Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,43,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 43, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 43);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 43 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(44.6910828688\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 10 x^{19} + \cdots + 58\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{380}\cdot 3^{41}\cdot 5^{10}\cdot 7^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.15 | ||
Root | \(0.500000 + 4.69874e8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.43.b.a.3.16 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.57912e6 | − | 1.38001e6i | 0.752984 | − | 0.658039i | ||||
\(3\) | − | 7.51798e9i | − | 0.718712i | −0.933201 | − | 0.359356i | \(-0.882996\pi\) | ||
0.933201 | − | 0.359356i | \(-0.117004\pi\) | |||||||
\(4\) | 5.89205e11 | − | 4.35840e12i | 0.133970 | − | 0.990985i | ||||
\(5\) | 5.33275e14 | 1.11836 | 0.559180 | − | 0.829047i | \(-0.311116\pi\) | ||||
0.559180 | + | 0.829047i | \(0.311116\pi\) | |||||||
\(6\) | −1.03749e16 | − | 1.18718e16i | −0.472941 | − | 0.541179i | ||||
\(7\) | 7.46884e17i | 1.33719i | 0.743625 | + | 0.668596i | \(0.233105\pi\) | ||||
−0.743625 | + | 0.668596i | \(0.766895\pi\) | |||||||
\(8\) | −5.08420e18 | − | 7.69555e18i | −0.551230 | − | 0.834353i | ||||
\(9\) | 5.28989e19 | 0.483453 | ||||||||
\(10\) | 8.42107e20 | − | 7.35924e20i | 0.842107 | − | 0.735924i | ||||
\(11\) | − | 6.22915e21i | − | 0.841749i | −0.907119 | − | 0.420874i | \(-0.861723\pi\) | ||
0.907119 | − | 0.420874i | \(-0.138277\pi\) | |||||||
\(12\) | −3.27664e22 | − | 4.42963e21i | −0.712233 | − | 0.0962856i | ||||
\(13\) | 4.81446e23 | 1.94867 | 0.974333 | − | 0.225111i | \(-0.0722746\pi\) | ||||
0.974333 | + | 0.225111i | \(0.0722746\pi\) | |||||||
\(14\) | 1.03071e24 | + | 1.17942e24i | 0.879925 | + | 1.00688i | ||||
\(15\) | − | 4.00915e24i | − | 0.803778i | ||||||
\(16\) | −1.86485e25 | − | 5.13598e24i | −0.964104 | − | 0.265524i | ||||
\(17\) | 7.46133e25 | 1.07991 | 0.539957 | − | 0.841693i | \(-0.318441\pi\) | ||||
0.539957 | + | 0.841693i | \(0.318441\pi\) | |||||||
\(18\) | 8.35338e25 | − | 7.30009e25i | 0.364032 | − | 0.318131i | ||||
\(19\) | 7.57016e26i | 1.05993i | 0.848018 | + | 0.529967i | \(0.177796\pi\) | ||||
−0.848018 | + | 0.529967i | \(0.822204\pi\) | |||||||
\(20\) | 3.14208e26 | − | 2.32423e27i | 0.149826 | − | 1.10828i | ||||
\(21\) | 5.61506e27 | 0.961057 | ||||||||
\(22\) | −8.59628e27 | − | 9.83659e27i | −0.553904 | − | 0.633823i | ||||
\(23\) | − | 2.53407e28i | − | 0.642000i | −0.947079 | − | 0.321000i | \(-0.895981\pi\) | ||
0.947079 | − | 0.321000i | \(-0.104019\pi\) | |||||||
\(24\) | −5.78550e28 | + | 3.82229e28i | −0.599660 | + | 0.396176i | ||||
\(25\) | 5.70088e28 | 0.250727 | ||||||||
\(26\) | 7.60262e29 | − | 6.64400e29i | 1.46731 | − | 1.28230i | ||||
\(27\) | − | 1.22030e30i | − | 1.06618i | ||||||
\(28\) | 3.25522e30 | + | 4.40067e29i | 1.32514 | + | 0.179143i | ||||
\(29\) | −1.54350e30 | −0.300711 | −0.150356 | − | 0.988632i | \(-0.548042\pi\) | ||||
−0.150356 | + | 0.988632i | \(0.548042\pi\) | |||||||
\(30\) | −5.53266e30 | − | 6.33094e30i | −0.528917 | − | 0.605232i | ||||
\(31\) | 1.96158e31i | 0.941911i | 0.882157 | + | 0.470956i | \(0.156091\pi\) | ||||
−0.882157 | + | 0.470956i | \(0.843909\pi\) | |||||||
\(32\) | −3.65359e31 | + | 1.76247e31i | −0.900680 | + | 0.434483i | ||||
\(33\) | −4.68307e31 | −0.604975 | ||||||||
\(34\) | 1.17823e32 | − | 1.02967e32i | 0.813157 | − | 0.710625i | ||||
\(35\) | 3.98295e32i | 1.49546i | ||||||||
\(36\) | 3.11683e31 | − | 2.30555e32i | 0.0647680 | − | 0.479095i | ||||
\(37\) | −6.73293e32 | −0.786988 | −0.393494 | − | 0.919327i | \(-0.628734\pi\) | ||||
−0.393494 | + | 0.919327i | \(0.628734\pi\) | |||||||
\(38\) | 1.04469e33 | + | 1.19542e33i | 0.697478 | + | 0.798114i | ||||
\(39\) | − | 3.61950e33i | − | 1.40053i | ||||||
\(40\) | −2.71128e33 | − | 4.10385e33i | −0.616473 | − | 0.933107i | ||||
\(41\) | 3.14869e33 | 0.426254 | 0.213127 | − | 0.977024i | \(-0.431635\pi\) | ||||
0.213127 | + | 0.977024i | \(0.431635\pi\) | |||||||
\(42\) | 8.86686e33 | − | 7.74882e33i | 0.723660 | − | 0.632413i | ||||
\(43\) | − | 7.71866e33i | − | 0.384330i | −0.981363 | − | 0.192165i | \(-0.938449\pi\) | ||
0.981363 | − | 0.192165i | \(-0.0615509\pi\) | |||||||
\(44\) | −2.71491e34 | − | 3.67024e33i | −0.834161 | − | 0.112769i | ||||
\(45\) | 2.82097e34 | 0.540674 | ||||||||
\(46\) | −3.49704e34 | − | 4.00161e34i | −0.422461 | − | 0.483415i | ||||
\(47\) | − | 1.95126e35i | − | 1.50059i | −0.661106 | − | 0.750293i | \(-0.729912\pi\) | ||
0.661106 | − | 0.750293i | \(-0.270088\pi\) | |||||||
\(48\) | −3.86122e34 | + | 1.40199e35i | −0.190835 | + | 0.692913i | ||||
\(49\) | −2.45862e35 | −0.788085 | ||||||||
\(50\) | 9.00238e34 | − | 7.86726e34i | 0.188794 | − | 0.164988i | ||||
\(51\) | − | 5.60941e35i | − | 0.776147i | ||||||
\(52\) | 2.83670e35 | − | 2.09834e36i | 0.261062 | − | 1.93110i | ||||
\(53\) | −3.91250e35 | −0.241358 | −0.120679 | − | 0.992692i | \(-0.538507\pi\) | ||||
−0.120679 | + | 0.992692i | \(0.538507\pi\) | |||||||
\(54\) | −1.68403e36 | − | 1.92701e36i | −0.701585 | − | 0.802813i | ||||
\(55\) | − | 3.32185e36i | − | 0.941378i | ||||||
\(56\) | 5.74768e36 | − | 3.79731e36i | 1.11569 | − | 0.737101i | ||||
\(57\) | 5.69123e36 | 0.761788 | ||||||||
\(58\) | −2.43738e36 | + | 2.13005e36i | −0.226431 | + | 0.197880i | ||||
\(59\) | − | 2.85242e36i | − | 0.185064i | −0.995710 | − | 0.0925319i | \(-0.970504\pi\) | ||
0.995710 | − | 0.0925319i | \(-0.0294960\pi\) | |||||||
\(60\) | −1.74735e37 | − | 2.36221e36i | −0.796533 | − | 0.107682i | ||||
\(61\) | −5.39160e37 | −1.73697 | −0.868483 | − | 0.495719i | \(-0.834905\pi\) | ||||
−0.868483 | + | 0.495719i | \(0.834905\pi\) | |||||||
\(62\) | 2.70699e37 | + | 3.09757e37i | 0.619814 | + | 0.709244i | ||||
\(63\) | 3.95093e37i | 0.646470i | ||||||||
\(64\) | −3.33724e37 | + | 7.82514e37i | −0.392291 | + | 0.919841i | ||||
\(65\) | 2.56743e38 | 2.17931 | ||||||||
\(66\) | −7.39513e37 | + | 6.46267e37i | −0.455537 | + | 0.398097i | ||||
\(67\) | 4.98954e37i | 0.224125i | 0.993701 | + | 0.112062i | \(0.0357456\pi\) | ||||
−0.993701 | + | 0.112062i | \(0.964254\pi\) | |||||||
\(68\) | 4.39625e37 | − | 3.25195e38i | 0.144676 | − | 1.07018i | ||||
\(69\) | −1.90511e38 | −0.461413 | ||||||||
\(70\) | 5.49649e38 | + | 6.28956e38i | 0.984072 | + | 1.12606i | ||||
\(71\) | 1.04801e39i | 1.39296i | 0.717575 | + | 0.696481i | \(0.245252\pi\) | ||||
−0.717575 | + | 0.696481i | \(0.754748\pi\) | |||||||
\(72\) | −2.68949e38 | − | 4.07086e38i | −0.266494 | − | 0.403370i | ||||
\(73\) | −1.07660e39 | −0.798497 | −0.399249 | − | 0.916843i | \(-0.630729\pi\) | ||||
−0.399249 | + | 0.916843i | \(0.630729\pi\) | |||||||
\(74\) | −1.06321e39 | + | 9.29150e38i | −0.592589 | + | 0.517868i | ||||
\(75\) | − | 4.28591e38i | − | 0.180201i | ||||||
\(76\) | 3.29938e39 | + | 4.46037e38i | 1.05038 | + | 0.141999i | ||||
\(77\) | 4.65245e39 | 1.12558 | ||||||||
\(78\) | −4.99494e39 | − | 5.71564e39i | −0.921603 | − | 1.05458i | ||||
\(79\) | 1.50373e39i | 0.212325i | 0.994349 | + | 0.106163i | \(0.0338564\pi\) | ||||
−0.994349 | + | 0.106163i | \(0.966144\pi\) | |||||||
\(80\) | −9.94478e39 | − | 2.73889e39i | −1.07821 | − | 0.296951i | ||||
\(81\) | −3.38607e39 | −0.282821 | ||||||||
\(82\) | 4.97217e39 | − | 4.34522e39i | 0.320963 | − | 0.280492i | ||||
\(83\) | − | 3.31555e40i | − | 1.65927i | −0.558310 | − | 0.829633i | \(-0.688550\pi\) | ||
0.558310 | − | 0.829633i | \(-0.311450\pi\) | |||||||
\(84\) | 3.30842e39 | − | 2.44727e40i | 0.128752 | − | 0.952393i | ||||
\(85\) | 3.97894e40 | 1.20773 | ||||||||
\(86\) | −1.06518e40 | − | 1.21887e40i | −0.252904 | − | 0.289394i | ||||
\(87\) | 1.16040e40i | 0.216125i | ||||||||
\(88\) | −4.79368e40 | + | 3.16703e40i | −0.702316 | + | 0.463997i | ||||
\(89\) | −1.74834e40 | −0.202039 | −0.101019 | − | 0.994884i | \(-0.532210\pi\) | ||||
−0.101019 | + | 0.994884i | \(0.532210\pi\) | |||||||
\(90\) | 4.45465e40 | − | 3.89296e40i | 0.407119 | − | 0.355784i | ||||
\(91\) | 3.59584e41i | 2.60574i | ||||||||
\(92\) | −1.10445e41 | − | 1.49309e40i | −0.636212 | − | 0.0860084i | ||||
\(93\) | 1.47471e41 | 0.676963 | ||||||||
\(94\) | −2.69276e41 | − | 3.08128e41i | −0.987444 | − | 1.12992i | ||||
\(95\) | 4.03698e41i | 1.18539i | ||||||||
\(96\) | 1.32502e41 | + | 2.74676e41i | 0.312268 | + | 0.647330i | ||||
\(97\) | 7.69142e41 | 1.45814 | 0.729071 | − | 0.684438i | \(-0.239952\pi\) | ||||
0.729071 | + | 0.684438i | \(0.239952\pi\) | |||||||
\(98\) | −3.88245e41 | + | 3.39291e41i | −0.593415 | + | 0.518591i | ||||
\(99\) | − | 3.29515e41i | − | 0.406946i | ||||||
\(100\) | 3.35898e40 | − | 2.48467e41i | 0.0335898 | − | 0.248467i | ||||
\(101\) | 1.00224e42 | 0.813246 | 0.406623 | − | 0.913596i | \(-0.366706\pi\) | ||||
0.406623 | + | 0.913596i | \(0.366706\pi\) | |||||||
\(102\) | −7.74103e41 | − | 8.85795e41i | −0.510735 | − | 0.584426i | ||||
\(103\) | 2.77198e42i | 1.49008i | 0.667021 | + | 0.745039i | \(0.267569\pi\) | ||||
−0.667021 | + | 0.745039i | \(0.732431\pi\) | |||||||
\(104\) | −2.44777e42 | − | 3.70499e42i | −1.07416 | − | 1.62588i | ||||
\(105\) | 2.99437e42 | 1.07481 | ||||||||
\(106\) | −6.17832e41 | + | 5.39928e41i | −0.181739 | + | 0.158823i | ||||
\(107\) | 3.31740e41i | 0.0801196i | 0.999197 | + | 0.0400598i | \(0.0127548\pi\) | ||||
−0.999197 | + | 0.0400598i | \(0.987245\pi\) | |||||||
\(108\) | −5.31857e42 | − | 7.19008e41i | −1.05656 | − | 0.142835i | ||||
