Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,41,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 41, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 41);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 41 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.4026855589\) |
Analytic rank: | \(0\) |
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: | \( x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.10 | ||
Root | \(229859. i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.41.b.a.2.3 |
$q$-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 \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.37915e6i | 1.31526i | 0.753340 | + | 0.657631i | \(0.228441\pi\) | ||||
−0.753340 | + | 0.657631i | \(0.771559\pi\) | |||||||
\(3\) | −3.48296e9 | + | 1.63234e8i | −0.998904 | + | 0.0468150i | ||||
\(4\) | −8.02549e11 | −0.729914 | ||||||||
\(5\) | − | 4.92196e13i | − | 0.516105i | −0.966131 | − | 0.258053i | \(-0.916919\pi\) | ||
0.966131 | − | 0.258053i | \(-0.0830808\pi\) | |||||||
\(6\) | −2.25124e14 | − | 4.80353e15i | −0.0615740 | − | 1.31382i | ||||
\(7\) | 5.39353e16 | 0.675946 | 0.337973 | − | 0.941156i | \(-0.390259\pi\) | ||||
0.337973 | + | 0.941156i | \(0.390259\pi\) | |||||||
\(8\) | 4.09556e17i | 0.355233i | ||||||||
\(9\) | 1.21044e19 | − | 1.13707e18i | 0.995617 | − | 0.0935274i | ||||
\(10\) | 6.78814e19 | 0.678814 | ||||||||
\(11\) | 2.19593e20i | 0.326412i | 0.986592 | + | 0.163206i | \(0.0521835\pi\) | ||||
−0.986592 | + | 0.163206i | \(0.947817\pi\) | |||||||
\(12\) | 2.79525e21 | − | 1.31003e20i | 0.729114 | − | 0.0341710i | ||||
\(13\) | 5.75209e21 | 0.302662 | 0.151331 | − | 0.988483i | \(-0.451644\pi\) | ||||
0.151331 | + | 0.988483i | \(0.451644\pi\) | |||||||
\(14\) | 7.43849e22i | 0.889046i | ||||||||
\(15\) | 8.03431e21 | + | 1.71430e23i | 0.0241615 | + | 0.515540i | ||||
\(16\) | −1.44725e24 | −1.19714 | ||||||||
\(17\) | 6.05210e24i | 1.48911i | 0.667560 | + | 0.744556i | \(0.267339\pi\) | ||||
−0.667560 | + | 0.744556i | \(0.732661\pi\) | |||||||
\(18\) | 1.56820e24 | + | 1.66938e25i | 0.123013 | + | 1.30950i | ||||
\(19\) | 3.89743e25 | 1.03683 | 0.518414 | − | 0.855130i | \(-0.326523\pi\) | ||||
0.518414 | + | 0.855130i | \(0.326523\pi\) | |||||||
\(20\) | 3.95012e25i | 0.376713i | ||||||||
\(21\) | −1.87854e26 | + | 8.80406e24i | −0.675205 | + | 0.0316444i | ||||
\(22\) | −3.02853e26 | −0.429317 | ||||||||
\(23\) | − | 2.93005e27i | − | 1.70733i | −0.520822 | − | 0.853666i | \(-0.674374\pi\) | ||
0.520822 | − | 0.853666i | \(-0.325626\pi\) | |||||||
\(24\) | −6.68534e25 | − | 1.42647e27i | −0.0166303 | − | 0.354844i | ||||
\(25\) | 6.67237e27 | 0.733635 | ||||||||
\(26\) | 7.93300e27i | 0.398080i | ||||||||
\(27\) | −4.19735e28 | + | 5.93623e27i | −0.990147 | + | 0.140035i | ||||
\(28\) | −4.32857e28 | −0.493383 | ||||||||
\(29\) | 2.25230e29i | 1.27253i | 0.771472 | + | 0.636264i | \(0.219521\pi\) | ||||
−0.771472 | + | 0.636264i | \(0.780479\pi\) | |||||||
\(30\) | −2.36428e29 | + | 1.10805e28i | −0.678070 | + | 0.0317787i | ||||
\(31\) | −5.05825e29 | −0.752950 | −0.376475 | − | 0.926427i | \(-0.622864\pi\) | ||||
−0.376475 | + | 0.926427i | \(0.622864\pi\) | |||||||
\(32\) | − | 1.54567e30i | − | 1.21932i | ||||||
\(33\) | −3.58451e28 | − | 7.64836e29i | −0.0152810 | − | 0.326054i | ||||
\(34\) | −8.34676e30 | −1.95857 | ||||||||
\(35\) | − | 2.65467e30i | − | 0.348859i | ||||||
\(36\) | −9.71436e30 | + | 9.12558e29i | −0.726715 | + | 0.0682670i | ||||
\(37\) | −3.44493e31 | −1.48986 | −0.744931 | − | 0.667141i | \(-0.767518\pi\) | ||||
−0.744931 | + | 0.667141i | \(0.767518\pi\) | |||||||
\(38\) | 5.37515e31i | 1.36370i | ||||||||
\(39\) | −2.00343e31 | + | 9.38935e29i | −0.302330 | + | 0.0141691i | ||||
\(40\) | 2.01582e31 | 0.183338 | ||||||||
\(41\) | − | 2.84139e31i | − | 0.157708i | −0.996886 | − | 0.0788541i | \(-0.974874\pi\) | ||
0.996886 | − | 0.0788541i | \(-0.0251261\pi\) | |||||||
\(42\) | −1.21421e31 | − | 2.59080e32i | −0.0416207 | − | 0.888071i | ||||
\(43\) | −3.37498e31 | −0.0722608 | −0.0361304 | − | 0.999347i | \(-0.511503\pi\) | ||||
−0.0361304 | + | 0.999347i | \(0.511503\pi\) | |||||||
\(44\) | − | 1.76235e32i | − | 0.238253i | ||||||
\(45\) | −5.59664e31 | − | 5.95773e32i | −0.0482700 | − | 0.513843i | ||||
\(46\) | 4.04098e33 | 2.24559 | ||||||||
\(47\) | 4.50279e33i | 1.62751i | 0.581205 | + | 0.813757i | \(0.302581\pi\) | ||||
−0.581205 | + | 0.813757i | \(0.697419\pi\) | |||||||
\(48\) | 5.04073e33 | − | 2.36241e32i | 1.19583 | − | 0.0560441i | ||||
\(49\) | −3.45779e33 | −0.543097 | ||||||||
\(50\) | 9.20222e33i | 0.964923i | ||||||||
\(51\) | −9.87907e32 | − | 2.10792e34i | −0.0697128 | − | 1.48748i | ||||
\(52\) | −4.61633e33 | −0.220918 | ||||||||
\(53\) | 1.59114e34i | 0.520224i | 0.965578 | + | 0.260112i | \(0.0837595\pi\) | ||||
−0.965578 | + | 0.260112i | \(0.916241\pi\) | |||||||
\(54\) | −8.18697e33 | − | 5.78878e34i | −0.184182 | − | 1.30230i | ||||
\(55\) | 1.08083e34 | 0.168463 | ||||||||
\(56\) | 2.20895e34i | 0.240119i | ||||||||
\(57\) | −1.35746e35 | + | 6.36193e33i | −1.03569 | + | 0.0485391i | ||||
\(58\) | −3.10627e35 | −1.67371 | ||||||||
\(59\) | 4.55972e35i | 1.74541i | 0.488245 | + | 0.872707i | \(0.337637\pi\) | ||||
−0.488245 | + | 0.872707i | \(0.662363\pi\) | |||||||
\(60\) | −6.44793e33 | − | 1.37581e35i | −0.0176358 | − | 0.376300i | ||||
\(61\) | 2.97372e35 | 0.584391 | 0.292196 | − | 0.956359i | \(-0.405614\pi\) | ||||
0.292196 | + | 0.956359i | \(0.405614\pi\) | |||||||
\(62\) | − | 6.97609e35i | − | 0.990327i | ||||||
\(63\) | 6.52853e35 | − | 6.13284e34i | 0.672983 | − | 0.0632194i | ||||
\(64\) | 5.40443e35 | 0.406584 | ||||||||
\(65\) | − | 2.83116e35i | − | 0.156206i | ||||||
\(66\) | 1.05482e36 | − | 4.94358e34i | 0.428846 | − | 0.0200985i | ||||
\(67\) | 1.49190e36 | 0.448996 | 0.224498 | − | 0.974475i | \(-0.427926\pi\) | ||||
0.224498 | + | 0.974475i | \(0.427926\pi\) | |||||||
\(68\) | − | 4.85711e36i | − | 1.08692i | ||||||
\(69\) | 4.78283e35 | + | 1.02052e37i | 0.0799287 | + | 1.70546i | ||||
\(70\) | 3.66120e36 | 0.458841 | ||||||||
\(71\) | 8.37384e36i | 0.790237i | 0.918630 | + | 0.395119i | \(0.129297\pi\) | ||||
−0.918630 | + | 0.395119i | \(0.870703\pi\) | |||||||
\(72\) | 4.65696e35 | + | 4.95742e36i | 0.0332240 | + | 0.353676i | ||||
\(73\) | −1.01281e37 | −0.548368 | −0.274184 | − | 0.961677i | \(-0.588408\pi\) | ||||
−0.274184 | + | 0.961677i | \(0.588408\pi\) | |||||||
\(74\) | − | 4.75109e37i | − | 1.95956i | ||||||
\(75\) | −2.32396e37 | + | 1.08916e36i | −0.732831 | + | 0.0343451i | ||||
\(76\) | −3.12788e37 | −0.756795 | ||||||||
\(77\) | 1.18438e37i | 0.220637i | ||||||||
\(78\) | −1.29493e36 | − | 2.76303e37i | −0.0186361 | − | 0.397644i | ||||
\(79\) | −9.72628e37 | −1.08494 | −0.542469 | − | 0.840076i | \(-0.682511\pi\) | ||||
−0.542469 | + | 0.840076i | \(0.682511\pi\) | |||||||
\(80\) | 7.12333e37i | 0.617850i | ||||||||
\(81\) | 1.45223e38 | − | 2.75271e37i | 0.982505 | − | 0.186235i | ||||
\(82\) | 3.91871e37 | 0.207428 | ||||||||
\(83\) | 3.08704e38i | 1.28227i | 0.767428 | + | 0.641136i | \(0.221536\pi\) | ||||
−0.767428 | + | 0.641136i | \(0.778464\pi\) | |||||||
\(84\) | 1.50762e38 | − | 7.06569e36i | 0.492842 | − | 0.0230977i | ||||
\(85\) | 2.97882e38 | 0.768539 | ||||||||
\(86\) | − | 4.65462e37i | − | 0.0950418i | ||||||
\(87\) | −3.67652e37 | − | 7.84469e38i | −0.0595734 | − | 1.27113i | ||||
\(88\) | −8.99359e37 | −0.115952 | ||||||||
\(89\) | − | 4.83862e38i | − | 0.497647i | −0.968549 | − | 0.248824i | \(-0.919956\pi\) | ||
0.968549 | − | 0.248824i | \(-0.0800440\pi\) | |||||||
\(90\) | 8.21662e38 | − | 7.71862e37i | 0.675838 | − | 0.0634877i | ||||
\(91\) | 3.10240e38 | 0.204583 | ||||||||
\(92\) | 2.35151e39i | 1.24621i | ||||||||
\(93\) | 1.76177e39 | − | 8.25677e37i | 0.752125 | − | 0.0352494i | ||||
\(94\) | −6.21004e39 | −2.14061 | ||||||||
\(95\) | − | 1.91830e39i | − | 0.535112i | ||||||
\(96\) | 2.52306e38 | + | 5.38351e39i | 0.0570824 | + | 1.21798i | ||||
\(97\) | −7.78530e39 | −1.43166 | −0.715831 | − | 0.698273i | \(-0.753952\pi\) | ||||
−0.715831 | + | 0.698273i | \(0.753952\pi\) | |||||||
\(98\) | − | 4.76882e39i | − | 0.714315i | ||||||
\(99\) | 2.49694e38 | + | 2.65804e39i | 0.0305284 | + | 0.324981i | ||||
\(100\) | −5.35491e39 | −0.535491 | ||||||||
\(101\) | − | 1.65661e40i | − | 1.35767i | −0.734293 | − | 0.678833i | \(-0.762486\pi\) | ||
0.734293 | − | 0.678833i | \(-0.237514\pi\) | |||||||
\(102\) | 2.90715e40 | − | 1.36247e39i | 1.95643 | − | 0.0916906i | ||||
\(103\) | 6.78762e39 | 0.375814 | 0.187907 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187907 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(104\) | 2.35580e39i | 0.107516i | ||||||||
\(105\) | 4.33333e38 | + | 9.24613e39i | 0.0163319 | + | 0.348477i | ||||
\(106\) | −2.19442e40 | −0.684231 | ||||||||
\(107\) | 3.91632e40i | 1.01205i | 0.862518 | + | 0.506026i | \(0.168886\pi\) | ||||
−0.862518 | + | 0.506026i | \(0.831114\pi\) | |||||||
\(108\) | 3.36858e40 | − | 4.76412e39i | 0.722722 | − | 0.102213i | ||||
