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 | 3.20 | ||
Root | \(0.500000 - 5.70227e8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.43.b.a.3.19 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.06680e6 | + | 355528.i | 0.985525 | + | 0.169529i | ||||
\(3\) | 9.12363e9i | 0.872210i | 0.899896 | + | 0.436105i | \(0.143642\pi\) | ||||
−0.899896 | + | 0.436105i | \(0.856358\pi\) | |||||||
\(4\) | 4.14525e12 | + | 1.46961e12i | 0.942520 | + | 0.334150i | ||||
\(5\) | −1.85810e14 | −0.389672 | −0.194836 | − | 0.980836i | \(-0.562418\pi\) | ||||
−0.194836 | + | 0.980836i | \(0.562418\pi\) | |||||||
\(6\) | −3.24370e15 | + | 1.88567e16i | −0.147865 | + | 0.859585i | ||||
\(7\) | 7.39963e17i | 1.32480i | 0.749149 | + | 0.662401i | \(0.230463\pi\) | ||||
−0.749149 | + | 0.662401i | \(0.769537\pi\) | |||||||
\(8\) | 8.04489e18 | + | 4.51113e18i | 0.872229 | + | 0.489098i | ||||
\(9\) | 2.61784e19 | 0.239249 | ||||||||
\(10\) | −3.84032e20 | − | 6.60607e19i | −0.384032 | − | 0.0660607i | ||||
\(11\) | − | 7.81812e20i | − | 0.105647i | −0.998604 | − | 0.0528233i | \(-0.983178\pi\) | ||
0.998604 | − | 0.0528233i | \(-0.0168220\pi\) | |||||||
\(12\) | −1.34081e22 | + | 3.78197e22i | −0.291449 | + | 0.822075i | ||||
\(13\) | −1.76158e23 | −0.713004 | −0.356502 | − | 0.934295i | \(-0.616031\pi\) | ||||
−0.356502 | + | 0.934295i | \(0.616031\pi\) | |||||||
\(14\) | −2.63078e23 | + | 1.52935e24i | −0.224592 | + | 1.30563i | ||||
\(15\) | − | 1.69526e24i | − | 0.339876i | ||||||
\(16\) | 1.50233e25 | + | 1.21838e25i | 0.776688 | + | 0.629886i | ||||
\(17\) | 1.77660e25 | 0.257135 | 0.128568 | − | 0.991701i | \(-0.458962\pi\) | ||||
0.128568 | + | 0.991701i | \(0.458962\pi\) | |||||||
\(18\) | 5.41055e25 | + | 9.30716e24i | 0.235786 | + | 0.0405597i | ||||
\(19\) | 8.99300e26i | 1.25915i | 0.776938 | + | 0.629577i | \(0.216772\pi\) | ||||
−0.776938 | + | 0.629577i | \(0.783228\pi\) | |||||||
\(20\) | −7.70229e26 | − | 2.73068e26i | −0.367274 | − | 0.130209i | ||||
\(21\) | −6.75115e27 | −1.15551 | ||||||||
\(22\) | 2.77956e26 | − | 1.61585e27i | 0.0179102 | − | 0.104117i | ||||
\(23\) | − | 2.55743e28i | − | 0.647917i | −0.946071 | − | 0.323959i | \(-0.894986\pi\) | ||
0.946071 | − | 0.323959i | \(-0.105014\pi\) | |||||||
\(24\) | −4.11579e28 | + | 7.33986e28i | −0.426596 | + | 0.760767i | ||||
\(25\) | −1.92848e29 | −0.848156 | ||||||||
\(26\) | −3.64083e29 | − | 6.26291e28i | −0.702683 | − | 0.120875i | ||||
\(27\) | 1.23714e30i | 1.08089i | ||||||||
\(28\) | −1.08746e30 | + | 3.06733e30i | −0.442683 | + | 1.24865i | ||||
\(29\) | −1.56307e30 | −0.304523 | −0.152262 | − | 0.988340i | \(-0.548656\pi\) | ||||
−0.152262 | + | 0.988340i | \(0.548656\pi\) | |||||||
\(30\) | 6.02713e29 | − | 3.50376e30i | 0.0576188 | − | 0.334956i | ||||
\(31\) | − | 3.90687e31i | − | 1.87600i | −0.346635 | − | 0.938000i | \(-0.612676\pi\) | ||
0.346635 | − | 0.938000i | \(-0.387324\pi\) | |||||||
\(32\) | 2.67185e31 | + | 3.05226e31i | 0.658661 | + | 0.752440i | ||||
\(33\) | 7.13296e30 | 0.0921461 | ||||||||
\(34\) | 3.67187e31 | + | 6.31630e30i | 0.253414 | + | 0.0435919i | ||||
\(35\) | − | 1.37493e32i | − | 0.516239i | ||||||
\(36\) | 1.08516e32 | + | 3.84720e31i | 0.225497 | + | 0.0799452i | ||||
\(37\) | 2.18801e32 | 0.255748 | 0.127874 | − | 0.991790i | \(-0.459185\pi\) | ||||
0.127874 | + | 0.991790i | \(0.459185\pi\) | |||||||
\(38\) | −3.19726e32 | + | 1.85867e33i | −0.213463 | + | 1.24093i | ||||
\(39\) | − | 1.60720e33i | − | 0.621889i | ||||||
\(40\) | −1.49482e33 | − | 8.38214e32i | −0.339883 | − | 0.190588i | ||||
\(41\) | −1.09206e34 | −1.47837 | −0.739186 | − | 0.673501i | \(-0.764790\pi\) | ||||
−0.739186 | + | 0.673501i | \(0.764790\pi\) | |||||||
\(42\) | −1.39532e34 | − | 2.40022e33i | −1.13878 | − | 0.195892i | ||||
\(43\) | 3.18319e34i | 1.58499i | 0.609881 | + | 0.792493i | \(0.291217\pi\) | ||||
−0.609881 | + | 0.792493i | \(0.708783\pi\) | |||||||
\(44\) | 1.14896e33 | − | 3.24080e33i | 0.0353018 | − | 0.0995741i | ||||
\(45\) | −4.86422e33 | −0.0932289 | ||||||||
\(46\) | 9.09238e33 | − | 5.28569e34i | 0.109841 | − | 0.638539i | ||||
\(47\) | 2.91371e34i | 0.224074i | 0.993704 | + | 0.112037i | \(0.0357375\pi\) | ||||
−0.993704 | + | 0.112037i | \(0.964262\pi\) | |||||||
\(48\) | −1.11160e35 | + | 1.37067e35i | −0.549393 | + | 0.677435i | ||||
\(49\) | −2.35572e35 | −0.755103 | ||||||||
\(50\) | −3.98578e35 | − | 6.85629e34i | −0.835879 | − | 0.143787i | ||||
\(51\) | 1.62090e35i | 0.224276i | ||||||||
\(52\) | −7.30218e35 | − | 2.58883e35i | −0.672020 | − | 0.238250i | ||||
\(53\) | −2.53747e36 | −1.56534 | −0.782669 | − | 0.622439i | \(-0.786142\pi\) | ||||
−0.782669 | + | 0.622439i | \(0.786142\pi\) | |||||||
\(54\) | −4.39838e35 | + | 2.55692e36i | −0.183241 | + | 1.06524i | ||||
\(55\) | 1.45269e35i | 0.0411676i | ||||||||
\(56\) | −3.33807e36 | + | 5.95292e36i | −0.647958 | + | 1.15553i | ||||
\(57\) | −8.20487e36 | −1.09825 | ||||||||
\(58\) | −3.23055e36 | − | 5.55715e35i | −0.300115 | − | 0.0516255i | ||||
\(59\) | − | 2.40962e36i | − | 0.156335i | −0.996940 | − | 0.0781675i | \(-0.975093\pi\) | ||
0.996940 | − | 0.0781675i | \(-0.0249069\pi\) | |||||||
\(60\) | 2.49137e36 | − | 7.02728e36i | 0.113570 | − | 0.320340i | ||||
\(61\) | 4.12023e37 | 1.32738 | 0.663690 | − | 0.748008i | \(-0.268989\pi\) | ||||
0.663690 | + | 0.748008i | \(0.268989\pi\) | |||||||
\(62\) | 1.38900e37 | − | 8.07469e37i | 0.318036 | − | 1.84885i | ||||
\(63\) | 1.93711e37i | 0.316958i | ||||||||
\(64\) | 4.43700e37 | + | 7.25831e37i | 0.521567 | + | 0.853210i | ||||
\(65\) | 3.27320e37 | 0.277838 | ||||||||
\(66\) | 1.47424e37 | + | 2.53597e36i | 0.0908123 | + | 0.0156214i | ||||
\(67\) | 3.27491e37i | 0.147106i | 0.997291 | + | 0.0735528i | \(0.0234337\pi\) | ||||
−0.997291 | + | 0.0735528i | \(0.976566\pi\) | |||||||
\(68\) | 7.36444e37 | + | 2.61090e37i | 0.242355 | + | 0.0859218i | ||||
\(69\) | 2.33331e38 | 0.565120 | ||||||||
\(70\) | 4.88825e37 | − | 2.84169e38i | 0.0875174 | − | 0.508766i | ||||
\(71\) | − | 5.97202e38i | − | 0.793772i | −0.917868 | − | 0.396886i | \(-0.870091\pi\) | ||
0.917868 | − | 0.396886i | \(-0.129909\pi\) | |||||||
\(72\) | 2.10603e38 | + | 1.18094e38i | 0.208680 | + | 0.117016i | ||||
\(73\) | 8.93872e38 | 0.662972 | 0.331486 | − | 0.943460i | \(-0.392450\pi\) | ||||
0.331486 | + | 0.943460i | \(0.392450\pi\) | |||||||
\(74\) | 4.52217e38 | + | 7.77898e37i | 0.252047 | + | 0.0433567i | ||||
\(75\) | − | 1.75948e39i | − | 0.739770i | ||||||
\(76\) | −1.32162e39 | + | 3.72782e39i | −0.420746 | + | 1.18678i | ||||
\(77\) | 5.78512e38 | 0.139961 | ||||||||
\(78\) | 5.71404e38 | − | 3.32175e39i | 0.105428 | − | 0.612888i | ||||
\(79\) | 7.24871e39i | 1.02351i | 0.859132 | + | 0.511754i | \(0.171004\pi\) | ||||
−0.859132 | + | 0.511754i | \(0.828996\pi\) | |||||||
\(80\) | −2.79149e39 | − | 2.26387e39i | −0.302654 | − | 0.245449i | ||||
\(81\) | −8.42279e39 | −0.703510 | ||||||||
\(82\) | −2.25706e40 | − | 3.88256e39i | −1.45697 | − | 0.250627i | ||||
\(83\) | 1.04180e40i | 0.521367i | 0.965424 | + | 0.260684i | \(0.0839479\pi\) | ||||
−0.965424 | + | 0.260684i | \(0.916052\pi\) | |||||||
\(84\) | −2.79852e40 | − | 9.92154e39i | −1.08909 | − | 0.386113i | ||||
\(85\) | −3.30110e39 | −0.100199 | ||||||||
\(86\) | −1.13171e40 | + | 6.57901e40i | −0.268701 | + | 1.56204i | ||||
\(87\) | − | 1.42609e40i | − | 0.265608i | ||||||
\(88\) | 3.52685e39 | − | 6.28959e39i | 0.0516715 | − | 0.0921481i | ||||
\(89\) | 1.28853e41 | 1.48903 | 0.744514 | − | 0.667607i | \(-0.232681\pi\) | ||||
0.744514 | + | 0.667607i | \(0.232681\pi\) | |||||||
\(90\) | −1.00534e40 | − | 1.72937e39i | −0.0918794 | − | 0.0158050i | ||||
\(91\) | − | 1.30350e41i | − | 0.944590i | ||||||
\(92\) | 3.75842e40 | − | 1.06012e41i | 0.216502 | − | 0.610675i | ||||
\(93\) | 3.56448e41 | 1.63627 | ||||||||
\(94\) | −1.03591e40 | + | 6.02204e40i | −0.0379870 | + | 0.220830i | ||||
\(95\) | − | 1.67099e41i | − | 0.490657i | ||||||
\(96\) | −2.78477e41 | + | 2.43769e41i | −0.656285 | + | 0.574491i | ||||
\(97\) | 5.53744e41 | 1.04979 | 0.524895 | − | 0.851167i | \(-0.324105\pi\) | ||||
0.524895 | + | 0.851167i | \(0.324105\pi\) | |||||||
\(98\) | −4.86879e41 | − | 8.37524e40i | −0.744173 | − | 0.128012i | ||||
\(99\) | − | 2.04666e40i | − | 0.0252759i | ||||||
\(100\) | −7.99403e41 | − | 2.83411e41i | −0.799403 | − | 0.283411i | ||||
\(101\) | 2.23693e42 | 1.81511 | 0.907555 | − | 0.419933i | \(-0.137947\pi\) | ||||
0.907555 | + | 0.419933i | \(0.137947\pi\) | |||||||
\(102\) | −5.76276e40 | + | 3.35007e41i | −0.0380213 | + | 0.221030i | ||||
\(103\) | 2.35307e42i | 1.26489i | 0.774604 | + | 0.632447i | \(0.217949\pi\) | ||||
−0.774604 | + | 0.632447i | \(0.782051\pi\) | |||||||
\(104\) | −1.41717e42 | − | 7.94672e41i | −0.621903 | − | 0.348729i | ||||
\(105\) | 1.25443e42 | 0.450269 | ||||||||
\(106\) | −5.24444e42 | − | 9.02142e41i | −1.54268 | − | 0.265370i | ||||
\(107\) | − | 7.40104e42i | − | 1.78745i | −0.448618 | − | 0.893724i | \(-0.648084\pi\) | ||
0.448618 | − | 0.893724i | \(-0.351916\pi\) | |||||||
\(108\) | −1.81811e42 | + | 5.12825e42i | −0.361178 | + | 1.01876i | ||||
\(109\) | 2.23024e42 | 0.365087 | 0.182543 | − | 0.983198i | \(-0.441567\pi\) | ||||
0.182543 | + | 0.983198i | \(0.441567\pi\) | |||||||
\(110\) | −5.16470e40 | + | 3.00241e41i | −0.00697909 | + | 0.0405717i | ||||
\(111\) | 1.99626e42i | 0.223066i | ||||||||
\(112\) | −9.01554e42 | + | 1.11167e43i | −0.834475 | + | 1.02896i | ||||
\(113\) | 9.60366e42 | 0.737547 | 0.368773 | − | 0.929519i | \(-0.379778\pi\) | ||||
