Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.8 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.27 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 41.3871i | − | 1.29335i | −0.762767 | − | 0.646673i | \(-0.776160\pi\) | ||
0.762767 | − | 0.646673i | \(-0.223840\pi\) | |||||||
\(3\) | 57.8259i | 0.237967i | 0.992896 | + | 0.118983i | \(0.0379635\pi\) | ||||
−0.992896 | + | 0.118983i | \(0.962036\pi\) | |||||||
\(4\) | −688.891 | −0.672745 | ||||||||
\(5\) | − | 4608.97i | − | 1.47487i | −0.675418 | − | 0.737435i | \(-0.736037\pi\) | ||
0.675418 | − | 0.737435i | \(-0.263963\pi\) | |||||||
\(6\) | 2393.24 | 0.307773 | ||||||||
\(7\) | − | 16533.3i | − | 0.983718i | −0.870675 | − | 0.491859i | \(-0.836318\pi\) | ||
0.870675 | − | 0.491859i | \(-0.163682\pi\) | |||||||
\(8\) | − | 13869.2i | − | 0.423255i | ||||||
\(9\) | 55705.2 | 0.943372 | ||||||||
\(10\) | −190752. | −1.90752 | ||||||||
\(11\) | 223001. | 1.38466 | 0.692330 | − | 0.721581i | \(-0.256584\pi\) | ||||
0.692330 | + | 0.721581i | \(0.256584\pi\) | |||||||
\(12\) | − | 39835.7i | − | 0.160091i | ||||||
\(13\) | 652651. | 1.75778 | 0.878890 | − | 0.477025i | \(-0.158285\pi\) | ||||
0.878890 | + | 0.477025i | \(0.158285\pi\) | |||||||
\(14\) | −684267. | −1.27229 | ||||||||
\(15\) | 266518. | 0.350970 | ||||||||
\(16\) | −1.27943e6 | −1.22016 | ||||||||
\(17\) | −577282. | −0.406577 | −0.203289 | − | 0.979119i | \(-0.565163\pi\) | ||||
−0.203289 | + | 0.979119i | \(0.565163\pi\) | |||||||
\(18\) | − | 2.30547e6i | − | 1.22011i | ||||||
\(19\) | − | 2.34685e6i | − | 0.947801i | −0.880578 | − | 0.473900i | \(-0.842846\pi\) | ||
0.880578 | − | 0.473900i | \(-0.157154\pi\) | |||||||
\(20\) | 3.17508e6i | 0.992211i | ||||||||
\(21\) | 956055. | 0.234092 | ||||||||
\(22\) | − | 9.22936e6i | − | 1.79085i | ||||||
\(23\) | −4.51196e6 | −0.701013 | −0.350506 | − | 0.936560i | \(-0.613990\pi\) | ||||
−0.350506 | + | 0.936560i | \(0.613990\pi\) | |||||||
\(24\) | 801999. | 0.100720 | ||||||||
\(25\) | −1.14770e7 | −1.17524 | ||||||||
\(26\) | − | 2.70113e7i | − | 2.27342i | ||||||
\(27\) | 6.63576e6i | 0.462458i | ||||||||
\(28\) | 1.13897e7i | 0.661791i | ||||||||
\(29\) | 9.59476e6i | 0.467783i | 0.972263 | + | 0.233891i | \(0.0751460\pi\) | ||||
−0.972263 | + | 0.233891i | \(0.924854\pi\) | |||||||
\(30\) | − | 1.10304e7i | − | 0.453926i | ||||||
\(31\) | 9.38059e6 | 0.327659 | 0.163829 | − | 0.986489i | \(-0.447615\pi\) | ||||
0.163829 | + | 0.986489i | \(0.447615\pi\) | |||||||
\(32\) | 3.87498e7i | 1.15483i | ||||||||
\(33\) | 1.28952e7i | 0.329503i | ||||||||
\(34\) | 2.38920e7i | 0.525845i | ||||||||
\(35\) | −7.62017e7 | −1.45086 | ||||||||
\(36\) | −3.83748e7 | −0.634648 | ||||||||
\(37\) | 9.20205e7i | 1.32702i | 0.748170 | + | 0.663508i | \(0.230933\pi\) | ||||
−0.748170 | + | 0.663508i | \(0.769067\pi\) | |||||||
\(38\) | −9.71292e7 | −1.22583 | ||||||||
\(39\) | 3.77401e7i | 0.418293i | ||||||||
\(40\) | −6.39227e7 | −0.624246 | ||||||||
\(41\) | −5.46246e7 | −0.471486 | −0.235743 | − | 0.971815i | \(-0.575752\pi\) | ||||
−0.235743 | + | 0.971815i | \(0.575752\pi\) | |||||||
\(42\) | − | 3.95683e7i | − | 0.302762i | ||||||
\(43\) | 1.46513e8 | + | 1.20552e7i | 0.996632 | + | 0.0820032i | ||||
\(44\) | −1.53623e8 | −0.931523 | ||||||||
\(45\) | − | 2.56743e8i | − | 1.39135i | ||||||
\(46\) | 1.86737e8i | 0.906652i | ||||||||
\(47\) | −5.77200e7 | −0.251673 | −0.125837 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125837 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(48\) | − | 7.39842e7i | − | 0.290357i | ||||||
\(49\) | 9.12383e6 | 0.0322996 | ||||||||
\(50\) | 4.74999e8i | 1.52000i | ||||||||
\(51\) | − | 3.33818e7i | − | 0.0967518i | ||||||
\(52\) | −4.49605e8 | −1.18254 | ||||||||
\(53\) | −3.80772e8 | −0.910512 | −0.455256 | − | 0.890361i | \(-0.650452\pi\) | ||||
−0.455256 | + | 0.890361i | \(0.650452\pi\) | |||||||
\(54\) | 2.74635e8 | 0.598118 | ||||||||
\(55\) | − | 1.02780e9i | − | 2.04219i | ||||||
\(56\) | −2.29304e8 | −0.416363 | ||||||||
\(57\) | 1.35709e8 | 0.225545 | ||||||||
\(58\) | 3.97099e8 | 0.605005 | ||||||||
\(59\) | 5.64392e8 | 0.789443 | 0.394721 | − | 0.918801i | \(-0.370841\pi\) | ||||
0.394721 | + | 0.918801i | \(0.370841\pi\) | |||||||
\(60\) | −1.83602e8 | −0.236113 | ||||||||
\(61\) | 6.10423e8i | 0.722739i | 0.932423 | + | 0.361370i | \(0.117691\pi\) | ||||
−0.932423 | + | 0.361370i | \(0.882309\pi\) | |||||||
\(62\) | − | 3.88235e8i | − | 0.423776i | ||||||
\(63\) | − | 9.20993e8i | − | 0.928012i | ||||||
\(64\) | 2.93605e8 | 0.273441 | ||||||||
\(65\) | − | 3.00805e9i | − | 2.59250i | ||||||
\(66\) | 5.33696e8 | 0.426161 | ||||||||
\(67\) | −1.39619e9 | −1.03412 | −0.517061 | − | 0.855949i | \(-0.672974\pi\) | ||||
−0.517061 | + | 0.855949i | \(0.672974\pi\) | |||||||
\(68\) | 3.97684e8 | 0.273523 | ||||||||
\(69\) | − | 2.60908e8i | − | 0.166818i | ||||||
\(70\) | 3.15377e9i | 1.87646i | ||||||||
\(71\) | 2.86201e9i | 1.58628i | 0.609040 | + | 0.793139i | \(0.291555\pi\) | ||||
−0.609040 | + | 0.793139i | \(0.708445\pi\) | |||||||
\(72\) | − | 7.72586e8i | − | 0.399286i | ||||||
\(73\) | 2.78136e9i | 1.34166i | 0.741611 | + | 0.670830i | \(0.234062\pi\) | ||||
−0.741611 | + | 0.670830i | \(0.765938\pi\) | |||||||
\(74\) | 3.80846e9 | 1.71629 | ||||||||
\(75\) | − | 6.63667e8i | − | 0.279669i | ||||||
\(76\) | 1.61672e9i | 0.637628i | ||||||||
\(77\) | − | 3.68695e9i | − | 1.36211i | ||||||
\(78\) | 1.56195e9 | 0.540998 | ||||||||
\(79\) | 3.46213e9 | 1.12514 | 0.562572 | − | 0.826748i | \(-0.309812\pi\) | ||||
0.562572 | + | 0.826748i | \(0.309812\pi\) | |||||||
\(80\) | 5.89685e9i | 1.79958i | ||||||||
\(81\) | 2.90562e9 | 0.833322 | ||||||||
\(82\) | 2.26075e9i | 0.609795i | ||||||||
\(83\) | 3.22198e9 | 0.817960 | 0.408980 | − | 0.912543i | \(-0.365885\pi\) | ||||
0.408980 | + | 0.912543i | \(0.365885\pi\) | |||||||
\(84\) | −6.58617e8 | −0.157484 | ||||||||
\(85\) | 2.66067e9i | 0.599649i | ||||||||
\(86\) | 4.98928e8 | − | 6.06376e9i | 0.106059 | − | 1.28899i | ||||
\(87\) | −5.54826e8 | −0.111317 | ||||||||
\(88\) | − | 3.09285e9i | − | 0.586064i | ||||||
\(89\) | 7.71319e8i | 0.138129i | 0.997612 | + | 0.0690644i | \(0.0220014\pi\) | ||||
−0.997612 | + | 0.0690644i | \(0.977999\pi\) | |||||||
\(90\) | −1.06259e10 | −1.79950 | ||||||||
\(91\) | − | 1.07905e10i | − | 1.72916i | ||||||
\(92\) | 3.10824e9 | 0.471602 | ||||||||
\(93\) | 5.42441e8i | 0.0779719i | ||||||||
\(94\) | 2.38886e9i | 0.325500i | ||||||||
\(95\) | −1.08166e10 | −1.39788 | ||||||||
\(96\) | −2.24074e9 | −0.274812 | ||||||||
\(97\) | 9.01361e9 | 1.04964 | 0.524820 | − | 0.851213i | \(-0.324133\pi\) | ||||
0.524820 | + | 0.851213i | \(0.324133\pi\) | |||||||
\(98\) | − | 3.77609e8i | − | 0.0417745i | ||||||
\(99\) | 1.24223e10 | 1.30625 | ||||||||
\(100\) | 7.90638e9 | 0.790638 | ||||||||
\(101\) | −1.63722e10 | −1.55775 | −0.778877 | − | 0.627177i | \(-0.784210\pi\) | ||||
−0.778877 | + | 0.627177i | \(0.784210\pi\) | |||||||
\(102\) | −1.38158e9 | −0.125134 | ||||||||
\(103\) | 1.12194e10 | 0.967799 | 0.483899 | − | 0.875124i | \(-0.339220\pi\) | ||||
0.483899 | + | 0.875124i | \(0.339220\pi\) | |||||||
\(104\) | − | 9.05175e9i | − | 0.743988i | ||||||
\(105\) | − | 4.40643e9i | − | 0.345255i | ||||||
\(106\) | 1.57590e10i | 1.17761i | ||||||||
\(107\) | −1.42067e10 | −1.01292 | −0.506460 | − | 0.862263i | \(-0.669046\pi\) | ||||
−0.506460 | + | 0.862263i | \(0.669046\pi\) | |||||||
\(108\) | − | 4.57131e9i | − | 0.311116i | ||||||
\(109\) | −1.56200e10 | −1.01519 | −0.507596 | − | 0.861595i | \(-0.669466\pi\) | ||||
−0.507596 | + | 0.861595i | \(0.669466\pi\) | |||||||
\(110\) | −4.25378e10 | −2.64126 | ||||||||
\(111\) | −5.32117e9 | −0.315785 | ||||||||
\(112\) | 2.11533e10i | 1.20029i | ||||||||
\(113\) | − | 3.16782e10i | − | 1.71937i | −0.510826 | − | 0.859684i | \(-0.670660\pi\) | ||
