Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,17,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, 17, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 17);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 17 \) |
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: | \(4.86973631570\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3814x^{2} + 2981440 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.4 | ||
Root | \(52.1196i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.17.b.a.2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 312.717i | 1.22155i | 0.791803 | + | 0.610776i | \(0.209143\pi\) | ||||
−0.791803 | + | 0.610776i | \(0.790857\pi\) | |||||||
\(3\) | −5369.70 | + | 3770.02i | −0.818427 | + | 0.574611i | ||||
\(4\) | −32256.2 | −0.492190 | ||||||||
\(5\) | − | 276758.i | − | 0.708501i | −0.935150 | − | 0.354251i | \(-0.884736\pi\) | ||
0.935150 | − | 0.354251i | \(-0.115264\pi\) | |||||||
\(6\) | −1.17895e6 | − | 1.67920e6i | −0.701917 | − | 0.999751i | ||||
\(7\) | −7.10881e6 | −1.23314 | −0.616570 | − | 0.787300i | \(-0.711478\pi\) | ||||
−0.616570 | + | 0.787300i | \(0.711478\pi\) | |||||||
\(8\) | 1.04072e7i | 0.620316i | ||||||||
\(9\) | 1.46206e7 | − | 4.04878e7i | 0.339645 | − | 0.940554i | ||||
\(10\) | 8.65472e7 | 0.865472 | ||||||||
\(11\) | 3.43468e8i | 1.60230i | 0.598462 | + | 0.801151i | \(0.295779\pi\) | ||||
−0.598462 | + | 0.801151i | \(0.704221\pi\) | |||||||
\(12\) | 1.73206e8 | − | 1.21607e8i | 0.402822 | − | 0.282818i | ||||
\(13\) | −7.14909e8 | −0.876403 | −0.438201 | − | 0.898877i | \(-0.644384\pi\) | ||||
−0.438201 | + | 0.898877i | \(0.644384\pi\) | |||||||
\(14\) | − | 2.22305e9i | − | 1.50635i | ||||||
\(15\) | 1.04338e9 | + | 1.48611e9i | 0.407112 | + | 0.579857i | ||||
\(16\) | −5.36845e9 | −1.24994 | ||||||||
\(17\) | 6.74629e8i | 0.0967105i | 0.998830 | + | 0.0483552i | \(0.0153980\pi\) | ||||
−0.998830 | + | 0.0483552i | \(0.984602\pi\) | |||||||
\(18\) | 1.26612e10 | + | 4.57212e9i | 1.14894 | + | 0.414894i | ||||
\(19\) | 4.70347e9 | 0.276942 | 0.138471 | − | 0.990366i | \(-0.455781\pi\) | ||||
0.138471 | + | 0.990366i | \(0.455781\pi\) | |||||||
\(20\) | 8.92717e9i | 0.348718i | ||||||||
\(21\) | 3.81722e10 | − | 2.68004e10i | 1.00924 | − | 0.708576i | ||||
\(22\) | −1.07408e11 | −1.95730 | ||||||||
\(23\) | 4.47377e10i | 0.571283i | 0.958337 | + | 0.285641i | \(0.0922066\pi\) | ||||
−0.958337 | + | 0.285641i | \(0.907793\pi\) | |||||||
\(24\) | −3.92353e10 | − | 5.58834e10i | −0.356440 | − | 0.507683i | ||||
\(25\) | 7.59927e10 | 0.498026 | ||||||||
\(26\) | − | 2.23564e11i | − | 1.07057i | ||||||
\(27\) | 7.41314e10 | + | 2.72527e11i | 0.262477 | + | 0.964938i | ||||
\(28\) | 2.29303e11 | 0.606940 | ||||||||
\(29\) | 3.75138e11i | 0.749906i | 0.927044 | + | 0.374953i | \(0.122341\pi\) | ||||
−0.927044 | + | 0.374953i | \(0.877659\pi\) | |||||||
\(30\) | −4.64732e11 | + | 3.26285e11i | −0.708325 | + | 0.497309i | ||||
\(31\) | 6.58929e11 | 0.772583 | 0.386291 | − | 0.922377i | \(-0.373756\pi\) | ||||
0.386291 | + | 0.922377i | \(0.373756\pi\) | |||||||
\(32\) | − | 9.96762e11i | − | 0.906550i | ||||||
\(33\) | −1.29488e12 | − | 1.84432e12i | −0.920700 | − | 1.31137i | ||||
\(34\) | −2.10968e11 | −0.118137 | ||||||||
\(35\) | 1.96742e12i | 0.873682i | ||||||||
\(36\) | −4.71605e11 | + | 1.30598e12i | −0.167170 | + | 0.462932i | ||||
\(37\) | 3.89028e11 | 0.110756 | 0.0553779 | − | 0.998465i | \(-0.482364\pi\) | ||||
0.0553779 | + | 0.998465i | \(0.482364\pi\) | |||||||
\(38\) | 1.47086e12i | 0.338299i | ||||||||
\(39\) | 3.83885e12 | − | 2.69522e12i | 0.717272 | − | 0.503590i | ||||
\(40\) | 2.88027e12 | 0.439495 | ||||||||
\(41\) | − | 4.14027e12i | − | 0.518511i | −0.965809 | − | 0.259256i | \(-0.916523\pi\) | ||
0.965809 | − | 0.259256i | \(-0.0834772\pi\) | |||||||
\(42\) | 8.38094e12 | + | 1.19371e13i | 0.865562 | + | 1.23283i | ||||
\(43\) | −1.68426e13 | −1.44099 | −0.720494 | − | 0.693461i | \(-0.756085\pi\) | ||||
−0.720494 | + | 0.693461i | \(0.756085\pi\) | |||||||
\(44\) | − | 1.10790e13i | − | 0.788638i | ||||||
\(45\) | −1.12053e13 | − | 4.04638e12i | −0.666384 | − | 0.240639i | ||||
\(46\) | −1.39903e13 | −0.697852 | ||||||||
\(47\) | 9.08356e12i | 0.381481i | 0.981640 | + | 0.190741i | \(0.0610889\pi\) | ||||
−0.981640 | + | 0.190741i | \(0.938911\pi\) | |||||||
\(48\) | 2.88269e13 | − | 2.02392e13i | 1.02298 | − | 0.718228i | ||||
\(49\) | 1.73022e13 | 0.520635 | ||||||||
\(50\) | 2.37642e13i | 0.608365i | ||||||||
\(51\) | −2.54336e12 | − | 3.62255e12i | −0.0555709 | − | 0.0791504i | ||||
\(52\) | 2.30602e13 | 0.431357 | ||||||||
\(53\) | 4.32802e13i | 0.695155i | 0.937651 | + | 0.347578i | \(0.112996\pi\) | ||||
−0.937651 | + | 0.347578i | \(0.887004\pi\) | |||||||
\(54\) | −8.52240e13 | + | 2.31822e13i | −1.17872 | + | 0.320630i | ||||
\(55\) | 9.50576e13 | 1.13523 | ||||||||
\(56\) | − | 7.39826e13i | − | 0.764937i | ||||||
\(57\) | −2.52562e13 | + | 1.77322e13i | −0.226657 | + | 0.159134i | ||||
\(58\) | −1.17312e14 | −0.916049 | ||||||||
\(59\) | − | 2.07085e14i | − | 1.41037i | −0.709024 | − | 0.705185i | \(-0.750864\pi\) | ||
0.709024 | − | 0.705185i | \(-0.249136\pi\) | |||||||
\(60\) | −3.36556e13 | − | 4.79362e13i | −0.200377 | − | 0.285400i | ||||
\(61\) | 1.10641e14 | 0.577136 | 0.288568 | − | 0.957459i | \(-0.406821\pi\) | ||||
0.288568 | + | 0.957459i | \(0.406821\pi\) | |||||||
\(62\) | 2.06059e14i | 0.943751i | ||||||||
\(63\) | −1.03935e14 | + | 2.87820e14i | −0.418830 | + | 1.15983i | ||||
\(64\) | −4.01216e13 | −0.142541 | ||||||||
\(65\) | 1.97857e14i | 0.620933i | ||||||||
\(66\) | 5.76750e14 | − | 4.04932e14i | 1.60190 | − | 1.12468i | ||||
\(67\) | 1.61981e14 | 0.398901 | 0.199451 | − | 0.979908i | \(-0.436084\pi\) | ||||
0.199451 | + | 0.979908i | \(0.436084\pi\) | |||||||
\(68\) | − | 2.17610e13i | − | 0.0476000i | ||||||
\(69\) | −1.68662e14 | − | 2.40228e14i | −0.328265 | − | 0.467553i | ||||
\(70\) | −6.15247e14 | −1.06725 | ||||||||
\(71\) | 8.06506e13i | 0.124894i | 0.998048 | + | 0.0624469i | \(0.0198904\pi\) | ||||
−0.998048 | + | 0.0624469i | \(0.980110\pi\) | |||||||
\(72\) | 4.21363e14 | + | 1.52159e14i | 0.583440 | + | 0.210687i | ||||
\(73\) | −8.85416e14 | −1.09790 | −0.548952 | − | 0.835854i | \(-0.684973\pi\) | ||||
−0.548952 | + | 0.835854i | \(0.684973\pi\) | |||||||
\(74\) | 1.21656e14i | 0.135294i | ||||||||
\(75\) | −4.08058e14 | + | 2.86494e14i | −0.407598 | + | 0.286171i | ||||
\(76\) | −1.51716e14 | −0.136308 | ||||||||
\(77\) | − | 2.44165e15i | − | 1.97586i | ||||||
\(78\) | 8.42843e14 | + | 1.20047e15i | 0.615162 | + | 0.876185i | ||||
\(79\) | 2.35142e15 | 1.54993 | 0.774967 | − | 0.632002i | \(-0.217766\pi\) | ||||
0.774967 | + | 0.632002i | \(0.217766\pi\) | |||||||
\(80\) | 1.48576e15i | 0.885584i | ||||||||
\(81\) | −1.42550e15 | − | 1.18391e15i | −0.769282 | − | 0.638909i | ||||
\(82\) | 1.29474e15 | 0.633389 | ||||||||
\(83\) | 3.93339e15i | 1.74640i | 0.487365 | + | 0.873198i | \(0.337958\pi\) | ||||
−0.487365 | + | 0.873198i | \(0.662042\pi\) | |||||||
\(84\) | −1.23129e15 | + | 8.64477e14i | −0.496736 | + | 0.348754i | ||||
\(85\) | 1.86709e14 | 0.0685195 | ||||||||
\(86\) | − | 5.26696e15i | − | 1.76024i | ||||||
\(87\) | −1.41428e15 | − | 2.01438e15i | −0.430904 | − | 0.613743i | ||||
\(88\) | −3.57453e15 | −0.993934 | ||||||||
\(89\) | 3.56666e15i | 0.906028i | 0.891503 | + | 0.453014i | \(0.149651\pi\) | ||||
−0.891503 | + | 0.453014i | \(0.850349\pi\) | |||||||
\(90\) | 1.26537e15 | − | 3.50410e15i | 0.293953 | − | 0.814023i | ||||
\(91\) | 5.08215e15 | 1.08073 | ||||||||
\(92\) | − | 1.44307e15i | − | 0.281180i | ||||||
\(93\) | −3.53825e15 | + | 2.48418e15i | −0.632303 | + | 0.443934i | ||||
\(94\) | −2.84059e15 | −0.465999 | ||||||||
\(95\) | − | 1.30172e15i | − | 0.196214i | ||||||
\(96\) | 3.75781e15 | + | 5.35231e15i | 0.520913 | + | 0.741945i | ||||
\(97\) | −1.51341e15 | −0.193100 | −0.0965502 | − | 0.995328i | \(-0.530781\pi\) | ||||
−0.0965502 | + | 0.995328i | \(0.530781\pi\) | |||||||
\(98\) | 5.41071e15i | 0.635983i | ||||||||
\(99\) | 1.39062e16 | + | 5.02171e15i | 1.50705 | + | 0.544214i | ||||
\(100\) | −2.45124e15 | −0.245124 | ||||||||
\(101\) | − | 1.00976e16i | − | 0.932499i | −0.884653 | − | 0.466249i | \(-0.845605\pi\) | ||
0.884653 | − | 0.466249i | \(-0.154395\pi\) | |||||||
\(102\) | 1.13284e15 | − | 7.95354e14i | 0.0966864 | − | 0.0678827i | ||||
\(103\) | −2.41924e15 | −0.190977 | −0.0954884 | − | 0.995431i | \(-0.530441\pi\) | ||||
−0.0954884 | + | 0.995431i | \(0.530441\pi\) | |||||||
\(104\) | − | 7.44018e15i | − | 0.543647i | ||||||
\(105\) | −7.41722e15 | − | 1.05645e16i | −0.502027 | − | 0.715045i | ||||
\(106\) | −1.35345e16 | −0.849169 | ||||||||
\(107\) | 1.15781e16i | 0.673857i | 0.941530 | + | 0.336929i | \(0.109388\pi\) | ||||
−0.941530 | + | 0.336929i | \(0.890612\pi\) | |||||||
\(108\) | −2.39120e15 | − | 8.79068e15i | −0.129189 | − | 0.474933i | ||||
\(109\) | −1.26180e16 | −0.633253 | −0.316627 | − | 0.948550i | \(-0.602550\pi\) | ||||
−0.316627 | + | 0.948550i | \(0.602550\pi\) | |||||||
