Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [64,12,Mod(17,64)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(64, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("64.17");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 64 = 2^{6} \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 64.e (of order \(4\), degree \(2\), not 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: | \(49.1739635558\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(21\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.17 | ||
Character | \(\chi\) | \(=\) | 64.17 |
Dual form | 64.12.e.a.49.17 |
$q$-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 \(\left(\mathbb{Z}/64\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(63\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 296.568 | + | 296.568i | 0.704623 | + | 0.704623i | 0.965399 | − | 0.260776i | \(-0.0839785\pi\) |
−0.260776 | + | 0.965399i | \(0.583978\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2867.98 | + | 2867.98i | −0.410432 | + | 0.410432i | −0.881889 | − | 0.471457i | \(-0.843728\pi\) |
0.471457 | + | 0.881889i | \(0.343728\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 8380.90i | − | 0.188474i | −0.995550 | − | 0.0942370i | \(-0.969959\pi\) | ||
0.995550 | − | 0.0942370i | \(-0.0300411\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 1242.24i | − | 0.00701249i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −84515.5 | + | 84515.5i | −0.158226 | + | 0.158226i | −0.781780 | − | 0.623554i | \(-0.785688\pi\) |
0.623554 | + | 0.781780i | \(0.285688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −385486. | − | 385486.i | −0.287952 | − | 0.287952i | 0.548318 | − | 0.836270i | \(-0.315268\pi\) |
−0.836270 | + | 0.548318i | \(0.815268\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.70110e6 | −0.578400 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.56551e6 | 0.267416 | 0.133708 | − | 0.991021i | \(-0.457311\pi\) | ||||
0.133708 | + | 0.991021i | \(0.457311\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −9.59253e6 | − | 9.59253e6i | −0.888768 | − | 0.888768i | 0.105637 | − | 0.994405i | \(-0.466312\pi\) |
−0.994405 | + | 0.105637i | \(0.966312\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.48550e6 | − | 2.48550e6i | 0.132803 | − | 0.132803i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 3.88214e7i | − | 1.25767i | −0.777537 | − | 0.628837i | \(-0.783531\pi\) | ||
0.777537 | − | 0.628837i | \(-0.216469\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.23775e7i | 0.663091i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.29045e7 | − | 5.29045e7i | 0.709564 | − | 0.709564i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.81048e7 | − | 8.81048e7i | −0.797647 | − | 0.797647i | 0.185077 | − | 0.982724i | \(-0.440746\pi\) |
−0.982724 | + | 0.185077i | \(0.940746\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.23333e7 | 0.453784 | 0.226892 | − | 0.973920i | \(-0.427144\pi\) | ||||
0.226892 | + | 0.973920i | \(0.427144\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −5.01291e7 | −0.222979 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.40363e7 | + | 2.40363e7i | 0.0773558 | + | 0.0773558i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.98585e7 | + | 9.98585e7i | −0.236742 | + | 0.236742i | −0.815500 | − | 0.578758i | \(-0.803538\pi\) |
0.578758 | + | 0.815500i | \(0.303538\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 2.28645e8i | − | 0.405795i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.13304e9i | 1.52733i | 0.645611 | + | 0.763667i | \(0.276603\pi\) | ||||
−0.645611 | + | 0.763667i | \(0.723397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.05585e9 | − | 1.05585e9i | 1.09528 | − | 1.09528i | 0.100329 | − | 0.994954i | \(-0.468010\pi\) |
0.994954 | − | 0.100329i | \(-0.0319897\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56273e6 | + | 3.56273e6i | 0.00287815 | + | 0.00287815i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.33450e9 | −0.848750 | −0.424375 | − | 0.905486i | \(-0.639506\pi\) | ||||
−0.424375 | + | 0.905486i | \(0.639506\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.90709e9 | 0.964478 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.64281e8 | + | 4.64281e8i | 0.188428 | + | 0.188428i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.50213e9 | − | 2.50213e9i | 0.821850 | − | 0.821850i | −0.164523 | − | 0.986373i | \(-0.552608\pi\) |
0.986373 | + | 0.164523i | \(0.0526085\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 4.84778e8i | − | 0.129882i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.68967e9i | − | 1.25249i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.81835e9 | − | 3.81835e9i | 0.695329 | − | 0.695329i | −0.268071 | − | 0.963399i | \(-0.586386\pi\) |
0.963399 | + | 0.268071i | \(0.0863861\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.73084e9 | − | 7.73084e9i | −1.17196 | − | 1.17196i | −0.981742 | − | 0.190218i | \(-0.939081\pi\) |
−0.190218 | − | 0.981742i | \(-0.560919\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.04111e7 | −0.00132167 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.21114e9 | 0.236370 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.91020e9 | − | 2.91020e9i | −0.263337 | − | 0.263337i | 0.563071 | − | 0.826408i | \(-0.309620\pi\) |
−0.826408 | + | 0.563071i | \(0.809620\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.15132e10 | − | 1.15132e10i | 0.886186 | − | 0.886186i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.77198e10i | − | 1.16557i | −0.812628 | − | 0.582783i | \(-0.801964\pi\) | ||
0.812628 | − | 0.582783i | \(-0.198036\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.04116e10i | − | 1.15239i | −0.817311 | − | 0.576197i | \(-0.804536\pi\) | ||
0.817311 | − | 0.576197i | \(-0.195464\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −9.60211e9 | + | 9.60211e9i | −0.467229 | + | 0.467229i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.08316e8 | + | 7.08316e8i | 0.0298214 | + | 0.0298214i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.60858e10 | 1.31943 | 0.659717 | − | 0.751514i | \(-0.270676\pi\) | ||||
0.659717 | + | 0.751514i | \(0.270676\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.11595e10 | 0.992938 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −5.73137e9 | − | 5.73137e9i | −0.159709 | − | 0.159709i | 0.622729 | − | 0.782438i | \(-0.286024\pi\) |
−0.782438 | + | 0.622729i | \(0.786024\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.48987e9 | + | 4.48987e9i | −0.109756 | + | 0.109756i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 5.22581e10i | − | 1.12408i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.07134e10i | 0.203367i | 0.994817 | + | 0.101684i | \(0.0324230\pi\) | ||||
−0.994817 | + | 0.101684i | \(0.967577\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.23072e9 | + | 3.23072e9i | −0.0542715 | + | 0.0542715i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.14517e10 | + | 2.14517e10i | 0.319746 | + | 0.319746i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 5.50224e10 | 0.729558 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.36209e9 | −0.0870475 | −0.0435238 | − | 0.999052i | \(-0.513858\pi\) | ||||
−0.0435238 | + | 0.999052i | \(0.513858\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.04989e8 | + | 1.04989e8i | 0.00110956 | + | 0.00110956i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.80812e10 | + | 8.80812e10i | −0.833903 | + | 0.833903i | −0.988048 | − | 0.154145i | \(-0.950738\pi\) |
0.154145 | + | 0.988048i | \(0.450738\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.00874e11i | − | 0.857383i | −0.903451 | − | 0.428691i | \(-0.858975\pi\) | ||
