Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,15,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, 15, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 15);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 15 \) |
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: | \(3.72986904456\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.1929141760.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 364x^{2} + 3640 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.3 | ||
Root | \(3.20795i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.15.b.a.2.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 38.4954i | 0.300745i | 0.988629 | + | 0.150373i | \(0.0480474\pi\) | ||||
−0.988629 | + | 0.150373i | \(0.951953\pi\) | |||||||
\(3\) | −824.672 | − | 2025.56i | −0.377079 | − | 0.926181i | ||||
\(4\) | 14902.1 | 0.909552 | ||||||||
\(5\) | − | 122931.i | − | 1.57351i | −0.617265 | − | 0.786755i | \(-0.711759\pi\) | ||
0.617265 | − | 0.786755i | \(-0.288241\pi\) | |||||||
\(6\) | 77974.7 | − | 31746.1i | 0.278545 | − | 0.113405i | ||||
\(7\) | −65585.1 | −0.0796378 | −0.0398189 | − | 0.999207i | \(-0.512678\pi\) | ||||
−0.0398189 | + | 0.999207i | \(0.512678\pi\) | |||||||
\(8\) | 1.20437e6i | 0.574289i | ||||||||
\(9\) | −3.42280e6 | + | 3.34084e6i | −0.715622 | + | 0.698487i | ||||
\(10\) | 4.73226e6 | 0.473226 | ||||||||
\(11\) | − | 6.41681e6i | − | 0.329284i | −0.986353 | − | 0.164642i | \(-0.947353\pi\) | ||
0.986353 | − | 0.164642i | \(-0.0526469\pi\) | |||||||
\(12\) | −1.22894e7 | − | 3.01851e7i | −0.342973 | − | 0.842410i | ||||
\(13\) | 6.71391e7 | 1.06997 | 0.534985 | − | 0.844861i | \(-0.320317\pi\) | ||||
0.534985 | + | 0.844861i | \(0.320317\pi\) | |||||||
\(14\) | − | 2.52473e6i | − | 0.0239507i | ||||||
\(15\) | −2.49003e8 | + | 1.01377e8i | −1.45736 | + | 0.593338i | ||||
\(16\) | 1.97793e8 | 0.736838 | ||||||||
\(17\) | 3.10586e8i | 0.756902i | 0.925621 | + | 0.378451i | \(0.123543\pi\) | ||||
−0.925621 | + | 0.378451i | \(0.876457\pi\) | |||||||
\(18\) | −1.28607e8 | − | 1.31762e8i | −0.210067 | − | 0.215220i | ||||
\(19\) | 2.64721e8 | 0.296151 | 0.148075 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148075 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(20\) | − | 1.83192e9i | − | 1.43119i | ||||||
\(21\) | 5.40863e7 | + | 1.32847e8i | 0.0300298 | + | 0.0737590i | ||||
\(22\) | 2.47018e8 | 0.0990306 | ||||||||
\(23\) | 3.74210e9i | 1.09906i | 0.835475 | + | 0.549529i | \(0.185193\pi\) | ||||
−0.835475 | + | 0.549529i | \(0.814807\pi\) | |||||||
\(24\) | 2.43952e9 | − | 9.93212e8i | 0.531895 | − | 0.216552i | ||||
\(25\) | −9.00839e9 | −1.47594 | ||||||||
\(26\) | 2.58455e9i | 0.321789i | ||||||||
\(27\) | 9.58976e9 | + | 4.17798e9i | 0.916772 | + | 0.399411i | ||||
\(28\) | −9.77357e8 | −0.0724347 | ||||||||
\(29\) | − | 2.30172e10i | − | 1.33434i | −0.744905 | − | 0.667170i | \(-0.767505\pi\) | ||
0.744905 | − | 0.667170i | \(-0.232495\pi\) | |||||||
\(30\) | −3.90256e9 | − | 9.58546e9i | −0.178444 | − | 0.438293i | ||||
\(31\) | 1.42829e10 | 0.519140 | 0.259570 | − | 0.965724i | \(-0.416419\pi\) | ||||
0.259570 | + | 0.965724i | \(0.416419\pi\) | |||||||
\(32\) | 2.73465e10i | 0.795889i | ||||||||
\(33\) | −1.29976e10 | + | 5.29177e9i | −0.304977 | + | 0.124166i | ||||
\(34\) | −1.19561e10 | −0.227635 | ||||||||
\(35\) | 8.06241e9i | 0.125311i | ||||||||
\(36\) | −5.10069e10 | + | 4.97856e10i | −0.650896 | + | 0.635311i | ||||
\(37\) | 7.16574e10 | 0.754830 | 0.377415 | − | 0.926044i | \(-0.376813\pi\) | ||||
0.377415 | + | 0.926044i | \(0.376813\pi\) | |||||||
\(38\) | 1.01905e10i | 0.0890660i | ||||||||
\(39\) | −5.53677e10 | − | 1.35994e11i | −0.403464 | − | 0.990986i | ||||
\(40\) | 1.48054e11 | 0.903650 | ||||||||
\(41\) | − | 9.96535e10i | − | 0.511688i | −0.966718 | − | 0.255844i | \(-0.917647\pi\) | ||
0.966718 | − | 0.255844i | \(-0.0823534\pi\) | |||||||
\(42\) | −5.11398e9 | + | 2.08207e9i | −0.0221827 | + | 0.00903131i | ||||
\(43\) | −2.62372e11 | −0.965248 | −0.482624 | − | 0.875828i | \(-0.660316\pi\) | ||||
−0.482624 | + | 0.875828i | \(0.660316\pi\) | |||||||
\(44\) | − | 9.56240e10i | − | 0.299501i | ||||||
\(45\) | 4.10692e11 | + | 4.20766e11i | 1.09908 | + | 1.12604i | ||||
\(46\) | −1.44054e11 | −0.330537 | ||||||||
\(47\) | 5.94893e11i | 1.17423i | 0.809503 | + | 0.587116i | \(0.199737\pi\) | ||||
−0.809503 | + | 0.587116i | \(0.800263\pi\) | |||||||
\(48\) | −1.63115e11 | − | 4.00642e11i | −0.277846 | − | 0.682445i | ||||
\(49\) | −6.73922e11 | −0.993658 | ||||||||
\(50\) | − | 3.46782e11i | − | 0.443881i | ||||||
\(51\) | 6.29110e11 | − | 2.56132e11i | 0.701028 | − | 0.285412i | ||||
\(52\) | 1.00051e12 | 0.973194 | ||||||||
\(53\) | − | 7.14608e11i | − | 0.608326i | −0.952620 | − | 0.304163i | \(-0.901623\pi\) | ||
0.952620 | − | 0.304163i | \(-0.0983768\pi\) | |||||||
\(54\) | −1.60833e11 | + | 3.69162e11i | −0.120121 | + | 0.275715i | ||||
\(55\) | −7.88822e11 | −0.518132 | ||||||||
\(56\) | − | 7.89889e10i | − | 0.0457351i | ||||||
\(57\) | −2.18308e11 | − | 5.36208e11i | −0.111672 | − | 0.274289i | ||||
\(58\) | 8.86056e11 | 0.401297 | ||||||||
\(59\) | 2.54506e12i | 1.02266i | 0.859383 | + | 0.511332i | \(0.170848\pi\) | ||||
−0.859383 | + | 0.511332i | \(0.829152\pi\) | |||||||
\(60\) | −3.71067e12 | + | 1.51074e12i | −1.32554 | + | 0.539672i | ||||
\(61\) | 2.14417e12 | 0.682260 | 0.341130 | − | 0.940016i | \(-0.389190\pi\) | ||||
0.341130 | + | 0.940016i | \(0.389190\pi\) | |||||||
\(62\) | 5.49826e11i | 0.156129i | ||||||||
\(63\) | 2.24485e11 | − | 2.19110e11i | 0.0569906 | − | 0.0556260i | ||||
\(64\) | 2.18793e12 | 0.497478 | ||||||||
\(65\) | − | 8.25344e12i | − | 1.68361i | ||||||
\(66\) | −2.03709e11 | − | 5.00349e11i | −0.0373424 | − | 0.0917203i | ||||
\(67\) | −3.16198e12 | −0.521717 | −0.260859 | − | 0.965377i | \(-0.584006\pi\) | ||||
−0.260859 | + | 0.965377i | \(0.584006\pi\) | |||||||
\(68\) | 4.62839e12i | 0.688442i | ||||||||
\(69\) | 7.57984e12 | − | 3.08601e12i | 1.01793 | − | 0.414432i | ||||
\(70\) | −3.10366e11 | −0.0376867 | ||||||||
\(71\) | 4.44830e12i | 0.489087i | 0.969638 | + | 0.244543i | \(0.0786380\pi\) | ||||
−0.969638 | + | 0.244543i | \(0.921362\pi\) | |||||||
\(72\) | −4.02362e12 | − | 4.12232e12i | −0.401134 | − | 0.410974i | ||||
\(73\) | −1.16545e13 | −1.05495 | −0.527475 | − | 0.849570i | \(-0.676861\pi\) | ||||
−0.527475 | + | 0.849570i | \(0.676861\pi\) | |||||||
\(74\) | 2.75848e12i | 0.227012i | ||||||||
\(75\) | 7.42897e12 | + | 1.82470e13i | 0.556545 | + | 1.36698i | ||||
\(76\) | 3.94490e12 | 0.269365 | ||||||||
\(77\) | 4.20848e11i | 0.0262234i | ||||||||
\(78\) | 5.23515e12 | − | 2.13140e12i | 0.298035 | − | 0.121340i | ||||
\(79\) | −1.15494e13 | −0.601411 | −0.300705 | − | 0.953717i | \(-0.597222\pi\) | ||||
−0.300705 | + | 0.953717i | \(0.597222\pi\) | |||||||
\(80\) | − | 2.43148e13i | − | 1.15942i | ||||||
\(81\) | 5.54323e11 | − | 2.28701e13i | 0.0242308 | − | 0.999706i | ||||
\(82\) | 3.83620e12 | 0.153888 | ||||||||
\(83\) | 1.72455e13i | 0.635519i | 0.948171 | + | 0.317760i | \(0.102930\pi\) | ||||
−0.948171 | + | 0.317760i | \(0.897070\pi\) | |||||||
\(84\) | 8.05999e11 | + | 1.97969e12i | 0.0273136 | + | 0.0670877i | ||||
\(85\) | 3.81805e13 | 1.19099 | ||||||||
\(86\) | − | 1.01001e13i | − | 0.290294i | ||||||
\(87\) | −4.66227e13 | + | 1.89817e13i | −1.23584 | + | 0.503152i | ||||
\(88\) | 7.72822e12 | 0.189104 | ||||||||
\(89\) | 9.51861e12i | 0.215201i | 0.994194 | + | 0.107600i | \(0.0343167\pi\) | ||||
−0.994194 | + | 0.107600i | \(0.965683\pi\) | |||||||
\(90\) | −1.61976e13 | + | 1.58097e13i | −0.338651 | + | 0.330542i | ||||
\(91\) | −4.40333e12 | −0.0852101 | ||||||||
\(92\) | 5.57652e13i | 0.999651i | ||||||||
\(93\) | −1.17787e13 | − | 2.89308e13i | −0.195757 | − | 0.480817i | ||||
\(94\) | −2.29007e13 | −0.353145 | ||||||||
\(95\) | − | 3.25423e13i | − | 0.465997i | ||||||
\(96\) | 5.53920e13 | − | 2.25519e13i | 0.737138 | − | 0.300113i | ||||
\(97\) | 8.81078e13 | 1.09047 | 0.545233 | − | 0.838285i | \(-0.316441\pi\) | ||||
0.545233 | + | 0.838285i | \(0.316441\pi\) | |||||||
\(98\) | − | 2.59429e13i | − | 0.298838i | ||||||
\(99\) | 2.14376e13 | + | 2.19635e13i | 0.230001 | + | 0.235643i | ||||
\(100\) | −1.34244e14 | −1.34244 | ||||||||
\(101\) | − | 1.49993e14i | − | 1.39901i | −0.714627 | − | 0.699506i | \(-0.753403\pi\) | ||
0.714627 | − | 0.699506i | \(-0.246597\pi\) | |||||||
\(102\) | 9.85990e12 | + | 2.42178e13i | 0.0858363 | + | 0.210831i | ||||
\(103\) | −1.66785e12 | −0.0135611 | −0.00678056 | − | 0.999977i | \(-0.502158\pi\) | ||||
−0.00678056 | + | 0.999977i | \(0.502158\pi\) | |||||||
\(104\) | 8.08604e13i | 0.614472i | ||||||||
\(105\) | 1.63309e13 | − | 6.64885e12i | 0.116061 | − | 0.0472521i | ||||
\(106\) | 2.75091e13 | 0.182951 | ||||||||
\(107\) | 2.47354e14i | 1.54039i | 0.637806 | + | 0.770197i | \(0.279842\pi\) | ||||
−0.637806 | + | 0.770197i | \(0.720158\pi\) | |||||||
\(108\) | 1.42908e14 | + | 6.22606e13i | 0.833852 | + | 0.363285i | ||||
\(109\) | −2.67988e14 | −1.46599 | −0.732994 | − | 0.680235i | \(-0.761878\pi\) | ||||