\(109\) | 1.47309e42 | 0.241142 | 0.120571 | − | 0.992705i | \(-0.461527\pi\) | ||||
0.120571 | + | 0.992705i | \(0.461527\pi\) | |||||||
\(110\) | −4.58418e42 | − | 5.24561e42i | −0.619463 | − | 0.708842i | ||||
\(111\) | 5.06181e42i | 0.565618i | ||||||||
\(112\) | 3.83598e42 | − | 1.39283e43i | 0.355057 | − | 1.28919i | ||||
\(113\) | 1.60332e42 | 0.123132 | 0.0615662 | − | 0.998103i | \(-0.480390\pi\) | ||||
0.0615662 | + | 0.998103i | \(0.480390\pi\) | |||||||
\(114\) | 8.98714e42 | − | 7.85394e42i | 0.573614 | − | 0.501286i | ||||
\(115\) | − | 1.35136e43i | − | 0.717986i | ||||||
\(116\) | −9.09440e41 | + | 6.72721e42i | −0.0402862 | + | 0.298001i | ||||
\(117\) | 2.54680e43 | 0.942088 | ||||||||
\(118\) | −3.93636e42 | − | 4.50432e42i | −0.121779 | − | 0.139350i | ||||
\(119\) | 5.57274e43i | 1.44405i | ||||||||
\(120\) | −3.08526e43 | + | 2.03833e43i | −0.670635 | + | 0.443067i | ||||
\(121\) | 1.59614e43 | 0.291459 | ||||||||
\(122\) | −8.51400e43 | + | 7.44045e43i | −1.30791 | + | 1.14299i | ||||
\(123\) | − | 2.36718e43i | − | 0.306354i | ||||||
\(124\) | 8.54934e43 | + | 1.15577e43i | 0.933421 | + | 0.126187i | ||||
\(125\) | −9.08514e43 | −0.837956 | ||||||||
\(126\) | 5.45232e43 | + | 6.23901e43i | 0.425402 | + | 0.486781i | ||||
\(127\) | 1.42876e44i | 0.944240i | 0.881534 | + | 0.472120i | \(0.156511\pi\) | ||||
−0.881534 | + | 0.472120i | \(0.843489\pi\) | |||||||
\(128\) | 5.52885e43 | + | 1.69623e44i | 0.309903 | + | 0.950768i | ||||
\(129\) | −5.80288e43 | −0.276223 | ||||||||
\(130\) | 4.05429e44 | − | 3.54308e44i | 1.64098 | − | 1.43407i | ||||
\(131\) | − | 5.31516e44i | − | 1.83155i | −0.401692 | − | 0.915775i | \(-0.631578\pi\) | ||
0.401692 | − | 0.915775i | \(-0.368422\pi\) | |||||||
\(132\) | −2.75928e43 | + | 2.04107e44i | −0.0810483 | + | 0.599522i | ||||
\(133\) | −5.65402e44 | −1.41734 | ||||||||
\(134\) | 6.88560e43 | + | 7.87909e43i | 0.147483 | + | 0.168762i | ||||
\(135\) | − | 6.50758e44i | − | 1.19237i | ||||||
\(136\) | −3.79349e44 | − | 5.74190e44i | −0.595281 | − | 0.901029i | ||||
\(137\) | 1.91399e44 | 0.257519 | 0.128759 | − | 0.991676i | \(-0.458901\pi\) | ||||
0.128759 | + | 0.991676i | \(0.458901\pi\) | |||||||
\(138\) | −3.00840e44 | + | 2.62907e44i | −0.347436 | + | 0.303628i | ||||
\(139\) | 1.48190e44i | 0.147065i | 0.997293 | + | 0.0735323i | \(0.0234272\pi\) | ||||
−0.997293 | + | 0.0735323i | \(0.976573\pi\) | |||||||
\(140\) | 1.73593e45 | + | 2.34677e44i | 1.48198 | + | 0.200346i | ||||
\(141\) | −1.46696e45 | −1.07849 | ||||||||
\(142\) | 1.44626e45 | + | 1.65493e45i | 0.916623 | + | 1.04888i | ||||
\(143\) | − | 2.99900e45i | − | 1.64029i | ||||||
\(144\) | −9.86485e44 | − | 2.71688e44i | −0.466099 | − | 0.128368i | ||||
\(145\) | −8.23113e44 | −0.336303 | ||||||||
\(146\) | −1.70008e45 | + | 1.48571e45i | −0.601256 | + | 0.525442i | ||||
\(147\) | 1.84838e45i | 0.566406i | ||||||||
\(148\) | −3.96707e44 | + | 2.93448e45i | −0.105432 | + | 0.779893i | ||||
\(149\) | 1.56939e45 | 0.362092 | 0.181046 | − | 0.983475i | \(-0.442052\pi\) | ||||
0.181046 | + | 0.983475i | \(0.442052\pi\) | |||||||
\(150\) | −5.91459e44 | − | 6.76798e44i | −0.118579 | − | 0.135688i | ||||
\(151\) | 5.27304e45i | 0.919486i | 0.888052 | + | 0.459743i | \(0.152059\pi\) | ||||
−0.888052 | + | 0.459743i | \(0.847941\pi\) | |||||||
\(152\) | 5.82565e45 | − | 3.84882e45i | 0.884360 | − | 0.584268i | ||||
\(153\) | 3.94696e45 | 0.522087 | ||||||||
\(154\) | 7.34679e45 | − | 6.42042e45i | 0.847544 | − | 0.740676i | ||||
\(155\) | 1.04606e46i | 1.05340i | ||||||||
\(156\) | −1.57753e46 | − | 2.13263e45i | −1.38790 | − | 0.187628i | ||||
\(157\) | 8.59406e44 | 0.0661158 | 0.0330579 | − | 0.999453i | \(-0.489475\pi\) | ||||
0.0330579 | + | 0.999453i | \(0.489475\pi\) | |||||||
\(158\) | 2.07516e45 | + | 2.37457e45i | 0.139718 | + | 0.159877i | ||||
\(159\) | 2.94141e45i | 0.173467i | ||||||||
\(160\) | −1.94837e46 | + | 9.39883e45i | −1.00728 | + | 0.485908i | ||||
\(161\) | 1.89266e46 | 0.858477 | ||||||||
\(162\) | −5.34702e45 | + | 4.67281e45i | −0.212959 | + | 0.186107i | ||||
\(163\) | − | 1.72880e45i | − | 0.0605070i | −0.999542 | − | 0.0302535i | \(-0.990369\pi\) | ||
0.999542 | − | 0.0302535i | \(-0.00963146\pi\) | |||||||
\(164\) | 1.85522e45 | − | 1.37233e46i | 0.0571051 | − | 0.422412i | ||||
\(165\) | −2.49736e46 | −0.676580 | ||||||||
\(166\) | −4.57549e46 | − | 5.23566e46i | −1.09186 | − | 1.24940i | ||||
\(167\) | − | 3.03185e46i | − | 0.637766i | −0.947794 | − | 0.318883i | \(-0.896692\pi\) | ||
0.947794 | − | 0.318883i | \(-0.103308\pi\) | |||||||
\(168\) | −2.85481e46 | − | 4.32110e46i | −0.529763 | − | 0.801861i | ||||
\(169\) | 1.70750e47 | 2.79730 | ||||||||
\(170\) | 6.28323e46 | − | 5.49097e46i | 0.909402 | − | 0.794734i | ||||
\(171\) | 4.00453e46i | 0.512428i | ||||||||
\(172\) | −3.36410e46 | − | 4.54787e45i | −0.380866 | − | 0.0514886i | ||||
\(173\) | −1.18082e47 | −1.18362 | −0.591812 | − | 0.806076i | \(-0.701587\pi\) | ||||
−0.591812 | + | 0.806076i | \(0.701587\pi\) | |||||||
\(174\) | 1.60137e46 | + | 1.83242e46i | 0.142219 | + | 0.162739i | ||||
\(175\) | 4.25789e46i | 0.335271i | ||||||||
\(176\) | −3.19928e46 | + | 1.16164e47i | −0.223504 | + | 0.811534i | ||||
\(177\) | −2.14445e46 | −0.133008 | ||||||||
\(178\) | −2.76084e46 | + | 2.41272e46i | −0.152132 | + | 0.132949i | ||||
\(179\) | 6.75465e45i | 0.0330894i | 0.999863 | + | 0.0165447i | \(0.00526659\pi\) | ||||
−0.999863 | + | 0.0165447i | \(0.994733\pi\) | |||||||
\(180\) | 1.66213e46 | − | 1.22949e47i | 0.0724339 | − | 0.535800i | ||||
\(181\) | −1.59754e47 | −0.619730 | −0.309865 | − | 0.950780i | \(-0.600284\pi\) | ||||
−0.309865 | + | 0.950780i | \(0.600284\pi\) | |||||||
\(182\) | 4.96229e47 | + | 5.67827e47i | 1.71468 | + | 1.96208i | ||||
\(183\) | 4.05340e47i | 1.24838i | ||||||||
\(184\) | −1.95011e47 | + | 1.28837e47i | −0.535654 | + | 0.353889i | ||||
\(185\) | −3.59050e47 | −0.880135 | ||||||||
\(186\) | 2.32875e47 | − | 2.03511e47i | 0.509742 | − | 0.445468i | ||||
\(187\) | − | 4.64778e47i | − | 0.909016i | ||||||
\(188\) | −8.50439e47 | − | 1.14969e47i | −1.48706 | − | 0.201033i | ||||
\(189\) | 9.11425e47 | 1.42568 | ||||||||
\(190\) | 5.57106e47 | + | 6.37488e47i | 0.780031 | + | 0.892578i | ||||
\(191\) | − | 1.30074e48i | − | 1.63114i | −0.578658 | − | 0.815570i | \(-0.696423\pi\) | ||
0.578658 | − | 0.815570i | \(-0.303577\pi\) | |||||||
\(192\) | 5.88293e47 | + | 2.50893e47i | 0.661101 | + | 0.281944i | ||||
\(193\) | −8.78035e47 | −0.884726 | −0.442363 | − | 0.896836i | \(-0.645860\pi\) | ||||
−0.442363 | + | 0.896836i | \(0.645860\pi\) | |||||||
\(194\) | 1.21457e48 | − | 1.06142e48i | 1.09796 | − | 0.959515i | ||||
\(195\) | − | 1.93019e48i | − | 1.56630i | ||||||
\(196\) | −1.44863e47 | + | 1.07156e48i | −0.105579 | + | 0.780981i | ||||
\(197\) | −2.97593e48 | −1.94909 | −0.974545 | − | 0.224191i | \(-0.928026\pi\) | ||||
−0.974545 | + | 0.224191i | \(0.928026\pi\) | |||||||
\(198\) | −4.54734e47 | − | 5.20345e47i | −0.267786 | − | 0.306424i | ||||
\(199\) | 2.69254e48i | 1.42642i | 0.700949 | + | 0.713211i | \(0.252760\pi\) | ||||
−0.700949 | + | 0.713211i | \(0.747240\pi\) | |||||||
\(200\) | −2.89844e47 | − | 4.38714e47i | −0.138208 | − | 0.209195i | ||||
\(201\) | 3.75113e47 | 0.161081 | ||||||||
\(202\) | 1.58265e48 | − | 1.38310e48i | 0.612361 | − | 0.535147i | ||||
\(203\) | − | 1.15282e48i | − | 0.402109i | ||||||
\(204\) | −2.44481e48 | − | 3.30509e47i | −0.769150 | − | 0.103980i | ||||
\(205\) | 1.67912e48 | 0.476706 | ||||||||
\(206\) | 3.82536e48 | + | 4.37730e48i | 0.980529 | + | 1.12200i | ||||
\(207\) | − | 1.34050e48i | − | 0.310377i | ||||||
\(208\) | −8.97825e48 | − | 2.47270e48i | −1.87872 | − | 0.517417i | ||||
\(209\) | 4.71557e48 | 0.892199 | ||||||||
\(210\) | 4.72848e48 | − | 4.13226e48i | 0.809312 | − | 0.707265i | ||||
\(211\) | 1.21220e49i | 1.87776i | 0.344239 | + | 0.938882i | \(0.388137\pi\) | ||||
−0.344239 | + | 0.938882i | \(0.611863\pi\) | |||||||
\(212\) | −2.30526e47 | + | 1.70523e48i | −0.0323346 | + | 0.239182i | ||||
\(213\) | 7.87891e48 | 1.00114 | ||||||||
\(214\) | 4.57804e47 | + | 5.23858e47i | 0.0527218 | + | 0.0603288i | ||||
\(215\) | − | 4.11617e48i | − | 0.429819i | ||||||
\(216\) | −9.39091e48 | + | 6.20427e48i | −0.889567 | + | 0.587708i | ||||
\(217\) | −1.46507e49 | −1.25952 | ||||||||
\(218\) | 2.32619e48 | − | 2.03288e48i | 0.181576 | − | 0.158681i | ||||
\(219\) | 8.09384e48i | 0.573890i | ||||||||
\(220\) | −1.44780e49 | − | 1.95725e48i | −0.932892 | − | 0.126116i | ||||
\(221\) | 3.59223e49 | 2.10439 | ||||||||
\(222\) | 6.98533e48 | + | 7.99321e48i | 0.372198 | + | 0.425901i | ||||
\(223\) | 1.96421e49i | 0.952325i | 0.879357 | + | 0.476162i | \(0.157973\pi\) | ||||
−0.879357 | + | 0.476162i | \(0.842027\pi\) | |||||||
\(224\) | −1.31636e49 | − | 2.72881e49i | −0.580988 | − | 1.20438i | ||||
\(225\) | 3.01570e48 | 0.121215 | ||||||||
\(226\) | 2.53183e48 | − | 2.21259e48i | 0.0927167 | − | 0.0810259i | ||||
\(227\) | 7.80948e48i | 0.260663i | 0.991470 | + | 0.130332i | \(0.0416042\pi\) | ||||
−0.991470 | + | 0.130332i | \(0.958396\pi\) | |||||||
\(228\) | 3.35330e48 | − | 2.48047e49i | 0.102056 | − | 0.754921i | ||||
\(229\) | −3.39479e49 | −0.942470 | −0.471235 | − | 0.882008i | \(-0.656192\pi\) | ||||
−0.471235 | + | 0.882008i | \(0.656192\pi\) | |||||||
\(230\) | −1.86489e49 | − | 2.13396e49i | −0.472463 | − | 0.540632i | ||||
\(231\) | − | 3.49771e49i | − | 0.808969i | ||||||
\(232\) | 7.84749e48 | + | 1.18781e49i | 0.165761 | + | 0.250900i | ||||
\(233\) | −2.49217e49 | −0.480953 | −0.240477 | − | 0.970655i | \(-0.577304\pi\) | ||||
