Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,39,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, 39, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 39);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 39 \) |
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: | \(27.4390407101\) |
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: | \( x^{12} + 17353504902 x^{10} + \cdots + 27\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{75}\cdot 3^{91}\cdot 5^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.5 | ||
Root | \(-18842.7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.39.b.a.2.8 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 226112.i | − | 0.431275i | −0.976473 | − | 0.215638i | \(-0.930817\pi\) | ||
0.976473 | − | 0.215638i | \(-0.0691830\pi\) | |||||||
\(3\) | −8.54601e8 | − | 7.87723e8i | −0.735292 | − | 0.677751i | ||||
\(4\) | 2.23751e11 | 0.814002 | ||||||||
\(5\) | − | 6.89065e12i | − | 0.361269i | −0.983550 | − | 0.180634i | \(-0.942185\pi\) | ||
0.983550 | − | 0.180634i | \(-0.0578150\pi\) | |||||||
\(6\) | −1.78114e14 | + | 1.93236e14i | −0.292297 | + | 0.317113i | ||||
\(7\) | 1.19822e16 | 1.05118 | 0.525588 | − | 0.850739i | \(-0.323845\pi\) | ||||
0.525588 | + | 0.850739i | \(0.323845\pi\) | |||||||
\(8\) | − | 1.12746e17i | − | 0.782334i | ||||||
\(9\) | 1.09835e17 | + | 1.34638e18i | 0.0813080 | + | 0.996689i | ||||
\(10\) | −1.55806e18 | −0.155806 | ||||||||
\(11\) | 1.21660e20i | 1.98924i | 0.103572 | + | 0.994622i | \(0.466973\pi\) | ||||
−0.103572 | + | 0.994622i | \(0.533027\pi\) | |||||||
\(12\) | −1.91218e20 | − | 1.76254e20i | −0.598529 | − | 0.551690i | ||||
\(13\) | 1.57410e21 | 1.07673 | 0.538367 | − | 0.842710i | \(-0.319041\pi\) | ||||
0.538367 | + | 0.842710i | \(0.319041\pi\) | |||||||
\(14\) | − | 2.70934e21i | − | 0.453346i | ||||||
\(15\) | −5.42793e21 | + | 5.88876e21i | −0.244850 | + | 0.265638i | ||||
\(16\) | 3.60109e22 | 0.476600 | ||||||||
\(17\) | 2.37425e23i | 0.993108i | 0.868006 | + | 0.496554i | \(0.165402\pi\) | ||||
−0.868006 | + | 0.496554i | \(0.834598\pi\) | |||||||
\(18\) | 3.04433e23 | − | 2.48351e22i | 0.429847 | − | 0.0350661i | ||||
\(19\) | −3.40129e23 | −0.171920 | −0.0859598 | − | 0.996299i | \(-0.527396\pi\) | ||||
−0.0859598 | + | 0.996299i | \(0.527396\pi\) | |||||||
\(20\) | − | 1.54179e24i | − | 0.294073i | ||||||
\(21\) | −1.02400e25 | − | 9.43870e24i | −0.772921 | − | 0.712435i | ||||
\(22\) | 2.75089e25 | 0.857912 | ||||||||
\(23\) | − | 1.60682e25i | − | 0.215347i | −0.994186 | − | 0.107674i | \(-0.965660\pi\) | ||
0.994186 | − | 0.107674i | \(-0.0343402\pi\) | |||||||
\(24\) | −8.88128e25 | + | 9.63531e25i | −0.530227 | + | 0.575244i | ||||
\(25\) | 3.16317e26 | 0.869485 | ||||||||
\(26\) | − | 3.55924e26i | − | 0.464369i | ||||||
\(27\) | 9.66709e26 | − | 1.23714e27i | 0.615722 | − | 0.787964i | ||||
\(28\) | 2.68104e27 | 0.855659 | ||||||||
\(29\) | − | 5.04838e27i | − | 0.827161i | −0.910468 | − | 0.413581i | \(-0.864278\pi\) | ||
0.910468 | − | 0.413581i | \(-0.135722\pi\) | |||||||
\(30\) | 1.33152e27 | + | 1.22732e27i | 0.114563 | + | 0.105598i | ||||
\(31\) | 1.48522e28 | 0.685358 | 0.342679 | − | 0.939452i | \(-0.388666\pi\) | ||||
0.342679 | + | 0.939452i | \(0.388666\pi\) | |||||||
\(32\) | − | 3.91340e28i | − | 0.987880i | ||||||
\(33\) | 9.58347e28 | − | 1.03971e29i | 1.34821 | − | 1.46267i | ||||
\(34\) | 5.36847e28 | 0.428303 | ||||||||
\(35\) | − | 8.25655e28i | − | 0.379757i | ||||||
\(36\) | 2.45757e28 | + | 3.01254e29i | 0.0661849 | + | 0.811306i | ||||
\(37\) | 4.44215e29 | 0.710822 | 0.355411 | − | 0.934710i | \(-0.384341\pi\) | ||||
0.355411 | + | 0.934710i | \(0.384341\pi\) | |||||||
\(38\) | 7.69074e28i | 0.0741447i | ||||||||
\(39\) | −1.34523e30 | − | 1.23996e30i | −0.791714 | − | 0.729757i | ||||
\(40\) | −7.76895e29 | −0.282633 | ||||||||
\(41\) | 2.53393e30i | 0.576635i | 0.957535 | + | 0.288318i | \(0.0930959\pi\) | ||||
−0.957535 | + | 0.288318i | \(0.906904\pi\) | |||||||
\(42\) | −2.13421e30 | + | 2.31540e30i | −0.307256 | + | 0.333342i | ||||
\(43\) | −1.36439e31 | −1.25614 | −0.628069 | − | 0.778158i | \(-0.716154\pi\) | ||||
−0.628069 | + | 0.778158i | \(0.716154\pi\) | |||||||
\(44\) | 2.72216e31i | 1.61925i | ||||||||
\(45\) | 9.27743e30 | − | 7.56836e29i | 0.360072 | − | 0.0293740i | ||||
\(46\) | −3.63323e30 | −0.0928740 | ||||||||
\(47\) | − | 1.20655e31i | − | 0.204967i | −0.994735 | − | 0.102484i | \(-0.967321\pi\) | ||
0.994735 | − | 0.102484i | \(-0.0326789\pi\) | |||||||
\(48\) | −3.07750e31 | − | 2.83666e31i | −0.350440 | − | 0.323016i | ||||
\(49\) | 1.36394e31 | 0.104971 | ||||||||
\(50\) | − | 7.15232e31i | − | 0.374987i | ||||||
\(51\) | 1.87025e32 | − | 2.02904e32i | 0.673080 | − | 0.730224i | ||||
\(52\) | 3.52207e32 | 0.876464 | ||||||||
\(53\) | 1.42820e32i | 0.247484i | 0.992314 | + | 0.123742i | \(0.0394896\pi\) | ||||
−0.992314 | + | 0.123742i | \(0.960510\pi\) | |||||||
\(54\) | −2.79732e32 | − | 2.18585e32i | −0.339829 | − | 0.265545i | ||||
\(55\) | 8.38319e32 | 0.718651 | ||||||||
\(56\) | − | 1.35095e33i | − | 0.822371i | ||||||
\(57\) | 2.90675e32 | + | 2.67928e32i | 0.126411 | + | 0.116519i | ||||
\(58\) | −1.14150e33 | −0.356734 | ||||||||
\(59\) | 5.18925e33i | 1.17197i | 0.810322 | + | 0.585984i | \(0.199292\pi\) | ||||
−0.810322 | + | 0.585984i | \(0.800708\pi\) | |||||||
\(60\) | −1.21450e33 | + | 1.31762e33i | −0.199308 | + | 0.216230i | ||||
\(61\) | −1.25756e34 | −1.50751 | −0.753755 | − | 0.657155i | \(-0.771760\pi\) | ||||
−0.753755 | + | 0.657155i | \(0.771760\pi\) | |||||||
\(62\) | − | 3.35826e33i | − | 0.295578i | ||||||
\(63\) | 1.31607e33 | + | 1.61326e34i | 0.0854691 | + | 1.04770i | ||||
\(64\) | 1.04993e33 | 0.0505521 | ||||||||
\(65\) | − | 1.08466e34i | − | 0.388990i | ||||||
\(66\) | −2.35092e34 | − | 2.16694e34i | −0.630815 | − | 0.581450i | ||||
\(67\) | 7.45504e34 | 1.50324 | 0.751621 | − | 0.659596i | \(-0.229273\pi\) | ||||
0.751621 | + | 0.659596i | \(0.229273\pi\) | |||||||
\(68\) | 5.31241e34i | 0.808392i | ||||||||
\(69\) | −1.26573e34 | + | 1.37319e34i | −0.145952 | + | 0.158343i | ||||
\(70\) | −1.86691e34 | −0.163780 | ||||||||
\(71\) | − | 2.70192e35i | − | 1.81035i | −0.425035 | − | 0.905177i | \(-0.639738\pi\) | ||
0.425035 | − | 0.905177i | \(-0.360262\pi\) | |||||||
\(72\) | 1.51799e35 | − | 1.23835e34i | 0.779744 | − | 0.0636101i | ||||
\(73\) | 1.76445e35 | 0.697389 | 0.348694 | − | 0.937236i | \(-0.386625\pi\) | ||||
0.348694 | + | 0.937236i | \(0.386625\pi\) | |||||||
\(74\) | − | 1.00443e35i | − | 0.306560i | ||||||
\(75\) | −2.70325e35 | − | 2.49170e35i | −0.639325 | − | 0.589294i | ||||
\(76\) | −7.61043e34 | −0.139943 | ||||||||
\(77\) | 1.45776e36i | 2.09105i | ||||||||
\(78\) | −2.80369e35 | + | 3.04173e35i | −0.314726 | + | 0.341447i | ||||
\(79\) | 4.16277e34 | 0.0366833 | 0.0183416 | − | 0.999832i | \(-0.494161\pi\) | ||||
0.0183416 | + | 0.999832i | \(0.494161\pi\) | |||||||
\(80\) | − | 2.48139e35i | − | 0.172181i | ||||||
\(81\) | −1.80067e36 | + | 2.95759e35i | −0.986778 | + | 0.162078i | ||||
\(82\) | 5.72953e35 | 0.248689 | ||||||||
\(83\) | − | 4.66415e35i | − | 0.160801i | −0.996763 | − | 0.0804006i | \(-0.974380\pi\) | ||
0.996763 | − | 0.0804006i | \(-0.0256199\pi\) | |||||||
\(84\) | −2.29122e36 | − | 2.11192e36i | −0.629159 | − | 0.579924i | ||||
\(85\) | 1.63601e36 | 0.358779 | ||||||||
\(86\) | 3.08505e36i | 0.541741i | ||||||||
\(87\) | −3.97673e36 | + | 4.31435e36i | −0.560609 | + | 0.608205i | ||||
\(88\) | 1.37167e37 | 1.55625 | ||||||||
\(89\) | − | 1.44520e37i | − | 1.32287i | −0.750002 | − | 0.661435i | \(-0.769948\pi\) | ||
0.750002 | − | 0.661435i | \(-0.230052\pi\) | |||||||
\(90\) | −1.71130e35 | − | 2.09774e36i | −0.0126683 | − | 0.155290i | ||||
\(91\) | 1.88613e37 | 1.13184 | ||||||||
\(92\) | − | 3.59529e36i | − | 0.175293i | ||||||
\(93\) | −1.26927e37 | − | 1.16994e37i | −0.503938 | − | 0.464502i | ||||
\(94\) | −2.72815e36 | −0.0883973 | ||||||||
\(95\) | 2.34371e36i | 0.0621092i | ||||||||
\(96\) | −3.08267e37 | + | 3.34439e37i | −0.669536 | + | 0.726380i | ||||
\(97\) | 4.27060e37 | 0.761773 | 0.380887 | − | 0.924622i | \(-0.375619\pi\) | ||||
0.380887 | + | 0.924622i | \(0.375619\pi\) | |||||||
\(98\) | − | 3.08405e36i | − | 0.0452716i | ||||||
\(99\) | −1.63801e38 | + | 1.33626e37i | −1.98266 | + | 0.161742i | ||||
\(100\) | 7.07762e37 | 0.707762 | ||||||||
\(101\) | 1.73179e38i | 1.43347i | 0.697343 | + | 0.716737i | \(0.254365\pi\) | ||||
−0.697343 | + | 0.716737i | \(0.745635\pi\) | |||||||
\(102\) | −4.58790e37 | − | 4.22887e37i | −0.314928 | − | 0.290283i | ||||
\(103\) | 4.09091e37 | 0.233299 | 0.116649 | − | 0.993173i | \(-0.462785\pi\) | ||||
0.116649 | + | 0.993173i | \(0.462785\pi\) | |||||||
\(104\) | − | 1.77474e38i | − | 0.842366i | ||||||
\(105\) | −6.50388e37 | + | 7.05606e37i | −0.257381 | + | 0.279232i | ||||
\(106\) | 3.22934e37 | 0.106734 | ||||||||
\(107\) | 1.64293e38i | 0.454283i | 0.973862 | + | 0.227142i | \(0.0729380\pi\) | ||||
−0.973862 | + | 0.227142i | \(0.927062\pi\) | |||||||
