(324\) | 6.90307e20 | 0.315798 | ||||||||
\(325\) | −3.23114e21 | −1.43995 | ||||||||
\(326\) | 1.02896e21 | 0.446733 | ||||||||
\(327\) | 2.85213e20 | 0.120646 | ||||||||
\(328\) | −3.74255e21 | −1.54255 | ||||||||
\(329\) | 5.73426e20 | 0.230310 | ||||||||
\(330\) | 4.34604e21 | 1.70108 | ||||||||
\(331\) | −1.60404e21 | −0.611895 | −0.305948 | − | 0.952048i | \(-0.598973\pi\) | ||||
−0.305948 | + | 0.952048i | \(0.598973\pi\) | |||||||
\(332\) | 5.32510e21 | 1.97995 | ||||||||
\(333\) | −5.75847e20 | −0.208704 | ||||||||
\(334\) | 2.80023e21 | 0.989347 | ||||||||
\(335\) | −6.06595e20 | −0.208938 | ||||||||
\(336\) | −2.75240e21 | −0.924331 | ||||||||
\(337\) | 1.94260e21 | 0.636106 | 0.318053 | − | 0.948073i | \(-0.396971\pi\) | ||||
0.318053 | + | 0.948073i | \(0.396971\pi\) | |||||||
\(338\) | −1.79407e21 | −0.572858 | ||||||||
\(339\) | 2.76282e21 | 0.860310 | ||||||||
\(340\) | 1.90983e22 | 5.79996 | ||||||||
\(341\) | −7.02693e19 | −0.0208139 | ||||||||
\(342\) | −1.64313e21 | −0.474734 | ||||||||
\(343\) | −1.91581e20 | −0.0539949 | ||||||||
\(344\) | 7.35729e21 | 2.02288 | ||||||||
\(345\) | 3.83983e21 | 1.03003 | ||||||||
\(346\) | 1.88900e21 | 0.494406 | ||||||||
\(347\) | 6.00428e21 | 1.53342 | 0.766708 | − | 0.641996i | \(-0.221893\pi\) | ||||
0.766708 | + | 0.641996i | \(0.221893\pi\) | |||||||
\(348\) | −7.96764e21 | −1.98567 | ||||||||
\(349\) | 6.16401e21 | 1.49916 | 0.749578 | − | 0.661916i | \(-0.230256\pi\) | ||||
0.749578 | + | 0.661916i | \(0.230256\pi\) | |||||||
\(350\) | 3.95359e21 | 0.938454 | ||||||||
\(351\) | −9.44283e20 | −0.218772 | ||||||||
\(352\) | −2.07138e22 | −4.68432 | ||||||||
\(353\) | −4.57956e21 | −1.01097 | −0.505486 | − | 0.862835i | \(-0.668687\pi\) | ||||
−0.505486 | + | 0.862835i | \(0.668687\pi\) | |||||||
\(354\) | −6.37787e21 | −1.37451 | ||||||||
\(355\) | −4.30561e21 | −0.905929 | ||||||||
\(356\) | 3.89136e21 | 0.799423 | ||||||||
\(357\) | 1.47451e21 | 0.295778 | ||||||||
\(358\) | 1.35588e22 | 2.65593 | ||||||||
\(359\) | −7.07727e20 | −0.135383 | −0.0676913 | − | 0.997706i | \(-0.521563\pi\) | ||||
−0.0676913 | + | 0.997706i | \(0.521563\pi\) | |||||||
\(360\) | 9.69993e21 | 1.81216 | ||||||||
\(361\) | −2.58720e21 | −0.472083 | ||||||||
\(362\) | 6.74952e21 | 1.20296 | ||||||||
\(363\) | −1.06782e19 | −0.00185905 | ||||||||
\(364\) | 7.18023e21 | 1.22117 | ||||||||
\(365\) | −4.65754e21 | −0.773868 | ||||||||
\(366\) | −1.08181e21 | −0.175615 | ||||||||
\(367\) | −2.02746e21 | −0.321581 | −0.160790 | − | 0.986989i | \(-0.551404\pi\) | ||||
−0.160790 | + | 0.986989i | \(0.551404\pi\) | |||||||
\(368\) | −3.23860e22 | −5.01938 | ||||||||
\(369\) | 9.40201e20 | 0.142396 | ||||||||
\(370\) | −1.24840e22 | −1.84773 | ||||||||
\(371\) | −2.64399e21 | −0.382455 | ||||||||
\(372\) | −2.41969e20 | −0.0342094 | ||||||||
\(373\) | −6.44473e21 | −0.890594 | −0.445297 | − | 0.895383i | \(-0.646902\pi\) | ||||
−0.445297 | + | 0.895383i | \(0.646902\pi\) | |||||||
\(374\) | 1.96369e22 | 2.65256 | ||||||||
\(375\) | −1.75559e21 | −0.231823 | ||||||||
\(376\) | 1.70443e22 | 2.20031 | ||||||||
\(377\) | 1.08991e22 | 1.37559 | ||||||||
\(378\) | 1.15542e21 | 0.142580 | ||||||||
\(379\) | 7.50017e20 | 0.0904978 | 0.0452489 | − | 0.998976i | \(-0.485592\pi\) | ||||
0.0452489 | + | 0.998976i | \(0.485592\pi\) | |||||||
\(380\) | −2.63507e22 | −3.10908 | ||||||||
\(381\) | 4.97151e21 | 0.573623 | ||||||||
\(382\) | −3.02801e22 | −3.41680 | ||||||||
\(383\) | 9.71613e21 | 1.07227 | 0.536134 | − | 0.844133i | \(-0.319884\pi\) | ||||
0.536134 | + | 0.844133i | \(0.319884\pi\) | |||||||
\(384\) | −2.69169e22 | −2.90543 | ||||||||
\(385\) | 5.38101e21 | 0.568130 | ||||||||
\(386\) | −2.30918e22 | −2.38487 | ||||||||
\(387\) | −1.84830e21 | −0.186736 | ||||||||
\(388\) | 1.20458e22 | 1.19060 | ||||||||
\(389\) | 1.53024e22 | 1.47975 | 0.739875 | − | 0.672744i | \(-0.234885\pi\) | ||||
0.739875 | + | 0.672744i | \(0.234885\pi\) | |||||||
\(390\) | −2.04714e22 | −1.93686 | ||||||||
\(391\) | 1.73497e22 | 1.60616 | ||||||||
\(392\) | −5.69449e21 | −0.515850 | ||||||||
\(393\) | −5.84051e21 | −0.517743 | ||||||||
\(394\) | 4.58472e20 | 0.0397736 | ||||||||
\(395\) | −1.54087e22 | −1.30825 | ||||||||
\(396\) | 1.13825e22 | 0.945868 | ||||||||
\(397\) | −9.93985e21 | −0.808464 | −0.404232 | − | 0.914657i | \(-0.632461\pi\) | ||||
−0.404232 | + | 0.914657i | \(0.632461\pi\) | |||||||
\(398\) | 5.92550e21 | 0.471758 | ||||||||
\(399\) | −2.03443e21 | −0.158553 | ||||||||
\(400\) | 7.03267e22 | 5.36550 | ||||||||
\(401\) | −6.58497e21 | −0.491843 | −0.245922 | − | 0.969290i | \(-0.579091\pi\) | ||||
−0.245922 | + | 0.969290i | \(0.579091\pi\) | |||||||
\(402\) | −2.14769e21 | −0.157054 | ||||||||
\(403\) | 3.30994e20 | 0.0236989 | ||||||||
\(404\) | −3.89232e22 | −2.72877 | ||||||||
\(405\) | −2.43681e21 | −0.167284 | ||||||||
\(406\) | −1.33360e22 | −0.896510 | ||||||||
\(407\) | −9.49521e21 | −0.625104 | ||||||||