\(109\) | 6.14356e39 | 0.109620 | 0.0548100 | − | 0.998497i | \(-0.482545\pi\) | ||||
0.0548100 | + | 0.998497i | \(0.482545\pi\) | |||||||
\(110\) | 1.49063e40i | 0.221573i | ||||||||
\(111\) | 1.19986e41 | − | 5.62330e39i | 1.48823 | − | 0.0697479i | ||||
\(112\) | −7.80580e40 | −0.809202 | ||||||||
\(113\) | 6.15450e40i | 0.534101i | 0.963682 | + | 0.267051i | \(0.0860491\pi\) | ||||
−0.963682 | + | 0.267051i | \(0.913951\pi\) | |||||||
\(114\) | −8.77407e39 | − | 1.87215e41i | −0.0638416 | − | 1.36220i | ||||
\(115\) | −1.44216e41 | −0.881163 | ||||||||
\(116\) | − | 1.80759e41i | − | 0.928836i | ||||||
\(117\) | 6.96254e40 | − | 6.54055e39i | 0.301336 | − | 0.0283072i | ||||
\(118\) | −6.28855e41 | −2.29568 | ||||||||
\(119\) | 3.26421e41i | 1.00656i | ||||||||
\(120\) | −7.02103e40 | + | 3.29050e39i | −0.183137 | + | 0.00858296i | ||||
\(121\) | 4.04371e41 | 0.893455 | ||||||||
\(122\) | 4.10122e41i | 0.768628i | ||||||||
\(123\) | 4.63811e39 | + | 9.89646e40i | 0.00738311 | + | 0.157535i | ||||
\(124\) | 4.05949e41 | 0.549589 | ||||||||
\(125\) | − | 7.76062e41i | − | 0.894738i | ||||||
\(126\) | 8.45812e40 | + | 9.00383e41i | 0.0831501 | + | 0.885149i | ||||
\(127\) | 8.82928e41 | 0.741056 | 0.370528 | − | 0.928821i | \(-0.379177\pi\) | ||||
0.370528 | + | 0.928821i | \(0.379177\pi\) | |||||||
\(128\) | − | 9.54129e41i | − | 0.684554i | ||||||
\(129\) | 1.17549e41 | − | 5.50912e39i | 0.0721815 | − | 0.00338289i | ||||
\(130\) | 3.90460e41 | 0.205451 | ||||||||
\(131\) | − | 3.17130e42i | − | 1.43157i | −0.698323 | − | 0.715783i | \(-0.746070\pi\) | ||
0.698323 | − | 0.715783i | \(-0.253930\pi\) | |||||||
\(132\) | 2.87675e40 | + | 6.13818e41i | 0.0111538 | + | 0.237991i | ||||
\(133\) | 2.10209e42 | 0.700839 | ||||||||
\(134\) | 2.05755e42i | 0.590547i | ||||||||
\(135\) | 2.92179e41 | + | 2.06592e42i | 0.0722726 | + | 0.511020i | ||||
\(136\) | −2.47867e42 | −0.528982 | ||||||||
\(137\) | 5.39384e42i | 0.994229i | 0.867685 | + | 0.497115i | \(0.165607\pi\) | ||||
−0.867685 | + | 0.497115i | \(0.834393\pi\) | |||||||
\(138\) | −1.40746e43 | + | 6.59625e41i | −2.24313 | + | 0.105127i | ||||
\(139\) | 9.90151e42 | 1.36586 | 0.682929 | − | 0.730485i | \(-0.260706\pi\) | ||||
0.682929 | + | 0.730485i | \(0.260706\pi\) | |||||||
\(140\) | 2.13051e42i | 0.254637i | ||||||||
\(141\) | −7.35008e41 | − | 1.56830e43i | −0.0761921 | − | 1.62573i | ||||
\(142\) | −1.15488e43 | −1.03937 | ||||||||
\(143\) | 1.26312e42i | 0.0987925i | ||||||||
\(144\) | −1.75181e43 | + | 1.64563e42i | −1.19189 | + | 0.111965i | ||||
\(145\) | 1.10858e43 | 0.656758 | ||||||||
\(146\) | − | 1.39682e43i | − | 0.721247i | ||||||
\(147\) | 1.20434e43 | − | 5.64429e41i | 0.542502 | − | 0.0254251i | ||||
\(148\) | 2.76473e43 | 1.08747 | ||||||||
\(149\) | 2.80166e43i | 0.963141i | 0.876407 | + | 0.481571i | \(0.159934\pi\) | ||||
−0.876407 | + | 0.481571i | \(0.840066\pi\) | |||||||
\(150\) | −1.50211e42 | − | 3.20510e43i | −0.0451729 | − | 0.963865i | ||||
\(151\) | 3.78370e43 | 0.996273 | 0.498136 | − | 0.867099i | \(-0.334018\pi\) | ||||
0.498136 | + | 0.867099i | \(0.334018\pi\) | |||||||
\(152\) | 1.59622e43i | 0.368316i | ||||||||
\(153\) | 6.88169e42 | + | 7.32569e43i | 0.139273 | + | 1.48259i | ||||
\(154\) | −1.63344e43 | −0.290195 | ||||||||
\(155\) | 2.48965e43i | 0.388602i | ||||||||
\(156\) | 1.60785e43 | − | 7.53542e41i | 0.220675 | − | 0.0103423i | ||||
\(157\) | −2.54079e43 | −0.306885 | −0.153443 | − | 0.988158i | \(-0.549036\pi\) | ||||
−0.153443 | + | 0.988158i | \(0.549036\pi\) | |||||||
\(158\) | − | 1.34140e44i | − | 1.42698i | ||||||
\(159\) | −2.59728e42 | − | 5.54187e43i | −0.0243543 | − | 0.519654i | ||||
\(160\) | −7.60773e43 | −0.629297 | ||||||||
\(161\) | − | 1.58033e44i | − | 1.15406i | ||||||
\(162\) | 3.79641e43 | + | 2.00285e44i | 0.244948 | + | 1.29225i | ||||
\(163\) | 3.84121e43 | 0.219137 | 0.109568 | − | 0.993979i | \(-0.465053\pi\) | ||||
0.109568 | + | 0.993979i | \(0.465053\pi\) | |||||||
\(164\) | 2.28036e43i | 0.115113i | ||||||||
\(165\) | −3.76449e43 | + | 1.76428e42i | −0.168278 | + | 0.00788659i | ||||
\(166\) | −4.25749e44 | −1.68652 | ||||||||
\(167\) | 5.27479e43i | 0.185300i | 0.995699 | + | 0.0926500i | \(0.0295338\pi\) | ||||
−0.995699 | + | 0.0926500i | \(0.970466\pi\) | |||||||
\(168\) | −3.60576e42 | − | 7.69369e43i | −0.0112412 | − | 0.239855i | ||||
\(169\) | −3.28102e44 | −0.908396 | ||||||||
\(170\) | 4.10825e44i | 1.01083i | ||||||||
\(171\) | 4.71760e44 | − | 4.43167e43i | 1.03228 | − | 0.0969718i | ||||
\(172\) | 2.70859e43 | 0.0527442 | ||||||||
\(173\) | 2.89150e44i | 0.501419i | 0.968062 | + | 0.250710i | \(0.0806639\pi\) | ||||
−0.968062 | + | 0.250710i | \(0.919336\pi\) | |||||||
\(174\) | 1.08190e45 | − | 5.07048e43i | 1.67187 | − | 0.0783546i | ||||
\(175\) | 3.59876e44 | 0.495898 | ||||||||
\(176\) | − | 3.17807e44i | − | 0.390760i | ||||||
\(177\) | −7.44301e43 | − | 1.58813e45i | −0.0817115 | − | 1.74350i | ||||
\(178\) | 6.67320e44 | 0.654537 | ||||||||
\(179\) | 2.25416e43i | 0.0197662i | 0.999951 | + | 0.00988312i | \(0.00314594\pi\) | ||||
−0.999951 | + | 0.00988312i | \(0.996854\pi\) | |||||||
\(180\) | 4.49158e43 | + | 4.78137e44i | 0.0352330 | + | 0.375062i | ||||
\(181\) | −1.60109e45 | −1.12420 | −0.562101 | − | 0.827069i | \(-0.690007\pi\) | ||||
−0.562101 | + | 0.827069i | \(0.690007\pi\) | |||||||
\(182\) | 4.27869e44i | 0.269081i | ||||||||
\(183\) | −1.03574e45 | + | 4.85412e43i | −0.583751 | + | 0.0273583i | ||||
\(184\) | 1.20002e45 | 0.606501 | ||||||||
\(185\) | 1.69558e45i | 0.768926i | ||||||||
\(186\) | 1.13873e44 | + | 2.42975e45i | 0.0463622 | + | 0.989241i | ||||
\(187\) | −1.32900e45 | −0.486064 | ||||||||
\(188\) | − | 3.61371e45i | − | 1.18795i | ||||||
\(189\) | −2.26385e45 | + | 3.20172e44i | −0.669286 | + | 0.0946558i | ||||
\(190\) | 2.64563e45 | 0.703813 | ||||||||
\(191\) | 2.81966e45i | 0.675350i | 0.941263 | + | 0.337675i | \(0.109641\pi\) | ||||
−0.941263 | + | 0.337675i | \(0.890359\pi\) | |||||||
\(192\) | −1.88234e45 | + | 8.82186e43i | −0.406139 | + | 0.0190342i | ||||
\(193\) | −7.64121e45 | −1.48599 | −0.742995 | − | 0.669297i | \(-0.766596\pi\) | ||||
−0.742995 | + | 0.669297i | \(0.766596\pi\) | |||||||
\(194\) | − | 1.07371e46i | − | 1.88301i | ||||||
\(195\) | 4.62140e43 | + | 9.86081e44i | 0.00731277 | + | 0.156034i | ||||
\(196\) | 2.77505e45 | 0.396414 | ||||||||
\(197\) | − | 9.28857e44i | − | 0.119846i | −0.998203 | − | 0.0599231i | \(-0.980914\pi\) | ||
0.998203 | − | 0.0599231i | \(-0.0190855\pi\) | |||||||
\(198\) | −3.66584e45 | + | 3.44366e44i | −0.427435 | + | 0.0401529i | ||||
\(199\) | 1.72349e46 | 1.81697 | 0.908486 | − | 0.417915i | \(-0.137239\pi\) | ||||
0.908486 | + | 0.417915i | \(0.137239\pi\) | |||||||
\(200\) | 2.73271e45i | 0.260612i | ||||||||
\(201\) | −5.19621e45 | + | 2.43528e44i | −0.448503 | + | 0.0210197i | ||||
\(202\) | 2.28472e46 | 1.78569 | ||||||||
\(203\) | 1.21479e46i | 0.860160i | ||||||||
\(204\) | 7.92844e44 | + | 1.69171e46i | 0.0508844 | + | 1.08573i | ||||
\(205\) | −1.39852e45 | −0.0813940 | ||||||||
\(206\) | 9.36116e45i | 0.494294i | ||||||||
\(207\) | −3.33168e45 | − | 3.54664e46i | −0.159682 | − | 1.69985i | ||||
\(208\) | −8.32472e45 | −0.362329 | ||||||||
\(209\) | 8.55851e45i | 0.338433i | ||||||||
\(210\) | −1.27518e46 | + | 5.97632e44i | −0.458338 | + | 0.0214807i | ||||
\(211\) | 1.43413e46 | 0.468749 | 0.234375 | − | 0.972146i | \(-0.424696\pi\) | ||||
0.234375 | + | 0.972146i | \(0.424696\pi\) | |||||||
\(212\) | − | 1.27697e46i | − | 0.379719i | ||||||
\(213\) | −1.36689e45 | − | 2.91658e46i | −0.0369950 | − | 0.789371i | ||||
\(214\) | −5.40120e46 | −1.33111 | ||||||||
\(215\) | 1.66115e45i | 0.0372942i | ||||||||
\(216\) | −2.43122e45 | − | 1.71905e46i | −0.0497450 | − | 0.351733i | ||||
\(217\) | −2.72818e46 | −0.508954 | ||||||||
\(218\) | 8.47290e45i | 0.144179i | ||||||||
\(219\) | 3.52759e46 | − | 1.65325e45i | 0.547767 | − | 0.0256718i | ||||
\(220\) | −8.67420e45 | −0.122963 | ||||||||
\(221\) | 3.48122e46i | 0.450698i | ||||||||
\(222\) | 7.75538e45 | + | 1.65479e47i | 0.0917368 | + | 1.95741i | ||||
\(223\) | −6.91711e46 | −0.747872 | −0.373936 | − | 0.927454i | \(-0.621992\pi\) | ||||
−0.373936 | + | 0.927454i | \(0.621992\pi\) | |||||||
\(224\) | − | 8.33661e46i | − | 0.824194i | ||||||
\(225\) | 8.07649e46 | − | 7.58699e45i | 0.730420 | − | 0.0686150i | ||||
\(226\) | −8.48799e46 | −0.702483 | ||||||||
\(227\) | − | 1.58759e45i | − | 0.0120288i | −0.999982 | − | 0.00601440i | \(-0.998086\pi\) | ||
0.999982 | − | 0.00601440i | \(-0.00191445\pi\) | |||||||
\(228\) | 1.08943e47 | − | 5.10576e45i | 0.755966 | − | 0.0354294i | ||||
\(229\) | 2.60363e47 | 1.65527 | 0.827636 | − | 0.561265i | \(-0.189685\pi\) | ||||
0.827636 | + | 0.561265i | \(0.189685\pi\) | |||||||
\(230\) | − | 1.98896e47i | − | 1.15896i | ||||||
\(231\) | −1.93331e45 | − | 4.12516e46i | −0.0103291 | − | 0.220395i | ||||
\(232\) | −9.22445e46 | −0.452044 | ||||||||
\(233\) | 1.26626e47i | 0.569384i | 0.958619 | + | 0.284692i | \(0.0918913\pi\) | ||||
