Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,18,Mod(1,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, 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("15.1");
S:= CuspForms(chi, 18);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 18 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(27.4833131017\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{849}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 212 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(15.0688\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −702.477 | −1.94034 | −0.970168 | − | 0.242432i | \(-0.922055\pi\) | ||||
−0.970168 | + | 0.242432i | \(0.922055\pi\) | |||||||
\(3\) | 6561.00 | 0.577350 | ||||||||
\(4\) | 362402. | 2.76491 | ||||||||
\(5\) | 390625. | 0.447214 | ||||||||
\(6\) | −4.60895e6 | −1.12025 | ||||||||
\(7\) | −2.67481e6 | −0.175372 | −0.0876858 | − | 0.996148i | \(-0.527947\pi\) | ||||
−0.0876858 | + | 0.996148i | \(0.527947\pi\) | |||||||
\(8\) | −1.62504e8 | −3.42451 | ||||||||
\(9\) | 4.30467e7 | 0.333333 | ||||||||
\(10\) | −2.74405e8 | −0.867745 | ||||||||
\(11\) | −9.86334e8 | −1.38735 | −0.693675 | − | 0.720288i | \(-0.744010\pi\) | ||||
−0.693675 | + | 0.720288i | \(0.744010\pi\) | |||||||
\(12\) | 2.37772e9 | 1.59632 | ||||||||
\(13\) | 2.81488e9 | 0.957065 | 0.478533 | − | 0.878070i | \(-0.341169\pi\) | ||||
0.478533 | + | 0.878070i | \(0.341169\pi\) | |||||||
\(14\) | 1.87899e9 | 0.340280 | ||||||||
\(15\) | 2.56289e9 | 0.258199 | ||||||||
\(16\) | 6.66544e10 | 3.87980 | ||||||||
\(17\) | 1.28501e10 | 0.446776 | 0.223388 | − | 0.974730i | \(-0.428288\pi\) | ||||
0.223388 | + | 0.974730i | \(0.428288\pi\) | |||||||
\(18\) | −3.02393e10 | −0.646779 | ||||||||
\(19\) | −1.22560e11 | −1.65555 | −0.827777 | − | 0.561057i | \(-0.810395\pi\) | ||||
−0.827777 | + | 0.561057i | \(0.810395\pi\) | |||||||
\(20\) | 1.41563e11 | 1.23650 | ||||||||
\(21\) | −1.75494e10 | −0.101251 | ||||||||
\(22\) | 6.92877e11 | 2.69193 | ||||||||
\(23\) | 1.14646e11 | 0.305263 | 0.152631 | − | 0.988283i | \(-0.451225\pi\) | ||||
0.152631 | + | 0.988283i | \(0.451225\pi\) | |||||||
\(24\) | −1.06619e12 | −1.97714 | ||||||||
\(25\) | 1.52588e11 | 0.200000 | ||||||||
\(26\) | −1.97739e12 | −1.85703 | ||||||||
\(27\) | 2.82430e11 | 0.192450 | ||||||||
\(28\) | −9.69355e11 | −0.484886 | ||||||||
\(29\) | −4.90027e12 | −1.81902 | −0.909510 | − | 0.415682i | \(-0.863543\pi\) | ||||
−0.909510 | + | 0.415682i | \(0.863543\pi\) | |||||||
\(30\) | −1.80037e12 | −0.500993 | ||||||||
\(31\) | 7.64406e12 | 1.60972 | 0.804859 | − | 0.593466i | \(-0.202241\pi\) | ||||
0.804859 | + | 0.593466i | \(0.202241\pi\) | |||||||
\(32\) | −2.55235e13 | −4.10361 | ||||||||
\(33\) | −6.47134e12 | −0.800987 | ||||||||
\(34\) | −9.02688e12 | −0.866896 | ||||||||
\(35\) | −1.04485e12 | −0.0784286 | ||||||||
\(36\) | 1.56002e13 | 0.921635 | ||||||||
\(37\) | 3.18983e12 | 0.149298 | 0.0746488 | − | 0.997210i | \(-0.476216\pi\) | ||||
0.0746488 | + | 0.997210i | \(0.476216\pi\) | |||||||
\(38\) | 8.60956e13 | 3.21233 | ||||||||
\(39\) | 1.84684e13 | 0.552562 | ||||||||
\(40\) | −6.34781e13 | −1.53149 | ||||||||
\(41\) | −5.53137e12 | −0.108186 | −0.0540928 | − | 0.998536i | \(-0.517227\pi\) | ||||
−0.0540928 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(42\) | 1.23281e13 | 0.196461 | ||||||||
\(43\) | 2.42435e13 | 0.316311 | 0.158155 | − | 0.987414i | \(-0.449445\pi\) | ||||
0.158155 | + | 0.987414i | \(0.449445\pi\) | |||||||
\(44\) | −3.57449e14 | −3.83589 | ||||||||
\(45\) | 1.68151e13 | 0.149071 | ||||||||
\(46\) | −8.05365e13 | −0.592313 | ||||||||
\(47\) | −5.82161e13 | −0.356625 | −0.178312 | − | 0.983974i | \(-0.557064\pi\) | ||||
−0.178312 | + | 0.983974i | \(0.557064\pi\) | |||||||
\(48\) | 4.37320e14 | 2.24000 | ||||||||
\(49\) | −2.25476e14 | −0.969245 | ||||||||
\(50\) | −1.07189e14 | −0.388067 | ||||||||
\(51\) | 8.43094e13 | 0.257946 | ||||||||
\(52\) | 1.02012e15 | 2.64620 | ||||||||
\(53\) | −6.45746e14 | −1.42468 | −0.712339 | − | 0.701835i | \(-0.752364\pi\) | ||||
−0.712339 | + | 0.701835i | \(0.752364\pi\) | |||||||
\(54\) | −1.98400e14 | −0.373418 | ||||||||
\(55\) | −3.85287e14 | −0.620442 | ||||||||
\(56\) | 4.34667e14 | 0.600562 | ||||||||
\(57\) | −8.04117e14 | −0.955835 | ||||||||
\(58\) | 3.44233e15 | 3.52951 | ||||||||
\(59\) | −1.04433e12 | −0.000925970 0 | −0.000462985 | − | 1.00000i | \(-0.500147\pi\) | ||||
−0.000462985 | 1.00000i | \(0.500147\pi\) | ||||||||
\(60\) | 9.28796e14 | 0.713896 | ||||||||
\(61\) | −1.56088e15 | −1.04247 | −0.521237 | − | 0.853412i | \(-0.674529\pi\) | ||||
−0.521237 | + | 0.853412i | \(0.674529\pi\) | |||||||
\(62\) | −5.36978e15 | −3.12340 | ||||||||
\(63\) | −1.15142e14 | −0.0584572 | ||||||||
\(64\) | 9.19314e15 | 4.08258 | ||||||||
\(65\) | 1.09956e15 | 0.428013 | ||||||||
\(66\) | 4.54597e15 | 1.55419 | ||||||||
\(67\) | 1.31151e15 | 0.394581 | 0.197290 | − | 0.980345i | \(-0.436786\pi\) | ||||
0.197290 | + | 0.980345i | \(0.436786\pi\) | |||||||
\(68\) | 4.65689e15 | 1.23529 | ||||||||
\(69\) | 7.52195e14 | 0.176244 | ||||||||
\(70\) | 7.33981e14 | 0.152178 | ||||||||
\(71\) | −7.09230e15 | −1.30344 | −0.651720 | − | 0.758459i | \(-0.725952\pi\) | ||||
−0.651720 | + | 0.758459i | \(0.725952\pi\) | |||||||
\(72\) | −6.99526e15 | −1.14150 | ||||||||
\(73\) | −1.17619e16 | −1.70700 | −0.853501 | − | 0.521091i | \(-0.825525\pi\) | ||||
−0.853501 | + | 0.521091i | \(0.825525\pi\) | |||||||
\(74\) | −2.24078e15 | −0.289688 | ||||||||
\(75\) | 1.00113e15 | 0.115470 | ||||||||
\(76\) | −4.44160e16 | −4.57745 | ||||||||
\(77\) | 2.63826e15 | 0.243302 | ||||||||
\(78\) | −1.29737e16 | −1.07216 | ||||||||
\(79\) | −7.14674e15 | −0.530003 | −0.265001 | − | 0.964248i | \(-0.585372\pi\) | ||||
−0.265001 | + | 0.964248i | \(0.585372\pi\) | |||||||
\(80\) | 2.60369e16 | 1.73510 | ||||||||
\(81\) | 1.85302e15 | 0.111111 | ||||||||
\(82\) | 3.88566e15 | 0.209917 | ||||||||
\(83\) | 9.04707e15 | 0.440904 | 0.220452 | − | 0.975398i | \(-0.429247\pi\) | ||||
0.220452 | + | 0.975398i | \(0.429247\pi\) | |||||||
\(84\) | −6.35994e15 | −0.279949 | ||||||||
\(85\) | 5.01956e15 | 0.199804 | ||||||||
\(86\) | −1.70305e16 | −0.613749 | ||||||||
\(87\) | −3.21507e16 | −1.05021 | ||||||||
\(88\) | 1.60283e17 | 4.75100 | ||||||||
\(89\) | −1.16786e16 | −0.314467 | −0.157233 | − | 0.987561i | \(-0.550257\pi\) | ||||
−0.157233 | + | 0.987561i | \(0.550257\pi\) | |||||||
\(90\) | −1.18122e16 | −0.289248 | ||||||||
\(91\) | −7.52927e15 | −0.167842 | ||||||||
\(92\) | 4.15481e16 | 0.844023 | ||||||||
\(93\) | 5.01527e16 | 0.929371 | ||||||||
\(94\) | 4.08955e16 | 0.691972 | ||||||||
\(95\) | −4.78750e16 | −0.740386 | ||||||||
\(96\) | −1.67460e17 | −2.36922 | ||||||||
\(97\) | −8.32538e16 | −1.07856 | −0.539280 | − | 0.842126i | \(-0.681304\pi\) | ||||
−0.539280 | + | 0.842126i | \(0.681304\pi\) | |||||||
\(98\) | 1.58392e17 | 1.88066 | ||||||||
\(99\) | −4.24585e16 | −0.462450 | ||||||||
\(100\) | 5.52981e16 | 0.552981 | ||||||||
\(101\) | −1.36210e16 | −0.125164 | −0.0625818 | − | 0.998040i | \(-0.519933\pi\) | ||||
−0.0625818 | + | 0.998040i | \(0.519933\pi\) | |||||||
\(102\) | −5.92254e16 | −0.500503 | ||||||||
\(103\) | 1.19030e17 | 0.925847 | 0.462923 | − | 0.886398i | \(-0.346801\pi\) | ||||
0.462923 | + | 0.886398i | \(0.346801\pi\) | |||||||
\(104\) | −4.57429e17 | −3.27748 | ||||||||
\(105\) | −6.85524e15 | −0.0452808 | ||||||||
\(106\) | 4.53622e17 | 2.76436 | ||||||||
\(107\) | 3.05375e17 | 1.71819 | 0.859096 | − | 0.511814i | \(-0.171026\pi\) | ||||
0.859096 | + | 0.511814i | \(0.171026\pi\) | |||||||
