Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,39,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, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
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: | \(36.5853876134\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 9 x^{17} + \cdots + 98\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{306}\cdot 3^{34}\cdot 5^{10}\cdot 19^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.15 | ||
Root | \(0.500000 - 4.14425e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.39.b.a.3.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 490276. | − | 185761.i | 0.935128 | − | 0.354311i | ||||
\(3\) | 6.63080e7i | 0.0570509i | 0.999593 | + | 0.0285254i | \(0.00908116\pi\) | ||||
−0.999593 | + | 0.0285254i | \(0.990919\pi\) | |||||||
\(4\) | 2.05863e11 | − | 1.82149e11i | 0.748927 | − | 0.662653i | ||||
\(5\) | −1.96572e13 | −1.03060 | −0.515301 | − | 0.857009i | \(-0.672320\pi\) | ||||
−0.515301 | + | 0.857009i | \(0.672320\pi\) | |||||||
\(6\) | 1.23175e13 | + | 3.25092e13i | 0.0202138 | + | 0.0533498i | ||||
\(7\) | 1.51470e16i | 1.32882i | 0.747370 | + | 0.664408i | \(0.231316\pi\) | ||||
−0.747370 | + | 0.664408i | \(0.768684\pi\) | |||||||
\(8\) | 6.70938e16 | − | 1.27545e17i | 0.465557 | − | 0.885018i | ||||
\(9\) | 1.34645e18 | 0.996745 | ||||||||
\(10\) | −9.63744e18 | + | 3.65154e18i | −0.963744 | + | 0.365154i | ||||
\(11\) | − | 1.12524e20i | − | 1.83986i | −0.392077 | − | 0.919932i | \(-0.628243\pi\) | ||
0.392077 | − | 0.919932i | \(-0.371757\pi\) | |||||||
\(12\) | 1.20779e19 | + | 1.36504e19i | 0.0378049 | + | 0.0427269i | ||||
\(13\) | −5.44284e20 | −0.372308 | −0.186154 | − | 0.982521i | \(-0.559602\pi\) | ||||
−0.186154 | + | 0.982521i | \(0.559602\pi\) | |||||||
\(14\) | 2.81373e21 | + | 7.42623e21i | 0.470814 | + | 1.24261i | ||||
\(15\) | − | 1.30343e21i | − | 0.0587967i | ||||||
\(16\) | 9.20167e21 | − | 7.49955e22i | 0.121783 | − | 0.992557i | ||||
\(17\) | −3.53724e23 | −1.47957 | −0.739784 | − | 0.672845i | \(-0.765072\pi\) | ||||
−0.739784 | + | 0.672845i | \(0.765072\pi\) | |||||||
\(18\) | 6.60135e23 | − | 2.50119e23i | 0.932084 | − | 0.353158i | ||||
\(19\) | − | 2.66676e24i | − | 1.34793i | −0.738765 | − | 0.673963i | \(-0.764591\pi\) | ||
0.738765 | − | 0.673963i | \(-0.235409\pi\) | |||||||
\(20\) | −4.04669e24 | + | 3.58052e24i | −0.771845 | + | 0.682931i | ||||
\(21\) | −1.00437e24 | −0.0758101 | ||||||||
\(22\) | −2.09027e25 | − | 5.51681e25i | −0.651885 | − | 1.72051i | ||||
\(23\) | − | 2.65998e25i | − | 0.356492i | −0.983986 | − | 0.178246i | \(-0.942958\pi\) | ||
0.983986 | − | 0.178246i | \(-0.0570423\pi\) | |||||||
\(24\) | 8.45722e24 | + | 4.44886e24i | 0.0504910 | + | 0.0265604i | ||||
\(25\) | 2.26061e25 | 0.0621392 | ||||||||
\(26\) | −2.66850e26 | + | 1.01107e26i | −0.348155 | + | 0.131913i | ||||
\(27\) | 1.78853e26i | 0.113916i | ||||||||
\(28\) | 2.75901e27 | + | 3.11822e27i | 0.880543 | + | 0.995186i | ||||
\(29\) | −1.06079e27 | −0.173807 | −0.0869033 | − | 0.996217i | \(-0.527697\pi\) | ||||
−0.0869033 | + | 0.996217i | \(0.527697\pi\) | |||||||
\(30\) | −2.42126e26 | − | 6.39039e26i | −0.0208323 | − | 0.0549824i | ||||
\(31\) | 6.94351e27i | 0.320411i | 0.987084 | + | 0.160205i | \(0.0512157\pi\) | ||||
−0.987084 | + | 0.160205i | \(0.948784\pi\) | |||||||
\(32\) | −9.41989e27 | − | 3.84778e28i | −0.237791 | − | 0.971316i | ||||
\(33\) | 7.46127e27 | 0.104966 | ||||||||
\(34\) | −1.73422e29 | + | 6.57082e28i | −1.38358 | + | 0.524228i | ||||
\(35\) | − | 2.97748e29i | − | 1.36948i | ||||||
\(36\) | 2.77186e29 | − | 2.45255e29i | 0.746489 | − | 0.660496i | ||||
\(37\) | −9.31975e29 | −1.49132 | −0.745661 | − | 0.666326i | \(-0.767866\pi\) | ||||
−0.745661 | + | 0.666326i | \(0.767866\pi\) | |||||||
\(38\) | −4.95381e29 | − | 1.30745e30i | −0.477585 | − | 1.26048i | ||||
\(39\) | − | 3.60904e28i | − | 0.0212405i | ||||||
\(40\) | −1.31887e30 | + | 2.50716e30i | −0.479803 | + | 0.912101i | ||||
\(41\) | −4.70553e29 | −0.107082 | −0.0535408 | − | 0.998566i | \(-0.517051\pi\) | ||||
−0.0535408 | + | 0.998566i | \(0.517051\pi\) | |||||||
\(42\) | −4.92418e29 | + | 1.86573e29i | −0.0708921 | + | 0.0268604i | ||||
\(43\) | − | 8.70134e30i | − | 0.801098i | −0.916275 | − | 0.400549i | \(-0.868819\pi\) | ||
0.916275 | − | 0.400549i | \(-0.131181\pi\) | |||||||
\(44\) | −2.04962e31 | − | 2.31647e31i | −1.21919 | − | 1.37792i | ||||
\(45\) | −2.64675e31 | −1.02725 | ||||||||
\(46\) | −4.94122e30 | − | 1.30413e31i | −0.126309 | − | 0.333366i | ||||
\(47\) | − | 5.03100e31i | − | 0.854664i | −0.904095 | − | 0.427332i | \(-0.859454\pi\) | ||
0.904095 | − | 0.427332i | \(-0.140546\pi\) | |||||||
\(48\) | 4.97280e30 | + | 6.10144e29i | 0.0566262 | + | 0.00694783i | ||||
\(49\) | −9.94977e31 | −0.765751 | ||||||||
\(50\) | 1.10832e31 | − | 4.19934e30i | 0.0581080 | − | 0.0220166i | ||||
\(51\) | − | 2.34547e31i | − | 0.0844106i | ||||||
\(52\) | −1.12048e32 | + | 9.91406e31i | −0.278831 | + | 0.246711i | ||||
\(53\) | 8.75485e32 | 1.51708 | 0.758538 | − | 0.651629i | \(-0.225914\pi\) | ||||
0.758538 | + | 0.651629i | \(0.225914\pi\) | |||||||
\(54\) | 3.32240e31 | + | 8.76874e31i | 0.0403617 | + | 0.106526i | ||||
\(55\) | 2.21191e33i | 1.89617i | ||||||||
\(56\) | 1.93192e33 | + | 1.01627e33i | 1.17603 | + | 0.618639i | ||||
\(57\) | 1.76828e32 | 0.0769003 | ||||||||
\(58\) | −5.20079e32 | + | 1.97053e32i | −0.162531 | + | 0.0615817i | ||||
\(59\) | − | 5.29322e33i | − | 1.19545i | −0.801701 | − | 0.597725i | \(-0.796071\pi\) | ||
0.801701 | − | 0.597725i | \(-0.203929\pi\) | |||||||
\(60\) | −2.37417e32 | − | 2.68328e32i | −0.0389618 | − | 0.0440344i | ||||
\(61\) | 4.70369e33 | 0.563860 | 0.281930 | − | 0.959435i | \(-0.409025\pi\) | ||||
0.281930 | + | 0.959435i | \(0.409025\pi\) | |||||||
\(62\) | 1.28984e33 | + | 3.40424e33i | 0.113525 | + | 0.299625i | ||||
\(63\) | 2.03948e34i | 1.32449i | ||||||||
\(64\) | −1.17660e34 | − | 1.71149e34i | −0.566514 | − | 0.824052i | ||||
\(65\) | 1.06991e34 | 0.383701 | ||||||||
\(66\) | 3.65808e33 | − | 1.38601e33i | 0.0981564 | − | 0.0371906i | ||||
\(67\) | − | 3.40887e34i | − | 0.687368i | −0.939085 | − | 0.343684i | \(-0.888325\pi\) | ||
0.939085 | − | 0.343684i | \(-0.111675\pi\) | |||||||
\(68\) | −7.28188e34 | + | 6.44303e34i | −1.10809 | + | 0.980439i | ||||
\(69\) | 1.76378e33 | 0.0203382 | ||||||||
\(70\) | −5.53099e34 | − | 1.45979e35i | −0.485222 | − | 1.28064i | ||||
\(71\) | − | 1.85895e34i | − | 0.124554i | −0.998059 | − | 0.0622771i | \(-0.980164\pi\) | ||
0.998059 | − | 0.0622771i | \(-0.0198362\pi\) | |||||||
\(72\) | 9.03388e34 | − | 1.71733e35i | 0.464042 | − | 0.882137i | ||||
\(73\) | −1.08290e35 | −0.428008 | −0.214004 | − | 0.976833i | \(-0.568651\pi\) | ||||
−0.214004 | + | 0.976833i | \(0.568651\pi\) | |||||||
\(74\) | −4.56925e35 | + | 1.73125e35i | −1.39458 | + | 0.528392i | ||||
\(75\) | 1.49897e33i | 0.00354509i | ||||||||
\(76\) | −4.85747e35 | − | 5.48989e35i | −0.893206 | − | 1.00950i | ||||
\(77\) | 1.70441e36 | 2.44484 | ||||||||
\(78\) | −6.70420e33 | − | 1.76943e34i | −0.00752574 | − | 0.0198626i | ||||
\(79\) | 1.22916e36i | 1.08316i | 0.840649 | + | 0.541581i | \(0.182174\pi\) | ||||
−0.840649 | + | 0.541581i | \(0.817826\pi\) | |||||||
\(80\) | −1.80879e35 | + | 1.47420e36i | −0.125510 | + | 1.02293i | ||||
\(81\) | 1.80700e36 | 0.990246 | ||||||||
\(82\) | −2.30701e35 | + | 8.74104e34i | −0.100135 | + | 0.0379402i | ||||
\(83\) | 3.51053e36i | 1.21029i | 0.796115 | + | 0.605145i | \(0.206885\pi\) | ||||
−0.796115 | + | 0.605145i | \(0.793115\pi\) | |||||||
\(84\) | −2.06763e35 | + | 1.82944e35i | −0.0567762 | + | 0.0502357i | ||||
\(85\) | 6.95321e36 | 1.52484 | ||||||||
\(86\) | −1.61637e36 | − | 4.26606e36i | −0.283838 | − | 0.749129i | ||||
\(87\) | − | 7.03387e34i | − | 0.00991582i | ||||||
\(88\) | −1.43519e37 | − | 7.54969e36i | −1.62831 | − | 0.856562i | ||||
\(89\) | 1.15872e37 | 1.06064 | 0.530322 | − | 0.847796i | \(-0.322071\pi\) | ||||
0.530322 | + | 0.847796i | \(0.322071\pi\) | |||||||
\(90\) | −1.29764e37 | + | 4.91663e36i | −0.960607 | + | 0.363965i | ||||
\(91\) | − | 8.24429e36i | − | 0.494728i | ||||||
\(92\) | −4.84512e36 | − | 5.47594e36i | −0.236231 | − | 0.266987i | ||||
\(93\) | −4.60411e35 | −0.0182797 | ||||||||
\(94\) | −9.34565e36 | − | 2.46658e37i | −0.302817 | − | 0.799220i | ||||
\(95\) | 5.24210e37i | 1.38917i | ||||||||
\(96\) | 2.55139e36 | − | 6.24614e35i | 0.0554144 | − | 0.0135662i | ||||
\(97\) | 1.01726e37 | 0.181455 | 0.0907275 | − | 0.995876i | \(-0.471081\pi\) | ||||
0.0907275 | + | 0.995876i | \(0.471081\pi\) | |||||||
\(98\) | −4.87813e37 | + | 1.84828e37i | −0.716075 | + | 0.271314i | ||||
\(99\) | − | 1.51509e38i | − | 1.83388i | ||||||
\(100\) | 4.65377e36 | − | 4.11767e36i | 0.0465377 | − | 0.0411767i | ||||
\(101\) | 2.00705e37 | 0.166132 | 0.0830658 | − | 0.996544i | \(-0.473529\pi\) | ||||
0.0830658 | + | 0.996544i | \(0.473529\pi\) | |||||||
\(102\) | −4.35698e36 | − | 1.14993e37i | −0.0299076 | − | 0.0789347i | ||||
\(103\) | 2.67993e38i | 1.52833i | 0.645022 | + | 0.764164i | \(0.276848\pi\) | ||||
−0.645022 | + | 0.764164i | \(0.723152\pi\) | |||||||
\(104\) | −3.65181e37 | + | 6.94205e37i | −0.173330 | + | 0.329499i | ||||
\(105\) | 1.97430e37 | 0.0781299 | ||||||||
\(106\) | 4.29229e38 | − | 1.62631e38i | 1.41866 | − | 0.537517i | ||||
\(107\) | − | 2.04553e38i | − | 0.565606i | −0.959178 | − | 0.282803i | \(-0.908736\pi\) | ||
0.959178 | − | 0.282803i | \(-0.0912643\pi\) | |||||||
\(108\) | 3.25778e37 | + | 3.68193e37i | 0.0754867 | + | 0.0853148i | ||||