−0.958619 | + | 0.284692i | \(0.908109\pi\) | |||||||
\(234\) | 9.02041e45 | + | 9.60240e46i | 0.0372314 | + | 0.396335i | ||||
\(235\) | 2.21626e47 | 0.839969 | ||||||||
\(236\) | − | 3.65940e47i | − | 1.27400i | ||||||
\(237\) | 3.38763e47 | − | 1.58766e46i | 1.08375 | − | 0.0507914i | ||||
\(238\) | −4.50185e47 | −1.32389 | ||||||||
\(239\) | 4.85091e47i | 1.31179i | 0.754850 | + | 0.655897i | \(0.227709\pi\) | ||||
−0.754850 | + | 0.655897i | \(0.772291\pi\) | |||||||
\(240\) | −1.16277e46 | − | 2.48103e47i | −0.0289247 | − | 0.617173i | ||||
\(241\) | −5.71937e47 | −1.30920 | −0.654602 | − | 0.755973i | \(-0.727164\pi\) | ||||
−0.654602 | + | 0.755973i | \(0.727164\pi\) | |||||||
\(242\) | 5.57690e47i | 1.17513i | ||||||||
\(243\) | −5.01313e47 | + | 1.19581e47i | −0.972709 | + | 0.232027i | ||||
\(244\) | −2.38656e47 | −0.426556 | ||||||||
\(245\) | 1.70191e47i | 0.280295i | ||||||||
\(246\) | −1.36487e47 | + | 6.39667e45i | −0.207200 | + | 0.00971072i | ||||
\(247\) | 2.24184e47 | 0.313809 | ||||||||
\(248\) | − | 2.07164e47i | − | 0.267473i | ||||||
\(249\) | −5.03909e46 | − | 1.07520e48i | −0.0600295 | − | 1.28087i | ||||
\(250\) | 1.07031e48 | 1.17682 | ||||||||
\(251\) | − | 1.04596e48i | − | 1.06180i | −0.847436 | − | 0.530898i | \(-0.821855\pi\) | ||
0.847436 | − | 0.530898i | \(-0.178145\pi\) | |||||||
\(252\) | −5.23946e47 | + | 4.92191e46i | −0.491220 | + | 0.0461448i | ||||
\(253\) | 6.43419e47 | 0.557293 | ||||||||
\(254\) | 1.21769e48i | 0.974683i | ||||||||
\(255\) | −1.03751e48 | + | 4.86244e46i | −0.767696 | + | 0.0359792i | ||||
\(256\) | 1.91011e48 | 1.30695 | ||||||||
\(257\) | − | 4.07243e47i | − | 0.257746i | −0.991661 | − | 0.128873i | \(-0.958864\pi\) | ||
0.991661 | − | 0.128873i | \(-0.0411359\pi\) | |||||||
\(258\) | 7.59791e45 | + | 1.62118e47i | 0.00444939 | + | 0.0949376i | ||||
\(259\) | −1.85803e48 | −1.00707 | ||||||||
\(260\) | 2.27214e47i | 0.114017i | ||||||||
\(261\) | 2.56104e47 | + | 2.72627e48i | 0.119016 | + | 1.26695i | ||||
\(262\) | 4.37371e48 | 1.88288 | ||||||||
\(263\) | − | 1.95587e48i | − | 0.780233i | −0.920765 | − | 0.390117i | \(-0.872435\pi\) | ||
0.920765 | − | 0.390117i | \(-0.127565\pi\) | |||||||
\(264\) | 3.13243e47 | − | 1.46806e46i | 0.115825 | − | 0.00542831i | ||||
\(265\) | 7.83152e47 | 0.268490 | ||||||||
\(266\) | 2.89910e48i | 0.921788i | ||||||||
\(267\) | 7.89827e46 | + | 1.68527e48i | 0.0232974 | + | 0.497102i | ||||
\(268\) | −1.19732e48 | −0.327728 | ||||||||
\(269\) | − | 3.91909e48i | − | 0.995724i | −0.867256 | − | 0.497862i | \(-0.834119\pi\) | ||
0.867256 | − | 0.497862i | \(-0.165881\pi\) | |||||||
\(270\) | −2.84922e48 | + | 4.02960e47i | −0.672125 | + | 0.0950574i | ||||
\(271\) | −3.29742e48 | −0.722418 | −0.361209 | − | 0.932485i | \(-0.617636\pi\) | ||||
−0.361209 | + | 0.932485i | \(0.617636\pi\) | |||||||
\(272\) | − | 8.75891e48i | − | 1.78268i | ||||||
\(273\) | −1.08055e48 | + | 5.06417e46i | −0.204359 | + | 0.00957757i | ||||
\(274\) | −7.43892e48 | −1.30767 | ||||||||
\(275\) | 1.46521e48i | 0.239467i | ||||||||
\(276\) | −3.83846e47 | − | 8.19021e48i | −0.0583411 | − | 1.24484i | ||||
\(277\) | 5.09477e47 | 0.0720327 | 0.0360163 | − | 0.999351i | \(-0.488533\pi\) | ||||
0.0360163 | + | 0.999351i | \(0.488533\pi\) | |||||||
\(278\) | 1.36557e49i | 1.79646i | ||||||||
\(279\) | −6.12269e48 | + | 5.75160e47i | −0.749650 | + | 0.0704214i | ||||
\(280\) | 1.08724e48 | 0.123926 | ||||||||
\(281\) | 1.31370e49i | 1.39435i | 0.716902 | + | 0.697174i | \(0.245559\pi\) | ||||
−0.716902 | + | 0.697174i | \(0.754441\pi\) | |||||||
\(282\) | 2.16293e49 | − | 1.01369e48i | 2.13826 | − | 0.100213i | ||||
\(283\) | 4.62045e48 | 0.425554 | 0.212777 | − | 0.977101i | \(-0.431749\pi\) | ||||
0.212777 | + | 0.977101i | \(0.431749\pi\) | |||||||
\(284\) | − | 6.72042e48i | − | 0.576806i | ||||||
\(285\) | 3.13132e47 | + | 6.68137e48i | 0.0250513 | + | 0.534526i | ||||
\(286\) | −1.74204e48 | −0.129938 | ||||||||
\(287\) | − | 1.53251e48i | − | 0.106602i | ||||||
\(288\) | −1.75754e48 | − | 1.87094e49i | −0.114040 | − | 1.21397i | ||||
\(289\) | −2.01099e49 | −1.21746 | ||||||||
\(290\) | 1.52890e49i | 0.863809i | ||||||||
\(291\) | 2.71159e49 | − | 1.27082e48i | 1.43009 | − | 0.0670233i | ||||
\(292\) | 8.12832e48 | 0.400262 | ||||||||
\(293\) | − | 2.66809e49i | − | 1.22701i | −0.789691 | − | 0.613505i | \(-0.789759\pi\) | ||
0.789691 | − | 0.613505i | \(-0.210241\pi\) | |||||||
\(294\) | 7.78433e47 | + | 1.66096e49i | 0.0334407 | + | 0.713532i | ||||
\(295\) | 2.24428e49 | 0.900817 | ||||||||
\(296\) | − | 1.41089e49i | − | 0.529249i | ||||||
\(297\) | −1.30356e48 | − | 9.21710e48i | −0.0457089 | − | 0.323195i | ||||
\(298\) | −3.86392e49 | −1.26678 | ||||||||
\(299\) | − | 1.68539e49i | − | 0.516745i | ||||||
\(300\) | 1.86509e49 | − | 8.74102e47i | 0.534904 | − | 0.0250690i | ||||
\(301\) | −1.82031e48 | −0.0488444 | ||||||||
\(302\) | 5.21831e49i | 1.31036i | ||||||||
\(303\) | 2.70415e48 | + | 5.76991e49i | 0.0635591 | + | 1.35618i | ||||
\(304\) | −5.64057e49 | −1.24123 | ||||||||
\(305\) | − | 1.46366e49i | − | 0.301607i | ||||||
\(306\) | −1.01032e50 | + | 9.49089e48i | −1.94999 | + | 0.183180i | ||||
\(307\) | 5.35320e49 | 0.967934 | 0.483967 | − | 0.875086i | \(-0.339195\pi\) | ||||
0.483967 | + | 0.875086i | \(0.339195\pi\) | |||||||
\(308\) | − | 9.50526e48i | − | 0.161046i | ||||||
\(309\) | −2.36410e49 | + | 1.10797e48i | −0.375402 | + | 0.0175937i | ||||
\(310\) | −3.43361e49 | −0.511113 | ||||||||
\(311\) | − | 7.51843e49i | − | 1.04935i | −0.851303 | − | 0.524674i | \(-0.824187\pi\) | ||
0.851303 | − | 0.524674i | \(-0.175813\pi\) | |||||||
\(312\) | −3.84547e47 | − | 8.20517e48i | −0.00503335 | − | 0.107398i | ||||
\(313\) | 9.48806e49 | 1.16491 | 0.582453 | − | 0.812864i | \(-0.302093\pi\) | ||||
0.582453 | + | 0.812864i | \(0.302093\pi\) | |||||||
\(314\) | − | 3.50414e49i | − | 0.403635i | ||||||
\(315\) | −3.01856e48 | − | 3.21332e49i | −0.0326279 | − | 0.347330i | ||||
\(316\) | 7.80582e49 | 0.791912 | ||||||||
\(317\) | 7.19460e49i | 0.685206i | 0.939480 | + | 0.342603i | \(0.111309\pi\) | ||||
−0.939480 | + | 0.342603i | \(0.888691\pi\) | |||||||
\(318\) | 7.64308e49 | − | 3.58204e48i | 0.683481 | − | 0.0320323i | ||||
\(319\) | −4.94591e49 | −0.415368 | ||||||||
\(320\) | − | 2.66004e49i | − | 0.209840i | ||||||
\(321\) | −6.39276e48 | − | 1.36404e50i | −0.0473792 | − | 1.01094i | ||||
\(322\) | 2.17951e50 | 1.51790 | ||||||||
\(323\) | 2.35876e50i | 1.54395i | ||||||||
\(324\) | −1.16549e50 | + | 2.20919e49i | −0.717145 | + | 0.135935i | ||||
\(325\) | 3.83801e49 | 0.222044 | ||||||||
\(326\) | 5.29761e49i | 0.288222i | ||||||||
\(327\) | −2.13978e49 | + | 1.00284e48i | −0.109500 | + | 0.00513186i | ||||
\(328\) | 1.16371e49 | 0.0560232 | ||||||||
\(329\) | 2.42859e50i | 1.10011i | ||||||||
\(330\) | −2.43321e48 | − | 5.19181e49i | −0.0103729 | − | 0.221330i | ||||
\(331\) | 2.91862e49 | 0.117116 | 0.0585582 | − | 0.998284i | \(-0.481350\pi\) | ||||
0.0585582 | + | 0.998284i | \(0.481350\pi\) | |||||||
\(332\) | − | 2.47750e50i | − | 0.935948i | ||||||
\(333\) | −4.16988e50 | + | 3.91714e49i | −1.48333 | + | 0.139343i | ||||
\(334\) | −7.27473e49 | −0.243718 | ||||||||
\(335\) | − | 7.34305e49i | − | 0.231729i | ||||||
\(336\) | 2.71873e50 | − | 1.27417e49i | 0.808314 | − | 0.0378828i | ||||
\(337\) | −1.25336e50 | −0.351138 | −0.175569 | − | 0.984467i | \(-0.556176\pi\) | ||||
−0.175569 | + | 0.984467i | \(0.556176\pi\) | |||||||
\(338\) | − | 4.52503e50i | − | 1.19478i | ||||||
\(339\) | −1.00462e49 | − | 2.14359e50i | −0.0250040 | − | 0.533516i | ||||
\(340\) | −2.39065e50 | −0.560968 | ||||||||
\(341\) | − | 1.11076e50i | − | 0.245772i | ||||||
\(342\) | 6.11195e49 | + | 6.50629e50i | 0.127543 | + | 1.35772i | ||||
\(343\) | −5.29892e50 | −1.04305 | ||||||||
\(344\) | − | 1.38225e49i | − | 0.0256694i | ||||||
\(345\) | 5.02298e50 | − | 2.35409e49i | 0.880197 | − | 0.0412516i | ||||
\(346\) | −3.98782e50 | −0.659498 | ||||||||
\(347\) | − | 3.21902e50i | − | 0.502497i | −0.967923 | − | 0.251249i | \(-0.919159\pi\) | ||
0.967923 | − | 0.251249i | \(-0.0808412\pi\) | |||||||
\(348\) | 2.95059e49 | + | 6.29575e50i | 0.0434835 | + | 0.927818i | ||||
\(349\) | 1.74668e50 | 0.243055 | 0.121527 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121527 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(350\) | 4.96324e50i | 0.652236i | ||||||||
\(351\) | −2.41435e50 | + | 3.41457e49i | −0.299680 | + | 0.0423832i | ||||
\(352\) | 3.39419e50 | 0.398000 | ||||||||
\(353\) | 4.50717e50i | 0.499356i | 0.968329 | + | 0.249678i | \(0.0803247\pi\) | ||||
−0.968329 | + | 0.249678i | \(0.919675\pi\) | |||||||
\(354\) | 2.19028e51 | − | 1.02650e50i | 2.29316 | − | 0.107472i | ||||
\(355\) | 4.12157e50 | 0.407846 | ||||||||
\(356\) | 3.88324e50i | 0.363240i | ||||||||
\(357\) | −5.32830e49 | − | 1.13691e51i | −0.0471221 | − | 1.00546i | ||||
\(358\) | −3.10883e49 | −0.0259978 | ||||||||
\(359\) | − | 3.54644e50i | − | 0.280481i | −0.990117 | − | 0.140241i | \(-0.955212\pi\) | ||
