Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,37,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, 37, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.2");
S:= CuspForms(chi, 37);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
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: | \(24.6273775978\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} + 1732091138 x^{8} + \cdots + 87\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{44}\cdot 3^{71}\cdot 5^{4}\cdot 7^{2}\cdot 13 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2.2 | ||
Root | \(-23576.4i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.2 |
Dual form | 3.37.b.b.2.9 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 424376.i | − | 1.61886i | −0.587213 | − | 0.809432i | \(-0.699775\pi\) | ||
0.587213 | − | 0.809432i | \(-0.300225\pi\) | |||||||
\(3\) | 3.83451e8 | − | 5.53148e7i | 0.989755 | − | 0.142777i | ||||
\(4\) | −1.11375e11 | −1.62072 | ||||||||
\(5\) | 3.68903e12i | 0.967058i | 0.875328 | + | 0.483529i | \(0.160645\pi\) | ||||
−0.875328 | + | 0.483529i | \(0.839355\pi\) | |||||||
\(6\) | −2.34743e13 | − | 1.62727e14i | −0.231137 | − | 1.60228i | ||||
\(7\) | −2.28183e15 | −1.40126 | −0.700629 | − | 0.713526i | \(-0.747097\pi\) | ||||
−0.700629 | + | 0.713526i | \(0.747097\pi\) | |||||||
\(8\) | 1.81020e16i | 1.00486i | ||||||||
\(9\) | 1.43975e17 | − | 4.24211e16i | 0.959229 | − | 0.282629i | ||||
\(10\) | 1.56554e18 | 1.56554 | ||||||||
\(11\) | 7.84145e18i | 1.41035i | 0.709032 | + | 0.705176i | \(0.249132\pi\) | ||||
−0.709032 | + | 0.705176i | \(0.750868\pi\) | |||||||
\(12\) | −4.27069e19 | + | 6.16070e18i | −1.60412 | + | 0.231402i | ||||
\(13\) | −7.34153e17 | −0.00652840 | −0.00326420 | − | 0.999995i | \(-0.501039\pi\) | ||||
−0.00326420 | + | 0.999995i | \(0.501039\pi\) | |||||||
\(14\) | 9.68352e20i | 2.26845i | ||||||||
\(15\) | 2.04058e20 | + | 1.41456e21i | 0.138074 | + | 0.957150i | ||||
\(16\) | 2.84165e19 | 0.00601742 | ||||||||
\(17\) | 1.60326e22i | 1.14005i | 0.821628 | + | 0.570024i | \(0.193066\pi\) | ||||
−0.821628 | + | 0.570024i | \(0.806934\pi\) | |||||||
\(18\) | −1.80025e22 | − | 6.10996e22i | −0.457538 | − | 1.55286i | ||||
\(19\) | 1.08973e23 | 1.04654 | 0.523270 | − | 0.852167i | \(-0.324712\pi\) | ||||
0.523270 | + | 0.852167i | \(0.324712\pi\) | |||||||
\(20\) | − | 4.10867e23i | − | 1.56733i | ||||||
\(21\) | −8.74970e23 | + | 1.26219e23i | −1.38690 | + | 0.200068i | ||||
\(22\) | 3.32772e24 | 2.28317 | ||||||||
\(23\) | 3.35294e24i | 1.03353i | 0.856126 | + | 0.516767i | \(0.172864\pi\) | ||||
−0.856126 | + | 0.516767i | \(0.827136\pi\) | |||||||
\(24\) | 1.00131e24 | + | 6.94125e24i | 0.143472 | + | 0.994569i | ||||
\(25\) | 9.42948e23 | 0.0647989 | ||||||||
\(26\) | 3.11557e23i | 0.0105686i | ||||||||
\(27\) | 5.28610e25 | − | 2.42304e25i | 0.909049 | − | 0.416689i | ||||
\(28\) | 2.54139e26 | 2.27105 | ||||||||
\(29\) | − | 1.36652e26i | − | 0.649312i | −0.945832 | − | 0.324656i | \(-0.894752\pi\) | ||
0.945832 | − | 0.324656i | \(-0.105248\pi\) | |||||||
\(30\) | 6.00307e26 | − | 8.65973e25i | 1.54950 | − | 0.223523i | ||||
\(31\) | −6.89506e26 | −0.986341 | −0.493171 | − | 0.869933i | \(-0.664162\pi\) | ||||
−0.493171 | + | 0.869933i | \(0.664162\pi\) | |||||||
\(32\) | 1.23190e27i | 0.995123i | ||||||||
\(33\) | 4.33748e26 | + | 3.00681e27i | 0.201366 | + | 1.39590i | ||||
\(34\) | 6.80384e27 | 1.84558 | ||||||||
\(35\) | − | 8.41774e27i | − | 1.35510i | ||||||
\(36\) | −1.60353e28 | + | 4.72465e27i | −1.55464 | + | 0.458063i | ||||
\(37\) | −1.67663e28 | −0.992670 | −0.496335 | − | 0.868131i | \(-0.665321\pi\) | ||||
−0.496335 | + | 0.868131i | \(0.665321\pi\) | |||||||
\(38\) | − | 4.62457e28i | − | 1.69421i | ||||||
\(39\) | −2.81512e26 | + | 4.06096e25i | −0.00646151 | + | 0.000932106i | ||||
\(40\) | −6.67790e28 | −0.971762 | ||||||||
\(41\) | 4.32262e28i | 0.403309i | 0.979457 | + | 0.201655i | \(0.0646318\pi\) | ||||
−0.979457 | + | 0.201655i | \(0.935368\pi\) | |||||||
\(42\) | 5.35642e28 | + | 3.71316e29i | 0.323882 | + | 2.24521i | ||||
\(43\) | −2.98235e29 | −1.18067 | −0.590333 | − | 0.807160i | \(-0.701004\pi\) | ||||
−0.590333 | + | 0.807160i | \(0.701004\pi\) | |||||||
\(44\) | − | 8.73342e29i | − | 2.28579i | ||||||
\(45\) | 1.56493e29 | + | 5.31129e29i | 0.273318 | + | 0.927630i | ||||
\(46\) | 1.42290e30 | 1.67315 | ||||||||
\(47\) | − | 9.90135e29i | − | 0.790556i | −0.918561 | − | 0.395278i | \(-0.870648\pi\) | ||
0.918561 | − | 0.395278i | \(-0.129352\pi\) | |||||||
\(48\) | 1.08963e28 | − | 1.57185e27i | 0.00595577 | − | 0.000859150i | ||||
\(49\) | 2.55501e30 | 0.963525 | ||||||||
\(50\) | − | 4.00164e29i | − | 0.104901i | ||||||
\(51\) | 8.86840e29 | + | 6.14772e30i | 0.162773 | + | 1.12837i | ||||
\(52\) | 8.17664e28 | 0.0105807 | ||||||||
\(53\) | 1.84427e31i | 1.69378i | 0.531765 | + | 0.846892i | \(0.321529\pi\) | ||||
−0.531765 | + | 0.846892i | \(0.678471\pi\) | |||||||
\(54\) | −1.02828e31 | − | 2.24329e31i | −0.674564 | − | 1.47163i | ||||
\(55\) | −2.89274e31 | −1.36389 | ||||||||
\(56\) | − | 4.13057e31i | − | 1.40807i | ||||||
\(57\) | 4.17860e31 | − | 6.02784e30i | 1.03582 | − | 0.149422i | ||||
\(58\) | −5.79919e31 | −1.05115 | ||||||||
\(59\) | 9.96164e31i | 1.32738i | 0.748008 | + | 0.663689i | \(0.231010\pi\) | ||||
−0.748008 | + | 0.663689i | \(0.768990\pi\) | |||||||
\(60\) | −2.27270e31 | − | 1.57547e32i | −0.223779 | − | 1.55127i | ||||
\(61\) | 2.76303e31 | 0.202045 | 0.101023 | − | 0.994884i | \(-0.467789\pi\) | ||||
0.101023 | + | 0.994884i | \(0.467789\pi\) | |||||||
\(62\) | 2.92609e32i | 1.59675i | ||||||||
\(63\) | −3.28527e32 | + | 9.67976e31i | −1.34413 | + | 0.396036i | ||||
\(64\) | 5.24742e32 | 1.61699 | ||||||||
\(65\) | − | 2.70832e30i | − | 0.00631334i | ||||||
\(66\) | 1.27602e33 | − | 1.84072e32i | 2.25978 | − | 0.325985i | ||||
\(67\) | 2.39988e31 | 0.0324222 | 0.0162111 | − | 0.999869i | \(-0.494840\pi\) | ||||
0.0162111 | + | 0.999869i | \(0.494840\pi\) | |||||||
\(68\) | − | 1.78563e33i | − | 1.84770i | ||||||
\(69\) | 1.85467e32 | + | 1.28569e33i | 0.147565 | + | 1.02294i | ||||
\(70\) | −3.57228e33 | −2.19372 | ||||||||
\(71\) | − | 1.79070e33i | − | 0.851869i | −0.904754 | − | 0.425935i | \(-0.859945\pi\) | ||
0.904754 | − | 0.425935i | \(-0.140055\pi\) | |||||||
\(72\) | 7.67907e32 | + | 2.60624e33i | 0.284004 | + | 0.963895i | ||||
\(73\) | 1.25926e33 | 0.363333 | 0.181666 | − | 0.983360i | \(-0.441851\pi\) | ||||
0.181666 | + | 0.983360i | \(0.441851\pi\) | |||||||
\(74\) | 7.11519e33i | 1.60700i | ||||||||
\(75\) | 3.61575e32 | − | 5.21590e31i | 0.0641350 | − | 0.00925180i | ||||
\(76\) | −1.21369e34 | −1.69615 | ||||||||
\(77\) | − | 1.78928e34i | − | 1.97627i | ||||||
\(78\) | 1.72337e31 | + | 1.19467e32i | 0.00150895 | + | 0.0104603i | ||||
\(79\) | −4.10710e33 | −0.285922 | −0.142961 | − | 0.989728i | \(-0.545662\pi\) | ||||
−0.142961 | + | 0.989728i | \(0.545662\pi\) | |||||||
\(80\) | 1.04829e32i | 0.00581919i | ||||||||
\(81\) | 1.89293e34 | − | 1.22152e34i | 0.840242 | − | 0.542212i | ||||
\(82\) | 1.83442e34 | 0.652903 | ||||||||
\(83\) | 4.33479e34i | 1.24040i | 0.784443 | + | 0.620201i | \(0.212949\pi\) | ||||
−0.784443 | + | 0.620201i | \(0.787051\pi\) | |||||||