\(108\) | 2.16302e38 | − | 2.76811e38i | 0.501198 | − | 0.641404i | ||||
\(109\) | 4.00261e38 | 0.778466 | 0.389233 | − | 0.921139i | \(-0.372740\pi\) | ||||
0.389233 | + | 0.921139i | \(0.372740\pi\) | |||||||
\(110\) | − | 1.89554e38i | − | 0.309937i | ||||||
\(111\) | −3.79627e38 | − | 3.49919e38i | −0.522662 | − | 0.481760i | ||||
\(112\) | 4.31492e38 | 0.500991 | ||||||||
\(113\) | − | 3.79863e38i | − | 0.372508i | −0.982502 | − | 0.186254i | \(-0.940365\pi\) | ||
0.982502 | − | 0.186254i | \(-0.0596348\pi\) | |||||||
\(114\) | 6.05818e37 | − | 6.57252e37i | 0.0502516 | − | 0.0545180i | ||||
\(115\) | −1.10721e38 | −0.0777982 | ||||||||
\(116\) | − | 1.12958e39i | − | 0.673310i | ||||||
\(117\) | 1.72891e38 | + | 2.11934e39i | 0.0875472 | + | 1.07317i | ||||
\(118\) | 1.17335e39 | 0.505441 | ||||||||
\(119\) | 2.84488e39i | 1.04393i | ||||||||
\(120\) | 6.63935e38 | + | 6.11978e38i | 0.207818 | + | 0.191555i | ||||
\(121\) | −1.10608e40 | −2.95709 | ||||||||
\(122\) | 2.84349e39i | 0.650152i | ||||||||
\(123\) | 1.99604e39 | − | 2.16550e39i | 0.390815 | − | 0.423995i | ||||
\(124\) | 3.32319e39 | 0.557883 | ||||||||
\(125\) | − | 4.68643e39i | − | 0.675386i | ||||||
\(126\) | 3.64779e39 | − | 2.97580e38i | 0.451845 | − | 0.0368607i | ||||
\(127\) | −6.98583e39 | −0.744641 | −0.372321 | − | 0.928104i | \(-0.621438\pi\) | ||||
−0.372321 | + | 0.928104i | \(0.621438\pi\) | |||||||
\(128\) | − | 1.09945e40i | − | 1.00968i | ||||||
\(129\) | 1.16601e40 | + | 1.07476e40i | 0.923628 | + | 0.851348i | ||||
\(130\) | −2.45255e39 | −0.167762 | ||||||||
\(131\) | 2.27888e40i | 1.34762i | 0.738906 | + | 0.673809i | \(0.235343\pi\) | ||||
−0.738906 | + | 0.673809i | \(0.764657\pi\) | |||||||
\(132\) | 2.14431e40 | − | 2.32636e40i | 1.09745 | − | 1.19062i | ||||
\(133\) | −4.07551e39 | −0.180718 | ||||||||
\(134\) | − | 1.68568e40i | − | 0.648311i | ||||||
\(135\) | −8.52468e39 | − | 6.66126e39i | −0.284667 | − | 0.222441i | ||||
\(136\) | 2.67688e40 | 0.776942 | ||||||||
\(137\) | − | 1.16139e40i | − | 0.293283i | −0.989190 | − | 0.146641i | \(-0.953154\pi\) | ||
0.989190 | − | 0.146641i | \(-0.0468464\pi\) | |||||||
\(138\) | 3.10496e39 | + | 2.86198e39i | 0.0682895 | + | 0.0629454i | ||||
\(139\) | −4.81953e40 | −0.924110 | −0.462055 | − | 0.886851i | \(-0.652888\pi\) | ||||
−0.462055 | + | 0.886851i | \(0.652888\pi\) | |||||||
\(140\) | − | 1.84741e40i | − | 0.309123i | ||||||
\(141\) | −9.50424e39 | + | 1.03112e40i | −0.138917 | + | 0.150711i | ||||
\(142\) | −6.10937e40 | −0.780761 | ||||||||
\(143\) | 1.91506e41i | 2.14189i | ||||||||
\(144\) | 3.95526e39 | + | 4.84843e40i | 0.0387514 | + | 0.475022i | ||||
\(145\) | −3.47866e40 | −0.298827 | ||||||||
\(146\) | − | 3.98964e40i | − | 0.300767i | ||||||
\(147\) | −1.16563e40 | − | 1.07441e40i | −0.0771846 | − | 0.0711444i | ||||
\(148\) | 9.93937e40 | 0.578610 | ||||||||
\(149\) | − | 2.78035e41i | − | 1.42416i | −0.702096 | − | 0.712082i | \(-0.747752\pi\) | ||
0.702096 | − | 0.712082i | \(-0.252248\pi\) | |||||||
\(150\) | −5.63405e40 | + | 6.11238e40i | −0.254148 | + | 0.275725i | ||||
\(151\) | 1.74842e41 | 0.695158 | 0.347579 | − | 0.937651i | \(-0.387004\pi\) | ||||
0.347579 | + | 0.937651i | \(0.387004\pi\) | |||||||
\(152\) | 3.83483e40i | 0.134499i | ||||||||
\(153\) | −3.19664e41 | + | 2.60776e40i | −0.989820 | + | 0.0807477i | ||||
\(154\) | 3.29619e41 | 0.901816 | ||||||||
\(155\) | − | 1.02341e41i | − | 0.247598i | ||||||
\(156\) | −3.00996e41 | − | 2.77441e41i | −0.644456 | − | 0.594024i | ||||
\(157\) | 8.83711e41 | 1.67578 | 0.837890 | − | 0.545840i | \(-0.183789\pi\) | ||||
0.837890 | + | 0.545840i | \(0.183789\pi\) | |||||||
\(158\) | − | 9.41255e39i | − | 0.0158206i | ||||||
\(159\) | 1.12503e41 | − | 1.22054e41i | 0.167733 | − | 0.181973i | ||||
\(160\) | −2.69658e41 | −0.356890 | ||||||||
\(161\) | − | 1.92534e41i | − | 0.226368i | ||||||
\(162\) | 6.68749e40 | + | 4.07155e41i | 0.0699001 | + | 0.425573i | ||||
\(163\) | −4.43978e41 | −0.412855 | −0.206427 | − | 0.978462i | \(-0.566184\pi\) | ||||
−0.206427 | + | 0.978462i | \(0.566184\pi\) | |||||||
\(164\) | 5.66969e41i | 0.469382i | ||||||||
\(165\) | −7.16429e41 | − | 6.60364e41i | −0.528418 | − | 0.487066i | ||||
\(166\) | −1.05462e41 | −0.0693495 | ||||||||
\(167\) | 2.19556e42i | 1.28805i | 0.765006 | + | 0.644023i | \(0.222736\pi\) | ||||
−0.765006 | + | 0.644023i | \(0.777264\pi\) | |||||||
\(168\) | −1.06418e42 | + | 1.15453e42i | −0.557362 | + | 0.604683i | ||||
\(169\) | 3.40580e41 | 0.159357 | ||||||||
\(170\) | − | 3.69923e41i | − | 0.154732i | ||||||
\(171\) | −3.73581e40 | − | 4.57943e41i | −0.0139784 | − | 0.171350i | ||||
\(172\) | −3.05283e42 | −1.02250 | ||||||||
\(173\) | − | 3.70657e42i | − | 1.11198i | −0.831189 | − | 0.555990i | \(-0.812339\pi\) | ||
0.831189 | − | 0.555990i | \(-0.187661\pi\) | |||||||
\(174\) | 9.75529e41 | + | 8.99188e41i | 0.262304 | + | 0.241777i | ||||
\(175\) | 3.79019e42 | 0.913982 | ||||||||
\(176\) | 4.38110e42i | 0.948074i | ||||||||
\(177\) | 4.08769e42 | − | 4.43474e42i | 0.794303 | − | 0.861739i | ||||
\(178\) | −3.26777e42 | −0.570521 | ||||||||
\(179\) | − | 5.09144e42i | − | 0.799159i | −0.916699 | − | 0.399579i | \(-0.869156\pi\) | ||
0.916699 | − | 0.399579i | \(-0.130844\pi\) | |||||||
\(180\) | 2.07583e42 | − | 1.69343e41i | 0.293100 | − | 0.0239105i | ||||
\(181\) | 3.83972e42 | 0.487985 | 0.243992 | − | 0.969777i | \(-0.421543\pi\) | ||||
0.243992 | + | 0.969777i | \(0.421543\pi\) | |||||||
\(182\) | − | 4.26476e42i | − | 0.488134i | ||||||
\(183\) | 1.07471e43 | + | 9.90606e42i | 1.10846 | + | 1.02172i | ||||
\(184\) | −1.81163e42 | −0.168474 | ||||||||
\(185\) | − | 3.06093e42i | − | 0.256798i | ||||||
\(186\) | −2.64538e42 | + | 2.86997e42i | −0.200328 | + | 0.217336i | ||||
\(187\) | −2.88852e43 | −1.97553 | ||||||||
\(188\) | − | 2.69966e42i | − | 0.166844i | ||||||
\(189\) | 1.15833e43 | − | 1.48237e43i | 0.647232 | − | 0.828289i | ||||
\(190\) | 5.29942e41 | 0.0267861 | ||||||||
\(191\) | 2.81633e43i | 1.28840i | 0.764858 | + | 0.644199i | \(0.222809\pi\) | ||||
−0.764858 | + | 0.644199i | \(0.777191\pi\) | |||||||
\(192\) | −8.97268e41 | − | 8.27051e41i | −0.0371705 | − | 0.0342617i | ||||
\(193\) | −1.91865e43 | −0.720124 | −0.360062 | − | 0.932928i | \(-0.617244\pi\) | ||||
−0.360062 | + | 0.932928i | \(0.617244\pi\) | |||||||
\(194\) | − | 9.65635e42i | − | 0.328534i | ||||||
\(195\) | −8.54410e42 | + | 9.26950e42i | −0.263638 | + | 0.286021i | ||||
\(196\) | 3.05184e42 | 0.0854469 | ||||||||
\(197\) | 5.56749e43i | 1.41514i | 0.706641 | + | 0.707572i | \(0.250210\pi\) | ||||
−0.706641 | + | 0.707572i | \(0.749790\pi\) | |||||||
\(198\) | 3.02145e42 | + | 3.70374e43i | 0.0697551 | + | 0.855071i | ||||
\(199\) | 3.53506e43 | 0.741631 | 0.370815 | − | 0.928707i | \(-0.379078\pi\) | ||||
0.370815 | + | 0.928707i | \(0.379078\pi\) | |||||||
\(200\) | − | 3.56635e43i | − | 0.680228i | ||||||
\(201\) | −6.37109e43 | − | 5.87251e43i | −1.10532 | − | 1.01882i | ||||
\(202\) | 3.91580e43 | 0.618222 | ||||||||
\(203\) | − | 6.04909e43i | − | 0.869492i | ||||||
\(204\) | 4.18471e43 | − | 4.53999e43i | 0.547888 | − | 0.594404i | ||||
\(205\) | 1.74604e43 | 0.208320 | ||||||||
\(206\) | − | 9.25005e42i | − | 0.100616i | ||||||
\(207\) | 2.16339e43 | − | 1.76486e42i | 0.214634 | − | 0.0175095i | ||||
\(208\) | 5.66848e43 | 0.513172 | ||||||||
\(209\) | − | 4.13802e43i | − | 0.341990i | ||||||
\(210\) | 1.59546e43 | + | 1.47061e43i | 0.120426 | + | 0.111002i | ||||
\(211\) | 1.99609e43 | 0.137662 | 0.0688311 | − | 0.997628i | \(-0.478073\pi\) | ||||
0.0688311 | + | 0.997628i | \(0.478073\pi\) | |||||||
\(212\) | 3.19561e43i | 0.201453i | ||||||||
\(213\) | −2.12836e44 | + | 2.30906e44i | −1.22697 | + | 1.33114i | ||||
\(214\) | 3.71487e43 | 0.195921 | ||||||||
\(215\) | 9.40153e43i | 0.453803i | ||||||||
\(216\) | −1.39483e44 | − | 1.08993e44i | −0.616451 | − | 0.481700i | ||||
\(217\) | 1.77962e44 | 0.720432 | ||||||||
\(218\) | − | 9.05039e43i | − | 0.335733i | ||||||
\(219\) | −1.50790e44 | − | 1.38990e44i | −0.512784 | − | 0.472656i | ||||
\(220\) | 1.87575e44 | 0.584983 | ||||||||
\(221\) | 3.73730e44i | 1.06931i | ||||||||
\(222\) | −7.91210e43 | + | 8.58384e43i | −0.207771 | + | 0.225411i | ||||
\(223\) | −6.72519e44 | −1.62148 | −0.810741 | − | 0.585406i | \(-0.800935\pi\) | ||||
−0.810741 | + | 0.585406i | \(0.800935\pi\) | |||||||
\(224\) | − | 4.68913e44i | − | 1.03844i | ||||||
\(225\) | 3.47427e43 | + | 4.25882e44i | 0.0706961 | + | 0.866606i | ||||
\(226\) | −8.58917e43 | −0.160654 | ||||||||
\(227\) | 3.07937e44i | 0.529628i | 0.964299 | + | 0.264814i | \(0.0853106\pi\) | ||||
−0.964299 | + | 0.264814i | \(0.914689\pi\) | |||||||
\(228\) | 6.50388e43 | + | 5.99491e43i | 0.102899 | + | 0.0948464i | ||||
\(229\) | 7.63372e44 | 1.11138 | 0.555690 | − | 0.831390i | \(-0.312454\pi\) | ||||
0.555690 | + | 0.831390i | \(0.312454\pi\) | |||||||
\(230\) | 2.50353e43i | 0.0335524i | ||||||||
\(231\) | 1.14832e45 | − | 1.24581e45i | 1.41721 | − | 1.53753i | ||||
\(232\) | −5.69186e44 | −0.647116 | ||||||||
