Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,41,Mod(2,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 41, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 41);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 41 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(30.4026855589\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 249659905422 x^{10} + \cdots + 12\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{63}\cdot 3^{98}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.11 | ||
Root | \(245022. i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.41.b.a.2.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.47013e6i | 1.40203i | 0.713148 | + | 0.701014i | \(0.247269\pi\) | ||||
−0.713148 | + | 0.701014i | \(0.752731\pi\) | |||||||
\(3\) | 1.53875e9 | + | 3.12889e9i | 0.441308 | + | 0.897356i | ||||
\(4\) | −1.06178e12 | −0.965680 | ||||||||
\(5\) | 3.18557e13i | 0.334032i | 0.985954 | + | 0.167016i | \(0.0534131\pi\) | ||||
−0.985954 | + | 0.167016i | \(0.946587\pi\) | |||||||
\(6\) | −4.59988e15 | + | 2.26216e15i | −1.25812 | + | 0.618726i | ||||
\(7\) | 7.85404e14 | 0.00984311 | 0.00492156 | − | 0.999988i | \(-0.498433\pi\) | ||||
0.00492156 | + | 0.999988i | \(0.498433\pi\) | |||||||
\(8\) | 5.54756e16i | 0.0481174i | ||||||||
\(9\) | −7.42219e18 | + | 9.62912e18i | −0.610495 | + | 0.792020i | ||||
\(10\) | −4.68322e19 | −0.468322 | ||||||||
\(11\) | − | 8.83914e20i | − | 1.31388i | −0.753942 | − | 0.656941i | \(-0.771850\pi\) | ||
0.753942 | − | 0.656941i | \(-0.228150\pi\) | |||||||
\(12\) | −1.63380e21 | − | 3.32218e21i | −0.426162 | − | 0.866559i | ||||
\(13\) | −1.50265e22 | −0.790664 | −0.395332 | − | 0.918538i | \(-0.629370\pi\) | ||||
−0.395332 | + | 0.918538i | \(0.629370\pi\) | |||||||
\(14\) | 1.15465e21i | 0.0138003i | ||||||||
\(15\) | −9.96730e22 | + | 4.90179e22i | −0.299745 | + | 0.147411i | ||||
\(16\) | −1.24899e24 | −1.03314 | ||||||||
\(17\) | − | 2.97100e24i | − | 0.731012i | −0.930809 | − | 0.365506i | \(-0.880896\pi\) | ||
0.930809 | − | 0.365506i | \(-0.119104\pi\) | |||||||
\(18\) | −1.41561e25 | − | 1.09116e25i | −1.11043 | − | 0.855930i | ||||
\(19\) | −6.09769e25 | −1.62216 | −0.811079 | − | 0.584936i | \(-0.801119\pi\) | ||||
−0.811079 | + | 0.584936i | \(0.801119\pi\) | |||||||
\(20\) | − | 3.38237e25i | − | 0.322568i | ||||||
\(21\) | 1.20854e24 | + | 2.45744e24i | 0.00434384 | + | 0.00883277i | ||||
\(22\) | 1.29947e27 | 1.84210 | ||||||||
\(23\) | 1.99164e27i | 1.16052i | 0.814431 | + | 0.580261i | \(0.197049\pi\) | ||||
−0.814431 | + | 0.580261i | \(0.802951\pi\) | |||||||
\(24\) | −1.73577e26 | + | 8.53628e25i | −0.0431784 | + | 0.0212346i | ||||
\(25\) | 8.08016e27 | 0.888423 | ||||||||
\(26\) | − | 2.20910e28i | − | 1.10853i | ||||||
\(27\) | −4.15493e28 | − | 8.40642e27i | −0.980140 | − | 0.198306i | ||||
\(28\) | −8.33924e26 | −0.00950530 | ||||||||
\(29\) | − | 8.61658e28i | − | 0.486827i | −0.969923 | − | 0.243414i | \(-0.921733\pi\) | ||
0.969923 | − | 0.243414i | \(-0.0782673\pi\) | |||||||
\(30\) | −7.20628e28 | − | 1.46532e29i | −0.206674 | − | 0.420251i | ||||
\(31\) | 3.82717e29 | 0.569696 | 0.284848 | − | 0.958573i | \(-0.408057\pi\) | ||||
0.284848 | + | 0.958573i | \(0.408057\pi\) | |||||||
\(32\) | − | 1.77519e30i | − | 1.40038i | ||||||
\(33\) | 2.76567e30 | − | 1.36012e30i | 1.17902 | − | 0.579826i | ||||
\(34\) | 4.36777e30 | 1.02490 | ||||||||
\(35\) | 2.50196e28i | 0.00328791i | ||||||||
\(36\) | 7.88071e30 | − | 1.02240e31i | 0.589543 | − | 0.764838i | ||||
\(37\) | −1.30186e31 | −0.563030 | −0.281515 | − | 0.959557i | \(-0.590837\pi\) | ||||
−0.281515 | + | 0.959557i | \(0.590837\pi\) | |||||||
\(38\) | − | 8.96441e31i | − | 2.27431i | ||||||
\(39\) | −2.31220e31 | − | 4.70163e31i | −0.348926 | − | 0.709507i | ||||
\(40\) | −1.76722e30 | −0.0160727 | ||||||||
\(41\) | 1.97826e32i | 1.09801i | 0.835820 | + | 0.549004i | \(0.184993\pi\) | ||||
−0.835820 | + | 0.549004i | \(0.815007\pi\) | |||||||
\(42\) | −3.61276e30 | + | 1.77671e30i | −0.0123838 | + | 0.00609019i | ||||
\(43\) | 8.12325e32 | 1.73925 | 0.869623 | − | 0.493717i | \(-0.164362\pi\) | ||||
0.869623 | + | 0.493717i | \(0.164362\pi\) | |||||||
\(44\) | 9.38519e32i | 1.26879i | ||||||||
\(45\) | −3.06743e32 | − | 2.36439e32i | −0.264560 | − | 0.203925i | ||||
\(46\) | −2.92797e33 | −1.62708 | ||||||||
\(47\) | 4.06950e33i | 1.47090i | 0.677577 | + | 0.735452i | \(0.263030\pi\) | ||||
−0.677577 | + | 0.735452i | \(0.736970\pi\) | |||||||
\(48\) | −1.92188e33 | − | 3.90795e33i | −0.455934 | − | 0.927096i | ||||
\(49\) | −6.36619e33 | −0.999903 | ||||||||
\(50\) | 1.18789e34i | 1.24559i | ||||||||
\(51\) | 9.29593e33 | − | 4.57162e33i | 0.655978 | − | 0.322601i | ||||
\(52\) | 1.59548e34 | 0.763528 | ||||||||
\(53\) | 2.48872e34i | 0.813690i | 0.913497 | + | 0.406845i | \(0.133371\pi\) | ||||
−0.913497 | + | 0.406845i | \(0.866629\pi\) | |||||||
\(54\) | 1.23586e34 | − | 6.10829e34i | 0.278030 | − | 1.37418i | ||||
\(55\) | 2.81577e34 | 0.438878 | ||||||||
\(56\) | 4.35708e31i | 0.000473625i | ||||||||
\(57\) | −9.38279e34 | − | 1.90790e35i | −0.715871 | − | 1.45565i | ||||
\(58\) | 1.26675e35 | 0.682545 | ||||||||
\(59\) | − | 1.16497e35i | − | 0.445938i | −0.974826 | − | 0.222969i | \(-0.928425\pi\) | ||
0.974826 | − | 0.222969i | \(-0.0715748\pi\) | |||||||
\(60\) | 1.05830e35 | − | 5.20460e34i | 0.289458 | − | 0.142352i | ||||
\(61\) | −5.58865e35 | −1.09827 | −0.549136 | − | 0.835733i | \(-0.685043\pi\) | ||||
−0.549136 | + | 0.835733i | \(0.685043\pi\) | |||||||
\(62\) | 5.62644e35i | 0.798730i | ||||||||
\(63\) | −5.82942e33 | + | 7.56275e33i | −0.00600917 | + | 0.00779595i | ||||
\(64\) | 1.23648e36 | 0.930223 | ||||||||
\(65\) | − | 4.78682e35i | − | 0.264107i | ||||||
\(66\) | 1.99955e36 | + | 4.06589e36i | 0.812932 | + | 1.65302i | ||||
\(67\) | −4.40203e36 | −1.32482 | −0.662410 | − | 0.749141i | \(-0.730466\pi\) | ||||
−0.662410 | + | 0.749141i | \(0.730466\pi\) | |||||||
\(68\) | 3.15454e36i | 0.705924i | ||||||||
\(69\) | −6.23160e36 | + | 3.06462e36i | −1.04140 | + | 0.512148i | ||||
\(70\) | −3.67822e34 | −0.00460974 | ||||||||
\(71\) | − | 1.87733e37i | − | 1.77163i | −0.464039 | − | 0.885815i | \(-0.653600\pi\) | ||
0.464039 | − | 0.885815i | \(-0.346400\pi\) | |||||||
\(72\) | −5.34181e35 | − | 4.11750e35i | −0.0381100 | − | 0.0293754i | ||||
\(73\) | 8.39273e35 | 0.0454408 | 0.0227204 | − | 0.999742i | \(-0.492767\pi\) | ||||
0.0227204 | + | 0.999742i | \(0.492767\pi\) | |||||||
\(74\) | − | 1.91391e37i | − | 0.789383i | ||||||
\(75\) | 1.24333e37 | + | 2.52819e37i | 0.392068 | + | 0.797231i | ||||
\(76\) | 6.47438e37 | 1.56649 | ||||||||
\(77\) | − | 6.94230e35i | − | 0.0129327i | ||||||
\(78\) | 6.91202e37 | − | 3.39924e37i | 0.994748 | − | 0.489204i | ||||
\(79\) | −8.62105e37 | −0.961653 | −0.480827 | − | 0.876816i | \(-0.659663\pi\) | ||||
−0.480827 | + | 0.876816i | \(0.659663\pi\) | |||||||
\(80\) | − | 3.97876e37i | − | 0.345102i | ||||||
\(81\) | −3.76310e37 | − | 1.42938e38i | −0.254593 | − | 0.967048i | ||||
\(82\) | −2.90830e38 | −1.53944 | ||||||||
\(83\) | 1.72703e38i | 0.717363i | 0.933460 | + | 0.358682i | \(0.116774\pi\) | ||||
−0.933460 | + | 0.358682i | \(0.883226\pi\) | |||||||
\(84\) | −1.28320e36 | − | 2.60925e36i | −0.00419476 | − | 0.00852963i | ||||
\(85\) | 9.46435e37 | 0.244181 | ||||||||
\(86\) | 1.19423e39i | 2.43847i | ||||||||
\(87\) | 2.69603e38 | − | 1.32587e38i | 0.436857 | − | 0.214841i | ||||
\(88\) | 4.90356e37 | 0.0632206 | ||||||||
\(89\) | 3.16586e38i | 0.325605i | 0.986659 | + | 0.162803i | \(0.0520534\pi\) | ||||
−0.986659 | + | 0.162803i | \(0.947947\pi\) | |||||||
\(90\) | 3.47597e38 | − | 4.50952e38i | 0.285908 | − | 0.370920i | ||||
\(91\) | −1.18019e37 | −0.00778259 | ||||||||
\(92\) | − | 2.11467e39i | − | 1.12069i | ||||||
\(93\) | 5.88904e38 | + | 1.19748e39i | 0.251412 | + | 0.511220i | ||||
\(94\) | −5.98270e39 | −2.06225 | ||||||||
\(95\) | − | 1.94246e39i | − | 0.541852i | ||||||
\(96\) | 5.55436e39 | − | 2.73156e39i | 1.25664 | − | 0.617997i | ||||
\(97\) | 2.49823e39 | 0.459408 | 0.229704 | − | 0.973261i | \(-0.426224\pi\) | ||||
0.229704 | + | 0.973261i | \(0.426224\pi\) | |||||||
\(98\) | − | 9.35914e39i | − | 1.40189i | ||||||
\(99\) | 8.51131e39 | + | 6.56057e39i | 1.04062 | + | 0.802118i | ||||
\(100\) | −8.57932e39 | −0.857932 | ||||||||
\(101\) | 1.38822e39i | 0.113771i | 0.998381 | + | 0.0568855i | \(0.0181170\pi\) | ||||
−0.998381 | + | 0.0568855i | \(0.981883\pi\) | |||||||
\(102\) | 6.72088e39 | + | 1.36662e40i | 0.452296 | + | 0.919699i | ||||
\(103\) | −5.22898e38 | −0.0289516 | −0.0144758 | − | 0.999895i | \(-0.504608\pi\) | ||||
−0.0144758 | + | 0.999895i | \(0.504608\pi\) | |||||||
\(104\) | − | 8.33606e38i | − | 0.0380447i | ||||||
\(105\) | −7.82836e37 | + | 3.84989e37i | −0.00295043 | + | 0.00145098i | ||||
\(106\) | −3.65875e40 | −1.14081 | ||||||||
\(107\) | 2.81098e40i | 0.726411i | 0.931709 | + | 0.363206i | \(0.118318\pi\) | ||||
−0.931709 | + | 0.363206i | \(0.881682\pi\) | |||||||
