Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,10,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("91.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(46.8682610909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 4522 x^{10} + 11094 x^{9} + 7471016 x^{8} - 18339296 x^{7} - 5497728352 x^{6} + \cdots + 170905444356096 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(24.5414\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 22.5414 | 0.996197 | 0.498099 | − | 0.867120i | \(-0.334032\pi\) | ||||
0.498099 | + | 0.867120i | \(0.334032\pi\) | |||||||
\(3\) | 66.2971 | 0.472551 | 0.236276 | − | 0.971686i | \(-0.424073\pi\) | ||||
0.236276 | + | 0.971686i | \(0.424073\pi\) | |||||||
\(4\) | −3.88662 | −0.00759106 | ||||||||
\(5\) | −391.554 | −0.280173 | −0.140087 | − | 0.990139i | \(-0.544738\pi\) | ||||
−0.140087 | + | 0.990139i | \(0.544738\pi\) | |||||||
\(6\) | 1494.43 | 0.470754 | ||||||||
\(7\) | 2401.00 | 0.377964 | ||||||||
\(8\) | −11628.8 | −1.00376 | ||||||||
\(9\) | −15287.7 | −0.776695 | ||||||||
\(10\) | −8826.17 | −0.279108 | ||||||||
\(11\) | 93595.7 | 1.92748 | 0.963738 | − | 0.266852i | \(-0.0859835\pi\) | ||||
0.963738 | + | 0.266852i | \(0.0859835\pi\) | |||||||
\(12\) | −257.672 | −0.00358716 | ||||||||
\(13\) | 28561.0 | 0.277350 | ||||||||
\(14\) | 54121.8 | 0.376527 | ||||||||
\(15\) | −25958.9 | −0.132396 | ||||||||
\(16\) | −260139. | −0.992351 | ||||||||
\(17\) | −385933. | −1.12071 | −0.560353 | − | 0.828254i | \(-0.689335\pi\) | ||||
−0.560353 | + | 0.828254i | \(0.689335\pi\) | |||||||
\(18\) | −344606. | −0.773742 | ||||||||
\(19\) | −1.01897e6 | −1.79379 | −0.896895 | − | 0.442244i | \(-0.854182\pi\) | ||||
−0.896895 | + | 0.442244i | \(0.854182\pi\) | |||||||
\(20\) | 1521.82 | 0.00212681 | ||||||||
\(21\) | 159179. | 0.178608 | ||||||||
\(22\) | 2.10978e6 | 1.92015 | ||||||||
\(23\) | 1.82565e6 | 1.36033 | 0.680163 | − | 0.733061i | \(-0.261909\pi\) | ||||
0.680163 | + | 0.733061i | \(0.261909\pi\) | |||||||
\(24\) | −770955. | −0.474328 | ||||||||
\(25\) | −1.79981e6 | −0.921503 | ||||||||
\(26\) | 643804. | 0.276295 | ||||||||
\(27\) | −2.31846e6 | −0.839579 | ||||||||
\(28\) | −9331.78 | −0.00286915 | ||||||||
\(29\) | −5.33916e6 | −1.40179 | −0.700894 | − | 0.713266i | \(-0.747215\pi\) | ||||
−0.700894 | + | 0.713266i | \(0.747215\pi\) | |||||||
\(30\) | −585149. | −0.131893 | ||||||||
\(31\) | −6.13823e6 | −1.19376 | −0.596878 | − | 0.802332i | \(-0.703592\pi\) | ||||
−0.596878 | + | 0.802332i | \(0.703592\pi\) | |||||||
\(32\) | 90052.9 | 0.0151818 | ||||||||
\(33\) | 6.20512e6 | 0.910830 | ||||||||
\(34\) | −8.69946e6 | −1.11645 | ||||||||
\(35\) | −940121. | −0.105896 | ||||||||
\(36\) | 59417.5 | 0.00589594 | ||||||||
\(37\) | −1.31232e7 | −1.15115 | −0.575576 | − | 0.817748i | \(-0.695222\pi\) | ||||
−0.575576 | + | 0.817748i | \(0.695222\pi\) | |||||||
\(38\) | −2.29690e7 | −1.78697 | ||||||||
\(39\) | 1.89351e6 | 0.131062 | ||||||||
\(40\) | 4.55330e6 | 0.281227 | ||||||||
\(41\) | 7.87529e6 | 0.435251 | 0.217625 | − | 0.976032i | \(-0.430169\pi\) | ||||
0.217625 | + | 0.976032i | \(0.430169\pi\) | |||||||
\(42\) | 3.58812e6 | 0.177928 | ||||||||
\(43\) | −4.05687e7 | −1.80960 | −0.904801 | − | 0.425835i | \(-0.859980\pi\) | ||||
−0.904801 | + | 0.425835i | \(0.859980\pi\) | |||||||
\(44\) | −363771. | −0.0146316 | ||||||||
\(45\) | 5.98596e6 | 0.217609 | ||||||||
\(46\) | 4.11527e7 | 1.35515 | ||||||||
\(47\) | 5.94709e7 | 1.77772 | 0.888862 | − | 0.458176i | \(-0.151497\pi\) | ||||
0.888862 | + | 0.458176i | \(0.151497\pi\) | |||||||
\(48\) | −1.72465e7 | −0.468937 | ||||||||
\(49\) | 5.76480e6 | 0.142857 | ||||||||
\(50\) | −4.05702e7 | −0.917999 | ||||||||
\(51\) | −2.55862e7 | −0.529591 | ||||||||
\(52\) | −111006. | −0.00210538 | ||||||||
\(53\) | 5.09403e7 | 0.886789 | 0.443394 | − | 0.896327i | \(-0.353774\pi\) | ||||
0.443394 | + | 0.896327i | \(0.353774\pi\) | |||||||
\(54\) | −5.22612e7 | −0.836387 | ||||||||
\(55\) | −3.66478e7 | −0.540027 | ||||||||
\(56\) | −2.79207e7 | −0.379385 | ||||||||
\(57\) | −6.75549e7 | −0.847657 | ||||||||
\(58\) | −1.20352e8 | −1.39646 | ||||||||
\(59\) | −616701. | −0.00662583 | −0.00331292 | − | 0.999995i | \(-0.501055\pi\) | ||||
−0.00331292 | + | 0.999995i | \(0.501055\pi\) | |||||||
\(60\) | 100892. | 0.00100503 | ||||||||
\(61\) | 5.11911e7 | 0.473380 | 0.236690 | − | 0.971585i | \(-0.423937\pi\) | ||||
0.236690 | + | 0.971585i | \(0.423937\pi\) | |||||||
\(62\) | −1.38364e8 | −1.18922 | ||||||||
\(63\) | −3.67058e7 | −0.293563 | ||||||||
\(64\) | 1.35221e8 | 1.00748 | ||||||||
\(65\) | −1.11832e7 | −0.0777061 | ||||||||
\(66\) | 1.39872e8 | 0.907367 | ||||||||
\(67\) | −1.58337e8 | −0.959947 | −0.479973 | − | 0.877283i | \(-0.659354\pi\) | ||||
−0.479973 | + | 0.877283i | \(0.659354\pi\) | |||||||
\(68\) | 1.49998e6 | 0.00850735 | ||||||||
\(69\) | 1.21036e8 | 0.642824 | ||||||||
\(70\) | −2.11916e7 | −0.105493 | ||||||||
\(71\) | 9.17625e6 | 0.0428551 | 0.0214276 | − | 0.999770i | \(-0.493179\pi\) | ||||
0.0214276 | + | 0.999770i | \(0.493179\pi\) | |||||||
\(72\) | 1.77777e8 | 0.779615 | ||||||||
\(73\) | −3.70094e8 | −1.52531 | −0.762657 | − | 0.646803i | \(-0.776106\pi\) | ||||
−0.762657 | + | 0.646803i | \(0.776106\pi\) | |||||||
\(74\) | −2.95815e8 | −1.14677 | ||||||||
\(75\) | −1.19322e8 | −0.435457 | ||||||||
\(76\) | 3.96036e6 | 0.0136168 | ||||||||
\(77\) | 2.24723e8 | 0.728517 | ||||||||
\(78\) | 4.26823e7 | 0.130564 | ||||||||
\(79\) | 2.66334e8 | 0.769317 | 0.384658 | − | 0.923059i | \(-0.374319\pi\) | ||||
0.384658 | + | 0.923059i | \(0.374319\pi\) | |||||||
\(80\) | 1.01858e8 | 0.278030 | ||||||||
\(81\) | 1.47201e8 | 0.379951 | ||||||||
\(82\) | 1.77520e8 | 0.433595 | ||||||||
\(83\) | −4.26490e8 | −0.986411 | −0.493205 | − | 0.869913i | \(-0.664175\pi\) | ||||
−0.493205 | + | 0.869913i | \(0.664175\pi\) | |||||||
\(84\) | −618670. | −0.00135582 | ||||||||
\(85\) | 1.51114e8 | 0.313992 | ||||||||
\(86\) | −9.14474e8 | −1.80272 | ||||||||
\(87\) | −3.53971e8 | −0.662416 | ||||||||
\(88\) | −1.08840e9 | −1.93472 | ||||||||
\(89\) | −1.11538e7 | −0.0188438 | −0.00942192 | − | 0.999956i | \(-0.502999\pi\) | ||||
−0.00942192 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(90\) | 1.34932e8 | 0.216782 | ||||||||
\(91\) | 6.85750e7 | 0.104828 | ||||||||
\(92\) | −7.09563e6 | −0.0103263 | ||||||||
\(93\) | −4.06947e8 | −0.564111 | ||||||||
\(94\) | 1.34056e9 | 1.77096 | ||||||||
\(95\) | 3.98983e8 | 0.502572 | ||||||||
\(96\) | 5.97025e6 | 0.00717417 | ||||||||
\(97\) | 4.95030e8 | 0.567752 | 0.283876 | − | 0.958861i | \(-0.408380\pi\) | ||||
0.283876 | + | 0.958861i | \(0.408380\pi\) | |||||||
\(98\) | 1.29947e8 | 0.142314 | ||||||||
\(99\) | −1.43086e9 | −1.49706 | ||||||||
\(100\) | 6.99518e6 | 0.00699518 | ||||||||
\(101\) | −9.32790e7 | −0.0891944 | −0.0445972 | − | 0.999005i | \(-0.514200\pi\) | ||||
−0.0445972 | + | 0.999005i | \(0.514200\pi\) | |||||||
\(102\) | −5.76749e8 | −0.527577 | ||||||||
\(103\) | 1.32347e8 | 0.115863 | 0.0579317 | − | 0.998321i | \(-0.481549\pi\) | ||||
0.0579317 | + | 0.998321i | \(0.481549\pi\) | |||||||
\(104\) | −3.32130e8 | −0.278393 | ||||||||
\(105\) | −6.23273e7 | −0.0500411 | ||||||||
\(106\) | 1.14826e9 | 0.883416 | ||||||||
\(107\) | −5.92037e8 | −0.436638 | −0.218319 | − | 0.975877i | \(-0.570057\pi\) | ||||
−0.218319 | + | 0.975877i | \(0.570057\pi\) | |||||||
\(108\) | 9.01096e6 | 0.00637330 | ||||||||
\(109\) | −7.00685e8 | −0.475449 | −0.237724 | − | 0.971333i | \(-0.576402\pi\) | ||||
−0.237724 | + | 0.971333i | \(0.576402\pi\) | |||||||