\(233\) | − | 9.50715e44i | − | 0.996066i | −0.867158 | − | 0.498033i | \(-0.834056\pi\) | ||
0.867158 | − | 0.498033i | \(-0.165944\pi\) | |||||||
\(234\) | 4.79208e44 | − | 3.90929e43i | 0.462831 | − | 0.0377569i | ||||
\(235\) | −8.31389e43 | −0.0740482 | ||||||||
\(236\) | 1.16110e45i | 0.953984i | ||||||||
\(237\) | −3.55751e43 | − | 3.27911e43i | −0.0269729 | − | 0.0248621i | ||||
\(238\) | 6.43263e44 | 0.450222 | ||||||||
\(239\) | − | 1.64609e45i | − | 1.06388i | −0.846782 | − | 0.531940i | \(-0.821463\pi\) | ||
0.846782 | − | 0.531940i | \(-0.178537\pi\) | |||||||
\(240\) | −1.95465e44 | + | 2.12060e44i | −0.116696 | + | 0.126603i | ||||
\(241\) | −1.63494e45 | −0.901942 | −0.450971 | − | 0.892539i | \(-0.648922\pi\) | ||||
−0.450971 | + | 0.892539i | \(0.648922\pi\) | |||||||
\(242\) | 2.50099e45i | 1.27532i | ||||||||
\(243\) | 1.77183e45 | + | 1.16568e45i | 0.835418 | + | 0.549615i | ||||
\(244\) | −2.81379e45 | −1.22712 | ||||||||
\(245\) | − | 9.39846e43i | − | 0.0379229i | ||||||
\(246\) | −4.89646e44 | − | 4.51329e44i | −0.182859 | − | 0.168549i | ||||
\(247\) | −5.35397e44 | −0.185112 | ||||||||
\(248\) | − | 1.67453e45i | − | 0.536179i | ||||||
\(249\) | −3.67406e44 | + | 3.98599e44i | −0.108983 | + | 0.118236i | ||||
\(250\) | −1.05966e45 | −0.291277 | ||||||||
\(251\) | 5.46320e42i | 0.00139202i | 1.00000 | 0.000696012i | \(0.000221547\pi\) | |||||
−1.00000 | 0.000696012i | \(0.999778\pi\) | ||||||||
\(252\) | 2.94472e44 | + | 3.60970e45i | 0.0695720 | + | 0.852826i | ||||
\(253\) | 1.95487e45 | 0.428378 | ||||||||
\(254\) | 1.57958e45i | 0.321145i | ||||||||
\(255\) | −1.39814e45 | − | 1.28872e45i | −0.263807 | − | 0.243163i | ||||
\(256\) | −2.19738e45 | −0.384899 | ||||||||
\(257\) | 2.10252e45i | 0.341988i | 0.985272 | + | 0.170994i | \(0.0546978\pi\) | ||||
−0.985272 | + | 0.170994i | \(0.945302\pi\) | |||||||
\(258\) | 2.43017e45 | − | 2.63649e45i | 0.367166 | − | 0.398338i | ||||
\(259\) | 5.32270e45 | 0.747199 | ||||||||
\(260\) | − | 2.42693e45i | − | 0.316639i | ||||||
\(261\) | 6.79703e45 | − | 5.54489e44i | 0.824422 | − | 0.0672548i | ||||
\(262\) | 5.15283e45 | 0.581194 | ||||||||
\(263\) | − | 1.06476e46i | − | 1.11710i | −0.829471 | − | 0.558550i | \(-0.811358\pi\) | ||
0.829471 | − | 0.558550i | \(-0.188642\pi\) | |||||||
\(264\) | −1.17223e46 | − | 1.08050e46i | −1.14430 | − | 1.05475i | ||||
\(265\) | 9.84123e44 | 0.0894083 | ||||||||
\(266\) | 9.21524e44i | 0.0779391i | ||||||||
\(267\) | −1.13842e46 | + | 1.23507e46i | −0.896576 | + | 0.972696i | ||||
\(268\) | 1.66807e46 | 1.22364 | ||||||||
\(269\) | − | 2.91439e45i | − | 0.199184i | −0.995028 | − | 0.0995921i | \(-0.968246\pi\) | ||
0.995028 | − | 0.0995921i | \(-0.0317538\pi\) | |||||||
\(270\) | −1.50619e45 | + | 1.92754e45i | −0.0959332 | + | 0.122770i | ||||
\(271\) | 9.28598e45 | 0.551329 | 0.275665 | − | 0.961254i | \(-0.411102\pi\) | ||||
0.275665 | + | 0.961254i | \(0.411102\pi\) | |||||||
\(272\) | 8.54988e45i | 0.473316i | ||||||||
\(273\) | −1.61189e46 | − | 1.48575e46i | −0.832231 | − | 0.767104i | ||||
\(274\) | −2.62604e45 | −0.126486 | ||||||||
\(275\) | 3.84832e46i | 1.72962i | ||||||||
\(276\) | −2.83209e45 | + | 3.07254e45i | −0.118805 | + | 0.128892i | ||||
\(277\) | −1.19106e46 | −0.466462 | −0.233231 | − | 0.972421i | \(-0.574930\pi\) | ||||
−0.233231 | + | 0.972421i | \(0.574930\pi\) | |||||||
\(278\) | 1.08976e46i | 0.398546i | ||||||||
\(279\) | 1.63129e45 | + | 1.99967e46i | 0.0557252 | + | 0.683089i | ||||
\(280\) | −9.30895e45 | −0.297097 | ||||||||
\(281\) | − | 2.75232e46i | − | 0.820880i | −0.911888 | − | 0.410440i | \(-0.865375\pi\) | ||
0.911888 | − | 0.410440i | \(-0.134625\pi\) | |||||||
\(282\) | 2.33148e45 | + | 2.14903e45i | 0.0649978 | + | 0.0599113i | ||||
\(283\) | −4.47611e46 | −1.16670 | −0.583350 | − | 0.812221i | \(-0.698258\pi\) | ||||
−0.583350 | + | 0.812221i | \(0.698258\pi\) | |||||||
\(284\) | − | 6.04557e46i | − | 1.47363i | ||||||
\(285\) | 1.84620e45 | − | 2.00294e45i | 0.0420945 | − | 0.0456684i | ||||
\(286\) | 4.33018e46 | 0.923743 | ||||||||
\(287\) | 3.03622e46i | 0.606145i | ||||||||
\(288\) | 5.26891e46 | − | 4.29828e45i | 0.984609 | − | 0.0803226i | ||||
\(289\) | 7.85087e44 | 0.0137360 | ||||||||
\(290\) | 7.86569e45i | 0.128877i | ||||||||
\(291\) | −3.64966e46 | − | 3.36405e46i | −0.560126 | − | 0.516292i | ||||
\(292\) | 3.94797e46 | 0.567676 | ||||||||
\(293\) | − | 9.08247e45i | − | 0.122382i | −0.998126 | − | 0.0611912i | \(-0.980510\pi\) | ||
0.998126 | − | 0.0611912i | \(-0.0194899\pi\) | |||||||
\(294\) | −2.42938e45 | + | 2.63563e45i | −0.0306828 | + | 0.0332878i | ||||
\(295\) | 3.57573e46 | 0.423396 | ||||||||
\(296\) | − | 5.00836e46i | − | 0.556100i | ||||||
\(297\) | 1.50511e47 | + | 1.17610e47i | 1.56745 | + | 1.22482i | ||||
\(298\) | −6.28672e46 | −0.614207 | ||||||||
\(299\) | − | 2.52930e46i | − | 0.231872i | ||||||
\(300\) | −6.04855e46 | − | 5.57521e46i | −0.520412 | − | 0.479686i | ||||
\(301\) | −1.63484e47 | −1.32042 | ||||||||
\(302\) | − | 3.95339e46i | − | 0.299804i | ||||||
\(303\) | 1.36417e47 | − | 1.47999e47i | 0.971538 | − | 1.05402i | ||||
\(304\) | −1.22484e46 | −0.0819369 | ||||||||
\(305\) | 8.66538e46i | 0.544616i | ||||||||
\(306\) | 5.89647e45 | + | 7.22800e46i | 0.0348245 | + | 0.426885i | ||||
\(307\) | −2.10043e47 | −1.16595 | −0.582975 | − | 0.812490i | \(-0.698111\pi\) | ||||
−0.582975 | + | 0.812490i | \(0.698111\pi\) | |||||||
\(308\) | 3.26176e47i | 1.70211i | ||||||||
\(309\) | −3.49609e46 | − | 3.22250e46i | −0.171543 | − | 0.158118i | ||||
\(310\) | −2.31406e46 | −0.106783 | ||||||||
\(311\) | 1.38306e47i | 0.600334i | 0.953887 | + | 0.300167i | \(0.0970425\pi\) | ||||
−0.953887 | + | 0.300167i | \(0.902958\pi\) | |||||||
\(312\) | −1.39800e47 | + | 1.51669e47i | −0.570914 | + | 0.619385i | ||||
\(313\) | −4.51251e46 | −0.173411 | −0.0867053 | − | 0.996234i | \(-0.527634\pi\) | ||||
−0.0867053 | + | 0.996234i | \(0.527634\pi\) | |||||||
\(314\) | − | 1.99818e47i | − | 0.722722i | ||||||
\(315\) | 1.11164e47 | − | 9.06859e45i | 0.378500 | − | 0.0308773i | ||||
\(316\) | 9.31425e45 | 0.0298602 | ||||||||
\(317\) | − | 3.49554e47i | − | 1.05533i | −0.849453 | − | 0.527665i | \(-0.823068\pi\) | ||
0.849453 | − | 0.527665i | \(-0.176932\pi\) | |||||||
\(318\) | −2.75980e46 | − | 2.54383e46i | −0.0784805 | − | 0.0723390i | ||||
\(319\) | 6.14188e47 | 1.64543 | ||||||||
\(320\) | − | 7.23467e45i | − | 0.0182629i | ||||||
\(321\) | 1.29417e47 | − | 1.40405e47i | 0.307891 | − | 0.334031i | ||||
\(322\) | −4.35342e46 | −0.0976269 | ||||||||
\(323\) | − | 8.07551e46i | − | 0.170735i | ||||||
\(324\) | −4.02902e47 | + | 6.61765e46i | −0.803239 | + | 0.131931i | ||||
\(325\) | 4.97914e47 | 0.936204 | ||||||||
\(326\) | 1.00389e47i | 0.178054i | ||||||||
\(327\) | −3.42063e47 | − | 3.15295e47i | −0.572400 | − | 0.527606i | ||||
\(328\) | 2.85691e47 | 0.451121 | ||||||||
\(329\) | − | 1.44571e47i | − | 0.215457i | ||||||
\(330\) | −1.49316e47 | + | 1.61993e47i | −0.210060 | + | 0.227894i | ||||
\(331\) | −8.82926e46 | −0.117272 | −0.0586358 | − | 0.998279i | \(-0.518675\pi\) | ||||
−0.0586358 | + | 0.998279i | \(0.518675\pi\) | |||||||
\(332\) | − | 1.04361e47i | − | 0.130892i | ||||||
\(333\) | 4.87904e46 | + | 5.98082e47i | 0.0577955 | + | 0.708468i | ||||
\(334\) | 4.96442e47 | 0.555502 | ||||||||
\(335\) | − | 5.13701e47i | − | 0.543074i | ||||||
\(336\) | −3.68753e47 | − | 3.39896e47i | −0.368374 | − | 0.339547i | ||||
\(337\) | −4.55217e47 | −0.429784 | −0.214892 | − | 0.976638i | \(-0.568940\pi\) | ||||
−0.214892 | + | 0.976638i | \(0.568940\pi\) | |||||||
\(338\) | − | 7.70093e46i | − | 0.0687268i | ||||||
\(339\) | −2.99227e47 | + | 3.24631e47i | −0.252468 | + | 0.273902i | ||||
\(340\) | 3.66059e47 | 0.292047 | ||||||||
\(341\) | 1.80692e48i | 1.36335i | ||||||||
\(342\) | −1.03547e47 | + | 8.44714e45i | −0.0738992 | + | 0.00602856i | ||||
\(343\) | −1.39348e48 | −0.940833 | ||||||||
\(344\) | 1.53830e48i | 0.982720i | ||||||||
\(345\) | 9.46220e46 | + | 8.72173e46i | 0.0572044 | + | 0.0527278i | ||||
\(346\) | −8.38103e47 | −0.479569 | ||||||||
\(347\) | − | 9.80357e47i | − | 0.531036i | −0.964106 | − | 0.265518i | \(-0.914457\pi\) | ||
0.964106 | − | 0.265518i | \(-0.0855430\pi\) | |||||||
\(348\) | −8.89797e47 | + | 9.65341e47i | −0.456337 | + | 0.495080i | ||||
\(349\) | −1.86070e47 | −0.0903635 | −0.0451817 | − | 0.998979i | \(-0.514387\pi\) | ||||
−0.0451817 | + | 0.998979i | \(0.514387\pi\) | |||||||
\(350\) | − | 8.57008e47i | − | 0.394178i | ||||||
\(351\) | 1.52170e48 | − | 1.94738e48i | 0.662969 | − | 0.848428i | ||||
\(352\) | 4.76105e48 | 1.96513 | ||||||||
\(353\) | 2.13190e47i | 0.0833773i | 0.999131 | + | 0.0416886i | \(0.0132738\pi\) | ||||
−0.999131 | + | 0.0416886i | \(0.986726\pi\) | |||||||
\(354\) | −1.00275e48 | − | 9.24278e47i | −0.371647 | − | 0.342563i | ||||
\(355\) | −1.86180e48 | −0.654024 | ||||||||
\(356\) | − | 3.23365e48i | − | 1.07682i | ||||||
\(357\) | 2.24098e48 | − | 2.43124e48i | 0.707525 | − | 0.767594i | ||||