−0.732994 | + | 0.680235i | \(0.761878\pi\) | |||||||
\(110\) | − | 3.03660e13i | − | 0.155826i | ||||||
\(111\) | −5.90939e13 | − | 1.45146e14i | −0.284631 | − | 0.699109i | ||||
\(112\) | −1.29723e13 | −0.0586801 | ||||||||
\(113\) | − | 2.60088e13i | − | 0.110553i | −0.998471 | − | 0.0552765i | \(-0.982396\pi\) | ||
0.998471 | − | 0.0552765i | \(-0.0176040\pi\) | |||||||
\(114\) | 2.06415e13 | − | 8.40386e12i | 0.0824912 | − | 0.0335849i | ||||
\(115\) | 4.60018e14 | 1.72938 | ||||||||
\(116\) | − | 3.43005e14i | − | 1.21365i | ||||||
\(117\) | −2.29804e14 | + | 2.24301e14i | −0.765695 | + | 0.747361i | ||||
\(118\) | −9.79729e13 | −0.307562 | ||||||||
\(119\) | − | 2.03698e13i | − | 0.0602780i | ||||||
\(120\) | −1.22096e14 | − | 2.99892e14i | −0.340748 | − | 0.836943i | ||||
\(121\) | 3.38574e14 | 0.891572 | ||||||||
\(122\) | 8.25407e13i | 0.205187i | ||||||||
\(123\) | −2.01854e14 | + | 8.21815e13i | −0.473916 | + | 0.192947i | ||||
\(124\) | 2.12845e14 | 0.472185 | ||||||||
\(125\) | 3.57098e14i | 0.748889i | ||||||||
\(126\) | 8.43472e12 | + | 8.64163e12i | 0.0167293 | + | 0.0171397i | ||||
\(127\) | −7.59996e14 | −1.42622 | −0.713108 | − | 0.701054i | \(-0.752713\pi\) | ||||
−0.713108 | + | 0.701054i | \(0.752713\pi\) | |||||||
\(128\) | 5.32271e14i | 0.945503i | ||||||||
\(129\) | 2.16371e14 | + | 5.31451e14i | 0.363975 | + | 0.893995i | ||||
\(130\) | 3.17719e14 | 0.506338 | ||||||||
\(131\) | − | 1.01894e15i | − | 1.53904i | −0.638623 | − | 0.769520i | \(-0.720496\pi\) | ||
0.638623 | − | 0.769520i | \(-0.279504\pi\) | |||||||
\(132\) | −1.93692e14 | + | 7.88585e13i | −0.277392 | + | 0.112936i | ||||
\(133\) | −1.73618e13 | −0.0235848 | ||||||||
\(134\) | − | 1.21722e14i | − | 0.156904i | ||||||
\(135\) | 5.13601e14 | − | 1.17887e15i | 0.628477 | − | 1.44255i | ||||
\(136\) | −3.74061e14 | −0.434680 | ||||||||
\(137\) | 4.70567e14i | 0.519491i | 0.965677 | + | 0.259745i | \(0.0836386\pi\) | ||||
−0.965677 | + | 0.259745i | \(0.916361\pi\) | |||||||
\(138\) | 1.18797e14 | + | 2.91789e14i | 0.124639 | + | 0.306137i | ||||
\(139\) | 2.98471e14 | 0.297714 | 0.148857 | − | 0.988859i | \(-0.452441\pi\) | ||||
0.148857 | + | 0.988859i | \(0.452441\pi\) | |||||||
\(140\) | 1.20147e14i | 0.113977i | ||||||||
\(141\) | 1.20499e15 | − | 4.90592e14i | 1.08755 | − | 0.442779i | ||||
\(142\) | −1.71239e14 | −0.147091 | ||||||||
\(143\) | − | 4.30819e14i | − | 0.352324i | ||||||
\(144\) | −6.77007e14 | + | 6.60797e14i | −0.527297 | + | 0.514672i | ||||
\(145\) | −2.82952e15 | −2.09960 | ||||||||
\(146\) | − | 4.48643e14i | − | 0.317271i | ||||||
\(147\) | 5.55765e14 | + | 1.36507e15i | 0.374688 | + | 0.920307i | ||||
\(148\) | 1.06785e15 | 0.686557 | ||||||||
\(149\) | 1.70696e15i | 1.04694i | 0.852045 | + | 0.523468i | \(0.175362\pi\) | ||||
−0.852045 | + | 0.523468i | \(0.824638\pi\) | |||||||
\(150\) | −7.02426e14 | + | 2.85981e14i | −0.411114 | + | 0.167378i | ||||
\(151\) | 2.46501e15 | 1.37714 | 0.688572 | − | 0.725168i | \(-0.258238\pi\) | ||||
0.688572 | + | 0.725168i | \(0.258238\pi\) | |||||||
\(152\) | 3.18822e14i | 0.170076i | ||||||||
\(153\) | −1.03762e15 | − | 1.06307e15i | −0.528686 | − | 0.541656i | ||||
\(154\) | −1.62007e13 | −0.00788658 | ||||||||
\(155\) | − | 1.75580e15i | − | 0.816872i | ||||||
\(156\) | −8.25096e14 | − | 2.02660e15i | −0.366971 | − | 0.901354i | ||||
\(157\) | 2.11414e14 | 0.0899158 | 0.0449579 | − | 0.998989i | \(-0.485685\pi\) | ||||
0.0449579 | + | 0.998989i | \(0.485685\pi\) | |||||||
\(158\) | − | 4.44600e14i | − | 0.180872i | ||||||
\(159\) | −1.44748e15 | + | 5.89317e14i | −0.563420 | + | 0.229387i | ||||
\(160\) | 3.36173e15 | 1.25234 | ||||||||
\(161\) | − | 2.45426e14i | − | 0.0875266i | ||||||
\(162\) | 8.80393e14 | + | 2.13389e13i | 0.300657 | + | 0.00728730i | ||||
\(163\) | −1.94446e15 | −0.636042 | −0.318021 | − | 0.948084i | \(-0.603018\pi\) | ||||
−0.318021 | + | 0.948084i | \(0.603018\pi\) | |||||||
\(164\) | − | 1.48505e15i | − | 0.465407i | ||||||
\(165\) | 6.50520e14 | + | 1.59780e15i | 0.195377 | + | 0.479884i | ||||
\(166\) | −6.63872e14 | −0.191129 | ||||||||
\(167\) | 4.09979e15i | 1.13174i | 0.824495 | + | 0.565869i | \(0.191459\pi\) | ||||
−0.824495 | + | 0.565869i | \(0.808541\pi\) | |||||||
\(168\) | −1.59996e14 | + | 6.51399e13i | −0.0423590 | + | 0.0172458i | ||||
\(169\) | 5.70278e14 | 0.144837 | ||||||||
\(170\) | 1.46977e15i | 0.358186i | ||||||||
\(171\) | −9.06087e14 | + | 8.84391e14i | −0.211932 | + | 0.206858i | ||||
\(172\) | −3.90990e15 | −0.877944 | ||||||||
\(173\) | 6.60096e14i | 0.142326i | 0.997465 | + | 0.0711630i | \(0.0226711\pi\) | ||||
−0.997465 | + | 0.0711630i | \(0.977329\pi\) | |||||||
\(174\) | −7.30706e14 | − | 1.79476e15i | −0.151321 | − | 0.371673i | ||||
\(175\) | 5.90817e14 | 0.117540 | ||||||||
\(176\) | − | 1.26920e15i | − | 0.242629i | ||||||
\(177\) | 5.15516e15 | − | 2.09884e15i | 0.947172 | − | 0.385626i | ||||
\(178\) | −3.66423e14 | −0.0647206 | ||||||||
\(179\) | − | 5.86552e15i | − | 0.996174i | −0.867127 | − | 0.498087i | \(-0.834036\pi\) | ||
0.867127 | − | 0.498087i | \(-0.165964\pi\) | |||||||
\(180\) | 6.12017e15 | + | 6.27031e15i | 0.999668 | + | 1.02419i | ||||
\(181\) | −1.98346e15 | −0.311655 | −0.155828 | − | 0.987784i | \(-0.549804\pi\) | ||||
−0.155828 | + | 0.987784i | \(0.549804\pi\) | |||||||
\(182\) | − | 1.69508e14i | − | 0.0256265i | ||||||
\(183\) | −1.76824e15 | − | 4.34314e15i | −0.257266 | − | 0.631897i | ||||
\(184\) | −4.50688e15 | −0.631177 | ||||||||
\(185\) | − | 8.80889e15i | − | 1.18773i | ||||||
\(186\) | 1.11370e15 | − | 4.53426e14i | 0.144604 | − | 0.0588729i | ||||
\(187\) | 1.99297e15 | 0.249236 | ||||||||
\(188\) | 8.86516e15i | 1.06803i | ||||||||
\(189\) | −6.28946e14 | − | 2.74013e14i | −0.0730097 | − | 0.0318082i | ||||
\(190\) | 1.25273e15 | 0.140146 | ||||||||
\(191\) | 1.70777e16i | 1.84160i | 0.390031 | + | 0.920802i | \(0.372464\pi\) | ||||
−0.390031 | + | 0.920802i | \(0.627536\pi\) | |||||||
\(192\) | −1.80433e15 | − | 4.43178e15i | −0.187588 | − | 0.460754i | ||||
\(193\) | 7.28710e15 | 0.730556 | 0.365278 | − | 0.930899i | \(-0.380974\pi\) | ||||
0.365278 | + | 0.930899i | \(0.380974\pi\) | |||||||
\(194\) | 3.39174e15i | 0.327952i | ||||||||
\(195\) | −1.67178e16 | + | 6.80638e15i | −1.55933 | + | 0.634854i | ||||
\(196\) | −1.00429e16 | −0.903784 | ||||||||
\(197\) | − | 1.34309e16i | − | 1.16639i | −0.812333 | − | 0.583194i | \(-0.801803\pi\) | ||
0.812333 | − | 0.583194i | \(-0.198197\pi\) | |||||||
\(198\) | −8.45492e14 | + | 8.25248e14i | −0.0708685 | + | 0.0691716i | ||||
\(199\) | 1.97699e16 | 1.59968 | 0.799839 | − | 0.600215i | \(-0.204918\pi\) | ||||
0.799839 | + | 0.600215i | \(0.204918\pi\) | |||||||
\(200\) | − | 1.08494e16i | − | 0.847613i | ||||||
\(201\) | 2.60760e15 | + | 6.40477e15i | 0.196729 | + | 0.483205i | ||||
\(202\) | 5.77404e15 | 0.420746 | ||||||||
\(203\) | 1.50959e15i | 0.106264i | ||||||||
\(204\) | 9.37506e15 | − | 3.81690e15i | 0.637622 | − | 0.259597i | ||||
\(205\) | −1.22504e16 | −0.805147 | ||||||||
\(206\) | − | 6.42044e13i | − | 0.00407844i | ||||||
\(207\) | −1.25018e16 | − | 1.28085e16i | −0.767678 | − | 0.786511i | ||||
\(208\) | 1.32797e16 | 0.788394 | ||||||||
\(209\) | − | 1.69866e15i | − | 0.0975177i | ||||||
\(210\) | 2.55950e14 | + | 6.28664e14i | 0.0142109 | + | 0.0349047i | ||||
\(211\) | −6.59808e15 | −0.354356 | −0.177178 | − | 0.984179i | \(-0.556697\pi\) | ||||
−0.177178 | + | 0.984179i | \(0.556697\pi\) | |||||||
\(212\) | − | 1.06492e16i | − | 0.553305i | ||||||
\(213\) | 9.01029e15 | − | 3.66839e15i | 0.452983 | − | 0.184424i | ||||
\(214\) | −9.52198e15 | −0.463266 | ||||||||
\(215\) | 3.22536e16i | 1.51883i | ||||||||
\(216\) | −5.03183e15 | + | 1.15496e16i | −0.229377 | + | 0.526492i | ||||
\(217\) | −9.36745e14 | −0.0413431 | ||||||||
\(218\) | − | 1.03163e16i | − | 0.440889i | ||||||
\(219\) | 9.61111e15 | + | 2.36068e16i | 0.397800 | + | 0.977075i | ||||
\(220\) | −1.17551e16 | −0.471268 | ||||||||
\(221\) | 2.08525e16i | 0.809863i | ||||||||
\(222\) | 5.58746e15 | − | 2.27484e15i | 0.210254 | − | 0.0856014i | ||||
\(223\) | −1.37296e16 | −0.500638 | −0.250319 | − | 0.968163i | \(-0.580535\pi\) | ||||
−0.250319 | + | 0.968163i | \(0.580535\pi\) | |||||||
\(224\) | − | 1.79353e15i | − | 0.0633829i | ||||||
\(225\) | 3.08339e16 | − | 3.00956e16i | 1.05621 | − | 1.03092i | ||||
\(226\) | 1.00122e15 | 0.0332483 | ||||||||
\(227\) | − | 4.03532e16i | − | 1.29926i | −0.760249 | − | 0.649632i | \(-0.774923\pi\) | ||
0.760249 | − | 0.649632i | \(-0.225077\pi\) | |||||||
\(228\) | −3.25325e15 | − | 7.99062e15i | −0.101572 | − | 0.249480i | ||||
\(229\) | −4.63973e16 | −1.40490 | −0.702448 | − | 0.711735i | \(-0.747910\pi\) | ||||
−0.702448 | + | 0.711735i | \(0.747910\pi\) | |||||||
\(230\) | 1.77086e16i | 0.520103i | ||||||||
\(231\) | 8.52451e14 | − | 3.47061e14i | 0.0242877 | − | 0.00988832i | ||||
\(232\) | 2.77213e16 | 0.766297 | ||||||||
\(233\) | − | 1.99408e16i | − | 0.534874i | −0.963575 | − | 0.267437i | \(-0.913823\pi\) | ||
0.963575 | − | 0.267437i | \(-0.0861768\pi\) | |||||||
\(234\) | −8.63456e15 | − | 8.84638e15i | −0.224765 | − | 0.230279i | ||||