−0.240477 | + | 0.970655i | \(0.577304\pi\) | |||||||
\(234\) | 4.02171e49 | − | 3.51460e49i | 0.709377 | − | 0.619931i | ||||
\(235\) | − | 1.04056e50i | − | 1.67819i | ||||||
\(236\) | −1.24320e49 | − | 1.68066e48i | −0.183396 | − | 0.0247929i | ||||
\(237\) | 1.13050e49 | 0.152601 | ||||||||
\(238\) | 7.69043e49 | + | 8.80004e49i | 0.950243 | + | 1.08735i | ||||
\(239\) | 2.26981e49i | 0.256823i | 0.991721 | + | 0.128412i | \(0.0409878\pi\) | ||||
−0.991721 | + | 0.128412i | \(0.959012\pi\) | |||||||
\(240\) | −2.05909e49 | + | 7.47647e49i | −0.213422 | + | 0.774926i | ||||
\(241\) | 5.53855e49 | 0.526064 | 0.263032 | − | 0.964787i | \(-0.415278\pi\) | ||||
0.263032 | + | 0.964787i | \(0.415278\pi\) | |||||||
\(242\) | 2.52049e49 | − | 2.20268e49i | 0.219464 | − | 0.191791i | ||||
\(243\) | − | 1.08068e50i | − | 0.862909i | ||||||
\(244\) | −3.17676e49 | + | 2.34988e50i | −0.232701 | + | 1.72131i | ||||
\(245\) | −1.31112e50 | −0.881362 | ||||||||
\(246\) | −3.26673e49 | − | 3.73807e49i | −0.201593 | − | 0.230680i | ||||
\(247\) | 3.64462e50i | 2.06546i | ||||||||
\(248\) | 1.50954e50 | − | 9.97306e49i | 0.785887 | − | 0.519210i | ||||
\(249\) | −2.49263e50 | −1.19253 | ||||||||
\(250\) | −1.43465e50 | + | 1.25376e50i | −0.630967 | + | 0.551408i | ||||
\(251\) | − | 6.78032e49i | − | 0.274222i | −0.990556 | − | 0.137111i | \(-0.956218\pi\) | ||
0.990556 | − | 0.137111i | \(-0.0437817\pi\) | |||||||
\(252\) | 1.72197e50 | + | 2.32791e49i | 0.640642 | + | 0.0866073i | ||||
\(253\) | −1.57851e50 | −0.540402 | ||||||||
\(254\) | 1.97171e50 | + | 2.25619e50i | 0.621347 | + | 0.710998i | ||||
\(255\) | − | 2.99136e50i | − | 0.868011i | ||||||
\(256\) | 3.21388e50 | + | 1.91556e50i | 0.858994 | + | 0.511985i | ||||
\(257\) | 4.98099e50 | 1.22665 | 0.613324 | − | 0.789831i | \(-0.289832\pi\) | ||||
0.613324 | + | 0.789831i | \(0.289832\pi\) | |||||||
\(258\) | −9.16345e49 | + | 8.00801e49i | −0.207991 | + | 0.181765i | ||||
\(259\) | − | 5.02872e50i | − | 1.05235i | ||||||
\(260\) | 1.51274e50 | − | 1.11899e51i | 0.291961 | − | 2.15966i | ||||
\(261\) | −8.16497e49 | −0.145380 | ||||||||
\(262\) | −7.33495e50 | − | 8.39328e50i | −1.20523 | − | 1.37913i | ||||
\(263\) | 4.90484e50i | 0.743968i | 0.928239 | + | 0.371984i | \(0.121322\pi\) | ||||
−0.928239 | + | 0.371984i | \(0.878678\pi\) | |||||||
\(264\) | 2.38096e50 | + | 3.60388e50i | 0.333481 | + | 0.504763i | ||||
\(265\) | −2.08644e50 | −0.269925 | ||||||||
\(266\) | −8.92839e50 | + | 7.80260e50i | −1.06723 | + | 0.932663i | ||||
\(267\) | 1.31440e50i | 0.145208i | ||||||||
\(268\) | 2.17464e50 | + | 2.93986e49i | 0.222104 | + | 0.0300259i | ||||
\(269\) | 4.60002e50 | 0.434472 | 0.217236 | − | 0.976119i | \(-0.430296\pi\) | ||||
0.217236 | + | 0.976119i | \(0.430296\pi\) | |||||||
\(270\) | −8.98050e50 | − | 1.02763e51i | −0.784624 | − | 0.897833i | ||||
\(271\) | 5.34679e50i | 0.432253i | 0.976365 | + | 0.216126i | \(0.0693423\pi\) | ||||
−0.976365 | + | 0.216126i | \(0.930658\pi\) | |||||||
\(272\) | −1.39143e51 | − | 3.83212e50i | −1.04115 | − | 0.286743i | ||||
\(273\) | 2.70335e51 | 1.87278 | ||||||||
\(274\) | 3.02243e50 | − | 2.64133e50i | 0.193907 | − | 0.169457i | ||||
\(275\) | − | 3.55116e50i | − | 0.211049i | ||||||
\(276\) | −1.12250e50 | + | 8.30324e50i | −0.0618153 | + | 0.457253i | ||||
\(277\) | −1.30079e51 | −0.663943 | −0.331972 | − | 0.943289i | \(-0.607714\pi\) | ||||
−0.331972 | + | 0.943289i | \(0.607714\pi\) | |||||||
\(278\) | 2.04503e50 | + | 2.34010e50i | 0.0967742 | + | 0.110737i | ||||
\(279\) | 1.03765e51i | 0.455370i | ||||||||
\(280\) | 3.06510e51 | − | 2.02501e51i | 1.24774 | − | 0.824344i | ||||
\(281\) | −9.36843e50 | −0.353862 | −0.176931 | − | 0.984223i | \(-0.556617\pi\) | ||||
−0.176931 | + | 0.984223i | \(0.556617\pi\) | |||||||
\(282\) | −2.31650e51 | + | 2.02441e51i | −0.812085 | + | 0.709688i | ||||
\(283\) | 4.65787e51i | 1.51591i | 0.652309 | + | 0.757953i | \(0.273801\pi\) | ||||
−0.652309 | + | 0.757953i | \(0.726199\pi\) | |||||||
\(284\) | 4.56764e51 | + | 6.17491e50i | 1.38041 | + | 0.186615i | ||||
\(285\) | 3.03499e51 | 0.851953 | ||||||||
\(286\) | −4.13865e51 | − | 4.73579e51i | −1.07937 | − | 1.23511i | ||||
\(287\) | 2.35171e51i | 0.569984i | ||||||||
\(288\) | −1.93271e51 | + | 9.32329e50i | −0.435436 | + | 0.210052i | ||||
\(289\) | 7.93447e50 | 0.166212 | ||||||||
\(290\) | −1.29980e51 | + | 1.13590e51i | −0.253231 | + | 0.221301i | ||||
\(291\) | − | 5.78240e51i | − | 1.04798i | ||||||
\(292\) | −6.34336e50 | + | 4.69224e51i | −0.106974 | + | 0.791299i | ||||
\(293\) | −4.50012e51 | −0.706324 | −0.353162 | − | 0.935562i | \(-0.614893\pi\) | ||||
−0.353162 | + | 0.935562i | \(0.614893\pi\) | |||||||
\(294\) | 2.55078e51 | + | 2.91882e51i | 0.372717 | + | 0.426495i | ||||
\(295\) | − | 1.52113e51i | − | 0.206968i | ||||||
\(296\) | 3.42316e51 | + | 5.18136e51i | 0.433811 | + | 0.656626i | ||||
\(297\) | −7.60146e51 | −0.897452 | ||||||||
\(298\) | 2.47826e51 | − | 2.16577e51i | 0.272650 | − | 0.238271i | ||||
\(299\) | − | 1.22002e52i | − | 1.25104i | ||||||
\(300\) | −1.86797e51 | − | 2.52528e50i | −0.178576 | − | 0.0241414i | ||||
\(301\) | 5.76494e51 | 0.513924 | ||||||||
\(302\) | 7.27684e51 | + | 8.32678e51i | 0.605058 | + | 0.692359i | ||||
\(303\) | − | 7.53480e51i | − | 0.584490i | ||||||
\(304\) | 3.88801e51 | − | 1.41172e52i | 0.281438 | − | 1.02189i | ||||
\(305\) | −2.87521e52 | −1.94255 | ||||||||
\(306\) | 6.23273e51 | − | 5.44684e51i | 0.393123 | − | 0.343554i | ||||
\(307\) | − | 2.88468e52i | − | 1.69899i | −0.527593 | − | 0.849497i | \(-0.676905\pi\) | ||
0.527593 | − | 0.849497i | \(-0.323095\pi\) | |||||||
\(308\) | 2.74125e51 | − | 2.02772e52i | 0.150794 | − | 1.11543i | ||||
\(309\) | 2.08397e52 | 1.07094 | ||||||||
\(310\) | 1.44357e52 | + | 1.65186e52i | 0.693175 | + | 0.793190i | ||||
\(311\) | 2.68748e52i | 1.20608i | 0.797710 | + | 0.603041i | \(0.206044\pi\) | ||||
−0.797710 | + | 0.603041i | \(0.793956\pi\) | |||||||
\(312\) | −2.78541e52 | + | 1.84023e52i | −1.16854 | + | 0.772014i | ||||
\(313\) | 3.94075e51 | 0.154578 | 0.0772890 | − | 0.997009i | \(-0.475374\pi\) | ||||
0.0772890 | + | 0.997009i | \(0.475374\pi\) | |||||||
\(314\) | 1.35711e51 | − | 1.18599e51i | 0.0497842 | − | 0.0435068i | ||||
\(315\) | 2.10694e52i | 0.722985i | ||||||||
\(316\) | 6.55386e51 | + | 8.86005e50i | 0.210411 | + | 0.0284451i | ||||
\(317\) | −3.19883e52 | −0.961052 | −0.480526 | − | 0.876980i | \(-0.659554\pi\) | ||||
−0.480526 | + | 0.876980i | \(0.659554\pi\) | |||||||
\(318\) | 4.05917e51 | + | 4.64485e51i | 0.114148 | + | 0.130618i | ||||
\(319\) | 9.61473e51i | 0.253124i | ||||||||
\(320\) | −1.77967e52 | + | 4.17296e52i | −0.438722 | + | 1.02871i | ||||
\(321\) | 2.49402e51 | 0.0575830 | ||||||||
\(322\) | 2.98874e52 | − | 2.61188e52i | 0.646420 | − | 0.564911i | ||||
\(323\) | 5.64834e52i | 1.14464i | ||||||||
\(324\) | −1.99509e51 | + | 1.47579e52i | −0.0378894 | + | 0.280271i | ||||
\(325\) | 2.74467e52 | 0.488584 | ||||||||
\(326\) | −2.38576e51 | − | 2.72999e51i | −0.0398160 | − | 0.0455608i | ||||
\(327\) | − | 1.10747e52i | − | 0.173312i | ||||||
\(328\) | −1.60086e52 | − | 2.42309e52i | −0.234964 | − | 0.355647i | ||||
\(329\) | 1.45737e53 | 2.00657 | ||||||||
\(330\) | −3.94364e52 | + | 3.44638e52i | −0.509454 | + | 0.445216i | ||||
\(331\) | − | 3.01946e52i | − | 0.366051i | −0.983108 | − | 0.183025i | \(-0.941411\pi\) | ||
0.983108 | − | 0.183025i | \(-0.0585891\pi\) | |||||||
\(332\) | −1.44505e53 | − | 1.95354e52i | −1.64431 | − | 0.222291i | ||||
\(333\) | −3.56165e52 | −0.380471 | ||||||||
\(334\) | −4.18397e52 | − | 4.78765e52i | −0.419675 | − | 0.480227i | ||||
\(335\) | 2.66080e52i | 0.250652i | ||||||||
\(336\) | −1.04712e53 | − | 2.88388e52i | −0.926559 | − | 0.255184i | ||||
\(337\) | 5.65477e51 | 0.0470097 | 0.0235048 | − | 0.999724i | \(-0.492517\pi\) | ||||
0.0235048 | + | 0.999724i | \(0.492517\pi\) | |||||||
\(338\) | 2.69634e53 | − | 2.35636e53i | 2.10632 | − | 1.84073i | ||||
\(339\) | − | 1.20537e52i | − | 0.0884968i | ||||||
\(340\) | 2.34441e52 | − | 1.73418e53i | 0.161799 | − | 1.19684i | ||||
\(341\) | 1.22190e53 | 0.792853 | ||||||||
\(342\) | 5.52628e52 | + | 6.32364e52i | 0.337198 | + | 0.385850i | ||||
\(343\) | 4.93778e52i | 0.283371i | ||||||||
\(344\) | −5.93994e52 | + | 3.92432e52i | −0.320667 | + | 0.211854i | ||||
\(345\) | −1.01595e53 | −0.516025 | ||||||||
\(346\) | −1.86465e53 | + | 1.62953e53i | −0.891250 | + | 0.778871i | ||||
\(347\) | 1.32477e53i | 0.595967i | 0.954571 | + | 0.297983i | \(0.0963140\pi\) | ||||
−0.954571 | + | 0.297983i | \(0.903686\pi\) | |||||||
\(348\) | 5.05751e52 | + | 6.83715e51i | 0.214177 | + | 0.0289542i | ||||
\(349\) | −3.71222e53 | −1.48013 | −0.740064 | − | 0.672536i | \(-0.765205\pi\) | ||||
−0.740064 | + | 0.672536i | \(0.765205\pi\) | |||||||
\(350\) | 5.87592e52 | + | 6.72373e52i | 0.220621 | + | 0.252454i | ||||
\(351\) | − | 5.87510e53i | − | 2.07762i | ||||||
\(352\) | 1.09787e53 | + | 2.27588e53i | 0.365726 | + | 0.758147i | ||||
\(353\) | 1.54798e52 | 0.0485844 | 0.0242922 | − | 0.999705i | \(-0.492267\pi\) | ||||
0.0242922 | + | 0.999705i | \(0.492267\pi\) | |||||||
\(354\) | −3.38634e52 | + | 2.95935e52i | −0.100153 | + | 0.0875242i | ||||
\(355\) | 5.58877e53i | 1.55783i | ||||||||
\(356\) | −1.03013e52 | + | 7.61995e52i | −0.0270671 | + | 0.200218i | ||||
\(357\) | 4.18958e53 | 1.03786 | ||||||||
\(358\) | 9.32147e51 | + | 1.06664e52i | 0.0217741 | + | 0.0249158i | ||||
\(359\) | − | 2.27556e53i | − | 0.501308i | −0.968077 | − | 0.250654i | \(-0.919354\pi\) | ||