\(110\) | 2.97262e16i | 1.38675i | ||||||||
\(111\) | −2.08896e15 | + | 1.46664e15i | −0.0906456 | + | 0.0636415i | ||||
\(112\) | 3.81633e16 | 1.54135 | ||||||||
\(113\) | − | 2.03120e16i | − | 0.764057i | −0.924151 | − | 0.382029i | \(-0.875226\pi\) | ||
0.924151 | − | 0.382029i | \(-0.124774\pi\) | |||||||
\(114\) | −5.54516e15 | − | 7.89805e15i | −0.194390 | − | 0.276873i | ||||
\(115\) | 1.23815e16 | 0.404755 | ||||||||
\(116\) | − | 1.21005e16i | − | 0.369096i | ||||||
\(117\) | −1.04524e16 | + | 2.89450e16i | −0.297666 | + | 0.824304i | ||||
\(118\) | 6.47591e16 | 1.72284 | ||||||||
\(119\) | − | 4.79581e15i | − | 0.119258i | ||||||
\(120\) | −1.54662e16 | + | 1.08587e16i | −0.359694 | + | 0.252538i | ||||
\(121\) | −7.20203e16 | −1.56737 | ||||||||
\(122\) | 3.45995e16i | 0.705003i | ||||||||
\(123\) | 1.56089e16 | + | 2.22320e16i | 0.297942 | + | 0.424364i | ||||
\(124\) | −2.12545e16 | −0.380258 | ||||||||
\(125\) | − | 6.32616e16i | − | 1.06135i | ||||||
\(126\) | −9.00062e16 | − | 3.25023e16i | −1.41680 | − | 0.511623i | ||||
\(127\) | 5.69808e16 | 0.841974 | 0.420987 | − | 0.907067i | \(-0.361684\pi\) | ||||
0.420987 | + | 0.907067i | \(0.361684\pi\) | |||||||
\(128\) | − | 7.78705e16i | − | 1.08067i | ||||||
\(129\) | 9.04395e16 | − | 6.34968e16i | 1.17934 | − | 0.828007i | ||||
\(130\) | −6.18733e16 | −0.758502 | ||||||||
\(131\) | 1.29909e17i | 1.49786i | 0.662651 | + | 0.748928i | \(0.269431\pi\) | ||||
−0.662651 | + | 0.748928i | \(0.730569\pi\) | |||||||
\(132\) | 4.17679e16 | + | 5.94907e16i | 0.453160 | + | 0.645442i | ||||
\(133\) | −3.34360e16 | −0.341509 | ||||||||
\(134\) | 5.06542e16i | 0.487279i | ||||||||
\(135\) | 7.54241e16 | − | 2.05165e16i | 0.683660 | − | 0.185966i | ||||
\(136\) | −7.02098e15 | −0.0599911 | ||||||||
\(137\) | 1.41617e17i | 1.14117i | 0.821238 | + | 0.570586i | \(0.193284\pi\) | ||||
−0.821238 | + | 0.570586i | \(0.806716\pi\) | |||||||
\(138\) | 7.51235e16 | − | 5.27436e16i | 0.571141 | − | 0.400993i | ||||
\(139\) | −3.68618e16 | −0.264520 | −0.132260 | − | 0.991215i | \(-0.542223\pi\) | ||||
−0.132260 | + | 0.991215i | \(0.542223\pi\) | |||||||
\(140\) | − | 6.34615e16i | − | 0.430018i | ||||||
\(141\) | −3.42452e16 | − | 4.87760e16i | −0.219203 | − | 0.312214i | ||||
\(142\) | −2.52208e16 | −0.152564 | ||||||||
\(143\) | − | 2.45548e17i | − | 1.40426i | ||||||
\(144\) | −7.84900e16 | + | 2.17356e17i | −0.424536 | + | 1.17563i | ||||
\(145\) | 1.03822e17 | 0.531309 | ||||||||
\(146\) | − | 2.76885e17i | − | 1.34115i | ||||||
\(147\) | −9.29077e16 | + | 6.52297e16i | −0.426102 | + | 0.299162i | ||||
\(148\) | −1.25486e16 | −0.0545130 | ||||||||
\(149\) | 3.06216e17i | 1.26049i | 0.776398 | + | 0.630243i | \(0.217045\pi\) | ||||
−0.776398 | + | 0.630243i | \(0.782955\pi\) | |||||||
\(150\) | −8.95917e16 | − | 1.27607e17i | −0.349573 | − | 0.497902i | ||||
\(151\) | −4.71608e17 | −1.74488 | −0.872440 | − | 0.488721i | \(-0.837463\pi\) | ||||
−0.872440 | + | 0.488721i | \(0.837463\pi\) | |||||||
\(152\) | 4.89498e16i | 0.171792i | ||||||||
\(153\) | 2.73142e16 | + | 9.86349e15i | 0.0909614 | + | 0.0328472i | ||||
\(154\) | 7.63545e17 | 2.41362 | ||||||||
\(155\) | − | 1.82364e17i | − | 0.547376i | ||||||
\(156\) | −1.23827e17 | + | 8.69376e16i | −0.353034 | + | 0.247862i | ||||
\(157\) | 5.59035e17 | 1.51440 | 0.757202 | − | 0.653181i | \(-0.226566\pi\) | ||||
0.757202 | + | 0.653181i | \(0.226566\pi\) | |||||||
\(158\) | 7.35330e17i | 1.89333i | ||||||||
\(159\) | −1.63167e17 | − | 2.32401e17i | −0.399444 | − | 0.568934i | ||||
\(160\) | −2.75862e17 | −0.642292 | ||||||||
\(161\) | − | 3.18032e17i | − | 0.704472i | ||||||
\(162\) | 3.70230e17 | − | 4.45777e17i | 0.780461 | − | 0.939719i | ||||
\(163\) | 2.34231e17 | 0.470050 | 0.235025 | − | 0.971989i | \(-0.424483\pi\) | ||||
0.235025 | + | 0.971989i | \(0.424483\pi\) | |||||||
\(164\) | 1.33549e17i | 0.255206i | ||||||||
\(165\) | −5.10430e17 | + | 3.58369e17i | −0.929105 | + | 0.652317i | ||||
\(166\) | −1.23004e18 | −2.13331 | ||||||||
\(167\) | − | 4.08862e17i | − | 0.675842i | −0.941175 | − | 0.337921i | \(-0.890276\pi\) | ||
0.941175 | − | 0.337921i | \(-0.109724\pi\) | |||||||
\(168\) | 2.78916e17 | + | 3.97264e17i | 0.439541 | + | 0.626045i | ||||
\(169\) | −1.54322e17 | −0.231918 | ||||||||
\(170\) | 5.83872e16i | 0.0837002i | ||||||||
\(171\) | 6.87675e16 | − | 1.90433e17i | 0.0940621 | − | 0.260479i | ||||
\(172\) | 5.43277e17 | 0.709241 | ||||||||
\(173\) | − | 2.03093e16i | − | 0.0253119i | −0.999920 | − | 0.0126560i | \(-0.995971\pi\) | ||
0.999920 | − | 0.0126560i | \(-0.00402863\pi\) | |||||||
\(174\) | 6.29931e17 | − | 4.42269e17i | 0.749719 | − | 0.526372i | ||||
\(175\) | −5.40218e17 | −0.614136 | ||||||||
\(176\) | − | 1.84389e18i | − | 2.00278i | ||||||
\(177\) | 7.80715e17 | + | 1.11198e18i | 0.810413 | + | 1.15428i | ||||
\(178\) | −1.11536e18 | −1.10676 | ||||||||
\(179\) | 1.38776e18i | 1.31671i | 0.752709 | + | 0.658354i | \(0.228747\pi\) | ||||
−0.752709 | + | 0.658354i | \(0.771253\pi\) | |||||||
\(180\) | 3.61441e17 | + | 1.30521e17i | 0.327988 | + | 0.118440i | ||||
\(181\) | 2.00744e18 | 1.74267 | 0.871334 | − | 0.490691i | \(-0.163256\pi\) | ||||
0.871334 | + | 0.490691i | \(0.163256\pi\) | |||||||
\(182\) | 1.58928e18i | 1.32017i | ||||||||
\(183\) | −5.94110e17 | + | 4.17120e17i | −0.472344 | + | 0.331629i | ||||
\(184\) | −4.65593e17 | −0.354376 | ||||||||
\(185\) | − | 1.07667e17i | − | 0.0784707i | ||||||
\(186\) | −7.76845e17 | − | 1.10647e18i | −0.542289 | − | 0.772391i | ||||
\(187\) | −2.31713e17 | −0.154959 | ||||||||
\(188\) | − | 2.93001e17i | − | 0.187761i | ||||||
\(189\) | −5.26986e17 | − | 1.93734e18i | −0.323671 | − | 1.18990i | ||||
\(190\) | 4.07072e17 | 0.239686 | ||||||||
\(191\) | − | 7.92402e17i | − | 0.447382i | −0.974660 | − | 0.223691i | \(-0.928189\pi\) | ||
0.974660 | − | 0.223691i | \(-0.0718107\pi\) | |||||||
\(192\) | 2.15441e17 | − | 1.51259e17i | 0.116659 | − | 0.0819053i | ||||
\(193\) | −2.85892e17 | −0.148506 | −0.0742528 | − | 0.997239i | \(-0.523657\pi\) | ||||
−0.0742528 | + | 0.997239i | \(0.523657\pi\) | |||||||
\(194\) | − | 4.73270e17i | − | 0.235882i | ||||||
\(195\) | −7.45925e17 | − | 1.06243e18i | −0.356795 | − | 0.508188i | ||||
\(196\) | −5.58104e17 | −0.256251 | ||||||||
\(197\) | 1.08139e18i | 0.476707i | 0.971178 | + | 0.238353i | \(0.0766077\pi\) | ||||
−0.971178 | + | 0.238353i | \(0.923392\pi\) | |||||||
\(198\) | −1.57038e18 | + | 4.34872e18i | −0.664786 | + | 1.84094i | ||||
\(199\) | 1.96655e18 | 0.799613 | 0.399806 | − | 0.916600i | \(-0.369077\pi\) | ||||
0.399806 | + | 0.916600i | \(0.369077\pi\) | |||||||
\(200\) | 7.90869e17i | 0.308933i | ||||||||
\(201\) | −8.69788e17 | + | 6.10671e17i | −0.326471 | + | 0.229213i | ||||
\(202\) | 3.15770e18 | 1.13910 | ||||||||
\(203\) | − | 2.66678e18i | − | 0.924739i | ||||||
\(204\) | 8.20393e16 | + | 1.16850e17i | 0.0273514 | + | 0.0389571i | ||||
\(205\) | −1.14586e18 | −0.367366 | ||||||||
\(206\) | − | 7.56538e17i | − | 0.233288i | ||||||
\(207\) | 1.81133e18 | + | 6.54093e17i | 0.537322 | + | 0.194033i | ||||
\(208\) | 3.83795e18 | 1.09545 | ||||||||
\(209\) | 1.61549e18i | 0.443745i | ||||||||
\(210\) | 3.30369e18 | − | 2.31949e18i | 0.873464 | − | 0.613252i | ||||
\(211\) | −5.56143e18 | −1.41556 | −0.707778 | − | 0.706435i | \(-0.750302\pi\) | ||||
−0.707778 | + | 0.706435i | \(0.750302\pi\) | |||||||
\(212\) | − | 1.39605e18i | − | 0.342149i | ||||||
\(213\) | −3.04054e17 | − | 4.33069e17i | −0.0717653 | − | 0.102216i | ||||
\(214\) | −3.62068e18 | −0.823152 | ||||||||
\(215\) | 4.66132e18i | 1.02094i | ||||||||
\(216\) | −2.83624e18 | + | 7.71498e17i | −0.598567 | + | 0.162819i | ||||
\(217\) | −4.68420e18 | −0.952703 | ||||||||
\(218\) | − | 3.94586e18i | − | 0.773552i | ||||||
\(219\) | 4.75442e18 | − | 3.33804e18i | 0.898554 | − | 0.630867i | ||||
\(220\) | −3.06619e18 | −0.558751 | ||||||||
\(221\) | − | 4.82298e17i | − | 0.0847573i | ||||||
\(222\) | −4.58645e17 | − | 6.53255e17i | −0.0777414 | − | 0.110728i | ||||
\(223\) | 8.62389e17 | 0.141015 | 0.0705074 | − | 0.997511i | \(-0.477538\pi\) | ||||
0.0705074 | + | 0.997511i | \(0.477538\pi\) | |||||||
\(224\) | 7.08579e18i | 1.11790i | ||||||||
\(225\) | 1.11106e18 | − | 3.07677e18i | 0.169152 | − | 0.468420i | ||||
\(226\) | 6.35193e18 | 0.933336 | ||||||||
\(227\) | − | 2.61451e18i | − | 0.370837i | −0.982660 | − | 0.185418i | \(-0.940636\pi\) | ||
0.982660 | − | 0.185418i | \(-0.0593641\pi\) | |||||||
\(228\) | 8.14669e17 | − | 5.71972e17i | 0.111558 | − | 0.0783242i | ||||
\(229\) | 5.58270e18 | 0.738176 | 0.369088 | − | 0.929394i | \(-0.379670\pi\) | ||||
0.369088 | + | 0.929394i | \(0.379670\pi\) | |||||||
\(230\) | 3.87192e18i | 0.494429i | ||||||||
\(231\) | 9.20505e18 | + | 1.31109e19i | 1.13535 | + | 1.61710i | ||||
\(232\) | −3.90412e18 | −0.465179 | ||||||||
\(233\) | − | 1.35764e19i | − | 1.56293i | −0.623952 | − | 0.781463i | \(-0.714474\pi\) | ||
0.623952 | − | 0.781463i | \(-0.285526\pi\) | |||||||
\(234\) | −9.05162e18 | − | 3.26865e18i | −1.00693 | − | 0.363615i | ||||