\(109\) | −3.50029e38 | −0.680770 | −0.340385 | − | 0.940286i | \(-0.610557\pi\) | ||||
−0.340385 | + | 0.940286i | \(0.610557\pi\) | |||||||
\(110\) | 4.10887e38 | + | 1.08445e39i | 0.671834 | + | 1.77316i | ||||
\(111\) | − | 6.17974e37i | − | 0.0850812i | ||||||
\(112\) | 1.13596e39 | + | 1.39378e38i | 1.31892 | + | 0.161827i | ||||
\(113\) | −9.40962e38 | −0.922745 | −0.461373 | − | 0.887206i | \(-0.652643\pi\) | ||||
−0.461373 | + | 0.887206i | \(0.652643\pi\) | |||||||
\(114\) | 8.66944e37 | − | 3.28477e37i | 0.0719116 | − | 0.0272466i | ||||
\(115\) | 5.22878e38i | 0.367402i | ||||||||
\(116\) | −2.18377e38 | + | 1.93221e38i | −0.130168 | + | 0.115173i | ||||
\(117\) | −7.32854e38 | −0.371096 | ||||||||
\(118\) | −9.83275e38 | − | 2.59514e39i | −0.423562 | − | 1.11790i | ||||
\(119\) | − | 5.35787e39i | − | 1.96607i | ||||||
\(120\) | −1.66245e38 | − | 8.74519e37i | −0.0520361 | − | 0.0273732i | ||||
\(121\) | −8.92132e39 | −2.38510 | ||||||||
\(122\) | 2.30611e39 | − | 8.73763e38i | 0.527281 | − | 0.199782i | ||||
\(123\) | − | 3.12014e37i | − | 0.00610910i | ||||||
\(124\) | 1.26475e39 | + | 1.42942e39i | 0.212321 | + | 0.239964i | ||||
\(125\) | 6.70686e39 | 0.966561 | ||||||||
\(126\) | 3.78856e39 | + | 9.99908e39i | 0.469282 | + | 1.23857i | ||||
\(127\) | 2.85766e39i | 0.304606i | 0.988334 | + | 0.152303i | \(0.0486690\pi\) | ||||
−0.988334 | + | 0.152303i | \(0.951331\pi\) | |||||||
\(128\) | −8.94789e39 | − | 6.20535e39i | −0.821734 | − | 0.569872i | ||||
\(129\) | 5.76969e38 | 0.0457033 | ||||||||
\(130\) | 5.24551e39 | − | 1.98747e39i | 0.358809 | − | 0.135950i | ||||
\(131\) | 2.19311e40i | 1.29690i | 0.761257 | + | 0.648450i | \(0.224582\pi\) | ||||
−0.761257 | + | 0.648450i | \(0.775418\pi\) | |||||||
\(132\) | 1.53600e39 | − | 1.35906e39i | 0.0786117 | − | 0.0695559i | ||||
\(133\) | 4.03935e40 | 1.79114 | ||||||||
\(134\) | −6.33236e39 | − | 1.67129e40i | −0.243542 | − | 0.642776i | ||||
\(135\) | − | 3.51574e39i | − | 0.117402i | ||||||
\(136\) | −2.37327e40 | + | 4.51155e40i | −0.688823 | + | 1.30944i | ||||
\(137\) | 2.40598e40 | 0.607578 | 0.303789 | − | 0.952739i | \(-0.401748\pi\) | ||||
0.303789 | + | 0.952739i | \(0.401748\pi\) | |||||||
\(138\) | 8.64741e38 | − | 3.27642e38i | 0.0190188 | − | 0.00720605i | ||||
\(139\) | − | 1.36580e40i | − | 0.261882i | −0.991390 | − | 0.130941i | \(-0.958200\pi\) | ||
0.991390 | − | 0.130941i | \(-0.0417998\pi\) | |||||||
\(140\) | −5.42343e40 | − | 6.12953e40i | −0.907489 | − | 1.02564i | ||||
\(141\) | 3.33596e39 | 0.0487593 | ||||||||
\(142\) | −3.45320e39 | − | 9.11397e39i | −0.0441309 | − | 0.116474i | ||||
\(143\) | 6.12453e40i | 0.684996i | ||||||||
\(144\) | 1.23896e40 | − | 1.00978e41i | 0.121387 | − | 0.989326i | ||||
\(145\) | 2.08521e40 | 0.179125 | ||||||||
\(146\) | −5.30918e40 | + | 2.01160e40i | −0.400242 | + | 0.151648i | ||||
\(147\) | − | 6.59749e39i | − | 0.0436867i | ||||||
\(148\) | −1.91860e41 | + | 1.69758e41i | −1.11689 | + | 0.988228i | ||||
\(149\) | 1.93459e41 | 0.990947 | 0.495474 | − | 0.868623i | \(-0.334995\pi\) | ||||
0.495474 | + | 0.868623i | \(0.334995\pi\) | |||||||
\(150\) | 2.78450e38 | + | 7.34907e38i | 0.00125607 | + | 0.00331511i | ||||
\(151\) | − | 1.17926e41i | − | 0.468865i | −0.972132 | − | 0.234433i | \(-0.924677\pi\) | ||
0.972132 | − | 0.234433i | \(-0.0753232\pi\) | |||||||
\(152\) | −3.40131e41 | − | 1.78923e41i | −1.19294 | − | 0.627536i | ||||
\(153\) | −4.76273e41 | −1.47475 | ||||||||
\(154\) | 8.35632e41 | − | 3.16613e41i | 2.28624 | − | 0.866235i | ||||
\(155\) | − | 1.36490e41i | − | 0.330216i | ||||||
\(156\) | −6.57382e39 | − | 7.42970e39i | −0.0140751 | − | 0.0159076i | ||||
\(157\) | −3.30992e41 | −0.627659 | −0.313830 | − | 0.949479i | \(-0.601612\pi\) | ||||
−0.313830 | + | 0.949479i | \(0.601612\pi\) | |||||||
\(158\) | 2.28330e41 | + | 6.02627e41i | 0.383776 | + | 1.01289i | ||||
\(159\) | 5.80517e40i | 0.0865505i | ||||||||
\(160\) | 1.85168e41 | + | 7.56364e41i | 0.245068 | + | 1.00104i | ||||
\(161\) | 4.02909e41 | 0.473713 | ||||||||
\(162\) | 8.85930e41 | − | 3.35671e41i | 0.926006 | − | 0.350855i | ||||
\(163\) | 3.31730e41i | 0.308475i | 0.988034 | + | 0.154238i | \(0.0492921\pi\) | ||||
−0.988034 | + | 0.154238i | \(0.950708\pi\) | |||||||
\(164\) | −9.68696e40 | + | 8.57105e40i | −0.0801963 | + | 0.0709579i | ||||
\(165\) | −1.46667e41 | −0.108178 | ||||||||
\(166\) | 6.52121e41 | + | 1.72113e42i | 0.428820 | + | 1.13178i | ||||
\(167\) | 7.73111e41i | 0.453554i | 0.973947 | + | 0.226777i | \(0.0728188\pi\) | ||||
−0.973947 | + | 0.226777i | \(0.927181\pi\) | |||||||
\(168\) | −6.73870e40 | + | 1.28102e41i | −0.0352939 | + | 0.0670933i | ||||
\(169\) | −1.84097e42 | −0.861387 | ||||||||
\(170\) | 3.40899e42 | − | 1.29164e42i | 1.42592 | − | 0.540270i | ||||
\(171\) | − | 3.59068e42i | − | 1.34354i | ||||||
\(172\) | −1.58494e42 | − | 1.79129e42i | −0.530850 | − | 0.599964i | ||||
\(173\) | −3.99307e42 | −1.19793 | −0.598964 | − | 0.800776i | \(-0.704421\pi\) | ||||
−0.598964 | + | 0.800776i | \(0.704421\pi\) | |||||||
\(174\) | −1.30662e40 | − | 3.44854e40i | −0.00351329 | − | 0.00927255i | ||||
\(175\) | 3.42415e41i | 0.0825715i | ||||||||
\(176\) | −8.43882e42 | − | 1.03541e42i | −1.82617 | − | 0.224064i | ||||
\(177\) | 3.50983e41 | 0.0682015 | ||||||||
\(178\) | 5.68095e42 | − | 2.15246e42i | 0.991838 | − | 0.375799i | ||||
\(179\) | − | 3.46266e42i | − | 0.543503i | −0.962367 | − | 0.271752i | \(-0.912397\pi\) | ||
0.962367 | − | 0.271752i | \(-0.0876029\pi\) | |||||||
\(180\) | −5.44869e42 | + | 4.82101e42i | −0.769333 | + | 0.680708i | ||||
\(181\) | 5.51272e42 | 0.700605 | 0.350302 | − | 0.936637i | \(-0.386079\pi\) | ||||
0.350302 | + | 0.936637i | \(0.386079\pi\) | |||||||
\(182\) | −1.53147e42 | − | 4.04198e42i | −0.175288 | − | 0.462634i | ||||
\(183\) | 3.11892e41i | 0.0321687i | ||||||||
\(184\) | −3.39267e42 | − | 1.78469e42i | −0.315502 | − | 0.165967i | ||||
\(185\) | 1.83200e43 | 1.53696 | ||||||||
\(186\) | −2.25728e41 | + | 8.55264e40i | −0.0170939 | + | 0.00647671i | ||||
\(187\) | 3.98026e43i | 2.72220i | ||||||||
\(188\) | −9.16390e42 | − | 1.03570e43i | −0.566345 | − | 0.640081i | ||||
\(189\) | −2.70909e42 | −0.151373 | ||||||||
\(190\) | 9.73778e42 | + | 2.57008e43i | 0.492200 | + | 1.29905i | ||||
\(191\) | − | 3.12782e43i | − | 1.43090i | −0.698666 | − | 0.715448i | \(-0.746223\pi\) | ||
0.698666 | − | 0.715448i | \(-0.253777\pi\) | |||||||
\(192\) | 1.13485e42 | − | 7.80182e41i | 0.0470129 | − | 0.0323201i | ||||
\(193\) | 4.29486e43 | 1.61198 | 0.805991 | − | 0.591928i | \(-0.201633\pi\) | ||||
0.805991 | + | 0.591928i | \(0.201633\pi\) | |||||||
\(194\) | 4.98738e42 | − | 1.88967e42i | 0.169684 | − | 0.0642916i | ||||
\(195\) | 7.09435e41i | 0.0218905i | ||||||||
\(196\) | −2.04829e43 | + | 1.81234e43i | −0.573491 | + | 0.507427i | ||||
\(197\) | −2.18683e43 | −0.555848 | −0.277924 | − | 0.960603i | \(-0.589646\pi\) | ||||
−0.277924 | + | 0.960603i | \(0.589646\pi\) | |||||||
\(198\) | −2.81445e43 | − | 7.42813e43i | −0.649763 | − | 1.71491i | ||||
\(199\) | 3.55448e43i | 0.745707i | 0.927890 | + | 0.372853i | \(0.121621\pi\) | ||||
−0.927890 | + | 0.372853i | \(0.878379\pi\) | |||||||
\(200\) | 1.51673e42 | − | 2.88328e42i | 0.0289293 | − | 0.0549943i | ||||
\(201\) | 2.26035e42 | 0.0392149 | ||||||||
\(202\) | 9.84009e42 | − | 3.72832e42i | 0.155354 | − | 0.0588623i | ||||
\(203\) | − | 1.60678e43i | − | 0.230957i | ||||||
\(204\) | −4.27224e42 | − | 4.82847e42i | −0.0559349 | − | 0.0632174i | ||||
\(205\) | 9.24973e42 | 0.110358 | ||||||||
\(206\) | 4.97827e43 | + | 1.31391e44i | 0.541504 | + | 1.42918i | ||||
\(207\) | − | 3.58155e43i | − | 0.355332i | ||||||
\(208\) | −5.00832e42 | + | 4.08189e43i | −0.0453408 | + | 0.369537i | ||||
\(209\) | −3.00076e44 | −2.48000 | ||||||||
\(210\) | 9.67955e42 | − | 3.66749e42i | 0.0730615 | − | 0.0276823i | ||||
\(211\) | − | 2.38247e44i | − | 1.64309i | −0.570147 | − | 0.821543i | \(-0.693114\pi\) | ||
0.570147 | − | 0.821543i | \(-0.306886\pi\) | |||||||
\(212\) | 1.80230e44 | − | 1.59468e44i | 1.13618 | − | 1.00529i | ||||
\(213\) | 1.23263e42 | 0.00710592 | ||||||||
\(214\) | −3.79980e43 | − | 1.00287e44i | −0.200401 | − | 0.528914i | ||||
\(215\) | 1.71044e44i | 0.825612i | ||||||||
\(216\) | 2.28117e43 | + | 1.19999e43i | 0.100818 | + | 0.0530344i | ||||
\(217\) | −1.05174e44 | −0.425767 | ||||||||
\(218\) | −1.71611e44 | + | 6.50217e43i | −0.636606 | + | 0.241204i | ||||
\(219\) | − | 7.18046e42i | − | 0.0244182i | ||||||
\(220\) | 4.02896e44 | + | 4.55352e44i | 1.25650 | + | 1.42009i | ||||
\(221\) | 1.92526e44 | 0.550855 | ||||||||
\(222\) | −1.14796e43 | − | 3.02978e43i | −0.0301452 | − | 0.0795618i | ||||
\(223\) | 8.77061e43i | 0.211465i | 0.994395 | + | 0.105732i | \(0.0337187\pi\) | ||||
−0.994395 | + | 0.105732i | \(0.966281\pi\) | |||||||
\(224\) | 5.82824e44 | − | 1.42683e44i | 1.29070 | − | 0.315981i | ||||
\(225\) | 3.04381e43 | 0.0619369 | ||||||||
\(226\) | −4.61331e44 | + | 1.74794e44i | −0.862884 | + | 0.326939i | ||||
\(227\) | 1.24442e44i | 0.214030i | 0.994257 | + | 0.107015i | \(0.0341293\pi\) | ||||
−0.994257 | + | 0.107015i | \(0.965871\pi\) | |||||||
\(228\) | 3.64024e43 | − | 3.22089e43i | 0.0575927 | − | 0.0509582i | ||||
\(229\) | 1.79974e44 | 0.262021 | 0.131010 | − | 0.991381i | \(-0.458178\pi\) | ||||
0.131010 | + | 0.991381i | \(0.458178\pi\) | |||||||
\(230\) | 9.71303e43 | + | 2.56354e44i | 0.130175 | + | 0.343567i | ||||
\(231\) | 1.13016e44i | 0.139480i | ||||||||
\(232\) | −7.11723e43 | + | 1.35298e44i | −0.0809169 | + | 0.153822i | ||||
\(233\) | 5.05917e44 | 0.530050 | 0.265025 | − | 0.964241i | \(-0.414620\pi\) | ||||