0.968077 | − | 0.250654i | \(-0.0806456\pi\) | |||||||
\(360\) | −1.43424e53 | − | 2.17089e53i | −0.298036 | − | 0.451113i | ||||
\(361\) | −6.29773e52 | −0.123462 | ||||||||
\(362\) | −2.52272e53 | + | 2.20462e53i | −0.466647 | + | 0.407807i | ||||
\(363\) | − | 1.19997e53i | − | 0.209475i | ||||||
\(364\) | 1.56721e54 | + | 2.11869e53i | 2.58225 | + | 0.349090i | ||||
\(365\) | −5.74123e53 | −0.893007 | ||||||||
\(366\) | 5.59372e53 | + | 6.40081e53i | 0.821482 | + | 0.940009i | ||||
\(367\) | − | 3.78230e53i | − | 0.524527i | −0.964996 | − | 0.262264i | \(-0.915531\pi\) | ||
0.964996 | − | 0.262264i | \(-0.0844690\pi\) | |||||||
\(368\) | −1.30149e53 | + | 4.72567e53i | −0.170466 | + | 0.618955i | ||||
\(369\) | 1.66562e53 | 0.206074 | ||||||||
\(370\) | −5.66984e53 | + | 4.95492e53i | −0.662727 | + | 0.579163i | ||||
\(371\) | − | 2.92218e53i | − | 0.322742i | ||||||
\(372\) | 8.68906e52 | − | 6.42738e53i | 0.0906925 | − | 0.670861i | ||||
\(373\) | −1.48546e54 | −1.46546 | −0.732732 | − | 0.680517i | \(-0.761755\pi\) | ||||
−0.732732 | + | 0.680517i | \(0.761755\pi\) | |||||||
\(374\) | −6.41397e53 | − | 7.33940e53i | −0.598168 | − | 0.684474i | ||||
\(375\) | 6.83019e53i | 0.602249i | ||||||||
\(376\) | −1.50160e54 | + | 9.92061e53i | −1.25202 | + | 0.827168i | ||||
\(377\) | −7.43115e53 | −0.585986 | ||||||||
\(378\) | 1.43925e54 | − | 1.25777e54i | 1.07352 | − | 0.938155i | ||||
\(379\) | − | 9.57606e53i | − | 0.675715i | −0.941197 | − | 0.337857i | \(-0.890298\pi\) | ||
0.941197 | − | 0.337857i | \(-0.109702\pi\) | |||||||
\(380\) | 1.75948e54 | + | 2.37860e53i | 1.17470 | + | 0.158806i | ||||
\(381\) | 1.07414e54 | 0.678637 | ||||||||
\(382\) | −1.79504e54 | − | 2.05403e54i | −1.07335 | − | 1.22822i | ||||
\(383\) | 1.07845e54i | 0.610416i | 0.952286 | + | 0.305208i | \(0.0987259\pi\) | ||||
−0.952286 | + | 0.305208i | \(0.901274\pi\) | |||||||
\(384\) | 1.27522e54 | − | 4.15658e53i | 0.683329 | − | 0.222731i | ||||
\(385\) | 2.48104e54 | 1.25880 | ||||||||
\(386\) | −1.38652e54 | + | 1.21170e54i | −0.666184 | + | 0.582184i | ||||
\(387\) | − | 4.08309e53i | − | 0.185805i | ||||||
\(388\) | 4.53182e53 | − | 3.35223e54i | 0.195347 | − | 1.44500i | ||||
\(389\) | 3.04929e54 | 1.24525 | 0.622627 | − | 0.782519i | \(-0.286065\pi\) | ||||
0.622627 | + | 0.782519i | \(0.286065\pi\) | |||||||
\(390\) | −2.66368e54 | − | 3.04801e54i | −1.03068 | − | 1.17940i | ||||
\(391\) | − | 1.89076e54i | − | 0.693304i | ||||||
\(392\) | 1.25001e54 | + | 1.89204e54i | 0.434416 | + | 0.657541i | ||||
\(393\) | −3.99592e54 | −1.31636 | ||||||||
\(394\) | −4.69936e54 | + | 4.10681e54i | −1.46763 | + | 1.28258i | ||||
\(395\) | 8.01902e53i | 0.237456i | ||||||||
\(396\) | −1.43616e54 | − | 1.94152e53i | −0.403277 | − | 0.0545184i | ||||
\(397\) | 6.05630e54 | 1.61290 | 0.806449 | − | 0.591303i | \(-0.201386\pi\) | ||||
0.806449 | + | 0.591303i | \(0.201386\pi\) | |||||||
\(398\) | 3.71573e54 | + | 4.25185e54i | 0.938641 | + | 1.07407i | ||||
\(399\) | 4.25069e54i | 1.01866i | ||||||||
\(400\) | −1.06313e54 | − | 2.92796e53i | −0.241727 | − | 0.0665741i | ||||
\(401\) | −1.98234e54 | −0.427707 | −0.213854 | − | 0.976866i | \(-0.568602\pi\) | ||||
−0.213854 | + | 0.976866i | \(0.568602\pi\) | |||||||
\(402\) | 5.92349e53 | − | 5.17659e53i | 0.121292 | − | 0.105998i | ||||
\(403\) | 9.44395e54i | 1.83547i | ||||||||
\(404\) | 5.90523e53 | − | 4.36815e54i | 0.108950 | − | 0.805915i | ||||
\(405\) | −1.80571e54 | −0.316295 | ||||||||
\(406\) | −1.59090e54 | − | 1.82044e54i | −0.264604 | − | 0.302782i | ||||
\(407\) | 4.19405e54i | 0.662446i | ||||||||
\(408\) | −4.31675e54 | + | 2.85194e54i | −0.647581 | + | 0.427835i | ||||
\(409\) | 1.90826e54 | 0.271924 | 0.135962 | − | 0.990714i | \(-0.456588\pi\) | ||||
0.135962 | + | 0.990714i | \(0.456588\pi\) | |||||||
\(410\) | 2.65153e54 | − | 2.31720e54i | 0.358952 | − | 0.313691i | ||||
\(411\) | − | 1.43894e54i | − | 0.185082i | ||||||
\(412\) | 1.20814e55 | + | 1.63327e54i | 1.47665 | + | 0.199625i | ||||
\(413\) | 2.13043e54 | 0.247466 | ||||||||
\(414\) | −1.84990e54 | − | 2.11681e54i | −0.204240 | − | 0.233709i | ||||
\(415\) | − | 1.76810e55i | − | 1.85565i | ||||||
\(416\) | −1.75901e55 | + | 8.48536e54i | −1.75512 | + | 0.846662i | ||||
\(417\) | 1.11409e54 | 0.105697 | ||||||||
\(418\) | 7.44645e54 | − | 6.50752e54i | 0.671812 | − | 0.587102i | ||||
\(419\) | − | 7.27140e53i | − | 0.0623912i | −0.999513 | − | 0.0311956i | \(-0.990069\pi\) | ||
0.999513 | − | 0.0311956i | \(-0.00993148\pi\) | |||||||
\(420\) | 1.76430e54 | − | 1.30507e55i | 0.143991 | − | 1.06512i | ||||
\(421\) | −2.07884e55 | −1.61397 | −0.806987 | − | 0.590569i | \(-0.798903\pi\) | ||||
−0.806987 | + | 0.590569i | \(0.798903\pi\) | |||||||
\(422\) | 1.67284e55 | + | 1.91420e55i | 1.23564 | + | 1.41393i | ||||
\(423\) | − | 1.03220e55i | − | 0.725462i | ||||||
\(424\) | 1.98919e54 | + | 3.01089e54i | 0.133044 | + | 0.201378i | ||||
\(425\) | 4.25361e54 | 0.270764 | ||||||||
\(426\) | 1.24418e55 | − | 1.08730e55i | 0.753841 | − | 0.658788i | ||||
\(427\) | − | 4.02690e55i | − | 2.32266i | ||||||
\(428\) | 1.44586e54 | + | 1.95463e53i | 0.0793974 | + | 0.0107336i | ||||
\(429\) | −2.25464e55 | −1.17889 | ||||||||
\(430\) | −5.68035e54 | − | 6.49993e54i | −0.282838 | − | 0.323647i | ||||
\(431\) | 2.20526e55i | 1.04577i | 0.852403 | + | 0.522885i | \(0.175144\pi\) | ||||
−0.852403 | + | 0.522885i | \(0.824856\pi\) | |||||||
\(432\) | −6.26745e54 | + | 2.27568e55i | −0.283095 | + | 1.02790i | ||||
\(433\) | 6.62429e54 | 0.285032 | 0.142516 | − | 0.989792i | \(-0.454481\pi\) | ||||
0.142516 | + | 0.989792i | \(0.454481\pi\) | |||||||
\(434\) | −2.31352e55 | + | 2.02181e55i | −0.948396 | + | 0.828811i | ||||
\(435\) | 6.18815e54i | 0.241705i | ||||||||
\(436\) | 8.67951e53 | − | 6.42032e54i | 0.0323057 | − | 0.238968i | ||||
\(437\) | 1.91833e55 | 0.680478 | ||||||||
\(438\) | 1.11696e55 | + | 1.27812e55i | 0.377642 | + | 0.432130i | ||||
\(439\) | 2.63874e55i | 0.850435i | 0.905091 | + | 0.425217i | \(0.139802\pi\) | ||||
−0.905091 | + | 0.425217i | \(0.860198\pi\) | |||||||
\(440\) | −2.55635e55 | + | 1.68890e55i | −0.785442 | + | 0.518916i | ||||
\(441\) | −1.30058e55 | −0.381002 | ||||||||
\(442\) | 5.67257e55 | − | 4.95730e55i | 1.58457 | − | 1.38477i | ||||
\(443\) | 8.61061e54i | 0.229380i | 0.993401 | + | 0.114690i | \(0.0365875\pi\) | ||||
−0.993401 | + | 0.114690i | \(0.963413\pi\) | |||||||
\(444\) | 2.20614e55 | + | 2.98244e54i | 0.560519 | + | 0.0757756i | ||||
\(445\) | −9.32345e54 | −0.225952 | ||||||||
\(446\) | 2.71062e55 | + | 3.10172e55i | 0.626667 | + | 0.717085i | ||||
\(447\) | − | 1.17986e55i | − | 0.260240i | ||||||
\(448\) | −5.84447e55 | − | 2.49253e55i | −1.23001 | − | 0.524569i | ||||
\(449\) | −2.26658e55 | −0.455196 | −0.227598 | − | 0.973755i | \(-0.573087\pi\) | ||||
−0.227598 | + | 0.973755i | \(0.573087\pi\) | |||||||
\(450\) | 4.76216e54 | − | 4.16169e54i | 0.0912728 | − | 0.0797641i | ||||
\(451\) | − | 1.96137e55i | − | 0.358799i | ||||||
\(452\) | 9.44682e53 | − | 6.98790e54i | 0.0164960 | − | 0.122022i | ||||
\(453\) | 3.96426e55 | 0.660846 | ||||||||
\(454\) | 1.07771e55 | + | 1.23321e55i | 0.171526 | + | 0.196275i | ||||
\(455\) | 1.91757e56i | 2.91416i | ||||||||
\(456\) | −2.89353e55 | − | 4.37971e55i | −0.419920 | − | 0.635600i | ||||
\(457\) | 1.02108e56 | 1.41521 | 0.707605 | − | 0.706608i | \(-0.249776\pi\) | ||||
0.707605 | + | 0.706608i | \(0.249776\pi\) | |||||||
\(458\) | −5.36079e55 | + | 4.68483e55i | −0.709665 | + | 0.620182i | ||||
\(459\) | − | 9.10508e55i | − | 1.15138i | ||||||
\(460\) | −5.88976e55 | − | 7.96227e54i | −0.711514 | − | 0.0961883i | ||||
\(461\) | 9.25084e54 | 0.106773 | 0.0533865 | − | 0.998574i | \(-0.482998\pi\) | ||||
0.0533865 | + | 0.998574i | \(0.482998\pi\) | |||||||
\(462\) | −4.82686e55 | − | 5.52330e55i | −0.532333 | − | 0.609140i | ||||
\(463\) | − | 1.47039e56i | − | 1.54965i | −0.632178 | − | 0.774823i | \(-0.717839\pi\) | ||
0.632178 | − | 0.774823i | \(-0.282161\pi\) | |||||||
\(464\) | 2.87840e55 | + | 7.92741e54i | 0.289917 | + | 0.0798461i | ||||
\(465\) | 7.86427e55 | 0.757088 | ||||||||
\(466\) | −3.93543e55 | + | 3.43921e55i | −0.362150 | + | 0.316486i | ||||
\(467\) | 1.55618e56i | 1.36901i | 0.729010 | + | 0.684503i | \(0.239981\pi\) | ||||
−0.729010 | + | 0.684503i | \(0.760019\pi\) | |||||||
\(468\) | 1.50059e55 | − | 1.11000e56i | 0.126211 | − | 0.933596i | ||||
\(469\) | −3.72661e55 | −0.299698 | ||||||||
\(470\) | −1.43598e56 | − | 1.64317e56i | −1.10432 | − | 1.26365i | ||||
\(471\) | − | 6.46100e54i | − | 0.0475183i | ||||||
\(472\) | −2.19510e55 | + | 1.45023e55i | −0.154409 | + | 0.102013i | ||||
\(473\) | −4.80807e55 | −0.323509 | ||||||||
\(474\) | 1.78520e55 | − | 1.56010e55i | 0.114906 | − | 0.100417i | ||||
\(475\) | 4.31565e55i | 0.265755i | ||||||||
\(476\) | 2.42882e56 | + | 3.28349e55i | 1.43103 | + | 0.193459i | ||||
\(477\) | −2.06967e55 | −0.116685 | ||||||||
\(478\) | 3.13236e55 | + | 3.58431e55i | 0.169000 | + | 0.193384i | ||||
\(479\) | − | 2.37266e56i | − | 1.22515i | −0.790412 | − | 0.612575i | \(-0.790134\pi\) | ||
0.790412 | − | 0.612575i | \(-0.209866\pi\) | |||||||
\(480\) | 7.06602e55 | + | 1.46478e56i | 0.349228 | + | 0.723947i | ||||
\(481\) | −3.24154e56 | −1.53358 | ||||||||
\(482\) | 8.74605e55 | − | 7.64325e55i | 0.396118 | − | 0.346170i | ||||
\(483\) | − | 1.42290e56i | − | 0.616998i | ||||||
\(484\) | 9.40450e54 | − | 6.95660e55i | 0.0390466 | − | 0.288831i | ||||
\(485\) | 4.10164e56 | 1.63073 | ||||||||
\(486\) | −1.49135e56 | − | 1.70652e56i | −0.567828 | − | 0.649757i | ||||