0.903451 | − | 0.428691i | \(-0.141025\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.42568e10i | 0.109013i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.90961e10 | + | 3.90961e10i | −0.269478 | + | 0.269478i | −0.828890 | − | 0.559412i | \(-0.811027\pi\) |
0.559412 | + | 0.828890i | \(0.311027\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.52858e11 | − | 1.52858e11i | −0.951576 | − | 0.951576i | 0.0473045 | − | 0.998881i | \(-0.484937\pi\) |
−0.998881 | + | 0.0473045i | \(0.984937\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.92296e10 | −0.333628 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.86408e10 | 0.452587 | 0.226293 | − | 0.974059i | \(-0.427339\pi\) | ||||
0.226293 | + | 0.974059i | \(0.427339\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.11339e11 | + | 1.11339e11i | 0.516190 | + | 0.516190i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.78867e8 | + | 4.78867e8i | −0.00201926 | + | 0.00201926i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 1.31204e10i | − | 0.0504011i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.71026e11i | 0.949929i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.36023e11 | + | 3.36023e11i | −1.07619 | + | 1.07619i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.32896e11 | − | 2.32896e11i | −0.682586 | − | 0.682586i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.85470e11 | −0.498142 | −0.249071 | − | 0.968485i | \(-0.580125\pi\) | ||||
−0.249071 | + | 0.968485i | \(0.580125\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 6.26263e11 | 1.54352 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.99872e11 | + | 1.99872e11i | 0.452646 | + | 0.452646i | 0.896232 | − | 0.443586i | \(-0.146294\pi\) |
−0.443586 | + | 0.896232i | \(0.646294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.03940e10 | + | 8.03940e10i | −0.167510 | + | 0.167510i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.03458e11i | 0.582456i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.03458e12i | 1.83147i | 0.401786 | + | 0.915734i | \(0.368390\pi\) | ||||
−0.401786 | + | 0.915734i | \(0.631610\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.75928e11 | + | 7.75928e11i | −1.26835 | + | 1.26835i | −0.321415 | + | 0.946938i | \(0.604158\pi\) |
−0.946938 | + | 0.321415i | \(0.895842\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.95769e11 | − | 3.95769e11i | −0.598049 | − | 0.598049i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.51591e10 | 0.0911228 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.05366e11 | 0.654760 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.65580e11 | + | 5.65580e11i | 0.679593 | + | 0.679593i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.48328e11 | + | 8.48328e11i | −0.946323 | + | 0.946323i | −0.998631 | − | 0.0523077i | \(-0.983342\pi\) |
0.0523077 | + | 0.998631i | \(0.483342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 8.18468e11i | − | 0.848454i | −0.905556 | − | 0.424227i | \(-0.860546\pi\) | ||
0.905556 | − | 0.424227i | \(-0.139454\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.94475e9i | − | 0.00187526i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.07451e11 | + | 2.07451e11i | −0.186247 | + | 0.186247i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.92527e11 | − | 5.92527e11i | −0.495747 | − | 0.495747i | 0.414364 | − | 0.910111i | \(-0.364004\pi\) |
−0.910111 | + | 0.414364i | \(0.864004\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.48410e12 | 1.15819 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.25358e11 | −0.237039 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.74040e11 | − | 2.74040e11i | −0.186544 | − | 0.186544i | 0.607656 | − | 0.794200i | \(-0.292110\pi\) |
−0.794200 | + | 0.607656i | \(0.792110\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.43770e11 | − | 1.43770e11i | 0.0915177 | − | 0.0915177i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 2.53745e12i | − | 1.51167i | −0.654762 | − | 0.755836i | \(-0.727231\pi\) | ||
0.654762 | − | 0.755836i | \(-0.272769\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 1.49496e12i | − | 0.834167i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.19162e10 | + | 1.19162e10i | −0.00623247 | + | 0.00623247i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.71348e11 | + | 5.71348e11i | 0.280315 | + | 0.280315i | 0.833235 | − | 0.552919i | \(-0.186486\pi\) |
−0.552919 | + | 0.833235i | \(0.686486\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.71352e11 | 0.124975 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.26480e12 | 0.979889 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.62660e12 | − | 1.62660e12i | −0.661592 | − | 0.661592i | 0.294163 | − | 0.955755i | \(-0.404959\pi\) |
−0.955755 | + | 0.294163i | \(0.904959\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.16199e11 | + | 5.16199e11i | −0.197508 | + | 0.197508i | −0.798931 | − | 0.601423i | \(-0.794601\pi\) |
0.601423 | + | 0.798931i | \(0.294601\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.58543e12i | − | 1.65158i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 5.72785e11i | − | 0.194333i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.32310e11 | + | 1.32310e11i | −0.0423121 | + | 0.0423121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.43387e11 | − | 4.43387e11i | −0.133734 | − | 0.133734i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.22938e12 | 0.634602 | 0.317301 | − | 0.948325i | \(-0.397224\pi\) | ||||
0.317301 | + | 0.948325i | \(0.397224\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.44625e11 | 0.0388758 | 0.0194379 | − | 0.999811i | \(-0.493812\pi\) | ||||
0.0194379 | + | 0.999811i | \(0.493812\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 6.55751e11 | + | 6.55751e11i | 0.166552 | + | 0.166552i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.27490e12 | − | 2.27490e12i | 0.546257 | − | 0.546257i | −0.379099 | − | 0.925356i | \(-0.623766\pi\) |
0.925356 | + | 0.379099i | \(0.123766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.80350e12i | 0.863956i | 0.901884 | + | 0.431978i | \(0.142184\pi\) | ||||
−0.901884 | + | 0.431978i | \(0.857816\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1.72614e12i | − | 0.371106i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −7.38398e11 | + | 7.38398e11i | −0.150336 | + | 0.150336i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.24954e12 | − | 3.24954e12i | −0.626867 | − | 0.626867i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.82255e10 | −0.00881942 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.62143e12 | 0.281252 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.90777e12 | + | 4.90777e12i | 0.807849 | + | 0.807849i | 0.984308 | − | 0.176459i | \(-0.0564642\pi\) |
−0.176459 | + | 0.984308i | \(0.556464\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.25511e12 | − | 5.25511e12i | 0.821285 | − | 0.821285i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.05633e12i | 0.899080i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 6.06218e11i | − | 0.0855264i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.05341e12 | − | 6.05341e12i | 0.812003 | − | 0.812003i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.03484e11 | − | 6.03484e11i | −0.0770031 | − | 0.0770031i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −4.65341e12 | −0.565060 | −0.282530 | − | 0.959259i | \(-0.591174\pi\) | ||||
−0.282530 | + | 0.959259i | \(0.591174\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.02206e10 | 0.00464992 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.96621e12 | − | 7.96621e12i | −0.877222 | − | 0.877222i | 0.116024 | − | 0.993246i | \(-0.462985\pi\) |
−0.993246 | + | 0.116024i | \(0.962985\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.29670e12 | + | 1.29670e12i | −0.136064 | + | 0.136064i | −0.771858 | − | 0.635794i | \(-0.780673\pi\) |