\(235\) | 2.51395e18 | 0.270280 | ||||||||
\(236\) | 6.67978e18i | 0.694170i | ||||||||
\(237\) | −1.26264e19 | + | 8.86490e18i | −1.26851 | + | 0.890609i | ||||
\(238\) | 1.49973e18 | 0.145679 | ||||||||
\(239\) | 8.32183e18i | 0.781692i | 0.920456 | + | 0.390846i | \(0.127818\pi\) | ||||
−0.920456 | + | 0.390846i | \(0.872182\pi\) | |||||||
\(240\) | −5.60136e18 | − | 7.97810e18i | −0.508866 | − | 0.724785i | ||||
\(241\) | 3.38184e18 | 0.297178 | 0.148589 | − | 0.988899i | \(-0.452527\pi\) | ||||
0.148589 | + | 0.988899i | \(0.452527\pi\) | |||||||
\(242\) | − | 2.25220e19i | − | 1.91463i | ||||||
\(243\) | 1.21179e19 | + | 9.83099e17i | 0.996725 | + | 0.0808625i | ||||
\(244\) | −3.56887e18 | −0.284061 | ||||||||
\(245\) | − | 4.78853e18i | − | 0.368870i | ||||||
\(246\) | −6.95234e18 | + | 4.88118e18i | −0.518382 | + | 0.363952i | ||||
\(247\) | −3.36255e18 | −0.242713 | ||||||||
\(248\) | 6.85759e18i | 0.479246i | ||||||||
\(249\) | −1.48290e19 | − | 2.11211e19i | −1.00350 | − | 1.42930i | ||||
\(250\) | 1.97830e19 | 1.29650 | ||||||||
\(251\) | 1.37972e19i | 0.875789i | 0.899026 | + | 0.437895i | \(0.144276\pi\) | ||||
−0.899026 | + | 0.437895i | \(0.855724\pi\) | |||||||
\(252\) | 3.35255e18 | − | 9.28397e18i | 0.206144 | − | 0.570859i | ||||
\(253\) | −1.53660e19 | −0.915368 | ||||||||
\(254\) | 1.78189e19i | 1.02852i | ||||||||
\(255\) | −1.00257e18 | + | 7.03897e17i | −0.0560782 | + | 0.0393720i | ||||
\(256\) | 2.17221e19 | 1.17756 | ||||||||
\(257\) | 1.93378e19i | 1.01611i | 0.861324 | + | 0.508057i | \(0.169636\pi\) | ||||
−0.861324 | + | 0.508057i | \(0.830364\pi\) | |||||||
\(258\) | 1.98566e19 | + | 2.82820e19i | 1.01145 | + | 1.44063i | ||||
\(259\) | −2.76552e18 | −0.136578 | ||||||||
\(260\) | − | 6.38211e18i | − | 0.305617i | ||||||
\(261\) | 1.51885e19 | + | 5.48474e18i | 0.705327 | + | 0.254702i | ||||
\(262\) | −4.06249e19 | −1.82971 | ||||||||
\(263\) | − | 4.15307e19i | − | 1.81436i | −0.420741 | − | 0.907181i | \(-0.638230\pi\) | ||
0.420741 | − | 0.907181i | \(-0.361770\pi\) | |||||||
\(264\) | 1.91941e19 | − | 1.34760e19i | 0.813462 | − | 0.571125i | ||||
\(265\) | 1.19781e19 | 0.492519 | ||||||||
\(266\) | − | 1.04560e19i | − | 0.417171i | ||||||
\(267\) | −1.34464e19 | − | 1.91519e19i | −0.520613 | − | 0.741518i | ||||
\(268\) | −5.22488e18 | −0.196335 | ||||||||
\(269\) | − | 4.45503e18i | − | 0.162492i | −0.996694 | − | 0.0812460i | \(-0.974110\pi\) | ||
0.996694 | − | 0.0812460i | \(-0.0258899\pi\) | |||||||
\(270\) | 6.41586e18 | + | 2.35864e19i | 0.227167 | + | 0.835127i | ||||
\(271\) | −1.72748e19 | −0.593827 | −0.296913 | − | 0.954904i | \(-0.595957\pi\) | ||||
−0.296913 | + | 0.954904i | \(0.595957\pi\) | |||||||
\(272\) | − | 3.62171e18i | − | 0.120882i | ||||||
\(273\) | −2.72896e19 | + | 1.91598e19i | −0.884497 | + | 0.620998i | ||||
\(274\) | −4.42862e19 | −1.39400 | ||||||||
\(275\) | 2.61010e19i | 0.797988i | ||||||||
\(276\) | 5.44040e18 | + | 7.74884e18i | 0.161569 | + | 0.230125i | ||||
\(277\) | 5.05204e19 | 1.45757 | 0.728784 | − | 0.684744i | \(-0.240086\pi\) | ||||
0.728784 | + | 0.684744i | \(0.240086\pi\) | |||||||
\(278\) | − | 1.15273e19i | − | 0.323125i | ||||||
\(279\) | 9.63395e18 | − | 2.66786e19i | 0.262404 | − | 0.726656i | ||||
\(280\) | −2.04753e19 | −0.541959 | ||||||||
\(281\) | − | 2.72214e18i | − | 0.0700260i | −0.999387 | − | 0.0350130i | \(-0.988853\pi\) | ||
0.999387 | − | 0.0350130i | \(-0.0111473\pi\) | |||||||
\(282\) | 1.52531e19 | − | 1.07091e19i | 0.381386 | − | 0.267768i | ||||
\(283\) | −3.84294e18 | −0.0934054 | −0.0467027 | − | 0.998909i | \(-0.514871\pi\) | ||||
−0.0467027 | + | 0.998909i | \(0.514871\pi\) | |||||||
\(284\) | − | 2.60148e18i | − | 0.0614715i | ||||||
\(285\) | 4.90752e18 | + | 6.98986e18i | 0.112747 | + | 0.160587i | ||||
\(286\) | 7.67872e19 | 1.71538 | ||||||||
\(287\) | 2.94324e19i | 0.639397i | ||||||||
\(288\) | −4.03567e19 | − | 1.45733e19i | −0.852659 | − | 0.307905i | ||||
\(289\) | 4.82061e19 | 0.990647 | ||||||||
\(290\) | 3.24671e19i | 0.649022i | ||||||||
\(291\) | 8.12657e18 | − | 5.70559e18i | 0.158039 | − | 0.110958i | ||||
\(292\) | 2.85601e19 | 0.540378 | ||||||||
\(293\) | 4.00496e19i | 0.737322i | 0.929564 | + | 0.368661i | \(0.120184\pi\) | ||||
−0.929564 | + | 0.368661i | \(0.879816\pi\) | |||||||
\(294\) | −2.03985e19 | − | 2.90539e19i | −0.365442 | − | 0.520505i | ||||
\(295\) | −5.73125e19 | −0.999249 | ||||||||
\(296\) | 4.04868e18i | 0.0687036i | ||||||||
\(297\) | −9.36042e19 | + | 2.54617e19i | −1.54612 | + | 0.420568i | ||||
\(298\) | −9.57592e19 | −1.53975 | ||||||||
\(299\) | − | 3.19834e19i | − | 0.500674i | ||||||
\(300\) | 1.31624e19 | − | 9.24121e18i | 0.200616 | − | 0.140851i | ||||
\(301\) | 1.19731e20 | 1.77694 | ||||||||
\(302\) | − | 1.47480e20i | − | 2.13146i | ||||||
\(303\) | 3.80683e19 | + | 5.42212e19i | 0.535824 | + | 0.763182i | ||||
\(304\) | −2.52503e19 | −0.346161 | ||||||||
\(305\) | − | 3.06209e19i | − | 0.408902i | ||||||
\(306\) | −3.08448e18 | + | 8.54163e18i | −0.0401246 | + | 0.111114i | ||||
\(307\) | −8.00171e19 | −1.01409 | −0.507044 | − | 0.861920i | \(-0.669262\pi\) | ||||
−0.507044 | + | 0.861920i | \(0.669262\pi\) | |||||||
\(308\) | 7.87582e19i | 0.972501i | ||||||||
\(309\) | 1.29906e19 | − | 9.12058e18i | 0.156301 | − | 0.109737i | ||||
\(310\) | 5.70284e19 | 0.668649 | ||||||||
\(311\) | − | 1.25107e20i | − | 1.42955i | −0.699355 | − | 0.714775i | \(-0.746529\pi\) | ||
0.699355 | − | 0.714775i | \(-0.253471\pi\) | |||||||
\(312\) | 2.80496e19 | + | 3.99515e19i | 0.312385 | + | 0.444935i | ||||
\(313\) | 4.69482e19 | 0.509641 | 0.254820 | − | 0.966988i | \(-0.417984\pi\) | ||||
0.254820 | + | 0.966988i | \(0.417984\pi\) | |||||||
\(314\) | 1.74820e20i | 1.84992i | ||||||||
\(315\) | 7.96565e19 | + | 2.87649e19i | 0.821744 | + | 0.296742i | ||||
\(316\) | −7.58478e19 | −0.762863 | ||||||||
\(317\) | 5.48514e19i | 0.537915i | 0.963152 | + | 0.268957i | \(0.0866791\pi\) | ||||
−0.963152 | + | 0.268957i | \(0.913321\pi\) | |||||||
\(318\) | 7.26760e19 | − | 5.10252e19i | 0.694983 | − | 0.487941i | ||||
\(319\) | −1.28848e20 | −1.20158 | ||||||||
\(320\) | 1.11040e19i | 0.100990i | ||||||||
\(321\) | −4.36498e19 | − | 6.21710e19i | −0.387206 | − | 0.551503i | ||||
\(322\) | 9.94541e19 | 0.860549 | ||||||||
\(323\) | 3.17309e18i | 0.0267832i | ||||||||
\(324\) | 4.59811e19 | + | 3.81885e19i | 0.378633 | + | 0.314465i | ||||
\(325\) | −5.43278e19 | −0.436471 | ||||||||
\(326\) | 7.32482e19i | 0.574191i | ||||||||
\(327\) | 6.77547e19 | − | 4.75700e19i | 0.518271 | − | 0.363874i | ||||
\(328\) | 4.30886e19 | 0.321641 | ||||||||
\(329\) | − | 6.45733e19i | − | 0.470420i | ||||||
\(330\) | −1.12068e20 | − | 1.59620e20i | −0.796840 | − | 1.13495i | ||||
\(331\) | −1.44398e20 | −1.00216 | −0.501081 | − | 0.865401i | \(-0.667064\pi\) | ||||
−0.501081 | + | 0.865401i | \(0.667064\pi\) | |||||||
\(332\) | − | 1.26876e20i | − | 0.859560i | ||||||
\(333\) | 5.68782e18 | − | 1.57509e19i | 0.0376177 | − | 0.104172i | ||||
\(334\) | 1.27858e20 | 0.825576 | ||||||||
\(335\) | − | 4.48295e19i | − | 0.282622i | ||||||
\(336\) | −2.04925e20 | + | 1.43876e20i | −1.26148 | + | 0.885676i | ||||
\(337\) | −1.23577e20 | −0.742846 | −0.371423 | − | 0.928464i | \(-0.621130\pi\) | ||||
−0.371423 | + | 0.928464i | \(0.621130\pi\) | |||||||
\(338\) | − | 4.82592e19i | − | 0.283300i | ||||||
\(339\) | 7.65768e19 | + | 1.09070e20i | 0.439035 | + | 0.625325i | ||||
\(340\) | −6.02253e18 | −0.0337246 | ||||||||
\(341\) | 2.26321e20i | 1.23791i | ||||||||
\(342\) | 5.95516e19 | + | 2.15048e19i | 0.318189 | + | 0.114902i | ||||
\(343\) | 1.13248e20 | 0.591125 | ||||||||
\(344\) | − | 1.75283e20i | − | 0.893868i | ||||||
\(345\) | −6.64851e19 | + | 4.66787e19i | −0.331262 | + | 0.232576i | ||||
\(346\) | 6.35106e18 | 0.0309198 | ||||||||
\(347\) | 2.90213e20i | 1.38064i | 0.723504 | + | 0.690320i | \(0.242530\pi\) | ||||
−0.723504 | + | 0.690320i | \(0.757470\pi\) | |||||||
\(348\) | 4.56192e19 | + | 6.49761e19i | 0.212087 | + | 0.302078i | ||||
\(349\) | 4.26107e20 | 1.93604 | 0.968021 | − | 0.250869i | \(-0.0807164\pi\) | ||||
0.968021 | + | 0.250869i | \(0.0807164\pi\) | |||||||
\(350\) | − | 1.68935e20i | − | 0.750199i | ||||||
\(351\) | −5.29972e19 | − | 1.94832e20i | −0.230036 | − | 0.845675i | ||||
\(352\) | 3.42356e20 | 1.45257 | ||||||||
\(353\) | − | 3.04382e20i | − | 1.26247i | −0.775591 | − | 0.631236i | \(-0.782548\pi\) | ||
0.775591 | − | 0.631236i | \(-0.217452\pi\) | |||||||
\(354\) | −3.47737e20 | + | 2.44143e20i | −1.41002 | + | 0.989962i | ||||
\(355\) | 2.23207e19 | 0.0884874 | ||||||||
\(356\) | − | 1.15047e20i | − | 0.445938i | ||||||
\(357\) | 1.80803e19 | + | 2.57520e19i | 0.0685267 | + | 0.0976036i | ||||
\(358\) | −4.33976e20 | −1.60843 | ||||||||
\(359\) | 6.70999e19i | 0.243202i | 0.992579 | + | 0.121601i | \(0.0388028\pi\) | ||||
−0.992579 | + | 0.121601i | \(0.961197\pi\) | |||||||
\(360\) | 4.21114e19 | − | 1.16616e20i | 0.149272 | − | 0.413368i | ||||
\(361\) | −2.66319e20 | −0.923303 | ||||||||
\(362\) | 6.27762e20i | 2.12876i | ||||||||