\(408\) | 4.38277e22 | 2.82577 | ||||||||
\(409\) | −5.74377e19 | −0.00362701 | −0.00181350 | − | 0.999998i | \(-0.500577\pi\) | ||||
−0.00181350 | + | 0.999998i | \(0.500577\pi\) | |||||||
\(410\) | 2.03829e22 | 1.26068 | ||||||||
\(411\) | 1.38550e22 | 0.839366 | ||||||||
\(412\) | −1.75113e22 | −1.03919 | ||||||||
\(413\) | −7.89671e21 | −0.459061 | ||||||||
\(414\) | 1.35951e22 | 0.774249 | ||||||||
\(415\) | −1.87978e22 | −1.04881 | ||||||||
\(416\) | 9.75695e22 | 5.33360 | ||||||||
\(417\) | −1.99711e22 | −1.06966 | ||||||||
\(418\) | −2.70938e22 | −1.42191 | ||||||||
\(419\) | −1.71702e22 | −0.882990 | −0.441495 | − | 0.897264i | \(-0.645552\pi\) | ||||
−0.441495 | + | 0.897264i | \(0.645552\pi\) | |||||||
\(420\) | 1.85293e22 | 0.933768 | ||||||||
\(421\) | 1.52694e22 | 0.754091 | 0.377045 | − | 0.926195i | \(-0.376940\pi\) | ||||
0.377045 | + | 0.926195i | \(0.376940\pi\) | |||||||
\(422\) | 4.52001e22 | 2.18768 | ||||||||
\(423\) | −4.28187e21 | −0.203114 | ||||||||
\(424\) | −7.85889e22 | −3.65386 | ||||||||
\(425\) | −3.76752e22 | −1.71692 | ||||||||
\(426\) | −1.52443e22 | −0.680966 | ||||||||
\(427\) | −1.33943e21 | −0.0586522 | ||||||||
\(428\) | 1.15903e23 | 4.97536 | ||||||||
\(429\) | −1.55704e22 | −0.655259 | ||||||||
\(430\) | −4.00698e22 | −1.65324 | ||||||||
\(431\) | 2.06204e22 | 0.834143 | 0.417072 | − | 0.908874i | \(-0.363056\pi\) | ||||
0.417072 | + | 0.908874i | \(0.363056\pi\) | |||||||
\(432\) | 2.05526e22 | 0.815184 | ||||||||
\(433\) | 2.90774e22 | 1.13086 | 0.565430 | − | 0.824797i | \(-0.308710\pi\) | ||||
0.565430 | + | 0.824797i | \(0.308710\pi\) | |||||||
\(434\) | −4.05002e20 | −0.0154452 | ||||||||
\(435\) | 2.81261e22 | 1.05184 | ||||||||
\(436\) | 1.61942e22 | 0.593917 | ||||||||
\(437\) | −2.39380e22 | −0.860986 | ||||||||
\(438\) | −1.64903e22 | −0.581699 | ||||||||
\(439\) | 4.31313e22 | 1.49226 | 0.746129 | − | 0.665802i | \(-0.231910\pi\) | ||||
0.746129 | + | 0.665802i | \(0.231910\pi\) | |||||||
\(440\) | 1.59943e23 | 5.42773 | ||||||||
\(441\) | 1.43057e21 | 0.0476190 | ||||||||
\(442\) | −9.24971e22 | −3.02022 | ||||||||
\(443\) | 4.15467e22 | 1.33078 | 0.665388 | − | 0.746497i | \(-0.268266\pi\) | ||||
0.665388 | + | 0.746497i | \(0.268266\pi\) | |||||||
\(444\) | −3.26963e22 | −1.02741 | ||||||||
\(445\) | −1.37367e22 | −0.423469 | ||||||||
\(446\) | −1.26214e23 | −3.81735 | ||||||||
\(447\) | 2.52549e22 | 0.749432 | ||||||||
\(448\) | −6.43992e22 | −1.87507 | ||||||||
\(449\) | −5.51324e22 | −1.57512 | −0.787559 | − | 0.616239i | \(-0.788655\pi\) | ||||
−0.787559 | + | 0.616239i | \(0.788655\pi\) | |||||||
\(450\) | −2.95221e22 | −0.827639 | ||||||||
\(451\) | 1.55031e22 | 0.426499 | ||||||||
\(452\) | 1.56872e23 | 4.23514 | ||||||||
\(453\) | −2.92625e22 | −0.775313 | ||||||||
\(454\) | −1.08594e23 | −2.82378 | ||||||||
\(455\) | −2.53465e22 | −0.646877 | ||||||||
\(456\) | −6.04707e22 | −1.51476 | ||||||||
\(457\) | 6.93022e22 | 1.70396 | 0.851980 | − | 0.523574i | \(-0.175402\pi\) | ||||
0.851980 | + | 0.523574i | \(0.175402\pi\) | |||||||
\(458\) | −5.80009e22 | −1.39984 | ||||||||
\(459\) | −1.10104e22 | −0.260852 | ||||||||
\(460\) | 2.18024e23 | 5.07063 | ||||||||
\(461\) | −7.17076e21 | −0.163722 | −0.0818610 | − | 0.996644i | \(-0.526086\pi\) | ||||
−0.0818610 | + | 0.996644i | \(0.526086\pi\) | |||||||
\(462\) | 1.90518e22 | 0.427050 | ||||||||
\(463\) | 2.59981e22 | 0.572141 | 0.286071 | − | 0.958209i | \(-0.407651\pi\) | ||||
0.286071 | + | 0.958209i | \(0.407651\pi\) | |||||||
\(464\) | −2.37222e23 | −5.12569 | ||||||||
\(465\) | 8.54162e20 | 0.0181213 | ||||||||
\(466\) | −8.19432e22 | −1.70700 | ||||||||
\(467\) | 5.59192e22 | 1.14385 | 0.571923 | − | 0.820308i | \(-0.306198\pi\) | ||||
0.571923 | + | 0.820308i | \(0.306198\pi\) | |||||||
\(468\) | −5.36160e22 | −1.07697 | ||||||||
\(469\) | −2.65914e21 | −0.0524532 | ||||||||
\(470\) | −9.28281e22 | −1.79824 | ||||||||
\(471\) | 3.20818e22 | 0.610354 | ||||||||
\(472\) | −2.34719e23 | −4.38572 | ||||||||
\(473\) | −3.04768e22 | −0.559305 | ||||||||
\(474\) | −5.45554e22 | −0.983381 | ||||||||
\(475\) | 5.19819e22 | 0.920357 | ||||||||
\(476\) | 8.37217e22 | 1.45606 | ||||||||
\(477\) | 1.97431e22 | 0.337294 | ||||||||
\(478\) | 2.00559e23 | 3.36593 | ||||||||
\(479\) | 2.79993e22 | 0.461631 | 0.230816 | − | 0.972998i | \(-0.425861\pi\) | ||||
0.230816 | + | 0.972998i | \(0.425861\pi\) | |||||||
\(480\) | 2.51787e23 | 4.07834 | ||||||||
\(481\) | 4.47259e22 | 0.711748 | ||||||||
\(482\) | −1.24532e23 | −1.94707 | ||||||||
\(483\) | 1.68327e22 | 0.258585 | ||||||||
\(484\) | −6.06304e20 | −0.00915176 | ||||||||
\(485\) | −4.25222e22 | −0.630682 | ||||||||
\(486\) | −8.62768e21 | −0.125744 | ||||||||
\(487\) | −6.23980e22 | −0.893664 | −0.446832 | − | 0.894618i | \(-0.647448\pi\) | ||||
−0.446832 | + | 0.894618i | \(0.647448\pi\) | |||||||
\(488\) | −3.98129e22 | −0.560344 | ||||||||
\(489\) | −9.51314e21 | −0.131583 | ||||||||
\(490\) | 3.10138e22 | 0.421588 | ||||||||