0.368773 | + | 0.929519i | \(0.379778\pi\) | |||||||
\(114\) | −1.69578e43 | − | 2.91706e42i | −1.08235 | − | 0.186185i | ||||
\(115\) | 4.75197e42i | 0.252475i | ||||||||
\(116\) | −6.47931e42 | − | 2.29710e42i | −0.287019 | − | 0.101756i | ||||
\(117\) | −4.61154e42 | −0.170586 | ||||||||
\(118\) | 8.56687e41 | − | 4.98019e42i | 0.0265033 | − | 0.154072i | ||||
\(119\) | 1.31462e43i | 0.340654i | ||||||||
\(120\) | 7.64755e42 | − | 1.36382e43i | 0.166233 | − | 0.296450i | ||||
\(121\) | 5.41525e43 | 0.988839 | ||||||||
\(122\) | 8.51568e43 | + | 1.46486e43i | 1.30817 | + | 0.225029i | ||||
\(123\) | − | 9.96351e43i | − | 1.28945i | ||||||
\(124\) | 5.74156e43 | − | 1.61949e44i | 0.626866 | − | 1.76817i | ||||
\(125\) | 7.80815e43 | 0.720175 | ||||||||
\(126\) | −6.88696e42 | + | 4.00361e43i | −0.0537336 | + | 0.312370i | ||||
\(127\) | 2.35239e44i | 1.55464i | 0.629103 | + | 0.777322i | \(0.283422\pi\) | ||||
−0.629103 | + | 0.777322i | \(0.716578\pi\) | |||||||
\(128\) | 6.58985e43 | + | 1.65789e44i | 0.369374 | + | 0.929281i | ||||
\(129\) | −2.90423e44 | −1.38244 | ||||||||
\(130\) | 6.76503e43 | + | 1.16371e43i | 0.273816 | + | 0.0471015i | ||||
\(131\) | − | 2.53620e44i | − | 0.873950i | −0.899474 | − | 0.436975i | \(-0.856050\pi\) | ||
0.899474 | − | 0.436975i | \(-0.143950\pi\) | |||||||
\(132\) | 2.95679e43 | + | 1.04826e43i | 0.0868495 | + | 0.0307906i | ||||
\(133\) | −6.65449e44 | −1.66813 | ||||||||
\(134\) | −1.16432e43 | + | 6.76858e43i | −0.0249386 | + | 0.144976i | ||||
\(135\) | − | 2.29873e44i | − | 0.421191i | ||||||
\(136\) | 1.42925e44 | + | 8.01447e43i | 0.224281 | + | 0.125764i | ||||
\(137\) | −1.20317e45 | −1.61881 | −0.809404 | − | 0.587252i | \(-0.800210\pi\) | ||||
−0.809404 | + | 0.587252i | \(0.800210\pi\) | |||||||
\(138\) | 4.82247e44 | + | 8.29555e43i | 0.556940 | + | 0.0958042i | ||||
\(139\) | 1.76849e45i | 1.75506i | 0.479525 | + | 0.877528i | \(0.340809\pi\) | ||||
−0.479525 | + | 0.877528i | \(0.659191\pi\) | |||||||
\(140\) | 2.02060e44 | − | 5.69941e44i | 0.172501 | − | 0.486565i | ||||
\(141\) | −2.65836e44 | −0.195440 | ||||||||
\(142\) | 2.12322e44 | − | 1.23429e45i | 0.134567 | − | 0.782282i | ||||
\(143\) | 1.37722e44i | 0.0753265i | ||||||||
\(144\) | 3.93287e44 | + | 3.18952e44i | 0.185822 | + | 0.150700i | ||||
\(145\) | 2.90434e44 | 0.118664 | ||||||||
\(146\) | 1.84745e45 | + | 3.17797e44i | 0.653376 | + | 0.112393i | ||||
\(147\) | − | 2.14927e45i | − | 0.658608i | ||||||
\(148\) | 9.06984e44 | + | 3.21551e44i | 0.241048 | + | 0.0854583i | ||||
\(149\) | 6.29694e44 | 0.145284 | 0.0726420 | − | 0.997358i | \(-0.476857\pi\) | ||||
0.0726420 | + | 0.997358i | \(0.476857\pi\) | |||||||
\(150\) | 6.25543e44 | − | 3.63648e45i | 0.125412 | − | 0.729062i | ||||
\(151\) | − | 2.84562e45i | − | 0.496204i | −0.968734 | − | 0.248102i | \(-0.920193\pi\) | ||
0.968734 | − | 0.248102i | \(-0.0798069\pi\) | |||||||
\(152\) | −4.05686e45 | + | 7.23477e45i | −0.615849 | + | 1.09827i | ||||
\(153\) | 4.65086e44 | 0.0615195 | ||||||||
\(154\) | 1.19567e45 | + | 2.05677e44i | 0.137935 | + | 0.0237274i | ||||
\(155\) | 7.25936e45i | 0.731025i | ||||||||
\(156\) | 2.36195e45 | − | 6.66224e45i | 0.207804 | − | 0.586143i | ||||
\(157\) | 1.97018e46 | 1.51570 | 0.757849 | − | 0.652430i | \(-0.226250\pi\) | ||||
0.757849 | + | 0.652430i | \(0.226250\pi\) | |||||||
\(158\) | −2.57712e45 | + | 1.49816e46i | −0.173514 | + | 1.00869i | ||||
\(159\) | − | 2.31509e46i | − | 1.36530i | ||||||
\(160\) | −4.96457e45 | − | 5.67141e45i | −0.256662 | − | 0.293205i | ||||
\(161\) | 1.89241e46 | 0.858362 | ||||||||
\(162\) | −1.74082e46 | − | 2.99454e45i | −0.693327 | − | 0.119265i | ||||
\(163\) | 8.93294e45i | 0.312647i | 0.987706 | + | 0.156324i | \(0.0499643\pi\) | ||||
−0.987706 | + | 0.156324i | \(0.950036\pi\) | |||||||
\(164\) | −4.52684e46 | − | 1.60489e46i | −1.39340 | − | 0.493998i | ||||
\(165\) | −1.32538e45 | −0.0359068 | ||||||||
\(166\) | −3.70388e45 | + | 2.15318e46i | −0.0883868 | + | 0.513820i | ||||
\(167\) | 4.98129e46i | 1.04784i | 0.851767 | + | 0.523921i | \(0.175531\pi\) | ||||
−0.851767 | + | 0.523921i | \(0.824469\pi\) | |||||||
\(168\) | −5.43123e46 | − | 3.04553e46i | −1.00787 | − | 0.565155i | ||||
\(169\) | −3.00092e46 | −0.491625 | ||||||||
\(170\) | −6.82270e45 | − | 1.17363e45i | −0.0987482 | − | 0.0169866i | ||||
\(171\) | 2.35423e46i | 0.301252i | ||||||||
\(172\) | −4.67804e46 | + | 1.31951e47i | −0.529623 | + | 1.49388i | ||||
\(173\) | 7.00878e46 | 0.702545 | 0.351273 | − | 0.936273i | \(-0.385749\pi\) | ||||
0.351273 | + | 0.936273i | \(0.385749\pi\) | |||||||
\(174\) | 5.07014e45 | − | 2.94743e46i | 0.0450283 | − | 0.261764i | ||||
\(175\) | − | 1.42701e47i | − | 1.12364i | ||||||
\(176\) | 9.52541e45 | − | 1.17454e46i | 0.0665454 | − | 0.0820545i | ||||
\(177\) | 2.19845e46 | 0.136357 | ||||||||
\(178\) | 2.66312e47 | + | 4.58107e46i | 1.46747 | + | 0.252433i | ||||
\(179\) | − | 2.19620e47i | − | 1.07586i | −0.842988 | − | 0.537932i | \(-0.819206\pi\) | ||
0.842988 | − | 0.537932i | \(-0.180794\pi\) | |||||||
\(180\) | −2.01634e46 | − | 7.14849e45i | −0.0878701 | − | 0.0311524i | ||||
\(181\) | 1.12159e47 | 0.435096 | 0.217548 | − | 0.976050i | \(-0.430194\pi\) | ||||
0.217548 | + | 0.976050i | \(0.430194\pi\) | |||||||
\(182\) | 4.63432e46 | − | 2.69408e47i | 0.160135 | − | 0.930917i | ||||
\(183\) | 3.75915e47i | 1.15775i | ||||||||
\(184\) | 1.15369e47 | − | 2.05743e47i | 0.316895 | − | 0.565132i | ||||
\(185\) | −4.06554e46 | −0.0996581 | ||||||||
\(186\) | 7.36705e47 | + | 1.26727e47i | 1.61258 | + | 0.277394i | ||||
\(187\) | − | 1.38897e46i | − | 0.0271655i | ||||||
\(188\) | −4.28201e46 | + | 1.20780e47i | −0.0748743 | + | 0.211194i | ||||
\(189\) | −9.15438e47 | −1.43196 | ||||||||
\(190\) | 5.94084e46 | − | 3.45360e47i | 0.0831806 | − | 0.483555i | ||||
\(191\) | 5.79692e47i | 0.726937i | 0.931606 | + | 0.363469i | \(0.118408\pi\) | ||||
−0.931606 | + | 0.363469i | \(0.881592\pi\) | |||||||
\(192\) | −6.62221e47 | + | 4.04815e47i | −0.744179 | + | 0.454916i | ||||
\(193\) | −1.31768e48 | −1.32772 | −0.663859 | − | 0.747858i | \(-0.731082\pi\) | ||||
−0.663859 | + | 0.747858i | \(0.731082\pi\) | |||||||
\(194\) | 1.14448e48 | + | 1.96871e47i | 1.03459 | + | 0.177970i | ||||
\(195\) | 2.98634e47i | 0.242333i | ||||||||
\(196\) | −9.76504e47 | − | 3.46198e47i | −0.711699 | − | 0.252318i | ||||
\(197\) | −9.14500e47 | −0.598953 | −0.299477 | − | 0.954104i | \(-0.596812\pi\) | ||||
−0.299477 | + | 0.954104i | \(0.596812\pi\) | |||||||
\(198\) | 7.27645e45 | − | 4.23003e46i | 0.00428500 | − | 0.0249100i | ||||
\(199\) | − | 7.99017e47i | − | 0.423293i | −0.977346 | − | 0.211647i | \(-0.932117\pi\) | ||
0.977346 | − | 0.211647i | \(-0.0678826\pi\) | |||||||
\(200\) | −1.55144e48 | − | 8.69963e47i | −0.739786 | − | 0.414831i | ||||
\(201\) | −2.98791e47 | −0.128307 | ||||||||
\(202\) | 4.62327e48 | + | 7.95290e47i | 1.78884 | + | 0.307714i | ||||
\(203\) | − | 1.15661e48i | − | 0.403433i | ||||||
\(204\) | −2.38209e47 | + | 6.71904e47i | −0.0749419 | + | 0.211385i | ||||
\(205\) | 2.02915e48 | 0.576081 | ||||||||
\(206\) | −8.36584e47 | + | 4.86333e48i | −0.214436 | + | 1.24658i | ||||
\(207\) | − | 6.69495e47i | − | 0.155014i | ||||||
\(208\) | −2.64648e48 | − | 2.14627e48i | −0.553781 | − | 0.449111i | ||||
\(209\) | 7.03083e47 | 0.133025 | ||||||||
\(210\) | 2.59266e48 | + | 4.45986e47i | 0.443751 | + | 0.0763336i | ||||
\(211\) | 5.02337e48i | 0.778151i | 0.921206 | + | 0.389076i | \(0.127206\pi\) | ||||
−0.921206 | + | 0.389076i | \(0.872794\pi\) | |||||||
\(212\) | −1.05184e49 | − | 3.72909e48i | −1.47536 | − | 0.523057i | ||||
\(213\) | 5.44865e48 | 0.692336 | ||||||||
\(214\) | 2.63128e48 | − | 1.52964e49i | 0.303024 | − | 1.76157i | ||||
\(215\) | − | 5.91470e48i | − | 0.617625i | ||||||
\(216\) | −5.58090e48 | + | 9.95266e48i | −0.528659 | + | 0.942780i | ||||
\(217\) | 2.89094e49 | 2.48533 | ||||||||
\(218\) | 4.60946e48 | + | 7.92914e47i | 0.359802 | + | 0.0618927i | ||||
\(219\) | 8.15536e48i | 0.578251i | ||||||||
\(220\) | −2.13488e47 | + | 6.02174e47i | −0.0137561 | + | 0.0388013i | ||||
\(221\) | −3.12962e48 | −0.183339 | ||||||||
\(222\) | −7.09725e47 | + | 4.12586e48i | −0.0378162 | + | 0.219838i | ||||
\(223\) | − | 2.97108e49i | − | 1.44050i | −0.693716 | − | 0.720249i | \(-0.744028\pi\) | ||
0.693716 | − | 0.720249i | \(-0.255972\pi\) | |||||||
\(224\) | −2.25856e49 | + | 1.97707e49i | −0.996834 | + | 0.872596i | ||||
\(225\) | −5.04846e48 | −0.202921 | ||||||||
\(226\) | 1.98488e49 | + | 3.41437e48i | 0.726871 | + | 0.125035i | ||||
\(227\) | 1.58388e49i | 0.528664i | 0.964432 | + | 0.264332i | \(0.0851515\pi\) | ||||
−0.964432 | + | 0.264332i | \(0.914848\pi\) | |||||||
\(228\) | −3.40112e49 | − | 1.20579e49i | −1.03512 | − | 0.366979i | ||||
\(229\) | 1.60852e48 | 0.0446562 | 0.0223281 | − | 0.999751i | \(-0.492892\pi\) | ||||
0.0223281 | + | 0.999751i | \(0.492892\pi\) | |||||||
\(230\) | −1.68946e48 | + | 9.82135e48i | −0.0428019 | + | 0.248821i | ||||
\(231\) | 5.27813e48i | 0.122075i | ||||||||
\(232\) | −1.25747e49 | − | 7.05121e48i | −0.265614 | − | 0.148942i | ||||
\(233\) | −5.90372e49 | −1.13933 | −0.569667 | − | 0.821876i | \(-0.692928\pi\) | ||||
−0.569667 | + | 0.821876i | \(0.692928\pi\) | |||||||
\(234\) | −9.53111e48 | − | 1.63953e48i | −0.168117 | − | 0.0289192i | ||||
\(235\) | − | 5.41397e48i | − | 0.0873154i | ||||||
\(236\) | 3.54120e48 | − | 9.98847e48i | 0.0522394 | − | 0.147349i | ||||
\(237\) | −6.61345e49 | −0.892715 | ||||||||