0.510826 | − | 0.859684i | \(-0.329340\pi\) | |||||||
\(114\) | − | 5.61658e9i | − | 0.291708i | ||||||
\(115\) | 2.07955e10i | 1.03390i | ||||||||
\(116\) | − | 6.60974e9i | − | 0.314698i | ||||||
\(117\) | 3.63560e10 | 1.65824 | ||||||||
\(118\) | − | 2.33585e10i | − | 1.02102i | ||||||
\(119\) | 9.54439e9i | 0.399957i | ||||||||
\(120\) | − | 3.69639e9i | − | 0.148550i | ||||||
\(121\) | 2.37920e10 | 0.917284 | ||||||||
\(122\) | 2.52636e10 | 0.934752 | ||||||||
\(123\) | − | 3.15871e9i | − | 0.112198i | ||||||
\(124\) | −6.46220e9 | −0.220431 | ||||||||
\(125\) | 7.88758e9i | 0.258460i | ||||||||
\(126\) | −3.81172e10 | −1.20024 | ||||||||
\(127\) | −4.98671e9 | −0.150937 | −0.0754684 | − | 0.997148i | \(-0.524045\pi\) | ||||
−0.0754684 | + | 0.997148i | \(0.524045\pi\) | |||||||
\(128\) | 2.75283e10i | 0.801180i | ||||||||
\(129\) | −6.97101e8 | + | 8.47226e9i | −0.0195140 | + | 0.237165i | ||||
\(130\) | −1.24494e11 | −3.35300 | ||||||||
\(131\) | 4.98746e10i | 1.29277i | 0.763010 | + | 0.646387i | \(0.223721\pi\) | ||||
−0.763010 | + | 0.646387i | \(0.776279\pi\) | |||||||
\(132\) | − | 8.88340e9i | − | 0.221671i | ||||||
\(133\) | −3.88012e10 | −0.932368 | ||||||||
\(134\) | 5.77844e10i | 1.33748i | ||||||||
\(135\) | 3.05840e10 | 0.682065 | ||||||||
\(136\) | 8.00644e9i | 0.172086i | ||||||||
\(137\) | − | 1.51873e10i | − | 0.314686i | −0.987544 | − | 0.157343i | \(-0.949707\pi\) | ||
0.987544 | − | 0.157343i | \(-0.0502929\pi\) | |||||||
\(138\) | −1.07982e10 | −0.215753 | ||||||||
\(139\) | −2.60375e10 | −0.501794 | −0.250897 | − | 0.968014i | \(-0.580726\pi\) | ||||
−0.250897 | + | 0.968014i | \(0.580726\pi\) | |||||||
\(140\) | 5.24946e10 | 0.976056 | ||||||||
\(141\) | − | 3.33771e9i | − | 0.0598898i | ||||||
\(142\) | 1.18450e11 | 2.05161 | ||||||||
\(143\) | 1.45542e11 | 2.43393 | ||||||||
\(144\) | −7.12708e10 | −1.15106 | ||||||||
\(145\) | 4.42220e10 | 0.689919 | ||||||||
\(146\) | 1.15112e11 | 1.73523 | ||||||||
\(147\) | 5.27593e8i | 0.00768622i | ||||||||
\(148\) | − | 6.33920e10i | − | 0.892742i | ||||||
\(149\) | − | 9.55286e10i | − | 1.30078i | −0.759603 | − | 0.650388i | \(-0.774607\pi\) | ||
0.759603 | − | 0.650388i | \(-0.225393\pi\) | |||||||
\(150\) | −2.74672e10 | −0.361708 | ||||||||
\(151\) | 1.25033e11i | 1.59272i | 0.604824 | + | 0.796360i | \(0.293244\pi\) | ||||
−0.604824 | + | 0.796360i | \(0.706756\pi\) | |||||||
\(152\) | −3.25489e10 | −0.401161 | ||||||||
\(153\) | −3.21576e10 | −0.383554 | ||||||||
\(154\) | −1.52592e11 | −1.76169 | ||||||||
\(155\) | − | 4.32349e10i | − | 0.483254i | ||||||
\(156\) | − | 2.59988e10i | − | 0.281404i | ||||||
\(157\) | − | 9.09771e10i | − | 0.953748i | −0.878972 | − | 0.476874i | \(-0.841770\pi\) | ||
0.878972 | − | 0.476874i | \(-0.158230\pi\) | |||||||
\(158\) | − | 1.43288e11i | − | 1.45520i | ||||||
\(159\) | − | 2.20185e10i | − | 0.216671i | ||||||
\(160\) | 1.78597e11 | 1.70323 | ||||||||
\(161\) | 7.45977e10i | 0.689598i | ||||||||
\(162\) | − | 1.20255e11i | − | 1.07777i | ||||||
\(163\) | 1.78007e11i | 1.54703i | 0.633776 | + | 0.773517i | \(0.281504\pi\) | ||||
−0.633776 | + | 0.773517i | \(0.718496\pi\) | |||||||
\(164\) | 3.76303e10 | 0.317190 | ||||||||
\(165\) | 5.94337e10 | 0.485974 | ||||||||
\(166\) | − | 1.33348e11i | − | 1.05791i | ||||||
\(167\) | 5.39108e10 | 0.415043 | 0.207522 | − | 0.978230i | \(-0.433460\pi\) | ||||
0.207522 | + | 0.978230i | \(0.433460\pi\) | |||||||
\(168\) | − | 1.32597e10i | − | 0.0990805i | ||||||
\(169\) | 2.88095e11 | 2.08979 | ||||||||
\(170\) | 1.10118e11 | 0.775554 | ||||||||
\(171\) | − | 1.30732e11i | − | 0.894129i | ||||||
\(172\) | −1.00932e11 | − | 8.30469e9i | −0.670479 | − | 0.0551672i | ||||
\(173\) | −2.11497e11 | −1.36481 | −0.682407 | − | 0.730972i | \(-0.739067\pi\) | ||||
−0.682407 | + | 0.730972i | \(0.739067\pi\) | |||||||
\(174\) | 2.29626e10i | 0.143971i | ||||||||
\(175\) | 1.89753e11i | 1.15611i | ||||||||
\(176\) | −2.85314e11 | −1.68951 | ||||||||
\(177\) | 3.26365e10i | 0.187861i | ||||||||
\(178\) | 3.19227e10 | 0.178648 | ||||||||
\(179\) | 1.44297e10i | 0.0785220i | 0.999229 | + | 0.0392610i | \(0.0125004\pi\) | ||||
−0.999229 | + | 0.0392610i | \(0.987500\pi\) | |||||||
\(180\) | 1.76868e11i | 0.936024i | ||||||||
\(181\) | 2.16492e11 | 1.11442 | 0.557211 | − | 0.830371i | \(-0.311871\pi\) | ||||
0.557211 | + | 0.830371i | \(0.311871\pi\) | |||||||
\(182\) | −4.46588e11 | −2.23640 | ||||||||
\(183\) | −3.52983e10 | −0.171988 | ||||||||
\(184\) | 6.25773e10i | 0.296707i | ||||||||
\(185\) | 4.24120e11 | 1.95718 | ||||||||
\(186\) | 2.24501e10 | 0.100845 | ||||||||
\(187\) | −1.28734e11 | −0.562971 | ||||||||
\(188\) | 3.97627e10 | 0.169312 | ||||||||
\(189\) | 1.09711e11 | 0.454928 | ||||||||
\(190\) | 4.47666e11i | 1.80795i | ||||||||
\(191\) | 1.17486e11i | 0.462188i | 0.972931 | + | 0.231094i | \(0.0742305\pi\) | ||||
−0.972931 | + | 0.231094i | \(0.925769\pi\) | |||||||
\(192\) | 1.69780e10i | 0.0650698i | ||||||||
\(193\) | −3.90134e11 | −1.45689 | −0.728445 | − | 0.685104i | \(-0.759757\pi\) | ||||
−0.728445 | + | 0.685104i | \(0.759757\pi\) | |||||||
\(194\) | − | 3.73047e11i | − | 1.35755i | ||||||
\(195\) | 1.73943e11 | 0.616928 | ||||||||
\(196\) | −6.28532e9 | −0.0217294 | ||||||||
\(197\) | −1.50033e11 | −0.505658 | −0.252829 | − | 0.967511i | \(-0.581361\pi\) | ||||
−0.252829 | + | 0.967511i | \(0.581361\pi\) | |||||||
\(198\) | − | 5.14123e11i | − | 1.68943i | ||||||
\(199\) | 2.20399e11i | 0.706227i | 0.935581 | + | 0.353113i | \(0.114877\pi\) | ||||
−0.935581 | + | 0.353113i | \(0.885123\pi\) | |||||||
\(200\) | 1.59177e11i | 0.497427i | ||||||||
\(201\) | − | 8.07362e10i | − | 0.246087i | ||||||
\(202\) | 6.77596e11i | 2.01472i | ||||||||
\(203\) | 1.58634e11 | 0.460166 | ||||||||
\(204\) | 2.29964e10i | 0.0650893i | ||||||||
\(205\) | 2.51763e11i | 0.695381i | ||||||||
\(206\) | − | 4.64340e11i | − | 1.25170i | ||||||
\(207\) | −2.51339e11 | −0.661316 | ||||||||
\(208\) | −8.35021e11 | −2.14477 | ||||||||
\(209\) | − | 5.23349e11i | − | 1.31238i | ||||||
\(210\) | −1.82369e11 | −0.446535 | ||||||||
\(211\) | − | 1.56284e11i | − | 0.373682i | −0.982390 | − | 0.186841i | \(-0.940175\pi\) | ||
0.982390 | − | 0.186841i | \(-0.0598249\pi\) | |||||||
\(212\) | 2.62310e11 | 0.612542 | ||||||||
\(213\) | −1.65498e11 | −0.377481 | ||||||||
\(214\) | 5.87975e11i | 1.31006i | ||||||||
\(215\) | 5.55619e10 | − | 6.75276e11i | 0.120944 | − | 1.46990i | ||||
\(216\) | 9.20327e10 | 0.195737 | ||||||||
\(217\) | − | 1.55093e11i | − | 0.322324i | ||||||
\(218\) | 6.46466e11i | 1.31299i | ||||||||
\(219\) | −1.60835e11 | −0.319271 | ||||||||
\(220\) | 7.08045e11i | 1.37388i | ||||||||
\(221\) | −3.76764e11 | −0.714673 | ||||||||
\(222\) | 2.20228e11i | 0.408420i | ||||||||
\(223\) | − | 8.73734e11i | − | 1.58436i | −0.610285 | − | 0.792182i | \(-0.708945\pi\) | ||
0.610285 | − | 0.792182i | \(-0.291055\pi\) | |||||||
\(224\) | 6.40664e11 | 1.13603 | ||||||||
\(225\) | −6.39327e11 | −1.10869 | ||||||||
\(226\) | −1.31107e12 | −2.22374 | ||||||||
\(227\) | − | 1.30562e11i | − | 0.216614i | −0.994117 | − | 0.108307i | \(-0.965457\pi\) | ||
0.994117 | − | 0.108307i | \(-0.0345430\pi\) | |||||||
\(228\) | −9.34884e10 | −0.151734 | ||||||||
\(229\) | 5.94053e11 | 0.943295 | 0.471648 | − | 0.881787i | \(-0.343659\pi\) | ||||
0.471648 | + | 0.881787i | \(0.343659\pi\) | |||||||
\(230\) | 8.60664e11 | 1.33719 | ||||||||
\(231\) | 2.13201e11 | 0.324138 | ||||||||
\(232\) | 1.33072e11 | 0.197991 | ||||||||
\(233\) | − | 9.83403e11i | − | 1.43203i | −0.698085 | − | 0.716015i | \(-0.745964\pi\) | ||
0.698085 | − | 0.716015i | \(-0.254036\pi\) | |||||||
\(234\) | − | 1.50467e12i | − | 2.14468i | ||||||
\(235\) | 2.66030e11i | 0.371185i | ||||||||
\(236\) | −3.88804e11 | −0.531093 | ||||||||
\(237\) | 2.00201e11i | 0.267747i | ||||||||
