Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,67,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, 67, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 67);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 67 \) |
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: | \(82.7604085389\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + \cdots + 56\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{216}\cdot 3^{291}\cdot 5^{20}\cdot 7^{10}\cdot 11^{6}\cdot 13^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.8 | ||
Root | \(-1.32287e8i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.67.b.b.2.13 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.76234e9i | − | 0.554410i | −0.960811 | − | 0.277205i | \(-0.910592\pi\) | ||
0.960811 | − | 0.277205i | \(-0.0894080\pi\) | |||||||
\(3\) | 4.09693e15 | − | 3.75743e15i | 0.736983 | − | 0.675912i | ||||
\(4\) | 5.11071e19 | 0.692630 | ||||||||
\(5\) | 1.11626e23i | 0.958860i | 0.877580 | + | 0.479430i | \(0.159157\pi\) | ||||
−0.877580 | + | 0.479430i | \(0.840843\pi\) | |||||||
\(6\) | −1.78942e25 | − | 1.95110e25i | −0.374732 | − | 0.408590i | ||||
\(7\) | 1.00296e28 | 1.29732 | 0.648659 | − | 0.761079i | \(-0.275330\pi\) | ||||
0.648659 | + | 0.761079i | \(0.275330\pi\) | |||||||
\(8\) | − | 5.94788e29i | − | 0.938410i | ||||||
\(9\) | 2.66653e30 | − | 3.07879e31i | 0.0862866 | − | 0.996270i | ||||
\(10\) | 5.31601e32 | 0.531601 | ||||||||
\(11\) | − | 2.71493e34i | − | 1.16896i | −0.811407 | − | 0.584481i | \(-0.801298\pi\) | ||
0.811407 | − | 0.584481i | \(-0.198702\pi\) | |||||||
\(12\) | 2.09382e35 | − | 1.92031e35i | 0.510456 | − | 0.468157i | ||||
\(13\) | −8.16964e36 | −1.41929 | −0.709647 | − | 0.704558i | \(-0.751146\pi\) | ||||
−0.709647 | + | 0.704558i | \(0.751146\pi\) | |||||||
\(14\) | − | 4.77642e37i | − | 0.719245i | ||||||
\(15\) | 4.19427e38 | + | 4.57324e38i | 0.648105 | + | 0.706663i | ||||
\(16\) | 9.38452e38 | 0.172366 | ||||||||
\(17\) | 3.36501e40i | 0.835935i | 0.908462 | + | 0.417968i | \(0.137257\pi\) | ||||
−0.908462 | + | 0.417968i | \(0.862743\pi\) | |||||||
\(18\) | −1.46622e41 | − | 1.26989e40i | −0.552342 | − | 0.0478381i | ||||
\(19\) | −2.59388e42 | −1.64090 | −0.820448 | − | 0.571721i | \(-0.806276\pi\) | ||||
−0.820448 | + | 0.571721i | \(0.806276\pi\) | |||||||
\(20\) | 5.70488e42i | 0.664135i | ||||||||
\(21\) | 4.10904e43 | − | 3.76854e43i | 0.956101 | − | 0.876872i | ||||
\(22\) | −1.29294e44 | −0.648084 | ||||||||
\(23\) | − | 7.82235e44i | − | 0.904313i | −0.891939 | − | 0.452157i | \(-0.850655\pi\) | ||
0.891939 | − | 0.452157i | \(-0.149345\pi\) | |||||||
\(24\) | −2.23488e45 | − | 2.43681e45i | −0.634283 | − | 0.691592i | ||||
\(25\) | 1.09216e45 | 0.0805869 | ||||||||
\(26\) | 3.89066e46i | 0.786870i | ||||||||
\(27\) | −1.04759e47 | − | 1.36155e47i | −0.609799 | − | 0.792556i | ||||
\(28\) | 5.12581e47 | 0.898561 | ||||||||
\(29\) | − | 2.09277e48i | − | 1.15236i | −0.817323 | − | 0.576180i | \(-0.804543\pi\) | ||
0.817323 | − | 0.576180i | \(-0.195457\pi\) | |||||||
\(30\) | 2.17793e48 | − | 1.99746e48i | 0.391781 | − | 0.359316i | ||||
\(31\) | −9.44360e48 | −0.575707 | −0.287854 | − | 0.957674i | \(-0.592942\pi\) | ||||
−0.287854 | + | 0.957674i | \(0.592942\pi\) | |||||||
\(32\) | − | 4.83568e49i | − | 1.03397i | ||||||
\(33\) | −1.02012e50 | − | 1.11229e50i | −0.790115 | − | 0.861504i | ||||
\(34\) | 1.60254e50 | 0.463450 | ||||||||
\(35\) | 1.11956e51i | 1.24395i | ||||||||
\(36\) | 1.36278e50 | − | 1.57348e51i | 0.0597647 | − | 0.690047i | ||||
\(37\) | 5.25278e51 | 0.932679 | 0.466340 | − | 0.884606i | \(-0.345572\pi\) | ||||
0.466340 | + | 0.884606i | \(0.345572\pi\) | |||||||
\(38\) | 1.23529e52i | 0.909729i | ||||||||
\(39\) | −3.34705e52 | + | 3.06969e52i | −1.04599 | + | 0.959317i | ||||
\(40\) | 6.63938e52 | 0.899804 | ||||||||
\(41\) | − | 2.65367e53i | − | 1.59213i | −0.605210 | − | 0.796066i | \(-0.706911\pi\) | ||
0.605210 | − | 0.796066i | \(-0.293089\pi\) | |||||||
\(42\) | −1.79471e53 | − | 1.95687e53i | −0.486146 | − | 0.530071i | ||||
\(43\) | 7.04522e53 | 0.877881 | 0.438941 | − | 0.898516i | \(-0.355354\pi\) | ||||
0.438941 | + | 0.898516i | \(0.355354\pi\) | |||||||
\(44\) | − | 1.38752e54i | − | 0.809658i | ||||||
\(45\) | 3.43673e54 | + | 2.97654e53i | 0.955284 | + | 0.0827368i | ||||
\(46\) | −3.72527e54 | −0.501360 | ||||||||
\(47\) | − | 5.54764e54i | − | 0.367180i | −0.983003 | − | 0.183590i | \(-0.941228\pi\) | ||
0.983003 | − | 0.183590i | \(-0.0587718\pi\) | |||||||
\(48\) | 3.84477e54 | − | 3.52617e54i | 0.127031 | − | 0.116504i | ||||
\(49\) | 4.08237e55 | 0.683033 | ||||||||
\(50\) | − | 5.20122e54i | − | 0.0446782i | ||||||
\(51\) | 1.26438e56 | + | 1.37862e56i | 0.565018 | + | 0.616070i | ||||
\(52\) | −4.17526e56 | −0.983045 | ||||||||
\(53\) | − | 5.01179e56i | − | 0.629345i | −0.949200 | − | 0.314673i | \(-0.898105\pi\) | ||
0.949200 | − | 0.314673i | \(-0.101895\pi\) | |||||||
\(54\) | −6.48418e56 | + | 4.98898e56i | −0.439401 | + | 0.338078i | ||||
\(55\) | 3.03057e57 | 1.12087 | ||||||||
\(56\) | − | 5.96546e57i | − | 1.21742i | ||||||
\(57\) | −1.06269e58 | + | 9.74634e57i | −1.20931 | + | 1.10910i | ||||
\(58\) | −9.96649e57 | −0.638879 | ||||||||
\(59\) | 2.39968e58i | 0.875057i | 0.899205 | + | 0.437528i | \(0.144146\pi\) | ||||
−0.899205 | + | 0.437528i | \(0.855854\pi\) | |||||||
\(60\) | 2.14357e58 | + | 2.33725e58i | 0.448897 | + | 0.489456i | ||||
\(61\) | 5.18967e58 | 0.629876 | 0.314938 | − | 0.949112i | \(-0.398016\pi\) | ||||
0.314938 | + | 0.949112i | \(0.398016\pi\) | |||||||
\(62\) | 4.49737e58i | 0.319178i | ||||||||
\(63\) | 2.67441e58 | − | 3.08789e59i | 0.111941 | − | 1.29248i | ||||
\(64\) | −1.61046e59 | −0.400878 | ||||||||
\(65\) | − | 9.11945e59i | − | 1.36090i | ||||||
\(66\) | −5.29710e59 | + | 4.85815e59i | −0.477626 | + | 0.438047i | ||||
\(67\) | 1.99087e60 | 1.09288 | 0.546442 | − | 0.837497i | \(-0.315982\pi\) | ||||
0.546442 | + | 0.837497i | \(0.315982\pi\) | |||||||
\(68\) | 1.71976e60i | 0.578994i | ||||||||
\(69\) | −2.93920e60 | − | 3.20476e60i | −0.611236 | − | 0.666463i | ||||
\(70\) | 5.33173e60 | 0.689656 | ||||||||
\(71\) | 1.53185e61i | 1.24077i | 0.784299 | + | 0.620383i | \(0.213023\pi\) | ||||
−0.784299 | + | 0.620383i | \(0.786977\pi\) | |||||||
\(72\) | −1.83123e61 | − | 1.58602e60i | −0.934910 | − | 0.0809723i | ||||
\(73\) | −8.33852e60 | −0.270044 | −0.135022 | − | 0.990843i | \(-0.543111\pi\) | ||||
−0.135022 | + | 0.990843i | \(0.543111\pi\) | |||||||
\(74\) | − | 2.50155e61i | − | 0.517086i | ||||||
\(75\) | 4.47449e60 | − | 4.10371e60i | 0.0593912 | − | 0.0544697i | ||||
\(76\) | −1.32566e62 | −1.13653 | ||||||||
\(77\) | − | 2.72296e62i | − | 1.51651i | ||||||
\(78\) | 1.46189e62 | + | 1.59398e62i | 0.531855 | + | 0.579910i | ||||
\(79\) | 2.10112e62 | 0.502062 | 0.251031 | − | 0.967979i | \(-0.419230\pi\) | ||||
0.251031 | + | 0.967979i | \(0.419230\pi\) | |||||||
\(80\) | 1.04756e62i | 0.165275i | ||||||||
\(81\) | −9.40784e62 | − | 1.64194e62i | −0.985109 | − | 0.171930i | ||||
\(82\) | −1.26377e63 | −0.882693 | ||||||||
\(83\) | − | 2.23637e63i | − | 1.04705i | −0.852011 | − | 0.523523i | \(-0.824617\pi\) | ||
0.852011 | − | 0.523523i | \(-0.175383\pi\) | |||||||
\(84\) | 2.10001e63 | − | 1.92599e63i | 0.662224 | − | 0.607348i | ||||
\(85\) | −3.75623e63 | −0.801545 | ||||||||
\(86\) | − | 3.35518e63i | − | 0.486706i | ||||||
\(87\) | −7.86345e63 | − | 8.57394e63i | −0.778893 | − | 0.849269i | ||||
\(88\) | −1.61481e64 | −1.09697 | ||||||||
\(89\) | 2.08278e62i | 0.00974479i | 0.999988 | + | 0.00487240i | \(0.00155094\pi\) | ||||
−0.999988 | + | 0.00487240i | \(0.998449\pi\) | |||||||
\(90\) | 1.41753e63 | − | 1.63669e64i | 0.0458701 | − | 0.529619i | ||||
\(91\) | −8.19379e64 | −1.84128 | ||||||||
\(92\) | − | 3.99778e64i | − | 0.626354i | ||||||
\(93\) | −3.86898e64 | + | 3.54837e64i | −0.424286 | + | 0.389127i | ||||
\(94\) | −2.64197e64 | −0.203568 | ||||||||
\(95\) | − | 2.89545e65i | − | 1.57339i | ||||||
\(96\) | −1.81698e65 | − | 1.98115e65i | −0.698874 | − | 0.762019i | ||||
\(97\) | 1.02926e65 | 0.281228 | 0.140614 | − | 0.990064i | \(-0.455092\pi\) | ||||
0.140614 | + | 0.990064i | \(0.455092\pi\) | |||||||
\(98\) | − | 1.94416e65i | − | 0.378680i | ||||||
\(99\) | −8.35870e65 | − | 7.23944e64i | −1.16460 | − | 0.100866i | ||||
\(100\) | 5.58169e64 | 0.0558169 | ||||||||
\(101\) | − | 1.71518e66i | − | 1.23511i | −0.786528 | − | 0.617554i | \(-0.788124\pi\) | ||
0.786528 | − | 0.617554i | \(-0.211876\pi\) | |||||||
\(102\) | 6.56548e65 | − | 6.02142e65i | 0.341555 | − | 0.313252i | ||||
\(103\) | −2.35799e66 | −0.889023 | −0.444511 | − | 0.895773i | \(-0.646623\pi\) | ||||
−0.444511 | + | 0.895773i | \(0.646623\pi\) | |||||||
\(104\) | 4.85921e66i | 1.33188i | ||||||||
\(105\) | 4.20667e66 | + | 4.58676e66i | 0.840798 | + | 0.916767i | ||||
\(106\) | −2.38679e66 | −0.348915 | ||||||||
\(107\) | 1.01687e67i | 1.09043i | 0.838295 | + | 0.545216i | \(0.183552\pi\) | ||||
−0.838295 | + | 0.545216i | \(0.816448\pi\) | |||||||