\(108\) | 1.02353e17 | 0.532106 | ||||||||
\(109\) | −2.94297e17 | −1.41469 | −0.707344 | − | 0.706869i | \(-0.750107\pi\) | ||||
−0.707344 | + | 0.706869i | \(0.750107\pi\) | |||||||
\(110\) | 2.70655e17 | 1.20387 | ||||||||
\(111\) | 2.09285e16 | 0.0861970 | ||||||||
\(112\) | −1.78288e17 | −0.680407 | ||||||||
\(113\) | −7.25034e16 | −0.256562 | −0.128281 | − | 0.991738i | \(-0.540946\pi\) | ||||
−0.128281 | + | 0.991738i | \(0.540946\pi\) | |||||||
\(114\) | 5.64873e17 | 1.85464 | ||||||||
\(115\) | 4.47838e16 | 0.136518 | ||||||||
\(116\) | −1.77587e18 | −5.02942 | ||||||||
\(117\) | 1.21171e17 | 0.319022 | ||||||||
\(118\) | 7.33620e14 | 0.00179669 | ||||||||
\(119\) | −3.43715e16 | −0.0783519 | ||||||||
\(120\) | −4.16480e17 | −0.884205 | ||||||||
\(121\) | 4.67408e17 | 0.924742 | ||||||||
\(122\) | 1.09648e18 | 2.02275 | ||||||||
\(123\) | −3.62913e16 | −0.0624610 | ||||||||
\(124\) | 2.77022e18 | 4.45072 | ||||||||
\(125\) | 5.96046e16 | 0.0894427 | ||||||||
\(126\) | 8.08844e16 | 0.113427 | ||||||||
\(127\) | −1.00107e18 | −1.31261 | −0.656304 | − | 0.754497i | \(-0.727881\pi\) | ||||
−0.656304 | + | 0.754497i | \(0.727881\pi\) | |||||||
\(128\) | −3.11255e18 | −3.81797 | ||||||||
\(129\) | 1.59062e17 | 0.182622 | ||||||||
\(130\) | −7.72418e17 | −0.830489 | ||||||||
\(131\) | 6.36150e17 | 0.640846 | 0.320423 | − | 0.947275i | \(-0.396175\pi\) | ||||
0.320423 | + | 0.947275i | \(0.396175\pi\) | |||||||
\(132\) | −2.34522e18 | −2.21465 | ||||||||
\(133\) | 3.27825e17 | 0.290337 | ||||||||
\(134\) | −9.21306e17 | −0.765620 | ||||||||
\(135\) | 1.10324e17 | 0.0860663 | ||||||||
\(136\) | −2.08819e18 | −1.52999 | ||||||||
\(137\) | 2.75383e17 | 0.189588 | 0.0947942 | − | 0.995497i | \(-0.469781\pi\) | ||||
0.0947942 | + | 0.995497i | \(0.469781\pi\) | |||||||
\(138\) | −5.28400e17 | −0.341972 | ||||||||
\(139\) | 3.61048e17 | 0.219755 | 0.109878 | − | 0.993945i | \(-0.464954\pi\) | ||||
0.109878 | + | 0.993945i | \(0.464954\pi\) | |||||||
\(140\) | −3.78654e17 | −0.216848 | ||||||||
\(141\) | −3.81956e17 | −0.205897 | ||||||||
\(142\) | 4.98218e18 | 2.52911 | ||||||||
\(143\) | −2.77641e18 | −1.32779 | ||||||||
\(144\) | 2.86926e18 | 1.29327 | ||||||||
\(145\) | −1.91417e18 | −0.813490 | ||||||||
\(146\) | 8.26248e18 | 3.31216 | ||||||||
\(147\) | −1.47935e18 | −0.559594 | ||||||||
\(148\) | 1.15600e18 | 0.412794 | ||||||||
\(149\) | −4.02824e18 | −1.35841 | −0.679207 | − | 0.733947i | \(-0.737676\pi\) | ||||
−0.679207 | + | 0.733947i | \(0.737676\pi\) | |||||||
\(150\) | −7.03270e17 | −0.224051 | ||||||||
\(151\) | −3.02464e18 | −0.910689 | −0.455345 | − | 0.890315i | \(-0.650484\pi\) | ||||
−0.455345 | + | 0.890315i | \(0.650484\pi\) | |||||||
\(152\) | 1.99165e19 | 5.66947 | ||||||||
\(153\) | 5.53154e17 | 0.148925 | ||||||||
\(154\) | −1.85331e18 | −0.472088 | ||||||||
\(155\) | 2.98596e18 | 0.719888 | ||||||||
\(156\) | 6.69300e18 | 1.52778 | ||||||||
\(157\) | −3.80909e18 | −0.823520 | −0.411760 | − | 0.911292i | \(-0.635086\pi\) | ||||
−0.411760 | + | 0.911292i | \(0.635086\pi\) | |||||||
\(158\) | 5.02042e18 | 1.02838 | ||||||||
\(159\) | −4.23674e18 | −0.822539 | ||||||||
\(160\) | −9.97012e18 | −1.83519 | ||||||||
\(161\) | −3.06657e17 | −0.0535345 | ||||||||
\(162\) | −1.30170e18 | −0.215593 | ||||||||
\(163\) | −7.01276e18 | −1.10229 | −0.551143 | − | 0.834411i | \(-0.685808\pi\) | ||||
−0.551143 | + | 0.834411i | \(0.685808\pi\) | |||||||
\(164\) | −2.00458e18 | −0.299123 | ||||||||
\(165\) | −2.52787e18 | −0.358212 | ||||||||
\(166\) | −6.35535e18 | −0.855502 | ||||||||
\(167\) | −5.20936e18 | −0.666337 | −0.333169 | − | 0.942867i | \(-0.608118\pi\) | ||||
−0.333169 | + | 0.942867i | \(0.608118\pi\) | |||||||
\(168\) | 2.85185e18 | 0.346735 | ||||||||
\(169\) | −7.26857e17 | −0.0840256 | ||||||||
\(170\) | −3.52613e18 | −0.387688 | ||||||||
\(171\) | −5.27581e18 | −0.551851 | ||||||||
\(172\) | 8.78590e18 | 0.874570 | ||||||||
\(173\) | 4.55714e18 | 0.431818 | 0.215909 | − | 0.976413i | \(-0.430729\pi\) | ||||
0.215909 | + | 0.976413i | \(0.430729\pi\) | |||||||
\(174\) | 2.25851e19 | 2.03776 | ||||||||
\(175\) | −4.08143e17 | −0.0350743 | ||||||||
\(176\) | −6.57436e19 | −5.38264 | ||||||||
\(177\) | −6.85187e15 | −0.000534609 0 | ||||||||
\(178\) | 8.20393e18 | 0.610171 | ||||||||
\(179\) | 1.27111e19 | 0.901428 | 0.450714 | − | 0.892668i | \(-0.351169\pi\) | ||||
0.450714 | + | 0.892668i | \(0.351169\pi\) | |||||||
\(180\) | 6.09383e18 | 0.412168 | ||||||||
\(181\) | 1.67839e19 | 1.08299 | 0.541494 | − | 0.840704i | \(-0.317859\pi\) | ||||
0.541494 | + | 0.840704i | \(0.317859\pi\) | |||||||
\(182\) | 5.28914e18 | 0.325670 | ||||||||
\(183\) | −1.02409e19 | −0.601872 | ||||||||
\(184\) | −1.86305e19 | −1.04538 | ||||||||
\(185\) | 1.24603e18 | 0.0667679 | ||||||||
\(186\) | −3.52311e19 | −1.80329 | ||||||||
\(187\) | −1.26745e19 | −0.619835 | ||||||||
\(188\) | −2.10976e19 | −0.986034 | ||||||||
\(189\) | −7.55445e17 | −0.0337503 | ||||||||
\(190\) | 3.36311e19 | 1.43660 | ||||||||
\(191\) | 1.93607e19 | 0.790930 | 0.395465 | − | 0.918481i | \(-0.370583\pi\) | ||||
0.395465 | + | 0.918481i | \(0.370583\pi\) | |||||||
\(192\) | 6.03162e19 | 2.35708 | ||||||||
\(193\) | 5.41103e18 | 0.202322 | 0.101161 | − | 0.994870i | \(-0.467744\pi\) | ||||
0.101161 | + | 0.994870i | \(0.467744\pi\) | |||||||
\(194\) | 5.84839e19 | 2.09277 | ||||||||
\(195\) | 7.21423e18 | 0.247113 | ||||||||
\(196\) | −8.17129e19 | −2.67987 | ||||||||
\(197\) | 1.69857e19 | 0.533483 | 0.266741 | − | 0.963768i | \(-0.414053\pi\) | ||||
0.266741 | + | 0.963768i | \(0.414053\pi\) | |||||||
\(198\) | 2.98261e19 | 0.897309 | ||||||||
\(199\) | −8.38703e18 | −0.241745 | −0.120872 | − | 0.992668i | \(-0.538569\pi\) | ||||
−0.120872 | + | 0.992668i | \(0.538569\pi\) | |||||||
\(200\) | −2.47961e19 | −0.684902 | ||||||||
\(201\) | 8.60482e18 | 0.227811 | ||||||||
\(202\) | 9.56845e18 | 0.242860 | ||||||||
\(203\) | 1.31073e19 | 0.319004 | ||||||||
\(204\) | 3.05539e19 | 0.713197 | ||||||||
\(205\) | −2.16069e18 | −0.0483821 | ||||||||
\(206\) | −8.36156e19 | −1.79645 | ||||||||
\(207\) | 4.93515e18 | 0.101754 | ||||||||
\(208\) | 1.87624e20 | 3.71322 | ||||||||
\(209\) | 1.20885e20 | 2.29683 | ||||||||
\(210\) | 4.81565e18 | 0.0878599 | ||||||||
\(211\) | 2.60946e19 | 0.457245 | 0.228623 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228623 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(212\) | −2.34020e20 | −3.93910 | ||||||||
\(213\) | −4.65326e19 | −0.752542 | ||||||||
\(214\) | −2.14519e20 | −3.33387 | ||||||||
\(215\) | 9.47013e18 | 0.141459 | ||||||||
\(216\) | −4.58959e19 | −0.659048 | ||||||||
\(217\) | −2.04464e19 | −0.282299 | ||||||||
\(218\) | 2.06737e20 | 2.74497 | ||||||||
\(219\) | −7.71700e19 | −0.985539 | ||||||||
\(220\) | −1.39629e20 | −1.71546 | ||||||||
\(221\) | 3.61715e19 | 0.427594 | ||||||||
\(222\) | −1.47018e19 | −0.167251 | ||||||||
\(223\) | 1.19753e19 | 0.131128 | 0.0655641 | − | 0.997848i | \(-0.479115\pi\) | ||||
0.0655641 | + | 0.997848i | \(0.479115\pi\) | |||||||
\(224\) | 6.82705e19 | 0.719656 | ||||||||
\(225\) | 6.56841e18 | 0.0666667 | ||||||||
\(226\) | 5.09320e19 | 0.497816 | ||||||||
\(227\) | 1.24200e20 | 1.16924 | 0.584619 | − | 0.811308i | \(-0.301244\pi\) | ||||
0.584619 | + | 0.811308i | \(0.301244\pi\) | |||||||
\(228\) | −2.91413e20 | −2.64279 | ||||||||
\(229\) | 1.03099e20 | 0.900853 | 0.450426 | − | 0.892814i | \(-0.351272\pi\) | ||||
0.450426 | + | 0.892814i | \(0.351272\pi\) | |||||||
\(230\) | −3.14596e19 | −0.264890 | ||||||||
\(231\) | 1.73096e19 | 0.140470 | ||||||||
\(232\) | 7.96313e20 | 6.22925 | ||||||||