0.635794 | + | 0.771858i | \(0.280673\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.20127e11i | 0.0420257i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4.73649e12i | 0.451855i | 0.974144 | + | 0.225928i | \(0.0725413\pi\) | ||||
−0.974144 | + | 0.225928i | \(0.927459\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.82732e12 | − | 3.82732e12i | 0.348355 | − | 0.348355i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.07019e13 | + | 1.07019e13i | 0.929704 | + | 0.929704i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.73692e13 | −1.44076 | −0.720381 | − | 0.693578i | \(-0.756033\pi\) | ||||
−0.720381 | + | 0.693578i | \(0.756033\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.51130e13 | −1.19745 | −0.598725 | − | 0.800955i | \(-0.704326\pi\) | ||||
−0.598725 | + | 0.800955i | \(0.704326\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.30983e11 | − | 1.30983e11i | −0.00991697 | − | 0.00991697i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.46949e12 | + | 5.46949e12i | −0.395853 | + | 0.395853i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.39557e12i | 0.511845i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 3.39948e12i | − | 0.225069i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.55409e12 | − | 7.55409e12i | 0.478604 | − | 0.478604i | −0.426081 | − | 0.904685i | \(-0.640106\pi\) |
0.904685 | + | 0.426081i | \(0.140106\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.28101e12 | + | 3.28101e12i | 0.198996 | + | 0.198996i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.66310e12 | −0.154674 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.57756e13 | −1.43409 | −0.717045 | − | 0.697027i | \(-0.754506\pi\) | ||||
−0.717045 | + | 0.697027i | \(0.754506\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.36904e11 | + | 8.36904e11i | 0.0446197 | + | 0.0446197i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.09447e11 | + | 1.09447e11i | −0.00559349 | + | 0.00559349i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.41102e13i | 1.67158i | 0.549047 | + | 0.835791i | \(0.314991\pi\) | ||||
−0.549047 | + | 0.835791i | \(0.685009\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.43521e13i | 0.674628i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.17724e12 | + | 3.17724e12i | −0.143297 | + | 0.143297i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.71092e13 | + | 2.71092e13i | 1.17349 | + | 1.17349i | 0.981372 | + | 0.192117i | \(0.0615354\pi\) |
0.192117 | + | 0.981372i | \(0.438465\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.37221e13 | 0.985876 | 0.492938 | − | 0.870065i | \(-0.335923\pi\) | ||||
0.492938 | + | 0.870065i | \(0.335923\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.91625e12 | −0.0764819 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.73640e12 | − | 2.73640e12i | −0.104918 | − | 0.104918i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.86303e13 | + | 2.86303e13i | −1.05484 | + | 1.05484i | −0.0564356 | + | 0.998406i | \(0.517974\pi\) |
−0.998406 | + | 0.0564356i | \(0.982026\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 8.98554e10i | − | 0.00318215i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.73419e13i | − | 0.590488i | −0.955422 | − | 0.295244i | \(-0.904599\pi\) | ||
0.955422 | − | 0.295244i | \(-0.0954010\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.78495e12 | + | 3.78495e12i | −0.123947 | + | 0.123947i | −0.766359 | − | 0.642412i | \(-0.777934\pi\) |
0.642412 | + | 0.766359i | \(0.277934\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.63179e13 | + | 1.63179e13i | 0.514063 | + | 0.514063i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 9.49589e12 | 0.287863 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.18211e13 | −0.928488 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.18336e12 | − | 2.18336e12i | −0.0613357 | − | 0.0613357i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.44335e13 | − | 3.44335e13i | 0.931556 | − | 0.931556i | −0.0662477 | − | 0.997803i | \(-0.521103\pi\) |
0.997803 | + | 0.0662477i | \(0.0211027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.19020e13i | 0.570771i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.94250e12i | 0.224542i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.49651e13 | + | 1.49651e13i | −0.362150 | + | 0.362150i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.84899e12 | − | 8.84899e12i | −0.206433 | − | 0.206433i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.22441e13 | −1.17518 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.43438e13 | 0.962020 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.03299e13 | − | 1.03299e13i | −0.216190 | − | 0.216190i | 0.590701 | − | 0.806891i | \(-0.298851\pi\) |
−0.806891 | + | 0.590701i | \(0.798851\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.99160e13 | − | 2.99160e13i | 0.604132 | − | 0.604132i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.78955e12i | 0.151820i | 0.997115 | + | 0.0759102i | \(0.0241862\pi\) | ||||
−0.997115 | + | 0.0759102i | \(0.975814\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.37500e13i | − | 1.76391i | −0.471330 | − | 0.881957i | \(-0.656226\pi\) | ||
0.471330 | − | 0.881957i | \(-0.343774\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.98589e10 | − | 2.98589e10i | 0.000542457 | − | 0.000542457i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.94124e13 | − | 2.94124e13i | −0.516065 | − | 0.516065i | 0.400313 | − | 0.916378i | \(-0.368901\pi\) |
−0.916378 | + | 0.400313i | \(0.868901\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.48924e13 | 0.252416 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.31893e13 | −0.379761 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.50172e13 | − | 1.50172e13i | −0.237671 | − | 0.237671i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.24811e13 | − | 1.24811e13i | 0.190938 | − | 0.190938i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 9.06657e13i | − | 1.34100i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.11843e13i | 0.159967i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.90138e13 | − | 8.90138e13i | 1.23141 | − | 1.23141i | 0.267990 | − | 0.963422i | \(-0.413640\pi\) |
0.963422 | − | 0.267990i | \(-0.0863596\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.24048e11 | + | 1.24048e11i | 0.00166015 | + | 0.00166015i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.66928e13 | 0.216164 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.94592e13 | 0.619844 | 0.309922 | − | 0.950762i | \(-0.399697\pi\) | ||||
0.309922 | + | 0.950762i | \(0.399697\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.62880e13 | + | 2.62880e13i | 0.318903 | + | 0.318903i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6.11328e12 | + | 6.11328e12i | −0.0718002 | + | 0.0718002i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.25549e13i | − | 0.370253i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6.60392e13i | 0.727439i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.93186e13 | − | 4.93186e13i | 0.526258 | − | 0.526258i | −0.393197 | − | 0.919454i | \(-0.628631\pi\) |
0.919454 | + | 0.393197i | \(0.128631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.31044e14 | − | 1.31044e14i | −1.35481 | − | 1.35481i | −0.880196 | − | 0.474610i | \(-0.842589\pi\) |
−0.474610 | − | 0.880196i | \(-0.657411\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.07879e13 | −0.408641 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.16944e14 | 1.13558 | 0.567791 | − | 0.823173i | \(-0.307798\pi\) | ||||
0.567791 | + | 0.823173i | \(0.307798\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.08200e13 | + | 5.08200e13i | 0.478386 | + | 0.478386i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.89109e12 | − | 3.89109e12i | 0.0355137 | − | 0.0355137i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 4.01208e13i | − | 0.355100i | −0.984112 | − | 0.177550i | \(-0.943183\pi\) | ||