\(235\) | 7.31305e16 | 1.84767 | ||||||||
\(236\) | 3.79267e16i | 0.930167i | ||||||||
\(237\) | 9.52451e15 | + | 2.33941e16i | 0.226780 | + | 0.557015i | ||||
\(238\) | 7.84145e14 | 0.0181283 | ||||||||
\(239\) | − | 7.55992e16i | − | 1.69720i | −0.529038 | − | 0.848598i | \(-0.677447\pi\) | ||
0.529038 | − | 0.848598i | \(-0.322553\pi\) | |||||||
\(240\) | −4.92511e16 | + | 2.00518e16i | −1.07383 | + | 0.437194i | ||||
\(241\) | −4.79554e16 | −1.01559 | −0.507795 | − | 0.861478i | \(-0.669539\pi\) | ||||
−0.507795 | + | 0.861478i | \(0.669539\pi\) | |||||||
\(242\) | 1.30336e16i | 0.268136i | ||||||||
\(243\) | −4.67818e16 | + | 1.77375e16i | −0.935046 | + | 0.354526i | ||||
\(244\) | 3.19526e16 | 0.620552 | ||||||||
\(245\) | 8.28455e16i | 1.56353i | ||||||||
\(246\) | −3.16361e15 | − | 7.77044e15i | −0.0580279 | − | 0.142528i | ||||
\(247\) | 1.77731e16 | 0.316873 | ||||||||
\(248\) | 1.72019e16i | 0.298136i | ||||||||
\(249\) | 3.49317e16 | − | 1.42219e16i | 0.588606 | − | 0.239641i | ||||
\(250\) | −1.37466e16 | −0.225225 | ||||||||
\(251\) | − | 5.85823e15i | − | 0.0933362i | −0.998910 | − | 0.0466681i | \(-0.985140\pi\) | ||
0.998910 | − | 0.0466681i | \(-0.0148603\pi\) | |||||||
\(252\) | 3.34530e15 | − | 3.26520e15i | 0.0518359 | − | 0.0505947i | ||||
\(253\) | 2.40124e16 | 0.361902 | ||||||||
\(254\) | − | 2.92564e16i | − | 0.428928i | ||||||
\(255\) | −3.14864e16 | − | 7.73368e16i | −0.449099 | − | 1.10307i | ||||
\(256\) | 1.53570e16 | 0.213122 | ||||||||
\(257\) | 1.74153e16i | 0.235179i | 0.993062 | + | 0.117590i | \(0.0375168\pi\) | ||||
−0.993062 | + | 0.117590i | \(0.962483\pi\) | |||||||
\(258\) | −2.04584e16 | + | 8.32930e15i | −0.268865 | + | 0.109464i | ||||
\(259\) | −4.69966e15 | −0.0601130 | ||||||||
\(260\) | − | 1.22994e17i | − | 1.53133i | ||||||
\(261\) | 7.68969e16 | + | 7.87833e16i | 0.932020 | + | 0.954884i | ||||
\(262\) | 3.92245e16 | 0.462859 | ||||||||
\(263\) | − | 1.15601e16i | − | 0.132823i | −0.997792 | − | 0.0664114i | \(-0.978845\pi\) | ||
0.997792 | − | 0.0664114i | \(-0.0211550\pi\) | |||||||
\(264\) | −6.37325e15 | − | 1.56540e16i | −0.0713073 | − | 0.175145i | ||||
\(265\) | −8.78471e16 | −0.957208 | ||||||||
\(266\) | − | 6.68348e14i | − | 0.00709302i | ||||||
\(267\) | 1.92805e16 | − | 7.84973e15i | 0.199315 | − | 0.0811477i | ||||
\(268\) | −4.71201e16 | −0.474529 | ||||||||
\(269\) | 1.20026e17i | 1.17764i | 0.808266 | + | 0.588818i | \(0.200407\pi\) | ||||
−0.808266 | + | 0.588818i | \(0.799593\pi\) | |||||||
\(270\) | 4.53812e16 | + | 1.97713e16i | 0.433840 | + | 0.189011i | ||||
\(271\) | −4.25215e16 | −0.396117 | −0.198058 | − | 0.980190i | \(-0.563464\pi\) | ||||
−0.198058 | + | 0.980190i | \(0.563464\pi\) | |||||||
\(272\) | 6.14319e16i | 0.557714i | ||||||||
\(273\) | 3.63130e15 | + | 8.91919e15i | 0.0321310 | + | 0.0789200i | ||||
\(274\) | −1.81147e16 | −0.156234 | ||||||||
\(275\) | 5.78052e16i | 0.486002i | ||||||||
\(276\) | 1.12956e17 | − | 4.59880e16i | 0.925858 | − | 0.376948i | ||||
\(277\) | −1.58094e17 | −1.26345 | −0.631725 | − | 0.775193i | \(-0.717653\pi\) | ||||
−0.631725 | + | 0.775193i | \(0.717653\pi\) | |||||||
\(278\) | 1.14898e16i | 0.0895360i | ||||||||
\(279\) | −4.88875e16 | + | 4.77169e16i | −0.371508 | + | 0.362612i | ||||
\(280\) | −9.71014e15 | −0.0719647 | ||||||||
\(281\) | − | 2.74660e17i | − | 1.98541i | −0.120551 | − | 0.992707i | \(-0.538466\pi\) | ||
0.120551 | − | 0.992707i | \(-0.461534\pi\) | |||||||
\(282\) | 1.88855e16 | + | 4.63866e16i | 0.133164 | + | 0.327076i | ||||
\(283\) | 2.87031e17 | 1.97435 | 0.987173 | − | 0.159653i | \(-0.0510375\pi\) | ||||
0.987173 | + | 0.159653i | \(0.0510375\pi\) | |||||||
\(284\) | 6.62891e16i | 0.444850i | ||||||||
\(285\) | −6.59163e16 | + | 2.68367e16i | −0.431597 | + | 0.175718i | ||||
\(286\) | 1.65845e16 | 0.105960 | ||||||||
\(287\) | 6.53579e15i | 0.0407497i | ||||||||
\(288\) | −9.13605e16 | − | 9.36018e16i | −0.555919 | − | 0.569556i | ||||
\(289\) | 7.19141e16 | 0.427100 | ||||||||
\(290\) | − | 1.08923e17i | − | 0.631444i | ||||||
\(291\) | −7.26600e16 | − | 1.78467e17i | −0.411192 | − | 1.00997i | ||||
\(292\) | −1.73676e17 | −0.959533 | ||||||||
\(293\) | 3.75542e16i | 0.202575i | 0.994857 | + | 0.101287i | \(0.0322961\pi\) | ||||
−0.994857 | + | 0.101287i | \(0.967704\pi\) | |||||||
\(294\) | −5.25488e16 | + | 2.13944e16i | −0.276778 | + | 0.112686i | ||||
\(295\) | 3.12865e17 | 1.60917 | ||||||||
\(296\) | 8.63022e16i | 0.433491i | ||||||||
\(297\) | 2.68093e16 | − | 6.15357e16i | 0.131520 | − | 0.301878i | ||||
\(298\) | −6.57102e16 | −0.314861 | ||||||||
\(299\) | 2.51241e17i | 1.17596i | ||||||||
\(300\) | 1.10707e17 | + | 2.71919e17i | 0.506206 | + | 1.24334i | ||||
\(301\) | 1.72077e16 | 0.0768702 | ||||||||
\(302\) | 9.48914e16i | 0.414170i | ||||||||
\(303\) | −3.03819e17 | + | 1.23695e17i | −1.29574 | + | 0.527538i | ||||
\(304\) | 5.23600e16 | 0.218215 | ||||||||
\(305\) | − | 2.63584e17i | − | 1.07354i | ||||||
\(306\) | 4.09235e16 | − | 3.99436e16i | 0.162900 | − | 0.159000i | ||||
\(307\) | −3.96983e17 | −1.54456 | −0.772278 | − | 0.635285i | \(-0.780883\pi\) | ||||
−0.772278 | + | 0.635285i | \(0.780883\pi\) | |||||||
\(308\) | 6.27151e15i | 0.0238516i | ||||||||
\(309\) | 1.37543e15 | + | 3.37832e15i | 0.00511362 | + | 0.0125601i | ||||
\(310\) | 6.75903e16 | 0.245670 | ||||||||
\(311\) | − | 2.59474e17i | − | 0.922086i | −0.887378 | − | 0.461043i | \(-0.847475\pi\) | ||
0.887378 | − | 0.461043i | \(-0.152525\pi\) | |||||||
\(312\) | 1.63787e17 | − | 6.66833e16i | 0.569112 | − | 0.231705i | ||||
\(313\) | 4.72356e17 | 1.60494 | 0.802470 | − | 0.596693i | \(-0.203519\pi\) | ||||
0.802470 | + | 0.596693i | \(0.203519\pi\) | |||||||
\(314\) | 8.13846e15i | 0.0270417i | ||||||||
\(315\) | −2.69353e16 | − | 2.75960e16i | −0.0875281 | − | 0.0896753i | ||||
\(316\) | −1.72111e17 | −0.547015 | ||||||||
\(317\) | 3.04249e17i | 0.945832i | 0.881108 | + | 0.472916i | \(0.156799\pi\) | ||||
−0.881108 | + | 0.472916i | \(0.843201\pi\) | |||||||
\(318\) | −2.26860e16 | − | 5.57213e16i | −0.0689871 | − | 0.169446i | ||||
\(319\) | −1.47697e17 | −0.439377 | ||||||||
\(320\) | − | 2.68963e17i | − | 0.782786i | ||||||
\(321\) | 5.01029e17 | − | 2.03986e17i | 1.42668 | − | 0.580851i | ||||
\(322\) | 9.44778e15 | 0.0263232 | ||||||||
\(323\) | 8.22186e16i | 0.224157i | ||||||||
\(324\) | 8.26058e15 | − | 3.40812e17i | 0.0220392 | − | 0.909285i | ||||
\(325\) | −6.04815e17 | −1.57921 | ||||||||
\(326\) | − | 7.48528e16i | − | 0.191287i | ||||||
\(327\) | 2.21003e17 | + | 5.42826e17i | 0.552794 | + | 1.35777i | ||||
\(328\) | 1.20020e17 | 0.293857 | ||||||||
\(329\) | − | 3.90162e16i | − | 0.0935133i | ||||||
\(330\) | −6.15081e16 | + | 2.50420e16i | −0.144323 | + | 0.0587586i | ||||
\(331\) | −2.80260e17 | −0.643820 | −0.321910 | − | 0.946770i | \(-0.604325\pi\) | ||||
−0.321910 | + | 0.946770i | \(0.604325\pi\) | |||||||
\(332\) | 2.56994e17i | 0.578038i | ||||||||
\(333\) | −2.45269e17 | + | 2.39396e17i | −0.540173 | + | 0.527239i | ||||
\(334\) | −1.57823e17 | −0.340365 | ||||||||
\(335\) | 3.88704e17i | 0.820928i | ||||||||
\(336\) | 1.06979e16 | + | 2.62762e16i | 0.0221271 | + | 0.0543484i | ||||
\(337\) | 3.66345e17 | 0.742131 | 0.371065 | − | 0.928607i | \(-0.378993\pi\) | ||||
0.371065 | + | 0.928607i | \(0.378993\pi\) | |||||||
\(338\) | 2.19531e16i | 0.0435590i | ||||||||
\(339\) | −5.26823e16 | + | 2.14487e16i | −0.102392 | + | 0.0416873i | ||||
\(340\) | 5.68970e17 | 1.08327 | ||||||||
\(341\) | − | 9.16506e16i | − | 0.170944i | ||||||
\(342\) | −3.40450e16 | − | 3.48802e16i | −0.0622115 | − | 0.0637376i | ||||
\(343\) | 8.86806e16 | 0.158771 | ||||||||
\(344\) | − | 3.15994e17i | − | 0.554331i | ||||||
\(345\) | −3.79365e17 | − | 9.31794e17i | −0.652113 | − | 1.60172i | ||||
\(346\) | −2.54107e16 | −0.0428039 | ||||||||
\(347\) | − | 1.96514e17i | − | 0.324405i | −0.986758 | − | 0.162202i | \(-0.948140\pi\) | ||
0.986758 | − | 0.162202i | \(-0.0518598\pi\) | |||||||
\(348\) | −6.94776e17 | + | 2.82867e17i | −1.12406 | + | 0.457643i | ||||
\(349\) | 8.35267e16 | 0.132449 | 0.0662243 | − | 0.997805i | \(-0.478905\pi\) | ||||
0.0662243 | + | 0.997805i | \(0.478905\pi\) | |||||||
\(350\) | 2.27437e16i | 0.0353497i | ||||||||
\(351\) | 6.43848e17 | + | 2.80505e17i | 0.980919 | + | 0.427358i | ||||
\(352\) | 1.75478e17 | 0.262074 | ||||||||
\(353\) | − | 7.48154e17i | − | 1.09539i | −0.836678 | − | 0.547694i | \(-0.815506\pi\) | ||
0.836678 | − | 0.547694i | \(-0.184494\pi\) | |||||||
\(354\) | 8.07956e16 | + | 1.98450e17i | 0.115975 | + | 0.284858i | ||||
\(355\) | 5.46832e17 | 0.769583 | ||||||||
\(356\) | 1.41847e17i | 0.195736i | ||||||||
\(357\) | −4.12603e16 | + | 1.67984e16i | −0.0558283 | + | 0.0227296i | ||||
\(358\) | 2.25796e17 | 0.299595 | ||||||||
\(359\) | 4.84462e16i | 0.0630374i | 0.999503 | + | 0.0315187i | \(0.0100344\pi\) | ||||
−0.999503 | + | 0.0315187i | \(0.989966\pi\) | |||||||
\(360\) | −5.06759e17 | + | 4.94625e17i | −0.646672 | + | 0.631188i | ||||
\(361\) | −7.28930e17 | −0.912295 | ||||||||
\(362\) | − | 7.63543e16i | − | 0.0937289i | ||||||