\(238\) | 3.95015e11 | 0.517283 | ||||||||
\(239\) | 1.42825e12 | 1.83154 | 0.915769 | − | 0.401705i | \(-0.131582\pi\) | ||||
0.915769 | + | 0.401705i | \(0.131582\pi\) | |||||||
\(240\) | −3.40991e11 | −0.428239 | ||||||||
\(241\) | 1.07910e12i | 1.32732i | 0.748036 | + | 0.663658i | \(0.230997\pi\) | ||||
−0.748036 | + | 0.663658i | \(0.769003\pi\) | |||||||
\(242\) | − | 9.84681e11i | − | 1.18637i | ||||||
\(243\) | 5.59855e11i | 0.660761i | ||||||||
\(244\) | − | 4.20515e11i | − | 0.486219i | ||||||
\(245\) | − | 4.20514e10i | − | 0.0476377i | ||||||
\(246\) | −1.30730e11 | −0.145111 | ||||||||
\(247\) | − | 1.53167e12i | − | 1.66602i | ||||||
\(248\) | − | 1.30101e11i | − | 0.138683i | ||||||
\(249\) | 1.86314e11i | 0.194647i | ||||||||
\(250\) | 3.26444e11 | 0.334279 | ||||||||
\(251\) | −1.49606e11 | −0.150169 | −0.0750846 | − | 0.997177i | \(-0.523923\pi\) | ||||
−0.0750846 | + | 0.997177i | \(0.523923\pi\) | |||||||
\(252\) | 6.34463e11i | 0.624315i | ||||||||
\(253\) | −1.00617e12 | −0.970664 | ||||||||
\(254\) | 2.06385e11i | 0.195214i | ||||||||
\(255\) | −1.53856e11 | −0.142696 | ||||||||
\(256\) | 1.43997e12 | 1.30964 | ||||||||
\(257\) | 2.14576e12i | 1.91389i | 0.290273 | + | 0.956944i | \(0.406254\pi\) | ||||
−0.290273 | + | 0.956944i | \(0.593746\pi\) | |||||||
\(258\) | 3.50642e11 | + | 2.88510e10i | 0.306737 | + | 0.0252384i | ||||
\(259\) | 1.52141e12 | 1.30541 | ||||||||
\(260\) | 2.07222e12i | 1.74409i | ||||||||
\(261\) | 5.34478e11i | 0.441293i | ||||||||
\(262\) | 2.06416e12 | 1.67200 | ||||||||
\(263\) | − | 4.92321e11i | − | 0.391264i | −0.980677 | − | 0.195632i | \(-0.937324\pi\) | ||
0.980677 | − | 0.195632i | \(-0.0626758\pi\) | |||||||
\(264\) | 1.78847e11 | 0.139464 | ||||||||
\(265\) | 1.75497e12i | 1.34289i | ||||||||
\(266\) | 1.60587e12i | 1.20588i | ||||||||
\(267\) | −4.46022e10 | −0.0328700 | ||||||||
\(268\) | 9.61825e11 | 0.695700 | ||||||||
\(269\) | 2.36892e10 | 0.0168186 | 0.00840930 | − | 0.999965i | \(-0.497323\pi\) | ||||
0.00840930 | + | 0.999965i | \(0.497323\pi\) | |||||||
\(270\) | − | 1.26578e12i | − | 0.882146i | ||||||
\(271\) | −8.95184e11 | −0.612444 | −0.306222 | − | 0.951960i | \(-0.599065\pi\) | ||||
−0.306222 | + | 0.951960i | \(0.599065\pi\) | |||||||
\(272\) | 7.38591e11 | 0.496089 | ||||||||
\(273\) | 6.23971e11 | 0.411482 | ||||||||
\(274\) | −6.28558e11 | −0.406998 | ||||||||
\(275\) | −2.55938e12 | −1.62731 | ||||||||
\(276\) | 1.79737e11i | 0.112226i | ||||||||
\(277\) | − | 1.22921e12i | − | 0.753752i | −0.926264 | − | 0.376876i | \(-0.876998\pi\) | ||
0.926264 | − | 0.376876i | \(-0.123002\pi\) | |||||||
\(278\) | 1.07762e12i | 0.648994i | ||||||||
\(279\) | 5.22547e11 | 0.309104 | ||||||||
\(280\) | 1.05686e12i | 0.614081i | ||||||||
\(281\) | −1.42026e12 | −0.810653 | −0.405327 | − | 0.914172i | \(-0.632842\pi\) | ||||
−0.405327 | + | 0.914172i | \(0.632842\pi\) | |||||||
\(282\) | −1.38138e11 | −0.0774582 | ||||||||
\(283\) | 3.23709e11 | 0.178329 | 0.0891646 | − | 0.996017i | \(-0.471580\pi\) | ||||
0.0891646 | + | 0.996017i | \(0.471580\pi\) | |||||||
\(284\) | − | 1.97161e12i | − | 1.06716i | ||||||
\(285\) | − | 6.25477e11i | − | 0.332650i | ||||||
\(286\) | − | 6.02355e12i | − | 3.14791i | ||||||
\(287\) | 9.03127e11i | 0.463809i | ||||||||
\(288\) | 2.15856e12i | 1.08944i | ||||||||
\(289\) | −1.68274e12 | −0.834695 | ||||||||
\(290\) | − | 1.83022e12i | − | 0.892304i | ||||||
\(291\) | 5.21220e11i | 0.249779i | ||||||||
\(292\) | − | 1.91605e12i | − | 0.902595i | ||||||
\(293\) | 3.98890e12 | 1.84720 | 0.923602 | − | 0.383354i | \(-0.125231\pi\) | ||||
0.923602 | + | 0.383354i | \(0.125231\pi\) | |||||||
\(294\) | 2.18356e10 | 0.00994094 | ||||||||
\(295\) | − | 2.60126e12i | − | 1.16433i | ||||||
\(296\) | 1.27625e12 | 0.561665 | ||||||||
\(297\) | 1.47978e12i | 0.640347i | ||||||||
\(298\) | −3.95365e12 | −1.68235 | ||||||||
\(299\) | −2.94473e12 | −1.23223 | ||||||||
\(300\) | 4.57194e11i | 0.188146i | ||||||||
\(301\) | 1.99312e11 | − | 2.42236e12i | 0.0806680 | − | 0.980405i | ||||
\(302\) | 5.17474e12 | 2.05994 | ||||||||
\(303\) | − | 9.46734e11i | − | 0.370694i | ||||||
\(304\) | 3.00263e12i | 1.15647i | ||||||||
\(305\) | 2.81342e12 | 1.06595 | ||||||||
\(306\) | 1.33091e12i | 0.496068i | ||||||||
\(307\) | −4.96244e12 | −1.81972 | −0.909858 | − | 0.414920i | \(-0.863810\pi\) | ||||
−0.909858 | + | 0.414920i | \(0.863810\pi\) | |||||||
\(308\) | 2.53991e12i | 0.916355i | ||||||||
\(309\) | 6.48774e11i | 0.230304i | ||||||||
\(310\) | −1.78937e12 | −0.625015 | ||||||||
\(311\) | 1.69678e12 | 0.583209 | 0.291605 | − | 0.956539i | \(-0.405811\pi\) | ||||
0.291605 | + | 0.956539i | \(0.405811\pi\) | |||||||
\(312\) | 5.23426e11 | 0.177044 | ||||||||
\(313\) | − | 3.31526e12i | − | 1.10356i | −0.833990 | − | 0.551779i | \(-0.813949\pi\) | ||
0.833990 | − | 0.551779i | \(-0.186051\pi\) | |||||||
\(314\) | −3.76528e12 | −1.23353 | ||||||||
\(315\) | −4.24483e12 | −1.36870 | ||||||||
\(316\) | −2.38503e12 | −0.756935 | ||||||||
\(317\) | 3.73328e10 | 0.0116626 | 0.00583129 | − | 0.999983i | \(-0.498144\pi\) | ||||
0.00583129 | + | 0.999983i | \(0.498144\pi\) | |||||||
\(318\) | −9.11281e11 | −0.280231 | ||||||||
\(319\) | 2.13964e12i | 0.647720i | ||||||||
\(320\) | − | 1.35322e12i | − | 0.403290i | ||||||
\(321\) | − | 8.21517e11i | − | 0.241041i | ||||||
\(322\) | 3.08738e12 | 0.891890 | ||||||||
\(323\) | 1.35479e12i | 0.385354i | ||||||||
\(324\) | −2.00165e12 | −0.560613 | ||||||||
\(325\) | −7.49047e12 | −2.06582 | ||||||||
\(326\) | 7.36720e12 | 2.00085 | ||||||||
\(327\) | − | 9.03240e11i | − | 0.241582i | ||||||
\(328\) | 7.57599e11i | 0.199559i | ||||||||
\(329\) | 9.54304e11i | 0.247575i | ||||||||
\(330\) | − | 2.45979e12i | − | 0.628533i | ||||||
\(331\) | 2.77022e12i | 0.697228i | 0.937266 | + | 0.348614i | \(0.113348\pi\) | ||||
−0.937266 | + | 0.348614i | \(0.886652\pi\) | |||||||
\(332\) | −2.21959e12 | −0.550278 | ||||||||
\(333\) | 5.12602e12i | 1.25187i | ||||||||
\(334\) | − | 2.23121e12i | − | 0.536795i | ||||||
\(335\) | 6.43502e12i | 1.52520i | ||||||||
\(336\) | −1.22321e12 | −0.285630 | ||||||||
\(337\) | −3.25059e12 | −0.747846 | −0.373923 | − | 0.927460i | \(-0.621988\pi\) | ||||
−0.373923 | + | 0.927460i | \(0.621988\pi\) | |||||||
\(338\) | − | 1.19234e13i | − | 2.70282i | ||||||
\(339\) | 1.83182e12 | 0.409152 | ||||||||
\(340\) | − | 1.83291e12i | − | 0.403410i | ||||||
\(341\) | 2.09188e12 | 0.453696 | ||||||||
\(342\) | −5.41060e12 | −1.15642 | ||||||||
\(343\) | − | 4.82111e12i | − | 1.01549i | ||||||
\(344\) | 1.67196e11 | − | 2.03202e12i | 0.0347082 | − | 0.421829i | ||||
\(345\) | −1.20252e12 | −0.246034 | ||||||||
\(346\) | 8.75324e12i | 1.76518i | ||||||||
\(347\) | 8.79337e12i | 1.74787i | 0.486047 | + | 0.873933i | \(0.338438\pi\) | ||||
−0.486047 | + | 0.873933i | \(0.661562\pi\) | |||||||
\(348\) | 3.82214e11 | 0.0748877 | ||||||||
\(349\) | − | 1.71043e12i | − | 0.330353i | −0.986264 | − | 0.165177i | \(-0.947181\pi\) | ||
0.986264 | − | 0.165177i | \(-0.0528194\pi\) | |||||||
\(350\) | 7.85332e12 | 1.49525 | ||||||||
\(351\) | 4.33084e12i | 0.812899i | ||||||||
\(352\) | 8.64124e12i | 1.59905i | ||||||||
\(353\) | −1.03009e13 | −1.87932 | −0.939661 | − | 0.342106i | \(-0.888860\pi\) | ||||
−0.939661 | + | 0.342106i | \(0.888860\pi\) | |||||||
\(354\) | 1.35073e12 | 0.242969 | ||||||||
\(355\) | 1.31909e13 | 2.33956 | ||||||||
\(356\) | − | 5.31355e11i | − | 0.0929254i | ||||||
\(357\) | −5.51913e11 | −0.0951765 | ||||||||
\(358\) | 5.97202e11 | 0.101556 | ||||||||
\(359\) | 5.05095e12 | 0.847034 | 0.423517 | − | 0.905888i | \(-0.360795\pi\) | ||||
0.423517 | + | 0.905888i | \(0.360795\pi\) | |||||||
\(360\) | −3.56083e12 | −0.588896 | ||||||||
\(361\) | 6.23369e11 | 0.101674 | ||||||||
\(362\) | − | 8.95999e12i | − | 1.44133i | ||||||