\(108\) | −5.35392e66 | − | 6.95849e66i | −0.422365 | − | 0.548948i | ||||
\(109\) | 2.22359e67 | 1.29414 | 0.647070 | − | 0.762431i | \(-0.275994\pi\) | ||||
0.647070 | + | 0.762431i | \(0.275994\pi\) | |||||||
\(110\) | − | 1.44326e67i | − | 0.621422i | ||||||
\(111\) | 2.15203e67 | − | 1.97370e67i | 0.687368 | − | 0.630409i | ||||
\(112\) | 9.41225e66 | 0.223614 | ||||||||
\(113\) | 1.00520e68i | 1.78099i | 0.454991 | + | 0.890496i | \(0.349642\pi\) | ||||
−0.454991 | + | 0.890496i | \(0.650358\pi\) | |||||||
\(114\) | 4.64154e67 | + | 5.06092e67i | 0.614896 | + | 0.670454i | ||||
\(115\) | 8.73178e67 | 0.867110 | ||||||||
\(116\) | − | 1.06955e68i | − | 0.798158i | ||||||
\(117\) | −2.17846e67 | + | 2.51526e68i | −0.122466 | + | 1.41400i | ||||
\(118\) | 1.14281e68 | 0.485140 | ||||||||
\(119\) | 3.37496e68i | 1.08447i | ||||||||
\(120\) | 2.72011e68 | − | 2.49471e68i | 0.663140 | − | 0.608188i | ||||
\(121\) | −1.97678e68 | −0.366472 | ||||||||
\(122\) | − | 2.47150e68i | − | 0.349209i | ||||||
\(123\) | −9.97098e68 | − | 1.08719e69i | −1.07614 | − | 1.17337i | ||||
\(124\) | −4.82635e68 | −0.398752 | ||||||||
\(125\) | 1.63473e69i | 1.03613i | ||||||||
\(126\) | −1.47056e69 | − | 1.27365e68i | −0.716563 | − | 0.0620613i | ||||
\(127\) | 1.97327e69 | 0.740736 | 0.370368 | − | 0.928885i | \(-0.379232\pi\) | ||||
0.370368 | + | 0.928885i | \(0.379232\pi\) | |||||||
\(128\) | − | 2.80115e69i | − | 0.811721i | ||||||
\(129\) | 2.88638e69 | − | 2.64720e69i | 0.646983 | − | 0.593370i | ||||
\(130\) | −4.34299e69 | −0.754498 | ||||||||
\(131\) | − | 4.38140e68i | − | 0.0591099i | −0.999563 | − | 0.0295549i | \(-0.990591\pi\) | ||
0.999563 | − | 0.0295549i | \(-0.00940900\pi\) | |||||||
\(132\) | −5.21352e69 | − | 5.68458e69i | −0.547257 | − | 0.596704i | ||||
\(133\) | −2.60155e70 | −2.12876 | ||||||||
\(134\) | − | 9.48119e69i | − | 0.605905i | ||||||
\(135\) | 1.51985e70 | − | 1.16938e70i | 0.759951 | − | 0.584712i | ||||
\(136\) | 2.00147e70 | 0.784450 | ||||||||
\(137\) | 2.37612e69i | 0.0731290i | 0.999331 | + | 0.0365645i | \(0.0116414\pi\) | ||||
−0.999331 | + | 0.0365645i | \(0.988359\pi\) | |||||||
\(138\) | −1.52622e70 | + | 1.39975e70i | −0.369494 | + | 0.338875i | ||||
\(139\) | −2.10404e70 | −0.401390 | −0.200695 | − | 0.979654i | \(-0.564320\pi\) | ||||
−0.200695 | + | 0.979654i | \(0.564320\pi\) | |||||||
\(140\) | 5.72174e70i | 0.861595i | ||||||||
\(141\) | −2.08449e70 | − | 2.27283e70i | −0.248181 | − | 0.270605i | ||||
\(142\) | 7.29518e70 | 0.687893 | ||||||||
\(143\) | 2.21800e71i | 1.65910i | ||||||||
\(144\) | 2.50241e69 | − | 2.88929e70i | 0.0148729 | − | 0.171723i | ||||
\(145\) | 2.33608e71 | 1.10495 | ||||||||
\(146\) | 3.97109e70i | 0.149715i | ||||||||
\(147\) | 1.67252e71 | − | 1.53392e71i | 0.503384 | − | 0.461670i | ||||
\(148\) | 2.68454e71 | 0.646002 | ||||||||
\(149\) | − | 1.98769e71i | − | 0.383003i | −0.981492 | − | 0.191501i | \(-0.938664\pi\) | ||
0.981492 | − | 0.191501i | \(-0.0613357\pi\) | |||||||
\(150\) | −1.95433e70 | − | 2.13091e70i | −0.0301985 | − | 0.0329270i | ||||
\(151\) | 1.99268e71 | 0.247286 | 0.123643 | − | 0.992327i | \(-0.460542\pi\) | ||||
0.123643 | + | 0.992327i | \(0.460542\pi\) | |||||||
\(152\) | 1.54281e72i | 1.53983i | ||||||||
\(153\) | 1.03602e72 | + | 8.97291e70i | 0.832817 | + | 0.0721300i | ||||
\(154\) | −1.29676e72 | −0.840770 | ||||||||
\(155\) | − | 1.05415e72i | − | 0.552023i | ||||||
\(156\) | −1.71058e72 | + | 1.56883e72i | −0.724487 | + | 0.664452i | ||||
\(157\) | −1.78221e72 | −0.611322 | −0.305661 | − | 0.952140i | \(-0.598877\pi\) | ||||
−0.305661 | + | 0.952140i | \(0.598877\pi\) | |||||||
\(158\) | − | 1.00063e72i | − | 0.278348i | ||||||
\(159\) | −1.88315e72 | − | 2.05330e72i | −0.425382 | − | 0.463817i | ||||
\(160\) | 5.39788e72 | 0.991435 | ||||||||
\(161\) | − | 7.84547e72i | − | 1.17318i | ||||||
\(162\) | −7.81946e71 | + | 4.48034e72i | −0.0953194 | + | 0.546154i | ||||
\(163\) | −1.88015e73 | −1.87069 | −0.935344 | − | 0.353739i | \(-0.884910\pi\) | ||||
−0.935344 | + | 0.353739i | \(0.884910\pi\) | |||||||
\(164\) | − | 1.35621e73i | − | 1.10276i | ||||||
\(165\) | 1.24160e73 | − | 1.13872e73i | 0.826062 | − | 0.757610i | ||||
\(166\) | −1.06503e73 | −0.580493 | ||||||||
\(167\) | 9.45676e72i | 0.422765i | 0.977403 | + | 0.211383i | \(0.0677966\pi\) | ||||
−0.977403 | + | 0.211383i | \(0.932203\pi\) | |||||||
\(168\) | −2.24148e73 | − | 2.44401e73i | −0.822866 | − | 0.897215i | ||||
\(169\) | 3.36100e73 | 1.01439 | ||||||||
\(170\) | 1.78885e73i | 0.444384i | ||||||||
\(171\) | −6.91666e72 | + | 7.98601e73i | −0.141587 | + | 1.63478i | ||||
\(172\) | 3.60061e73 | 0.608047 | ||||||||
\(173\) | − | 2.80759e73i | − | 0.391573i | −0.980647 | − | 0.195786i | \(-0.937274\pi\) | ||
0.980647 | − | 0.195786i | \(-0.0627259\pi\) | |||||||
\(174\) | −4.08320e73 | + | 3.74484e73i | −0.470843 | + | 0.431826i | ||||
\(175\) | 1.09538e73 | 0.104547 | ||||||||
\(176\) | − | 2.54783e73i | − | 0.201490i | ||||||
\(177\) | 9.01663e73 | + | 9.83131e73i | 0.591461 | + | 0.644902i | ||||
\(178\) | 9.91890e71 | 0.00540261 | ||||||||
\(179\) | − | 7.97451e73i | − | 0.361039i | −0.983571 | − | 0.180519i | \(-0.942222\pi\) | ||
0.983571 | − | 0.180519i | \(-0.0577779\pi\) | |||||||
\(180\) | 1.75641e74 | + | 1.52122e73i | 0.661658 | + | 0.0573060i | ||||
\(181\) | 2.41480e74 | 0.757683 | 0.378841 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378841 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(182\) | 3.90216e74i | 1.02082i | ||||||||
\(183\) | 2.12617e74 | − | 1.94998e74i | 0.464207 | − | 0.425740i | ||||
\(184\) | −4.65264e74 | −0.848617 | ||||||||
\(185\) | 5.86347e74i | 0.894309i | ||||||||
\(186\) | 1.68986e74 | + | 1.84254e74i | 0.215736 | + | 0.235228i | ||||
\(187\) | 9.13579e74 | 0.977176 | ||||||||
\(188\) | − | 2.83523e74i | − | 0.254320i | ||||||
\(189\) | −1.05069e75 | − | 1.36558e75i | −0.791103 | − | 1.02820i | ||||
\(190\) | −1.37891e75 | −0.872303 | ||||||||
\(191\) | − | 2.34298e75i | − | 1.24643i | −0.782050 | − | 0.623215i | \(-0.785826\pi\) | ||
0.782050 | − | 0.623215i | \(-0.214174\pi\) | |||||||
\(192\) | −6.59796e74 | + | 6.05121e74i | −0.295440 | + | 0.270958i | ||||
\(193\) | −1.66241e75 | −0.627116 | −0.313558 | − | 0.949569i | \(-0.601521\pi\) | ||||
−0.313558 | + | 0.949569i | \(0.601521\pi\) | |||||||
\(194\) | − | 4.90170e74i | − | 0.155915i | ||||||
\(195\) | −3.42657e75 | − | 3.73617e75i | −0.919851 | − | 1.00296i | ||||
\(196\) | 2.08638e75 | 0.473089 | ||||||||
\(197\) | 6.66851e75i | 1.27833i | 0.769070 | + | 0.639165i | \(0.220720\pi\) | ||||
−0.769070 | + | 0.639165i | \(0.779280\pi\) | |||||||
\(198\) | −3.44767e74 | + | 3.98070e75i | −0.0559210 | + | 0.645667i | ||||
\(199\) | −3.43455e75 | −0.471756 | −0.235878 | − | 0.971783i | \(-0.575797\pi\) | ||||
−0.235878 | + | 0.971783i | \(0.575797\pi\) | |||||||
\(200\) | − | 6.49602e74i | − | 0.0756236i | ||||||
\(201\) | 8.15645e75 | − | 7.48055e75i | 0.805436 | − | 0.738693i | ||||
\(202\) | −8.16829e75 | −0.684756 | ||||||||
\(203\) | − | 2.09896e76i | − | 1.49498i | ||||||
\(204\) | 6.46189e75 | + | 7.04574e75i | 0.391349 | + | 0.426708i | ||||
\(205\) | 2.96218e76 | 1.52663 | ||||||||
\(206\) | 1.12295e76i | 0.492883i | ||||||||
\(207\) | −2.40834e76 | − | 2.08585e75i | −0.900940 | − | 0.0780301i | ||||
\(208\) | −7.66681e75 | −0.244638 | ||||||||
\(209\) | 7.04221e76i | 1.91815i | ||||||||
\(210\) | 2.18437e76 | − | 2.00336e76i | 0.508264 | − | 0.466146i | ||||
\(211\) | 2.69113e76 | 0.535321 | 0.267660 | − | 0.963513i | \(-0.413750\pi\) | ||||
0.267660 | + | 0.963513i | \(0.413750\pi\) | |||||||
\(212\) | − | 2.56138e76i | − | 0.435904i | ||||||
\(213\) | 5.75582e76 | + | 6.27587e76i | 0.838649 | + | 0.914423i | ||||
\(214\) | 4.84266e76 | 0.604546 | ||||||||
\(215\) | 7.86430e76i | 0.841765i | ||||||||
\(216\) | −8.09835e76 | + | 6.23094e76i | −0.743743 | + | 0.572242i | ||||
\(217\) | −9.47151e76 | −0.746875 | ||||||||
\(218\) | − | 1.05895e77i | − | 0.717483i | ||||||
\(219\) | −3.41624e76 | + | 3.13315e76i | −0.199018 | + | 0.182526i | ||||
\(220\) | 1.54884e77 | 0.776349 | ||||||||
\(221\) | − | 2.74910e77i | − | 1.18644i | ||||||
\(222\) | −9.39942e76 | − | 1.02487e77i | −0.349505 | − | 0.381084i | ||||
\(223\) | −2.32321e77 | −0.744780 | −0.372390 | − | 0.928076i | \(-0.621462\pi\) | ||||
−0.372390 | + | 0.928076i | \(0.621462\pi\) | |||||||
\(224\) | − | 4.84998e77i | − | 1.34139i | ||||||
\(225\) | 2.91227e75 | − | 3.36252e76i | 0.00695358 | − | 0.0802864i | ||||
\(226\) | 4.78708e77 | 0.987399 | ||||||||
\(227\) | 2.54284e77i | 0.453383i | 0.973967 | + | 0.226692i | \(0.0727909\pi\) | ||||
−0.973967 | + | 0.226692i | \(0.927209\pi\) | |||||||
\(228\) | −5.43112e77 | + | 4.98107e77i | −0.837606 | + | 0.768197i | ||||
\(229\) | −2.66886e77 | −0.356250 | −0.178125 | − | 0.984008i | \(-0.557003\pi\) | ||||
−0.178125 | + | 0.984008i | \(0.557003\pi\) | |||||||
\(230\) | − | 4.15837e77i | − | 0.480734i | ||||||
\(231\) | −1.02313e78 | − | 1.11558e78i | −1.02503 | − | 1.11765i | ||||