\(108\) | 4.41160e40 | + | 8.92574e39i | 0.946502 | + | 0.191500i | ||||
\(109\) | −9.91057e40 | −1.76835 | −0.884176 | − | 0.467154i | \(-0.845279\pi\) | ||||
−0.884176 | + | 0.467154i | \(0.845279\pi\) | |||||||
\(110\) | 4.13956e40i | 0.615319i | ||||||||
\(111\) | −2.00324e40 | − | 4.07339e40i | −0.248470 | − | 0.505238i | ||||
\(112\) | −9.80964e38 | −0.0101693 | ||||||||
\(113\) | 4.74724e39i | 0.0411977i | 0.999788 | + | 0.0205988i | \(0.00655728\pi\) | ||||
−0.999788 | + | 0.0205988i | \(0.993443\pi\) | |||||||
\(114\) | 2.80486e41 | − | 1.37939e41i | 2.04087 | − | 1.00367i | ||||
\(115\) | −6.34451e40 | −0.387651 | ||||||||
\(116\) | 9.14888e40i | 0.470120i | ||||||||
\(117\) | 1.11530e41 | − | 1.44692e41i | 0.482696 | − | 0.626222i | ||||
\(118\) | 1.71266e41 | 0.625217 | ||||||||
\(119\) | − | 2.33344e39i | − | 0.00719543i | ||||||
\(120\) | −2.71930e39 | − | 5.52942e39i | −0.00709303 | − | 0.0144230i | ||||
\(121\) | −3.28711e41 | −0.726284 | ||||||||
\(122\) | − | 8.21605e41i | − | 1.53981i | ||||||
\(123\) | −6.18974e41 | + | 3.04403e41i | −0.985304 | + | 0.484560i | ||||
\(124\) | −4.06360e41 | −0.550145 | ||||||||
\(125\) | 5.47126e41i | 0.630793i | ||||||||
\(126\) | −1.11182e40 | − | 8.57002e39i | −0.0109301 | − | 0.00842502i | ||||
\(127\) | 8.29339e41 | 0.696078 | 0.348039 | − | 0.937480i | \(-0.386848\pi\) | ||||
0.348039 | + | 0.937480i | \(0.386848\pi\) | |||||||
\(128\) | − | 1.34053e41i | − | 0.0961781i | ||||||
\(129\) | 1.24996e42 | + | 2.54167e42i | 0.767543 | + | 1.56072i | ||||
\(130\) | 7.03725e41 | 0.370285 | ||||||||
\(131\) | 3.01248e42i | 1.35987i | 0.733272 | + | 0.679935i | \(0.237992\pi\) | ||||
−0.733272 | + | 0.679935i | \(0.762008\pi\) | |||||||
\(132\) | −2.93652e42 | + | 1.44414e42i | −1.13856 | + | 0.559927i | ||||
\(133\) | −4.78915e40 | −0.0159671 | ||||||||
\(134\) | − | 6.47156e42i | − | 1.85743i | ||||||
\(135\) | 2.67793e41 | − | 1.32358e42i | 0.0662405 | − | 0.327398i | ||||
\(136\) | 1.64818e41 | 0.0351744 | ||||||||
\(137\) | − | 1.97127e42i | − | 0.363359i | −0.983358 | − | 0.181679i | \(-0.941847\pi\) | ||
0.983358 | − | 0.181679i | \(-0.0581533\pi\) | |||||||
\(138\) | −4.50540e42 | − | 9.16128e42i | −0.718045 | − | 1.46007i | ||||
\(139\) | 2.34490e42 | 0.323466 | 0.161733 | − | 0.986835i | \(-0.448292\pi\) | ||||
0.161733 | + | 0.986835i | \(0.448292\pi\) | |||||||
\(140\) | − | 2.65653e40i | − | 0.00317507i | ||||||
\(141\) | −1.27330e43 | + | 6.26193e42i | −1.31992 | + | 0.649121i | ||||
\(142\) | 2.75992e43 | 2.48387 | ||||||||
\(143\) | 1.32822e43i | 1.03884i | ||||||||
\(144\) | 9.27026e42 | − | 1.20267e43i | 0.630728 | − | 0.818270i | ||||
\(145\) | 2.74488e42 | 0.162616 | ||||||||
\(146\) | 1.23384e42i | 0.0637093i | ||||||||
\(147\) | −9.79594e42 | − | 1.99191e43i | −0.441265 | − | 0.897269i | ||||
\(148\) | 1.38229e43 | 0.543707 | ||||||||
\(149\) | 2.99713e43i | 1.03034i | 0.857088 | + | 0.515170i | \(0.172271\pi\) | ||||
−0.857088 | + | 0.515170i | \(0.827729\pi\) | |||||||
\(150\) | −3.71677e43 | + | 1.82786e43i | −1.11774 | + | 0.549690i | ||||
\(151\) | −7.32154e43 | −1.92781 | −0.963904 | − | 0.266252i | \(-0.914215\pi\) | ||||
−0.963904 | + | 0.266252i | \(0.914215\pi\) | |||||||
\(152\) | − | 3.38273e42i | − | 0.0780541i | ||||||
\(153\) | 2.86081e43 | + | 2.20513e43i | 0.578976 | + | 0.446279i | ||||
\(154\) | 1.02061e42 | 0.0181320 | ||||||||
\(155\) | 1.21917e43i | 0.190297i | ||||||||
\(156\) | 2.45504e43 | + | 4.99208e43i | 0.336951 | + | 0.685156i | ||||
\(157\) | 2.98232e43 | 0.360214 | 0.180107 | − | 0.983647i | \(-0.442356\pi\) | ||||
0.180107 | + | 0.983647i | \(0.442356\pi\) | |||||||
\(158\) | − | 1.26741e44i | − | 1.34826i | ||||||
\(159\) | −7.78692e43 | + | 3.82951e43i | −0.730169 | + | 0.359088i | ||||
\(160\) | 5.65499e43 | 0.467770 | ||||||||
\(161\) | 1.56424e42i | 0.0114231i | ||||||||
\(162\) | 2.10138e44 | − | 5.53226e43i | 1.35583 | − | 0.356946i | ||||
\(163\) | 6.16652e43 | 0.351794 | 0.175897 | − | 0.984409i | \(-0.443717\pi\) | ||||
0.175897 | + | 0.984409i | \(0.443717\pi\) | |||||||
\(164\) | − | 2.10047e44i | − | 1.06032i | ||||||
\(165\) | 4.33276e43 | + | 8.81023e43i | 0.193680 | + | 0.393830i | ||||
\(166\) | −2.53897e44 | −1.00576 | ||||||||
\(167\) | − | 1.03723e44i | − | 0.364373i | −0.983264 | − | 0.182186i | \(-0.941683\pi\) | ||
0.983264 | − | 0.182186i | \(-0.0583174\pi\) | |||||||
\(168\) | −1.36328e41 | + | 6.70443e40i | −0.000425010 | + | 0.000209014i | ||||
\(169\) | −1.35392e44 | −0.374851 | ||||||||
\(170\) | 1.39138e44i | 0.342349i | ||||||||
\(171\) | 4.52582e44 | − | 5.87154e44i | 0.990319 | − | 1.28478i | ||||
\(172\) | −8.62508e44 | −1.67955 | ||||||||
\(173\) | 4.64474e44i | 0.805451i | 0.915321 | + | 0.402726i | \(0.131937\pi\) | ||||
−0.915321 | + | 0.402726i | \(0.868063\pi\) | |||||||
\(174\) | 1.94921e44 | + | 3.96352e44i | 0.301213 | + | 0.612486i | ||||
\(175\) | 6.34619e42 | 0.00874485 | ||||||||
\(176\) | 1.10400e45i | 1.35743i | ||||||||
\(177\) | 3.64506e44 | − | 1.79259e44i | 0.400165 | − | 0.196796i | ||||
\(178\) | −4.65423e44 | −0.456507 | ||||||||
\(179\) | 7.06105e44i | 0.619168i | 0.950872 | + | 0.309584i | \(0.100190\pi\) | ||||
−0.950872 | + | 0.309584i | \(0.899810\pi\) | |||||||
\(180\) | 3.25692e44 | + | 2.51046e44i | 0.255480 | + | 0.196926i | ||||
\(181\) | 1.48674e45 | 1.04391 | 0.521955 | − | 0.852973i | \(-0.325203\pi\) | ||||
0.521955 | + | 0.852973i | \(0.325203\pi\) | |||||||
\(182\) | − | 1.73504e43i | − | 0.0109114i | ||||||
\(183\) | −8.59951e44 | − | 1.74862e45i | −0.484676 | − | 0.985541i | ||||
\(184\) | −1.10487e44 | −0.0558413 | ||||||||
\(185\) | − | 4.14719e44i | − | 0.188070i | ||||||
\(186\) | −1.76045e45 | + | 8.65766e44i | −0.716745 | + | 0.352486i | ||||
\(187\) | −2.62611e45 | −0.960463 | ||||||||
\(188\) | − | 4.32090e45i | − | 1.42042i | ||||||
\(189\) | −3.26330e43 | − | 6.60244e42i | −0.00964763 | − | 0.00195195i | ||||
\(190\) | 2.85568e45 | 0.759692 | ||||||||
\(191\) | − | 7.76747e45i | − | 1.86043i | −0.367020 | − | 0.930213i | \(-0.619622\pi\) | ||
0.367020 | − | 0.930213i | \(-0.380378\pi\) | |||||||
\(192\) | 1.90263e45 | + | 3.86880e45i | 0.410515 | + | 0.834741i | ||||
\(193\) | 5.76691e45 | 1.12149 | 0.560747 | − | 0.827987i | \(-0.310514\pi\) | ||||
0.560747 | + | 0.827987i | \(0.310514\pi\) | |||||||
\(194\) | 3.67273e45i | 0.644102i | ||||||||
\(195\) | 1.49774e45 | − | 7.36569e44i | 0.236998 | − | 0.116552i | ||||
\(196\) | 6.75947e45 | 0.965587 | ||||||||
\(197\) | 6.43416e45i | 0.830170i | 0.909783 | + | 0.415085i | \(0.136248\pi\) | ||||
−0.909783 | + | 0.415085i | \(0.863752\pi\) | |||||||
\(198\) | −9.64491e45 | + | 1.25127e46i | −1.12459 | + | 1.45898i | ||||
\(199\) | −4.76778e45 | −0.502638 | −0.251319 | − | 0.967904i | \(-0.580864\pi\) | ||||
−0.251319 | + | 0.967904i | \(0.580864\pi\) | |||||||
\(200\) | 4.48252e44i | 0.0427486i | ||||||||
\(201\) | −6.77360e45 | − | 1.37734e46i | −0.584654 | − | 1.18883i | ||||
\(202\) | −2.04087e45 | −0.159510 | ||||||||
\(203\) | − | 6.76750e43i | − | 0.00479190i | ||||||
\(204\) | −9.87020e45 | + | 4.85403e45i | −0.633465 | + | 0.311530i | ||||
\(205\) | −6.30188e45 | −0.366769 | ||||||||
\(206\) | − | 7.68729e44i | − | 0.0405909i | ||||||
\(207\) | −1.91777e46 | − | 1.47823e46i | −0.919157 | − | 0.708493i | ||||
\(208\) | 1.87680e46 | 0.816868 | ||||||||
\(209\) | 5.38983e46i | 2.13132i | ||||||||
\(210\) | −5.65984e43 | − | 1.15087e44i | −0.00203432 | − | 0.00413658i | ||||
\(211\) | 4.75899e46 | 1.55548 | 0.777742 | − | 0.628583i | \(-0.216365\pi\) | ||||
0.777742 | + | 0.628583i | \(0.216365\pi\) | |||||||
\(212\) | − | 2.64247e46i | − | 0.785764i | ||||||
\(213\) | 5.87394e46 | − | 2.88873e46i | 1.58978 | − | 0.781834i | ||||
\(214\) | −4.13252e46 | −1.01845 | ||||||||
\(215\) | 2.58772e46i | 0.580963i | ||||||||
\(216\) | 4.66351e44 | − | 2.30497e45i | 0.00954197 | − | 0.0471618i | ||||
\(217\) | 3.00587e44 | 0.00560759 | ||||||||
\(218\) | − | 1.45698e47i | − | 2.47928i | ||||||
\(219\) | 1.29143e45 | + | 2.62599e45i | 0.0200534 | + | 0.0407766i | ||||
\(220\) | −2.98972e46 | −0.423816 | ||||||||
\(221\) | 4.46439e46i | 0.577985i | ||||||||
\(222\) | 5.98842e46 | − | 2.94503e46i | 0.708358 | − | 0.348361i | ||||
\(223\) | −1.24456e47 | −1.34561 | −0.672804 | − | 0.739821i | \(-0.734910\pi\) | ||||
−0.672804 | + | 0.739821i | \(0.734910\pi\) | |||||||
\(224\) | − | 1.39424e45i | − | 0.0137841i | ||||||
\(225\) | −5.99725e46 | + | 7.78048e46i | −0.542377 | + | 0.703649i | ||||
\(226\) | −6.97908e45 | −0.0577603 | ||||||||
\(227\) | 9.40746e46i | 0.712780i | 0.934337 | + | 0.356390i | \(0.115992\pi\) | ||||
−0.934337 | + | 0.356390i | \(0.884008\pi\) | |||||||
\(228\) | 9.96243e46 | + | 2.02576e47i | 0.691303 | + | 1.40570i | ||||
\(229\) | 4.05603e45 | 0.0257864 | 0.0128932 | − | 0.999917i | \(-0.495896\pi\) | ||||
0.0128932 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(230\) | − | 9.32726e46i | − | 0.543498i | ||||||
\(231\) | 2.17217e45 | − | 1.06824e45i | 0.0116052 | − | 0.00570729i | ||||
\(232\) | 4.78010e45 | 0.0234249 | ||||||||