0.984112 | − | 0.177550i | \(-0.0568171\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.75428e13i | 0.579815i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −8.03775e13 | + | 8.03775e13i | −0.669342 | + | 0.669342i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.85401e13 | + | 5.85401e13i | 0.472980 | + | 0.472980i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.48808e14 | 1.16671 | 0.583354 | − | 0.812218i | \(-0.301740\pi\) | ||||
0.583354 | + | 0.812218i | \(0.301740\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.40751e12 | 0.0107104 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.09701e13 | − | 2.09701e13i | −0.154897 | − | 0.154897i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −9.75473e13 | + | 9.75473e13i | −0.699547 | + | 0.699547i | −0.964313 | − | 0.264766i | \(-0.914705\pi\) |
0.264766 | + | 0.964313i | \(0.414705\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.38139e14i | − | 0.961932i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.79263e13i | 0.459368i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.24977e14 | + | 1.24977e14i | −0.820944 | + | 0.820944i | −0.986243 | − | 0.165299i | \(-0.947141\pi\) |
0.165299 | + | 0.986243i | \(0.447141\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.50044e13 | − | 5.50044e13i | −0.351002 | − | 0.351002i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.86299e13 | 0.301516 | 0.150758 | − | 0.988571i | \(-0.451829\pi\) | ||||
0.150758 | + | 0.988571i | \(0.451829\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.06288e12 | −0.0244793 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.31162e12 | − | 1.31162e12i | −0.00768067 | − | 0.00768067i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.60395e12 | − | 8.60395e12i | 0.0489751 | − | 0.0489751i | −0.682195 | − | 0.731170i | \(-0.738975\pi\) |
0.731170 | + | 0.682195i | \(0.238975\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 6.07755e13i | − | 0.336323i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.18551e14i | 0.637890i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.03494e14 | + | 1.03494e14i | −0.541539 | + | 0.541539i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.00648e13 | − | 4.00648e13i | −0.203899 | − | 0.203899i | 0.597769 | − | 0.801668i | \(-0.296054\pi\) |
−0.801668 | + | 0.597769i | \(0.796054\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.76845e13 | −0.236062 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.93054e14 | 1.89304 | 0.946518 | − | 0.322652i | \(-0.104574\pi\) | ||||
0.946518 | + | 0.322652i | \(0.104574\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.78835e13 | − | 2.78835e13i | −0.130668 | − | 0.130668i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −8.93648e13 | + | 8.93648e13i | −0.407534 | + | 0.407534i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1.68792e13i | − | 0.0749173i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 3.20804e14i | − | 1.38599i | −0.720941 | − | 0.692997i | \(-0.756290\pi\) | ||
0.720941 | − | 0.692997i | \(-0.243710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.06822e14 | + | 3.06822e14i | −1.29049 | + | 1.29049i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.20012e13 | − | 3.20012e13i | −0.131051 | − | 0.131051i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.28750e13 | 0.131099 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.60231e14 | −1.78742 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.19903e14 | + | 1.19903e14i | 0.453580 | + | 0.453580i | 0.896541 | − | 0.442961i | \(-0.146072\pi\) |
−0.442961 | + | 0.896541i | \(0.646072\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.87949e13 | − | 6.87949e13i | 0.253516 | − | 0.253516i | −0.568895 | − | 0.822410i | \(-0.692629\pi\) |
0.822410 | + | 0.568895i | \(0.192629\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.65777e12i | 0.00595185i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.06874e13i | 0.177321i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.47914e13 | + | 6.47914e13i | −0.220884 | + | 0.220884i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.93241e13 | + | 1.93241e13i | 0.0642072 | + | 0.0642072i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.48651e14 | 0.805314 | 0.402657 | − | 0.915351i | \(-0.368087\pi\) | ||||
0.402657 | + | 0.915351i | \(0.368087\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.94573e13 | 0.250871 | 0.125435 | − | 0.992102i | \(-0.459967\pi\) | ||||
0.125435 | + | 0.992102i | \(0.459967\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.49875e14 | + | 1.49875e14i | 0.461359 | + | 0.461359i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3.72395e14 | + | 3.72395e14i | −1.11778 | + | 1.11778i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.46704e14i | 1.60029i | 0.599809 | + | 0.800143i | \(0.295243\pi\) | ||||
−0.599809 | + | 0.800143i | \(0.704757\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | − | 2.36906e12i | − | 0.00676339i | ||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.74563e13 | − | 7.74563e13i | 0.215693 | − | 0.215693i | −0.590988 | − | 0.806681i | \(-0.701262\pi\) |
0.806681 | + | 0.590988i | \(0.201262\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.07258e13 | − | 3.07258e13i | −0.0834686 | − | 0.0834686i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.03174e14 | −1.33360 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.23108e14 | 0.318369 | 0.159184 | − | 0.987249i | \(-0.449114\pi\) | ||||
0.159184 | + | 0.987249i | \(0.449114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.57594e13 | − | 9.57594e13i | −0.241663 | − | 0.241663i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.42731e14 | − | 2.42731e14i | 0.597841 | − | 0.597841i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 1.85313e13i | − | 0.0445495i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.91954e14i | 1.38915i | 0.719421 | + | 0.694574i | \(0.244407\pi\) | ||||
−0.719421 | + | 0.694574i | \(0.755593\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.28228e13 | − | 8.28228e13i | 0.189749 | − | 0.189749i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.14114e14 | + | 3.14114e14i | 0.702639 | + | 0.702639i | 0.964976 | − | 0.262337i | \(-0.0844932\pi\) |
−0.262337 | + | 0.964976i | \(0.584493\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.18707e14 | −0.477713 | −0.238857 | − | 0.971055i | \(-0.576773\pi\) | ||||
−0.238857 | + | 0.971055i | \(0.576773\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.23046e14 | −0.262469 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.13426e13 | + | 1.13426e13i | 0.0236304 | + | 0.0236304i | 0.718823 | − | 0.695193i | \(-0.244681\pi\) |
−0.695193 | + | 0.718823i | \(0.744681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.43901e13 | + | 2.43901e13i | −0.0496322 | + | 0.0496322i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 3.51449e14i | − | 0.698629i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.78472e14i | 0.346604i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.10582e14 | − | 3.10582e14i | 0.589333 | − | 0.589333i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.10825e12 | − | 3.10825e12i | −0.00576322 | − | 0.00576322i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.93567e14 | 0.531939 | 0.265969 | − | 0.963981i | \(-0.414308\pi\) | ||||
0.265969 | + | 0.963981i | \(0.414308\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.69881e13 | 0.136341 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −9.64907e13 | − | 9.64907e13i | −0.167023 | − | 0.167023i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 2.11143e13 | − | 2.11143e13i | 0.0357271 | − | 0.0357271i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.66029e13i | − | 0.0440069i | −0.999758 | − | 0.0220034i | \(-0.992996\pi\) | ||