\(233\) | 1.13357e20 | 0.854919 | 0.427459 | − | 0.904035i | \(-0.359409\pi\) | ||||
0.427459 | + | 0.904035i | \(0.359409\pi\) | |||||||
\(234\) | −8.51201e19 | −0.619010 | ||||||||
\(235\) | −2.27407e19 | −0.159487 | ||||||||
\(236\) | −3.78468e17 | −0.00256022 | ||||||||
\(237\) | −4.68898e19 | −0.305997 | ||||||||
\(238\) | 2.41452e19 | 0.152029 | ||||||||
\(239\) | −8.29065e19 | −0.503740 | −0.251870 | − | 0.967761i | \(-0.581046\pi\) | ||||
−0.251870 | + | 0.967761i | \(0.581046\pi\) | |||||||
\(240\) | 1.70828e20 | 1.00176 | ||||||||
\(241\) | −1.62688e20 | −0.920896 | −0.460448 | − | 0.887687i | \(-0.652311\pi\) | ||||
−0.460448 | + | 0.887687i | \(0.652311\pi\) | |||||||
\(242\) | −3.28343e20 | −1.79431 | ||||||||
\(243\) | 1.21577e19 | 0.0641500 | ||||||||
\(244\) | −5.65664e20 | −2.88234 | ||||||||
\(245\) | −8.80765e19 | −0.433459 | ||||||||
\(246\) | 2.54938e19 | 0.121195 | ||||||||
\(247\) | −3.44992e20 | −1.58447 | ||||||||
\(248\) | −1.24219e21 | −5.51250 | ||||||||
\(249\) | 5.93578e19 | 0.254556 | ||||||||
\(250\) | −4.18709e19 | −0.173549 | ||||||||
\(251\) | 4.10409e20 | 1.64433 | 0.822167 | − | 0.569247i | \(-0.192765\pi\) | ||||
0.822167 | + | 0.569247i | \(0.192765\pi\) | |||||||
\(252\) | −4.17276e19 | −0.161629 | ||||||||
\(253\) | −1.13080e20 | −0.423507 | ||||||||
\(254\) | 7.03232e20 | 2.54690 | ||||||||
\(255\) | 3.29333e19 | 0.115357 | ||||||||
\(256\) | 9.81533e20 | 3.32556 | ||||||||
\(257\) | −1.69582e20 | −0.555839 | −0.277920 | − | 0.960604i | \(-0.589645\pi\) | ||||
−0.277920 | + | 0.960604i | \(0.589645\pi\) | |||||||
\(258\) | −1.11737e20 | −0.354348 | ||||||||
\(259\) | −8.53218e18 | −0.0261826 | ||||||||
\(260\) | 3.98484e20 | 1.18341 | ||||||||
\(261\) | −2.10941e20 | −0.606340 | ||||||||
\(262\) | −4.46881e20 | −1.24346 | ||||||||
\(263\) | −3.50624e20 | −0.944534 | −0.472267 | − | 0.881456i | \(-0.656564\pi\) | ||||
−0.472267 | + | 0.881456i | \(0.656564\pi\) | |||||||
\(264\) | 1.05162e21 | 2.74299 | ||||||||
\(265\) | −2.52245e20 | −0.637136 | ||||||||
\(266\) | −2.30289e20 | −0.563352 | ||||||||
\(267\) | −7.66231e19 | −0.181557 | ||||||||
\(268\) | 4.75294e20 | 1.09098 | ||||||||
\(269\) | 2.92843e20 | 0.651240 | 0.325620 | − | 0.945501i | \(-0.394427\pi\) | ||||
0.325620 | + | 0.945501i | \(0.394427\pi\) | |||||||
\(270\) | −7.75001e19 | −0.166998 | ||||||||
\(271\) | 5.64043e20 | 1.17780 | 0.588902 | − | 0.808204i | \(-0.299560\pi\) | ||||
0.588902 | + | 0.808204i | \(0.299560\pi\) | |||||||
\(272\) | 8.56515e20 | 1.73340 | ||||||||
\(273\) | −4.93995e19 | −0.0969037 | ||||||||
\(274\) | −1.93450e20 | −0.367865 | ||||||||
\(275\) | −1.50503e20 | −0.277470 | ||||||||
\(276\) | 2.72597e20 | 0.487297 | ||||||||
\(277\) | 7.92843e20 | 1.37439 | 0.687194 | − | 0.726474i | \(-0.258842\pi\) | ||||
0.687194 | + | 0.726474i | \(0.258842\pi\) | |||||||
\(278\) | −2.53628e20 | −0.426399 | ||||||||
\(279\) | 3.29052e20 | 0.536573 | ||||||||
\(280\) | 1.69792e20 | 0.268580 | ||||||||
\(281\) | −4.07531e20 | −0.625399 | −0.312700 | − | 0.949852i | \(-0.601233\pi\) | ||||
−0.312700 | + | 0.949852i | \(0.601233\pi\) | |||||||
\(282\) | 2.68315e20 | 0.399510 | ||||||||
\(283\) | 9.05800e20 | 1.30872 | 0.654362 | − | 0.756182i | \(-0.272937\pi\) | ||||
0.654362 | + | 0.756182i | \(0.272937\pi\) | |||||||
\(284\) | −2.57026e21 | −3.60389 | ||||||||
\(285\) | −3.14108e20 | −0.427462 | ||||||||
\(286\) | 1.95037e21 | 2.57635 | ||||||||
\(287\) | 1.47953e19 | 0.0189727 | ||||||||
\(288\) | −1.09870e21 | −1.36787 | ||||||||
\(289\) | −6.62116e20 | −0.800391 | ||||||||
\(290\) | 1.34466e21 | 1.57845 | ||||||||
\(291\) | −5.46228e20 | −0.622707 | ||||||||
\(292\) | −4.26254e21 | −4.71970 | ||||||||
\(293\) | 1.22920e21 | 1.32205 | 0.661025 | − | 0.750364i | \(-0.270122\pi\) | ||||
0.661025 | + | 0.750364i | \(0.270122\pi\) | |||||||
\(294\) | 1.03921e21 | 1.08580 | ||||||||
\(295\) | −4.07943e17 | −0.000414106 0 | ||||||||
\(296\) | −5.18359e20 | −0.511271 | ||||||||
\(297\) | −2.78570e20 | −0.266996 | ||||||||
\(298\) | 2.82974e21 | 2.63578 | ||||||||
\(299\) | 3.22716e20 | 0.292157 | ||||||||
\(300\) | 3.62811e20 | 0.319264 | ||||||||
\(301\) | −6.48468e19 | −0.0554719 | ||||||||
\(302\) | 2.12474e21 | 1.76704 | ||||||||
\(303\) | −8.93675e19 | −0.0722632 | ||||||||
\(304\) | −8.16918e21 | −6.42322 | ||||||||
\(305\) | −6.09717e20 | −0.466208 | ||||||||
\(306\) | −3.88578e20 | −0.288965 | ||||||||
\(307\) | −1.33769e21 | −0.967565 | −0.483783 | − | 0.875188i | \(-0.660738\pi\) | ||||
−0.483783 | + | 0.875188i | \(0.660738\pi\) | |||||||
\(308\) | 9.56108e20 | 0.672707 | ||||||||
\(309\) | 7.80954e20 | 0.534538 | ||||||||
\(310\) | −2.09757e21 | −1.39683 | ||||||||
\(311\) | −8.26556e19 | −0.0535561 | −0.0267781 | − | 0.999641i | \(-0.508525\pi\) | ||||
−0.0267781 | + | 0.999641i | \(0.508525\pi\) | |||||||
\(312\) | −3.00119e21 | −1.89226 | ||||||||
\(313\) | −2.88314e20 | −0.176905 | −0.0884523 | − | 0.996080i | \(-0.528192\pi\) | ||||
−0.0884523 | + | 0.996080i | \(0.528192\pi\) | |||||||
\(314\) | 2.67580e21 | 1.59791 | ||||||||
\(315\) | −4.49772e19 | −0.0261429 | ||||||||
\(316\) | −2.58999e21 | −1.46541 | ||||||||
\(317\) | −3.17162e21 | −1.74694 | −0.873468 | − | 0.486882i | \(-0.838134\pi\) | ||||
−0.873468 | + | 0.486882i | \(0.838134\pi\) | |||||||
\(318\) | 2.97621e21 | 1.59600 | ||||||||
\(319\) | 4.83331e21 | 2.52362 | ||||||||
\(320\) | 3.59107e21 | 1.82578 | ||||||||
\(321\) | 2.00357e21 | 0.991999 | ||||||||
\(322\) | 2.15420e20 | 0.103875 | ||||||||
\(323\) | −1.57491e21 | −0.739662 | ||||||||
\(324\) | 6.71538e20 | 0.307212 | ||||||||
\(325\) | 4.29517e20 | 0.191413 | ||||||||
\(326\) | 4.92630e21 | 2.13881 | ||||||||
\(327\) | −1.93088e21 | −0.816771 | ||||||||
\(328\) | 8.98868e20 | 0.370483 | ||||||||
\(329\) | 1.55717e20 | 0.0625419 | ||||||||
\(330\) | 1.77577e21 | 0.695053 | ||||||||
\(331\) | −1.58984e21 | −0.606478 | −0.303239 | − | 0.952915i | \(-0.598068\pi\) | ||||
−0.303239 | + | 0.952915i | \(0.598068\pi\) | |||||||
\(332\) | 3.27867e21 | 1.21906 | ||||||||
\(333\) | 1.37312e20 | 0.0497659 | ||||||||
\(334\) | 3.65945e21 | 1.29292 | ||||||||
\(335\) | 5.12309e20 | 0.176462 | ||||||||
\(336\) | −1.16975e21 | −0.392833 | ||||||||
\(337\) | −3.01551e20 | −0.0987432 | −0.0493716 | − | 0.998780i | \(-0.515722\pi\) | ||||
−0.0493716 | + | 0.998780i | \(0.515722\pi\) | |||||||
\(338\) | 5.10600e20 | 0.163038 | ||||||||
\(339\) | −4.75695e20 | −0.148126 | ||||||||
\(340\) | 1.81910e21 | 0.552440 | ||||||||
\(341\) | −7.53960e21 | −2.23324 | ||||||||
\(342\) | 3.70613e21 | 1.07078 | ||||||||
\(343\) | 1.22535e21 | 0.345350 | ||||||||
\(344\) | −3.93967e21 | −1.08321 | ||||||||
\(345\) | 2.93826e20 | 0.0788185 | ||||||||
\(346\) | −3.20129e21 | −0.837873 | ||||||||
\(347\) | −3.81902e21 | −0.975331 | −0.487665 | − | 0.873031i | \(-0.662151\pi\) | ||||
−0.487665 | + | 0.873031i | \(0.662151\pi\) | |||||||
\(348\) | −1.16515e22 | −2.90374 | ||||||||
\(349\) | −3.13624e20 | −0.0762769 | −0.0381384 | − | 0.999272i | \(-0.512143\pi\) | ||||
−0.0381384 | + | 0.999272i | \(0.512143\pi\) | |||||||
\(350\) | 2.86711e20 | 0.0680560 | ||||||||
\(351\) | 7.95006e20 | 0.184187 | ||||||||
\(352\) | 2.51747e22 | 5.69314 | ||||||||
\(353\) | −4.65586e21 | −1.02781 | −0.513907 | − | 0.857846i | \(-0.671802\pi\) | ||||
−0.513907 | + | 0.857846i | \(0.671802\pi\) | |||||||
\(354\) | 4.81328e18 | 0.00103732 | ||||||||
\(355\) | −2.77043e21 | −0.582916 | ||||||||
\(356\) | −4.23234e21 | −0.869471 | ||||||||
\(357\) | −2.25511e20 | −0.0452365 | ||||||||
\(358\) | −8.92923e21 | −1.74907 | ||||||||