\(232\) | −1.24476e78 | −1.08139 | ||||||||
\(233\) | 1.67239e78i | 1.26064i | 0.776335 | + | 0.630321i | \(0.217077\pi\) | ||||
−0.776335 | + | 0.630321i | \(0.782923\pi\) | |||||||
\(234\) | 1.19785e78 | + | 1.03746e77i | 0.783935 | + | 0.0678964i | ||||
\(235\) | 6.19260e77 | 0.352074 | ||||||||
\(236\) | 1.22640e78i | 0.606091i | ||||||||
\(237\) | 8.60816e77 | − | 7.89484e77i | 0.370011 | − | 0.339350i | ||||
\(238\) | 1.60727e78 | 0.601242 | ||||||||
\(239\) | − | 2.67411e78i | − | 0.871062i | −0.900174 | − | 0.435531i | \(-0.856561\pi\) | ||
0.900174 | − | 0.435531i | \(-0.143439\pi\) | |||||||
\(240\) | 3.93612e77 | + | 4.29177e77i | 0.111711 | + | 0.121805i | ||||
\(241\) | 3.51268e78 | 0.869112 | 0.434556 | − | 0.900645i | \(-0.356905\pi\) | ||||
0.434556 | + | 0.900645i | \(0.356905\pi\) | |||||||
\(242\) | 9.41409e77i | 0.203175i | ||||||||
\(243\) | −4.47127e78 | + | 2.86224e78i | −0.842218 | + | 0.539138i | ||||
\(244\) | 2.65229e78 | 0.436271 | ||||||||
\(245\) | 4.55699e78i | 0.654933i | ||||||||
\(246\) | −5.17756e78 | + | 4.74852e78i | −0.650529 | + | 0.596623i | ||||
\(247\) | 2.11911e79 | 2.32891 | ||||||||
\(248\) | 5.61694e78i | 0.540250i | ||||||||
\(249\) | −8.40300e78 | − | 9.16224e78i | −0.707711 | − | 0.771655i | ||||
\(250\) | 7.78513e78 | 0.574441 | ||||||||
\(251\) | 1.00593e79i | 0.650632i | 0.945605 | + | 0.325316i | \(0.105471\pi\) | ||||
−0.945605 | + | 0.325316i | \(0.894529\pi\) | |||||||
\(252\) | 1.36681e78 | − | 1.57813e79i | 0.0775338 | − | 0.895210i | ||||
\(253\) | −2.12372e79 | −1.05711 | ||||||||
\(254\) | − | 9.39738e78i | − | 0.410671i | ||||||
\(255\) | −1.53890e79 | + | 1.41138e79i | −0.590725 | + | 0.541774i | ||||
\(256\) | −2.52231e79 | −0.850904 | ||||||||
\(257\) | − | 7.80840e78i | − | 0.231616i | −0.993272 | − | 0.115808i | \(-0.963054\pi\) | ||
0.993272 | − | 0.115808i | \(-0.0369458\pi\) | |||||||
\(258\) | −1.26069e79 | − | 1.37459e79i | −0.328970 | − | 0.358694i | ||||
\(259\) | 5.26830e79 | 1.20998 | ||||||||
\(260\) | − | 4.66068e79i | − | 0.942603i | ||||||
\(261\) | −6.44320e79 | − | 5.58044e78i | −1.14806 | − | 0.0994332i | ||||
\(262\) | −2.08657e78 | −0.0327711 | ||||||||
\(263\) | − | 8.43767e79i | − | 1.16865i | −0.811521 | − | 0.584323i | \(-0.801360\pi\) | ||
0.811521 | − | 0.584323i | \(-0.198640\pi\) | |||||||
\(264\) | −6.61576e79 | + | 6.06754e79i | −0.808445 | + | 0.741452i | ||||
\(265\) | 5.59446e79 | 0.603454 | ||||||||
\(266\) | 1.23895e80i | 1.18021i | ||||||||
\(267\) | 7.82590e77 | + | 8.53300e77i | 0.00658662 | + | 0.00718174i | ||||
\(268\) | 1.01747e80 | 0.756964 | ||||||||
\(269\) | − | 1.40981e80i | − | 0.927543i | −0.885955 | − | 0.463771i | \(-0.846496\pi\) | ||
0.885955 | − | 0.463771i | \(-0.153504\pi\) | |||||||
\(270\) | −5.56900e79 | − | 7.23803e79i | −0.324170 | − | 0.421324i | ||||
\(271\) | 2.33299e80 | 1.20206 | 0.601031 | − | 0.799225i | \(-0.294757\pi\) | ||||
0.601031 | + | 0.799225i | \(0.294757\pi\) | |||||||
\(272\) | 3.15790e79i | 0.144087i | ||||||||
\(273\) | −3.35694e80 | + | 3.07876e80i | −1.35699 | + | 1.24454i | ||||
\(274\) | 1.13159e79 | 0.0405434 | ||||||||
\(275\) | − | 2.96513e79i | − | 0.0942031i | ||||||
\(276\) | −1.50214e80 | − | 1.63786e80i | −0.423360 | − | 0.461612i | ||||
\(277\) | 5.90165e80 | 1.47619 | 0.738093 | − | 0.674698i | \(-0.235726\pi\) | ||||
0.738093 | + | 0.674698i | \(0.235726\pi\) | |||||||
\(278\) | 1.00202e80i | 0.222534i | ||||||||
\(279\) | −2.51816e79 | + | 2.90749e80i | −0.0496758 | + | 0.573560i | ||||
\(280\) | 6.65901e80 | 1.16733 | ||||||||
\(281\) | 1.26663e81i | 1.97397i | 0.160808 | + | 0.986986i | \(0.448590\pi\) | ||||
−0.160808 | + | 0.986986i | \(0.551410\pi\) | |||||||
\(282\) | −1.08240e80 | + | 9.92704e79i | −0.150026 | + | 0.137594i | ||||
\(283\) | 1.62778e80 | 0.200744 | 0.100372 | − | 0.994950i | \(-0.467997\pi\) | ||||
0.100372 | + | 0.994950i | \(0.467997\pi\) | |||||||
\(284\) | 7.82883e80i | 0.859392i | ||||||||
\(285\) | −1.08794e81 | − | 1.18624e81i | −1.06347 | − | 1.15956i | ||||
\(286\) | 1.05629e81 | 0.919821 | ||||||||
\(287\) | − | 2.66151e81i | − | 2.06550i | ||||||
\(288\) | −1.48881e81 | − | 1.28945e80i | −1.03012 | − | 0.0892179i | ||||
\(289\) | 4.88092e80 | 0.301213 | ||||||||
\(290\) | − | 1.11252e81i | − | 0.612596i | ||||||
\(291\) | 4.21681e80 | − | 3.86738e80i | 0.207260 | − | 0.190085i | ||||
\(292\) | −4.26158e80 | −0.187041 | ||||||||
\(293\) | 1.13023e81i | 0.443133i | 0.975145 | + | 0.221567i | \(0.0711170\pi\) | ||||
−0.975145 | + | 0.221567i | \(0.928883\pi\) | |||||||
\(294\) | −7.30507e80 | − | 7.96511e80i | −0.255954 | − | 0.279081i | ||||
\(295\) | −2.67866e81 | −0.839057 | ||||||||
\(296\) | − | 3.12429e81i | − | 0.875236i | ||||||
\(297\) | −3.69652e81 | + | 2.84413e81i | −0.926468 | + | 0.712832i | ||||
\(298\) | −9.46606e80 | −0.212340 | ||||||||
\(299\) | 6.39058e81i | 1.28349i | ||||||||
\(300\) | 2.28678e80 | − | 2.09728e80i | 0.0411361 | − | 0.0377273i | ||||
\(301\) | 7.06605e81 | 1.13889 | ||||||||
\(302\) | − | 9.48984e80i | − | 0.137098i | ||||||
\(303\) | −6.44469e81 | − | 7.02698e81i | −0.834824 | − | 0.910253i | ||||
\(304\) | −2.43423e81 | −0.282835 | ||||||||
\(305\) | 5.79302e81i | 0.603963i | ||||||||
\(306\) | 4.27321e80 | − | 4.93387e81i | 0.0399896 | − | 0.461722i | ||||
\(307\) | 2.32712e82 | 1.95548 | 0.977738 | − | 0.209829i | \(-0.0672908\pi\) | ||||
0.977738 | + | 0.209829i | \(0.0672908\pi\) | |||||||
\(308\) | − | 1.39162e82i | − | 1.05038i | ||||||
\(309\) | −9.66051e81 | + | 8.85998e81i | −0.655194 | + | 0.600901i | ||||
\(310\) | −5.02023e81 | −0.306047 | ||||||||
\(311\) | 5.11858e81i | 0.280580i | 0.990110 | + | 0.140290i | \(0.0448035\pi\) | ||||
−0.990110 | + | 0.140290i | \(0.955196\pi\) | |||||||
\(312\) | 1.82581e82 | + | 1.99078e82i | 0.900233 | + | 0.981572i | ||||
\(313\) | 5.81970e81 | 0.258189 | 0.129094 | − | 0.991632i | \(-0.458793\pi\) | ||||
0.129094 | + | 0.991632i | \(0.458793\pi\) | |||||||
\(314\) | 8.48749e81i | 0.338923i | ||||||||
\(315\) | 3.44689e82 | + | 2.98534e81i | 1.23931 | + | 0.107336i | ||||
\(316\) | 1.07382e82 | 0.347743 | ||||||||
\(317\) | 1.66865e82i | 0.486867i | 0.969918 | + | 0.243434i | \(0.0782738\pi\) | ||||
−0.969918 | + | 0.243434i | \(0.921726\pi\) | |||||||
\(318\) | −9.77849e81 | + | 8.96819e81i | −0.257144 | + | 0.235836i | ||||
\(319\) | −5.68173e82 | −1.34706 | ||||||||
\(320\) | − | 1.79770e82i | − | 0.384386i | ||||||
\(321\) | 3.82081e82 | + | 4.16603e82i | 0.737036 | + | 0.803630i | ||||
\(322\) | −3.73628e82 | −0.650423 | ||||||||
\(323\) | − | 8.72845e82i | − | 1.37168i | ||||||
\(324\) | −4.80807e82 | − | 8.39146e81i | −0.682316 | − | 0.119084i | ||||
\(325\) | −8.92253e81 | −0.114377 | ||||||||
\(326\) | 8.95391e82i | 1.03713i | ||||||||
\(327\) | 9.10991e82 | − | 8.35501e82i | 0.953758 | − | 0.874724i | ||||
\(328\) | −1.57837e83 | −1.49407 | ||||||||
\(329\) | − | 5.56403e82i | − | 0.476349i | ||||||
\(330\) | −5.42296e82 | − | 5.91294e82i | −0.420026 | − | 0.457977i | ||||
\(331\) | 9.56493e82 | 0.670437 | 0.335219 | − | 0.942140i | \(-0.391190\pi\) | ||||
0.335219 | + | 0.942140i | \(0.391190\pi\) | |||||||
\(332\) | − | 1.14294e83i | − | 0.725216i | ||||||
\(333\) | 1.40067e82 | − | 1.61722e83i | 0.0804777 | − | 0.929201i | ||||
\(334\) | 4.50364e82 | 0.234385 | ||||||||
\(335\) | 2.22233e83i | 1.04792i | ||||||||
\(336\) | 3.85613e82 | − | 3.53659e82i | 0.164800 | − | 0.151143i | ||||
\(337\) | −4.91700e83 | −1.90508 | −0.952540 | − | 0.304412i | \(-0.901540\pi\) | ||||
−0.952540 | + | 0.304412i | \(0.901540\pi\) | |||||||
\(338\) | − | 1.60062e83i | − | 0.562390i | ||||||
\(339\) | 3.77696e83 | + | 4.11822e83i | 1.20379 | + | 1.31256i | ||||
\(340\) | −1.91970e83 | −0.555174 | ||||||||
\(341\) | 2.56387e83i | 0.672980i | ||||||||
\(342\) | 3.80321e83 | + | 3.29395e82i | 0.906336 | + | 0.0784974i | ||||
\(343\) | −1.90005e83 | −0.411207 | ||||||||
\(344\) | − | 4.19042e83i | − | 0.823813i | ||||||
\(345\) | 3.57735e83 | − | 3.28091e83i | 0.639045 | − | 0.586090i | ||||
\(346\) | −1.33707e83 | −0.217092 | ||||||||
\(347\) | 1.12779e84i | 1.66478i | 0.554193 | + | 0.832388i | \(0.313027\pi\) | ||||
−0.554193 | + | 0.832388i | \(0.686973\pi\) | |||||||
\(348\) | −4.01878e83 | − | 4.38189e83i | −0.539485 | − | 0.588229i | ||||
\(349\) | 1.60460e84 | 1.95942 | 0.979710 | − | 0.200421i | \(-0.0642309\pi\) | ||||
0.979710 | + | 0.200421i | \(0.0642309\pi\) | |||||||
\(350\) | − | 5.21660e82i | − | 0.0579618i | ||||||
\(351\) | 8.55843e83 | + | 1.11234e84i | 0.865484 | + | 1.12487i | ||||
\(352\) | −1.31286e84 | −1.20867 | ||||||||
\(353\) | 5.07192e83i | 0.425214i | 0.977138 | + | 0.212607i | \(0.0681954\pi\) | ||||
−0.977138 | + | 0.212607i | \(0.931805\pi\) | |||||||
\(354\) | 4.68201e83 | − | 4.29403e83i | 0.357540 | − | 0.327912i | ||||
\(355\) | −1.70994e84 | −1.18972 | ||||||||
\(356\) | 1.06445e82i | 0.00674954i | ||||||||
\(357\) | 1.26812e84 | + | 1.38270e84i | 0.733008 | + | 0.799238i | ||||
\(358\) | −3.79773e83 | −0.200163 | ||||||||