\(233\) | − | 8.72200e46i | − | 0.392191i | −0.980585 | − | 0.196095i | \(-0.937174\pi\) | ||
0.980585 | − | 0.196095i | \(-0.0628263\pi\) | |||||||
\(234\) | 2.12717e47 | + | 1.63964e47i | 0.877980 | + | 0.676753i | ||||
\(235\) | −1.29637e47 | −0.491328 | ||||||||
\(236\) | 1.23694e47i | 0.430633i | ||||||||
\(237\) | −1.32656e47 | − | 2.69743e47i | −0.424385 | − | 0.862945i | ||||
\(238\) | 3.43046e45 | 0.0100882 | ||||||||
\(239\) | 3.37265e47i | 0.912039i | 0.889970 | + | 0.456020i | \(0.150725\pi\) | ||||
−0.889970 | + | 0.456020i | \(0.849275\pi\) | |||||||
\(240\) | 1.24491e47 | − | 6.12230e46i | 0.309679 | − | 0.152296i | ||||
\(241\) | −7.05542e47 | −1.61503 | −0.807517 | − | 0.589844i | \(-0.799189\pi\) | ||||
−0.807517 | + | 0.589844i | \(0.799189\pi\) | |||||||
\(242\) | − | 4.83248e47i | − | 1.01827i | ||||||
\(243\) | 3.89333e47 | − | 3.37689e47i | 0.755433 | − | 0.655226i | ||||
\(244\) | 5.93389e47 | 1.06058 | ||||||||
\(245\) | − | 2.02800e47i | − | 0.333999i | ||||||
\(246\) | −4.47513e47 | − | 9.09973e47i | −0.679366 | − | 1.38142i | ||||
\(247\) | 9.16271e47 | 1.28258 | ||||||||
\(248\) | 2.12314e46i | 0.0274123i | ||||||||
\(249\) | −5.40370e47 | + | 2.65747e47i | −0.643730 | + | 0.316578i | ||||
\(250\) | −8.04347e47 | −0.884389 | ||||||||
\(251\) | 1.12398e48i | 1.14100i | 0.821298 | + | 0.570499i | \(0.193250\pi\) | ||||
−0.821298 | + | 0.570499i | \(0.806750\pi\) | |||||||
\(252\) | 6.18954e45 | − | 8.02995e45i | 0.00580293 | − | 0.00752839i | ||||
\(253\) | 1.76043e48 | 1.52479 | ||||||||
\(254\) | 1.21924e48i | 0.975920i | ||||||||
\(255\) | 1.45632e47 | + | 2.96129e47i | 0.107759 | + | 0.219117i | ||||
\(256\) | 1.55660e48 | 1.06507 | ||||||||
\(257\) | − | 1.62765e48i | − | 1.03015i | −0.857146 | − | 0.515073i | \(-0.827765\pi\) | ||
0.857146 | − | 0.515073i | \(-0.172235\pi\) | |||||||
\(258\) | −3.73659e48 | + | 1.83761e48i | −2.18817 | + | 1.07612i | ||||
\(259\) | −1.02249e46 | −0.00554197 | ||||||||
\(260\) | 5.08253e47i | 0.255043i | ||||||||
\(261\) | 8.29701e47 | + | 6.39539e47i | 0.385577 | + | 0.297206i | ||||
\(262\) | −4.42874e48 | −1.90658 | ||||||||
\(263\) | − | 1.72240e48i | − | 0.687098i | −0.939135 | − | 0.343549i | \(-0.888371\pi\) | ||
0.939135 | − | 0.343549i | \(-0.111629\pi\) | |||||||
\(264\) | 7.54534e46 | + | 1.53427e47i | 0.0278997 | + | 0.0567313i | ||||
\(265\) | −7.92801e47 | −0.271798 | ||||||||
\(266\) | − | 7.04068e46i | − | 0.0223863i | ||||||
\(267\) | −9.90561e47 | + | 4.87145e47i | −0.292184 | + | 0.143692i | ||||
\(268\) | 4.67397e48 | 1.27935 | ||||||||
\(269\) | − | 3.60605e48i | − | 0.916192i | −0.888903 | − | 0.458096i | \(-0.848532\pi\) | ||
0.888903 | − | 0.458096i | \(-0.151468\pi\) | |||||||
\(270\) | 1.94584e48 | + | 3.93691e47i | 0.459021 | + | 0.0928710i | ||||
\(271\) | 4.48842e48 | 0.983349 | 0.491674 | − | 0.870779i | \(-0.336385\pi\) | ||||
0.491674 | + | 0.870779i | \(0.336385\pi\) | |||||||
\(272\) | 3.71076e48i | 0.755239i | ||||||||
\(273\) | −1.81601e46 | − | 3.69268e46i | −0.00343452 | − | 0.00698375i | ||||
\(274\) | 2.89803e48 | 0.509439 | ||||||||
\(275\) | − | 7.14216e48i | − | 1.16728i | ||||||
\(276\) | 6.61657e48 | − | 3.25394e48i | 1.00566 | − | 0.494571i | ||||
\(277\) | −4.95445e48 | −0.700488 | −0.350244 | − | 0.936659i | \(-0.613901\pi\) | ||||
−0.350244 | + | 0.936659i | \(0.613901\pi\) | |||||||
\(278\) | 3.44731e48i | 0.453508i | ||||||||
\(279\) | −2.84060e48 | + | 3.68522e48i | −0.347797 | + | 0.451211i | ||||
\(280\) | −1.38798e45 | −0.000158206 | ||||||||
\(281\) | − | 3.18401e48i | − | 0.337947i | −0.985621 | − | 0.168973i | \(-0.945955\pi\) | ||
0.985621 | − | 0.168973i | \(-0.0540452\pi\) | |||||||
\(282\) | −9.20586e48 | − | 1.87192e49i | −0.910085 | − | 1.85057i | ||||
\(283\) | −1.24165e49 | −1.14359 | −0.571794 | − | 0.820397i | \(-0.693752\pi\) | ||||
−0.571794 | + | 0.820397i | \(0.693752\pi\) | |||||||
\(284\) | 1.99330e49i | 1.71083i | ||||||||
\(285\) | 6.07775e48 | − | 2.98896e48i | 0.486234 | − | 0.239124i | ||||
\(286\) | −1.95265e49 | −1.45648 | ||||||||
\(287\) | 1.55373e47i | 0.0108078i | ||||||||
\(288\) | 1.70935e49 | + | 1.31758e49i | 1.10913 | + | 0.854922i | ||||
\(289\) | 7.69112e48 | 0.465621 | ||||||||
\(290\) | 4.03533e48i | 0.227992i | ||||||||
\(291\) | 3.84415e48 | + | 7.81669e48i | 0.202740 | + | 0.412252i | ||||
\(292\) | −8.91120e47 | −0.0438813 | ||||||||
\(293\) | 3.17462e49i | 1.45996i | 0.683471 | + | 0.729978i | \(0.260470\pi\) | ||||
−0.683471 | + | 0.729978i | \(0.739530\pi\) | |||||||
\(294\) | 2.92837e49 | − | 1.44013e49i | 1.25800 | − | 0.618666i | ||||
\(295\) | 3.71110e48 | 0.148957 | ||||||||
\(296\) | − | 7.22217e47i | − | 0.0270915i | ||||||
\(297\) | −7.43055e48 | + | 3.67260e49i | −0.260551 | + | 1.28779i | ||||
\(298\) | −4.40618e49 | −1.44457 | ||||||||
\(299\) | − | 2.99274e49i | − | 0.917583i | ||||||
\(300\) | −1.32014e49 | − | 2.68437e49i | −0.378612 | − | 0.769870i | ||||
\(301\) | 6.38004e47 | 0.0171196 | ||||||||
\(302\) | − | 1.07636e50i | − | 2.70284i | ||||||
\(303\) | −4.34359e48 | + | 2.13612e48i | −0.102093 | + | 0.0502080i | ||||
\(304\) | 7.61596e49 | 1.67592 | ||||||||
\(305\) | − | 1.78031e49i | − | 0.366858i | ||||||
\(306\) | −3.24184e49 | + | 4.20577e49i | −0.625695 | + | 0.811741i | ||||
\(307\) | −1.26028e49 | −0.227877 | −0.113939 | − | 0.993488i | \(-0.536347\pi\) | ||||
−0.113939 | + | 0.993488i | \(0.536347\pi\) | |||||||
\(308\) | 7.37117e47i | 0.0124888i | ||||||||
\(309\) | −8.04607e47 | − | 1.63609e48i | −0.0127766 | − | 0.0259799i | ||||
\(310\) | −1.79234e49 | −0.266801 | ||||||||
\(311\) | 4.17051e49i | 0.582079i | 0.956711 | + | 0.291039i | \(0.0940011\pi\) | ||||
−0.956711 | + | 0.291039i | \(0.905999\pi\) | |||||||
\(312\) | 2.60826e48 | − | 1.28271e48i | 0.0341396 | − | 0.0167894i | ||||
\(313\) | 8.98638e49 | 1.10331 | 0.551656 | − | 0.834072i | \(-0.313996\pi\) | ||||
0.551656 | + | 0.834072i | \(0.313996\pi\) | |||||||
\(314\) | 4.38440e49i | 0.505030i | ||||||||
\(315\) | −2.40917e47 | − | 1.85701e47i | −0.00260409 | − | 0.00200725i | ||||
\(316\) | 9.15363e49 | 0.928649 | ||||||||
\(317\) | 3.17725e49i | 0.302598i | 0.988488 | + | 0.151299i | \(0.0483456\pi\) | ||||
−0.988488 | + | 0.151299i | \(0.951654\pi\) | |||||||
\(318\) | −5.62988e49 | − | 1.14478e50i | −0.503451 | − | 1.02372i | ||||
\(319\) | −7.61631e49 | −0.639633 | ||||||||
\(320\) | 3.93889e49i | 0.310724i | ||||||||
\(321\) | −8.79524e49 | + | 4.32539e49i | −0.651849 | + | 0.320571i | ||||
\(322\) | −2.29964e48 | −0.0160156 | ||||||||
\(323\) | 1.81162e50i | 1.18582i | ||||||||
\(324\) | 3.99557e49 | + | 1.51769e50i | 0.245855 | + | 0.933859i | ||||
\(325\) | −1.21417e50 | −0.702444 | ||||||||
\(326\) | 9.06560e49i | 0.493224i | ||||||||
\(327\) | −1.52498e50 | − | 3.10090e50i | −0.780388 | − | 1.58684i | ||||
\(328\) | −1.09745e49 | −0.0528333 | ||||||||
\(329\) | 3.19620e48i | 0.0144783i | ||||||||
\(330\) | −1.29522e50 | + | 6.36973e49i | −0.552160 | + | 0.271545i | ||||
\(331\) | 2.81121e50 | 1.12806 | 0.564031 | − | 0.825754i | \(-0.309250\pi\) | ||||
0.564031 | + | 0.825754i | \(0.309250\pi\) | |||||||
\(332\) | − | 1.83373e50i | − | 0.692744i | ||||||
\(333\) | 9.66269e49 | − | 1.25358e50i | 0.343727 | − | 0.445931i | ||||
\(334\) | 1.52487e50 | 0.510861 | ||||||||
\(335\) | − | 1.40230e50i | − | 0.442532i | ||||||
\(336\) | −1.50945e48 | − | 3.06932e48i | −0.00448781 | − | 0.00912551i | ||||
\(337\) | 2.00107e50 | 0.560613 | 0.280307 | − | 0.959910i | \(-0.409564\pi\) | ||||
0.280307 | + | 0.959910i | \(0.409564\pi\) | |||||||
\(338\) | − | 1.99044e50i | − | 0.525551i | ||||||
\(339\) | −1.48536e49 | + | 7.30480e48i | −0.0369690 | + | 0.0181809i | ||||
\(340\) | −1.00490e50 | −0.235801 | ||||||||
\(341\) | − | 3.38288e50i | − | 0.748513i | ||||||
\(342\) | 8.63193e50 | + | 6.65355e50i | 1.80130 | + | 1.38845i | ||||
\(343\) | −1.00005e49 | −0.0196853 | ||||||||
\(344\) | 4.50642e49i | 0.0836880i | ||||||||
\(345\) | −9.76258e49 | − | 1.98512e50i | −0.171074 | − | 0.347861i | ||||
\(346\) | −6.82838e50 | −1.12926 | ||||||||
\(347\) | − | 2.08623e49i | − | 0.0325666i | −0.999867 | − | 0.0162833i | \(-0.994817\pi\) | ||
0.999867 | − | 0.0162833i | \(-0.00518337\pi\) | |||||||
\(348\) | −2.86258e50 | + | 1.40778e50i | −0.421864 | + | 0.207467i | ||||
\(349\) | −5.22713e50 | −0.727369 | −0.363684 | − | 0.931522i | \(-0.618481\pi\) | ||||
−0.363684 | + | 0.931522i | \(0.618481\pi\) | |||||||
\(350\) | 9.32974e48i | 0.0122605i | ||||||||
\(351\) | 6.24342e50 | + | 1.26319e50i | 0.774961 | + | 0.156793i | ||||
\(352\) | −1.56911e51 | −1.83993 | ||||||||
\(353\) | − | 4.45127e50i | − | 0.493162i | −0.969122 | − | 0.246581i | \(-0.920693\pi\) | ||
0.969122 | − | 0.246581i | \(-0.0793071\pi\) | |||||||
\(354\) | 2.63535e50 | + | 5.35871e50i | 0.275913 | + | 0.561042i | ||||
\(355\) | 5.98037e50 | 0.591781 | ||||||||
\(356\) | − | 3.36143e50i | − | 0.314430i | ||||||
\(357\) | 7.30106e48 | − | 3.59057e48i | 0.00645686 | − | 0.00317540i | ||||
\(358\) | −1.03807e51 | −0.868091 | ||||||||