\(110\) | −8.26091e8 | −0.537973 | ||||||||
\(111\) | −8.70031e8 | −0.543978 | ||||||||
\(112\) | −6.24594e8 | −0.375074 | ||||||||
\(113\) | 1.52540e9 | 0.880100 | 0.440050 | − | 0.897973i | \(-0.354961\pi\) | ||||
0.440050 | + | 0.897973i | \(0.354961\pi\) | |||||||
\(114\) | −1.52278e9 | −0.844434 | ||||||||
\(115\) | −7.14842e8 | −0.381127 | ||||||||
\(116\) | 2.07513e7 | 0.0106411 | ||||||||
\(117\) | −4.36632e8 | −0.215417 | ||||||||
\(118\) | −1.39013e7 | −0.00660064 | ||||||||
\(119\) | −9.26626e8 | −0.423587 | ||||||||
\(120\) | 3.01871e8 | 0.132894 | ||||||||
\(121\) | 6.40221e9 | 2.71516 | ||||||||
\(122\) | 1.15392e9 | 0.471580 | ||||||||
\(123\) | 5.22109e8 | 0.205678 | ||||||||
\(124\) | 2.38570e7 | 0.00906187 | ||||||||
\(125\) | 1.46948e9 | 0.538354 | ||||||||
\(126\) | −8.27398e8 | −0.292447 | ||||||||
\(127\) | 3.21186e9 | 1.09557 | 0.547785 | − | 0.836619i | \(-0.315471\pi\) | ||||
0.547785 | + | 0.836619i | \(0.315471\pi\) | |||||||
\(128\) | 3.00196e9 | 0.988462 | ||||||||
\(129\) | −2.68959e9 | −0.855129 | ||||||||
\(130\) | −2.52084e8 | −0.0774106 | ||||||||
\(131\) | −4.15853e9 | −1.23373 | −0.616863 | − | 0.787070i | \(-0.711597\pi\) | ||||
−0.616863 | + | 0.787070i | \(0.711597\pi\) | |||||||
\(132\) | −2.41170e7 | −0.00691417 | ||||||||
\(133\) | −2.44655e9 | −0.677989 | ||||||||
\(134\) | −3.56914e9 | −0.956296 | ||||||||
\(135\) | 9.07801e8 | 0.235228 | ||||||||
\(136\) | 4.48794e9 | 1.12492 | ||||||||
\(137\) | 7.05191e9 | 1.71027 | 0.855134 | − | 0.518407i | \(-0.173475\pi\) | ||||
0.855134 | + | 0.518407i | \(0.173475\pi\) | |||||||
\(138\) | 2.72831e9 | 0.640379 | ||||||||
\(139\) | −4.37330e9 | −0.993670 | −0.496835 | − | 0.867845i | \(-0.665505\pi\) | ||||
−0.496835 | + | 0.867845i | \(0.665505\pi\) | |||||||
\(140\) | 3.65390e6 | 0.000803859 0 | ||||||||
\(141\) | 3.94275e9 | 0.840065 | ||||||||
\(142\) | 2.06845e8 | 0.0426921 | ||||||||
\(143\) | 2.67319e9 | 0.534585 | ||||||||
\(144\) | 3.97693e9 | 0.770755 | ||||||||
\(145\) | 2.09057e9 | 0.392743 | ||||||||
\(146\) | −8.34243e9 | −1.51951 | ||||||||
\(147\) | 3.82189e8 | 0.0675073 | ||||||||
\(148\) | 5.10050e7 | 0.00873846 | ||||||||
\(149\) | 1.47718e9 | 0.245525 | 0.122762 | − | 0.992436i | \(-0.460825\pi\) | ||||
0.122762 | + | 0.992436i | \(0.460825\pi\) | |||||||
\(150\) | −2.68969e9 | −0.433801 | ||||||||
\(151\) | −6.20770e9 | −0.971705 | −0.485852 | − | 0.874041i | \(-0.661491\pi\) | ||||
−0.485852 | + | 0.874041i | \(0.661491\pi\) | |||||||
\(152\) | 1.18494e10 | 1.80053 | ||||||||
\(153\) | 5.90003e9 | 0.870448 | ||||||||
\(154\) | 5.06557e9 | 0.725747 | ||||||||
\(155\) | 2.40345e9 | 0.334458 | ||||||||
\(156\) | −7.35936e6 | −0.000994900 0 | ||||||||
\(157\) | 2.93653e9 | 0.385732 | 0.192866 | − | 0.981225i | \(-0.438222\pi\) | ||||
0.192866 | + | 0.981225i | \(0.438222\pi\) | |||||||
\(158\) | 6.00354e9 | 0.766391 | ||||||||
\(159\) | 3.37719e9 | 0.419053 | ||||||||
\(160\) | −3.52606e7 | −0.00425353 | ||||||||
\(161\) | 4.38339e9 | 0.514155 | ||||||||
\(162\) | 3.31811e9 | 0.378507 | ||||||||
\(163\) | 2.14103e7 | 0.00237563 | 0.00118782 | − | 0.999999i | \(-0.499622\pi\) | ||||
0.00118782 | + | 0.999999i | \(0.499622\pi\) | |||||||
\(164\) | −3.06083e7 | −0.00330401 | ||||||||
\(165\) | −2.42964e9 | −0.255190 | ||||||||
\(166\) | −9.61367e9 | −0.982659 | ||||||||
\(167\) | 1.16485e10 | 1.15890 | 0.579448 | − | 0.815009i | \(-0.303268\pi\) | ||||
0.579448 | + | 0.815009i | \(0.303268\pi\) | |||||||
\(168\) | −1.85106e9 | −0.179279 | ||||||||
\(169\) | 8.15731e8 | 0.0769231 | ||||||||
\(170\) | 3.40631e9 | 0.312798 | ||||||||
\(171\) | 1.55777e10 | 1.39323 | ||||||||
\(172\) | 1.57675e8 | 0.0137368 | ||||||||
\(173\) | −9.63553e9 | −0.817839 | −0.408920 | − | 0.912570i | \(-0.634094\pi\) | ||||
−0.408920 | + | 0.912570i | \(0.634094\pi\) | |||||||
\(174\) | −7.97899e9 | −0.659897 | ||||||||
\(175\) | −4.32134e9 | −0.348295 | ||||||||
\(176\) | −2.43479e10 | −1.91273 | ||||||||
\(177\) | −4.08855e7 | −0.00313105 | ||||||||
\(178\) | −2.51423e8 | −0.0187722 | ||||||||
\(179\) | 1.02545e10 | 0.746578 | 0.373289 | − | 0.927715i | \(-0.378230\pi\) | ||||
0.373289 | + | 0.927715i | \(0.378230\pi\) | |||||||
\(180\) | −2.32652e7 | −0.00165189 | ||||||||
\(181\) | 1.64816e10 | 1.14142 | 0.570711 | − | 0.821151i | \(-0.306668\pi\) | ||||
0.570711 | + | 0.821151i | \(0.306668\pi\) | |||||||
\(182\) | 1.54577e9 | 0.104430 | ||||||||
\(183\) | 3.39382e9 | 0.223696 | ||||||||
\(184\) | −2.12301e10 | −1.36544 | ||||||||
\(185\) | 5.13845e9 | 0.322522 | ||||||||
\(186\) | −9.17313e9 | −0.561965 | ||||||||
\(187\) | −3.61217e10 | −2.16013 | ||||||||
\(188\) | −2.31141e8 | −0.0134948 | ||||||||
\(189\) | −5.56661e9 | −0.317331 | ||||||||
\(190\) | 8.99362e9 | 0.500661 | ||||||||
\(191\) | 9.70454e9 | 0.527624 | 0.263812 | − | 0.964574i | \(-0.415020\pi\) | ||||
0.263812 | + | 0.964574i | \(0.415020\pi\) | |||||||
\(192\) | 8.96476e9 | 0.476084 | ||||||||
\(193\) | −3.14916e10 | −1.63375 | −0.816877 | − | 0.576812i | \(-0.804297\pi\) | ||||
−0.816877 | + | 0.576812i | \(0.804297\pi\) | |||||||
\(194\) | 1.11587e10 | 0.565593 | ||||||||
\(195\) | −7.41412e8 | −0.0367201 | ||||||||
\(196\) | −2.24056e7 | −0.00108444 | ||||||||
\(197\) | 1.44276e10 | 0.682492 | 0.341246 | − | 0.939974i | \(-0.389151\pi\) | ||||
0.341246 | + | 0.939974i | \(0.389151\pi\) | |||||||
\(198\) | −3.22536e10 | −1.49137 | ||||||||
\(199\) | 1.13380e10 | 0.512505 | 0.256252 | − | 0.966610i | \(-0.417512\pi\) | ||||
0.256252 | + | 0.966610i | \(0.417512\pi\) | |||||||
\(200\) | 2.09296e10 | 0.924967 | ||||||||
\(201\) | −1.04973e10 | −0.453624 | ||||||||
\(202\) | −2.10264e9 | −0.0888553 | ||||||||
\(203\) | −1.28193e10 | −0.529826 | ||||||||
\(204\) | 9.94441e7 | 0.00402016 | ||||||||
\(205\) | −3.08360e9 | −0.121946 | ||||||||
\(206\) | 2.98328e9 | 0.115423 | ||||||||
\(207\) | −2.79100e10 | −1.05656 | ||||||||
\(208\) | −7.42983e9 | −0.275229 | ||||||||
\(209\) | −9.53715e10 | −3.45748 | ||||||||
\(210\) | −1.40494e9 | −0.0498508 | ||||||||
\(211\) | 1.04589e10 | 0.363257 | 0.181628 | − | 0.983367i | \(-0.441863\pi\) | ||||
0.181628 | + | 0.983367i | \(0.441863\pi\) | |||||||
\(212\) | −1.97986e8 | −0.00673167 | ||||||||
\(213\) | 6.08359e8 | 0.0202512 | ||||||||
\(214\) | −1.33453e10 | −0.434978 | ||||||||
\(215\) | 1.58848e10 | 0.507002 | ||||||||
\(216\) | 2.69608e10 | 0.842736 | ||||||||
\(217\) | −1.47379e10 | −0.451197 | ||||||||
\(218\) | −1.57944e10 | −0.473641 | ||||||||
\(219\) | −2.45362e10 | −0.720789 | ||||||||
\(220\) | 1.42436e8 | 0.00409938 | ||||||||
\(221\) | −1.10226e10 | −0.310828 | ||||||||
\(222\) | −1.96117e10 | −0.541909 | ||||||||
\(223\) | −2.88573e10 | −0.781418 | −0.390709 | − | 0.920514i | \(-0.627770\pi\) | ||||
−0.390709 | + | 0.920514i | \(0.627770\pi\) | |||||||
\(224\) | 2.16217e8 | 0.00573818 | ||||||||
\(225\) | 2.75150e10 | 0.715727 | ||||||||
\(226\) | 3.43847e10 | 0.876753 | ||||||||
\(227\) | −1.01009e10 | −0.252490 | −0.126245 | − | 0.991999i | \(-0.540293\pi\) | ||||
−0.126245 | + | 0.991999i | \(0.540293\pi\) | |||||||
\(228\) | 2.62561e8 | 0.00643462 | ||||||||
\(229\) | −6.00090e10 | −1.44197 | −0.720986 | − | 0.692949i | \(-0.756311\pi\) | ||||
−0.720986 | + | 0.692949i | \(0.756311\pi\) | |||||||
\(230\) | −1.61135e10 | −0.379678 | ||||||||
\(231\) | 1.48985e10 | 0.344262 | ||||||||
\(232\) | 6.20880e10 | 1.40706 | ||||||||
\(233\) | −1.49600e10 | −0.332530 | −0.166265 | − | 0.986081i | \(-0.553171\pi\) | ||||
−0.166265 | + | 0.986081i | \(0.553171\pi\) | |||||||