0.990117 | − | 0.140241i | \(-0.0447876\pi\) | |||||||
\(360\) | 2.44003e50 | − | 2.29214e49i | 0.182534 | − | 0.0171471i | ||||
\(361\) | 1.05992e50 | 0.0750116 | ||||||||
\(362\) | − | 2.20815e51i | − | 1.47862i | ||||||
\(363\) | −1.40841e51 | + | 6.60071e49i | −0.892476 | + | 0.0418271i | ||||
\(364\) | −2.48983e50 | −0.149328 | ||||||||
\(365\) | 4.98503e50i | 0.283016i | ||||||||
\(366\) | −6.69457e49 | − | 1.42844e51i | −0.0359833 | − | 0.767785i | ||||
\(367\) | −1.94434e51 | −0.989578 | −0.494789 | − | 0.869013i | \(-0.664755\pi\) | ||||
−0.494789 | + | 0.869013i | \(0.664755\pi\) | |||||||
\(368\) | 4.24052e51i | 2.04391i | ||||||||
\(369\) | −3.23088e49 | − | 3.43933e50i | −0.0147500 | − | 0.157017i | ||||
\(370\) | −2.33847e51 | −1.01134 | ||||||||
\(371\) | 8.58184e50i | 0.351643i | ||||||||
\(372\) | −1.41391e51 | + | 6.62647e49i | −0.548987 | + | 0.0257290i | ||||
\(373\) | 3.70930e51 | 1.36494 | 0.682472 | − | 0.730912i | \(-0.260905\pi\) | ||||
0.682472 | + | 0.730912i | \(0.260905\pi\) | |||||||
\(374\) | − | 1.83290e51i | − | 0.639301i | ||||||
\(375\) | 1.26680e50 | + | 2.70299e51i | 0.0418872 | + | 0.893757i | ||||
\(376\) | −1.84415e51 | −0.578147 | ||||||||
\(377\) | 1.29554e51i | 0.385146i | ||||||||
\(378\) | −4.41566e50 | − | 3.12219e51i | −0.124497 | − | 0.880286i | ||||
\(379\) | 4.60053e51 | 1.23034 | 0.615168 | − | 0.788396i | \(-0.289088\pi\) | ||||
0.615168 | + | 0.788396i | \(0.289088\pi\) | |||||||
\(380\) | 1.53953e51i | 0.390586i | ||||||||
\(381\) | −3.07521e51 | + | 1.44124e50i | −0.740244 | + | 0.0346925i | ||||
\(382\) | −3.88874e51 | −0.888263 | ||||||||
\(383\) | − | 2.47639e51i | − | 0.536839i | −0.963302 | − | 0.268420i | \(-0.913499\pi\) | ||
0.963302 | − | 0.268420i | \(-0.0865014\pi\) | |||||||
\(384\) | 1.55746e50 | + | 3.32319e51i | 0.0320474 | + | 0.683803i | ||||
\(385\) | 5.82949e50 | 0.113872 | ||||||||
\(386\) | − | 1.05384e52i | − | 1.95447i | ||||||
\(387\) | −4.08521e50 | + | 3.83761e49i | −0.0719440 | + | 0.00675836i | ||||
\(388\) | 6.24809e51 | 1.04499 | ||||||||
\(389\) | − | 2.87226e51i | − | 0.456281i | −0.973628 | − | 0.228140i | \(-0.926735\pi\) | ||
0.973628 | − | 0.228140i | \(-0.0732645\pi\) | |||||||
\(390\) | −1.35996e51 | + | 6.37362e49i | −0.205226 | + | 0.00961821i | ||||
\(391\) | 1.77329e52 | 2.54241 | ||||||||
\(392\) | − | 1.41616e51i | − | 0.192926i | ||||||
\(393\) | 5.17664e50 | + | 1.10455e52i | 0.0670188 | + | 1.43000i | ||||
\(394\) | 1.28103e51 | 0.157629 | ||||||||
\(395\) | 4.78724e51i | 0.559943i | ||||||||
\(396\) | −2.00392e50 | − | 2.13321e51i | −0.0222831 | − | 0.237208i | ||||
\(397\) | −2.27883e51 | −0.240936 | −0.120468 | − | 0.992717i | \(-0.538440\pi\) | ||||
−0.120468 | + | 0.992717i | \(0.538440\pi\) | |||||||
\(398\) | 2.37696e52i | 2.38980i | ||||||||
\(399\) | −7.32150e51 | + | 3.43132e50i | −0.700071 | + | 0.0328098i | ||||
\(400\) | −9.65661e51 | −0.878264 | ||||||||
\(401\) | − | 2.26183e52i | − | 1.95692i | −0.206432 | − | 0.978461i | \(-0.566185\pi\) | ||
0.206432 | − | 0.978461i | \(-0.433815\pi\) | |||||||
\(402\) | −3.35862e50 | − | 7.16637e51i | −0.0276465 | − | 0.589900i | ||||
\(403\) | −2.90955e51 | −0.227890 | ||||||||
\(404\) | 1.32951e52i | 0.990980i | ||||||||
\(405\) | −1.35488e51 | − | 7.14782e51i | −0.0961168 | − | 0.507076i | ||||
\(406\) | −1.67538e52 | −1.13134 | ||||||||
\(407\) | − | 7.56485e51i | − | 0.486309i | ||||||
\(408\) | 8.63313e51 | − | 4.04603e50i | 0.528402 | − | 0.0247643i | ||||
\(409\) | −2.07287e52 | −1.20811 | −0.604053 | − | 0.796944i | \(-0.706448\pi\) | ||||
−0.604053 | + | 0.796944i | \(0.706448\pi\) | |||||||
\(410\) | − | 1.92878e51i | − | 0.107054i | ||||||
\(411\) | −8.80457e50 | − | 1.87865e52i | −0.0465449 | − | 0.993139i | ||||
\(412\) | −5.44740e51 | −0.274312 | ||||||||
\(413\) | 2.45930e52i | 1.17981i | ||||||||
\(414\) | 4.89135e52 | − | 4.59489e51i | 2.23574 | − | 0.210024i | ||||
\(415\) | 1.51943e52 | 0.661787 | ||||||||
\(416\) | − | 8.89083e51i | − | 0.369042i | ||||||
\(417\) | −3.44866e52 | + | 1.61626e51i | −1.36436 | + | 0.0639426i | ||||
\(418\) | −1.18035e52 | −0.445128 | ||||||||
\(419\) | − | 1.57114e52i | − | 0.564852i | −0.959289 | − | 0.282426i | \(-0.908861\pi\) | ||
0.959289 | − | 0.282426i | \(-0.0911392\pi\) | |||||||
\(420\) | −3.47771e50 | − | 7.42047e51i | −0.0119209 | − | 0.254358i | ||||
\(421\) | 1.39208e52 | 0.455013 | 0.227507 | − | 0.973777i | \(-0.426943\pi\) | ||||
0.227507 | + | 0.973777i | \(0.426943\pi\) | |||||||
\(422\) | 1.97789e52i | 0.616528i | ||||||||
\(423\) | 5.12001e51 | + | 5.45035e52i | 0.152217 | + | 1.62038i | ||||
\(424\) | −6.51660e51 | −0.184801 | ||||||||
\(425\) | 4.03819e52i | 1.09247i | ||||||||
\(426\) | 4.02240e52 | − | 1.88515e51i | 1.03823 | − | 0.0486581i | ||||
\(427\) | 1.60388e52 | 0.395017 | ||||||||
\(428\) | − | 3.14304e52i | − | 0.738711i | ||||||
\(429\) | −2.06184e50 | − | 4.39940e51i | −0.00462497 | − | 0.0986842i | ||||
\(430\) | −2.29099e51 | −0.0490516 | ||||||||
\(431\) | − | 2.35434e52i | − | 0.481199i | −0.970625 | − | 0.240599i | \(-0.922656\pi\) | ||
0.970625 | − | 0.240599i | \(-0.0773440\pi\) | |||||||
\(432\) | 6.07462e52 | − | 8.59122e51i | 1.18534 | − | 0.167641i | ||||
\(433\) | 3.12129e51 | 0.0581536 | 0.0290768 | − | 0.999577i | \(-0.490743\pi\) | ||||
0.0290768 | + | 0.999577i | \(0.490743\pi\) | |||||||
\(434\) | − | 3.76257e52i | − | 0.669407i | ||||||
\(435\) | −3.86113e52 | + | 1.80957e51i | −0.656038 | + | 0.0307461i | ||||
\(436\) | −4.93051e51 | −0.0800133 | ||||||||
\(437\) | − | 1.14197e53i | − | 1.77021i | ||||||
\(438\) | 2.28009e51 | + | 4.86508e52i | 0.0337652 | + | 0.720457i | ||||
\(439\) | −1.93419e52 | −0.273658 | −0.136829 | − | 0.990595i | \(-0.543691\pi\) | ||||
−0.136829 | + | 0.990595i | \(0.543691\pi\) | |||||||
\(440\) | 4.42661e51i | 0.0598436i | ||||||||
\(441\) | −4.18544e52 | + | 3.93177e51i | −0.540716 | + | 0.0507944i | ||||
\(442\) | −4.80113e52 | −0.592786 | ||||||||
\(443\) | 1.63741e53i | 1.93233i | 0.257920 | + | 0.966166i | \(0.416963\pi\) | ||||
−0.257920 | + | 0.966166i | \(0.583037\pi\) | |||||||
\(444\) | −9.62944e52 | + | 4.51297e51i | −1.08628 | + | 0.0509100i | ||||
\(445\) | −2.38155e52 | −0.256839 | ||||||||
\(446\) | − | 9.53975e52i | − | 0.983648i | ||||||
\(447\) | −4.57326e51 | − | 9.75807e52i | −0.0450895 | − | 0.962085i | ||||
\(448\) | 2.91489e52 | 0.274829 | ||||||||
\(449\) | 1.35291e53i | 1.21995i | 0.792420 | + | 0.609975i | \(0.208821\pi\) | ||||
−0.792420 | + | 0.609975i | \(0.791179\pi\) | |||||||
\(450\) | 1.04636e52 | + | 1.11387e53i | 0.0902467 | + | 0.960693i | ||||
\(451\) | 6.23951e51 | 0.0514778 | ||||||||
\(452\) | − | 4.93929e52i | − | 0.389848i | ||||||
\(453\) | −1.31785e53 | + | 6.17629e51i | −0.995181 | + | 0.0466405i | ||||
\(454\) | 2.18953e51 | 0.0158210 | ||||||||
\(455\) | − | 1.52699e52i | − | 0.105587i | ||||||
\(456\) | −2.60557e51 | − | 5.55956e52i | −0.0172427 | − | 0.367912i | ||||
\(457\) | 3.02271e53 | 1.91457 | 0.957287 | − | 0.289141i | \(-0.0933695\pi\) | ||||
0.957287 | + | 0.289141i | \(0.0933695\pi\) | |||||||
\(458\) | 3.59080e53i | 2.17712i | ||||||||
\(459\) | −3.59266e52 | − | 2.54027e53i | −0.208527 | − | 1.47444i | ||||
\(460\) | 1.15740e53 | 0.643173 | ||||||||
\(461\) | − | 1.80944e53i | − | 0.962776i | −0.876507 | − | 0.481388i | \(-0.840133\pi\) | ||
0.876507 | − | 0.481388i | \(-0.159867\pi\) | |||||||
\(462\) | 5.68922e52 | − | 2.66633e51i | 0.289877 | − | 0.0135855i | ||||
\(463\) | 2.11666e53 | 1.03284 | 0.516419 | − | 0.856336i | \(-0.327265\pi\) | ||||
0.516419 | + | 0.856336i | \(0.327265\pi\) | |||||||
\(464\) | − | 3.25965e53i | − | 1.52339i | ||||||
\(465\) | −4.06395e51 | − | 8.67136e52i | −0.0181924 | − | 0.388176i | ||||
\(466\) | −1.74637e53 | −0.748889 | ||||||||
\(467\) | 1.47795e53i | 0.607185i | 0.952802 | + | 0.303592i | \(0.0981861\pi\) | ||||
−0.952802 | + | 0.303592i | \(0.901814\pi\) | |||||||
\(468\) | −5.58778e52 | + | 5.24911e51i | −0.219949 | + | 0.0206618i | ||||
\(469\) | 8.04658e52 | 0.303497 | ||||||||
\(470\) | 3.05656e53i | 1.10478i | ||||||||
\(471\) | 8.84948e52 | − | 4.14743e51i | 0.306549 | − | 0.0143668i | ||||
\(472\) | −1.86746e53 | −0.620029 | ||||||||
\(473\) | − | 7.41124e51i | − | 0.0235868i | ||||||
\(474\) | 2.18962e52 | + | 4.67205e53i | 0.0668040 | + | 1.42541i | ||||
\(475\) | 2.60051e53 | 0.760653 | ||||||||
\(476\) | − | 2.61969e53i | − | 0.734702i | ||||||
\(477\) | 1.80924e52 | + | 1.92597e53i | 0.0486552 | + | 0.517944i | ||||
\(478\) | −6.69015e53 | −1.72535 | ||||||||
\(479\) | 9.58337e52i | 0.237033i | 0.992952 | + | 0.118516i | \(0.0378138\pi\) | ||||
−0.992952 | + | 0.118516i | \(0.962186\pi\) | |||||||
\(480\) | 2.64974e53 | − | 1.24184e52i | 0.628607 | − | 0.0294605i | ||||
\(481\) | −1.98155e53 | −0.450925 | ||||||||
\(482\) | − | 7.88789e53i | − | 1.72195i | ||||||
\(483\) | 2.57963e52 | + | 5.50422e53i | 0.0540275 | + | 1.15280i | ||||
\(484\) | −3.24528e53 | −0.652146 | ||||||||
\(485\) | 3.83190e53i | 0.738889i | ||||||||