\(363\) | 1.37579e12i | 0.218283i | ||||||||
\(364\) | 7.43348e12i | 1.16328i | ||||||||
\(365\) | 1.28192e13 | 1.97878 | ||||||||
\(366\) | 1.46089e12i | 0.222440i | ||||||||
\(367\) | −4.47428e12 | −0.672037 | −0.336018 | − | 0.941855i | \(-0.609080\pi\) | ||||
−0.336018 | + | 0.941855i | \(0.609080\pi\) | |||||||
\(368\) | 5.77273e12 | 0.855347 | ||||||||
\(369\) | −3.04287e12 | −0.444787 | ||||||||
\(370\) | − | 1.75531e13i | − | 2.53131i | ||||||
\(371\) | 6.29543e12i | 0.895687i | ||||||||
\(372\) | − | 3.73683e11i | − | 0.0524551i | ||||||
\(373\) | − | 8.44273e12i | − | 1.16933i | −0.811273 | − | 0.584667i | \(-0.801225\pi\) | ||
0.811273 | − | 0.584667i | \(-0.198775\pi\) | |||||||
\(374\) | 5.32794e12i | 0.728117i | ||||||||
\(375\) | −4.56107e11 | −0.0615049 | ||||||||
\(376\) | 8.00530e11i | 0.106522i | ||||||||
\(377\) | 6.26203e12i | 0.822259i | ||||||||
\(378\) | − | 4.54063e12i | − | 0.588379i | ||||||
\(379\) | 5.87700e12 | 0.751553 | 0.375777 | − | 0.926710i | \(-0.377376\pi\) | ||||
0.375777 | + | 0.926710i | \(0.377376\pi\) | |||||||
\(380\) | 7.45142e12 | 0.940418 | ||||||||
\(381\) | − | 2.88361e11i | − | 0.0359179i | ||||||
\(382\) | 4.86240e12 | 0.597769 | ||||||||
\(383\) | − | 1.11495e13i | − | 1.35288i | −0.736496 | − | 0.676442i | \(-0.763521\pi\) | ||
0.736496 | − | 0.676442i | \(-0.236479\pi\) | |||||||
\(384\) | −1.59185e12 | −0.190654 | ||||||||
\(385\) | −1.69930e13 | −2.00894 | ||||||||
\(386\) | 1.61465e13i | 1.88426i | ||||||||
\(387\) | 8.16155e12 | + | 6.71535e11i | 0.940195 | + | 0.0773596i | ||||
\(388\) | −6.20939e12 | −0.706139 | ||||||||
\(389\) | − | 1.73137e13i | − | 1.94375i | −0.235495 | − | 0.971876i | \(-0.575671\pi\) | ||
0.235495 | − | 0.971876i | \(-0.424329\pi\) | |||||||
\(390\) | − | 7.19900e12i | − | 0.797901i | ||||||
\(391\) | 2.60467e12 | 0.285016 | ||||||||
\(392\) | − | 1.26540e11i | − | 0.0136709i | ||||||
\(393\) | −2.88404e12 | −0.307637 | ||||||||
\(394\) | 6.20944e12i | 0.653991i | ||||||||
\(395\) | − | 1.59569e13i | − | 1.65944i | ||||||
\(396\) | −8.55761e12 | −0.878772 | ||||||||
\(397\) | −4.73758e12 | −0.480401 | −0.240201 | − | 0.970723i | \(-0.577213\pi\) | ||||
−0.240201 | + | 0.970723i | \(0.577213\pi\) | |||||||
\(398\) | 9.12167e12 | 0.913396 | ||||||||
\(399\) | − | 2.24372e12i | − | 0.221873i | ||||||
\(400\) | 1.46840e13 | 1.43398 | ||||||||
\(401\) | −7.21764e11 | −0.0696103 | −0.0348051 | − | 0.999394i | \(-0.511081\pi\) | ||||
−0.0348051 | + | 0.999394i | \(0.511081\pi\) | |||||||
\(402\) | −3.34143e12 | −0.318275 | ||||||||
\(403\) | 6.12226e12 | 0.575952 | ||||||||
\(404\) | 1.12786e13 | 1.04797 | ||||||||
\(405\) | − | 1.33919e13i | − | 1.22904i | ||||||
\(406\) | − | 6.56538e12i | − | 0.595154i | ||||||
\(407\) | 2.05207e13i | 1.83747i | ||||||||
\(408\) | −4.62979e11 | −0.0409506 | ||||||||
\(409\) | 5.76963e12i | 0.504117i | 0.967712 | + | 0.252059i | \(0.0811076\pi\) | ||||
−0.967712 | + | 0.252059i | \(0.918892\pi\) | |||||||
\(410\) | 1.04197e13 | 0.899368 | ||||||||
\(411\) | 8.78219e11 | 0.0748848 | ||||||||
\(412\) | −7.72897e12 | −0.651081 | ||||||||
\(413\) | − | 9.33128e12i | − | 0.776589i | ||||||
\(414\) | 1.04022e13i | 0.855310i | ||||||||
\(415\) | − | 1.48500e13i | − | 1.20638i | ||||||
\(416\) | 2.52901e13i | 2.02994i | ||||||||
\(417\) | − | 1.50564e12i | − | 0.119410i | ||||||
\(418\) | −2.16599e13 | −1.69736 | ||||||||
\(419\) | − | 1.13276e13i | − | 0.877138i | −0.898698 | − | 0.438569i | \(-0.855486\pi\) | ||
0.898698 | − | 0.438569i | \(-0.144514\pi\) | |||||||
\(420\) | 3.03555e12i | 0.232269i | ||||||||
\(421\) | − | 3.42831e12i | − | 0.259221i | −0.991565 | − | 0.129610i | \(-0.958627\pi\) | ||
0.991565 | − | 0.129610i | \(-0.0413727\pi\) | |||||||
\(422\) | −6.46814e12 | −0.483300 | ||||||||
\(423\) | −3.21530e12 | −0.237421 | ||||||||
\(424\) | 5.28100e12i | 0.385378i | ||||||||
\(425\) | 6.62545e12 | 0.477827 | ||||||||
\(426\) | 6.84949e12i | 0.488214i | ||||||||
\(427\) | 1.00923e13 | 0.710971 | ||||||||
\(428\) | 9.78689e12 | 0.681437 | ||||||||
\(429\) | 8.41609e12i | 0.579194i | ||||||||
\(430\) | −2.79477e13 | − | 2.29955e12i | −1.90109 | − | 0.156423i | ||||
\(431\) | −3.30836e11 | −0.0222447 | −0.0111223 | − | 0.999938i | \(-0.503540\pi\) | ||||
−0.0111223 | + | 0.999938i | \(0.503540\pi\) | |||||||
\(432\) | − | 8.48999e12i | − | 0.564272i | ||||||
\(433\) | 1.76261e13i | 1.15802i | 0.815320 | + | 0.579010i | \(0.196561\pi\) | ||||
−0.815320 | + | 0.579010i | \(0.803439\pi\) | |||||||
\(434\) | −6.41883e12 | −0.416876 | ||||||||
\(435\) | 2.55718e12i | 0.164178i | ||||||||
\(436\) | 1.07605e13 | 0.682965 | ||||||||
\(437\) | 1.05889e13i | 0.664420i | ||||||||
\(438\) | 6.65647e12i | 0.412927i | ||||||||
\(439\) | 1.04849e13 | 0.643047 | 0.321524 | − | 0.946902i | \(-0.395805\pi\) | ||||
0.321524 | + | 0.946902i | \(0.395805\pi\) | |||||||
\(440\) | −1.42548e13 | −0.864368 | ||||||||
\(441\) | 5.08244e11 | 0.0304705 | ||||||||
\(442\) | 1.55931e13i | 0.924320i | ||||||||
\(443\) | 2.43587e13 | 1.42770 | 0.713849 | − | 0.700300i | \(-0.246950\pi\) | ||||
0.713849 | + | 0.700300i | \(0.246950\pi\) | |||||||
\(444\) | 3.66570e12 | 0.212443 | ||||||||
\(445\) | 3.55499e12 | 0.203722 | ||||||||
\(446\) | −3.61613e13 | −2.04913 | ||||||||
\(447\) | 5.52403e12 | 0.309541 | ||||||||
\(448\) | − | 4.85427e12i | − | 0.268989i | ||||||
\(449\) | 1.91626e12i | 0.105008i | 0.998621 | + | 0.0525041i | \(0.0167202\pi\) | ||||
−0.998621 | + | 0.0525041i | \(0.983280\pi\) | |||||||
\(450\) | 2.64599e13i | 1.43392i | ||||||||
\(451\) | −1.21813e13 | −0.652848 | ||||||||
\(452\) | 2.18228e13i | 1.15670i | ||||||||
\(453\) | −7.23013e12 | −0.379014 | ||||||||
\(454\) | −5.40357e12 | −0.280157 | ||||||||
\(455\) | −4.97331e13 | −2.55029 | ||||||||
\(456\) | − | 1.88217e12i | − | 0.0954629i | ||||||
\(457\) | − | 2.13528e13i | − | 1.07121i | −0.844469 | − | 0.535604i | \(-0.820084\pi\) | ||
0.844469 | − | 0.535604i | \(-0.179916\pi\) | |||||||
\(458\) | − | 2.45861e13i | − | 1.22001i | ||||||
\(459\) | − | 3.83070e12i | − | 0.188025i | ||||||
\(460\) | − | 1.43258e13i | − | 0.695552i | ||||||
\(461\) | 2.01606e13 | 0.968275 | 0.484138 | − | 0.874992i | \(-0.339133\pi\) | ||||
0.484138 | + | 0.874992i | \(0.339133\pi\) | |||||||
\(462\) | − | 8.82378e12i | − | 0.419223i | ||||||
\(463\) | − | 2.86432e13i | − | 1.34622i | −0.739542 | − | 0.673110i | \(-0.764958\pi\) | ||
0.739542 | − | 0.673110i | \(-0.235042\pi\) | |||||||
\(464\) | − | 1.22758e13i | − | 0.570770i | ||||||
\(465\) | 2.50010e12 | 0.114998 | ||||||||
\(466\) | −4.07002e13 | −1.85211 | ||||||||
\(467\) | 1.24624e13i | 0.561070i | 0.959844 | + | 0.280535i | \(0.0905119\pi\) | ||||
−0.959844 | + | 0.280535i | \(0.909488\pi\) | |||||||
\(468\) | −2.50453e13 | −1.11557 | ||||||||
\(469\) | 2.30838e13i | 1.01728i | ||||||||
\(470\) | 1.10102e13 | 0.480071 | ||||||||
\(471\) | 5.26083e12 | 0.226960 | ||||||||
\(472\) | − | 7.82766e12i | − | 0.334135i | ||||||
\(473\) | 3.26726e13 | + | 2.68831e12i | 1.38000 | + | 0.113547i | ||||
\(474\) | 8.28573e12 | 0.346289 | ||||||||
\(475\) | 2.69347e13i | 1.11390i | ||||||||
\(476\) | − | 6.57504e12i | − | 0.269069i | ||||||
\(477\) | −2.12110e13 | −0.858951 | ||||||||
\(478\) | − | 5.91113e13i | − | 2.36881i | ||||||
\(479\) | −2.65412e13 | −1.05255 | −0.526275 | − | 0.850314i | \(-0.676412\pi\) | ||||
−0.526275 | + | 0.850314i | \(0.676412\pi\) | |||||||
\(480\) | 1.03275e13i | 0.405312i | ||||||||
\(481\) | 6.00573e13i | 2.33260i | ||||||||
\(482\) | 4.46606e13 | 1.71668 | ||||||||
\(483\) | −4.31368e12 | −0.164101 | ||||||||
\(484\) | −1.63901e13 | −0.617098 | ||||||||
\(485\) | − | 4.15435e13i | − | 1.54808i | ||||||
\(486\) | 2.31708e13 | 0.854592 | ||||||||
\(487\) | 4.21082e13 | 1.53717 | 0.768584 | − | 0.639749i | \(-0.220962\pi\) | ||||
0.768584 | + | 0.639749i | \(0.220962\pi\) | |||||||