0.999758 | − | 0.0220034i | \(-0.00700448\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 1.62543e14i | − | 0.262887i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.66005e14 | − | 8.66005e14i | 1.36953 | − | 1.36953i | 0.508428 | − | 0.861104i | \(-0.330227\pi\) |
0.861104 | − | 0.508428i | \(-0.169773\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.37929e14 | − | 1.37929e14i | −0.213304 | − | 0.213304i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.02212e11 | −0.000910795 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.48508e14 | −0.219679 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.86185e14 | − | 5.86185e14i | −0.848168 | − | 0.848168i | 0.141736 | − | 0.989904i | \(-0.454732\pi\) |
−0.989904 | + | 0.141736i | \(0.954732\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.52526e14 | − | 7.52526e14i | 1.06516 | − | 1.06516i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.63209e14i | 0.226006i | 0.993595 | + | 0.113003i | \(0.0360470\pi\) | ||||
−0.993595 | + | 0.113003i | \(0.963953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 5.05231e14i | − | 0.684522i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.43357e14 | − | 4.43357e14i | 0.587774 | − | 0.587774i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.22280e14 | − | 2.22280e14i | −0.288372 | − | 0.288372i | 0.548065 | − | 0.836436i | \(-0.315365\pi\) |
−0.836436 | + | 0.548065i | \(0.815365\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.71067e14 | −0.217196 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.01498e15 | −1.26128 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.89305e14 | + | 2.89305e14i | 0.351898 | + | 0.351898i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.12786e14 | − | 1.12786e14i | 0.134294 | − | 0.134294i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.38886e14i | 0.395033i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 1.24751e15i | − | 1.42375i | −0.702304 | − | 0.711877i | \(-0.747845\pi\) | ||
0.702304 | − | 0.711877i | \(-0.252155\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.96253e13 | − | 4.96253e13i | 0.0554555 | − | 0.0554555i | −0.678835 | − | 0.734291i | \(-0.737515\pi\) |
0.734291 | + | 0.678835i | \(0.237515\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 8.04743e13 | + | 8.04743e13i | 0.0880605 | + | 0.0880605i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.13239e14 | 0.121349 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.54291e14 | −0.581744 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.74332e12 | − | 4.74332e12i | −0.00487598 | − | 0.00487598i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.36771e14 | − | 4.36771e14i | 0.439799 | − | 0.439799i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.24254e14i | − | 0.221205i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.64796e14i | − | 0.932346i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.61178e14 | + | 1.61178e14i | −0.152605 | + | 0.152605i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.45723e14 | + | 9.45723e14i | 0.877363 | + | 0.877363i | 0.993261 | − | 0.115898i | \(-0.0369747\pi\) |
−0.115898 | + | 0.993261i | \(0.536975\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.06176e14 | −0.278338 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.76790e14 | 0.781115 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.14467e15 | − | 1.14467e15i | −0.999428 | − | 0.999428i | 0.000571894 | − | 1.00000i | \(-0.499818\pi\) |
−1.00000 | 0.000571894i | \(0.999818\pi\) | ||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.60357e12 | + | 9.60357e12i | −0.00821835 | + | 0.00821835i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.69030e15i | 1.41785i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.02432e14i | − | 0.248679i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.69870e14 | − | 1.69870e14i | 0.136932 | − | 0.136932i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 1.26785e15 | + | 1.26785e15i | 1.00199 | + | 1.00199i | 0.999998 | + | 0.00199459i | \(0.000634897\pi\) |
0.00199459 | + | 0.999998i | \(0.499365\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.14033e14 | −0.630778 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.84779e13 | −0.0596282 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.53526e14 | + | 9.53526e14i | 0.710455 | + | 0.710455i | 0.966630 | − | 0.256175i | \(-0.0824624\pi\) |
−0.256175 | + | 0.966630i | \(0.582462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.54220e14 | + | 2.54220e14i | −0.185756 | + | 0.185756i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.61144e14i | − | 0.187143i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.93700e14i | 0.417301i | 0.977990 | + | 0.208650i | \(0.0669071\pi\) | ||||
−0.977990 | + | 0.208650i | \(0.933093\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.83062e14 | + | 3.83062e14i | −0.264101 | + | 0.264101i | −0.826718 | − | 0.562617i | \(-0.809795\pi\) |
0.562617 | + | 0.826718i | \(0.309795\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 6.61163e14 | + | 6.61163e14i | 0.447155 | + | 0.447155i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.25694e15 | 0.833952 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.21498e15 | −0.790867 | −0.395434 | − | 0.918495i | \(-0.629406\pi\) | ||||
−0.395434 | + | 0.918495i | \(0.629406\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.28912e13 | + | 4.28912e13i | 0.0273928 | + | 0.0273928i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.80341e13 | + | 4.80341e13i | −0.0301010 | + | 0.0301010i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.22938e14i | 0.260076i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.74676e12i | − | 0.00165754i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.85634e14 | + | 8.85634e14i | −0.524499 | + | 0.524499i | −0.918927 | − | 0.394428i | \(-0.870943\pi\) |
0.394428 | + | 0.918927i | \(0.370943\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.93859e14 | − | 6.93859e14i | −0.403308 | − | 0.403308i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.34932e15 | 0.769811 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.11099e14 | −0.118218 | −0.0591092 | − | 0.998252i | \(-0.518826\pi\) | ||||
−0.0591092 | + | 0.998252i | \(0.518826\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.76292e13 | + | 3.76292e13i | 0.0206862 | + | 0.0206862i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.12800e15 | + | 1.12800e15i | −0.608763 | + | 0.608763i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.04958e15i | 0.556122i | 0.960563 | + | 0.278061i | \(0.0896917\pi\) | ||||
−0.960563 | + | 0.278061i | \(0.910308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.43484e15i | 0.746436i | 0.927744 | + | 0.373218i | \(0.121746\pi\) | ||||
−0.927744 | + | 0.373218i | \(0.878254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3.61517e12 | + | 3.61517e12i | −0.00184665 | + | 0.00184665i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7.77298e14 | − | 7.77298e14i | −0.389882 | − | 0.389882i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.30297e15 | −1.13436 | −0.567181 | − | 0.823593i | \(-0.691966\pi\) | ||||
−0.567181 | + | 0.823593i | \(0.691966\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.37970e14 | −0.211860 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.14431e14 | + | 5.14431e14i | 0.244399 | + | 0.244399i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.01165e15 | + | 1.01165e15i | −0.472058 | + | 0.472058i | −0.902580 | − | 0.430522i | \(-0.858330\pi\) |
0.430522 | + | 0.902580i | \(0.358330\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 1.92742e15i | − | 0.883410i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.46635e15i | 1.11042i | 0.831711 | + | 0.555209i | \(0.187362\pi\) | ||||