\(359\) | 3.57780e21 | 0.684405 | 0.342203 | − | 0.939626i | \(-0.388827\pi\) | ||||
0.342203 | + | 0.939626i | \(0.388827\pi\) | |||||||
\(360\) | −2.73252e21 | −0.510496 | ||||||||
\(361\) | 9.54059e21 | 1.74086 | ||||||||
\(362\) | −1.17903e22 | −2.10136 | ||||||||
\(363\) | 3.06667e21 | 0.533900 | ||||||||
\(364\) | −2.72862e21 | −0.464068 | ||||||||
\(365\) | −4.59450e21 | −0.763395 | ||||||||
\(366\) | 7.19400e21 | 1.16783 | ||||||||
\(367\) | −5.72348e21 | −0.907818 | −0.453909 | − | 0.891048i | \(-0.649971\pi\) | ||||
−0.453909 | + | 0.891048i | \(0.649971\pi\) | |||||||
\(368\) | 7.64170e21 | 1.18436 | ||||||||
\(369\) | −2.38107e20 | −0.0360619 | ||||||||
\(370\) | −8.75305e20 | −0.129552 | ||||||||
\(371\) | 1.72725e21 | 0.249848 | ||||||||
\(372\) | 1.81754e22 | 2.56962 | ||||||||
\(373\) | 7.79326e21 | 1.07695 | 0.538473 | − | 0.842643i | \(-0.319001\pi\) | ||||
0.538473 | + | 0.842643i | \(0.319001\pi\) | |||||||
\(374\) | 8.90352e21 | 1.20269 | ||||||||
\(375\) | 3.91066e20 | 0.0516398 | ||||||||
\(376\) | 9.46034e21 | 1.22127 | ||||||||
\(377\) | −1.37937e22 | −1.74092 | ||||||||
\(378\) | 5.30683e20 | 0.0654869 | ||||||||
\(379\) | 4.41273e21 | 0.532444 | 0.266222 | − | 0.963912i | \(-0.414225\pi\) | ||||
0.266222 | + | 0.963912i | \(0.414225\pi\) | |||||||
\(380\) | −1.73500e22 | −2.04710 | ||||||||
\(381\) | −6.56805e21 | −0.757834 | ||||||||
\(382\) | −1.36005e22 | −1.53467 | ||||||||
\(383\) | 7.42094e21 | 0.818973 | 0.409486 | − | 0.912316i | \(-0.365708\pi\) | ||||
0.409486 | + | 0.912316i | \(0.365708\pi\) | |||||||
\(384\) | −2.04215e22 | −2.20430 | ||||||||
\(385\) | 1.03057e21 | 0.108808 | ||||||||
\(386\) | −3.80112e21 | −0.392572 | ||||||||
\(387\) | 1.04360e21 | 0.105437 | ||||||||
\(388\) | −3.01713e22 | −2.98212 | ||||||||
\(389\) | 4.44977e21 | 0.430295 | 0.215147 | − | 0.976582i | \(-0.430977\pi\) | ||||
0.215147 | + | 0.976582i | \(0.430977\pi\) | |||||||
\(390\) | −5.06783e21 | −0.479483 | ||||||||
\(391\) | 1.47322e21 | 0.136384 | ||||||||
\(392\) | 3.66407e22 | 3.31919 | ||||||||
\(393\) | 4.17378e21 | 0.369993 | ||||||||
\(394\) | −1.19321e22 | −1.03514 | ||||||||
\(395\) | −2.79170e21 | −0.237024 | ||||||||
\(396\) | −1.53870e22 | −1.27863 | ||||||||
\(397\) | −4.94222e20 | −0.0401979 | −0.0200989 | − | 0.999798i | \(-0.506398\pi\) | ||||
−0.0200989 | + | 0.999798i | \(0.506398\pi\) | |||||||
\(398\) | 5.89170e21 | 0.469066 | ||||||||
\(399\) | 2.15086e21 | 0.167626 | ||||||||
\(400\) | 1.01707e22 | 0.775960 | ||||||||
\(401\) | 2.49341e22 | 1.86237 | 0.931187 | − | 0.364542i | \(-0.118775\pi\) | ||||
0.931187 | + | 0.364542i | \(0.118775\pi\) | |||||||
\(402\) | −6.04469e21 | −0.442031 | ||||||||
\(403\) | 2.15171e22 | 1.54061 | ||||||||
\(404\) | −4.93628e21 | −0.346066 | ||||||||
\(405\) | 7.23836e20 | 0.0496904 | ||||||||
\(406\) | −9.20757e21 | −0.618976 | ||||||||
\(407\) | −3.14624e21 | −0.207128 | ||||||||
\(408\) | −1.37006e22 | −0.883340 | ||||||||
\(409\) | 7.82942e21 | 0.494404 | 0.247202 | − | 0.968964i | \(-0.420489\pi\) | ||||
0.247202 | + | 0.968964i | \(0.420489\pi\) | |||||||
\(410\) | 1.51783e21 | 0.0938775 | ||||||||
\(411\) | 1.80679e21 | 0.109459 | ||||||||
\(412\) | 4.31366e22 | 2.55988 | ||||||||
\(413\) | 2.79339e18 | 0.000162389 0 | ||||||||
\(414\) | −3.46683e21 | −0.197438 | ||||||||
\(415\) | 3.53401e21 | 0.197178 | ||||||||
\(416\) | −7.18457e22 | −3.92742 | ||||||||
\(417\) | 2.36884e21 | 0.126876 | ||||||||
\(418\) | −8.49191e22 | −4.45663 | ||||||||
\(419\) | −1.37314e20 | −0.00706150 | −0.00353075 | − | 0.999994i | \(-0.501124\pi\) | ||||
−0.00353075 | + | 0.999994i | \(0.501124\pi\) | |||||||
\(420\) | −2.48435e21 | −0.125197 | ||||||||
\(421\) | −1.84158e21 | −0.0909481 | −0.0454740 | − | 0.998966i | \(-0.514480\pi\) | ||||
−0.0454740 | + | 0.998966i | \(0.514480\pi\) | |||||||
\(422\) | −1.83308e22 | −0.887209 | ||||||||
\(423\) | −2.50601e21 | −0.118875 | ||||||||
\(424\) | 1.04936e23 | 4.87883 | ||||||||
\(425\) | 1.96077e21 | 0.0893552 | ||||||||
\(426\) | 3.26881e22 | 1.46018 | ||||||||
\(427\) | 4.17505e21 | 0.182820 | ||||||||
\(428\) | 1.10669e23 | 4.75064 | ||||||||
\(429\) | −1.82161e22 | −0.766597 | ||||||||
\(430\) | −6.65255e21 | −0.274477 | ||||||||
\(431\) | −3.30639e21 | −0.133751 | −0.0668756 | − | 0.997761i | \(-0.521303\pi\) | ||||
−0.0668756 | + | 0.997761i | \(0.521303\pi\) | |||||||
\(432\) | 1.88252e22 | 0.746668 | ||||||||
\(433\) | 1.49902e22 | 0.582990 | 0.291495 | − | 0.956572i | \(-0.405847\pi\) | ||||
0.291495 | + | 0.956572i | \(0.405847\pi\) | |||||||
\(434\) | 1.43631e22 | 0.547755 | ||||||||
\(435\) | −1.25589e22 | −0.469669 | ||||||||
\(436\) | −1.06654e23 | −3.91148 | ||||||||
\(437\) | −1.40511e22 | −0.505379 | ||||||||
\(438\) | 5.42102e22 | 1.91228 | ||||||||
\(439\) | 5.27352e22 | 1.82453 | 0.912267 | − | 0.409597i | \(-0.134331\pi\) | ||||
0.912267 | + | 0.409597i | \(0.134331\pi\) | |||||||
\(440\) | 6.26106e22 | 2.12471 | ||||||||
\(441\) | −9.70600e21 | −0.323082 | ||||||||
\(442\) | −2.54096e22 | −0.829676 | ||||||||
\(443\) | 2.21332e22 | 0.708944 | 0.354472 | − | 0.935067i | \(-0.384661\pi\) | ||||
0.354472 | + | 0.935067i | \(0.384661\pi\) | |||||||
\(444\) | 7.58452e21 | 0.238327 | ||||||||
\(445\) | −4.56194e21 | −0.140634 | ||||||||
\(446\) | −8.41239e21 | −0.254433 | ||||||||
\(447\) | −2.64293e22 | −0.784280 | ||||||||
\(448\) | −2.45899e22 | −0.715968 | ||||||||
\(449\) | 1.01171e22 | 0.289041 | 0.144521 | − | 0.989502i | \(-0.453836\pi\) | ||||
0.144521 | + | 0.989502i | \(0.453836\pi\) | |||||||
\(450\) | −4.61416e21 | −0.129356 | ||||||||
\(451\) | 5.45578e21 | 0.150091 | ||||||||
\(452\) | −2.62754e22 | −0.709369 | ||||||||
\(453\) | −1.98447e22 | −0.525787 | ||||||||
\(454\) | −8.72479e22 | −2.26872 | ||||||||
\(455\) | −2.94112e21 | −0.0750613 | ||||||||
\(456\) | 1.30672e23 | 3.27327 | ||||||||
\(457\) | −7.09706e22 | −1.74498 | −0.872490 | − | 0.488632i | \(-0.837496\pi\) | ||||
−0.872490 | + | 0.488632i | \(0.837496\pi\) | |||||||
\(458\) | −7.24248e22 | −1.74796 | ||||||||
\(459\) | 3.62924e21 | 0.0859821 | ||||||||
\(460\) | 1.62297e22 | 0.377459 | ||||||||
\(461\) | 1.09889e22 | 0.250899 | 0.125449 | − | 0.992100i | \(-0.459963\pi\) | ||||
0.125449 | + | 0.992100i | \(0.459963\pi\) | |||||||
\(462\) | −1.21596e22 | −0.272560 | ||||||||
\(463\) | 1.78028e22 | 0.391787 | 0.195893 | − | 0.980625i | \(-0.437239\pi\) | ||||
0.195893 | + | 0.980625i | \(0.437239\pi\) | |||||||
\(464\) | −3.26625e23 | −7.05743 | ||||||||
\(465\) | 1.95909e22 | 0.415628 | ||||||||
\(466\) | −7.96310e22 | −1.65883 | ||||||||
\(467\) | 7.82704e22 | 1.60105 | 0.800524 | − | 0.599301i | \(-0.204555\pi\) | ||||
0.800524 | + | 0.599301i | \(0.204555\pi\) | |||||||
\(468\) | 4.39127e22 | 0.882065 | ||||||||
\(469\) | −3.50804e21 | −0.0691983 | ||||||||
\(470\) | 1.59748e22 | 0.309459 | ||||||||
\(471\) | −2.49914e22 | −0.475459 | ||||||||
\(472\) | 1.69708e20 | 0.00317100 | ||||||||
\(473\) | −2.39122e22 | −0.438834 | ||||||||
\(474\) | 3.29390e22 | 0.593737 | ||||||||
\(475\) | −1.87012e22 | −0.331111 | ||||||||
\(476\) | −1.24563e22 | −0.216636 | ||||||||
\(477\) | −2.77973e22 | −0.474893 | ||||||||
\(478\) | 5.82399e22 | 0.977425 | ||||||||
\(479\) | −1.17366e23 | −1.93504 | −0.967522 | − | 0.252785i | \(-0.918653\pi\) | ||||
−0.967522 | + | 0.252785i | \(0.918653\pi\) | |||||||
\(480\) | −6.54140e22 | −1.05955 | ||||||||
\(481\) | 8.97899e21 | 0.142888 | ||||||||
\(482\) | 1.14285e23 | 1.78685 | ||||||||
\(483\) | −2.01198e21 | −0.0309081 | ||||||||
\(484\) | 1.69390e23 | 2.55683 | ||||||||
\(485\) | −3.25210e22 | −0.482347 | ||||||||