\(491\) | 4.41349e22 | 0.589644 | 0.294822 | − | 0.955552i | \(-0.404740\pi\) | ||||
0.294822 | + | 0.955552i | \(0.404740\pi\) | |||||||
\(492\) | 5.33842e22 | 0.700986 | ||||||||
\(493\) | 1.27084e23 | 1.64018 | ||||||||
\(494\) | 1.27622e23 | 1.61900 | ||||||||
\(495\) | −4.01809e22 | −0.501043 | ||||||||
\(496\) | −7.20420e21 | −0.0883062 | ||||||||
\(497\) | −1.88746e22 | −0.227430 | ||||||||
\(498\) | −6.65548e22 | −0.788370 | ||||||||
\(499\) | −6.21080e22 | −0.723257 | −0.361629 | − | 0.932322i | \(-0.617779\pi\) | ||||
−0.361629 | + | 0.932322i | \(0.617779\pi\) | |||||||
\(500\) | −9.96814e22 | −1.14122 | ||||||||
\(501\) | −2.58893e22 | −0.291406 | ||||||||
\(502\) | −1.50799e22 | −0.166885 | ||||||||
\(503\) | −5.47475e22 | −0.595713 | −0.297856 | − | 0.954611i | \(-0.596272\pi\) | ||||
−0.297856 | + | 0.954611i | \(0.596272\pi\) | |||||||
\(504\) | 4.25217e22 | 0.454937 | ||||||||
\(505\) | 1.37401e23 | 1.44548 | ||||||||
\(506\) | 2.24172e23 | 2.31901 | ||||||||
\(507\) | 1.65869e22 | 0.168732 | ||||||||
\(508\) | 2.82280e23 | 2.82383 | ||||||||
\(509\) | 9.52145e22 | 0.936703 | 0.468352 | − | 0.883542i | \(-0.344848\pi\) | ||||
0.468352 | + | 0.883542i | \(0.344848\pi\) | |||||||
\(510\) | −2.38698e23 | −2.30941 | ||||||||
\(511\) | −2.04173e22 | −0.194277 | ||||||||
\(512\) | −4.89249e23 | −4.57862 | ||||||||
\(513\) | 1.51914e22 | 0.139830 | ||||||||
\(514\) | 3.88010e23 | 3.51283 | ||||||||
\(515\) | 6.18158e22 | 0.550475 | ||||||||
\(516\) | −1.04945e23 | −0.919265 | ||||||||
\(517\) | −7.06043e22 | −0.608361 | ||||||||
\(518\) | −5.47262e22 | −0.463866 | ||||||||
\(519\) | −1.74645e22 | −0.145625 | ||||||||
\(520\) | −7.53391e23 | −6.18005 | ||||||||
\(521\) | −1.00893e23 | −0.814221 | −0.407110 | − | 0.913379i | \(-0.633464\pi\) | ||||
−0.407110 | + | 0.913379i | \(0.633464\pi\) | |||||||
\(522\) | 9.95823e22 | 0.790647 | ||||||||
\(523\) | 4.21022e22 | 0.328883 | 0.164441 | − | 0.986387i | \(-0.447418\pi\) | ||||
0.164441 | + | 0.986387i | \(0.447418\pi\) | |||||||
\(524\) | −3.31621e23 | −2.54875 | ||||||||
\(525\) | −3.65525e22 | −0.276416 | ||||||||
\(526\) | 1.69210e23 | 1.25906 | ||||||||
\(527\) | 3.85941e21 | 0.0282573 | ||||||||
\(528\) | 3.38895e23 | 2.44161 | ||||||||
\(529\) | 5.70112e22 | 0.404191 | ||||||||
\(530\) | 4.28017e23 | 2.98618 | ||||||||
\(531\) | 5.89660e22 | 0.404854 | ||||||||
\(532\) | −1.15514e23 | −0.780523 | ||||||||
\(533\) | −7.30252e22 | −0.485614 | ||||||||
\(534\) | −4.86356e22 | −0.318312 | ||||||||
\(535\) | −4.09144e23 | −2.63554 | ||||||||
\(536\) | −7.90394e22 | −0.501121 | ||||||||
\(537\) | −1.25357e23 | −0.782288 | ||||||||
\(538\) | 3.23447e23 | 1.98680 | ||||||||
\(539\) | 2.35888e22 | 0.142627 | ||||||||
\(540\) | −1.38361e23 | −0.823506 | ||||||||
\(541\) | 2.78620e23 | 1.63243 | 0.816217 | − | 0.577745i | \(-0.196067\pi\) | ||||
0.816217 | + | 0.577745i | \(0.196067\pi\) | |||||||
\(542\) | 3.48366e23 | 2.00929 | ||||||||
\(543\) | −6.24021e22 | −0.354324 | ||||||||
\(544\) | 1.13766e24 | 6.35950 | ||||||||
\(545\) | −5.71664e22 | −0.314609 | ||||||||
\(546\) | −8.97409e22 | −0.486243 | ||||||||
\(547\) | 4.35097e22 | 0.232110 | 0.116055 | − | 0.993243i | \(-0.462975\pi\) | ||||
0.116055 | + | 0.993243i | \(0.462975\pi\) | |||||||
\(548\) | 7.86681e23 | 4.13203 | ||||||||
\(549\) | 1.00018e22 | 0.0517264 | ||||||||
\(550\) | −4.86793e23 | −2.47892 | ||||||||
\(551\) | −1.75342e23 | −0.879221 | ||||||||
\(552\) | 5.00330e23 | 2.47044 | ||||||||
\(553\) | −6.75473e22 | −0.328431 | ||||||||
\(554\) | −5.60982e22 | −0.268606 | ||||||||
\(555\) | 1.15420e23 | 0.544238 | ||||||||
\(556\) | −1.13395e24 | −5.26572 | ||||||||
\(557\) | −2.26465e23 | −1.03570 | −0.517848 | − | 0.855473i | \(-0.673267\pi\) | ||||
−0.517848 | + | 0.855473i | \(0.673267\pi\) | |||||||
\(558\) | 3.02421e21 | 0.0136214 | ||||||||
\(559\) | 1.43557e23 | 0.636829 | ||||||||
\(560\) | 5.51675e23 | 2.41038 | ||||||||
\(561\) | −1.81551e23 | −0.781295 | ||||||||
\(562\) | −5.59506e23 | −2.37162 | ||||||||
\(563\) | −2.13808e23 | −0.892693 | −0.446347 | − | 0.894860i | \(-0.647275\pi\) | ||||
−0.446347 | + | 0.894860i | \(0.647275\pi\) | |||||||
\(564\) | −2.43123e23 | −0.999892 | ||||||||
\(565\) | −5.53764e23 | −2.24343 | ||||||||
\(566\) | 2.26285e23 | 0.903057 | ||||||||
\(567\) | −1.06823e22 | −0.0419961 | ||||||||
\(568\) | −5.61022e23 | −2.17279 | ||||||||
\(569\) | −6.03782e22 | −0.230370 | −0.115185 | − | 0.993344i | \(-0.536746\pi\) | ||||
−0.115185 | + | 0.993344i | \(0.536746\pi\) | |||||||
\(570\) | 3.29340e23 | 1.23796 | ||||||||
\(571\) | 3.26516e23 | 1.20920 | 0.604600 | − | 0.796529i | \(-0.293333\pi\) | ||||
0.604600 | + | 0.796529i | \(0.293333\pi\) | |||||||
\(572\) | −8.84080e23 | −3.22571 | ||||||||
\(573\) | 2.79952e23 | 1.00640 | ||||||||
\(574\) | 8.93530e22 | 0.316488 | ||||||||
\(575\) | −4.30094e23 | −1.50102 | ||||||||
\(576\) | 4.80879e23 | 1.65366 | ||||||||