\(234\) | −9.84228e9 | −0.214597 | ||||||||
\(235\) | −2.32861e10 | −0.498071 | ||||||||
\(236\) | 2.39688e6 | 5.02971e−5 0 | ||||||||
\(237\) | 1.76572e10 | 0.363541 | ||||||||
\(238\) | −2.08874e10 | −0.421977 | ||||||||
\(239\) | −5.33741e10 | −1.05813 | −0.529066 | − | 0.848581i | \(-0.677458\pi\) | ||||
−0.529066 | + | 0.848581i | \(0.677458\pi\) | |||||||
\(240\) | 6.75292e9 | 0.131384 | ||||||||
\(241\) | 1.32320e10 | 0.252667 | 0.126334 | − | 0.991988i | \(-0.459679\pi\) | ||||
0.126334 | + | 0.991988i | \(0.459679\pi\) | |||||||
\(242\) | 1.44314e11 | 2.70484 | ||||||||
\(243\) | 5.53931e10 | 1.01913 | ||||||||
\(244\) | −1.98961e8 | −0.00359346 | ||||||||
\(245\) | −2.25723e9 | −0.0400248 | ||||||||
\(246\) | 1.17690e10 | 0.204896 | ||||||||
\(247\) | −2.91029e10 | −0.497508 | ||||||||
\(248\) | 7.13802e10 | 1.19824 | ||||||||
\(249\) | −2.82751e10 | −0.466129 | ||||||||
\(250\) | 3.31240e10 | 0.536307 | ||||||||
\(251\) | 5.18625e9 | 0.0824748 | 0.0412374 | − | 0.999149i | \(-0.486870\pi\) | ||||
0.0412374 | + | 0.999149i | \(0.486870\pi\) | |||||||
\(252\) | 1.42661e8 | 0.00222846 | ||||||||
\(253\) | 1.70873e11 | 2.62200 | ||||||||
\(254\) | 7.23997e10 | 1.09140 | ||||||||
\(255\) | 1.00184e10 | 0.148377 | ||||||||
\(256\) | −1.56487e9 | −0.0227719 | ||||||||
\(257\) | −8.01772e10 | −1.14644 | −0.573221 | − | 0.819401i | \(-0.694306\pi\) | ||||
−0.573221 | + | 0.819401i | \(0.694306\pi\) | |||||||
\(258\) | −6.06270e10 | −0.851877 | ||||||||
\(259\) | −3.15088e10 | −0.435094 | ||||||||
\(260\) | 4.34648e7 | 0.000589872 0 | ||||||||
\(261\) | 8.16235e10 | 1.08876 | ||||||||
\(262\) | −9.37389e10 | −1.22903 | ||||||||
\(263\) | 6.08567e8 | 0.00784346 | 0.00392173 | − | 0.999992i | \(-0.498752\pi\) | ||||
0.00392173 | + | 0.999992i | \(0.498752\pi\) | |||||||
\(264\) | −7.21581e10 | −0.914255 | ||||||||
\(265\) | −1.99459e10 | −0.248455 | ||||||||
\(266\) | −5.51487e10 | −0.675410 | ||||||||
\(267\) | −7.39467e8 | −0.00890467 | ||||||||
\(268\) | 6.15398e8 | 0.00728701 | ||||||||
\(269\) | −6.55756e10 | −0.763584 | −0.381792 | − | 0.924248i | \(-0.624693\pi\) | ||||
−0.381792 | + | 0.924248i | \(0.624693\pi\) | |||||||
\(270\) | 2.04631e10 | 0.234333 | ||||||||
\(271\) | 2.61259e10 | 0.294245 | 0.147123 | − | 0.989118i | \(-0.452999\pi\) | ||||
0.147123 | + | 0.989118i | \(0.452999\pi\) | |||||||
\(272\) | 1.00396e11 | 1.11214 | ||||||||
\(273\) | 4.54632e9 | 0.0495368 | ||||||||
\(274\) | 1.58960e11 | 1.70376 | ||||||||
\(275\) | −1.68454e11 | −1.77617 | ||||||||
\(276\) | −4.70419e8 | −0.00487971 | ||||||||
\(277\) | 6.74230e10 | 0.688096 | 0.344048 | − | 0.938952i | \(-0.388202\pi\) | ||||
0.344048 | + | 0.938952i | \(0.388202\pi\) | |||||||
\(278\) | −9.85801e10 | −0.989892 | ||||||||
\(279\) | 9.38394e10 | 0.927185 | ||||||||
\(280\) | 1.09325e10 | 0.106294 | ||||||||
\(281\) | 4.36337e10 | 0.417487 | 0.208744 | − | 0.977970i | \(-0.433063\pi\) | ||||
0.208744 | + | 0.977970i | \(0.433063\pi\) | |||||||
\(282\) | 8.88749e10 | 0.836871 | ||||||||
\(283\) | −1.65395e11 | −1.53279 | −0.766395 | − | 0.642370i | \(-0.777951\pi\) | ||||
−0.766395 | + | 0.642370i | \(0.777951\pi\) | |||||||
\(284\) | −3.56646e7 | −0.000325316 0 | ||||||||
\(285\) | 2.64514e10 | 0.237491 | ||||||||
\(286\) | 6.02573e10 | 0.532553 | ||||||||
\(287\) | 1.89086e10 | 0.164509 | ||||||||
\(288\) | −1.37670e9 | −0.0117916 | ||||||||
\(289\) | 3.03566e10 | 0.255984 | ||||||||
\(290\) | 4.71243e10 | 0.391250 | ||||||||
\(291\) | 3.28190e10 | 0.268292 | ||||||||
\(292\) | 1.43842e9 | 0.0115788 | ||||||||
\(293\) | 5.54864e10 | 0.439827 | 0.219914 | − | 0.975519i | \(-0.429422\pi\) | ||||
0.219914 | + | 0.975519i | \(0.429422\pi\) | |||||||
\(294\) | 8.61507e9 | 0.0672506 | ||||||||
\(295\) | 2.41472e8 | 0.00185638 | ||||||||
\(296\) | 1.52607e11 | 1.15548 | ||||||||
\(297\) | −2.16997e11 | −1.61827 | ||||||||
\(298\) | 3.32977e10 | 0.244591 | ||||||||
\(299\) | 5.21425e10 | 0.377287 | ||||||||
\(300\) | 4.63760e8 | 0.00330558 | ||||||||
\(301\) | −9.74054e10 | −0.683965 | ||||||||
\(302\) | −1.39930e11 | −0.968009 | ||||||||
\(303\) | −6.18413e9 | −0.0421489 | ||||||||
\(304\) | 2.65075e11 | 1.78007 | ||||||||
\(305\) | −2.00441e10 | −0.132629 | ||||||||
\(306\) | 1.32995e11 | 0.867138 | ||||||||
\(307\) | −2.95750e11 | −1.90021 | −0.950105 | − | 0.311932i | \(-0.899024\pi\) | ||||
−0.950105 | + | 0.311932i | \(0.899024\pi\) | |||||||
\(308\) | −8.73415e8 | −0.00553022 | ||||||||
\(309\) | 8.77421e9 | 0.0547514 | ||||||||
\(310\) | 5.41770e10 | 0.333187 | ||||||||
\(311\) | 2.21826e11 | 1.34460 | 0.672298 | − | 0.740281i | \(-0.265308\pi\) | ||||
0.672298 | + | 0.740281i | \(0.265308\pi\) | |||||||
\(312\) | −2.20192e10 | −0.131555 | ||||||||
\(313\) | −3.12860e11 | −1.84247 | −0.921236 | − | 0.389004i | \(-0.872819\pi\) | ||||
−0.921236 | + | 0.389004i | \(0.872819\pi\) | |||||||
\(314\) | 6.61933e10 | 0.384265 | ||||||||
\(315\) | 1.43723e10 | 0.0822486 | ||||||||
\(316\) | −1.03514e9 | −0.00583993 | ||||||||
\(317\) | 1.52625e11 | 0.848903 | 0.424451 | − | 0.905451i | \(-0.360467\pi\) | ||||
0.424451 | + | 0.905451i | \(0.360467\pi\) | |||||||
\(318\) | 7.61266e10 | 0.417459 | ||||||||
\(319\) | −4.99723e11 | −2.70191 | ||||||||
\(320\) | −5.29464e10 | −0.282268 | ||||||||
\(321\) | −3.92503e10 | −0.206334 | ||||||||
\(322\) | 9.88077e10 | 0.512200 | ||||||||
\(323\) | 3.93256e11 | 2.01031 | ||||||||
\(324\) | −5.72115e8 | −0.00288423 | ||||||||
\(325\) | −5.14044e10 | −0.255579 | ||||||||
\(326\) | 4.82618e8 | 0.00236660 | ||||||||
\(327\) | −4.64534e10 | −0.224674 | ||||||||
\(328\) | −9.15801e10 | −0.436887 | ||||||||
\(329\) | 1.42790e11 | 0.671916 | ||||||||
\(330\) | −5.47674e10 | −0.254220 | ||||||||
\(331\) | −2.19954e11 | −1.00718 | −0.503589 | − | 0.863943i | \(-0.667987\pi\) | ||||
−0.503589 | + | 0.863943i | \(0.667987\pi\) | |||||||
\(332\) | 1.65761e9 | 0.00748790 | ||||||||
\(333\) | 2.00624e11 | 0.894094 | ||||||||
\(334\) | 2.62572e11 | 1.15449 | ||||||||
\(335\) | 6.19977e10 | 0.268951 | ||||||||
\(336\) | −4.14087e10 | −0.177241 | ||||||||
\(337\) | −1.30279e11 | −0.550224 | −0.275112 | − | 0.961412i | \(-0.588715\pi\) | ||||
−0.275112 | + | 0.961412i | \(0.588715\pi\) | |||||||
\(338\) | 1.83877e10 | 0.0766306 | ||||||||
\(339\) | 1.01130e11 | 0.415892 | ||||||||
\(340\) | −5.87322e8 | −0.00238353 | ||||||||
\(341\) | −5.74512e11 | −2.30093 | ||||||||
\(342\) | 3.51144e11 | 1.38793 | ||||||||
\(343\) | 1.38413e10 | 0.0539949 | ||||||||
\(344\) | 4.71765e11 | 1.81640 | ||||||||
\(345\) | −4.73919e10 | −0.180102 | ||||||||
\(346\) | −2.17198e11 | −0.814729 | ||||||||
\(347\) | −2.65960e11 | −0.984768 | −0.492384 | − | 0.870378i | \(-0.663874\pi\) | ||||
−0.492384 | + | 0.870378i | \(0.663874\pi\) | |||||||
\(348\) | 1.37575e9 | 0.00502844 | ||||||||
\(349\) | −2.10746e11 | −0.760405 | −0.380203 | − | 0.924903i | \(-0.624146\pi\) | ||||
−0.380203 | + | 0.924903i | \(0.624146\pi\) | |||||||
\(350\) | −9.74090e10 | −0.346971 | ||||||||
\(351\) | −6.62174e10 | −0.232857 | ||||||||
\(352\) | 8.42857e9 | 0.0292625 | ||||||||
\(353\) | 2.15031e11 | 0.737081 | 0.368540 | − | 0.929612i | \(-0.379858\pi\) | ||||
0.368540 | + | 0.929612i | \(0.379858\pi\) | |||||||
\(354\) | −9.21615e8 | −0.00311914 | ||||||||
\(355\) | −3.59300e9 | −0.0120069 | ||||||||
\(356\) | 4.33508e7 | 0.000143045 0 | ||||||||
\(357\) | −6.14326e10 | −0.200167 | ||||||||
\(358\) | 2.31150e11 | 0.743739 | ||||||||
\(359\) | −2.50831e11 | −0.796995 | −0.398497 | − | 0.917169i | \(-0.630468\pi\) | ||||
−0.398497 | + | 0.917169i | \(0.630468\pi\) | |||||||