\(486\) | −8.54048e21 | −0.124473 | ||||||||
\(487\) | 4.40441e22 | 0.630800 | 0.315400 | − | 0.948959i | \(-0.397861\pi\) | ||||
0.315400 | + | 0.948959i | \(0.397861\pi\) | |||||||
\(488\) | 2.53648e23 | 3.56996 | ||||||||
\(489\) | −4.60107e22 | −0.636405 | ||||||||
\(490\) | 6.18717e22 | 0.841057 | ||||||||
\(491\) | −9.19512e21 | −0.122847 | −0.0614235 | − | 0.998112i | \(-0.519564\pi\) | ||||
−0.0614235 | + | 0.998112i | \(0.519564\pi\) | |||||||
\(492\) | −1.31520e22 | −0.172699 | ||||||||
\(493\) | −6.29689e22 | −0.812695 | ||||||||
\(494\) | 2.42349e23 | 3.07441 | ||||||||
\(495\) | −1.65853e22 | −0.206814 | ||||||||
\(496\) | 5.09511e23 | 6.24539 | ||||||||
\(497\) | 1.89705e22 | 0.228586 | ||||||||
\(498\) | −4.16975e22 | −0.493924 | ||||||||
\(499\) | −9.12259e22 | −1.06234 | −0.531170 | − | 0.847265i | \(-0.678247\pi\) | ||||
−0.531170 | + | 0.847265i | \(0.678247\pi\) | |||||||
\(500\) | 2.16008e22 | 0.247301 | ||||||||
\(501\) | −3.41786e22 | −0.384710 | ||||||||
\(502\) | −2.88303e23 | −3.19056 | ||||||||
\(503\) | −4.20493e22 | −0.457542 | −0.228771 | − | 0.973480i | \(-0.573471\pi\) | ||||
−0.228771 | + | 0.973480i | \(0.573471\pi\) | |||||||
\(504\) | 1.87110e22 | 0.200187 | ||||||||
\(505\) | −5.32071e21 | −0.0559749 | ||||||||
\(506\) | 7.94359e22 | 0.821746 | ||||||||
\(507\) | −4.76891e21 | −0.0485122 | ||||||||
\(508\) | −3.62791e23 | −3.62924 | ||||||||
\(509\) | 3.12071e22 | 0.307010 | 0.153505 | − | 0.988148i | \(-0.450944\pi\) | ||||
0.153505 | + | 0.988148i | \(0.450944\pi\) | |||||||
\(510\) | −2.31349e22 | −0.223832 | ||||||||
\(511\) | 3.14609e22 | 0.299360 | ||||||||
\(512\) | −2.81536e23 | −2.63475 | ||||||||
\(513\) | −3.46146e22 | −0.318612 | ||||||||
\(514\) | 1.19128e23 | 1.07852 | ||||||||
\(515\) | 4.64960e22 | 0.414051 | ||||||||
\(516\) | 5.76443e22 | 0.504933 | ||||||||
\(517\) | 5.74206e22 | 0.494764 | ||||||||
\(518\) | 5.99366e21 | 0.0508030 | ||||||||
\(519\) | 2.98994e22 | 0.249310 | ||||||||
\(520\) | −1.78683e23 | −1.46573 | ||||||||
\(521\) | −1.71736e23 | −1.38593 | −0.692965 | − | 0.720971i | \(-0.743696\pi\) | ||||
−0.692965 | + | 0.720971i | \(0.743696\pi\) | |||||||
\(522\) | 1.48181e23 | 1.17650 | ||||||||
\(523\) | −3.54202e22 | −0.276686 | −0.138343 | − | 0.990384i | \(-0.544178\pi\) | ||||
−0.138343 | + | 0.990384i | \(0.544178\pi\) | |||||||
\(524\) | 2.30542e23 | 1.77188 | ||||||||
\(525\) | −2.67783e21 | −0.0202502 | ||||||||
\(526\) | 2.46305e23 | 1.83271 | ||||||||
\(527\) | 9.82268e22 | 0.719184 | ||||||||
\(528\) | −4.31344e23 | −3.10767 | ||||||||
\(529\) | −1.27906e23 | −0.906815 | ||||||||
\(530\) | 1.77196e23 | 1.23626 | ||||||||
\(531\) | −4.49551e19 | −0.000308657 0 | ||||||||
\(532\) | 1.18804e23 | 0.802755 | ||||||||
\(533\) | −1.55701e22 | −0.103541 | ||||||||
\(534\) | 5.38260e22 | 0.352283 | ||||||||
\(535\) | 1.19287e23 | 0.768399 | ||||||||
\(536\) | −2.13126e23 | −1.35125 | ||||||||
\(537\) | 8.33973e22 | 0.520440 | ||||||||
\(538\) | −2.05716e23 | −1.26363 | ||||||||
\(539\) | 2.22395e23 | 1.34468 | ||||||||
\(540\) | 3.99816e22 | 0.237965 | ||||||||
\(541\) | −1.03474e23 | −0.606257 | −0.303128 | − | 0.952950i | \(-0.598031\pi\) | ||||
−0.303128 | + | 0.952950i | \(0.598031\pi\) | |||||||
\(542\) | −3.96227e23 | −2.28534 | ||||||||
\(543\) | 1.10119e23 | 0.625264 | ||||||||
\(544\) | −3.27979e23 | −1.83339 | ||||||||
\(545\) | −1.14960e23 | −0.632668 | ||||||||
\(546\) | 3.47020e22 | 0.188026 | ||||||||
\(547\) | 2.96616e23 | 1.58235 | 0.791176 | − | 0.611589i | \(-0.209469\pi\) | ||||
0.791176 | + | 0.611589i | \(0.209469\pi\) | |||||||
\(548\) | 9.97992e22 | 0.524194 | ||||||||
\(549\) | −6.71906e22 | −0.347491 | ||||||||
\(550\) | 1.05725e23 | 0.538385 | ||||||||
\(551\) | 6.00578e23 | 3.01149 | ||||||||
\(552\) | −1.22235e23 | −0.603548 | ||||||||
\(553\) | 1.91162e22 | 0.0929474 | ||||||||
\(554\) | −5.56954e23 | −2.66678 | ||||||||
\(555\) | 8.17518e21 | 0.0385485 | ||||||||
\(556\) | 1.30845e23 | 0.607603 | ||||||||
\(557\) | −5.46640e22 | −0.249996 | −0.124998 | − | 0.992157i | \(-0.539892\pi\) | ||||
−0.124998 | + | 0.992157i | \(0.539892\pi\) | |||||||
\(558\) | −2.31151e23 | −1.04113 | ||||||||
\(559\) | 6.82427e22 | 0.302730 | ||||||||
\(560\) | −6.96437e22 | −0.304287 | ||||||||
\(561\) | −8.31572e22 | −0.357862 | ||||||||
\(562\) | 2.86281e23 | 1.21349 | ||||||||
\(563\) | −1.18516e23 | −0.494829 | −0.247414 | − | 0.968910i | \(-0.579581\pi\) | ||||
−0.247414 | + | 0.968910i | \(0.579581\pi\) | |||||||
\(564\) | −1.38422e23 | −0.569287 | ||||||||
\(565\) | −2.83217e22 | −0.114738 | ||||||||
\(566\) | −6.36304e23 | −2.53936 | ||||||||
\(567\) | −4.95647e21 | −0.0194857 | ||||||||
\(568\) | 1.15253e24 | 4.46365 | ||||||||
\(569\) | −4.39785e23 | −1.67798 | −0.838988 | − | 0.544149i | \(-0.816853\pi\) | ||||
−0.838988 | + | 0.544149i | \(0.816853\pi\) | |||||||
\(570\) | 2.20654e23 | 0.829421 | ||||||||
\(571\) | −4.89721e22 | −0.181360 | −0.0906800 | − | 0.995880i | \(-0.528904\pi\) | ||||
−0.0906800 | + | 0.995880i | \(0.528904\pi\) | |||||||
\(572\) | −1.00618e24 | −3.67120 | ||||||||
\(573\) | 1.27026e23 | 0.456644 | ||||||||
\(574\) | −1.03934e22 | −0.0368134 | ||||||||
\(575\) | 1.74937e22 | 0.0610526 | ||||||||
\(576\) | 3.95735e23 | 1.36086 | ||||||||
\(577\) | 5.15333e23 | 1.74620 | 0.873099 | − | 0.487543i | \(-0.162107\pi\) | ||||
0.873099 | + | 0.487543i | \(0.162107\pi\) | |||||||
\(578\) | 4.65121e23 | 1.55303 | ||||||||
\(579\) | 3.55018e22 | 0.116811 | ||||||||
\(580\) | −6.93698e23 | −2.24922 | ||||||||
\(581\) | −2.41992e22 | −0.0773220 | ||||||||
\(582\) | 3.83713e23 | 1.20826 | ||||||||
\(583\) | 6.36922e23 | 1.97653 | ||||||||
\(584\) | 1.91136e24 | 5.84565 | ||||||||
\(585\) | 4.73326e22 | 0.142671 | ||||||||
\(586\) | −8.63485e23 | −2.56522 | ||||||||
\(587\) | −3.59992e22 | −0.105407 | −0.0527035 | − | 0.998610i | \(-0.516784\pi\) | ||||
−0.0527035 | + | 0.998610i | \(0.516784\pi\) | |||||||
\(588\) | −5.36118e23 | −1.54722 | ||||||||
\(589\) | −9.36857e23 | −2.66498 | ||||||||
\(590\) | 2.86570e20 | 0.000803506 0 | ||||||||
\(591\) | 1.11443e23 | 0.308006 | ||||||||
\(592\) | 2.12616e23 | 0.579245 | ||||||||
\(593\) | −3.67652e23 | −0.987351 | −0.493676 | − | 0.869646i | \(-0.664347\pi\) | ||||
−0.493676 | + | 0.869646i | \(0.664347\pi\) | |||||||
\(594\) | 1.95689e23 | 0.518062 | ||||||||
\(595\) | −1.34264e22 | −0.0350400 | ||||||||
\(596\) | −1.45984e24 | −3.75588 | ||||||||
\(597\) | −5.50273e22 | −0.139571 | ||||||||
\(598\) | −2.26701e23 | −0.566882 | ||||||||
\(599\) | −6.97132e23 | −1.71865 | −0.859324 | − | 0.511432i | \(-0.829115\pi\) | ||||
−0.859324 | + | 0.511432i | \(0.829115\pi\) | |||||||
\(600\) | −1.62687e23 | −0.395429 | ||||||||
\(601\) | 3.44330e23 | 0.825166 | 0.412583 | − | 0.910920i | \(-0.364627\pi\) | ||||
0.412583 | + | 0.910920i | \(0.364627\pi\) | |||||||
\(602\) | 4.55534e22 | 0.107634 | ||||||||
\(603\) | 5.64562e22 | 0.131527 | ||||||||
\(604\) | −1.09614e24 | −2.51797 | ||||||||
\(605\) | 1.82581e23 | 0.413557 | ||||||||
\(606\) | 6.27786e22 | 0.140215 | ||||||||
\(607\) | −3.08234e23 | −0.678855 | −0.339427 | − | 0.940632i | \(-0.610233\pi\) | ||||
−0.339427 | + | 0.940632i | \(0.610233\pi\) | |||||||
\(608\) | 3.12816e24 | 6.79374 | ||||||||
\(609\) | 8.59970e22 | 0.184177 | ||||||||
\(610\) | 4.28312e23 | 0.904601 | ||||||||
\(611\) | −1.63872e23 | −0.341313 | ||||||||
\(612\) | 2.00464e23 | 0.411765 | ||||||||
\(613\) | −4.35176e23 | −0.881558 | −0.440779 | − | 0.897616i | \(-0.645298\pi\) | ||||
−0.440779 | + | 0.897616i | \(0.645298\pi\) | |||||||
\(614\) | 9.39699e23 | 1.87740 | ||||||||