\(487\) | 2.28960e56i | 0.834931i | 0.908693 | + | 0.417465i | \(0.137082\pi\) | ||||
−0.908693 | + | 0.417465i | \(0.862918\pi\) | |||||||
\(488\) | 2.74120e56 | + | 4.14913e56i | 0.957468 | + | 1.44924i | ||||
\(489\) | −1.29971e55 | −0.0434871 | ||||||||
\(490\) | −2.07042e56 | + | 1.80935e56i | −0.663652 | + | 0.579971i | ||||
\(491\) | 2.89726e56i | 0.889766i | 0.895589 | + | 0.444883i | \(0.146755\pi\) | ||||
−0.895589 | + | 0.444883i | \(0.853245\pi\) | |||||||
\(492\) | −1.03171e56 | − | 1.39475e55i | −0.303593 | − | 0.0410422i | ||||
\(493\) | −1.15166e56 | −0.324742 | ||||||||
\(494\) | 5.02961e56 | + | 5.75530e56i | 1.35915 | + | 1.55526i | ||||
\(495\) | − | 1.75722e56i | − | 0.455112i | ||||||
\(496\) | 1.00746e56 | − | 3.65805e56i | 0.250100 | − | 0.908101i | ||||
\(497\) | −7.82740e56 | −1.86266 | ||||||||
\(498\) | −3.93616e56 | + | 3.43984e56i | −0.897959 | + | 0.784734i | ||||
\(499\) | 4.36402e56i | 0.954497i | 0.878768 | + | 0.477249i | \(0.158366\pi\) | ||||
−0.878768 | + | 0.477249i | \(0.841634\pi\) | |||||||
\(500\) | −5.35300e55 | + | 3.95967e56i | −0.112261 | + | 0.830402i | ||||
\(501\) | −2.27934e56 | −0.458370 | ||||||||
\(502\) | −9.35689e55 | − | 1.07069e56i | −0.180449 | − | 0.206485i | ||||
\(503\) | − | 6.10709e56i | − | 1.12955i | −0.825244 | − | 0.564777i | \(-0.808962\pi\) | ||
0.825244 | − | 0.564777i | \(-0.191038\pi\) | |||||||
\(504\) | 3.04046e56 | − | 2.00873e56i | 0.539384 | − | 0.356354i | ||||
\(505\) | 5.34468e56 | 0.909501 | ||||||||
\(506\) | −2.49266e56 | + | 2.17836e56i | −0.406914 | + | 0.355606i | ||||
\(507\) | − | 1.28369e57i | − | 2.01045i | ||||||
\(508\) | 6.22713e56 | + | 8.41835e55i | 0.935728 | + | 0.126500i | ||||
\(509\) | 5.22818e55 | 0.0753837 | 0.0376918 | − | 0.999289i | \(-0.487999\pi\) | ||||
0.0376918 | + | 0.999289i | \(0.487999\pi\) | |||||||
\(510\) | −4.12810e56 | − | 4.72372e56i | −0.571185 | − | 0.653598i | ||||
\(511\) | − | 8.04093e56i | − | 1.06774i | ||||||
\(512\) | 7.71860e56 | − | 1.41027e56i | 0.983715 | − | 0.179735i | ||||
\(513\) | 9.23789e56 | 1.13008 | ||||||||
\(514\) | 7.86559e56 | − | 6.87381e56i | 0.923647 | − | 0.807183i | ||||
\(515\) | 1.47823e57i | 1.66644i | ||||||||
\(516\) | −3.41908e55 | + | 2.52913e56i | −0.0370054 | + | 0.273733i | ||||
\(517\) | −1.21547e57 | −1.26312 | ||||||||
\(518\) | −6.93967e56 | − | 7.94095e56i | −0.692490 | − | 0.792406i | ||||
\(519\) | 8.87735e56i | 0.850685i | ||||||||
\(520\) | −1.30533e57 | − | 1.97578e57i | −1.20130 | − | 1.81831i | ||||
\(521\) | 1.33475e56 | 0.117980 | 0.0589901 | − | 0.998259i | \(-0.481212\pi\) | ||||
0.0589901 | + | 0.998259i | \(0.481212\pi\) | |||||||
\(522\) | −1.28935e56 | + | 1.12677e56i | −0.109469 | + | 0.0956656i | ||||
\(523\) | − | 2.78450e56i | − | 0.227098i | −0.993532 | − | 0.113549i | \(-0.963778\pi\) | ||
0.993532 | − | 0.113549i | \(-0.0362218\pi\) | |||||||
\(524\) | −2.31656e57 | − | 3.13171e56i | −1.81504 | − | 0.245372i | ||||
\(525\) | 3.20108e56 | 0.240963 | ||||||||
\(526\) | 6.76872e56 | + | 7.74534e56i | 0.489560 | + | 0.560196i | ||||
\(527\) | 1.46360e57i | 1.01718i | ||||||||
\(528\) | 8.73321e56 | + | 2.40521e56i | 0.583259 | + | 0.160635i | ||||
\(529\) | 9.15853e56 | 0.587837 | ||||||||
\(530\) | −3.29474e56 | + | 2.87930e56i | −0.203249 | + | 0.177621i | ||||
\(531\) | − | 1.50890e56i | − | 0.0894696i | ||||||
\(532\) | −3.33138e56 | + | 2.46425e57i | −0.189880 | + | 1.40456i | ||||
\(533\) | 1.51593e57 | 0.830628 | ||||||||
\(534\) | 1.81388e56 | + | 2.07559e56i | 0.0955524 | + | 0.109339i | ||||
\(535\) | 1.76909e56i | 0.0896025i | ||||||||
\(536\) | 3.83973e56 | − | 2.53678e56i | 0.186999 | − | 0.123544i | ||||
\(537\) | 5.07814e55 | 0.0237818 | ||||||||
\(538\) | 7.26399e56 | − | 6.34806e56i | 0.327150 | − | 0.285899i | ||||
\(539\) | 1.53151e57i | 0.663370i | ||||||||
\(540\) | −2.83626e57 | − | 3.83429e56i | −1.18162 | − | 0.159741i | ||||
\(541\) | 1.78358e57 | 0.714742 | 0.357371 | − | 0.933962i | \(-0.383673\pi\) | ||||
0.357371 | + | 0.933962i | \(0.383673\pi\) | |||||||
\(542\) | 7.37861e56 | + | 8.44323e56i | 0.284439 | + | 0.325479i | ||||
\(543\) | 1.20103e57i | 0.445408i | ||||||||
\(544\) | −2.72607e57 | + | 1.31504e57i | −0.972656 | + | 0.469204i | ||||
\(545\) | 7.85563e56 | 0.269683 | ||||||||
\(546\) | 4.26892e57 | − | 3.73064e57i | 1.41017 | − | 1.23236i | ||||
\(547\) | − | 1.43548e57i | − | 0.456315i | −0.973624 | − | 0.228157i | \(-0.926730\pi\) | ||
0.973624 | − | 0.228157i | \(-0.0732701\pi\) | |||||||
\(548\) | 1.12773e56 | − | 8.34195e56i | 0.0344997 | − | 0.255197i | ||||
\(549\) | −2.85210e57 | −0.839741 | ||||||||
\(550\) | −4.90063e56 | − | 5.60772e56i | −0.138879 | − | 0.158917i | ||||
\(551\) | − | 1.16846e57i | − | 0.318735i | ||||||
\(552\) | 9.68597e56 | + | 1.46609e57i | 0.254345 | + | 0.384981i | ||||
\(553\) | −1.12311e57 | −0.283920 | ||||||||
\(554\) | −2.05410e57 | + | 1.79509e57i | −0.499938 | + | 0.436900i | ||||
\(555\) | 2.69934e57i | 0.632564i | ||||||||
\(556\) | 6.45871e56 | + | 8.73142e55i | 0.145739 | + | 0.0197022i | ||||
\(557\) | −1.17398e57 | −0.255095 | −0.127548 | − | 0.991832i | \(-0.540711\pi\) | ||||
−0.127548 | + | 0.991832i | \(0.540711\pi\) | |||||||
\(558\) | 1.43197e57 | + | 1.63858e57i | 0.299651 | + | 0.342886i | ||||
\(559\) | − | 3.71612e57i | − | 0.748931i | ||||||
\(560\) | 2.04563e57 | − | 7.42759e57i | 0.397081 | − | 1.44178i | ||||
\(561\) | −3.49419e57 | −0.653321 | ||||||||
\(562\) | −1.47939e57 | + | 1.29285e57i | −0.266452 | + | 0.232855i | ||||
\(563\) | − | 6.40650e57i | − | 1.11159i | −0.831319 | − | 0.555795i | \(-0.812414\pi\) | ||
0.831319 | − | 0.555795i | \(-0.187586\pi\) | |||||||
\(564\) | −8.64337e56 | + | 6.39358e57i | −0.144485 | + | 1.06877i | ||||
\(565\) | 8.55010e56 | 0.137706 | ||||||||
\(566\) | 6.42790e57 | + | 7.35535e57i | 0.997526 | + | 1.14145i | ||||
\(567\) | − | 2.52900e57i | − | 0.378186i | ||||||
\(568\) | 8.06500e57 | − | 5.32828e57i | 1.16222 | − | 0.767843i | ||||
\(569\) | −8.87740e57 | −1.23290 | −0.616451 | − | 0.787393i | \(-0.711430\pi\) | ||||
−0.616451 | + | 0.787393i | \(0.711430\pi\) | |||||||
\(570\) | 4.79262e57 | − | 4.18831e57i | 0.641507 | − | 0.560618i | ||||
\(571\) | − | 6.67045e57i | − | 0.860591i | −0.902688 | − | 0.430295i | \(-0.858409\pi\) | ||
0.902688 | − | 0.430295i | \(-0.141591\pi\) | |||||||
\(572\) | −1.30709e58 | − | 1.76703e57i | −1.62550 | − | 0.219749i | ||||
\(573\) | −9.77898e57 | −1.17232 | ||||||||
\(574\) | 3.24537e57 | + | 3.71363e57i | 0.375072 | + | 0.429189i | ||||
\(575\) | − | 1.44464e57i | − | 0.160967i | ||||||
\(576\) | −1.76537e57 | + | 4.13942e57i | −0.189654 | + | 0.444700i | ||||
\(577\) | 3.75671e57 | 0.389148 | 0.194574 | − | 0.980888i | \(-0.437667\pi\) | ||||
0.194574 | + | 0.980888i | \(0.437667\pi\) | |||||||
\(578\) | 1.25295e57 | − | 1.09496e57i | 0.125155 | − | 0.109374i | ||||
\(579\) | 6.60106e57i | 0.635863i | ||||||||
\(580\) | −4.84982e56 | + | 3.58746e57i | −0.0450544 | + | 0.333272i | ||||
\(581\) | 2.47633e58 | 2.21876 | ||||||||
\(582\) | −7.97975e57 | − | 9.13111e57i | −0.689615 | − | 0.789116i | ||||
\(583\) | 2.43716e57i | 0.203163i | ||||||||
\(584\) | 5.47364e57 | + | 8.28501e57i | 0.440156 | + | 0.666229i | ||||
\(585\) | 1.35814e58 | 1.05359 | ||||||||
\(586\) | −7.10623e57 | + | 6.21019e57i | −0.531850 | + | 0.464788i | ||||
\(587\) | − | 1.13033e58i | − | 0.816219i | −0.912933 | − | 0.408109i | \(-0.866188\pi\) | ||
0.912933 | − | 0.408109i | \(-0.133812\pi\) | |||||||
\(588\) | 8.05600e57 | + | 1.08908e57i | 0.561300 | + | 0.0758812i | ||||
\(589\) | −1.48495e58 | −0.998365 | ||||||||
\(590\) | −2.09917e57 | − | 2.40204e57i | −0.136193 | − | 0.155843i | ||||
\(591\) | 2.23730e58i | 1.40083i | ||||||||
\(592\) | 1.25559e58 | + | 3.45802e57i | 0.758738 | + | 0.208964i | ||||
\(593\) | −3.29525e58 | −1.92194 | −0.960969 | − | 0.276656i | \(-0.910774\pi\) | ||||
−0.960969 | + | 0.276656i | \(0.910774\pi\) | |||||||
\(594\) | −1.20036e58 | + | 1.04901e58i | −0.675767 | + | 0.590558i | ||||
\(595\) | 2.97181e58i | 1.61497i | ||||||||
\(596\) | 9.24691e56 | − | 6.84003e57i | 0.0485093 | − | 0.358828i | ||||
\(597\) | 2.02425e58 | 1.02519 | ||||||||
\(598\) | −1.68364e58 | − | 1.92656e58i | −0.823235 | − | 0.942015i | ||||
\(599\) | 5.10173e57i | 0.240854i | 0.992722 | + | 0.120427i | \(0.0384264\pi\) | ||||
−0.992722 | + | 0.120427i | \(0.961574\pi\) | |||||||
\(600\) | −3.29824e57 | + | 2.17904e57i | −0.150351 | + | 0.0993321i | ||||
\(601\) | 1.55884e58 | 0.686178 | 0.343089 | − | 0.939303i | \(-0.388527\pi\) | ||||
0.343089 | + | 0.939303i | \(0.388527\pi\) | |||||||
\(602\) | 9.10354e57 | − | 7.95566e57i | 0.386976 | − | 0.338182i | ||||
\(603\) | 2.63941e57i | 0.108354i | ||||||||
\(604\) | 2.29820e58 | + | 3.10690e57i | 0.911198 | + | 0.123183i | ||||
\(605\) | 8.51179e57 | 0.325955 | ||||||||
\(606\) | −1.03981e58 | − | 1.18984e58i | −0.384617 | − | 0.440111i | ||||
\(607\) | 2.55219e58i | 0.911905i | 0.890004 | + | 0.455953i | \(0.150701\pi\) | ||||
−0.890004 | + | 0.455953i | \(0.849299\pi\) | |||||||
\(608\) | −1.33422e58 | − | 2.76583e58i | −0.460524 | − | 0.954662i | ||||
\(609\) | −8.66687e57 | −0.289001 | ||||||||
\(610\) | −4.54030e58 | + | 3.96781e58i | −1.46271 | + | 1.27827i | ||||
\(611\) | − | 9.39428e58i | − | 2.92414i | ||||||
\(612\) | 2.32557e57 | − | 1.72024e58i | 0.0699438 | − | 0.517381i | ||||
\(613\) | 5.28802e58 | 1.53682 | 0.768410 | − | 0.639958i | \(-0.221048\pi\) | ||||
0.768410 | + | 0.639958i | \(0.221048\pi\) | |||||||
\(614\) | −3.98088e58 | − | 4.55526e58i | −1.11800 | − | 1.27932i | ||||