\(363\) | 3.86727e20 | − | 2.71518e20i | 1.28278 | − | 0.900629i | ||||
\(364\) | −1.63931e20 | −0.531924 | ||||||||
\(365\) | 2.45046e20i | 0.777866i | ||||||||
\(366\) | −1.30441e20 | − | 1.85789e20i | −0.405102 | − | 0.576993i | ||||
\(367\) | −1.14079e20 | −0.346639 | −0.173320 | − | 0.984866i | \(-0.555449\pi\) | ||||
−0.173320 | + | 0.984866i | \(0.555449\pi\) | |||||||
\(368\) | − | 2.40172e20i | − | 0.714069i | ||||||
\(369\) | −1.67630e20 | − | 6.05333e19i | −0.487688 | − | 0.176110i | ||||
\(370\) | 3.36692e19 | 0.0958561 | ||||||||
\(371\) | − | 3.07670e20i | − | 0.857224i | ||||||
\(372\) | 1.14130e20 | − | 8.01301e19i | 0.311213 | − | 0.218500i | ||||
\(373\) | −8.72192e19 | −0.232778 | −0.116389 | − | 0.993204i | \(-0.537132\pi\) | ||||
−0.116389 | + | 0.993204i | \(0.537132\pi\) | |||||||
\(374\) | − | 7.24608e19i | − | 0.189291i | ||||||
\(375\) | 2.38497e20 | + | 3.39696e20i | 0.609865 | + | 0.868640i | ||||
\(376\) | −9.45342e19 | −0.236639 | ||||||||
\(377\) | − | 2.68189e20i | − | 0.657220i | ||||||
\(378\) | 6.05841e20 | − | 1.64798e20i | 1.45353 | − | 0.395382i | ||||
\(379\) | 4.07877e20 | 0.958111 | 0.479056 | − | 0.877785i | \(-0.340979\pi\) | ||||
0.479056 | + | 0.877785i | \(0.340979\pi\) | |||||||
\(380\) | 4.19886e19i | 0.0965746i | ||||||||
\(381\) | −3.05970e20 | + | 2.14819e20i | −0.689094 | + | 0.483807i | ||||
\(382\) | 2.47798e20 | 0.546501 | ||||||||
\(383\) | 9.15624e20i | 1.97755i | 0.149422 | + | 0.988774i | \(0.452259\pi\) | ||||
−0.149422 | + | 0.988774i | \(0.547741\pi\) | |||||||
\(384\) | 2.93574e20 | + | 4.18141e20i | 0.620965 | + | 0.884450i | ||||
\(385\) | −6.75746e20 | −1.39990 | ||||||||
\(386\) | − | 8.94033e19i | − | 0.181407i | ||||||
\(387\) | −2.46249e20 | + | 6.81917e20i | −0.489425 | + | 1.35533i | ||||
\(388\) | 4.88169e19 | 0.0950422 | ||||||||
\(389\) | − | 9.02288e20i | − | 1.72087i | −0.509559 | − | 0.860436i | \(-0.670191\pi\) | ||
0.509559 | − | 0.860436i | \(-0.329809\pi\) | |||||||
\(390\) | 3.32241e20 | − | 2.33264e20i | 0.620778 | − | 0.435843i | ||||
\(391\) | −3.01814e19 | −0.0552490 | ||||||||
\(392\) | 1.80067e20i | 0.322958i | ||||||||
\(393\) | −4.89761e20 | − | 6.97574e20i | −0.860684 | − | 1.22589i | ||||
\(394\) | −3.38169e20 | −0.582322 | ||||||||
\(395\) | − | 6.50775e20i | − | 1.09813i | ||||||
\(396\) | −4.48562e20 | − | 1.61981e20i | −0.741756 | − | 0.267857i | ||||
\(397\) | 1.05321e21 | 1.70684 | 0.853419 | − | 0.521226i | \(-0.174525\pi\) | ||||
0.853419 | + | 0.521226i | \(0.174525\pi\) | |||||||
\(398\) | 6.14973e20i | 0.976769i | ||||||||
\(399\) | 1.79541e20 | − | 1.26055e20i | 0.279500 | − | 0.196234i | ||||
\(400\) | −4.07963e20 | −0.622502 | ||||||||
\(401\) | − | 2.31809e20i | − | 0.346717i | −0.984859 | − | 0.173358i | \(-0.944538\pi\) | ||
0.984859 | − | 0.173358i | \(-0.0554619\pi\) | |||||||
\(402\) | −1.90967e20 | − | 2.71998e20i | −0.279995 | − | 0.398802i | ||||
\(403\) | −4.71074e20 | −0.677094 | ||||||||
\(404\) | 3.25711e20i | 0.458967i | ||||||||
\(405\) | −3.27657e20 | + | 3.94518e20i | −0.452668 | + | 0.545038i | ||||
\(406\) | 8.33949e20 | 1.12962 | ||||||||
\(407\) | 1.33618e20i | 0.177464i | ||||||||
\(408\) | 3.77005e19 | − | 2.64692e19i | 0.0490983 | − | 0.0344715i | ||||
\(409\) | −2.32833e19 | −0.0297343 | −0.0148671 | − | 0.999889i | \(-0.504733\pi\) | ||||
−0.0148671 | + | 0.999889i | \(0.504733\pi\) | |||||||
\(410\) | − | 3.58329e20i | − | 0.448757i | ||||||
\(411\) | −5.33900e20 | − | 7.60442e20i | −0.655730 | − | 0.933966i | ||||
\(412\) | 7.80354e19 | 0.0939970 | ||||||||
\(413\) | 1.47213e21i | 1.73918i | ||||||||
\(414\) | −2.04546e20 | + | 5.66434e20i | −0.237022 | + | 0.656367i | ||||
\(415\) | 1.08860e21 | 1.23732 | ||||||||
\(416\) | 7.12594e20i | 0.794503i | ||||||||
\(417\) | 1.97937e20 | − | 1.38970e20i | 0.216490 | − | 0.151996i | ||||
\(418\) | −5.05191e20 | −0.542058 | ||||||||
\(419\) | − | 3.12205e20i | − | 0.328645i | −0.986407 | − | 0.164323i | \(-0.947456\pi\) | ||
0.986407 | − | 0.164323i | \(-0.0525438\pi\) | |||||||
\(420\) | 2.39251e20 | + | 3.40769e20i | 0.247093 | + | 0.351938i | ||||
\(421\) | 1.66124e21 | 1.68336 | 0.841679 | − | 0.539978i | \(-0.181567\pi\) | ||||
0.841679 | + | 0.539978i | \(0.181567\pi\) | |||||||
\(422\) | − | 1.73916e21i | − | 1.72918i | ||||||
\(423\) | 3.67773e20 | + | 1.32807e20i | 0.358803 | + | 0.129568i | ||||
\(424\) | −4.50424e20 | −0.431216 | ||||||||
\(425\) | 5.12669e19i | 0.0481643i | ||||||||
\(426\) | 1.35428e20 | − | 9.50831e19i | 0.124863 | − | 0.0876651i | ||||
\(427\) | −7.86528e20 | −0.711690 | ||||||||
\(428\) | − | 3.73466e20i | − | 0.331666i | ||||||
\(429\) | 9.25721e20 | + | 1.31852e21i | 0.806904 | + | 1.14929i | ||||
\(430\) | −1.45768e21 | −1.24713 | ||||||||
\(431\) | 1.02197e20i | 0.0858259i | 0.999079 | + | 0.0429129i | \(0.0136638\pi\) | ||||
−0.999079 | + | 0.0429129i | \(0.986336\pi\) | |||||||
\(432\) | −3.97970e20 | − | 1.46305e21i | −0.328081 | − | 1.20611i | ||||
\(433\) | −2.16790e21 | −1.75443 | −0.877216 | − | 0.480096i | \(-0.840602\pi\) | ||||
−0.877216 | + | 0.480096i | \(0.840602\pi\) | |||||||
\(434\) | − | 1.46483e21i | − | 1.16378i | ||||||
\(435\) | −5.57495e20 | + | 3.91413e20i | −0.434838 | + | 0.305296i | ||||
\(436\) | 4.07007e20 | 0.311681 | ||||||||
\(437\) | 2.10422e20i | 0.158212i | ||||||||
\(438\) | 1.04386e21 | + | 1.48679e21i | 0.770638 | + | 1.09763i | ||||
\(439\) | −7.18216e20 | −0.520641 | −0.260321 | − | 0.965522i | \(-0.583828\pi\) | ||||
−0.260321 | + | 0.965522i | \(0.583828\pi\) | |||||||
\(440\) | 9.89281e20i | 0.704203i | ||||||||
\(441\) | 2.52969e20 | − | 7.00528e20i | 0.176831 | − | 0.489685i | ||||
\(442\) | 1.50823e20 | 0.103536 | ||||||||
\(443\) | − | 2.80285e20i | − | 0.188960i | −0.995527 | − | 0.0944802i | \(-0.969881\pi\) | ||
0.995527 | − | 0.0944802i | \(-0.0301189\pi\) | |||||||
\(444\) | 6.73819e19 | − | 4.73083e19i | 0.0446149 | − | 0.0313237i | ||||
\(445\) | 9.87103e20 | 0.641922 | ||||||||
\(446\) | 2.69684e20i | 0.172257i | ||||||||
\(447\) | −1.15444e21 | − | 1.64429e21i | −0.724289 | − | 1.03162i | ||||
\(448\) | 2.85217e20 | 0.175772 | ||||||||
\(449\) | 1.90690e21i | 1.15440i | 0.816603 | + | 0.577200i | \(0.195855\pi\) | ||||
−0.816603 | + | 0.577200i | \(0.804145\pi\) | |||||||
\(450\) | 9.62161e20 | + | 3.47448e20i | 0.572200 | + | 0.206628i | ||||
\(451\) | 1.42205e21 | 0.830812 | ||||||||
\(452\) | 6.55189e20i | 0.376062i | ||||||||
\(453\) | 2.53239e21 | − | 1.77797e21i | 1.42806 | − | 1.00263i | ||||
\(454\) | 8.17602e20 | 0.452997 | ||||||||
\(455\) | − | 1.40653e21i | − | 0.765697i | ||||||
\(456\) | −1.84542e20 | − | 2.62846e20i | −0.0987133 | − | 0.140599i | ||||
\(457\) | −1.24426e21 | −0.654005 | −0.327002 | − | 0.945024i | \(-0.606038\pi\) | ||||
−0.327002 | + | 0.945024i | \(0.606038\pi\) | |||||||
\(458\) | 1.74581e21i | 0.901721i | ||||||||
\(459\) | −1.83855e20 | + | 5.00112e19i | −0.0933196 | + | 0.0253843i | ||||
\(460\) | −3.99381e20 | −0.199216 | ||||||||
\(461\) | 1.67655e21i | 0.821879i | 0.911663 | + | 0.410940i | \(0.134799\pi\) | ||||
−0.911663 | + | 0.410940i | \(0.865201\pi\) | |||||||
\(462\) | −4.10001e21 | + | 2.87858e21i | −1.97537 | + | 1.38689i | ||||
\(463\) | −2.07466e21 | −0.982422 | −0.491211 | − | 0.871041i | \(-0.663446\pi\) | ||||
−0.491211 | + | 0.871041i | \(0.663446\pi\) | |||||||
\(464\) | − | 2.01391e21i | − | 0.937336i | ||||||
\(465\) | 6.87517e20 | + | 9.79240e20i | 0.314528 | + | 0.447987i | ||||
\(466\) | 4.24559e21 | 1.90920 | ||||||||
\(467\) | − | 1.45238e21i | − | 0.642016i | −0.947076 | − | 0.321008i | \(-0.895978\pi\) | ||
0.947076 | − | 0.321008i | \(-0.104022\pi\) | |||||||
\(468\) | 3.37155e20 | − | 9.33657e20i | 0.146508 | − | 0.405715i | ||||
\(469\) | −1.15149e21 | −0.491901 | ||||||||
\(470\) | 7.86156e20i | 0.330161i | ||||||||
\(471\) | −3.00185e21 | + | 2.10757e21i | −1.23943 | + | 0.870193i | ||||
\(472\) | 2.15517e21 | 0.874875 | ||||||||
\(473\) | − | 5.78487e21i | − | 2.30890i | ||||||
\(474\) | −2.77221e21 | − | 3.94850e21i | −1.08793 | − | 1.54955i | ||||
\(475\) | 3.57429e20 | 0.137924 | ||||||||
\(476\) | 1.54694e20i | 0.0586974i | ||||||||
\(477\) | 1.75232e21 | + | 6.32782e20i | 0.653831 | + | 0.236106i | ||||
\(478\) | −2.60238e21 | −0.954878 | ||||||||
\(479\) | 5.43994e20i | 0.196295i | 0.995172 | + | 0.0981477i | \(0.0312918\pi\) | ||||
−0.995172 | + | 0.0981477i | \(0.968708\pi\) | |||||||
\(480\) | 1.48130e21 | − | 1.04001e21i | 0.525669 | − | 0.369068i | ||||
\(481\) | −2.78119e20 | −0.0970668 | ||||||||
\(482\) | 1.05756e21i | 0.363019i | ||||||||
\(483\) | 1.19899e21 | + | 1.70774e21i | 0.404797 | + | 0.576559i | ||||
\(484\) | 2.32310e21 | 0.771446 | ||||||||
\(485\) | 4.18849e20i | 0.136812i | ||||||||
\(486\) | −3.07432e20 | + | 3.78946e21i | −0.0987778 | + | 1.21755i | ||||
\(487\) | 8.43207e20 | 0.266503 | 0.133252 | − | 0.991082i | \(-0.457458\pi\) | ||||
0.133252 | + | 0.991082i | \(0.457458\pi\) | |||||||
\(488\) | 1.15146e21i | 0.358007i | ||||||||
\(489\) | −1.25775e21 | + | 8.83057e20i | −0.384702 | + | 0.270096i | ||||
\(490\) | 1.49746e21 | 0.450595 | ||||||||