0.265025 | + | 0.964241i | \(0.414620\pi\) | |||||||
\(234\) | −3.59301e44 | + | 1.36136e44i | −0.347022 | + | 0.131484i | ||||
\(235\) | 9.88953e44i | 0.880818i | ||||||||
\(236\) | −9.64152e44 | − | 1.08968e45i | −0.792169 | − | 0.895305i | ||||
\(237\) | −8.15031e43 | −0.0617953 | ||||||||
\(238\) | −9.95283e44 | − | 2.62683e45i | −0.696602 | − | 1.83853i | ||||
\(239\) | − | 2.69834e45i | − | 1.74396i | −0.489540 | − | 0.871981i | \(-0.662835\pi\) | ||
0.489540 | − | 0.871981i | \(-0.337165\pi\) | |||||||
\(240\) | −9.77511e43 | − | 1.19937e43i | −0.0583590 | − | 0.00716044i | ||||
\(241\) | 5.53361e44 | 0.305270 | 0.152635 | − | 0.988283i | \(-0.451224\pi\) | ||||
0.152635 | + | 0.988283i | \(0.451224\pi\) | |||||||
\(242\) | −4.37391e45 | + | 1.65723e45i | −2.23037 | + | 0.845069i | ||||
\(243\) | 3.61423e44i | 0.170410i | ||||||||
\(244\) | 9.68317e44 | − | 8.56770e44i | 0.422290 | − | 0.373644i | ||||
\(245\) | 1.95584e45 | 0.789184 | ||||||||
\(246\) | −5.79601e42 | − | 1.52973e43i | −0.00216452 | − | 0.00571278i | ||||
\(247\) | 1.45148e45i | 0.501843i | ||||||||
\(248\) | 8.85607e44 | + | 4.65867e44i | 0.283569 | + | 0.149169i | ||||
\(249\) | −2.32777e44 | −0.0690481 | ||||||||
\(250\) | 3.28821e45 | − | 1.24587e45i | 0.903857 | − | 0.342463i | ||||
\(251\) | 4.98974e45i | 1.27139i | 0.771942 | + | 0.635693i | \(0.219286\pi\) | ||||
−0.771942 | + | 0.635693i | \(0.780714\pi\) | |||||||
\(252\) | 3.71488e45 | + | 4.19854e45i | 0.877677 | + | 0.991947i | ||||
\(253\) | −2.99313e45 | −0.655898 | ||||||||
\(254\) | 5.30841e44 | + | 1.40104e45i | 0.107926 | + | 0.284846i | ||||
\(255\) | 4.61053e44i | 0.0869937i | ||||||||
\(256\) | −5.53965e45 | − | 1.38017e45i | −0.970338 | − | 0.241753i | ||||
\(257\) | 7.77277e45 | 1.26429 | 0.632145 | − | 0.774850i | \(-0.282175\pi\) | ||||
0.632145 | + | 0.774850i | \(0.282175\pi\) | |||||||
\(258\) | 2.82874e44 | − | 1.07178e44i | 0.0427384 | − | 0.0161932i | ||||
\(259\) | − | 1.41166e46i | − | 1.98169i | ||||||
\(260\) | 2.20255e45 | − | 1.94882e45i | 0.287364 | − | 0.254260i | ||||
\(261\) | −1.42830e45 | −0.173241 | ||||||||
\(262\) | 4.07395e45 | + | 1.07523e46i | 0.459506 | + | 1.21277i | ||||
\(263\) | 1.14587e46i | 1.20220i | 0.799175 | + | 0.601098i | \(0.205270\pi\) | ||||
−0.799175 | + | 0.601098i | \(0.794730\pi\) | |||||||
\(264\) | 5.00605e44 | − | 9.51644e44i | 0.0488676 | − | 0.0928967i | ||||
\(265\) | −1.72096e46 | −1.56350 | ||||||||
\(266\) | 1.98040e46 | − | 7.50355e45i | 1.67495 | − | 0.634623i | ||||
\(267\) | 7.68327e44i | 0.0605107i | ||||||||
\(268\) | −6.20921e45 | − | 7.01762e45i | −0.455486 | − | 0.514788i | ||||
\(269\) | −1.98031e46 | −1.35344 | −0.676722 | − | 0.736238i | \(-0.736600\pi\) | ||||
−0.676722 | + | 0.736238i | \(0.736600\pi\) | |||||||
\(270\) | −6.53089e44 | − | 1.72368e45i | −0.0415969 | − | 0.109786i | ||||
\(271\) | − | 2.30949e46i | − | 1.37120i | −0.727980 | − | 0.685598i | \(-0.759541\pi\) | ||
0.727980 | − | 0.685598i | \(-0.240459\pi\) | |||||||
\(272\) | −3.25485e45 | + | 2.65277e46i | −0.180186 | + | 1.46855i | ||||
\(273\) | 5.46662e44 | 0.0282247 | ||||||||
\(274\) | 1.17960e46 | − | 4.46939e45i | 0.568163 | − | 0.215272i | ||||
\(275\) | − | 2.54374e45i | − | 0.114328i | ||||||
\(276\) | 3.63098e44 | − | 3.21271e44i | 0.0152318 | − | 0.0134772i | ||||
\(277\) | 4.88443e45 | 0.191293 | 0.0956463 | − | 0.995415i | \(-0.469508\pi\) | ||||
0.0956463 | + | 0.995415i | \(0.469508\pi\) | |||||||
\(278\) | −2.53712e45 | − | 6.69618e45i | −0.0927877 | − | 0.244893i | ||||
\(279\) | 9.34913e45i | 0.319368i | ||||||||
\(280\) | −3.79761e46 | − | 1.99770e46i | −1.21201 | − | 0.637570i | ||||
\(281\) | 1.79224e45 | 0.0534535 | 0.0267268 | − | 0.999643i | \(-0.491492\pi\) | ||||
0.0267268 | + | 0.999643i | \(0.491492\pi\) | |||||||
\(282\) | 1.63554e45 | − | 6.19692e44i | 0.0455962 | − | 0.0172760i | ||||
\(283\) | 1.24037e46i | 0.323301i | 0.986848 | + | 0.161651i | \(0.0516818\pi\) | ||||
−0.986848 | + | 0.161651i | \(0.948318\pi\) | |||||||
\(284\) | −3.38604e45 | − | 3.82689e45i | −0.0825361 | − | 0.0932819i | ||||
\(285\) | −3.47593e45 | −0.0792535 | ||||||||
\(286\) | 1.13770e46 | + | 3.00271e46i | 0.242702 | + | 0.640559i | ||||
\(287\) | − | 7.12747e45i | − | 0.142292i | ||||||
\(288\) | −1.26835e46 | − | 5.18086e46i | −0.237017 | − | 0.968155i | ||||
\(289\) | 6.79649e46 | 1.18912 | ||||||||
\(290\) | 1.02233e46 | − | 3.87351e45i | 0.167505 | − | 0.0634662i | ||||
\(291\) | 6.74525e44i | 0.0103522i | ||||||||
\(292\) | −2.22929e46 | + | 1.97248e46i | −0.320547 | + | 0.283621i | ||||
\(293\) | 7.42285e46 | 1.00020 | 0.500099 | − | 0.865968i | \(-0.333297\pi\) | ||||
0.500099 | + | 0.865968i | \(0.333297\pi\) | |||||||
\(294\) | −1.22556e45 | − | 3.23459e45i | −0.0154787 | − | 0.0408527i | ||||
\(295\) | 1.04050e47i | 1.23203i | ||||||||
\(296\) | −6.25297e46 | + | 1.18868e47i | −0.694295 | + | 1.31985i | ||||
\(297\) | 2.01253e46 | 0.209590 | ||||||||
\(298\) | 9.48485e46 | − | 3.59372e46i | 0.926662 | − | 0.351104i | ||||
\(299\) | 1.44779e46i | 0.132725i | ||||||||
\(300\) | 2.73034e44 | + | 3.08582e44i | 0.00234916 | + | 0.00265501i | ||||
\(301\) | 1.31799e47 | 1.06451 | ||||||||
\(302\) | −2.19061e46 | − | 5.78164e46i | −0.166124 | − | 0.438449i | ||||
\(303\) | 1.33084e45i | 0.00947795i | ||||||||
\(304\) | −1.99995e47 | − | 2.45387e46i | −1.33789 | − | 0.164154i | ||||
\(305\) | −9.24611e46 | −0.581115 | ||||||||
\(306\) | −2.33505e47 | + | 8.84731e46i | −1.37908 | + | 0.522521i | ||||
\(307\) | 1.04591e47i | 0.580582i | 0.956938 | + | 0.290291i | \(0.0937521\pi\) | ||||
−0.956938 | + | 0.290291i | \(0.906248\pi\) | |||||||
\(308\) | 3.50876e47 | − | 3.10456e47i | 1.83101 | − | 1.62008i | ||||
\(309\) | −1.77701e46 | −0.0871924 | ||||||||
\(310\) | −2.53545e46 | − | 6.69177e46i | −0.116999 | − | 0.308794i | ||||
\(311\) | − | 3.96335e47i | − | 1.72034i | −0.510006 | − | 0.860171i | \(-0.670357\pi\) | ||
0.510006 | − | 0.860171i | \(-0.329643\pi\) | |||||||
\(312\) | −4.60313e45 | − | 2.42144e45i | −0.0187982 | − | 0.00988865i | ||||
\(313\) | −4.94711e47 | −1.90112 | −0.950559 | − | 0.310544i | \(-0.899489\pi\) | ||||
−0.950559 | + | 0.310544i | \(0.899489\pi\) | |||||||
\(314\) | −1.62277e47 | + | 6.14855e46i | −0.586942 | + | 0.222387i | ||||
\(315\) | − | 4.00904e47i | − | 1.36502i | ||||||
\(316\) | 2.23889e47 | + | 2.53039e47i | 0.717760 | + | 0.811209i | ||||
\(317\) | −1.49550e47 | −0.451503 | −0.225751 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225751 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(318\) | 1.07837e46 | + | 2.84613e46i | 0.0306658 | + | 0.0809357i | ||||
\(319\) | 1.19365e47i | 0.319781i | ||||||||
\(320\) | 2.31287e47 | + | 3.36430e47i | 0.583850 | + | 0.849269i | ||||
\(321\) | 1.35635e46 | 0.0322683 | ||||||||
\(322\) | 1.97537e47 | − | 7.48448e46i | 0.442982 | − | 0.167842i | ||||
\(323\) | 9.43297e47i | 1.99435i | ||||||||
\(324\) | 3.71996e47 | − | 3.29143e47i | 0.741622 | − | 0.656189i | ||||
\(325\) | −1.23041e46 | −0.0231349 | ||||||||
\(326\) | 6.16226e46 | + | 1.62639e47i | 0.109296 | + | 0.288464i | ||||
\(327\) | − | 2.32097e46i | − | 0.0388385i | ||||||
\(328\) | −3.15712e46 | + | 6.00164e46i | −0.0498526 | + | 0.0947692i | ||||
\(329\) | 7.62048e47 | 1.13569 | ||||||||
\(330\) | −7.19075e46 | + | 2.72451e46i | −0.101160 | + | 0.0383287i | ||||
\(331\) | − | 1.19326e48i | − | 1.58491i | −0.609931 | − | 0.792454i | \(-0.708803\pi\) | ||
0.609931 | − | 0.792454i | \(-0.291197\pi\) | |||||||
\(332\) | 6.39439e47 | + | 7.22691e47i | 0.802002 | + | 0.906419i | ||||
\(333\) | −1.25486e48 | −1.48647 | ||||||||
\(334\) | 1.43614e47 | + | 3.79038e47i | 0.160699 | + | 0.424131i | ||||
\(335\) | 6.70087e47i | 0.708402i | ||||||||
\(336\) | −9.24187e45 | + | 7.53231e46i | −0.00923238 | + | 0.0752458i | ||||
\(337\) | 1.78825e47 | 0.168834 | 0.0844170 | − | 0.996431i | \(-0.473097\pi\) | ||||
0.0844170 | + | 0.996431i | \(0.473097\pi\) | |||||||
\(338\) | −9.02581e47 | + | 3.41980e47i | −0.805507 | + | 0.305199i | ||||
\(339\) | − | 6.23933e46i | − | 0.0526434i | ||||||
\(340\) | 1.43141e48 | − | 1.26652e48i | 1.14200 | − | 1.01044i | ||||
\(341\) | 7.81315e47 | 0.589513 | ||||||||
\(342\) | −6.67008e47 | − | 1.76042e48i | −0.476031 | − | 1.25638i | ||||
\(343\) | 4.61032e47i | 0.311274i | ||||||||
\(344\) | −1.10981e48 | − | 5.83806e47i | −0.708986 | − | 0.372957i | ||||
\(345\) | −3.46710e46 | −0.0209606 | ||||||||
\(346\) | −1.95770e48 | + | 7.41757e47i | −1.12021 | + | 0.424439i | ||||
\(347\) | − | 5.47196e47i | − | 0.296403i | −0.988957 | − | 0.148202i | \(-0.952652\pi\) | ||
0.988957 | − | 0.148202i | \(-0.0473485\pi\) | |||||||
\(348\) | −1.28121e46 | − | 1.44802e46i | −0.00657074 | − | 0.00742622i | ||||
\(349\) | −6.65771e46 | −0.0323327 | −0.0161664 | − | 0.999869i | \(-0.505146\pi\) | ||||
−0.0161664 | + | 0.999869i | \(0.505146\pi\) | |||||||
\(350\) | 6.36075e46 | + | 1.67878e47i | 0.0292560 | + | 0.0772149i | ||||
\(351\) | − | 9.73469e46i | − | 0.0424118i | ||||||
\(352\) | −4.32969e48 | + | 1.05997e48i | −1.78709 | + | 0.437504i | ||||
\(353\) | 4.18240e48 | 1.63571 | 0.817854 | − | 0.575426i | \(-0.195164\pi\) | ||||
0.817854 | + | 0.575426i | \(0.195164\pi\) | |||||||
\(354\) | 1.72079e47 | − | 6.51990e46i | 0.0637771 | − | 0.0241646i | ||||
\(355\) | 3.65416e47i | 0.128366i | ||||||||
\(356\) | 2.38539e48 | − | 2.11060e48i | 0.794346 | − | 0.702839i | ||||
\(357\) | 3.55269e47 | 0.112166 | ||||||||
\(358\) | −6.43228e47 | − | 1.69766e48i | −0.192569 | − | 0.508245i | ||||
\(359\) | 3.19911e48i | 0.908312i | 0.890922 | + | 0.454156i | \(0.150059\pi\) | ||||