\(84\) | 9.74499e34 | − | 1.40576e34i | 2.24778 | − | 0.324254i | ||||
\(85\) | −5.91448e34 | −1.10249 | ||||||||
\(86\) | 1.26564e35i | 1.91134i | ||||||||
\(87\) | −7.55890e33 | − | 5.23995e34i | −0.0927069 | − | 0.642659i | ||||
\(88\) | −1.41946e35 | −1.41721 | ||||||||
\(89\) | − | 5.33521e34i | − | 0.434642i | −0.976100 | − | 0.217321i | \(-0.930268\pi\) | ||
0.976100 | − | 0.217321i | \(-0.0697318\pi\) | |||||||
\(90\) | 2.25398e35 | − | 6.64117e34i | 1.50171 | − | 0.442466i | ||||
\(91\) | 1.67521e33 | 0.00914797 | ||||||||
\(92\) | − | 3.73434e35i | − | 1.67507i | ||||||
\(93\) | −2.64392e35 | + | 3.81399e34i | −0.976236 | + | 0.140827i | ||||
\(94\) | −4.20189e35 | −1.27980 | ||||||||
\(95\) | 4.02007e35i | 1.01206i | ||||||||
\(96\) | 6.81425e34 | + | 4.72375e35i | 0.142081 | + | 0.984928i | ||||
\(97\) | −1.24213e35 | −0.214919 | −0.107460 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107460 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(98\) | − | 1.08428e36i | − | 1.55982i | ||||||
\(99\) | 3.32643e35 | + | 1.12897e36i | 0.398606 | + | 1.35285i | ||||
\(100\) | −1.05021e35 | −0.105021 | ||||||||
\(101\) | 4.71676e35i | 0.394330i | 0.980370 | + | 0.197165i | \(0.0631734\pi\) | ||||
−0.980370 | + | 0.197165i | \(0.936827\pi\) | |||||||
\(102\) | 2.60894e36 | − | 3.76353e35i | 1.82668 | − | 0.263507i | ||||
\(103\) | −1.54044e36 | −0.904847 | −0.452424 | − | 0.891803i | \(-0.649440\pi\) | ||||
−0.452424 | + | 0.891803i | \(0.649440\pi\) | |||||||
\(104\) | − | 1.32897e34i | − | 0.00656015i | ||||||
\(105\) | −4.65626e35 | − | 3.22779e36i | −0.193477 | − | 1.34121i | ||||
\(106\) | 7.82661e36 | 2.74201 | ||||||||
\(107\) | − | 3.09814e36i | − | 0.916627i | −0.888791 | − | 0.458314i | \(-0.848454\pi\) | ||
0.888791 | − | 0.458314i | \(-0.151546\pi\) | |||||||
\(108\) | −5.88740e36 | + | 2.69866e36i | −1.47332 | + | 0.675338i | ||||
\(109\) | −1.74804e36 | −0.370573 | −0.185287 | − | 0.982685i | \(-0.559321\pi\) | ||||
−0.185287 | + | 0.982685i | \(0.559321\pi\) | |||||||
\(110\) | 1.22761e37i | 2.20796i | ||||||||
\(111\) | −6.42904e36 | + | 9.27422e35i | −0.982500 | + | 0.141731i | ||||
\(112\) | −6.48415e34 | −0.00843196 | ||||||||
\(113\) | − | 2.20649e36i | − | 0.244506i | −0.992499 | − | 0.122253i | \(-0.960988\pi\) | ||
0.992499 | − | 0.122253i | \(-0.0390120\pi\) | |||||||
\(114\) | −2.55807e36 | − | 1.77330e37i | −0.241894 | − | 1.67685i | ||||
\(115\) | −1.23691e37 | −0.999486 | ||||||||
\(116\) | 1.52197e37i | 1.05235i | ||||||||
\(117\) | −1.05700e35 | + | 3.11436e34i | −0.00626223 | + | 0.00184511i | ||||
\(118\) | 4.22748e37 | 2.14885 | ||||||||
\(119\) | − | 3.65836e37i | − | 1.59750i | ||||||
\(120\) | −2.56065e37 | + | 3.69387e36i | −0.961806 | + | 0.138745i | ||||
\(121\) | −3.05756e37 | −0.989095 | ||||||||
\(122\) | − | 1.17256e37i | − | 0.327084i | ||||||
\(123\) | 2.39105e36 | + | 1.65752e37i | 0.0575833 | + | 0.399177i | ||||
\(124\) | 7.67938e37 | 1.59859 | ||||||||
\(125\) | 5.71611e37i | 1.02972i | ||||||||
\(126\) | 4.10785e37 | + | 1.39419e38i | 0.641129 | + | 2.17596i | ||||
\(127\) | 9.04828e37 | 1.22489 | 0.612447 | − | 0.790511i | \(-0.290185\pi\) | ||||
0.612447 | + | 0.790511i | \(0.290185\pi\) | |||||||
\(128\) | − | 1.38032e38i | − | 1.62256i | ||||||
\(129\) | −1.14359e38 | + | 1.64968e37i | −1.16857 | + | 0.168572i | ||||
\(130\) | −1.14934e36 | −0.0102204 | ||||||||
\(131\) | 1.02918e37i | 0.0797274i | 0.999205 | + | 0.0398637i | \(0.0126924\pi\) | ||||
−0.999205 | + | 0.0398637i | \(0.987308\pi\) | |||||||
\(132\) | −4.83088e37 | − | 3.34884e38i | −0.326359 | − | 2.26237i | ||||
\(133\) | −2.48659e38 | −1.46647 | ||||||||
\(134\) | − | 1.01845e37i | − | 0.0524872i | ||||||
\(135\) | 8.93867e37 | + | 1.95006e38i | 0.402963 | + | 0.879103i | ||||
\(136\) | −2.90222e38 | −1.14559 | ||||||||
\(137\) | 3.34355e36i | 0.0115674i | 0.999983 | + | 0.00578372i | \(0.00184103\pi\) | ||||
−0.999983 | + | 0.00578372i | \(0.998159\pi\) | |||||||
\(138\) | 5.45615e38 | − | 7.87077e37i | 1.65601 | − | 0.238888i | ||||
\(139\) | −3.57808e37 | −0.0953639 | −0.0476820 | − | 0.998863i | \(-0.515183\pi\) | ||||
−0.0476820 | + | 0.998863i | \(0.515183\pi\) | |||||||
\(140\) | 9.37527e38i | 2.19624i | ||||||||
\(141\) | −5.47691e37 | − | 3.79668e38i | −0.112873 | − | 0.782457i | ||||
\(142\) | −7.59930e38 | −1.37906 | ||||||||
\(143\) | − | 5.75682e36i | − | 0.00920734i | ||||||
\(144\) | 4.09126e36 | − | 1.20546e36i | 0.00577208 | − | 0.00170070i | ||||
\(145\) | 5.04115e38 | 0.627922 | ||||||||
\(146\) | − | 5.34400e38i | − | 0.588187i | ||||||
\(147\) | 9.79721e38 | − | 1.41330e38i | 0.953653 | − | 0.137569i | ||||
\(148\) | 1.86734e39 | 1.60884 | ||||||||
\(149\) | − | 1.50133e39i | − | 1.14584i | −0.819612 | − | 0.572919i | \(-0.805811\pi\) | ||
0.819612 | − | 0.572919i | \(-0.194189\pi\) | |||||||
\(150\) | −2.21350e37 | − | 1.53443e38i | −0.0149774 | − | 0.103826i | ||||
\(151\) | 6.27675e38 | 0.376834 | 0.188417 | − | 0.982089i | \(-0.439664\pi\) | ||||
0.188417 | + | 0.982089i | \(0.439664\pi\) | |||||||
\(152\) | 1.97264e39i | 1.05163i | ||||||||
\(153\) | 6.80120e38 | + | 2.30830e39i | 0.322211 | + | 1.09357i | ||||
\(154\) | −7.59328e39 | −3.19931 | ||||||||
\(155\) | − | 2.54361e39i | − | 0.953849i | ||||||
\(156\) | 3.13535e37 | − | 4.52290e36i | 0.0104723 | − | 0.00151068i | ||||
\(157\) | 1.36826e39 | 0.407358 | 0.203679 | − | 0.979038i | \(-0.434710\pi\) | ||||
0.203679 | + | 0.979038i | \(0.434710\pi\) | |||||||
\(158\) | 1.74295e39i | 0.462869i | ||||||||
\(159\) | 1.02015e39 | + | 7.07186e39i | 0.241834 | + | 1.67643i | ||||
\(160\) | −4.54453e39 | −0.962342 | ||||||||
\(161\) | − | 7.65083e39i | − | 1.44825i | ||||||
\(162\) | −5.18382e39 | − | 8.03313e39i | −0.877767 | − | 1.36024i | ||||
\(163\) | 1.03735e40 | 1.57235 | 0.786175 | − | 0.618004i | \(-0.212058\pi\) | ||||
0.786175 | + | 0.618004i | \(0.212058\pi\) | |||||||
\(164\) | − | 4.81433e39i | − | 0.653652i | ||||||
\(165\) | −1.10922e40 | + | 1.60011e39i | −1.34992 | + | 0.194733i | ||||
\(166\) | 1.83958e40 | 2.00804 | ||||||||
\(167\) | 1.58942e40i | 1.55719i | 0.627527 | + | 0.778595i | \(0.284067\pi\) | ||||
−0.627527 | + | 0.778595i | \(0.715933\pi\) | |||||||
\(168\) | −2.28482e39 | − | 1.58387e40i | −0.201041 | − | 1.39365i | ||||
\(169\) | −1.26457e40 | −0.999957 | ||||||||
\(170\) | 2.50996e40i | 1.78479i | ||||||||
\(171\) | 1.56895e40 | − | 4.62277e39i | 1.00387 | − | 0.295782i | ||||
\(172\) | 3.32160e40 | 1.91353 | ||||||||
\(173\) | 2.10599e39i | 0.109301i | 0.998506 | + | 0.0546507i | \(0.0174045\pi\) | ||||
−0.998506 | + | 0.0546507i | \(0.982595\pi\) | |||||||
\(174\) | −2.22371e40 | + | 3.20781e39i | −1.04038 | + | 0.150080i | ||||
\(175\) | −2.15164e39 | −0.0908000 | ||||||||
\(176\) | 2.22826e38i | 0.00848668i | ||||||||
\(177\) | 5.51026e39 | + | 3.81980e40i | 0.189519 | + | 1.31378i | ||||
\(178\) | −2.26413e40 | −0.703626 | ||||||||
\(179\) | − | 5.73503e40i | − | 1.61132i | −0.592380 | − | 0.805659i | \(-0.701812\pi\) | ||
0.592380 | − | 0.805659i | \(-0.298188\pi\) | |||||||
\(180\) | −1.74294e40 | − | 5.91546e40i | −0.442973 | − | 1.50343i | ||||
\(181\) | 1.65060e40 | 0.379688 | 0.189844 | − | 0.981814i | \(-0.439202\pi\) | ||||