\(615\) | − | 1.26236e58i | − | 0.342614i | ||||||
\(616\) | −2.36540e58 | − | 3.58032e58i | −0.620454 | − | 0.939132i | ||||
\(617\) | 3.28812e58 | 0.833602 | 0.416801 | − | 0.908998i | \(-0.363151\pi\) | ||||
0.416801 | + | 0.908998i | \(0.363151\pi\) | |||||||
\(618\) | 3.29085e58 | − | 2.87590e58i | 0.806398 | − | 0.704718i | ||||
\(619\) | 5.81480e58i | 1.37731i | 0.725090 | + | 0.688654i | \(0.241798\pi\) | ||||
−0.725090 | + | 0.688654i | \(0.758202\pi\) | |||||||
\(620\) | 4.55915e58 | + | 6.16344e57i | 1.04390 | + | 0.141123i | ||||
\(621\) | −3.09234e58 | −0.684484 | ||||||||
\(622\) | 3.70874e58 | + | 4.24385e58i | 0.793649 | + | 0.908160i | ||||
\(623\) | − | 1.30580e58i | − | 0.270165i | ||||||
\(624\) | −1.85897e58 | + | 6.74983e58i | −0.371874 | + | 1.35026i | ||||
\(625\) | −6.14111e58 | −1.18786 | ||||||||
\(626\) | 6.22292e57 | − | 5.43827e57i | 0.116395 | − | 0.101718i | ||||
\(627\) | − | 3.54515e58i | − | 0.641234i | ||||||
\(628\) | 5.06366e56 | − | 3.74563e57i | 0.00885751 | − | 0.0655198i | ||||
\(629\) | −5.02366e58 | −0.849878 | ||||||||
\(630\) | 2.90759e58 | + | 3.32711e58i | 0.475753 | + | 0.544396i | ||||
\(631\) | − | 3.70156e58i | − | 0.585825i | −0.956139 | − | 0.292913i | \(-0.905375\pi\) | ||
0.956139 | − | 0.292913i | \(-0.0946245\pi\) | |||||||
\(632\) | 1.15720e58 | − | 7.64527e57i | 0.177154 | − | 0.117040i | ||||
\(633\) | 9.11326e58 | 1.34957 | ||||||||
\(634\) | −5.05135e58 | + | 4.41441e58i | −0.723657 | + | 0.632410i | ||||
\(635\) | 7.61925e58i | 1.05600i | ||||||||
\(636\) | 1.28199e58 | + | 1.73309e57i | 0.171903 | + | 0.0232393i | ||||
\(637\) | −1.18369e59 | −1.53571 | ||||||||
\(638\) | 1.32684e58 | + | 1.51828e58i | 0.166565 | + | 0.190598i | ||||
\(639\) | 5.54385e58i | 0.673431i | ||||||||
\(640\) | 2.94840e58 | + | 9.04556e58i | 0.346582 | + | 1.06330i | ||||
\(641\) | −3.15478e58 | −0.358881 | −0.179440 | − | 0.983769i | \(-0.557429\pi\) | ||||
−0.179440 | + | 0.983769i | \(0.557429\pi\) | |||||||
\(642\) | 3.93836e57 | − | 3.44176e57i | 0.0433590 | − | 0.0378918i | ||||
\(643\) | 7.19598e57i | 0.0766760i | 0.999265 | + | 0.0383380i | \(0.0122064\pi\) | ||||
−0.999265 | + | 0.0383380i | \(0.987794\pi\) | |||||||
\(644\) | 1.11516e58 | − | 8.24896e58i | 0.115010 | − | 0.850739i | ||||
\(645\) | −3.09453e58 | −0.308916 | ||||||||
\(646\) | 7.79475e58 | + | 8.91942e58i | 0.753216 | + | 0.861894i | ||||
\(647\) | − | 8.89244e58i | − | 0.831823i | −0.909405 | − | 0.415912i | \(-0.863463\pi\) | ||
0.909405 | − | 0.415912i | \(-0.136537\pi\) | |||||||
\(648\) | 1.72155e58 | + | 2.60577e58i | 0.155899 | + | 0.235972i | ||||
\(649\) | −1.77682e58 | −0.155777 | ||||||||
\(650\) | 4.33416e58 | − | 3.78766e58i | 0.367896 | − | 0.321507i | ||||
\(651\) | 1.10144e59i | 0.905230i | ||||||||
\(652\) | −7.53481e57 | − | 1.01862e57i | −0.0599616 | − | 0.00810610i | ||||
\(653\) | 1.50401e59 | 1.15898 | 0.579488 | − | 0.814981i | \(-0.303253\pi\) | ||||
0.579488 | + | 0.814981i | \(0.303253\pi\) | |||||||
\(654\) | −1.52831e58 | − | 1.74882e58i | −0.114046 | − | 0.130501i | ||||
\(655\) | − | 2.83444e59i | − | 2.04833i | ||||||
\(656\) | −5.87183e58 | − | 1.61716e58i | −0.410954 | − | 0.113181i | ||||
\(657\) | −5.69509e58 | −0.386036 | ||||||||
\(658\) | 2.30136e59 | − | 2.01118e59i | 1.51092 | − | 1.32040i | ||||
\(659\) | 5.37852e58i | 0.342034i | 0.985268 | + | 0.171017i | \(0.0547053\pi\) | ||||
−0.985268 | + | 0.171017i | \(0.945295\pi\) | |||||||
\(660\) | −1.47146e58 | + | 1.08845e59i | −0.0906411 | + | 0.670481i | ||||
\(661\) | 9.15978e58 | 0.546581 | 0.273290 | − | 0.961932i | \(-0.411888\pi\) | ||||
0.273290 | + | 0.961932i | \(0.411888\pi\) | |||||||
\(662\) | −4.16688e58 | − | 4.76809e58i | −0.240876 | − | 0.275630i | ||||
\(663\) | − | 2.70063e59i | − | 1.51245i | ||||||
\(664\) | −2.55150e59 | + | 1.68569e59i | −1.38441 | + | 0.914637i | ||||
\(665\) | −3.01515e59 | −1.58509 | ||||||||
\(666\) | −5.62428e58 | + | 4.91510e58i | −0.286489 | + | 0.250365i | ||||
\(667\) | 3.91136e58i | 0.193057i | ||||||||
\(668\) | −1.32140e59 | − | 1.78638e58i | −0.632017 | − | 0.0854412i | ||||
\(669\) | 1.47669e59 | 0.684448 | ||||||||
\(670\) | 3.67192e58 | + | 4.20172e58i | 0.164939 | + | 0.188737i | ||||
\(671\) | 3.35851e59i | 1.46209i | ||||||||
\(672\) | −2.05151e59 | + | 9.89638e58i | −0.865605 | + | 0.417563i | ||||
\(673\) | −4.69261e58 | −0.191910 | −0.0959552 | − | 0.995386i | \(-0.530591\pi\) | ||||
−0.0959552 | + | 0.995386i | \(0.530591\pi\) | |||||||
\(674\) | 8.92958e57 | − | 7.80363e57i | 0.0353975 | − | 0.0309342i | ||||
\(675\) | − | 6.95680e58i | − | 0.267319i | ||||||
\(676\) | 1.00606e59 | − | 7.44195e59i | 0.374753 | − | 2.77208i | ||||
\(677\) | 4.75164e59 | 1.71586 | 0.857929 | − | 0.513768i | \(-0.171751\pi\) | ||||
0.857929 | + | 0.513768i | \(0.171751\pi\) | |||||||
\(678\) | −1.66342e58 | − | 1.90343e58i | −0.0582343 | − | 0.0666367i | ||||
\(679\) | 5.74459e59i | 1.94982i | ||||||||
\(680\) | −2.02297e59 | − | 3.06201e59i | −0.665737 | − | 1.00767i | ||||
\(681\) | 5.87116e58 | 0.187342 | ||||||||
\(682\) | 1.92952e59 | − | 1.68623e59i | 0.597006 | − | 0.521728i | ||||
\(683\) | − | 2.38223e59i | − | 0.714740i | −0.933963 | − | 0.357370i | \(-0.883674\pi\) | ||
0.933963 | − | 0.357370i | \(-0.116326\pi\) | |||||||
\(684\) | 1.74533e59 | + | 2.35949e58i | 0.507809 | + | 0.0686498i | ||||
\(685\) | 1.02069e59 | 0.287998 | ||||||||
\(686\) | 6.81418e58 | + | 7.79736e58i | 0.186469 | + | 0.213374i | ||||
\(687\) | 2.55220e59i | 0.677365i | ||||||||
\(688\) | −3.96429e58 | + | 1.43941e59i | −0.102049 | + | 0.370534i | ||||
\(689\) | −1.88366e59 | −0.470326 | ||||||||
\(690\) | −1.60431e59 | + | 1.40202e59i | −0.388559 | + | 0.339565i | ||||
\(691\) | − | 4.10554e58i | − | 0.0964565i | −0.998836 | − | 0.0482282i | \(-0.984643\pi\) | ||
0.998836 | − | 0.0482282i | \(-0.0153575\pi\) | |||||||
\(692\) | −6.95742e58 | + | 5.14646e59i | −0.158570 | + | 1.17295i | ||||
\(693\) | 2.46110e59 | 0.544165 | ||||||||
\(694\) | 1.82819e59 | + | 2.09198e59i | 0.392169 | + | 0.448753i | ||||
\(695\) | 7.90260e58i | 0.164471i | ||||||||
\(696\) | 8.92995e58 | − | 5.89973e58i | 0.180325 | − | 0.119135i | ||||
\(697\) | 2.34934e59 | 0.460318 | ||||||||
\(698\) | −5.86204e59 | + | 5.12289e59i | −1.11451 | + | 0.973982i | ||||
\(699\) | 1.87361e59i | 0.345667i | ||||||||
\(700\) | 1.85576e59 | + | 2.50877e58i | 0.332248 | + | 0.0449161i | ||||
\(701\) | −3.63509e59 | −0.631593 | −0.315796 | − | 0.948827i | \(-0.602272\pi\) | ||||
−0.315796 | + | 0.948827i | \(0.602272\pi\) | |||||||
\(702\) | −8.10769e59 | − | 9.27751e59i | −1.36715 | − | 1.56441i | ||||
\(703\) | − | 5.09693e59i | − | 0.834156i | ||||||
\(704\) | 4.87440e59 | + | 2.07882e59i | 0.774275 | + | 0.330210i | ||||
\(705\) | −7.82291e59 | −1.20614 | ||||||||
\(706\) | 2.44445e58 | − | 2.13623e58i | 0.0365833 | − | 0.0319704i | ||||
\(707\) | 7.48555e59i | 1.08747i | ||||||||
\(708\) | −1.26352e58 | + | 9.34636e58i | −0.0178190 | + | 0.131809i | ||||
\(709\) | 4.75727e59 | 0.651308 | 0.325654 | − | 0.945489i | \(-0.394416\pi\) | ||||
0.325654 | + | 0.945489i | \(0.394416\pi\) | |||||||
\(710\) | 7.71254e59 | + | 8.82534e59i | 1.02511 | + | 1.17302i | ||||
\(711\) | 7.95457e58i | 0.102649i | ||||||||
\(712\) | 8.88889e58 | + | 1.34544e59i | 0.111370 | + | 0.168572i | ||||
\(713\) | 4.97078e59 | 0.604707 | ||||||||
\(714\) | 6.61586e59 | − | 5.78165e59i | 0.781490 | − | 0.682951i | ||||
\(715\) | − | 1.59929e60i | − | 1.83443i | ||||||
\(716\) | 2.94395e58 | + | 3.97987e57i | 0.0327912 | + | 0.00443298i | ||||
\(717\) | 1.70644e59 | 0.184582 | ||||||||
\(718\) | −3.14029e59 | − | 3.59338e59i | −0.329880 | − | 0.377477i | ||||
\(719\) | − | 4.79953e59i | − | 0.489657i | −0.969566 | − | 0.244829i | \(-0.921268\pi\) | ||
0.969566 | − | 0.244829i | \(-0.0787317\pi\) | |||||||
\(720\) | −5.26068e59 | − | 1.44884e59i | −0.521266 | − | 0.143562i | ||||
\(721\) | −2.07035e60 | −1.99252 | ||||||||
\(722\) | −9.94488e58 | + | 8.69091e58i | −0.0929648 | + | 0.0812427i | ||||
\(723\) | − | 4.16387e59i | − | 0.378088i | ||||||
\(724\) | −9.41280e58 | + | 6.96274e59i | −0.0830250 | + | 0.614144i | ||||
\(725\) | −8.79933e58 | −0.0753966 | ||||||||
\(726\) | −1.65597e59 | − | 1.89490e59i | −0.137843 | − | 0.157731i | ||||
\(727\) | − | 1.68327e60i | − | 1.36123i | −0.732643 | − | 0.680613i | \(-0.761713\pi\) | ||
0.732643 | − | 0.680613i | \(-0.238287\pi\) | |||||||
\(728\) | 2.76720e60 | − | 1.82820e60i | 2.17411 | − | 1.43636i | ||||
\(729\) | −1.18295e60 | −0.903004 | ||||||||
\(730\) | −9.06610e59 | + | 7.92294e59i | −0.672420 | + | 0.587633i | ||||
\(731\) | − | 5.75915e59i | − | 0.415043i | ||||||
\(732\) | 1.76663e60 | + | 2.38828e59i | 1.23712 | + | 0.167245i | ||||
\(733\) | −6.39885e59 | −0.435430 | −0.217715 | − | 0.976012i | \(-0.569860\pi\) | ||||
−0.217715 | + | 0.976012i | \(0.569860\pi\) | |||||||
\(734\) | −5.21960e59 | − | 5.97271e59i | −0.345159 | − | 0.394961i | ||||
\(735\) | 9.85697e59i | 0.633446i | ||||||||
\(736\) | 4.46624e59 | + | 9.25847e59i | 0.278938 | + | 0.578236i | ||||
\(737\) | 3.10806e59 | 0.188657 | ||||||||
\(738\) | 2.63022e59 | − | 2.29857e59i | 0.155170 | − | 0.135605i | ||||
\(739\) | 1.71279e60i | 0.982132i | 0.871122 | + | 0.491066i | \(0.163393\pi\) | ||||
−0.871122 | + | 0.491066i | \(0.836607\pi\) | |||||||
\(740\) | −2.11554e59 | + | 1.56489e60i | −0.117911 | + | 0.872201i | ||||
\(741\) | 2.74002e60 | 1.48447 | ||||||||
\(742\) | −4.03264e59 | − | 4.61449e59i | −0.212377 | − | 0.243020i | ||||
\(743\) | 3.39513e60i | 1.73816i | 0.494668 | + | 0.869082i | \(0.335290\pi\) | ||||