\(491\) | 6.07036e21i | 1.79706i | 0.438911 | + | 0.898530i | \(0.355364\pi\) | ||||
−0.438911 | + | 0.898530i | \(0.644636\pi\) | |||||||
\(492\) | −5.03484e20 | − | 7.17120e20i | −0.146644 | − | 0.208868i | ||||
\(493\) | −2.53079e20 | −0.0725237 | ||||||||
\(494\) | − | 1.05153e21i | − | 0.296487i | ||||||
\(495\) | 1.38980e21 | − | 3.84867e21i | 0.385577 | − | 1.06775i | ||||
\(496\) | −3.53743e21 | −0.965682 | ||||||||
\(497\) | − | 5.73330e20i | − | 0.154012i | ||||||
\(498\) | 6.60495e21 | − | 4.63728e21i | 1.74596 | − | 1.22583i | ||||
\(499\) | 1.14493e21 | 0.297834 | 0.148917 | − | 0.988850i | \(-0.452421\pi\) | ||||
0.148917 | + | 0.988850i | \(0.452421\pi\) | |||||||
\(500\) | 2.04058e21i | 0.522388i | ||||||||
\(501\) | 1.54142e21 | + | 2.19547e21i | 0.388346 | + | 0.553127i | ||||
\(502\) | −4.31461e21 | −1.06982 | ||||||||
\(503\) | − | 4.27994e21i | − | 1.04446i | −0.852803 | − | 0.522232i | \(-0.825099\pi\) | ||
0.852803 | − | 0.522232i | \(-0.174901\pi\) | |||||||
\(504\) | −2.99539e21 | − | 1.08167e21i | −0.719464 | − | 0.259807i | ||||
\(505\) | −2.79460e21 | −0.660677 | ||||||||
\(506\) | − | 4.80520e21i | − | 1.11817i | ||||||
\(507\) | 8.28663e20 | − | 5.81797e20i | 0.189808 | − | 0.133262i | ||||
\(508\) | −1.83798e21 | −0.414412 | ||||||||
\(509\) | 4.76935e21i | 1.05856i | 0.848446 | + | 0.529282i | \(0.177539\pi\) | ||||
−0.848446 | + | 0.529282i | \(0.822461\pi\) | |||||||
\(510\) | −2.20121e20 | − | 3.13522e20i | −0.0480950 | − | 0.0685025i | ||||
\(511\) | 6.29425e21 | 1.35387 | ||||||||
\(512\) | 1.68955e21i | 0.357775i | ||||||||
\(513\) | 3.48674e20 | + | 1.28182e21i | 0.0726911 | + | 0.267232i | ||||
\(514\) | −6.04727e21 | −1.24124 | ||||||||
\(515\) | 6.69544e20i | 0.135307i | ||||||||
\(516\) | −2.91723e21 | + | 2.04816e21i | −0.580462 | + | 0.407537i | ||||
\(517\) | −3.11991e21 | −0.611248 | ||||||||
\(518\) | − | 8.64827e20i | − | 0.166837i | ||||||
\(519\) | 7.65663e19 | + | 1.09055e20i | 0.0145445 | + | 0.0207160i | ||||
\(520\) | −2.05913e21 | −0.385175 | ||||||||
\(521\) | − | 6.64803e21i | − | 1.22459i | −0.790629 | − | 0.612295i | \(-0.790246\pi\) | ||
0.790629 | − | 0.612295i | \(-0.209754\pi\) | |||||||
\(522\) | −1.71517e21 | + | 4.74970e21i | −0.311132 | + | 0.861593i | ||||
\(523\) | −5.95294e20 | −0.106345 | −0.0531727 | − | 0.998585i | \(-0.516933\pi\) | ||||
−0.0531727 | + | 0.998585i | \(0.516933\pi\) | |||||||
\(524\) | − | 4.19038e21i | − | 0.737231i | ||||||
\(525\) | 2.90081e21 | − | 2.03663e21i | 0.502625 | − | 0.352889i | ||||
\(526\) | 1.29874e22 | 2.21634 | ||||||||
\(527\) | 4.44533e20i | 0.0747169i | ||||||||
\(528\) | 6.95150e21 | + | 9.90112e21i | 1.15082 | + | 1.63913i | ||||
\(529\) | 4.13115e21 | 0.673636 | ||||||||
\(530\) | 3.74578e21i | 0.601637i | ||||||||
\(531\) | −8.38441e21 | − | 3.02771e21i | −1.32653 | − | 0.479025i | ||||
\(532\) | 1.07852e21 | 0.168087 | ||||||||
\(533\) | 2.95992e21i | 0.454425i | ||||||||
\(534\) | 5.98913e21 | − | 4.20492e21i | 0.905803 | − | 0.635957i | ||||
\(535\) | 3.20434e21 | 0.477429 | ||||||||
\(536\) | 1.68576e21i | 0.247445i | ||||||||
\(537\) | −5.23187e21 | − | 7.45184e21i | −0.756594 | − | 1.07763i | ||||
\(538\) | 1.39316e21 | 0.198492 | ||||||||
\(539\) | 5.94275e21i | 0.834214i | ||||||||
\(540\) | −2.43290e21 | + | 6.61783e20i | −0.336491 | + | 0.0915305i | ||||
\(541\) | −6.55475e21 | −0.893260 | −0.446630 | − | 0.894719i | \(-0.647376\pi\) | ||||
−0.446630 | + | 0.894719i | \(0.647376\pi\) | |||||||
\(542\) | − | 5.40214e21i | − | 0.725390i | ||||||
\(543\) | −1.07794e22 | + | 7.56810e21i | −1.42625 | + | 1.00136i | ||||
\(544\) | 6.72445e20 | 0.0876729 | ||||||||
\(545\) | 3.49213e21i | 0.448661i | ||||||||
\(546\) | −5.99161e21 | − | 8.53394e21i | −0.758581 | − | 1.08046i | ||||
\(547\) | 1.34210e22 | 1.67451 | 0.837253 | − | 0.546816i | \(-0.184160\pi\) | ||||
0.837253 | + | 0.546816i | \(0.184160\pi\) | |||||||
\(548\) | − | 4.56803e21i | − | 0.561674i | ||||||
\(549\) | 1.61764e21 | − | 4.47962e21i | 0.196022 | − | 0.542828i | ||||
\(550\) | −8.16225e21 | −0.974784 | ||||||||
\(551\) | 1.76445e21i | 0.207681i | ||||||||
\(552\) | 2.50010e21 | − | 1.75530e21i | 0.290031 | − | 0.203628i | ||||
\(553\) | −1.67158e22 | −1.91129 | ||||||||
\(554\) | 1.57986e22i | 1.78050i | ||||||||
\(555\) | 4.05906e20 | + | 5.78138e20i | 0.0450901 | + | 0.0642225i | ||||
\(556\) | 1.18902e21 | 0.130194 | ||||||||
\(557\) | − | 1.06083e22i | − | 1.14500i | −0.819905 | − | 0.572500i | \(-0.805974\pi\) | ||
0.819905 | − | 0.572500i | \(-0.194026\pi\) | |||||||
\(558\) | 8.34285e21 | + | 3.01270e21i | 0.887648 | + | 0.320540i | ||||
\(559\) | 1.20409e22 | 1.26289 | ||||||||
\(560\) | − | 1.05620e22i | − | 1.09205i | ||||||
\(561\) | 1.24423e21 | − | 8.73563e20i | 0.126823 | − | 0.0890413i | ||||
\(562\) | 8.51259e20 | 0.0855404 | ||||||||
\(563\) | − | 1.02060e22i | − | 1.01109i | −0.862801 | − | 0.505544i | \(-0.831292\pi\) | ||
0.862801 | − | 0.505544i | \(-0.168708\pi\) | |||||||
\(564\) | 1.10462e21 | + | 1.57333e21i | 0.107890 | + | 0.153669i | ||||
\(565\) | −5.62153e21 | −0.541336 | ||||||||
\(566\) | − | 1.20175e21i | − | 0.114100i | ||||||
\(567\) | 1.01336e22 | + | 8.41620e21i | 0.948633 | + | 0.787864i | ||||
\(568\) | −8.39345e20 | −0.0774736 | ||||||||
\(569\) | 1.29597e22i | 1.17950i | 0.807587 | + | 0.589749i | \(0.200773\pi\) | ||||
−0.807587 | + | 0.589749i | \(0.799227\pi\) | |||||||
\(570\) | −2.18585e21 | + | 1.53467e21i | −0.196165 | + | 0.137726i | ||||
\(571\) | −2.34308e21 | −0.207347 | −0.103673 | − | 0.994611i | \(-0.533060\pi\) | ||||
−0.103673 | + | 0.994611i | \(0.533060\pi\) | |||||||
\(572\) | 7.92045e21i | 0.691164i | ||||||||
\(573\) | 2.98737e21 | + | 4.25496e21i | 0.257071 | + | 0.366150i | ||||
\(574\) | −9.20403e21 | −0.781057 | ||||||||
\(575\) | 3.39974e21i | 0.284514i | ||||||||
\(576\) | −5.86602e20 | + | 1.62443e21i | −0.0484132 | + | 0.134067i | ||||
\(577\) | 1.87414e22 | 1.52544 | 0.762720 | − | 0.646729i | \(-0.223864\pi\) | ||||
0.762720 | + | 0.646729i | \(0.223864\pi\) | |||||||
\(578\) | 1.50749e22i | 1.21013i | ||||||||
\(579\) | 1.53515e21 | − | 1.07782e21i | 0.121541 | − | 0.0853329i | ||||
\(580\) | −3.34892e21 | −0.261505 | ||||||||
\(581\) | − | 2.79617e22i | − | 2.15355i | ||||||
\(582\) | 1.78424e21 | + | 2.54132e21i | 0.135541 | + | 0.193052i | ||||
\(583\) | −1.48653e22 | −1.11385 | ||||||||
\(584\) | − | 9.21468e21i | − | 0.681047i | ||||||
\(585\) | 8.01078e21 | + | 2.89279e21i | 0.584021 | + | 0.210897i | ||||
\(586\) | −1.25242e22 | −0.900677 | ||||||||
\(587\) | 3.32847e21i | 0.236124i | 0.993006 | + | 0.118062i | \(0.0376681\pi\) | ||||
−0.993006 | + | 0.118062i | \(0.962332\pi\) | |||||||
\(588\) | 2.99685e21 | − | 2.10406e21i | 0.209723 | − | 0.147245i | ||||
\(589\) | 3.09925e21 | 0.213961 | ||||||||
\(590\) | − | 1.79226e22i | − | 1.22063i | ||||||
\(591\) | −4.07685e21 | − | 5.80672e21i | −0.273921 | − | 0.390150i | ||||
\(592\) | −2.08847e21 | −0.138438 | ||||||||
\(593\) | 1.79460e22i | 1.17363i | 0.809722 | + | 0.586814i | \(0.199618\pi\) | ||||
−0.809722 | + | 0.586814i | \(0.800382\pi\) | |||||||
\(594\) | −7.96233e21 | − | 2.92717e22i | −0.513746 | − | 1.88867i | ||||
\(595\) | −1.32728e21 | −0.0844942 | ||||||||
\(596\) | − | 9.87737e21i | − | 0.620399i | ||||||
\(597\) | −1.05598e22 | + | 7.41392e21i | −0.654424 | + | 0.459466i | ||||
\(598\) | 1.00018e22 | 0.611600 | ||||||||
\(599\) | 5.13326e21i | 0.309727i | 0.987936 | + | 0.154863i | \(0.0494938\pi\) | ||||
−0.987936 | + | 0.154863i | \(0.950506\pi\) | |||||||
\(600\) | −2.98159e21 | − | 4.24673e21i | −0.177516 | − | 0.252839i | ||||
\(601\) | −2.68398e21 | −0.157682 | −0.0788411 | − | 0.996887i | \(-0.525122\pi\) | ||||
−0.0788411 | + | 0.996887i | \(0.525122\pi\) | |||||||
\(602\) | 3.74418e22i | 2.17063i | ||||||||
\(603\) | 2.36826e21 | − | 6.55824e21i | 0.135485 | − | 0.375188i | ||||
\(604\) | 1.52123e22 | 0.858813 | ||||||||
\(605\) | 1.99322e22i | 1.11049i | ||||||||
\(606\) | −1.69559e22 | + | 1.19046e22i | −0.932267 | + | 0.654537i | ||||
\(607\) | −9.52751e21 | −0.516975 | −0.258488 | − | 0.966015i | \(-0.583224\pi\) | ||||
−0.258488 | + | 0.966015i | \(0.583224\pi\) | |||||||
\(608\) | − | 4.68824e21i | − | 0.251062i | ||||||
\(609\) | 1.00538e22 | + | 1.43198e22i | 0.531365 | + | 0.756831i | ||||
\(610\) | 9.57569e21 | 0.499495 | ||||||||
\(611\) | − | 6.49391e21i | − | 0.334331i | ||||||
\(612\) | −8.81052e20 | − | 3.18158e20i | −0.0447703 | − | 0.0161671i | ||||
\(613\) | 2.23921e22 | 1.12308 | 0.561541 | − | 0.827449i | \(-0.310209\pi\) | ||||
0.561541 | + | 0.827449i | \(0.310209\pi\) | |||||||
\(614\) | − | 2.50227e22i | − | 1.23876i | ||||||
\(615\) | 6.15290e21 | − | 4.31990e21i | 0.300662 | − | 0.211092i | ||||
\(616\) | 2.54106e22 | 1.22566 | ||||||||
\(617\) | − | 1.75829e22i | − | 0.837162i | −0.908179 | − | 0.418581i | \(-0.862528\pi\) | ||
0.908179 | − | 0.418581i | \(-0.137472\pi\) | |||||||
\(618\) | 2.85216e21 | + | 4.06238e21i | 0.134050 | + | 0.190929i | ||||
\(619\) | −2.16013e22 | −1.00220 | −0.501101 | − | 0.865389i | \(-0.667071\pi\) | ||||