\(488\) | 8.46608e12 | 0.305903 | ||||||||
\(489\) | −1.02934e13 | −0.368142 | ||||||||
\(490\) | −1.74039e12 | −0.0616120 | ||||||||
\(491\) | 2.85436e12i | 0.100023i | 0.998749 | + | 0.0500116i | \(0.0159258\pi\) | ||||
−0.998749 | + | 0.0500116i | \(0.984074\pi\) | |||||||
\(492\) | 2.17601e12i | 0.0754805i | ||||||||
\(493\) | − | 5.53888e12i | − | 0.190190i | ||||||
\(494\) | −6.33915e13 | −2.15475 | ||||||||
\(495\) | − | 5.72540e13i | − | 1.92655i | ||||||
\(496\) | −1.20018e13 | −0.399796 | ||||||||
\(497\) | 4.73186e13 | 1.56045 | ||||||||
\(498\) | 7.71098e12 | 0.251746 | ||||||||
\(499\) | 2.05715e12i | 0.0664909i | 0.999447 | + | 0.0332455i | \(0.0105843\pi\) | ||||
−0.999447 | + | 0.0332455i | \(0.989416\pi\) | |||||||
\(500\) | − | 5.43368e12i | − | 0.173878i | ||||||
\(501\) | 3.11744e12i | 0.0987665i | ||||||||
\(502\) | 6.19176e12i | 0.194221i | ||||||||
\(503\) | − | 1.19595e13i | − | 0.371428i | −0.982604 | − | 0.185714i | \(-0.940540\pi\) | ||
0.982604 | − | 0.185714i | \(-0.0594598\pi\) | |||||||
\(504\) | −1.27734e13 | −0.392785 | ||||||||
\(505\) | 7.54588e13i | 2.29749i | ||||||||
\(506\) | 4.16425e13i | 1.25541i | ||||||||
\(507\) | 1.66594e13i | 0.497300i | ||||||||
\(508\) | 3.43529e12 | 0.101542 | ||||||||
\(509\) | −3.54611e12 | −0.103792 | −0.0518960 | − | 0.998652i | \(-0.516526\pi\) | ||||
−0.0518960 | + | 0.998652i | \(0.516526\pi\) | |||||||
\(510\) | 6.36764e12i | 0.184556i | ||||||||
\(511\) | 4.59852e13 | 1.31982 | ||||||||
\(512\) | − | 3.14071e13i | − | 0.892643i | ||||||
\(513\) | 1.55731e13 | 0.438318 | ||||||||
\(514\) | 8.88069e13 | 2.47532 | ||||||||
\(515\) | − | 5.17101e13i | − | 1.42738i | ||||||
\(516\) | 4.80226e11 | − | 5.83646e12i | 0.0131280 | − | 0.159552i | ||||
\(517\) | −1.28716e13 | −0.348482 | ||||||||
\(518\) | − | 6.29666e13i | − | 1.68834i | ||||||
\(519\) | − | 1.22300e13i | − | 0.324780i | ||||||
\(520\) | −4.17193e13 | −1.09729 | ||||||||
\(521\) | 1.30995e13i | 0.341244i | 0.985337 | + | 0.170622i | \(0.0545777\pi\) | ||||
−0.985337 | + | 0.170622i | \(0.945422\pi\) | |||||||
\(522\) | 2.21205e13 | 0.570745 | ||||||||
\(523\) | − | 9.28471e12i | − | 0.237279i | −0.992937 | − | 0.118640i | \(-0.962147\pi\) | ||
0.992937 | − | 0.118640i | \(-0.0378533\pi\) | |||||||
\(524\) | − | 3.43581e13i | − | 0.869707i | ||||||
\(525\) | −1.09726e13 | −0.275115 | ||||||||
\(526\) | −2.03757e13 | −0.506040 | ||||||||
\(527\) | −5.41524e12 | −0.133219 | ||||||||
\(528\) | − | 1.64985e13i | − | 0.402046i | ||||||
\(529\) | −2.10688e13 | −0.508581 | ||||||||
\(530\) | 7.26330e13 | 1.73682 | ||||||||
\(531\) | 3.14395e13 | 0.744738 | ||||||||
\(532\) | 2.67298e13 | 0.627246 | ||||||||
\(533\) | −3.56508e13 | −0.828768 | ||||||||
\(534\) | 1.84596e12i | 0.0425124i | ||||||||
\(535\) | 6.54784e13i | 1.49393i | ||||||||
\(536\) | 1.93641e13i | 0.437697i | ||||||||
\(537\) | −8.34409e11 | −0.0186856 | ||||||||
\(538\) | − | 9.80428e11i | − | 0.0217523i | ||||||
\(539\) | 2.03462e12 | 0.0447239 | ||||||||
\(540\) | −2.10690e13 | −0.458856 | ||||||||
\(541\) | −4.80610e13 | −1.03707 | −0.518533 | − | 0.855057i | \(-0.673522\pi\) | ||||
−0.518533 | + | 0.855057i | \(0.673522\pi\) | |||||||
\(542\) | 3.70491e13i | 0.792102i | ||||||||
\(543\) | 1.25189e13i | 0.265195i | ||||||||
\(544\) | − | 2.23695e13i | − | 0.469529i | ||||||
\(545\) | 7.19920e13i | 1.49728i | ||||||||
\(546\) | − | 2.58243e13i | − | 0.532189i | ||||||
\(547\) | 9.25834e13 | 1.89059 | 0.945293 | − | 0.326223i | \(-0.105776\pi\) | ||||
0.945293 | + | 0.326223i | \(0.105776\pi\) | |||||||
\(548\) | 1.04624e13i | 0.211703i | ||||||||
\(549\) | 3.40037e13i | 0.681812i | ||||||||
\(550\) | 1.05925e14i | 2.10468i | ||||||||
\(551\) | 2.25175e13 | 0.443365 | ||||||||
\(552\) | −3.61859e12 | −0.0706063 | ||||||||
\(553\) | − | 5.72406e13i | − | 1.10682i | ||||||
\(554\) | −5.08736e13 | −0.974863 | ||||||||
\(555\) | 2.45251e13i | 0.465742i | ||||||||
\(556\) | 1.79370e13 | 0.337579 | ||||||||
\(557\) | −7.83003e13 | −1.46045 | −0.730226 | − | 0.683206i | \(-0.760585\pi\) | ||||
−0.730226 | + | 0.683206i | \(0.760585\pi\) | |||||||
\(558\) | − | 2.16267e13i | − | 0.399779i | ||||||
\(559\) | 9.56221e13 | + | 7.86782e12i | 1.75186 | + | 0.144144i | ||||
\(560\) | 9.74947e13 | 1.77028 | ||||||||
\(561\) | − | 7.44418e12i | − | 0.133968i | ||||||
\(562\) | 5.87803e13i | 1.04846i | ||||||||
\(563\) | 8.52093e13 | 1.50642 | 0.753208 | − | 0.657782i | \(-0.228505\pi\) | ||||
0.753208 | + | 0.657782i | \(0.228505\pi\) | |||||||
\(564\) | 2.29932e12i | 0.0402905i | ||||||||
\(565\) | −1.46004e14 | −2.53584 | ||||||||
\(566\) | − | 1.33974e13i | − | 0.230641i | ||||||
\(567\) | − | 4.80395e13i | − | 0.819754i | ||||||
\(568\) | 3.96938e13 | 0.671399 | ||||||||
\(569\) | −5.42162e13 | −0.909009 | −0.454504 | − | 0.890744i | \(-0.650184\pi\) | ||||
−0.454504 | + | 0.890744i | \(0.650184\pi\) | |||||||
\(570\) | −2.58867e13 | −0.430231 | ||||||||
\(571\) | 7.67443e13i | 1.26434i | 0.774828 | + | 0.632172i | \(0.217837\pi\) | ||||
−0.774828 | + | 0.632172i | \(0.782163\pi\) | |||||||
\(572\) | −1.00262e14 | −1.63741 | ||||||||
\(573\) | −6.79372e12 | −0.109985 | ||||||||
\(574\) | 3.73778e13 | 0.599866 | ||||||||
\(575\) | 5.17836e13 | 0.823860 | ||||||||
\(576\) | 1.63553e13 | 0.257957 | ||||||||
\(577\) | 1.18461e14i | 1.85223i | 0.377240 | + | 0.926115i | \(0.376873\pi\) | ||||
−0.377240 | + | 0.926115i | \(0.623127\pi\) | |||||||
\(578\) | 6.96437e13i | 1.07955i | ||||||||
\(579\) | − | 2.25598e13i | − | 0.346691i | ||||||
\(580\) | −3.04641e13 | −0.464139 | ||||||||
\(581\) | − | 5.32700e13i | − | 0.804641i | ||||||
\(582\) | 2.15718e13 | 0.323051 | ||||||||
\(583\) | −8.49125e13 | −1.26075 | ||||||||
\(584\) | 3.85752e13 | 0.567864 | ||||||||
\(585\) | − | 1.67564e14i | − | 2.44569i | ||||||
\(586\) | − | 1.65089e14i | − | 2.38907i | ||||||
\(587\) | − | 5.26291e13i | − | 0.755154i | −0.925978 | − | 0.377577i | \(-0.876757\pi\) | ||
0.925978 | − | 0.377577i | \(-0.123243\pi\) | |||||||
\(588\) | − | 3.63454e11i | − | 0.00517086i | ||||||
\(589\) | − | 2.20148e13i | − | 0.310555i | ||||||
\(590\) | −1.07659e14 | −1.50588 | ||||||||
\(591\) | − | 8.67582e12i | − | 0.120330i | ||||||
\(592\) | − | 1.17734e14i | − | 1.61917i | ||||||
\(593\) | − | 1.12040e14i | − | 1.52791i | −0.645267 | − | 0.763957i | \(-0.723254\pi\) | ||
0.645267 | − | 0.763957i | \(-0.276746\pi\) | |||||||
\(594\) | 6.12438e13 | 0.828190 | ||||||||
\(595\) | 4.39898e13 | 0.589885 | ||||||||
\(596\) | 6.58088e13i | 0.875089i | ||||||||
\(597\) | −1.27448e13 | −0.168058 | ||||||||
\(598\) | 1.21874e14i | 1.59369i | ||||||||
\(599\) | −2.65090e13 | −0.343764 | −0.171882 | − | 0.985118i | \(-0.554985\pi\) | ||||
−0.171882 | + | 0.985118i | \(0.554985\pi\) | |||||||
\(600\) | −9.20453e12 | −0.118371 | ||||||||
\(601\) | 5.75764e13i | 0.734298i | 0.930162 | + | 0.367149i | \(0.119666\pi\) | ||||
−0.930162 | + | 0.367149i | \(0.880334\pi\) | |||||||
\(602\) | −1.00254e14 | − | 8.24895e12i | −1.26800 | − | 0.104332i | ||||
\(603\) | −7.77752e13 | −0.975562 | ||||||||
\(604\) | − | 8.61339e13i | − | 1.07149i | ||||||
\(605\) | − | 1.09657e14i | − | 1.35288i | ||||||
\(606\) | −3.91826e13 | −0.479435 | ||||||||
\(607\) | 7.18754e13i | 0.872241i | 0.899888 | + | 0.436121i | \(0.143648\pi\) | ||||
−0.899888 | + | 0.436121i | \(0.856352\pi\) | |||||||
\(608\) | 9.09399e13 | 1.09455 | ||||||||
\(609\) | 9.17313e12i | 0.109504i | ||||||||
\(610\) | − | 1.16439e14i | − | 1.37864i | ||||||
\(611\) | −3.76710e13 | −0.442386 | ||||||||
\(612\) | 2.21530e13 | 0.258034 | ||||||||
\(613\) | −4.70443e13 | −0.543507 | −0.271753 | − | 0.962367i | \(-0.587603\pi\) | ||||
−0.271753 | + | 0.962367i | \(0.587603\pi\) | |||||||
\(614\) | 2.05381e14i | 2.35352i | ||||||||
\(615\) | −1.45584e13 | −0.165477 | ||||||||
\(616\) | −5.11351e13 | −0.576521 | ||||||||