−0.890922 | + | 0.454156i | \(0.849941\pi\) | |||||||
\(360\) | −1.77580e48 | + | 3.37578e48i | −0.478242 | + | 0.909132i | ||||
\(361\) | −3.19748e48 | −0.816903 | ||||||||
\(362\) | 2.70276e48 | − | 1.02405e48i | 0.655155 | − | 0.248232i | ||||
\(363\) | − | 5.91555e47i | − | 0.136072i | ||||||
\(364\) | −1.50169e48 | − | 1.69720e48i | −0.327833 | − | 0.370515i | ||||
\(365\) | 2.12866e48 | 0.441106 | ||||||||
\(366\) | 5.79375e46 | + | 1.52913e47i | 0.0113977 | + | 0.0300819i | ||||
\(367\) | − | 9.43287e48i | − | 1.76193i | −0.473181 | − | 0.880965i | \(-0.656895\pi\) | ||
0.473181 | − | 0.880965i | \(-0.343105\pi\) | |||||||
\(368\) | −1.99487e48 | − | 2.44763e47i | −0.353839 | − | 0.0434147i | ||||
\(369\) | −6.33578e47 | −0.106733 | ||||||||
\(370\) | 8.98185e48 | − | 3.40314e48i | 1.43725 | − | 0.544562i | ||||
\(371\) | 1.32610e49i | 2.01591i | ||||||||
\(372\) | −9.47817e46 | + | 8.38631e46i | −0.0136902 | + | 0.0121131i | ||||
\(373\) | 2.35364e48 | 0.323051 | 0.161526 | − | 0.986869i | \(-0.448359\pi\) | ||||
0.161526 | + | 0.986869i | \(0.448359\pi\) | |||||||
\(374\) | 7.39378e48 | + | 1.95143e49i | 0.964508 | + | 2.54561i | ||||
\(375\) | 4.44719e47i | 0.0551431i | ||||||||
\(376\) | −6.41677e48 | − | 3.37549e48i | −0.756393 | − | 0.397895i | ||||
\(377\) | 5.77370e47 | 0.0647096 | ||||||||
\(378\) | −1.32820e48 | + | 5.03244e47i | −0.141553 | + | 0.0536333i | ||||
\(379\) | − | 1.20823e48i | − | 0.122463i | −0.998124 | − | 0.0612316i | \(-0.980497\pi\) | ||
0.998124 | − | 0.0612316i | \(-0.0195028\pi\) | |||||||
\(380\) | 9.54840e48 | + | 1.07916e49i | 0.920540 | + | 1.04039i | ||||
\(381\) | −1.89485e47 | −0.0173781 | ||||||||
\(382\) | −5.81028e48 | − | 1.53350e49i | −0.506983 | − | 1.33807i | ||||
\(383\) | − | 1.05467e49i | − | 0.875667i | −0.899056 | − | 0.437833i | \(-0.855746\pi\) | ||
0.899056 | − | 0.437833i | \(-0.144254\pi\) | |||||||
\(384\) | 4.11465e47 | − | 5.93317e47i | 0.0325117 | − | 0.0468806i | ||||
\(385\) | −3.35039e49 | −2.51966 | ||||||||
\(386\) | 2.10567e49 | − | 7.97818e48i | 1.50741 | − | 0.571143i | ||||
\(387\) | − | 1.17160e49i | − | 0.798490i | ||||||
\(388\) | 2.09417e48 | − | 1.85292e48i | 0.135897 | − | 0.120242i | ||||
\(389\) | −1.29236e49 | −0.798622 | −0.399311 | − | 0.916815i | \(-0.630751\pi\) | ||||
−0.399311 | + | 0.916815i | \(0.630751\pi\) | |||||||
\(390\) | 1.31785e47 | + | 3.47819e47i | 0.00775604 | + | 0.0204704i | ||||
\(391\) | 9.40900e48i | 0.527455i | ||||||||
\(392\) | −6.67568e48 | + | 1.26904e49i | −0.356500 | + | 0.677703i | ||||
\(393\) | −1.45421e48 | −0.0739892 | ||||||||
\(394\) | −1.07215e49 | + | 4.06227e48i | −0.519789 | + | 0.196943i | ||||
\(395\) | − | 2.41618e49i | − | 1.11631i | ||||||
\(396\) | −2.75972e49 | − | 3.11902e49i | −1.21522 | − | 1.37344i | ||||
\(397\) | 1.72773e49 | 0.725197 | 0.362598 | − | 0.931945i | \(-0.381890\pi\) | ||||
0.362598 | + | 0.931945i | \(0.381890\pi\) | |||||||
\(398\) | 6.60285e48 | + | 1.74268e49i | 0.264212 | + | 0.697331i | ||||
\(399\) | 2.67841e48i | 0.102186i | ||||||||
\(400\) | 2.08014e47 | − | 1.69535e48i | 0.00756750 | − | 0.0616766i | ||||
\(401\) | 3.76027e49 | 1.30460 | 0.652299 | − | 0.757962i | \(-0.273805\pi\) | ||||
0.652299 | + | 0.757962i | \(0.273805\pi\) | |||||||
\(402\) | 1.10820e48 | − | 4.19886e47i | 0.0366709 | − | 0.0138943i | ||||
\(403\) | − | 3.77925e48i | − | 0.119291i | ||||||
\(404\) | 4.13178e48 | − | 3.65581e48i | 0.124420 | − | 0.110088i | ||||
\(405\) | −3.55205e49 | −1.02055 | ||||||||
\(406\) | −2.98477e48 | − | 7.87765e48i | −0.0818307 | − | 0.215974i | ||||
\(407\) | 1.04870e50i | 2.74383i | ||||||||
\(408\) | −2.99152e48 | − | 1.57367e48i | −0.0747049 | − | 0.0392979i | ||||
\(409\) | 5.19798e49 | 1.23906 | 0.619530 | − | 0.784973i | \(-0.287323\pi\) | ||||
0.619530 | + | 0.784973i | \(0.287323\pi\) | |||||||
\(410\) | 4.53492e48 | − | 1.71824e48i | 0.103199 | − | 0.0391013i | ||||
\(411\) | 1.59536e48i | 0.0346628i | ||||||||
\(412\) | 4.88146e49 | + | 5.51700e49i | 1.01275 | + | 1.14461i | ||||
\(413\) | 8.01765e49 | 1.58853 | ||||||||
\(414\) | −6.65313e48 | − | 1.75595e49i | −0.125898 | − | 0.332281i | ||||
\(415\) | − | 6.90071e49i | − | 1.24733i | ||||||
\(416\) | 5.12710e48 | + | 2.09429e49i | 0.0885316 | + | 0.361629i | ||||
\(417\) | 9.05633e47 | 0.0149406 | ||||||||
\(418\) | −1.47120e50 | + | 5.57425e49i | −2.31912 | + | 0.878692i | ||||
\(419\) | 5.41652e49i | 0.815932i | 0.912997 | + | 0.407966i | \(0.133762\pi\) | ||||
−0.912997 | + | 0.407966i | \(0.866238\pi\) | |||||||
\(420\) | 4.06437e48 | − | 3.59617e48i | 0.0585136 | − | 0.0517730i | ||||
\(421\) | −1.23888e49 | −0.170479 | −0.0852395 | − | 0.996360i | \(-0.527166\pi\) | ||||
−0.0852395 | + | 0.996360i | \(0.527166\pi\) | |||||||
\(422\) | −4.42570e49 | − | 1.16807e50i | −0.582164 | − | 1.53649i | ||||
\(423\) | − | 6.77402e49i | − | 0.851882i | ||||||
\(424\) | 5.87396e49 | − | 1.11663e50i | 0.706285 | − | 1.34264i | ||||
\(425\) | −7.99632e48 | −0.0919391 | ||||||||
\(426\) | 6.04329e47 | − | 2.28975e47i | 0.00664494 | − | 0.00251771i | ||||
\(427\) | 7.12469e49i | 0.749266i | ||||||||
\(428\) | −3.72590e49 | − | 4.21100e49i | −0.374800 | − | 0.423598i | ||||
\(429\) | −4.06105e48 | −0.0390796 | ||||||||
\(430\) | 3.17733e49 | + | 8.38586e49i | 0.292524 | + | 0.772053i | ||||
\(431\) | − | 8.98078e49i | − | 0.791127i | −0.918439 | − | 0.395563i | \(-0.870549\pi\) | ||
0.918439 | − | 0.395563i | \(-0.129451\pi\) | |||||||
\(432\) | 1.34132e49 | + | 1.64575e48i | 0.113068 | + | 0.0138730i | ||||
\(433\) | −7.55037e49 | −0.609113 | −0.304557 | − | 0.952494i | \(-0.598508\pi\) | ||||
−0.304557 | + | 0.952494i | \(0.598508\pi\) | |||||||
\(434\) | −5.15641e49 | + | 1.95372e49i | −0.398146 | + | 0.150854i | ||||
\(435\) | 1.38266e48i | 0.0102193i | ||||||||
\(436\) | −7.20581e49 | + | 6.37572e49i | −0.509847 | + | 0.451114i | ||||
\(437\) | −7.09355e49 | −0.480525 | ||||||||
\(438\) | −1.33385e48 | − | 3.52041e48i | −0.00865166 | − | 0.0228342i | ||||
\(439\) | 3.61707e49i | 0.224663i | 0.993671 | + | 0.112331i | \(0.0358318\pi\) | ||||
−0.993671 | + | 0.112331i | \(0.964168\pi\) | |||||||
\(440\) | 2.82117e50 | + | 1.48406e50i | 1.67814 | + | 0.882773i | ||||
\(441\) | −1.33969e50 | −0.763258 | ||||||||
\(442\) | 9.43911e49 | − | 3.57639e49i | 0.515119 | − | 0.195174i | ||||
\(443\) | − | 1.91270e50i | − | 0.999945i | −0.866041 | − | 0.499972i | \(-0.833343\pi\) | ||
0.866041 | − | 0.499972i | \(-0.166657\pi\) | |||||||
\(444\) | −1.12563e49 | − | 1.27218e49i | −0.0563793 | − | 0.0637196i | ||||
\(445\) | −2.27772e50 | −1.09310 | ||||||||
\(446\) | 1.62924e49 | + | 4.30002e49i | 0.0749243 | + | 0.197746i | ||||
\(447\) | 1.28279e49i | 0.0565344i | ||||||||
\(448\) | 2.59240e50 | − | 1.78220e50i | 1.09501 | − | 0.752792i | ||||
\(449\) | 2.29714e50 | 0.930050 | 0.465025 | − | 0.885297i | \(-0.346045\pi\) | ||||
0.465025 | + | 0.885297i | \(0.346045\pi\) | |||||||
\(450\) | 1.49231e49 | − | 5.65422e48i | 0.0579189 | − | 0.0219450i | ||||
\(451\) | 5.29487e49i | 0.197016i | ||||||||
\(452\) | −1.93710e50 | + | 1.71395e50i | −0.691069 | + | 0.611459i | ||||
\(453\) | 7.81945e48 | 0.0267492 | ||||||||
\(454\) | 2.31165e49 | + | 6.10109e49i | 0.0758334 | + | 0.200146i | ||||
\(455\) | 1.62059e50i | 0.509868i | ||||||||
\(456\) | 1.18640e49 | − | 2.25534e49i | 0.0358015 | − | 0.0680581i | ||||
\(457\) | −5.45645e49 | −0.157944 | −0.0789718 | − | 0.996877i | \(-0.525164\pi\) | ||||
−0.0789718 | + | 0.996877i | \(0.525164\pi\) | |||||||
\(458\) | 8.82369e49 | − | 3.34322e49i | 0.245023 | − | 0.0928369i | ||||
\(459\) | − | 6.32646e49i | − | 0.168546i | ||||||
\(460\) | 9.52414e49 | + | 1.07641e50i | 0.243460 | + | 0.275157i | ||||
\(461\) | 8.67754e49 | 0.212853 | 0.106426 | − | 0.994321i | \(-0.466059\pi\) | ||||
0.106426 | + | 0.994321i | \(0.466059\pi\) | |||||||
\(462\) | 2.09940e49 | + | 5.54091e49i | 0.0494194 | + | 0.130432i | ||||
\(463\) | 5.84414e49i | 0.132033i | 0.997819 | + | 0.0660164i | \(0.0210290\pi\) | ||||
−0.997819 | + | 0.0660164i | \(0.978971\pi\) | |||||||
\(464\) | −9.76102e48 | + | 7.95543e49i | −0.0211667 | + | 0.172513i | ||||
\(465\) | 9.05037e48 | 0.0188391 | ||||||||
\(466\) | 2.48039e50 | − | 9.39798e49i | 0.495665 | − | 0.187803i | ||||
\(467\) | − | 3.77723e48i | − | 0.00724691i | −0.999993 | − | 0.00362345i | \(-0.998847\pi\) | ||
0.999993 | − | 0.00362345i | \(-0.00115338\pi\) | |||||||
\(468\) | −1.50868e50 | + | 1.33488e50i | −0.277924 | + | 0.245908i | ||||
\(469\) | 5.16342e50 | 0.913385 | ||||||||
\(470\) | 1.83709e50 | + | 4.84860e50i | 0.312084 | + | 0.823677i | ||||
\(471\) | − | 2.19474e49i | − | 0.0358085i | ||||||
\(472\) | −6.75121e50 | − | 3.55142e50i | −1.05800 | − | 0.556550i | ||||
\(473\) | −9.79114e50 | −1.47391 | ||||||||
\(474\) | −3.99590e49 | + | 1.51401e49i | −0.0577865 | + | 0.0218948i | ||||
\(475\) | − | 6.02851e49i | − | 0.0837590i | ||||||
\(476\) | −9.75927e50 | − | 1.10299e51i | −1.30282 | − | 1.47244i | ||||
\(477\) | 1.17880e51 | 1.51214 | ||||||||
\(478\) | −5.01247e50 | − | 1.32293e51i | −0.617905 | − | 1.63083i | ||||
\(479\) | 7.21096e50i | 0.854316i | 0.904177 | + | 0.427158i | \(0.140485\pi\) | ||||
−0.904177 | + | 0.427158i | \(0.859515\pi\) | |||||||
\(480\) | −5.01530e49 | + | 1.22781e49i | −0.0571102 | + | 0.0139813i | ||||
\(481\) | 5.07259e50 | 0.555231 | ||||||||
\(482\) | 2.71300e50 | − | 1.02793e50i | 0.285467 | − | 0.108161i | ||||
\(483\) | 2.67161e49i | 0.0270257i | ||||||||
\(484\) | −1.83657e51 | + | 1.62501e51i | −1.78627 | + | 1.58049i | ||||
\(485\) | −1.99964e50 | −0.187008 | ||||||||
\(486\) | 6.71383e49 | + | 1.77197e50i | 0.0603783 | + | 0.159355i | ||||