\(238\) | −4.67383e48 | + | 2.71705e49i | −0.0577507 | + | 0.335723i | ||||
\(239\) | 7.38705e49i | 0.835825i | 0.908487 | + | 0.417912i | \(0.137238\pi\) | ||||
−0.908487 | + | 0.417912i | \(0.862762\pi\) | |||||||
\(240\) | 2.06547e49 | − | 2.54685e49i | 0.214083 | − | 0.263978i | ||||
\(241\) | 2.17016e49 | 0.206127 | 0.103063 | − | 0.994675i | \(-0.467136\pi\) | ||||
0.103063 | + | 0.994675i | \(0.467136\pi\) | |||||||
\(242\) | 1.11922e50 | + | 1.92527e49i | 0.974526 | + | 0.167637i | ||||
\(243\) | 5.85203e49i | 0.467277i | ||||||||
\(244\) | 1.70794e50 | + | 6.05512e49i | 1.25108 | + | 0.443544i | ||||
\(245\) | 4.37717e49 | 0.294243 | ||||||||
\(246\) | 3.54230e49 | − | 2.05925e50i | 0.218599 | − | 1.27079i | ||||
\(247\) | − | 1.58419e50i | − | 0.897782i | ||||||
\(248\) | 1.76244e50 | − | 3.14303e50i | 0.917547 | − | 1.63630i | ||||
\(249\) | −9.50498e49 | −0.454742 | ||||||||
\(250\) | 1.61379e50 | + | 2.77602e49i | 0.709751 | + | 0.122090i | ||||
\(251\) | − | 7.60536e49i | − | 0.307590i | −0.988103 | − | 0.153795i | \(-0.950850\pi\) | ||
0.988103 | − | 0.153795i | \(-0.0491495\pi\) | |||||||
\(252\) | −2.84679e49 | + | 8.02979e49i | −0.105912 | + | 0.298740i | ||||
\(253\) | −1.99943e49 | −0.0684503 | ||||||||
\(254\) | −8.36340e49 | + | 4.86191e50i | −0.263557 | + | 1.53214i | ||||
\(255\) | − | 3.01180e49i | − | 0.0873942i | ||||||
\(256\) | 7.72560e49 | + | 3.66081e50i | 0.206487 | + | 0.978449i | ||||
\(257\) | −3.66538e50 | −0.902659 | −0.451329 | − | 0.892357i | \(-0.649050\pi\) | ||||
−0.451329 | + | 0.892357i | \(0.649050\pi\) | |||||||
\(258\) | −6.00244e50 | − | 1.03253e50i | −1.36243 | − | 0.234364i | ||||
\(259\) | 1.61905e50i | 0.338816i | ||||||||
\(260\) | 1.35682e50 | + | 4.81031e49i | 0.261868 | + | 0.0928395i | ||||
\(261\) | −4.09187e49 | −0.0728571 | ||||||||
\(262\) | 9.01690e49 | − | 5.24181e50i | 0.148160 | − | 0.861300i | ||||
\(263\) | − | 9.90397e48i | − | 0.0150224i | −0.999972 | − | 0.00751119i | \(-0.997609\pi\) | ||
0.999972 | − | 0.00751119i | \(-0.00239091\pi\) | |||||||
\(264\) | 5.73839e49 | + | 3.21777e49i | 0.0803725 | + | 0.0450684i | ||||
\(265\) | 4.71488e50 | 0.609968 | ||||||||
\(266\) | −1.37535e51 | − | 2.36586e50i | −1.64398 | − | 0.282796i | ||||
\(267\) | 1.17560e51i | 1.29875i | ||||||||
\(268\) | −4.81284e49 | + | 1.35753e50i | −0.0491553 | + | 0.138650i | ||||
\(269\) | 1.35233e50 | 0.127727 | 0.0638637 | − | 0.997959i | \(-0.479658\pi\) | ||||
0.0638637 | + | 0.997959i | \(0.479658\pi\) | |||||||
\(270\) | 8.17264e49 | − | 4.75101e50i | 0.0714041 | − | 0.415095i | ||||
\(271\) | − | 1.61523e51i | − | 1.30580i | −0.757442 | − | 0.652902i | \(-0.773551\pi\) | ||
0.757442 | − | 0.652902i | \(-0.226449\pi\) | |||||||
\(272\) | 2.66904e50 | + | 2.16457e50i | 0.199714 | + | 0.161966i | ||||
\(273\) | 1.18927e51 | 0.823881 | ||||||||
\(274\) | −2.48671e51 | − | 4.27761e50i | −1.59538 | − | 0.274435i | ||||
\(275\) | 1.50771e50i | 0.0896048i | ||||||||
\(276\) | 9.67212e50 | + | 3.42904e50i | 0.532637 | + | 0.188835i | ||||
\(277\) | 1.90483e51 | 0.972258 | 0.486129 | − | 0.873887i | \(-0.338408\pi\) | ||||
0.486129 | + | 0.873887i | \(0.338408\pi\) | |||||||
\(278\) | −6.28746e50 | + | 3.65510e51i | −0.297533 | + | 1.72965i | ||||
\(279\) | − | 1.02276e51i | − | 0.448832i | ||||||
\(280\) | 6.20247e50 | − | 1.10611e51i | 0.252491 | − | 0.450279i | ||||
\(281\) | 1.31260e51 | 0.495792 | 0.247896 | − | 0.968787i | \(-0.420261\pi\) | ||||
0.247896 | + | 0.968787i | \(0.420261\pi\) | |||||||
\(282\) | −5.49429e50 | − | 9.45121e49i | −0.192611 | − | 0.0331326i | ||||
\(283\) | 2.85209e51i | 0.928214i | 0.885779 | + | 0.464107i | \(0.153625\pi\) | ||||
−0.885779 | + | 0.464107i | \(0.846375\pi\) | |||||||
\(284\) | 8.77652e50 | − | 2.47555e51i | 0.265239 | − | 0.748146i | ||||
\(285\) | 1.52455e51 | 0.427956 | ||||||||
\(286\) | −4.89642e49 | + | 2.84644e50i | −0.0127700 | + | 0.0742362i | ||||
\(287\) | − | 8.08081e51i | − | 1.95855i | ||||||
\(288\) | 6.99448e50 | + | 7.99033e50i | 0.157584 | + | 0.180021i | ||||
\(289\) | −4.45807e51 | −0.933881 | ||||||||
\(290\) | 6.00269e50 | + | 1.03258e50i | 0.116947 | + | 0.0201170i | ||||
\(291\) | 5.05215e51i | 0.915638i | ||||||||
\(292\) | 3.70532e51 | + | 1.31364e51i | 0.624865 | + | 0.221532i | ||||
\(293\) | 1.08229e51 | 0.169872 | 0.0849361 | − | 0.996386i | \(-0.472931\pi\) | ||||
0.0849361 | + | 0.996386i | \(0.472931\pi\) | |||||||
\(294\) | 7.64126e50 | − | 4.44210e51i | 0.111653 | − | 0.649075i | ||||
\(295\) | 4.47732e50i | 0.0609194i | ||||||||
\(296\) | 1.76023e51 | + | 9.87039e50i | 0.223071 | + | 0.125086i | ||||
\(297\) | 9.67211e50 | 0.114192 | ||||||||
\(298\) | 1.30145e51 | + | 2.23874e50i | 0.143181 | + | 0.0246299i | ||||
\(299\) | 4.50512e51i | 0.461968i | ||||||||
\(300\) | 2.58574e51 | − | 7.29346e51i | 0.247194 | − | 0.697248i | ||||
\(301\) | −2.35545e52 | −2.09979 | ||||||||
\(302\) | 1.01170e51 | − | 5.88131e51i | 0.0841210 | − | 0.489022i | ||||
\(303\) | 2.04089e52i | 1.58316i | ||||||||
\(304\) | −1.09569e52 | + | 1.35105e52i | −0.793124 | + | 0.977969i | ||||
\(305\) | −7.65581e51 | −0.517243 | ||||||||
\(306\) | 9.61237e50 | + | 1.65351e50i | 0.0606290 | + | 0.0104293i | ||||
\(307\) | − | 1.27509e52i | − | 0.750990i | −0.926824 | − | 0.375495i | \(-0.877473\pi\) | ||
0.926824 | − | 0.375495i | \(-0.122527\pi\) | |||||||
\(308\) | 2.39807e51 | + | 8.50185e50i | 0.131916 | + | 0.0467680i | ||||
\(309\) | −2.14686e52 | −1.10325 | ||||||||
\(310\) | −2.58090e51 | + | 1.50036e52i | −0.123930 | + | 0.720444i | ||||
\(311\) | − | 2.22773e52i | − | 0.999755i | −0.866096 | − | 0.499878i | \(-0.833378\pi\) | ||
0.866096 | − | 0.499878i | \(-0.166622\pi\) | |||||||
\(312\) | 7.25029e51 | − | 1.29298e52i | 0.304165 | − | 0.542430i | ||||
\(313\) | −1.24552e52 | −0.488562 | −0.244281 | − | 0.969704i | \(-0.578552\pi\) | ||||
−0.244281 | + | 0.969704i | \(0.578552\pi\) | |||||||
\(314\) | 4.07196e52 | + | 7.00453e51i | 1.49376 | + | 0.256955i | ||||
\(315\) | − | 3.59934e51i | − | 0.123510i | ||||||
\(316\) | −1.06528e52 | + | 3.00477e52i | −0.342005 | + | 0.964677i | ||||
\(317\) | 5.30020e52 | 1.59239 | 0.796193 | − | 0.605043i | \(-0.206844\pi\) | ||||
0.796193 | + | 0.605043i | \(0.206844\pi\) | |||||||
\(318\) | 8.23080e51 | − | 4.78483e52i | 0.231458 | − | 1.34554i | ||||
\(319\) | 1.22203e51i | 0.0321719i | ||||||||
\(320\) | −8.24440e51 | − | 1.34867e52i | −0.203240 | − | 0.332472i | ||||
\(321\) | 6.75243e52 | 1.55903 | ||||||||
\(322\) | 3.91122e52 | + | 6.72803e51i | 0.845938 | + | 0.145517i | ||||
\(323\) | 1.59769e52i | 0.323773i | ||||||||
\(324\) | −3.49145e52 | − | 1.23782e52i | −0.663072 | − | 0.235078i | ||||
\(325\) | 3.39718e52 | 0.604738 | ||||||||
\(326\) | −3.17591e51 | + | 1.84626e52i | −0.0530028 | + | 0.308122i | ||||
\(327\) | 2.03479e52i | 0.318432i | ||||||||
\(328\) | −8.78547e52 | − | 4.92640e52i | −1.28948 | − | 0.723068i | ||||
\(329\) | −2.15604e52 | −0.296854 | ||||||||
\(330\) | −2.73928e51 | − | 4.71208e50i | −0.0353870 | − | 0.00608724i | ||||
\(331\) | − | 5.66239e52i | − | 0.686455i | −0.939252 | − | 0.343227i | \(-0.888480\pi\) | ||
0.939252 | − | 0.343227i | \(-0.111520\pi\) | |||||||
\(332\) | −1.53103e52 | + | 4.31851e52i | −0.174215 | + | 0.491399i | ||||
\(333\) | 5.72787e51 | 0.0611877 | ||||||||
\(334\) | −1.77099e52 | + | 1.02953e53i | −0.177640 | + | 1.03268i | ||||
\(335\) | − | 6.08512e51i | − | 0.0573229i | ||||||
\(336\) | −1.01425e53 | − | 8.22544e52i | −0.897467 | − | 0.727837i | ||||
\(337\) | 4.43746e52 | 0.368898 | 0.184449 | − | 0.982842i | \(-0.440950\pi\) | ||||
0.184449 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(338\) | −6.20230e52 | − | 1.06691e52i | −0.484509 | − | 0.0833447i | ||||
\(339\) | 8.76202e52i | 0.643296i | ||||||||
\(340\) | −1.36839e52 | − | 4.85132e51i | −0.0944391 | − | 0.0334814i | ||||
\(341\) | −3.05443e52 | −0.198193 | ||||||||
\(342\) | −8.36993e51 | + | 4.86570e52i | −0.0510709 | + | 0.296891i | ||||
\(343\) | 5.65343e52i | 0.324441i | ||||||||
\(344\) | −1.43598e53 | + | 2.56085e53i | −0.775213 | + | 1.38247i | ||||
\(345\) | −4.33552e52 | −0.220212 | ||||||||
\(346\) | 1.44857e53 | + | 2.49182e52i | 0.692376 | + | 0.119102i | ||||
\(347\) | − | 2.18997e53i | − | 0.985189i | −0.870259 | − | 0.492594i | \(-0.836049\pi\) | ||
0.870259 | − | 0.492594i | \(-0.163951\pi\) | |||||||
\(348\) | 2.09579e52 | − | 5.91148e52i | 0.0887531 | − | 0.250341i | ||||
\(349\) | 9.12545e52 | 0.363848 | 0.181924 | − | 0.983313i | \(-0.441767\pi\) | ||||
0.181924 | + | 0.983313i | \(0.441767\pi\) | |||||||
\(350\) | 5.07340e52 | − | 2.94933e53i | 0.190489 | − | 1.10737i | ||||
\(351\) | − | 2.17932e53i | − | 0.770676i | ||||||
\(352\) | 2.38629e52 | − | 2.08888e52i | 0.0794927 | − | 0.0695854i | ||||
\(353\) | −1.04883e53 | −0.329183 | −0.164591 | − | 0.986362i | \(-0.552631\pi\) | ||||
−0.164591 | + | 0.986362i | \(0.552631\pi\) | |||||||
\(354\) | 4.54374e52 | + | 7.81609e51i | 0.134383 | + | 0.0231165i | ||||
\(355\) | 1.10966e53i | 0.309311i | ||||||||
\(356\) | 5.34125e53 | + | 1.89363e53i | 1.40344 | + | 0.497559i | ||||
\(357\) | −1.19941e53 | −0.297122 | ||||||||
\(358\) | 7.80809e52 | − | 4.53909e53i | 0.182390 | − | 1.06029i | ||||
\(359\) | 5.78396e53i | 1.27421i | 0.770776 | + | 0.637106i | \(0.219869\pi\) | ||||
−0.770776 | + | 0.637106i | \(0.780131\pi\) | |||||||
\(360\) | −3.91321e52 | − | 2.19431e52i | −0.0813169 | − | 0.0455980i | ||||
\(361\) | −2.98645e53 | −0.585469 | ||||||||
\(362\) | 2.31810e53 | + | 3.98757e52i | 0.428798 | + | 0.0737613i | ||||
\(363\) | 4.94067e53i | 0.862475i | ||||||||