\(359\) | − | 1.65366e84i | − | 0.794929i | −0.917618 | − | 0.397464i | \(-0.869890\pi\) | ||
0.917618 | − | 0.397464i | \(-0.130110\pi\) | |||||||
\(360\) | 1.77041e83 | − | 2.04413e84i | 0.0776411 | − | 0.896448i | ||||
\(361\) | 4.22938e84 | 1.69254 | ||||||||
\(362\) | − | 1.15001e84i | − | 0.420067i | ||||||
\(363\) | −8.09872e83 | + | 7.42761e83i | −0.270083 | + | 0.247702i | ||||
\(364\) | −4.18760e84 | −1.27532 | ||||||||
\(365\) | − | 9.30796e83i | − | 0.258935i | ||||||
\(366\) | −9.28648e83 | − | 1.01255e84i | −0.236035 | − | 0.257361i | ||||
\(367\) | −4.67354e84 | −1.08559 | −0.542794 | − | 0.839866i | \(-0.682634\pi\) | ||||
−0.542794 | + | 0.839866i | \(0.682634\pi\) | |||||||
\(368\) | − | 7.34090e83i | − | 0.155873i | ||||||
\(369\) | −8.17008e84 | − | 7.07608e83i | −1.58619 | − | 0.137380i | ||||
\(370\) | 2.79238e84 | 0.495813 | ||||||||
\(371\) | − | 5.02660e84i | − | 0.816461i | ||||||
\(372\) | −1.97732e84 | + | 1.81347e84i | −0.293873 | + | 0.269521i | ||||
\(373\) | 3.60604e84 | 0.490501 | 0.245250 | − | 0.969460i | \(-0.421130\pi\) | ||||
0.245250 | + | 0.969460i | \(0.421130\pi\) | |||||||
\(374\) | − | 4.35077e84i | − | 0.541756i | ||||||
\(375\) | 6.14238e84 | + | 6.69737e84i | 0.700334 | + | 0.763611i | ||||
\(376\) | −3.29967e84 | −0.344565 | ||||||||
\(377\) | 1.70972e85i | 1.63554i | ||||||||
\(378\) | −6.50334e84 | + | 5.00372e84i | −0.570042 | + | 0.438595i | ||||
\(379\) | 1.99630e85 | 1.60373 | 0.801866 | − | 0.597504i | \(-0.203841\pi\) | ||||
0.801866 | + | 0.597504i | \(0.203841\pi\) | |||||||
\(380\) | − | 1.47978e85i | − | 1.08978i | ||||||
\(381\) | 8.08435e84 | − | 7.41443e84i | 0.545910 | − | 0.500672i | ||||
\(382\) | −1.11581e85 | −0.691033 | ||||||||
\(383\) | 1.29127e85i | 0.733598i | 0.930300 | + | 0.366799i | \(0.119546\pi\) | ||||
−0.930300 | + | 0.366799i | \(0.880454\pi\) | |||||||
\(384\) | −1.05251e85 | − | 1.14761e85i | −0.548652 | − | 0.598225i | ||||
\(385\) | 3.03953e85 | 1.45413 | ||||||||
\(386\) | 7.91698e84i | 0.347679i | ||||||||
\(387\) | 1.87863e84 | − | 2.16908e85i | 0.0757494 | − | 0.874607i | ||||
\(388\) | 5.26025e84 | 0.194787 | ||||||||
\(389\) | 4.51592e85i | 1.53606i | 0.640412 | + | 0.768032i | \(0.278764\pi\) | ||||
−0.640412 | + | 0.768032i | \(0.721236\pi\) | |||||||
\(390\) | −1.77929e85 | + | 1.63185e85i | −0.556052 | + | 0.509974i | ||||
\(391\) | 2.63223e85 | 0.755947 | ||||||||
\(392\) | − | 2.42815e85i | − | 0.640965i | ||||||
\(393\) | −1.64628e84 | − | 1.79503e84i | −0.0399531 | − | 0.0435630i | ||||
\(394\) | 3.17577e85 | 0.708719 | ||||||||
\(395\) | 2.34540e85i | 0.481408i | ||||||||
\(396\) | −4.27189e85 | − | 3.69987e84i | −0.806638 | − | 0.0698627i | ||||
\(397\) | 1.54656e85 | 0.268708 | 0.134354 | − | 0.990933i | \(-0.457104\pi\) | ||||
0.134354 | + | 0.990933i | \(0.457104\pi\) | |||||||
\(398\) | 1.63565e85i | 0.261546i | ||||||||
\(399\) | −1.06584e86 | + | 9.77514e85i | −1.56886 | + | 1.43886i | ||||
\(400\) | 1.02494e84 | 0.0138905 | ||||||||
\(401\) | − | 5.34957e85i | − | 0.667659i | −0.942634 | − | 0.333829i | \(-0.891659\pi\) | ||
0.942634 | − | 0.333829i | \(-0.108341\pi\) | |||||||
\(402\) | −3.56250e85 | − | 3.88438e85i | −0.409538 | − | 0.446541i | ||||
\(403\) | 7.71508e85 | 0.817098 | ||||||||
\(404\) | − | 8.76580e85i | − | 0.855473i | ||||||
\(405\) | 1.83283e85 | − | 1.05016e86i | 0.164856 | − | 0.944582i | ||||
\(406\) | −9.99595e85 | −0.828829 | ||||||||
\(407\) | − | 1.42609e86i | − | 1.09027i | ||||||
\(408\) | 8.19989e85 | − | 7.52040e85i | 0.578126 | − | 0.530219i | ||||
\(409\) | −1.53999e86 | −1.00150 | −0.500748 | − | 0.865593i | \(-0.666942\pi\) | ||||
−0.500748 | + | 0.865593i | \(0.666942\pi\) | |||||||
\(410\) | − | 1.41069e86i | − | 0.846379i | ||||||
\(411\) | 8.92811e84 | + | 9.73479e84i | 0.0494287 | + | 0.0538948i | ||||
\(412\) | −1.20510e86 | −0.615764 | ||||||||
\(413\) | 2.40677e86i | 1.13523i | ||||||||
\(414\) | −9.93355e84 | + | 1.14693e86i | −0.0432607 | + | 0.499490i | ||||
\(415\) | 2.49637e86 | 1.00397 | ||||||||
\(416\) | 3.95058e86i | 1.46751i | ||||||||
\(417\) | −8.62012e85 | + | 7.90580e85i | −0.295817 | + | 0.271304i | ||||
\(418\) | 3.35374e86 | 1.06344 | ||||||||
\(419\) | − | 2.41715e86i | − | 0.708339i | −0.935181 | − | 0.354170i | \(-0.884764\pi\) | ||
0.935181 | − | 0.354170i | \(-0.115236\pi\) | |||||||
\(420\) | 2.14991e86 | + | 2.34416e86i | 0.582362 | + | 0.634980i | ||||
\(421\) | −3.82162e86 | −0.957058 | −0.478529 | − | 0.878072i | \(-0.658830\pi\) | ||||
−0.478529 | + | 0.878072i | \(0.658830\pi\) | |||||||
\(422\) | − | 1.28161e86i | − | 0.296787i | ||||||
\(423\) | −1.70800e86 | − | 1.47929e85i | −0.365810 | − | 0.0316827i | ||||
\(424\) | −2.98095e86 | −0.590584 | ||||||||
\(425\) | 3.67512e85i | 0.0673655i | ||||||||
\(426\) | 2.98879e86 | − | 2.74112e86i | 0.506965 | − | 0.464955i | ||||
\(427\) | 5.20500e86 | 0.817149 | ||||||||
\(428\) | 5.19690e86i | 0.755266i | ||||||||
\(429\) | 8.33400e86 | + | 9.08700e86i | 1.12141 | + | 1.22273i | ||||
\(430\) | 3.74525e86 | 0.466683 | ||||||||
\(431\) | − | 1.00679e87i | − | 1.16196i | −0.813918 | − | 0.580979i | \(-0.802670\pi\) | ||
0.813918 | − | 0.580979i | \(-0.197330\pi\) | |||||||
\(432\) | −9.83112e85 | − | 1.27775e86i | −0.105109 | − | 0.136610i | ||||
\(433\) | −1.35263e87 | −1.33992 | −0.669962 | − | 0.742396i | \(-0.733690\pi\) | ||||
−0.669962 | + | 0.742396i | \(0.733690\pi\) | |||||||
\(434\) | 4.51066e86i | 0.414075i | ||||||||
\(435\) | 9.57075e86 | − | 8.77766e86i | 0.814330 | − | 0.746850i | ||||
\(436\) | 1.13641e87 | 0.896360 | ||||||||
\(437\) | 2.02903e87i | 1.48388i | ||||||||
\(438\) | 1.49211e86 | + | 1.62693e86i | 0.101194 | + | 0.110337i | ||||
\(439\) | −2.91566e87 | −1.83403 | −0.917017 | − | 0.398848i | \(-0.869410\pi\) | ||||
−0.917017 | + | 0.398848i | \(0.869410\pi\) | |||||||
\(440\) | − | 1.80255e87i | − | 1.05184i | ||||||
\(441\) | 1.08858e86 | − | 1.25688e87i | 0.0589366 | − | 0.680486i | ||||
\(442\) | −1.30921e87 | −0.657772 | ||||||||
\(443\) | − | 2.75569e86i | − | 0.128501i | −0.997934 | − | 0.0642506i | \(-0.979534\pi\) | ||
0.997934 | − | 0.0642506i | \(-0.0204657\pi\) | |||||||
\(444\) | 1.09984e87 | − | 1.00870e87i | 0.476092 | − | 0.436640i | ||||
\(445\) | −2.32492e85 | −0.00934390 | ||||||||
\(446\) | 1.10639e87i | 0.412913i | ||||||||
\(447\) | −7.46862e86 | − | 8.14343e86i | −0.258876 | − | 0.282266i | ||||
\(448\) | −1.61522e87 | −0.520066 | ||||||||
\(449\) | − | 2.94185e87i | − | 0.880017i | −0.897994 | − | 0.440009i | \(-0.854975\pi\) | ||
0.897994 | − | 0.440009i | \(-0.145025\pi\) | |||||||
\(450\) | −1.60135e86 | − | 1.38692e85i | −0.0445115 | − | 0.00385513i | ||||
\(451\) | −7.20452e87 | −1.86114 | ||||||||
\(452\) | 5.13726e87i | 1.23357i | ||||||||
\(453\) | 8.16389e86 | − | 7.48738e86i | 0.182245 | − | 0.167143i | ||||
\(454\) | 1.21099e87 | 0.251360 | ||||||||
\(455\) | − | 9.14640e87i | − | 1.76553i | ||||||
\(456\) | 5.79701e87 | + | 6.32078e87i | 1.04079 | + | 1.13483i | ||||
\(457\) | 2.81675e87 | 0.470450 | 0.235225 | − | 0.971941i | \(-0.424417\pi\) | ||||
0.235225 | + | 0.971941i | \(0.424417\pi\) | |||||||
\(458\) | 1.27100e87i | 0.197509i | ||||||||
\(459\) | 4.58164e87 | − | 3.52515e87i | 0.662525 | − | 0.509752i | ||||
\(460\) | 4.46256e87 | 0.600586 | ||||||||
\(461\) | 1.02715e88i | 1.28678i | 0.765539 | + | 0.643389i | \(0.222472\pi\) | ||||
−0.765539 | + | 0.643389i | \(0.777528\pi\) | |||||||
\(462\) | −5.31276e87 | + | 4.87251e87i | −0.619633 | + | 0.568287i | ||||
\(463\) | −2.23256e87 | −0.242455 | −0.121227 | − | 0.992625i | \(-0.538683\pi\) | ||||
−0.121227 | + | 0.992625i | \(0.538683\pi\) | |||||||
\(464\) | − | 1.96396e87i | − | 0.198628i | ||||||
\(465\) | −3.96091e87 | − | 4.31879e87i | −0.373119 | − | 0.406831i | ||||
\(466\) | 7.96448e87 | 0.698912 | ||||||||
\(467\) | − | 1.05727e86i | − | 0.00864431i | −0.999991 | − | 0.00432216i | \(-0.998624\pi\) | ||
0.999991 | − | 0.00432216i | \(-0.00137579\pi\) | |||||||
\(468\) | −1.11335e87 | + | 1.28548e88i | −0.0848237 | + | 0.979379i | ||||
\(469\) | 1.99675e88 | 1.41782 | ||||||||
\(470\) | − | 2.94913e87i | − | 0.195193i | ||||||
\(471\) | −7.30159e87 | + | 6.69653e87i | −0.450534 | + | 0.413200i | ||||
\(472\) | 1.42730e88 | 0.821162 | ||||||||
\(473\) | − | 1.91273e88i | − | 1.02621i | ||||||
\(474\) | −3.75979e87 | − | 4.09950e87i | −0.188139 | − | 0.205138i | ||||
\(475\) | −2.83292e87 | −0.132235 | ||||||||
\(476\) | 1.72484e88i | 0.751139i | ||||||||
\(477\) | −1.54302e88 | − | 1.33641e87i | −0.626998 | − | 0.0543041i | ||||
\(478\) | −1.27350e88 | −0.482925 | ||||||||
\(479\) | 3.13406e88i | 1.10927i | 0.832095 | + | 0.554633i | \(0.187141\pi\) | ||||
−0.832095 | + | 0.554633i | \(0.812859\pi\) | |||||||
\(480\) | 2.21148e88 | − | 2.02822e88i | 0.730670 | − | 0.670122i | ||||
\(481\) | −4.29133e88 | −1.32375 | ||||||||
\(482\) | − | 1.67286e88i | − | 0.481844i | ||||||
\(483\) | −2.94788e88 | − | 3.21424e88i | −0.792967 | − | 0.864614i | ||||
\(484\) | −1.01027e88 | −0.253829 | ||||||||