\(615\) | −1.41763e22 | −0.0279334 | ||||||||
\(616\) | −4.28727e23 | −0.833190 | ||||||||
\(617\) | 6.04231e23 | 1.15819 | 0.579094 | − | 0.815261i | \(-0.303406\pi\) | ||||
0.579094 | + | 0.815261i | \(0.303406\pi\) | |||||||
\(618\) | −5.48602e23 | −1.03718 | ||||||||
\(619\) | −3.33503e23 | −0.621913 | −0.310956 | − | 0.950424i | \(-0.600649\pi\) | ||||
−0.310956 | + | 0.950424i | \(0.600649\pi\) | |||||||
\(620\) | 1.08212e24 | 1.99042 | ||||||||
\(621\) | 3.23795e22 | 0.0587479 | ||||||||
\(622\) | 5.80637e22 | 0.103917 | ||||||||
\(623\) | 3.12379e22 | 0.0551485 | ||||||||
\(624\) | 1.23100e24 | 2.14383 | ||||||||
\(625\) | 2.32831e22 | 0.0400000 | ||||||||
\(626\) | 2.02534e23 | 0.343255 | ||||||||
\(627\) | 7.93128e23 | 1.32608 | ||||||||
\(628\) | −1.38042e24 | −2.27695 | ||||||||
\(629\) | 4.09896e22 | 0.0667026 | ||||||||
\(630\) | 3.15955e22 | 0.0507259 | ||||||||
\(631\) | 7.67831e23 | 1.21623 | 0.608116 | − | 0.793848i | \(-0.291926\pi\) | ||||
0.608116 | + | 0.793848i | \(0.291926\pi\) | |||||||
\(632\) | 1.16137e24 | 1.81500 | ||||||||
\(633\) | 1.71206e23 | 0.263991 | ||||||||
\(634\) | 2.22799e24 | 3.38964 | ||||||||
\(635\) | −3.91045e23 | −0.587016 | ||||||||
\(636\) | −1.53540e24 | −2.27424 | ||||||||
\(637\) | −6.34688e23 | −0.927631 | ||||||||
\(638\) | −3.39529e24 | −4.89667 | ||||||||
\(639\) | −3.05300e23 | −0.434480 | ||||||||
\(640\) | −1.21584e24 | −1.70745 | ||||||||
\(641\) | −1.34739e24 | −1.86724 | −0.933620 | − | 0.358264i | \(-0.883369\pi\) | ||||
−0.933620 | + | 0.358264i | \(0.883369\pi\) | |||||||
\(642\) | −1.40746e24 | −1.92481 | ||||||||
\(643\) | 1.07291e24 | 1.44800 | 0.723999 | − | 0.689801i | \(-0.242302\pi\) | ||||
0.723999 | + | 0.689801i | \(0.242302\pi\) | |||||||
\(644\) | −1.11133e23 | −0.148018 | ||||||||
\(645\) | 6.21335e22 | 0.0816711 | ||||||||
\(646\) | 1.10634e24 | 1.43519 | ||||||||
\(647\) | 2.56767e23 | 0.328740 | 0.164370 | − | 0.986399i | \(-0.447441\pi\) | ||||
0.164370 | + | 0.986399i | \(0.447441\pi\) | |||||||
\(648\) | −3.01123e23 | −0.380501 | ||||||||
\(649\) | 1.03006e21 | 0.00128465 | ||||||||
\(650\) | −3.01726e23 | −0.371406 | ||||||||
\(651\) | −1.34149e23 | −0.162985 | ||||||||
\(652\) | −2.54144e24 | −3.04772 | ||||||||
\(653\) | 9.55573e23 | 1.13110 | 0.565551 | − | 0.824713i | \(-0.308664\pi\) | ||||
0.565551 | + | 0.824713i | \(0.308664\pi\) | |||||||
\(654\) | 1.35640e24 | 1.58481 | ||||||||
\(655\) | 2.48496e23 | 0.286595 | ||||||||
\(656\) | −3.68690e23 | −0.419739 | ||||||||
\(657\) | −5.06312e23 | −0.569001 | ||||||||
\(658\) | −1.09388e23 | −0.121352 | ||||||||
\(659\) | −4.48249e23 | −0.490901 | −0.245450 | − | 0.969409i | \(-0.578936\pi\) | ||||
−0.245450 | + | 0.969409i | \(0.578936\pi\) | |||||||
\(660\) | −9.16103e23 | −0.990424 | ||||||||
\(661\) | 3.31071e23 | 0.353353 | 0.176677 | − | 0.984269i | \(-0.443465\pi\) | ||||
0.176677 | + | 0.984269i | \(0.443465\pi\) | |||||||
\(662\) | 1.11682e24 | 1.17677 | ||||||||
\(663\) | 2.37321e23 | 0.246872 | ||||||||
\(664\) | −1.47018e24 | −1.50988 | ||||||||
\(665\) | 1.28057e23 | 0.129843 | ||||||||
\(666\) | −9.64583e22 | −0.0965625 | ||||||||
\(667\) | −5.61799e23 | −0.555279 | ||||||||
\(668\) | −1.88788e24 | −1.84236 | ||||||||
\(669\) | 7.85701e22 | 0.0757069 | ||||||||
\(670\) | −3.59885e23 | −0.342396 | ||||||||
\(671\) | 1.53955e24 | 1.44628 | ||||||||
\(672\) | 4.47923e23 | 0.415494 | ||||||||
\(673\) | −9.61434e23 | −0.880626 | −0.440313 | − | 0.897844i | \(-0.645132\pi\) | ||||
−0.440313 | + | 0.897844i | \(0.645132\pi\) | |||||||
\(674\) | 2.11833e23 | 0.191595 | ||||||||
\(675\) | 4.30953e22 | 0.0384900 | ||||||||
\(676\) | −2.63414e23 | −0.232323 | ||||||||
\(677\) | 1.08092e24 | 0.941432 | 0.470716 | − | 0.882285i | \(-0.343996\pi\) | ||||
0.470716 | + | 0.882285i | \(0.343996\pi\) | |||||||
\(678\) | 3.34165e23 | 0.287414 | ||||||||
\(679\) | 2.22688e23 | 0.189149 | ||||||||
\(680\) | −8.15698e23 | −0.684232 | ||||||||
\(681\) | 8.14879e23 | 0.675060 | ||||||||
\(682\) | 5.29640e24 | 4.33325 | ||||||||
\(683\) | 4.56949e23 | 0.369226 | 0.184613 | − | 0.982811i | \(-0.440897\pi\) | ||||
0.184613 | + | 0.982811i | \(0.440897\pi\) | |||||||
\(684\) | −1.91196e24 | −1.52582 | ||||||||
\(685\) | 1.07571e23 | 0.0847865 | ||||||||
\(686\) | −8.60778e23 | −0.670095 | ||||||||
\(687\) | 6.76434e23 | 0.520107 | ||||||||
\(688\) | 1.61594e24 | 1.22722 | ||||||||
\(689\) | −1.81770e24 | −1.36351 | ||||||||
\(690\) | −2.06406e23 | −0.152934 | ||||||||
\(691\) | −1.38418e24 | −1.01305 | −0.506523 | − | 0.862226i | \(-0.669070\pi\) | ||||
−0.506523 | + | 0.862226i | \(0.669070\pi\) | |||||||
\(692\) | 1.65152e24 | 1.19394 | ||||||||
\(693\) | 1.13568e23 | 0.0811007 | ||||||||
\(694\) | 2.68278e24 | 1.89247 | ||||||||
\(695\) | 1.41035e23 | 0.0982776 | ||||||||
\(696\) | 5.22461e24 | 3.59646 | ||||||||
\(697\) | −7.10785e22 | −0.0483348 | ||||||||
\(698\) | 2.20314e23 | 0.148003 | ||||||||
\(699\) | 7.43739e23 | 0.493588 | ||||||||
\(700\) | −1.47912e23 | −0.0969772 | ||||||||
\(701\) | 9.18978e22 | 0.0595254 | 0.0297627 | − | 0.999557i | \(-0.490525\pi\) | ||||
0.0297627 | + | 0.999557i | \(0.490525\pi\) | |||||||
\(702\) | −5.58473e23 | −0.357385 | ||||||||
\(703\) | −3.90946e23 | −0.247170 | ||||||||
\(704\) | −9.06751e24 | −5.66396 | ||||||||
\(705\) | −1.49202e23 | −0.0920801 | ||||||||
\(706\) | 3.27063e24 | 1.99431 | ||||||||
\(707\) | 3.64336e22 | 0.0219501 | ||||||||
\(708\) | −2.48313e21 | −0.00147814 | ||||||||
\(709\) | −1.54021e24 | −0.905913 | −0.452956 | − | 0.891533i | \(-0.649631\pi\) | ||||
−0.452956 | + | 0.891533i | \(0.649631\pi\) | |||||||
\(710\) | 1.94616e24 | 1.13105 | ||||||||
\(711\) | −3.07644e23 | −0.176668 | ||||||||
\(712\) | 1.89781e24 | 1.07690 | ||||||||
\(713\) | 8.76365e23 | 0.491387 | ||||||||
\(714\) | 1.58417e23 | 0.0877740 | ||||||||
\(715\) | −1.08454e24 | −0.593804 | ||||||||
\(716\) | 4.60651e24 | 2.49236 | ||||||||
\(717\) | −5.43949e23 | −0.290834 | ||||||||
\(718\) | −2.51332e24 | −1.32798 | ||||||||
\(719\) | 3.23522e24 | 1.68931 | 0.844654 | − | 0.535313i | \(-0.179806\pi\) | ||||
0.844654 | + | 0.535313i | \(0.179806\pi\) | |||||||
\(720\) | 1.12080e24 | 0.578366 | ||||||||
\(721\) | −3.18382e23 | −0.162367 | ||||||||
\(722\) | −6.70204e24 | −3.37786 | ||||||||
\(723\) | −1.06740e24 | −0.531679 | ||||||||
\(724\) | 6.08250e24 | 2.99436 | ||||||||
\(725\) | −7.47722e23 | −0.363804 | ||||||||
\(726\) | −2.15426e24 | −1.03595 | ||||||||
\(727\) | −2.33512e24 | −1.10986 | −0.554929 | − | 0.831898i | \(-0.687255\pi\) | ||||
−0.554929 | + | 0.831898i | \(0.687255\pi\) | |||||||
\(728\) | 1.22354e24 | 0.574777 | ||||||||
\(729\) | 7.97664e22 | 0.0370370 | ||||||||
\(730\) | 3.22753e24 | 1.48124 | ||||||||
\(731\) | 3.11531e23 | 0.141320 | ||||||||
\(732\) | −3.71132e24 | −1.66412 | ||||||||
\(733\) | 1.81465e24 | 0.804282 | 0.402141 | − | 0.915578i | \(-0.368266\pi\) | ||||
0.402141 | + | 0.915578i | \(0.368266\pi\) | |||||||
\(734\) | 4.02061e24 | 1.76147 | ||||||||
\(735\) | −5.77870e23 | −0.250258 | ||||||||
\(736\) | −2.92618e24 | −1.25268 | ||||||||
\(737\) | −1.29359e24 | −0.547422 | ||||||||
\(738\) | 1.67265e23 | 0.0699722 | ||||||||
\(739\) | −1.21901e24 | −0.504114 | −0.252057 | − | 0.967712i | \(-0.581107\pi\) | ||||
−0.252057 | + | 0.967712i | \(0.581107\pi\) | |||||||
\(740\) | 4.51562e23 | 0.184607 | ||||||||
\(741\) | −2.26349e24 | −0.914797 | ||||||||
\(742\) | −1.21335e24 | −0.484790 | ||||||||
\(743\) | 4.70556e23 | 0.185869 | 0.0929344 | − | 0.995672i | \(-0.470375\pi\) | ||||
0.0929344 | + | 0.995672i | \(0.470375\pi\) | |||||||
\(744\) | −8.15001e24 | −3.18264 | ||||||||