\(577\) | 4.82707e23 | 1.63565 | 0.817823 | − | 0.575469i | \(-0.195181\pi\) | ||||
0.817823 | + | 0.575469i | \(0.195181\pi\) | |||||||
\(578\) | −4.91469e23 | −1.64100 | ||||||||
\(579\) | 2.13493e23 | 0.702450 | ||||||||
\(580\) | 1.59699e24 | 5.17802 | ||||||||
\(581\) | −8.24043e22 | −0.263301 | ||||||||
\(582\) | −1.50552e23 | −0.474070 | ||||||||
\(583\) | 3.25546e23 | 1.01025 | ||||||||
\(584\) | −6.06877e23 | −1.85606 | ||||||||
\(585\) | 1.89267e23 | 0.570492 | ||||||||
\(586\) | 8.69026e23 | 2.58168 | ||||||||
\(587\) | 1.01172e23 | 0.296235 | 0.148118 | − | 0.988970i | \(-0.452679\pi\) | ||||
0.148118 | + | 0.988970i | \(0.452679\pi\) | |||||||
\(588\) | 8.12270e22 | 0.234419 | ||||||||
\(589\) | −5.32497e21 | −0.0151474 | ||||||||
\(590\) | 1.27834e24 | 3.58431 | ||||||||
\(591\) | −4.23876e21 | −0.0117151 | ||||||||
\(592\) | −9.73474e23 | −2.65210 | ||||||||
\(593\) | −7.06394e23 | −1.89707 | −0.948533 | − | 0.316679i | \(-0.897432\pi\) | ||||
−0.948533 | + | 0.316679i | \(0.897432\pi\) | |||||||
\(594\) | −1.42263e23 | −0.376623 | ||||||||
\(595\) | −2.95541e23 | −0.771301 | ||||||||
\(596\) | 1.43396e24 | 3.68930 | ||||||||
\(597\) | −5.47837e22 | −0.138953 | ||||||||
\(598\) | −1.05593e24 | −2.64044 | ||||||||
\(599\) | −2.23905e23 | −0.551997 | −0.275998 | − | 0.961158i | \(-0.589008\pi\) | ||||
−0.275998 | + | 0.961158i | \(0.589008\pi\) | |||||||
\(600\) | −1.08648e24 | −2.64079 | ||||||||
\(601\) | −2.44409e22 | −0.0585711 | −0.0292856 | − | 0.999571i | \(-0.509323\pi\) | ||||
−0.0292856 | + | 0.999571i | \(0.509323\pi\) | |||||||
\(602\) | −1.75655e23 | −0.415039 | ||||||||
\(603\) | 1.98562e22 | 0.0462594 | ||||||||
\(604\) | −1.66151e24 | −3.81671 | ||||||||
\(605\) | 2.14028e21 | 0.00484785 | ||||||||
\(606\) | 4.86475e23 | 1.08653 | ||||||||
\(607\) | −8.77084e23 | −1.93169 | −0.965845 | − | 0.259122i | \(-0.916567\pi\) | ||||
−0.965845 | + | 0.259122i | \(0.916567\pi\) | |||||||
\(608\) | −1.56968e24 | −3.40902 | ||||||||
\(609\) | 1.23297e23 | 0.264062 | ||||||||
\(610\) | 2.16832e23 | 0.457951 | ||||||||
\(611\) | 3.32572e23 | 0.692684 | ||||||||
\(612\) | −6.25164e23 | −1.28412 | ||||||||
\(613\) | −5.80620e23 | −1.17619 | −0.588096 | − | 0.808791i | \(-0.700122\pi\) | ||||
−0.588096 | + | 0.808791i | \(0.700122\pi\) | |||||||
\(614\) | 1.44114e24 | 2.87922 | ||||||||
\(615\) | −1.88448e23 | −0.371325 | ||||||||
\(616\) | 7.01146e23 | 1.36261 | ||||||||
\(617\) | 8.08554e23 | 1.54983 | 0.774917 | − | 0.632063i | \(-0.217792\pi\) | ||||
0.774917 | + | 0.632063i | \(0.217792\pi\) | |||||||
\(618\) | 2.18863e23 | 0.413780 | ||||||||
\(619\) | 9.05655e22 | 0.168885 | 0.0844427 | − | 0.996428i | \(-0.473089\pi\) | ||||
0.0844427 | + | 0.996428i | \(0.473089\pi\) | |||||||
\(620\) | 4.84989e22 | 0.0892078 | ||||||||
\(621\) | −1.25693e23 | −0.228051 | ||||||||
\(622\) | −4.79532e23 | −0.858221 | ||||||||
\(623\) | −6.02177e22 | −0.106310 | ||||||||
\(624\) | −1.59632e24 | −2.78004 | ||||||||
\(625\) | −3.85436e23 | −0.662174 | ||||||||
\(626\) | 1.03714e24 | 1.75774 | ||||||||
\(627\) | 2.50493e23 | 0.418815 | ||||||||
\(628\) | 1.82159e24 | 3.00465 | ||||||||
\(629\) | 5.21506e23 | 0.848650 | ||||||||
\(630\) | −2.31585e23 | −0.371805 | ||||||||
\(631\) | 1.00909e23 | 0.159838 | 0.0799188 | − | 0.996801i | \(-0.474534\pi\) | ||||
0.0799188 | + | 0.996801i | \(0.474534\pi\) | |||||||
\(632\) | −2.00775e24 | −3.13772 | ||||||||
\(633\) | −4.17893e23 | −0.644368 | ||||||||
\(634\) | −2.03107e24 | −3.09005 | ||||||||
\(635\) | −9.96462e23 | −1.49584 | ||||||||
\(636\) | 1.12100e24 | 1.66043 | ||||||||
\(637\) | −1.11112e23 | −0.162396 | ||||||||
\(638\) | 1.64202e24 | 2.36812 | ||||||||
\(639\) | 1.40940e23 | 0.200575 | ||||||||
\(640\) | 5.39507e24 | 7.57648 | ||||||||
\(641\) | −1.07424e24 | −1.48870 | −0.744351 | − | 0.667789i | \(-0.767241\pi\) | ||||
−0.744351 | + | 0.667789i | \(0.767241\pi\) | |||||||
\(642\) | −1.44860e24 | −1.98107 | ||||||||
\(643\) | 8.84469e23 | 1.19368 | 0.596842 | − | 0.802359i | \(-0.296422\pi\) | ||||
0.596842 | + | 0.802359i | \(0.296422\pi\) | |||||||
\(644\) | 9.55753e23 | 1.27296 | ||||||||
\(645\) | 3.70462e23 | 0.486951 | ||||||||
\(646\) | 1.48807e24 | 1.93040 | ||||||||
\(647\) | −8.12876e22 | −0.104073 | −0.0520365 | − | 0.998645i | \(-0.516571\pi\) | ||||
−0.0520365 | + | 0.998645i | \(0.516571\pi\) | |||||||
\(648\) | −3.17517e23 | −0.401217 | ||||||||
\(649\) | 9.72298e23 | 1.21260 | ||||||||
\(650\) | 2.29298e24 | 2.82251 | ||||||||
\(651\) | 3.74440e21 | 0.00454930 | ||||||||
\(652\) | −5.40151e23 | −0.647755 | ||||||||
\(653\) | 2.70011e23 | 0.319610 | 0.159805 | − | 0.987149i | \(-0.448913\pi\) | ||||
0.159805 | + | 0.987149i | \(0.448913\pi\) | |||||||
\(654\) | −2.02401e23 | −0.236484 | ||||||||
\(655\) | 1.17064e24 | 1.35012 | ||||||||
\(656\) | 1.58942e24 | 1.80949 | ||||||||
\(657\) | 1.52460e23 | 0.171336 | ||||||||
\(658\) | −4.06932e23 | −0.451442 | ||||||||