\(360\) | −6.96095e10 | −0.218427 | ||||||||
\(361\) | 7.15618e11 | 2.21768 | ||||||||
\(362\) | 3.71518e11 | 1.13708 | ||||||||
\(363\) | 4.24448e11 | 1.28305 | ||||||||
\(364\) | −2.66525e8 | −0.000795759 0 | ||||||||
\(365\) | 1.44912e11 | 0.427352 | ||||||||
\(366\) | 7.65014e10 | 0.222846 | ||||||||
\(367\) | −4.69761e11 | −1.35170 | −0.675849 | − | 0.737040i | \(-0.736223\pi\) | ||||
−0.675849 | + | 0.737040i | \(0.736223\pi\) | |||||||
\(368\) | −4.74924e11 | −1.34992 | ||||||||
\(369\) | −1.20395e11 | −0.338057 | ||||||||
\(370\) | 1.15828e11 | 0.321295 | ||||||||
\(371\) | 1.22308e11 | 0.335175 | ||||||||
\(372\) | 1.58165e9 | 0.00428220 | ||||||||
\(373\) | 3.42061e11 | 0.914984 | 0.457492 | − | 0.889214i | \(-0.348748\pi\) | ||||
0.457492 | + | 0.889214i | \(0.348748\pi\) | |||||||
\(374\) | −8.14232e11 | −2.15192 | ||||||||
\(375\) | 9.74220e10 | 0.254400 | ||||||||
\(376\) | −6.91575e11 | −1.78441 | ||||||||
\(377\) | −1.52492e11 | −0.388786 | ||||||||
\(378\) | −1.25479e11 | −0.316124 | ||||||||
\(379\) | 2.27292e11 | 0.565859 | 0.282929 | − | 0.959141i | \(-0.408694\pi\) | ||||
0.282929 | + | 0.959141i | \(0.408694\pi\) | |||||||
\(380\) | −1.55070e9 | −0.00381505 | ||||||||
\(381\) | 2.12937e11 | 0.517712 | ||||||||
\(382\) | 2.18754e11 | 0.525618 | ||||||||
\(383\) | 1.97764e11 | 0.469627 | 0.234814 | − | 0.972040i | \(-0.424552\pi\) | ||||
0.234814 | + | 0.972040i | \(0.424552\pi\) | |||||||
\(384\) | 1.99021e11 | 0.467099 | ||||||||
\(385\) | −8.79913e10 | −0.204111 | ||||||||
\(386\) | −7.09864e11 | −1.62754 | ||||||||
\(387\) | 6.20202e11 | 1.40551 | ||||||||
\(388\) | −1.92399e9 | −0.00430984 | ||||||||
\(389\) | 7.21867e11 | 1.59839 | 0.799197 | − | 0.601069i | \(-0.205258\pi\) | ||||
0.799197 | + | 0.601069i | \(0.205258\pi\) | |||||||
\(390\) | −1.67124e10 | −0.0365805 | ||||||||
\(391\) | −7.04581e11 | −1.52453 | ||||||||
\(392\) | −6.70377e10 | −0.143394 | ||||||||
\(393\) | −2.75698e11 | −0.582999 | ||||||||
\(394\) | 3.25219e11 | 0.679897 | ||||||||
\(395\) | −1.04284e11 | −0.215542 | ||||||||
\(396\) | 5.56122e9 | 0.0113643 | ||||||||
\(397\) | 8.41609e9 | 0.0170041 | 0.00850204 | − | 0.999964i | \(-0.497294\pi\) | ||||
0.00850204 | + | 0.999964i | \(0.497294\pi\) | |||||||
\(398\) | 2.55574e11 | 0.510556 | ||||||||
\(399\) | −1.62199e11 | −0.320384 | ||||||||
\(400\) | 4.68201e11 | 0.914455 | ||||||||
\(401\) | −6.75074e10 | −0.130377 | −0.0651886 | − | 0.997873i | \(-0.520765\pi\) | ||||
−0.0651886 | + | 0.997873i | \(0.520765\pi\) | |||||||
\(402\) | −2.36624e11 | −0.451899 | ||||||||
\(403\) | −1.75314e11 | −0.331088 | ||||||||
\(404\) | 3.62540e8 | 0.000677080 0 | ||||||||
\(405\) | −5.76371e10 | −0.106452 | ||||||||
\(406\) | −2.88965e11 | −0.527811 | ||||||||
\(407\) | −1.22828e12 | −2.21882 | ||||||||
\(408\) | 2.97537e11 | 0.531582 | ||||||||
\(409\) | 2.10564e11 | 0.372074 | 0.186037 | − | 0.982543i | \(-0.440436\pi\) | ||||
0.186037 | + | 0.982543i | \(0.440436\pi\) | |||||||
\(410\) | −6.95086e10 | −0.121482 | ||||||||
\(411\) | 4.67521e11 | 0.808189 | ||||||||
\(412\) | −5.14382e8 | −0.000879526 0 | ||||||||
\(413\) | −1.48070e9 | −0.00250433 | ||||||||
\(414\) | −6.29131e11 | −1.05254 | ||||||||
\(415\) | 1.66994e11 | 0.276366 | ||||||||
\(416\) | 2.57200e9 | 0.00421067 | ||||||||
\(417\) | −2.89937e11 | −0.469560 | ||||||||
\(418\) | −2.14980e12 | −3.44434 | ||||||||
\(419\) | 9.95463e10 | 0.157784 | 0.0788918 | − | 0.996883i | \(-0.474862\pi\) | ||||
0.0788918 | + | 0.996883i | \(0.474862\pi\) | |||||||
\(420\) | 2.42243e8 | 0.000379865 0 | ||||||||
\(421\) | −4.42260e10 | −0.0686133 | −0.0343067 | − | 0.999411i | \(-0.510922\pi\) | ||||
−0.0343067 | + | 0.999411i | \(0.510922\pi\) | |||||||
\(422\) | 2.35757e11 | 0.361875 | ||||||||
\(423\) | −9.09173e11 | −1.38075 | ||||||||
\(424\) | −5.92374e11 | −0.890123 | ||||||||
\(425\) | 6.94607e11 | 1.03273 | ||||||||
\(426\) | 1.37132e10 | 0.0201742 | ||||||||
\(427\) | 1.22910e11 | 0.178921 | ||||||||
\(428\) | 2.30102e9 | 0.00331455 | ||||||||
\(429\) | 1.77224e11 | 0.252619 | ||||||||
\(430\) | 3.58066e11 | 0.505074 | ||||||||
\(431\) | −8.65731e11 | −1.20847 | −0.604234 | − | 0.796807i | \(-0.706521\pi\) | ||||
−0.604234 | + | 0.796807i | \(0.706521\pi\) | |||||||
\(432\) | 6.03120e11 | 0.833158 | ||||||||
\(433\) | 1.08066e12 | 1.47738 | 0.738689 | − | 0.674046i | \(-0.235445\pi\) | ||||
0.738689 | + | 0.674046i | \(0.235445\pi\) | |||||||
\(434\) | −3.32212e11 | −0.449481 | ||||||||
\(435\) | 1.38599e11 | 0.185591 | ||||||||
\(436\) | 2.72330e9 | 0.00360916 | ||||||||
\(437\) | −1.86029e12 | −2.44014 | ||||||||
\(438\) | −5.53079e11 | −0.718048 | ||||||||
\(439\) | 7.82505e10 | 0.100553 | 0.0502767 | − | 0.998735i | \(-0.483990\pi\) | ||||
0.0502767 | + | 0.998735i | \(0.483990\pi\) | |||||||
\(440\) | 4.26169e11 | 0.542057 | ||||||||
\(441\) | −8.81305e10 | −0.110956 | ||||||||
\(442\) | −2.48465e11 | −0.309646 | ||||||||
\(443\) | 8.02517e11 | 0.990005 | 0.495002 | − | 0.868892i | \(-0.335167\pi\) | ||||
0.495002 | + | 0.868892i | \(0.335167\pi\) | |||||||
\(444\) | 3.38148e9 | 0.00412937 | ||||||||
\(445\) | 4.36733e9 | 0.00527954 | ||||||||
\(446\) | −6.50483e11 | −0.778447 | ||||||||
\(447\) | 9.79327e10 | 0.116023 | ||||||||
\(448\) | 3.24666e11 | 0.380790 | ||||||||
\(449\) | 7.23243e11 | 0.839800 | 0.419900 | − | 0.907570i | \(-0.362065\pi\) | ||||
0.419900 | + | 0.907570i | \(0.362065\pi\) | |||||||
\(450\) | 6.20225e11 | 0.713005 | ||||||||
\(451\) | 7.37093e11 | 0.838935 | ||||||||
\(452\) | −5.92867e9 | −0.00668089 | ||||||||
\(453\) | −4.11552e11 | −0.459180 | ||||||||
\(454\) | −2.27688e11 | −0.251530 | ||||||||
\(455\) | −2.68508e10 | −0.0293701 | ||||||||
\(456\) | 7.85582e11 | 0.850844 | ||||||||
\(457\) | 2.75313e11 | 0.295260 | 0.147630 | − | 0.989043i | \(-0.452836\pi\) | ||||
0.147630 | + | 0.989043i | \(0.452836\pi\) | |||||||
\(458\) | −1.35269e12 | −1.43649 | ||||||||
\(459\) | 8.94769e11 | 0.940922 | ||||||||
\(460\) | 2.77832e9 | 0.00289316 | ||||||||
\(461\) | −6.14394e10 | −0.0633567 | −0.0316783 | − | 0.999498i | \(-0.510085\pi\) | ||||
−0.0316783 | + | 0.999498i | \(0.510085\pi\) | |||||||
\(462\) | 3.35833e11 | 0.342952 | ||||||||
\(463\) | 1.05539e12 | 1.06733 | 0.533666 | − | 0.845695i | \(-0.320814\pi\) | ||||
0.533666 | + | 0.845695i | \(0.320814\pi\) | |||||||
\(464\) | 1.38892e12 | 1.39107 | ||||||||
\(465\) | 1.59342e11 | 0.158049 | ||||||||
\(466\) | −3.37220e11 | −0.331266 | ||||||||
\(467\) | 1.58916e12 | 1.54612 | 0.773059 | − | 0.634334i | \(-0.218725\pi\) | ||||
0.773059 | + | 0.634334i | \(0.218725\pi\) | |||||||
\(468\) | 1.69702e9 | 0.00163524 | ||||||||
\(469\) | −3.80168e11 | −0.362826 | ||||||||
\(470\) | −5.24900e11 | −0.496177 | ||||||||
\(471\) | 1.94683e11 | 0.182278 | ||||||||
\(472\) | 7.17149e9 | 0.00665074 | ||||||||
\(473\) | −3.79705e12 | −3.48796 | ||||||||
\(474\) | 3.98017e11 | 0.362159 | ||||||||
\(475\) | 1.83396e12 | 1.65298 | ||||||||
\(476\) | 3.60145e9 | 0.00321548 | ||||||||
\(477\) | −7.78760e11 | −0.688765 | ||||||||
\(478\) | −1.20312e12 | −1.05411 | ||||||||
\(479\) | −1.20954e12 | −1.04981 | −0.524906 | − | 0.851160i | \(-0.675900\pi\) | ||||
−0.524906 | + | 0.851160i | \(0.675900\pi\) | |||||||
\(480\) | −2.33767e9 | −0.00201001 | ||||||||
\(481\) | −3.74812e11 | −0.319272 | ||||||||
\(482\) | 2.98267e11 | 0.251706 | ||||||||
\(483\) | 2.90606e11 | 0.242965 | ||||||||
\(484\) | −2.48830e10 | −0.0206109 | ||||||||
\(485\) | −1.93831e11 | −0.159069 | ||||||||
\(486\) | 1.24864e12 | 1.01525 | ||||||||