−0.831711 | + | 0.555209i | \(0.812638\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.54673e14 | + | 4.54673e14i | −0.201095 | + | 0.201095i | −0.800469 | − | 0.599374i | \(-0.795416\pi\) |
0.599374 | + | 0.800469i | \(0.295416\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.05383e15 | − | 2.05383e15i | −0.892400 | − | 0.892400i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.97878e13 | 0.0383295 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.45046e14 | −0.102780 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.80865e14 | + | 4.80865e14i | 0.198176 | + | 0.198176i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.56330e14 | + | 1.56330e14i | −0.0633088 | + | 0.0633088i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.74681e15i | − | 1.09312i | −0.837420 | − | 0.546560i | \(-0.815937\pi\) | ||
0.837420 | − | 0.546560i | \(-0.184063\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.91097e15i | 1.13846i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5.31925e14 | − | 5.31925e14i | 0.204454 | − | 0.204454i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.35156e14 | − | 7.35156e14i | −0.277723 | − | 0.277723i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.20122e13 | −0.00817352 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.33345e15 | 1.58167 | 0.790833 | − | 0.612032i | \(-0.209648\pi\) | ||||
0.790833 | + | 0.612032i | \(0.209648\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.47930e15 | − | 2.47930e15i | −0.889545 | − | 0.889545i | 0.104934 | − | 0.994479i | \(-0.466537\pi\) |
−0.994479 | + | 0.104934i | \(0.966537\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.79611e15 | + | 1.79611e15i | −0.633512 | + | 0.633512i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.92897e15i | 0.668885i | 0.942416 | + | 0.334443i | \(0.108548\pi\) | ||||
−0.942416 | + | 0.334443i | \(0.891452\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.45420e14i | 0.220038i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.79785e14 | − | 1.79785e14i | 0.0602639 | − | 0.0602639i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 6.57083e14 | + | 6.57083e14i | 0.216570 | + | 0.216570i | 0.807051 | − | 0.590481i | \(-0.201062\pi\) |
−0.590481 | + | 0.807051i | \(0.701062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.14646e15 | −0.371561 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.53561e13 | −0.00808115 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.43636e15 | + | 3.43636e15i | 1.07703 | + | 1.07703i | 0.996774 | + | 0.0802587i | \(0.0255747\pi\) |
0.0802587 | + | 0.996774i | \(0.474425\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.46547e15 | − | 2.46547e15i | 0.759963 | − | 0.759963i | −0.216353 | − | 0.976315i | \(-0.569416\pi\) |
0.976315 | + | 0.216353i | \(0.0694161\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.57948e14i | − | 0.108516i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 4.61137e14i | − | 0.137503i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.42035e15 | + | 3.42035e15i | −1.00318 | + | 1.00318i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.38005e15 | − | 1.38005e15i | −0.398154 | − | 0.398154i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.30675e15 | 0.370868 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.59870e15 | 1.56316 | 0.781581 | − | 0.623803i | \(-0.214413\pi\) | ||||
0.781581 | + | 0.623803i | \(0.214413\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.71291e15 | + | 1.71291e15i | 0.470505 | + | 0.470505i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.69257e14 | − | 9.69257e14i | 0.261940 | − | 0.261940i | −0.563902 | − | 0.825842i | \(-0.690700\pi\) |
0.825842 | + | 0.563902i | \(0.190700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.17009e13i | 0.0164062i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 4.72504e15i | − | 1.23622i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −6.09310e14 | + | 6.09310e14i | −0.156864 | + | 0.156864i | −0.781176 | − | 0.624311i | \(-0.785380\pi\) |
0.624311 | + | 0.781176i | \(0.285380\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.96715e15 | − | 2.96715e15i | −0.751693 | − | 0.751693i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.69116e14 | −0.191748 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.92907e15 | −0.473307 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.63310e14 | + | 2.63310e14i | 0.0635826 | + | 0.0635826i | 0.738183 | − | 0.674600i | \(-0.235684\pi\) |
−0.674600 | + | 0.738183i | \(0.735684\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.79900e11 | − | 8.79900e11i | 0.000209122 | − | 0.000209122i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 4.45070e15i | − | 1.04115i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.77379e15i | 0.408434i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.40469e15 | + | 1.40469e15i | −0.318388 | + | 0.318388i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.81857e15 | + | 3.81857e15i | 0.852024 | + | 0.852024i | 0.990382 | − | 0.138358i | \(-0.0441824\pi\) |
−0.138358 | + | 0.990382i | \(0.544182\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.91579e15 | 0.420817 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.27012e15 | 0.490918 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 7.38200e14 | + | 7.38200e14i | 0.157169 | + | 0.157169i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −2.06573e15 | + | 2.06573e15i | −0.433031 | + | 0.433031i | −0.889658 | − | 0.456627i | \(-0.849057\pi\) |
0.456627 | + | 0.889658i | \(0.349057\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 4.48273e13i | − | 0.00925252i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.80808e15i | − | 0.570712i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.86875e14 | + | 1.86875e14i | −0.0373997 | + | 0.0373997i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.15116e15 | − | 5.15116e15i | −1.01519 | − | 1.01519i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.28686e15 | 1.80244 | 0.901218 | − | 0.433366i | \(-0.142674\pi\) | ||||
0.901218 | + | 0.433366i | \(0.142674\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.45416e14 | −0.161594 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −4.48203e15 | − | 4.48203e15i | −0.843751 | − | 0.843751i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.85261e15 | − | 2.85261e15i | 0.528912 | − | 0.528912i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 7.23879e15i | − | 1.32198i | −0.750393 | − | 0.660992i | \(-0.770136\pi\) | ||
0.750393 | − | 0.660992i | \(-0.229864\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 5.59749e15i | − | 1.00691i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.65295e15 | − | 1.65295e15i | 0.292897 | − | 0.292897i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.06411e15 | + | 1.06411e15i | 0.185743 | + | 0.185743i | 0.793853 | − | 0.608110i | \(-0.208072\pi\) |
−0.608110 | + | 0.793853i | \(0.708072\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.24415e15 | −0.557854 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 4.91914e14 | 0.0833333 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.11437e15 | − | 2.11437e15i | −0.352887 | − | 0.352887i | 0.508295 | − | 0.861183i | \(-0.330276\pi\) |
−0.861183 | + | 0.508295i | \(0.830276\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.19329e15 | + | 2.19329e15i | −0.360658 | + | 0.360658i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 5.36629e15i | − | 0.869432i | −0.900568 | − | 0.434716i | \(-0.856849\pi\) | ||
0.900568 | − | 0.434716i | \(-0.143151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 4.86598e15i | − | 0.776803i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7.11975e12 | + | 7.11975e12i | −0.00111996 | + | 0.00111996i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.27661e14 | + | 3.27661e14i | 0.0507896 | + | 0.0507896i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.27521e15 | 0.958536 | 0.479268 | − | 0.877669i | \(-0.340902\pi\) | ||||