\(486\) | −1.64921e53 | − | 6.91386e53i | −0.305176 | − | 1.27937i | ||||
\(487\) | 2.13753e53 | 0.379605 | 0.189803 | − | 0.981822i | \(-0.439215\pi\) | ||||
0.189803 | + | 0.981822i | \(0.439215\pi\) | |||||||
\(488\) | 1.21791e53i | 0.207595i | ||||||||
\(489\) | −1.33788e53 | + | 6.27015e51i | −0.218897 | + | 0.0102589i | ||||
\(490\) | −2.34720e53 | −0.368662 | ||||||||
\(491\) | − | 1.17512e54i | − | 1.77195i | −0.463734 | − | 0.885975i | \(-0.653491\pi\) | ||
0.463734 | − | 0.885975i | \(-0.346509\pi\) | |||||||
\(492\) | −3.72232e51 | − | 7.94240e52i | −0.00538904 | − | 0.114987i | ||||
\(493\) | −1.36312e54 | −1.89494 | ||||||||
\(494\) | 3.09183e53i | 0.412741i | ||||||||
\(495\) | 1.30828e53 | − | 1.22899e52i | 0.167724 | − | 0.0157559i | ||||
\(496\) | 7.32056e53 | 0.901386 | ||||||||
\(497\) | 4.51645e53i | 0.534158i | ||||||||
\(498\) | 1.48287e54 | − | 6.94967e52i | 1.68467 | − | 0.0789546i | ||||
\(499\) | 7.55269e53 | 0.824310 | 0.412155 | − | 0.911114i | \(-0.364776\pi\) | ||||
0.412155 | + | 0.911114i | \(0.364776\pi\) | |||||||
\(500\) | 6.22828e53i | 0.653083i | ||||||||
\(501\) | −8.61024e51 | − | 1.83719e53i | −0.00867482 | − | 0.185097i | ||||
\(502\) | 1.44254e54 | 1.39654 | ||||||||
\(503\) | 1.44044e54i | 1.34009i | 0.742318 | + | 0.670047i | \(0.233726\pi\) | ||||
−0.742318 | + | 0.670047i | \(0.766274\pi\) | |||||||
\(504\) | 2.51174e52 | + | 2.67380e53i | 0.0224577 | + | 0.239066i | ||||
\(505\) | −8.15378e53 | −0.700699 | ||||||||
\(506\) | 8.87373e53i | 0.732986i | ||||||||
\(507\) | 1.14277e54 | − | 5.35574e52i | 0.907400 | − | 0.0425265i | ||||
\(508\) | −7.08594e53 | −0.540908 | ||||||||
\(509\) | − | 1.97937e54i | − | 1.45268i | −0.687334 | − | 0.726341i | \(-0.741219\pi\) | ||
0.687334 | − | 0.726341i | \(-0.258781\pi\) | |||||||
\(510\) | −6.70605e52 | − | 1.43089e54i | −0.0473220 | − | 1.00972i | ||||
\(511\) | −5.46263e53 | −0.370667 | ||||||||
\(512\) | 1.58526e54i | 1.03443i | ||||||||
\(513\) | −1.63589e54 | + | 2.31361e53i | −1.02661 | + | 0.145192i | ||||
\(514\) | 5.61650e53 | 0.339003 | ||||||||
\(515\) | − | 3.34084e53i | − | 0.193960i | ||||||
\(516\) | −9.43392e52 | + | 4.42134e51i | −0.0526863 | + | 0.00246922i | ||||
\(517\) | −9.88784e53 | −0.531240 | ||||||||
\(518\) | − | 2.56251e54i | − | 1.32456i | ||||||
\(519\) | −4.71990e52 | − | 1.00710e54i | −0.0234739 | − | 0.500869i | ||||
\(520\) | 1.15952e53 | 0.0554894 | ||||||||
\(521\) | − | 2.44544e53i | − | 0.112617i | −0.998413 | − | 0.0563084i | \(-0.982067\pi\) | ||
0.998413 | − | 0.0563084i | \(-0.0179330\pi\) | |||||||
\(522\) | −3.75995e54 | + | 3.53206e53i | −1.66637 | + | 0.156537i | ||||
\(523\) | 4.06306e54 | 1.73309 | 0.866543 | − | 0.499103i | \(-0.166337\pi\) | ||||
0.866543 | + | 0.499103i | \(0.166337\pi\) | |||||||
\(524\) | 2.54513e54i | 1.04492i | ||||||||
\(525\) | −1.25343e54 | + | 5.87440e52i | −0.495354 | + | 0.0232155i | ||||
\(526\) | 2.69744e54 | 1.02621 | ||||||||
\(527\) | − | 3.06130e54i | − | 1.12123i | ||||||
\(528\) | 5.18769e52 | + | 1.10691e54i | 0.0182934 | + | 0.390332i | ||||
\(529\) | −5.63998e54 | −1.91498 | ||||||||
\(530\) | 1.08009e54i | 0.353135i | ||||||||
\(531\) | 5.18475e53 | + | 5.51926e54i | 0.163244 | + | 1.73776i | ||||
\(532\) | −1.68703e54 | −0.511553 | ||||||||
\(533\) | − | 1.63439e53i | − | 0.0477323i | ||||||
\(534\) | −2.32425e54 | + | 1.08929e53i | −0.653819 | + | 0.0306421i | ||||
\(535\) | 1.92760e54 | 0.522325 | ||||||||
\(536\) | 6.11015e53i | 0.159498i | ||||||||
\(537\) | −3.67955e51 | − | 7.85115e52i | −0.000925356 | − | 0.0197446i | ||||
\(538\) | 5.40502e54 | 1.30964 | ||||||||
\(539\) | − | 7.59309e53i | − | 0.177273i | ||||||
\(540\) | −2.34488e53 | − | 1.65800e54i | −0.0527528 | − | 0.373001i | ||||
\(541\) | −3.89611e54 | −0.844668 | −0.422334 | − | 0.906440i | \(-0.638789\pi\) | ||||
−0.422334 | + | 0.906440i | \(0.638789\pi\) | |||||||
\(542\) | − | 4.54765e54i | − | 0.950169i | ||||||
\(543\) | 5.57653e54 | − | 2.61352e53i | 1.12297 | − | 0.0526295i | ||||
\(544\) | 9.35455e54 | 1.81570 | ||||||||
\(545\) | − | 3.02384e53i | − | 0.0565755i | ||||||
\(546\) | −6.98426e52 | − | 1.49025e54i | −0.0125970 | − | 0.268786i | ||||
\(547\) | 4.78615e54 | 0.832223 | 0.416112 | − | 0.909314i | \(-0.363393\pi\) | ||||
0.416112 | + | 0.909314i | \(0.363393\pi\) | |||||||
\(548\) | − | 4.32882e54i | − | 0.725702i | ||||||
\(549\) | 3.59951e54 | − | 3.38134e53i | 0.581830 | − | 0.0546566i | ||||
\(550\) | −2.02075e54 | −0.314962 | ||||||||
\(551\) | 8.77820e54i | 1.31939i | ||||||||
\(552\) | −4.17962e54 | + | 1.95884e53i | −0.605836 | + | 0.0283933i | ||||
\(553\) | −5.24590e54 | −0.733360 | ||||||||
\(554\) | 7.02647e53i | 0.0947418i | ||||||||
\(555\) | −2.76777e53 | − | 5.90565e54i | −0.0359973 | − | 0.768083i | ||||
\(556\) | −7.94645e54 | −0.996959 | ||||||||
\(557\) | 1.04373e55i | 1.26324i | 0.775280 | + | 0.631618i | \(0.217609\pi\) | ||||
−0.775280 | + | 0.631618i | \(0.782391\pi\) | |||||||
\(558\) | −7.93234e53 | − | 8.44413e54i | −0.0926226 | − | 0.985986i | ||||
\(559\) | −1.94132e53 | −0.0218706 | ||||||||
\(560\) | 3.84198e54i | 0.417633i | ||||||||
\(561\) | 4.62886e54 | − | 2.16938e53i | 0.485531 | − | 0.0227551i | ||||
\(562\) | −1.81180e55 | −1.83393 | ||||||||
\(563\) | − | 3.11876e53i | − | 0.0304659i | −0.999884 | − | 0.0152330i | \(-0.995151\pi\) | ||
0.999884 | − | 0.0152330i | \(-0.00484899\pi\) | |||||||
\(564\) | 5.89880e53 | + | 1.25864e55i | 0.0556137 | + | 1.18664i | ||||
\(565\) | 3.02922e54 | 0.275653 | ||||||||
\(566\) | 6.37230e54i | 0.559716i | ||||||||
\(567\) | 7.83264e54 | − | 1.48468e54i | 0.664120 | − | 0.125885i | ||||
\(568\) | −3.42956e54 | −0.280719 | ||||||||
\(569\) | − | 6.48098e54i | − | 0.512148i | −0.966657 | − | 0.256074i | \(-0.917571\pi\) | ||
0.966657 | − | 0.256074i | \(-0.0824291\pi\) | |||||||
\(570\) | −9.21463e54 | + | 4.31857e53i | −0.703041 | + | 0.0329490i | ||||
\(571\) | −1.66814e54 | −0.122888 | −0.0614442 | − | 0.998111i | \(-0.519571\pi\) | ||||
−0.0614442 | + | 0.998111i | \(0.519571\pi\) | |||||||
\(572\) | − | 1.01372e54i | − | 0.0721101i | ||||||
\(573\) | −4.60264e53 | − | 9.82076e54i | −0.0316165 | − | 0.674610i | ||||
\(574\) | 2.11357e54 | 0.140210 | ||||||||
\(575\) | − | 1.95504e55i | − | 1.25256i | ||||||
\(576\) | 6.54173e54 | − | 6.14524e53i | 0.404802 | − | 0.0380268i | ||||
\(577\) | −8.58415e54 | −0.513075 | −0.256538 | − | 0.966534i | \(-0.582582\pi\) | ||||
−0.256538 | + | 0.966534i | \(0.582582\pi\) | |||||||
\(578\) | − | 2.77346e55i | − | 1.60127i | ||||||
\(579\) | 2.66140e55 | − | 1.24730e54i | 1.48436 | − | 0.0695667i | ||||
\(580\) | −8.89687e54 | −0.479377 | ||||||||
\(581\) | 1.66500e55i | 0.866746i | ||||||||
\(582\) | 1.75266e54 | + | 3.73970e55i | 0.0881532 | + | 1.88095i | ||||
\(583\) | −3.49403e54 | −0.169807 | ||||||||
\(584\) | − | 4.14804e54i | − | 0.194799i | ||||||
\(585\) | −3.21923e53 | − | 3.42694e54i | −0.0146095 | − | 0.155521i | ||||
\(586\) | 3.67971e55 | 1.61384 | ||||||||
\(587\) | 8.79766e54i | 0.372911i | 0.982463 | + | 0.186455i | \(0.0597000\pi\) | ||||
−0.982463 | + | 0.186455i | \(0.940300\pi\) | |||||||
\(588\) | −9.66539e54 | + | 4.52982e53i | −0.395980 | + | 0.0185581i | ||||
\(589\) | −1.97142e55 | −0.780679 | ||||||||
\(590\) | 3.09520e55i | 1.18481i | ||||||||
\(591\) | 1.51621e53 | + | 3.23517e54i | 0.00561060 | + | 0.119715i | ||||
\(592\) | 4.98569e55 | 1.78357 | ||||||||
\(593\) | − | 1.89933e55i | − | 0.656910i | −0.944520 | − | 0.328455i | \(-0.893472\pi\) | ||
0.944520 | − | 0.328455i | \(-0.106528\pi\) | |||||||
\(594\) | 1.27118e55 | − | 1.79780e54i | 0.425087 | − | 0.0601192i | ||||
\(595\) | 1.60663e55 | 0.519491 | ||||||||
\(596\) | − | 2.24847e55i | − | 0.703011i | ||||||
\(597\) | −6.00286e55 | + | 2.81333e54i | −1.81498 | + | 0.0850616i | ||||
\(598\) | 2.32441e55 | 0.679655 | ||||||||
\(599\) | 3.37089e55i | 0.953252i | 0.879106 | + | 0.476626i | \(0.158140\pi\) | ||||
−0.879106 | + | 0.476626i | \(0.841860\pi\) | |||||||
\(600\) | −4.46071e53 | − | 9.51793e54i | −0.0122005 | − | 0.260326i | ||||
\(601\) | −4.50788e55 | −1.19257 | −0.596283 | − | 0.802774i | \(-0.703356\pi\) | ||||
−0.596283 | + | 0.802774i | \(0.703356\pi\) | |||||||
\(602\) | − | 2.51048e54i | − | 0.0642432i | ||||||
\(603\) | 1.80585e55 | − | 1.69640e54i | 0.447028 | − | 0.0419934i | ||||
\(604\) | −3.03661e55 | −0.727194 | ||||||||
\(605\) | − | 1.99030e55i | − | 0.461117i | ||||||
\(606\) | −7.95758e55 | + | 3.72943e54i | −1.78373 | + | 0.0835969i | ||||
\(607\) | 4.11803e55 | 0.893133 | 0.446566 | − | 0.894751i | \(-0.352647\pi\) | ||||
0.446566 | + | 0.894751i | \(0.352647\pi\) | |||||||
\(608\) | − | 6.02414e55i | − | 1.26422i | ||||||
\(609\) | −1.98294e54 | − | 4.23105e55i | −0.0402684 | − | 0.859217i | ||||
\(610\) | 2.01860e55 | 0.396693 | ||||||||
\(611\) | 2.59004e55i | 0.492587i | ||||||||
\(612\) | −5.52289e54 | − | 5.87922e55i | −0.101657 | − | 1.08216i | ||||
\(613\) | −8.47769e55 | −1.51032 | −0.755159 | − | 0.655542i | \(-0.772440\pi\) | ||||