\(487\) | −8.91824e11 | −0.718454 | −0.359227 | − | 0.933250i | \(-0.616960\pi\) | ||||
−0.359227 | + | 0.933250i | \(0.616960\pi\) | |||||||
\(488\) | −5.95291e11 | −0.475160 | ||||||||
\(489\) | 1.41944e9 | 0.00112261 | ||||||||
\(490\) | −5.08811e10 | −0.0398725 | ||||||||
\(491\) | −7.46715e10 | −0.0579813 | −0.0289906 | − | 0.999580i | \(-0.509229\pi\) | ||||
−0.0289906 | + | 0.999580i | \(0.509229\pi\) | |||||||
\(492\) | −2.02924e9 | −0.00156131 | ||||||||
\(493\) | 2.06056e12 | 1.57099 | ||||||||
\(494\) | −6.56019e11 | −0.495616 | ||||||||
\(495\) | 5.60260e11 | 0.419437 | ||||||||
\(496\) | 1.59679e12 | 1.18462 | ||||||||
\(497\) | 2.20322e10 | 0.0161977 | ||||||||
\(498\) | −6.37359e11 | −0.464357 | ||||||||
\(499\) | 1.33765e12 | 0.965808 | 0.482904 | − | 0.875673i | \(-0.339582\pi\) | ||||
0.482904 | + | 0.875673i | \(0.339582\pi\) | |||||||
\(500\) | −5.71130e9 | −0.00408668 | ||||||||
\(501\) | 7.72259e11 | 0.547638 | ||||||||
\(502\) | 1.16905e11 | 0.0821612 | ||||||||
\(503\) | 4.15314e11 | 0.289281 | 0.144641 | − | 0.989484i | \(-0.453797\pi\) | ||||
0.144641 | + | 0.989484i | \(0.453797\pi\) | |||||||
\(504\) | 4.26844e11 | 0.294667 | ||||||||
\(505\) | 3.65238e10 | 0.0249899 | ||||||||
\(506\) | 3.85172e12 | 2.61202 | ||||||||
\(507\) | 5.40806e10 | 0.0363501 | ||||||||
\(508\) | −1.24833e10 | −0.00831653 | ||||||||
\(509\) | −1.12069e12 | −0.740039 | −0.370020 | − | 0.929024i | \(-0.620649\pi\) | ||||
−0.370020 | + | 0.929024i | \(0.620649\pi\) | |||||||
\(510\) | 2.25828e11 | 0.147813 | ||||||||
\(511\) | −8.88596e11 | −0.576515 | ||||||||
\(512\) | −1.57228e12 | −1.01115 | ||||||||
\(513\) | 2.36244e12 | 1.50603 | ||||||||
\(514\) | −1.80730e12 | −1.14208 | ||||||||
\(515\) | −5.18210e10 | −0.0324618 | ||||||||
\(516\) | 1.04534e10 | 0.00649134 | ||||||||
\(517\) | 5.56622e12 | 3.42652 | ||||||||
\(518\) | −7.10252e11 | −0.433440 | ||||||||
\(519\) | −6.38807e11 | −0.386471 | ||||||||
\(520\) | 1.30047e11 | 0.0779982 | ||||||||
\(521\) | −8.83586e11 | −0.525387 | −0.262693 | − | 0.964879i | \(-0.584611\pi\) | ||||
−0.262693 | + | 0.964879i | \(0.584611\pi\) | |||||||
\(522\) | 1.83991e12 | 1.08462 | ||||||||
\(523\) | −2.69371e11 | −0.157432 | −0.0787161 | − | 0.996897i | \(-0.525082\pi\) | ||||
−0.0787161 | + | 0.996897i | \(0.525082\pi\) | |||||||
\(524\) | 1.61626e10 | 0.00936529 | ||||||||
\(525\) | −2.86493e11 | −0.164587 | ||||||||
\(526\) | 1.37179e10 | 0.00781364 | ||||||||
\(527\) | 2.36895e12 | 1.33785 | ||||||||
\(528\) | −1.61419e12 | −0.903864 | ||||||||
\(529\) | 1.53186e12 | 0.850488 | ||||||||
\(530\) | −4.49608e11 | −0.247510 | ||||||||
\(531\) | 9.42794e9 | 0.00514626 | ||||||||
\(532\) | 9.50883e9 | 0.00514665 | ||||||||
\(533\) | 2.24926e11 | 0.120717 | ||||||||
\(534\) | −1.66686e10 | −0.00887081 | ||||||||
\(535\) | 2.31814e11 | 0.122334 | ||||||||
\(536\) | 1.84127e12 | 0.963556 | ||||||||
\(537\) | 6.79842e11 | 0.352796 | ||||||||
\(538\) | −1.47816e12 | −0.760680 | ||||||||
\(539\) | 5.39561e11 | 0.275354 | ||||||||
\(540\) | −3.52828e9 | −0.00178563 | ||||||||
\(541\) | −7.05511e11 | −0.354092 | −0.177046 | − | 0.984203i | \(-0.556654\pi\) | ||||
−0.177046 | + | 0.984203i | \(0.556654\pi\) | |||||||
\(542\) | 5.88914e11 | 0.293127 | ||||||||
\(543\) | 1.09268e12 | 0.539380 | ||||||||
\(544\) | −3.47544e10 | −0.0170143 | ||||||||
\(545\) | 2.74356e11 | 0.133208 | ||||||||
\(546\) | 1.02480e11 | 0.0493484 | ||||||||
\(547\) | −2.49219e12 | −1.19025 | −0.595126 | − | 0.803633i | \(-0.702898\pi\) | ||||
−0.595126 | + | 0.803633i | \(0.702898\pi\) | |||||||
\(548\) | −2.74081e10 | −0.0129828 | ||||||||
\(549\) | −7.82594e11 | −0.367672 | ||||||||
\(550\) | −3.79720e12 | −1.76942 | ||||||||
\(551\) | 5.44046e12 | 2.51451 | ||||||||
\(552\) | −1.40750e12 | −0.645240 | ||||||||
\(553\) | 6.39468e11 | 0.290774 | ||||||||
\(554\) | 1.51981e12 | 0.685479 | ||||||||
\(555\) | 3.40664e11 | 0.152408 | ||||||||
\(556\) | 1.69974e10 | 0.00754301 | ||||||||
\(557\) | −2.05323e12 | −0.903836 | −0.451918 | − | 0.892060i | \(-0.649260\pi\) | ||||
−0.451918 | + | 0.892060i | \(0.649260\pi\) | |||||||
\(558\) | 2.11527e12 | 0.923659 | ||||||||
\(559\) | −1.15868e12 | −0.501893 | ||||||||
\(560\) | 2.44562e11 | 0.105086 | ||||||||
\(561\) | −2.39476e12 | −1.02077 | ||||||||
\(562\) | 9.83562e11 | 0.415900 | ||||||||
\(563\) | −4.20623e12 | −1.76443 | −0.882216 | − | 0.470845i | \(-0.843949\pi\) | ||||
−0.882216 | + | 0.470845i | \(0.843949\pi\) | |||||||
\(564\) | −1.53240e10 | −0.00637698 | ||||||||
\(565\) | −5.97278e11 | −0.246580 | ||||||||
\(566\) | −3.72822e12 | −1.52696 | ||||||||
\(567\) | 3.53429e11 | 0.143608 | ||||||||
\(568\) | −1.06709e11 | −0.0430162 | ||||||||
\(569\) | −1.08108e12 | −0.432367 | −0.216184 | − | 0.976353i | \(-0.569361\pi\) | ||||
−0.216184 | + | 0.976353i | \(0.569361\pi\) | |||||||
\(570\) | 5.96251e11 | 0.236588 | ||||||||
\(571\) | −2.15704e12 | −0.849173 | −0.424586 | − | 0.905387i | \(-0.639581\pi\) | ||||
−0.424586 | + | 0.905387i | \(0.639581\pi\) | |||||||
\(572\) | −1.03897e10 | −0.00405807 | ||||||||
\(573\) | 6.43383e11 | 0.249329 | ||||||||
\(574\) | 4.26225e11 | 0.163884 | ||||||||
\(575\) | −3.28583e12 | −1.25354 | ||||||||
\(576\) | −2.06722e12 | −0.782502 | ||||||||
\(577\) | 1.24361e12 | 0.467083 | 0.233541 | − | 0.972347i | \(-0.424969\pi\) | ||||
0.233541 | + | 0.972347i | \(0.424969\pi\) | |||||||
\(578\) | 6.84280e11 | 0.255011 | ||||||||
\(579\) | −2.08780e12 | −0.772032 | ||||||||
\(580\) | −8.12526e9 | −0.00298134 | ||||||||
\(581\) | −1.02400e12 | −0.372828 | ||||||||
\(582\) | 7.39786e11 | 0.267271 | ||||||||
\(583\) | 4.76779e12 | 1.70926 | ||||||||
\(584\) | 4.30375e12 | 1.53105 | ||||||||
\(585\) | 1.70965e11 | 0.0603540 | ||||||||
\(586\) | 1.25074e12 | 0.438154 | ||||||||
\(587\) | −9.64442e11 | −0.335278 | −0.167639 | − | 0.985848i | \(-0.553614\pi\) | ||||
−0.167639 | + | 0.985848i | \(0.553614\pi\) | |||||||
\(588\) | −1.48543e9 | −0.000512452 0 | ||||||||
\(589\) | 6.25469e12 | 2.14135 | ||||||||
\(590\) | 5.44311e9 | 0.00184932 | ||||||||
\(591\) | 9.56511e11 | 0.322512 | ||||||||
\(592\) | 3.41386e12 | 1.14235 | ||||||||
\(593\) | −4.96432e12 | −1.64859 | −0.824297 | − | 0.566158i | \(-0.808429\pi\) | ||||
−0.824297 | + | 0.566158i | \(0.808429\pi\) | |||||||
\(594\) | −4.89142e12 | −1.61211 | ||||||||
\(595\) | 3.62824e11 | 0.118678 | ||||||||
\(596\) | −5.74124e9 | −0.00186379 | ||||||||
\(597\) | 7.51677e11 | 0.242185 | ||||||||
\(598\) | 1.17536e12 | 0.375852 | ||||||||
\(599\) | 2.35087e12 | 0.746120 | 0.373060 | − | 0.927807i | \(-0.378309\pi\) | ||||
0.373060 | + | 0.927807i | \(0.378309\pi\) | |||||||
\(600\) | 1.38757e12 | 0.437094 | ||||||||
\(601\) | −2.37861e12 | −0.743682 | −0.371841 | − | 0.928296i | \(-0.621273\pi\) | ||||
−0.371841 | + | 0.928296i | \(0.621273\pi\) | |||||||
\(602\) | −2.19565e12 | −0.681364 | ||||||||
\(603\) | 2.42062e12 | 0.745586 | ||||||||
\(604\) | 2.41270e10 | 0.00737627 | ||||||||
\(605\) | −2.50681e12 | −0.760715 | ||||||||
\(606\) | −1.39399e11 | −0.0419886 | ||||||||
\(607\) | −5.88382e12 | −1.75918 | −0.879590 | − | 0.475733i | \(-0.842183\pi\) | ||||
−0.879590 | + | 0.475733i | \(0.842183\pi\) | |||||||
\(608\) | −9.17615e10 | −0.0272329 | ||||||||
\(609\) | −8.49884e11 | −0.250370 | ||||||||
\(610\) | −4.51821e11 | −0.132124 | ||||||||
\(611\) | 1.69855e12 | 0.493052 | ||||||||
\(612\) | −2.29312e10 | −0.00660762 | ||||||||
\(613\) | −2.45729e12 | −0.702884 | −0.351442 | − | 0.936210i | \(-0.614309\pi\) | ||||
−0.351442 | + | 0.936210i | \(0.614309\pi\) | |||||||
\(614\) | −6.66660e12 | −1.89298 | ||||||||