\(487\) | − | 2.11552e51i | − | 1.82965i | −0.403852 | − | 0.914824i | \(-0.632329\pi\) | ||
0.403852 | − | 0.914824i | \(-0.367671\pi\) | |||||||
\(488\) | 3.15588e50 | − | 5.99930e50i | 0.262509 | − | 0.499027i | ||||
\(489\) | −2.19964e49 | −0.0175988 | ||||||||
\(490\) | 9.58902e50 | − | 3.63319e50i | 0.737987 | − | 0.279617i | ||||
\(491\) | − | 4.41488e50i | − | 0.326867i | −0.986554 | − | 0.163433i | \(-0.947743\pi\) | ||
0.986554 | − | 0.163433i | \(-0.0522569\pi\) | |||||||
\(492\) | −5.68329e48 | − | 6.42323e48i | −0.00404821 | − | 0.00457527i | ||||
\(493\) | 3.75226e50 | 0.257159 | ||||||||
\(494\) | 2.69628e50 | + | 7.11624e50i | 0.177809 | + | 0.469287i | ||||
\(495\) | 2.97824e51i | 1.89000i | ||||||||
\(496\) | 5.20732e50 | + | 6.38919e49i | 0.318026 | + | 0.0390206i | ||||
\(497\) | 2.81575e50 | 0.165509 | ||||||||
\(498\) | −1.14125e50 | + | 4.32408e49i | −0.0645688 | + | 0.0244645i | ||||
\(499\) | 2.54282e51i | 1.38486i | 0.721486 | + | 0.692429i | \(0.243460\pi\) | ||||
−0.721486 | + | 0.692429i | \(0.756540\pi\) | |||||||
\(500\) | 1.38070e51 | − | 1.22165e51i | 0.723883 | − | 0.640494i | ||||
\(501\) | −5.12634e49 | −0.0258756 | ||||||||
\(502\) | 9.26901e50 | + | 2.44635e51i | 0.450467 | + | 1.18891i | ||||
\(503\) | − | 1.68910e51i | − | 0.790430i | −0.918589 | − | 0.395215i | \(-0.870670\pi\) | ||
0.918589 | − | 0.395215i | \(-0.129330\pi\) | |||||||
\(504\) | 2.60124e51 | + | 1.36836e51i | 1.17220 | + | 0.616626i | ||||
\(505\) | −3.94529e50 | −0.171215 | ||||||||
\(506\) | −1.46746e51 | + | 5.56008e50i | −0.613348 | + | 0.232392i | ||||
\(507\) | − | 1.22071e50i | − | 0.0491429i | ||||||
\(508\) | 5.20518e50 | + | 5.88287e50i | 0.201848 | + | 0.228128i | ||||
\(509\) | −7.42254e50 | −0.277278 | −0.138639 | − | 0.990343i | \(-0.544273\pi\) | ||||
−0.138639 | + | 0.990343i | \(0.544273\pi\) | |||||||
\(510\) | 8.56458e49 | + | 2.26043e50i | 0.0308228 | + | 0.0813502i | ||||
\(511\) | − | 1.64026e51i | − | 0.568744i | ||||||
\(512\) | −2.97234e51 | + | 3.52389e50i | −0.993045 | + | 0.117732i | ||||
\(513\) | 4.76958e50 | 0.153550 | ||||||||
\(514\) | 3.81080e51 | − | 1.44388e51i | 1.18227 | − | 0.447952i | ||||
\(515\) | − | 5.26798e51i | − | 1.57510i | ||||||
\(516\) | 1.18777e50 | − | 1.05094e50i | 0.0342284 | − | 0.0302854i | ||||
\(517\) | −5.66111e51 | −1.57247 | ||||||||
\(518\) | −2.62233e51 | − | 6.92106e51i | −0.702136 | − | 1.85313i | ||||
\(519\) | − | 2.64772e50i | − | 0.0683428i | ||||||
\(520\) | 7.17842e50 | − | 1.36461e51i | 0.178635 | − | 0.339582i | ||||
\(521\) | −6.51392e51 | −1.56288 | −0.781440 | − | 0.623981i | \(-0.785514\pi\) | ||||
−0.781440 | + | 0.623981i | \(0.785514\pi\) | |||||||
\(522\) | −7.00263e50 | + | 2.65323e50i | −0.162002 | + | 0.0613812i | ||||
\(523\) | 5.37549e51i | 1.19918i | 0.800306 | + | 0.599592i | \(0.204671\pi\) | ||||
−0.800306 | + | 0.599592i | \(0.795329\pi\) | |||||||
\(524\) | 3.99472e51 | + | 4.51482e51i | 0.859394 | + | 0.971283i | ||||
\(525\) | −2.27049e49 | −0.00471077 | ||||||||
\(526\) | 2.12858e51 | + | 5.61792e51i | 0.425952 | + | 1.12421i | ||||
\(527\) | − | 2.45609e51i | − | 0.474069i | ||||||
\(528\) | 6.86562e49 | − | 5.59562e50i | 0.0127831 | − | 0.104185i | ||||
\(529\) | 4.85992e51 | 0.872913 | ||||||||
\(530\) | −8.43743e51 | + | 3.19687e51i | −1.46207 | + | 0.553966i | ||||
\(531\) | − | 7.12708e51i | − | 1.19156i | ||||||
\(532\) | 8.31555e51 | − | 7.35762e51i | 1.34144 | − | 1.18691i | ||||
\(533\) | 2.56114e50 | 0.0398673 | ||||||||
\(534\) | 1.42725e50 | + | 3.76692e50i | 0.0214396 | + | 0.0565852i | ||||
\(535\) | 4.02093e51i | 0.582914i | ||||||||
\(536\) | −4.34783e51 | − | 2.28714e51i | −0.608333 | − | 0.320009i | ||||
\(537\) | 2.29602e50 | 0.0310073 | ||||||||
\(538\) | −9.70900e51 | + | 3.67865e51i | −1.26564 | + | 0.479541i | ||||
\(539\) | 1.11959e52i | 1.40888i | ||||||||
\(540\) | −6.40387e50 | − | 7.23763e50i | −0.0777967 | − | 0.0879255i | ||||
\(541\) | 1.53182e52 | 1.79664 | 0.898319 | − | 0.439343i | \(-0.144789\pi\) | ||||
0.898319 | + | 0.439343i | \(0.144789\pi\) | |||||||
\(542\) | −4.29014e51 | − | 1.13229e52i | −0.485830 | − | 1.28224i | ||||
\(543\) | 3.65538e50i | 0.0399701i | ||||||||
\(544\) | 3.33204e51 | + | 1.36105e52i | 0.351829 | + | 1.43713i | ||||
\(545\) | 6.88057e51 | 0.701602 | ||||||||
\(546\) | 2.68016e50 | − | 1.01549e50i | 0.0263937 | − | 0.0100003i | ||||
\(547\) | 9.03610e50i | 0.0859452i | 0.999076 | + | 0.0429726i | \(0.0136828\pi\) | ||||
−0.999076 | + | 0.0429726i | \(0.986317\pi\) | |||||||
\(548\) | 4.95304e51 | − | 4.38247e51i | 0.455032 | − | 0.402613i | ||||
\(549\) | 6.33330e51 | 0.562025 | ||||||||
\(550\) | −4.72528e50 | − | 1.24713e51i | −0.0405076 | − | 0.106911i | ||||
\(551\) | 2.82887e51i | 0.234278i | ||||||||
\(552\) | 1.18339e50 | − | 2.24961e50i | 0.00946859 | − | 0.0179997i | ||||
\(553\) | −1.86181e52 | −1.43932 | ||||||||
\(554\) | 2.39472e51 | − | 9.07338e50i | 0.178883 | − | 0.0677772i | ||||
\(555\) | 1.21476e51i | 0.0876848i | ||||||||
\(556\) | −2.48778e51 | − | 2.81168e51i | −0.173537 | − | 0.196130i | ||||
\(557\) | 1.86424e52 | 1.25676 | 0.628381 | − | 0.777906i | \(-0.283718\pi\) | ||||
0.628381 | + | 0.777906i | \(0.283718\pi\) | |||||||
\(558\) | 1.73671e51 | + | 4.58366e51i | 0.113156 | + | 0.298650i | ||||
\(559\) | 4.73600e51i | 0.298255i | ||||||||
\(560\) | −2.23297e52 | − | 2.73977e51i | −1.35929 | − | 0.166779i | ||||
\(561\) | −2.63923e51 | −0.155304 | ||||||||
\(562\) | 8.78693e50 | − | 3.32929e50i | 0.0499858 | − | 0.0189392i | ||||
\(563\) | − | 3.00821e52i | − | 1.65443i | −0.561886 | − | 0.827214i | \(-0.689924\pi\) | ||
0.561886 | − | 0.827214i | \(-0.310076\pi\) | |||||||
\(564\) | 6.86752e50 | − | 6.07640e50i | 0.0365172 | − | 0.0323105i | ||||
\(565\) | 1.84966e52 | 0.950982 | ||||||||
\(566\) | 2.30412e51 | + | 6.08122e51i | 0.114549 | + | 0.302328i | ||||
\(567\) | 2.73707e52i | 1.31585i | ||||||||
\(568\) | −2.37098e51 | − | 1.24724e51i | −0.110233 | − | 0.0579870i | ||||
\(569\) | −2.41460e52 | −1.08571 | −0.542854 | − | 0.839827i | \(-0.682656\pi\) | ||||
−0.542854 | + | 0.839827i | \(0.682656\pi\) | |||||||
\(570\) | −1.70417e51 | + | 6.45693e50i | −0.0741122 | + | 0.0280804i | ||||
\(571\) | − | 8.82025e50i | − | 0.0371018i | −0.999828 | − | 0.0185509i | \(-0.994095\pi\) | ||
0.999828 | − | 0.0185509i | \(-0.00590527\pi\) | |||||||
\(572\) | 1.11557e52 | + | 1.26082e52i | 0.453914 | + | 0.513012i | ||||
\(573\) | 2.07400e51 | 0.0816338 | ||||||||
\(574\) | −1.32401e51 | − | 3.49443e51i | −0.0504156 | − | 0.133061i | ||||
\(575\) | − | 6.01319e50i | − | 0.0221521i | ||||||
\(576\) | −1.58424e52 | − | 2.30444e52i | −0.564670 | − | 0.821370i | ||||
\(577\) | −4.57479e52 | −1.57772 | −0.788862 | − | 0.614571i | \(-0.789329\pi\) | ||||
−0.788862 | + | 0.614571i | \(0.789329\pi\) | |||||||
\(578\) | 3.33216e52 | − | 1.26252e52i | 1.11198 | − | 0.421319i | ||||
\(579\) | 2.84784e51i | 0.0919649i | ||||||||
\(580\) | 4.29268e51 | − | 3.79817e51i | 0.134152 | − | 0.118698i | ||||
\(581\) | −5.31742e52 | −1.60825 | ||||||||
\(582\) | 1.25301e50 | + | 3.30703e50i | 0.00366789 | + | 0.00968059i | ||||
\(583\) | − | 9.85135e52i | − | 2.79121i | ||||||
\(584\) | −7.26556e51 | + | 1.38117e52i | −0.199262 | + | 0.378795i | ||||
\(585\) | 1.44058e52 | 0.382452 | ||||||||
\(586\) | 3.63924e52 | − | 1.37888e52i | 0.935312 | − | 0.354381i | ||||
\(587\) | 9.15612e51i | 0.227818i | 0.993491 | + | 0.113909i | \(0.0363372\pi\) | ||||
−0.993491 | + | 0.113909i | \(0.963663\pi\) | |||||||
\(588\) | −1.20172e51 | − | 1.35818e51i | −0.0289491 | − | 0.0327182i | ||||
\(589\) | 1.85167e52 | 0.431890 | ||||||||
\(590\) | 1.93284e52 | + | 5.10131e52i | 0.436523 | + | 1.15211i | ||||
\(591\) | − | 1.45004e51i | − | 0.0317116i | ||||||
\(592\) | −8.57572e51 | + | 6.98939e52i | −0.181618 | + | 1.48022i | ||||
\(593\) | 7.62371e51 | 0.156361 | 0.0781803 | − | 0.996939i | \(-0.475089\pi\) | ||||
0.0781803 | + | 0.996939i | \(0.475089\pi\) | |||||||
\(594\) | 9.86697e51 | − | 3.73851e51i | 0.195993 | − | 0.0742601i | ||||
\(595\) | 1.05320e53i | 2.02624i | ||||||||
\(596\) | 3.98262e52 | − | 3.52383e52i | 0.742147 | − | 0.656654i | ||||
\(597\) | −2.35691e51 | −0.0425432 | ||||||||
\(598\) | 2.68943e51 | + | 7.09816e51i | 0.0470259 | + | 0.124115i | ||||
\(599\) | 7.08756e52i | 1.20057i | 0.799787 | + | 0.600284i | \(0.204946\pi\) | ||||
−0.799787 | + | 0.600284i | \(0.795054\pi\) | |||||||
\(600\) | 1.91185e50 | + | 1.00571e50i | 0.00313747 | + | 0.00165044i | ||||
\(601\) | −4.74698e52 | −0.754749 | −0.377375 | − | 0.926061i | \(-0.623173\pi\) | ||||
−0.377375 | + | 0.926061i | \(0.623173\pi\) | |||||||
\(602\) | 6.46181e52 | − | 2.44832e52i | 0.995454 | − | 0.377168i | ||||
\(603\) | − | 4.58989e52i | − | 0.685130i | ||||||
\(604\) | −2.14801e52 | − | 2.42767e52i | −0.310695 | − | 0.351146i | ||||
\(605\) | 1.75368e53 | 2.45809 | ||||||||
\(606\) | 2.47218e50 | + | 6.52477e50i | 0.00335814 | + | 0.00886309i | ||||
\(607\) | − | 6.14799e52i | − | 0.809372i | −0.914456 | − | 0.404686i | \(-0.867381\pi\) | ||
0.914456 | − | 0.404686i | \(-0.132619\pi\) | |||||||
\(608\) | −1.02611e53 | + | 2.51206e52i | −1.30926 | + | 0.320525i | ||||
\(609\) | 1.06542e51 | 0.0131763 | ||||||||
\(610\) | −4.53315e52 | + | 1.71757e52i | −0.543417 | + | 0.205896i | ||||
\(611\) | 2.73830e52i | 0.318198i | ||||||||
\(612\) | −9.80473e52 | + | 8.67525e52i | −1.10448 | + | 0.977248i | ||||
\(613\) | −6.77869e52 | −0.740282 | −0.370141 | − | 0.928976i | \(-0.620691\pi\) | ||||
−0.370141 | + | 0.928976i | \(0.620691\pi\) | |||||||
\(614\) | 1.94289e52 | + | 5.12783e52i | 0.205707 | + | 0.542918i | ||||