\(363\) | −2.79213e17 | − | 6.85802e17i | −0.336193 | − | 0.825757i | ||||
\(364\) | −6.56188e16 | −0.0775030 | ||||||||
\(365\) | 1.43269e18i | 1.65998i | ||||||||
\(366\) | 1.67191e17 | − | 6.80690e16i | 0.190040 | − | 0.0773716i | ||||
\(367\) | −4.80054e17 | −0.535338 | −0.267669 | − | 0.963511i | \(-0.586253\pi\) | ||||
−0.267669 | + | 0.963511i | \(0.586253\pi\) | |||||||
\(368\) | 7.40163e17i | 0.809827i | ||||||||
\(369\) | 3.32927e17 | + | 3.41094e17i | 0.357408 | + | 0.366176i | ||||
\(370\) | 3.39102e17 | 0.357205 | ||||||||
\(371\) | 4.68677e16i | 0.0484458i | ||||||||
\(372\) | −1.75527e17 | − | 4.31130e17i | −0.178051 | − | 0.437328i | ||||
\(373\) | 6.20045e17 | 0.617250 | 0.308625 | − | 0.951184i | \(-0.400131\pi\) | ||||
0.308625 | + | 0.951184i | \(0.400131\pi\) | |||||||
\(374\) | 7.67203e16i | 0.0749564i | ||||||||
\(375\) | 7.23323e17 | − | 2.94489e17i | 0.693607 | − | 0.282390i | ||||
\(376\) | −7.16472e17 | −0.674349 | ||||||||
\(377\) | − | 1.54535e18i | − | 1.42770i | ||||||
\(378\) | 1.05482e16 | − | 2.42115e16i | 0.00956616 | − | 0.0219573i | ||||
\(379\) | −1.19985e18 | −1.06820 | −0.534100 | − | 0.845421i | \(-0.679349\pi\) | ||||
−0.534100 | + | 0.845421i | \(0.679349\pi\) | |||||||
\(380\) | − | 4.84948e17i | − | 0.423848i | ||||||
\(381\) | 6.26748e17 | + | 1.53942e18i | 0.537797 | + | 1.32093i | ||||
\(382\) | −6.57413e17 | −0.553854 | ||||||||
\(383\) | − | 1.56394e18i | − | 1.29368i | −0.762624 | − | 0.646842i | \(-0.776089\pi\) | ||
0.762624 | − | 0.646842i | \(-0.223911\pi\) | |||||||
\(384\) | 1.07815e18 | − | 4.38949e17i | 0.875707 | − | 0.356530i | ||||
\(385\) | 5.17350e16 | 0.0412629 | ||||||||
\(386\) | 2.80520e17i | 0.219711i | ||||||||
\(387\) | 8.98048e17 | − | 8.76545e17i | 0.690753 | − | 0.674214i | ||||
\(388\) | 1.31299e18 | 0.991836 | ||||||||
\(389\) | 1.32813e18i | 0.985359i | 0.870211 | + | 0.492680i | \(0.163983\pi\) | ||||
−0.870211 | + | 0.492680i | \(0.836017\pi\) | |||||||
\(390\) | −2.62014e17 | − | 6.43559e17i | −0.190929 | − | 0.468960i | ||||
\(391\) | −1.16224e18 | −0.831879 | ||||||||
\(392\) | − | 8.11652e17i | − | 0.570647i | ||||||
\(393\) | −2.06392e18 | + | 8.40292e17i | −1.42543 | + | 0.580340i | ||||
\(394\) | 5.17030e17 | 0.350786 | ||||||||
\(395\) | 1.41978e18i | 0.946326i | ||||||||
\(396\) | 3.19465e17 | + | 3.27302e17i | 0.209198 | + | 0.214330i | ||||
\(397\) | 1.26662e18 | 0.814915 | 0.407457 | − | 0.913224i | \(-0.366416\pi\) | ||||
0.407457 | + | 0.913224i | \(0.366416\pi\) | |||||||
\(398\) | 7.61050e17i | 0.481096i | ||||||||
\(399\) | 1.43178e16 | + | 3.51672e16i | 0.00889334 | + | 0.0218438i | ||||
\(400\) | −1.78180e18 | −1.08752 | ||||||||
\(401\) | 1.97233e18i | 1.18296i | 0.806320 | + | 0.591479i | \(0.201456\pi\) | ||||
−0.806320 | + | 0.591479i | \(0.798544\pi\) | |||||||
\(402\) | −2.46554e17 | + | 1.00380e17i | −0.145322 | + | 0.0591653i | ||||
\(403\) | 9.58940e17 | 0.555464 | ||||||||
\(404\) | − | 2.23521e18i | − | 1.27247i | ||||||
\(405\) | −2.81143e18 | − | 6.81432e16i | −1.57305 | − | 0.0381274i | ||||
\(406\) | −5.81121e16 | −0.0319584 | ||||||||
\(407\) | − | 4.59812e17i | − | 0.248553i | ||||||
\(408\) | 3.08478e17 | + | 7.57682e17i | 0.163909 | + | 0.402593i | ||||
\(409\) | 1.78192e18 | 0.930731 | 0.465366 | − | 0.885119i | \(-0.345923\pi\) | ||||
0.465366 | + | 0.885119i | \(0.345923\pi\) | |||||||
\(410\) | − | 4.71586e17i | − | 0.242144i | ||||||
\(411\) | 9.53161e17 | − | 3.88064e17i | 0.481142 | − | 0.195889i | ||||
\(412\) | −2.48544e16 | −0.0123346 | ||||||||
\(413\) | − | 1.66918e17i | − | 0.0814427i | ||||||
\(414\) | 4.93067e17 | − | 4.81261e17i | 0.236539 | − | 0.230876i | ||||
\(415\) | 2.12000e18 | 0.999996 | ||||||||
\(416\) | 1.83602e18i | 0.851578i | ||||||||
\(417\) | −2.46141e17 | − | 6.04571e17i | −0.112262 | − | 0.275737i | ||||
\(418\) | 6.53908e16 | 0.0293280 | ||||||||
\(419\) | − | 2.33841e18i | − | 1.03139i | −0.856773 | − | 0.515694i | \(-0.827534\pi\) | ||
0.856773 | − | 0.515694i | \(-0.172466\pi\) | |||||||
\(420\) | 2.43365e17 | − | 9.90819e16i | 0.105563 | − | 0.0429783i | ||||
\(421\) | −2.14596e18 | −0.915478 | −0.457739 | − | 0.889087i | \(-0.651341\pi\) | ||||
−0.457739 | + | 0.889087i | \(0.651341\pi\) | |||||||
\(422\) | − | 2.53996e17i | − | 0.106571i | ||||||
\(423\) | −1.98745e18 | − | 2.03620e18i | −0.820186 | − | 0.840307i | ||||
\(424\) | 8.60653e17 | 0.349355 | ||||||||
\(425\) | − | 2.79788e18i | − | 1.11714i | ||||||
\(426\) | 1.41216e17 | + | 3.46855e17i | 0.0554648 | + | 0.136232i | ||||
\(427\) | −1.40626e17 | −0.0543337 | ||||||||
\(428\) | 3.68609e18i | 1.40107i | ||||||||
\(429\) | −8.72648e17 | + | 3.55284e17i | −0.326316 | + | 0.132854i | ||||
\(430\) | −1.24161e18 | −0.456781 | ||||||||
\(431\) | 1.47411e18i | 0.533567i | 0.963756 | + | 0.266784i | \(0.0859609\pi\) | ||||
−0.963756 | + | 0.266784i | \(0.914039\pi\) | |||||||
\(432\) | 1.89679e18 | + | 8.26376e17i | 0.675512 | + | 0.294301i | ||||
\(433\) | 4.14642e18 | 1.45297 | 0.726487 | − | 0.687181i | \(-0.241152\pi\) | ||||
0.726487 | + | 0.687181i | \(0.241152\pi\) | |||||||
\(434\) | − | 3.60604e16i | − | 0.0124338i | ||||||
\(435\) | 2.33342e18 | + | 5.73135e18i | 0.791715 | + | 1.94461i | ||||
\(436\) | −3.99359e18 | −1.33339 | ||||||||
\(437\) | 9.90613e17i | 0.325487i | ||||||||
\(438\) | −9.08752e17 | + | 3.69984e17i | −0.293851 | + | 0.119636i | ||||
\(439\) | −5.26499e18 | −1.67551 | −0.837753 | − | 0.546049i | \(-0.816131\pi\) | ||||
−0.837753 | + | 0.546049i | \(0.816131\pi\) | |||||||
\(440\) | − | 9.50034e17i | − | 0.297557i | ||||||
\(441\) | 2.30670e18 | − | 2.25147e18i | 0.711084 | − | 0.694057i | ||||
\(442\) | −8.02724e17 | −0.243562 | ||||||||
\(443\) | − | 2.03378e18i | − | 0.607404i | −0.952767 | − | 0.303702i | \(-0.901777\pi\) | ||
0.952767 | − | 0.303702i | \(-0.0982228\pi\) | |||||||
\(444\) | −8.80624e17 | − | 2.16299e18i | −0.258887 | − | 0.635876i | ||||
\(445\) | 1.17013e18 | 0.338620 | ||||||||
\(446\) | − | 5.28526e17i | − | 0.150565i | ||||||
\(447\) | 3.45755e18 | − | 1.40768e18i | 0.969652 | − | 0.394778i | ||||
\(448\) | −1.43496e17 | −0.0396180 | ||||||||
\(449\) | 2.95114e18i | 0.802168i | 0.916041 | + | 0.401084i | \(0.131367\pi\) | ||||
−0.916041 | + | 0.401084i | \(0.868633\pi\) | |||||||
\(450\) | 1.15854e18 | + | 1.18696e18i | 0.310045 | + | 0.317651i | ||||
\(451\) | −6.39458e17 | −0.168491 | ||||||||
\(452\) | − | 3.87586e17i | − | 0.100554i | ||||||
\(453\) | −2.03282e18 | − | 4.99301e18i | −0.519293 | − | 1.27548i | ||||
\(454\) | 1.55341e18 | 0.390747 | ||||||||
\(455\) | 5.41303e17i | 0.134079i | ||||||||
\(456\) | 6.45793e17 | − | 2.62924e17i | 0.157521 | − | 0.0641322i | ||||
\(457\) | −2.32324e18 | −0.558060 | −0.279030 | − | 0.960282i | \(-0.590013\pi\) | ||||
−0.279030 | + | 0.960282i | \(0.590013\pi\) | |||||||
\(458\) | − | 1.78608e18i | − | 0.422516i | ||||||
\(459\) | −1.29762e18 | + | 2.97845e18i | −0.302315 | + | 0.693906i | ||||
\(460\) | 6.85524e18 | 1.57296 | ||||||||
\(461\) | − | 3.05191e18i | − | 0.689709i | −0.938656 | − | 0.344854i | \(-0.887928\pi\) | ||
0.938656 | − | 0.344854i | \(-0.112072\pi\) | |||||||
\(462\) | 1.33603e16 | + | 3.28154e16i | 0.00297387 | + | 0.00730440i | ||||
\(463\) | 9.23063e17 | 0.202379 | 0.101189 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101189 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(464\) | − | 4.55265e18i | − | 0.983192i | ||||||
\(465\) | −3.55648e18 | + | 1.44796e18i | −0.756571 | + | 0.308025i | ||||
\(466\) | 7.67630e17 | 0.160861 | ||||||||
\(467\) | 5.58017e18i | 1.15194i | 0.817472 | + | 0.575969i | \(0.195375\pi\) | ||||
−0.817472 | + | 0.575969i | \(0.804625\pi\) | |||||||
\(468\) | −3.42456e18 | + | 3.34256e18i | −0.696439 | + | 0.679764i | ||||
\(469\) | 2.07379e17 | 0.0415484 | ||||||||
\(470\) | 2.81519e18i | 0.555677i | ||||||||
\(471\) | −1.74347e17 | − | 4.28231e17i | −0.0339054 | − | 0.0832783i | ||||
\(472\) | −3.06519e18 | −0.587305 | ||||||||
\(473\) | 1.68360e18i | 0.317841i | ||||||||
\(474\) | −9.00564e17 | + | 3.66650e17i | −0.167520 | + | 0.0682029i | ||||
\(475\) | −2.38471e18 | −0.437100 | ||||||||
\(476\) | − | 3.03553e17i | − | 0.0548260i | ||||||
\(477\) | 2.38739e18 | + | 2.44596e18i | 0.424908 | + | 0.435332i | ||||
\(478\) | 2.91022e18 | 0.510424 | ||||||||
\(479\) | 8.34404e18i | 1.44221i | 0.692827 | + | 0.721104i | \(0.256365\pi\) | ||||
−0.692827 | + | 0.721104i | \(0.743635\pi\) | |||||||
\(480\) | −2.77232e18 | − | 6.80937e18i | −0.472232 | − | 1.15989i | ||||
\(481\) | 4.81101e18 | 0.807646 | ||||||||
\(482\) | − | 1.84606e18i | − | 0.305434i | ||||||
\(483\) | −4.97125e17 | + | 2.02396e17i | −0.0810655 | + | 0.0330045i | ||||
\(484\) | 5.04547e18 | 0.810931 | ||||||||
\(485\) | − | 1.08311e19i | − | 1.71586i | ||||||
\(486\) | −6.82812e17 | − | 1.80088e18i | −0.106622 | − | 0.281211i | ||||
\(487\) | −6.93256e18 | −1.06707 | −0.533533 | − | 0.845779i | \(-0.679136\pi\) | ||||
−0.533533 | + | 0.845779i | \(0.679136\pi\) | |||||||
\(488\) | 2.58238e18i | 0.391815i | ||||||||
\(489\) | 1.60354e18 | + | 3.93862e18i | 0.239838 | + | 0.589090i | ||||
\(490\) | −3.18917e18 | −0.470225 | ||||||||