−0.755159 | + | 0.655542i | \(0.772440\pi\) | |||||||
\(614\) | 7.38288e55i | 1.27309i | ||||||||
\(615\) | 4.87100e54 | − | 2.28286e53i | 0.0813048 | − | 0.00381046i | ||||
\(616\) | −4.85071e54 | −0.0783775 | ||||||||
\(617\) | 1.03563e56i | 1.61996i | 0.586460 | + | 0.809978i | \(0.300521\pi\) | ||||
−0.586460 | + | 0.809978i | \(0.699479\pi\) | |||||||
\(618\) | −1.52806e54 | − | 3.26046e55i | −0.0231404 | − | 0.493752i | ||||
\(619\) | 1.56701e55 | 0.229752 | 0.114876 | − | 0.993380i | \(-0.463353\pi\) | ||||
0.114876 | + | 0.993380i | \(0.463353\pi\) | |||||||
\(620\) | − | 1.99807e55i | − | 0.283646i | ||||||
\(621\) | 1.73934e55 | + | 1.22984e56i | 0.239085 | + | 1.69051i | ||||
\(622\) | 1.03691e56 | 1.38017 | ||||||||
\(623\) | − | 2.60972e55i | − | 0.336383i | ||||||
\(624\) | 2.89947e55 | − | 1.35888e54i | 0.361932 | − | 0.0169624i | ||||
\(625\) | 2.24874e55 | 0.271856 | ||||||||
\(626\) | 1.30855e56i | 1.53216i | ||||||||
\(627\) | −1.39704e54 | − | 2.98090e55i | −0.0158437 | − | 0.338062i | ||||
\(628\) | 2.03911e55 | 0.224000 | ||||||||
\(629\) | − | 2.08491e56i | − | 2.21857i | ||||||
\(630\) | 4.43165e55 | − | 4.16306e54i | 0.456830 | − | 0.0429142i | ||||
\(631\) | 7.98242e55 | 0.797164 | 0.398582 | − | 0.917133i | \(-0.369502\pi\) | ||||
0.398582 | + | 0.917133i | \(0.369502\pi\) | |||||||
\(632\) | − | 3.98346e55i | − | 0.385406i | ||||||
\(633\) | −4.99503e55 | + | 2.34099e54i | −0.468235 | + | 0.0219445i | ||||
\(634\) | −9.92244e55 | −0.901226 | ||||||||
\(635\) | − | 4.34574e55i | − | 0.382463i | ||||||
\(636\) | 2.08444e54 | + | 4.44763e55i | 0.0177765 | + | 0.379303i | ||||
\(637\) | −1.98895e55 | −0.164375 | ||||||||
\(638\) | − | 6.82117e55i | − | 0.546318i | ||||||
\(639\) | 9.52168e54 | + | 1.01360e56i | 0.0739088 | + | 0.786774i | ||||
\(640\) | −4.69619e55 | −0.353302 | ||||||||
\(641\) | − | 1.21501e56i | − | 0.885969i | −0.896529 | − | 0.442985i | \(-0.853920\pi\) | ||
0.896529 | − | 0.442985i | \(-0.146080\pi\) | |||||||
\(642\) | 1.88122e56 | − | 8.81659e54i | 1.32965 | − | 0.0623160i | ||||
\(643\) | 1.48311e56 | 1.01614 | 0.508072 | − | 0.861315i | \(-0.330358\pi\) | ||||
0.508072 | + | 0.861315i | \(0.330358\pi\) | |||||||
\(644\) | 1.26829e56i | 0.842368i | ||||||||
\(645\) | −2.71157e53 | − | 5.78574e54i | −0.00174593 | − | 0.0372533i | ||||
\(646\) | −3.25310e56 | −2.03070 | ||||||||
\(647\) | − | 1.11424e56i | − | 0.674364i | −0.941439 | − | 0.337182i | \(-0.890526\pi\) | ||
0.941439 | − | 0.337182i | \(-0.109474\pi\) | |||||||
\(648\) | 1.12739e55 | + | 5.94770e55i | 0.0661568 | + | 0.349019i | ||||
\(649\) | −1.00129e56 | −0.569723 | ||||||||
\(650\) | 5.29320e55i | 0.292046i | ||||||||
\(651\) | 9.50214e55 | − | 4.45331e54i | 0.508396 | − | 0.0238267i | ||||
\(652\) | −3.08276e55 | −0.159951 | ||||||||
\(653\) | 2.87225e56i | 1.44530i | 0.691213 | + | 0.722651i | \(0.257077\pi\) | ||||
−0.691213 | + | 0.722651i | \(0.742923\pi\) | |||||||
\(654\) | −1.38306e54 | − | 2.95108e55i | −0.00674975 | − | 0.144021i | ||||
\(655\) | −1.56090e56 | −0.738839 | ||||||||
\(656\) | 4.11221e55i | 0.188799i | ||||||||
\(657\) | −1.22595e56 | + | 1.15164e55i | −0.545964 | + | 0.0512874i | ||||
\(658\) | −3.34940e56 | −1.44693 | ||||||||
\(659\) | 1.81493e55i | 0.0760593i | 0.999277 | + | 0.0380296i | \(0.0121081\pi\) | ||||
−0.999277 | + | 0.0380296i | \(0.987892\pi\) | |||||||
\(660\) | 3.02119e55 | − | 1.41592e54i | 0.122829 | − | 0.00575654i | ||||
\(661\) | 2.14598e55 | 0.0846440 | 0.0423220 | − | 0.999104i | \(-0.486524\pi\) | ||||
0.0423220 | + | 0.999104i | \(0.486524\pi\) | |||||||
\(662\) | 4.02522e55i | 0.154039i | ||||||||
\(663\) | −5.68253e54 | − | 1.21249e56i | −0.0210994 | − | 0.450204i | ||||
\(664\) | −1.26431e56 | −0.455505 | ||||||||
\(665\) | − | 1.03464e56i | − | 0.361707i | ||||||
\(666\) | −5.40234e55 | − | 5.75089e56i | −0.183272 | − | 1.95097i | ||||
\(667\) | 6.59936e56 | 2.17263 | ||||||||
\(668\) | − | 4.23328e55i | − | 0.135253i | ||||||
\(669\) | 2.40920e56 | − | 1.12911e55i | 0.747052 | − | 0.0350116i | ||||
\(670\) | 1.01272e56 | 0.304785 | ||||||||
\(671\) | 6.53010e55i | 0.190752i | ||||||||
\(672\) | 1.36082e55 | + | 2.90361e56i | 0.0385846 | + | 0.823290i | ||||
\(673\) | 5.09730e56 | 1.40294 | 0.701470 | − | 0.712699i | \(-0.252527\pi\) | ||||
0.701470 | + | 0.712699i | \(0.252527\pi\) | |||||||
\(674\) | − | 1.72857e56i | − | 0.461838i | ||||||
\(675\) | −2.80063e56 | + | 3.96087e55i | −0.726406 | + | 0.102734i | ||||
\(676\) | 2.63318e56 | 0.663051 | ||||||||
\(677\) | 1.61926e56i | 0.395860i | 0.980216 | + | 0.197930i | \(0.0634219\pi\) | ||||
−0.980216 | + | 0.197930i | \(0.936578\pi\) | |||||||
\(678\) | 2.95633e56 | − | 1.38553e55i | 0.701713 | − | 0.0328868i | ||||
\(679\) | −4.19902e56 | −0.967727 | ||||||||
\(680\) | 1.21999e56i | 0.273011i | ||||||||
\(681\) | 2.59149e53 | + | 5.52953e54i | 0.000563128 | + | 0.0120156i | ||||
\(682\) | 1.53190e56 | 0.323254 | ||||||||
\(683\) | 7.57766e56i | 1.55282i | 0.630229 | + | 0.776410i | \(0.282961\pi\) | ||||
−0.630229 | + | 0.776410i | \(0.717039\pi\) | |||||||
\(684\) | −3.78611e56 | + | 3.55663e55i | −0.753478 | + | 0.0707811i | ||||
\(685\) | 2.65483e56 | 0.513127 | ||||||||
\(686\) | − | 7.30802e56i | − | 1.37188i | ||||||
\(687\) | −9.06834e56 | + | 4.25000e55i | −1.65346 | + | 0.0774916i | ||||
\(688\) | 4.88445e55 | 0.0865062 | ||||||||
\(689\) | 9.15236e55i | 0.157452i | ||||||||
\(690\) | 3.24665e55 | + | 6.92746e56i | 0.0542567 | + | 1.15769i | ||||
\(691\) | −2.89353e56 | −0.469750 | −0.234875 | − | 0.972026i | \(-0.575468\pi\) | ||||
−0.234875 | + | 0.972026i | \(0.575468\pi\) | |||||||
\(692\) | − | 2.32057e56i | − | 0.365993i | ||||||
\(693\) | 1.34673e55 | + | 1.43362e56i | 0.0206356 | + | 0.219670i | ||||
\(694\) | 4.43951e56 | 0.660915 | ||||||||
\(695\) | − | 4.87349e56i | − | 0.704927i | ||||||
\(696\) | 3.21284e56 | − | 1.50574e55i | 0.451548 | − | 0.0211624i | ||||
\(697\) | 1.71964e56 | 0.234845 | ||||||||
\(698\) | 2.40893e56i | 0.319680i | ||||||||
\(699\) | −2.06697e55 | − | 4.41034e56i | −0.0266557 | − | 0.568760i | ||||
\(700\) | −2.88818e56 | −0.361963 | ||||||||
\(701\) | − | 1.26479e57i | − | 1.54049i | −0.637751 | − | 0.770243i | \(-0.720135\pi\) | ||
0.637751 | − | 0.770243i | \(-0.279865\pi\) | |||||||
\(702\) | −4.70921e55 | − | 3.32976e56i | −0.0557450 | − | 0.394158i | ||||
\(703\) | −1.34264e57 | −1.54473 | ||||||||
\(704\) | 1.18678e56i | 0.132714i | ||||||||
\(705\) | −7.71914e56 | + | 3.61768e55i | −0.839048 | + | 0.0393231i | ||||
\(706\) | −6.21608e56 | −0.656783 | ||||||||
\(707\) | − | 8.93497e56i | − | 0.917709i | ||||||
\(708\) | 5.97339e55 | + | 1.27456e57i | 0.0596424 | + | 1.27261i | ||||
\(709\) | 1.45309e57 | 1.41048 | 0.705239 | − | 0.708969i | \(-0.250840\pi\) | ||||
0.705239 | + | 0.708969i | \(0.250840\pi\) | |||||||
\(710\) | 5.68428e56i | 0.536424i | ||||||||
\(711\) | −1.17731e57 | + | 1.10595e56i | −1.08018 | + | 0.101471i | ||||
\(712\) | 1.98169e56 | 0.176781 | ||||||||
\(713\) | 1.48209e57i | 1.28554i | ||||||||
\(714\) | 1.56798e57 | − | 7.34854e55i | 1.32244 | − | 0.0619779i | ||||
\(715\) | 6.21703e55 | 0.0509873 | ||||||||
\(716\) | − | 1.80907e55i | − | 0.0144277i | ||||||
\(717\) | −7.91833e55 | − | 1.68955e57i | −0.0614116 | − | 1.31036i | ||||
\(718\) | 4.89108e56 | 0.368906 | ||||||||
\(719\) | 1.31015e57i | 0.961045i | 0.876982 | + | 0.480523i | \(0.159553\pi\) | ||||
−0.876982 | + | 0.480523i | \(0.840447\pi\) | |||||||
\(720\) | 8.09975e55 | + | 8.62234e56i | 0.0577859 | + | 0.615142i | ||||
\(721\) | 3.66092e56 | 0.254030 | ||||||||
\(722\) | 1.46179e56i | 0.0986600i | ||||||||
\(723\) | 1.99204e57 | − | 9.33595e55i | 1.30777 | − | 0.0612904i | ||||
\(724\) | 1.28495e57 | 0.820571 | ||||||||
\(725\) | 1.50282e57i | 0.933571i | ||||||||
\(726\) | −9.10338e55 | − | 1.94241e57i | −0.0550136 | − | 1.17384i | ||||
\(727\) | −6.53644e56 | −0.384285 | −0.192142 | − | 0.981367i | \(-0.561544\pi\) | ||||
−0.192142 | + | 0.981367i | \(0.561544\pi\) | |||||||
\(728\) | 1.27061e56i | 0.0726748i | ||||||||
\(729\) | 1.72653e57 | − | 4.98328e56i | 0.960781 | − | 0.277310i | ||||
\(730\) | −6.87511e56 | −0.372240 | ||||||||
\(731\) | − | 2.04257e56i | − | 0.107604i | ||||||
\(732\) | 8.31229e56 | − | 3.89567e55i | 0.426088 | − | 0.0199692i | ||||
\(733\) | −1.72547e57 | −0.860651 | −0.430325 | − | 0.902674i | \(-0.641601\pi\) | ||||
−0.430325 | + | 0.902674i | \(0.641601\pi\) | |||||||
\(734\) | − | 2.68153e57i | − | 1.30155i | ||||||
\(735\) | −2.77810e55 | − | 5.92770e56i | −0.0131220 | − | 0.279988i | ||||
\(736\) | −4.52888e57 | −2.08178 | ||||||||
\(737\) | 3.27610e56i | 0.146557i | ||||||||
\(738\) | 4.74336e56 | − | 4.45587e55i | 0.206518 | − | 0.0194002i | ||||
\(739\) | 4.69133e56 | 0.198796 | 0.0993979 | − | 0.995048i | \(-0.468308\pi\) | ||||
0.0993979 | + | 0.995048i | \(0.468308\pi\) | |||||||
\(740\) | − | 1.36079e57i | − | 0.561250i | ||||||
\(741\) | −7.80823e56 | + | 3.65944e55i | −0.313465 | + | 0.0146910i | ||||
\(742\) | −1.18357e57 | −0.462503 | ||||||||