\(485\) | 1.14892e88i | 0.269658i | ||||||||
\(486\) | 1.36310e88 | + | 2.12937e88i | 0.298903 | + | 0.466934i | ||||
\(487\) | 6.55251e88 | 1.34262 | 0.671308 | − | 0.741179i | \(-0.265733\pi\) | ||||
0.671308 | + | 0.741179i | \(0.265733\pi\) | |||||||
\(488\) | − | 3.08675e88i | − | 0.591082i | ||||||
\(489\) | −7.70284e88 | + | 7.06454e88i | −1.37866 | + | 1.26442i | ||||
\(490\) | 2.17019e88 | 0.363101 | ||||||||
\(491\) | − | 1.03456e89i | − | 1.61833i | −0.587582 | − | 0.809165i | \(-0.699920\pi\) | ||
0.587582 | − | 0.809165i | \(-0.300080\pi\) | |||||||
\(492\) | −5.09587e88 | − | 5.55630e88i | −0.745367 | − | 0.812714i | ||||
\(493\) | 7.04221e88 | 0.963297 | ||||||||
\(494\) | − | 1.00919e89i | − | 1.29117i | ||||||
\(495\) | 8.08110e87 | − | 9.33049e88i | 0.0967162 | − | 1.11669i | ||||
\(496\) | −8.86236e87 | −0.0992326 | ||||||||
\(497\) | 1.53638e89i | 1.60967i | ||||||||
\(498\) | −4.36337e88 | + | 4.00180e88i | −0.427813 | + | 0.392362i | ||||
\(499\) | −4.58449e88 | −0.420700 | −0.210350 | − | 0.977626i | \(-0.567460\pi\) | ||||
−0.210350 | + | 0.977626i | \(0.567460\pi\) | |||||||
\(500\) | 8.35462e88i | 0.717656i | ||||||||
\(501\) | 3.55332e88 | + | 3.87437e88i | 0.285752 | + | 0.311570i | ||||
\(502\) | 4.79059e88 | 0.360717 | ||||||||
\(503\) | 1.87043e89i | 1.31886i | 0.751767 | + | 0.659429i | \(0.229202\pi\) | ||||
−0.751767 | + | 0.659429i | \(0.770798\pi\) | |||||||
\(504\) | −1.83664e89 | − | 1.59071e88i | −1.21288 | − | 0.105047i | ||||
\(505\) | 1.91459e89 | 1.18430 | ||||||||
\(506\) | 1.01139e89i | 0.586071i | ||||||||
\(507\) | 1.37698e89 | − | 1.26287e89i | 0.747591 | − | 0.685641i | ||||
\(508\) | 1.00848e89 | 0.513056 | ||||||||
\(509\) | 1.10894e89i | 0.528714i | 0.964425 | + | 0.264357i | \(0.0851598\pi\) | ||||
−0.964425 | + | 0.264357i | \(0.914840\pi\) | |||||||
\(510\) | 6.72147e88 | + | 7.32878e88i | 0.300365 | + | 0.327503i | ||||
\(511\) | −8.36317e88 | −0.350333 | ||||||||
\(512\) | − | 8.65670e88i | − | 0.339972i | ||||||
\(513\) | 2.71732e89 | + | 3.53170e89i | 1.00062 | + | 1.30050i | ||||
\(514\) | −3.71863e88 | −0.128410 | ||||||||
\(515\) | − | 2.63213e89i | − | 0.852449i | ||||||
\(516\) | 1.47514e89 | − | 1.35290e89i | 0.448120 | − | 0.410986i | ||||
\(517\) | −1.50615e89 | −0.429219 | ||||||||
\(518\) | − | 2.50895e89i | − | 0.670825i | ||||||
\(519\) | −1.05493e89 | − | 1.15025e89i | −0.264669 | − | 0.288582i | ||||
\(520\) | −5.42414e89 | −1.27709 | ||||||||
\(521\) | − | 3.29116e89i | − | 0.727284i | −0.931539 | − | 0.363642i | \(-0.881533\pi\) | ||
0.931539 | − | 0.363642i | \(-0.118467\pi\) | |||||||
\(522\) | −2.65759e88 | + | 3.06847e89i | −0.0551267 | + | 0.636496i | ||||
\(523\) | 3.94819e89 | 0.768851 | 0.384425 | − | 0.923156i | \(-0.374400\pi\) | ||||
0.384425 | + | 0.923156i | \(0.374400\pi\) | |||||||
\(524\) | − | 2.23921e88i | − | 0.0409413i | ||||||
\(525\) | 4.48772e88 | − | 4.11584e88i | 0.0770492 | − | 0.0706645i | ||||
\(526\) | −4.01831e89 | −0.647908 | ||||||||
\(527\) | − | 3.17779e89i | − | 0.481254i | ||||||
\(528\) | −9.57331e88 | − | 1.04383e89i | −0.136189 | − | 0.148494i | ||||
\(529\) | 1.36341e89 | 0.182218 | ||||||||
\(530\) | − | 2.66427e89i | − | 0.334561i | ||||||
\(531\) | 7.38810e89 | + | 6.39881e88i | 0.871793 | + | 0.0755057i | ||||
\(532\) | −1.32957e90 | −1.47445 | ||||||||
\(533\) | 2.16795e90i | 2.25970i | ||||||||
\(534\) | 4.06370e87 | − | 3.72696e87i | 0.00398163 | − | 0.00365169i | ||||
\(535\) | −1.13509e90 | −1.04557 | ||||||||
\(536\) | − | 1.18414e90i | − | 1.02557i | ||||||
\(537\) | −2.99637e89 | − | 3.26710e89i | −0.244030 | − | 0.266079i | ||||
\(538\) | −6.71397e89 | −0.514239 | ||||||||
\(539\) | − | 1.10834e90i | − | 0.798440i | ||||||
\(540\) | 7.76749e89 | − | 5.97637e89i | 0.526365 | − | 0.404989i | ||||
\(541\) | −6.61490e89 | −0.421710 | −0.210855 | − | 0.977517i | \(-0.567625\pi\) | ||||
−0.210855 | + | 0.977517i | \(0.567625\pi\) | |||||||
\(542\) | − | 1.11105e90i | − | 0.666435i | ||||||
\(543\) | 9.89325e89 | − | 9.07344e89i | 0.558399 | − | 0.512127i | ||||
\(544\) | 1.62722e90 | 0.864333 | ||||||||
\(545\) | 2.48211e90i | 1.24090i | ||||||||
\(546\) | 1.46621e90 | + | 1.59869e90i | 0.689985 | + | 0.752327i | ||||
\(547\) | 2.03418e90 | 0.901170 | 0.450585 | − | 0.892734i | \(-0.351215\pi\) | ||||
0.450585 | + | 0.892734i | \(0.351215\pi\) | |||||||
\(548\) | 1.21436e89i | 0.0506513i | ||||||||
\(549\) | 1.38384e89 | − | 1.59779e90i | 0.0543498 | − | 0.627526i | ||||
\(550\) | −1.41210e89 | −0.0522271 | ||||||||
\(551\) | 5.42840e90i | 1.89090i | ||||||||
\(552\) | −1.90616e90 | + | 1.74820e90i | −0.625416 | + | 0.573590i | ||||
\(553\) | 2.10733e90 | 0.651334 | ||||||||
\(554\) | − | 2.81057e90i | − | 0.818412i | ||||||
\(555\) | 2.20316e90 | + | 2.40222e90i | 0.604474 | + | 0.659090i | ||||
\(556\) | −1.07531e90 | −0.278015 | ||||||||
\(557\) | 6.52629e89i | 0.159017i | 0.996834 | + | 0.0795087i | \(0.0253352\pi\) | ||||
−0.996834 | + | 0.0795087i | \(0.974665\pi\) | |||||||
\(558\) | 1.38464e90 | + | 1.19924e89i | 0.317987 | + | 0.0275408i | ||||
\(559\) | −5.75569e90 | −1.24597 | ||||||||
\(560\) | 1.05065e90i | 0.214414i | ||||||||
\(561\) | 3.74287e90 | − | 3.43271e90i | 0.720162 | − | 0.660485i | ||||
\(562\) | 6.03212e90 | 1.09439 | ||||||||
\(563\) | − | 8.83877e89i | − | 0.151222i | −0.997137 | − | 0.0756110i | \(-0.975909\pi\) | ||
0.997137 | − | 0.0756110i | \(-0.0240907\pi\) | |||||||
\(564\) | −1.06532e90 | − | 1.16158e90i | −0.171898 | − | 0.187429i | ||||
\(565\) | −1.12206e91 | −1.70772 | ||||||||
\(566\) | − | 7.75203e89i | − | 0.111294i | ||||||
\(567\) | −9.43565e90 | − | 1.64679e90i | −1.27800 | − | 0.223047i | ||||
\(568\) | 9.11125e90 | 1.16435 | ||||||||
\(569\) | − | 1.29091e91i | − | 1.55665i | −0.627862 | − | 0.778325i | \(-0.716070\pi\) | ||
0.627862 | − | 0.778325i | \(-0.283930\pi\) | |||||||
\(570\) | −5.64930e90 | + | 5.18117e90i | −0.642872 | + | 0.589600i | ||||
\(571\) | 7.71993e90 | 0.829128 | 0.414564 | − | 0.910020i | \(-0.363934\pi\) | ||||
0.414564 | + | 0.910020i | \(0.363934\pi\) | |||||||
\(572\) | 1.13356e91i | 1.14914i | ||||||||
\(573\) | −8.80361e90 | − | 9.59904e90i | −0.842477 | − | 0.918598i | ||||
\(574\) | −1.26750e91 | −1.14513 | ||||||||
\(575\) | − | 8.54324e89i | − | 0.0728758i | ||||||
\(576\) | −4.29435e89 | + | 4.95828e90i | −0.0345904 | + | 0.399382i | ||||
\(577\) | 2.03705e91 | 1.54953 | 0.774766 | − | 0.632248i | \(-0.217867\pi\) | ||||
0.774766 | + | 0.632248i | \(0.217867\pi\) | |||||||
\(578\) | − | 2.32446e90i | − | 0.166995i | ||||||
\(579\) | −6.81079e90 | + | 6.24641e90i | −0.462173 | + | 0.423875i | ||||
\(580\) | 1.19390e91 | 0.765322 | ||||||||
\(581\) | − | 2.24298e91i | − | 1.35835i | ||||||
\(582\) | −1.84178e90 | − | 2.00819e90i | −0.105385 | − | 0.114907i | ||||
\(583\) | −1.36067e91 | −0.735681 | ||||||||
\(584\) | 4.95966e90i | 0.253412i | ||||||||
\(585\) | −2.80769e91 | − | 2.43173e90i | −1.35583 | − | 0.117428i | ||||
\(586\) | 5.38253e90 | 0.245677 | ||||||||
\(587\) | − | 1.91542e91i | − | 0.826431i | −0.910633 | − | 0.413215i | \(-0.864406\pi\) | ||
0.910633 | − | 0.413215i | \(-0.135594\pi\) | |||||||
\(588\) | 8.54776e90 | − | 7.83944e90i | 0.348659 | − | 0.319767i | ||||
\(589\) | 2.44956e91 | 0.944676 | ||||||||
\(590\) | 1.27567e91i | 0.465181i | ||||||||
\(591\) | 2.50565e91 | + | 2.73204e91i | 0.864038 | + | 0.942107i | ||||
\(592\) | 4.92948e90 | 0.160762 | ||||||||
\(593\) | 4.05156e91i | 1.24973i | 0.780731 | + | 0.624867i | \(0.214847\pi\) | ||||
−0.780731 | + | 0.624867i | \(0.785153\pi\) | |||||||
\(594\) | 1.35447e91 | + | 1.76041e91i | 0.395201 | + | 0.513643i | ||||
\(595\) | −3.76733e91 | −1.03986 | ||||||||
\(596\) | − | 1.01585e91i | − | 0.265279i | ||||||
\(597\) | −1.40711e91 | + | 1.29051e91i | −0.347676 | + | 0.318866i | ||||
\(598\) | 3.04341e91 | 0.711577 | ||||||||
\(599\) | 5.55907e91i | 1.23003i | 0.788514 | + | 0.615017i | \(0.210851\pi\) | ||||
−0.788514 | + | 0.615017i | \(0.789149\pi\) | |||||||
\(600\) | −2.44084e90 | − | 2.66137e90i | −0.0511149 | − | 0.0557333i | ||||
\(601\) | 5.83160e91 | 1.15593 | 0.577963 | − | 0.816063i | \(-0.303848\pi\) | ||||
0.577963 | + | 0.816063i | \(0.303848\pi\) | |||||||
\(602\) | − | 3.36509e91i | − | 0.631412i | ||||||
\(603\) | 5.30871e90 | − | 6.12946e91i | 0.0943012 | − | 1.08881i | ||||
\(604\) | 1.01840e91 | 0.171277 | ||||||||
\(605\) | − | 2.20660e91i | − | 0.351395i | ||||||
\(606\) | −3.34649e91 | + | 3.06918e91i | −0.504653 | + | 0.462835i | ||||
\(607\) | −1.20208e91 | −0.171675 | −0.0858375 | − | 0.996309i | \(-0.527357\pi\) | ||||
−0.0858375 | + | 0.996309i | \(0.527357\pi\) | |||||||
\(608\) | 1.25432e92i | 1.69664i | ||||||||
\(609\) | −7.88669e91 | − | 8.59928e91i | −1.01047 | − | 1.10177i | ||||
\(610\) | 2.75883e91 | 0.334843 | ||||||||
\(611\) | 4.53222e91i | 0.521136i | ||||||||
\(612\) | 5.29478e91 | + | 4.58579e90i | 0.576834 | + | 0.0499594i | ||||
\(613\) | 2.30231e91 | 0.237667 | 0.118833 | − | 0.992914i | \(-0.462085\pi\) | ||||