\(491\) | − | 9.61225e18i | − | 1.39719i | −0.715518 | − | 0.698594i | \(-0.753809\pi\) | ||
0.715518 | − | 0.698594i | \(-0.246191\pi\) | |||||||
\(492\) | −3.00805e18 | + | 1.22468e18i | −0.431051 | + | 0.175495i | ||||
\(493\) | 7.14882e18 | 1.00996 | ||||||||
\(494\) | 6.84183e17i | 0.0952980i | ||||||||
\(495\) | 2.69998e18 | − | 2.63533e18i | 0.370787 | − | 0.361908i | ||||
\(496\) | 2.82506e18 | 0.382522 | ||||||||
\(497\) | − | 2.91742e17i | − | 0.0389498i | ||||||
\(498\) | 5.47477e17 | + | 1.34471e18i | 0.0720710 | + | 0.177020i | ||||
\(499\) | 9.37657e17 | 0.121714 | 0.0608569 | − | 0.998146i | \(-0.480617\pi\) | ||||
0.0608569 | + | 0.998146i | \(0.480617\pi\) | |||||||
\(500\) | 5.32151e18i | 0.681153i | ||||||||
\(501\) | 8.30435e18 | − | 3.38098e18i | 1.04819 | − | 0.426755i | ||||
\(502\) | 2.25515e17 | 0.0280704 | ||||||||
\(503\) | 2.44187e18i | 0.299741i | 0.988706 | + | 0.149870i | \(0.0478857\pi\) | ||||
−0.988706 | + | 0.149870i | \(0.952114\pi\) | |||||||
\(504\) | 2.63889e17 | + | 2.70363e17i | 0.0319454 | + | 0.0327291i | ||||
\(505\) | −1.84387e19 | −2.20136 | ||||||||
\(506\) | 9.24366e17i | 0.108840i | ||||||||
\(507\) | −4.70292e17 | − | 1.15513e18i | −0.0546150 | − | 0.134145i | ||||
\(508\) | −1.13255e19 | −1.29722 | ||||||||
\(509\) | 3.91889e18i | 0.442730i | 0.975191 | + | 0.221365i | \(0.0710512\pi\) | ||||
−0.975191 | + | 0.221365i | \(0.928949\pi\) | |||||||
\(510\) | 2.97711e18 | − | 1.21208e18i | 0.331745 | − | 0.135064i | ||||
\(511\) | 7.64359e17 | 0.0840139 | ||||||||
\(512\) | 9.31191e18i | 1.00960i | ||||||||
\(513\) | 2.53861e18 | + | 1.10600e18i | 0.271503 | + | 0.118286i | ||||
\(514\) | −6.70409e17 | −0.0707291 | ||||||||
\(515\) | 2.05029e17i | 0.0213386i | ||||||||
\(516\) | 3.22439e18 | + | 7.91973e18i | 0.331054 | + | 0.813135i | ||||
\(517\) | 3.81732e18 | 0.386656 | ||||||||
\(518\) | − | 1.80915e17i | − | 0.0180787i | ||||||
\(519\) | 1.33706e18 | − | 5.44363e17i | 0.131820 | − | 0.0536682i | ||||
\(520\) | 9.94020e18 | 0.966878 | ||||||||
\(521\) | − | 6.73712e18i | − | 0.646562i | −0.946303 | − | 0.323281i | \(-0.895214\pi\) | ||
0.946303 | − | 0.323281i | \(-0.104786\pi\) | |||||||
\(522\) | −3.03279e18 | + | 2.96018e18i | −0.287177 | + | 0.280301i | ||||
\(523\) | −3.28728e18 | −0.307132 | −0.153566 | − | 0.988138i | \(-0.549076\pi\) | ||||
−0.153566 | + | 0.988138i | \(0.549076\pi\) | |||||||
\(524\) | − | 1.51844e19i | − | 1.39984i | ||||||
\(525\) | −4.87230e17 | − | 1.19673e18i | −0.0443220 | − | 0.108864i | ||||
\(526\) | 4.45012e17 | 0.0399458 | ||||||||
\(527\) | 4.43607e18i | 0.392938i | ||||||||
\(528\) | −2.57084e18 | + | 1.04668e18i | −0.224718 | + | 0.0914903i | ||||
\(529\) | −2.41049e18 | −0.207929 | ||||||||
\(530\) | − | 3.38171e18i | − | 0.287876i | ||||||
\(531\) | −8.50263e18 | − | 8.71121e18i | −0.714318 | − | 0.731842i | ||||
\(532\) | −2.58727e17 | −0.0214516 | ||||||||
\(533\) | − | 6.69064e18i | − | 0.547491i | ||||||
\(534\) | 3.02179e17 | + | 7.42210e17i | 0.0244048 | + | 0.0599430i | ||||
\(535\) | 3.04073e19 | 2.42383 | ||||||||
\(536\) | − | 3.80820e18i | − | 0.299616i | ||||||
\(537\) | −1.18809e19 | + | 4.83713e18i | −0.922637 | + | 0.375637i | ||||
\(538\) | −4.62047e18 | −0.354169 | ||||||||
\(539\) | 4.32443e18i | 0.327196i | ||||||||
\(540\) | 7.65373e18 | − | 1.75677e19i | 0.571633 | − | 1.31208i | ||||
\(541\) | −7.23423e18 | −0.533349 | −0.266675 | − | 0.963787i | \(-0.585925\pi\) | ||||
−0.266675 | + | 0.963787i | \(0.585925\pi\) | |||||||
\(542\) | − | 1.63688e18i | − | 0.119130i | ||||||
\(543\) | 1.63571e18 | + | 4.01762e18i | 0.117519 | + | 0.288649i | ||||
\(544\) | −8.49346e18 | −0.602410 | ||||||||
\(545\) | 3.29439e19i | 2.30675i | ||||||||
\(546\) | −3.43348e17 | + | 1.39788e17i | −0.0237348 | + | 0.00966324i | ||||
\(547\) | 1.41948e19 | 0.968764 | 0.484382 | − | 0.874857i | \(-0.339045\pi\) | ||||
0.484382 | + | 0.874857i | \(0.339045\pi\) | |||||||
\(548\) | 7.01244e18i | 0.472504i | ||||||||
\(549\) | −7.33906e18 | + | 7.16333e18i | −0.488241 | + | 0.476550i | ||||
\(550\) | −2.22523e18 | −0.146163 | ||||||||
\(551\) | − | 6.09314e18i | − | 0.395166i | ||||||
\(552\) | 3.71670e18 | + | 9.12895e18i | 0.238004 | + | 0.584584i | ||||
\(553\) | 7.57472e17 | 0.0478950 | ||||||||
\(554\) | − | 6.08590e18i | − | 0.379976i | ||||||
\(555\) | −1.78429e19 | + | 7.26445e18i | −1.10006 | + | 0.447870i | ||||
\(556\) | 4.44785e18 | 0.270786 | ||||||||
\(557\) | − | 7.43862e18i | − | 0.447205i | −0.974680 | − | 0.223602i | \(-0.928218\pi\) | ||
0.974680 | − | 0.223602i | \(-0.0717817\pi\) | |||||||
\(558\) | −1.83688e18 | − | 1.88194e18i | −0.109054 | − | 0.111729i | ||||
\(559\) | −1.76154e19 | −1.03279 | ||||||||
\(560\) | 1.59469e18i | 0.0923338i | ||||||||
\(561\) | −1.64355e18 | − | 4.03688e18i | −0.0939816 | − | 0.230837i | ||||
\(562\) | 1.05731e19 | 0.597104 | ||||||||
\(563\) | − | 2.60682e19i | − | 1.45396i | −0.686658 | − | 0.726981i | \(-0.740923\pi\) | ||
0.686658 | − | 0.726981i | \(-0.259077\pi\) | |||||||
\(564\) | 1.79569e19 | − | 7.31085e18i | 0.989185 | − | 0.402730i | ||||
\(565\) | −3.19727e18 | −0.173956 | ||||||||
\(566\) | 1.10494e19i | 0.593775i | ||||||||
\(567\) | −3.63554e16 | + | 1.49994e18i | −0.00192969 | + | 0.0796144i | ||||
\(568\) | −5.35741e18 | −0.280877 | ||||||||
\(569\) | 3.01258e19i | 1.56010i | 0.625717 | + | 0.780051i | \(0.284807\pi\) | ||||
−0.625717 | + | 0.780051i | \(0.715193\pi\) | |||||||
\(570\) | −1.03309e18 | − | 2.53747e18i | −0.0528463 | − | 0.129801i | ||||
\(571\) | 1.99425e19 | 1.00769 | 0.503845 | − | 0.863794i | \(-0.331918\pi\) | ||||
0.503845 | + | 0.863794i | \(0.331918\pi\) | |||||||
\(572\) | − | 6.42011e18i | − | 0.320457i | ||||||
\(573\) | 3.45919e19 | − | 1.40835e19i | 1.70566 | − | 0.694431i | ||||
\(574\) | −2.51598e17 | −0.0122553 | ||||||||
\(575\) | − | 3.37103e19i | − | 1.62214i | ||||||
\(576\) | −7.48884e18 | + | 7.30953e18i | −0.356006 | + | 0.347482i | ||||
\(577\) | −1.29010e19 | −0.605886 | −0.302943 | − | 0.953009i | \(-0.597969\pi\) | ||||
−0.302943 | + | 0.953009i | \(0.597969\pi\) | |||||||
\(578\) | 2.76836e18i | 0.128448i | ||||||||
\(579\) | −6.00947e18 | − | 1.47604e19i | −0.275477 | − | 0.676627i | ||||
\(580\) | −4.21657e19 | −1.90969 | ||||||||
\(581\) | − | 1.13105e18i | − | 0.0506113i | ||||||
\(582\) | 6.87017e18 | − | 2.79708e18i | 0.303743 | − | 0.123664i | ||||
\(583\) | −4.58550e18 | −0.200312 | ||||||||
\(584\) | − | 1.40363e19i | − | 0.605846i | ||||||
\(585\) | 2.75734e19 | + | 2.82499e19i | 1.17598 | + | 1.20483i | ||||
\(586\) | −1.44566e18 | −0.0609234 | ||||||||
\(587\) | 8.63543e18i | 0.359598i | 0.983703 | + | 0.179799i | \(0.0575447\pi\) | ||||
−0.983703 | + | 0.179799i | \(0.942455\pi\) | |||||||
\(588\) | 8.28206e18 | + | 2.03424e19i | 0.340798 | + | 0.837067i | ||||
\(589\) | 3.78098e18 | 0.153744 | ||||||||
\(590\) | 1.20439e19i | 0.483951i | ||||||||
\(591\) | −2.72052e19 | + | 1.10761e19i | −1.08029 | + | 0.439821i | ||||
\(592\) | 1.41734e19 | 0.556187 | ||||||||
\(593\) | 2.44611e19i | 0.948620i | 0.880358 | + | 0.474310i | \(0.157302\pi\) | ||||
−0.880358 | + | 0.474310i | \(0.842698\pi\) | |||||||
\(594\) | 2.36884e18 | + | 1.03203e18i | 0.0907885 | + | 0.0395539i | ||||
\(595\) | −2.50407e18 | −0.0948480 | ||||||||
\(596\) | 2.54373e19i | 0.952243i | ||||||||
\(597\) | −1.63037e19 | − | 4.00450e19i | −0.603205 | − | 1.48159i | ||||
\(598\) | −9.67163e18 | −0.353664 | ||||||||
\(599\) | − | 4.76145e18i | − | 0.172088i | −0.996291 | − | 0.0860442i | \(-0.972577\pi\) | ||
0.996291 | − | 0.0860442i | \(-0.0274226\pi\) | |||||||
\(600\) | −2.19762e19 | + | 8.94724e18i | −0.785043 | + | 0.319617i | ||||
\(601\) | −5.34152e18 | −0.188601 | −0.0943004 | − | 0.995544i | \(-0.530061\pi\) | ||||
−0.0943004 | + | 0.995544i | \(0.530061\pi\) | |||||||
\(602\) | 6.62419e17i | 0.0231184i | ||||||||
\(603\) | 1.08228e19 | − | 1.05637e19i | 0.373353 | − | 0.364413i | ||||
\(604\) | 3.67338e19 | 1.25258 | ||||||||
\(605\) | − | 4.16211e19i | − | 1.40290i | ||||||
\(606\) | −4.76169e18 | − | 1.16957e19i | −0.158655 | − | 0.389687i | ||||
\(607\) | 2.37460e19 | 0.782115 | 0.391057 | − | 0.920366i | \(-0.372109\pi\) | ||||
0.391057 | + | 0.920366i | \(0.372109\pi\) | |||||||
\(608\) | 7.23920e18i | 0.235703i | ||||||||
\(609\) | 3.05775e18 | − | 1.24491e18i | 0.0984196 | − | 0.0400699i | ||||
\(610\) | 1.01468e19 | 0.322863 | ||||||||
\(611\) | 3.99406e19i | 1.25639i | ||||||||
\(612\) | −1.54627e19 | − | 1.58420e19i | −0.480868 | − | 0.492664i | ||||
\(613\) | −2.13066e19 | −0.655074 | −0.327537 | − | 0.944838i | \(-0.606219\pi\) | ||||
−0.327537 | + | 0.944838i | \(0.606219\pi\) | |||||||
\(614\) | − | 1.52820e19i | − | 0.464518i | ||||||
\(615\) | 1.01026e19 | + | 2.48140e19i | 0.303604 | + | 0.745712i | ||||
\(616\) | −5.06857e17 | −0.0150598 | ||||||||
\(617\) | − | 6.07266e19i | − | 1.78395i | −0.452085 | − | 0.891975i | \(-0.649320\pi\) | ||
0.452085 | − | 0.891975i | \(-0.350680\pi\) | |||||||
\(618\) | −1.30050e17 | + | 5.29476e16i | −0.00377738 | + | 0.00153790i | ||||
\(619\) | 3.06934e19 | 0.881476 | 0.440738 | − | 0.897636i | \(-0.354717\pi\) | ||||