\(364\) | 1.91564e53 | − | 5.40335e53i | 0.315635 | − | 0.890295i | ||||
\(365\) | −1.66091e53 | −0.258342 | ||||||||
\(366\) | −1.33648e53 | + | 7.76939e53i | −0.196273 | + | 1.14100i | ||||
\(367\) | − | 6.95425e52i | − | 0.0964412i | −0.998837 | − | 0.0482206i | \(-0.984645\pi\) | ||
0.998837 | − | 0.0482206i | \(-0.0153551\pi\) | |||||||
\(368\) | 3.11592e53 | − | 3.84211e53i | 0.408114 | − | 0.503229i | ||||
\(369\) | −2.85883e53 | −0.353700 | ||||||||
\(370\) | −8.40265e52 | − | 1.44541e52i | −0.0982155 | − | 0.0168949i | ||||
\(371\) | − | 1.87764e54i | − | 2.07376i | ||||||
\(372\) | 1.47756e54 | + | 5.23838e53i | 1.54221 | + | 0.546758i | ||||
\(373\) | 2.05688e53 | 0.202919 | 0.101460 | − | 0.994840i | \(-0.467649\pi\) | ||||
0.101460 | + | 0.994840i | \(0.467649\pi\) | |||||||
\(374\) | 4.93816e51 | − | 2.87071e52i | 0.00460534 | − | 0.0267723i | ||||
\(375\) | 7.12387e53i | 0.628144i | ||||||||
\(376\) | −1.31441e53 | + | 2.34405e53i | −0.109594 | + | 0.195444i | ||||
\(377\) | 2.75347e53 | 0.217126 | ||||||||
\(378\) | −1.89202e54 | − | 3.25464e53i | −1.41123 | − | 0.242759i | ||||
\(379\) | − | 1.30408e54i | − | 0.920195i | −0.887868 | − | 0.460097i | \(-0.847814\pi\) | ||
0.887868 | − | 0.460097i | \(-0.152186\pi\) | |||||||
\(380\) | 2.45570e53 | − | 6.92667e53i | 0.163953 | − | 0.462454i | ||||
\(381\) | −2.14623e54 | −1.35598 | ||||||||
\(382\) | −2.06097e53 | + | 1.19811e54i | −0.123237 | + | 0.716415i | ||||
\(383\) | 3.01942e54i | 1.70903i | 0.519429 | + | 0.854514i | \(0.326145\pi\) | ||||
−0.519429 | + | 0.854514i | \(0.673855\pi\) | |||||||
\(384\) | −1.51260e54 | + | 6.01233e53i | −0.810528 | + | 0.322171i | ||||
\(385\) | −1.07493e53 | −0.0545389 | ||||||||
\(386\) | −2.72337e54 | − | 4.68471e53i | −1.30850 | − | 0.225086i | ||||
\(387\) | 8.33310e53i | 0.379207i | ||||||||
\(388\) | 2.29540e54 | + | 8.13786e53i | 0.989448 | + | 0.350787i | ||||
\(389\) | 2.49607e54 | 1.01933 | 0.509666 | − | 0.860372i | \(-0.329769\pi\) | ||||
0.509666 | + | 0.860372i | \(0.329769\pi\) | |||||||
\(390\) | −1.06173e53 | + | 6.17216e53i | −0.0410824 | + | 0.238825i | ||||
\(391\) | − | 4.54353e53i | − | 0.166602i | ||||||
\(392\) | −1.89515e54 | − | 1.06270e54i | −0.658622 | − | 0.369319i | ||||
\(393\) | 2.31394e54 | 0.762268 | ||||||||
\(394\) | −1.89008e54 | − | 3.25130e53i | −0.590283 | − | 0.101540i | ||||
\(395\) | − | 1.34688e54i | − | 0.398833i | ||||||
\(396\) | 3.00779e52 | − | 8.48391e52i | 0.00844594 | − | 0.0238230i | ||||
\(397\) | 2.13047e54 | 0.567380 | 0.283690 | − | 0.958916i | \(-0.408441\pi\) | ||||
0.283690 | + | 0.958916i | \(0.408441\pi\) | |||||||
\(398\) | 2.84073e53 | − | 1.65140e54i | 0.0717604 | − | 0.417166i | ||||
\(399\) | − | 6.07130e54i | − | 1.45496i | ||||||
\(400\) | −2.89722e54 | − | 2.34962e54i | −0.658752 | − | 0.534241i | ||||
\(401\) | 7.18819e54 | 1.55091 | 0.775457 | − | 0.631401i | \(-0.217520\pi\) | ||||
0.775457 | + | 0.631401i | \(0.217520\pi\) | |||||||
\(402\) | −6.17540e53 | − | 1.06228e53i | −0.126450 | − | 0.0217517i | ||||
\(403\) | 6.88226e54i | 1.33760i | ||||||||
\(404\) | 9.27261e54 | + | 3.28740e54i | 1.71078 | + | 0.606519i | ||||
\(405\) | 1.56504e54 | 0.274138 | ||||||||
\(406\) | 4.11209e53 | − | 2.39049e54i | 0.0683936 | − | 0.397594i | ||||
\(407\) | − | 1.71061e53i | − | 0.0270190i | ||||||
\(408\) | −7.31210e53 | + | 1.30400e54i | −0.109693 | + | 0.195620i | ||||
\(409\) | −2.09361e54 | −0.298337 | −0.149168 | − | 0.988812i | \(-0.547660\pi\) | ||||
−0.149168 | + | 0.988812i | \(0.547660\pi\) | |||||||
\(410\) | 4.19384e54 | + | 7.21420e53i | 0.567742 | + | 0.0976623i | ||||
\(411\) | − | 1.09773e55i | − | 1.41194i | ||||||
\(412\) | −3.45810e54 | + | 9.75407e54i | −0.422664 | + | 1.19219i | ||||
\(413\) | 1.78303e54 | 0.207113 | ||||||||
\(414\) | 2.38024e53 | − | 1.38371e54i | 0.0262793 | − | 0.152770i | ||||
\(415\) | − | 1.93577e54i | − | 0.203162i | ||||||
\(416\) | −4.70667e54 | − | 5.37680e54i | −0.469628 | − | 0.536492i | ||||
\(417\) | −1.61350e55 | −1.53078 | ||||||||
\(418\) | 1.45313e54 | + | 2.49966e53i | 0.131100 | + | 0.0225517i | ||||
\(419\) | 1.55694e55i | 1.33591i | 0.744200 | + | 0.667957i | \(0.232831\pi\) | ||||
−0.744200 | + | 0.667957i | \(0.767169\pi\) | |||||||
\(420\) | 5.19993e54 | + | 1.84352e54i | 0.424387 | + | 0.150457i | ||||
\(421\) | −2.08192e55 | −1.61636 | −0.808182 | − | 0.588933i | \(-0.799548\pi\) | ||||
−0.808182 | + | 0.588933i | \(0.799548\pi\) | |||||||
\(422\) | −1.78595e54 | + | 1.03823e55i | −0.131919 | + | 0.766888i | ||||
\(423\) | 7.62764e53i | 0.0536096i | ||||||||
\(424\) | −2.04137e55 | − | 1.14469e55i | −1.36533 | − | 0.765603i | ||||
\(425\) | −3.42614e54 | −0.218091 | ||||||||
\(426\) | 1.12612e55 | + | 1.93715e54i | 0.682315 | + | 0.117371i | ||||
\(427\) | 3.04882e55i | 1.75852i | ||||||||
\(428\) | 1.08766e55 | − | 3.06791e55i | 0.597276 | − | 1.68470i | ||||
\(429\) | −1.25653e54 | −0.0657005 | ||||||||
\(430\) | 2.10284e54 | − | 1.22245e55i | 0.104705 | − | 0.608685i | ||||
\(431\) | − | 2.86805e55i | − | 1.36008i | −0.733176 | − | 0.680039i | \(-0.761963\pi\) | ||
0.733176 | − | 0.680039i | \(-0.238037\pi\) | |||||||
\(432\) | −1.50730e55 | + | 1.85860e55i | −0.680835 | + | 0.839511i | ||||
\(433\) | −1.45804e55 | −0.627370 | −0.313685 | − | 0.949527i | \(-0.601564\pi\) | ||||
−0.313685 | + | 0.949527i | \(0.601564\pi\) | |||||||
\(434\) | 5.97498e55 | + | 1.02781e55i | 2.44936 | + | 0.421335i | ||||
\(435\) | 2.64982e54i | 0.103500i | ||||||||
\(436\) | 9.24491e54 | + | 3.27758e54i | 0.344101 | + | 0.121994i | ||||
\(437\) | 2.29990e55 | 0.815827 | ||||||||
\(438\) | −2.89946e54 | + | 1.68555e55i | −0.0980303 | + | 0.569881i | ||||
\(439\) | 1.17124e55i | 0.377477i | 0.982027 | + | 0.188738i | \(0.0604398\pi\) | ||||
−0.982027 | + | 0.188738i | \(0.939560\pi\) | |||||||
\(440\) | −6.55325e53 | + | 1.16867e54i | −0.0201350 | + | 0.0359076i | ||||
\(441\) | −6.16690e54 | −0.180658 | ||||||||
\(442\) | −6.46829e54 | − | 1.11267e54i | −0.180685 | − | 0.0310812i | ||||
\(443\) | − | 5.65522e55i | − | 1.50651i | −0.657730 | − | 0.753254i | \(-0.728483\pi\) | ||
0.657730 | − | 0.753254i | \(-0.271517\pi\) | |||||||
\(444\) | −2.93372e54 | + | 8.27498e54i | −0.0745376 | + | 0.210244i | ||||
\(445\) | −2.39421e55 | −0.580233 | ||||||||
\(446\) | 1.05630e55 | − | 6.14062e55i | 0.244206 | − | 1.41965i | ||||
\(447\) | 5.74509e54i | 0.126718i | ||||||||
\(448\) | −5.37088e55 | + | 3.28322e55i | −1.13034 | + | 0.690973i | ||||
\(449\) | 7.97841e55 | 1.60230 | 0.801148 | − | 0.598466i | \(-0.204223\pi\) | ||||
0.801148 | + | 0.598466i | \(0.204223\pi\) | |||||||
\(450\) | −1.04341e55 | − | 1.79487e54i | −0.199984 | − | 0.0344009i | ||||
\(451\) | 8.53782e54i | 0.156185i | ||||||||
\(452\) | 3.98095e55 | + | 1.41136e55i | 0.695152 | + | 0.246451i | ||||
\(453\) | 2.59623e55 | 0.432794 | ||||||||
\(454\) | −5.63115e54 | + | 3.27356e55i | −0.0896239 | + | 0.521012i | ||||
\(455\) | 2.42204e55i | 0.368080i | ||||||||
\(456\) | −6.60073e55 | − | 3.70133e55i | −0.957923 | − | 0.537150i | ||||
\(457\) | 1.70643e55 | 0.236509 | 0.118254 | − | 0.992983i | \(-0.462270\pi\) | ||||
0.118254 | + | 0.992983i | \(0.462270\pi\) | |||||||
\(458\) | 3.32448e54 | + | 5.71874e53i | 0.0440098 | + | 0.00757051i | ||||
\(459\) | 2.19790e55i | 0.277934i | ||||||||
\(460\) | −6.98353e54 | + | 1.96981e55i | −0.0843646 | + | 0.237963i | ||||
\(461\) | 1.02450e56 | 1.18247 | 0.591236 | − | 0.806499i | \(-0.298640\pi\) | ||||
0.591236 | + | 0.806499i | \(0.298640\pi\) | |||||||
\(462\) | −1.87652e54 | + | 1.09088e55i | −0.0206953 | + | 0.120308i | ||||
\(463\) | − | 1.09737e56i | − | 1.15652i | −0.815854 | − | 0.578258i | \(-0.803733\pi\) | ||
0.815854 | − | 0.578258i | \(-0.196267\pi\) | |||||||
\(464\) | −2.34825e55 | − | 1.90441e55i | −0.236520 | − | 0.191815i | ||||
\(465\) | −6.62316e55 | −0.637608 | ||||||||
\(466\) | −1.22018e56 | − | 2.09894e55i | −1.12284 | − | 0.193150i | ||||
\(467\) | 9.47914e55i | 0.833900i | 0.908929 | + | 0.416950i | \(0.136901\pi\) | ||||
−0.908929 | + | 0.416950i | \(0.863099\pi\) | |||||||
\(468\) | −1.91160e55 | − | 6.77715e54i | −0.160781 | − | 0.0570012i | ||||
\(469\) | −2.42332e55 | −0.194886 | ||||||||
\(470\) | 1.92482e54 | − | 1.11896e55i | 0.0148025 | − | 0.0860515i | ||||
\(471\) | 1.79752e56i | 1.32201i | ||||||||
\(472\) | 1.08701e55 | − | 1.93851e55i | 0.0764631 | − | 0.136360i | ||||
\(473\) | 2.48866e55 | 0.167449 | ||||||||
\(474\) | −1.36687e56 | − | 2.35127e55i | −0.879793 | − | 0.151341i | ||||
\(475\) | − | 1.73428e56i | − | 1.06796i | ||||||
\(476\) | −1.93197e55 | + | 5.44941e55i | −0.113829 | + | 0.321073i | ||||
\(477\) | −6.64270e55 | −0.374506 | ||||||||
\(478\) | −2.62630e55 | + | 1.52675e56i | −0.141696 | + | 0.823727i | ||||
\(479\) | − | 2.36040e56i | − | 1.21882i | −0.792854 | − | 0.609411i | \(-0.791406\pi\) | ||
0.792854 | − | 0.609411i | \(-0.208594\pi\) | |||||||
\(480\) | 5.17438e55 | − | 4.52948e55i | 0.255736 | − | 0.223863i | ||||
\(481\) | −3.85435e55 | −0.182350 | ||||||||
\(482\) | 4.48528e55 | + | 7.71553e54i | 0.203143 | + | 0.0349444i | ||||
\(483\) | 1.72656e56i | 0.748672i | ||||||||
\(484\) | 2.24475e56 | + | 7.95829e55i | 0.932000 | + | 0.330420i | ||||
\(485\) | −1.02891e56 | −0.409074 | ||||||||
\(486\) | −2.08056e55 | + | 1.20949e56i | −0.0792170 | + | 0.460513i | ||||
\(487\) | 1.06895e56i | 0.389807i | 0.980822 | + | 0.194904i | \(0.0624394\pi\) | ||||
−0.980822 | + | 0.194904i | \(0.937561\pi\) | |||||||
\(488\) | 3.31468e56 | + | 1.85869e56i | 1.15778 | + | 0.649218i | ||||