\(659\) | 4.89100e23 | 0.535638 | 0.267819 | − | 0.963469i | \(-0.413697\pi\) | ||||
0.267819 | + | 0.963469i | \(0.413697\pi\) | |||||||
\(660\) | −2.28145e24 | −2.46654 | ||||||||
\(661\) | −9.68394e23 | −1.03357 | −0.516785 | − | 0.856115i | \(-0.672871\pi\) | ||||
−0.516785 | + | 0.856115i | \(0.672871\pi\) | |||||||
\(662\) | 1.13831e24 | 1.19941 | ||||||||
\(663\) | 8.55173e23 | 0.889589 | ||||||||
\(664\) | −2.44936e24 | −2.51549 | ||||||||
\(665\) | 4.07770e23 | 0.413457 | ||||||||
\(666\) | 4.08650e23 | 0.409091 | ||||||||
\(667\) | 1.45077e24 | 1.43393 | ||||||||
\(668\) | −1.46998e24 | −1.43454 | ||||||||
\(669\) | 1.16690e24 | 1.12438 | ||||||||
\(670\) | 4.30470e23 | 0.409550 | ||||||||
\(671\) | 1.64920e23 | 0.154929 | ||||||||
\(672\) | 1.10376e24 | 1.02385 | ||||||||
\(673\) | −3.89550e23 | −0.356808 | −0.178404 | − | 0.983957i | \(-0.557093\pi\) | ||||
−0.178404 | + | 0.983957i | \(0.557093\pi\) | |||||||
\(674\) | −1.37857e24 | −1.24686 | ||||||||
\(675\) | 2.72944e23 | 0.243776 | ||||||||
\(676\) | 9.41795e23 | 0.830634 | ||||||||
\(677\) | −3.92236e23 | −0.341621 | −0.170810 | − | 0.985304i | \(-0.554639\pi\) | ||||
−0.170810 | + | 0.985304i | \(0.554639\pi\) | |||||||
\(678\) | −1.96063e24 | −1.68634 | ||||||||
\(679\) | −1.86405e23 | −0.158331 | ||||||||
\(680\) | −8.78457e24 | −7.36876 | ||||||||
\(681\) | 1.00399e24 | 0.831727 | ||||||||
\(682\) | 4.98666e22 | 0.0407984 | ||||||||
\(683\) | 9.51983e23 | 0.769225 | 0.384612 | − | 0.923078i | \(-0.374335\pi\) | ||||
0.384612 | + | 0.923078i | \(0.374335\pi\) | |||||||
\(684\) | 8.62562e23 | 0.688357 | ||||||||
\(685\) | −2.77702e24 | −2.18881 | ||||||||
\(686\) | 1.35956e23 | 0.105838 | ||||||||
\(687\) | 5.36242e23 | 0.412315 | ||||||||
\(688\) | −3.12456e24 | −2.37294 | ||||||||
\(689\) | −1.53344e24 | −1.15028 | ||||||||
\(690\) | −2.72493e24 | −2.01901 | ||||||||
\(691\) | −1.40863e23 | −0.103094 | −0.0515470 | − | 0.998671i | \(-0.516415\pi\) | ||||
−0.0515470 | + | 0.998671i | \(0.516415\pi\) | |||||||
\(692\) | −9.91628e23 | −0.716881 | ||||||||
\(693\) | −1.76142e23 | −0.125785 | ||||||||
\(694\) | −4.26093e24 | −3.00572 | ||||||||
\(695\) | 4.00289e24 | 2.78935 | ||||||||
\(696\) | 3.66484e24 | 2.52276 | ||||||||
\(697\) | −8.51477e23 | −0.579021 | ||||||||
\(698\) | −4.37428e24 | −2.93857 | ||||||||
\(699\) | 7.57599e23 | 0.502786 | ||||||||
\(700\) | −2.07544e24 | −1.36074 | ||||||||
\(701\) | 1.06778e24 | 0.691637 | 0.345818 | − | 0.938301i | \(-0.387601\pi\) | ||||
0.345818 | + | 0.938301i | \(0.387601\pi\) | |||||||
\(702\) | 6.70110e23 | 0.428826 | ||||||||
\(703\) | −7.19541e23 | −0.454921 | ||||||||
\(704\) | 7.92928e24 | 4.95297 | ||||||||
\(705\) | 8.58233e23 | 0.529661 | ||||||||
\(706\) | 3.24989e24 | 1.98166 | ||||||||
\(707\) | 6.02325e23 | 0.362882 | ||||||||
\(708\) | 3.34806e24 | 1.99302 | ||||||||
\(709\) | 1.61640e24 | 0.950729 | 0.475364 | − | 0.879789i | \(-0.342316\pi\) | ||||
0.475364 | + | 0.879789i | \(0.342316\pi\) | |||||||
\(710\) | 3.05548e24 | 1.77575 | ||||||||
\(711\) | 5.04387e23 | 0.289649 | ||||||||
\(712\) | −1.78989e24 | −1.01566 | ||||||||
\(713\) | 4.40583e22 | 0.0247040 | ||||||||
\(714\) | −1.04638e24 | −0.579770 | ||||||||
\(715\) | 3.12084e24 | 1.70872 | ||||||||
\(716\) | −7.11771e24 | −3.85105 | ||||||||
\(717\) | −1.85425e24 | −0.991415 | ||||||||
\(718\) | 5.02238e23 | 0.265370 | ||||||||
\(719\) | −1.04728e24 | −0.546847 | −0.273423 | − | 0.961894i | \(-0.588156\pi\) | ||||
−0.273423 | + | 0.961894i | \(0.588156\pi\) | |||||||
\(720\) | −4.11945e24 | −2.12575 | ||||||||
\(721\) | 2.70983e23 | 0.138195 | ||||||||
\(722\) | 1.83600e24 | 0.925352 | ||||||||
\(723\) | 1.15135e24 | 0.573497 | ||||||||
\(724\) | −3.54316e24 | −1.74427 | ||||||||
\(725\) | −3.15037e24 | −1.53281 | ||||||||
\(726\) | 7.57779e21 | 0.00364402 | ||||||||
\(727\) | 9.16926e23 | 0.435805 | 0.217902 | − | 0.975971i | \(-0.430079\pi\) | ||||
0.217902 | + | 0.975971i | \(0.430079\pi\) | |||||||
\(728\) | −3.30265e24 | −1.55148 | ||||||||
\(729\) | 7.97664e22 | 0.0370370 | ||||||||
\(730\) | 3.30522e24 | 1.51690 | ||||||||
\(731\) | 1.67388e24 | 0.759321 | ||||||||
\(732\) | 5.67896e23 | 0.254639 | ||||||||
\(733\) | −1.94460e24 | −0.861879 | −0.430940 | − | 0.902381i | \(-0.641818\pi\) | ||||
−0.430940 | + | 0.902381i | \(0.641818\pi\) | |||||||
\(734\) | 1.43878e24 | 0.630346 | ||||||||
\(735\) | −2.86735e23 | −0.124176 | ||||||||
\(736\) | 1.29874e25 | 5.55981 | ||||||||
\(737\) | 3.27412e23 | 0.138555 | ||||||||
\(738\) | −6.67213e23 | −0.279117 | ||||||||
\(739\) | −3.20437e24 | −1.32515 | −0.662574 | − | 0.748996i | \(-0.730536\pi\) | ||||
−0.662574 | + | 0.748996i | \(0.730536\pi\) | |||||||
\(740\) | 6.55347e24 | 2.67918 | ||||||||
\(741\) | −1.17992e24 | −0.476866 | ||||||||
\(742\) | 1.87630e24 | 0.749669 | ||||||||
\(743\) | −2.70961e24 | −1.07029 | −0.535146 | − | 0.844759i | \(-0.679744\pi\) | ||||
−0.535146 | + | 0.844759i | \(0.679744\pi\) | |||||||
\(744\) | 1.11297e23 | 0.0434625 | ||||||||