\(358\) | −1.15124e48 | −0.344657 | ||||||||
\(359\) | 2.43115e48i | 0.690267i | 0.938554 | + | 0.345133i | \(0.112166\pi\) | ||||
−0.938554 | + | 0.345133i | \(0.887834\pi\) | |||||||
\(360\) | −8.53303e46 | − | 1.04600e48i | −0.0229803 | − | 0.281697i | ||||
\(361\) | −3.79846e48 | −0.970444 | ||||||||
\(362\) | − | 8.68208e47i | − | 0.210456i | ||||||
\(363\) | 9.45258e48 | + | 8.71286e48i | 2.17433 | + | 2.00417i | ||||
\(364\) | 4.22023e48 | 0.921318 | ||||||||
\(365\) | − | 1.21582e48i | − | 0.251945i | ||||||
\(366\) | 2.23988e48 | − | 2.43005e48i | 0.440641 | − | 0.478051i | ||||
\(367\) | −9.76811e48 | −1.82455 | −0.912274 | − | 0.409580i | \(-0.865675\pi\) | ||||
−0.912274 | + | 0.409580i | \(0.865675\pi\) | |||||||
\(368\) | − | 5.78632e47i | − | 0.102635i | ||||||
\(369\) | −3.41163e48 | + | 2.78314e47i | −0.574726 | + | 0.0468851i | ||||
\(370\) | −6.92115e47 | −0.110750 | ||||||||
\(371\) | 1.71131e48i | 0.260150i | ||||||||
\(372\) | −2.84000e48 | − | 2.61775e48i | −0.410207 | − | 0.378106i | ||||
\(373\) | 6.19042e47 | 0.0849674 | 0.0424837 | − | 0.999097i | \(-0.486473\pi\) | ||||
0.0424837 | + | 0.999097i | \(0.486473\pi\) | |||||||
\(374\) | 6.53130e48i | 0.851999i | ||||||||
\(375\) | −3.69161e48 | + | 4.00503e48i | −0.457743 | + | 0.496606i | ||||
\(376\) | −1.36033e48 | −0.160353 | ||||||||
\(377\) | − | 7.94665e48i | − | 0.890633i | ||||||
\(378\) | −3.35182e48 | − | 2.61914e48i | −0.357220 | − | 0.279135i | ||||
\(379\) | −6.49689e48 | −0.658507 | −0.329254 | − | 0.944242i | \(-0.606797\pi\) | ||||
−0.329254 | + | 0.944242i | \(0.606797\pi\) | |||||||
\(380\) | 5.24408e47i | 0.0505570i | ||||||||
\(381\) | 5.97010e48 | + | 5.50290e48i | 0.547529 | + | 0.504681i | ||||
\(382\) | 6.36808e48 | 0.555654 | ||||||||
\(383\) | 6.98738e48i | 0.580147i | 0.957004 | + | 0.290073i | \(0.0936797\pi\) | ||||
−0.957004 | + | 0.290073i | \(0.906320\pi\) | |||||||
\(384\) | −8.66060e48 | + | 9.39588e48i | −0.684313 | + | 0.742411i | ||||
\(385\) | 1.00449e49 | 0.755429 | ||||||||
\(386\) | 4.33831e48i | 0.310572i | ||||||||
\(387\) | −1.49858e48 | − | 1.83698e49i | −0.102134 | − | 1.25198i | ||||
\(388\) | 9.55551e48 | 0.620085 | ||||||||
\(389\) | − | 8.22924e48i | − | 0.508531i | −0.967134 | − | 0.254266i | \(-0.918166\pi\) | ||
0.967134 | − | 0.254266i | \(-0.0818337\pi\) | |||||||
\(390\) | 2.09595e48 | + | 1.93193e48i | 0.123354 | + | 0.113701i | ||||
\(391\) | 3.81500e48 | 0.213863 | ||||||||
\(392\) | − | 1.53779e48i | − | 0.0821227i | ||||||
\(393\) | 1.79513e49 | − | 1.94753e49i | 0.913349 | − | 0.990892i | ||||
\(394\) | 1.25888e49 | 0.610317 | ||||||||
\(395\) | − | 2.86842e47i | − | 0.0132525i | ||||||
\(396\) | −3.66506e49 | + | 2.98989e48i | −1.61389 | + | 0.131658i | ||||
\(397\) | −1.02385e47 | −0.00429749 | −0.00214875 | − | 0.999998i | \(-0.500684\pi\) | ||||
−0.00214875 | + | 0.999998i | \(0.500684\pi\) | |||||||
\(398\) | − | 7.99320e48i | − | 0.319847i | ||||||
\(399\) | 3.48294e48 | + | 3.21038e48i | 0.132880 | + | 0.122482i | ||||
\(400\) | 1.13909e49 | 0.414397 | ||||||||
\(401\) | − | 4.44850e49i | − | 1.54337i | −0.636004 | − | 0.771686i | \(-0.719414\pi\) | ||
0.636004 | − | 0.771686i | \(-0.280586\pi\) | |||||||
\(402\) | −1.32785e49 | + | 1.44058e49i | −0.439393 | + | 0.476698i | ||||
\(403\) | 2.33788e49 | 0.737949 | ||||||||
\(404\) | 3.87491e49i | 1.16685i | ||||||||
\(405\) | 2.03798e48 | + | 1.24078e49i | 0.0585536 | + | 0.356492i | ||||
\(406\) | −1.36778e49 | −0.374990 | ||||||||
\(407\) | 5.40434e49i | 1.41400i | ||||||||
\(408\) | −2.28766e49 | − | 2.10864e49i | −0.571279 | − | 0.526573i | ||||
\(409\) | −4.50122e49 | −1.07297 | −0.536484 | − | 0.843910i | \(-0.680248\pi\) | ||||
−0.536484 | + | 0.843910i | \(0.680248\pi\) | |||||||
\(410\) | − | 3.94802e48i | − | 0.0898434i | ||||||
\(411\) | −9.14853e48 | + | 9.92524e48i | −0.198773 | + | 0.215649i | ||||
\(412\) | 9.15345e48 | 0.189906 | ||||||||
\(413\) | 6.21788e49i | 1.23195i | ||||||||
\(414\) | −3.99056e47 | − | 4.89170e48i | −0.00755140 | − | 0.0925665i | ||||
\(415\) | −3.21391e48 | −0.0580924 | ||||||||
\(416\) | − | 6.16008e49i | − | 1.06368i | ||||||
\(417\) | 4.11878e49 | + | 3.79646e49i | 0.679491 | + | 0.626316i | ||||
\(418\) | −9.35659e48 | −0.147492 | ||||||||
\(419\) | − | 1.20666e50i | − | 1.81768i | −0.417140 | − | 0.908842i | \(-0.636967\pi\) | ||
0.417140 | − | 0.908842i | \(-0.363033\pi\) | |||||||
\(420\) | −1.45525e49 | + | 1.57880e49i | −0.209508 | + | 0.227295i | ||||
\(421\) | 8.94542e48 | 0.123095 | 0.0615475 | − | 0.998104i | \(-0.480396\pi\) | ||||
0.0615475 | + | 0.998104i | \(0.480396\pi\) | |||||||
\(422\) | − | 4.51342e48i | − | 0.0593703i | ||||||
\(423\) | 1.62447e49 | − | 1.32521e48i | 0.204289 | − | 0.0166655i | ||||
\(424\) | 1.61024e49 | 0.193615 | ||||||||
\(425\) | 7.51015e49i | 0.863493i | ||||||||
\(426\) | 5.22108e49 | + | 4.81250e49i | 0.574087 | + | 0.529161i | ||||
\(427\) | −1.50683e50 | −1.58466 | ||||||||
\(428\) | 3.67607e49i | 0.369787i | ||||||||
\(429\) | 1.50853e50 | − | 1.63661e50i | 1.45167 | − | 1.57491i | ||||
\(430\) | 2.12580e49 | 0.195714 | ||||||||
\(431\) | − | 5.54855e49i | − | 0.488778i | −0.969677 | − | 0.244389i | \(-0.921413\pi\) | ||
0.969677 | − | 0.244389i | \(-0.0785874\pi\) | |||||||
\(432\) | 3.48121e49 | − | 4.45504e49i | 0.293453 | − | 0.375544i | ||||
\(433\) | −9.80377e48 | −0.0790903 | −0.0395451 | − | 0.999218i | \(-0.512591\pi\) | ||||
−0.0395451 | + | 0.999218i | \(0.512591\pi\) | |||||||
\(434\) | − | 4.02395e49i | − | 0.310705i | ||||||
\(435\) | 2.97287e49 | + | 2.74022e49i | 0.219725 | + | 0.202530i | ||||
\(436\) | 8.95588e49 | 0.633672 | ||||||||
\(437\) | 5.46528e48i | 0.0370224i | ||||||||
\(438\) | −3.14273e49 | + | 3.40955e49i | −0.203845 | + | 0.221151i | ||||
\(439\) | −1.14042e50 | −0.708336 | −0.354168 | − | 0.935182i | \(-0.615236\pi\) | ||||
−0.354168 | + | 0.935182i | \(0.615236\pi\) | |||||||
\(440\) | − | 9.45173e49i | − | 0.562225i | ||||||
\(441\) | 1.49809e48 | + | 1.83638e49i | 0.00853502 | + | 0.104624i | ||||
\(442\) | 8.45051e49 | 0.461169 | ||||||||
\(443\) | 2.75252e50i | 1.43900i | 0.694494 | + | 0.719499i | \(0.255628\pi\) | ||||
−0.694494 | + | 0.719499i | \(0.744372\pi\) | |||||||
\(444\) | −8.49420e49 | − | 7.82947e49i | −0.425447 | − | 0.392153i | ||||
\(445\) | −9.95836e49 | −0.477912 | ||||||||
\(446\) | 1.52065e50i | 0.699305i | ||||||||
\(447\) | −2.19015e50 | + | 2.37609e50i | −0.965229 | + | 1.04718i | ||||
\(448\) | 1.25805e49 | 0.0531392 | ||||||||
\(449\) | 4.10948e49i | 0.166382i | 0.996534 | + | 0.0831910i | \(0.0265112\pi\) | ||||
−0.996534 | + | 0.0831910i | \(0.973489\pi\) | |||||||
\(450\) | 9.62973e49 | − | 7.85575e48i | 0.373746 | − | 0.0304895i | ||||
\(451\) | −3.08279e50 | −1.14707 | ||||||||
\(452\) | − | 8.49947e49i | − | 0.303223i | ||||||
\(453\) | −1.49420e50 | − | 1.37727e50i | −0.511144 | − | 0.471144i | ||||
\(454\) | 6.96285e49 | 0.228416 | ||||||||
\(455\) | − | 1.29966e50i | − | 0.408897i | ||||||
\(456\) | 3.02078e49 | − | 3.27725e49i | 0.0911565 | − | 0.0988957i | ||||
\(457\) | 3.29920e50 | 0.954993 | 0.477497 | − | 0.878634i | \(-0.341544\pi\) | ||||
0.477497 | + | 0.878634i | \(0.341544\pi\) | |||||||
\(458\) | − | 1.72608e50i | − | 0.479310i | ||||||
\(459\) | 2.93727e50 | + | 2.29521e50i | 0.782533 | + | 0.611478i | ||||
\(460\) | −2.47739e49 | −0.0633279 | ||||||||
\(461\) | − | 2.19869e50i | − | 0.539319i | −0.962956 | − | 0.269660i | \(-0.913089\pi\) | ||
0.962956 | − | 0.269660i | \(-0.0869112\pi\) | |||||||
\(462\) | −2.81693e50 | − | 2.59648e50i | −0.663098 | − | 0.611207i | ||||
\(463\) | 4.94759e50 | 1.11778 | 0.558888 | − | 0.829243i | \(-0.311228\pi\) | ||||
0.558888 | + | 0.829243i | \(0.311228\pi\) | |||||||
\(464\) | − | 1.81797e50i | − | 0.394225i | ||||||
\(465\) | −8.06165e49 | + | 8.74609e49i | −0.167810 | + | 0.182057i | ||||
\(466\) | −2.14969e50 | −0.429578 | ||||||||
\(467\) | 8.34023e50i | 1.60014i | 0.599908 | + | 0.800069i | \(0.295204\pi\) | ||||
−0.599908 | + | 0.800069i | \(0.704796\pi\) | |||||||
\(468\) | 3.86846e49 | + | 4.74204e50i | 0.0712635 | + | 0.873562i | ||||
\(469\) | 8.93281e50 | 1.58017 | ||||||||
\(470\) | 1.87987e49i | 0.0319352i | ||||||||
\(471\) | −7.55220e50 | − | 6.96120e50i | −1.23219 | − | 1.13576i | ||||
\(472\) | 5.85068e50 | 0.916871 | ||||||||
\(473\) | − | 1.65992e51i | − | 2.49877i | ||||||
\(474\) | −7.41449e48 | + | 8.04398e48i | −0.0107224 | + | 0.0116327i | ||||
\(475\) | −1.07589e50 | −0.149482 | ||||||||
\(476\) | 6.36546e50i | 0.849762i | ||||||||
\(477\) | −1.92290e50 | + | 1.56867e49i | −0.246665 | + | 0.0201225i | ||||
\(478\) | −3.72201e50 | −0.458826 | ||||||||
\(479\) | 1.93838e50i | 0.229649i | 0.993386 | + | 0.114824i | \(0.0366306\pi\) | ||||
−0.993386 | + | 0.114824i | \(0.963369\pi\) | |||||||
\(480\) | 2.30450e50 | + | 2.12416e50i | 0.262418 | + | 0.241882i | ||||
\(481\) | 6.99239e50 | 0.765366 | ||||||||
\(482\) | 3.69681e50i | 0.388985i | ||||||||
\(483\) | −1.51663e50 | + | 1.64539e50i | −0.153421 | + | 0.166446i | ||||
\(484\) | −2.47487e51 | −2.40708 | ||||||||