\(489\) | −8.15008e55 | −0.272694 | ||||||||
\(490\) | 9.04671e55 | + | 1.55621e55i | 0.289983 | + | 0.0498826i | ||||
\(491\) | − | 1.68700e56i | − | 0.518088i | −0.965865 | − | 0.259044i | \(-0.916592\pi\) | ||
0.965865 | − | 0.259044i | \(-0.0834075\pi\) | |||||||
\(492\) | 1.46424e56 | − | 4.13012e56i | 0.430870 | − | 1.21533i | ||||
\(493\) | −2.77695e55 | −0.0783038 | ||||||||
\(494\) | 5.63223e55 | − | 3.27419e56i | 0.152200 | − | 0.884787i | ||||
\(495\) | 3.80290e54i | 0.00984932i | ||||||||
\(496\) | 4.76003e56 | − | 5.86941e56i | 1.18167 | − | 1.45707i | ||||
\(497\) | 4.41907e56 | 1.05159 | ||||||||
\(498\) | −1.96449e56 | − | 3.37928e55i | −0.448159 | − | 0.0770919i | ||||
\(499\) | 2.28193e56i | 0.499105i | 0.968361 | + | 0.249552i | \(0.0802835\pi\) | ||||
−0.968361 | + | 0.249552i | \(0.919717\pi\) | |||||||
\(500\) | 3.23667e56 | + | 1.14749e56i | 0.678779 | + | 0.240646i | ||||
\(501\) | −4.54475e56 | −0.913939 | ||||||||
\(502\) | 2.70392e55 | − | 1.57187e56i | 0.0521454 | − | 0.303137i | ||||
\(503\) | 1.52058e56i | 0.281243i | 0.990063 | + | 0.140622i | \(0.0449101\pi\) | ||||
−0.990063 | + | 0.140622i | \(0.955090\pi\) | |||||||
\(504\) | −8.73854e55 | + | 1.55838e56i | −0.155024 | + | 0.276460i | ||||
\(505\) | −4.15644e56 | −0.707298 | ||||||||
\(506\) | −4.13241e55 | − | 7.10853e54i | −0.0674595 | − | 0.0116043i | ||||
\(507\) | − | 2.73793e56i | − | 0.428801i | ||||||
\(508\) | −3.45709e56 | + | 9.75123e56i | −0.519484 | + | 1.46528i | ||||
\(509\) | 6.45110e55 | 0.0930165 | 0.0465083 | − | 0.998918i | \(-0.485191\pi\) | ||||
0.0465083 | + | 0.998918i | \(0.485191\pi\) | |||||||
\(510\) | 1.07078e55 | − | 6.22478e55i | 0.0148158 | − | 0.0861292i | ||||
\(511\) | 6.61433e56i | 0.878308i | ||||||||
\(512\) | 2.95202e55 | + | 7.84082e56i | 0.0376228 | + | 0.999292i | ||||
\(513\) | −1.11256e57 | −1.36100 | ||||||||
\(514\) | −7.57559e56 | − | 1.30314e56i | −0.889593 | − | 0.153027i | ||||
\(515\) | − | 4.37225e56i | − | 0.492894i | ||||||
\(516\) | −1.20387e57 | − | 4.26807e56i | −1.30298 | − | 0.461943i | ||||
\(517\) | 2.27797e55 | 0.0236727 | ||||||||
\(518\) | −5.75616e55 | + | 3.34624e56i | −0.0574391 | + | 0.333912i | ||||
\(519\) | 6.39455e56i | 0.612767i | ||||||||
\(520\) | 2.63325e56 | + | 1.47658e56i | 0.242338 | + | 0.135890i | ||||
\(521\) | 7.31241e56 | 0.646351 | 0.323176 | − | 0.946339i | \(-0.395250\pi\) | ||||
0.323176 | + | 0.946339i | \(0.395250\pi\) | |||||||
\(522\) | −8.45707e55 | − | 1.45478e55i | −0.0718025 | − | 0.0123514i | ||||
\(523\) | − | 1.53270e57i | − | 1.25004i | −0.780610 | − | 0.625018i | \(-0.785092\pi\) | ||
0.780610 | − | 0.625018i | \(-0.214908\pi\) | |||||||
\(524\) | 3.72722e56 | − | 1.05132e57i | 0.292030 | − | 0.823715i | ||||
\(525\) | 1.30195e57 | 0.980049 | ||||||||
\(526\) | 3.52114e54 | − | 2.04695e55i | 0.00254673 | − | 0.0148049i | ||||
\(527\) | − | 6.94093e56i | − | 0.482386i | ||||||
\(528\) | 1.07161e56 | + | 8.69063e55i | 0.0715687 | + | 0.0580415i | ||||
\(529\) | 9.03960e56 | 0.580203 | ||||||||
\(530\) | 9.74470e56 | + | 1.67627e56i | 0.601139 | + | 0.103407i | ||||
\(531\) | − | 6.30801e55i | − | 0.0374031i | ||||||
\(532\) | −2.75845e57 | − | 9.77948e56i | −1.57225 | − | 0.557406i | ||||
\(533\) | 1.92374e57 | 1.05409 | ||||||||
\(534\) | −4.17959e56 | + | 2.42973e57i | −0.220175 | + | 1.27995i | ||||
\(535\) | 1.37519e57i | 0.696519i | ||||||||
\(536\) | −1.47736e56 | + | 2.63463e56i | −0.0719490 | + | 0.128310i | ||||
\(537\) | 2.00373e57 | 0.938380 | ||||||||
\(538\) | 2.79499e56 | + | 4.80790e55i | 0.125879 | + | 0.0216535i | ||||
\(539\) | 1.84173e56i | 0.0797741i | ||||||||
\(540\) | 3.37823e56 | − | 9.52881e56i | 0.140741 | − | 0.396981i | ||||
\(541\) | 7.70270e55 | 0.0308674 | 0.0154337 | − | 0.999881i | \(-0.495087\pi\) | ||||
0.0154337 | + | 0.999881i | \(0.495087\pi\) | |||||||
\(542\) | 5.74258e56 | − | 3.33834e57i | 0.221372 | − | 1.28690i | ||||
\(543\) | 1.02330e57i | 0.379495i | ||||||||
\(544\) | 4.74680e56 | + | 5.42264e56i | 0.169365 | + | 0.193479i | ||||
\(545\) | −4.14402e56 | −0.142264 | ||||||||
\(546\) | 2.45798e57 | + | 4.22818e56i | 0.811955 | + | 0.139672i | ||||
\(547\) | − | 3.11561e56i | − | 0.0990396i | −0.998773 | − | 0.0495198i | \(-0.984231\pi\) | ||
0.998773 | − | 0.0495198i | \(-0.0157691\pi\) | |||||||
\(548\) | −4.98744e57 | − | 1.76819e57i | −1.52576 | − | 0.540925i | ||||
\(549\) | 1.07861e57 | 0.317575 | ||||||||
\(550\) | −5.36033e55 | + | 3.11613e56i | −0.0151906 | + | 0.0883078i | ||||
\(551\) | − | 1.40567e57i | − | 0.383442i | ||||||
\(552\) | 1.87712e57 | + | 1.05258e57i | 0.492914 | + | 0.276399i | ||||
\(553\) | −5.36378e57 | −1.35595 | ||||||||
\(554\) | 3.93690e57 | + | 6.77221e56i | 0.958185 | + | 0.164826i | ||||
\(555\) | − | 3.70925e56i | − | 0.0869228i | ||||||
\(556\) | −2.59898e57 | + | 7.33081e57i | −0.586452 | + | 1.65418i | ||||
\(557\) | −5.75909e57 | −1.25139 | −0.625697 | − | 0.780066i | \(-0.715186\pi\) | ||||
−0.625697 | + | 0.780066i | \(0.715186\pi\) | |||||||
\(558\) | 3.63618e56 | − | 2.11383e57i | 0.0760900 | − | 0.442335i | ||||
\(559\) | − | 5.60745e57i | − | 1.13010i | ||||||
\(560\) | 1.67518e57 | − | 2.06560e57i | 0.325172 | − | 0.400956i | ||||
\(561\) | 1.26724e56 | 0.0236940 | ||||||||
\(562\) | 2.71287e57 | + | 4.66665e56i | 0.488615 | + | 0.0840510i | ||||
\(563\) | 7.98057e57i | 1.38471i | 0.721559 | + | 0.692353i | \(0.243426\pi\) | ||||
−0.721559 | + | 0.692353i | \(0.756574\pi\) | |||||||
\(564\) | −1.10196e57 | − | 3.90675e56i | −0.184206 | − | 0.0653061i | ||||
\(565\) | −1.78446e57 | −0.287401 | ||||||||
\(566\) | −1.01400e57 | + | 5.89469e57i | −0.157359 | + | 0.914778i | ||||
\(567\) | − | 6.23255e57i | − | 0.932012i | ||||||
\(568\) | 2.69406e57 | − | 4.80443e57i | 0.388232 | − | 0.692351i | ||||
\(569\) | −1.97666e57 | −0.274521 | −0.137260 | − | 0.990535i | \(-0.543830\pi\) | ||||
−0.137260 | + | 0.990535i | \(0.543830\pi\) | |||||||
\(570\) | 3.15093e57 | + | 5.42020e56i | 0.421762 | + | 0.0725510i | ||||
\(571\) | 1.39663e58i | 1.80186i | 0.433961 | + | 0.900932i | \(0.357116\pi\) | ||||
−0.433961 | + | 0.900932i | \(0.642884\pi\) | |||||||
\(572\) | −2.02398e56 | + | 5.70893e56i | −0.0251704 | + | 0.0709967i | ||||
\(573\) | −5.28890e57 | −0.634042 | ||||||||
\(574\) | 2.87295e57 | − | 1.67014e58i | 0.332031 | − | 1.93020i | ||||
\(575\) | 4.93196e57i | 0.549535i | ||||||||
\(576\) | 1.16154e57 | + | 1.90011e57i | 0.124785 | + | 0.204130i | ||||
\(577\) | −4.09717e57 | −0.424416 | −0.212208 | − | 0.977225i | \(-0.568065\pi\) | ||||
−0.212208 | + | 0.977225i | \(0.568065\pi\) | |||||||
\(578\) | −9.21391e57 | − | 1.58497e57i | −0.920364 | − | 0.158320i | ||||
\(579\) | − | 1.20220e58i | − | 1.15805i | ||||||
\(580\) | 1.20392e57 | + | 4.26825e56i | 0.111843 | + | 0.0396517i | ||||
\(581\) | −7.70892e57 | −0.690709 | ||||||||
\(582\) | −1.79618e57 | + | 1.04418e58i | −0.155227 | + | 0.902384i | ||||
\(583\) | 1.98382e57i | 0.165373i | ||||||||
\(584\) | 7.19111e57 | + | 4.03237e57i | 0.578264 | + | 0.324258i | ||||
\(585\) | 8.56871e56 | 0.0664726 | ||||||||
\(586\) | 2.23687e57 | + | 3.84783e56i | 0.167413 | + | 0.0287983i | ||||
\(587\) | 2.25118e57i | 0.162559i | 0.996691 | + | 0.0812794i | \(0.0259006\pi\) | ||||
−0.996691 | + | 0.0812794i | \(0.974099\pi\) | |||||||
\(588\) | 3.15858e57 | − | 8.90926e57i | 0.220074 | − | 0.620751i | ||||
\(589\) | 3.51344e58 | 2.36217 | ||||||||
\(590\) | −1.59181e56 | + | 9.25371e56i | −0.0103276 | + | 0.0600376i | ||||
\(591\) | − | 8.34355e57i | − | 0.522413i | ||||||
\(592\) | 3.28712e57 | + | 2.66582e57i | 0.198637 | + | 0.161092i | ||||
\(593\) | 1.62838e58 | 0.949743 | 0.474872 | − | 0.880055i | \(-0.342494\pi\) | ||||
0.474872 | + | 0.880055i | \(0.342494\pi\) | |||||||
\(594\) | 1.99903e57 | + | 3.43870e56i | 0.112539 | + | 0.0193588i | ||||
\(595\) | − | 2.44269e57i | − | 0.132743i | ||||||
\(596\) | 2.61024e57 | + | 9.25403e56i | 0.136933 | + | 0.0485467i | ||||
\(597\) | 7.28993e57 | 0.369201 | ||||||||
\(598\) | −1.60170e57 | + | 9.31117e57i | −0.0783168 | + | 0.455281i | ||||
\(599\) | − | 1.87184e58i | − | 0.883702i | −0.897088 | − | 0.441851i | \(-0.854322\pi\) | ||
0.897088 | − | 0.441851i | \(-0.145678\pi\) | |||||||
\(600\) | 7.93722e57 | − | 1.41548e58i | 0.361820 | − | 0.645249i | ||||
\(601\) | 6.65480e57 | 0.292935 | 0.146467 | − | 0.989215i | \(-0.453210\pi\) | ||||
0.146467 | + | 0.989215i | \(0.453210\pi\) | |||||||
\(602\) | −4.86823e58 | − | 8.37427e57i | −2.06940 | − | 0.355976i | ||||
\(603\) | 8.57321e56i | 0.0351949i | ||||||||
\(604\) | 4.18194e57 | − | 1.17958e58i | 0.165807 | − | 0.467682i | ||||
\(605\) | −1.00621e58 | −0.385323 | ||||||||
\(606\) | −7.25593e57 | + | 4.21810e58i | −0.268391 | + | 1.56024i | ||||
\(607\) | 9.04232e57i | 0.323085i | 0.986866 | + | 0.161543i | \(0.0516470\pi\) | ||||
−0.986866 | + | 0.161543i | \(0.948353\pi\) | |||||||
\(608\) | −2.74489e58 | + | 2.40279e58i | −0.947437 | + | 0.829356i | ||||
\(609\) | 1.05525e58 | 0.351879 | ||||||||
\(610\) | −1.58230e58 | − | 2.72186e57i | −0.509756 | − | 0.0876877i | ||||
\(611\) | − | 5.13273e57i | − | 0.159766i | ||||||
\(612\) | 1.92789e57 | + | 6.83493e56i | 0.0579834 | + | 0.0205567i | ||||
\(613\) | −1.40615e58 | −0.408659 | −0.204329 | − | 0.978902i | \(-0.565501\pi\) | ||||
−0.204329 | + | 0.978902i | \(0.565501\pi\) | |||||||
\(614\) | 4.53329e57 | − | 2.63535e58i | 0.127314 | − | 0.740119i | ||||
\(615\) | 1.85132e58i | 0.502463i | ||||||||
\(616\) | 4.65407e57 | + | 2.60974e57i | 0.122078 | + | 0.0684546i | ||||