0.479268 | + | 0.877669i | \(0.340902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 4.48060e15 | 0.674471 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.34735e15 | + | 2.34735e15i | 0.348233 | + | 0.348233i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.57647e15 | − | 5.57647e15i | 0.815327 | − | 0.815327i | −0.170100 | − | 0.985427i | \(-0.554409\pi\) |
0.985427 | + | 0.170100i | \(0.0544091\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.94608e15i | 0.280435i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.13565e15i | 1.29755i | 0.760981 | + | 0.648775i | \(0.224718\pi\) | ||||
−0.760981 | + | 0.648775i | \(0.775282\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.28109e15 | + | 1.28109e15i | −0.179347 | + | 0.179347i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.57750e12 | + | 5.57750e12i | 0.000769665 | + | 0.000769665i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.94384e15 | −0.400443 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.05572e16 | −1.41564 | −0.707822 | − | 0.706390i | \(-0.750322\pi\) | ||||
−0.707822 | + | 0.706390i | \(0.750322\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.64420e15 | − | 7.64420e15i | −1.01049 | − | 1.01049i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.20745e14 | − | 4.20745e14i | 0.0548317 | − | 0.0548317i | −0.679159 | − | 0.733991i | \(-0.737655\pi\) |
0.733991 | + | 0.679159i | \(0.237655\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.34197e15i | 0.300900i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.96397e14i | 0.0628802i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.08687e16 | − | 1.08687e16i | 1.35744 | − | 1.35744i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.49760e15 | + | 1.49760e15i | 0.184422 | + | 0.184422i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.32228e15 | −1.13196 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.39871e15 | 0.406941 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.07370e15 | + | 6.07370e15i | 0.717121 | + | 0.717121i | 0.968015 | − | 0.250894i | \(-0.0807246\pi\) |
−0.250894 | + | 0.968015i | \(0.580725\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.01160e16 | + | 1.01160e16i | −1.17784 | + | 1.17784i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 7.42889e14i | − | 0.0853009i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.96026e15i | 0.674936i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.25638e15 | + | 4.25638e15i | −0.475358 | + | 0.475358i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 7.43572e15 | + | 7.43572e15i | 0.819034 | + | 0.819034i | 0.985968 | − | 0.166934i | \(-0.0533866\pi\) |
−0.166934 | + | 0.985968i | \(0.553387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.08918e15 | −0.226970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.33086e13 | 0.00142611 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.72510e15 | + | 1.72510e15i | 0.182338 | + | 0.182338i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.33122e14 | − | 9.33122e14i | 0.0972884 | − | 0.0972884i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.60794e16i | 1.65374i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.62426e15i | 0.367708i | 0.982954 | + | 0.183854i | \(0.0588573\pi\) | ||||
−0.982954 | + | 0.183854i | \(0.941143\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.45703e15 | − | 5.45703e15i | 0.546187 | − | 0.546187i | −0.379149 | − | 0.925336i | \(-0.623783\pi\) |
0.925336 | + | 0.379149i | \(0.123783\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.03521e15 | + | 7.03521e15i | 0.694671 | + | 0.694671i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.57188e15 | 0.153128 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.02566e16 | −1.94691 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.01333e12 | + | 4.01333e12i | 0.000380578 | + | 0.000380578i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.79173e14 | − | 7.79173e14i | 0.0729032 | − | 0.0729032i | −0.669715 | − | 0.742618i | \(-0.733584\pi\) |
0.742618 | + | 0.669715i | \(0.233584\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.87740e16i | 1.73323i | 0.498975 | + | 0.866616i | \(0.333710\pi\) | ||||
−0.498975 | + | 0.866616i | \(0.666290\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 1.62305e15i | − | 0.147855i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.96952e15 | + | 3.96952e15i | −0.356827 | + | 0.356827i | −0.862642 | − | 0.505815i | \(-0.831192\pi\) |
0.505815 | + | 0.862642i | \(0.331192\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.56186e15 | − | 8.56186e15i | −0.759483 | − | 0.759483i | 0.216745 | − | 0.976228i | \(-0.430456\pi\) |
−0.976228 | + | 0.216745i | \(0.930456\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.69816e16 | −1.48653 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.98557e15 | 0.257917 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.27737e15 | + | 7.27737e15i | 0.620439 | + | 0.620439i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.82675e15 | − | 3.82675e15i | 0.321989 | − | 0.321989i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.76310e16i | 1.46415i | 0.681224 | + | 0.732075i | \(0.261448\pi\) | ||||
−0.681224 | + | 0.732075i | \(0.738552\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.32441e15i | 0.272481i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.14304e15 | − | 5.14304e15i | 0.416072 | − | 0.416072i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.28752e15 | + | 4.28752e15i | 0.342369 | + | 0.342369i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.27144e15 | 0.179037 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.24499e15 | −0.174671 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.87665e15 | + | 3.87665e15i | 0.297744 | + | 0.297744i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 8.96322e15 | − | 8.96322e15i | 0.679586 | − | 0.679586i | −0.280320 | − | 0.959907i | \(-0.590441\pi\) |
0.959907 | + | 0.280320i | \(0.0904407\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 6.83511e13i | − | 0.00511602i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.38540e16i | − | 1.02372i | −0.859069 | − | 0.511859i | \(-0.828957\pi\) | ||
0.859069 | − | 0.511859i | \(-0.171043\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.36023e14 | − | 9.36023e14i | 0.0682848 | − | 0.0682848i | −0.672140 | − | 0.740424i | \(-0.734625\pi\) |
0.740424 | + | 0.672140i | \(0.234625\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.81617e15 | + | 2.81617e15i | 0.202835 | + | 0.202835i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.24799e16 | −1.59858 | −0.799291 | − | 0.600945i | \(-0.794791\pi\) | ||||
−0.799291 | + | 0.600945i | \(0.794791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.27723e15 | −0.230101 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −9.43710e15 | − | 9.43710e15i | −0.654234 | − | 0.654234i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.04981e15 | + | 3.04981e15i | −0.208768 | + | 0.208768i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.24368e15i | 0.151657i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.14549e12i | 0.000610420i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.95188e15 | + | 1.95188e15i | −0.128650 | + | 0.128650i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.07874e14 | + | 4.07874e14i | 0.0265478 | + | 0.0265478i | 0.720256 | − | 0.693708i | \(-0.244024\pi\) |
−0.693708 | + | 0.720256i | \(0.744024\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.04237e16 | 1.31279 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.29668e15 | −0.0823122 | −0.0411561 | − | 0.999153i | \(-0.513104\pi\) | ||||