\(743\) | − | 2.04139e57i | − | 0.776514i | −0.921551 | − | 0.388257i | \(-0.873077\pi\) | ||
0.921551 | − | 0.388257i | \(-0.126923\pi\) | |||||||
\(744\) | 3.38161e55 | + | 7.21543e56i | 0.0125218 | + | 0.267180i | ||||
\(745\) | 1.37897e57 | 0.497083 | ||||||||
\(746\) | 5.11568e57i | 1.79526i | ||||||||
\(747\) | 3.51019e56 | + | 3.73666e57i | 0.119927 | + | 1.27665i | ||||
\(748\) | 1.06659e57 | 0.354785 | ||||||||
\(749\) | 2.11228e57i | 0.684092i | ||||||||
\(750\) | −3.72784e57 | + | 1.74710e56i | −1.17553 | + | 0.0550926i | ||||
\(751\) | −3.33553e57 | −1.02416 | −0.512078 | − | 0.858939i | \(-0.671124\pi\) | ||||
−0.512078 | + | 0.858939i | \(0.671124\pi\) | |||||||
\(752\) | − | 6.51668e57i | − | 1.94836i | ||||||
\(753\) | 1.70736e56 | + | 3.64304e57i | 0.0497080 | + | 1.06063i | ||||
\(754\) | −1.78675e57 | −0.506568 | ||||||||
\(755\) | − | 1.86233e57i | − | 0.514182i | ||||||
\(756\) | 1.81685e57 | − | 2.56954e56i | 0.488521 | − | 0.0690907i | ||||
\(757\) | 4.96840e57 | 1.30106 | 0.650532 | − | 0.759479i | \(-0.274546\pi\) | ||||
0.650532 | + | 0.759479i | \(0.274546\pi\) | |||||||
\(758\) | 6.34483e57i | 1.61821i | ||||||||
\(759\) | −2.24100e57 | + | 1.05028e56i | −0.556682 | + | 0.0260897i | ||||
\(760\) | 7.85653e56 | 0.190090 | ||||||||
\(761\) | − | 5.68523e57i | − | 1.33985i | −0.742430 | − | 0.669923i | \(-0.766327\pi\) | ||
0.742430 | − | 0.669923i | \(-0.233673\pi\) | |||||||
\(762\) | −1.98769e56 | − | 4.24118e57i | −0.0456298 | − | 0.973614i | ||||
\(763\) | 3.31354e56 | 0.0740972 | ||||||||
\(764\) | − | 2.26291e57i | − | 0.492948i | ||||||
\(765\) | 3.60568e57 | − | 3.38714e56i | 0.765170 | − | 0.0718794i | ||||
\(766\) | 3.41533e57 | 0.706085 | ||||||||
\(767\) | 2.62279e57i | 0.528271i | ||||||||
\(768\) | −6.65285e57 | + | 3.11795e56i | −1.30552 | + | 0.0611850i | ||||
\(769\) | 3.56826e57 | 0.682228 | 0.341114 | − | 0.940022i | \(-0.389196\pi\) | ||||
0.341114 | + | 0.940022i | \(0.389196\pi\) | |||||||
\(770\) | 8.03976e56i | 0.149771i | ||||||||
\(771\) | 6.64759e55 | + | 1.41841e57i | 0.0120664 | + | 0.257463i | ||||
\(772\) | 6.13245e57 | 1.08465 | ||||||||
\(773\) | − | 4.57545e57i | − | 0.788577i | −0.918987 | − | 0.394289i | \(-0.870991\pi\) | ||
0.918987 | − | 0.394289i | \(-0.129009\pi\) | |||||||
\(774\) | −5.29265e55 | − | 5.63412e56i | −0.00888901 | − | 0.0946253i | ||||
\(775\) | −3.37505e57 | −0.552391 | ||||||||
\(776\) | − | 3.18852e57i | − | 0.508574i | ||||||
\(777\) | 6.47146e57 | − | 3.03294e56i | 1.00596 | − | 0.0471458i | ||||
\(778\) | 3.96129e57 | 0.600129 | ||||||||
\(779\) | − | 1.10741e57i | − | 0.163516i | ||||||
\(780\) | −3.70891e55 | − | 7.91378e56i | −0.00533769 | − | 0.113892i | ||||
\(781\) | −1.83884e57 | −0.257943 | ||||||||
\(782\) | 2.44564e58i | 3.34393i | ||||||||
\(783\) | −1.33702e57 | − | 9.45370e57i | −0.178198 | − | 1.25999i | ||||
\(784\) | 5.00430e57 | 0.650163 | ||||||||
\(785\) | 1.25057e57i | 0.158385i | ||||||||
\(786\) | −1.52334e58 | + | 7.13937e56i | −1.88082 | + | 0.0881473i | ||||
\(787\) | 4.35653e57 | 0.524380 | 0.262190 | − | 0.965016i | \(-0.415555\pi\) | ||||
0.262190 | + | 0.965016i | \(0.415555\pi\) | |||||||
\(788\) | 7.45453e56i | 0.0874774i | ||||||||
\(789\) | 3.19264e56 | + | 6.81221e57i | 0.0365266 | + | 0.779378i | ||||
\(790\) | −6.60234e57 | −0.736471 | ||||||||
\(791\) | 3.31944e57i | 0.361024i | ||||||||
\(792\) | −1.08862e57 | + | 1.02264e56i | −0.115444 | + | 0.0108447i | ||||
\(793\) | 1.71051e57 | 0.176873 | ||||||||
\(794\) | − | 3.14285e57i | − | 0.316894i | ||||||
\(795\) | −2.72769e57 | + | 1.27837e56i | −0.268196 | + | 0.0125694i | ||||
\(796\) | −1.38319e58 | −1.32623 | ||||||||
\(797\) | − | 1.01655e58i | − | 0.950527i | −0.879844 | − | 0.475263i | \(-0.842353\pi\) | ||
0.879844 | − | 0.475263i | \(-0.157647\pi\) | |||||||
\(798\) | −4.73232e56 | − | 1.00975e58i | −0.0431535 | − | 0.920777i | ||||
\(799\) | −2.72513e58 | −2.42355 | ||||||||
\(800\) | − | 1.03133e58i | − | 0.894535i | ||||||
\(801\) | −5.50188e56 | − | 5.85685e57i | −0.0465437 | − | 0.495466i | ||||
\(802\) | 3.11941e58 | 2.57386 | ||||||||
\(803\) | − | 2.22407e57i | − | 0.178994i | ||||||
\(804\) | 4.17022e57 | − | 1.95443e56i | 0.327369 | − | 0.0153426i | ||||
\(805\) | −7.77832e57 | −0.595618 | ||||||||
\(806\) | − | 4.01271e57i | − | 0.299735i | ||||||
\(807\) | 6.39727e56 | + | 1.36500e58i | 0.0466148 | + | 0.994633i | ||||
\(808\) | 6.78475e57 | 0.482288 | ||||||||
\(809\) | 2.07322e58i | 1.43772i | 0.695155 | + | 0.718860i | \(0.255336\pi\) | ||||
−0.695155 | + | 0.718860i | \(0.744664\pi\) | |||||||
\(810\) | 9.85794e57 | − | 1.86858e57i | 0.666938 | − | 0.126419i | ||||
\(811\) | −9.48084e57 | −0.625792 | −0.312896 | − | 0.949787i | \(-0.601299\pi\) | ||||
−0.312896 | + | 0.949787i | \(0.601299\pi\) | |||||||
\(812\) | − | 9.74926e57i | − | 0.627843i | ||||||
\(813\) | 1.14848e58 | − | 5.38251e56i | 0.721626 | − | 0.0338200i | ||||
\(814\) | 1.04331e58 | 0.639623 | ||||||||
\(815\) | − | 1.89063e57i | − | 0.113098i | ||||||
\(816\) | 1.42975e57 | + | 3.05070e58i | 0.0834560 | + | 1.78072i | ||||
\(817\) | −1.31538e57 | −0.0749220 | ||||||||
\(818\) | − | 2.85880e58i | − | 1.58898i | ||||||
\(819\) | 3.75526e57 | − | 3.52766e56i | 0.203687 | − | 0.0191341i | ||||
\(820\) | 1.12238e57 | 0.0594107 | ||||||||
\(821\) | 1.82148e58i | 0.940939i | 0.882416 | + | 0.470469i | \(0.155915\pi\) | ||||
−0.882416 | + | 0.470469i | \(0.844085\pi\) | |||||||
\(822\) | 2.59095e58 | − | 1.21428e57i | 1.30624 | − | 0.0612187i | ||||
\(823\) | −8.22694e57 | −0.404801 | −0.202400 | − | 0.979303i | \(-0.564874\pi\) | ||||
−0.202400 | + | 0.979303i | \(0.564874\pi\) | |||||||
\(824\) | 2.77991e57i | 0.133502i | ||||||||
\(825\) | −2.39172e56 | − | 5.10327e57i | −0.0112107 | − | 0.239205i | ||||
\(826\) | −3.39175e58 | −1.55175 | ||||||||
\(827\) | − | 1.59628e57i | − | 0.0712850i | −0.999365 | − | 0.0356425i | \(-0.988652\pi\) | ||
0.999365 | − | 0.0356425i | \(-0.0113478\pi\) | |||||||
\(828\) | 2.67384e57 | + | 2.84635e58i | 0.116554 | + | 1.24074i | ||||
\(829\) | 1.05730e58 | 0.449893 | 0.224946 | − | 0.974371i | \(-0.427779\pi\) | ||||
0.224946 | + | 0.974371i | \(0.427779\pi\) | |||||||
\(830\) | 2.09552e58i | 0.870423i | ||||||||
\(831\) | −1.77449e57 | + | 8.31639e55i | −0.0719537 | + | 0.00337221i | ||||
\(832\) | 3.10868e57 | 0.123058 | ||||||||
\(833\) | − | 2.09269e58i | − | 0.808733i | ||||||
\(834\) | −2.22907e57 | − | 4.75622e58i | −0.0841013 | − | 1.79449i | ||||
\(835\) | 2.59623e57 | 0.0956343 | ||||||||
\(836\) | − | 6.86862e57i | − | 0.247027i | ||||||
\(837\) | 2.12312e58 | − | 3.00269e57i | 0.745531 | − | 0.105439i | ||||
\(838\) | 2.16684e58 | 0.742928 | ||||||||
\(839\) | − | 1.81513e58i | − | 0.607670i | −0.952725 | − | 0.303835i | \(-0.901733\pi\) | ||
0.952725 | − | 0.303835i | \(-0.0982671\pi\) | |||||||
\(840\) | −3.78681e57 | + | 1.77474e56i | −0.123791 | + | 0.00580162i | ||||
\(841\) | −1.94017e58 | −0.619326 | ||||||||
\(842\) | 1.91990e58i | 0.598461i | ||||||||
\(843\) | −2.14441e57 | − | 4.57558e58i | −0.0652764 | − | 1.39282i | ||||
\(844\) | −1.15096e58 | −0.342147 | ||||||||
\(845\) | 1.61491e58i | 0.468828i | ||||||||
\(846\) | −7.51686e58 | + | 7.06127e57i | −2.13122 | + | 0.200205i | ||||
\(847\) | 2.18099e58 | 0.603928 | ||||||||
\(848\) | − | 2.30278e58i | − | 0.622781i | ||||||
\(849\) | −1.60928e58 | + | 7.54213e56i | −0.425088 | + | 0.0199223i | ||||
\(850\) | −5.56927e58 | −1.43688 | ||||||||
\(851\) | 1.00938e59i | 2.54369i | ||||||||
\(852\) | 1.09700e57 | + | 2.34070e58i | 0.0270032 | + | 0.576173i | ||||
\(853\) | −1.57273e58 | −0.378157 | −0.189079 | − | 0.981962i | \(-0.560550\pi\) | ||||
−0.189079 | + | 0.981962i | \(0.560550\pi\) | |||||||
\(854\) | 2.21200e58i | 0.519551i | ||||||||
\(855\) | −2.18125e57 | − | 2.32199e58i | −0.0500476 | − | 0.532767i | ||||
\(856\) | −1.60395e58 | −0.359514 | ||||||||
\(857\) | − | 2.48359e58i | − | 0.543830i | −0.962321 | − | 0.271915i | \(-0.912343\pi\) | ||
0.962321 | − | 0.271915i | \(-0.0876570\pi\) | |||||||
\(858\) | 6.06744e57 | − | 2.84359e56i | 0.129796 | − | 0.00608305i | ||||
\(859\) | 7.97374e58 | 1.66647 | 0.833237 | − | 0.552916i | \(-0.186485\pi\) | ||||
0.833237 | + | 0.552916i | \(0.186485\pi\) | |||||||
\(860\) | − | 1.33316e57i | − | 0.0272216i | ||||||
\(861\) | 2.50158e56 | + | 5.33768e57i | 0.00499058 | + | 0.106485i | ||||
\(862\) | 3.24700e58 | 0.632903 | ||||||||
\(863\) | − | 5.20595e58i | − | 0.991480i | −0.868471 | − | 0.495740i | \(-0.834897\pi\) | ||
0.868471 | − | 0.495740i | \(-0.165103\pi\) | |||||||
\(864\) | 9.17545e57 | + | 6.48771e58i | 0.170747 | + | 1.20730i | ||||
\(865\) | 1.42319e58 | 0.258785 | ||||||||
\(866\) | 4.30474e57i | 0.0764872i | ||||||||
\(867\) | 7.00420e58 | − | 3.28262e57i | 1.21612 | − | 0.0569952i | ||||
\(868\) | 2.18950e58 | 0.371493 | ||||||||
\(869\) | − | 2.13583e58i | − | 0.354137i | ||||||
\(870\) | −2.49567e57 | − | 5.32508e58i | −0.0404392 | − | 0.862862i | ||||
\(871\) | 8.58151e57 | 0.135894 | ||||||||
\(872\) | 2.51613e57i | 0.0389407i | ||||||||