0.440738 | + | 0.897636i | \(0.354717\pi\) | |||||||
\(620\) | − | 2.61652e19i | − | 0.742987i | ||||||
\(621\) | −1.56344e19 | + | 3.58859e19i | −0.438976 | + | 1.00759i | ||||
\(622\) | 9.98856e18 | 0.277313 | ||||||||
\(623\) | − | 6.24279e17i | − | 0.0171381i | ||||||
\(624\) | −1.09514e19 | − | 2.68987e19i | −0.297287 | − | 0.730196i | ||||
\(625\) | −1.10846e19 | −0.297551 | ||||||||
\(626\) | 1.81835e19i | 0.482678i | ||||||||
\(627\) | −3.44074e18 | + | 1.40084e18i | −0.0903191 | + | 0.0367719i | ||||
\(628\) | 3.15051e18 | 0.0817831 | ||||||||
\(629\) | 2.22558e19i | 0.571332i | ||||||||
\(630\) | 1.06232e18 | − | 1.03688e18i | 0.0269694 | − | 0.0263237i | ||||
\(631\) | 2.16168e18 | 0.0542734 | 0.0271367 | − | 0.999632i | \(-0.491361\pi\) | ||||
0.0271367 | + | 0.999632i | \(0.491361\pi\) | |||||||
\(632\) | − | 1.39098e19i | − | 0.345384i | ||||||
\(633\) | 5.44125e18 | + | 1.33648e19i | 0.133620 | + | 0.328198i | ||||
\(634\) | −1.17122e19 | −0.284454 | ||||||||
\(635\) | 9.34267e19i | 2.24417i | ||||||||
\(636\) | −2.15705e19 | + | 8.78207e18i | −0.512460 | + | 0.208640i | ||||
\(637\) | −4.52465e19 | −1.06318 | ||||||||
\(638\) | − | 5.68566e18i | − | 0.132141i | ||||||
\(639\) | −1.48611e19 | − | 1.52256e19i | −0.341621 | − | 0.350001i | ||||
\(640\) | 6.54324e19 | 1.48776 | ||||||||
\(641\) | − | 4.45341e17i | − | 0.0100158i | −0.999987 | − | 0.00500791i | \(-0.998406\pi\) | ||
0.999987 | − | 0.00500791i | \(-0.00159407\pi\) | |||||||
\(642\) | 7.85251e18 | + | 1.92873e19i | 0.174688 | + | 0.429069i | ||||
\(643\) | −4.21110e19 | −0.926656 | −0.463328 | − | 0.886187i | \(-0.653345\pi\) | ||||
−0.463328 | + | 0.886187i | \(0.653345\pi\) | |||||||
\(644\) | − | 3.65737e18i | − | 0.0796100i | ||||||
\(645\) | 6.53315e19 | − | 2.65986e19i | 1.40671 | − | 0.572719i | ||||
\(646\) | −3.16504e18 | −0.0674142 | ||||||||
\(647\) | 1.01166e19i | 0.213160i | 0.994304 | + | 0.106580i | \(0.0339900\pi\) | ||||
−0.994304 | + | 0.106580i | \(0.966010\pi\) | |||||||
\(648\) | 2.75441e19 | + | 6.67611e17i | 0.574120 | + | 0.0139155i | ||||
\(649\) | 1.63311e19 | 0.336747 | ||||||||
\(650\) | − | 2.32826e19i | − | 0.474939i | ||||||
\(651\) | 7.72508e17 | + | 1.89743e18i | 0.0155896 | + | 0.0382912i | ||||
\(652\) | −2.89766e19 | −0.578514 | ||||||||
\(653\) | − | 6.72302e19i | − | 1.32792i | −0.747768 | − | 0.663960i | \(-0.768874\pi\) | ||
0.747768 | − | 0.663960i | \(-0.231126\pi\) | |||||||
\(654\) | −2.08963e19 | + | 8.50758e18i | −0.408343 | + | 0.166250i | ||||
\(655\) | −1.25259e20 | −2.42170 | ||||||||
\(656\) | − | 1.97108e19i | − | 0.377031i | ||||||
\(657\) | 3.98909e19 | − | 3.89357e19i | 0.754946 | − | 0.736870i | ||||
\(658\) | 1.50194e18 | 0.0281237 | ||||||||
\(659\) | − | 2.11715e18i | − | 0.0392241i | −0.999808 | − | 0.0196121i | \(-0.993757\pi\) | ||
0.999808 | − | 0.0196121i | \(-0.00624312\pi\) | |||||||
\(660\) | 9.69411e18 | + | 2.38107e19i | 0.177705 | + | 0.436479i | ||||
\(661\) | 8.18053e19 | 1.48379 | 0.741893 | − | 0.670518i | \(-0.233928\pi\) | ||||
0.741893 | + | 0.670518i | \(0.233928\pi\) | |||||||
\(662\) | − | 1.07887e19i | − | 0.193626i | ||||||
\(663\) | 4.22379e19 | − | 1.71964e19i | 0.750079 | − | 0.305382i | ||||
\(664\) | −2.07700e19 | −0.364972 | ||||||||
\(665\) | 2.13429e18i | 0.0371109i | ||||||||
\(666\) | −9.21566e18 | − | 9.44173e18i | −0.158565 | − | 0.162455i | ||||
\(667\) | 8.61327e19 | 1.46652 | ||||||||
\(668\) | 6.10954e19i | 1.02937i | ||||||||
\(669\) | 1.13224e19 | + | 2.78101e19i | 0.188780 | + | 0.463681i | ||||
\(670\) | −1.49633e19 | −0.246890 | ||||||||
\(671\) | − | 1.37587e19i | − | 0.224657i | ||||||
\(672\) | −3.63289e18 | + | 1.47907e18i | −0.0587040 | + | 0.0239004i | ||||
\(673\) | −5.70739e19 | −0.912709 | −0.456354 | − | 0.889798i | \(-0.650845\pi\) | ||||
−0.456354 | + | 0.889798i | \(0.650845\pi\) | |||||||
\(674\) | 1.41026e19i | 0.223192i | ||||||||
\(675\) | −8.63883e19 | − | 3.76369e19i | −1.35310 | − | 0.589504i | ||||
\(676\) | 8.49834e18 | 0.131737 | ||||||||
\(677\) | 5.97269e19i | 0.916325i | 0.888868 | + | 0.458163i | \(0.151492\pi\) | ||||
−0.888868 | + | 0.458163i | \(0.848508\pi\) | |||||||
\(678\) | −8.25677e17 | − | 2.02803e18i | −0.0125373 | − | 0.0307940i | ||||
\(679\) | −5.77856e18 | −0.0868423 | ||||||||
\(680\) | 4.59835e19i | 0.683974i | ||||||||
\(681\) | −8.17378e19 | + | 3.32782e19i | −1.20335 | + | 0.489925i | ||||
\(682\) | 3.52813e18 | 0.0514107 | ||||||||
\(683\) | − | 6.68549e19i | − | 0.964248i | −0.876103 | − | 0.482124i | \(-0.839866\pi\) | ||
0.876103 | − | 0.482124i | \(-0.160134\pi\) | |||||||
\(684\) | −1.35026e19 | + | 1.31793e19i | −0.192763 | + | 0.188148i | ||||
\(685\) | 5.78471e19 | 0.817424 | ||||||||
\(686\) | 3.41380e18i | 0.0477495i | ||||||||
\(687\) | 3.82626e19 | + | 9.39804e19i | 0.529757 | + | 1.30119i | ||||
\(688\) | −5.18955e19 | −0.711231 | ||||||||
\(689\) | − | 4.79781e19i | − | 0.650891i | ||||||
\(690\) | 3.58698e19 | − | 1.46038e19i | 0.481709 | − | 0.196120i | ||||
\(691\) | 7.46966e19 | 0.993012 | 0.496506 | − | 0.868033i | \(-0.334616\pi\) | ||||
0.496506 | + | 0.868033i | \(0.334616\pi\) | |||||||
\(692\) | 9.83682e18i | 0.129453i | ||||||||
\(693\) | −1.40599e18 | − | 1.44048e18i | −0.0183167 | − | 0.0187661i | ||||
\(694\) | 7.56489e18 | 0.0975632 | ||||||||
\(695\) | − | 3.66912e19i | − | 0.468456i | ||||||
\(696\) | −2.28610e19 | − | 5.61510e19i | −0.288955 | − | 0.709729i | ||||
\(697\) | 3.09510e19 | 0.387298 | ||||||||
\(698\) | 3.21539e18i | 0.0398333i | ||||||||
\(699\) | −4.03913e19 | + | 1.64447e19i | −0.495390 | + | 0.201690i | ||||
\(700\) | 8.80441e18 | 0.106909 | ||||||||
\(701\) | − | 3.02354e18i | − | 0.0363488i | −0.999835 | − | 0.0181744i | \(-0.994215\pi\) | ||
0.999835 | − | 0.0181744i | \(-0.00578541\pi\) | |||||||
\(702\) | −1.07982e19 | + | 2.47852e19i | −0.128526 | + | 0.295007i | ||||
\(703\) | 1.89692e19 | 0.223544 | ||||||||
\(704\) | − | 1.40395e19i | − | 0.163811i | ||||||
\(705\) | −6.03087e19 | − | 1.48130e20i | −0.696717 | − | 1.71127i | ||||
\(706\) | 2.88005e19 | 0.329433 | ||||||||
\(707\) | 9.83731e18i | 0.111414i | ||||||||
\(708\) | 7.68227e19 | − | 3.12771e19i | 0.861503 | − | 0.350747i | ||||
\(709\) | 1.23202e19 | 0.136803 | 0.0684013 | − | 0.997658i | \(-0.478210\pi\) | ||||
0.0684013 | + | 0.997658i | \(0.478210\pi\) | |||||||
\(710\) | 2.10505e19i | 0.231448i | ||||||||
\(711\) | 3.95314e19 | − | 3.85849e19i | 0.430383 | − | 0.420078i | ||||
\(712\) | −1.14639e19 | −0.123587 | ||||||||
\(713\) | 5.34480e19i | 0.570565i | ||||||||
\(714\) | −6.46663e17 | − | 1.58833e18i | −0.00683582 | − | 0.0167901i | ||||
\(715\) | −5.29608e19 | −0.554386 | ||||||||
\(716\) | − | 8.74086e19i | − | 0.906072i | ||||||
\(717\) | −1.53131e20 | + | 6.23446e19i | −1.57191 | + | 0.639977i | ||||
\(718\) | −1.86496e18 | −0.0189582 | ||||||||
\(719\) | 8.17486e18i | 0.0822958i | 0.999153 | + | 0.0411479i | \(0.0131015\pi\) | ||||
−0.999153 | + | 0.0411479i | \(0.986899\pi\) | |||||||
\(720\) | 8.12320e19 | + | 8.32248e19i | 0.809841 | + | 0.829708i | ||||
\(721\) | 1.09386e17 | 0.00107998 | ||||||||
\(722\) | − | 2.80604e19i | − | 0.274368i | ||||||
\(723\) | 3.95475e19 | + | 9.71365e19i | 0.382958 | + | 0.940620i | ||||
\(724\) | −2.95578e19 | −0.283467 | ||||||||
\(725\) | 2.07348e20i | 1.96940i | ||||||||
\(726\) | 2.64002e19 | − | 1.07484e19i | 0.248343 | − | 0.101109i | ||||
\(727\) | −3.07501e19 | −0.286487 | −0.143244 | − | 0.989687i | \(-0.545753\pi\) | ||||
−0.143244 | + | 0.989687i | \(0.545753\pi\) | |||||||
\(728\) | − | 5.30324e18i | − | 0.0489352i | ||||||
\(729\) | 7.45080e19 | + | 8.01316e19i | 0.680942 | + | 0.732337i | ||||
\(730\) | −5.51519e19 | −0.499230 | ||||||||
\(731\) | − | 8.14892e19i | − | 0.730598i | ||||||
\(732\) | −2.63505e19 | − | 6.47219e19i | −0.233997 | − | 0.574743i | ||||
\(733\) | −8.18832e19 | −0.720223 | −0.360112 | − | 0.932909i | \(-0.617261\pi\) | ||||
−0.360112 | + | 0.932909i | \(0.617261\pi\) | |||||||
\(734\) | − | 1.84799e19i | − | 0.161000i | ||||||
\(735\) | 1.67808e20 | − | 6.83204e19i | 1.44811 | − | 0.589575i | ||||
\(736\) | −1.02334e20 | −0.874729 | ||||||||
\(737\) | 2.02898e19i | 0.171793i | ||||||||
\(738\) | −1.31305e19 | + | 1.28161e19i | −0.110126 | + | 0.107489i | ||||
\(739\) | −8.38576e19 | −0.696677 | −0.348338 | − | 0.937369i | \(-0.613254\pi\) | ||||
−0.348338 | + | 0.937369i | \(0.613254\pi\) | |||||||
\(740\) | − | 1.31271e20i | − | 1.08031i | ||||||
\(741\) | −1.46570e19 | − | 3.60005e19i | −0.119486 | − | 0.293482i | ||||
\(742\) | −1.80419e18 | −0.0145698 | ||||||||
\(743\) | 9.95254e19i | 0.796182i | 0.917346 | + | 0.398091i | \(0.130327\pi\) | ||||
−0.917346 | + | 0.398091i | \(0.869673\pi\) | |||||||
\(744\) | 3.48434e19 | − | 1.41859e19i | 0.276128 | − | 0.112421i | ||||
\(745\) | 2.09838e20 | 1.64736 | ||||||||
\(746\) | 2.38689e19i | 0.185635i | ||||||||
\(747\) | −5.76145e19 | − | 5.90278e19i | −0.443902 | − | 0.454792i | ||||
\(748\) | 2.96995e19 | 0.226693 | ||||||||
\(749\) | − | 1.62227e19i | − | 0.122674i | ||||||
\(750\) | 1.13365e19 | + | 2.78446e19i | 0.0849276 | + | 0.208599i | ||||