\(617\) | −5.58230e58 | −1.41522 | −0.707612 | − | 0.706602i | \(-0.750227\pi\) | ||||
−0.707612 | + | 0.706602i | \(0.750227\pi\) | |||||||
\(618\) | −4.43712e58 | − | 7.63268e57i | −1.08728 | − | 0.187033i | ||||
\(619\) | − | 3.89176e57i | − | 0.0921812i | −0.998937 | − | 0.0460906i | \(-0.985324\pi\) | ||
0.998937 | − | 0.0460906i | \(-0.0146763\pi\) | |||||||
\(620\) | −1.06684e58 | + | 3.00918e58i | −0.244272 | + | 0.689006i | ||||
\(621\) | 3.16390e58 | 0.700325 | ||||||||
\(622\) | 7.92019e57 | − | 4.60426e58i | 0.169487 | − | 0.985284i | ||||
\(623\) | 9.53461e58i | 1.97267i | ||||||||
\(624\) | 1.95818e58 | − | 2.41455e58i | 0.391719 | − | 0.483014i | ||||
\(625\) | 2.93403e58 | 0.567523 | ||||||||
\(626\) | −2.57424e58 | − | 4.42817e57i | −0.481490 | − | 0.0828254i | ||||
\(627\) | 6.41467e57i | 0.116026i | ||||||||
\(628\) | 8.16687e58 | + | 2.89539e58i | 1.42858 | + | 0.506471i | ||||
\(629\) | 3.88721e57 | 0.0657620 | ||||||||
\(630\) | 1.27967e57 | − | 7.43911e57i | 0.0209385 | − | 0.121722i | ||||
\(631\) | − | 1.14571e59i | − | 1.81326i | −0.421930 | − | 0.906628i | \(-0.638647\pi\) | ||
0.421930 | − | 0.906628i | \(-0.361353\pi\) | |||||||
\(632\) | −3.26999e58 | + | 5.83151e58i | −0.500596 | + | 0.892734i | ||||
\(633\) | −4.58314e58 | −0.678711 | ||||||||
\(634\) | 1.09544e59 | + | 1.88437e58i | 1.56934 | + | 0.269955i | ||||
\(635\) | − | 4.37098e58i | − | 0.605802i | ||||||
\(636\) | 3.40228e58 | − | 9.59663e58i | 0.456216 | − | 1.28683i | ||||
\(637\) | 4.14979e58 | 0.538391 | ||||||||
\(638\) | −4.34465e56 | + | 2.52568e57i | −0.00545406 | + | 0.0317062i | ||||
\(639\) | − | 1.56338e58i | − | 0.189910i | ||||||
\(640\) | −1.22446e58 | − | 3.08053e58i | −0.143935 | − | 0.362115i | ||||
\(641\) | −1.31593e59 | −1.49697 | −0.748484 | − | 0.663152i | \(-0.769218\pi\) | ||||
−0.748484 | + | 0.663152i | \(0.769218\pi\) | |||||||
\(642\) | 1.39559e59 | + | 2.40068e58i | 1.53646 | + | 0.264301i | ||||
\(643\) | − | 8.14606e58i | − | 0.867995i | −0.900914 | − | 0.433997i | \(-0.857103\pi\) | ||
0.900914 | − | 0.433997i | \(-0.142897\pi\) | |||||||
\(644\) | 7.84449e58 | + | 2.78109e58i | 0.809024 | + | 0.286822i | ||||
\(645\) | 5.39635e58 | 0.538699 | ||||||||
\(646\) | −5.68025e57 | + | 3.30211e58i | −0.0548889 | + | 0.319087i | ||||
\(647\) | 5.88617e58i | 0.550609i | 0.961357 | + | 0.275304i | \(0.0887786\pi\) | ||||
−0.961357 | + | 0.275304i | \(0.911221\pi\) | |||||||
\(648\) | −6.77604e58 | − | 3.79963e58i | −0.613622 | − | 0.344085i | ||||
\(649\) | −1.88387e57 | −0.0165163 | ||||||||
\(650\) | 7.02127e58 | + | 1.20779e58i | 0.595985 | + | 0.102521i | ||||
\(651\) | 2.63758e59i | 2.16773i | ||||||||
\(652\) | −1.31279e58 | + | 3.70292e58i | −0.104471 | + | 0.294676i | ||||
\(653\) | −1.57717e59 | −1.21535 | −0.607675 | − | 0.794186i | \(-0.707898\pi\) | ||||
−0.607675 | + | 0.794186i | \(0.707898\pi\) | |||||||
\(654\) | −7.23425e57 | + | 4.20550e58i | −0.0539835 | + | 0.313823i | ||||
\(655\) | 4.71252e58i | 0.340554i | ||||||||
\(656\) | −1.64063e59 | − | 1.33054e59i | −1.14823 | − | 0.931206i | ||||
\(657\) | 2.34002e58 | 0.158616 | ||||||||
\(658\) | −4.45609e58 | − | 7.66532e57i | −0.292557 | − | 0.0503253i | ||||
\(659\) | − | 1.50895e59i | − | 0.959579i | −0.877384 | − | 0.479789i | \(-0.840713\pi\) | ||
0.877384 | − | 0.479789i | \(-0.159287\pi\) | |||||||
\(660\) | −5.49401e57 | − | 1.94778e57i | −0.0338429 | − | 0.0119983i | ||||
\(661\) | −1.26109e59 | −0.752517 | −0.376259 | − | 0.926515i | \(-0.622790\pi\) | ||||
−0.376259 | + | 0.926515i | \(0.622790\pi\) | |||||||
\(662\) | 2.01314e58 | − | 1.17030e59i | 0.116374 | − | 0.676518i | ||||
\(663\) | − | 2.85535e58i | − | 0.159910i | ||||||
\(664\) | −4.69969e58 | + | 8.38115e58i | −0.254999 | + | 0.454752i | ||||
\(665\) | 1.23647e59 | 0.650024 | ||||||||
\(666\) | 1.18383e58 | + | 2.03642e57i | 0.0603020 | + | 0.0103731i | ||||
\(667\) | 3.99745e58i | 0.197306i | ||||||||
\(668\) | −7.32054e58 | + | 2.06487e59i | −0.350137 | + | 0.987613i | ||||
\(669\) | 2.71070e59 | 1.25642 | ||||||||
\(670\) | 2.16343e57 | − | 1.25767e58i | 0.00971789 | − | 0.0564932i | ||||
\(671\) | − | 3.22125e58i | − | 0.140233i | ||||||
\(672\) | −1.80380e59 | − | 2.06062e59i | −0.761087 | − | 0.869449i | ||||
\(673\) | −2.35126e59 | −0.961577 | −0.480789 | − | 0.876837i | \(-0.659650\pi\) | ||||
−0.480789 | + | 0.876837i | \(0.659650\pi\) | |||||||
\(674\) | 9.17132e58 | + | 1.57764e58i | 0.363558 | + | 0.0625389i | ||||
\(675\) | − | 2.38580e59i | − | 0.916759i | ||||||
\(676\) | −1.24396e59 | − | 4.41018e58i | −0.463367 | − | 0.164277i | ||||
\(677\) | 3.55696e59 | 1.28445 | 0.642225 | − | 0.766516i | \(-0.278012\pi\) | ||||
0.642225 | + | 0.766516i | \(0.278012\pi\) | |||||||
\(678\) | −3.11514e58 | + | 1.81093e59i | −0.109057 | + | 0.633984i | ||||
\(679\) | 4.09750e59i | 1.39076i | ||||||||
\(680\) | −2.65570e58 | − | 1.48917e58i | −0.0873961 | − | 0.0490069i | ||||
\(681\) | −1.44508e59 | −0.461106 | ||||||||
\(682\) | −6.31289e58 | − | 1.08594e58i | −0.195324 | − | 0.0335995i | ||||
\(683\) | − | 2.95984e59i | − | 0.888042i | −0.896016 | − | 0.444021i | \(-0.853552\pi\) | ||
0.896016 | − | 0.444021i | \(-0.146448\pi\) | |||||||
\(684\) | −3.45979e58 | + | 9.75885e58i | −0.100663 | + | 0.283936i | ||||
\(685\) | 2.23561e59 | 0.630805 | ||||||||
\(686\) | −2.00995e58 | + | 1.16845e59i | −0.0550021 | + | 0.319745i | ||||
\(687\) | 1.46755e58i | 0.0389496i | ||||||||
\(688\) | −3.87833e59 | + | 4.78221e59i | −0.998361 | + | 1.23104i | ||||
\(689\) | 4.46996e59 | 1.11609 | ||||||||
\(690\) | −8.96063e58 | − | 1.54140e58i | −0.217024 | − | 0.0373322i | ||||
\(691\) | − | 2.15531e58i | − | 0.0506372i | −0.999679 | − | 0.0253186i | \(-0.991940\pi\) | ||
0.999679 | − | 0.0253186i | \(-0.00806003\pi\) | |||||||
\(692\) | 2.90531e59 | + | 1.03002e59i | 0.662163 | + | 0.234756i | ||||
\(693\) | 1.51445e58 | 0.0334856 | ||||||||
\(694\) | 7.78596e58 | − | 4.52622e59i | 0.167018 | − | 0.970928i | ||||
\(695\) | − | 3.28603e59i | − | 0.683897i | ||||||
\(696\) | 6.43326e58 | − | 1.14727e59i | 0.129908 | − | 0.231671i | ||||
\(697\) | −1.94014e59 | −0.380142 | ||||||||
\(698\) | 1.88604e59 | + | 3.24435e58i | 0.358582 | + | 0.0616828i | ||||
\(699\) | − | 5.38633e59i | − | 0.993739i | ||||||
\(700\) | 2.09714e59 | − | 5.91529e59i | 0.375464 | − | 1.05905i | ||||
\(701\) | 7.18112e59 | 1.24771 | 0.623855 | − | 0.781540i | \(-0.285565\pi\) | ||||
0.623855 | + | 0.781540i | \(0.285565\pi\) | |||||||
\(702\) | 7.74810e58 | − | 4.50421e59i | 0.130652 | − | 0.759521i | ||||
\(703\) | 1.96768e59i | 0.322027i | ||||||||
\(704\) | 5.67463e58 | − | 3.46890e58i | 0.0901388 | − | 0.0551018i | ||||
\(705\) | 4.93950e58 | 0.0761574 | ||||||||
\(706\) | −2.16772e59 | − | 3.72889e58i | −0.324418 | − | 0.0558060i | ||||
\(707\) | 1.65524e60i | 2.40466i | ||||||||
\(708\) | 9.11311e58 | + | 3.23085e58i | 0.128519 | + | 0.0455637i | ||||
\(709\) | −4.70042e59 | −0.643525 | −0.321762 | − | 0.946820i | \(-0.604275\pi\) | ||||
−0.321762 | + | 0.946820i | \(0.604275\pi\) | |||||||
\(710\) | −3.94516e58 | + | 2.29345e59i | −0.0524372 | + | 0.304834i | ||||
\(711\) | 1.89760e59i | 0.244874i | ||||||||
\(712\) | 1.03660e60 | + | 5.81270e59i | 1.29877 | + | 0.728280i | ||||
\(713\) | −9.99154e59 | −1.21549 | ||||||||
\(714\) | −2.47893e59 | − | 4.26423e58i | −0.292821 | − | 0.0503707i | ||||
\(715\) | − | 2.55902e58i | − | 0.0293526i | ||||||
\(716\) | 3.22755e59 | − | 9.10377e59i | 0.359500 | − | 1.01402i | ||||
\(717\) | −6.73967e59 | −0.729015 | ||||||||
\(718\) | −2.05636e59 | + | 1.19543e60i | −0.216016 | + | 1.25577i | ||||
\(719\) | − | 1.41173e60i | − | 1.44027i | −0.693834 | − | 0.720135i | \(-0.744080\pi\) | ||
0.693834 | − | 0.720135i | \(-0.255920\pi\) | |||||||
\(720\) | −7.30767e58 | − | 5.92645e58i | −0.0724097 | − | 0.0587236i | ||||
\(721\) | −1.74119e60 | −1.67573 | ||||||||
\(722\) | −6.17238e59 | − | 1.06177e59i | −0.576994 | − | 0.0992539i | ||||
\(723\) | 1.97998e59i | 0.179786i | ||||||||
\(724\) | 4.64927e59 | + | 1.64830e59i | 0.410086 | + | 0.145387i | ||||
\(725\) | 3.01435e59 | 0.258283 | ||||||||
\(726\) | −1.75655e59 | + | 1.02114e60i | −0.146214 | + | 0.849991i | ||||
\(727\) | − | 3.94107e59i | − | 0.318707i | −0.987222 | − | 0.159353i | \(-0.949059\pi\) | ||
0.987222 | − | 0.159353i | \(-0.0509409\pi\) | |||||||
\(728\) | 5.88028e59 | − | 1.04866e60i | 0.461997 | − | 0.823899i | ||||
\(729\) | −1.45553e60 | −1.11107 | ||||||||
\(730\) | −3.43275e59 | − | 5.90498e58i | −0.254602 | − | 0.0437964i | ||||
\(731\) | 5.65526e59i | 0.407556i | ||||||||
\(732\) | −5.52447e59 | + | 1.55826e60i | −0.386864 | + | 1.09121i | ||||
\(733\) | 3.63598e59 | 0.247422 | 0.123711 | − | 0.992318i | \(-0.460520\pi\) | ||||
0.123711 | + | 0.992318i | \(0.460520\pi\) | |||||||
\(734\) | 2.47243e58 | − | 1.43730e59i | 0.0163496 | − | 0.0950453i | ||||
\(735\) | 3.99356e59i | 0.256641i | ||||||||
\(736\) | 7.80594e59 | − | 6.83307e59i | 0.487519 | − | 0.426758i | ||||
\(737\) | 2.56037e58 | 0.0155412 | ||||||||
\(738\) | −5.90862e59 | − | 1.01639e59i | −0.348580 | − | 0.0599623i | ||||
\(739\) | 7.19815e59i | 0.412750i | 0.978473 | + | 0.206375i | \(0.0661668\pi\) | ||||
−0.978473 | + | 0.206375i | \(0.933833\pi\) | |||||||
\(740\) | −1.68527e59 | − | 5.97475e58i | −0.0939297 | − | 0.0333007i | ||||
\(741\) | 1.44535e60 | 0.783054 | ||||||||
\(742\) | 6.67552e59 | − | 3.88069e60i | 0.351563 | − | 2.04375i | ||||
\(743\) | − | 1.83146e59i | − | 0.0937631i | −0.998900 | − | 0.0468816i | \(-0.985072\pi\) | ||
0.998900 | − | 0.0468816i | \(-0.0149283\pi\) | |||||||