\(745\) | −5.06195e24 | −1.95429 | ||||||||
\(746\) | 4.57350e24 | 1.74570 | ||||||||
\(747\) | 6.15327e23 | 0.232210 | ||||||||
\(748\) | −1.03084e25 | −3.84616 | ||||||||
\(749\) | −1.79357e24 | −0.661643 | ||||||||
\(750\) | 1.24585e24 | 0.454408 | ||||||||
\(751\) | 7.73264e23 | 0.278861 | 0.139431 | − | 0.990232i | \(-0.455473\pi\) | ||||
0.139431 | + | 0.990232i | \(0.455473\pi\) | |||||||
\(752\) | −7.23853e24 | −2.58106 | ||||||||
\(753\) | 1.39420e23 | 0.0491551 | ||||||||
\(754\) | −7.73453e24 | −2.69636 | ||||||||
\(755\) | 5.86521e24 | 2.02178 | ||||||||
\(756\) | −6.06536e23 | −0.206738 | ||||||||
\(757\) | 2.29385e24 | 0.773125 | 0.386563 | − | 0.922263i | \(-0.373662\pi\) | ||||
0.386563 | + | 0.922263i | \(0.373662\pi\) | |||||||
\(758\) | −5.32250e23 | −0.177389 | ||||||||
\(759\) | −2.07256e24 | −0.683049 | ||||||||
\(760\) | 1.21204e25 | 3.95004 | ||||||||
\(761\) | 2.50959e24 | 0.808786 | 0.404393 | − | 0.914585i | \(-0.367483\pi\) | ||||
0.404393 | + | 0.914585i | \(0.367483\pi\) | |||||||
\(762\) | −3.52803e24 | −1.12439 | ||||||||
\(763\) | −2.50601e23 | −0.0789814 | ||||||||
\(764\) | 1.58956e25 | 4.95430 | ||||||||
\(765\) | 2.20686e24 | 0.680224 | ||||||||
\(766\) | −6.89505e24 | −2.10181 | ||||||||
\(767\) | −4.57988e24 | −1.38068 | ||||||||
\(768\) | 9.49485e24 | 2.83086 | ||||||||
\(769\) | −7.81121e23 | −0.230327 | −0.115163 | − | 0.993347i | \(-0.536739\pi\) | ||||
−0.115163 | + | 0.993347i | \(0.536739\pi\) | |||||||
\(770\) | −3.81863e24 | −1.11362 | ||||||||
\(771\) | −3.58732e24 | −1.03468 | ||||||||
\(772\) | 1.21220e25 | 3.45802 | ||||||||
\(773\) | −5.75821e24 | −1.62466 | −0.812329 | − | 0.583199i | \(-0.801801\pi\) | ||||
−0.812329 | + | 0.583199i | \(0.801801\pi\) | |||||||
\(774\) | 1.31164e24 | 0.366030 | ||||||||
\(775\) | −9.56735e22 | −0.0264075 | ||||||||
\(776\) | −5.54064e24 | −1.51264 | ||||||||
\(777\) | 5.05966e23 | 0.136629 | ||||||||
\(778\) | −1.08594e25 | −2.90053 | ||||||||
\(779\) | 1.17481e24 | 0.310385 | ||||||||
\(780\) | 1.07465e25 | 2.80842 | ||||||||
\(781\) | 2.32397e24 | 0.600754 | ||||||||
\(782\) | −1.23122e25 | −3.14832 | ||||||||
\(783\) | −9.20679e23 | −0.232880 | ||||||||
\(784\) | 2.41839e24 | 0.605117 | ||||||||
\(785\) | −6.43030e24 | −1.59162 | ||||||||
\(786\) | 4.14472e24 | 1.01485 | ||||||||
\(787\) | 3.31374e24 | 0.802664 | 0.401332 | − | 0.915933i | \(-0.368547\pi\) | ||||
0.401332 | + | 0.915933i | \(0.368547\pi\) | |||||||
\(788\) | −2.40675e23 | −0.0576711 | ||||||||
\(789\) | −1.56442e24 | −0.370849 | ||||||||
\(790\) | 1.09348e25 | 2.56436 | ||||||||
\(791\) | −2.42754e24 | −0.563205 | ||||||||
\(792\) | −5.23557e24 | −1.20171 | ||||||||
\(793\) | −7.76836e23 | −0.176403 | ||||||||
\(794\) | 7.05381e24 | 1.58471 | ||||||||
\(795\) | −3.95719e24 | −0.879561 | ||||||||
\(796\) | −3.11059e24 | −0.684041 | ||||||||
\(797\) | 5.01788e24 | 1.09175 | 0.545877 | − | 0.837866i | \(-0.316197\pi\) | ||||
0.545877 | + | 0.837866i | \(0.316197\pi\) | |||||||
\(798\) | 1.44373e24 | 0.310787 | ||||||||
\(799\) | 3.87780e24 | 0.825920 | ||||||||
\(800\) | −2.82023e25 | −5.94320 | ||||||||
\(801\) | 4.49656e23 | 0.0937570 | ||||||||
\(802\) | 4.67302e24 | 0.964086 | ||||||||
\(803\) | 2.51392e24 | 0.513180 | ||||||||
\(804\) | 1.12743e24 | 0.227726 | ||||||||
\(805\) | −3.37385e24 | −0.674312 | ||||||||
\(806\) | −2.34890e23 | −0.0464533 | ||||||||
\(807\) | −2.99040e24 | −0.585200 | ||||||||
\(808\) | 1.79033e25 | 3.46686 | ||||||||
\(809\) | −6.53004e24 | −1.25128 | −0.625638 | − | 0.780114i | \(-0.715161\pi\) | ||||
−0.625638 | + | 0.780114i | \(0.715161\pi\) | |||||||
\(810\) | 1.72928e24 | 0.327901 | ||||||||
\(811\) | 4.78535e24 | 0.897917 | 0.448959 | − | 0.893553i | \(-0.351795\pi\) | ||||
0.448959 | + | 0.893553i | \(0.351795\pi\) | |||||||
\(812\) | 7.00074e24 | 1.29992 | ||||||||
\(813\) | −3.22078e24 | −0.591823 | ||||||||
\(814\) | 6.73827e24 | 1.22530 | ||||||||
\(815\) | 1.90676e24 | 0.343128 | ||||||||
\(816\) | −1.86131e25 | −3.31477 | ||||||||
\(817\) | −2.30951e24 | −0.407036 | ||||||||
\(818\) | 4.07606e22 | 0.00710948 | ||||||||
\(819\) | 8.29691e23 | 0.143220 | ||||||||
\(820\) | −1.07000e25 | −1.82796 | ||||||||
\(821\) | 7.93062e24 | 1.34088 | 0.670441 | − | 0.741963i | \(-0.266105\pi\) | ||||
0.670441 | + | 0.741963i | \(0.266105\pi\) | |||||||
\(822\) | −9.83220e24 | −1.64528 | ||||||||
\(823\) | 8.24812e24 | 1.36602 | 0.683009 | − | 0.730410i | \(-0.260671\pi\) | ||||
0.683009 | + | 0.730410i | \(0.260671\pi\) | |||||||
\(824\) | 8.05460e24 | 1.32027 | ||||||||
\(825\) | 4.50060e24 | 0.730150 | ||||||||
\(826\) | 5.60390e24 | 0.899828 | ||||||||
\(827\) | −2.36975e24 | −0.376623 | −0.188311 | − | 0.982109i | \(-0.560301\pi\) | ||||
−0.188311 | + | 0.982109i | \(0.560301\pi\) | |||||||
\(828\) | −7.13677e24 | −1.12265 | ||||||||
\(829\) | 2.92107e24 | 0.454808 | 0.227404 | − | 0.973800i | \(-0.426976\pi\) | ||||
0.227404 | + | 0.973800i | \(0.426976\pi\) | |||||||