\(751\) | 5.86701e19 | 0.435449 | 0.217725 | − | 0.976010i | \(-0.430137\pi\) | ||||
0.217725 | + | 0.976010i | \(0.430137\pi\) | |||||||
\(752\) | 1.17666e20i | 0.865218i | ||||||||
\(753\) | −1.18662e19 | + | 4.83112e18i | −0.0864462 | + | 0.0351952i | ||||
\(754\) | 5.94890e19 | 0.429376 | ||||||||
\(755\) | − | 3.03024e20i | − | 2.16695i | ||||||
\(756\) | −9.37262e18 | − | 4.08337e18i | −0.0664061 | − | 0.0289312i | ||||
\(757\) | −1.57745e20 | −1.10735 | −0.553676 | − | 0.832732i | \(-0.686775\pi\) | ||||
−0.553676 | + | 0.832732i | \(0.686775\pi\) | |||||||
\(758\) | − | 4.61887e19i | − | 0.321256i | ||||||
\(759\) | −1.98023e19 | − | 4.86384e19i | −0.136466 | − | 0.335187i | ||||
\(760\) | 3.91930e19 | 0.267617 | ||||||||
\(761\) | − | 2.25035e20i | − | 1.52250i | −0.648459 | − | 0.761249i | \(-0.724586\pi\) | ||
0.648459 | − | 0.761249i | \(-0.275414\pi\) | |||||||
\(762\) | −5.92605e19 | + | 2.41269e19i | −0.397265 | + | 0.161740i | ||||
\(763\) | 1.75761e19 | 0.116748 | ||||||||
\(764\) | 2.54494e20i | 1.67503i | ||||||||
\(765\) | −1.30684e20 | + | 1.27555e20i | −0.852301 | + | 0.831893i | ||||
\(766\) | 6.02044e19 | 0.389069 | ||||||||
\(767\) | 1.70873e20i | 1.09422i | ||||||||
\(768\) | −1.26645e19 | − | 3.11066e19i | −0.0803638 | − | 0.197389i | ||||
\(769\) | 1.08395e20 | 0.681591 | 0.340795 | − | 0.940137i | \(-0.389304\pi\) | ||||
0.340795 | + | 0.940137i | \(0.389304\pi\) | |||||||
\(770\) | 1.99156e18i | 0.0124096i | ||||||||
\(771\) | 3.52757e19 | − | 1.43619e19i | 0.217819 | − | 0.0886813i | ||||
\(772\) | 1.08593e20 | 0.664479 | ||||||||
\(773\) | 2.03020e20i | 1.23107i | 0.788109 | + | 0.615536i | \(0.211060\pi\) | ||||
−0.788109 | + | 0.615536i | \(0.788940\pi\) | |||||||
\(774\) | 3.37430e19 | + | 3.45707e19i | 0.202767 | + | 0.207741i | ||||
\(775\) | −1.28666e20 | −0.766216 | ||||||||
\(776\) | 1.06114e20i | 0.626242i | ||||||||
\(777\) | 3.87568e18 | + | 9.51944e18i | 0.0226674 | + | 0.0556755i | ||||
\(778\) | −5.11270e19 | −0.296342 | ||||||||
\(779\) | − | 2.63804e19i | − | 0.151537i | ||||||
\(780\) | −2.49131e20 | + | 1.01429e20i | −1.41829 | + | 0.577433i | ||||
\(781\) | 2.85439e19 | 0.161048 | ||||||||
\(782\) | − | 4.47411e19i | − | 0.250184i | ||||||
\(783\) | 9.61653e19 | − | 2.20729e20i | 0.532950 | − | 1.22329i | ||||
\(784\) | −1.33297e20 | −0.732164 | ||||||||
\(785\) | − | 2.59892e19i | − | 0.141483i | ||||||
\(786\) | −3.23474e19 | − | 7.94516e19i | −0.174535 | − | 0.428691i | ||||
\(787\) | 1.68006e20 | 0.898464 | 0.449232 | − | 0.893415i | \(-0.351698\pi\) | ||||
0.449232 | + | 0.893415i | \(0.351698\pi\) | |||||||
\(788\) | − | 2.00149e20i | − | 1.06089i | ||||||
\(789\) | −2.34157e19 | + | 9.53332e18i | −0.123018 | + | 0.0500847i | ||||
\(790\) | −5.46549e19 | −0.284603 | ||||||||
\(791\) | 1.70579e18i | 0.00880420i | ||||||||
\(792\) | −2.64522e19 | + | 2.58188e19i | −0.135327 | + | 0.132087i | ||||
\(793\) | 1.43958e20 | 0.729999 | ||||||||
\(794\) | 4.87590e19i | 0.245082i | ||||||||
\(795\) | 7.24451e19 | + | 1.77939e20i | 0.360943 | + | 0.886548i | ||||
\(796\) | 2.94613e20 | 1.45499 | ||||||||
\(797\) | − | 1.61596e20i | − | 0.791084i | −0.918448 | − | 0.395542i | \(-0.870557\pi\) | ||
0.918448 | − | 0.395542i | \(-0.129443\pi\) | |||||||
\(798\) | −1.35378e18 | + | 5.51168e17i | −0.00656942 | + | 0.00267463i | ||||
\(799\) | −1.84766e20 | −0.888778 | ||||||||
\(800\) | − | 2.46348e20i | − | 1.17468i | ||||||
\(801\) | −3.18002e19 | − | 3.25803e19i | −0.150315 | − | 0.154002i | ||||
\(802\) | −7.59257e19 | −0.355769 | ||||||||
\(803\) | 7.47845e19i | 0.347378i | ||||||||
\(804\) | 3.88587e19 | + | 9.54445e19i | 0.178935 | + | 0.439500i | ||||
\(805\) | −3.01704e19 | −0.137724 | ||||||||
\(806\) | 3.69148e19i | 0.167053i | ||||||||
\(807\) | 2.43121e20 | − | 9.89825e19i | 1.09070 | − | 0.444062i | ||||
\(808\) | 1.80647e20 | 0.803437 | ||||||||
\(809\) | − | 1.11551e20i | − | 0.491852i | −0.969289 | − | 0.245926i | \(-0.920908\pi\) | ||
0.969289 | − | 0.245926i | \(-0.0790921\pi\) | |||||||
\(810\) | 2.62320e18 | − | 1.08227e20i | 0.0114666 | − | 0.473087i | ||||
\(811\) | −4.47129e20 | −1.93770 | −0.968850 | − | 0.247647i | \(-0.920343\pi\) | ||||
−0.968850 | + | 0.247647i | \(0.920343\pi\) | |||||||
\(812\) | 2.24960e19i | 0.0966526i | ||||||||
\(813\) | 3.50663e19 | + | 8.61297e19i | 0.149367 | + | 0.366876i | ||||
\(814\) | 1.77007e19 | 0.0747513 | ||||||||
\(815\) | 2.39034e20i | 1.00082i | ||||||||
\(816\) | 1.24434e20 | − | 5.06612e19i | 0.516544 | − | 0.210302i | ||||
\(817\) | −6.94555e19 | −0.285859 | ||||||||
\(818\) | 6.85956e19i | 0.279913i | ||||||||
\(819\) | 1.50717e19 | − | 1.47108e19i | 0.0609782 | − | 0.0595182i | ||||
\(820\) | −1.82557e20 | −0.732323 | ||||||||
\(821\) | 2.52577e20i | 1.00460i | 0.864694 | + | 0.502299i | \(0.167512\pi\) | ||||
−0.864694 | + | 0.502299i | \(0.832488\pi\) | |||||||
\(822\) | 1.49387e19 | + | 3.66923e19i | 0.0589128 | + | 0.144701i | ||||
\(823\) | −4.42630e20 | −1.73078 | −0.865390 | − | 0.501099i | \(-0.832929\pi\) | ||||
−0.865390 | + | 0.501099i | \(0.832929\pi\) | |||||||
\(824\) | − | 2.00871e18i | − | 0.00778800i | ||||||
\(825\) | 1.17088e20 | − | 4.76703e19i | 0.450126 | − | 0.183261i | ||||
\(826\) | 6.42557e18 | 0.0244935 | ||||||||
\(827\) | 2.72278e20i | 1.02914i | 0.857448 | + | 0.514570i | \(0.172049\pi\) | ||||
−0.857448 | + | 0.514570i | \(0.827951\pi\) | |||||||
\(828\) | −1.86303e20 | − | 1.90873e20i | −0.698244 | − | 0.715373i | ||||
\(829\) | 1.07852e20 | 0.400816 | 0.200408 | − | 0.979713i | \(-0.435773\pi\) | ||||
0.200408 | + | 0.979713i | \(0.435773\pi\) | |||||||
\(830\) | 8.16101e19i | 0.300744i | ||||||||
\(831\) | 1.30376e20 | + | 3.20229e20i | 0.476421 | + | 1.17018i | ||||
\(832\) | 1.46896e20 | 0.532286 | ||||||||
\(833\) | − | 2.09311e20i | − | 0.752101i | ||||||
\(834\) | 2.32732e19 | − | 9.47529e18i | 0.0829265 | − | 0.0337622i | ||||
\(835\) | 5.03989e20 | 1.78080 | ||||||||
\(836\) | − | 2.53137e19i | − | 0.0886975i | ||||||
\(837\) | 1.36969e20 | + | 5.96736e19i | 0.475933 | + | 0.207350i | ||||
\(838\) | 9.00179e19 | 0.310185 | ||||||||
\(839\) | − | 4.86182e20i | − | 1.66137i | −0.556746 | − | 0.830683i | \(-0.687950\pi\) | ||
0.556746 | − | 0.830683i | \(-0.312050\pi\) | |||||||
\(840\) | 8.00768e18 | + | 1.96684e19i | 0.0271364 | + | 0.0666523i | ||||
\(841\) | −2.32233e20 | −0.780464 | ||||||||
\(842\) | − | 8.26098e19i | − | 0.275326i | ||||||
\(843\) | −5.56340e20 | + | 2.26505e20i | −1.83885 | + | 0.748659i | ||||
\(844\) | −9.83252e19 | −0.322306 | ||||||||
\(845\) | − | 7.01045e19i | − | 0.227902i | ||||||
\(846\) | 7.83843e19 | − | 7.65075e19i | 0.252718 | − | 0.246667i | ||||
\(847\) | −2.22054e19 | −0.0710028 | ||||||||
\(848\) | − | 1.41345e20i | − | 0.448238i | ||||||
\(849\) | −2.36706e20 | − | 5.81397e20i | −0.744485 | − | 1.82860i | ||||
\(850\) | 1.07706e20 | 0.335974 | ||||||||
\(851\) | 2.68149e20i | 0.829602i | ||||||||
\(852\) | 1.34272e20 | − | 5.46668e19i | 0.412011 | − | 0.167744i | ||||
\(853\) | 4.29971e20 | 1.30857 | 0.654284 | − | 0.756249i | \(-0.272970\pi\) | ||||
0.654284 | + | 0.756249i | \(0.272970\pi\) | |||||||
\(854\) | − | 5.41344e18i | − | 0.0163406i | ||||||
\(855\) | 1.08719e20 | + | 1.11386e20i | 0.325493 | + | 0.333478i | ||||
\(856\) | −2.97906e20 | −0.884631 | ||||||||
\(857\) | − | 4.88235e20i | − | 1.43801i | −0.695003 | − | 0.719007i | \(-0.744597\pi\) | ||
0.695003 | − | 0.719007i | \(-0.255403\pi\) | |||||||
\(858\) | −1.36768e19 | − | 3.35930e19i | −0.0399553 | − | 0.0981380i | ||||
\(859\) | 4.60333e20 | 1.33389 | 0.666945 | − | 0.745107i | \(-0.267601\pi\) | ||||
0.666945 | + | 0.745107i | \(0.267601\pi\) | |||||||
\(860\) | 4.80646e20i | 1.38145i | ||||||||
\(861\) | 1.32386e19 | − | 5.38988e18i | 0.0377416 | − | 0.0153659i | ||||
\(862\) | −5.67465e19 | −0.160468 | ||||||||
\(863\) | 2.76671e20i | 0.776047i | 0.921650 | + | 0.388023i | \(0.126842\pi\) | ||||
−0.921650 | + | 0.388023i | \(0.873158\pi\) | |||||||
\(864\) | −1.14253e20 | + | 2.62247e20i | −0.317887 | + | 0.729649i | ||||
\(865\) | 8.11459e19 | 0.223952 | ||||||||
\(866\) | 1.59618e20i | 0.436975i | ||||||||
\(867\) | −5.93056e19 | − | 1.45666e20i | −0.161050 | − | 0.395572i | ||||
\(868\) | −1.39595e19 | −0.0376037 | ||||||||
\(869\) | 7.41106e19i | 0.198035i | ||||||||
\(870\) | −2.20631e20 | + | 8.98261e19i | −0.584832 | + | 0.238105i | ||||
\(871\) | −2.12292e20 | −0.558222 | ||||||||
\(872\) | − | 3.22757e20i | − | 0.841901i | ||||||
\(873\) | −3.01575e20 | + | 2.94354e20i | −0.780362 | + | 0.761677i | ||||
\(874\) | −3.81340e19 | −0.0978887 | ||||||||
\(875\) | − | 2.34203e19i | − | 0.0596398i | ||||||
\(876\) | 1.43226e20 | + | 3.51791e20i | 0.361820 | + | 0.888701i | ||||
\(877\) | −2.56763e20 | −0.643480 | −0.321740 | − | 0.946828i | \(-0.604268\pi\) | ||||
−0.321740 | + | 0.946828i | \(0.604268\pi\) | |||||||
\(878\) | − | 2.02678e20i | − | 0.503901i | ||||||
\(879\) | 7.60682e19 | − | 3.09699e19i | 0.187621 | − | 0.0763867i | ||||
\(880\) | −1.56024e20 | −0.381779 | ||||||||
\(881\) | 3.46483e20i | 0.841106i | 0.907268 | + | 0.420553i | \(0.138164\pi\) | ||||