\(615\) | 6.13331e50i | 0.00629604i | ||||||||
\(616\) | 1.14355e53 | − | 2.17388e53i | 1.13821 | − | 2.16373i | ||||
\(617\) | −4.25379e51 | −0.0410542 | −0.0205271 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205271 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(618\) | −8.71225e51 | + | 3.30099e51i | −0.0815360 | + | 0.0308932i | ||||
\(619\) | − | 1.72464e53i | − | 1.56523i | −0.622508 | − | 0.782614i | \(-0.713886\pi\) | ||
0.622508 | − | 0.782614i | \(-0.286114\pi\) | |||||||
\(620\) | −2.48614e52 | − | 2.80983e52i | −0.218818 | − | 0.247308i | ||||
\(621\) | 4.75746e51 | 0.0406102 | ||||||||
\(622\) | −7.36236e52 | − | 1.94313e53i | −0.609537 | − | 1.60874i | ||||
\(623\) | 1.75512e53i | 1.40940i | ||||||||
\(624\) | −2.70662e51 | − | 3.32092e50i | −0.0210824 | − | 0.00258673i | ||||
\(625\) | −1.40062e53 | −1.05828 | ||||||||
\(626\) | −2.42545e53 | + | 9.18981e52i | −1.77779 | + | 0.673588i | ||||
\(627\) | − | 1.98974e52i | − | 0.141486i | ||||||
\(628\) | −6.81392e52 | + | 6.02897e52i | −0.470071 | + | 0.415920i | ||||
\(629\) | 3.29662e53 | 2.20651 | ||||||||
\(630\) | −7.44724e52 | − | 1.96554e53i | −0.483643 | − | 1.27647i | ||||
\(631\) | 8.27177e52i | 0.521244i | 0.965441 | + | 0.260622i | \(0.0839276\pi\) | ||||
−0.965441 | + | 0.260622i | \(0.916072\pi\) | |||||||
\(632\) | 1.56772e53 | + | 8.24689e52i | 0.958617 | + | 0.504273i | ||||
\(633\) | 1.57977e52 | 0.0937394 | ||||||||
\(634\) | −7.33208e52 | + | 2.77806e52i | −0.422213 | + | 0.159973i | ||||
\(635\) | − | 5.61734e52i | − | 0.313928i | ||||||
\(636\) | 1.05740e52 | + | 1.19507e52i | 0.0573529 | + | 0.0648200i | ||||
\(637\) | 5.41550e52 | 0.285095 | ||||||||
\(638\) | 2.21733e52 | + | 5.85216e52i | 0.113302 | + | 0.299036i | ||||
\(639\) | − | 2.50299e52i | − | 0.124149i | ||||||
\(640\) | 1.75890e53 | + | 1.21980e53i | 0.846880 | + | 0.587311i | ||||
\(641\) | 5.20892e52 | 0.243470 | 0.121735 | − | 0.992563i | \(-0.461154\pi\) | ||||
0.121735 | + | 0.992563i | \(0.461154\pi\) | |||||||
\(642\) | 6.64986e51 | − | 2.51957e51i | 0.0301750 | − | 0.0114330i | ||||
\(643\) | 1.70216e53i | 0.749880i | 0.927049 | + | 0.374940i | \(0.122337\pi\) | ||||
−0.927049 | + | 0.374940i | \(0.877663\pi\) | |||||||
\(644\) | 8.29442e52 | − | 7.33892e52i | 0.354776 | − | 0.313907i | ||||
\(645\) | −1.13416e52 | −0.0471019 | ||||||||
\(646\) | 1.75228e53 | + | 4.62476e53i | 0.706620 | + | 1.86497i | ||||
\(647\) | 2.79328e52i | 0.109379i | 0.998503 | + | 0.0546895i | \(0.0174169\pi\) | ||||
−0.998503 | + | 0.0546895i | \(0.982583\pi\) | |||||||
\(648\) | 1.21239e53 | − | 2.30473e53i | 0.461016 | − | 0.876386i | ||||
\(649\) | −5.95617e53 | −2.19947 | ||||||||
\(650\) | −6.03243e51 | + | 2.28563e51i | −0.0216341 | + | 0.00819696i | ||||
\(651\) | − | 6.97385e51i | − | 0.0242904i | ||||||
\(652\) | 6.04241e52 | + | 6.82911e52i | 0.204412 | + | 0.231025i | ||||
\(653\) | 2.06931e53 | 0.679947 | 0.339973 | − | 0.940435i | \(-0.389582\pi\) | ||||
0.339973 | + | 0.940435i | \(0.389582\pi\) | |||||||
\(654\) | −4.31146e51 | − | 1.13792e52i | −0.0137609 | − | 0.0363189i | ||||
\(655\) | − | 4.31104e53i | − | 1.33659i | ||||||
\(656\) | −4.32987e51 | + | 3.52893e52i | −0.0130407 | + | 0.106285i | ||||
\(657\) | −1.45807e53 | −0.426615 | ||||||||
\(658\) | 3.73614e53 | − | 1.41559e53i | 1.06202 | − | 0.402388i | ||||
\(659\) | 1.73819e53i | 0.480038i | 0.970768 | + | 0.240019i | \(0.0771536\pi\) | ||||
−0.970768 | + | 0.240019i | \(0.922846\pi\) | |||||||
\(660\) | −3.01935e52 | + | 2.67153e52i | −0.0810174 | + | 0.0716844i | ||||
\(661\) | 4.10114e53 | 1.06924 | 0.534622 | − | 0.845091i | \(-0.320454\pi\) | ||||
0.534622 | + | 0.845091i | \(0.320454\pi\) | |||||||
\(662\) | −2.21662e53 | − | 5.85028e53i | −0.561551 | − | 1.48209i | ||||
\(663\) | 1.27660e52i | 0.0314267i | ||||||||
\(664\) | 4.47749e53 | + | 2.35535e53i | 1.07113 | + | 0.563459i | ||||
\(665\) | −7.94022e53 | −1.84596 | ||||||||
\(666\) | −6.15229e53 | + | 2.33105e53i | −1.39004 | + | 0.526672i | ||||
\(667\) | 2.82168e52i | 0.0619608i | ||||||||
\(668\) | 1.40821e53 | + | 1.59155e53i | 0.300549 | + | 0.339679i | ||||
\(669\) | −5.81562e51 | −0.0120642 | ||||||||
\(670\) | 1.24476e53 | + | 3.28528e53i | 0.250995 | + | 0.662446i | ||||
\(671\) | − | 5.29280e53i | − | 1.03743i | ||||||
\(672\) | 9.46105e51 | + | 3.86459e52i | 0.0180270 | + | 0.0736355i | ||||
\(673\) | −5.18635e53 | −0.960673 | −0.480337 | − | 0.877084i | \(-0.659485\pi\) | ||||
−0.480337 | + | 0.877084i | \(0.659485\pi\) | |||||||
\(674\) | 8.76735e52 | − | 3.32187e52i | 0.157881 | − | 0.0598198i | ||||
\(675\) | 4.04317e51i | 0.00707865i | ||||||||
\(676\) | −3.78988e53 | + | 3.35329e53i | −0.645116 | + | 0.570800i | ||||
\(677\) | 5.47375e53 | 0.905942 | 0.452971 | − | 0.891525i | \(-0.350364\pi\) | ||||
0.452971 | + | 0.891525i | \(0.350364\pi\) | |||||||
\(678\) | −1.15903e52 | − | 3.05900e52i | −0.0186522 | − | 0.0492283i | ||||
\(679\) | 1.54085e53i | 0.241120i | ||||||||
\(680\) | 4.66517e53 | − | 8.86844e53i | 0.709902 | − | 1.34951i | ||||
\(681\) | −8.25149e51 | −0.0122106 | ||||||||
\(682\) | 3.83060e53 | − | 1.45138e53i | 0.551269 | − | 0.208871i | ||||
\(683\) | 5.49786e53i | 0.769485i | 0.923024 | + | 0.384743i | \(0.125710\pi\) | ||||
−0.923024 | + | 0.384743i | \(0.874290\pi\) | |||||||
\(684\) | −6.54036e53 | − | 7.39189e53i | −0.890299 | − | 1.00621i | ||||
\(685\) | −4.72948e53 | −0.626171 | ||||||||
\(686\) | 8.56419e52 | + | 2.26033e53i | 0.110288 | + | 0.291081i | ||||
\(687\) | 1.19337e52i | 0.0149485i | ||||||||
\(688\) | −6.52561e53 | − | 8.00669e52i | −0.795135 | − | 0.0975602i | ||||
\(689\) | −4.76513e53 | −0.564819 | ||||||||
\(690\) | −1.69983e52 | + | 6.44052e51i | −0.0196008 | + | 0.00742657i | ||||
\(691\) | − | 1.13297e54i | − | 1.27097i | −0.772113 | − | 0.635485i | \(-0.780800\pi\) | ||
0.772113 | − | 0.635485i | \(-0.219200\pi\) | |||||||
\(692\) | −8.22026e53 | + | 7.27331e53i | −0.897160 | + | 0.793810i | ||||
\(693\) | 2.29491e54 | 2.43688 | ||||||||
\(694\) | −1.01648e53 | − | 2.68277e53i | −0.105019 | − | 0.277175i | ||||
\(695\) | 2.68477e53i | 0.269896i | ||||||||
\(696\) | −8.97132e51 | − | 4.71929e51i | −0.00877568 | − | 0.00461638i | ||||
\(697\) | 1.66446e53 | 0.158434 | ||||||||
\(698\) | −3.26412e52 | + | 1.23674e52i | −0.0302352 | + | 0.0114558i | ||||
\(699\) | 3.35464e52i | 0.0302398i | ||||||||
\(700\) | 6.23704e52 | + | 7.04908e52i | 0.0547162 | + | 0.0618400i | ||||
\(701\) | 2.04413e54 | 1.74529 | 0.872643 | − | 0.488359i | \(-0.162404\pi\) | ||||
0.872643 | + | 0.488359i | \(0.162404\pi\) | |||||||
\(702\) | −1.80833e52 | − | 4.77269e52i | −0.0150270 | − | 0.0396605i | ||||
\(703\) | 2.48535e54i | 2.01019i | ||||||||
\(704\) | −1.92584e54 | + | 1.32397e54i | −1.51614 | + | 1.04231i | ||||
\(705\) | −6.55755e52 | −0.0502514 | ||||||||
\(706\) | 2.05053e54 | − | 7.76927e53i | 1.52960 | − | 0.579550i | ||||
\(707\) | 3.04008e53i | 0.220758i | ||||||||
\(708\) | 7.22545e52 | − | 6.39310e52i | 0.0510779 | − | 0.0451939i | ||||
\(709\) | −7.38765e52 | −0.0508426 | −0.0254213 | − | 0.999677i | \(-0.508093\pi\) | ||||
−0.0254213 | + | 0.999677i | \(0.508093\pi\) | |||||||
\(710\) | 6.78801e52 | + | 1.79155e53i | 0.0454814 | + | 0.120038i | ||||
\(711\) | 1.65501e54i | 1.07964i | ||||||||
\(712\) | 7.77432e53 | − | 1.47789e54i | 0.493790 | − | 0.938690i | ||||
\(713\) | 1.84696e53 | 0.114224 | ||||||||
\(714\) | 1.74180e53 | − | 6.59953e52i | 0.104890 | − | 0.0397417i | ||||
\(715\) | − | 1.20391e54i | − | 0.705958i | ||||||
\(716\) | −6.30718e53 | − | 7.12835e53i | −0.360154 | − | 0.407044i | ||||
\(717\) | 1.78922e53 | 0.0994945 | ||||||||
\(718\) | 5.94271e53 | + | 1.56845e54i | 0.321825 | + | 0.849387i | ||||
\(719\) | − | 3.02966e54i | − | 1.59788i | −0.601408 | − | 0.798942i | \(-0.705393\pi\) | ||
0.601408 | − | 0.798942i | \(-0.294607\pi\) | |||||||
\(720\) | −2.43545e53 | + | 1.98494e54i | −0.125101 | + | 1.01960i | ||||
\(721\) | −4.05930e54 | −2.03086 | ||||||||
\(722\) | −1.56765e54 | + | 5.93967e53i | −0.763908 | + | 0.289438i | ||||
\(723\) | 3.66923e52i | 0.0174159i | ||||||||
\(724\) | 1.13487e54 | − | 1.00413e54i | 0.524702 | − | 0.464258i | ||||
\(725\) | −2.39803e52 | −0.0108002 | ||||||||
\(726\) | −1.09888e53 | − | 2.90025e53i | −0.0482119 | − | 0.127245i | ||||
\(727\) | − | 2.55388e54i | − | 1.09156i | −0.837929 | − | 0.545779i | \(-0.816234\pi\) | ||
0.837929 | − | 0.545779i | \(-0.183766\pi\) | |||||||
\(728\) | −1.05151e54 | − | 5.53141e53i | −0.437843 | − | 0.230324i | ||||
\(729\) | 2.41703e54 | 0.980524 | ||||||||
\(730\) | 1.04363e54 | − | 3.95423e53i | 0.412490 | − | 0.156289i | ||||
\(731\) | 3.07787e54i | 1.18528i | ||||||||
\(732\) | 5.68107e52 | + | 6.42072e52i | 0.0213167 | + | 0.0240920i | ||||
\(733\) | −3.07753e54 | −1.12519 | −0.562595 | − | 0.826732i | \(-0.690197\pi\) | ||||
−0.562595 | + | 0.826732i | \(0.690197\pi\) | |||||||
\(734\) | −1.75226e54 | − | 4.62471e54i | −0.624272 | − | 1.64763i | ||||
\(735\) | 1.29688e53i | 0.0450236i | ||||||||
\(736\) | −1.02350e54 | + | 2.50568e53i | −0.346267 | + | 0.0847708i | ||||
\(737\) | −3.83581e54 | −1.26466 | ||||||||
\(738\) | −3.10628e53 | + | 1.17694e53i | −0.0998090 | + | 0.0378167i | ||||
\(739\) | − | 4.93005e54i | − | 1.54386i | −0.635709 | − | 0.771929i | \(-0.719292\pi\) | ||
0.635709 | − | 0.771929i | \(-0.280708\pi\) | |||||||
\(740\) | 3.77141e54 | − | 3.33696e54i | 1.15107 | − | 1.01847i | ||||
\(741\) | −9.62445e52 | −0.0286306 | ||||||||
\(742\) | 2.46338e54 | + | 6.50155e54i | 0.714261 | + | 1.88514i | ||||
\(743\) | − | 3.20011e54i | − | 0.904434i | −0.891908 | − | 0.452217i | \(-0.850633\pi\) | ||