\(745\) | −1.57353e24 | −0.607501 | ||||||||
\(746\) | −5.47458e24 | −2.08964 | ||||||||
\(747\) | 3.89447e23 | 0.146968 | ||||||||
\(748\) | −4.59325e24 | −1.71379 | ||||||||
\(749\) | −8.16820e23 | −0.301322 | ||||||||
\(750\) | −2.74715e23 | −0.100199 | ||||||||
\(751\) | −3.20027e24 | −1.15411 | −0.577056 | − | 0.816705i | \(-0.695798\pi\) | ||||
−0.577056 | + | 0.816705i | \(0.695798\pi\) | |||||||
\(752\) | −3.88036e24 | −1.38363 | ||||||||
\(753\) | 2.69269e24 | 0.949356 | ||||||||
\(754\) | 9.68975e24 | 3.37797 | ||||||||
\(755\) | −1.18150e24 | −0.407273 | ||||||||
\(756\) | −2.73775e23 | −0.0933164 | ||||||||
\(757\) | −5.33142e24 | −1.79692 | −0.898458 | − | 0.439060i | \(-0.855312\pi\) | ||||
−0.898458 | + | 0.439060i | \(0.855312\pi\) | |||||||
\(758\) | −3.09984e24 | −1.03312 | ||||||||
\(759\) | −7.41916e23 | −0.244512 | ||||||||
\(760\) | 7.77988e24 | 2.53546 | ||||||||
\(761\) | 3.19775e24 | 1.03057 | 0.515283 | − | 0.857020i | \(-0.327687\pi\) | ||||
0.515283 | + | 0.857020i | \(0.327687\pi\) | |||||||
\(762\) | 4.61390e24 | 1.47045 | ||||||||
\(763\) | 7.87188e23 | 0.248096 | ||||||||
\(764\) | 7.01636e24 | 2.18685 | ||||||||
\(765\) | 2.16076e23 | 0.0666014 | ||||||||
\(766\) | −5.21304e24 | −1.58908 | ||||||||
\(767\) | −2.93967e21 | −0.000886214 0 | ||||||||
\(768\) | 6.43984e24 | 1.92001 | ||||||||
\(769\) | −3.24975e24 | −0.958245 | −0.479122 | − | 0.877748i | \(-0.659045\pi\) | ||||
−0.479122 | + | 0.877748i | \(0.659045\pi\) | |||||||
\(770\) | −7.23950e23 | −0.211124 | ||||||||
\(771\) | −1.11263e24 | −0.320914 | ||||||||
\(772\) | 1.96097e24 | 0.559401 | ||||||||
\(773\) | 4.35391e24 | 1.22844 | 0.614220 | − | 0.789135i | \(-0.289471\pi\) | ||||
0.614220 | + | 0.789135i | \(0.289471\pi\) | |||||||
\(774\) | −7.33108e23 | −0.204583 | ||||||||
\(775\) | 1.16639e24 | 0.321944 | ||||||||
\(776\) | 1.35291e25 | 3.69354 | ||||||||
\(777\) | −5.59797e22 | −0.0151165 | ||||||||
\(778\) | −3.12586e24 | −0.834917 | ||||||||
\(779\) | 6.77925e23 | 0.179107 | ||||||||
\(780\) | 2.61445e24 | 0.683245 | ||||||||
\(781\) | 6.99538e24 | 1.80833 | ||||||||
\(782\) | −1.03490e24 | −0.264631 | ||||||||
\(783\) | −1.38398e24 | −0.350070 | ||||||||
\(784\) | −1.50290e25 | −3.76048 | ||||||||
\(785\) | −1.48792e24 | −0.368289 | ||||||||
\(786\) | −2.93199e24 | −0.717910 | ||||||||
\(787\) | 1.67282e24 | 0.405194 | 0.202597 | − | 0.979262i | \(-0.435062\pi\) | ||||
0.202597 | + | 0.979262i | \(0.435062\pi\) | |||||||
\(788\) | 6.15565e24 | 1.47503 | ||||||||
\(789\) | −2.30044e24 | −0.545327 | ||||||||
\(790\) | 1.96110e24 | 0.459907 | ||||||||
\(791\) | 1.93933e23 | 0.0449936 | ||||||||
\(792\) | 6.89966e24 | 1.58367 | ||||||||
\(793\) | −4.39368e24 | −0.997715 | ||||||||
\(794\) | 3.47180e23 | 0.0779974 | ||||||||
\(795\) | −1.65498e24 | −0.367850 | ||||||||
\(796\) | −3.03948e24 | −0.668402 | ||||||||
\(797\) | 9.07285e23 | 0.197400 | 0.0987002 | − | 0.995117i | \(-0.468532\pi\) | ||||
0.0987002 | + | 0.995117i | \(0.468532\pi\) | |||||||
\(798\) | −1.51093e24 | −0.325251 | ||||||||
\(799\) | −7.48082e23 | −0.159331 | ||||||||
\(800\) | −3.89458e24 | −0.820721 | ||||||||
\(801\) | −5.02724e23 | −0.104822 | ||||||||
\(802\) | −1.75156e25 | −3.61363 | ||||||||
\(803\) | 1.16012e25 | 2.36821 | ||||||||
\(804\) | 3.11840e24 | 0.629877 | ||||||||
\(805\) | −1.19788e23 | −0.0239413 | ||||||||
\(806\) | −1.51153e25 | −2.98929 | ||||||||
\(807\) | 1.92135e24 | 0.375994 | ||||||||
\(808\) | 2.21347e24 | 0.428624 | ||||||||
\(809\) | −9.92795e23 | −0.190238 | −0.0951189 | − | 0.995466i | \(-0.530323\pi\) | ||||
−0.0951189 | + | 0.995466i | \(0.530323\pi\) | |||||||
\(810\) | −5.08478e23 | −0.0964161 | ||||||||
\(811\) | 5.63576e24 | 1.05749 | 0.528744 | − | 0.848781i | \(-0.322663\pi\) | ||||
0.528744 | + | 0.848781i | \(0.322663\pi\) | |||||||
\(812\) | 4.75011e24 | 0.882017 | ||||||||
\(813\) | 3.70068e24 | 0.680006 | ||||||||
\(814\) | 2.21016e24 | 0.401898 | ||||||||
\(815\) | −2.73936e24 | −0.492957 | ||||||||
\(816\) | 5.61959e24 | 1.00078 | ||||||||
\(817\) | −2.97129e24 | −0.523670 | ||||||||
\(818\) | −5.49999e24 | −0.959310 | ||||||||
\(819\) | −3.24110e23 | −0.0559474 | ||||||||
\(820\) | −7.83038e23 | −0.133772 | ||||||||
\(821\) | −9.18781e24 | −1.55344 | −0.776721 | − | 0.629845i | \(-0.783118\pi\) | ||||
−0.776721 | + | 0.629845i | \(0.783118\pi\) | |||||||
\(822\) | −1.26923e24 | −0.212387 | ||||||||
\(823\) | 6.83078e24 | 1.13128 | 0.565642 | − | 0.824651i | \(-0.308628\pi\) | ||||
0.565642 | + | 0.824651i | \(0.308628\pi\) | |||||||
\(824\) | −1.93428e25 | −3.17057 | ||||||||
\(825\) | −9.87448e23 | −0.160197 | ||||||||
\(826\) | −1.96229e21 | −0.000315089 0 | ||||||||
\(827\) | −9.93808e24 | −1.57945 | −0.789724 | − | 0.613462i | \(-0.789776\pi\) | ||||
−0.789724 | + | 0.613462i | \(0.789776\pi\) | |||||||
\(828\) | 1.78851e24 | 0.281341 | ||||||||
\(829\) | 1.00372e25 | 1.56278 | 0.781391 | − | 0.624042i | \(-0.214511\pi\) | ||||
0.781391 | + | 0.624042i | \(0.214511\pi\) | |||||||
\(830\) | −2.48256e24 | −0.382592 | ||||||||
\(831\) | 5.20185e24 | 0.793503 | ||||||||
\(832\) | 2.58776e25 | 3.90729 | ||||||||
\(833\) | −2.89738e24 | −0.433035 | ||||||||
\(834\) | −1.66405e24 | −0.246182 | ||||||||
\(835\) | −2.03491e24 | −0.297995 | ||||||||
\(836\) | 4.38090e25 | 6.35053 | ||||||||
\(837\) | 2.15891e24 | 0.309790 | ||||||||
\(838\) | 9.64602e22 | 0.0137017 | ||||||||
\(839\) | 1.16269e25 | 1.63489 | 0.817446 | − | 0.576005i | \(-0.195389\pi\) | ||||
0.817446 | + | 0.576005i | \(0.195389\pi\) | |||||||
\(840\) | 1.11400e24 | 0.155065 | ||||||||
\(841\) | 1.67555e25 | 2.30883 | ||||||||
\(842\) | 1.29367e24 | 0.176470 | ||||||||
\(843\) | −2.67381e24 | −0.361074 | ||||||||
\(844\) | 9.45671e24 | 1.26424 | ||||||||
\(845\) | −2.83928e23 | −0.0375774 | ||||||||
\(846\) | 1.76042e24 | 0.230657 | ||||||||
\(847\) | −1.25023e24 | −0.162174 | ||||||||
\(848\) | −4.30419e25 | −5.52747 | ||||||||
\(849\) | 5.94296e24 | 0.755592 | ||||||||
\(850\) | −1.37739e24 | −0.173379 | ||||||||
\(851\) | 3.65703e23 | 0.0455750 | ||||||||
\(852\) | −1.68635e25 | −2.08071 | ||||||||
\(853\) | 1.09678e23 | 0.0133984 | 0.00669922 | − | 0.999978i | \(-0.497868\pi\) | ||||
0.00669922 | + | 0.999978i | \(0.497868\pi\) | |||||||
\(854\) | −2.93287e24 | −0.354733 | ||||||||
\(855\) | −2.06086e24 | −0.246795 | ||||||||
\(856\) | −4.96246e25 | −5.88397 | ||||||||
\(857\) | 1.52818e25 | 1.79406 | 0.897030 | − | 0.441970i | \(-0.145720\pi\) | ||||
0.897030 | + | 0.441970i | \(0.145720\pi\) | |||||||
\(858\) | 1.27964e25 | 1.48746 | ||||||||
\(859\) | −1.62639e25 | −1.87190 | −0.935951 | − | 0.352130i | \(-0.885457\pi\) | ||||
−0.935951 | + | 0.352130i | \(0.885457\pi\) | |||||||
\(860\) | 3.43199e24 | 0.391119 | ||||||||
\(861\) | 9.70723e22 | 0.0109539 | ||||||||
\(862\) | 2.32266e24 | 0.259522 | ||||||||
\(863\) | −8.64833e24 | −0.956842 | −0.478421 | − | 0.878130i | \(-0.658791\pi\) | ||||
−0.478421 | + | 0.878130i | \(0.658791\pi\) | |||||||
\(864\) | −7.20859e24 | −0.789739 | ||||||||
\(865\) | 1.78013e24 | 0.193115 | ||||||||
\(866\) | −1.05303e25 | −1.13120 | ||||||||
\(867\) | −4.34414e24 | −0.462106 | ||||||||
\(868\) | −7.40981e24 | −0.780530 | ||||||||
\(869\) | 7.04908e24 | 0.735299 | ||||||||
\(870\) | 8.82231e24 | 0.911316 | ||||||||
\(871\) | 3.69175e24 | 0.377640 | ||||||||
\(872\) | 4.78244e25 | 4.84462 | ||||||||
\(873\) | −3.58381e24 | −0.359520 | ||||||||
\(874\) | 9.87056e24 | 0.980606 | ||||||||
\(875\) | −1.59431e23 | −0.0156857 | ||||||||
\(876\) | −2.79665e25 | −2.72492 | ||||||||
\(877\) | 1.02051e25 | 0.984740 | 0.492370 | − | 0.870386i | \(-0.336131\pi\) | ||||