\(615\) | −2.04434e11 | −0.0576255 | ||||||||
\(616\) | −2.61326e12 | −0.731256 | ||||||||
\(617\) | 1.18050e12 | 0.327931 | 0.163966 | − | 0.986466i | \(-0.447571\pi\) | ||||
0.163966 | + | 0.986466i | \(0.447571\pi\) | |||||||
\(618\) | 1.97783e11 | 0.0545432 | ||||||||
\(619\) | −5.82546e12 | −1.59486 | −0.797430 | − | 0.603412i | \(-0.793807\pi\) | ||||
−0.797430 | + | 0.603412i | \(0.793807\pi\) | |||||||
\(620\) | −9.34130e9 | −0.00253889 | ||||||||
\(621\) | −4.23270e12 | −1.14210 | ||||||||
\(622\) | 5.00027e12 | 1.33948 | ||||||||
\(623\) | −2.67804e10 | −0.00712230 | ||||||||
\(624\) | −4.92576e11 | −0.130060 | ||||||||
\(625\) | 2.93987e12 | 0.770671 | ||||||||
\(626\) | −7.05230e12 | −1.83547 | ||||||||
\(627\) | −6.32285e12 | −1.63384 | ||||||||
\(628\) | −1.14132e10 | −0.00292811 | ||||||||
\(629\) | 5.06469e12 | 1.29010 | ||||||||
\(630\) | 3.23971e11 | 0.0819358 | ||||||||
\(631\) | 5.20483e12 | 1.30700 | 0.653498 | − | 0.756928i | \(-0.273301\pi\) | ||||
0.653498 | + | 0.756928i | \(0.273301\pi\) | |||||||
\(632\) | −3.09715e12 | −0.772209 | ||||||||
\(633\) | 6.93392e11 | 0.171657 | ||||||||
\(634\) | 3.44037e12 | 0.845674 | ||||||||
\(635\) | −1.25762e12 | −0.306949 | ||||||||
\(636\) | −1.31259e10 | −0.00318106 | ||||||||
\(637\) | 1.64648e11 | 0.0396214 | ||||||||
\(638\) | −1.12644e13 | −2.69164 | ||||||||
\(639\) | −1.40284e11 | −0.0332854 | ||||||||
\(640\) | −1.17543e12 | −0.276941 | ||||||||
\(641\) | −4.11424e12 | −0.962561 | −0.481281 | − | 0.876567i | \(-0.659828\pi\) | ||||
−0.481281 | + | 0.876567i | \(0.659828\pi\) | |||||||
\(642\) | −8.84756e11 | −0.205549 | ||||||||
\(643\) | 2.85804e12 | 0.659354 | 0.329677 | − | 0.944094i | \(-0.393060\pi\) | ||||
0.329677 | + | 0.944094i | \(0.393060\pi\) | |||||||
\(644\) | −1.70366e10 | −0.00390298 | ||||||||
\(645\) | 1.05312e12 | 0.239584 | ||||||||
\(646\) | 8.86452e12 | 2.00267 | ||||||||
\(647\) | −8.06581e12 | −1.80958 | −0.904792 | − | 0.425855i | \(-0.859973\pi\) | ||||
−0.904792 | + | 0.425855i | \(0.859973\pi\) | |||||||
\(648\) | −1.71177e12 | −0.381380 | ||||||||
\(649\) | −5.77206e10 | −0.0127711 | ||||||||
\(650\) | −1.15873e12 | −0.254607 | ||||||||
\(651\) | −9.77079e11 | −0.213214 | ||||||||
\(652\) | −8.32139e7 | −1.80336e−5 0 | ||||||||
\(653\) | −3.40144e12 | −0.732072 | −0.366036 | − | 0.930601i | \(-0.619285\pi\) | ||||
−0.366036 | + | 0.930601i | \(0.619285\pi\) | |||||||
\(654\) | −1.04712e12 | −0.223819 | ||||||||
\(655\) | 1.62829e12 | 0.345657 | ||||||||
\(656\) | −2.04867e12 | −0.431921 | ||||||||
\(657\) | 5.65789e12 | 1.18470 | ||||||||
\(658\) | 3.21867e12 | 0.669361 | ||||||||
\(659\) | 3.72618e12 | 0.769625 | 0.384812 | − | 0.922995i | \(-0.374266\pi\) | ||||
0.384812 | + | 0.922995i | \(0.374266\pi\) | |||||||
\(660\) | 9.44310e9 | 0.00193717 | ||||||||
\(661\) | 6.25787e12 | 1.27503 | 0.637515 | − | 0.770438i | \(-0.279963\pi\) | ||||
0.637515 | + | 0.770438i | \(0.279963\pi\) | |||||||
\(662\) | −4.95807e12 | −1.00335 | ||||||||
\(663\) | −7.30769e11 | −0.146882 | ||||||||
\(664\) | 4.95957e12 | 0.990119 | ||||||||
\(665\) | 9.57958e11 | 0.189954 | ||||||||
\(666\) | 4.52233e12 | 0.890694 | ||||||||
\(667\) | −9.74746e12 | −1.90689 | ||||||||
\(668\) | −4.52732e10 | −0.00879725 | ||||||||
\(669\) | −1.91315e12 | −0.369260 | ||||||||
\(670\) | 1.39751e12 | 0.267929 | ||||||||
\(671\) | 4.79127e12 | 0.912429 | ||||||||
\(672\) | 1.43346e10 | 0.00271158 | ||||||||
\(673\) | 1.01140e13 | 1.90044 | 0.950220 | − | 0.311579i | \(-0.100858\pi\) | ||||
0.950220 | + | 0.311579i | \(0.100858\pi\) | |||||||
\(674\) | −2.93667e12 | −0.548132 | ||||||||
\(675\) | 4.17278e12 | 0.773675 | ||||||||
\(676\) | −3.17044e9 | −0.000583928 0 | ||||||||
\(677\) | −8.92555e11 | −0.163300 | −0.0816500 | − | 0.996661i | \(-0.526019\pi\) | ||||
−0.0816500 | + | 0.996661i | \(0.526019\pi\) | |||||||
\(678\) | 2.27960e12 | 0.414310 | ||||||||
\(679\) | 1.18857e12 | 0.214590 | ||||||||
\(680\) | −1.75727e12 | −0.315173 | ||||||||
\(681\) | −6.69660e11 | −0.119314 | ||||||||
\(682\) | −1.29503e13 | −2.29218 | ||||||||
\(683\) | 1.05244e12 | 0.185056 | 0.0925282 | − | 0.995710i | \(-0.470505\pi\) | ||||
0.0925282 | + | 0.995710i | \(0.470505\pi\) | |||||||
\(684\) | −6.05448e10 | −0.0105761 | ||||||||
\(685\) | −2.76120e12 | −0.479172 | ||||||||
\(686\) | 3.12002e11 | 0.0537896 | ||||||||
\(687\) | −3.97842e12 | −0.681406 | ||||||||
\(688\) | 1.05535e13 | 1.79576 | ||||||||
\(689\) | 1.45491e12 | 0.245951 | ||||||||
\(690\) | −1.06828e12 | −0.179417 | ||||||||
\(691\) | 9.39665e12 | 1.56791 | 0.783956 | − | 0.620816i | \(-0.213199\pi\) | ||||
0.783956 | + | 0.620816i | \(0.213199\pi\) | |||||||
\(692\) | 3.74497e10 | 0.00620827 | ||||||||
\(693\) | −3.43550e12 | −0.565836 | ||||||||
\(694\) | −5.99511e12 | −0.981023 | ||||||||
\(695\) | 1.71238e12 | 0.278400 | ||||||||
\(696\) | 4.11625e12 | 0.664906 | ||||||||
\(697\) | −3.03934e12 | −0.487788 | ||||||||
\(698\) | −4.75051e12 | −0.757514 | ||||||||
\(699\) | −9.91807e11 | −0.157138 | ||||||||
\(700\) | 1.67954e10 | 0.00264393 | ||||||||
\(701\) | −6.60089e11 | −0.103246 | −0.0516228 | − | 0.998667i | \(-0.516439\pi\) | ||||
−0.0516228 | + | 0.998667i | \(0.516439\pi\) | |||||||
\(702\) | −1.49263e12 | −0.231972 | ||||||||
\(703\) | 1.33722e13 | 2.06492 | ||||||||
\(704\) | 1.26561e13 | 1.94188 | ||||||||
\(705\) | −1.54380e12 | −0.235364 | ||||||||
\(706\) | 4.84709e12 | 0.734278 | ||||||||
\(707\) | −2.23963e11 | −0.0337123 | ||||||||
\(708\) | 1.58906e8 | 2.37680e−5 0 | ||||||||
\(709\) | 1.24774e12 | 0.185446 | 0.0927228 | − | 0.995692i | \(-0.470443\pi\) | ||||
0.0927228 | + | 0.995692i | \(0.470443\pi\) | |||||||
\(710\) | −8.09911e10 | −0.0119612 | ||||||||
\(711\) | −4.07164e12 | −0.597525 | ||||||||
\(712\) | 1.29706e11 | 0.0189147 | ||||||||
\(713\) | −1.12063e13 | −1.62390 | ||||||||
\(714\) | −1.38477e12 | −0.199406 | ||||||||
\(715\) | −1.04670e12 | −0.149777 | ||||||||
\(716\) | −3.98553e10 | −0.00566732 | ||||||||
\(717\) | −3.53855e12 | −0.500021 | ||||||||
\(718\) | −5.65406e12 | −0.793964 | ||||||||
\(719\) | 9.24139e12 | 1.28961 | 0.644803 | − | 0.764349i | \(-0.276939\pi\) | ||||
0.644803 | + | 0.764349i | \(0.276939\pi\) | |||||||
\(720\) | −1.55718e12 | −0.215945 | ||||||||
\(721\) | 3.17765e11 | 0.0437922 | ||||||||
\(722\) | 1.61310e13 | 2.20925 | ||||||||
\(723\) | 8.77243e11 | 0.119398 | ||||||||
\(724\) | −6.40578e10 | −0.00866460 | ||||||||
\(725\) | 9.60948e12 | 1.29175 | ||||||||
\(726\) | 9.56763e12 | 1.27817 | ||||||||
\(727\) | 2.56696e12 | 0.340811 | 0.170406 | − | 0.985374i | \(-0.445492\pi\) | ||||
0.170406 | + | 0.985374i | \(0.445492\pi\) | |||||||
\(728\) | −7.97444e11 | −0.105223 | ||||||||
\(729\) | 7.75047e11 | 0.101638 | ||||||||
\(730\) | 3.26651e12 | 0.425727 | ||||||||
\(731\) | 1.56568e13 | 2.02803 | ||||||||
\(732\) | −1.31905e10 | −0.00169809 | ||||||||
\(733\) | −1.35156e13 | −1.72929 | −0.864647 | − | 0.502380i | \(-0.832458\pi\) | ||||
−0.864647 | + | 0.502380i | \(0.832458\pi\) | |||||||
\(734\) | −1.05891e13 | −1.34656 | ||||||||
\(735\) | −1.49648e11 | −0.0189137 | ||||||||
\(736\) | 1.64406e11 | 0.0206522 | ||||||||
\(737\) | −1.48197e13 | −1.85027 | ||||||||
\(738\) | −2.71387e12 | −0.336772 | ||||||||
\(739\) | 8.83237e12 | 1.08937 | 0.544687 | − | 0.838639i | \(-0.316648\pi\) | ||||
0.544687 | + | 0.838639i | \(0.316648\pi\) | |||||||
\(740\) | −1.99712e10 | −0.00244828 | ||||||||
\(741\) | −1.92944e12 | −0.235098 | ||||||||
\(742\) | 2.75698e12 | 0.333900 | ||||||||