0.118833 | + | 0.992914i | \(0.462085\pi\) | |||||||
\(614\) | − | 1.10825e92i | − | 1.08413i | ||||||
\(615\) | 1.21359e92 | − | 1.11302e92i | 1.12510 | − | 1.03187i | ||||
\(616\) | −1.61958e92 | −1.42311 | ||||||||
\(617\) | − | 1.79035e92i | − | 1.49117i | −0.666409 | − | 0.745587i | \(-0.732169\pi\) | ||
0.666409 | − | 0.745587i | \(-0.267831\pi\) | |||||||
\(618\) | 4.21943e91 | + | 4.60066e91i | 0.333145 | + | 0.363246i | ||||
\(619\) | −2.15496e92 | −1.61305 | −0.806524 | − | 0.591201i | \(-0.798654\pi\) | ||||
−0.806524 | + | 0.591201i | \(0.798654\pi\) | |||||||
\(620\) | − | 5.38746e91i | − | 0.382348i | ||||||
\(621\) | −1.06505e92 | + | 8.19461e91i | −0.716719 | + | 0.551449i | ||||
\(622\) | 2.43764e91 | 0.155556 | ||||||||
\(623\) | 2.08893e90i | 0.0126421i | ||||||||
\(624\) | −3.14104e91 | + | 2.88075e91i | −0.180294 | + | 0.165354i | ||||
\(625\) | −1.67677e92 | −0.912919 | ||||||||
\(626\) | − | 2.77154e91i | − | 0.143142i | ||||||
\(627\) | 2.64606e92 | + | 2.88514e92i | 1.29650 | + | 1.41364i | ||||
\(628\) | −9.10835e91 | −0.423420 | ||||||||
\(629\) | 1.76757e92i | 0.779659i | ||||||||
\(630\) | 1.42172e91 | − | 1.64153e92i | 0.0595081 | − | 0.687084i | ||||
\(631\) | 1.80767e91 | 0.0718044 | 0.0359022 | − | 0.999355i | \(-0.488570\pi\) | ||||
0.0359022 | + | 0.999355i | \(0.488570\pi\) | |||||||
\(632\) | − | 1.24972e92i | − | 0.471141i | ||||||
\(633\) | 1.10254e92 | − | 1.01118e92i | 0.394522 | − | 0.361829i | ||||
\(634\) | 7.94670e91 | 0.269924 | ||||||||
\(635\) | 2.20268e92i | 0.710262i | ||||||||
\(636\) | −9.62421e91 | − | 1.04938e92i | −0.294632 | − | 0.321253i | ||||
\(637\) | −3.33515e92 | −0.969425 | ||||||||
\(638\) | 2.70583e92i | 0.746825i | ||||||||
\(639\) | 4.71624e92 | + | 4.08472e91i | 1.23614 | + | 0.107062i | ||||
\(640\) | 3.12681e92 | 0.778327 | ||||||||
\(641\) | − | 1.97841e92i | − | 0.467737i | −0.972268 | − | 0.233868i | \(-0.924862\pi\) | ||
0.972268 | − | 0.233868i | \(-0.0751385\pi\) | |||||||
\(642\) | 1.98400e92 | − | 1.81960e92i | 0.445540 | − | 0.408620i | ||||
\(643\) | 4.43786e92 | 0.946698 | 0.473349 | − | 0.880875i | \(-0.343045\pi\) | ||||
0.473349 | + | 0.880875i | \(0.343045\pi\) | |||||||
\(644\) | − | 4.00959e92i | − | 0.812581i | ||||||
\(645\) | 2.95496e92 | + | 3.22195e92i | 0.568959 | + | 0.620366i | ||||
\(646\) | −4.15678e92 | −0.760474 | ||||||||
\(647\) | − | 9.41682e91i | − | 0.163705i | −0.996644 | − | 0.0818527i | \(-0.973916\pi\) | ||
0.996644 | − | 0.0818527i | \(-0.0260837\pi\) | |||||||
\(648\) | −9.76604e91 | + | 5.59567e92i | −0.161341 | + | 0.924437i | ||||
\(649\) | 6.51496e92 | 1.02291 | ||||||||
\(650\) | 4.24921e91i | 0.0634115i | ||||||||
\(651\) | −3.88041e92 | + | 3.55886e92i | −0.550434 | + | 0.504822i | ||||
\(652\) | −9.60889e92 | −1.29569 | ||||||||
\(653\) | 9.87640e92i | 1.26609i | 0.774116 | + | 0.633044i | \(0.218195\pi\) | ||||
−0.774116 | + | 0.633044i | \(0.781805\pi\) | |||||||
\(654\) | −3.97894e92 | − | 4.33845e92i | −0.484955 | − | 0.528773i | ||||
\(655\) | 4.89078e91 | 0.0566781 | ||||||||
\(656\) | − | 2.49034e92i | − | 0.274430i | ||||||
\(657\) | −2.22349e91 | + | 2.56726e92i | −0.0233012 | + | 0.269037i | ||||
\(658\) | −2.64978e92 | −0.264092 | ||||||||
\(659\) | 8.84049e92i | 0.838026i | 0.907980 | + | 0.419013i | \(0.137624\pi\) | ||||
−0.907980 | + | 0.419013i | \(0.862376\pi\) | |||||||
\(660\) | 6.34547e92 | − | 5.81965e92i | 0.572156 | − | 0.524743i | ||||
\(661\) | 2.08708e93 | 1.79016 | 0.895080 | − | 0.445906i | \(-0.147118\pi\) | ||||
0.895080 | + | 0.445906i | \(0.147118\pi\) | |||||||
\(662\) | − | 4.55515e92i | − | 0.371697i | ||||||
\(663\) | −1.03295e93 | − | 1.12629e93i | −0.801927 | − | 0.874384i | ||||
\(664\) | −1.33016e93 | −0.982559 | ||||||||
\(665\) | − | 2.90400e93i | − | 2.04119i | ||||||
\(666\) | −7.70176e92 | − | 6.67046e91i | −0.515158 | − | 0.0446176i | ||||
\(667\) | −1.63704e93 | −1.04209 | ||||||||
\(668\) | 4.83308e92i | 0.292820i | ||||||||
\(669\) | −9.51803e92 | + | 8.72931e92i | −0.548890 | + | 0.503405i | ||||
\(670\) | 1.05835e93 | 0.580978 | ||||||||
\(671\) | − | 1.40896e93i | − | 0.736301i | ||||||
\(672\) | −1.82235e93 | − | 1.98700e93i | −0.906661 | − | 0.988581i | ||||
\(673\) | 3.12867e92 | 0.148205 | 0.0741025 | − | 0.997251i | \(-0.476391\pi\) | ||||
0.0741025 | + | 0.997251i | \(0.476391\pi\) | |||||||
\(674\) | 2.34164e93i | 1.05620i | ||||||||
\(675\) | −1.14413e92 | − | 1.48703e92i | −0.0491418 | − | 0.0638697i | ||||
\(676\) | 1.71771e93 | 0.702600 | ||||||||
\(677\) | 1.53207e93i | 0.596834i | 0.954436 | + | 0.298417i | \(0.0964586\pi\) | ||||
−0.954436 | + | 0.298417i | \(0.903541\pi\) | |||||||
\(678\) | 1.96124e93 | − | 1.79872e93i | 0.727696 | − | 0.667394i | ||||
\(679\) | 1.03230e93 | 0.364842 | ||||||||
\(680\) | 2.23416e93i | 0.752178i | ||||||||
\(681\) | 9.55454e92 | + | 1.04178e93i | 0.306447 | + | 0.334135i | ||||
\(682\) | 1.22100e93 | 0.373106 | ||||||||
\(683\) | − | 2.57622e93i | − | 0.750066i | −0.927011 | − | 0.375033i | \(-0.877631\pi\) | ||
0.927011 | − | 0.375033i | \(-0.122369\pi\) | |||||||
\(684\) | −3.53490e92 | + | 4.08142e93i | −0.0980677 | + | 1.13230i | ||||
\(685\) | −2.65237e92 | −0.0701204 | ||||||||
\(686\) | 9.04871e92i | 0.227977i | ||||||||
\(687\) | −1.09341e93 | + | 1.00281e93i | −0.262550 | + | 0.240794i | ||||
\(688\) | 6.61160e92 | 0.151317 | ||||||||
\(689\) | 4.09445e93i | 0.893226i | ||||||||
\(690\) | −1.56248e93 | − | 1.70366e93i | −0.324934 | − | 0.354293i | ||||
\(691\) | 4.05213e93 | 0.803356 | 0.401678 | − | 0.915781i | \(-0.368427\pi\) | ||||
0.401678 | + | 0.915781i | \(0.368427\pi\) | |||||||
\(692\) | − | 1.43488e93i | − | 0.271215i | ||||||
\(693\) | −8.38341e93 | − | 7.26084e92i | −1.51086 | − | 0.130855i | ||||
\(694\) | 5.37092e93 | 0.922968 | ||||||||
\(695\) | − | 2.34866e93i | − | 0.384877i | ||||||
\(696\) | −5.09968e93 | + | 4.67709e93i | −0.796962 | + | 0.730921i | ||||
\(697\) | 8.92962e93 | 1.33092 | ||||||||
\(698\) | − | 7.64165e93i | − | 1.08632i | ||||||
\(699\) | 6.28389e93 | + | 6.85166e93i | 0.852082 | + | 0.929071i | ||||
\(700\) | 5.59819e92 | 0.0724123 | ||||||||
\(701\) | 5.64714e93i | 0.696842i | 0.937338 | + | 0.348421i | \(0.113282\pi\) | ||||
−0.937338 | + | 0.348421i | \(0.886718\pi\) | |||||||
\(702\) | 5.29734e93 | − | 4.07582e93i | 0.623639 | − | 0.479833i | ||||
\(703\) | −1.36251e94 | −1.53043 | ||||||||
\(704\) | 4.37230e93i | 0.468611i | ||||||||
\(705\) | 2.53707e93 | − | 2.32683e93i | 0.259472 | − | 0.237971i | ||||
\(706\) | 2.41542e93 | 0.235743 | ||||||||
\(707\) | − | 1.72025e94i | − | 1.60233i | ||||||
\(708\) | 4.60813e93 | + | 5.02449e93i | 0.409664 | + | 0.446678i | ||||
\(709\) | −1.03680e94 | −0.879772 | −0.439886 | − | 0.898054i | \(-0.644981\pi\) | ||||
−0.439886 | + | 0.898054i | \(0.644981\pi\) | |||||||
\(710\) | 8.14332e93i | 0.659593i | ||||||||
\(711\) | 5.60271e92 | − | 6.46892e93i | 0.0433213 | − | 0.500190i | ||||
\(712\) | 1.23881e92 | 0.00914462 | ||||||||
\(713\) | 7.38712e93i | 0.520620i | ||||||||
\(714\) | 6.58488e93 | − | 6.03922e93i | 0.443105 | − | 0.406387i | ||||
\(715\) | −2.47587e94 | −1.59085 | ||||||||
\(716\) | − | 4.07554e93i | − | 0.250066i | ||||||
\(717\) | −1.00478e94 | − | 1.09557e94i | −0.588761 | − | 0.641958i | ||||
\(718\) | −7.87527e93 | −0.440716 | ||||||||
\(719\) | − | 1.26419e94i | − | 0.675709i | −0.941198 | − | 0.337854i | \(-0.890299\pi\) | ||
0.941198 | − | 0.337854i | \(-0.109701\pi\) | |||||||
\(720\) | 3.22521e93 | + | 2.79334e92i | 0.164659 | + | 0.0142610i | ||||
\(721\) | −2.36496e94 | −1.15335 | ||||||||
\(722\) | − | 2.01418e94i | − | 0.938361i | ||||||
\(723\) | 1.43912e94 | − | 1.31987e94i | 0.640521 | − | 0.587443i | ||||
\(724\) | 1.23413e94 | 0.524794 | ||||||||
\(725\) | − | 2.28563e93i | − | 0.0928651i | ||||||
\(726\) | 3.53728e93 | + | 3.85689e93i | 0.137329 | + | 0.149737i | ||||
\(727\) | 2.43739e94 | 0.904251 | 0.452126 | − | 0.891954i | \(-0.350666\pi\) | ||||
0.452126 | + | 0.891954i | \(0.350666\pi\) | |||||||
\(728\) | 4.87357e94i | 1.72787i | ||||||||
\(729\) | −7.56381e93 | + | 2.85269e94i | −0.256290 | + | 0.966600i | ||||
\(730\) | −4.43277e93 | −0.143556 | ||||||||
\(731\) | 2.37073e94i | 0.733852i | ||||||||
\(732\) | 1.08662e94 | − | 9.96579e93i | 0.321524 | − | 0.294881i | ||||
\(733\) | −1.42262e94 | −0.402399 | −0.201199 | − | 0.979550i | \(-0.564484\pi\) | ||||
−0.201199 | + | 0.979550i | \(0.564484\pi\) | |||||||
\(734\) | 2.22570e94i | 0.601861i | ||||||||
\(735\) | 1.71226e94 | + | 1.86697e94i | 0.442677 | + | 0.482675i | ||||
\(736\) | −3.78264e94 | −0.935034 | ||||||||
\(737\) | − | 5.40507e94i | − | 1.27754i | ||||||
\(738\) | −3.36987e93 | + | 3.89087e94i | −0.0761646 | + | 0.879401i | ||||
\(739\) | 6.47461e94 | 1.39942 | 0.699708 | − | 0.714429i | \(-0.253313\pi\) | ||||
0.699708 | + | 0.714429i | \(0.253313\pi\) | |||||||
\(740\) | 2.99665e94i | 0.619425i | ||||||||
\(741\) | 8.68183e94 | − | 7.96241e94i | 1.71637 | − | 1.57414i | ||||
\(742\) | −2.39384e94 | −0.452654 | ||||||||