\(744\) | 2.86758e60 | + | 1.60798e60i | 1.42720 | + | 0.800294i | ||||
\(745\) | −1.17004e59 | −0.0566132 | ||||||||
\(746\) | 4.25115e59 | + | 7.31278e58i | 0.199982 | + | 0.0344007i | ||||
\(747\) | 2.72726e59i | 0.124737i | ||||||||
\(748\) | 2.04123e58 | − | 5.75761e58i | 0.00907735 | − | 0.0256040i | ||||
\(749\) | 5.47649e60 | 2.36802 | ||||||||
\(750\) | −2.53273e59 | + | 1.47236e60i | −0.106489 | + | 0.619052i | ||||
\(751\) | − | 2.98766e60i | − | 1.22150i | −0.791824 | − | 0.610749i | \(-0.790868\pi\) | ||
0.791824 | − | 0.610749i | \(-0.209132\pi\) | |||||||
\(752\) | −3.55000e59 | + | 4.37736e59i | −0.141141 | + | 0.174035i | ||||
\(753\) | 6.93885e59 | 0.268283 | ||||||||
\(754\) | 5.69087e59 | + | 9.78937e58i | 0.213984 | + | 0.0368092i | ||||
\(755\) | 5.28745e59i | 0.193357i | ||||||||
\(756\) | −3.79472e60 | − | 1.34533e60i | −1.34965 | − | 0.478490i | ||||
\(757\) | 1.80666e60 | 0.624976 | 0.312488 | − | 0.949922i | \(-0.398838\pi\) | ||||
0.312488 | + | 0.949922i | \(0.398838\pi\) | |||||||
\(758\) | 4.63636e59 | − | 2.69526e60i | 0.156000 | − | 0.906875i | ||||
\(759\) | − | 1.82421e59i | − | 0.0597030i | ||||||
\(760\) | 7.53806e59 | − | 1.34429e60i | 0.239979 | − | 0.427966i | ||||
\(761\) | −9.77729e59 | −0.302790 | −0.151395 | − | 0.988473i | \(-0.548376\pi\) | ||||
−0.151395 | + | 0.988473i | \(0.548376\pi\) | |||||||
\(762\) | −4.43582e60 | − | 7.63045e59i | −1.33635 | − | 0.229877i | ||||
\(763\) | 1.65030e60i | 0.483668i | ||||||||
\(764\) | −8.51920e59 | + | 2.40297e60i | −0.242906 | + | 0.685153i | ||||
\(765\) | −8.64177e58 | −0.0239724 | ||||||||
\(766\) | −1.07349e60 | + | 6.24052e60i | −0.289730 | + | 1.68429i | ||||
\(767\) | 4.24474e59i | 0.111468i | ||||||||
\(768\) | −3.33999e60 | + | 7.04855e59i | −0.853413 | + | 0.180100i | ||||
\(769\) | −4.50113e60 | −1.11910 | −0.559549 | − | 0.828797i | \(-0.689026\pi\) | ||||
−0.559549 | + | 0.828797i | \(0.689026\pi\) | |||||||
\(770\) | −2.22167e59 | − | 3.82169e58i | −0.0537495 | − | 0.00924592i | ||||
\(771\) | − | 3.34416e60i | − | 0.787308i | ||||||
\(772\) | −5.46210e60 | − | 1.93647e60i | −1.25140 | − | 0.443657i | ||||
\(773\) | 5.68528e60 | 1.26760 | 0.633801 | − | 0.773497i | \(-0.281494\pi\) | ||||
0.633801 | + | 0.773497i | \(0.281494\pi\) | |||||||
\(774\) | −2.96265e59 | + | 1.72228e60i | −0.0642866 | + | 0.373718i | ||||
\(775\) | 7.53432e60i | 1.59114i | ||||||||
\(776\) | 4.45481e60 | + | 2.49801e60i | 0.915657 | + | 0.513450i | ||||
\(777\) | −1.47716e60 | −0.295519 | ||||||||
\(778\) | 5.15887e60 | + | 8.87423e59i | 1.00458 | + | 0.172806i | ||||
\(779\) | − | 9.82085e60i | − | 1.86150i | ||||||
\(780\) | −4.38875e59 | + | 1.23791e60i | −0.0809756 | + | 0.228404i | ||||
\(781\) | −4.66899e59 | −0.0838594 | ||||||||
\(782\) | 1.61535e59 | − | 9.39055e59i | 0.0282439 | − | 0.164191i | ||||
\(783\) | − | 1.93374e60i | − | 0.329155i | ||||||
\(784\) | −3.53907e60 | − | 2.87015e60i | −0.586479 | − | 0.475629i | ||||
\(785\) | −3.66079e60 | −0.590625 | ||||||||
\(786\) | 4.78243e60 | + | 8.22668e59i | 0.751234 | + | 0.129226i | ||||
\(787\) | 2.10897e60i | 0.322553i | 0.986909 | + | 0.161276i | \(0.0515610\pi\) | ||||
−0.986909 | + | 0.161276i | \(0.948439\pi\) | |||||||
\(788\) | −3.79083e60 | − | 1.34396e60i | −0.564525 | − | 0.200140i | ||||
\(789\) | 9.03601e58 | 0.0131027 | ||||||||
\(790\) | 4.78855e59 | − | 2.78373e60i | 0.0676137 | − | 0.393060i | ||||
\(791\) | 7.10635e60i | 0.977104i | ||||||||
\(792\) | 9.23275e58 | − | 1.64652e59i | 0.0123624 | − | 0.0220464i | ||||
\(793\) | −7.25812e60 | −0.946427 | ||||||||
\(794\) | 4.40324e60 | + | 7.57441e59i | 0.559168 | + | 0.0961874i | ||||
\(795\) | 4.30168e60i | 0.532021i | ||||||||
\(796\) | 1.17424e60 | − | 3.31212e60i | 0.141443 | − | 0.398962i | ||||
\(797\) | 3.04020e60 | 0.356679 | 0.178339 | − | 0.983969i | \(-0.442928\pi\) | ||||
0.178339 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(798\) | 2.15852e60 | − | 1.25481e61i | 0.246658 | − | 1.43390i | ||||
\(799\) | 5.17649e59i | 0.0576173i | ||||||||
\(800\) | −5.15261e60 | − | 5.88623e60i | −0.558647 | − | 0.638186i | ||||
\(801\) | 3.37316e60 | 0.356249 | ||||||||
\(802\) | 1.48565e61 | + | 2.55560e60i | 1.52846 | + | 0.262925i | ||||
\(803\) | − | 6.98840e59i | − | 0.0700408i | ||||||
\(804\) | −1.23856e60 | − | 4.39105e59i | −0.120932 | − | 0.0428738i | ||||
\(805\) | −3.51628e60 | −0.334480 | ||||||||
\(806\) | −2.44683e60 | + | 1.42242e61i | −0.226761 | + | 1.31823i | ||||
\(807\) | 1.23381e60i | 0.111405i | ||||||||
\(808\) | 1.79958e61 | + | 1.00911e61i | 1.58319 | + | 0.887766i | ||||
\(809\) | −1.23032e61 | −1.05463 | −0.527315 | − | 0.849670i | \(-0.676801\pi\) | ||||
−0.527315 | + | 0.849670i | \(0.676801\pi\) | |||||||
\(810\) | 3.23462e60 | + | 5.56415e59i | 0.270170 | + | 0.0464744i | ||||
\(811\) | − | 6.49185e60i | − | 0.528361i | −0.964473 | − | 0.264180i | \(-0.914899\pi\) | ||
0.964473 | − | 0.264180i | \(-0.0851015\pi\) | |||||||
\(812\) | 1.69977e60 | − | 4.79445e60i | 0.134807 | − | 0.380244i | ||||
\(813\) | 1.47367e61 | 1.13894 | ||||||||
\(814\) | 6.08170e58 | − | 3.53549e59i | 0.00458050 | − | 0.0266279i | ||||
\(815\) | − | 1.65983e60i | − | 0.121830i | ||||||
\(816\) | −1.97487e60 | + | 2.43513e60i | −0.141268 | + | 0.174193i | ||||
\(817\) | −2.86264e61 | −1.99574 | ||||||||
\(818\) | −4.32707e60 | − | 7.44338e59i | −0.294019 | − | 0.0505767i | ||||
\(819\) | − | 3.41237e60i | − | 0.225993i | ||||||
\(820\) | 8.41133e60 | + | 2.98205e60i | 0.542967 | + | 0.192497i | ||||
\(821\) | 1.89733e61 | 1.19382 | 0.596908 | − | 0.802309i | \(-0.296396\pi\) | ||||
0.596908 | + | 0.802309i | \(0.296396\pi\) | |||||||
\(822\) | 3.90273e60 | − | 2.26878e61i | 0.239365 | − | 1.39150i | ||||
\(823\) | − | 1.75773e61i | − | 1.05089i | −0.850829 | − | 0.525443i | \(-0.823900\pi\) | ||
0.850829 | − | 0.525443i | \(-0.176100\pi\) | |||||||
\(824\) | −1.06150e61 | + | 1.89302e61i | −0.618656 | + | 1.10328i | ||||
\(825\) | −1.37558e60 | −0.0781542 | ||||||||
\(826\) | 3.68516e60 | + | 6.33917e59i | 0.204115 | + | 0.0351117i | ||||
\(827\) | 1.42009e61i | 0.766831i | 0.923576 | + | 0.383416i | \(0.125252\pi\) | ||||
−0.923576 | + | 0.383416i | \(0.874748\pi\) | |||||||
\(828\) | 9.83895e59 | − | 2.77522e60i | 0.0517979 | − | 0.146104i | ||||
\(829\) | −5.95082e60 | −0.305444 | −0.152722 | − | 0.988269i | \(-0.548804\pi\) | ||||
−0.152722 | + | 0.988269i | \(0.548804\pi\) | |||||||
\(830\) | 6.88219e59 | − | 4.00084e60i | 0.0344419 | − | 0.200222i | ||||
\(831\) | 1.73790e61i | 0.848014i | ||||||||
\(832\) | −7.81613e60 | − | 1.27861e61i | −0.371879 | − | 0.608342i | ||||
\(833\) | −4.18517e60 | −0.194164 | ||||||||
\(834\) | −3.33478e61 | − | 5.73645e60i | −1.50862 | − | 0.259511i | ||||
\(835\) | − | 9.25575e60i | − | 0.408315i | ||||||
\(836\) | 2.91445e60 | + | 1.03326e60i | 0.125379 | + | 0.0444504i | ||||
\(837\) | 4.83334e61 | 2.02774 | ||||||||
\(838\) | −5.53537e60 | + | 3.21789e61i | −0.226476 | + | 1.31658i | ||||
\(839\) | − | 1.32492e61i | − | 0.528675i | −0.964430 | − | 0.264338i | \(-0.914847\pi\) | ||
0.964430 | − | 0.264338i | \(-0.0851533\pi\) | |||||||
\(840\) | 1.00918e61 | + | 5.65891e60i | 0.392738 | + | 0.220225i | ||||
\(841\) | −2.39029e61 | −0.907265 | ||||||||
\(842\) | −4.30290e61 | − | 7.40179e60i | −1.59297 | − | 0.274020i | ||||
\(843\) | 1.19757e61i | 0.432434i | ||||||||
\(844\) | −7.38239e60 | + | 2.08231e61i | −0.260019 | + | 0.733423i | ||||
\(845\) | 5.57602e60 | 0.191573 | ||||||||
\(846\) | −2.71184e59 | + | 1.57648e60i | −0.00908837 | + | 0.0528336i | ||||
\(847\) | 4.00708e61i | 1.31002i | ||||||||
\(848\) | −3.81212e61 | − | 3.09160e61i | −1.21578 | − | 0.985984i | ||||
\(849\) | −2.60214e61 | −0.809597 | ||||||||
\(850\) | −7.08113e60 | − | 1.21809e60i | −0.214934 | − | 0.0369727i | ||||
\(851\) | − | 5.59568e60i | − | 0.165704i | ||||||
\(852\) | 2.25860e61 | + | 8.00737e60i | 0.652541 | + | 0.231344i | ||||
\(853\) | 2.31643e61 | 0.652964 | 0.326482 | − | 0.945203i | \(-0.394137\pi\) | ||||
0.326482 | + | 0.945203i | \(0.394137\pi\) | |||||||
\(854\) | −1.08394e61 | + | 6.30129e61i | −0.298119 | + | 1.73306i | ||||
\(855\) | − | 4.37439e60i | − | 0.117389i | ||||||
\(856\) | 3.33870e61 | − | 5.95406e61i | 0.874236 | − | 1.55906i | ||||
\(857\) | 3.00133e61 | 0.766860 | 0.383430 | − | 0.923570i | \(-0.374743\pi\) | ||||
0.383430 | + | 0.923570i | \(0.374743\pi\) | |||||||
\(858\) | −2.59699e60 | − | 4.46731e59i | −0.0647495 | − | 0.0111381i | ||||
\(859\) | − | 1.33009e60i | − | 0.0323611i | −0.999869 | − | 0.0161806i | \(-0.994849\pi\) | ||
0.999869 | − | 0.0161806i | \(-0.00515065\pi\) | |||||||
\(860\) | 8.69228e60 | − | 2.45179e61i | 0.206379 | − | 0.582124i | ||||
\(861\) | 7.37263e61 | 1.70827 | ||||||||
\(862\) | 1.01967e61 | − | 5.92767e61i | 0.230573 | − | 1.34039i | ||||
\(863\) | − | 7.89149e61i | − | 1.74153i | −0.491695 | − | 0.870767i | \(-0.663623\pi\) | ||
0.491695 | − | 0.870767i | \(-0.336377\pi\) | |||||||
\(864\) | −3.77607e61 | + | 3.30545e61i | −0.813301 | + | 0.711938i | ||||
\(865\) | −1.30230e61 | −0.273762 | ||||||||
\(866\) | −3.01347e61 | − | 5.18374e60i | −0.618289 | − | 0.106357i | ||||
\(867\) | − | 4.06737e61i | − | 0.814541i | ||||||
\(868\) | 1.19836e62 | + | 4.24854e61i | 2.34247 | + | 0.830473i | ||||
\(869\) | 5.66712e60 | 0.108130 | ||||||||
\(870\) | −9.42083e59 | + | 5.47663e60i | −0.0175463 | + | 0.102002i | ||||
\(871\) | − | 5.76902e60i | − | 0.104887i | ||||||
\(872\) | 1.79421e61 | + | 1.00609e61i | 0.318439 | + | 0.178563i | ||||
\(873\) | 1.44961e61 | 0.251162 | ||||||||