0.189844 | + | 0.981814i | \(0.439202\pi\) | |||||||
\(182\) | − | 7.10919e38i | − | 0.0148093i | ||||||
\(183\) | 1.05949e40 | − | 1.52836e39i | 0.199975 | − | 0.0288474i | ||||
\(184\) | −6.06950e40 | −1.03856 | ||||||||
\(185\) | − | 6.18513e40i | − | 0.959969i | ||||||
\(186\) | 1.61856e40 | + | 1.12201e41i | 0.227980 | + | 1.58039i | ||||
\(187\) | −1.25719e41 | −1.60787 | ||||||||
\(188\) | 1.10276e41i | 1.28127i | ||||||||
\(189\) | −1.20620e41 | + | 5.52895e40i | −1.27381 | + | 0.583889i | ||||
\(190\) | 1.70602e41 | 1.63840 | ||||||||
\(191\) | − | 8.35822e40i | − | 0.730320i | −0.930945 | − | 0.365160i | \(-0.881014\pi\) | ||
0.930945 | − | 0.365160i | \(-0.118986\pi\) | |||||||
\(192\) | 2.01213e41 | − | 2.90260e40i | 1.60042 | − | 0.230869i | ||||
\(193\) | 2.00501e41 | 1.45240 | 0.726199 | − | 0.687484i | \(-0.241285\pi\) | ||||
0.726199 | + | 0.687484i | \(0.241285\pi\) | |||||||
\(194\) | 5.27130e40i | 0.347925i | ||||||||
\(195\) | −1.49810e38 | − | 1.03851e39i | −0.000901401 | − | 0.00624866i | ||||
\(196\) | −2.84564e41 | −1.56161 | ||||||||
\(197\) | − | 1.55876e41i | − | 0.780524i | −0.920704 | − | 0.390262i | \(-0.872384\pi\) | ||
0.920704 | − | 0.390262i | \(-0.127616\pi\) | |||||||
\(198\) | 4.79109e41 | − | 1.41165e41i | 2.19008 | − | 0.645290i | ||||
\(199\) | −4.16157e41 | −1.73741 | −0.868704 | − | 0.495331i | \(-0.835047\pi\) | ||||
−0.868704 | + | 0.495331i | \(0.835047\pi\) | |||||||
\(200\) | 1.70693e40i | 0.0651141i | ||||||||
\(201\) | 9.20237e39 | − | 1.32749e39i | 0.0320901 | − | 0.00462916i | ||||
\(202\) | 2.00168e41 | 0.638366 | ||||||||
\(203\) | 3.11817e41i | 0.909853i | ||||||||
\(204\) | −9.87719e40 | − | 6.84703e41i | −0.263810 | − | 1.82877i | ||||
\(205\) | −1.59463e41 | −0.390023 | ||||||||
\(206\) | 6.53726e41i | 1.46482i | ||||||||
\(207\) | 1.42235e41 | + | 4.82740e41i | 0.292106 | + | 0.991395i | ||||
\(208\) | −2.08620e37 | −3.92841e−5 | ||||||||
\(209\) | 8.54509e41i | 1.47599i | ||||||||
\(210\) | −1.36980e42 | + | 1.97600e41i | −2.17124 | + | 0.313213i | ||||
\(211\) | 3.08375e41 | 0.448740 | 0.224370 | − | 0.974504i | \(-0.427968\pi\) | ||||
0.224370 | + | 0.974504i | \(0.427968\pi\) | |||||||
\(212\) | − | 2.05405e42i | − | 2.74515i | ||||||
\(213\) | −9.90523e40 | − | 6.86647e41i | −0.121627 | − | 0.843142i | ||||
\(214\) | −1.31477e42 | −1.48390 | ||||||||
\(215\) | − | 1.10020e42i | − | 1.14177i | ||||||
\(216\) | 4.38619e41 | + | 9.56891e41i | 0.418716 | + | 0.913471i | ||||
\(217\) | 1.57333e42 | 1.38212 | ||||||||
\(218\) | 7.41825e41i | 0.599908i | ||||||||
\(219\) | 4.82866e41 | − | 6.96559e40i | 0.359611 | − | 0.0518757i | ||||
\(220\) | 3.22179e42 | 2.21049 | ||||||||
\(221\) | − | 1.17704e40i | − | 0.00744269i | ||||||
\(222\) | 3.93575e41 | + | 2.72833e42i | 0.229443 | + | 1.59053i | ||||
\(223\) | −1.52920e42 | −0.822196 | −0.411098 | − | 0.911591i | \(-0.634855\pi\) | ||||
−0.411098 | + | 0.911591i | \(0.634855\pi\) | |||||||
\(224\) | − | 2.81099e42i | − | 1.39442i | ||||||
\(225\) | 1.35761e41 | − | 4.00009e40i | 0.0621570 | − | 0.0183140i | ||||
\(226\) | −9.36380e41 | −0.395822 | ||||||||
\(227\) | 3.16945e42i | 1.23742i | 0.785619 | + | 0.618711i | \(0.212345\pi\) | ||||
−0.785619 | + | 0.618711i | \(0.787655\pi\) | |||||||
\(228\) | −4.65392e42 | + | 6.71352e41i | −1.67877 | + | 0.242172i | ||||
\(229\) | 3.13587e42 | 1.04549 | 0.522745 | − | 0.852489i | \(-0.324908\pi\) | ||||
0.522745 | + | 0.852489i | \(0.324908\pi\) | |||||||
\(230\) | 5.24914e42i | 1.61803i | ||||||||
\(231\) | −9.89738e41 | − | 6.86103e42i | −0.282166 | − | 1.95602i | ||||
\(232\) | 2.47368e42 | 0.652470 | ||||||||
\(233\) | − | 1.98672e42i | − | 0.484987i | −0.970153 | − | 0.242494i | \(-0.922035\pi\) | ||
0.970153 | − | 0.242494i | \(-0.0779654\pi\) | |||||||
\(234\) | 1.32166e40 | + | 4.48564e40i | 0.00298699 | + | 0.0101377i | ||||
\(235\) | 3.65264e42 | 0.764514 | ||||||||
\(236\) | − | 1.10948e43i | − | 2.15131i | ||||||
\(237\) | −1.57487e42 | + | 2.27183e41i | −0.282993 | + | 0.0408231i | ||||
\(238\) | −1.55252e43 | −2.58614 | ||||||||
\(239\) | 5.72357e42i | 0.884106i | 0.896989 | + | 0.442053i | \(0.145750\pi\) | ||||
−0.896989 | + | 0.442053i | \(0.854250\pi\) | |||||||
\(240\) | 5.79861e39 | + | 4.01969e40i | 0.000830848 | + | 0.00575957i | ||||
\(241\) | −1.81774e42 | −0.241672 | −0.120836 | − | 0.992673i | \(-0.538557\pi\) | ||||
−0.120836 | + | 0.992673i | \(0.538557\pi\) | |||||||
\(242\) | 1.29755e43i | 1.60121i | ||||||||
\(243\) | 6.58279e42 | − | 5.73099e42i | 0.754218 | − | 0.656624i | ||||
\(244\) | −3.07733e42 | −0.327459 | ||||||||
\(245\) | 9.42551e42i | 0.931784i | ||||||||
\(246\) | 7.03409e42 | − | 1.01470e42i | 0.646214 | − | 0.0932196i | ||||
\(247\) | −8.00032e40 | −0.00683223 | ||||||||
\(248\) | − | 1.24814e43i | − | 0.991139i | ||||||
\(249\) | 2.39778e42 | + | 1.66218e43i | 0.177101 | + | 1.22769i | ||||
\(250\) | 2.42578e43 | 1.66698 | ||||||||
\(251\) | 9.57719e42i | 0.612507i | 0.951950 | + | 0.306253i | \(0.0990755\pi\) | ||||
−0.951950 | + | 0.306253i | \(0.900924\pi\) | |||||||
\(252\) | 3.65897e43 | − | 1.07808e43i | 2.17846 | − | 0.641864i | ||||
\(253\) | −2.62919e43 | −1.45765 | ||||||||
\(254\) | − | 3.83987e43i | − | 1.98294i | ||||||
\(255\) | −2.26791e43 | + | 3.27158e42i | −1.09120 | + | 0.157411i | ||||
\(256\) | −2.25174e43 | −1.00972 | ||||||||
\(257\) | − | 3.16415e43i | − | 1.32270i | −0.750077 | − | 0.661350i | \(-0.769984\pi\) | ||
0.750077 | − | 0.661350i | \(-0.230016\pi\) | |||||||
\(258\) | 7.00085e42 | + | 4.85311e43i | 0.272895 | + | 1.89176i | ||||
\(259\) | 3.82577e43 | 1.39099 | ||||||||
\(260\) | 3.01639e41i | 0.0102322i | ||||||||
\(261\) | −5.79694e42 | − | 1.96745e43i | −0.183514 | − | 0.622839i | ||||
\(262\) | 4.36759e42 | 0.129068 | ||||||||
\(263\) | 1.63619e43i | 0.451472i | 0.974189 | + | 0.225736i | \(0.0724787\pi\) | ||||
−0.974189 | + | 0.225736i | \(0.927521\pi\) | |||||||
\(264\) | −5.44294e43 | + | 7.85172e42i | −1.40269 | + | 0.202346i | ||||
\(265\) | −6.80356e43 | −1.63799 | ||||||||
\(266\) | 1.05525e44i | 2.37402i | ||||||||
\(267\) | −2.95116e42 | − | 2.04579e43i | −0.0620570 | − | 0.430189i | ||||
\(268\) | −2.67287e42 | −0.0525474 | ||||||||
\(269\) | − | 5.32556e43i | − | 0.979094i | −0.871977 | − | 0.489547i | \(-0.837162\pi\) | ||
0.871977 | − | 0.489547i | \(-0.162838\pi\) | |||||||
\(270\) | 8.27557e43 | − | 3.79335e43i | 1.42315 | − | 0.652342i | ||||
\(271\) | −2.55880e43 | −0.411708 | −0.205854 | − | 0.978583i | \(-0.565997\pi\) | ||||
−0.205854 | + | 0.978583i | \(0.565997\pi\) | |||||||
\(272\) | 4.55590e41i | 0.00686015i | ||||||||
\(273\) | 6.42362e41 | − | 9.26640e40i | 0.00905425 | − | 0.00130612i | ||||
\(274\) | 1.41892e42 | 0.0187261 | ||||||||
\(275\) | 7.39407e42i | 0.0913893i | ||||||||
\(276\) | −2.06564e43 | − | 1.43194e44i | −0.239162 | − | 1.65791i | ||||
\(277\) | 1.43545e44 | 1.55723 | 0.778613 | − | 0.627504i | \(-0.215924\pi\) | ||||
0.778613 | + | 0.627504i | \(0.215924\pi\) | |||||||
\(278\) | 1.51845e43i | 0.154381i | ||||||||
\(279\) | −9.92717e43 | + | 2.92496e43i | −0.946128 | + | 0.278769i | ||||
\(280\) | 1.52378e44 | 1.36169 | ||||||||
\(281\) | − | 8.99700e41i | − | 0.00754022i | −0.999993 | − | 0.00377011i | \(-0.998800\pi\) | ||