\(359\) | 2.36020e51i | 1.86663i | 0.359054 | + | 0.933317i | \(0.383100\pi\) | ||||
−0.359054 | + | 0.933317i | \(0.616900\pi\) | |||||||
\(360\) | 1.31166e49 | − | 1.70167e49i | 0.00981232 | − | 0.0127299i | ||||
\(361\) | 2.30517e51 | 1.63140 | ||||||||
\(362\) | 2.18570e51i | 1.46359i | ||||||||
\(363\) | −5.05802e50 | − | 1.02850e51i | −0.320515 | − | 0.651735i | ||||
\(364\) | 1.25310e49 | 0.00751549 | ||||||||
\(365\) | 2.67357e49i | 0.0151787i | ||||||||
\(366\) | 2.57071e51 | − | 1.26424e51i | 1.38176 | − | 0.679529i | ||||
\(367\) | 7.49900e50 | 0.381665 | 0.190832 | − | 0.981623i | \(-0.438881\pi\) | ||||
0.190832 | + | 0.981623i | \(0.438881\pi\) | |||||||
\(368\) | − | 2.48754e51i | − | 1.19898i | ||||||
\(369\) | −1.90489e51 | − | 1.46830e51i | −0.869645 | − | 0.670328i | ||||
\(370\) | 6.09691e50 | 0.263679 | ||||||||
\(371\) | 1.95465e49i | 0.00800924i | ||||||||
\(372\) | −6.25284e50 | − | 1.27145e51i | −0.242783 | − | 0.493675i | ||||
\(373\) | −3.43410e51 | −1.26368 | −0.631838 | − | 0.775100i | \(-0.717699\pi\) | ||||
−0.631838 | + | 0.775100i | \(0.717699\pi\) | |||||||
\(374\) | − | 3.86073e51i | − | 1.34660i | ||||||
\(375\) | −1.71189e51 | + | 8.41887e50i | −0.566046 | + | 0.278374i | ||||
\(376\) | −2.25758e50 | −0.0707760 | ||||||||
\(377\) | 1.29477e51i | 0.384917i | ||||||||
\(378\) | 9.70646e48 | − | 4.79748e49i | 0.00273668 | − | 0.0135262i | ||||
\(379\) | −6.62305e50 | −0.177123 | −0.0885613 | − | 0.996071i | \(-0.528227\pi\) | ||||
−0.0885613 | + | 0.996071i | \(0.528227\pi\) | |||||||
\(380\) | 2.06246e51i | 0.523256i | ||||||||
\(381\) | 1.27614e51 | + | 2.59491e51i | 0.307185 | + | 0.624629i | ||||
\(382\) | 1.14192e52 | 2.60837 | ||||||||
\(383\) | − | 5.12395e51i | − | 1.11078i | −0.831589 | − | 0.555391i | \(-0.812568\pi\) | ||
0.831589 | − | 0.555391i | \(-0.187432\pi\) | |||||||
\(384\) | 4.19436e50 | − | 2.06273e50i | 0.0863060 | − | 0.0424442i | ||||
\(385\) | 2.21152e49 | 0.00431993 | ||||||||
\(386\) | 8.47813e51i | 1.57237i | ||||||||
\(387\) | −6.02923e51 | + | 7.82198e51i | −1.06180 | + | 1.37752i | ||||
\(388\) | −2.65257e51 | −0.443641 | ||||||||
\(389\) | − | 2.31289e51i | − | 0.367420i | −0.982980 | − | 0.183710i | \(-0.941189\pi\) | ||
0.982980 | − | 0.183710i | \(-0.0588107\pi\) | |||||||
\(390\) | 1.08285e51 | + | 2.20188e51i | 0.163410 | + | 0.332277i | ||||
\(391\) | 5.91716e51 | 0.848356 | ||||||||
\(392\) | − | 3.53168e50i | − | 0.0481127i | ||||||
\(393\) | −9.42569e51 | + | 4.63543e51i | −1.22029 | + | 0.600122i | ||||
\(394\) | −9.45906e51 | −1.16392 | ||||||||
\(395\) | − | 2.74630e51i | − | 0.321223i | ||||||
\(396\) | −9.03711e51 | − | 6.96586e51i | −1.00491 | − | 0.774589i | ||||
\(397\) | 1.17777e52 | 1.24523 | 0.622616 | − | 0.782528i | \(-0.286070\pi\) | ||||
0.622616 | + | 0.782528i | \(0.286070\pi\) | |||||||
\(398\) | − | 7.00927e51i | − | 0.704712i | ||||||
\(399\) | −7.36928e49 | − | 1.49847e50i | −0.00704640 | − | 0.0143282i | ||||
\(400\) | −1.00921e52 | −0.917867 | ||||||||
\(401\) | 4.24297e51i | 0.367098i | 0.983011 | + | 0.183549i | \(0.0587587\pi\) | ||||
−0.983011 | + | 0.183549i | \(0.941241\pi\) | |||||||
\(402\) | 2.02488e52 | − | 9.95809e51i | 1.66678 | − | 0.819700i | ||||
\(403\) | −5.75091e51 | −0.450438 | ||||||||
\(404\) | − | 1.47398e51i | − | 0.109866i | ||||||
\(405\) | 4.55341e51 | − | 1.19876e51i | 0.323025 | − | 0.0850420i | ||||
\(406\) | 9.94912e49 | 0.00671837 | ||||||||
\(407\) | 1.15074e52i | 0.739754i | ||||||||
\(408\) | 2.53613e50 | + | 5.15697e50i | 0.0155227 | + | 0.0315640i | ||||
\(409\) | 2.21554e52 | 1.29126 | 0.645630 | − | 0.763651i | \(-0.276595\pi\) | ||||
0.645630 | + | 0.763651i | \(0.276595\pi\) | |||||||
\(410\) | − | 9.26460e51i | − | 0.514221i | ||||||
\(411\) | 6.16789e51 | − | 3.03329e51i | 0.326062 | − | 0.160353i | ||||
\(412\) | 5.55201e50 | 0.0279580 | ||||||||
\(413\) | − | 9.14972e49i | − | 0.00438942i | ||||||
\(414\) | 2.17319e52 | − | 2.81938e52i | 0.993326 | − | 1.28868i | ||||
\(415\) | −5.50160e51 | −0.239622 | ||||||||
\(416\) | 2.66749e52i | 1.10723i | ||||||||
\(417\) | 3.60820e51 | + | 7.33692e51i | 0.142748 | + | 0.290264i | ||||
\(418\) | −7.92376e52 | −2.98817 | ||||||||
\(419\) | − | 3.58632e52i | − | 1.28934i | −0.764460 | − | 0.644672i | \(-0.776994\pi\) | ||
0.764460 | − | 0.644672i | \(-0.223006\pi\) | |||||||
\(420\) | 8.31197e49 | − | 4.08772e49i | 0.00284917 | − | 0.00140118i | ||||
\(421\) | 2.87166e52 | 0.938621 | 0.469311 | − | 0.883033i | \(-0.344502\pi\) | ||||
0.469311 | + | 0.883033i | \(0.344502\pi\) | |||||||
\(422\) | 6.99634e52i | 2.18083i | ||||||||
\(423\) | −3.91857e52 | − | 3.02046e52i | −1.16499 | − | 0.897978i | ||||
\(424\) | −1.38063e51 | −0.0391526 | ||||||||
\(425\) | − | 2.40062e52i | − | 0.649448i | ||||||
\(426\) | 4.24681e52 | + | 8.63547e52i | 1.09615 | + | 2.22892i | ||||
\(427\) | −4.38935e50 | −0.0108104 | ||||||||
\(428\) | − | 2.98464e52i | − | 0.701481i | ||||||
\(429\) | −4.15584e52 | + | 2.04379e52i | −0.932208 | + | 0.458448i | ||||
\(430\) | −3.80429e52 | −0.814526 | ||||||||
\(431\) | 2.54987e52i | 0.521162i | 0.965452 | + | 0.260581i | \(0.0839141\pi\) | ||||
−0.965452 | + | 0.260581i | \(0.916086\pi\) | |||||||
\(432\) | 5.18947e52 | + | 1.04996e52i | 1.01262 | + | 0.204878i | ||||
\(433\) | −5.65399e52 | −1.05341 | −0.526705 | − | 0.850048i | \(-0.676573\pi\) | ||||
−0.526705 | + | 0.850048i | \(0.676573\pi\) | |||||||
\(434\) | 4.41903e50i | 0.00786199i | ||||||||
\(435\) | 4.22367e51 | + | 8.58840e51i | 0.0717636 | + | 0.145924i | ||||
\(436\) | 1.05228e53 | 1.70766 | ||||||||
\(437\) | − | 1.21444e53i | − | 1.88255i | ||||||
\(438\) | −3.86055e51 | + | 1.89857e51i | −0.0571699 | + | 0.0281154i | ||||
\(439\) | 7.68897e52 | 1.08787 | 0.543936 | − | 0.839127i | \(-0.316933\pi\) | ||||
0.543936 | + | 0.839127i | \(0.316933\pi\) | |||||||
\(440\) | 1.56207e51i | 0.0211177i | ||||||||
\(441\) | 4.72511e52 | − | 6.13008e52i | 0.610436 | − | 0.791944i | ||||
\(442\) | −6.56324e52 | −0.810350 | ||||||||
\(443\) | 7.92880e52i | 0.935692i | 0.883810 | + | 0.467846i | \(0.154970\pi\) | ||||
−0.883810 | + | 0.467846i | \(0.845030\pi\) | |||||||
\(444\) | 2.12699e52 | + | 4.32503e52i | 0.239942 | + | 0.487898i | ||||
\(445\) | −1.00851e52 | −0.108762 | ||||||||
\(446\) | − | 1.82967e53i | − | 1.88658i | ||||||
\(447\) | −9.37769e52 | + | 4.61183e52i | −0.924582 | + | 0.454697i | ||||
\(448\) | 9.71135e50 | 0.00915629 | ||||||||
\(449\) | 1.28592e53i | 1.15955i | 0.814777 | + | 0.579774i | \(0.196859\pi\) | ||||
−0.814777 | + | 0.579774i | \(0.803141\pi\) | |||||||
\(450\) | −1.14383e53 | − | 8.81674e52i | −0.986535 | − | 0.760428i | ||||
\(451\) | 1.74861e53 | 1.44265 | ||||||||
\(452\) | − | 5.04051e51i | − | 0.0397838i | ||||||
\(453\) | −1.12660e53 | − | 2.29083e53i | −0.850756 | − | 1.72993i | ||||
\(454\) | −1.38302e53 | −0.999336 | ||||||||
\(455\) | − | 3.75959e50i | − | 0.00259963i | ||||||
\(456\) | 1.05842e52 | − | 5.20516e51i | 0.0700423 | − | 0.0344459i | ||||
\(457\) | 2.32780e53 | 1.47442 | 0.737209 | − | 0.675665i | \(-0.236143\pi\) | ||||
0.737209 | + | 0.675665i | \(0.236143\pi\) | |||||||
\(458\) | 5.96290e51i | 0.0361533i | ||||||||
\(459\) | −2.49755e52 | + | 1.23443e53i | −0.144964 | + | 0.716494i | ||||
\(460\) | 6.73645e52 | 0.374347 | ||||||||
\(461\) | 3.68046e53i | 1.95832i | 0.203089 | + | 0.979160i | \(0.434902\pi\) | ||||
−0.203089 | + | 0.979160i | \(0.565098\pi\) | |||||||
\(462\) | 1.57046e51 | + | 3.19337e51i | 0.00800178 | + | 0.0162708i | ||||
\(463\) | −9.46582e52 | −0.461890 | −0.230945 | − | 0.972967i | \(-0.574182\pi\) | ||||
−0.230945 | + | 0.972967i | \(0.574182\pi\) | |||||||
\(464\) | 1.07620e53i | 0.502962i | ||||||||
\(465\) | −3.81465e52 | + | 1.87600e52i | −0.170764 | + | 0.0839794i | ||||
\(466\) | 1.28225e53 | 0.549862 | ||||||||
\(467\) | 3.32159e53i | 1.36461i | 0.731068 | + | 0.682304i | \(0.239022\pi\) | ||||
−0.731068 | + | 0.682304i | \(0.760978\pi\) | |||||||
\(468\) | −1.18420e53 | + | 1.53631e53i | −0.466130 | + | 0.604730i | ||||
\(469\) | −3.45737e51 | −0.0130404 | ||||||||
\(470\) | − | 1.90584e53i | − | 0.688856i | ||||||
\(471\) | 4.58903e52 | + | 9.33134e52i | 0.158965 | + | 0.323240i | ||||
\(472\) | 6.46274e51 | 0.0214574 | ||||||||
\(473\) | − | 7.18025e53i | − | 2.28516i | ||||||
\(474\) | 3.96558e53 | − | 1.95022e53i | 1.20987 | − | 0.595000i | ||||
\(475\) | −4.92703e53 | −1.44116 | ||||||||
\(476\) | 2.47759e51i | 0.00694849i | ||||||||
\(477\) | −2.39642e53 | − | 1.84718e53i | −0.644459 | − | 0.496753i | ||||
\(478\) | −4.95824e53 | −1.27870 | ||||||||
\(479\) | 2.50146e53i | 0.618705i | 0.950947 | + | 0.309353i | \(0.100112\pi\) | ||||
−0.950947 | + | 0.309353i | \(0.899888\pi\) | |||||||
\(480\) | 8.70159e52 | + | 1.76938e53i | 0.206431 | + | 0.419756i | ||||
\(481\) | 1.95625e53 | 0.445167 | ||||||||
\(482\) | − | 1.03724e54i | − | 2.26432i | ||||||
\(483\) | −4.89433e51 | + | 2.40697e51i | −0.0102506 | + | 0.00504113i | ||||
\(484\) | 3.49017e53 | 0.701358 | ||||||||
\(485\) | 7.95831e52i | 0.153457i | ||||||||