−0.0411561 | + | 0.999153i | \(0.513104\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.46438e16 | − | 1.46438e16i | −0.918056 | − | 0.918056i | 0.0788318 | − | 0.996888i | \(-0.474881\pi\) |
−0.996888 | + | 0.0788318i | \(0.974881\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.49541e15 | + | 6.49541e15i | −0.402178 | + | 0.402178i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.45969e16i | − | 0.892648i | −0.894871 | − | 0.446324i | \(-0.852733\pi\) | ||
0.894871 | − | 0.446324i | \(-0.147267\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.55441e15i | 0.0938869i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.63346e15 | + | 2.63346e15i | −0.157108 | + | 0.157108i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.28012e16 | + | 1.28012e16i | 0.754342 | + | 0.754342i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.33014e15 | 0.543077 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −8.87633e15 | −0.510358 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.37291e15 | − | 6.37291e15i | −0.361959 | − | 0.361959i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.91712e15 | − | 3.91712e15i | 0.219776 | − | 0.219776i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.24865e15i | − | 0.290914i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 2.96090e15i | − | 0.162128i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.79943e14 | − | 1.79943e14i | 0.00973408 | − | 0.00973408i | −0.702223 | − | 0.711957i | \(-0.747809\pi\) |
0.711957 | + | 0.702223i | \(0.247809\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.09418e14 | + | 1.09418e14i | 0.00584774 | + | 0.00584774i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.66120e15 | −0.246120 | −0.123060 | − | 0.992399i | \(-0.539271\pi\) | ||||
−0.123060 | + | 0.992399i | \(0.539271\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.68780e14 | 0.0505401 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.31509e16 | + | 1.31509e16i | 0.677862 | + | 0.677862i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.67510e15 | − | 1.67510e15i | 0.0853120 | − | 0.0853120i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 7.32403e15i | − | 0.368565i | −0.982873 | − | 0.184283i | \(-0.941004\pi\) | ||
0.982873 | − | 0.184283i | \(-0.0589962\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 6.12703e15i | − | 0.304665i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.83072e15 | + | 6.83072e15i | −0.335627 | + | 0.335627i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.23317e15 | − | 3.23317e15i | −0.156981 | − | 0.156981i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.25310e14 | −0.00601239 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.83734e15 | 0.181946 | 0.0909732 | − | 0.995853i | \(-0.471002\pi\) | ||||
0.0909732 | + | 0.995853i | \(0.471002\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.82938e16 | − | 1.82938e16i | −0.857196 | − | 0.857196i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.31013e15 | + | 2.31013e15i | −0.106976 | + | 0.106976i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 7.58928e14i | − | 0.0347325i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.42166e15i | 0.154764i | 0.997002 | + | 0.0773818i | \(0.0246560\pi\) | ||||
−0.997002 | + | 0.0773818i | \(0.975344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.78032e16 | − | 2.78032e16i | 1.24289 | − | 1.24289i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.01665e15 | − | 4.01665e15i | −0.177468 | − | 0.177468i | 0.612783 | − | 0.790251i | \(-0.290050\pi\) |
−0.790251 | + | 0.612783i | \(0.790050\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.39862e16 | 1.92089 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.54325e15 | 0.109778 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.64810e16 | + | 2.64810e16i | 1.12982 | + | 1.12982i | 0.990206 | + | 0.139617i | \(0.0445870\pi\) |
0.139617 | + | 0.990206i | \(0.455413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.86838e15 | + | 7.86838e15i | −0.331834 | + | 0.331834i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1.74455e16i | − | 0.727263i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1.46484e16i | − | 0.603640i | −0.953365 | − | 0.301820i | \(-0.902406\pi\) | ||
0.953365 | − | 0.301820i | \(-0.0975942\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.39383e15 | + | 6.39383e15i | −0.260461 | + | 0.260461i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.41662e15 | + | 4.41662e15i | 0.177858 | + | 0.177858i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.67068e15 | 0.345184 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.01764e16 | −0.794080 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.85668e13 | + | 4.85668e13i | 0.00188971 | + | 0.00188971i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.14783e14 | + | 4.14783e14i | −0.0159559 | + | 0.0159559i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 5.90633e15i | − | 0.224632i | −0.993673 | − | 0.112316i | \(-0.964173\pi\) | ||
0.993673 | − | 0.112316i | \(-0.0358270\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 8.90726e15i | − | 0.334937i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.00686e15 | + | 4.00686e15i | −0.148970 | + | 0.148970i | −0.777658 | − | 0.628688i | \(-0.783592\pi\) |
0.628688 | + | 0.777658i | \(0.283592\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6.50298e15 | + | 6.50298e15i | 0.239052 | + | 0.239052i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.40296e15 | 0.269079 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 3.72683e16 | 1.33943 | 0.669714 | − | 0.742619i | \(-0.266417\pi\) | ||||
0.669714 | + | 0.742619i | \(0.266417\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.05447e14 | − | 9.05447e14i | −0.0321779 | − | 0.0321779i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.89887e14 | + | 1.89887e14i | −0.00667292 | + | 0.00667292i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.32496e16i | − | 1.50293i | −0.659776 | − | 0.751463i | \(-0.729349\pi\) | ||
0.659776 | − | 0.751463i | \(-0.270651\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.30487e16i | 0.448403i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.31690e15 | + | 3.31690e15i | −0.112717 | + | 0.112717i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −4.09897e16 | − | 4.09897e16i | −1.37751 | − | 1.37751i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.69777e16 | −1.22895 | −0.614476 | − | 0.788936i | \(-0.710632\pi\) | ||||
−0.614476 | + | 0.788936i | \(0.710632\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 5.27972e16 | 1.73536 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.09084e16 | − | 1.09084e16i | −0.354595 | − | 0.354595i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.76589e16 | − | 3.76589e16i | 1.21072 | − | 1.21072i | 0.239932 | − | 0.970790i | \(-0.422875\pi\) |
0.970790 | − | 0.239932i | \(-0.0771253\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.05659e16i | 0.335968i |
(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 | 64.12.e.a.17.17 | 42 | ||
4.3 | odd | 2 | 16.12.e.a.13.12 | yes | 42 | ||
8.3 | odd | 2 | 128.12.e.b.33.17 | 42 | |||
8.5 | even | 2 | 128.12.e.a.33.5 | 42 | |||
16.3 | odd | 4 | 128.12.e.b.97.17 | 42 | |||
16.5 | even | 4 | inner | 64.12.e.a.49.17 | 42 | ||
16.11 | odd | 4 | 16.12.e.a.5.12 | ✓ | 42 | ||
16.13 | even | 4 | 128.12.e.a.97.5 | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.12.e.a.5.12 | ✓ | 42 | 16.11 | odd | 4 | ||
16.12.e.a.13.12 | yes | 42 | 4.3 | odd | 2 | ||
64.12.e.a.17.17 | 42 | 1.1 | even | 1 | trivial | ||
64.12.e.a.49.17 | 42 | 16.5 | even | 4 | inner | ||
128.12.e.a.33.5 | 42 | 8.5 | even | 2 | |||
128.12.e.a.97.5 | 42 | 16.13 | even | 4 | |||
128.12.e.b.33.17 | 42 | 8.3 | odd | 2 | |||
128.12.e.b.97.17 | 42 | 16.3 | odd | 4 |