−0.501101 | + | 0.865389i | \(0.667071\pi\) | |||||||
\(620\) | 5.88237e21i | 0.269413i | ||||||||
\(621\) | −1.21922e22 | + | 3.31647e21i | −0.551253 | + | 0.149949i | ||||
\(622\) | 3.91232e22 | 1.74627 | ||||||||
\(623\) | − | 2.53547e22i | − | 1.11726i | ||||||
\(624\) | −2.06086e22 | + | 1.44692e22i | −0.896546 | + | 0.629457i | ||||
\(625\) | −5.91261e21 | −0.253945 | ||||||||
\(626\) | 1.46815e22i | 0.622553i | ||||||||
\(627\) | −6.09042e21 | − | 8.67469e21i | −0.254981 | − | 0.363173i | ||||
\(628\) | −1.80323e22 | −0.745375 | ||||||||
\(629\) | 2.62449e20i | 0.0107113i | ||||||||
\(630\) | −8.99529e21 | + | 2.49100e22i | −0.362486 | + | 1.00380i | ||||
\(631\) | −2.28393e22 | −0.908757 | −0.454379 | − | 0.890809i | \(-0.650139\pi\) | ||||
−0.454379 | + | 0.890809i | \(0.650139\pi\) | |||||||
\(632\) | 2.44716e22i | 0.961449i | ||||||||
\(633\) | 2.98632e22 | − | 2.09667e22i | 1.15853 | − | 0.813393i | ||||
\(634\) | −1.71530e22 | −0.657091 | ||||||||
\(635\) | − | 1.57699e22i | − | 0.596540i | ||||||
\(636\) | 5.26315e21 | + | 7.49639e21i | 0.196602 | + | 0.280024i | ||||
\(637\) | −1.23695e22 | −0.456286 | ||||||||
\(638\) | − | 4.02929e22i | − | 1.46779i | ||||||
\(639\) | 3.26536e21 | + | 1.17916e21i | 0.117469 | + | 0.0424196i | ||||
\(640\) | −2.15513e22 | −0.765657 | ||||||||
\(641\) | 2.43535e22i | 0.854470i | 0.904141 | + | 0.427235i | \(0.140512\pi\) | ||||
−0.904141 | + | 0.427235i | \(0.859488\pi\) | |||||||
\(642\) | 1.94420e22 | − | 1.36500e22i | 0.673690 | − | 0.472992i | ||||
\(643\) | −3.79348e22 | −1.29822 | −0.649112 | − | 0.760693i | \(-0.724859\pi\) | ||||
−0.649112 | + | 0.760693i | \(0.724859\pi\) | |||||||
\(644\) | 1.02585e22i | 0.346734i | ||||||||
\(645\) | −1.75733e22 | − | 2.50299e22i | −0.586644 | − | 0.835567i | ||||
\(646\) | −9.92281e20 | −0.0327171 | ||||||||
\(647\) | 1.51186e22i | 0.492354i | 0.969225 | + | 0.246177i | \(0.0791744\pi\) | ||||
−0.969225 | + | 0.246177i | \(0.920826\pi\) | |||||||
\(648\) | 1.23212e22 | − | 1.48354e22i | 0.396325 | − | 0.477198i | ||||
\(649\) | 7.11271e22 | 2.25984 | ||||||||
\(650\) | − | 1.69893e22i | − | 0.533173i | ||||||
\(651\) | 2.51527e22 | − | 1.76595e22i | 0.779718 | − | 0.547433i | ||||
\(652\) | −7.55541e21 | −0.231354 | ||||||||
\(653\) | 3.13376e22i | 0.947896i | 0.880553 | + | 0.473948i | \(0.157172\pi\) | ||||
−0.880553 | + | 0.473948i | \(0.842828\pi\) | |||||||
\(654\) | 1.48760e22 | + | 2.11881e22i | 0.444491 | + | 0.633096i | ||||
\(655\) | 3.59535e22 | 1.06123 | ||||||||
\(656\) | 2.22268e22i | 0.648107i | ||||||||
\(657\) | −1.29453e22 | + | 3.58485e22i | −0.372898 | + | 1.03264i | ||||
\(658\) | 2.01932e22 | 0.574642 | ||||||||
\(659\) | 2.15993e22i | 0.607235i | 0.952794 | + | 0.303617i | \(0.0981945\pi\) | ||||
−0.952794 | + | 0.303617i | \(0.901806\pi\) | |||||||
\(660\) | 1.64645e22 | − | 1.15596e22i | 0.457297 | − | 0.321064i | ||||
\(661\) | −5.48959e22 | −1.50636 | −0.753179 | − | 0.657815i | \(-0.771481\pi\) | ||||
−0.753179 | + | 0.657815i | \(0.771481\pi\) | |||||||
\(662\) | − | 4.51558e22i | − | 1.22419i | ||||||
\(663\) | 1.81827e21 | + | 2.58980e21i | 0.0487025 | + | 0.0693677i | ||||
\(664\) | −4.09355e22 | −1.08332 | ||||||||
\(665\) | 9.25370e21i | 0.241959i | ||||||||
\(666\) | 4.92557e21 | + | 1.77868e21i | 0.127251 | + | 0.0459520i | ||||
\(667\) | −1.67828e22 | −0.428408 | ||||||||
\(668\) | 1.31883e22i | 0.332643i | ||||||||
\(669\) | −4.63077e21 | + | 3.25123e21i | −0.115410 | + | 0.0810286i | ||||
\(670\) | 1.40190e22 | 0.345238 | ||||||||
\(671\) | 3.80017e22i | 0.924747i | ||||||||
\(672\) | −2.67136e22 | − | 3.80486e22i | −0.642359 | − | 0.914922i | ||||
\(673\) | 2.63360e22 | 0.625791 | 0.312896 | − | 0.949787i | \(-0.398701\pi\) | ||||
0.312896 | + | 0.949787i | \(0.398701\pi\) | |||||||
\(674\) | − | 3.86447e22i | − | 0.907426i | ||||||
\(675\) | 5.63344e21 | + | 2.07101e22i | 0.130721 | + | 0.480564i | ||||
\(676\) | 4.97784e21 | 0.114148 | ||||||||
\(677\) | − | 8.67255e22i | − | 1.96534i | −0.185365 | − | 0.982670i | \(-0.559347\pi\) | ||
0.185365 | − | 0.982670i | \(-0.440653\pi\) | |||||||
\(678\) | −3.41079e22 | + | 2.39469e22i | −0.763867 | + | 0.536305i | ||||
\(679\) | 1.07586e22 | 0.238120 | ||||||||
\(680\) | 1.94312e21i | 0.0425037i | ||||||||
\(681\) | 9.85675e21 | + | 1.40391e22i | 0.213087 | + | 0.303503i | ||||
\(682\) | −7.07745e22 | −1.51217 | ||||||||
\(683\) | − | 5.07014e22i | − | 1.07067i | −0.844641 | − | 0.535333i | \(-0.820186\pi\) | ||
0.844641 | − | 0.535333i | \(-0.179814\pi\) | |||||||
\(684\) | −2.21818e21 | + | 6.14263e21i | −0.0462965 | + | 0.128205i | ||||
\(685\) | 3.91937e22 | 0.808522 | ||||||||
\(686\) | 3.54147e22i | 0.722090i | ||||||||
\(687\) | −2.99774e22 | + | 2.10469e22i | −0.604143 | + | 0.424164i | ||||
\(688\) | 9.04184e22 | 1.80115 | ||||||||
\(689\) | − | 3.09414e22i | − | 0.609236i | ||||||
\(690\) | −1.45972e22 | − | 2.07911e22i | −0.284104 | − | 0.404654i | ||||
\(691\) | 6.54722e22 | 1.25960 | 0.629800 | − | 0.776758i | \(-0.283137\pi\) | ||||
0.629800 | + | 0.776758i | \(0.283137\pi\) | |||||||
\(692\) | 6.55099e20i | 0.0124583i | ||||||||
\(693\) | −9.88567e22 | − | 3.56984e22i | −1.85841 | − | 0.671092i | ||||
\(694\) | −9.07546e22 | −1.68653 | ||||||||
\(695\) | 1.02018e22i | 0.187413i | ||||||||
\(696\) | 2.09640e22 | − | 1.47186e22i | 0.380715 | − | 0.267297i | ||||
\(697\) | 2.79315e21 | 0.0501455 | ||||||||
\(698\) | 1.33251e23i | 2.36498i | ||||||||
\(699\) | 5.11834e22 | + | 7.29014e22i | 0.898074 | + | 1.27914i | ||||
\(700\) | 1.74254e22 | 0.302272 | ||||||||
\(701\) | 1.53086e21i | 0.0262537i | 0.999914 | + | 0.0131269i | \(0.00417853\pi\) | ||||
−0.999914 | + | 0.0131269i | \(0.995821\pi\) | |||||||
\(702\) | 6.09274e22 | − | 1.65731e22i | 1.03304 | − | 0.281001i | ||||
\(703\) | 1.82978e21 | 0.0306730 | ||||||||
\(704\) | − | 1.37805e22i | − | 0.228393i | ||||||
\(705\) | −1.34992e22 | + | 9.47764e21i | −0.221204 | + | 0.155306i | ||||
\(706\) | 9.51857e22 | 1.54218 | ||||||||
\(707\) | 7.17821e22i | 1.14990i | ||||||||
\(708\) | −2.51829e22 | − | 3.58684e22i | −0.398878 | − | 0.568128i | ||||
\(709\) | 1.08542e22 | 0.169991 | 0.0849956 | − | 0.996381i | \(-0.472912\pi\) | ||||
0.0849956 | + | 0.996381i | \(0.472912\pi\) | |||||||
\(710\) | 6.98008e21i | 0.108092i | ||||||||
\(711\) | 3.43792e22 | − | 9.52037e22i | 0.526428 | − | 1.45780i | ||||
\(712\) | −3.71189e22 | −0.562024 | ||||||||
\(713\) | 2.94790e22i | 0.441363i | ||||||||
\(714\) | −8.05311e21 | + | 5.65402e21i | −0.119228 | + | 0.0837089i | ||||
\(715\) | −6.79575e22 | −0.994922 | ||||||||
\(716\) | − | 4.47638e22i | − | 0.648071i | ||||||
\(717\) | −3.13735e22 | − | 4.46857e22i | −0.449169 | − | 0.639758i | ||||
\(718\) | −2.09833e22 | −0.297083 | ||||||||
\(719\) | − | 1.17168e23i | − | 1.64051i | −0.571997 | − | 0.820256i | \(-0.693831\pi\) | ||
0.571997 | − | 0.820256i | \(-0.306169\pi\) | |||||||
\(720\) | 6.01552e22 | + | 2.17228e22i | 0.832939 | + | 0.300784i | ||||
\(721\) | 1.71979e22 | 0.235501 | ||||||||
\(722\) | − | 8.32825e22i | − | 1.12786i | ||||||
\(723\) | −1.81595e22 | + | 1.27496e22i | −0.243219 | + | 0.170762i | ||||
\(724\) | −6.47524e22 | −0.857724 | ||||||||
\(725\) | 2.85077e22i | 0.373472i | ||||||||
\(726\) | 8.49084e22 | + | 1.20936e23i | 1.10017 | + | 1.56698i | ||||
\(727\) | −6.75278e22 | −0.865381 | −0.432691 | − | 0.901542i | \(-0.642436\pi\) | ||||
−0.432691 | + | 0.901542i | \(0.642436\pi\) | |||||||
\(728\) | 5.28908e22i | 0.670393i | ||||||||
\(729\) | −6.87755e22 | + | 4.04056e22i | −0.862211 | + | 0.506549i | ||||
\(730\) | −7.66302e22 | −0.950205 | ||||||||
\(731\) | − | 1.13625e22i | − | 0.139359i | ||||||
\(732\) | 1.91637e22 | − | 1.34547e22i | 0.232483 | − | 0.163225i | ||||
\(733\) | −8.14391e22 | −0.977240 | −0.488620 | − | 0.872497i | \(-0.662500\pi\) | ||||
−0.488620 | + | 0.872497i | \(0.662500\pi\) | |||||||
\(734\) | − | 3.56745e22i | − | 0.423438i | ||||||
\(735\) | 1.80529e22 | + | 2.57130e22i | 0.211957 | + | 0.301894i | ||||
\(736\) | 4.45929e22 | 0.517897 | ||||||||
\(737\) | 5.56352e22i | 0.639160i | ||||||||
\(738\) | 1.89298e22 | − | 5.24209e22i | 0.215127 | − | 0.595736i | ||||
\(739\) | 2.72207e22 | 0.306016 | 0.153008 | − | 0.988225i | \(-0.451104\pi\) | ||||
0.153008 | + | 0.988225i | \(0.451104\pi\) | |||||||
\(740\) | 3.47292e21i | 0.0386225i | ||||||||
\(741\) | 1.80559e22 | − | 1.26769e22i | 0.198643 | − | 0.139465i | ||||
\(742\) | 9.62139e22 | 1.04714 | ||||||||
\(743\) | − | 1.77551e22i | − | 0.191167i | −0.995421 | − | 0.0955833i | \(-0.969528\pi\) | ||
0.995421 | − | 0.0955833i | \(-0.0304716\pi\) | |||||||
\(744\) | −2.58533e22 | − | 3.68232e22i | −0.275380 | − | 0.392227i | ||||
\(745\) | 8.47479e22 | 0.893056 | ||||||||
\(746\) | − | 2.72750e22i | − | 0.284350i | ||||||
\(747\) | 1.59254e23 | + | 5.75086e22i | 1.64258 | + | 0.593155i | ||||
\(748\) | 7.47419e21 | 0.0762695 | ||||||||
\(749\) | − | 8.23067e22i | − | 0.830961i | ||||||
\(750\) | −1.06229e23 | + | 7.45823e22i | −1.06109 | + | 0.744982i | ||||
\(751\) | −2.88558e22 | −0.285177 | −0.142588 | − | 0.989782i | \(-0.545543\pi\) | ||||