\(873\) | −9.42362e58 | + | 8.85247e57i | −1.42539 | + | 0.133900i | ||||
\(874\) | 1.57494e59 | 2.32829 | ||||||||
\(875\) | − | 4.18571e58i | − | 0.604795i | ||||||
\(876\) | −2.83106e58 | + | 1.32682e57i | −0.399823 | + | 0.0187382i | ||||
\(877\) | −5.67389e58 | −0.783230 | −0.391615 | − | 0.920129i | \(-0.628083\pi\) | ||||
−0.391615 | + | 0.920129i | \(0.628083\pi\) | |||||||
\(878\) | − | 2.66754e58i | − | 0.359932i | ||||||
\(879\) | 4.35523e57 | + | 9.29286e58i | 0.0574425 | + | 1.22567i | ||||
\(880\) | −1.56424e58 | −0.201673 | ||||||||
\(881\) | − | 9.54440e58i | − | 1.20290i | −0.798910 | − | 0.601451i | \(-0.794589\pi\) | ||
0.798910 | − | 0.601451i | \(-0.205411\pi\) | |||||||
\(882\) | −5.42251e57 | − | 5.77236e58i | −0.0668080 | − | 0.711184i | ||||
\(883\) | 1.39324e59 | 1.67807 | 0.839036 | − | 0.544076i | \(-0.183120\pi\) | ||||
0.839036 | + | 0.544076i | \(0.183120\pi\) | |||||||
\(884\) | − | 2.79385e58i | − | 0.328971i | ||||||
\(885\) | −7.81674e58 | + | 3.66342e57i | −0.899830 | + | 0.0421718i | ||||
\(886\) | −2.25823e59 | −2.54152 | ||||||||
\(887\) | 1.44700e59i | 1.59220i | 0.605167 | + | 0.796098i | \(0.293106\pi\) | ||||
−0.605167 | + | 0.796098i | \(0.706894\pi\) | |||||||
\(888\) | 2.30306e57 | + | 4.91409e58i | 0.0247768 | + | 0.528669i | ||||
\(889\) | 4.76210e58 | 0.500914 | ||||||||
\(890\) | − | 3.28453e58i | − | 0.337810i | ||||||
\(891\) | 6.04478e57 | + | 3.18900e58i | 0.0607892 | + | 0.320701i | ||||
\(892\) | 5.55132e58 | 0.545883 | ||||||||
\(893\) | 1.75493e59i | 1.68745i | ||||||||
\(894\) | 1.34579e59 | − | 6.30722e57i | 1.26539 | − | 0.0593045i | ||||
\(895\) | 1.10949e57 | 0.0102015 | ||||||||
\(896\) | − | 5.14612e58i | − | 0.462721i | ||||||
\(897\) | 2.75112e57 | + | 5.87014e58i | 0.0241914 | + | 0.516178i | ||||
\(898\) | −1.86587e59 | −1.60456 | ||||||||
\(899\) | − | 1.13927e59i | − | 0.958150i | ||||||
\(900\) | −6.48178e58 | + | 6.08893e57i | −0.533144 | + | 0.0500831i | ||||
\(901\) | −9.62972e58 | −0.774672 | ||||||||
\(902\) | 8.60524e57i | 0.0677068i | ||||||||
\(903\) | 6.34006e57 | − | 2.97136e56i | 0.0487908 | − | 0.00228665i | ||||
\(904\) | −2.52061e58 | −0.189731 | ||||||||
\(905\) | 7.88051e58i | 0.580206i | ||||||||
\(906\) | −8.51804e57 | − | 1.81752e59i | −0.0613445 | − | 1.30892i | ||||
\(907\) | −1.05800e59 | −0.745314 | −0.372657 | − | 0.927969i | \(-0.621553\pi\) | ||||
−0.372657 | + | 0.927969i | \(0.621553\pi\) | |||||||
\(908\) | 1.27412e57i | 0.00877999i | ||||||||
\(909\) | −1.88369e58 | − | 2.00522e59i | −0.126979 | − | 1.35171i | ||||
\(910\) | 2.10595e58 | 0.138874 | ||||||||
\(911\) | − | 2.09761e59i | − | 1.35319i | −0.736357 | − | 0.676593i | \(-0.763456\pi\) | ||
0.736357 | − | 0.676593i | \(-0.236544\pi\) | |||||||
\(912\) | 1.96459e59 | − | 9.20732e57i | 1.23987 | − | 0.0581081i | ||||
\(913\) | −6.77893e58 | −0.418548 | ||||||||
\(914\) | 4.16877e59i | 2.51817i | ||||||||
\(915\) | 2.38918e57 | + | 5.09786e58i | 0.0141198 | + | 0.301277i | ||||
\(916\) | −2.08954e59 | −1.20821 | ||||||||
\(917\) | − | 1.71045e59i | − | 0.967661i | ||||||
\(918\) | 3.50343e59 | − | 4.95483e58i | 1.93927 | − | 0.274268i | ||||
\(919\) | 3.09625e59 | 1.67697 | 0.838487 | − | 0.544921i | \(-0.183440\pi\) | ||||
0.838487 | + | 0.544921i | \(0.183440\pi\) | |||||||
\(920\) | − | 5.90645e58i | − | 0.313018i | ||||||
\(921\) | −1.86450e59 | + | 8.73823e57i | −0.966873 | + | 0.0453139i | ||||
\(922\) | 2.49549e59 | 1.26630 | ||||||||
\(923\) | 4.81670e58i | 0.239175i | ||||||||
\(924\) | 1.55158e57 | + | 3.31065e58i | 0.00753937 | + | 0.160869i | ||||
\(925\) | −2.29859e59 | −1.09302 | ||||||||
\(926\) | 2.91920e59i | 1.35845i | ||||||||
\(927\) | 8.21599e58 | − | 7.71803e57i | 0.374167 | − | 0.0351489i | ||||
\(928\) | 3.48132e59 | 1.55162 | ||||||||
\(929\) | 2.84934e58i | 0.124288i | 0.998067 | + | 0.0621440i | \(0.0197938\pi\) | ||||
−0.998067 | + | 0.0621440i | \(0.980206\pi\) | |||||||
\(930\) | 1.19591e59 | − | 5.60481e57i | 0.510553 | − | 0.0239278i | ||||
\(931\) | −1.34765e59 | −0.563098 | ||||||||
\(932\) | − | 1.01624e59i | − | 0.415602i | ||||||
\(933\) | 1.22726e58 | + | 2.61864e59i | 0.0491252 | + | 1.04820i | ||||
\(934\) | −2.03831e59 | −0.798607 | ||||||||
\(935\) | 6.54130e58i | 0.250860i | ||||||||
\(936\) | 2.67872e57 | + | 2.85155e58i | 0.0100557 | + | 0.107044i | ||||
\(937\) | 2.58554e59 | 0.950078 | 0.475039 | − | 0.879965i | \(-0.342434\pi\) | ||||
0.475039 | + | 0.879965i | \(0.342434\pi\) | |||||||
\(938\) | 1.10975e59i | 0.399178i | ||||||||
\(939\) | −3.30466e59 | + | 1.54877e58i | −1.16363 | + | 0.0545351i | ||||
\(940\) | −1.77866e59 | −0.613105 | ||||||||
\(941\) | − | 3.55530e59i | − | 1.19973i | −0.800101 | − | 0.599865i | \(-0.795221\pi\) | ||
0.800101 | − | 0.599865i | \(-0.204779\pi\) | |||||||
\(942\) | 5.71994e57 | + | 1.22048e59i | 0.0188962 | + | 0.403192i | ||||
\(943\) | −8.32541e58 | −0.269260 | ||||||||
\(944\) | − | 6.59907e59i | − | 2.08950i | ||||||
\(945\) | 1.57588e58 | + | 1.11426e59i | 0.0488524 | + | 0.345422i | ||||
\(946\) | 1.02212e58 | 0.0310228 | ||||||||
\(947\) | − | 3.80294e59i | − | 1.13011i | −0.825054 | − | 0.565053i | \(-0.808856\pi\) | ||
0.825054 | − | 0.565053i | \(-0.191144\pi\) | |||||||
\(948\) | −2.71874e59 | + | 1.27417e58i | −0.791044 | + | 0.0370734i | ||||
\(949\) | −5.82579e58 | −0.165970 | ||||||||
\(950\) | 3.58650e59i | 1.00046i | ||||||||
\(951\) | −1.17440e58 | − | 2.50585e59i | −0.0320779 | − | 0.684455i | ||||
\(952\) | −1.33688e59 | −0.357564 | ||||||||
\(953\) | 2.95999e59i | 0.775234i | 0.921821 | + | 0.387617i | \(0.126702\pi\) | ||||
−0.921821 | + | 0.387617i | \(0.873298\pi\) | |||||||
\(954\) | −2.65621e59 | + | 2.49522e58i | −0.681232 | + | 0.0639943i | ||||
\(955\) | 1.38783e59 | 0.348552 | ||||||||
\(956\) | − | 3.89310e59i | − | 0.957497i | ||||||
\(957\) | 1.72264e59 | − | 8.07340e57i | 0.414912 | − | 0.0194454i | ||||
\(958\) | −1.32169e59 | −0.311760 | ||||||||
\(959\) | 2.90918e59i | 0.672045i | ||||||||
\(960\) | 4.34209e57 | + | 9.26483e58i | 0.00982368 | + | 0.209610i | ||||
\(961\) | −1.95444e59 | −0.433066 | ||||||||
\(962\) | − | 2.73287e59i | − | 0.593085i | ||||||
\(963\) | 4.45315e58 | + | 4.74046e59i | 0.0946545 | + | 1.00761i | ||||
\(964\) | 4.59008e59 | 0.955607 | ||||||||
\(965\) | 3.76098e59i | 0.766928i | ||||||||
\(966\) | −7.59116e59 | + | 3.55770e58i | −1.51623 | + | 0.0710603i | ||||
\(967\) | 9.40566e59 | 1.84018 | 0.920089 | − | 0.391709i | \(-0.128116\pi\) | ||||
0.920089 | + | 0.391709i | \(0.128116\pi\) | |||||||
\(968\) | 1.65613e59i | 0.317385i | ||||||||
\(969\) | −3.85030e58 | − | 8.21548e59i | −0.0722802 | − | 1.54226i | ||||
\(970\) | −5.28477e59 | −0.971833 | ||||||||
\(971\) | 7.90172e59i | 1.42343i | 0.702467 | + | 0.711717i | \(0.252082\pi\) | ||||
−0.702467 | + | 0.711717i | \(0.747918\pi\) | |||||||
\(972\) | 4.02328e59 | − | 9.59699e58i | 0.709995 | − | 0.169360i | ||||
\(973\) | 5.34041e59 | 0.923246 | ||||||||
\(974\) | 2.94797e59i | 0.499280i | ||||||||
\(975\) | −1.33676e59 | + | 6.26493e57i | −0.221800 | + | 0.0103950i | ||||
\(976\) | −4.30373e59 | −0.699598 | ||||||||
\(977\) | 2.31628e59i | 0.368892i | 0.982843 | + | 0.184446i | \(0.0590491\pi\) | ||||
−0.982843 | + | 0.184446i | \(0.940951\pi\) | |||||||
\(978\) | −8.64749e57 | − | 1.84514e59i | −0.0134931 | − | 0.287906i | ||||
\(979\) | 1.06253e59 | 0.162438 | ||||||||
\(980\) | − | 1.36587e59i | − | 0.204592i | ||||||
\(981\) | 7.43639e58 | − | 6.98568e57i | 0.109140 | − | 0.0102525i | ||||
\(982\) | 1.62067e60 | 2.33058 | ||||||||
\(983\) | 1.31841e59i | 0.185772i | 0.995677 | + | 0.0928862i | \(0.0296093\pi\) | ||||
−0.995677 | + | 0.0928862i | \(0.970391\pi\) | |||||||
\(984\) | −4.05316e58 | + | 1.89957e57i | −0.0559618 | + | 0.00262273i | ||||
\(985\) | −4.57180e58 | −0.0618533 | ||||||||
\(986\) | − | 1.87995e60i | − | 2.49234i | ||||||
\(987\) | −3.96428e58 | − | 8.45869e59i | −0.0515017 | − | 1.09891i | ||||
\(988\) | −1.79918e59 | −0.229053 | ||||||||
\(989\) | 9.88886e58i | 0.123373i | ||||||||
\(990\) | 1.69496e58 | + | 1.80432e59i | 0.0207231 | + | 0.220602i | ||||
\(991\) | 3.29149e59 | 0.394384 | 0.197192 | − | 0.980365i | \(-0.436818\pi\) | ||||
0.197192 | + | 0.980365i | \(0.436818\pi\) | |||||||
\(992\) | 7.81838e59i | 0.918086i | ||||||||
\(993\) | −1.01654e59 | + | 4.76418e57i | −0.116988 | + | 0.00548281i | ||||
\(994\) | −6.22887e59 | −0.702558 | ||||||||
\(995\) | − | 8.48298e59i | − | 0.937749i | ||||||
\(996\) | 4.04412e58 | + | 8.62903e59i | 0.0438164 | + | 0.934922i | ||||
\(997\) | −4.87393e59 | −0.517578 | −0.258789 | − | 0.965934i | \(-0.583323\pi\) | ||||
−0.258789 | + | 0.965934i | \(0.583323\pi\) | |||||||
\(998\) | 1.04163e60i | 1.08418i | ||||||||
\(999\) | 1.44596e60 | − | 2.04499e59i | 1.47518 | − | 0.208632i |
(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 | 3.41.b.a.2.10 | yes | 12 | |
3.2 | odd | 2 | inner | 3.41.b.a.2.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.41.b.a.2.3 | ✓ | 12 | 3.2 | odd | 2 | inner | |
3.41.b.a.2.10 | yes | 12 | 1.1 | even | 1 | trivial |