0.999993 | − | 0.00377011i | \(-0.00120007\pi\) | |||||||
\(282\) | −1.61122e44 | + | 2.32427e43i | −1.26669 | + | 0.182727i | ||||
\(283\) | 1.89987e44 | 1.40142 | 0.700709 | − | 0.713447i | \(-0.252867\pi\) | ||||
0.700709 | + | 0.713447i | \(0.252867\pi\) | |||||||
\(284\) | 1.99440e44i | 1.38064i | ||||||||
\(285\) | 2.22369e43 | + | 1.54150e44i | 0.144500 | + | 1.00170i | ||||
\(286\) | −2.44306e42 | −0.0149054 | ||||||||
\(287\) | − | 9.86348e43i | − | 0.565140i | ||||||
\(288\) | 5.22586e43 | + | 1.77363e44i | 0.281250 | + | 0.954551i | ||||
\(289\) | −5.92738e43 | −0.299710 | ||||||||
\(290\) | − | 2.13934e44i | − | 1.01652i | ||||||
\(291\) | −4.76296e43 | + | 6.87082e42i | −0.212718 | + | 0.0306856i | ||||
\(292\) | −1.40251e44 | −0.588862 | ||||||||
\(293\) | − | 7.55971e43i | − | 0.298461i | −0.988802 | − | 0.149231i | \(-0.952320\pi\) | ||
0.988802 | − | 0.149231i | \(-0.0476797\pi\) | |||||||
\(294\) | −5.99769e43 | − | 4.15770e44i | −0.222706 | − | 1.54384i | ||||
\(295\) | −3.67488e44 | −1.28365 | ||||||||
\(296\) | − | 3.03503e44i | − | 0.997499i | ||||||
\(297\) | 1.90001e44 | + | 4.14506e44i | 0.587679 | + | 1.28208i | ||||
\(298\) | −6.37128e44 | −1.85496 | ||||||||
\(299\) | − | 2.46157e42i | − | 0.00674731i | ||||||
\(300\) | −4.02704e43 | + | 5.80922e42i | −0.103945 | + | 0.0149946i | ||||
\(301\) | 6.80522e44 | 1.65442 | ||||||||
\(302\) | − | 2.66370e44i | − | 0.610043i | ||||||
\(303\) | 2.60907e43 | + | 1.80865e44i | 0.0563013 | + | 0.390290i | ||||
\(304\) | 3.09664e42 | 0.00629747 | ||||||||
\(305\) | 1.01929e44i | 0.195389i | ||||||||
\(306\) | 9.79584e44 | − | 2.88626e44i | 1.77034 | − | 0.521615i | ||||
\(307\) | 3.14505e44 | 0.535965 | 0.267983 | − | 0.963424i | \(-0.413643\pi\) | ||||
0.267983 | + | 0.963424i | \(0.413643\pi\) | |||||||
\(308\) | 1.99282e45i | 3.20298i | ||||||||
\(309\) | −5.90684e44 | + | 8.52092e43i | −0.895577 | + | 0.129192i | ||||
\(310\) | −1.07945e45 | −1.54415 | ||||||||
\(311\) | − | 3.59597e44i | − | 0.485432i | −0.970097 | − | 0.242716i | \(-0.921962\pi\) | ||
0.970097 | − | 0.242716i | \(-0.0780384\pi\) | |||||||
\(312\) | −7.35115e41 | − | 5.09594e42i | −0.000936640 | − | 0.00649294i | ||||
\(313\) | 5.83770e44 | 0.702173 | 0.351086 | − | 0.936343i | \(-0.385812\pi\) | ||||
0.351086 | + | 0.936343i | \(0.385812\pi\) | |||||||
\(314\) | − | 5.80658e44i | − | 0.659457i | ||||||
\(315\) | −3.57090e44 | − | 1.21195e45i | −0.382990 | − | 1.29985i | ||||
\(316\) | 4.57429e44 | 0.463400 | ||||||||
\(317\) | − | 1.00111e45i | − | 0.958113i | −0.877784 | − | 0.479057i | \(-0.840979\pi\) | ||
0.877784 | − | 0.479057i | \(-0.159021\pi\) | |||||||
\(318\) | 3.00113e45 | − | 4.32928e44i | 2.71391 | − | 0.391496i | ||||
\(319\) | 1.07155e45 | 0.915758 | ||||||||
\(320\) | 1.93579e45i | 1.56372i | ||||||||
\(321\) | −1.71373e44 | − | 1.18799e45i | −0.130873 | − | 0.907236i | ||||
\(322\) | −3.24682e45 | −2.34451 | ||||||||
\(323\) | 1.74713e45i | 1.19311i | ||||||||
\(324\) | −2.10825e45 | + | 1.36047e45i | −1.36180 | + | 0.878774i | ||||
\(325\) | −6.92268e41 | −0.000423033 | ||||||||
\(326\) | − | 4.40227e45i | − | 2.54542i | ||||||
\(327\) | −6.70288e44 | + | 9.66925e43i | −0.366777 | + | 0.0529094i | ||||
\(328\) | −7.82483e44 | −0.405271 | ||||||||
\(329\) | 2.25932e45i | 1.10777i | ||||||||
\(330\) | 6.79048e44 | + | 4.70727e45i | 0.315246 | + | 2.18534i | ||||
\(331\) | −4.28276e45 | −1.88287 | −0.941435 | − | 0.337195i | \(-0.890522\pi\) | ||||
−0.941435 | + | 0.337195i | \(0.890522\pi\) | |||||||
\(332\) | − | 4.82788e45i | − | 2.01035i | ||||||
\(333\) | −2.41392e45 | + | 7.11242e44i | −0.952198 | + | 0.280557i | ||||
\(334\) | 6.74510e45 | 2.52088 | ||||||||
\(335\) | 8.85324e43i | 0.0313542i | ||||||||
\(336\) | −2.48635e43 | + | 3.58669e42i | −0.00834557 | + | 0.00120389i | ||||
\(337\) | 2.41522e45 | 0.768454 | 0.384227 | − | 0.923239i | \(-0.374468\pi\) | ||||
0.384227 | + | 0.923239i | \(0.374468\pi\) | |||||||
\(338\) | 5.36652e45i | 1.61880i | ||||||||
\(339\) | −1.22052e44 | − | 8.46081e44i | −0.0349099 | − | 0.242001i | ||||
\(340\) | 6.58726e45 | 1.78683 | ||||||||
\(341\) | − | 5.40672e45i | − | 1.39109i | ||||||
\(342\) | −1.96179e45 | − | 6.65823e45i | −0.478831 | − | 1.62513i | ||||
\(343\) | 2.20705e44 | 0.0511114 | ||||||||
\(344\) | − | 5.39867e45i | − | 1.18641i | ||||||
\(345\) | −4.74295e45 | + | 6.84194e44i | −0.989246 | + | 0.142704i | ||||
\(346\) | 8.93730e44 | 0.176944 | ||||||||
\(347\) | 8.25781e45i | 1.55215i | 0.630640 | + | 0.776076i | \(0.282793\pi\) | ||||
−0.630640 | + | 0.776076i | \(0.717207\pi\) | |||||||
\(348\) | 8.41873e44 | + | 5.83600e45i | 0.150252 | + | 1.04157i | ||||
\(349\) | 4.21970e45 | 0.715194 | 0.357597 | − | 0.933876i | \(-0.383596\pi\) | ||||
0.357597 | + | 0.933876i | \(0.383596\pi\) | |||||||
\(350\) | 9.13106e44i | 0.146993i | ||||||||
\(351\) | −3.88081e43 | + | 1.77888e43i | −0.00593463 | + | 0.00272031i | ||||
\(352\) | −9.65990e45 | −1.40347 | ||||||||
\(353\) | 1.36665e46i | 1.88675i | 0.331735 | + | 0.943373i | \(0.392366\pi\) | ||||
−0.331735 | + | 0.943373i | \(0.607634\pi\) | |||||||
\(354\) | 1.62103e46 | − | 2.33842e45i | 2.12683 | − | 0.306806i | ||||
\(355\) | 6.60596e45 | 0.823807 | ||||||||
\(356\) | 5.94210e45i | 0.704434i | ||||||||
\(357\) | −2.02362e45 | − | 1.40280e46i | −0.228087 | − | 1.58114i | ||||
\(358\) | −2.43381e46 | −2.60850 | ||||||||
\(359\) | − | 1.37555e46i | − | 1.40209i | −0.713115 | − | 0.701047i | \(-0.752716\pi\) | ||
0.713115 | − | 0.701047i | \(-0.247284\pi\) | |||||||
\(360\) | −9.61452e45 | + | 2.83284e45i | −0.932143 | + | 0.274648i | ||||
\(361\) | 1.03270e45 | 0.0952456 | ||||||||
\(362\) | − | 7.00474e45i | − | 0.614664i | ||||||
\(363\) | −1.17242e46 | + | 1.69128e45i | −0.978962 | + | 0.141220i | ||||
\(364\) | −1.86577e44 | −0.0148263 | ||||||||
\(365\) | 4.64546e45i | 0.351364i | ||||||||
\(366\) | −6.48601e44 | − | 4.49621e45i | −0.0467001 | − | 0.323733i | ||||
\(367\) | 2.84960e46 | 1.95341 | 0.976707 | − | 0.214580i | \(-0.0688381\pi\) | ||||
0.976707 | + | 0.214580i | \(0.0688381\pi\) | |||||||
\(368\) | 9.52786e43i | 0.00621920i | ||||||||
\(369\) | 1.83370e45 | + | 6.22350e45i | 0.113987 | + | 0.386866i | ||||
\(370\) | −2.62482e46 | −1.55406 | ||||||||
\(371\) | − | 4.20830e46i | − | 2.37343i | ||||||
\(372\) | 2.94467e46 | − | 4.24783e45i | 1.58221 | − | 0.228241i | ||||
\(373\) | −9.28379e45 | −0.475299 | −0.237649 | − | 0.971351i | \(-0.576377\pi\) | ||||
−0.237649 | + | 0.971351i | \(0.576377\pi\) | |||||||
\(374\) | 5.33520e46i | 2.60292i | ||||||||
\(375\) | 3.16185e45 | + | 2.19185e46i | 0.147021 | + | 1.01917i | ||||
\(376\) | 1.79234e46 | 0.794402 | ||||||||
\(377\) | 1.00324e44i | 0.00423896i | ||||||||
\(378\) | 2.34635e46 | + | 5.11880e46i | 0.945238 | + | 2.06213i | ||||
\(379\) | −2.44149e46 | −0.937884 | −0.468942 | − | 0.883229i | \(-0.655365\pi\) | ||||
−0.468942 | + | 0.883229i | \(0.655365\pi\) | |||||||
\(380\) | − | 4.47735e46i | − | 1.64028i | ||||||
\(381\) | 3.46957e46 | − | 5.00504e45i | 1.21235 | − | 0.174887i | ||||
\(382\) | −3.54702e46 | −1.18229 | ||||||||
\(383\) | 4.74363e46i | 1.50846i | 0.656613 | + | 0.754228i | \(0.271989\pi\) | ||||