\(486\) | 4.96447e53 | + | 5.72371e53i | 0.918645 | + | 1.05914i | ||||
\(487\) | 3.98927e53 | 0.708457 | 0.354229 | − | 0.935159i | \(-0.384743\pi\) | ||||
0.354229 | + | 0.935159i | \(0.384743\pi\) | |||||||
\(488\) | − | 3.10034e52i | − | 0.0528460i | ||||||
\(489\) | 9.48871e52 | + | 1.92943e53i | 0.155249 | + | 0.315684i | ||||
\(490\) | 2.98142e53 | 0.468276 | ||||||||
\(491\) | − | 4.07385e53i | − | 0.614292i | −0.951662 | − | 0.307146i | \(-0.900626\pi\) | ||
0.951662 | − | 0.307146i | \(-0.0993740\pi\) | |||||||
\(492\) | 6.57212e53 | − | 3.23208e53i | 0.951488 | − | 0.467930i | ||||
\(493\) | −2.55999e53 | −0.355877 | ||||||||
\(494\) | 1.34704e54i | 1.79821i | ||||||||
\(495\) | −2.08992e53 | + | 2.71134e53i | −0.267933 | + | 0.347600i | ||||
\(496\) | −4.78010e53 | −0.588577 | ||||||||
\(497\) | − | 1.47446e52i | − | 0.0174384i | ||||||
\(498\) | −3.90683e53 | − | 7.94415e53i | −0.443851 | − | 0.902527i | ||||
\(499\) | −7.38488e53 | −0.805995 | −0.402998 | − | 0.915201i | \(-0.632032\pi\) | ||||
−0.402998 | + | 0.915201i | \(0.632032\pi\) | |||||||
\(500\) | − | 5.80925e53i | − | 0.609144i | ||||||
\(501\) | 3.24538e53 | − | 1.59603e53i | 0.326972 | − | 0.160801i | ||||
\(502\) | −1.65240e54 | −1.59971 | ||||||||
\(503\) | 8.34228e53i | 0.776114i | 0.921635 | + | 0.388057i | \(0.126854\pi\) | ||||
−0.921635 | + | 0.388057i | \(0.873146\pi\) | |||||||
\(504\) | −4.19548e50 | − | 3.23391e50i | −0.000375121 | − | 0.000289146i | ||||
\(505\) | −4.42228e52 | −0.0380031 | ||||||||
\(506\) | 2.58807e54i | 2.13779i | ||||||||
\(507\) | −2.08334e53 | − | 4.23626e53i | −0.165425 | − | 0.336375i | ||||
\(508\) | −8.80573e53 | −0.672188 | ||||||||
\(509\) | − | 2.04133e54i | − | 1.49816i | −0.662480 | − | 0.749080i | \(-0.730496\pi\) | ||
0.662480 | − | 0.749080i | \(-0.269504\pi\) | |||||||
\(510\) | −4.35348e53 | + | 2.14099e53i | −0.307209 | + | 0.151081i | ||||
\(511\) | 6.59169e50 | 0.000447279 | ||||||||
\(512\) | 2.14101e54i | 1.39707i | ||||||||
\(513\) | 2.53355e54 | + | 5.12597e53i | 1.58994 | + | 0.321684i | ||||
\(514\) | 2.39286e54 | 1.44429 | ||||||||
\(515\) | − | 1.66573e52i | − | 0.00967075i | ||||||
\(516\) | −1.32718e54 | − | 2.69869e54i | −0.741201 | − | 1.50716i | ||||
\(517\) | 3.59709e54 | 1.93259 | ||||||||
\(518\) | − | 1.50320e52i | − | 0.00776999i | ||||||
\(519\) | −1.45329e54 | + | 7.14707e53i | −0.722776 | + | 0.355452i | ||||
\(520\) | 2.65551e52 | 0.0127081 | ||||||||
\(521\) | − | 2.09664e54i | − | 0.965539i | −0.875747 | − | 0.482770i | \(-0.839631\pi\) | ||
0.875747 | − | 0.482770i | \(-0.160369\pi\) | |||||||
\(522\) | −9.40207e53 | + | 1.21977e54i | −0.416690 | + | 0.540590i | ||||
\(523\) | −7.49003e53 | −0.319484 | −0.159742 | − | 0.987159i | \(-0.551066\pi\) | ||||
−0.159742 | + | 0.987159i | \(0.551066\pi\) | |||||||
\(524\) | − | 3.19858e54i | − | 1.31320i | ||||||
\(525\) | 9.76517e51 | + | 1.98565e52i | 0.00385917 | + | 0.00784724i | ||||
\(526\) | 2.53215e54 | 0.963330 | ||||||||
\(527\) | − | 1.13705e54i | − | 0.416455i | ||||||
\(528\) | −3.45429e54 | + | 1.69878e54i | −1.21809 | + | 0.599043i | ||||
\(529\) | −1.02143e54 | −0.346812 | ||||||||
\(530\) | − | 1.16552e54i | − | 0.381068i | ||||||
\(531\) | 1.12176e54 | + | 8.64662e53i | 0.353192 | + | 0.272243i | ||||
\(532\) | 5.08501e52 | 0.0154191 | ||||||||
\(533\) | − | 2.97263e54i | − | 0.868155i | ||||||
\(534\) | −7.16168e53 | − | 1.45626e54i | −0.201460 | − | 0.409649i | ||||
\(535\) | −8.95460e53 | −0.242644 | ||||||||
\(536\) | − | 2.44205e53i | − | 0.0637469i | ||||||
\(537\) | −2.20932e54 | + | 1.08652e54i | −0.555614 | + | 0.273244i | ||||
\(538\) | 5.30137e54 | 1.28453 | ||||||||
\(539\) | 5.62716e54i | 1.31375i | ||||||||
\(540\) | −2.84336e53 | + | 1.40535e54i | −0.0639671 | + | 0.316162i | ||||
\(541\) | −2.63120e54 | −0.570438 | −0.285219 | − | 0.958462i | \(-0.592066\pi\) | ||||
−0.285219 | + | 0.958462i | \(0.592066\pi\) | |||||||
\(542\) | 6.59857e54i | 1.37868i | ||||||||
\(543\) | 2.28771e54 | + | 4.65183e54i | 0.460686 | + | 0.936758i | ||||
\(544\) | −5.27408e54 | −1.02369 | ||||||||
\(545\) | − | 3.15709e54i | − | 0.590686i | ||||||
\(546\) | 5.42873e52 | − | 2.66978e52i | 0.00979141 | − | 0.00481529i | ||||
\(547\) | −4.02299e54 | −0.699523 | −0.349762 | − | 0.936839i | \(-0.613737\pi\) | ||||
−0.349762 | + | 0.936839i | \(0.613737\pi\) | |||||||
\(548\) | 2.09305e54i | 0.350888i | ||||||||
\(549\) | 4.14800e54 | − | 5.38137e54i | 0.670489 | − | 0.869854i | ||||
\(550\) | 1.04999e55 | 1.63656 | ||||||||
\(551\) | 5.25412e54i | 0.789711i | ||||||||
\(552\) | −1.70012e53 | − | 3.45702e53i | −0.0246432 | − | 0.0501095i | ||||
\(553\) | −6.77101e52 | −0.00946566 | ||||||||
\(554\) | − | 7.28370e54i | − | 0.982103i | ||||||
\(555\) | 1.29761e54 | − | 6.38147e53i | 0.168766 | − | 0.0829967i | ||||
\(556\) | −2.48976e54 | −0.312364 | ||||||||
\(557\) | 3.05699e54i | 0.369991i | 0.982739 | + | 0.184995i | \(0.0592270\pi\) | ||||
−0.982739 | + | 0.184995i | \(0.940773\pi\) | |||||||
\(558\) | −5.41777e54 | − | 4.17605e54i | −0.632610 | − | 0.487620i | ||||
\(559\) | −1.22064e55 | −1.37516 | ||||||||
\(560\) | − | 3.12493e52i | − | 0.00339688i | ||||||
\(561\) | −4.04091e54 | − | 8.21680e54i | −0.423860 | − | 0.861877i | ||||
\(562\) | 4.68092e54 | 0.473811 | ||||||||
\(563\) | 1.63777e55i | 1.59988i | 0.600083 | + | 0.799938i | \(0.295134\pi\) | ||||
−0.600083 | + | 0.799938i | \(0.704866\pi\) | |||||||
\(564\) | 1.35196e55 | − | 6.64877e54i | 1.27462 | − | 0.626843i | ||||
\(565\) | −1.51227e53 | −0.0137613 | ||||||||
\(566\) | − | 1.82539e55i | − | 1.60334i | ||||||
\(567\) | −2.95556e52 | − | 1.12264e53i | −0.00250598 | − | 0.00951877i | ||||
\(568\) | 1.04146e54 | 0.0852462 | ||||||||
\(569\) | − | 1.09842e55i | − | 0.868010i | −0.900910 | − | 0.434005i | \(-0.857100\pi\) | ||
0.900910 | − | 0.434005i | \(-0.142900\pi\) | |||||||
\(570\) | 4.39416e54 | + | 8.93509e54i | 0.335258 | + | 0.681714i | ||||
\(571\) | −1.49352e55 | −1.10024 | −0.550120 | − | 0.835085i | \(-0.685418\pi\) | ||||
−0.550120 | + | 0.835085i | \(0.685418\pi\) | |||||||
\(572\) | − | 1.41027e55i | − | 1.00319i | ||||||
\(573\) | 2.43035e55 | − | 1.19522e55i | 1.66946 | − | 0.821021i | ||||
\(574\) | −2.28419e53 | −0.0151528 | ||||||||
\(575\) | 1.60927e55i | 1.03103i | ||||||||
\(576\) | −9.17738e54 | + | 1.19062e55i | −0.567896 | + | 0.736755i | ||||
\(577\) | 7.87830e54 | 0.470887 | 0.235443 | − | 0.971888i | \(-0.424346\pi\) | ||||
0.235443 | + | 0.971888i | \(0.424346\pi\) | |||||||
\(578\) | 1.13070e55i | 0.652814i | ||||||||
\(579\) | 8.87381e54 | + | 1.80440e55i | 0.494925 | + | 1.00638i | ||||
\(580\) | −2.91445e54 | −0.157035 | ||||||||
\(581\) | 1.35642e53i | 0.00706109i | ||||||||
\(582\) | −1.14916e55 | + | 5.65140e54i | −0.577989 | + | 0.284247i | ||||
\(583\) | 2.19981e55 | 1.06909 | ||||||||
\(584\) | 4.65592e52i | 0.00218649i | ||||||||
\(585\) | 4.60928e54 | + | 3.55287e54i | 0.209178 | + | 0.161236i | ||||
\(586\) | −4.66711e55 | −2.04690 | ||||||||
\(587\) | 2.21712e54i | 0.0939782i | 0.998895 | + | 0.0469891i | \(0.0149626\pi\) | ||||
−0.998895 | + | 0.0469891i | \(0.985037\pi\) | |||||||
\(588\) | 1.04011e55 | + | 2.11496e55i | 0.426121 | + | 0.866475i | ||||
\(589\) | −2.33369e55 | −0.924138 | ||||||||
\(590\) | 5.45580e54i | 0.208842i | ||||||||
\(591\) | −2.01317e55 | + | 9.90053e54i | −0.744958 | + | 0.366361i | ||||
\(592\) | 1.62602e55 | 0.581690 | ||||||||
\(593\) | − | 4.82567e55i | − | 1.66903i | −0.550987 | − | 0.834514i | \(-0.685749\pi\) | ||
0.550987 | − | 0.834514i | \(-0.314251\pi\) | |||||||
\(594\) | −5.39920e55 | − | 1.09239e55i | −1.80551 | − | 0.365299i | ||||
\(595\) | 7.43334e52 | 0.00240350 | ||||||||
\(596\) | − | 3.18229e55i | − | 0.994979i | ||||||
\(597\) | −7.33641e54 | − | 1.49179e55i | −0.221818 | − | 0.451045i | ||||
\(598\) | 4.39972e55 | 1.28648 | ||||||||
\(599\) | 6.29039e55i | 1.77886i | 0.457075 | + | 0.889428i | \(0.348897\pi\) | ||||
−0.457075 | + | 0.889428i | \(0.651103\pi\) | |||||||
\(600\) | −1.40253e54 | + | 6.89745e53i | −0.0383607 | + | 0.0188653i | ||||
\(601\) | 1.93988e55 | 0.513198 | 0.256599 | − | 0.966518i | \(-0.417398\pi\) | ||||
0.256599 | + | 0.966518i | \(0.417398\pi\) | |||||||
\(602\) | 9.37950e53i | 0.0240021i | ||||||||
\(603\) | 3.26727e55 | − | 4.23877e55i | 0.808796 | − | 1.04928i | ||||
\(604\) | 7.77384e55 | 1.86164 | ||||||||
\(605\) | − | 1.04713e55i | − | 0.242602i | ||||||
\(606\) | −3.14038e54 | − | 6.38564e54i | −0.0703930 | − | 0.143137i | ||||
\(607\) | −1.78014e55 | −0.386082 | −0.193041 | − | 0.981191i | \(-0.561835\pi\) | ||||
−0.193041 | + | 0.981191i | \(0.561835\pi\) | |||||||
\(608\) | 1.08245e56i | 2.27163i | ||||||||
\(609\) | 2.11747e53 | − | 1.04135e53i | 0.00430004 | − | 0.00211470i | ||||
\(610\) | 2.61728e55 | 0.514345 | ||||||||
\(611\) | − | 6.11505e55i | − | 1.16299i | ||||||
\(612\) | −3.03754e55 | − | 2.34136e55i | −0.559106 | − | 0.430963i | ||||
\(613\) | 2.54745e55 | 0.453833 | 0.226916 | − | 0.973914i | \(-0.427136\pi\) | ||||
0.226916 | + | 0.973914i | \(0.427136\pi\) | |||||||