\(617\) | −5.09966e13 | −0.570316 | −0.285158 | − | 0.958481i | \(-0.592046\pi\) | ||||
−0.285158 | + | 0.958481i | \(0.592046\pi\) | |||||||
\(618\) | 2.68509e13 | 0.297863 | ||||||||
\(619\) | −4.92566e13 | −0.542014 | −0.271007 | − | 0.962577i | \(-0.587357\pi\) | ||||
−0.271007 | + | 0.962577i | \(0.587357\pi\) | |||||||
\(620\) | 2.97841e13i | 0.325107i | ||||||||
\(621\) | − | 2.99403e13i | − | 0.324189i | ||||||
\(622\) | − | 7.02249e13i | − | 0.754292i | ||||||
\(623\) | 1.27525e13 | 0.135880 | ||||||||
\(624\) | − | 4.82859e13i | − | 0.510384i | ||||||
\(625\) | −7.57262e13 | −0.794047 | ||||||||
\(626\) | −1.37209e14 | −1.42728 | ||||||||
\(627\) | 3.02631e13 | 0.312303 | ||||||||
\(628\) | 6.26733e13i | 0.641629i | ||||||||
\(629\) | − | 5.31217e13i | − | 0.539534i | ||||||
\(630\) | 1.75681e14i | 1.77020i | ||||||||
\(631\) | 9.10936e13i | 0.910629i | 0.890331 | + | 0.455314i | \(0.150473\pi\) | ||||
−0.890331 | + | 0.455314i | \(0.849527\pi\) | |||||||
\(632\) | − | 4.80170e13i | − | 0.476223i | ||||||
\(633\) | 9.03726e12 | 0.0889238 | ||||||||
\(634\) | − | 1.54510e12i | − | 0.0150838i | ||||||
\(635\) | 2.29836e13i | 0.222612i | ||||||||
\(636\) | 1.51683e13i | 0.145765i | ||||||||
\(637\) | 5.95468e12 | 0.0567755 | ||||||||
\(638\) | 8.85535e13 | 0.837727 | ||||||||
\(639\) | 1.59429e14i | 1.49645i | ||||||||
\(640\) | 1.26877e14 | 1.18164 | ||||||||
\(641\) | 5.43369e13i | 0.502117i | 0.967972 | + | 0.251058i | \(0.0807786\pi\) | ||||
−0.967972 | + | 0.251058i | \(0.919221\pi\) | |||||||
\(642\) | −3.40002e13 | −0.311750 | ||||||||
\(643\) | −1.67473e14 | −1.52367 | −0.761835 | − | 0.647772i | \(-0.775701\pi\) | ||||
−0.761835 | + | 0.647772i | \(0.775701\pi\) | |||||||
\(644\) | − | 5.13897e13i | − | 0.463924i | ||||||
\(645\) | 3.90484e13 | + | 3.21292e12i | 0.349788 | + | 0.0287807i | ||||
\(646\) | 5.60709e13 | 0.498396 | ||||||||
\(647\) | − | 1.83630e14i | − | 1.61966i | −0.586667 | − | 0.809828i | \(-0.699560\pi\) | ||
0.586667 | − | 0.809828i | \(-0.300440\pi\) | |||||||
\(648\) | − | 4.02986e13i | − | 0.352707i | ||||||
\(649\) | 1.25860e14 | 1.09311 | ||||||||
\(650\) | 3.10008e14i | 2.67182i | ||||||||
\(651\) | 8.96837e12 | 0.0767023 | ||||||||
\(652\) | − | 1.22628e14i | − | 1.04076i | ||||||
\(653\) | − | 1.76238e14i | − | 1.48434i | −0.670210 | − | 0.742172i | \(-0.733796\pi\) | ||
0.670210 | − | 0.742172i | \(-0.266204\pi\) | |||||||
\(654\) | −3.73824e13 | −0.312449 | ||||||||
\(655\) | 2.29870e14 | 1.90667 | ||||||||
\(656\) | 6.98883e13 | 0.575288 | ||||||||
\(657\) | 1.54936e14i | 1.26569i | ||||||||
\(658\) | 3.94958e13 | 0.320200 | ||||||||
\(659\) | −1.92062e14 | −1.54531 | −0.772653 | − | 0.634829i | \(-0.781070\pi\) | ||||
−0.772653 | + | 0.634829i | \(0.781070\pi\) | |||||||
\(660\) | −4.09433e13 | −0.326937 | ||||||||
\(661\) | −8.62903e13 | −0.683841 | −0.341920 | − | 0.939729i | \(-0.611077\pi\) | ||||
−0.341920 | + | 0.939729i | \(0.611077\pi\) | |||||||
\(662\) | 1.14652e14 | 0.901758 | ||||||||
\(663\) | − | 2.17867e13i | − | 0.170068i | ||||||
\(664\) | − | 4.46862e13i | − | 0.346205i | ||||||
\(665\) | 1.78834e14i | 1.37512i | ||||||||
\(666\) | 2.12151e14 | 1.61910 | ||||||||
\(667\) | − | 4.32912e13i | − | 0.327922i | ||||||
\(668\) | −3.71387e13 | −0.279218 | ||||||||
\(669\) | 5.05245e13 | 0.377026 | ||||||||
\(670\) | 2.66327e14 | 1.97261 | ||||||||
\(671\) | 1.36125e14i | 1.00075i | ||||||||
\(672\) | 3.70470e13i | 0.270337i | ||||||||
\(673\) | − | 9.34892e13i | − | 0.677152i | −0.940939 | − | 0.338576i | \(-0.890055\pi\) | ||
0.940939 | − | 0.338576i | \(-0.109945\pi\) | |||||||
\(674\) | 1.34532e14i | 0.967224i | ||||||||
\(675\) | − | 7.61585e13i | − | 0.543500i | ||||||
\(676\) | −1.98466e14 | −1.40589 | ||||||||
\(677\) | − | 2.15946e13i | − | 0.151845i | −0.997114 | − | 0.0759227i | \(-0.975810\pi\) | ||
0.997114 | − | 0.0759227i | \(-0.0241902\pi\) | |||||||
\(678\) | − | 7.58138e13i | − | 0.529175i | ||||||
\(679\) | − | 1.49025e14i | − | 1.03255i | ||||||
\(680\) | 3.69014e13 | 0.253804 | ||||||||
\(681\) | 7.54985e12 | 0.0515469 | ||||||||
\(682\) | − | 8.65769e13i | − | 0.586786i | ||||||
\(683\) | 9.87064e13 | 0.664113 | 0.332056 | − | 0.943260i | \(-0.392258\pi\) | ||||
0.332056 | + | 0.943260i | \(0.392258\pi\) | |||||||
\(684\) | 9.00597e13i | 0.601520i | ||||||||
\(685\) | −6.99978e13 | −0.464121 | ||||||||
\(686\) | −1.99532e14 | −1.31338 | ||||||||
\(687\) | 3.43516e13i | 0.224473i | ||||||||
\(688\) | −1.87454e14 | − | 1.54237e13i | −1.21605 | − | 0.100057i | ||||
\(689\) | −2.48511e14 | −1.60048 | ||||||||
\(690\) | 4.97687e13i | 0.318208i | ||||||||
\(691\) | 1.90466e14i | 1.20900i | 0.796605 | + | 0.604500i | \(0.206627\pi\) | ||||
−0.796605 | + | 0.604500i | \(0.793373\pi\) | |||||||
\(692\) | 1.45698e14 | 0.918172 | ||||||||
\(693\) | − | 2.05382e14i | − | 1.28498i | ||||||
\(694\) | 3.63932e14 | 2.26060 | ||||||||
\(695\) | 1.20006e14i | 0.740081i | ||||||||
\(696\) | 7.69499e12i | 0.0471153i | ||||||||
\(697\) | 3.15338e13 | 0.191695 | ||||||||
\(698\) | −7.07897e13 | −0.427261 | ||||||||
\(699\) | 5.68662e13 | 0.340775 | ||||||||
\(700\) | − | 1.30719e14i | − | 0.777765i | ||||||
\(701\) | −2.16231e14 | −1.27740 | −0.638701 | − | 0.769455i | \(-0.720528\pi\) | ||||
−0.638701 | + | 0.769455i | \(0.720528\pi\) | |||||||
\(702\) | 1.79241e14 | 1.05136 | ||||||||
\(703\) | 2.15958e14 | 1.25775 | ||||||||
\(704\) | 6.54742e13 | 0.378623 | ||||||||
\(705\) | −1.53834e13 | −0.0883297 | ||||||||
\(706\) | 4.26324e14i | 2.43061i | ||||||||
\(707\) | 2.70686e14i | 1.53239i | ||||||||
\(708\) | − | 2.24829e13i | − | 0.126382i | ||||||
\(709\) | 2.91700e14 | 1.62819 | 0.814096 | − | 0.580730i | \(-0.197233\pi\) | ||||
0.814096 | + | 0.580730i | \(0.197233\pi\) | |||||||
\(710\) | − | 5.45934e14i | − | 3.02585i | ||||||
\(711\) | 1.92859e14 | 1.06143 | ||||||||
\(712\) | 1.06976e13 | 0.0584636 | ||||||||
\(713\) | −4.23248e13 | −0.229693 | ||||||||
\(714\) | 2.28421e13i | 0.123096i | ||||||||
\(715\) | − | 6.70798e14i | − | 3.58973i | ||||||
\(716\) | − | 9.94047e12i | − | 0.0528253i | ||||||
\(717\) | 8.25901e13i | 0.435845i | ||||||||
\(718\) | − | 2.09044e14i | − | 1.09551i | ||||||
\(719\) | −1.88232e13 | −0.0979601 | −0.0489800 | − | 0.998800i | \(-0.515597\pi\) | ||||
−0.0489800 | + | 0.998800i | \(0.515597\pi\) | |||||||
\(720\) | 3.28485e14i | 1.69767i | ||||||||
\(721\) | − | 1.85495e14i | − | 0.952041i | ||||||
\(722\) | − | 2.57994e13i | − | 0.131499i | ||||||
\(723\) | −6.23996e13 | −0.315857 | ||||||||
\(724\) | −1.49140e14 | −0.749722 | ||||||||
\(725\) | − | 1.10119e14i | − | 0.549758i | ||||||
\(726\) | 5.69401e13 | 0.282316 | ||||||||
\(727\) | 3.32311e14i | 1.63634i | 0.574979 | + | 0.818168i | \(0.305010\pi\) | ||||
−0.574979 | + | 0.818168i | \(0.694990\pi\) | |||||||
\(728\) | −1.49656e14 | −0.731874 | ||||||||
\(729\) | 1.39200e14 | 0.676083 | ||||||||
\(730\) | − | 5.30549e14i | − | 2.55924i | ||||||
\(731\) | −8.45794e13 | − | 6.95923e12i | −0.405208 | − | 0.0333407i | ||||
\(732\) | 2.43166e13 | 0.115704 | ||||||||
\(733\) | 1.30904e14i | 0.618631i | 0.950960 | + | 0.309315i | \(0.100100\pi\) | ||||
−0.950960 | + | 0.309315i | \(0.899900\pi\) | |||||||
\(734\) | 1.85178e14i | 0.869176i | ||||||||
\(735\) | 2.43166e12 | 0.0113362 | ||||||||
\(736\) | − | 1.74837e14i | − | 0.809553i | ||||||
\(737\) | −3.11353e14 | −1.43191 | ||||||||
\(738\) | 1.25936e14i | 0.575263i | ||||||||
\(739\) | − | 1.81148e14i | − | 0.821885i | −0.911661 | − | 0.410942i | \(-0.865200\pi\) | ||
0.911661 | − | 0.410942i | \(-0.134800\pi\) | |||||||
\(740\) | −2.92172e14 | −1.31668 | ||||||||
\(741\) | 8.85704e13 | 0.396458 | ||||||||
\(742\) | 2.60550e14 | 1.15843 | ||||||||
\(743\) | 6.15807e12i | 0.0271957i | 0.999908 | + | 0.0135979i | \(0.00432847\pi\) | ||||
−0.999908 | + | 0.0135979i | \(0.995672\pi\) | |||||||