−0.142588 | + | 0.989782i | \(0.545543\pi\) | |||||||
\(752\) | − | 4.87646e22i | − | 0.476828i | ||||||
\(753\) | −5.20155e22 | − | 7.40865e22i | −0.503238 | − | 0.716770i | ||||
\(754\) | 8.38674e22 | 0.802828 | ||||||||
\(755\) | 1.30521e23i | 1.23625i | ||||||||
\(756\) | 1.69986e22 | + | 6.24913e22i | 0.159308 | + | 0.585659i | ||||
\(757\) | −5.88768e22 | −0.545981 | −0.272990 | − | 0.962017i | \(-0.588013\pi\) | ||||
−0.272990 | + | 0.962017i | \(0.588013\pi\) | |||||||
\(758\) | 1.27550e23i | 1.17038i | ||||||||
\(759\) | 8.25106e22 | − | 5.79300e22i | 0.749162 | − | 0.525980i | ||||
\(760\) | 1.35473e22 | 0.121715 | ||||||||
\(761\) | 4.74458e22i | 0.421814i | 0.977506 | + | 0.210907i | \(0.0676417\pi\) | ||||
−0.977506 | + | 0.210907i | \(0.932358\pi\) | |||||||
\(762\) | −6.71776e22 | − | 9.56821e22i | −0.590996 | − | 0.841765i | ||||
\(763\) | 8.96987e22 | 0.780890 | ||||||||
\(764\) | 2.55599e22i | 0.220197i | ||||||||
\(765\) | 2.72980e21 | − | 7.55943e21i | 0.0232723 | − | 0.0644463i | ||||
\(766\) | −2.86331e23 | −2.41568 | ||||||||
\(767\) | 1.48047e23i | 1.23605i | ||||||||
\(768\) | −1.16641e23 | + | 8.18926e22i | −0.963743 | + | 0.676636i | ||||
\(769\) | 1.15591e23 | 0.945176 | 0.472588 | − | 0.881283i | \(-0.343320\pi\) | ||||
0.472588 | + | 0.881283i | \(0.343320\pi\) | |||||||
\(770\) | − | 2.11318e23i | − | 1.71005i | ||||||
\(771\) | −7.29039e22 | − | 1.03838e23i | −0.583870 | − | 0.831615i | ||||
\(772\) | 9.22178e21 | 0.0730931 | ||||||||
\(773\) | − | 6.88499e22i | − | 0.540091i | −0.962848 | − | 0.270046i | \(-0.912961\pi\) | ||
0.962848 | − | 0.270046i | \(-0.0870388\pi\) | |||||||
\(774\) | −2.13247e23 | − | 7.70062e22i | −1.65560 | − | 0.597858i | ||||
\(775\) | 5.00738e22 | 0.384766 | ||||||||
\(776\) | − | 1.57503e22i | − | 0.119783i | ||||||
\(777\) | 1.48500e22 | − | 1.04261e22i | 0.111779 | − | 0.0784789i | ||||
\(778\) | 2.82161e23 | 2.10213 | ||||||||
\(779\) | − | 1.94736e22i | − | 0.143598i | ||||||
\(780\) | 2.40607e22 | + | 3.42700e22i | 0.175611 | + | 0.250125i | ||||
\(781\) | −2.77009e22 | −0.200118 | ||||||||
\(782\) | − | 9.43824e21i | − | 0.0674896i | ||||||
\(783\) | −1.02235e23 | + | 2.78095e22i | −0.723613 | + | 0.196833i | ||||
\(784\) | −9.28861e22 | −0.650762 | ||||||||
\(785\) | − | 1.54718e23i | − | 1.07296i | ||||||
\(786\) | 2.18144e23 | − | 1.53157e23i | 1.49748 | − | 1.05137i | ||||
\(787\) | −1.50748e23 | −1.02436 | −0.512181 | − | 0.858877i | \(-0.671162\pi\) | ||||
−0.512181 | + | 0.858877i | \(0.671162\pi\) | |||||||
\(788\) | − | 3.48814e22i | − | 0.234631i | ||||||
\(789\) | 1.56572e23 | + | 2.23008e23i | 1.04255 | + | 1.48492i | ||||
\(790\) | 2.03509e23 | 1.34142 | ||||||||
\(791\) | 1.44394e23i | 0.942190i | ||||||||
\(792\) | −5.22618e22 | + | 1.44725e23i | −0.337585 | + | 0.934848i | ||||
\(793\) | −7.90984e22 | −0.505804 | ||||||||
\(794\) | 3.29358e23i | 2.08499i | ||||||||
\(795\) | −6.43190e22 | + | 4.51579e22i | −0.403090 | + | 0.283006i | ||||
\(796\) | −6.34333e22 | −0.393562 | ||||||||
\(797\) | − | 8.61549e22i | − | 0.529192i | −0.964359 | − | 0.264596i | \(-0.914761\pi\) | ||
0.964359 | − | 0.264596i | \(-0.0852387\pi\) | |||||||
\(798\) | 3.94194e22 | + | 5.61457e22i | 0.239711 | + | 0.341424i | ||||
\(799\) | −6.12803e21 | −0.0368932 | ||||||||
\(800\) | − | 7.57467e22i | − | 0.451485i | ||||||
\(801\) | 1.44406e23 | + | 5.21467e22i | 0.852168 | + | 0.307728i | ||||
\(802\) | 7.24906e22 | 0.423533 | ||||||||
\(803\) | − | 3.04112e23i | − | 1.75917i | ||||||
\(804\) | 2.80561e22 | − | 1.96979e22i | 0.160686 | − | 0.112816i | ||||
\(805\) | −8.80180e22 | −0.499119 | ||||||||
\(806\) | − | 1.47313e23i | − | 0.827106i | ||||||
\(807\) | 1.67955e22 | + | 2.39221e22i | 0.0933696 | + | 0.132988i | ||||
\(808\) | 1.05088e23 | 0.578444 | ||||||||
\(809\) | 2.92416e23i | 1.59372i | 0.604161 | + | 0.796862i | \(0.293508\pi\) | ||||
−0.604161 | + | 0.796862i | \(0.706492\pi\) | |||||||
\(810\) | −1.23373e23 | − | 1.02464e23i | −0.665792 | − | 0.552958i | ||||
\(811\) | −1.92966e23 | −1.03113 | −0.515564 | − | 0.856851i | \(-0.672418\pi\) | ||||
−0.515564 | + | 0.856851i | \(0.672418\pi\) | |||||||
\(812\) | 8.60202e22i | 0.455148i | ||||||||
\(813\) | 9.27607e22 | − | 6.51265e22i | 0.486004 | − | 0.341219i | ||||
\(814\) | −4.17848e22 | −0.216782 | ||||||||
\(815\) | − | 6.48255e22i | − | 0.333031i | ||||||
\(816\) | 1.36539e22 | + | 1.94475e22i | 0.0694602 | + | 0.0989332i | ||||
\(817\) | −7.92184e22 | −0.399070 | ||||||||
\(818\) | − | 7.28108e21i | − | 0.0363220i | ||||||
\(819\) | 7.43041e22 | − | 2.05765e23i | 0.367064 | − | 1.01648i | ||||
\(820\) | 3.69609e22 | 0.180814 | ||||||||
\(821\) | 1.31465e23i | 0.636892i | 0.947941 | + | 0.318446i | \(0.103161\pi\) | ||||
−0.947941 | + | 0.318446i | \(0.896839\pi\) | |||||||
\(822\) | 2.37803e23 | − | 1.66960e23i | 1.14089 | − | 0.801009i | ||||
\(823\) | 1.51869e22 | 0.0721556 | 0.0360778 | − | 0.999349i | \(-0.488514\pi\) | ||||
0.0360778 | + | 0.999349i | \(0.488514\pi\) | |||||||
\(824\) | − | 2.51774e22i | − | 0.118466i | ||||||
\(825\) | −9.84014e22 | − | 1.40155e23i | −0.458532 | − | 0.653095i | ||||
\(826\) | −4.60360e23 | −2.12450 | ||||||||
\(827\) | − | 2.24491e23i | − | 1.02602i | −0.858383 | − | 0.513009i | \(-0.828531\pi\) | ||
0.858383 | − | 0.513009i | \(-0.171469\pi\) | |||||||
\(828\) | −5.84266e22 | − | 2.10985e22i | −0.264465 | − | 0.0955014i | ||||
\(829\) | 8.92207e22 | 0.399972 | 0.199986 | − | 0.979799i | \(-0.435910\pi\) | ||||
0.199986 | + | 0.979799i | \(0.435910\pi\) | |||||||
\(830\) | 3.40424e23i | 1.51146i | ||||||||
\(831\) | −2.71279e23 | + | 1.90463e23i | −1.19291 | + | 0.837534i | ||||
\(832\) | 2.86833e22 | 0.124923 | ||||||||
\(833\) | 1.16726e22i | 0.0503508i | ||||||||
\(834\) | 4.34583e22 | + | 6.18983e22i | 0.185671 | + | 0.264454i | ||||
\(835\) | −1.13156e23 | −0.478835 | ||||||||
\(836\) | − | 5.21095e22i | − | 0.218407i | ||||||
\(837\) | 4.88473e22 | + | 1.79576e23i | 0.202786 | + | 0.745495i | ||||
\(838\) | 9.76319e22 | 0.401458 | ||||||||
\(839\) | − | 3.14887e23i | − | 1.28250i | −0.767331 | − | 0.641252i | \(-0.778416\pi\) | ||
0.767331 | − | 0.641252i | \(-0.221584\pi\) | |||||||
\(840\) | 1.09946e23 | − | 7.71923e22i | 0.443554 | − | 0.311415i | ||||
\(841\) | 1.09518e23 | 0.437641 | ||||||||
\(842\) | 5.19500e23i | 2.05631i | ||||||||
\(843\) | 1.02625e22 | + | 1.46170e22i | 0.0402377 | + | 0.0573111i | ||||
\(844\) | 1.79391e23 | 0.696723 | ||||||||
\(845\) | 4.27099e22i | 0.164314i | ||||||||
\(846\) | −4.15311e22 | + | 1.15009e23i | −0.158274 | + | 0.438297i | ||||
\(847\) | 5.11979e23 | 1.93279 | ||||||||
\(848\) | − | 2.32347e23i | − | 0.868902i | ||||||
\(849\) | 2.06354e22 | − | 1.44880e22i | 0.0764455 | − | 0.0536717i | ||||
\(850\) | −1.60320e22 | −0.0588352 | ||||||||
\(851\) | 1.74042e22i | 0.0632729i | ||||||||
\(852\) | 9.80764e21 | + | 1.39692e22i | 0.0353222 | + | 0.0503099i | ||||
\(853\) | 4.24442e23 | 1.51435 | 0.757174 | − | 0.653213i | \(-0.226580\pi\) | ||||
0.757174 | + | 0.653213i | \(0.226580\pi\) | |||||||
\(854\) | − | 2.45961e23i | − | 0.869367i | ||||||
\(855\) | −5.27038e22 | − | 1.90320e22i | −0.184550 | − | 0.0666431i | ||||
\(856\) | −1.20496e23 | −0.418005 | ||||||||
\(857\) | − | 1.01944e23i | − | 0.350359i | −0.984536 | − | 0.175180i | \(-0.943949\pi\) | ||
0.984536 | − | 0.175180i | \(-0.0560506\pi\) | |||||||
\(858\) | −4.12324e23 | + | 2.89489e23i | −1.40391 | + | 0.985676i | ||||
\(859\) | −3.39798e23 | −1.14624 | −0.573120 | − | 0.819472i | \(-0.694267\pi\) | ||||
−0.573120 | + | 0.819472i | \(0.694267\pi\) | |||||||
\(860\) | − | 1.50356e23i | − | 0.502498i | ||||||
\(861\) | −1.10961e23 | − | 1.58043e23i | −0.367404 | − | 0.523300i | ||||
\(862\) | −3.19587e22 | −0.104841 | ||||||||
\(863\) | 2.27685e23i | 0.740028i | 0.929026 | + | 0.370014i | \(0.120647\pi\) | ||||
−0.929026 | + | 0.370014i | \(0.879353\pi\) | |||||||
\(864\) | 2.71645e23 | − | 7.38914e22i | 0.874765 | − | 0.237949i | ||||
\(865\) | −5.62076e21 | −0.0179335 | ||||||||
\(866\) | − | 6.77941e23i | − | 2.14313i | ||||||
\(867\) | −2.58852e23 | + | 1.81738e23i | −0.810772 | + | 0.569236i | ||||
\(868\) | 1.51094e23 | 0.468911 | ||||||||
\(869\) | 8.07636e23i | 2.48346i | ||||||||
\(870\) | −1.22402e23 | − | 1.74339e23i | −0.372935 | − | 0.531177i | ||||
\(871\) | −1.15802e23 | −0.349598 | ||||||||
\(872\) | − | 1.31317e23i | − | 0.392817i | ||||||
\(873\) | −2.21270e22 | + | 6.12746e22i | −0.0655856 | + | 0.181621i | ||||
\(874\) | −6.58027e22 | −0.193265 | ||||||||
\(875\) | 4.49714e23i | 1.30880i | ||||||||
\(876\) | −1.53359e23 | + | 1.07672e23i | −0.442260 | + | 0.310507i | ||||
\(877\) | −3.55043e22 | −0.101458 | −0.0507288 | − | 0.998712i | \(-0.516154\pi\) | ||||
−0.0507288 | + | 0.998712i | \(0.516154\pi\) | |||||||
\(878\) | − | 2.24599e23i | − | 0.635991i | ||||||
\(879\) | −1.50988e23 | − | 2.15054e23i | −0.423673 | − | 0.603444i | ||||
\(880\) | −5.10311e23 | −1.41897 | ||||||||
\(881\) | − | 5.58469e23i | − | 1.53883i | −0.638747 | − | 0.769417i | \(-0.720547\pi\) | ||