−0.656613 | + | 0.754228i | \(0.728011\pi\) | |||||||
\(384\) | −7.63522e45 | − | 5.29286e46i | −0.231664 | − | 1.60594i | ||||
\(385\) | 6.60072e46 | 1.91117 | ||||||||
\(386\) | − | 8.50879e46i | − | 2.35124i | ||||||
\(387\) | −4.29385e46 | + | 1.26515e46i | −1.13253 | + | 0.333690i | ||||
\(388\) | 1.38342e46 | 0.348325 | ||||||||
\(389\) | − | 4.50416e45i | − | 0.108273i | −0.998534 | − | 0.0541366i | \(-0.982759\pi\) | ||
0.998534 | − | 0.0541366i | \(-0.0172406\pi\) | |||||||
\(390\) | −4.40717e44 | + | 6.35757e43i | −0.0101157 | + | 0.00145925i | ||||
\(391\) | −5.37563e46 | −1.17828 | ||||||||
\(392\) | 4.62508e46i | 0.968212i | ||||||||
\(393\) | 5.69289e44 | + | 3.94640e45i | 0.0113833 | + | 0.0789106i | ||||
\(394\) | −6.61498e46 | −1.26356 | ||||||||
\(395\) | − | 1.51512e46i | − | 0.276503i | ||||||
\(396\) | −3.70481e46 | − | 1.25740e47i | −0.646030 | − | 2.19260i | ||||
\(397\) | 1.06014e47 | 1.76658 | 0.883292 | − | 0.468823i | \(-0.155322\pi\) | ||||
0.883292 | + | 0.468823i | \(0.155322\pi\) | |||||||
\(398\) | 1.76607e47i | 2.81263i | ||||||||
\(399\) | −9.53485e46 | + | 1.37545e46i | −1.45145 | + | 0.209379i | ||||
\(400\) | 2.67952e43 | 0.000389922 | ||||||||
\(401\) | 6.06638e46i | 0.843977i | 0.906601 | + | 0.421989i | \(0.138668\pi\) | ||||
−0.906601 | + | 0.421989i | \(0.861332\pi\) | |||||||
\(402\) | −5.63354e44 | − | 3.90526e45i | −0.00749398 | − | 0.0519495i | ||||
\(403\) | 5.06203e44 | 0.00643923 | ||||||||
\(404\) | − | 5.25330e46i | − | 0.639099i | ||||||
\(405\) | 4.50621e46 | + | 6.98308e46i | 0.524350 | + | 0.812563i | ||||
\(406\) | 1.32328e47 | 1.47293 | ||||||||
\(407\) | − | 1.31472e47i | − | 1.40002i | ||||||
\(408\) | −1.11286e47 | + | 1.60536e46i | −1.13386 | + | 0.163565i | ||||
\(409\) | −1.18079e47 | −1.15120 | −0.575602 | − | 0.817730i | \(-0.695232\pi\) | ||||
−0.575602 | + | 0.817730i | \(0.695232\pi\) | |||||||
\(410\) | 6.76722e46i | 0.631395i | ||||||||
\(411\) | 1.84948e44 | + | 1.28209e45i | 0.00165157 | + | 0.0114489i | ||||
\(412\) | 1.71567e47 | 1.46651 | ||||||||
\(413\) | − | 2.27308e47i | − | 1.86000i | ||||||
\(414\) | 2.04863e47 | − | 6.03611e46i | 1.60493 | − | 0.472880i | ||||
\(415\) | −1.59912e47 | −1.19954 | ||||||||
\(416\) | − | 9.04406e44i | − | 0.00649656i | ||||||
\(417\) | −1.37202e46 | + | 1.97921e45i | −0.0943869 | + | 0.0136158i | ||||
\(418\) | 3.62633e47 | 2.38943 | ||||||||
\(419\) | 7.53107e46i | 0.475340i | 0.971346 | + | 0.237670i | \(0.0763837\pi\) | ||||
−0.971346 | + | 0.237670i | \(0.923616\pi\) | |||||||
\(420\) | 5.18591e46 | + | 3.59496e47i | 0.313573 | + | 2.17374i | ||||
\(421\) | 6.19282e46 | 0.358766 | 0.179383 | − | 0.983779i | \(-0.442590\pi\) | ||||
0.179383 | + | 0.983779i | \(0.442590\pi\) | |||||||
\(422\) | − | 1.30867e47i | − | 0.726450i | ||||||
\(423\) | −4.20026e46 | − | 1.42555e47i | −0.223434 | − | 0.758325i | ||||
\(424\) | −3.33850e47 | −1.70202 | ||||||||
\(425\) | 1.51179e46i | 0.0738739i | ||||||||
\(426\) | −2.91396e47 | + | 4.20354e46i | −1.36493 | + | 0.196898i | ||||
\(427\) | −6.30476e46 | −0.283117 | ||||||||
\(428\) | 3.45056e47i | 1.48560i | ||||||||
\(429\) | −3.18438e44 | − | 2.20746e45i | −0.00131460 | − | 0.00911301i | ||||
\(430\) | −4.66898e47 | −1.84837 | ||||||||
\(431\) | 9.70486e46i | 0.368467i | 0.982883 | + | 0.184233i | \(0.0589802\pi\) | ||||
−0.982883 | + | 0.184233i | \(0.941020\pi\) | |||||||
\(432\) | 1.50212e45 | − | 6.88541e44i | 0.00547013 | − | 0.00250739i | ||||
\(433\) | 2.41609e47 | 0.843977 | 0.421988 | − | 0.906601i | \(-0.361332\pi\) | ||||
0.421988 | + | 0.906601i | \(0.361332\pi\) | |||||||
\(434\) | − | 6.67684e47i | − | 2.23746i | ||||||
\(435\) | 1.93304e47 | − | 2.78850e46i | 0.621489 | − | 0.0896529i | ||||
\(436\) | 1.94688e47 | 0.600596 | ||||||||
\(437\) | 3.65381e47i | 1.08163i | ||||||||
\(438\) | −2.95602e46 | − | 2.04916e47i | −0.0839796 | − | 0.582161i | ||||
\(439\) | −4.81019e47 | −1.31160 | −0.655800 | − | 0.754935i | \(-0.727668\pi\) | ||||
−0.655800 | + | 0.754935i | \(0.727668\pi\) | |||||||
\(440\) | − | 5.23644e47i | − | 1.37053i | ||||||
\(441\) | 3.67858e47 | − | 1.08386e47i | 0.924241 | − | 0.272320i | ||||
\(442\) | −4.99506e45 | −0.0120487 | ||||||||
\(443\) | 2.10611e47i | 0.487769i | 0.969804 | + | 0.243885i | \(0.0784218\pi\) | ||||
−0.969804 | + | 0.243885i | \(0.921578\pi\) | |||||||
\(444\) | 7.16035e47 | − | 1.03292e47i | 1.59236 | − | 0.229706i | ||||
\(445\) | 1.96818e47 | 0.420324 | ||||||||
\(446\) | 6.48953e47i | 1.33102i | ||||||||
\(447\) | −8.30458e46 | − | 5.75687e47i | −0.163600 | − | 1.13410i | ||||
\(448\) | −1.19737e48 | −2.26582 | ||||||||
\(449\) | 1.01455e48i | 1.84433i | 0.386798 | + | 0.922164i | \(0.373581\pi\) | ||||
−0.386798 | + | 0.922164i | \(0.626419\pi\) | |||||||
\(450\) | −1.69754e46 | − | 5.76137e46i | −0.0296479 | − | 0.100624i | ||||
\(451\) | −3.38956e47 | −0.568808 | ||||||||
\(452\) | 2.45748e47i | 0.396276i | ||||||||
\(453\) | 2.40683e47 | − | 3.47197e46i | 0.372973 | − | 0.0538033i | ||||
\(454\) | 1.34504e48 | 2.00322 | ||||||||
\(455\) | 6.17991e45i | 0.00884662i | ||||||||
\(456\) | 1.09116e47 | + | 7.56411e47i | 0.150149 | + | 1.04086i | ||||
\(457\) | 1.30325e48 | 1.72400 | 0.861999 | − | 0.506909i | \(-0.169212\pi\) | ||||
0.861999 | + | 0.506909i | \(0.169212\pi\) | |||||||
\(458\) | − | 1.33079e48i | − | 1.69251i | ||||||
\(459\) | 3.88476e47 | + | 8.47498e47i | 0.475046 | + | 1.03636i | ||||
\(460\) | 1.37761e48 | 1.61989 | ||||||||
\(461\) | − | 8.28935e47i | − | 0.937354i | −0.883369 | − | 0.468677i | \(-0.844731\pi\) | ||
0.883369 | − | 0.468677i | \(-0.155269\pi\) | |||||||
\(462\) | −2.91165e48 | + | 4.20021e47i | −3.16653 | + | 0.456789i | ||||
\(463\) | −1.38341e48 | −1.44709 | −0.723543 | − | 0.690279i | \(-0.757488\pi\) | ||||
−0.723543 | + | 0.690279i | \(0.757488\pi\) | |||||||
\(464\) | − | 3.88317e45i | − | 0.00390718i | ||||||
\(465\) | −1.40699e47 | − | 9.75350e47i | −0.136188 | − | 0.944077i | ||||
\(466\) | −8.43116e47 | −0.785129 | ||||||||
\(467\) | − | 3.62292e47i | − | 0.324605i | −0.986741 | − | 0.162302i | \(-0.948108\pi\) | ||
0.986741 | − | 0.162302i | \(-0.0518920\pi\) | |||||||
\(468\) | 1.17723e46 | − | 3.46862e45i | 0.0101493 | − | 0.00299041i | ||||
\(469\) | −5.47611e46 | −0.0454319 | ||||||||
\(470\) | − | 1.55009e48i | − | 1.23764i | ||||||
\(471\) | 5.24663e47 | − | 7.56853e46i | 0.403185 | − | 0.0581614i | ||||
\(472\) | −1.80326e48 | −1.33384 | ||||||||
\(473\) | − | 2.33860e48i | − | 1.66516i | ||||||
\(474\) | 9.64110e46 | + | 6.68337e47i | 0.0660871 | + | 0.458127i | ||||
\(475\) | 1.02756e47 | 0.0678146 | ||||||||
\(476\) | 4.07451e48i | 2.58911i | ||||||||
\(477\) | 7.82357e47 | + | 2.65529e48i | 0.478712 | + | 1.62473i | ||||
\(478\) | 2.42894e48 | 1.43125 | ||||||||
\(479\) | 1.80871e48i | 1.02643i | 0.858259 | + | 0.513216i | \(0.171546\pi\) | ||||
−0.858259 | + | 0.513216i | \(0.828454\pi\) | |||||||
\(480\) | −1.74261e48 | + | 2.51380e47i | −0.952482 | + | 0.137400i | ||||
\(481\) | 1.23090e46 | 0.00648054 | ||||||||
\(482\) | 7.71405e47i | 0.391233i | ||||||||
\(483\) | −4.23204e47 | − | 2.93372e48i | −0.206777 | − | 1.43341i | ||||
\(484\) | 3.40536e48 | 1.60305 | ||||||||