\(744\) | 7.52323e12 | 0.0330019 | ||||||||
\(745\) | −4.40289e14 | −1.91847 | ||||||||
\(746\) | −3.49420e14 | −1.51235 | ||||||||
\(747\) | 1.79481e14 | 0.771640 | ||||||||
\(748\) | 8.86839e13 | 0.378736 | ||||||||
\(749\) | 2.34885e14i | 0.996428i | ||||||||
\(750\) | 1.88769e13i | 0.0795472i | ||||||||
\(751\) | − | 3.33417e14i | − | 1.39569i | −0.716251 | − | 0.697843i | \(-0.754143\pi\) | ||
0.716251 | − | 0.697843i | \(-0.245857\pi\) | |||||||
\(752\) | 7.38486e13 | 0.307081 | ||||||||
\(753\) | − | 8.65111e12i | − | 0.0357353i | ||||||
\(754\) | 2.59167e14 | 1.06347 | ||||||||
\(755\) | 5.76272e14 | 2.34905 | ||||||||
\(756\) | −7.55791e13 | −0.306050 | ||||||||
\(757\) | 5.95588e13i | 0.239589i | 0.992799 | + | 0.119794i | \(0.0382236\pi\) | ||||
−0.992799 | + | 0.119794i | \(0.961776\pi\) | |||||||
\(758\) | − | 2.43232e14i | − | 0.972019i | ||||||
\(759\) | − | 5.81827e13i | − | 0.230986i | ||||||
\(760\) | 1.50017e14i | 0.591660i | ||||||||
\(761\) | − | 1.10350e14i | − | 0.432363i | −0.976353 | − | 0.216182i | \(-0.930640\pi\) | ||
0.976353 | − | 0.216182i | \(-0.0693603\pi\) | |||||||
\(762\) | −1.19344e13 | −0.0464543 | ||||||||
\(763\) | 2.58251e14i | 0.998662i | ||||||||
\(764\) | − | 8.09349e13i | − | 0.310935i | ||||||
\(765\) | 1.48213e14i | 0.565692i | ||||||||
\(766\) | −4.61444e14 | −1.74975 | ||||||||
\(767\) | 3.68351e14 | 1.38767 | ||||||||
\(768\) | 8.32675e13i | 0.311652i | ||||||||
\(769\) | −1.86002e14 | −0.691650 | −0.345825 | − | 0.938299i | \(-0.612401\pi\) | ||||
−0.345825 | + | 0.938299i | \(0.612401\pi\) | |||||||
\(770\) | 7.03293e14i | 2.59826i | ||||||||
\(771\) | −1.24081e14 | −0.455441 | ||||||||
\(772\) | 2.68759e14 | 0.980115 | ||||||||
\(773\) | 2.76888e14i | 1.00324i | 0.865087 | + | 0.501622i | \(0.167263\pi\) | ||||
−0.865087 | + | 0.501622i | \(0.832737\pi\) | |||||||
\(774\) | 2.77929e13 | − | 3.37783e14i | 0.100053 | − | 1.21600i | ||||
\(775\) | −1.07661e14 | −0.385079 | ||||||||
\(776\) | − | 1.25012e14i | − | 0.444265i | ||||||
\(777\) | 8.79767e13i | 0.310644i | ||||||||
\(778\) | −7.16561e14 | −2.51394 | ||||||||
\(779\) | 1.28196e14i | 0.446875i | ||||||||
\(780\) | −1.19828e14 | −0.415035 | ||||||||
\(781\) | 6.38231e14i | 2.19646i | ||||||||
\(782\) | − | 1.07800e14i | − | 0.368624i | ||||||
\(783\) | −6.36686e13 | −0.216330 | ||||||||
\(784\) | −1.16733e13 | −0.0394106 | ||||||||
\(785\) | −4.19311e14 | −1.40666 | ||||||||
\(786\) | 1.19362e14i | 0.397881i | ||||||||
\(787\) | 5.43190e14 | 1.79919 | 0.899597 | − | 0.436721i | \(-0.143860\pi\) | ||||
0.899597 | + | 0.436721i | \(0.143860\pi\) | |||||||
\(788\) | 1.03357e14 | 0.340179 | ||||||||
\(789\) | 2.84689e13 | 0.0931078 | ||||||||
\(790\) | −6.60408e14 | −2.14623 | ||||||||
\(791\) | −5.23747e14 | −1.69137 | ||||||||
\(792\) | − | 1.72287e14i | − | 0.552876i | ||||||
\(793\) | 3.98393e14i | 1.27042i | ||||||||
\(794\) | 1.96075e14i | 0.621325i | ||||||||
\(795\) | −1.01483e14 | −0.319562 | ||||||||
\(796\) | − | 1.51831e14i | − | 0.475110i | ||||||
\(797\) | −2.71342e14 | −0.843772 | −0.421886 | − | 0.906649i | \(-0.638632\pi\) | ||||
−0.421886 | + | 0.906649i | \(0.638632\pi\) | |||||||
\(798\) | −9.28609e13 | −0.286958 | ||||||||
\(799\) | 3.33207e13 | 0.102325 | ||||||||
\(800\) | − | 4.44731e14i | − | 1.35721i | ||||||
\(801\) | 4.29665e13i | 0.130307i | ||||||||
\(802\) | 2.98717e13i | 0.0900302i | ||||||||
\(803\) | 6.20246e14i | 1.85774i | ||||||||
\(804\) | 5.56184e13i | 0.165553i | ||||||||
\(805\) | 3.43819e14 | 1.01707 | ||||||||
\(806\) | − | 2.53382e14i | − | 0.744905i | ||||||
\(807\) | 1.36985e12i | 0.00400226i | ||||||||
\(808\) | 2.27069e14i | 0.659326i | ||||||||
\(809\) | 1.12185e14 | 0.323736 | 0.161868 | − | 0.986812i | \(-0.448248\pi\) | ||||
0.161868 | + | 0.986812i | \(0.448248\pi\) | |||||||
\(810\) | −5.54251e14 | −1.58958 | ||||||||
\(811\) | − | 1.39238e14i | − | 0.396876i | −0.980113 | − | 0.198438i | \(-0.936413\pi\) | ||
0.980113 | − | 0.198438i | \(-0.0635869\pi\) | |||||||
\(812\) | −1.09281e14 | −0.309574 | ||||||||
\(813\) | − | 5.17648e13i | − | 0.145741i | ||||||
\(814\) | 8.49290e14 | 2.37648 | ||||||||
\(815\) | 8.20430e14 | 2.28167 | ||||||||
\(816\) | 4.27097e13i | 0.118053i | ||||||||
\(817\) | 2.82917e13 | − | 3.43845e14i | 0.0777227 | − | 0.944609i | ||||
\(818\) | 2.38788e14 | 0.651998 | ||||||||
\(819\) | − | 6.01087e14i | − | 1.63124i | ||||||
\(820\) | − | 1.73437e14i | − | 0.467814i | ||||||
\(821\) | −1.49950e14 | −0.402003 | −0.201002 | − | 0.979591i | \(-0.564420\pi\) | ||||
−0.201002 | + | 0.979591i | \(0.564420\pi\) | |||||||
\(822\) | − | 3.63469e13i | − | 0.0968520i | ||||||
\(823\) | 3.18025e14 | 0.842290 | 0.421145 | − | 0.906993i | \(-0.361628\pi\) | ||||
0.421145 | + | 0.906993i | \(0.361628\pi\) | |||||||
\(824\) | − | 1.55605e14i | − | 0.409625i | ||||||
\(825\) | − | 1.47998e14i | − | 0.387246i | ||||||
\(826\) | −3.86194e14 | −1.00440 | ||||||||
\(827\) | 6.29025e13 | 0.162607 | 0.0813037 | − | 0.996689i | \(-0.474092\pi\) | ||||
0.0813037 | + | 0.996689i | \(0.474092\pi\) | |||||||
\(828\) | 1.73145e14 | 0.444896 | ||||||||
\(829\) | 3.86270e14i | 0.986548i | 0.869874 | + | 0.493274i | \(0.164200\pi\) | ||||
−0.869874 | + | 0.493274i | \(0.835800\pi\) | |||||||
\(830\) | −6.14598e14 | −1.56027 | ||||||||
\(831\) | 7.10804e13 | 0.179368 | ||||||||
\(832\) | 1.91622e14 | 0.480649 | ||||||||
\(833\) | −5.26702e12 | −0.0131323 | ||||||||
\(834\) | −6.23142e13 | −0.154439 | ||||||||
\(835\) | − | 2.48473e14i | − | 0.612135i | ||||||
\(836\) | 3.60530e14i | 0.882898i | ||||||||
\(837\) | 6.22474e13i | 0.151528i | ||||||||
\(838\) | −4.68816e14 | −1.13444 | ||||||||
\(839\) | 9.58197e13i | 0.230486i | 0.993337 | + | 0.115243i | \(0.0367647\pi\) | ||||
−0.993337 | + | 0.115243i | \(0.963235\pi\) | |||||||
\(840\) | −6.11137e13 | −0.146131 | ||||||||
\(841\) | 3.28648e14 | 0.781179 | ||||||||
\(842\) | −1.41888e14 | −0.335262 | ||||||||
\(843\) | − | 8.21276e13i | − | 0.192908i | ||||||
\(844\) | 1.07663e14i | 0.251392i | ||||||||
\(845\) | − | 1.32782e15i | − | 3.08217i | ||||||
\(846\) | 1.33072e14i | 0.307068i | ||||||||
\(847\) | − | 3.93361e14i | − | 0.902349i | ||||||
\(848\) | 4.87171e14 | 1.11097 | ||||||||
\(849\) | 1.87188e13i | 0.0424364i | ||||||||
\(850\) | − | 2.74208e14i | − | 0.617996i | ||||||
\(851\) | − | 4.15192e14i | − | 0.930254i | ||||||
\(852\) | 1.14010e14 | 0.253949 | ||||||||
\(853\) | 2.13948e14 | 0.473766 | 0.236883 | − | 0.971538i | \(-0.423874\pi\) | ||||
0.236883 | + | 0.971538i | \(0.423874\pi\) | |||||||
\(854\) | − | 4.17692e14i | − | 0.919532i | ||||||
\(855\) | −6.02538e14 | −1.31872 | ||||||||
\(856\) | 1.97036e14i | 0.428723i | ||||||||
\(857\) | −2.11784e14 | −0.458130 | −0.229065 | − | 0.973411i | \(-0.573567\pi\) | ||||
−0.229065 | + | 0.973411i | \(0.573567\pi\) | |||||||
\(858\) | 3.48317e14 | 0.749098 | ||||||||
\(859\) | 8.17276e13i | 0.174744i | 0.996176 | + | 0.0873722i | \(0.0278469\pi\) | ||||
−0.996176 | + | 0.0873722i | \(0.972153\pi\) | |||||||
\(860\) | −3.82761e13 | + | 4.65191e14i | −0.0813645 | + | 0.988869i | ||||
\(861\) | −5.22241e13 | −0.110371 | ||||||||
\(862\) | 1.36923e13i | 0.0287701i | ||||||||
\(863\) | − | 3.44739e14i | − | 0.720171i | −0.932919 | − | 0.360086i | \(-0.882747\pi\) | ||
0.932919 | − | 0.360086i | \(-0.117253\pi\) | |||||||
\(864\) | −2.57134e14 | −0.534062 | ||||||||
\(865\) | 9.74783e14i | 2.01292i | ||||||||
\(866\) | 7.29492e14 | 1.49772 | ||||||||
\(867\) | − | 9.73059e13i | − | 0.198630i | ||||||
\(868\) | 1.06842e14i | 0.216842i | ||||||||
\(869\) | 7.72059e14 | 1.55794 | ||||||||
\(870\) | 1.05834e14 | 0.212339 | ||||||||
\(871\) | −9.11228e14 | −1.81776 | ||||||||
\(872\) | 2.16637e14i | 0.429685i | ||||||||
\(873\) | 5.02105e14 | 0.990200 | ||||||||
\(874\) | 4.38243e14 | 0.859325 | ||||||||
\(875\) | 1.30408e14 | 0.254252 | ||||||||