\(485\) | − | 2.94272e50i | − | 0.275205i | ||||||
\(486\) | 2.63574e50 | − | 4.00634e50i | 0.237035 | − | 0.360295i | ||||
\(487\) | −7.70368e50 | −0.666267 | −0.333133 | − | 0.942880i | \(-0.608106\pi\) | ||||
−0.333133 | + | 0.942880i | \(0.608106\pi\) | |||||||
\(488\) | 1.41785e51i | 1.17938i | ||||||||
\(489\) | 3.79424e50 | + | 3.49732e50i | 0.303569 | + | 0.279813i | ||||
\(490\) | −2.12511e49 | −0.0163552 | ||||||||
\(491\) | 2.08113e51i | 1.54081i | 0.637552 | + | 0.770407i | \(0.279947\pi\) | ||||
−0.637552 | + | 0.770407i | \(0.720053\pi\) | |||||||
\(492\) | 4.46615e50 | − | 4.84533e50i | 0.318124 | − | 0.345133i | ||||
\(493\) | 1.19861e51 | 0.821460 | ||||||||
\(494\) | 1.21060e50i | 0.0798341i | ||||||||
\(495\) | 9.20769e49 | + | 1.12870e51i | 0.0584321 | + | 0.716272i | ||||
\(496\) | 5.34840e50 | 0.326642 | ||||||||
\(497\) | − | 3.23750e51i | − | 1.90300i | ||||||
\(498\) | 9.01282e49 | + | 8.30751e49i | 0.0509921 | + | 0.0470017i | ||||
\(499\) | −3.02207e51 | −1.64586 | −0.822932 | − | 0.568140i | \(-0.807663\pi\) | ||||
−0.822932 | + | 0.568140i | \(0.807663\pi\) | |||||||
\(500\) | − | 1.04859e51i | − | 0.549766i | ||||||
\(501\) | 1.72949e51 | − | 1.87632e51i | 0.872974 | − | 0.947090i | ||||
\(502\) | 1.23530e48 | 0.000600345 | ||||||||
\(503\) | − | 2.14049e50i | − | 0.100166i | −0.998745 | − | 0.0500831i | \(-0.984051\pi\) | ||
0.998745 | − | 0.0500831i | \(-0.0159486\pi\) | |||||||
\(504\) | 1.81889e51 | − | 1.48382e50i | 0.819648 | − | 0.0668654i | ||||
\(505\) | 1.19332e51 | 0.517869 | ||||||||
\(506\) | − | 4.42020e50i | − | 0.184749i | ||||||
\(507\) | −2.91060e50 | − | 2.68283e50i | −0.117174 | − | 0.108004i | ||||
\(508\) | −1.56309e51 | −0.606139 | ||||||||
\(509\) | 1.75144e51i | 0.654272i | 0.944977 | + | 0.327136i | \(0.106083\pi\) | ||||
−0.944977 | + | 0.327136i | \(0.893917\pi\) | |||||||
\(510\) | −2.91397e50 | + | 3.16136e50i | −0.104870 | + | 0.113773i | ||||
\(511\) | 2.11421e51 | 0.733078 | ||||||||
\(512\) | − | 2.52528e51i | − | 0.843685i | ||||||
\(513\) | −3.28806e50 | + | 4.20786e50i | −0.105855 | + | 0.135466i | ||||
\(514\) | 4.75406e50 | 0.147491 | ||||||||
\(515\) | − | 2.81890e50i | − | 0.0842835i | ||||||
\(516\) | 2.60896e51 | + | 2.40479e51i | 0.751835 | + | 0.692999i | ||||
\(517\) | 1.46789e51 | 0.407730 | ||||||||
\(518\) | − | 1.20353e51i | − | 0.322249i | ||||||
\(519\) | −2.91976e51 | + | 3.16764e51i | −0.753645 | + | 0.817629i | ||||
\(520\) | −1.22291e51 | −0.304320 | ||||||||
\(521\) | 5.56561e50i | 0.133535i | 0.997769 | + | 0.0667676i | \(0.0212686\pi\) | ||||
−0.997769 | + | 0.0667676i | \(0.978731\pi\) | |||||||
\(522\) | −1.25377e50 | − | 1.53689e51i | −0.0290054 | − | 0.355553i | ||||
\(523\) | −5.01335e51 | −1.11840 | −0.559198 | − | 0.829034i | \(-0.688891\pi\) | ||||
−0.559198 | + | 0.829034i | \(0.688891\pi\) | |||||||
\(524\) | 5.09902e51i | 1.09696i | ||||||||
\(525\) | −3.23910e51 | − | 2.98562e51i | −0.672043 | − | 0.619452i | ||||
\(526\) | −2.40755e51 | −0.481778 | ||||||||
\(527\) | 3.52627e51i | 0.680635i | ||||||||
\(528\) | 3.45109e51 | − | 3.74409e51i | 0.642558 | − | 0.697111i | ||||
\(529\) | 5.30928e51 | 0.953626 | ||||||||
\(530\) | − | 2.22523e50i | − | 0.0385596i | ||||||
\(531\) | −6.98669e51 | + | 5.69961e50i | −1.16809 | + | 0.0952905i | ||||
\(532\) | −9.11900e50 | −0.147105 | ||||||||
\(533\) | 3.98866e51i | 0.620883i | ||||||||
\(534\) | 2.79264e51 | + | 2.57410e51i | 0.419500 | + | 0.386671i | ||||
\(535\) | 1.13208e51 | 0.164118 | ||||||||
\(536\) | − | 8.40527e51i | − | 1.17604i | ||||||
\(537\) | −4.01065e51 | + | 4.35115e51i | −0.541630 | + | 0.587615i | ||||
\(538\) | −6.58981e50 | −0.0859033 | ||||||||
\(539\) | 1.65938e51i | 0.208814i | ||||||||
\(540\) | −1.90741e51 | − | 1.49046e51i | −0.231719 | − | 0.181067i | ||||
\(541\) | 6.87237e51 | 0.806044 | 0.403022 | − | 0.915190i | \(-0.367960\pi\) | ||||
0.403022 | + | 0.915190i | \(0.367960\pi\) | |||||||
\(542\) | − | 2.09968e51i | − | 0.237775i | ||||||
\(543\) | −3.28143e51 | − | 3.02464e51i | −0.358811 | − | 0.330732i | ||||
\(544\) | 9.29137e51 | 0.981072 | ||||||||
\(545\) | − | 2.75806e51i | − | 0.281235i | ||||||
\(546\) | −3.35946e51 | + | 3.64467e51i | −0.330833 | + | 0.358921i | ||||
\(547\) | 1.32047e52 | 1.25594 | 0.627970 | − | 0.778237i | \(-0.283886\pi\) | ||||
0.627970 | + | 0.778237i | \(0.283886\pi\) | |||||||
\(548\) | − | 2.59862e51i | − | 0.238733i | ||||||
\(549\) | −1.38124e51 | − | 1.69315e52i | −0.122573 | − | 1.50252i | ||||
\(550\) | 8.70153e51 | 0.745941 | ||||||||
\(551\) | 1.71710e51i | 0.142205i | ||||||||
\(552\) | 1.54822e51 | + | 1.42707e51i | 0.123877 | + | 0.114183i | ||||
\(553\) | 4.98794e50 | 0.0385606 | ||||||||
\(554\) | 2.69312e51i | 0.201174i | ||||||||
\(555\) | −2.41117e51 | + | 2.61588e51i | −0.174045 | + | 0.188821i | ||||
\(556\) | −1.07838e52 | −0.752227 | ||||||||
\(557\) | − | 6.23704e51i | − | 0.420465i | −0.977651 | − | 0.210233i | \(-0.932578\pi\) | ||
0.977651 | − | 0.210233i | \(-0.0674221\pi\) | |||||||
\(558\) | 4.52149e51 | − | 3.68855e50i | 0.294599 | − | 0.0240329i | ||||
\(559\) | −2.14768e52 | −1.35253 | ||||||||
\(560\) | − | 2.97326e51i | − | 0.180992i | ||||||
\(561\) | 2.46853e52 | + | 2.27535e52i | 1.45259 | + | 1.33892i | ||||
\(562\) | −6.22335e51 | −0.354025 | ||||||||
\(563\) | 1.16923e52i | 0.643043i | 0.946902 | + | 0.321522i | \(0.104194\pi\) | ||||
−0.946902 | + | 0.321522i | \(0.895806\pi\) | |||||||
\(564\) | −2.12658e51 | + | 2.30713e51i | −0.113078 | + | 0.122679i | ||||
\(565\) | −2.61750e51 | −0.134576 | ||||||||
\(566\) | 1.01211e52i | 0.503168i | ||||||||
\(567\) | −2.15761e52 | + | 3.54386e51i | −1.03728 | + | 0.170372i | ||||
\(568\) | −3.04631e52 | −1.41630 | ||||||||
\(569\) | − | 3.70607e52i | − | 1.66641i | −0.552968 | − | 0.833203i | \(-0.686505\pi\) | ||
0.552968 | − | 0.833203i | \(-0.313495\pi\) | |||||||
\(570\) | −4.52889e50 | − | 4.17448e50i | −0.0196956 | − | 0.0181543i | ||||
\(571\) | −1.98355e51 | −0.0834367 | −0.0417184 | − | 0.999129i | \(-0.513283\pi\) | ||||
−0.0417184 | + | 0.999129i | \(0.513283\pi\) | |||||||
\(572\) | 4.28496e52i | 1.74350i | ||||||||
\(573\) | 2.21849e52 | − | 2.40684e52i | 0.873213 | − | 0.947349i | ||||
\(574\) | 6.86526e51 | 0.261416 | ||||||||
\(575\) | − | 5.08265e51i | − | 0.187241i | ||||||
\(576\) | 1.15319e50 | + | 1.41360e51i | 0.00411029 | + | 0.0503847i | ||||
\(577\) | 1.96715e52 | 0.678417 | 0.339209 | − | 0.940711i | \(-0.389841\pi\) | ||||
0.339209 | + | 0.940711i | \(0.389841\pi\) | |||||||
\(578\) | − | 1.77518e50i | − | 0.00592398i | ||||||
\(579\) | 1.63968e52 | + | 1.51137e52i | 0.529501 | + | 0.488065i | ||||
\(580\) | −7.78355e51 | −0.243246 | ||||||||
\(581\) | − | 5.58870e51i | − | 0.169030i | ||||||
\(582\) | −7.60654e51 | + | 8.25233e51i | −0.222664 | + | 0.241568i | ||||
\(583\) | −1.73755e52 | −0.492307 | ||||||||
\(584\) | − | 1.98935e52i | − | 0.545591i | ||||||
\(585\) | 1.46036e52 | − | 1.19133e51i | 0.387702 | − | 0.0316280i | ||||
\(586\) | −2.05366e51 | −0.0527805 | ||||||||
\(587\) | 4.11855e52i | 1.02476i | 0.858760 | + | 0.512379i | \(0.171236\pi\) | ||||
−0.858760 | + | 0.512379i | \(0.828764\pi\) | |||||||
\(588\) | −2.60810e51 | − | 2.40400e51i | −0.0628284 | − | 0.0579117i | ||||
\(589\) | −5.05166e51 | −0.117827 | ||||||||
\(590\) | − | 8.08517e51i | − | 0.182600i | ||||||
\(591\) | 4.38564e52 | − | 4.75798e52i | 0.959115 | − | 1.04054i | ||||
\(592\) | 1.59966e52 | 0.338778 | ||||||||
\(593\) | − | 3.40678e52i | − | 0.698724i | −0.936988 | − | 0.349362i | \(-0.886398\pi\) | ||
0.936988 | − | 0.349362i | \(-0.113602\pi\) | |||||||
\(594\) | 2.65931e52 | − | 3.40323e52i | 0.528235 | − | 0.676003i | ||||
\(595\) | 1.96031e52 | 0.377140 | ||||||||
\(596\) | − | 6.22106e52i | − | 1.15927i | ||||||
\(597\) | −3.02106e52 | − | 2.78465e52i | −0.545315 | − | 0.502641i | ||||
\(598\) | −5.71907e51 | −0.100001 | ||||||||
\(599\) | 1.29821e52i | 0.219904i | 0.993937 | + | 0.109952i | \(0.0350698\pi\) | ||||
−0.993937 | + | 0.109952i | \(0.964930\pi\) | |||||||
\(600\) | −2.80930e52 | + | 3.04781e52i | −0.461025 | + | 0.500166i | ||||
\(601\) | −2.33958e52 | −0.371983 | −0.185992 | − | 0.982551i | \(-0.559550\pi\) | ||||
−0.185992 | + | 0.982551i | \(0.559550\pi\) | |||||||
\(602\) | 3.69659e52i | 0.569466i | ||||||||
\(603\) | 8.18825e51 | + | 1.00373e53i | 0.122226 | + | 1.49826i | ||||
\(604\) | 3.91210e52 | 0.565860 | ||||||||
\(605\) | 7.62162e52i | 1.06830i | ||||||||
\(606\) | −3.34645e52 | − | 3.08457e52i | −0.454574 | − | 0.419000i | ||||
\(607\) | −2.92954e52 | −0.385668 | −0.192834 | − | 0.981231i | \(-0.561768\pi\) | ||||
−0.192834 | + | 0.981231i | \(0.561768\pi\) | |||||||
\(608\) | 1.33106e52i | 0.169836i | ||||||||
\(609\) | −4.76501e52 | + | 5.16956e52i | −0.589299 | + | 0.639330i | ||||
\(610\) | 1.95935e52 | 0.234879 | ||||||||
\(611\) | − | 1.89922e52i | − | 0.220695i | ||||||
\(612\) | −7.15251e52 | + | 5.83489e51i | −0.805715 | + | 0.0657288i | ||||
\(613\) | −1.95347e52 | −0.213332 | −0.106666 | − | 0.994295i | \(-0.534018\pi\) | ||||