−0.907268 | + | 0.420553i | \(0.861836\pi\) | |||||||
\(882\) | 8.66711e19 | + | 8.87973e19i | 0.208735 | + | 0.213855i | ||||
\(883\) | 8.21926e20 | 1.96385 | 0.981924 | − | 0.189278i | \(-0.0606147\pi\) | ||||
0.981924 | + | 0.189278i | \(0.0606147\pi\) | |||||||
\(884\) | 3.10746e20i | 0.736612i | ||||||||
\(885\) | −2.58011e20 | − | 6.33726e20i | −0.606786 | − | 1.49039i | ||||
\(886\) | 7.82912e19 | 0.182674 | ||||||||
\(887\) | − | 3.45271e20i | − | 0.799271i | −0.916674 | − | 0.399636i | \(-0.869137\pi\) | ||
0.916674 | − | 0.399636i | \(-0.130863\pi\) | |||||||
\(888\) | 1.74810e20 | − | 7.11710e19i | 0.401491 | − | 0.163460i | ||||
\(889\) | 4.98445e19 | 0.113581 | ||||||||
\(890\) | 4.50445e19i | 0.101838i | ||||||||
\(891\) | −1.46753e20 | − | 3.55699e18i | −0.329187 | − | 0.00797882i | ||||
\(892\) | −2.04600e20 | −0.455356 | ||||||||
\(893\) | 1.57481e20i | 0.347750i | ||||||||
\(894\) | 5.41894e19 | + | 1.33100e20i | 0.118728 | + | 0.291618i | ||||
\(895\) | −7.21051e20 | −1.56749 | ||||||||
\(896\) | − | 3.49091e19i | − | 0.0752978i | ||||||
\(897\) | 5.08904e20 | − | 2.07192e20i | 1.08915 | − | 0.443430i | ||||
\(898\) | −1.13605e20 | −0.241248 | ||||||||
\(899\) | − | 3.28752e20i | − | 0.692709i | ||||||
\(900\) | 4.59490e20 | − | 4.48488e20i | 0.960680 | − | 0.937677i | ||||
\(901\) | 2.21947e20 | 0.460443 | ||||||||
\(902\) | − | 2.46162e19i | − | 0.0506728i | ||||||
\(903\) | −1.41907e19 | − | 3.48553e19i | −0.0289862 | − | 0.0711958i | ||||
\(904\) | 3.13242e19 | 0.0634894 | ||||||||
\(905\) | 2.43828e20i | 0.490393i | ||||||||
\(906\) | 1.92208e20 | − | 7.82543e19i | 0.383596 | − | 0.156175i | ||||
\(907\) | −3.86876e20 | −0.766162 | −0.383081 | − | 0.923715i | \(-0.625137\pi\) | ||||
−0.383081 | + | 0.923715i | \(0.625137\pi\) | |||||||
\(908\) | − | 6.01348e20i | − | 1.18175i | ||||||
\(909\) | 5.01103e20 | + | 5.13396e20i | 0.977192 | + | 1.00116i | ||||
\(910\) | −2.08377e19 | −0.0403236 | ||||||||
\(911\) | − | 1.87671e20i | − | 0.360387i | −0.983631 | − | 0.180193i | \(-0.942328\pi\) | ||
0.983631 | − | 0.180193i | \(-0.0576724\pi\) | |||||||
\(912\) | −4.31799e19 | − | 1.06058e20i | −0.0822844 | − | 0.202107i | ||||
\(913\) | 1.10661e20 | 0.209266 | ||||||||
\(914\) | − | 8.94341e19i | − | 0.167834i | ||||||
\(915\) | −5.33904e20 | + | 2.17370e20i | −0.994296 | + | 0.404811i | ||||
\(916\) | −6.91417e20 | −1.27783 | ||||||||
\(917\) | 6.68274e19i | 0.122566i | ||||||||
\(918\) | −1.14656e20 | − | 4.99525e19i | −0.208689 | − | 0.0909197i | ||||
\(919\) | 4.07867e20 | 0.736733 | 0.368366 | − | 0.929681i | \(-0.379917\pi\) | ||||
0.368366 | + | 0.929681i | \(0.379917\pi\) | |||||||
\(920\) | 5.54033e20i | 0.993164i | ||||||||
\(921\) | 3.27381e20 | + | 8.04112e20i | 0.582420 | + | 1.43054i | ||||
\(922\) | 1.17485e20 | 0.207427 | ||||||||
\(923\) | 2.98655e20i | 0.523308i | ||||||||
\(924\) | 1.27033e19 | − | 5.17195e18i | 0.0220909 | − | 0.00899394i | ||||
\(925\) | −6.45518e20 | −1.11408 | ||||||||
\(926\) | 3.55337e19i | 0.0608644i | ||||||||
\(927\) | 5.70871e18 | − | 5.57202e18i | 0.00970464 | − | 0.00947227i | ||||
\(928\) | 6.29441e20 | 1.06199 | ||||||||
\(929\) | 5.28931e20i | 0.885705i | 0.896594 | + | 0.442853i | \(0.146033\pi\) | ||||
−0.896594 | + | 0.442853i | \(0.853967\pi\) | |||||||
\(930\) | −5.57399e19 | − | 1.36908e20i | −0.0926372 | − | 0.227535i | ||||
\(931\) | −1.78401e20 | −0.294273 | ||||||||
\(932\) | − | 2.97160e20i | − | 0.486496i | ||||||
\(933\) | −5.25580e20 | + | 2.13981e20i | −0.854018 | + | 0.347699i | ||||
\(934\) | −2.14811e20 | −0.346440 | ||||||||
\(935\) | − | 2.44997e20i | − | 0.392175i | ||||||
\(936\) | −2.70142e20 | − | 2.76769e20i | −0.429201 | − | 0.439730i | ||||
\(937\) | 4.76361e19 | 0.0751207 | 0.0375603 | − | 0.999294i | \(-0.488041\pi\) | ||||
0.0375603 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(938\) | 7.98313e18i | 0.0124955i | ||||||||
\(939\) | −3.89539e20 | − | 9.56784e20i | −0.605190 | − | 1.48646i | ||||
\(940\) | 1.08980e21 | 1.68055 | ||||||||
\(941\) | − | 4.29127e20i | − | 0.656839i | −0.944532 | − | 0.328419i | \(-0.893484\pi\) | ||
0.944532 | − | 0.328419i | \(-0.106516\pi\) | |||||||
\(942\) | 1.64849e19 | − | 6.71156e18i | 0.0250456 | − | 0.0101969i | ||||
\(943\) | 3.72913e20 | 0.562375 | ||||||||
\(944\) | 5.03395e20i | 0.753538i | ||||||||
\(945\) | −3.36846e19 | + | 7.73166e19i | −0.0500505 | + | 0.114882i | ||||
\(946\) | −6.48107e19 | −0.0955891 | ||||||||
\(947\) | 3.75227e20i | 0.549343i | 0.961538 | + | 0.274672i | \(0.0885691\pi\) | ||||
−0.961538 | + | 0.274672i | \(0.911431\pi\) | |||||||
\(948\) | 1.41935e20 | + | 3.48621e20i | 0.206268 | + | 0.506635i | ||||
\(949\) | −7.82469e20 | −1.12877 | ||||||||
\(950\) | − | 9.18004e19i | − | 0.131456i | ||||||
\(951\) | 6.16273e20 | − | 2.50906e20i | 0.876011 | − | 0.356654i | ||||
\(952\) | 2.45328e19 | 0.0346170 | ||||||||
\(953\) | − | 2.80481e20i | − | 0.392874i | −0.980516 | − | 0.196437i | \(-0.937063\pi\) | ||
0.980516 | − | 0.196437i | \(-0.0629372\pi\) | |||||||
\(954\) | −9.41582e19 | + | 9.19036e19i | −0.130924 | + | 0.127789i | ||||
\(955\) | 2.09937e21 | 2.89778 | ||||||||
\(956\) | − | 1.12659e21i | − | 1.54369i | ||||||
\(957\) | 1.21802e20 | + | 2.99169e20i | 0.165680 | + | 0.406942i | ||||
\(958\) | −3.21207e20 | −0.433737 | ||||||||
\(959\) | − | 3.08622e19i | − | 0.0413711i | ||||||
\(960\) | −5.44801e20 | + | 2.21807e20i | −0.725002 | + | 0.295172i | ||||
\(961\) | −5.52943e20 | −0.730494 | ||||||||
\(962\) | 1.85202e20i | 0.242896i | ||||||||
\(963\) | −8.26370e20 | − | 8.46642e20i | −1.07595 | − | 1.10234i | ||||
\(964\) | −7.14637e20 | −0.923732 | ||||||||
\(965\) | − | 8.95806e20i | − | 1.14954i | ||||||
\(966\) | −7.79133e18 | − | 1.91370e19i | −0.00992594 | − | 0.0243801i | ||||
\(967\) | 5.81177e19 | 0.0735060 | 0.0367530 | − | 0.999324i | \(-0.488299\pi\) | ||||
0.0367530 | + | 0.999324i | \(0.488299\pi\) | |||||||
\(968\) | 4.07769e20i | 0.512020i | ||||||||
\(969\) | 1.66539e20 | − | 6.78034e19i | 0.207610 | − | 0.0845250i | ||||
\(970\) | 4.16949e20 | 0.516037 | ||||||||
\(971\) | 5.64465e20i | 0.693589i | 0.937941 | + | 0.346795i | \(0.112730\pi\) | ||||
−0.937941 | + | 0.346795i | \(0.887270\pi\) | |||||||
\(972\) | −6.97147e20 | + | 2.64326e20i | −0.850473 | + | 0.322460i | ||||
\(973\) | −1.95753e19 | −0.0237093 | ||||||||
\(974\) | − | 2.66872e20i | − | 0.320915i | ||||||
\(975\) | 4.98774e20 | + | 1.22509e21i | 0.595486 | + | 1.46263i | ||||
\(976\) | 4.24102e20 | 0.502715 | ||||||||
\(977\) | 1.62939e21i | 1.91762i | 0.284052 | + | 0.958809i | \(0.408321\pi\) | ||||
−0.284052 | + | 0.958809i | \(0.591679\pi\) | |||||||
\(978\) | −1.51619e20 | + | 6.17290e19i | −0.177166 | + | 0.0721303i | ||||
\(979\) | 6.10791e19 | 0.0708621 | ||||||||
\(980\) | 1.23457e21i | 1.42211i | ||||||||
\(981\) | 9.17270e20 | − | 8.95307e20i | 1.04909 | − | 1.02397i | ||||
\(982\) | 3.70028e20 | 0.420198 | ||||||||
\(983\) | − | 1.91394e20i | − | 0.215801i | −0.994162 | − | 0.107900i | \(-0.965587\pi\) | ||
0.994162 | − | 0.107900i | \(-0.0344128\pi\) | |||||||
\(984\) | −9.89770e19 | − | 2.43107e20i | −0.110807 | − | 0.272165i | ||||
\(985\) | −1.65107e21 | −1.83532 | ||||||||
\(986\) | 2.75197e20i | 0.303742i | ||||||||
\(987\) | −7.90295e19 | + | 3.21755e19i | −0.0866102 | + | 0.0352619i | ||||
\(988\) | 2.64857e20 | 0.288212 | ||||||||
\(989\) | − | 9.81825e20i | − | 1.06086i | ||||||
\(990\) | 1.01448e20 | + | 1.03937e20i | 0.108842 | + | 0.111512i | ||||
\(991\) | −7.98378e20 | −0.850536 | −0.425268 | − | 0.905067i | \(-0.639820\pi\) | ||||
−0.425268 | + | 0.905067i | \(0.639820\pi\) | |||||||
\(992\) | 3.90588e20i | 0.413178i | ||||||||
\(993\) | 2.31122e20 | + | 5.67682e20i | 0.242771 | + | 0.596294i | ||||
\(994\) | 1.12307e19 | 0.0117140 | ||||||||
\(995\) | − | 2.43032e21i | − | 2.51711i | ||||||
\(996\) | 5.20556e20 | − | 2.11936e20i | 0.535368 | − | 0.217966i | ||||
\(997\) | −5.86353e19 | −0.0598816 | −0.0299408 | − | 0.999552i | \(-0.509532\pi\) | ||||
−0.0299408 | + | 0.999552i | \(0.509532\pi\) | |||||||
\(998\) | 3.60955e19i | 0.0366049i | ||||||||
\(999\) | 6.87178e20 | + | 2.99383e20i | 0.692007 | + | 0.301487i |
(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 | 3.15.b.a.2.3 | yes | 4 | |
3.2 | odd | 2 | inner | 3.15.b.a.2.2 | ✓ | 4 | |
4.3 | odd | 2 | 48.15.e.b.17.4 | 4 | |||
5.2 | odd | 4 | 75.15.d.b.74.4 | 8 | |||
5.3 | odd | 4 | 75.15.d.b.74.5 | 8 | |||
5.4 | even | 2 | 75.15.c.d.26.2 | 4 | |||
12.11 | even | 2 | 48.15.e.b.17.3 | 4 | |||
15.2 | even | 4 | 75.15.d.b.74.6 | 8 | |||
15.8 | even | 4 | 75.15.d.b.74.3 | 8 | |||
15.14 | odd | 2 | 75.15.c.d.26.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.15.b.a.2.2 | ✓ | 4 | 3.2 | odd | 2 | inner | |
3.15.b.a.2.3 | yes | 4 | 1.1 | even | 1 | trivial | |
48.15.e.b.17.3 | 4 | 12.11 | even | 2 | |||
48.15.e.b.17.4 | 4 | 4.3 | odd | 2 | |||
75.15.c.d.26.2 | 4 | 5.4 | even | 2 | |||
75.15.c.d.26.3 | 4 | 15.14 | odd | 2 | |||
75.15.d.b.74.3 | 8 | 15.8 | even | 4 | |||
75.15.d.b.74.4 | 8 | 5.2 | odd | 4 | |||
75.15.d.b.74.5 | 8 | 5.3 | odd | 4 | |||
75.15.d.b.74.6 | 8 | 15.2 | even | 4 |