\(743\) | − | 3.38589e94i | − | 0.612410i | −0.951966 | − | 0.306205i | \(-0.900941\pi\) | ||
0.951966 | − | 0.306205i | \(-0.0990592\pi\) | |||||||
\(744\) | 2.11053e94 | + | 2.30122e94i | 0.365161 | + | 0.398155i | ||||
\(745\) | 2.21878e94 | 0.367246 | ||||||||
\(746\) | − | 1.71732e94i | − | 0.271938i | ||||||
\(747\) | −6.88530e94 | − | 5.96334e93i | −1.04314 | − | 0.0903461i | ||||
\(748\) | 4.66903e94 | 0.676822 | ||||||||
\(749\) | 1.01987e95i | 1.41464i | ||||||||
\(750\) | 3.18952e94 | − | 2.92521e94i | 0.423353 | − | 0.388272i | ||||
\(751\) | −1.25300e95 | −1.59160 | −0.795801 | − | 0.605559i | \(-0.792950\pi\) | ||||
−0.795801 | + | 0.605559i | \(0.792950\pi\) | |||||||
\(752\) | − | 5.20619e93i | − | 0.0632894i | ||||||
\(753\) | 3.77972e94 | + | 4.12123e94i | 0.439770 | + | 0.479505i | ||||
\(754\) | 8.14227e94 | 0.906757 | ||||||||
\(755\) | 2.22435e94i | 0.237112i | ||||||||
\(756\) | −5.36975e94 | − | 6.97906e94i | −0.547942 | − | 0.712160i | ||||
\(757\) | −6.88341e94 | −0.672418 | −0.336209 | − | 0.941787i | \(-0.609145\pi\) | ||||
−0.336209 | + | 0.941787i | \(0.609145\pi\) | |||||||
\(758\) | − | 9.50706e94i | − | 0.889124i | ||||||
\(759\) | −8.70072e94 | + | 7.97972e94i | −0.779070 | + | 0.714511i | ||||
\(760\) | −1.72218e95 | −1.47649 | ||||||||
\(761\) | 8.72317e94i | 0.716111i | 0.933700 | + | 0.358056i | \(0.116560\pi\) | ||||
−0.933700 | + | 0.358056i | \(0.883440\pi\) | |||||||
\(762\) | −3.53100e94 | − | 3.85004e94i | −0.277577 | − | 0.302657i | ||||
\(763\) | 2.23017e95 | 1.67891 | ||||||||
\(764\) | − | 1.19743e95i | − | 0.863315i | ||||||
\(765\) | −1.00161e94 | + | 1.15646e95i | −0.0691626 | + | 0.798555i | ||||
\(766\) | 6.14948e94 | 0.406714 | ||||||||
\(767\) | − | 1.96045e95i | − | 1.24196i | ||||||
\(768\) | −1.03337e95 | + | 9.47743e94i | −0.627101 | + | 0.575136i | ||||
\(769\) | −8.94550e94 | −0.520038 | −0.260019 | − | 0.965603i | \(-0.583729\pi\) | ||||
−0.260019 | + | 0.965603i | \(0.583729\pi\) | |||||||
\(770\) | − | 1.44753e95i | − | 0.806181i | ||||||
\(771\) | −2.93396e94 | − | 3.19905e94i | −0.156552 | − | 0.170697i | ||||
\(772\) | −8.49610e94 | −0.434359 | ||||||||
\(773\) | − | 1.48435e95i | − | 0.727130i | −0.931569 | − | 0.363565i | \(-0.881560\pi\) | ||
0.931569 | − | 0.363565i | \(-0.118440\pi\) | |||||||
\(774\) | −1.03299e95 | − | 8.94667e93i | −0.484890 | − | 0.0419962i | ||||
\(775\) | −1.03139e94 | −0.0463945 | ||||||||
\(776\) | − | 6.12193e94i | − | 0.263907i | ||||||
\(777\) | 2.15839e95 | − | 1.97953e95i | 0.891735 | − | 0.817841i | ||||
\(778\) | 2.15063e95 | 0.851608 | ||||||||
\(779\) | 6.88329e95i | 2.61252i | ||||||||
\(780\) | −1.75122e95 | − | 1.90945e95i | −0.637117 | − | 0.694682i | ||||
\(781\) | 4.15886e95 | 1.45041 | ||||||||
\(782\) | − | 1.25356e95i | − | 0.419104i | ||||||
\(783\) | −2.84942e95 | + | 2.19236e95i | −0.913309 | + | 0.702708i | ||||
\(784\) | 3.83111e94 | 0.117732 | ||||||||
\(785\) | − | 1.98941e95i | − | 0.586172i | ||||||
\(786\) | −8.54854e93 | + | 7.84016e93i | −0.0241517 | + | 0.0221504i | ||||
\(787\) | 6.31584e95 | 1.71106 | 0.855529 | − | 0.517754i | \(-0.173232\pi\) | ||||
0.855529 | + | 0.517754i | \(0.173232\pi\) | |||||||
\(788\) | 3.40808e95i | 0.885410i | ||||||||
\(789\) | −3.17040e95 | − | 3.45686e95i | −0.789901 | − | 0.861271i | ||||
\(790\) | 1.11696e95 | 0.266897 | ||||||||
\(791\) | 1.00817e96i | 2.31051i | ||||||||
\(792\) | −4.30594e94 | + | 4.97166e95i | −0.0946535 | + | 1.09287i | ||||
\(793\) | −4.23977e95 | −0.893979 | ||||||||
\(794\) | − | 7.36526e94i | − | 0.148974i | ||||||
\(795\) | 2.29201e95 | − | 2.10208e95i | 0.444735 | − | 0.407882i | ||||
\(796\) | −1.75530e95 | −0.326753 | ||||||||
\(797\) | − | 5.07830e95i | − | 0.906972i | −0.891263 | − | 0.453486i | \(-0.850180\pi\) | ||
0.891263 | − | 0.453486i | \(-0.149820\pi\) | |||||||
\(798\) | 4.65526e95 | + | 5.07587e95i | 0.797716 | + | 0.869792i | ||||
\(799\) | 1.86679e95 | 0.306938 | ||||||||
\(800\) | − | 5.28133e94i | − | 0.0833246i | ||||||
\(801\) | 6.41243e93 | + | 5.55379e92i | 0.00970845 | + | 0.000840846i | ||||
\(802\) | −2.54765e95 | −0.370156 | ||||||||
\(803\) | 2.26385e95i | 0.315671i | ||||||||
\(804\) | 4.16852e95 | − | 3.82309e95i | 0.557869 | − | 0.511641i | ||||
\(805\) | 8.75759e95 | 1.12492 | ||||||||
\(806\) | − | 3.67419e95i | − | 0.453007i | ||||||
\(807\) | −5.29725e95 | − | 5.77587e95i | −0.626937 | − | 0.683583i | ||||
\(808\) | −1.02017e96 | −1.15904 | ||||||||
\(809\) | 2.63427e95i | 0.287315i | 0.989627 | + | 0.143658i | \(0.0458864\pi\) | ||||
−0.989627 | + | 0.143658i | \(0.954114\pi\) | |||||||
\(810\) | −5.00122e95 | − | 8.72856e94i | −0.523685 | − | 0.0913980i | ||||
\(811\) | −2.78615e95 | −0.280102 | −0.140051 | − | 0.990144i | \(-0.544727\pi\) | ||||
−0.140051 | + | 0.990144i | \(0.544727\pi\) | |||||||
\(812\) | − | 1.07272e96i | − | 1.03547i | ||||||
\(813\) | 9.55812e95 | − | 8.76607e95i | 0.885899 | − | 0.812488i | ||||
\(814\) | −6.79155e95 | −0.604454 | ||||||||
\(815\) | − | 2.09874e96i | − | 1.79373i | ||||||
\(816\) | 1.18656e95 | + | 1.29377e95i | 0.0973901 | + | 0.106190i | ||||
\(817\) | −1.82745e96 | −1.44051 | ||||||||
\(818\) | 7.33397e95i | 0.555239i | ||||||||
\(819\) | −2.18490e95 | + | 2.52269e96i | −0.158877 | + | 1.83441i | ||||
\(820\) | 1.51388e96 | 1.05739 | ||||||||
\(821\) | 1.59159e96i | 1.06784i | 0.845534 | + | 0.533921i | \(0.179282\pi\) | ||||
−0.845534 | + | 0.533921i | \(0.820718\pi\) | |||||||
\(822\) | 4.63604e94 | − | 4.25187e94i | 0.0298798 | − | 0.0274038i | ||||
\(823\) | −1.01941e96 | −0.631181 | −0.315591 | − | 0.948895i | \(-0.602203\pi\) | ||||
−0.315591 | + | 0.948895i | \(0.602203\pi\) | |||||||
\(824\) | 1.40250e96i | 0.834268i | ||||||||
\(825\) | −1.11413e95 | − | 1.21479e95i | −0.0636730 | − | 0.0694260i | ||||
\(826\) | 1.14619e96 | 0.629381 | ||||||||
\(827\) | − | 3.10475e96i | − | 1.63812i | −0.573708 | − | 0.819060i | \(-0.694496\pi\) | ||
0.573708 | − | 0.819060i | \(-0.305504\pi\) | |||||||
\(828\) | −1.23083e96 | − | 1.06602e95i | −0.624018 | − | 0.0540460i | ||||
\(829\) | −2.62690e96 | −1.27980 | −0.639902 | − | 0.768456i | \(-0.721025\pi\) | ||||
−0.639902 | + | 0.768456i | \(0.721025\pi\) | |||||||
\(830\) | − | 1.18886e96i | − | 0.556611i | ||||||
\(831\) | 2.41787e96 | − | 2.21751e96i | 1.08792 | − | 0.997772i | ||||
\(832\) | 1.31569e96 | 0.568963 | ||||||||
\(833\) | 1.37372e96i | 0.570971i | ||||||||
\(834\) | 3.76501e95 | + | 4.10520e95i | 0.150414 | + | 0.164004i | ||||
\(835\) | −1.05562e96 | −0.405373 | ||||||||
\(836\) | 3.59907e96i | 1.32856i | ||||||||
\(837\) | 9.89301e95 | + | 1.28580e96i | 0.351066 | + | 0.456280i | ||||
\(838\) | −1.15113e96 | −0.392710 | ||||||||
\(839\) | − | 3.27888e96i | − | 1.07543i | −0.843128 | − | 0.537713i | \(-0.819288\pi\) | ||
0.843128 | − | 0.537713i | \(-0.180712\pi\) | |||||||
\(840\) | 2.72815e96 | − | 2.50208e96i | 0.860303 | − | 0.789014i | ||||
\(841\) | −1.08156e96 | −0.327932 | ||||||||
\(842\) | 1.81999e96i | 0.530602i | ||||||||
\(843\) | 4.75928e96 | + | 5.18929e96i | 1.33423 | + | 1.45478i | ||||
\(844\) | 1.37536e96 | 0.370779 | ||||||||
\(845\) | 3.75175e96i | 0.972663i | ||||||||
\(846\) | −7.04490e94 | + | 8.13408e95i | −0.0175652 | + | 0.202809i | ||||
\(847\) | −1.98262e96 | −0.475430 | ||||||||
\(848\) | − | 4.70332e95i | − | 0.108478i | ||||||
\(849\) | 6.66889e95 | − | 6.11626e95i | 0.147945 | − | 0.135685i | ||||
\(850\) | 1.75022e95 | 0.0373481 | ||||||||
\(851\) | − | 4.10891e96i | − | 0.843434i | ||||||
\(852\) | 2.94163e96 | + | 3.20742e96i | 0.580873 | + | 0.633357i | ||||
\(853\) | 4.09685e96 | 0.778273 | 0.389136 | − | 0.921180i | \(-0.372773\pi\) | ||||
0.389136 | + | 0.921180i | \(0.372773\pi\) | |||||||
\(854\) | − | 2.47880e96i | − | 0.453035i | ||||||
\(855\) | −8.91447e96 | − | 7.72079e95i | −1.56752 | − | 0.135763i | ||||
\(856\) | 6.04820e96 | 1.02327 | ||||||||
\(857\) | 6.48094e96i | 1.05504i | 0.849541 | + | 0.527522i | \(0.176879\pi\) | ||||
−0.849541 | + | 0.527522i | \(0.823121\pi\) | |||||||
\(858\) | 4.32754e96 | − | 3.96893e96i | 0.677892 | − | 0.621718i | ||||
\(859\) | −1.57468e96 | −0.237366 | −0.118683 | − | 0.992932i | \(-0.537867\pi\) | ||||
−0.118683 | + | 0.992932i | \(0.537867\pi\) | |||||||
\(860\) | 4.01921e96i | 0.583032i | ||||||||
\(861\) | −1.00004e97 | − | 1.09040e97i | −1.39610 | − | 1.52224i | ||||
\(862\) | −4.79470e96 | −0.644201 | ||||||||
\(863\) | − | 8.93981e96i | − | 1.15604i | −0.816023 | − | 0.578019i | \(-0.803826\pi\) | ||
0.816023 | − | 0.578019i | \(-0.196174\pi\) | |||||||
\(864\) | −6.58404e96 | + | 5.06581e96i | −0.819481 | + | 0.630515i | ||||
\(865\) | 3.13400e96 | 0.375464 | ||||||||
\(866\) | 6.44171e96i | 0.742866i | ||||||||
\(867\) | 1.99968e96 | − | 1.83397e96i | 0.221988 | − | 0.203593i | ||||
\(868\) | −4.84061e96 | −0.517308 | ||||||||
\(869\) | − | 5.70441e96i | − | 0.586892i | ||||||
\(870\) | −4.18022e96 | − | 4.55792e96i | −0.414061 | − | 0.451472i | ||||
\(871\) | −1.62647e97 | −1.55112 | ||||||||
\(872\) | − | 1.32257e97i | − | 1.21443i | ||||||