−0.494668 | + | 0.869082i | \(0.664710\pi\) | |||||||
\(744\) | −7.49773e59 | − | 1.13487e60i | −0.373162 | − | 0.564826i | ||||
\(745\) | 8.36916e59 | 0.404949 | ||||||||
\(746\) | −2.34572e60 | + | 2.04994e60i | −1.10347 | + | 0.964332i | ||||
\(747\) | − | 1.75389e60i | − | 0.802177i | ||||||
\(748\) | −2.02569e60 | − | 2.73849e59i | −0.900821 | − | 0.121780i | ||||
\(749\) | −2.47771e59 | −0.107135 | ||||||||
\(750\) | 9.42572e59 | + | 1.07857e60i | 0.396303 | + | 0.453484i | ||||
\(751\) | − | 6.43064e59i | − | 0.262915i | −0.991322 | − | 0.131458i | \(-0.958034\pi\) | ||
0.991322 | − | 0.131458i | \(-0.0419657\pi\) | |||||||
\(752\) | −1.00216e60 | + | 3.63881e60i | −0.398441 | + | 1.44672i | ||||
\(753\) | −5.09743e59 | −0.197086 | ||||||||
\(754\) | −1.17347e60 | + | 1.02550e60i | −0.441238 | + | 0.385602i | ||||
\(755\) | 2.81198e60i | 1.02832i | ||||||||
\(756\) | 5.37015e59 | − | 3.97235e60i | 0.190998 | − | 1.41283i | ||||
\(757\) | 1.59596e60 | 0.552088 | 0.276044 | − | 0.961145i | \(-0.410977\pi\) | ||||
0.276044 | + | 0.961145i | \(0.410977\pi\) | |||||||
\(758\) | −1.32150e60 | − | 1.51218e60i | −0.444647 | − | 0.508802i | ||||
\(759\) | 1.18672e60i | 0.388394i | ||||||||
\(760\) | 3.10668e60 | − | 2.05248e60i | 0.989032 | − | 0.653421i | ||||
\(761\) | 3.03237e60 | 0.939083 | 0.469541 | − | 0.882910i | \(-0.344419\pi\) | ||||
0.469541 | + | 0.882910i | \(0.344419\pi\) | |||||||
\(762\) | 1.69620e60 | − | 1.48233e60i | 0.511003 | − | 0.446570i | ||||
\(763\) | 1.10023e60i | 0.322453i | ||||||||
\(764\) | −5.66917e60 | − | 7.66405e59i | −1.61644 | − | 0.218523i | ||||
\(765\) | 2.10482e60 | 0.583881 | ||||||||
\(766\) | 1.48827e60 | + | 1.70300e60i | 0.401677 | + | 0.459633i | ||||
\(767\) | − | 1.37329e60i | − | 0.360628i | ||||||
\(768\) | 1.44012e60 | − | 2.41619e60i | 0.367970 | − | 0.617370i | ||||
\(769\) | −7.39821e60 | −1.83939 | −0.919694 | − | 0.392636i | \(-0.871563\pi\) | ||||
−0.919694 | + | 0.392636i | \(0.871563\pi\) | |||||||
\(770\) | 3.91786e60 | − | 3.42385e60i | 0.947859 | − | 0.828342i | ||||
\(771\) | − | 3.74470e60i | − | 0.881607i | ||||||
\(772\) | −5.17342e59 | + | 3.82683e60i | −0.118526 | + | 0.876750i | ||||
\(773\) | 5.30130e60 | 1.18199 | 0.590993 | − | 0.806676i | \(-0.298736\pi\) | ||||
0.590993 | + | 0.806676i | \(0.298736\pi\) | |||||||
\(774\) | −5.63469e59 | − | 6.44769e59i | −0.122267 | − | 0.139909i | ||||
\(775\) | 1.11827e60i | 0.236163i | ||||||||
\(776\) | −3.91047e60 | − | 5.91897e60i | −0.803772 | − | 1.21661i | ||||
\(777\) | −3.78058e60 | −0.756340 | ||||||||
\(778\) | 4.81521e60 | − | 4.20805e60i | 0.937656 | − | 0.819425i | ||||
\(779\) | 2.38361e60i | 0.451802i | ||||||||
\(780\) | −8.41255e60 | − | 1.13728e60i | −1.55218 | − | 0.209836i | ||||
\(781\) | 6.52820e60 | 1.17252 | ||||||||
\(782\) | −2.60926e60 | − | 2.98573e60i | −0.456221 | − | 0.522047i | ||||
\(783\) | 1.88354e60i | 0.320611i | ||||||||
\(784\) | 4.58495e60 | + | 1.26274e60i | 0.759796 | + | 0.209255i | ||||
\(785\) | 4.58300e59 | 0.0739413 | ||||||||
\(786\) | −6.31005e60 | + | 5.51441e60i | −0.991196 | + | 0.866214i | ||||
\(787\) | − | 6.74513e60i | − | 1.03162i | −0.856702 | − | 0.515811i | \(-0.827491\pi\) | ||
0.856702 | − | 0.515811i | \(-0.172509\pi\) | |||||||
\(788\) | −1.75343e60 | + | 1.29703e61i | −0.261119 | + | 1.93152i | ||||
\(789\) | 3.68745e60 | 0.534699 | ||||||||
\(790\) | 1.10663e60 | + | 1.26630e60i | 0.156255 | + | 0.178800i | ||||
\(791\) | 1.19749e60i | 0.164652i | ||||||||
\(792\) | −2.53580e60 | + | 1.67532e60i | −0.339537 | + | 0.224321i | ||||
\(793\) | −2.59577e61 | −3.38477 | ||||||||
\(794\) | 9.56364e60 | − | 8.35775e60i | 1.21449 | − | 1.06135i | ||||
\(795\) | 1.56858e60i | 0.193998i | ||||||||
\(796\) | 1.17352e61 | + | 1.58646e60i | 1.41356 | + | 0.191097i | ||||
\(797\) | 6.46199e60 | 0.758126 | 0.379063 | − | 0.925371i | \(-0.376246\pi\) | ||||
0.379063 | + | 0.925371i | \(0.376246\pi\) | |||||||
\(798\) | 5.86598e60 | + | 6.71235e60i | 0.670316 | + | 0.767033i | ||||
\(799\) | − | 1.45590e61i | − | 1.62050i | ||||||
\(800\) | −2.08287e60 | + | 1.00476e60i | −0.225825 | + | 0.108937i | ||||
\(801\) | −9.24851e59 | −0.0976763 | ||||||||
\(802\) | −3.13036e60 | + | 2.73565e60i | −0.322057 | + | 0.281448i | ||||
\(803\) | 6.70629e60i | 0.672134i | ||||||||
\(804\) | 2.21018e59 | − | 1.63489e60i | 0.0215800 | − | 0.159629i | ||||
\(805\) | 1.00931e61 | 0.960086 | ||||||||
\(806\) | 1.30327e61 | + | 1.49131e61i | 1.20781 | + | 1.38208i | ||||
\(807\) | − | 3.45828e60i | − | 0.312260i | ||||||
\(808\) | −5.09557e60 | − | 7.71277e60i | −0.448285 | − | 0.678534i | ||||
\(809\) | −1.09013e61 | −0.934455 | −0.467227 | − | 0.884137i | \(-0.654747\pi\) | ||||
−0.467227 | + | 0.884137i | \(0.654747\pi\) | |||||||
\(810\) | −2.85143e60 | + | 2.49189e60i | −0.238165 | + | 0.208134i | ||||
\(811\) | − | 7.79618e59i | − | 0.0634518i | −0.999497 | − | 0.0317259i | \(-0.989900\pi\) | ||
0.999497 | − | 0.0317259i | \(-0.0101004\pi\) | |||||||
\(812\) | −5.02444e60 | − | 6.79246e59i | −0.398484 | − | 0.0538704i | ||||
\(813\) | 4.01970e60 | 0.310665 | ||||||||
\(814\) | 5.78781e60 | + | 6.62291e60i | 0.435915 | + | 0.498811i | ||||
\(815\) | − | 9.21928e59i | − | 0.0676686i | ||||||
\(816\) | −2.88098e60 | + | 1.04607e61i | −0.206085 | + | 0.748286i | ||||
\(817\) | 5.84315e60 | 0.407365 | ||||||||
\(818\) | 3.01337e60 | − | 2.63341e60i | 0.204754 | − | 0.178936i | ||||
\(819\) | 1.90216e61i | 1.25975i | ||||||||
\(820\) | 9.89344e59 | − | 7.31827e60i | 0.0638641 | − | 0.472408i | ||||
\(821\) | −2.21652e61 | −1.39465 | −0.697326 | − | 0.716754i | \(-0.745627\pi\) | ||||
−0.697326 | + | 0.716754i | \(0.745627\pi\) | |||||||
\(822\) | −1.98575e60 | − | 2.27226e60i | −0.121791 | − | 0.139364i | ||||
\(823\) | − | 6.02862e59i | − | 0.0360430i | −0.999838 | − | 0.0180215i | \(-0.994263\pi\) | ||
0.999838 | − | 0.0180215i | \(-0.00573674\pi\) | |||||||
\(824\) | 2.13319e61 | − | 1.40933e61i | 1.24325 | − | 0.821376i | ||||
\(825\) | −2.66976e60 | −0.151684 | ||||||||
\(826\) | 3.36420e60 | − | 2.94001e60i | 0.186338 | − | 0.162842i | ||||
\(827\) | − | 1.02519e60i | − | 0.0553589i | −0.999617 | − | 0.0276794i | \(-0.991188\pi\) | ||
0.999617 | − | 0.0276794i | \(-0.00881176\pi\) | |||||||
\(828\) | −5.84243e60 | − | 7.89827e59i | −0.307579 | − | 0.0415810i | ||||
\(829\) | 1.03234e61 | 0.529880 | 0.264940 | − | 0.964265i | \(-0.414648\pi\) | ||||
0.264940 | + | 0.964265i | \(0.414648\pi\) | |||||||
\(830\) | −2.43999e61 | − | 2.79205e61i | −1.22109 | − | 1.39728i | ||||
\(831\) | 9.77929e60i | 0.477184i | ||||||||
\(832\) | −1.60670e61 | + | 3.76739e61i | −0.764444 | + | 1.79246i | ||||
\(833\) | −1.83445e61 | −0.851063 | ||||||||
\(834\) | 1.75928e60 | − | 1.53745e60i | 0.0795882 | − | 0.0695528i | ||||
\(835\) | − | 1.61681e61i | − | 0.713251i | ||||||
\(836\) | 2.77843e60 | − | 2.05523e61i | 0.119528 | − | 0.884156i | ||||
\(837\) | 2.39372e61 | 1.00424 | ||||||||
\(838\) | −1.00346e60 | − | 1.14824e60i | −0.0410559 | − | 0.0469796i | ||||
\(839\) | − | 4.48263e61i | − | 1.78868i | −0.447392 | − | 0.894338i | \(-0.647647\pi\) | ||
0.447392 | − | 0.894338i | \(-0.352353\pi\) | |||||||
\(840\) | −1.52240e61 | − | 2.30433e61i | −0.592466 | − | 0.896769i | ||||
\(841\) | −2.39637e61 | −0.909573 | ||||||||
\(842\) | −3.28274e61 | + | 2.86881e61i | −1.21530 | + | 1.06206i | ||||
\(843\) | 7.04317e60i | 0.254325i | ||||||||
\(844\) | 5.28323e61 | + | 7.14231e60i | 1.86084 | + | 0.251563i | ||||
\(845\) | 9.10565e61 | 3.12839 | ||||||||
\(846\) | −1.42444e61 | − | 1.62997e61i | −0.477383 | − | 0.546262i | ||||
\(847\) | 1.19213e61i | 0.389736i | ||||||||
\(848\) | 7.29623e60 | + | 2.00945e60i | 0.232694 | + | 0.0640863i | ||||
\(849\) | 3.50178e61 | 1.08950 | ||||||||
\(850\) | 6.71697e60 | − | 5.87002e60i | 0.203881 | − | 0.178173i | ||||
\(851\) | 1.70617e61i | 0.505246i | ||||||||
\(852\) | 4.64229e60 | − | 3.43394e61i | 0.134122 | − | 0.992114i | ||||
\(853\) | −1.74705e61 | −0.492467 | −0.246233 | − | 0.969211i | \(-0.579193\pi\) | ||||
−0.246233 | + | 0.969211i | \(0.579193\pi\) | |||||||
\(854\) | −5.55715e61 | − | 6.35896e61i | −1.52840 | − | 1.74892i | ||||
\(855\) | 2.13552e61i | 0.573079i | ||||||||
\(856\) | 2.55292e60 | − | 1.68663e60i | 0.0668481 | − | 0.0441643i | ||||
\(857\) | −3.89100e61 | −0.994177 | −0.497088 | − | 0.867700i | \(-0.665598\pi\) | ||||
−0.497088 | + | 0.867700i | \(0.665598\pi\) | |||||||
\(858\) | −3.56036e61 | + | 3.11143e61i | −0.887689 | + | 0.775759i | ||||
\(859\) | 2.54821e61i | 0.619982i | 0.950739 | + | 0.309991i | \(0.100326\pi\) | ||||
−0.950739 | + | 0.309991i | \(0.899674\pi\) | |||||||
\(860\) | −1.79399e61 | − | 2.42527e60i | −0.425944 | − | 0.0575827i | ||||
\(861\) | 1.76801e61 | 0.409655 | ||||||||
\(862\) | 3.04327e61 | + | 3.48237e61i | 0.688157 | + | 0.787448i | ||||
\(863\) | 7.90313e61i | 1.74410i | 0.489413 | + | 0.872052i | \(0.337211\pi\) | ||||
−0.489413 | + | 0.872052i | \(0.662789\pi\) | |||||||
\(864\) | 2.15075e61 | + | 4.45849e61i | 0.463235 | + | 0.960283i | ||||
\(865\) | −6.29699e61 | −1.32372 | ||||||||
\(866\) | 1.04606e61 | − | 9.14158e60i | 0.214625 | − | 0.187562i | ||||
\(867\) | − | 5.96512e60i | − | 0.119459i | ||||||
\(868\) | −8.63226e60 | + | 6.38536e61i | −0.168737 | + | 1.24816i | ||||
\(869\) | 9.36697e60 | 0.178724 | ||||||||
\(870\) | 8.53969e60 | + | 9.77184e60i | 0.159052 | + | 0.182000i | ||||
\(871\) | 2.40220e61i | 0.436744i | ||||||||
\(872\) | −7.48949e60 | − | 1.13362e61i | −0.132925 | − | 0.201198i | ||||
\(873\) | 4.06868e61 | 0.704943 | ||||||||