−0.106666 | + | 0.994295i | \(0.534018\pi\) | |||||||
\(614\) | 4.74934e52i | 0.502845i | ||||||||
\(615\) | −1.49217e52 | − | 1.37540e52i | −0.153176 | − | 0.141189i | ||||
\(616\) | 1.64357e53 | 1.63590 | ||||||||
\(617\) | − | 2.89268e52i | − | 0.279179i | −0.990209 | − | 0.139589i | \(-0.955422\pi\) | ||
0.990209 | − | 0.139589i | \(-0.0445783\pi\) | |||||||
\(618\) | −7.28648e51 | + | 7.90510e51i | −0.0681925 | + | 0.0739821i | ||||
\(619\) | −1.54732e53 | −1.40430 | −0.702148 | − | 0.712031i | \(-0.747776\pi\) | ||||
−0.702148 | + | 0.712031i | \(0.747776\pi\) | |||||||
\(620\) | − | 2.28989e52i | − | 0.201546i | ||||||
\(621\) | −1.98786e52 | − | 1.55333e52i | −0.169686 | − | 0.132594i | ||||
\(622\) | 3.12727e52 | 0.258909 | ||||||||
\(623\) | − | 1.73167e53i | − | 1.39057i | ||||||
\(624\) | −4.84429e52 | − | 4.46519e52i | −0.377331 | − | 0.347803i | ||||
\(625\) | 8.27828e52 | 0.625489 | ||||||||
\(626\) | 1.02033e52i | 0.0747877i | ||||||||
\(627\) | −3.25962e52 | + | 3.53636e52i | −0.231784 | + | 0.251462i | ||||
\(628\) | 1.97731e53 | 1.36409 | ||||||||
\(629\) | 1.05468e53i | 0.705923i | ||||||||
\(630\) | −2.05052e51 | − | 2.51357e52i | −0.0133166 | − | 0.163238i | ||||
\(631\) | 3.10238e52 | 0.195496 | 0.0977478 | − | 0.995211i | \(-0.468836\pi\) | ||||
0.0977478 | + | 0.995211i | \(0.468836\pi\) | |||||||
\(632\) | − | 4.69337e51i | − | 0.0286986i | ||||||
\(633\) | −1.70586e52 | − | 1.57237e52i | −0.101222 | − | 0.0933006i | ||||
\(634\) | −7.90385e52 | −0.455138 | ||||||||
\(635\) | 4.81369e52i | 0.269016i | ||||||||
\(636\) | 2.51726e52 | − | 2.73098e52i | 0.136535 | − | 0.148126i | ||||
\(637\) | 2.14698e52 | 0.113026 | ||||||||
\(638\) | − | 1.38875e53i | − | 0.709631i | ||||||
\(639\) | 3.63780e53 | − | 2.96765e52i | 1.80436 | − | 0.147196i | ||||
\(640\) | −7.57590e52 | −0.364766 | ||||||||
\(641\) | 9.53340e52i | 0.445600i | 0.974864 | + | 0.222800i | \(0.0715197\pi\) | ||||
−0.974864 | + | 0.222800i | \(0.928480\pi\) | |||||||
\(642\) | −3.17473e52 | − | 2.92629e52i | −0.144059 | − | 0.132786i | ||||
\(643\) | 9.32636e52 | 0.410869 | 0.205435 | − | 0.978671i | \(-0.434139\pi\) | ||||
0.205435 | + | 0.978671i | \(0.434139\pi\) | |||||||
\(644\) | − | 4.30796e52i | − | 0.184264i | ||||||
\(645\) | 7.40580e52 | − | 8.03456e52i | 0.307565 | − | 0.333678i | ||||
\(646\) | −1.82597e52 | −0.0736337 | ||||||||
\(647\) | − | 7.58255e52i | − | 0.296916i | −0.988919 | − | 0.148458i | \(-0.952569\pi\) | ||
0.988919 | − | 0.148458i | \(-0.0474310\pi\) | |||||||
\(648\) | 3.33458e52 | + | 2.03019e53i | 0.126799 | + | 0.771990i | ||||
\(649\) | −6.31326e53 | −2.33133 | ||||||||
\(650\) | − | 1.12585e53i | − | 0.403762i | ||||||
\(651\) | −1.52087e53 | − | 1.40185e53i | −0.529728 | − | 0.488274i | ||||
\(652\) | −9.93406e52 | −0.336064 | ||||||||
\(653\) | 4.34569e53i | 1.42794i | 0.700178 | + | 0.713968i | \(0.253104\pi\) | ||||
−0.700178 | + | 0.713968i | \(0.746896\pi\) | |||||||
\(654\) | −7.12921e52 | + | 7.73448e52i | −0.227543 | + | 0.246862i | ||||
\(655\) | 1.57030e53 | 0.486852 | ||||||||
\(656\) | 9.12491e52i | 0.274825i | ||||||||
\(657\) | 1.93799e52 | + | 2.37562e53i | 0.0567033 | + | 0.695080i | ||||
\(658\) | −3.26894e52 | −0.0929211 | ||||||||
\(659\) | 1.35861e53i | 0.375207i | 0.982245 | + | 0.187603i | \(0.0600720\pi\) | ||||
−0.982245 | + | 0.187603i | \(0.939928\pi\) | |||||||
\(660\) | −1.60302e53 | − | 1.47757e53i | −0.430134 | − | 0.396473i | ||||
\(661\) | −1.47594e53 | −0.384805 | −0.192402 | − | 0.981316i | \(-0.561628\pi\) | ||||
−0.192402 | + | 0.981316i | \(0.561628\pi\) | |||||||
\(662\) | 1.99641e52i | 0.0505763i | ||||||||
\(663\) | 2.94396e53 | − | 3.19390e53i | 0.724728 | − | 0.786258i | ||||
\(664\) | −5.25866e52 | −0.125800 | ||||||||
\(665\) | 2.80829e52i | 0.0652877i | ||||||||
\(666\) | 1.35234e53 | − | 1.10321e52i | 0.305545 | − | 0.0249258i | ||||
\(667\) | −8.11186e52 | −0.178127 | ||||||||
\(668\) | 4.91258e53i | 1.04847i | ||||||||
\(669\) | 5.74735e53 | + | 5.29759e53i | 1.19226 | + | 1.09896i | ||||
\(670\) | −1.16154e53 | −0.234214 | ||||||||
\(671\) | − | 1.52995e54i | − | 2.99881i | ||||||
\(672\) | −3.69374e53 | + | 4.00733e53i | −0.703801 | + | 0.763553i | ||||
\(673\) | −9.61367e52 | −0.178075 | −0.0890375 | − | 0.996028i | \(-0.528379\pi\) | ||||
−0.0890375 | + | 0.996028i | \(0.528379\pi\) | |||||||
\(674\) | 1.02930e53i | 0.185355i | ||||||||
\(675\) | 3.05786e53 | − | 3.91327e53i | 0.535361 | − | 0.685123i | ||||
\(676\) | 7.62051e52 | 0.129717 | ||||||||
\(677\) | − | 6.32159e53i | − | 1.04627i | −0.852251 | − | 0.523133i | \(-0.824763\pi\) | ||
0.852251 | − | 0.523133i | \(-0.175237\pi\) | |||||||
\(678\) | 7.34031e52 | + | 6.76589e52i | 0.118127 | + | 0.108883i | ||||
\(679\) | 5.11714e53 | 0.800758 | ||||||||
\(680\) | − | 1.84454e53i | − | 0.280685i | ||||||
\(681\) | 2.42570e53 | − | 2.63164e53i | 0.358956 | − | 0.389431i | ||||
\(682\) | 4.08567e53 | 0.587977 | ||||||||
\(683\) | 1.06104e54i | 1.48504i | 0.669823 | + | 0.742521i | \(0.266370\pi\) | ||||
−0.669823 | + | 0.742521i | \(0.733630\pi\) | |||||||
\(684\) | −8.35892e51 | − | 1.02465e53i | −0.0113785 | − | 0.139479i | ||||
\(685\) | −8.00272e52 | −0.105954 | ||||||||
\(686\) | 3.15083e53i | 0.405758i | ||||||||
\(687\) | −6.52379e53 | − | 6.01326e53i | −0.817188 | − | 0.753238i | ||||
\(688\) | −4.91329e53 | −0.598676 | ||||||||
\(689\) | 2.24813e53i | 0.266475i | ||||||||
\(690\) | 1.97209e52 | − | 2.13952e52i | 0.0227402 | − | 0.0246708i | ||||
\(691\) | 1.68158e54 | 1.88640 | 0.943201 | − | 0.332224i | \(-0.107799\pi\) | ||||
0.943201 | + | 0.332224i | \(0.107799\pi\) | |||||||
\(692\) | − | 8.29350e53i | − | 0.905153i | ||||||
\(693\) | −1.96270e54 | + | 1.60114e53i | −2.08412 | + | 0.170019i | ||||
\(694\) | −2.21671e53 | −0.229023 | ||||||||
\(695\) | 3.32097e53i | 0.333852i | ||||||||
\(696\) | 4.86427e53 | + | 4.48361e53i | 0.475819 | + | 0.438583i | ||||
\(697\) | −6.01618e53 | −0.572661 | ||||||||
\(698\) | 4.20727e52i | 0.0389715i | ||||||||
\(699\) | −7.48901e53 | + | 8.12483e53i | −0.675084 | + | 0.732399i | ||||
\(700\) | 8.48058e53 | 0.743983 | ||||||||
\(701\) | 1.79665e53i | 0.153398i | 0.997054 | + | 0.0766991i | \(0.0244381\pi\) | ||||
−0.997054 | + | 0.0766991i | \(0.975562\pi\) | |||||||
\(702\) | −4.40326e53 | − | 3.44075e53i | −0.365906 | − | 0.285922i | ||||
\(703\) | −1.51091e53 | −0.122204 | ||||||||
\(704\) | 1.27734e53i | 0.100560i | ||||||||
\(705\) | 7.10506e52 | + | 6.54904e52i | 0.0544471 | + | 0.0501862i | ||||
\(706\) | 4.82049e52 | 0.0359586 | ||||||||
\(707\) | 2.07508e54i | 1.50683i | ||||||||
\(708\) | 9.14625e53 | − | 9.92277e53i | 0.646564 | − | 0.701457i | ||||
\(709\) | −1.48779e53 | −0.102391 | −0.0511955 | − | 0.998689i | \(-0.516303\pi\) | ||||
−0.0511955 | + | 0.998689i | \(0.516303\pi\) | |||||||
\(710\) | 4.20976e53i | 0.282064i | ||||||||
\(711\) | 4.57219e51 | + | 5.60467e52i | 0.00298264 | + | 0.0365618i | ||||
\(712\) | −1.62941e54 | −1.03493 | ||||||||
\(713\) | − | 2.38648e53i | − | 0.147590i | ||||||
\(714\) | −5.49734e53 | − | 5.06714e53i | −0.331045 | − | 0.305138i | ||||
\(715\) | 1.31960e54 | 0.773797 | ||||||||
\(716\) | − | 1.13922e54i | − | 0.650517i | ||||||
\(717\) | −1.29666e54 | + | 1.40675e54i | −0.721046 | + | 0.782263i | ||||
\(718\) | 5.49713e53 | 0.297695 | ||||||||
\(719\) | − | 2.13138e54i | − | 1.12412i | −0.827097 | − | 0.562059i | \(-0.810009\pi\) | ||
0.827097 | − | 0.562059i | \(-0.189991\pi\) | |||||||
\(720\) | 3.34089e53 | − | 2.72543e52i | 0.171611 | − | 0.0139997i | ||||
\(721\) | 4.90183e53 | 0.245238 | ||||||||
\(722\) | 8.58878e53i | 0.418528i | ||||||||
\(723\) | 1.39722e54 | + | 1.28788e54i | 0.663191 | + | 0.611292i | ||||
\(724\) | 8.59141e53 | 0.397220 | ||||||||
\(725\) | − | 1.59689e54i | − | 0.719204i | ||||||
\(726\) | 1.97009e54 | − | 2.13735e54i | 0.864349 | − | 0.937733i | ||||
\(727\) | −1.08624e54 | −0.464273 | −0.232137 | − | 0.972683i | \(-0.574572\pi\) | ||||
−0.232137 | + | 0.972683i | \(0.574572\pi\) | |||||||
\(728\) | − | 2.12654e54i | − | 0.885475i | ||||||
\(729\) | −5.95981e53 | − | 2.39190e54i | −0.241774 | − | 0.970333i | ||||
\(730\) | −2.74912e53 | −0.108658 | ||||||||
\(731\) | − | 3.23940e54i | − | 1.24748i | ||||||
\(732\) | 2.40467e54 | + | 2.21649e54i | 0.902288 | + | 0.831679i | ||||
\(733\) | 1.44131e54 | 0.526967 | 0.263483 | − | 0.964664i | \(-0.415129\pi\) | ||||
0.263483 | + | 0.964664i | \(0.415129\pi\) | |||||||
\(734\) | 2.20869e54i | 0.786883i | ||||||||
\(735\) | −7.40339e52 | + | 8.03194e52i | −0.0257022 | + | 0.0278844i | ||||
\(736\) | −6.28814e53 | −0.212737 | ||||||||
\(737\) | 9.06983e54i | 2.99031i | ||||||||
\(738\) | 6.29304e52 | + | 7.71412e53i | 0.0202204 | + | 0.247865i | ||||
\(739\) | −3.45110e54 | −1.08072 | −0.540360 | − | 0.841434i | \(-0.681712\pi\) | ||||
−0.540360 | + | 0.841434i | \(0.681712\pi\) | |||||||
\(740\) | − | 6.84887e53i | − | 0.209034i | ||||||
\(741\) | 4.57551e53 | + | 4.21745e53i | 0.136111 | + | 0.125460i | ||||
\(742\) | 3.86947e53 | 0.112196 | ||||||||