\(873\) | 2.74456e95 | − | 3.16888e96i | 0.0242662 | − | 0.280179i | ||||
\(874\) | 9.66291e96 | 0.822680 | ||||||||
\(875\) | 1.63956e97i | 1.34419i | ||||||||
\(876\) | −1.74594e96 | + | 1.60126e96i | −0.137846 | + | 0.126423i | ||||
\(877\) | 8.72612e96 | 0.663490 | 0.331745 | − | 0.943369i | \(-0.392363\pi\) | ||||
0.331745 | + | 0.943369i | \(0.392363\pi\) | |||||||
\(878\) | 1.38854e97i | 1.01681i | ||||||||
\(879\) | 4.24675e96 | + | 4.63046e96i | 0.299519 | + | 0.326581i | ||||
\(880\) | 2.84404e96 | 0.193200 | ||||||||
\(881\) | − | 3.81448e96i | − | 0.249592i | −0.992182 | − | 0.124796i | \(-0.960172\pi\) | ||
0.992182 | − | 0.124796i | \(-0.0398277\pi\) | |||||||
\(882\) | −5.98567e96 | − | 5.18417e95i | −0.377268 | − | 0.0326750i | ||||
\(883\) | 2.47898e97 | 1.50511 | 0.752556 | − | 0.658528i | \(-0.228821\pi\) | ||||
0.752556 | + | 0.658528i | \(0.228821\pi\) | |||||||
\(884\) | − | 1.40498e97i | − | 0.821762i | ||||||
\(885\) | −1.09743e97 | + | 1.00649e97i | −0.618371 | + | 0.567129i | ||||
\(886\) | −1.31235e96 | −0.0712424 | ||||||||
\(887\) | − | 2.39028e97i | − | 1.25017i | −0.780556 | − | 0.625085i | \(-0.785064\pi\) | ||
0.780556 | − | 0.625085i | \(-0.214936\pi\) | |||||||
\(888\) | −1.17393e97 | − | 1.28000e97i | −0.591582 | − | 0.645033i | ||||
\(889\) | 1.97910e97 | 0.960970 | ||||||||
\(890\) | 1.10721e95i | 0.00518035i | ||||||||
\(891\) | −4.45775e96 | + | 2.55416e97i | −0.200979 | + | 1.15156i | ||||
\(892\) | −1.18732e97 | −0.515857 | ||||||||
\(893\) | 1.43899e97i | 0.602504i | ||||||||
\(894\) | −3.87818e96 | + | 3.55681e96i | −0.156491 | + | 0.143523i | ||||
\(895\) | 8.90163e96 | 0.346186 | ||||||||
\(896\) | − | 2.80943e97i | − | 1.05306i | ||||||
\(897\) | 2.40122e97 | + | 2.61818e97i | 0.867523 | + | 0.945907i | ||||
\(898\) | −1.40101e97 | −0.487890 | ||||||||
\(899\) | 1.97633e97i | 0.663422i | ||||||||
\(900\) | 1.48837e95 | − | 1.71849e96i | 0.00481626 | − | 0.0556088i | ||||
\(901\) | 1.68647e97 | 0.526092 | ||||||||
\(902\) | 3.43104e97i | 1.03183i | ||||||||
\(903\) | 2.89491e97 | − | 2.65502e97i | 0.839343 | − | 0.769790i | ||||
\(904\) | 5.97878e97 | 1.67130 | ||||||||
\(905\) | 2.69554e97i | 0.726512i | ||||||||
\(906\) | −3.56574e96 | − | 3.88792e96i | −0.0926659 | − | 0.101039i | ||||
\(907\) | −6.60749e96 | −0.165575 | −0.0827877 | − | 0.996567i | \(-0.526382\pi\) | ||||
−0.0827877 | + | 0.996567i | \(0.526382\pi\) | |||||||
\(908\) | 1.29957e97i | 0.314027i | ||||||||
\(909\) | −5.28069e97 | − | 4.57358e96i | −1.23050 | − | 0.106573i | ||||
\(910\) | −4.35583e97 | −0.978824 | ||||||||
\(911\) | 9.53247e96i | 0.206585i | 0.994651 | + | 0.103293i | \(0.0329378\pi\) | ||||
−0.994651 | + | 0.103293i | \(0.967062\pi\) | |||||||
\(912\) | −9.97288e96 | + | 9.14646e96i | −0.208445 | + | 0.191172i | ||||
\(913\) | −6.07158e97 | −1.22396 | ||||||||
\(914\) | − | 1.34143e97i | − | 0.260822i | ||||||
\(915\) | 2.17669e97 | + | 2.37336e97i | 0.408226 | + | 0.445110i | ||||
\(916\) | −1.36398e97 | −0.246750 | ||||||||
\(917\) | − | 4.39435e96i | − | 0.0766843i | ||||||
\(918\) | −1.67880e97 | − | 2.18193e97i | −0.282612 | − | 0.367310i | ||||
\(919\) | 6.29938e96 | 0.102302 | 0.0511512 | − | 0.998691i | \(-0.483711\pi\) | ||||
0.0511512 | + | 0.998691i | \(0.483711\pi\) | |||||||
\(920\) | − | 5.19356e97i | − | 0.813705i | ||||||
\(921\) | 9.53405e97 | − | 8.74400e97i | 1.44115 | − | 1.32173i | ||||
\(922\) | 4.89164e97 | 0.713402 | ||||||||
\(923\) | − | 1.25146e98i | − | 1.76101i | ||||||
\(924\) | −5.22893e97 | − | 5.70138e97i | −0.709967 | − | 0.774114i | ||||
\(925\) | 5.73686e96 | 0.0751618 | ||||||||
\(926\) | 1.06322e97i | 0.134419i | ||||||||
\(927\) | −6.28764e96 | + | 7.25975e97i | −0.0767108 | + | 0.885707i | ||||
\(928\) | −1.01200e98 | −1.19151 | ||||||||
\(929\) | − | 5.56128e97i | − | 0.631912i | −0.948774 | − | 0.315956i | \(-0.897675\pi\) | ||
0.948774 | − | 0.315956i | \(-0.102325\pi\) | |||||||
\(930\) | −2.05675e97 | + | 1.88632e97i | −0.225551 | + | 0.206861i | ||||
\(931\) | −1.05892e98 | −1.12079 | ||||||||
\(932\) | 8.54709e97i | 0.873158i | ||||||||
\(933\) | 1.92327e97 | + | 2.09705e97i | 0.189647 | + | 0.206783i | ||||
\(934\) | −5.03510e95 | −0.00479249 | ||||||||
\(935\) | 1.01979e98i | 0.936975i | ||||||||
\(936\) | 1.49605e98 | + | 1.29572e97i | 1.32691 | + | 0.114923i | ||||
\(937\) | −4.54606e97 | −0.389250 | −0.194625 | − | 0.980878i | \(-0.562349\pi\) | ||||
−0.194625 | + | 0.980878i | \(0.562349\pi\) | |||||||
\(938\) | − | 9.50921e97i | − | 0.786051i | ||||||
\(939\) | 2.38429e97 | − | 2.18671e97i | 0.190281 | − | 0.174513i | ||||
\(940\) | 3.16486e97 | 0.243857 | ||||||||
\(941\) | 2.46857e98i | 1.83649i | 0.396015 | + | 0.918244i | \(0.370393\pi\) | ||||
−0.396015 | + | 0.918244i | \(0.629607\pi\) | |||||||
\(942\) | 3.18912e97 | + | 3.47727e97i | 0.229082 | + | 0.249780i | ||||
\(943\) | −2.07579e98 | −1.43979 | ||||||||
\(944\) | 2.25198e97i | 0.150830i | ||||||||
\(945\) | 1.52434e98 | − | 1.17284e98i | 0.985897 | − | 0.758557i | ||||
\(946\) | −9.10907e97 | −0.568940 | ||||||||
\(947\) | 6.48446e97i | 0.391133i | 0.980690 | + | 0.195566i | \(0.0626545\pi\) | ||||
−0.980690 | + | 0.195566i | \(0.937345\pi\) | |||||||
\(948\) | 4.39938e97 | − | 4.03482e97i | 0.256281 | − | 0.235044i | ||||
\(949\) | 6.81227e97 | 0.383272 | ||||||||
\(950\) | 1.34914e97i | 0.0733123i | ||||||||
\(951\) | 6.26986e97 | + | 6.83636e97i | 0.329079 | + | 0.358813i | ||||
\(952\) | 2.00739e98 | 1.01768 | ||||||||
\(953\) | − | 1.90568e98i | − | 0.933221i | −0.884463 | − | 0.466610i | \(-0.845475\pi\) | ||
0.884463 | − | 0.466610i | \(-0.154525\pi\) | |||||||
\(954\) | −6.36443e96 | + | 7.34841e97i | −0.0301067 | + | 0.347614i | ||||
\(955\) | 2.61538e98 | 1.19515 | ||||||||
\(956\) | − | 1.36666e98i | − | 0.603324i | ||||||
\(957\) | −2.32777e98 | + | 2.13487e98i | −0.992763 | + | 0.910496i | ||||
\(958\) | 1.49255e98 | 0.614987 | ||||||||
\(959\) | 2.38314e97i | 0.0948715i | ||||||||
\(960\) | −6.75473e97 | − | 7.36504e97i | −0.259811 | − | 0.283285i | ||||
\(961\) | −1.79892e98 | −0.668561 | ||||||||
\(962\) | 2.04368e98i | 0.733897i | ||||||||
\(963\) | 3.13071e98 | + | 2.71150e97i | 1.08637 | + | 0.0940898i | ||||
\(964\) | 1.79523e98 | 0.601973 | ||||||||
\(965\) | − | 1.85569e98i | − | 0.601316i | ||||||
\(966\) | −1.53073e98 | + | 1.40388e98i | −0.479350 | + | 0.439629i | ||||
\(967\) | −7.99314e97 | −0.241904 | −0.120952 | − | 0.992658i | \(-0.538595\pi\) | ||||
−0.120952 | + | 0.992658i | \(0.538595\pi\) | |||||||
\(968\) | 1.17576e98i | 0.343901i | ||||||||
\(969\) | −3.27966e98 | − | 3.57598e98i | −0.927136 | − | 1.01091i | ||||
\(970\) | 5.47157e97 | 0.149501 | ||||||||
\(971\) | − | 9.84731e97i | − | 0.260066i | −0.991510 | − | 0.130033i | \(-0.958492\pi\) | ||
0.991510 | − | 0.130033i | \(-0.0415083\pi\) | |||||||
\(972\) | −2.28514e98 | + | 1.46281e98i | −0.583345 | + | 0.373423i | ||||
\(973\) | −2.11026e98 | −0.520730 | ||||||||
\(974\) | − | 3.12053e98i | − | 0.744359i | ||||||
\(975\) | −3.65550e97 | + | 3.35258e97i | −0.0842935 | + | 0.0773085i | ||||
\(976\) | 4.87025e97 | 0.108569 | ||||||||
\(977\) | − | 1.73034e98i | − | 0.372916i | −0.982463 | − | 0.186458i | \(-0.940299\pi\) | ||
0.982463 | − | 0.186458i | \(-0.0597008\pi\) | |||||||
\(978\) | 3.36437e98 | + | 3.66836e98i | 0.701007 | + | 0.764345i | ||||
\(979\) | 5.65460e96 | 0.0113913 | ||||||||
\(980\) | 2.32894e98i | 0.453627i | ||||||||
\(981\) | 5.92928e97 | − | 6.84598e98i | 0.111667 | − | 1.28931i | ||||
\(982\) | −4.92693e98 | −0.897217 | ||||||||
\(983\) | 2.14187e97i | 0.0377161i | 0.999822 | + | 0.0188580i | \(0.00600306\pi\) | ||||
−0.999822 | + | 0.0188580i | \(0.993997\pi\) | |||||||
\(984\) | −6.46647e98 | + | 5.93062e98i | −1.10111 | + | 1.00986i | ||||
\(985\) | −7.44379e98 | −1.22574 | ||||||||
\(986\) | − | 3.35374e98i | − | 0.534061i | ||||||
\(987\) | −2.09065e98 | − | 2.27955e98i | −0.321970 | − | 0.351061i | ||||
\(988\) | 1.08301e99 | 1.61308 | ||||||||
\(989\) | − | 5.51102e98i | − | 0.793879i | ||||||
\(990\) | −4.44350e98 | − | 3.84850e97i | −0.619104 | − | 0.0536204i | ||||
\(991\) | −1.39208e98 | −0.187600 | −0.0938001 | − | 0.995591i | \(-0.529901\pi\) | ||||
−0.0938001 | + | 0.995591i | \(0.529901\pi\) | |||||||
\(992\) | 4.56663e98i | 0.595265i | ||||||||
\(993\) | 3.91869e98 | − | 3.59396e98i | 0.494100 | − | 0.453156i | ||||
\(994\) | 7.31674e98 | 0.892416 | ||||||||
\(995\) | − | 3.83385e98i | − | 0.452348i | ||||||
\(996\) | −4.29453e98 | − | 4.68255e98i | −0.490182 | − | 0.534471i | ||||
\(997\) | 9.29444e98 | 1.02632 | 0.513160 | − | 0.858293i | \(-0.328475\pi\) | ||||
0.513160 | + | 0.858293i | \(0.328475\pi\) | |||||||
\(998\) | 2.18329e98i | 0.233240i | ||||||||
\(999\) | −5.50275e98 | − | 7.15193e98i | −0.568747 | − | 0.739200i |
(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 | 3.67.b.b.2.8 | ✓ | 20 | |
3.2 | odd | 2 | inner | 3.67.b.b.2.13 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.67.b.b.2.8 | ✓ | 20 | 1.1 | even | 1 | trivial | |
3.67.b.b.2.13 | yes | 20 | 3.2 | odd | 2 | inner |