0.492370 | + | 0.870386i | \(0.336131\pi\) | |||||||
\(878\) | −3.70452e25 | −3.54021 | ||||||||
\(879\) | 8.06479e24 | 0.763286 | ||||||||
\(880\) | −2.56811e25 | −2.40719 | ||||||||
\(881\) | −9.18419e23 | −0.0852601 | −0.0426301 | − | 0.999091i | \(-0.513574\pi\) | ||||
−0.0426301 | + | 0.999091i | \(0.513574\pi\) | |||||||
\(882\) | 6.81824e24 | 0.626887 | ||||||||
\(883\) | 8.44090e24 | 0.768640 | 0.384320 | − | 0.923200i | \(-0.374436\pi\) | ||||
0.384320 | + | 0.923200i | \(0.374436\pi\) | |||||||
\(884\) | 1.31086e25 | 1.18226 | ||||||||
\(885\) | −2.67651e21 | −0.000239084 0 | ||||||||
\(886\) | −1.55480e25 | −1.37559 | ||||||||
\(887\) | −1.20407e25 | −1.05512 | −0.527558 | − | 0.849519i | \(-0.676892\pi\) | ||||
−0.527558 | + | 0.849519i | \(0.676892\pi\) | |||||||
\(888\) | −3.40096e24 | −0.295183 | ||||||||
\(889\) | 2.67768e24 | 0.230194 | ||||||||
\(890\) | 3.20466e24 | 0.272877 | ||||||||
\(891\) | −1.82770e24 | −0.154150 | ||||||||
\(892\) | 4.33988e24 | 0.362557 | ||||||||
\(893\) | 7.13498e24 | 0.590412 | ||||||||
\(894\) | 1.85660e25 | 1.52177 | ||||||||
\(895\) | 4.96526e24 | 0.403131 | ||||||||
\(896\) | 8.32548e24 | 0.669563 | ||||||||
\(897\) | 2.11734e24 | 0.168677 | ||||||||
\(898\) | −7.10700e24 | −0.560838 | ||||||||
\(899\) | −3.74580e25 | −2.92811 | ||||||||
\(900\) | 2.38040e24 | 0.184327 | ||||||||
\(901\) | −8.29789e24 | −0.636512 | ||||||||
\(902\) | −3.83256e24 | −0.291228 | ||||||||
\(903\) | −4.25460e23 | −0.0320267 | ||||||||
\(904\) | 1.17821e25 | 0.878599 | ||||||||
\(905\) | 6.55620e24 | 0.484327 | ||||||||
\(906\) | 1.39404e25 | 1.02020 | ||||||||
\(907\) | −2.51467e25 | −1.82314 | −0.911568 | − | 0.411150i | \(-0.865127\pi\) | ||||
−0.911568 | + | 0.411150i | \(0.865127\pi\) | |||||||
\(908\) | 4.50104e25 | 3.23284 | ||||||||
\(909\) | −5.86340e23 | −0.0417212 | ||||||||
\(910\) | 2.06607e24 | 0.145644 | ||||||||
\(911\) | −8.57548e24 | −0.598897 | −0.299448 | − | 0.954112i | \(-0.596803\pi\) | ||||
−0.299448 | + | 0.954112i | \(0.596803\pi\) | |||||||
\(912\) | −5.35980e25 | −3.70845 | ||||||||
\(913\) | −8.92343e24 | −0.611688 | ||||||||
\(914\) | 4.98552e25 | 3.38585 | ||||||||
\(915\) | −4.00036e24 | −0.269165 | ||||||||
\(916\) | 3.73633e25 | 2.49077 | ||||||||
\(917\) | −1.70158e24 | −0.112386 | ||||||||
\(918\) | −2.54946e24 | −0.166834 | ||||||||
\(919\) | 1.26569e25 | 0.820626 | 0.410313 | − | 0.911945i | \(-0.365419\pi\) | ||||
0.410313 | + | 0.911945i | \(0.365419\pi\) | |||||||
\(920\) | −7.27753e24 | −0.467507 | ||||||||
\(921\) | −8.77661e24 | −0.558624 | ||||||||
\(922\) | −7.71948e24 | −0.486828 | ||||||||
\(923\) | −1.99640e25 | −1.24748 | ||||||||
\(924\) | 6.27303e24 | 0.388388 | ||||||||
\(925\) | 4.86729e23 | 0.0298595 | ||||||||
\(926\) | −1.25060e25 | −0.760198 | ||||||||
\(927\) | 5.12384e24 | 0.308616 | ||||||||
\(928\) | 1.25072e26 | 7.46454 | ||||||||
\(929\) | −1.61298e25 | −0.953881 | −0.476941 | − | 0.878936i | \(-0.658254\pi\) | ||||
−0.476941 | + | 0.878936i | \(0.658254\pi\) | |||||||
\(930\) | −1.37622e25 | −0.806457 | ||||||||
\(931\) | 2.76343e25 | 1.60464 | ||||||||
\(932\) | 4.10810e25 | 2.36377 | ||||||||
\(933\) | −5.42304e23 | −0.0309206 | ||||||||
\(934\) | −5.49832e25 | −3.10657 | ||||||||
\(935\) | −4.95097e24 | −0.277199 | ||||||||
\(936\) | −1.96908e25 | −1.09249 | ||||||||
\(937\) | 2.27726e24 | 0.125206 | 0.0626032 | − | 0.998038i | \(-0.480060\pi\) | ||||
0.0626032 | + | 0.998038i | \(0.480060\pi\) | |||||||
\(938\) | 2.46432e24 | 0.134268 | ||||||||
\(939\) | −1.89163e24 | −0.102136 | ||||||||
\(940\) | −8.24126e24 | −0.440968 | ||||||||
\(941\) | −1.42919e25 | −0.757839 | −0.378919 | − | 0.925430i | \(-0.623704\pi\) | ||||
−0.378919 | + | 0.925430i | \(0.623704\pi\) | |||||||
\(942\) | 1.75559e25 | 0.922551 | ||||||||
\(943\) | −6.34151e23 | −0.0330251 | ||||||||
\(944\) | −6.96095e22 | −0.00359258 | ||||||||
\(945\) | −2.95096e23 | −0.0150936 | ||||||||
\(946\) | 1.67978e25 | 0.851486 | ||||||||
\(947\) | −1.82863e24 | −0.0918653 | −0.0459326 | − | 0.998945i | \(-0.514626\pi\) | ||||
−0.0459326 | + | 0.998945i | \(0.514626\pi\) | |||||||
\(948\) | −1.69929e25 | −0.846053 | ||||||||
\(949\) | −3.31084e25 | −1.63371 | ||||||||
\(950\) | 1.31372e25 | 0.642467 | ||||||||
\(951\) | −2.08090e25 | −1.00859 | ||||||||
\(952\) | 5.58550e24 | 0.268317 | ||||||||
\(953\) | 1.66599e25 | 0.793201 | 0.396601 | − | 0.917991i | \(-0.370190\pi\) | ||||
0.396601 | + | 0.917991i | \(0.370190\pi\) | |||||||
\(954\) | 1.95269e25 | 0.921452 | ||||||||
\(955\) | 7.56278e24 | 0.353715 | ||||||||
\(956\) | −3.00455e25 | −1.39279 | ||||||||
\(957\) | 3.17113e25 | 1.45701 | ||||||||
\(958\) | 8.24470e25 | 3.75464 | ||||||||
\(959\) | −7.36596e23 | −0.0332484 | ||||||||
\(960\) | 2.35610e25 | 1.05412 | ||||||||
\(961\) | 3.58816e25 | 1.59119 | ||||||||
\(962\) | −6.30753e24 | −0.277250 | ||||||||
\(963\) | 1.31454e25 | 0.572731 | ||||||||
\(964\) | −5.89584e25 | −2.54619 | ||||||||
\(965\) | 2.11368e24 | 0.0904810 | ||||||||
\(966\) | 1.41337e24 | 0.0599722 | ||||||||
\(967\) | −3.59794e25 | −1.51331 | −0.756657 | − | 0.653812i | \(-0.773169\pi\) | ||||
−0.756657 | + | 0.653812i | \(0.773169\pi\) | |||||||
\(968\) | −7.59556e25 | −3.16679 | ||||||||
\(969\) | −1.03330e25 | −0.427044 | ||||||||
\(970\) | 2.28453e25 | 0.935915 | ||||||||
\(971\) | −2.68946e25 | −1.09220 | −0.546099 | − | 0.837721i | \(-0.683888\pi\) | ||||
−0.546099 | + | 0.837721i | \(0.683888\pi\) | |||||||
\(972\) | 4.40596e24 | 0.177369 | ||||||||
\(973\) | −9.65735e23 | −0.0385389 | ||||||||
\(974\) | −3.09400e25 | −1.22396 | ||||||||
\(975\) | 2.81806e24 | 0.110512 | ||||||||
\(976\) | −1.04039e26 | −4.04459 | ||||||||
\(977\) | 1.26185e25 | 0.486301 | 0.243151 | − | 0.969989i | \(-0.421819\pi\) | ||||
0.243151 | + | 0.969989i | \(0.421819\pi\) | |||||||
\(978\) | 3.23215e25 | 1.23484 | ||||||||
\(979\) | 1.15190e25 | 0.436276 | ||||||||
\(980\) | −3.19191e25 | −1.19847 | ||||||||
\(981\) | −1.26685e25 | −0.471563 | ||||||||
\(982\) | 6.45936e24 | 0.238365 | ||||||||
\(983\) | −2.72481e25 | −0.996852 | −0.498426 | − | 0.866932i | \(-0.666088\pi\) | ||||
−0.498426 | + | 0.866932i | \(0.666088\pi\) | |||||||
\(984\) | 5.89747e24 | 0.213898 | ||||||||
\(985\) | 6.63504e24 | 0.238581 | ||||||||
\(986\) | 4.42342e25 | 1.57690 | ||||||||
\(987\) | 1.02166e24 | 0.0361086 | ||||||||
\(988\) | −1.25026e26 | −4.38092 | ||||||||
\(989\) | 2.77944e24 | 0.0965580 | ||||||||
\(990\) | 1.16508e25 | 0.401289 | ||||||||
\(991\) | −2.34443e25 | −0.800593 | −0.400296 | − | 0.916386i | \(-0.631093\pi\) | ||||
−0.400296 | + | 0.916386i | \(0.631093\pi\) | |||||||
\(992\) | −1.95103e26 | −6.60565 | ||||||||
\(993\) | −1.04309e25 | −0.350150 | ||||||||
\(994\) | −1.33264e25 | −0.443535 | ||||||||
\(995\) | −3.27619e24 | −0.108112 | ||||||||
\(996\) | 2.15114e25 | 0.703823 | ||||||||
\(997\) | 5.52750e25 | 1.79316 | 0.896582 | − | 0.442877i | \(-0.146042\pi\) | ||||
0.896582 | + | 0.442877i | \(0.146042\pi\) | |||||||
\(998\) | 6.40841e25 | 2.06130 | ||||||||
\(999\) | 9.00902e23 | 0.0287323 |
(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 | 15.18.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 45.18.a.b.1.2 | 2 | |||
5.2 | odd | 4 | 75.18.b.b.49.1 | 4 | |||
5.3 | odd | 4 | 75.18.b.b.49.4 | 4 | |||
5.4 | even | 2 | 75.18.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.18.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
45.18.a.b.1.2 | 2 | 3.2 | odd | 2 | |||
75.18.a.c.1.2 | 2 | 5.4 | even | 2 | |||
75.18.b.b.49.1 | 4 | 5.2 | odd | 4 | |||
75.18.b.b.49.4 | 4 | 5.3 | odd | 4 |