\(485\) | − | 4.58226e47i | − | 0.207840i | ||||||
\(486\) | −2.43209e48 | − | 2.79357e48i | −1.06299 | − | 1.22098i | ||||
\(487\) | −3.17507e48 | −1.33731 | −0.668655 | − | 0.743573i | \(-0.733130\pi\) | ||||
−0.668655 | + | 0.743573i | \(0.733130\pi\) | |||||||
\(488\) | 5.00164e47i | 0.203028i | ||||||||
\(489\) | 3.97774e48 | − | 5.73809e47i | 1.55624 | − | 0.224496i | ||||
\(490\) | 3.99996e48 | 1.50843 | ||||||||
\(491\) | − | 8.71878e47i | − | 0.316948i | −0.987363 | − | 0.158474i | \(-0.949343\pi\) | ||
0.987363 | − | 0.158474i | \(-0.0506575\pi\) | |||||||
\(492\) | −2.66304e47 | − | 1.84606e48i | −0.0933266 | − | 0.646955i | ||||
\(493\) | 2.19089e48 | 0.740246 | ||||||||
\(494\) | 3.39514e46i | 0.0110604i | ||||||||
\(495\) | −4.16482e48 | + | 1.22713e48i | −1.30829 | + | 0.385475i | ||||
\(496\) | −1.95933e46 | −0.00593523 | ||||||||
\(497\) | 4.08607e48i | 1.19369i | ||||||||
\(498\) | 7.05389e48 | − | 1.01756e48i | 1.98747 | − | 0.286703i | ||||
\(499\) | −6.75309e48 | −1.83524 | −0.917620 | − | 0.397459i | \(-0.869892\pi\) | ||||
−0.917620 | + | 0.397459i | \(0.869892\pi\) | |||||||
\(500\) | − | 6.36632e48i | − | 1.66889i | ||||||
\(501\) | 8.79183e47 | + | 6.09464e48i | 0.222331 | + | 1.54124i | ||||
\(502\) | 4.06432e48 | 0.991566 | ||||||||
\(503\) | − | 2.21878e48i | − | 0.522264i | −0.965303 | − | 0.261132i | \(-0.915904\pi\) | ||
0.965303 | − | 0.261132i | \(-0.0840958\pi\) | |||||||
\(504\) | −1.75223e48 | − | 5.94700e48i | −0.397962 | − | 1.35067i | ||||
\(505\) | −1.74003e48 | −0.381340 | ||||||||
\(506\) | 1.11576e49i | 2.35973i | ||||||||
\(507\) | −4.84900e48 | + | 6.99493e47i | −0.989713 | + | 0.142771i | ||||
\(508\) | −1.00775e49 | −1.98521 | ||||||||
\(509\) | − | 1.47051e48i | − | 0.279606i | −0.990179 | − | 0.139803i | \(-0.955353\pi\) | ||
0.990179 | − | 0.139803i | \(-0.0446470\pi\) | |||||||
\(510\) | 1.38838e48 | + | 9.62447e48i | 0.254827 | + | 1.76650i | ||||
\(511\) | −2.87342e48 | −0.509123 | ||||||||
\(512\) | 7.03553e46i | 0.0120348i | ||||||||
\(513\) | 5.76044e48 | − | 2.64047e48i | 0.951356 | − | 0.436082i | ||||
\(514\) | −1.34279e49 | −2.14127 | ||||||||
\(515\) | − | 5.68274e48i | − | 0.875040i | ||||||
\(516\) | 1.27367e49 | − | 1.83734e48i | 1.89393 | − | 0.273209i | ||||
\(517\) | 7.76409e48 | 1.11496 | ||||||||
\(518\) | − | 1.62356e49i | − | 2.25182i | ||||||
\(519\) | 1.16492e47 | + | 8.07544e47i | 0.0156058 | + | 0.108182i | ||||
\(520\) | 4.90260e46 | 0.00634405 | ||||||||
\(521\) | 1.54623e48i | 0.193284i | 0.995319 | + | 0.0966419i | \(0.0308101\pi\) | ||||
−0.995319 | + | 0.0966419i | \(0.969190\pi\) | |||||||
\(522\) | −8.34940e48 | + | 2.46008e48i | −1.00829 | + | 0.297085i | ||||
\(523\) | 3.66724e48 | 0.427867 | 0.213934 | − | 0.976848i | \(-0.431372\pi\) | ||||
0.213934 | + | 0.976848i | \(0.431372\pi\) | |||||||
\(524\) | − | 1.14625e48i | − | 0.129216i | ||||||
\(525\) | −8.25051e47 | + | 1.19018e47i | −0.0898697 | + | 0.0129642i | ||||
\(526\) | 6.94360e48 | 0.730872 | ||||||||
\(527\) | − | 1.10546e49i | − | 1.12448i | ||||||
\(528\) | 1.23256e46 | + | 8.54429e46i | 0.00121170 | + | 0.00839974i | ||||
\(529\) | −7.17672e47 | −0.0681905 | ||||||||
\(530\) | 2.88726e49i | 2.65168i | ||||||||
\(531\) | 4.22584e48 | + | 1.43423e49i | 0.375155 | + | 1.27326i | ||||
\(532\) | 2.76944e49 | 2.37674 | ||||||||
\(533\) | − | 3.17347e46i | − | 0.00263296i | ||||||
\(534\) | −8.68185e48 | + | 1.25240e48i | −0.696418 | + | 0.100462i | ||||
\(535\) | 1.14291e49 | 0.886432 | ||||||||
\(536\) | 4.34427e47i | 0.0325800i | ||||||||
\(537\) | −3.17232e48 | − | 2.19910e49i | −0.230059 | − | 1.59481i | ||||
\(538\) | −2.26004e49 | −1.58502 | ||||||||
\(539\) | 2.00350e49i | 1.35891i | ||||||||
\(540\) | −9.95545e48 | − | 2.17188e49i | −0.653091 | − | 1.42478i | ||||
\(541\) | −3.99340e48 | −0.253391 | −0.126696 | − | 0.991942i | \(-0.540437\pi\) | ||||
−0.126696 | + | 0.991942i | \(0.540437\pi\) | |||||||
\(542\) | 1.08589e49i | 0.666500i | ||||||||
\(543\) | 6.32924e48 | − | 9.13025e47i | 0.375798 | − | 0.0542108i | ||||
\(544\) | −1.97506e49 | −1.13449 | ||||||||
\(545\) | − | 6.44858e48i | − | 0.358366i | ||||||
\(546\) | −3.93243e46 | − | 2.72603e47i | −0.00211443 | − | 0.0146576i | ||||
\(547\) | 7.48376e48 | 0.389357 | 0.194678 | − | 0.980867i | \(-0.437634\pi\) | ||||
0.194678 | + | 0.980867i | \(0.437634\pi\) | |||||||
\(548\) | − | 3.72388e47i | − | 0.0187476i | ||||||
\(549\) | 3.97808e48 | − | 1.17211e48i | 0.193808 | − | 0.0571038i | ||||
\(550\) | 3.13786e48 | 0.147947 | ||||||||
\(551\) | − | 1.48915e49i | − | 0.679530i | ||||||
\(552\) | −2.32736e49 | + | 3.35733e48i | −1.02792 | + | 0.148283i | ||||
\(553\) | 9.37169e48 | 0.400650 | ||||||||
\(554\) | − | 6.09169e49i | − | 2.52094i | ||||||
\(555\) | −3.42129e48 | − | 2.37169e49i | −0.137062 | − | 0.950134i | ||||
\(556\) | 3.98510e48 | 0.154558 | ||||||||
\(557\) | 4.55904e49i | 1.71190i | 0.517055 | + | 0.855952i | \(0.327028\pi\) | ||||
−0.517055 | + | 0.855952i | \(0.672972\pi\) | |||||||
\(558\) | 1.24128e49 | + | 4.21285e49i | 0.451288 | + | 1.53165i | ||||
\(559\) | 2.18951e47 | 0.00770785 | ||||||||
\(560\) | − | 2.39202e47i | − | 0.00815419i | ||||||
\(561\) | −4.82070e49 | + | 6.95411e48i | −1.59140 | + | 0.229567i | ||||
\(562\) | −3.81811e47 | −0.0122066 | ||||||||
\(563\) | 4.47479e49i | 1.38555i | 0.721155 | + | 0.692774i | \(0.243612\pi\) | ||||
−0.721155 | + | 0.692774i | \(0.756388\pi\) | |||||||
\(564\) | 6.09992e48 | + | 4.22856e49i | 0.182936 | + | 1.26815i | ||||
\(565\) | 8.13981e48 | 0.236452 | ||||||||
\(566\) | − | 8.06258e49i | − | 2.26871i | ||||||
\(567\) | −4.31934e49 | + | 2.78729e49i | −1.17740 | + | 0.759779i | ||||
\(568\) | 3.24153e49 | 0.856013 | ||||||||
\(569\) | 1.68421e49i | 0.430898i | 0.976515 | + | 0.215449i | \(0.0691215\pi\) | ||||
−0.976515 | + | 0.215449i | \(0.930879\pi\) | |||||||
\(570\) | 6.54175e49 | − | 9.43680e48i | 1.62161 | − | 0.233925i | ||||
\(571\) | 6.75389e49 | 1.62220 | 0.811100 | − | 0.584908i | \(-0.198869\pi\) | ||||
0.811100 | + | 0.584908i | \(0.198869\pi\) | |||||||
\(572\) | 6.41167e47i | 0.0149225i | ||||||||
\(573\) | −4.62333e48 | − | 3.20497e49i | −0.104273 | − | 0.722838i | ||||
\(574\) | −4.18582e49 | −0.914885 | ||||||||
\(575\) | 3.16165e48i | 0.0669718i | ||||||||
\(576\) | 7.55498e49 | − | 2.22601e49i | 1.55106 | − | 0.457007i | ||||
\(577\) | 2.31892e49 | 0.461446 | 0.230723 | − | 0.973019i | \(-0.425891\pi\) | ||||
0.230723 | + | 0.973019i | \(0.425891\pi\) | |||||||
\(578\) | 2.51543e49i | 0.485190i | ||||||||
\(579\) | 7.68825e49 | − | 1.10907e49i | 1.43752 | − | 0.207369i | ||||
\(580\) | −5.61459e49 | −1.01769 | ||||||||
\(581\) | − | 9.89125e49i | − | 1.73812i | ||||||
\(582\) | 2.91581e48 | + | 2.02129e49i | 0.0496758 | + | 0.344361i | ||||
\(583\) | −1.44617e50 | −2.38883 | ||||||||
\(584\) | 2.27952e49i | 0.365100i | ||||||||
\(585\) | −1.14890e47 | − | 3.89930e47i | −0.00178433 | − | 0.00605594i | ||||
\(586\) | −3.20816e49 | −0.483168 | ||||||||
\(587\) | − | 8.44537e49i | − | 1.23348i | −0.787166 | − | 0.616741i | \(-0.788452\pi\) | ||
0.787166 | − | 0.616741i | \(-0.211548\pi\) | |||||||
\(588\) | −1.09117e50 | + | 1.57406e49i | −1.54561 | + | 0.222962i | ||||
\(589\) | −7.51378e49 | −1.03225 | ||||||||