\(876\) | 1.10797e14 | 0.214788 | ||||||||
\(877\) | 1.71265e14 | 0.330119 | 0.165060 | − | 0.986284i | \(-0.447218\pi\) | ||||
0.165060 | + | 0.986284i | \(0.447218\pi\) | |||||||
\(878\) | − | 4.33941e14i | − | 0.831683i | ||||||
\(879\) | 2.30662e14i | 0.439573i | ||||||||
\(880\) | 1.31500e15i | 2.49180i | ||||||||
\(881\) | −4.99862e14 | −0.941826 | −0.470913 | − | 0.882180i | \(-0.656075\pi\) | ||||
−0.470913 | + | 0.882180i | \(0.656075\pi\) | |||||||
\(882\) | − | 2.10348e13i | − | 0.0394089i | ||||||
\(883\) | 1.29329e13 | 0.0240931 | 0.0120466 | − | 0.999927i | \(-0.496165\pi\) | ||||
0.0120466 | + | 0.999927i | \(0.496165\pi\) | |||||||
\(884\) | 2.59549e14 | 0.480793 | ||||||||
\(885\) | 1.50420e14 | 0.277071 | ||||||||
\(886\) | − | 1.00814e15i | − | 1.84651i | ||||||
\(887\) | − | 5.80801e14i | − | 1.05781i | −0.848680 | − | 0.528907i | \(-0.822602\pi\) | ||
0.848680 | − | 0.528907i | \(-0.177398\pi\) | |||||||
\(888\) | 7.38003e13i | 0.133658i | ||||||||
\(889\) | 8.24469e13i | 0.148479i | ||||||||
\(890\) | − | 1.47131e14i | − | 0.263483i | ||||||
\(891\) | 6.47955e14 | 1.15387 | ||||||||
\(892\) | 6.01907e14i | 1.06587i | ||||||||
\(893\) | 1.35460e14i | 0.238536i | ||||||||
\(894\) | − | 2.28623e14i | − | 0.400344i | ||||||
\(895\) | 6.65059e13 | 0.115810 | ||||||||
\(896\) | 4.55135e14 | 0.788135 | ||||||||
\(897\) | − | 1.70282e14i | − | 0.293229i | ||||||
\(898\) | 7.93084e13 | 0.135812 | ||||||||
\(899\) | 9.00046e13i | 0.153273i | ||||||||
\(900\) | 4.40426e14 | 0.745866 | ||||||||
\(901\) | 2.19813e14 | 0.370193 | ||||||||
\(902\) | 5.04150e14i | 0.844358i | ||||||||
\(903\) | 1.40075e14 | + | 1.15254e13i | 0.233304 | + | 0.0191963i | ||||
\(904\) | −4.39352e14 | −0.727730 | ||||||||
\(905\) | − | 9.97807e14i | − | 1.64363i | ||||||
\(906\) | 2.99234e14i | 0.490196i | ||||||||
\(907\) | −3.95800e14 | −0.644821 | −0.322410 | − | 0.946600i | \(-0.604493\pi\) | ||||
−0.322410 | + | 0.946600i | \(0.604493\pi\) | |||||||
\(908\) | 8.99427e13i | 0.145726i | ||||||||
\(909\) | −9.12013e14 | −1.46954 | ||||||||
\(910\) | 2.05831e15i | 3.29840i | ||||||||
\(911\) | − | 5.06840e14i | − | 0.807753i | −0.914813 | − | 0.403877i | \(-0.867663\pi\) | ||
0.914813 | − | 0.403877i | \(-0.132337\pi\) | |||||||
\(912\) | −1.73630e14 | −0.275201 | ||||||||
\(913\) | 7.18504e14 | 1.13260 | ||||||||
\(914\) | −8.83731e14 | −1.38544 | ||||||||
\(915\) | 1.62689e14i | 0.253660i | ||||||||
\(916\) | −4.09237e14 | −0.634597 | ||||||||
\(917\) | 8.24593e14 | 1.27172 | ||||||||
\(918\) | −1.58542e14 | −0.243181 | ||||||||
\(919\) | −2.79234e14 | −0.425981 | −0.212990 | − | 0.977054i | \(-0.568320\pi\) | ||||
−0.212990 | + | 0.977054i | \(0.568320\pi\) | |||||||
\(920\) | 2.88417e14 | 0.437604 | ||||||||
\(921\) | − | 2.86958e14i | − | 0.433032i | ||||||
\(922\) | − | 8.34388e14i | − | 1.25232i | ||||||
\(923\) | 1.86789e15i | 2.78833i | ||||||||
\(924\) | −1.46872e14 | −0.218062 | ||||||||
\(925\) | − | 1.05612e15i | − | 1.55956i | ||||||
\(926\) | −1.18546e15 | −1.74113 | ||||||||
\(927\) | 6.24981e14 | 0.912994 | ||||||||
\(928\) | −3.71795e14 | −0.540212 | ||||||||
\(929\) | − | 8.33263e14i | − | 1.20421i | −0.798416 | − | 0.602107i | \(-0.794328\pi\) | ||
0.798416 | − | 0.602107i | \(-0.205672\pi\) | |||||||
\(930\) | − | 1.03472e14i | − | 0.148733i | ||||||
\(931\) | − | 2.14122e13i | − | 0.0306136i | ||||||
\(932\) | 6.77457e14i | 0.963390i | ||||||||
\(933\) | 9.81180e13i | 0.138784i | ||||||||
\(934\) | 5.15782e14 | 0.725658 | ||||||||
\(935\) | 5.93333e14i | 0.830310i | ||||||||
\(936\) | − | 5.04229e14i | − | 0.701857i | ||||||
\(937\) | − | 1.98336e14i | − | 0.274602i | −0.990529 | − | 0.137301i | \(-0.956157\pi\) | ||
0.990529 | − | 0.137301i | \(-0.0438427\pi\) | |||||||
\(938\) | 9.55369e14 | 1.31570 | ||||||||
\(939\) | 1.91708e14 | 0.262610 | ||||||||
\(940\) | − | 1.83265e14i | − | 0.249713i | ||||||
\(941\) | 7.26328e12 | 0.00984430 | 0.00492215 | − | 0.999988i | \(-0.498433\pi\) | ||||
0.00492215 | + | 0.999988i | \(0.498433\pi\) | |||||||
\(942\) | − | 2.17730e14i | − | 0.293538i | ||||||
\(943\) | 2.46464e14 | 0.330518 | ||||||||
\(944\) | −7.22099e14 | −0.963246 | ||||||||
\(945\) | − | 5.05656e14i | − | 0.670960i | ||||||
\(946\) | 1.11261e14 | − | 1.35222e15i | 0.146855 | − | 1.78481i | ||||
\(947\) | 3.67266e13 | 0.0482204 | 0.0241102 | − | 0.999709i | \(-0.492325\pi\) | ||||
0.0241102 | + | 0.999709i | \(0.492325\pi\) | |||||||
\(948\) | − | 1.37917e14i | − | 0.180125i | ||||||
\(949\) | 1.81526e15i | 2.35834i | ||||||||
\(950\) | 1.11475e15 | 1.44065 | ||||||||
\(951\) | 2.15880e12i | 0.00277531i | ||||||||
\(952\) | 1.32373e14 | 0.169284 | ||||||||
\(953\) | 5.18570e14i | 0.659694i | 0.944034 | + | 0.329847i | \(0.106997\pi\) | ||||
−0.944034 | + | 0.329847i | \(0.893003\pi\) | |||||||
\(954\) | 8.77860e14i | 1.11092i | ||||||||
\(955\) | 5.41489e14 | 0.681668 | ||||||||
\(956\) | −9.83911e14 | −1.23216 | ||||||||
\(957\) | −1.23727e14 | −0.154136 | ||||||||
\(958\) | 1.09846e15i | 1.36131i | ||||||||
\(959\) | −2.51097e14 | −0.309562 | ||||||||
\(960\) | 7.82510e13 | 0.0959696 | ||||||||
\(961\) | −7.31633e14 | −0.892640 | ||||||||
\(962\) | 2.48560e15 | 3.01686 | ||||||||
\(963\) | −7.91389e14 | −0.955561 | ||||||||
\(964\) | − | 7.43378e14i | − | 0.892945i | ||||||
\(965\) | 1.79811e15i | 2.14873i | ||||||||
\(966\) | 1.78531e14i | 0.212240i | ||||||||
\(967\) | −1.07633e15 | −1.27295 | −0.636477 | − | 0.771296i | \(-0.719609\pi\) | ||||
−0.636477 | + | 0.771296i | \(0.719609\pi\) | |||||||
\(968\) | − | 3.29976e14i | − | 0.388245i | ||||||
\(969\) | −7.83421e13 | −0.0917014 | ||||||||
\(970\) | −1.71936e15 | −2.00221 | ||||||||
\(971\) | −8.42511e14 | −0.976066 | −0.488033 | − | 0.872825i | \(-0.662286\pi\) | ||||
−0.488033 | + | 0.872825i | \(0.662286\pi\) | |||||||
\(972\) | − | 3.85679e14i | − | 0.444523i | ||||||
\(973\) | 4.30487e14i | 0.493624i | ||||||||
\(974\) | − | 1.74273e15i | − | 1.98809i | ||||||
\(975\) | − | 4.33143e14i | − | 0.491596i | ||||||
\(976\) | − | 7.80993e14i | − | 0.881857i | ||||||
\(977\) | −1.32957e15 | −1.49361 | −0.746806 | − | 0.665042i | \(-0.768413\pi\) | ||||
−0.746806 | + | 0.665042i | \(0.768413\pi\) | |||||||
\(978\) | 4.26015e14i | 0.476136i | ||||||||
\(979\) | 1.72005e14i | 0.191261i | ||||||||
\(980\) | 2.89688e13i | 0.0320480i | ||||||||
\(981\) | −8.70114e14 | −0.957703 | ||||||||
\(982\) | 1.18134e14 | 0.129365 | ||||||||
\(983\) | − | 3.03156e14i | − | 0.330292i | −0.986269 | − | 0.165146i | \(-0.947190\pi\) | ||
0.986269 | − | 0.165146i | \(-0.0528096\pi\) | |||||||
\(984\) | −4.38089e13 | −0.0474883 | ||||||||
\(985\) | 6.91499e14i | 0.745780i | ||||||||
\(986\) | −2.29238e14 | −0.245981 | ||||||||
\(987\) | −5.51835e13 | −0.0589146 | ||||||||
\(988\) | 1.05516e15i | 1.12081i | ||||||||
\(989\) | −6.61062e14 | − | 5.43924e13i | −0.698652 | − | 0.0574853i | ||||
\(990\) | −2.36958e15 | −2.49170 | ||||||||
\(991\) | − | 8.24185e14i | − | 0.862296i | −0.902281 | − | 0.431148i | \(-0.858109\pi\) | ||
0.902281 | − | 0.431148i | \(-0.141891\pi\) | |||||||
\(992\) | 3.63496e14i | 0.378391i | ||||||||
\(993\) | −1.60191e14 | −0.165917 | ||||||||
\(994\) | − | 1.95838e15i | − | 2.01820i | ||||||
\(995\) | 1.01581e15 | 1.04159 | ||||||||
\(996\) | − | 1.28350e14i | − | 0.130948i | ||||||
\(997\) | − | 5.47068e14i | − | 0.555348i | −0.960675 | − | 0.277674i | \(-0.910436\pi\) | ||
0.960675 | − | 0.277674i | \(-0.0895635\pi\) | |||||||
\(998\) | 8.51393e13 | 0.0859958 | ||||||||
\(999\) | −6.10626e14 | −0.613688 |
(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 | 43.11.b.b.42.8 | ✓ | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.27 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.8 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.11.b.b.42.27 | yes | 34 | 43.42 | odd | 2 | inner |