\(743\) | − | 4.33606e54i | − | 1.22548i | −0.790283 | − | 0.612742i | \(-0.790066\pi\) | ||
0.790283 | − | 0.612742i | \(-0.209934\pi\) | |||||||
\(744\) | −1.31906e54 | + | 1.43105e54i | −0.363396 | + | 0.394248i | ||||
\(745\) | −1.91584e54 | −0.514506 | ||||||||
\(746\) | − | 1.39973e53i | − | 0.0366443i | ||||||
\(747\) | 6.27972e53 | − | 5.12288e52i | 0.160269 | − | 0.0130744i | ||||
\(748\) | −6.46309e54 | −1.60809 | ||||||||
\(749\) | 1.96860e54i | 0.477532i | ||||||||
\(750\) | 9.05588e53 | + | 8.34720e53i | 0.214174 | + | 0.197413i | ||||
\(751\) | 4.67397e54 | 1.07777 | 0.538886 | − | 0.842379i | \(-0.318845\pi\) | ||||
0.538886 | + | 0.842379i | \(0.318845\pi\) | |||||||
\(752\) | − | 4.34488e53i | − | 0.0976875i | ||||||
\(753\) | 4.30349e51 | − | 4.66886e51i | 0.000943445 | − | 0.00102354i | ||||
\(754\) | −1.79684e54 | −0.384108 | ||||||||
\(755\) | − | 1.20477e54i | − | 0.251139i | ||||||
\(756\) | 2.59179e54 | − | 3.31681e54i | 0.526848 | − | 0.674228i | ||||
\(757\) | −7.66727e54 | −1.51991 | −0.759957 | − | 0.649974i | \(-0.774780\pi\) | ||||
−0.759957 | + | 0.649974i | \(0.774780\pi\) | |||||||
\(758\) | 1.46903e54i | 0.283998i | ||||||||
\(759\) | −1.67063e54 | − | 1.53990e54i | −0.314983 | − | 0.290334i | ||||
\(760\) | 2.64245e53 | 0.0485901 | ||||||||
\(761\) | − | 1.93757e54i | − | 0.347495i | −0.984790 | − | 0.173748i | \(-0.944412\pi\) | ||
0.984790 | − | 0.173748i | \(-0.0555877\pi\) | |||||||
\(762\) | 1.24427e54 | − | 1.34991e54i | 0.217657 | − | 0.236136i | ||||
\(763\) | 4.79602e54 | 0.818305 | ||||||||
\(764\) | 6.30158e54i | 1.04876i | ||||||||
\(765\) | 1.79692e53 | + | 2.20269e54i | 0.0291716 | + | 0.357591i | ||||
\(766\) | 1.57993e54 | 0.250203 | ||||||||
\(767\) | 8.16839e54i | 1.26190i | ||||||||
\(768\) | 1.87789e54 | + | 1.73093e54i | 0.283013 | + | 0.260865i | ||||
\(769\) | 7.88156e54 | 1.15881 | 0.579405 | − | 0.815040i | \(-0.303285\pi\) | ||||
0.579405 | + | 0.815040i | \(0.303285\pi\) | |||||||
\(770\) | − | 2.27129e54i | − | 0.325798i | ||||||
\(771\) | 1.65620e54 | − | 1.79681e54i | 0.231782 | − | 0.251461i | ||||
\(772\) | −4.29300e54 | −0.586182 | ||||||||
\(773\) | − | 1.36258e55i | − | 1.81532i | −0.419711 | − | 0.907658i | \(-0.637869\pi\) | ||
0.419711 | − | 0.907658i | \(-0.362131\pi\) | |||||||
\(774\) | −4.15365e54 | + | 3.38847e53i | −0.539948 | + | 0.0440479i | ||||
\(775\) | 4.69799e54 | 0.595909 | ||||||||
\(776\) | − | 4.81494e54i | − | 0.595961i | ||||||
\(777\) | −4.54879e54 | − | 4.19281e54i | −0.549409 | − | 0.506415i | ||||
\(778\) | −1.86073e54 | −0.219317 | ||||||||
\(779\) | − | 8.61863e53i | − | 0.0991349i | ||||||
\(780\) | −1.91175e54 | + | 2.07406e54i | −0.214602 | + | 0.232822i | ||||
\(781\) | 3.28716e55 | 3.60124 | ||||||||
\(782\) | − | 8.62619e53i | − | 0.0922339i | ||||||
\(783\) | −6.24554e54 | − | 4.88032e54i | −0.651773 | − | 0.509301i | ||||
\(784\) | 4.91168e53 | 0.0500294 | ||||||||
\(785\) | − | 6.08934e54i | − | 0.605406i | ||||||
\(786\) | −4.40362e54 | − | 4.05901e54i | −0.427347 | − | 0.393905i | ||||
\(787\) | −1.47597e55 | −1.39816 | −0.699082 | − | 0.715042i | \(-0.746408\pi\) | ||||
−0.699082 | + | 0.715042i | \(0.746408\pi\) | |||||||
\(788\) | 1.24573e55i | 1.15193i | ||||||||
\(789\) | −8.38735e54 | + | 9.09944e54i | −0.757115 | + | 0.821394i | ||||
\(790\) | −6.48586e52 | −0.00571548 | ||||||||
\(791\) | − | 4.55161e54i | − | 0.391572i | ||||||
\(792\) | 1.50658e54 | + | 1.84679e55i | 0.126536 | + | 1.55110i | ||||
\(793\) | −1.97952e55 | −1.62319 | ||||||||
\(794\) | 2.31504e52i | 0.00185340i | ||||||||
\(795\) | −8.41033e53 | − | 7.75217e53i | −0.0657412 | − | 0.0605966i | ||||
\(796\) | 7.90973e54 | 0.603689 | ||||||||
\(797\) | 1.62351e55i | 1.20989i | 0.796266 | + | 0.604946i | \(0.206805\pi\) | ||||
−0.796266 | + | 0.604946i | \(0.793195\pi\) | |||||||
\(798\) | 7.25906e53 | − | 7.87536e53i | 0.0528233 | − | 0.0573080i | ||||
\(799\) | 2.86464e54 | 0.203555 | ||||||||
\(800\) | − | 1.23787e55i | − | 0.858947i | ||||||
\(801\) | 1.94578e55 | − | 1.58734e54i | 1.31849 | − | 0.107560i | ||||
\(802\) | −1.00586e55 | −0.665618 | ||||||||
\(803\) | 2.14664e55i | 1.38728i | ||||||||
\(804\) | −1.42554e55 | − | 1.31398e55i | −0.899733 | − | 0.829323i | ||||
\(805\) | −1.32668e54 | −0.0817796 | ||||||||
\(806\) | − | 5.28624e54i | − | 0.318259i | ||||||
\(807\) | −2.29574e54 | + | 2.49065e54i | −0.134997 | + | 0.146459i | ||||
\(808\) | 1.95253e55 | 1.12146 | ||||||||
\(809\) | 3.79732e54i | 0.213037i | 0.994311 | + | 0.106518i | \(0.0339703\pi\) | ||||
−0.994311 | + | 0.106518i | \(0.966030\pi\) | |||||||
\(810\) | 2.80556e54 | − | 4.60812e53i | 0.153746 | − | 0.0252527i | ||||
\(811\) | −2.36495e55 | −1.26598 | −0.632988 | − | 0.774162i | \(-0.718172\pi\) | ||||
−0.632988 | + | 0.774162i | \(0.718172\pi\) | |||||||
\(812\) | − | 1.35349e55i | − | 0.707768i | ||||||
\(813\) | −7.93581e54 | − | 7.31478e54i | −0.405388 | − | 0.373664i | ||||
\(814\) | 1.22199e55 | 0.609823 | ||||||||
\(815\) | 3.05930e54i | 0.149151i | ||||||||
\(816\) | 6.73494e54 | − | 7.30674e54i | 0.320790 | − | 0.348025i | ||||
\(817\) | 4.64068e54 | 0.215955 | ||||||||
\(818\) | 1.01778e55i | 0.462745i | ||||||||
\(819\) | 2.07163e54 | + | 2.53944e55i | 0.0920275 | + | 1.12809i | ||||
\(820\) | 3.90679e54 | 0.169573 | ||||||||
\(821\) | − | 3.82353e55i | − | 1.62160i | −0.585320 | − | 0.810802i | \(-0.699031\pi\) | ||
0.585320 | − | 0.810802i | \(-0.300969\pi\) | |||||||
\(822\) | 2.24422e54 | + | 2.06860e54i | 0.0930039 | + | 0.0857257i | ||||
\(823\) | 1.60310e54 | 0.0649178 | 0.0324589 | − | 0.999473i | \(-0.489666\pi\) | ||||
0.0324589 | + | 0.999473i | \(0.489666\pi\) | |||||||
\(824\) | − | 4.61234e54i | − | 0.182518i | ||||||
\(825\) | 3.03141e55 | − | 3.28878e55i | 1.17225 | − | 1.27177i | ||||
\(826\) | 1.40594e55 | 0.531308 | ||||||||
\(827\) | 1.56013e55i | 0.576178i | 0.957604 | + | 0.288089i | \(0.0930198\pi\) | ||||
−0.957604 | + | 0.288089i | \(0.906980\pi\) | |||||||
\(828\) | 4.84062e54 | − | 3.94889e53i | 0.174713 | − | 0.0142527i | ||||
\(829\) | −5.01082e55 | −1.76755 | −0.883777 | − | 0.467908i | \(-0.845008\pi\) | ||||
−0.883777 | + | 0.467908i | \(0.845008\pi\) | |||||||
\(830\) | 7.26704e53i | 0.0250538i | ||||||||
\(831\) | 1.01788e55 | + | 9.38222e54i | 0.342986 | + | 0.316145i | ||||
\(832\) | 1.65269e54 | 0.0544312 | ||||||||
\(833\) | 3.23834e54i | 0.104248i | ||||||||
\(834\) | 8.58427e54 | − | 9.31307e54i | 0.270115 | − | 0.293048i | ||||
\(835\) | 1.51288e55 | 0.465331 | ||||||||
\(836\) | − | 9.25887e54i | − | 0.278380i | ||||||
\(837\) | 1.43577e55 | − | 1.83742e55i | 0.421990 | − | 0.540038i | ||||
\(838\) | −2.72841e55 | −0.783922 | ||||||||
\(839\) | 2.86261e55i | 0.804052i | 0.915628 | + | 0.402026i | \(0.131694\pi\) | ||||
−0.915628 | + | 0.402026i | \(0.868306\pi\) | |||||||
\(840\) | 7.95544e54 | + | 7.33288e54i | 0.218453 | + | 0.201358i | ||||
\(841\) | 1.17637e55 | 0.315805 | ||||||||
\(842\) | − | 2.02267e54i | − | 0.0530879i | ||||||
\(843\) | −2.16807e55 | + | 2.35214e55i | −0.556352 | + | 0.603586i | ||||
\(844\) | 4.46628e54 | 0.112057 | ||||||||
\(845\) | − | 2.34682e54i | − | 0.0575707i | ||||||
\(846\) | −2.99647e53 | − | 3.67312e54i | −0.00718741 | − | 0.0881046i | ||||
\(847\) | −1.32533e56 | −3.10842 | ||||||||
\(848\) | 5.14308e54i | 0.117951i | ||||||||
\(849\) | 3.82529e55 | + | 3.52594e55i | 0.857864 | + | 0.790731i | ||||
\(850\) | 1.69814e55 | 0.372403 | ||||||||
\(851\) | − | 7.13776e54i | − | 0.153074i | ||||||
\(852\) | −4.76224e55 | + | 5.16655e55i | −0.998754 | + | 1.08355i | ||||
\(853\) | 6.28932e55 | 1.28995 | 0.644973 | − | 0.764205i | \(-0.276868\pi\) | ||||
0.644973 | + | 0.764205i | \(0.276868\pi\) | |||||||
\(854\) | 3.40714e55i | 0.683424i | ||||||||
\(855\) | −3.15552e54 | + | 2.57422e53i | −0.0619035 | + | 0.00504997i | ||||
\(856\) | 1.85234e55 | 0.355401 | ||||||||
\(857\) | − | 3.58908e55i | − | 0.673515i | −0.941591 | − | 0.336758i | \(-0.890670\pi\) | ||
0.941591 | − | 0.336758i | \(-0.109330\pi\) | |||||||
\(858\) | −3.70058e55 | − | 3.41098e55i | −0.679221 | − | 0.626068i | ||||
\(859\) | 6.89794e54 | 0.123837 | 0.0619183 | − | 0.998081i | \(-0.480278\pi\) | ||||
0.0619183 | + | 0.998081i | \(0.480278\pi\) | |||||||
\(860\) | 2.10360e55i | 0.369397i | ||||||||
\(861\) | 2.39170e55 | − | 2.59476e55i | 0.410815 | − | 0.445694i | ||||
\(862\) | −1.25460e55 | −0.210798 | ||||||||
\(863\) | − | 2.38411e55i | − | 0.391850i | −0.980619 | − | 0.195925i | \(-0.937229\pi\) | ||
0.980619 | − | 0.195925i | \(-0.0627710\pi\) | |||||||
\(864\) | −4.84141e55 | − | 3.78312e55i | −0.778414 | − | 0.608259i | ||||
\(865\) | −2.55407e55 | −0.401723 | ||||||||
\(866\) | 2.21676e54i | 0.0341097i | ||||||||
\(867\) | −6.70936e53 | − | 6.18432e53i | −0.0100999 | − | 0.00930955i | ||||
\(868\) | 3.98193e55 | 0.586433 | ||||||||
\(869\) | 5.06444e54i | 0.0729720i | ||||||||
\(870\) | 6.19599e54 | − | 6.72203e54i | 0.0873464 | − | 0.0947621i | ||||
\(871\) | 1.17350e56 | 1.61859 | ||||||||
\(872\) | − | 4.51279e55i | − | 0.609020i | ||||||