\(590\) | 1.55953e50i | 2.07806i | ||||||||
\(591\) | −8.62223e48 | − | 5.97707e49i | −0.111441 | − | 0.772527i | ||||
\(592\) | −4.76437e47 | −0.00597331 | ||||||||
\(593\) | 1.19791e50i | 1.45693i | 0.685083 | + | 0.728465i | \(0.259766\pi\) | ||||
−0.685083 | + | 0.728465i | \(0.740234\pi\) | |||||||
\(594\) | 1.75906e50 | − | 8.06319e49i | 2.07551 | − | 0.951373i | ||||
\(595\) | 1.34958e50 | 1.54488 | ||||||||
\(596\) | 1.67211e50i | 1.85709i | ||||||||
\(597\) | −1.59576e50 | + | 2.30196e49i | −1.71961 | + | 0.248062i | ||||
\(598\) | −1.04463e48 | −0.0109230 | ||||||||
\(599\) | 1.84673e49i | 0.187379i | 0.995601 | + | 0.0936895i | \(0.0298661\pi\) | ||||
−0.995601 | + | 0.0936895i | \(0.970134\pi\) | |||||||
\(600\) | 9.44183e47 | + | 6.54523e48i | 0.00929681 | + | 0.0644470i | ||||
\(601\) | −1.81640e49 | −0.173569 | −0.0867844 | − | 0.996227i | \(-0.527659\pi\) | ||||
−0.0867844 | + | 0.996227i | \(0.527659\pi\) | |||||||
\(602\) | − | 2.88797e50i | − | 2.67828i | ||||||
\(603\) | 3.45523e48 | − | 1.01805e48i | 0.0311004 | − | 0.00916346i | ||||
\(604\) | −6.99074e49 | −0.610743 | ||||||||
\(605\) | − | 1.12794e50i | − | 0.956512i | ||||||
\(606\) | 7.67547e49 | − | 1.10723e49i | 0.631826 | − | 0.0911441i | ||||
\(607\) | −2.81069e49 | −0.224604 | −0.112302 | − | 0.993674i | \(-0.535822\pi\) | ||||
−0.112302 | + | 0.993674i | \(0.535822\pi\) | |||||||
\(608\) | 1.34245e50i | 1.04144i | ||||||||
\(609\) | 1.72481e49 | + | 1.19567e50i | 0.129906 | + | 0.900532i | ||||
\(610\) | 4.32562e49 | 0.316309 | ||||||||
\(611\) | 7.26911e47i | 0.00516106i | ||||||||
\(612\) | −7.57485e49 | − | 2.57087e50i | −0.522214 | − | 1.77237i | ||||
\(613\) | 6.55578e49 | 0.438870 | 0.219435 | − | 0.975627i | \(-0.429579\pi\) | ||||
0.219435 | + | 0.975627i | \(0.429579\pi\) | |||||||
\(614\) | − | 1.33468e50i | − | 0.867655i | ||||||
\(615\) | −6.11463e49 | + | 8.82067e48i | −0.386027 | + | 0.0556864i | ||||
\(616\) | 3.23897e50 | 1.98588 | ||||||||
\(617\) | − | 1.44551e50i | − | 0.860771i | −0.902645 | − | 0.430385i | \(-0.858378\pi\) | ||
0.902645 | − | 0.430385i | \(-0.141622\pi\) | |||||||
\(618\) | 3.61607e49 | + | 2.50672e50i | 0.209144 | + | 1.44982i | ||||
\(619\) | 2.86652e50 | 1.61036 | 0.805180 | − | 0.593031i | \(-0.202069\pi\) | ||||
0.805180 | + | 0.593031i | \(0.202069\pi\) | |||||||
\(620\) | 2.83295e50i | 1.54592i | ||||||||
\(621\) | 8.12429e49 | + | 1.77239e50i | 0.430662 | + | 0.939532i | ||||
\(622\) | −1.52604e50 | −0.785849 | ||||||||
\(623\) | 1.21740e50i | 0.609046i | ||||||||
\(624\) | −7.99957e45 | + | 1.15398e45i | −3.88816e−5 | + | 5.60887e-6i | ||||
\(625\) | −1.97147e50 | −0.931002 | ||||||||
\(626\) | − | 2.47738e50i | − | 1.13672i | ||||||
\(627\) | 4.72670e49 | + | 3.27663e50i | 0.210738 | + | 1.46087i | ||||
\(628\) | −1.52391e50 | −0.660214 | ||||||||
\(629\) | − | 2.68807e50i | − | 1.13169i | ||||||
\(630\) | −5.14320e50 | + | 1.51540e50i | −2.10428 | + | 0.620008i | ||||
\(631\) | 1.51022e50 | 0.600500 | 0.300250 | − | 0.953861i | \(-0.402930\pi\) | ||||
0.300250 | + | 0.953861i | \(0.402930\pi\) | |||||||
\(632\) | − | 7.43468e49i | − | 0.287313i | ||||||
\(633\) | 1.18247e50 | − | 1.70577e49i | 0.444143 | − | 0.0640699i | ||||
\(634\) | −4.24848e50 | −1.55106 | ||||||||
\(635\) | 3.33794e50i | 1.18454i | ||||||||
\(636\) | −1.13620e50 | − | 7.87630e50i | −0.391945 | − | 2.71703i | ||||
\(637\) | −1.87577e48 | −0.00629027 | ||||||||
\(638\) | − | 4.54740e50i | − | 1.48249i | ||||||
\(639\) | −7.59635e49 | − | 2.57817e50i | −0.240763 | − | 0.817138i | ||||
\(640\) | 5.09205e50 | 1.56911 | ||||||||
\(641\) | 2.02582e50i | 0.606954i | 0.952839 | + | 0.303477i | \(0.0981476\pi\) | ||||
−0.952839 | + | 0.303477i | \(0.901852\pi\) | |||||||
\(642\) | −5.04152e50 | + | 7.27265e49i | −1.46869 | + | 0.211866i | ||||
\(643\) | 3.57163e50 | 1.01174 | 0.505870 | − | 0.862610i | \(-0.331172\pi\) | ||||
0.505870 | + | 0.862610i | \(0.331172\pi\) | |||||||
\(644\) | 8.52112e50i | 2.34720i | ||||||||
\(645\) | −6.08574e49 | − | 4.21873e50i | −0.163019 | − | 1.13007i | ||||
\(646\) | 7.41438e50 | 1.93148 | ||||||||
\(647\) | − | 2.86314e50i | − | 0.725381i | −0.931910 | − | 0.362690i | \(-0.881858\pi\) | ||
0.931910 | − | 0.362690i | \(-0.118142\pi\) | |||||||
\(648\) | 2.21119e50 | + | 3.42659e50i | 0.544849 | + | 0.844329i | ||||
\(649\) | −7.81137e50 | −1.87207 | ||||||||
\(650\) | 2.93782e47i | 0.000684833i | ||||||||
\(651\) | 6.03297e50 | − | 8.70286e49i | 1.36796 | − | 0.197335i | ||||
\(652\) | −1.15535e51 | −2.54834 | ||||||||
\(653\) | 5.19777e50i | 1.11527i | 0.830086 | + | 0.557635i | \(0.188291\pi\) | ||||
−0.830086 | + | 0.557635i | \(0.811709\pi\) | |||||||
\(654\) | 4.10339e49 | + | 2.84454e50i | 0.0856532 | + | 0.593762i | ||||
\(655\) | −3.79668e49 | −0.0771011 | ||||||||
\(656\) | 1.22834e48i | 0.00242688i | ||||||||
\(657\) | 1.81303e50 | − | 5.34193e49i | 0.348520 | − | 0.102688i | ||||
\(658\) | 9.58799e50 | 1.79334 | ||||||||
\(659\) | − | 6.61615e50i | − | 1.20411i | −0.798453 | − | 0.602057i | \(-0.794348\pi\) | ||
0.798453 | − | 0.602057i | \(-0.205652\pi\) | |||||||
\(660\) | 1.23540e51 | − | 1.78213e50i | 2.18784 | − | 0.315608i | ||||
\(661\) | −2.77874e50 | −0.478875 | −0.239437 | − | 0.970912i | \(-0.576963\pi\) | ||||
−0.239437 | + | 0.970912i | \(0.576963\pi\) | |||||||
\(662\) | 1.81750e51i | 3.04811i | ||||||||
\(663\) | −6.51077e47 | − | 4.51337e48i | −0.00106265 | − | 0.00736643i | ||||
\(664\) | −7.84685e50 | −1.24644 | ||||||||
\(665\) | − | 9.17310e50i | − | 1.41816i | ||||||
\(666\) | 3.01834e50 | + | 1.02441e51i | 0.454184 | + | 1.54148i | ||||
\(667\) | 4.58187e50 | 0.671085 | ||||||||
\(668\) | − | 1.77022e51i | − | 2.52377i | ||||||
\(669\) | −5.86372e50 | + | 8.45872e49i | −0.813773 | + | 0.117391i | ||||
\(670\) | 3.75710e49 | 0.0507582 | ||||||||
\(671\) | 2.16661e50i | 0.284955i | ||||||||
\(672\) | −1.55489e50 | − | 1.07788e51i | −0.199092 | − | 1.38014i | ||||
\(673\) | −1.06983e51 | −1.33366 | −0.666828 | − | 0.745211i | \(-0.732349\pi\) | ||||
−0.666828 | + | 0.745211i | \(0.732349\pi\) | |||||||
\(674\) | − | 1.02496e51i | − | 1.24402i | ||||||
\(675\) | 4.98451e49 | − | 2.28480e49i | 0.0589054 | − | 0.0270010i | ||||
\(676\) | 1.40841e51 | 1.62065 | ||||||||
\(677\) | 6.04437e50i | 0.677259i | 0.940920 | + | 0.338630i | \(0.109963\pi\) | ||||
−0.940920 | + | 0.338630i | \(0.890037\pi\) | |||||||
\(678\) | −3.59056e50 | + | 5.17957e49i | −0.391767 | + | 0.0565144i | ||||
\(679\) | 2.83433e50 | 0.301158 | ||||||||
\(680\) | − | 1.07064e51i | − | 1.10786i | ||||||
\(681\) | 1.75317e50 | + | 1.21533e51i | 0.176676 | + | 1.22474i | ||||
\(682\) | −2.29448e51 | −2.25199 | ||||||||
\(683\) | 1.98977e51i | 1.90209i | 0.309054 | + | 0.951045i | \(0.399988\pi\) | ||||
−0.309054 | + | 0.951045i | \(0.600012\pi\) | |||||||
\(684\) | −1.74742e51 | + | 5.14862e50i | −1.62700 | + | 0.479381i | ||||
\(685\) | −1.23345e49 | −0.0111864 | ||||||||
\(686\) | − | 9.36617e49i | − | 0.0827424i | ||||||
\(687\) | 1.20245e51 | − | 1.73460e50i | 1.03478 | − | 0.149272i | ||||
\(688\) | −8.47479e48 | −0.00710456 | ||||||||
\(689\) | − | 1.35397e49i | − | 0.0110577i | ||||||
\(690\) | 2.90355e50 | + | 2.01279e51i | 0.231018 | + | 1.60146i | ||||