\(874\) | 4.75342e61 | + | 8.17678e60i | 0.804019 | + | 0.138306i | ||||
\(875\) | 5.77774e61i | 0.954090i | ||||||||
\(876\) | −1.19852e61 | + | 3.38060e61i | −0.193223 | + | 0.545013i | ||||
\(877\) | 1.97462e61 | 0.310808 | 0.155404 | − | 0.987851i | \(-0.450332\pi\) | ||||
0.155404 | + | 0.987851i | \(0.450332\pi\) | |||||||
\(878\) | −4.16408e60 | + | 2.42071e61i | −0.0639932 | + | 0.372013i | ||||
\(879\) | 9.87438e60i | 0.148164i | ||||||||
\(880\) | −1.76992e60 | + | 2.18242e60i | −0.0259309 | + | 0.0319743i | ||||
\(881\) | −1.24161e62 | −1.77619 | −0.888095 | − | 0.459659i | \(-0.847972\pi\) | ||||
−0.888095 | + | 0.459659i | \(0.847972\pi\) | |||||||
\(882\) | −1.27457e61 | − | 2.19251e60i | −0.178043 | − | 0.0306267i | ||||
\(883\) | − | 2.67978e61i | − | 0.365531i | −0.983157 | − | 0.182765i | \(-0.941495\pi\) | ||
0.983157 | − | 0.182765i | \(-0.0585049\pi\) | |||||||
\(884\) | −1.29730e61 | − | 4.59931e60i | −0.172800 | − | 0.0612626i | ||||
\(885\) | −4.08494e60 | −0.0531346 | ||||||||
\(886\) | 2.01059e61 | − | 1.16882e62i | 0.255397 | − | 1.48470i | ||||
\(887\) | 1.30509e62i | 1.61899i | 0.587124 | + | 0.809497i | \(0.300260\pi\) | ||||
−0.587124 | + | 0.809497i | \(0.699740\pi\) | |||||||
\(888\) | −9.00538e60 | + | 1.60597e61i | −0.109101 | + | 0.194565i | ||||
\(889\) | −1.74068e62 | −2.05960 | ||||||||
\(890\) | −4.94835e61 | − | 8.51209e60i | −0.571834 | − | 0.0983662i | ||||
\(891\) | 6.58503e60i | 0.0743235i | ||||||||
\(892\) | 4.36632e61 | − | 1.23159e62i | 0.481342 | − | 1.35770i | ||||
\(893\) | −2.62030e61 | −0.282144 | ||||||||
\(894\) | −2.04254e60 | + | 1.18739e61i | −0.0214824 | + | 0.124884i | ||||
\(895\) | 4.08076e61i | 0.419234i | ||||||||
\(896\) | −1.22678e62 | + | 4.87624e61i | −1.23111 | + | 0.489347i | ||||
\(897\) | −4.11030e61 | −0.402933 | ||||||||
\(898\) | 1.64897e62 | + | 2.83655e61i | 1.57910 | + | 0.271636i | ||||
\(899\) | 6.10671e61i | 0.571286i | ||||||||
\(900\) | −2.09271e61 | − | 7.41926e60i | −0.191257 | − | 0.0678060i | ||||
\(901\) | −4.50807e61 | −0.402504 | ||||||||
\(902\) | −3.03543e60 | + | 1.76459e61i | −0.0264779 | + | 0.153924i | ||||
\(903\) | − | 2.14902e62i | − | 1.83146i | ||||||
\(904\) | 7.72604e61 | + | 4.33234e61i | 0.643310 | + | 0.360732i | ||||
\(905\) | −2.08403e61 | −0.169545 | ||||||||
\(906\) | 5.36589e61 | + | 9.23034e60i | 0.426530 | + | 0.0733712i | ||||
\(907\) | 1.86719e62i | 1.45022i | 0.688631 | + | 0.725112i | \(0.258212\pi\) | ||||
−0.688631 | + | 0.725112i | \(0.741788\pi\) | |||||||
\(908\) | −2.32769e61 | + | 6.56559e61i | −0.176653 | + | 0.498277i | ||||
\(909\) | 5.85592e61 | 0.434264 | ||||||||
\(910\) | −8.61104e60 | + | 5.00587e61i | −0.0624003 | + | 0.362753i | ||||
\(911\) | − | 1.33909e62i | − | 0.948253i | −0.880457 | − | 0.474126i | \(-0.842764\pi\) | ||
0.880457 | − | 0.474126i | \(-0.157236\pi\) | |||||||
\(912\) | −1.23264e62 | − | 9.99663e61i | −0.852995 | − | 0.691770i | ||||
\(913\) | 8.14490e60 | 0.0550807 | ||||||||
\(914\) | 3.52684e61 | + | 6.06682e60i | 0.233085 | + | 0.0400951i | ||||
\(915\) | − | 6.98488e61i | − | 0.451145i | ||||||
\(916\) | 6.66771e60 | + | 2.36389e60i | 0.0420893 | + | 0.0149219i | ||||
\(917\) | 1.87670e62 | 1.15781 | ||||||||
\(918\) | −7.81415e60 | + | 4.54261e61i | −0.0471179 | + | 0.273911i | ||||
\(919\) | − | 9.20724e61i | − | 0.542630i | −0.962491 | − | 0.271315i | \(-0.912542\pi\) | ||
0.962491 | − | 0.271315i | \(-0.0874585\pi\) | |||||||
\(920\) | −2.14367e61 | + | 3.82291e61i | −0.123485 | + | 0.220216i | ||||
\(921\) | 1.16334e62 | 0.655021 | ||||||||
\(922\) | 2.11742e62 | + | 3.64237e61i | 1.16536 | + | 0.200463i | ||||
\(923\) | 1.05202e62i | 0.565963i | ||||||||
\(924\) | −7.75677e60 | + | 2.18791e61i | −0.0407915 | + | 0.115059i | ||||
\(925\) | −4.21954e61 | −0.216914 | ||||||||
\(926\) | 3.90145e61 | − | 2.26803e62i | 0.196063 | − | 1.13977i | ||||
\(927\) | 6.15998e61i | 0.302625i | ||||||||
\(928\) | −4.17629e61 | − | 4.77089e61i | −0.200578 | − | 0.229135i | ||||
\(929\) | 2.24606e62 | 1.05461 | 0.527304 | − | 0.849677i | \(-0.323203\pi\) | ||||
0.527304 | + | 0.849677i | \(0.323203\pi\) | |||||||
\(930\) | −1.36887e62 | − | 2.35472e61i | −0.628378 | − | 0.108093i | ||||
\(931\) | − | 2.11850e62i | − | 0.950790i | ||||||
\(932\) | −2.44724e62 | − | 8.67614e61i | −1.07384 | − | 0.380708i | ||||
\(933\) | 2.03249e62 | 0.871997 | ||||||||
\(934\) | −3.37010e61 | + | 1.95914e62i | −0.141370 | + | 0.821830i | ||||
\(935\) | 2.58084e60i | 0.0105856i | ||||||||
\(936\) | −3.70993e61 | − | 2.08033e61i | −0.148790 | − | 0.0834331i | ||||
\(937\) | −4.19898e62 | −1.64669 | −0.823345 | − | 0.567541i | \(-0.807895\pi\) | ||||
−0.823345 | + | 0.567541i | \(0.807895\pi\) | |||||||
\(938\) | −5.00850e61 | − | 8.61556e60i | −0.192065 | − | 0.0330388i | ||||
\(939\) | − | 1.13637e62i | − | 0.426129i | ||||||
\(940\) | 7.95641e60 | − | 2.24422e61i | 0.0291764 | − | 0.0822965i | ||||
\(941\) | 4.11281e62 | 1.47488 | 0.737439 | − | 0.675414i | \(-0.236035\pi\) | ||||
0.737439 | + | 0.675414i | \(0.236035\pi\) | |||||||
\(942\) | −6.39067e61 | + | 3.71510e62i | −0.224118 | + | 1.30287i | ||||
\(943\) | 2.79286e62i | 0.957863i | ||||||||
\(944\) | 2.93583e61 | − | 3.62005e61i | 0.0984733 | − | 0.121424i | ||||
\(945\) | 1.70098e62 | 0.557995 | ||||||||
\(946\) | 5.14355e61 | + | 8.84787e60i | 0.165025 | + | 0.0283874i | ||||
\(947\) | 1.14975e62i | 0.360789i | 0.983594 | + | 0.180395i | \(0.0577375\pi\) | ||||
−0.983594 | + | 0.180395i | \(0.942262\pi\) | |||||||
\(948\) | −2.74144e62 | − | 9.71917e61i | −0.841401 | − | 0.298301i | ||||
\(949\) | −1.57463e62 | −0.472702 | ||||||||
\(950\) | 6.16586e61 | − | 3.58441e62i | 0.181050 | − | 1.05250i | ||||
\(951\) | 4.83571e62i | 1.38889i | ||||||||
\(952\) | −5.93041e61 | + | 1.05760e62i | −0.166613 | + | 0.297128i | ||||
\(953\) | 5.01879e62 | 1.37927 | 0.689633 | − | 0.724159i | \(-0.257772\pi\) | ||||
0.689633 | + | 0.724159i | \(0.257772\pi\) | |||||||
\(954\) | −1.37291e62 | − | 2.36167e61i | −0.369085 | − | 0.0634896i | ||||
\(955\) | − | 1.07713e62i | − | 0.283267i | ||||||
\(956\) | −1.08561e62 | + | 3.06212e62i | −0.279291 | + | 0.787782i | ||||
\(957\) | −1.11493e61 | −0.0280606 | ||||||||
\(958\) | 8.39189e61 | − | 4.87847e62i | 0.206626 | − | 1.20118i | ||||
\(959\) | − | 8.90302e62i | − | 2.14460i | ||||||
\(960\) | 1.23047e62 | − | 7.52188e61i | 0.289986 | − | 0.177268i | ||||
\(961\) | −1.09266e63 | −2.51938 | ||||||||
\(962\) | −7.96616e61 | − | 1.37033e61i | −0.179710 | − | 0.0309135i | ||||
\(963\) | − | 1.93748e62i | − | 0.427646i | ||||||
\(964\) | 8.99586e61 | + | 3.18929e61i | 0.194279 | + | 0.0688773i | ||||
\(965\) | 2.44838e62 | 0.517375 | ||||||||
\(966\) | −6.13840e61 | + | 3.56845e62i | −0.126922 | + | 0.737836i | ||||
\(967\) | 7.61171e62i | 1.54002i | 0.638032 | + | 0.770010i | \(0.279749\pi\) | ||||
−0.638032 | + | 0.770010i | \(0.720251\pi\) | |||||||
\(968\) | 4.35651e62 | + | 2.44289e62i | 0.862494 | + | 0.483639i | ||||
\(969\) | −1.45768e62 | −0.282398 | ||||||||
\(970\) | −2.12655e62 | − | 3.65807e61i | −0.403153 | − | 0.0693499i | ||||
\(971\) | − | 5.06333e62i | − | 0.939360i | −0.882837 | − | 0.469680i | \(-0.844369\pi\) | ||
0.882837 | − | 0.469680i | \(-0.155631\pi\) | |||||||
\(972\) | −8.60018e61 | + | 2.42581e62i | −0.156141 | + | 0.440418i | ||||
\(973\) | −1.30862e63 | −2.32510 | ||||||||
\(974\) | −3.80042e61 | + | 2.20931e62i | −0.0660836 | + | 0.384165i | ||||
\(975\) | 3.09946e62i | 0.527459i | ||||||||
\(976\) | 6.18996e62 | + | 5.02000e62i | 1.03096 | + | 0.836098i | ||||
\(977\) | 5.75301e61 | 0.0937797 | 0.0468899 | − | 0.998900i | \(-0.485069\pi\) | ||||
0.0468899 | + | 0.998900i | \(0.485069\pi\) | |||||||
\(978\) | −1.68446e62 | − | 2.89758e61i | −0.268747 | − | 0.0462296i | ||||
\(979\) | − | 1.00738e62i | − | 0.157311i | ||||||
\(980\) | 1.81444e62 | + | 6.43272e61i | 0.277329 | + | 0.0983211i | ||||
\(981\) | 5.83843e61 | 0.0873468 | ||||||||
\(982\) | 5.99776e61 | − | 3.48669e62i | 0.0878310 | − | 0.510589i | ||||
\(983\) | 5.65404e62i | 0.810466i | 0.914213 | + | 0.405233i | \(0.132810\pi\) | ||||
−0.914213 | + | 0.405233i | \(0.867190\pi\) | |||||||
\(984\) | 4.49467e62 | − | 8.01553e62i | 0.630668 | − | 1.12470i | ||||
\(985\) | 1.69923e62 | 0.233395 | ||||||||
\(986\) | −5.73939e61 | − | 9.87283e60i | −0.0771703 | − | 0.0132748i | ||||
\(987\) | − | 1.96709e62i | − | 0.258919i | ||||||
\(988\) | 2.32813e62 | − | 6.56685e62i | 0.299994 | − | 0.846177i | ||||
\(989\) | 8.14080e62 | 1.02694 | ||||||||
\(990\) | −1.35204e60 | + | 7.85983e60i | −0.00166974 | + | 0.00970675i | ||||
\(991\) | 1.77300e62i | 0.214369i | 0.994239 | + | 0.107184i | \(0.0341835\pi\) | ||||
−0.994239 | + | 0.107184i | \(0.965816\pi\) | |||||||
\(992\) | 1.19248e63 | − | 1.04385e63i | 1.41158 | − | 1.23565i | ||||
\(993\) | 5.16615e62 | 0.598733 | ||||||||
\(994\) | 9.13333e62 | + | 1.57110e62i | 1.03637 | + | 0.178275i | ||||
\(995\) | 1.48465e62i | 0.164946i | ||||||||
\(996\) | −3.94005e62 | − | 1.39686e62i | −0.428603 | − | 0.151952i | ||||
\(997\) | −6.85556e62 | −0.730205 | −0.365102 | − | 0.930967i | \(-0.618966\pi\) | ||||
−0.365102 | + | 0.930967i | \(0.618966\pi\) | |||||||
\(998\) | −8.11291e61 | + | 4.71629e62i | −0.0846127 | + | 0.491880i | ||||
\(999\) | 2.70687e62i | 0.276435i |
(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.3.20 | yes | 20 | |
4.3 | odd | 2 | inner | 4.43.b.a.3.19 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.43.b.a.3.19 | ✓ | 20 | 4.3 | odd | 2 | inner | |
4.43.b.a.3.20 | yes | 20 | 1.1 | even | 1 | trivial |