0.891908 | − | 0.452217i | \(-0.149367\pi\) | |||||||
\(744\) | −3.08907e52 | + | 5.87229e52i | −0.00851024 | + | 0.0161779i | ||||
\(745\) | −3.80286e54 | −1.02127 | ||||||||
\(746\) | 1.15393e54 | − | 4.37214e53i | 0.302094 | − | 0.114461i | ||||
\(747\) | 4.72678e54i | 1.20635i | ||||||||
\(748\) | 7.24998e54 | + | 8.19390e54i | 1.80388 | + | 2.03873i | ||||
\(749\) | 3.09837e54 | 0.751586 | ||||||||
\(750\) | 8.26115e52 | + | 2.18035e53i | 0.0195378 | + | 0.0515658i | ||||
\(751\) | 4.56831e54i | 1.05341i | 0.850048 | + | 0.526705i | \(0.176573\pi\) | ||||
−0.850048 | + | 0.526705i | \(0.823427\pi\) | |||||||
\(752\) | −3.77302e54 | − | 4.62936e53i | −0.848302 | − | 0.104084i | ||||
\(753\) | −3.30860e53 | −0.0725337 | ||||||||
\(754\) | 2.83071e53 | − | 1.07253e53i | 0.0605117 | − | 0.0229273i | ||||
\(755\) | 2.31809e54i | 0.483213i | ||||||||
\(756\) | −5.57703e53 | + | 4.93457e53i | −0.113368 | + | 0.100308i | ||||
\(757\) | 6.13782e54 | 1.21673 | 0.608363 | − | 0.793659i | \(-0.291827\pi\) | ||||
0.608363 | + | 0.793659i | \(0.291827\pi\) | |||||||
\(758\) | −2.24443e53 | − | 5.92368e53i | −0.0433901 | − | 0.114519i | ||||
\(759\) | − | 1.98469e53i | − | 0.0374195i | ||||||
\(760\) | 6.68601e54 | + | 3.51712e54i | 1.22944 | + | 0.646739i | ||||
\(761\) | −5.99687e53 | −0.107551 | −0.0537757 | − | 0.998553i | \(-0.517126\pi\) | ||||
−0.0537757 | + | 0.998553i | \(0.517126\pi\) | |||||||
\(762\) | −9.29002e52 | + | 3.51990e52i | −0.0162507 | + | 0.00615724i | ||||
\(763\) | − | 5.30189e54i | − | 0.904617i | ||||||
\(764\) | −5.69728e54 | − | 6.43904e54i | −0.948187 | − | 1.07164i | ||||
\(765\) | 9.36218e54 | 1.51988 | ||||||||
\(766\) | −1.95916e54 | − | 5.17078e54i | −0.310259 | − | 0.818860i | ||||
\(767\) | 2.88102e54i | 0.445076i | ||||||||
\(768\) | 9.15161e52 | − | 3.67323e53i | 0.0137922 | − | 0.0553586i | ||||
\(769\) | −1.31746e55 | −1.93703 | −0.968515 | − | 0.248953i | \(-0.919913\pi\) | ||||
−0.968515 | + | 0.248953i | \(0.919913\pi\) | |||||||
\(770\) | −1.64262e55 | + | 6.22372e54i | −2.35620 | + | 0.892743i | ||||
\(771\) | 5.15397e53i | 0.0721288i | ||||||||
\(772\) | 8.84155e54 | − | 7.82303e54i | 1.20726 | − | 1.06818i | ||||
\(773\) | 1.13927e55 | 1.51781 | 0.758903 | − | 0.651203i | \(-0.225735\pi\) | ||||
0.758903 | + | 0.651203i | \(0.225735\pi\) | |||||||
\(774\) | −2.17637e54 | − | 5.74406e54i | −0.282914 | − | 0.746690i | ||||
\(775\) | 1.56966e53i | 0.0199101i | ||||||||
\(776\) | 6.82519e53 | − | 1.29746e54i | 0.0844776 | − | 0.160591i | ||||
\(777\) | 9.36047e53 | 0.113057 | ||||||||
\(778\) | −6.33614e54 | + | 2.40071e54i | −0.746814 | + | 0.282961i | ||||
\(779\) | 1.25485e54i | 0.144338i | ||||||||
\(780\) | 1.29223e53 | + | 1.46047e53i | 0.0145058 | + | 0.0163944i | ||||
\(781\) | −2.09177e54 | −0.229163 | ||||||||
\(782\) | 1.74783e54 | + | 4.61301e54i | 0.186883 | + | 0.493237i | ||||
\(783\) | − | 1.89725e53i | − | 0.0197994i | ||||||
\(784\) | −9.15545e53 | + | 7.46187e54i | −0.0932555 | + | 0.760051i | ||||
\(785\) | 6.50636e54 | 0.646867 | ||||||||
\(786\) | −7.12964e53 | + | 2.70136e53i | −0.0691894 | + | 0.0262152i | ||||
\(787\) | 2.78592e54i | 0.263906i | 0.991256 | + | 0.131953i | \(0.0421248\pi\) | ||||
−0.991256 | + | 0.131953i | \(0.957875\pi\) | |||||||
\(788\) | −4.50188e54 | + | 3.98327e54i | −0.416289 | + | 0.368334i | ||||
\(789\) | −7.59802e53 | −0.0685863 | ||||||||
\(790\) | −4.48832e54 | − | 1.18459e55i | −0.395521 | − | 1.04389i | ||||
\(791\) | − | 1.42528e55i | − | 1.22616i | ||||||
\(792\) | −1.93242e55 | − | 1.01653e55i | −1.62301 | − | 0.853774i | ||||
\(793\) | −2.56014e54 | −0.209930 | ||||||||
\(794\) | 8.47064e54 | − | 3.20945e54i | 0.678152 | − | 0.256946i | ||||
\(795\) | − | 1.14113e54i | − | 0.0891990i | ||||||
\(796\) | 6.47444e54 | + | 7.31738e54i | 0.494144 | + | 0.558480i | ||||
\(797\) | −9.56674e54 | −0.712945 | −0.356472 | − | 0.934306i | \(-0.616021\pi\) | ||||
−0.356472 | + | 0.934306i | \(0.616021\pi\) | |||||||
\(798\) | 4.97545e53 | + | 1.31316e54i | 0.0362058 | + | 0.0955572i | ||||
\(799\) | 1.77959e55i | 1.26453i | ||||||||
\(800\) | −2.12947e53 | − | 8.69833e53i | −0.0147762 | − | 0.0603568i | ||||
\(801\) | 1.56017e55 | 1.05719 | ||||||||
\(802\) | 1.84357e55 | − | 6.98513e54i | 1.21996 | − | 0.462234i | ||||
\(803\) | 1.21852e55i | 0.787477i | ||||||||
\(804\) | 4.65324e53 | − | 4.11720e53i | 0.0293691 | − | 0.0259859i | ||||
\(805\) | −7.92004e54 | −0.488209 | ||||||||
\(806\) | −7.02037e53 | − | 1.85287e54i | −0.0422663 | − | 0.111553i | ||||
\(807\) | − | 1.31311e54i | − | 0.0772152i | ||||||
\(808\) | 1.34661e54 | − | 2.55988e54i | 0.0773437 | − | 0.147029i | ||||
\(809\) | 8.57158e54 | 0.480883 | 0.240441 | − | 0.970664i | \(-0.422708\pi\) | ||||
0.240441 | + | 0.970664i | \(0.422708\pi\) | |||||||
\(810\) | −1.74149e55 | + | 6.59833e54i | −0.954344 | + | 0.361592i | ||||
\(811\) | − | 2.53774e55i | − | 1.35847i | −0.733921 | − | 0.679235i | \(-0.762312\pi\) | ||
0.733921 | − | 0.679235i | \(-0.237688\pi\) | |||||||
\(812\) | −2.92672e54 | − | 3.30777e54i | −0.153044 | − | 0.172970i | ||||
\(813\) | 1.53138e54 | 0.0782279 | ||||||||
\(814\) | 1.94808e55 | + | 5.14152e55i | 0.972170 | + | 2.56583i | ||||
\(815\) | − | 6.52087e54i | − | 0.317915i | ||||||
\(816\) | −1.75900e54 | − | 2.15823e53i | −0.0837823 | − | 0.0102798i | ||||
\(817\) | −2.32044e55 | −1.07982 | ||||||||
\(818\) | 2.54845e55 | − | 9.65584e54i | 1.15868 | − | 0.439013i | ||||
\(819\) | − | 1.11006e55i | − | 0.493118i | ||||||
\(820\) | 1.90418e54 | − | 1.68482e54i | 0.0826504 | − | 0.0731293i | ||||
\(821\) | −2.00404e55 | −0.849937 | −0.424969 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424969 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(822\) | 2.96356e53 | + | 7.82167e53i | 0.0122814 | + | 0.0324142i | ||||
\(823\) | 1.64036e55i | 0.664266i | 0.943233 | + | 0.332133i | \(0.107768\pi\) | ||||
−0.943233 | + | 0.332133i | \(0.892232\pi\) | |||||||
\(824\) | 3.41811e55 | + | 1.79807e55i | 1.35260 | + | 0.711523i | ||||
\(825\) | 1.68670e53 | 0.00652249 | ||||||||
\(826\) | 3.93086e55 | − | 1.48937e55i | 1.48548 | − | 0.562835i | ||||
\(827\) | 2.11921e55i | 0.782651i | 0.920252 | + | 0.391326i | \(0.127983\pi\) | ||||
−0.920252 | + | 0.391326i | \(0.872017\pi\) | |||||||
\(828\) | −6.52374e54 | − | 7.37310e54i | −0.235462 | − | 0.266118i | ||||
\(829\) | −2.59284e55 | −0.914617 | −0.457308 | − | 0.889308i | \(-0.651186\pi\) | ||||
−0.457308 | + | 0.889308i | \(0.651186\pi\) | |||||||
\(830\) | −1.28188e55 | − | 3.38326e55i | −0.441942 | − | 1.16641i | ||||
\(831\) | 3.23877e53i | 0.0109134i | ||||||||
\(832\) | 6.40406e54 | + | 9.31537e54i | 0.210917 | + | 0.306801i | ||||
\(833\) | 3.51947e55 | 1.13298 | ||||||||
\(834\) | 4.44010e53 | − | 1.68232e53i | 0.0139713 | − | 0.00529362i | ||||
\(835\) | − | 1.51972e55i | − | 0.467433i | ||||||
\(836\) | −6.17747e55 | + | 5.46584e55i | −1.85734 | + | 1.64338i | ||||
\(837\) | −1.24187e54 | −0.0364999 | ||||||||
\(838\) | 1.00618e55 | + | 2.65559e55i | 0.289094 | + | 0.763001i | ||||
\(839\) | 1.99481e55i | 0.560305i | 0.959955 | + | 0.280153i | \(0.0903851\pi\) | ||||
−0.959955 | + | 0.280153i | \(0.909615\pi\) | |||||||
\(840\) | 1.32464e54 | − | 2.51812e54i | 0.0363739 | − | 0.0691464i | ||||
\(841\) | −3.61245e55 | −0.969791 | ||||||||
\(842\) | −6.07396e54 | + | 2.30137e54i | −0.159420 | + | 0.0604027i | ||||
\(843\) | 1.18840e53i | 0.00304957i | ||||||||
\(844\) | −4.33963e55 | − | 4.90463e55i | −1.08880 | − | 1.23055i | ||||
\(845\) | 3.61882e55 | 0.887747 | ||||||||
\(846\) | −1.25835e55 | − | 3.32114e55i | −0.301832 | − | 0.796618i | ||||
\(847\) | − | 1.35131e56i | − | 3.16936i | ||||||
\(848\) | 8.05592e54 | − | 6.56574e55i | 0.184754 | − | 1.50578i | ||||
\(849\) | −8.22462e53 | −0.0184446 | ||||||||
\(850\) | −3.92040e54 | + | 1.48541e54i | −0.0859748 | + | 0.0325751i | ||||
\(851\) | 2.47904e55i | 0.531645i | ||||||||
\(852\) | 2.53753e53 | − | 2.24522e53i | 0.00532181 | − | 0.00470875i | ||||
\(853\) | −8.25116e55 | −1.69232 | −0.846162 | − | 0.532925i | \(-0.821093\pi\) | ||||
−0.846162 | + | 0.532925i | \(0.821093\pi\) | |||||||
\(854\) | 1.32349e55 | + | 3.49307e55i | 0.265474 | + | 0.700660i | ||||
\(855\) | 7.05825e55i | 1.38465i | ||||||||
\(856\) | −2.60896e55 | − | 1.37242e55i | −0.500571 | − | 0.263322i | ||||
\(857\) | 5.82193e55 | 1.09253 | 0.546263 | − | 0.837614i | \(-0.316050\pi\) | ||||
0.546263 | + | 0.837614i | \(0.316050\pi\) | |||||||
\(858\) | −1.99104e54 | + | 7.54386e53i | −0.0365444 | + | 0.0138463i | ||||
\(859\) | 1.82991e55i | 0.328518i | 0.986417 | + | 0.164259i | \(0.0525233\pi\) | ||||
−0.986417 | + | 0.164259i | \(0.947477\pi\) | |||||||
\(860\) | 3.11554e55 | + | 3.52116e55i | 0.547094 | + | 0.618323i | ||||
\(861\) | 4.72609e53 | 0.00811786 | ||||||||
\(862\) | −1.66828e55 | − | 4.40306e55i | −0.280305 | − | 0.739804i | ||||
\(863\) | 2.09673e55i | 0.344618i | 0.985043 | + | 0.172309i | \(0.0551228\pi\) | ||||
−0.985043 | + | 0.172309i | \(0.944877\pi\) | |||||||
\(864\) | 6.88187e54 | − | 1.68478e54i | 0.110648 | − | 0.0270883i | ||||
\(865\) | 7.84923e55 | 1.23459 | ||||||||
\(866\) | −3.70176e55 | + | 1.40256e55i | −0.569598 | + | 0.215816i | ||||
\(867\) | 4.50662e54i | 0.0678403i | ||||||||
\(868\) | −2.16514e55 | + | 1.91572e55i | −0.318868 | + | 0.282136i | ||||
\(869\) | 1.38310e56 | 1.99287 | ||||||||
\(870\) | 2.56844e53 | + | 6.77885e53i | 0.00362080 | + | 0.00955631i | ||||
\(871\) | 1.85539e55i | 0.255912i | ||||||||
\(872\) | −2.34848e55 | + | 4.46442e55i | −0.316937 | + | 0.602493i | ||||
\(873\) | 1.36969e55 | 0.180864 | ||||||||