\(830\) | 1.33399e25 | 2.05583 | ||||||||
\(831\) | 5.18650e23 | 0.0791163 | ||||||||
\(832\) | −3.73498e25 | −5.63949 | ||||||||
\(833\) | −1.29557e24 | −0.193632 | ||||||||
\(834\) | 1.41725e25 | 2.09669 | ||||||||
\(835\) | 5.18910e24 | 0.759900 | ||||||||
\(836\) | 1.42229e25 | 2.06174 | ||||||||
\(837\) | −2.79601e22 | −0.00401210 | ||||||||
\(838\) | 1.21848e25 | 1.73079 | ||||||||
\(839\) | −5.56183e24 | −0.782062 | −0.391031 | − | 0.920378i | \(-0.627881\pi\) | ||||
−0.391031 | + | 0.920378i | \(0.627881\pi\) | |||||||
\(840\) | −8.52281e24 | −1.18634 | ||||||||
\(841\) | 3.36949e24 | 0.464300 | ||||||||
\(842\) | −1.08359e25 | −1.47813 | ||||||||
\(843\) | 5.17286e24 | 0.698548 | ||||||||
\(844\) | −2.37278e25 | −3.17210 | ||||||||
\(845\) | −3.32458e24 | −0.440002 | ||||||||
\(846\) | 3.03863e24 | 0.398134 | ||||||||
\(847\) | 9.38237e21 | 0.00121704 | ||||||||
\(848\) | 3.33758e25 | 4.28615 | ||||||||
\(849\) | −2.09209e24 | −0.265990 | ||||||||
\(850\) | 2.67362e25 | 3.36541 | ||||||||
\(851\) | 5.95343e24 | 0.741935 | ||||||||
\(852\) | 8.00249e24 | 0.987389 | ||||||||
\(853\) | −1.36694e25 | −1.66986 | −0.834932 | − | 0.550353i | \(-0.814493\pi\) | ||||
−0.834932 | + | 0.550353i | \(0.814493\pi\) | |||||||
\(854\) | 9.50529e23 | 0.114967 | ||||||||
\(855\) | −3.04488e24 | −0.364635 | ||||||||
\(856\) | −5.33115e25 | −6.32112 | ||||||||
\(857\) | −8.64762e24 | −1.01522 | −0.507609 | − | 0.861587i | \(-0.669471\pi\) | ||||
−0.507609 | + | 0.861587i | \(0.669471\pi\) | |||||||
\(858\) | 1.10495e25 | 1.28440 | ||||||||
\(859\) | −2.98424e23 | −0.0343472 | −0.0171736 | − | 0.999853i | \(-0.505467\pi\) | ||||
−0.0171736 | + | 0.999853i | \(0.505467\pi\) | |||||||
\(860\) | 2.10346e25 | 2.39717 | ||||||||
\(861\) | −8.26105e23 | −0.0932198 | ||||||||
\(862\) | −1.46333e25 | −1.63504 | ||||||||
\(863\) | −7.54136e24 | −0.834368 | −0.417184 | − | 0.908822i | \(-0.636983\pi\) | ||||
−0.417184 | + | 0.908822i | \(0.636983\pi\) | |||||||
\(864\) | −8.24199e24 | −0.902953 | ||||||||
\(865\) | 3.50049e24 | 0.379745 | ||||||||
\(866\) | −2.06348e25 | −2.21665 | ||||||||
\(867\) | 4.54383e24 | 0.483348 | ||||||||
\(868\) | 2.12606e23 | 0.0223953 | ||||||||
\(869\) | 8.31689e24 | 0.867547 | ||||||||
\(870\) | −1.99597e25 | −2.06177 | ||||||||
\(871\) | −1.54223e24 | −0.157759 | ||||||||
\(872\) | −7.44878e24 | −0.754562 | ||||||||
\(873\) | 1.39192e24 | 0.139634 | ||||||||
\(874\) | 1.69876e25 | 1.68766 | ||||||||
\(875\) | 1.54254e24 | 0.151764 | ||||||||
\(876\) | 8.65658e24 | 0.843454 | ||||||||
\(877\) | 4.83896e24 | 0.466934 | 0.233467 | − | 0.972365i | \(-0.424993\pi\) | ||||
0.233467 | + | 0.972365i | \(0.424993\pi\) | |||||||
\(878\) | −3.06081e25 | −2.92505 | ||||||||
\(879\) | −8.03450e24 | −0.760420 | ||||||||
\(880\) | −6.79261e25 | −6.36698 | ||||||||
\(881\) | −1.14844e25 | −1.06614 | −0.533068 | − | 0.846072i | \(-0.678961\pi\) | ||||
−0.533068 | + | 0.846072i | \(0.678961\pi\) | |||||||
\(882\) | −1.01520e24 | −0.0933404 | ||||||||
\(883\) | 1.40332e25 | 1.27788 | 0.638942 | − | 0.769255i | \(-0.279372\pi\) | ||||
0.638942 | + | 0.769255i | \(0.279372\pi\) | |||||||
\(884\) | 4.85563e25 | 4.37927 | ||||||||
\(885\) | −1.18188e25 | −1.05574 | ||||||||
\(886\) | −2.94836e25 | −2.60852 | ||||||||
\(887\) | 1.16146e25 | 1.01778 | 0.508888 | − | 0.860833i | \(-0.330057\pi\) | ||||
0.508888 | + | 0.860833i | \(0.330057\pi\) | |||||||
\(888\) | 1.50392e25 | 1.30531 | ||||||||
\(889\) | −4.36820e24 | −0.375524 | ||||||||
\(890\) | 9.74823e24 | 0.830062 | ||||||||
\(891\) | 1.31528e24 | 0.110932 | ||||||||
\(892\) | 6.62562e25 | 5.53510 | ||||||||
\(893\) | −5.35035e24 | −0.442736 | ||||||||
\(894\) | −1.79221e25 | −1.46900 | ||||||||
\(895\) | 2.51258e25 | 2.03997 | ||||||||
\(896\) | 2.36505e25 | 1.90205 | ||||||||
\(897\) | 9.76252e24 | 0.777725 | ||||||||
\(898\) | 3.91247e25 | 3.08746 | ||||||||
\(899\) | 3.22720e23 | 0.0252272 | ||||||||
\(900\) | 1.54976e25 | 1.20006 | ||||||||
\(901\) | −1.78800e25 | −1.37153 | ||||||||
\(902\) | −1.10018e25 | −0.836001 | ||||||||
\(903\) | 1.62400e24 | 0.122247 | ||||||||
\(904\) | −7.21554e25 | −5.38068 | ||||||||
\(905\) | 1.25075e25 | 0.923971 | ||||||||
\(906\) | 2.07661e25 | 1.51973 | ||||||||
\(907\) | −1.29818e25 | −0.941182 | −0.470591 | − | 0.882351i | \(-0.655959\pi\) | ||||
−0.470591 | + | 0.882351i | \(0.655959\pi\) | |||||||
\(908\) | 5.70063e25 | 4.09443 | ||||||||
\(909\) | −4.49766e24 | −0.320032 | ||||||||
\(910\) | 1.79871e25 | 1.26797 | ||||||||
\(911\) | −3.94564e24 | −0.275557 | −0.137778 | − | 0.990463i | \(-0.543996\pi\) | ||||
−0.137778 | + | 0.990463i | \(0.543996\pi\) | |||||||
\(912\) | 2.56812e25 | 1.77689 | ||||||||
\(913\) | 1.01462e25 | 0.695507 | ||||||||
\(914\) | −4.91803e25 | −3.34002 | ||||||||
\(915\) | −2.00470e24 | −0.134887 | ||||||||
\(916\) | 3.04476e25 | 2.02974 | ||||||||
\(917\) | 5.13175e24 | 0.338942 | ||||||||
\(918\) | 7.81351e24 | 0.511309 | ||||||||