\(614\) | − | 1.85278e55i | − | 0.319490i | ||||||
\(615\) | −9.69700e54 | − | 1.97179e55i | −0.161858 | − | 0.329123i | ||||
\(616\) | 3.85128e52 | 0.000622287 | ||||||||
\(617\) | − | 5.04493e55i | − | 0.789137i | −0.918867 | − | 0.394568i | \(-0.870894\pi\) | ||
0.918867 | − | 0.394568i | \(-0.129106\pi\) | |||||||
\(618\) | 2.40526e54 | − | 1.18288e54i | 0.0364245 | − | 0.0179131i | ||||
\(619\) | −1.10845e56 | −1.62519 | −0.812595 | − | 0.582829i | \(-0.801946\pi\) | ||||
−0.812595 | + | 0.582829i | \(0.801946\pi\) | |||||||
\(620\) | − | 1.29449e55i | − | 0.183766i | ||||||
\(621\) | 1.67425e55 | − | 8.27511e55i | 0.230139 | − | 1.13747i | ||||
\(622\) | −6.13121e55 | −0.816090 | ||||||||
\(623\) | 2.48648e53i | 0.00320497i | ||||||||
\(624\) | 2.88792e55 | + | 5.87230e55i | 0.360490 | + | 0.733021i | ||||
\(625\) | 5.60595e55 | 0.677718 | ||||||||
\(626\) | 1.32112e56i | 1.54687i | ||||||||
\(627\) | −1.68642e56 | + | 8.29358e55i | −1.91256 | + | 0.940570i | ||||
\(628\) | −3.16656e55 | −0.347852 | ||||||||
\(629\) | 3.86784e55i | 0.411582i | ||||||||
\(630\) | 2.73004e53 | − | 3.54180e53i | 0.00281422 | − | 0.00365101i | ||||
\(631\) | 6.65827e55 | 0.664927 | 0.332464 | − | 0.943116i | \(-0.392120\pi\) | ||||
0.332464 | + | 0.943116i | \(0.392120\pi\) | |||||||
\(632\) | − | 4.78258e54i | − | 0.0462723i | ||||||
\(633\) | 7.32288e55 | + | 1.48903e56i | 0.686448 | + | 1.39582i | ||||
\(634\) | −4.67098e55 | −0.424251 | ||||||||
\(635\) | 2.64192e55i | 0.232512i | ||||||||
\(636\) | 8.26797e55 | − | 4.06608e55i | 0.705110 | − | 0.346764i | ||||
\(637\) | 9.56618e55 | 0.790587 | ||||||||
\(638\) | − | 1.11970e56i | − | 0.896783i | ||||||
\(639\) | 1.80770e56 | + | 1.39339e56i | 1.40317 | + | 1.08157i | ||||
\(640\) | 4.27035e54 | 0.0321266 | ||||||||
\(641\) | − | 9.15350e55i | − | 0.667462i | −0.942668 | − | 0.333731i | \(-0.891692\pi\) | ||
0.942668 | − | 0.333731i | \(-0.108308\pi\) | |||||||
\(642\) | −6.35889e55 | − | 1.29302e56i | −0.449449 | − | 0.913911i | ||||
\(643\) | 5.36382e54 | 0.0367498 | 0.0183749 | − | 0.999831i | \(-0.494151\pi\) | ||||
0.0183749 | + | 0.999831i | \(0.494151\pi\) | |||||||
\(644\) | − | 1.66087e54i | − | 0.0110311i | ||||||
\(645\) | −8.09669e55 | + | 3.98185e55i | −0.521331 | + | 0.256384i | ||||
\(646\) | −2.66333e56 | −1.66255 | ||||||||
\(647\) | − | 7.57259e55i | − | 0.458309i | −0.973390 | − | 0.229155i | \(-0.926404\pi\) | ||
0.973390 | − | 0.229155i | \(-0.0735962\pi\) | |||||||
\(648\) | 7.92959e54 | − | 2.08760e54i | 0.0465319 | − | 0.0122503i | ||||
\(649\) | −1.02973e56 | −0.585909 | ||||||||
\(650\) | − | 1.78499e56i | − | 0.984845i | ||||||
\(651\) | 4.62527e53 | + | 9.40503e53i | 0.00247467 | + | 0.00503200i | ||||
\(652\) | −6.54747e55 | −0.339720 | ||||||||
\(653\) | 1.47287e56i | 0.741140i | 0.928804 | + | 0.370570i | \(0.120838\pi\) | ||||
−0.928804 | + | 0.370570i | \(0.879162\pi\) | |||||||
\(654\) | 4.55874e56 | − | 2.24193e56i | 2.22479 | − | 1.09412i | ||||
\(655\) | −9.59647e55 | −0.454240 | ||||||||
\(656\) | − | 2.47083e56i | − | 1.13440i | ||||||
\(657\) | −6.22924e54 | + | 8.08146e54i | −0.0277414 | + | 0.0359900i | ||||
\(658\) | −4.69884e54 | −0.0202989 | ||||||||
\(659\) | − | 3.56702e55i | − | 0.149485i | −0.997203 | − | 0.0747425i | \(-0.976187\pi\) | ||
0.997203 | − | 0.0747425i | \(-0.0238135\pi\) | |||||||
\(660\) | −4.60042e55 | − | 9.35450e55i | −0.187033 | − | 0.380314i | ||||
\(661\) | 1.95144e56 | 0.769707 | 0.384854 | − | 0.922978i | \(-0.374252\pi\) | ||||
0.384854 | + | 0.922978i | \(0.374252\pi\) | |||||||
\(662\) | 4.13285e56i | 1.58157i | ||||||||
\(663\) | −1.39686e56 | + | 6.86956e55i | −0.518658 | + | 0.255069i | ||||
\(664\) | −9.58083e54 | −0.0345177 | ||||||||
\(665\) | − | 1.52562e54i | − | 0.00533351i | ||||||
\(666\) | 1.84293e56 | + | 1.42054e56i | 0.625208 | + | 0.481914i | ||||
\(667\) | 1.71611e56 | 0.564974 | ||||||||
\(668\) | 1.10131e56i | 0.351868i | ||||||||
\(669\) | −1.91506e56 | − | 3.89408e56i | −0.593827 | − | 1.20749i | ||||
\(670\) | 2.06157e56 | 0.620442 | ||||||||
\(671\) | 4.93988e56i | 1.44300i | ||||||||
\(672\) | 4.36242e54 | − | 2.14538e54i | 0.0123692 | − | 0.00608301i | ||||
\(673\) | −3.95837e56 | −1.08947 | −0.544735 | − | 0.838609i | \(-0.683370\pi\) | ||||
−0.544735 | + | 0.838609i | \(0.683370\pi\) | |||||||
\(674\) | 2.94183e56i | 0.785995i | ||||||||
\(675\) | −3.35725e56 | − | 6.79252e55i | −0.870779 | − | 0.176180i | ||||
\(676\) | 1.43756e56 | 0.361986 | ||||||||
\(677\) | 1.03199e56i | 0.252292i | 0.992012 | + | 0.126146i | \(0.0402607\pi\) | ||||
−0.992012 | + | 0.126146i | \(0.959739\pi\) | |||||||
\(678\) | −1.07390e55 | − | 2.18367e55i | −0.0254901 | − | 0.0518315i | ||||
\(679\) | 1.96212e54 | 0.00452200 | ||||||||
\(680\) | 5.25040e54i | 0.0117494i | ||||||||
\(681\) | −2.94349e56 | + | 1.44757e56i | −0.639617 | + | 0.314555i | ||||
\(682\) | 4.97329e56 | 1.04944 | ||||||||
\(683\) | − | 6.20211e56i | − | 1.27094i | −0.772125 | − | 0.635471i | \(-0.780806\pi\) | ||
0.772125 | − | 0.635471i | \(-0.219194\pi\) | |||||||
\(684\) | −4.80541e56 | + | 6.23426e56i | −0.956331 | + | 1.24069i | ||||
\(685\) | 6.27964e55 | 0.121373 | ||||||||
\(686\) | − | 1.47021e55i | − | 0.0275993i | ||||||
\(687\) | 6.24120e54 | + | 1.26909e55i | 0.0113798 | + | 0.0231396i | ||||
\(688\) | −1.01459e57 | −1.79689 | ||||||||
\(689\) | − | 3.73969e56i | − | 0.643355i | ||||||
\(690\) | 2.91839e56 | − | 1.43523e56i | 0.487711 | − | 0.239850i | ||||
\(691\) | 7.95190e56 | 1.29095 | 0.645476 | − | 0.763780i | \(-0.276659\pi\) | ||||
0.645476 | + | 0.763780i | \(0.276659\pi\) | |||||||
\(692\) | − | 4.93167e56i | − | 0.777808i | ||||||
\(693\) | 6.68482e54 | + | 5.15270e54i | 0.0102429 | + | 0.00789533i | ||||
\(694\) | 3.06703e55 | 0.0456593 | ||||||||
\(695\) | 7.46985e55i | 0.108048i | ||||||||
\(696\) | 7.35536e54 | + | 1.49564e55i | 0.0103376 | + | 0.0210204i | ||||
\(697\) | 5.87740e56 | 0.802657 | ||||||||
\(698\) | − | 7.68457e56i | − | 1.01979i | ||||||
\(699\) | 2.72901e56 | − | 1.34209e56i | 0.351935 | − | 0.173077i | ||||
\(700\) | −6.73824e54 | −0.00844472 | ||||||||
\(701\) | 3.53553e56i | 0.430620i | 0.976546 | + | 0.215310i | \(0.0690762\pi\) | ||||
−0.976546 | + | 0.215310i | \(0.930924\pi\) | |||||||
\(702\) | −1.85706e56 | + | 9.17865e56i | −0.219829 | + | 1.08652i | ||||
\(703\) | 7.93837e56 | 0.913324 | ||||||||
\(704\) | − | 1.09294e57i | − | 1.22220i | ||||||
\(705\) | −1.99478e56 | − | 4.05619e56i | −0.216827 | − | 0.440896i | ||||
\(706\) | 6.54395e56 | 0.691426 | ||||||||
\(707\) | 1.09031e54i | 0.00111986i | ||||||||
\(708\) | −3.87023e56 | + | 1.90333e56i | −0.386431 | + | 0.190042i | ||||
\(709\) | 5.27547e55 | 0.0512079 | 0.0256039 | − | 0.999672i | \(-0.491849\pi\) | ||||
0.0256039 | + | 0.999672i | \(0.491849\pi\) | |||||||
\(710\) | 8.79193e56i | 0.829693i | ||||||||
\(711\) | 6.39871e56 | − | 8.30131e56i | 0.587084 | − | 0.761649i | ||||
\(712\) | −1.75628e55 | −0.0156673 | ||||||||
\(713\) | 7.62233e56i | 0.661145i | ||||||||
\(714\) | 5.27861e54 | + | 1.07335e55i | 0.00445200 | + | 0.00905270i | ||||
\(715\) | −4.23113e56 | −0.347005 | ||||||||
\(716\) | − | 7.49726e56i | − | 0.597919i | ||||||
\(717\) | −1.05526e57 | + | 5.18965e56i | −0.818424 | + | 0.402490i | ||||
\(718\) | −3.46980e57 | −2.61707 | ||||||||
\(719\) | 1.10786e57i | 0.812660i | 0.913726 | + | 0.406330i | \(0.133192\pi\) | ||||
−0.913726 | + | 0.406330i | \(0.866808\pi\) | |||||||
\(720\) | 3.83119e56 | + | 2.95311e56i | 0.273328 | + | 0.210683i | ||||
\(721\) | −4.10686e53 | −0.000284974 | ||||||||
\(722\) | 3.38891e57i | 2.28726i | ||||||||
\(723\) | −1.08565e57 | − | 2.20756e57i | −0.712728 | − | 1.44926i | ||||
\(724\) | −1.57858e57 | −1.00808 | ||||||||
\(725\) | − | 6.96233e56i | − | 0.432509i | ||||||
\(726\) | 1.51203e57 | − | 7.43596e56i | 0.913750 | − | 0.449371i | ||||
\(727\) | 2.26670e57 | 1.33262 | 0.666308 | − | 0.745677i | \(-0.267874\pi\) | ||||
0.666308 | + | 0.745677i | \(0.267874\pi\) | |||||||
\(728\) | − | 6.54718e53i | − | 0.000374478i | ||||||
\(729\) | 1.65567e57 | + | 6.98562e56i | 0.921349 | + | 0.388735i | ||||
\(730\) | −3.93050e55 | −0.0212809 | ||||||||
\(731\) | − | 2.41342e57i | − | 1.27141i | ||||||
\(732\) | 9.13075e56 | + | 1.85665e57i | 0.468042 | + | 0.951717i | ||||
\(733\) | −2.19626e57 | −1.09548 | −0.547740 | − | 0.836648i | \(-0.684512\pi\) | ||||
−0.547740 | + | 0.836648i | \(0.684512\pi\) | |||||||
\(734\) | 1.10245e57i | 0.535104i | ||||||||
\(735\) | 6.34537e56 | − | 3.12057e56i | 0.299716 | − | 0.147397i | ||||
\(736\) | 3.53553e57 | 1.62517 | ||||||||
\(737\) | 3.89101e57i | 1.74066i | ||||||||
\(738\) | 2.15859e57 | − | 2.80043e57i | 0.939818 | − | 1.21927i | ||||
\(739\) | −3.97320e57 | −1.68365 | −0.841824 | − | 0.539752i | \(-0.818518\pi\) | ||||
−0.841824 | + | 0.539752i | \(0.818518\pi\) | |||||||
\(740\) | 4.40339e56i | 0.181615i | ||||||||
\(741\) | 1.40991e57 | + | 2.86691e57i | 0.566013 | + | 1.15093i | ||||
\(742\) | −2.87360e55 | −0.0112292 | ||||||||
\(743\) | − | 2.93565e57i | − | 1.11668i | −0.829613 | − | 0.558339i | \(-0.811439\pi\) | ||