\(743\) | 1.24941e13 | 1.50402 | 0.752012 | − | 0.659149i | \(-0.229083\pi\) | ||||
0.752012 | + | 0.659149i | \(0.229083\pi\) | |||||||
\(744\) | 4.73230e12 | 0.566231 | ||||||||
\(745\) | −5.78396e11 | −0.0687894 | ||||||||
\(746\) | 7.71052e12 | 0.911505 | ||||||||
\(747\) | 6.52005e12 | 0.766141 | ||||||||
\(748\) | 1.40391e11 | 0.0163977 | ||||||||
\(749\) | −1.42148e12 | −0.165034 | ||||||||
\(750\) | 2.19603e12 | 0.253432 | ||||||||
\(751\) | 9.68723e11 | 0.111127 | 0.0555636 | − | 0.998455i | \(-0.482304\pi\) | ||||
0.0555636 | + | 0.998455i | \(0.482304\pi\) | |||||||
\(752\) | −1.54707e13 | −1.76413 | ||||||||
\(753\) | 3.43833e11 | 0.0389736 | ||||||||
\(754\) | −3.43737e12 | −0.387307 | ||||||||
\(755\) | 2.43065e12 | 0.272246 | ||||||||
\(756\) | 2.16353e10 | 0.00240888 | ||||||||
\(757\) | −4.86384e11 | −0.0538330 | −0.0269165 | − | 0.999638i | \(-0.508569\pi\) | ||||
−0.0269165 | + | 0.999638i | \(0.508569\pi\) | |||||||
\(758\) | 5.12348e12 | 0.563707 | ||||||||
\(759\) | 1.13284e13 | 1.23903 | ||||||||
\(760\) | −4.63969e12 | −0.504461 | ||||||||
\(761\) | −2.85734e12 | −0.308838 | −0.154419 | − | 0.988005i | \(-0.549351\pi\) | ||||
−0.154419 | + | 0.988005i | \(0.549351\pi\) | |||||||
\(762\) | 4.79989e12 | 0.515744 | ||||||||
\(763\) | −1.68235e12 | −0.179703 | ||||||||
\(764\) | −3.77179e10 | −0.00400523 | ||||||||
\(765\) | −2.31018e12 | −0.243876 | ||||||||
\(766\) | 4.45788e12 | 0.467841 | ||||||||
\(767\) | −1.76136e10 | −0.00183768 | ||||||||
\(768\) | −1.03746e11 | −0.0107609 | ||||||||
\(769\) | −1.72096e13 | −1.77461 | −0.887303 | − | 0.461187i | \(-0.847424\pi\) | ||||
−0.887303 | + | 0.461187i | \(0.847424\pi\) | |||||||
\(770\) | −1.98344e12 | −0.203335 | ||||||||
\(771\) | −5.31551e12 | −0.541752 | ||||||||
\(772\) | 1.22396e11 | 0.0124019 | ||||||||
\(773\) | −1.26196e12 | −0.127127 | −0.0635636 | − | 0.997978i | \(-0.520247\pi\) | ||||
−0.0635636 | + | 0.997978i | \(0.520247\pi\) | |||||||
\(774\) | 1.39802e13 | 1.40016 | ||||||||
\(775\) | 1.10476e13 | 1.10005 | ||||||||
\(776\) | −5.75660e12 | −0.569886 | ||||||||
\(777\) | −2.08894e12 | −0.205604 | ||||||||
\(778\) | 1.62719e13 | 1.59232 | ||||||||
\(779\) | −8.02471e12 | −0.780748 | ||||||||
\(780\) | 2.88159e9 | 0.000278744 0 | ||||||||
\(781\) | 8.58857e11 | 0.0826022 | ||||||||
\(782\) | −1.58822e13 | −1.51873 | ||||||||
\(783\) | 1.23786e13 | 1.17691 | ||||||||
\(784\) | −1.49965e12 | −0.141764 | ||||||||
\(785\) | −1.14981e12 | −0.108072 | ||||||||
\(786\) | −6.21462e12 | −0.580782 | ||||||||
\(787\) | −3.34979e12 | −0.311265 | −0.155633 | − | 0.987815i | \(-0.549742\pi\) | ||||
−0.155633 | + | 0.987815i | \(0.549742\pi\) | |||||||
\(788\) | −5.60748e10 | −0.00518084 | ||||||||
\(789\) | 4.03462e10 | 0.00370644 | ||||||||
\(790\) | −2.35071e12 | −0.214722 | ||||||||
\(791\) | 3.66249e12 | 0.332646 | ||||||||
\(792\) | 1.66392e13 | 1.50269 | ||||||||
\(793\) | 1.46207e12 | 0.131292 | ||||||||
\(794\) | 1.89710e11 | 0.0169394 | ||||||||
\(795\) | −1.32235e12 | −0.117407 | ||||||||
\(796\) | −4.40666e10 | −0.00389046 | ||||||||
\(797\) | −1.97846e13 | −1.73686 | −0.868429 | − | 0.495813i | \(-0.834870\pi\) | ||||
−0.868429 | + | 0.495813i | \(0.834870\pi\) | |||||||
\(798\) | −3.65620e12 | −0.319166 | ||||||||
\(799\) | −2.29518e13 | −1.99231 | ||||||||
\(800\) | −1.62078e11 | −0.0139901 | ||||||||
\(801\) | 1.70516e11 | 0.0146359 | ||||||||
\(802\) | −1.52171e12 | −0.129881 | ||||||||
\(803\) | −3.46392e13 | −2.94001 | ||||||||
\(804\) | 4.07991e10 | 0.00344349 | ||||||||
\(805\) | −1.71634e12 | −0.144053 | ||||||||
\(806\) | −3.95182e12 | −0.329829 | ||||||||
\(807\) | −4.34747e12 | −0.360833 | ||||||||
\(808\) | 1.08472e12 | 0.0895298 | ||||||||
\(809\) | 1.17947e12 | 0.0968093 | 0.0484046 | − | 0.998828i | \(-0.484586\pi\) | ||||
0.0484046 | + | 0.998828i | \(0.484586\pi\) | |||||||
\(810\) | −1.29922e12 | −0.106047 | ||||||||
\(811\) | 2.03470e13 | 1.65161 | 0.825803 | − | 0.563959i | \(-0.190723\pi\) | ||||
0.825803 | + | 0.563959i | \(0.190723\pi\) | |||||||
\(812\) | 4.98239e10 | 0.00402194 | ||||||||
\(813\) | 1.73207e12 | 0.139046 | ||||||||
\(814\) | −2.76870e13 | −2.21038 | ||||||||
\(815\) | −8.38330e9 | −0.000665589 0 | ||||||||
\(816\) | 6.65598e12 | 0.525541 | ||||||||
\(817\) | 4.13384e13 | 3.24604 | ||||||||
\(818\) | 4.74640e12 | 0.370659 | ||||||||
\(819\) | −1.04835e12 | −0.0814198 | ||||||||
\(820\) | 1.19848e10 | 0.000925696 0 | ||||||||
\(821\) | −3.20868e12 | −0.246480 | −0.123240 | − | 0.992377i | \(-0.539329\pi\) | ||||
−0.123240 | + | 0.992377i | \(0.539329\pi\) | |||||||
\(822\) | 1.05386e13 | 0.805116 | ||||||||
\(823\) | −2.87132e12 | −0.218163 | −0.109082 | − | 0.994033i | \(-0.534791\pi\) | ||||
−0.109082 | + | 0.994033i | \(0.534791\pi\) | |||||||
\(824\) | −1.53903e12 | −0.116299 | ||||||||
\(825\) | −1.11680e13 | −0.839333 | ||||||||
\(826\) | −3.33770e10 | −0.00249481 | ||||||||
\(827\) | 1.28110e13 | 0.952377 | 0.476188 | − | 0.879343i | \(-0.342018\pi\) | ||||
0.476188 | + | 0.879343i | \(0.342018\pi\) | |||||||
\(828\) | 1.08476e11 | 0.00802041 | ||||||||
\(829\) | −5.07698e12 | −0.373345 | −0.186672 | − | 0.982422i | \(-0.559770\pi\) | ||||
−0.186672 | + | 0.982422i | \(0.559770\pi\) | |||||||
\(830\) | 3.76427e12 | 0.275315 | ||||||||
\(831\) | 4.46995e12 | 0.325160 | ||||||||
\(832\) | 3.86205e12 | 0.279423 | ||||||||
\(833\) | −2.22483e12 | −0.160101 | ||||||||
\(834\) | −6.53557e12 | −0.467774 | ||||||||
\(835\) | −4.56100e12 | −0.324692 | ||||||||
\(836\) | 3.70673e11 | 0.0262460 | ||||||||
\(837\) | 1.42312e13 | 1.00225 | ||||||||
\(838\) | 2.24391e12 | 0.157184 | ||||||||
\(839\) | −7.11401e12 | −0.495662 | −0.247831 | − | 0.968803i | \(-0.579718\pi\) | ||||
−0.247831 | + | 0.968803i | \(0.579718\pi\) | |||||||
\(840\) | 7.24791e11 | 0.0502292 | ||||||||
\(841\) | 1.39995e13 | 0.965007 | ||||||||
\(842\) | −9.96916e11 | −0.0683524 | ||||||||
\(843\) | 2.89278e12 | 0.197284 | ||||||||
\(844\) | −4.06497e10 | −0.00275750 | ||||||||
\(845\) | −3.19403e11 | −0.0215518 | ||||||||
\(846\) | −2.04940e13 | −1.37550 | ||||||||
\(847\) | 1.53717e13 | 1.02623 | ||||||||
\(848\) | −1.32516e13 | −0.880006 | ||||||||
\(849\) | −1.09652e13 | −0.724321 | ||||||||
\(850\) | 1.56574e13 | 1.02881 | ||||||||
\(851\) | −2.39584e13 | −1.56594 | ||||||||
\(852\) | −2.36446e9 | −0.000153728 0 | ||||||||
\(853\) | 1.39575e13 | 0.902690 | 0.451345 | − | 0.892350i | \(-0.350944\pi\) | ||||
0.451345 | + | 0.892350i | \(0.350944\pi\) | |||||||
\(854\) | 2.77056e12 | 0.178241 | ||||||||
\(855\) | −6.09953e12 | −0.390345 | ||||||||
\(856\) | 6.88467e12 | 0.438280 | ||||||||
\(857\) | 2.19454e13 | 1.38973 | 0.694865 | − | 0.719141i | \(-0.255464\pi\) | ||||
0.694865 | + | 0.719141i | \(0.255464\pi\) | |||||||
\(858\) | 3.99488e12 | 0.251658 | ||||||||
\(859\) | −2.71253e13 | −1.69983 | −0.849916 | − | 0.526918i | \(-0.823347\pi\) | ||||
−0.849916 | + | 0.526918i | \(0.823347\pi\) | |||||||
\(860\) | −6.17384e10 | −0.00384868 | ||||||||
\(861\) | 1.25358e12 | 0.0777390 | ||||||||
\(862\) | −1.95148e13 | −1.20387 | ||||||||
\(863\) | −1.34740e13 | −0.826893 | −0.413447 | − | 0.910528i | \(-0.635675\pi\) | ||||
−0.413447 | + | 0.910528i | \(0.635675\pi\) | |||||||
\(864\) | −2.08784e11 | −0.0127463 | ||||||||
\(865\) | 3.77283e12 | 0.229137 | ||||||||
\(866\) | 2.43595e13 | 1.47176 | ||||||||
\(867\) | 2.01255e12 | 0.120966 | ||||||||
\(868\) | 5.72806e10 | 0.00342507 | ||||||||
\(869\) | 2.49277e13 | 1.48284 | ||||||||
\(870\) | 3.12420e12 | 0.184886 | ||||||||
\(871\) | −4.52228e12 | −0.266241 | ||||||||
\(872\) | 8.14812e12 | 0.477236 | ||||||||