0.638747 | − | 0.769417i | \(-0.279453\pi\) | |||||||
\(882\) | 2.19067e23 | + | 7.91078e22i | 0.598176 | + | 0.216008i | ||||
\(883\) | 5.61513e23 | 1.51941 | 0.759704 | − | 0.650269i | \(-0.225344\pi\) | ||||
0.759704 | + | 0.650269i | \(0.225344\pi\) | |||||||
\(884\) | 1.55571e22i | 0.0417168i | ||||||||
\(885\) | 3.07751e23 | − | 2.16069e23i | 0.817812 | − | 0.574179i | ||||
\(886\) | 8.76502e22 | 0.230825 | ||||||||
\(887\) | 2.60967e22i | 0.0681076i | 0.999420 | + | 0.0340538i | \(0.0108418\pi\) | ||||
−0.999420 | + | 0.0340538i | \(0.989158\pi\) | |||||||
\(888\) | −1.52636e22 | − | 2.17402e22i | −0.0394778 | − | 0.0562289i | ||||
\(889\) | −4.05066e23 | −1.03827 | ||||||||
\(890\) | 3.08684e23i | 0.784142i | ||||||||
\(891\) | 4.06635e23 | − | 4.89612e23i | 1.02373 | − | 1.23262i | ||||
\(892\) | −2.78174e22 | −0.0694061 | ||||||||
\(893\) | 4.27242e22i | 0.105648i | ||||||||
\(894\) | 5.14198e23 | − | 3.61014e23i | 1.26017 | − | 0.884757i | ||||
\(895\) | 3.84073e23 | 0.932889 | ||||||||
\(896\) | 5.53567e23i | 1.33262i | ||||||||
\(897\) | 1.20578e23 | + | 1.71741e23i | 0.287693 | + | 0.409765i | ||||
\(898\) | −5.96320e23 | −1.41016 | ||||||||
\(899\) | 2.47189e23i | 0.579364i | ||||||||
\(900\) | −3.58386e22 | + | 9.92450e22i | −0.0832550 | + | 0.230552i | ||||
\(901\) | −2.91980e22 | −0.0672288 | ||||||||
\(902\) | 4.44700e23i | 1.01488i | ||||||||
\(903\) | −6.42917e23 | + | 4.51387e23i | −1.45430 | + | 1.02105i | ||||
\(904\) | 2.11391e23 | 0.473957 | ||||||||
\(905\) | − | 5.55576e23i | − | 1.23468i | ||||||
\(906\) | 5.56003e23 | + | 7.91923e23i | 1.22476 | + | 1.74445i | ||||
\(907\) | 4.66455e23 | 1.01848 | 0.509238 | − | 0.860626i | \(-0.329927\pi\) | ||||
0.509238 | + | 0.860626i | \(0.329927\pi\) | |||||||
\(908\) | 8.43341e22i | 0.182522i | ||||||||
\(909\) | −4.08830e23 | − | 1.47633e23i | −0.877065 | − | 0.316719i | ||||
\(910\) | 4.39846e23 | 0.935339 | ||||||||
\(911\) | − | 6.96041e22i | − | 0.146719i | −0.997306 | − | 0.0733597i | \(-0.976628\pi\) | ||
0.997306 | − | 0.0733597i | \(-0.0233721\pi\) | |||||||
\(912\) | 1.35587e23 | − | 9.51942e22i | 0.283307 | − | 0.198908i | ||||
\(913\) | −1.35099e24 | −2.79825 | ||||||||
\(914\) | − | 3.89101e23i | − | 0.798901i | ||||||
\(915\) | 1.15441e23 | + | 1.64425e23i | 0.234959 | + | 0.334656i | ||||
\(916\) | −1.80077e23 | −0.363323 | ||||||||
\(917\) | − | 9.23501e23i | − | 1.84707i | ||||||
\(918\) | −1.56394e22 | − | 5.74945e22i | −0.0310083 | − | 0.113995i | ||||
\(919\) | 1.90324e23 | 0.374084 | 0.187042 | − | 0.982352i | \(-0.440110\pi\) | ||||
0.187042 | + | 0.982352i | \(0.440110\pi\) | |||||||
\(920\) | 1.28857e23i | 0.251076i | ||||||||
\(921\) | 4.29668e23 | − | 3.01666e23i | 0.829957 | − | 0.582706i | ||||
\(922\) | −5.24285e23 | −1.00397 | ||||||||
\(923\) | − | 5.76578e22i | − | 0.109457i | ||||||
\(924\) | −2.96920e23 | − | 4.22908e23i | −0.558809 | − | 0.795921i | ||||
\(925\) | 2.95633e22 | 0.0551593 | ||||||||
\(926\) | − | 6.48781e23i | − | 1.20008i | ||||||
\(927\) | −3.53707e22 | + | 9.79495e22i | −0.0648644 | + | 0.179624i | ||||
\(928\) | 3.73923e23 | 0.679827 | ||||||||
\(929\) | − | 3.31139e22i | − | 0.0596877i | −0.999555 | − | 0.0298438i | \(-0.990499\pi\) | ||
0.999555 | − | 0.0298438i | \(-0.00950100\pi\) | |||||||
\(930\) | −3.06226e23 | + | 2.14998e23i | −0.547240 | + | 0.384213i | ||||
\(931\) | 8.13804e22 | 0.144186 | ||||||||
\(932\) | 4.37924e23i | 0.769257i | ||||||||
\(933\) | 4.71657e23 | + | 6.71788e23i | 0.821435 | + | 1.16998i | ||||
\(934\) | 4.54185e23 | 0.784256 | ||||||||
\(935\) | 6.41286e22i | 0.109789i | ||||||||
\(936\) | −3.01236e23 | − | 1.08780e23i | −0.511329 | − | 0.184647i | ||||
\(937\) | −7.97266e23 | −1.34180 | −0.670898 | − | 0.741550i | \(-0.734091\pi\) | ||||
−0.670898 | + | 0.741550i | \(0.734091\pi\) | |||||||
\(938\) | − | 3.60091e23i | − | 0.600883i | ||||||
\(939\) | −2.52098e23 | + | 1.76996e23i | −0.417104 | + | 0.292845i | ||||
\(940\) | −8.10905e22 | −0.133029 | ||||||||
\(941\) | 8.32522e23i | 1.35419i | 0.735897 | + | 0.677094i | \(0.236761\pi\) | ||||
−0.735897 | + | 0.677094i | \(0.763239\pi\) | |||||||
\(942\) | −6.59075e23 | − | 9.38731e23i | −1.06299 | − | 1.51403i | ||||
\(943\) | 1.85226e23 | 0.296217 | ||||||||
\(944\) | 1.11173e24i | 1.76288i | ||||||||
\(945\) | −5.36176e23 | + | 1.45848e23i | −0.843049 | + | 0.229322i | ||||
\(946\) | 1.80903e24 | 2.82044 | ||||||||
\(947\) | 7.14569e20i | 0.00110470i | 1.00000 | 0.000552350i | \(0.000175818\pi\) | |||||
−1.00000 | 0.000552350i | \(0.999824\pi\) | ||||||||
\(948\) | 4.07280e23 | − | 2.85948e23i | 0.624347 | − | 0.438349i | ||||
\(949\) | 6.32991e23 | 0.962206 | ||||||||
\(950\) | 1.11774e23i | 0.168482i | ||||||||
\(951\) | −2.06791e23 | − | 2.94535e23i | −0.309091 | − | 0.440244i | ||||
\(952\) | 4.99108e22 | 0.0739774 | ||||||||
\(953\) | 6.28939e23i | 0.924412i | 0.886773 | + | 0.462206i | \(0.152942\pi\) | ||||
−0.886773 | + | 0.462206i | \(0.847058\pi\) | |||||||
\(954\) | −1.97882e23 | + | 5.47980e23i | −0.288416 | + | 0.798689i | ||||
\(955\) | −2.19304e23 | −0.316971 | ||||||||
\(956\) | − | 2.68431e23i | − | 0.384741i | ||||||
\(957\) | 6.91873e23 | − | 4.85758e23i | 0.983402 | − | 0.690438i | ||||
\(958\) | −1.70116e23 | −0.239785 | ||||||||
\(959\) | − | 1.00673e24i | − | 1.40723i | ||||||
\(960\) | −4.18623e22 | − | 5.96251e22i | −0.0580300 | − | 0.0826531i | ||||
\(961\) | −2.93236e23 | −0.403116 | ||||||||
\(962\) | − | 8.69728e22i | − | 0.118572i | ||||||
\(963\) | 4.68772e23 | + | 1.69279e23i | 0.633799 | + | 0.228872i | ||||
\(964\) | −1.09085e23 | −0.146268 | ||||||||
\(965\) | 7.91229e22i | 0.105216i | ||||||||
\(966\) | −5.34039e23 | + | 3.74944e23i | −0.704297 | + | 0.494481i | ||||
\(967\) | 7.80856e23 | 1.02131 | 0.510657 | − | 0.859784i | \(-0.329402\pi\) | ||||
0.510657 | + | 0.859784i | \(0.329402\pi\) | |||||||
\(968\) | − | 7.49528e23i | − | 0.972266i | ||||||
\(969\) | −1.19626e22 | − | 1.70386e22i | −0.0153899 | − | 0.0219201i | ||||
\(970\) | −1.30982e23 | −0.167123 | ||||||||
\(971\) | 1.10738e24i | 1.40134i | 0.713486 | + | 0.700669i | \(0.247115\pi\) | ||||
−0.713486 | + | 0.700669i | \(0.752885\pi\) | |||||||
\(972\) | −3.90876e23 | − | 3.17110e22i | −0.490579 | − | 0.0397998i | ||||
\(973\) | 2.62043e23 | 0.326190 | ||||||||
\(974\) | 2.63685e23i | 0.325548i | ||||||||
\(975\) | 2.91724e23 | − | 2.04817e23i | 0.357220 | − | 0.250801i | ||||
\(976\) | −5.93972e23 | −0.721385 | ||||||||
\(977\) | − | 1.41210e24i | − | 1.70102i | −0.525956 | − | 0.850512i | \(-0.676292\pi\) | ||
0.525956 | − | 0.850512i | \(-0.323708\pi\) | |||||||
\(978\) | −2.76147e23 | − | 3.93321e23i | −0.329936 | − | 0.469933i | ||||
\(979\) | −1.22503e24 | −1.45173 | ||||||||
\(980\) | 1.54460e23i | 0.181555i | ||||||||
\(981\) | −1.84482e23 | + | 5.10873e23i | −0.215081 | + | 0.595608i | ||||
\(982\) | −1.89831e24 | −2.19520 | ||||||||
\(983\) | 3.91385e23i | 0.448928i | 0.974482 | + | 0.224464i | \(0.0720630\pi\) | ||||
−0.974482 | + | 0.224464i | \(0.927937\pi\) | |||||||
\(984\) | −2.31373e23 | + | 1.62445e23i | −0.263240 | + | 0.184818i | ||||
\(985\) | 2.99283e23 | 0.337747 | ||||||||
\(986\) | − | 7.91421e22i | − | 0.0885916i | ||||||
\(987\) | 2.43443e23 | + | 3.46739e23i | 0.270308 | + | 0.385004i | ||||
\(988\) | 1.08463e23 | 0.119461 | ||||||||
\(989\) | − | 7.53498e23i | − | 0.823212i | ||||||
\(990\) | 1.20355e24 | + | 4.34615e23i | 1.30431 | + | 0.471002i | ||||
\(991\) | 4.73437e23 | 0.508947 | 0.254474 | − | 0.967080i | \(-0.418098\pi\) | ||||
0.254474 | + | 0.967080i | \(0.418098\pi\) | |||||||
\(992\) | − | 6.56796e23i | − | 0.700385i | ||||||
\(993\) | 7.75375e23 | − | 5.44384e23i | 0.820196 | − | 0.575853i | ||||
\(994\) | 1.79290e23 | 0.188133 | ||||||||
\(995\) | − | 5.44258e23i | − | 0.566527i | ||||||
\(996\) | 4.78326e23 | + | 6.81288e23i | 0.493912 | + | 0.703487i | ||||
\(997\) | −4.33201e23 | −0.443739 | −0.221870 | − | 0.975076i | \(-0.571216\pi\) | ||||
−0.221870 | + | 0.975076i | \(0.571216\pi\) | |||||||
\(998\) | 3.58039e23i | 0.363819i | ||||||||
\(999\) | 2.88392e22 | + | 1.06021e23i | 0.0290709 | + | 0.106873i |
(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 | 3.17.b.a.2.4 | yes | 4 | |
3.2 | odd | 2 | inner | 3.17.b.a.2.1 | ✓ | 4 | |
4.3 | odd | 2 | 48.17.e.b.17.3 | 4 | |||
5.2 | odd | 4 | 75.17.d.b.74.2 | 8 | |||
5.3 | odd | 4 | 75.17.d.b.74.7 | 8 | |||
5.4 | even | 2 | 75.17.c.d.26.1 | 4 | |||
12.11 | even | 2 | 48.17.e.b.17.4 | 4 | |||
15.2 | even | 4 | 75.17.d.b.74.8 | 8 | |||
15.8 | even | 4 | 75.17.d.b.74.1 | 8 | |||
15.14 | odd | 2 | 75.17.c.d.26.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.17.b.a.2.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
3.17.b.a.2.4 | yes | 4 | 1.1 | even | 1 | trivial | |
48.17.e.b.17.3 | 4 | 4.3 | odd | 2 | |||
48.17.e.b.17.4 | 4 | 12.11 | even | 2 | |||
75.17.c.d.26.1 | 4 | 5.4 | even | 2 | |||
75.17.c.d.26.4 | 4 | 15.14 | odd | 2 | |||
75.17.d.b.74.1 | 8 | 15.8 | even | 4 | |||
75.17.d.b.74.2 | 8 | 5.2 | odd | 4 | |||
75.17.d.b.74.7 | 8 | 5.3 | odd | 4 | |||
75.17.d.b.74.8 | 8 | 15.2 | even | 4 |