0.829613 | − | 0.558339i | \(-0.188561\pi\) | |||||||
\(744\) | −6.64307e55 | + | 3.26698e55i | −0.0245986 | + | 0.0120973i | ||||
\(745\) | −9.54759e56 | −0.344166 | ||||||||
\(746\) | − | 5.04857e57i | − | 1.77171i | ||||||
\(747\) | −1.66298e57 | − | 1.28184e57i | −0.568166 | − | 0.437947i | ||||
\(748\) | 2.78834e57 | 0.927500 | ||||||||
\(749\) | 2.20776e55i | 0.00715015i | ||||||||
\(750\) | −1.23769e57 | − | 2.51671e57i | −0.390288 | − | 0.793612i | ||||
\(751\) | −3.66179e56 | −0.112433 | −0.0562166 | − | 0.998419i | \(-0.517904\pi\) | ||||
−0.0562166 | + | 0.998419i | \(0.517904\pi\) | |||||||
\(752\) | − | 5.08277e57i | − | 1.51965i | ||||||
\(753\) | −3.51681e57 | + | 1.72952e57i | −1.02388 | + | 0.503531i | ||||
\(754\) | −1.90349e57 | −0.539664 | ||||||||
\(755\) | − | 2.33233e57i | − | 0.643949i | ||||||
\(756\) | 3.46489e55 | + | 7.01032e54i | 0.00931652 | + | 0.00188496i | ||||
\(757\) | 1.69184e57 | 0.443039 | 0.221520 | − | 0.975156i | \(-0.428898\pi\) | ||||
0.221520 | + | 0.975156i | \(0.428898\pi\) | |||||||
\(758\) | − | 9.73676e56i | − | 0.248331i | ||||||
\(759\) | 2.70886e57 | + | 5.50820e57i | 0.672901 | + | 1.36828i | ||||
\(760\) | 1.07759e56 | 0.0260725 | ||||||||
\(761\) | 1.28568e57i | 0.302999i | 0.988457 | + | 0.151499i | \(0.0484102\pi\) | ||||
−0.988457 | + | 0.151499i | \(0.951590\pi\) | |||||||
\(762\) | −3.81486e57 | + | 1.87610e57i | −0.875747 | + | 0.430681i | ||||
\(763\) | −7.78380e55 | −0.0174061 | ||||||||
\(764\) | 8.24732e57i | 1.79658i | ||||||||
\(765\) | −7.02462e56 | + | 9.11333e56i | −0.149071 | + | 0.193396i | ||||
\(766\) | 7.53288e57 | 1.55735 | ||||||||
\(767\) | 1.75055e57i | 0.352587i | ||||||||
\(768\) | 2.39521e57 | + | 4.87042e57i | 0.470023 | + | 0.955744i | ||||
\(769\) | 3.55428e57 | 0.679555 | 0.339777 | − | 0.940506i | \(-0.389648\pi\) | ||||
0.339777 | + | 0.940506i | \(0.389648\pi\) | |||||||
\(770\) | 3.25123e55i | 0.00605665i | ||||||||
\(771\) | 5.09273e57 | − | 2.50454e57i | 0.924407 | − | 0.454611i | ||||
\(772\) | −6.12317e57 | −1.08301 | ||||||||
\(773\) | 9.17318e57i | 1.58099i | 0.612466 | + | 0.790497i | \(0.290178\pi\) | ||||
−0.612466 | + | 0.790497i | \(0.709822\pi\) | |||||||
\(774\) | −1.14993e58 | − | 8.86377e57i | −1.93132 | − | 1.48867i | ||||
\(775\) | 3.09241e57 | 0.506131 | ||||||||
\(776\) | 1.38591e56i | 0.0221055i | ||||||||
\(777\) | −1.57335e55 | − | 3.19926e55i | −0.00244571 | − | 0.00497312i | ||||
\(778\) | 3.40025e57 | 0.515133 | ||||||||
\(779\) | − | 1.20628e58i | − | 1.78114i | ||||||
\(780\) | −1.59027e57 | + | 7.82072e56i | −0.228864 | + | 0.112552i | ||||
\(781\) | −1.65940e58 | −2.32771 | ||||||||
\(782\) | 8.69900e57i | 1.18942i | ||||||||
\(783\) | −7.24346e56 | + | 3.58013e57i | −0.0965408 | + | 0.477159i | ||||
\(784\) | 7.95132e57 | 1.03304 | ||||||||
\(785\) | 9.50040e56i | 0.120323i | ||||||||
\(786\) | −6.81470e57 | − | 1.38570e58i | −0.841387 | − | 1.71088i | ||||
\(787\) | −1.58399e57 | −0.190659 | −0.0953297 | − | 0.995446i | \(-0.530391\pi\) | ||||
−0.0953297 | + | 0.995446i | \(0.530391\pi\) | |||||||
\(788\) | − | 6.83164e57i | − | 0.801679i | ||||||
\(789\) | 5.38919e57 | − | 2.65033e57i | 0.616572 | − | 0.303222i | ||||
\(790\) | 4.03743e57 | 0.450363 | ||||||||
\(791\) | 3.72851e54i | 0.000405513i | ||||||||
\(792\) | −3.63952e56 | + | 4.72170e56i | −0.0385958 | + | 0.0500720i | ||||
\(793\) | 8.39780e57 | 0.868364 | ||||||||
\(794\) | 1.73148e58i | 1.74585i | ||||||||
\(795\) | −1.21992e57 | − | 2.48058e57i | −0.119947 | − | 0.243900i | ||||
\(796\) | 5.06232e57 | 0.485387 | ||||||||
\(797\) | − | 5.79622e57i | − | 0.541974i | −0.962583 | − | 0.270987i | \(-0.912650\pi\) | ||
0.962583 | − | 0.270987i | \(-0.0873500\pi\) | |||||||
\(798\) | 2.20295e56 | − | 1.08338e56i | 0.0200885 | − | 0.00987925i | ||||
\(799\) | 1.20905e58 | 1.07525 | ||||||||
\(800\) | − | 1.43438e58i | − | 1.24413i | ||||||
\(801\) | −3.04844e57 | − | 2.34976e57i | −0.257886 | − | 0.198780i | ||||
\(802\) | −6.23773e57 | −0.514682 | ||||||||
\(803\) | − | 7.41845e56i | − | 0.0597038i | ||||||
\(804\) | 7.19205e57 | + | 1.46243e58i | 0.564588 | + | 1.14803i | ||||
\(805\) | −4.98300e55 | −0.00381569 | ||||||||
\(806\) | − | 8.45459e57i | − | 0.631527i | ||||||
\(807\) | 1.12829e58 | − | 5.54880e57i | 0.822150 | − | 0.404323i | ||||
\(808\) | −7.70124e55 | −0.00547436 | ||||||||
\(809\) | − | 7.60503e57i | − | 0.527389i | −0.964606 | − | 0.263694i | \(-0.915059\pi\) | ||
0.964606 | − | 0.263694i | \(-0.0849410\pi\) | |||||||
\(810\) | 1.76234e57 | + | 6.69411e57i | 0.119231 | + | 0.452890i | ||||
\(811\) | −1.24011e57 | −0.0818548 | −0.0409274 | − | 0.999162i | \(-0.513031\pi\) | ||||
−0.0409274 | + | 0.999162i | \(0.513031\pi\) | |||||||
\(812\) | 7.18557e55i | 0.00462744i | ||||||||
\(813\) | 6.90654e57 | + | 1.40438e58i | 0.433960 | + | 0.882414i | ||||
\(814\) | −1.69173e58 | −1.03716 | ||||||||
\(815\) | 1.96439e57i | 0.117510i | ||||||||
\(816\) | −1.16105e58 | + | 5.70991e57i | −0.677718 | + | 0.333293i | ||||
\(817\) | −4.95331e58 | −2.82133 | ||||||||
\(818\) | 3.25714e58i | 1.81038i | ||||||||
\(819\) | 8.75960e55 | − | 1.13642e56i | 0.00475123 | − | 0.00616397i | ||||
\(820\) | 6.69119e57 | 0.354182 | ||||||||
\(821\) | − | 2.11936e58i | − | 1.09482i | −0.836865 | − | 0.547409i | \(-0.815614\pi\) | ||
0.836865 | − | 0.547409i | \(-0.184386\pi\) | |||||||
\(822\) | 4.45933e57 | + | 9.06761e57i | 0.224819 | + | 0.457148i | ||||
\(823\) | −1.61545e58 | −0.794874 | −0.397437 | − | 0.917630i | \(-0.630100\pi\) | ||||
−0.397437 | + | 0.917630i | \(0.630100\pi\) | |||||||
\(824\) | − | 2.90081e55i | − | 0.00139308i | ||||||
\(825\) | 2.23470e58 | − | 1.09900e58i | 1.04747 | − | 0.515131i | ||||
\(826\) | 1.34513e56 | 0.00615408 | ||||||||
\(827\) | 9.15034e57i | 0.408627i | 0.978906 | + | 0.204313i | \(0.0654962\pi\) | ||||
−0.978906 | + | 0.204313i | \(0.934504\pi\) | |||||||
\(828\) | 2.03624e58 | + | 1.56955e58i | 0.887612 | + | 0.684177i | ||||
\(829\) | 1.73502e58 | 0.738269 | 0.369135 | − | 0.929376i | \(-0.379654\pi\) | ||||
0.369135 | + | 0.929376i | \(0.379654\pi\) | |||||||
\(830\) | − | 8.08808e57i | − | 0.335957i | ||||||
\(831\) | −7.62364e57 | − | 1.55019e58i | −0.309131 | − | 0.628587i | ||||
\(832\) | −1.85800e58 | −0.735493 | ||||||||
\(833\) | 1.89140e58i | 0.730941i | ||||||||
\(834\) | −1.07862e58 | + | 5.30454e57i | −0.406958 | + | 0.200137i | ||||
\(835\) | 3.30418e57 | 0.121712 | ||||||||
\(836\) | − | 5.72280e58i | − | 2.05818i | ||||||
\(837\) | −1.59016e58 | − | 3.21728e57i | −0.558382 | − | 0.112974i | ||||
\(838\) | 5.27236e58 | 1.80769 | ||||||||
\(839\) | 3.59646e58i | 1.20403i | 0.798486 | + | 0.602014i | \(0.205635\pi\) | ||||
−0.798486 | + | 0.602014i | \(0.794365\pi\) | |||||||
\(840\) | −2.13575e54 | − | 4.34283e54i | −6.98175e−5 | − | 0.000141967i | ||||
\(841\) | 2.39025e58 | 0.762999 | ||||||||
\(842\) | 4.22171e58i | 1.31597i | ||||||||
\(843\) | 9.96241e57 | − | 4.89939e57i | 0.303259 | − | 0.149139i | ||||
\(844\) | −5.05298e58 | −1.50210 | ||||||||
\(845\) | − | 4.31301e57i | − | 0.125212i | ||||||
\(846\) | 4.44048e58 | − | 5.76082e58i | 1.25899 | − | 1.63334i | ||||
\(847\) | −2.58171e56 | −0.00714890 | ||||||||
\(848\) | − | 3.10839e58i | − | 0.840657i | ||||||
\(849\) | −1.91058e58 | − | 3.88497e58i | −0.504674 | − | 1.02621i | ||||
\(850\) | 3.52922e58 | 0.910543 | ||||||||
\(851\) | − | 2.59284e58i | − | 0.653409i | ||||||
\(852\) | −6.23681e58 | + | 3.06718e58i | −1.53522 | + | 0.755002i | ||||
\(853\) | 6.51802e58 | 1.56724 | 0.783619 | − | 0.621242i | \(-0.213371\pi\) | ||||
0.783619 | + | 0.621242i | \(0.213371\pi\) | |||||||
\(854\) | − | 6.45292e56i | − | 0.0151565i | ||||||
\(855\) | 1.87042e58 | + | 1.44173e58i | 0.429158 | + | 0.330798i | ||||
\(856\) | −1.55941e57 | −0.0349530 | ||||||||
\(857\) | 6.66361e58i | 1.45913i | 0.683913 | + | 0.729564i | \(0.260277\pi\) | ||||
−0.683913 | + | 0.729564i | \(0.739723\pi\) | |||||||
\(858\) | −3.00464e58 | − | 6.10963e58i | −0.642756 | − | 1.30698i | ||||
\(859\) | −8.25379e58 | −1.72500 | −0.862502 | − | 0.506053i | \(-0.831104\pi\) | ||||
−0.862502 | + | 0.506053i | \(0.831104\pi\) | |||||||
\(860\) | − | 2.74758e58i | − | 0.561025i | ||||||
\(861\) | −4.86145e56 | + | 2.39080e56i | −0.00969845 | + | 0.00476957i | ||||
\(862\) | −3.74865e58 | −0.730683 | ||||||||
\(863\) | 3.26696e58i | 0.622197i | 0.950378 | + | 0.311098i | \(0.100697\pi\) | ||||
−0.950378 | + | 0.311098i | \(0.899303\pi\) | |||||||
\(864\) | −1.49230e58 | + | 7.37577e58i | −0.277703 | + | 1.37256i | ||||
\(865\) | −1.47962e58 | −0.269046 | ||||||||
\(866\) | − | 8.31212e58i | − | 1.47691i | ||||||
\(867\) | 1.18347e58 | + | 2.40647e58i | 0.205482 | + | 0.417828i | ||||
\(868\) | −3.19157e56 | −0.00541513 | ||||||||
\(869\) | 7.62027e58i | 1.26350i | ||||||||
\(870\) | −1.26261e58 | + | 6.20935e57i | −0.204590 | + | 0.100615i | ||||
\(871\) | 6.61473e58 | 1.04749 | ||||||||
\(872\) | − | 5.49795e57i | − | 0.0850885i | ||||||
\(873\) | −1.85424e58 | + | 2.40558e58i | −0.280466 | + | 0.363860i | ||||