\(873\) | 4.69062e54 | + | 5.74984e55i | 0.0619383 | + | 0.759251i | ||||
\(874\) | 1.23577e54 | 0.0159669 | ||||||||
\(875\) | − | 5.61540e55i | − | 0.709950i | ||||||
\(876\) | −3.37394e55 | − | 3.10991e55i | −0.417407 | − | 0.384743i | ||||
\(877\) | 1.23658e56 | 1.49703 | 0.748515 | − | 0.663118i | \(-0.230767\pi\) | ||||
0.748515 | + | 0.663118i | \(0.230767\pi\) | |||||||
\(878\) | 2.57863e55i | 0.305488i | ||||||||
\(879\) | −7.15447e54 | + | 7.76189e54i | −0.0829448 | + | 0.0899868i | ||||
\(880\) | 3.01886e55 | 0.342509 | ||||||||
\(881\) | − | 8.97270e55i | − | 0.996279i | −0.867097 | − | 0.498139i | \(-0.834017\pi\) | ||
0.867097 | − | 0.498139i | \(-0.165983\pi\) | |||||||
\(882\) | 4.15229e54 | − | 3.38737e53i | 0.0451217 | − | 0.00368094i | ||||
\(883\) | −1.21876e55 | −0.129618 | −0.0648089 | − | 0.997898i | \(-0.520644\pi\) | ||||
−0.0648089 | + | 0.997898i | \(0.520644\pi\) | |||||||
\(884\) | 8.36226e55i | 0.870423i | ||||||||
\(885\) | −3.05582e55 | − | 2.81669e55i | −0.311319 | − | 0.286957i | ||||
\(886\) | 6.22380e55 | 0.620604 | ||||||||
\(887\) | 1.89933e56i | 1.85376i | 0.375363 | + | 0.926878i | \(0.377518\pi\) | ||||
−0.375363 | + | 0.926878i | \(0.622482\pi\) | |||||||
\(888\) | −3.94520e55 | + | 4.28015e55i | −0.376897 | + | 0.408896i | ||||
\(889\) | −8.37059e55 | −0.782749 | ||||||||
\(890\) | 2.25171e55i | 0.206111i | ||||||||
\(891\) | −3.59822e55 | − | 2.19070e56i | −0.322412 | − | 1.96294i | ||||
\(892\) | −1.50477e56 | −1.31989 | ||||||||
\(893\) | 4.10381e54i | 0.0352379i | ||||||||
\(894\) | 5.37264e55 | + | 4.95219e55i | 0.451621 | + | 0.416279i | ||||
\(895\) | −3.50833e55 | −0.288711 | ||||||||
\(896\) | − | 1.31738e56i | − | 1.06135i | ||||||
\(897\) | −1.99239e55 | + | 2.16154e55i | −0.157151 | + | 0.170493i | ||||
\(898\) | 9.29205e54 | 0.0717565 | ||||||||
\(899\) | − | 7.49794e55i | − | 0.566902i | ||||||
\(900\) | 7.77371e54 | + | 9.52916e55i | 0.0575468 | + | 0.705419i | ||||
\(901\) | −3.39090e55 | −0.245779 | ||||||||
\(902\) | 6.97057e55i | 0.494702i | ||||||||
\(903\) | 1.39714e56 | + | 1.28781e56i | 0.970896 | + | 0.894917i | ||||
\(904\) | −4.28281e55 | −0.291426 | ||||||||
\(905\) | − | 2.64582e55i | − | 0.176294i | ||||||
\(906\) | −3.11418e55 | + | 3.37857e55i | −0.203193 | + | 0.220444i | ||||
\(907\) | 2.49440e55 | 0.159378 | 0.0796890 | − | 0.996820i | \(-0.474607\pi\) | ||||
0.0796890 | + | 0.996820i | \(0.474607\pi\) | |||||||
\(908\) | 6.89013e55i | 0.431118i | ||||||||
\(909\) | −2.33165e56 | + | 1.90212e55i | −1.42873 | + | 0.116553i | ||||
\(910\) | −2.93870e55 | −0.176347 | ||||||||
\(911\) | 6.13735e55i | 0.360688i | 0.983604 | + | 0.180344i | \(0.0577211\pi\) | ||||
−0.983604 | + | 0.180344i | \(0.942279\pi\) | |||||||
\(912\) | 1.04675e55 | + | 9.64832e54i | 0.0602476 | + | 0.0555328i | ||||
\(913\) | 5.67443e55 | 0.319873 | ||||||||
\(914\) | − | 7.45989e55i | − | 0.411865i | ||||||
\(915\) | 6.82592e55 | − | 7.40544e55i | 0.369114 | − | 0.400452i | ||||
\(916\) | 1.70805e56 | 0.904664 | ||||||||
\(917\) | 2.73061e56i | 1.41658i | ||||||||
\(918\) | 5.18975e55 | − | 6.64153e55i | 0.263715 | − | 0.337487i | ||||
\(919\) | −2.68199e56 | −1.33494 | −0.667472 | − | 0.744635i | \(-0.732623\pi\) | ||||
−0.667472 | + | 0.744635i | \(0.732623\pi\) | |||||||
\(920\) | 1.24833e55i | 0.0608642i | ||||||||
\(921\) | 1.79503e56 | + | 1.65456e56i | 0.857313 | + | 0.790223i | ||||
\(922\) | −4.97151e55 | −0.232595 | ||||||||
\(923\) | − | 4.25309e56i | − | 1.94927i | ||||||
\(924\) | 2.56937e56 | − | 2.78751e56i | 1.15361 | − | 1.25155i | ||||
\(925\) | 1.40513e56 | 0.618049 | ||||||||
\(926\) | − | 1.11871e56i | − | 0.482069i | ||||||
\(927\) | 4.49325e54 | + | 5.50791e55i | 0.0189691 | + | 0.232526i | ||||
\(928\) | −1.97563e56 | −0.817136 | ||||||||
\(929\) | − | 1.08404e56i | − | 0.439284i | −0.975581 | − | 0.219642i | \(-0.929511\pi\) | ||
0.975581 | − | 0.219642i | \(-0.0704889\pi\) | |||||||
\(930\) | 1.97760e55 | + | 1.82284e55i | 0.0785167 | + | 0.0723723i | ||||
\(931\) | −4.63917e54 | −0.0180466 | ||||||||
\(932\) | − | 2.12724e56i | − | 0.810799i | ||||||
\(933\) | 1.08947e56 | − | 1.18196e56i | 0.406877 | − | 0.441421i | ||||
\(934\) | 1.88583e56 | 0.690100 | ||||||||
\(935\) | 1.99038e56i | 0.713699i | ||||||||
\(936\) | 2.38947e56 | − | 1.94929e55i | 0.839577 | − | 0.0684911i | ||||
\(937\) | −3.80879e56 | −1.31140 | −0.655699 | − | 0.755023i | \(-0.727626\pi\) | ||||
−0.655699 | + | 0.755023i | \(0.727626\pi\) | |||||||
\(938\) | − | 2.01982e56i | − | 0.681489i | ||||||
\(939\) | 3.85639e55 | + | 3.55461e55i | 0.127507 | + | 0.117529i | ||||
\(940\) | −1.86024e55 | −0.0602754 | ||||||||
\(941\) | 3.50183e56i | 1.11197i | 0.831194 | + | 0.555983i | \(0.187658\pi\) | ||||
−0.831194 | + | 0.555983i | \(0.812342\pi\) | |||||||
\(942\) | −1.57401e56 | + | 1.70765e56i | −0.489825 | + | 0.531412i | ||||
\(943\) | 4.07158e55 | 0.124177 | ||||||||
\(944\) | 1.86869e56i | 0.558561i | ||||||||
\(945\) | −1.02145e56 | − | 7.98168e55i | −0.299235 | − | 0.233825i | ||||
\(946\) | −3.75329e56 | −1.07766 | ||||||||
\(947\) | 4.44911e56i | 1.25206i | 0.779801 | + | 0.626028i | \(0.215320\pi\) | ||||
−0.779801 | + | 0.626028i | \(0.784680\pi\) | |||||||
\(948\) | −7.95997e54 | − | 7.33705e54i | −0.0219560 | − | 0.0202378i | ||||
\(949\) | 2.77742e56 | 0.750902 | ||||||||
\(950\) | 2.43271e55i | 0.0644677i | ||||||||
\(951\) | −2.75352e56 | + | 2.98729e56i | −0.715250 | + | 0.775975i | ||||
\(952\) | 3.20750e56 | 0.816703 | ||||||||
\(953\) | 8.74426e55i | 0.218252i | 0.994028 | + | 0.109126i | \(0.0348052\pi\) | ||||
−0.994028 | + | 0.109126i | \(0.965195\pi\) | |||||||
\(954\) | 3.54695e54 | + | 4.34792e55i | 0.00867832 | + | 0.106380i | ||||
\(955\) | 1.94064e56 | 0.465458 | ||||||||
\(956\) | − | 3.68314e56i | − | 0.866001i | ||||||
\(957\) | −5.24886e56 | − | 4.83810e56i | −1.20987 | − | 1.11519i | ||||
\(958\) | 4.38292e55 | 0.0990419 | ||||||||
\(959\) | − | 1.39160e56i | − | 0.308292i | ||||||
\(960\) | −5.69892e54 | + | 6.18276e54i | −0.0123777 | + | 0.0134286i | ||||
\(961\) | −2.49031e56 | −0.530284 | ||||||||
\(962\) | − | 1.58107e56i | − | 0.330084i | ||||||
\(963\) | −2.21200e56 | + | 1.80451e55i | −0.452779 | + | 0.0369369i | ||||
\(964\) | −3.65820e56 | −0.734182 | ||||||||
\(965\) | 1.32208e56i | 0.260158i | ||||||||
\(966\) | 3.72044e55 | + | 3.42930e55i | 0.0717843 | + | 0.0661667i | ||||
\(967\) | 9.29193e56 | 1.75794 | 0.878968 | − | 0.476881i | \(-0.158233\pi\) | ||||
0.878968 | + | 0.476881i | \(0.158233\pi\) | |||||||
\(968\) | 1.24706e57i | 2.31343i | ||||||||
\(969\) | −6.36127e55 | + | 6.90134e55i | −0.115716 | + | 0.125540i | ||||
\(970\) | −6.65386e55 | −0.118689 | ||||||||
\(971\) | − | 7.25349e56i | − | 1.26877i | −0.773019 | − | 0.634383i | \(-0.781254\pi\) | ||
0.773019 | − | 0.634383i | \(-0.218746\pi\) | |||||||
\(972\) | 3.96450e56 | + | 2.60821e56i | 0.680032 | + | 0.447388i | ||||
\(973\) | −5.77488e56 | −0.971403 | ||||||||
\(974\) | 1.74190e56i | 0.287344i | ||||||||
\(975\) | −4.25518e56 | − | 3.92219e56i | −0.688383 | − | 0.634513i | ||||
\(976\) | −4.52857e56 | −0.718480 | ||||||||
\(977\) | − | 8.84780e56i | − | 1.37670i | −0.725380 | − | 0.688349i | \(-0.758336\pi\) | ||
0.725380 | − | 0.688349i | \(-0.241664\pi\) | |||||||
\(978\) | 7.90788e55 | − | 8.57926e55i | 0.120676 | − | 0.130922i | ||||
\(979\) | 1.75823e57 | 2.63151 | ||||||||
\(980\) | − | 2.10292e55i | − | 0.0308693i | ||||||
\(981\) | 4.39627e55 | + | 5.38903e56i | 0.0632955 | + | 0.775888i | ||||
\(982\) | 4.70569e56 | 0.664515 | ||||||||
\(983\) | − | 6.99045e56i | − | 0.968252i | −0.874998 | − | 0.484126i | \(-0.839138\pi\) | ||
0.874998 | − | 0.484126i | \(-0.160862\pi\) | |||||||
\(984\) | −2.44152e56 | − | 2.25046e56i | −0.331706 | − | 0.305748i | ||||
\(985\) | 3.83636e56 | 0.511247 | ||||||||
\(986\) | − | 2.71021e56i | − | 0.354276i | ||||||
\(987\) | −1.13882e56 | + | 1.23551e56i | −0.146026 | + | 0.158424i | ||||
\(988\) | −1.19796e56 | −0.150681 | ||||||||
\(989\) | 2.19233e56i | 0.270506i | ||||||||
\(990\) | 2.55212e56 | − | 2.08197e55i | 0.308910 | − | 0.0252003i | ||||
\(991\) | 3.94493e56 | 0.468424 | 0.234212 | − | 0.972185i | \(-0.424749\pi\) | ||||
0.234212 | + | 0.972185i | \(0.424749\pi\) | |||||||
\(992\) | − | 5.81224e56i | − | 0.677052i | ||||||
\(993\) | 7.54550e55 | + | 6.95502e55i | 0.0862288 | + | 0.0794808i | ||||
\(994\) | −7.32040e56 | −0.820717 | ||||||||
\(995\) | − | 2.43588e56i | − | 0.267928i | ||||||
\(996\) | −8.22075e55 | + | 8.91870e55i | −0.0887124 | + | 0.0962441i | ||||
\(997\) | 3.13678e56 | 0.332106 | 0.166053 | − | 0.986117i | \(-0.446898\pi\) | ||||
0.166053 | + | 0.986117i | \(0.446898\pi\) | |||||||
\(998\) | 6.83327e56i | 0.709820i | ||||||||
\(999\) | 4.29427e56 | − | 5.49555e56i | 0.437668 | − | 0.560102i |
(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 | 3.39.b.a.2.5 | ✓ | 12 | |
3.2 | odd | 2 | inner | 3.39.b.a.2.8 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.39.b.a.2.5 | ✓ | 12 | 1.1 | even | 1 | trivial | |
3.39.b.a.2.8 | yes | 12 | 3.2 | odd | 2 | inner |