\(919\) | 7.63928e24 | 0.495302 | 0.247651 | − | 0.968849i | \(-0.420341\pi\) | ||||
0.247651 | + | 0.968849i | \(0.420341\pi\) | |||||||
\(920\) | −1.00283e26 | −6.44216 | ||||||||
\(921\) | −1.33239e25 | −0.848058 | ||||||||
\(922\) | 5.08872e24 | 0.320919 | ||||||||
\(923\) | −1.09468e25 | −0.684023 | ||||||||
\(924\) | −1.00012e25 | −0.619216 | ||||||||
\(925\) | −1.29280e25 | −0.793096 | ||||||||
\(926\) | −1.84495e25 | −1.12148 | ||||||||
\(927\) | −2.02347e24 | −0.121876 | ||||||||
\(928\) | 9.51305e25 | 5.67756 | ||||||||
\(929\) | 2.66866e25 | 1.57819 | 0.789096 | − | 0.614270i | \(-0.210549\pi\) | ||||
0.789096 | + | 0.614270i | \(0.210549\pi\) | |||||||
\(930\) | −6.06156e23 | −0.0355205 | ||||||||
\(931\) | 1.78755e24 | 0.103797 | ||||||||
\(932\) | 4.30161e25 | 2.47512 | ||||||||
\(933\) | 4.43347e24 | 0.252784 | ||||||||
\(934\) | −3.96830e25 | −2.24211 | ||||||||
\(935\) | 3.63891e25 | 2.03738 | ||||||||
\(936\) | 2.46615e25 | 1.36828 | ||||||||
\(937\) | −2.54191e25 | −1.39757 | −0.698784 | − | 0.715333i | \(-0.746275\pi\) | ||||
−0.698784 | + | 0.715333i | \(0.746275\pi\) | |||||||
\(938\) | 1.88706e24 | 0.102816 | ||||||||
\(939\) | −9.58877e24 | −0.517732 | ||||||||
\(940\) | 4.87301e25 | 2.60742 | ||||||||
\(941\) | 9.03633e24 | 0.479160 | 0.239580 | − | 0.970877i | \(-0.422990\pi\) | ||||
0.239580 | + | 0.970877i | \(0.422990\pi\) | |||||||
\(942\) | −2.27669e25 | −1.19638 | ||||||||
\(943\) | −9.72032e24 | −0.506210 | ||||||||
\(944\) | 9.96825e25 | 5.14466 | ||||||||
\(945\) | 2.14110e24 | 0.109513 | ||||||||
\(946\) | 2.16278e25 | 1.09632 | ||||||||
\(947\) | 8.97578e24 | 0.450918 | 0.225459 | − | 0.974253i | \(-0.427612\pi\) | ||||
0.225459 | + | 0.974253i | \(0.427612\pi\) | |||||||
\(948\) | 2.86388e25 | 1.42589 | ||||||||
\(949\) | −1.18415e25 | −0.584311 | ||||||||
\(950\) | −3.68889e25 | −1.80404 | ||||||||
\(951\) | 1.87781e25 | 0.910157 | ||||||||
\(952\) | −3.85091e25 | −1.84990 | ||||||||
\(953\) | −3.56154e25 | −1.69569 | −0.847847 | − | 0.530240i | \(-0.822102\pi\) | ||||
−0.847847 | + | 0.530240i | \(0.822102\pi\) | |||||||
\(954\) | −1.40107e25 | −0.661146 | ||||||||
\(955\) | −5.61120e25 | −2.62438 | ||||||||
\(956\) | −1.05283e26 | −4.88054 | ||||||||
\(957\) | −1.51812e25 | −0.697516 | ||||||||
\(958\) | −1.98697e25 | −0.904866 | ||||||||
\(959\) | −1.21737e25 | −0.549494 | ||||||||
\(960\) | −9.63847e25 | −4.31224 | ||||||||
\(961\) | −2.25403e25 | −0.999565 | ||||||||
\(962\) | −3.17397e25 | −1.39513 | ||||||||
\(963\) | 1.33929e25 | 0.583514 | ||||||||
\(964\) | 6.53730e25 | 2.82321 | ||||||||
\(965\) | −4.27913e25 | −1.83178 | ||||||||
\(966\) | −1.19453e25 | −0.506865 | ||||||||
\(967\) | 2.47463e25 | 1.04084 | 0.520422 | − | 0.853909i | \(-0.325774\pi\) | ||||
0.520422 | + | 0.853909i | \(0.325774\pi\) | |||||||
\(968\) | 2.78878e23 | 0.0116272 | ||||||||
\(969\) | −1.37579e25 | −0.568589 | ||||||||
\(970\) | 3.01758e25 | 1.23623 | ||||||||
\(971\) | −1.14088e25 | −0.463315 | −0.231657 | − | 0.972797i | \(-0.574415\pi\) | ||||
−0.231657 | + | 0.972797i | \(0.574415\pi\) | |||||||
\(972\) | 4.52910e24 | 0.182326 | ||||||||
\(973\) | 1.75475e25 | 0.700256 | ||||||||
\(974\) | 4.42807e25 | 1.75172 | ||||||||
\(975\) | −2.11995e25 | −0.831354 | ||||||||
\(976\) | 1.69081e25 | 0.657311 | ||||||||
\(977\) | 4.13224e25 | 1.59251 | 0.796255 | − | 0.604962i | \(-0.206812\pi\) | ||||
0.796255 | + | 0.604962i | \(0.206812\pi\) | |||||||
\(978\) | 6.75099e24 | 0.257921 | ||||||||
\(979\) | 7.41442e24 | 0.280818 | ||||||||
\(980\) | −1.62807e25 | −0.611295 | ||||||||
\(981\) | 1.87128e24 | 0.0696550 | ||||||||
\(982\) | −3.13203e25 | −1.15579 | ||||||||
\(983\) | 3.64968e25 | 1.33521 | 0.667606 | − | 0.744515i | \(-0.267319\pi\) | ||||
0.667606 | + | 0.744515i | \(0.267319\pi\) | |||||||
\(984\) | −2.45548e25 | −0.890592 | ||||||||
\(985\) | 8.49593e23 | 0.0305494 | ||||||||
\(986\) | −9.01849e25 | −3.21499 | ||||||||
\(987\) | 3.76225e24 | 0.132969 | ||||||||
\(988\) | −6.69950e25 | −2.34752 | ||||||||
\(989\) | 1.91087e25 | 0.663839 | ||||||||
\(990\) | 2.85143e25 | 0.982119 | ||||||||
\(991\) | 3.75564e25 | 1.28250 | 0.641250 | − | 0.767332i | \(-0.278416\pi\) | ||||
0.641250 | + | 0.767332i | \(0.278416\pi\) | |||||||
\(992\) | 2.88902e24 | 0.0978140 | ||||||||
\(993\) | −1.05241e25 | −0.353278 | ||||||||
\(994\) | 1.33943e25 | 0.445797 | ||||||||
\(995\) | 1.09805e25 | 0.362349 | ||||||||
\(996\) | 3.49380e25 | 1.14312 | ||||||||
\(997\) | 1.11835e25 | 0.362801 | 0.181400 | − | 0.983409i | \(-0.441937\pi\) | ||||
0.181400 | + | 0.983409i | \(0.441937\pi\) | |||||||
\(998\) | 4.40749e25 | 1.41769 | ||||||||
\(999\) | −3.77813e24 | −0.120495 |
(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 | 21.18.a.d.1.1 | ✓ | 5 | |
3.2 | odd | 2 | 63.18.a.f.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.18.a.d.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial | |
63.18.a.f.1.5 | 5 | 3.2 | odd | 2 |