\(874\) | 3.02928e61 | − | 2.64731e61i | 0.512389 | − | 0.447781i | ||||
\(875\) | − | 6.78554e61i | − | 1.12051i | ||||||
\(876\) | 3.52762e61 | + | 4.76893e60i | 0.568716 | + | 0.0768838i | ||||
\(877\) | −3.55428e61 | −0.559449 | −0.279725 | − | 0.960080i | \(-0.590243\pi\) | ||||
−0.279725 | + | 0.960080i | \(0.590243\pi\) | |||||||
\(878\) | 3.64148e61 | + | 4.16689e61i | 0.559619 | + | 0.640364i | ||||
\(879\) | 3.38318e61i | 0.507643i | ||||||||
\(880\) | −1.70610e61 | + | 6.19475e61i | −0.249958 | + | 0.907586i | ||||
\(881\) | −7.63111e60 | −0.109168 | −0.0545838 | − | 0.998509i | \(-0.517383\pi\) | ||||
−0.0545838 | + | 0.998509i | \(0.517383\pi\) | |||||||
\(882\) | −2.05378e61 | + | 1.79481e61i | −0.286888 | + | 0.250714i | ||||
\(883\) | − | 1.26270e62i | − | 1.72236i | −0.508298 | − | 0.861181i | \(-0.669725\pi\) | ||
0.508298 | − | 0.861181i | \(-0.330275\pi\) | |||||||
\(884\) | 2.11656e61 | − | 1.56564e62i | 0.281924 | − | 2.08542i | ||||
\(885\) | −1.14358e61 | −0.148750 | ||||||||
\(886\) | 1.18827e61 | + | 1.35972e61i | 0.150941 | + | 0.172719i | ||||
\(887\) | − | 1.06440e62i | − | 1.32041i | −0.751085 | − | 0.660206i | \(-0.770469\pi\) | ||
0.751085 | − | 0.660206i | \(-0.229531\pi\) | |||||||
\(888\) | 3.89534e61 | − | 2.57352e61i | 0.471925 | − | 0.311785i | ||||
\(889\) | −1.06712e62 | −1.26263 | ||||||||
\(890\) | −1.47229e61 | + | 1.28664e61i | −0.170138 | + | 0.148685i | ||||
\(891\) | 2.10924e61i | 0.238064i | ||||||||
\(892\) | 8.56080e61 | + | 1.15732e61i | 0.943740 | + | 0.127583i | ||||
\(893\) | 1.47714e62 | 1.59052 | ||||||||
\(894\) | −1.62822e61 | − | 1.86315e61i | −0.171248 | − | 0.195957i | ||||
\(895\) | 3.60209e60i | 0.0370059i | ||||||||
\(896\) | −1.26688e62 | + | 4.12940e61i | −1.27136 | + | 0.414400i | ||||
\(897\) | −9.17209e61 | −0.899140 | ||||||||
\(898\) | −3.57921e61 | + | 3.12790e61i | −0.342755 | + | 0.299537i | ||||
\(899\) | − | 3.02771e61i | − | 0.283244i | ||||||
\(900\) | 1.77687e60 | − | 1.31436e61i | 0.0162391 | − | 0.120122i | ||||
\(901\) | −2.91925e61 | −0.260646 | ||||||||
\(902\) | −2.70670e61 | − | 3.09724e61i | −0.236104 | − | 0.270170i | ||||
\(903\) | − | 4.33407e61i | − | 0.369363i | ||||||
\(904\) | −8.15159e60 | − | 1.23384e61i | −0.0678743 | − | 0.102736i | ||||
\(905\) | −8.51931e61 | −0.693081 | ||||||||
\(906\) | 6.26006e61 | − | 5.47071e61i | 0.497606 | − | 0.434862i | ||||
\(907\) | − | 1.94296e62i | − | 1.50908i | −0.656256 | − | 0.754538i | \(-0.727861\pi\) | ||
0.656256 | − | 0.754538i | \(-0.272139\pi\) | |||||||
\(908\) | 3.40369e61 | + | 4.60138e60i | 0.258313 | + | 0.0349209i | ||||
\(909\) | 5.30173e61 | 0.393166 | ||||||||
\(910\) | 2.64627e62 | + | 3.02808e62i | 1.91763 | + | 2.19431i | ||||
\(911\) | − | 3.70463e60i | − | 0.0262337i | −0.999914 | − | 0.0131168i | \(-0.995825\pi\) | ||
0.999914 | − | 0.0131168i | \(-0.00417534\pi\) | |||||||
\(912\) | −1.06133e62 | − | 2.92300e61i | −0.734443 | − | 0.202273i | ||||
\(913\) | −2.06531e62 | −1.39668 | ||||||||
\(914\) | 1.61241e62 | − | 1.40910e62i | 1.06563 | − | 0.931263i | ||||
\(915\) | 2.16158e62i | 1.39614i | ||||||||
\(916\) | −2.00023e61 | + | 1.47958e62i | −0.126262 | + | 0.933974i | ||||
\(917\) | 3.96980e62 | 2.44914 | ||||||||
\(918\) | −1.25651e62 | − | 1.43780e62i | −0.757651 | − | 0.866968i | ||||
\(919\) | 6.62041e61i | 0.390175i | 0.980786 | + | 0.195087i | \(0.0624990\pi\) | ||||
−0.980786 | + | 0.195087i | \(0.937501\pi\) | |||||||
\(920\) | −1.03995e62 | + | 6.87058e61i | −0.599054 | + | 0.395776i | ||||
\(921\) | −2.16870e62 | −1.22109 | ||||||||
\(922\) | 1.46082e61 | − | 1.27662e61i | 0.0803984 | − | 0.0702608i | ||||
\(923\) | 5.04560e62i | 2.71442i | ||||||||
\(924\) | −1.52444e62 | − | 2.06086e61i | −0.801676 | − | 0.108377i | ||||
\(925\) | −3.83836e61 | −0.197319 | ||||||||
\(926\) | −2.02915e62 | − | 2.32193e62i | −1.01973 | − | 1.16686i | ||||
\(927\) | 1.46635e62i | 0.720382i | ||||||||
\(928\) | 5.63934e61 | − | 2.72038e61i | 0.270845 | − | 0.130654i | ||||
\(929\) | 6.43967e61 | 0.302366 | 0.151183 | − | 0.988506i | \(-0.451692\pi\) | ||||
0.151183 | + | 0.988506i | \(0.451692\pi\) | |||||||
\(930\) | 1.24186e62 | − | 1.08528e62i | 0.570075 | − | 0.498193i | ||||
\(931\) | − | 1.86121e62i | − | 0.835319i | ||||||
\(932\) | −1.46840e61 | + | 1.08619e62i | −0.0644331 | + | 0.476617i | ||||
\(933\) | 2.02044e62 | 0.866825 | ||||||||
\(934\) | 2.14754e62 | + | 2.45740e62i | 0.900859 | + | 1.03084i | ||||
\(935\) | − | 2.47854e62i | − | 1.01661i | ||||||
\(936\) | −1.29484e62 | − | 1.95990e62i | −0.519307 | − | 0.786034i | ||||
\(937\) | 4.19397e62 | 1.64473 | 0.822364 | − | 0.568962i | \(-0.192655\pi\) | ||||
0.822364 | + | 0.568962i | \(0.192655\pi\) | |||||||
\(938\) | −5.88477e61 | + | 5.14275e61i | −0.225668 | + | 0.197213i | ||||
\(939\) | − | 2.96265e61i | − | 0.111097i | ||||||
\(940\) | −4.53518e62 | − | 6.13103e61i | −1.66307 | − | 0.224827i | ||||
\(941\) | 1.00265e62 | 0.359555 | 0.179778 | − | 0.983707i | \(-0.442462\pi\) | ||||
0.179778 | + | 0.983707i | \(0.442462\pi\) | |||||||
\(942\) | −8.91623e60 | − | 1.02027e61i | −0.0312689 | − | 0.0357805i | ||||
\(943\) | − | 7.97901e61i | − | 0.273655i | ||||||
\(944\) | −1.46500e61 | + | 5.31934e61i | −0.0491389 | + | 0.178421i | ||||
\(945\) | 4.86040e62 | 1.59443 | ||||||||
\(946\) | −7.59253e61 | + | 6.63518e61i | −0.243597 | + | 0.212882i | ||||
\(947\) | 4.46412e62i | 1.40083i | 0.713734 | + | 0.700417i | \(0.247003\pi\) | ||||
−0.713734 | + | 0.700417i | \(0.752997\pi\) | |||||||
\(948\) | 6.66097e60 | − | 4.92718e61i | 0.0204438 | − | 0.151225i | ||||
\(949\) | −5.18324e62 | −1.55600 | ||||||||
\(950\) | 5.95563e61 | + | 6.81494e61i | 0.174877 | + | 0.200109i | ||||
\(951\) | 2.40488e62i | 0.690720i | ||||||||
\(952\) | 4.28853e62 | − | 2.83329e62i | 1.20485 | − | 0.796005i | ||||
\(953\) | −6.33284e62 | −1.74039 | −0.870197 | − | 0.492704i | \(-0.836008\pi\) | ||||
−0.870197 | + | 0.492704i | \(0.836008\pi\) | |||||||
\(954\) | −3.26826e61 | + | 2.85616e61i | −0.0878620 | + | 0.0767834i | ||||
\(955\) | − | 6.93655e62i | − | 1.82420i | ||||||
\(956\) | 9.89275e61 | + | 1.33738e61i | 0.254508 | + | 0.0344065i | ||||
\(957\) | 7.22834e61 | 0.181923 | ||||||||
\(958\) | −3.27429e62 | − | 3.74672e62i | −0.806197 | − | 0.922519i | ||||
\(959\) | 1.42953e62i | 0.344352i | ||||||||
\(960\) | 3.13722e62 | + | 1.33795e62i | 0.739348 | + | 0.315315i | ||||
\(961\) | 4.89228e61 | 0.112803 | ||||||||
\(962\) | −5.11879e62 | + | 4.47336e62i | −1.15476 | + | 1.00915i | ||||
\(963\) | 1.75487e61i | 0.0387341i | ||||||||
\(964\) | 3.26334e61 | − | 2.41392e62i | 0.0704766 | − | 0.521322i | ||||
\(965\) | −4.68235e62 | −0.989441 | ||||||||
\(966\) | −1.96361e62 | − | 2.24693e62i | −0.406009 | − | 0.464590i | ||||
\(967\) | − | 5.23915e62i | − | 1.06000i | −0.847998 | − | 0.529999i | \(-0.822192\pi\) | ||
0.847998 | − | 0.529999i | \(-0.177808\pi\) | |||||||
\(968\) | −8.11507e61 | − | 1.22831e62i | −0.160661 | − | 0.243180i | ||||
\(969\) | 4.24641e62 | 0.822665 | ||||||||
\(970\) | 6.47699e62 | − | 5.66030e62i | 1.22791 | − | 1.07308i | ||||
\(971\) | 4.94294e61i | 0.0917026i | 0.998948 | + | 0.0458513i | \(0.0146000\pi\) | ||||
−0.998948 | + | 0.0458513i | \(0.985400\pi\) | |||||||
\(972\) | −4.71003e62 | − | 6.36741e61i | −0.855130 | − | 0.115604i | ||||
\(973\) | −1.10681e62 | −0.196654 | ||||||||
\(974\) | 3.15966e62 | + | 3.61555e62i | 0.549417 | + | 0.628690i | ||||
\(975\) | − | 2.06344e62i | − | 0.351151i | ||||||
\(976\) | 1.00545e63 | + | 2.76911e62i | 1.67462 | + | 0.461206i | ||||
\(977\) | 5.52585e62 | 0.900769 | 0.450384 | − | 0.892835i | \(-0.351287\pi\) | ||||
0.450384 | + | 0.892835i | \(0.351287\pi\) | |||||||
\(978\) | −2.05240e61 | + | 1.79361e61i | −0.0327451 | + | 0.0286162i | ||||
\(979\) | 1.08907e62i | 0.170066i | ||||||||
\(980\) | −7.72517e61 | + | 5.71438e62i | −0.118076 | + | 0.873417i | ||||
\(981\) | 7.79249e61 | 0.116581 | ||||||||
\(982\) | 3.99824e62 | + | 4.57512e62i | 0.585501 | + | 0.669979i | ||||
\(983\) | 6.10031e62i | 0.874436i | 0.899355 | + | 0.437218i | \(0.144036\pi\) | ||||
−0.899355 | + | 0.437218i | \(0.855964\pi\) | |||||||
\(984\) | −1.82168e62 | + | 1.20352e62i | −0.255608 | + | 0.168872i | ||||
\(985\) | −1.58699e63 | −2.17978 | ||||||||
\(986\) | −1.81861e62 | + | 1.58930e62i | −0.244526 | + | 0.213693i | ||||
\(987\) | − | 1.09565e63i | − | 1.44215i | ||||||
\(988\) | 1.58847e63 | + | 2.14743e62i | 2.04684 | + | 0.276709i | ||||
\(989\) | −1.95597e62 | −0.246740 | ||||||||
\(990\) | −2.42498e62 | − | 2.77487e62i | −0.299481 | − | 0.342692i | ||||
\(991\) | − | 8.93543e62i | − | 1.08036i | −0.841549 | − | 0.540181i | \(-0.818356\pi\) | ||
0.841549 | − | 0.540181i | \(-0.181644\pi\) | |||||||
\(992\) | −3.45723e62 | − | 7.16681e62i | −0.409244 | − | 0.848361i | ||||
\(993\) | −2.27002e62 | −0.263085 | ||||||||
\(994\) | −1.23604e63 | + | 1.08019e63i | −1.40255 | + | 1.22570i | ||||
\(995\) | 1.43587e63i | 1.59525i | ||||||||
\(996\) | −1.46867e62 | + | 1.08639e63i | −0.159763 | + | 1.18178i | ||||
\(997\) | −8.66565e62 | −0.923003 | −0.461501 | − | 0.887140i | \(-0.652689\pi\) | ||||
−0.461501 | + | 0.887140i | \(0.652689\pi\) | |||||||
\(998\) | 6.02237e62 | + | 6.89131e62i | 0.628096 | + | 0.718721i | ||||
\(999\) | 8.21622e62i | 0.839067i |
(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 | 4.43.b.a.3.15 | ✓ | 20 | |
4.3 | odd | 2 | inner | 4.43.b.a.3.16 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.43.b.a.3.15 | ✓ | 20 | 1.1 | even | 1 | trivial | |
4.43.b.a.3.16 | yes | 20 | 4.3 | odd | 2 | inner |