\(873\) | −7.56787e12 | −0.440970 | ||||||||
\(874\) | −4.19335e13 | −2.43086 | ||||||||
\(875\) | 3.52821e12 | 0.203479 | ||||||||
\(876\) | 9.53628e10 | 0.00547155 | ||||||||
\(877\) | −2.38700e13 | −1.36255 | −0.681277 | − | 0.732026i | \(-0.738575\pi\) | ||||
−0.681277 | + | 0.732026i | \(0.738575\pi\) | |||||||
\(878\) | 1.76387e12 | 0.100171 | ||||||||
\(879\) | 3.67858e12 | 0.207841 | ||||||||
\(880\) | 9.53351e12 | 0.535897 | ||||||||
\(881\) | −6.58056e12 | −0.368020 | −0.184010 | − | 0.982924i | \(-0.558908\pi\) | ||||
−0.184010 | + | 0.982924i | \(0.558908\pi\) | |||||||
\(882\) | −1.98658e12 | −0.110535 | ||||||||
\(883\) | 1.75753e12 | 0.0972925 | 0.0486462 | − | 0.998816i | \(-0.484509\pi\) | ||||
0.0486462 | + | 0.998816i | \(0.484509\pi\) | |||||||
\(884\) | 4.28408e10 | 0.00235952 | ||||||||
\(885\) | 1.60089e10 | 0.000877235 0 | ||||||||
\(886\) | 1.80898e13 | 0.986240 | ||||||||
\(887\) | 1.35188e12 | 0.0733299 | 0.0366649 | − | 0.999328i | \(-0.488327\pi\) | ||||
0.0366649 | + | 0.999328i | \(0.488327\pi\) | |||||||
\(888\) | 1.01174e13 | 0.546023 | ||||||||
\(889\) | 7.71167e12 | 0.414086 | ||||||||
\(890\) | 9.84456e10 | 0.00525946 | ||||||||
\(891\) | 1.37774e13 | 0.732347 | ||||||||
\(892\) | 1.12157e11 | 0.00593179 | ||||||||
\(893\) | −6.05992e13 | −3.18886 | ||||||||
\(894\) | 2.20754e12 | 0.115582 | ||||||||
\(895\) | −4.01518e12 | −0.209171 | ||||||||
\(896\) | 7.20771e12 | 0.373604 | ||||||||
\(897\) | 3.45690e12 | 0.178287 | ||||||||
\(898\) | 1.63029e13 | 0.836606 | ||||||||
\(899\) | 3.27730e13 | 1.67339 | ||||||||
\(900\) | −1.06940e11 | −0.00543313 | ||||||||
\(901\) | −1.96596e13 | −0.993830 | ||||||||
\(902\) | 1.66151e13 | 0.835744 | ||||||||
\(903\) | −6.45770e12 | −0.323208 | ||||||||
\(904\) | −1.77386e13 | −0.883408 | ||||||||
\(905\) | −6.45345e12 | −0.319796 | ||||||||
\(906\) | −9.27695e12 | −0.457434 | ||||||||
\(907\) | −1.78688e13 | −0.876726 | −0.438363 | − | 0.898798i | \(-0.644442\pi\) | ||||
−0.438363 | + | 0.898798i | \(0.644442\pi\) | |||||||
\(908\) | 3.92584e10 | 0.00191666 | ||||||||
\(909\) | 1.42602e12 | 0.0692769 | ||||||||
\(910\) | −6.05254e11 | −0.0292585 | ||||||||
\(911\) | −2.20038e13 | −1.05843 | −0.529217 | − | 0.848486i | \(-0.677514\pi\) | ||||
−0.529217 | + | 0.848486i | \(0.677514\pi\) | |||||||
\(912\) | 1.75737e13 | 0.841174 | ||||||||
\(913\) | −3.99177e13 | −1.90128 | ||||||||
\(914\) | 6.20593e12 | 0.294137 | ||||||||
\(915\) | −1.32886e12 | −0.0626738 | ||||||||
\(916\) | 2.33233e11 | 0.0109461 | ||||||||
\(917\) | −9.98463e12 | −0.466305 | ||||||||
\(918\) | 2.01693e13 | 0.937344 | ||||||||
\(919\) | 4.13313e12 | 0.191144 | 0.0955718 | − | 0.995423i | \(-0.469532\pi\) | ||||
0.0955718 | + | 0.995423i | \(0.469532\pi\) | |||||||
\(920\) | 8.31275e12 | 0.382560 | ||||||||
\(921\) | −1.96073e13 | −0.897946 | ||||||||
\(922\) | −1.38493e12 | −0.0631158 | ||||||||
\(923\) | 2.62083e11 | 0.0118859 | ||||||||
\(924\) | −5.79048e10 | −0.00261331 | ||||||||
\(925\) | 2.36193e13 | 1.06079 | ||||||||
\(926\) | 2.37900e13 | 1.06327 | ||||||||
\(927\) | −2.02328e12 | −0.0899906 | ||||||||
\(928\) | −4.80807e11 | −0.0212816 | ||||||||
\(929\) | 3.08089e12 | 0.135708 | 0.0678541 | − | 0.997695i | \(-0.478385\pi\) | ||||
0.0678541 | + | 0.997695i | \(0.478385\pi\) | |||||||
\(930\) | 3.59178e12 | 0.157448 | ||||||||
\(931\) | −5.87418e12 | −0.256256 | ||||||||
\(932\) | 5.81441e10 | 0.00252426 | ||||||||
\(933\) | 1.47064e13 | 0.635390 | ||||||||
\(934\) | 3.58219e13 | 1.54024 | ||||||||
\(935\) | 1.41436e13 | 0.605212 | ||||||||
\(936\) | 5.07750e12 | 0.216226 | ||||||||
\(937\) | −1.74551e13 | −0.739766 | −0.369883 | − | 0.929078i | \(-0.620602\pi\) | ||||
−0.369883 | + | 0.929078i | \(0.620602\pi\) | |||||||
\(938\) | −8.56951e12 | −0.361446 | ||||||||
\(939\) | −2.07417e13 | −0.870662 | ||||||||
\(940\) | 9.05042e10 | 0.00378088 | ||||||||
\(941\) | −8.49435e12 | −0.353165 | −0.176582 | − | 0.984286i | \(-0.556504\pi\) | ||||
−0.176582 | + | 0.984286i | \(0.556504\pi\) | |||||||
\(942\) | 4.38842e12 | 0.181585 | ||||||||
\(943\) | 1.43776e13 | 0.592083 | ||||||||
\(944\) | 1.60428e11 | 0.00657516 | ||||||||
\(945\) | 2.17963e12 | 0.0889077 | ||||||||
\(946\) | −8.55908e13 | −3.47470 | ||||||||
\(947\) | 6.95169e12 | 0.280876 | 0.140438 | − | 0.990089i | \(-0.455149\pi\) | ||||
0.140438 | + | 0.990089i | \(0.455149\pi\) | |||||||
\(948\) | −6.86268e10 | −0.00275966 | ||||||||
\(949\) | −1.05703e13 | −0.423046 | ||||||||
\(950\) | 4.13399e13 | 1.64670 | ||||||||
\(951\) | 1.01186e13 | 0.401150 | ||||||||
\(952\) | 1.07755e13 | 0.425180 | ||||||||
\(953\) | 9.03759e12 | 0.354923 | 0.177462 | − | 0.984128i | \(-0.443211\pi\) | ||||
0.177462 | + | 0.984128i | \(0.443211\pi\) | |||||||
\(954\) | −1.75543e13 | −0.686146 | ||||||||
\(955\) | −3.79985e12 | −0.147826 | ||||||||
\(956\) | 2.07445e11 | 0.00803234 | ||||||||
\(957\) | −3.31301e13 | −1.27679 | ||||||||
\(958\) | −2.72648e13 | −1.04582 | ||||||||
\(959\) | 1.69316e13 | 0.646421 | ||||||||
\(960\) | −3.51019e12 | −0.133386 | ||||||||
\(961\) | 1.12382e13 | 0.425053 | ||||||||
\(962\) | −8.44878e12 | −0.318058 | ||||||||
\(963\) | 9.05088e12 | 0.339135 | ||||||||
\(964\) | −5.14278e10 | −0.00191801 | ||||||||
\(965\) | 1.23307e13 | 0.457734 | ||||||||
\(966\) | 6.55066e12 | 0.242041 | ||||||||
\(967\) | −2.87825e12 | −0.105854 | −0.0529272 | − | 0.998598i | \(-0.516855\pi\) | ||||
−0.0529272 | + | 0.998598i | \(0.516855\pi\) | |||||||
\(968\) | −7.44499e13 | −2.72537 | ||||||||
\(969\) | 2.60717e13 | 0.949975 | ||||||||
\(970\) | −4.36922e12 | −0.158464 | ||||||||
\(971\) | 1.36281e13 | 0.491980 | 0.245990 | − | 0.969272i | \(-0.420887\pi\) | ||||
0.245990 | + | 0.969272i | \(0.420887\pi\) | |||||||
\(972\) | −2.15292e11 | −0.00773625 | ||||||||
\(973\) | −1.05003e13 | −0.375572 | ||||||||
\(974\) | −2.01029e13 | −0.715722 | ||||||||
\(975\) | −3.40796e12 | −0.120774 | ||||||||
\(976\) | −1.33168e13 | −0.469760 | ||||||||
\(977\) | −7.83200e12 | −0.275009 | −0.137505 | − | 0.990501i | \(-0.543908\pi\) | ||||
−0.137505 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(978\) | 3.19962e10 | 0.00111834 | ||||||||
\(979\) | −1.04395e12 | −0.0363210 | ||||||||
\(980\) | 8.77301e9 | 0.000303830 0 | ||||||||
\(981\) | 1.07119e13 | 0.369279 | ||||||||
\(982\) | −1.68320e12 | −0.0577608 | ||||||||
\(983\) | 5.00319e13 | 1.70906 | 0.854528 | − | 0.519405i | \(-0.173846\pi\) | ||||
0.854528 | + | 0.519405i | \(0.173846\pi\) | |||||||
\(984\) | −6.07149e12 | −0.206451 | ||||||||
\(985\) | −5.64920e12 | −0.191216 | ||||||||
\(986\) | 4.64478e13 | 1.56502 | ||||||||
\(987\) | 9.46654e12 | 0.317515 | ||||||||
\(988\) | 1.13112e11 | 0.00377661 | ||||||||
\(989\) | −7.40644e13 | −2.46165 | ||||||||
\(990\) | 1.26290e13 | 0.417842 | ||||||||
\(991\) | 5.33015e13 | 1.75553 | 0.877765 | − | 0.479091i | \(-0.159034\pi\) | ||||
0.877765 | + | 0.479091i | \(0.159034\pi\) | |||||||
\(992\) | −5.52766e11 | −0.0181233 | ||||||||
\(993\) | −1.45823e13 | −0.475943 | ||||||||
\(994\) | 4.96635e11 | 0.0161361 | ||||||||
\(995\) | −4.43944e12 | −0.143590 | ||||||||
\(996\) | 1.09894e11 | 0.00353842 | ||||||||
\(997\) | −3.21504e13 | −1.03052 | −0.515262 | − | 0.857033i | \(-0.672305\pi\) | ||||
−0.515262 | + | 0.857033i | \(0.672305\pi\) | |||||||
\(998\) | 3.01525e13 | 0.962136 | ||||||||
\(999\) | 3.04256e13 | 0.966483 |
(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 | 91.10.a.a.1.9 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.10.a.a.1.9 | ✓ | 12 | 1.1 | even | 1 | trivial |