\(874\) | 1.78538e59 | 2.63939 | ||||||||
\(875\) | 4.29715e56i | 0.00620897i | ||||||||
\(876\) | −1.37121e57 | − | 2.78821e57i | −0.0193652 | − | 0.0393771i | ||||
\(877\) | −1.90902e58 | −0.263524 | −0.131762 | − | 0.991281i | \(-0.542063\pi\) | ||||
−0.131762 | + | 0.991281i | \(0.542063\pi\) | |||||||
\(878\) | 1.13038e59i | 1.52523i | ||||||||
\(879\) | −9.93303e58 | + | 4.88494e58i | −1.31010 | + | 0.644290i | ||||
\(880\) | −3.51688e58 | −0.453423 | ||||||||
\(881\) | − | 1.22884e59i | − | 1.54874i | −0.632733 | − | 0.774370i | \(-0.718067\pi\) | ||
0.632733 | − | 0.774370i | \(-0.281933\pi\) | |||||||
\(882\) | 9.01203e58 | + | 6.94653e58i | 1.11033 | + | 0.855847i | ||||
\(883\) | 2.29805e58 | 0.276787 | 0.138393 | − | 0.990377i | \(-0.455806\pi\) | ||||
0.138393 | + | 0.990377i | \(0.455806\pi\) | |||||||
\(884\) | − | 4.74018e58i | − | 0.558148i | ||||||
\(885\) | 5.71043e57 | + | 1.16116e58i | 0.0657361 | + | 0.133668i | ||||
\(886\) | −1.16564e59 | −1.31187 | ||||||||
\(887\) | 1.96194e58i | 0.215881i | 0.994157 | + | 0.107940i | \(0.0344255\pi\) | ||||
−0.994157 | + | 0.107940i | \(0.965574\pi\) | |||||||
\(888\) | 2.25974e57 | − | 1.11131e57i | 0.0243108 | − | 0.0119557i | ||||
\(889\) | 6.51366e56 | 0.00685157 | ||||||||
\(890\) | − | 1.48264e58i | − | 0.152488i | ||||||
\(891\) | −1.26345e59 | + | 3.32626e58i | −1.27059 | + | 0.334504i | ||||
\(892\) | 1.32144e59 | 1.29943 | ||||||||
\(893\) | − | 2.48146e59i | − | 2.38604i | ||||||
\(894\) | −6.77999e58 | − | 1.37864e59i | −0.637498 | − | 1.29629i | ||||
\(895\) | −2.24935e58 | −0.206822 | ||||||||
\(896\) | − | 1.05286e56i | − | 0.000946692i | ||||||
\(897\) | 9.36394e58 | − | 4.60507e58i | 0.823398 | − | 0.404937i | ||||
\(898\) | −1.89048e59 | −1.62572 | ||||||||
\(899\) | − | 3.29771e58i | − | 0.277344i | ||||||
\(900\) | 6.36774e58 | − | 8.26113e58i | 0.523763 | − | 0.679500i | ||||
\(901\) | 7.39399e58 | 0.594817 | ||||||||
\(902\) | 2.57068e59i | 2.02264i | ||||||||
\(903\) | 9.81725e56 | + | 1.99624e57i | 0.00755501 | + | 0.0153624i | ||||
\(904\) | −2.63356e56 | −0.00198233 | ||||||||
\(905\) | 4.73612e58i | 0.348699i | ||||||||
\(906\) | 3.36782e59 | − | 1.65625e59i | 2.42541 | − | 1.19278i | ||||
\(907\) | −1.32909e59 | −0.936284 | −0.468142 | − | 0.883653i | \(-0.655076\pi\) | ||||
−0.468142 | + | 0.883653i | \(0.655076\pi\) | |||||||
\(908\) | − | 9.98862e58i | − | 0.688317i | ||||||
\(909\) | −1.33673e58 | − | 1.03036e58i | −0.0901089 | − | 0.0694565i | ||||
\(910\) | 5.52709e56 | 0.00364476 | ||||||||
\(911\) | 9.58216e56i | 0.00618153i | 0.999995 | + | 0.00309077i | \(0.000983823\pi\) | ||||
−0.999995 | + | 0.00309077i | \(0.999016\pi\) | |||||||
\(912\) | 1.17190e59 | + | 2.38295e59i | 0.739597 | + | 1.50390i | ||||
\(913\) | 1.52655e59 | 0.942530 | ||||||||
\(914\) | 3.42217e59i | 2.06717i | ||||||||
\(915\) | 5.57037e58 | − | 2.73944e58i | 0.329202 | − | 0.161897i | ||||
\(916\) | −4.30660e57 | −0.0249015 | ||||||||
\(917\) | 2.36601e57i | 0.0133854i | ||||||||
\(918\) | −1.81477e59 | − | 3.67173e58i | −1.00454 | − | 0.203244i | ||||
\(919\) | 8.88524e58 | 0.481237 | 0.240619 | − | 0.970620i | \(-0.422650\pi\) | ||||
0.240619 | + | 0.970620i | \(0.422650\pi\) | |||||||
\(920\) | − | 3.51965e57i | − | 0.0186528i | ||||||
\(921\) | −1.93926e58 | − | 3.94329e58i | −0.100564 | − | 0.204487i | ||||
\(922\) | −5.41076e59 | −2.74562 | ||||||||
\(923\) | 2.82097e59i | 1.40076i | ||||||||
\(924\) | −2.30635e57 | + | 1.13423e57i | −0.0112069 | + | 0.00551142i | ||||
\(925\) | −1.05193e59 | −0.500209 | ||||||||
\(926\) | − | 1.39160e59i | − | 0.647582i | ||||||
\(927\) | 3.88105e57 | − | 5.03505e57i | 0.0176748 | − | 0.0229302i | ||||
\(928\) | −1.52960e59 | −0.681741 | ||||||||
\(929\) | − | 3.17122e59i | − | 1.38329i | −0.722239 | − | 0.691643i | \(-0.756887\pi\) | ||
0.722239 | − | 0.691643i | \(-0.243113\pi\) | |||||||
\(930\) | −2.75796e58 | − | 5.60804e58i | −0.117741 | − | 0.239416i | ||||
\(931\) | 3.88190e59 | 1.62200 | ||||||||
\(932\) | 9.26081e58i | 0.378731i | ||||||||
\(933\) | −1.30491e59 | + | 6.41736e58i | −0.522332 | + | 0.256876i | ||||
\(934\) | −4.88317e59 | −1.91322 | ||||||||
\(935\) | − | 8.36567e58i | − | 0.320825i | ||||||
\(936\) | 8.02689e57 | + | 6.18718e57i | 0.0301322 | + | 0.0232261i | ||||
\(937\) | 3.88543e59 | 1.42773 | 0.713866 | − | 0.700282i | \(-0.246942\pi\) | ||||
0.713866 | + | 0.700282i | \(0.246942\pi\) | |||||||
\(938\) | − | 5.08279e57i | − | 0.0182829i | ||||||
\(939\) | 1.38278e59 | + | 2.81174e59i | 0.486900 | + | 0.990063i | ||||
\(940\) | 1.37646e59 | 0.474466 | ||||||||
\(941\) | − | 1.95897e59i | − | 0.661051i | −0.943797 | − | 0.330525i | \(-0.892774\pi\) | ||
0.943797 | − | 0.330525i | \(-0.107226\pi\) | |||||||
\(942\) | −1.37183e59 | + | 6.74648e58i | −0.453192 | + | 0.222874i | ||||
\(943\) | −3.93997e59 | −1.27426 | ||||||||
\(944\) | 1.45504e59i | 0.460717i | ||||||||
\(945\) | 2.10326e56 | − | 1.03955e57i | 0.000652013 | − | 0.00322261i | ||||
\(946\) | 1.05559e60 | 3.20386 | ||||||||
\(947\) | 4.05743e59i | 1.20573i | 0.797842 | + | 0.602866i | \(0.205975\pi\) | ||||
−0.797842 | + | 0.602866i | \(0.794025\pi\) | |||||||
\(948\) | 1.40851e59 | + | 2.86407e59i | 0.409820 | + | 0.833329i | ||||
\(949\) | −1.26114e58 | −0.0359284 | ||||||||
\(950\) | − | 7.24338e59i | − | 2.02055i | ||||||
\(951\) | −9.94125e58 | + | 4.88898e58i | −0.271538 | + | 0.133539i | ||||
\(952\) | 1.29449e56 | 0.000346226 | ||||||||
\(953\) | − | 4.59879e59i | − | 1.20444i | −0.798330 | − | 0.602220i | \(-0.794283\pi\) | ||
0.798330 | − | 0.602220i | \(-0.205717\pi\) | |||||||
\(954\) | 2.71559e59 | − | 3.52305e59i | 0.696461 | − | 0.903549i | ||||
\(955\) | 2.47439e59 | 0.621441 | ||||||||
\(956\) | − | 3.58100e59i | − | 0.880738i | ||||||
\(957\) | −1.17196e59 | − | 2.38306e59i | −0.282275 | − | 0.573979i | ||||
\(958\) | −3.67748e59 | −0.867442 | ||||||||
\(959\) | − | 1.54825e57i | − | 0.00357658i | ||||||
\(960\) | −1.23244e59 | + | 6.06096e58i | −0.278830 | + | 0.137125i | ||||
\(961\) | −3.04830e59 | −0.675446 | ||||||||
\(962\) | 2.87595e59i | 0.624137i | ||||||||
\(963\) | −2.70673e59 | − | 2.08636e59i | −0.575333 | − | 0.443470i | ||||
\(964\) | 7.49128e59 | 1.55961 | ||||||||
\(965\) | 1.83709e59i | 0.374615i | ||||||||
\(966\) | −3.53856e57 | − | 7.19531e57i | −0.00706780 | − | 0.0143717i | ||||
\(967\) | −6.05101e59 | −1.18386 | −0.591928 | − | 0.805991i | \(-0.701633\pi\) | ||||
−0.591928 | + | 0.805991i | \(0.701633\pi\) | |||||||
\(968\) | − | 1.82354e58i | − | 0.0349469i | ||||||
\(969\) | −5.66837e59 | + | 2.78763e59i | −1.06410 | + | 0.523310i | ||||
\(970\) | −1.16998e59 | −0.215151 | ||||||||
\(971\) | 4.08611e59i | 0.736081i | 0.929810 | + | 0.368040i | \(0.119971\pi\) | ||||
−0.929810 | + | 0.368040i | \(0.880029\pi\) | |||||||
\(972\) | −4.13385e59 | + | 3.58550e59i | −0.729506 | + | 0.632739i | ||||
\(973\) | 1.84169e57 | 0.00318391 | ||||||||
\(974\) | 5.86475e59i | 0.993277i | ||||||||
\(975\) | −1.86830e59 | − | 3.79899e59i | −0.309994 | − | 0.630342i | ||||
\(976\) | 6.98018e59 | 1.13467 | ||||||||
\(977\) | 5.00416e59i | 0.796966i | 0.917176 | + | 0.398483i | \(0.130463\pi\) | ||||
−0.917176 | + | 0.398483i | \(0.869537\pi\) | |||||||
\(978\) | −2.83652e59 | + | 1.39497e59i | −0.442598 | + | 0.217664i | ||||
\(979\) | 2.79835e59 | 0.427807 | ||||||||
\(980\) | 2.15328e59i | 0.322537i | ||||||||
\(981\) | 7.35581e59 | − | 9.54301e59i | 1.07957 | − | 1.40057i | ||||
\(982\) | 5.98909e59 | 0.861254 | ||||||||
\(983\) | 3.00318e59i | 0.423167i | 0.977360 | + | 0.211583i | \(0.0678620\pi\) | ||||
−0.977360 | + | 0.211583i | \(0.932138\pi\) | |||||||
\(984\) | −1.68870e58 | − | 3.43379e58i | −0.0233158 | − | 0.0474103i | ||||
\(985\) | −2.04965e59 | −0.277303 | ||||||||
\(986\) | − | 3.76352e59i | − | 0.498949i | ||||||
\(987\) | −1.00006e58 | + | 4.91814e57i | −0.0129922 | + | 0.00638937i | ||||
\(988\) | −9.72875e59 | −1.23856 | ||||||||
\(989\) | 1.61786e60i | 2.01843i | ||||||||
\(990\) | −3.98603e59 | − | 3.07246e59i | −0.487345 | − | 0.375649i | ||||
\(991\) | 8.35257e58 | 0.100080 | 0.0500400 | − | 0.998747i | \(-0.484065\pi\) | ||||
0.0500400 | + | 0.998747i | \(0.484065\pi\) | |||||||
\(992\) | − | 6.79394e59i | − | 0.797789i | ||||||
\(993\) | 4.32573e59 | + | 8.79595e59i | 0.497823 | + | 1.01227i | ||||
\(994\) | 2.16765e58 | 0.0244490 | ||||||||
\(995\) | − | 1.51881e59i | − | 0.167897i | ||||||
\(996\) | 5.73752e59 | − | 2.82164e59i | 0.621637 | − | 0.305713i | ||||
\(997\) | 6.98796e58 | 0.0742074 | 0.0371037 | − | 0.999311i | \(-0.488187\pi\) | ||||
0.0371037 | + | 0.999311i | \(0.488187\pi\) | |||||||
\(998\) | − | 1.08567e60i | − | 1.13003i | ||||||
\(999\) | 5.40915e59 | + | 1.09440e59i | 0.551848 | + | 0.111652i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3.41.b.a.2.11 | yes | 12 | |
3.2 | odd | 2 | inner | 3.41.b.a.2.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.41.b.a.2.2 | ✓ | 12 | 3.2 | odd | 2 | inner | |
3.41.b.a.2.11 | yes | 12 | 1.1 | even | 1 | trivial |