\(874\) | −3.47780e55 | + | 1.31771e55i | −0.449352 | + | 0.170256i | ||||
\(875\) | 1.01589e56i | 1.28438i | ||||||||
\(876\) | −1.30791e54 | − | 1.47819e54i | −0.0161808 | − | 0.0182875i | ||||
\(877\) | −3.38473e55 | −0.409762 | −0.204881 | − | 0.978787i | \(-0.565681\pi\) | ||||
−0.204881 | + | 0.978787i | \(0.565681\pi\) | |||||||
\(878\) | 6.71912e54 | + | 1.77336e55i | 0.0796006 | + | 0.210088i | ||||
\(879\) | 4.92194e54i | 0.0570621i | ||||||||
\(880\) | 1.65883e56 | + | 2.03533e55i | 1.88205 | + | 0.230921i | ||||
\(881\) | 7.01856e55 | 0.779302 | 0.389651 | − | 0.920963i | \(-0.372596\pi\) | ||||
0.389651 | + | 0.920963i | \(0.372596\pi\) | |||||||
\(882\) | −6.56819e55 | + | 2.48863e55i | −0.713744 | + | 0.270431i | ||||
\(883\) | − | 3.63229e55i | − | 0.386302i | −0.981169 | − | 0.193151i | \(-0.938129\pi\) | ||
0.981169 | − | 0.193151i | \(-0.0618708\pi\) | |||||||
\(884\) | 3.96341e55 | − | 3.50684e55i | 0.412550 | − | 0.365025i | ||||
\(885\) | −6.89933e54 | −0.0702885 | ||||||||
\(886\) | −3.55305e55 | − | 9.37751e55i | −0.354292 | − | 0.935076i | ||||
\(887\) | 1.42465e55i | 0.139047i | 0.997580 | + | 0.0695233i | \(0.0221478\pi\) | ||||
−0.997580 | + | 0.0695233i | \(0.977852\pi\) | |||||||
\(888\) | −7.88192e54 | − | 4.14622e54i | −0.0752984 | − | 0.0396101i | ||||
\(889\) | −4.32850e55 | −0.404766 | ||||||||
\(890\) | −1.11671e56 | + | 4.23113e55i | −1.02219 | + | 0.387299i | ||||
\(891\) | − | 2.03332e56i | − | 1.82192i | ||||||
\(892\) | 1.59755e55 | + | 1.80555e55i | 0.140128 | + | 0.158372i | ||||
\(893\) | −1.34165e56 | −1.15202 | ||||||||
\(894\) | 2.38293e54 | + | 6.28921e54i | 0.0200308 | + | 0.0528668i | ||||
\(895\) | 6.80661e55i | 0.560135i | ||||||||
\(896\) | 9.39927e55 | − | 1.35534e56i | 0.757254 | − | 1.09193i | ||||
\(897\) | −9.59999e53 | −0.00757207 | ||||||||
\(898\) | 1.12623e56 | − | 4.26719e55i | 0.869716 | − | 0.329527i | ||||
\(899\) | − | 7.36559e54i | − | 0.0556895i | ||||||
\(900\) | 6.26609e54 | − | 5.54425e54i | 0.0463862 | − | 0.0410427i | ||||
\(901\) | −3.09680e56 | −2.24462 | ||||||||
\(902\) | 9.83581e54 | + | 2.59595e55i | 0.0698049 | + | 0.184235i | ||||
\(903\) | 8.73936e54i | 0.0607313i | ||||||||
\(904\) | −6.31327e55 | + | 1.20015e56i | −0.429590 | + | 0.816646i | ||||
\(905\) | −1.08364e56 | −0.722044 | ||||||||
\(906\) | 3.83369e54 | − | 1.45255e54i | 0.0250139 | − | 0.00947753i | ||||
\(907\) | − | 9.16025e55i | − | 0.585287i | −0.956222 | − | 0.292643i | \(-0.905465\pi\) | ||
0.956222 | − | 0.292643i | \(-0.0945349\pi\) | |||||||
\(908\) | 2.26669e55 | + | 2.56180e55i | 0.141828 | + | 0.160293i | ||||
\(909\) | 2.70240e55 | 0.165591 | ||||||||
\(910\) | 3.01043e55 | + | 7.94538e55i | 0.180652 | + | 0.476791i | ||||
\(911\) | − | 2.11413e56i | − | 1.24246i | −0.783628 | − | 0.621231i | \(-0.786633\pi\) | ||
0.783628 | − | 0.621231i | \(-0.213367\pi\) | |||||||
\(912\) | 1.62711e54 | − | 1.32613e55i | 0.00936515 | − | 0.0763279i | ||||
\(913\) | 3.95021e56 | 2.22677 | ||||||||
\(914\) | −2.67516e55 | + | 1.01360e55i | −0.147697 | + | 0.0559612i | ||||
\(915\) | − | 6.13091e54i | − | 0.0331531i | ||||||
\(916\) | 3.70501e55 | − | 3.27820e55i | 0.196234 | − | 0.173629i | ||||
\(917\) | −3.32192e56 | −1.72334 | ||||||||
\(918\) | −1.17521e55 | − | 3.10171e55i | −0.0597179 | − | 0.157612i | ||||
\(919\) | 1.66961e56i | 0.831037i | 0.909585 | + | 0.415518i | \(0.136400\pi\) | ||||
−0.909585 | + | 0.415518i | \(0.863600\pi\) | |||||||
\(920\) | 6.66902e55 | + | 3.50818e55i | 0.325157 | + | 0.171046i | ||||
\(921\) | −6.93519e54 | −0.0331227 | ||||||||
\(922\) | 4.25439e55 | − | 1.61195e55i | 0.199044 | − | 0.0754161i | ||||
\(923\) | 1.01179e55i | 0.0463725i | ||||||||
\(924\) | 2.05857e55 | + | 2.32659e55i | 0.0924269 | + | 0.104461i | ||||
\(925\) | −2.10683e55 | −0.0926695 | ||||||||
\(926\) | 1.08561e55 | + | 2.86524e55i | 0.0467807 | + | 0.123468i | ||||
\(927\) | 3.60841e56i | 1.52335i | ||||||||
\(928\) | 9.99250e54 | + | 4.08168e55i | 0.0413297 | + | 0.168821i | ||||
\(929\) | −7.86208e55 | −0.318595 | −0.159298 | − | 0.987231i | \(-0.550923\pi\) | ||||
−0.159298 | + | 0.987231i | \(0.550923\pi\) | |||||||
\(930\) | 4.43718e54 | − | 1.68121e54i | 0.0176170 | − | 0.00667490i | ||||
\(931\) | 2.65337e56i | 1.03217i | ||||||||
\(932\) | 1.04150e56 | − | 9.21521e55i | 0.396969 | − | 0.351239i | ||||
\(933\) | 2.62802e55 | 0.0981469 | ||||||||
\(934\) | −7.01663e53 | − | 1.85189e54i | −0.00256766 | − | 0.00677678i | ||||
\(935\) | − | 7.82406e56i | − | 2.80551i | ||||||
\(936\) | −4.91700e55 | + | 9.34716e55i | −0.172766 | + | 0.328427i | ||||
\(937\) | 4.45530e56 | 1.53400 | 0.766999 | − | 0.641649i | \(-0.221749\pi\) | ||||
0.766999 | + | 0.641649i | \(0.221749\pi\) | |||||||
\(938\) | 2.53150e56 | − | 9.59164e55i | 0.854131 | − | 0.323623i | ||||
\(939\) | − | 3.28033e55i | − | 0.108460i | ||||||
\(940\) | 1.80136e56 | + | 2.03589e56i | 0.583676 | + | 0.659668i | ||||
\(941\) | −5.63415e54 | −0.0178906 | −0.00894532 | − | 0.999960i | \(-0.502847\pi\) | ||||
−0.00894532 | + | 0.999960i | \(0.502847\pi\) | |||||||
\(942\) | −4.07698e54 | − | 1.07603e55i | −0.0126874 | − | 0.0334855i | ||||
\(943\) | 1.25166e55i | 0.0381738i | ||||||||
\(944\) | −3.96967e56 | − | 4.87065e55i | −1.18655 | − | 0.145586i | ||||
\(945\) | 5.32531e55 | 0.156006 | ||||||||
\(946\) | −4.80036e56 | + | 1.81881e56i | −1.37830 | + | 0.522224i | ||||
\(947\) | 4.03250e56i | 1.13481i | 0.823438 | + | 0.567407i | \(0.192053\pi\) | ||||
−0.823438 | + | 0.567407i | \(0.807947\pi\) | |||||||
\(948\) | −1.67785e55 | + | 1.48457e55i | −0.0462802 | + | 0.0409488i | ||||
\(949\) | 5.89403e55 | 0.159351 | ||||||||
\(950\) | −1.11986e55 | − | 2.95563e55i | −0.0296767 | − | 0.0783253i | ||||
\(951\) | − | 9.91636e54i | − | 0.0257586i | ||||||
\(952\) | −6.83366e56 | − | 3.59480e56i | −1.74001 | − | 0.915318i | ||||
\(953\) | 6.40790e56 | 1.59938 | 0.799689 | − | 0.600415i | \(-0.204998\pi\) | ||||
0.799689 | + | 0.600415i | \(0.204998\pi\) | |||||||
\(954\) | 5.77938e56 | − | 2.18976e56i | 1.41404 | − | 0.535768i | ||||
\(955\) | 6.14841e56i | 1.47468i | ||||||||
\(956\) | −4.91499e56 | − | 5.55490e56i | −1.15564 | − | 1.30610i | ||||
\(957\) | −7.91482e54 | −0.0182438 | ||||||||
\(958\) | 1.33952e56 | + | 3.53536e56i | 0.302694 | + | 0.798894i | ||||
\(959\) | 3.64435e56i | 0.807359i | ||||||||
\(960\) | −2.23080e55 | + | 1.53362e55i | −0.0484515 | + | 0.0333091i | ||||
\(961\) | 4.21405e56 | 0.897337 | ||||||||
\(962\) | 2.48697e56 | − | 9.42291e55i | 0.519212 | − | 0.196725i | ||||
\(963\) | − | 2.75421e56i | − | 0.563765i | ||||||
\(964\) | 1.13917e56 | − | 1.00794e56i | 0.228625 | − | 0.202288i | ||||
\(965\) | −8.44248e56 | −1.66131 | ||||||||
\(966\) | 4.96281e54 | + | 1.30983e55i | 0.00957552 | + | 0.0252725i | ||||
\(967\) | − | 5.40199e56i | − | 1.02200i | −0.859581 | − | 0.511000i | \(-0.829275\pi\) | ||
0.859581 | − | 0.511000i | \(-0.170725\pi\) | |||||||
\(968\) | −5.98565e56 | + | 1.13787e57i | −1.11040 | + | 2.11086i | ||||
\(969\) | −6.25482e55 | −0.113779 | ||||||||
\(970\) | −9.80378e55 | + | 3.71456e55i | −0.174876 | + | 0.0662590i | ||||
\(971\) | − | 5.69092e56i | − | 0.995445i | −0.867336 | − | 0.497722i | \(-0.834170\pi\) | ||
0.867336 | − | 0.497722i | \(-0.165830\pi\) | |||||||
\(972\) | 6.58326e55 | + | 7.44037e55i | 0.112923 | + | 0.127625i | ||||
\(973\) | 2.06878e56 | 0.347992 | ||||||||
\(974\) | −3.92982e56 | − | 1.03719e57i | −0.648265 | − | 1.71096i | ||||
\(975\) | − | 8.15863e53i | − | 0.00131987i | ||||||
\(976\) | 4.32818e55 | − | 3.52755e56i | 0.0686687 | − | 0.559663i | ||||
\(977\) | −5.87734e56 | −0.914501 | −0.457250 | − | 0.889338i | \(-0.651166\pi\) | ||||
−0.457250 | + | 0.889338i | \(0.651166\pi\) | |||||||
\(978\) | −1.07843e55 | + | 4.08607e54i | −0.0164571 | + | 0.00623544i | ||||
\(979\) | − | 1.30385e57i | − | 1.95144i | ||||||
\(980\) | 4.02636e56 | − | 3.56254e56i | 0.591041 | − | 0.522955i | ||||
\(981\) | −4.71298e56 | −0.678554 | ||||||||
\(982\) | −8.20114e55 | − | 2.16451e56i | −0.115813 | − | 0.305662i | ||||
\(983\) | 1.33516e57i | 1.84934i | 0.380769 | + | 0.924670i | \(0.375659\pi\) | ||||
−0.380769 | + | 0.924670i | \(0.624341\pi\) | |||||||
\(984\) | −3.97957e54 | − | 2.09342e54i | −0.00540666 | − | 0.00284413i | ||||
\(985\) | 4.29868e56 | 0.572857 | ||||||||
\(986\) | 1.83964e56 | − | 6.97024e55i | 0.240476 | − | 0.0911143i | ||||
\(987\) | 5.05299e55i | 0.0647921i | ||||||||
\(988\) | 2.64384e56 | + | 2.98806e56i | 0.332548 | + | 0.375844i | ||||
\(989\) | −2.31454e56 | −0.285585 | ||||||||
\(990\) | 5.53241e56 | + | 1.46016e57i | 0.669647 | + | 1.76739i | ||||
\(991\) | 1.01541e57i | 1.20571i | 0.797852 | + | 0.602853i | \(0.205970\pi\) | ||||
−0.797852 | + | 0.602853i | \(0.794030\pi\) | |||||||
\(992\) | 2.67171e56 | − | 6.54071e55i | 0.311220 | − | 0.0761909i | ||||
\(993\) | 7.91229e55 | 0.0904204 | ||||||||
\(994\) | 1.38050e56 | − | 5.23057e55i | 0.154772 | − | 0.0586419i | ||||
\(995\) | − | 6.98710e56i | − | 0.768526i | ||||||
\(996\) | −4.79202e55 | + | 4.23999e55i | −0.0517120 | + | 0.0457549i | ||||
\(997\) | 6.90908e56 | 0.731497 | 0.365748 | − | 0.930714i | \(-0.380813\pi\) | ||||
0.365748 | + | 0.930714i | \(0.380813\pi\) | |||||||
\(998\) | 4.72357e56 | + | 1.24668e57i | 0.490671 | + | 1.29502i | ||||
\(999\) | − | 1.66687e56i | − | 0.169885i |
(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 | 4.39.b.a.3.15 | ✓ | 18 | |
4.3 | odd | 2 | inner | 4.39.b.a.3.16 | yes | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.39.b.a.3.15 | ✓ | 18 | 1.1 | even | 1 | trivial | |
4.39.b.a.3.16 | yes | 18 | 4.3 | odd | 2 | inner |