\(691\) | −1.77535e51 | −1.37619 | −0.688097 | − | 0.725619i | \(-0.741554\pi\) | ||||
−0.688097 | + | 0.725619i | \(0.741554\pi\) | |||||||
\(692\) | − | 2.34555e50i | − | 0.177147i | ||||||
\(693\) | −7.59033e50 | − | 2.57612e51i | −0.558550 | − | 1.89569i | ||||
\(694\) | 3.50441e51 | 2.51272 | ||||||||
\(695\) | − | 1.31997e50i | − | 0.0922225i | ||||||
\(696\) | 9.48538e50 | − | 1.36831e50i | 0.645785 | − | 0.0931578i | ||||
\(697\) | −6.93029e50 | −0.459792 | ||||||||
\(698\) | − | 1.79074e51i | − | 1.15780i | ||||||
\(699\) | −1.09895e50 | − | 7.61811e50i | −0.0692451 | − | 0.480019i | ||||
\(700\) | 2.39640e50 | 0.147162 | ||||||||
\(701\) | 2.09034e51i | 1.25110i | 0.780183 | + | 0.625551i | \(0.215126\pi\) | ||||
−0.780183 | + | 0.625551i | \(0.784874\pi\) | |||||||
\(702\) | 7.54914e48 | + | 1.64692e49i | 0.00440382 | + | 0.00960736i | ||||
\(703\) | −1.82708e51 | −1.03887 | ||||||||
\(704\) | 4.11474e51i | 2.28052i | ||||||||
\(705\) | 1.40061e51 | − | 2.02045e50i | 0.756681 | − | 0.109155i | ||||
\(706\) | 5.79974e51 | 3.05438 | ||||||||
\(707\) | − | 1.07628e51i | − | 0.552558i | ||||||
\(708\) | −6.13706e50 | − | 4.25431e51i | −0.307158 | − | 2.12927i | ||||
\(709\) | 2.67147e51 | 1.30352 | 0.651761 | − | 0.758424i | \(-0.274030\pi\) | ||||
0.651761 | + | 0.758424i | \(0.274030\pi\) | |||||||
\(710\) | − | 2.80341e51i | − | 1.33363i | ||||||
\(711\) | −5.91320e50 | + | 1.74227e50i | −0.274265 | + | 0.0808098i | ||||
\(712\) | 9.65782e50 | 0.436756 | ||||||||
\(713\) | − | 2.31187e51i | − | 1.01942i | ||||||
\(714\) | −5.95316e51 | + | 8.58773e50i | −2.55964 | + | 0.369242i | ||||
\(715\) | 2.12371e49 | 0.00890403 | ||||||||
\(716\) | 6.38740e51i | 2.61150i | ||||||||
\(717\) | 3.16598e50 | + | 2.19471e51i | 0.126230 | + | 0.875049i | ||||
\(718\) | −5.83751e51 | −2.26980 | ||||||||
\(719\) | 9.98772e50i | 0.378745i | 0.981905 | + | 0.189372i | \(0.0606453\pi\) | ||||
−0.981905 | + | 0.189372i | \(0.939355\pi\) | |||||||
\(720\) | 4.44697e48 | + | 1.50928e49i | 0.00164467 | + | 0.00558194i | ||||
\(721\) | 3.51502e51 | 1.26792 | ||||||||
\(722\) | − | 4.38253e50i | − | 0.154190i | ||||||
\(723\) | −6.97016e50 | + | 1.00548e50i | −0.239196 | + | 0.0345052i | ||||
\(724\) | −1.83836e51 | −0.615369 | ||||||||
\(725\) | − | 1.28856e50i | − | 0.0420747i | ||||||
\(726\) | 7.17739e50 | + | 4.97548e51i | 0.228616 | + | 1.58481i | ||||
\(727\) | −2.95088e51 | −0.916921 | −0.458461 | − | 0.888715i | \(-0.651599\pi\) | ||||
−0.458461 | + | 0.888715i | \(0.651599\pi\) | |||||||
\(728\) | 3.03247e49i | 0.00919247i | ||||||||
\(729\) | 2.20717e51 | − | 2.56168e51i | 0.652740 | − | 0.757582i | ||||
\(730\) | 1.97142e51 | 0.568811 | ||||||||
\(731\) | − | 4.78149e51i | − | 1.34602i | ||||||
\(732\) | −1.18001e51 | + | 1.70222e50i | −0.324104 | + | 0.0467537i | ||||
\(733\) | 2.86424e51 | 0.767605 | 0.383803 | − | 0.923415i | \(-0.374614\pi\) | ||||
0.383803 | + | 0.923415i | \(0.374614\pi\) | |||||||
\(734\) | − | 1.20930e52i | − | 3.16231i | ||||||
\(735\) | 5.21370e50 | + | 3.61422e51i | 0.133038 | + | 0.922238i | ||||
\(736\) | −4.13049e51 | −1.02849 | ||||||||
\(737\) | 1.88185e50i | 0.0457268i | ||||||||
\(738\) | 2.64110e51 | − | 7.78179e50i | 0.626283 | − | 0.184529i | ||||
\(739\) | −5.73726e50 | −0.132771 | −0.0663857 | − | 0.997794i | \(-0.521147\pi\) | ||||
−0.0663857 | + | 0.997794i | \(0.521147\pi\) | |||||||
\(740\) | 6.88869e51i | 1.55584i | ||||||||
\(741\) | −3.06773e49 | + | 4.42536e48i | −0.00676223 | + | 0.000975486i | ||||
\(742\) | −1.78590e52 | −3.84226 | ||||||||
\(743\) | − | 6.56790e51i | − | 1.37920i | −0.724189 | − | 0.689601i | \(-0.757786\pi\) | ||
0.724189 | − | 0.689601i | \(-0.242214\pi\) | |||||||
\(744\) | −6.90409e50 | − | 4.78603e51i | −0.141512 | − | 0.980985i | ||||
\(745\) | 5.53846e51 | 1.10809 | ||||||||
\(746\) | 3.93982e51i | 0.769444i | ||||||||
\(747\) | 1.83887e51 | + | 6.24102e51i | 0.350573 | + | 1.18983i | ||||
\(748\) | 1.40019e52 | 2.60591 | ||||||||
\(749\) | 7.06942e51i | 1.28443i | ||||||||
\(750\) | 9.30167e51 | − | 1.34181e51i | 1.64990 | − | 0.238007i | ||||
\(751\) | −8.72757e50 | −0.151138 | −0.0755692 | − | 0.997141i | \(-0.524077\pi\) | ||||
−0.0755692 | + | 0.997141i | \(0.524077\pi\) | |||||||
\(752\) | − | 2.81361e49i | − | 0.00475711i | ||||||
\(753\) | 5.29760e50 | + | 3.67239e51i | 0.0874520 | + | 0.606232i | ||||
\(754\) | 4.25750e49 | 0.00686231 | ||||||||
\(755\) | 2.31551e51i | 0.364420i | ||||||||
\(756\) | 1.34340e52 | − | 6.15788e51i | 2.06450 | − | 0.946322i | ||||
\(757\) | −1.51978e51 | −0.228064 | −0.114032 | − | 0.993477i | \(-0.536377\pi\) | ||||
−0.114032 | + | 0.993477i | \(0.536377\pi\) | |||||||
\(758\) | 1.03611e52i | 1.51831i | ||||||||
\(759\) | −1.00817e52 | + | 1.45433e51i | −1.44271 | + | 0.208119i | ||||
\(760\) | −7.27713e51 | −1.01699 | ||||||||
\(761\) | 6.48495e50i | 0.0885080i | 0.999020 | + | 0.0442540i | \(0.0140911\pi\) | ||||
−0.999020 | + | 0.0442540i | \(0.985909\pi\) | |||||||
\(762\) | −2.12402e51 | − | 1.47240e52i | −0.283118 | − | 1.96262i | ||||
\(763\) | 3.98873e51 | 0.519269 | ||||||||
\(764\) | 9.30898e51i | 1.18365i | ||||||||
\(765\) | −8.51538e51 | + | 2.50898e51i | −1.05754 | + | 0.311596i | ||||
\(766\) | 2.01308e52 | 2.44199 | ||||||||
\(767\) | − | 7.31337e49i | − | 0.00866565i | ||||||
\(768\) | −8.63434e51 | + | 1.24555e51i | −0.999372 | + | 0.144164i | ||||
\(769\) | −1.21318e52 | −1.37168 | −0.685838 | − | 0.727754i | \(-0.740564\pi\) | ||||
−0.685838 | + | 0.727754i | \(0.740564\pi\) | |||||||
\(770\) | − | 2.80119e52i | − | 3.09392i | ||||||
\(771\) | −1.75025e51 | − | 1.21330e52i | −0.188851 | − | 1.30915i | ||||
\(772\) | −2.23309e52 | −2.35393 | ||||||||
\(773\) | − | 8.56661e51i | − | 0.882222i | −0.897453 | − | 0.441111i | \(-0.854584\pi\) | ||
0.897453 | − | 0.441111i | \(-0.145416\pi\) | |||||||
\(774\) | 5.36897e51 | + | 1.82220e52i | 0.540199 | + | 1.83341i | ||||
\(775\) | −6.50168e50 | −0.0639138 | ||||||||
\(776\) | − | 2.24851e51i | − | 0.215965i | ||||||
\(777\) | 1.46700e52 | − | 2.11622e51i | 1.37674 | − | 0.198601i | ||||
\(778\) | −1.91145e51 | −0.175279 | ||||||||
\(779\) | 4.71051e51i | 0.422079i | ||||||||
\(780\) | 1.66851e49 | + | 1.15664e50i | 0.00146092 | + | 0.0101273i | ||||
\(781\) | 1.40417e52 | 1.20144 | ||||||||
\(782\) | 2.28129e52i | 1.90747i | ||||||||
\(783\) | −3.31114e51 | − | 7.22357e51i | −0.270561 | − | 0.590256i | ||||
\(784\) | 7.26043e49 | 0.00579793 | ||||||||
\(785\) | 5.04757e51i | 0.393939i | ||||||||
\(786\) | 1.67476e51 | − | 2.41592e50i | 0.127746 | − | 0.0184280i | ||||
\(787\) | −1.54435e52 | −1.15133 | −0.575666 | − | 0.817685i | \(-0.695257\pi\) | ||||
−0.575666 | + | 0.817685i | \(0.695257\pi\) | |||||||
\(788\) | 1.73607e52i | 1.26501i | ||||||||
\(789\) | 9.05057e50 | + | 6.27400e51i | 0.0644599 | + | 0.446847i | ||||
\(790\) | −6.42981e51 | −0.447621 | ||||||||
\(791\) | 5.03483e51i | 0.342616i | ||||||||
\(792\) | −2.04367e52 | + | 6.02150e51i | −1.35943 | + | 0.400545i | ||||
\(793\) | −2.02849e49 | −0.00131903 | ||||||||
\(794\) | − | 4.49898e52i | − | 2.85986i | ||||||
\(795\) | −2.60883e52 | + | 3.76338e51i | −1.62121 | + | 0.233867i | ||||
\(796\) | 4.63496e52 | 2.81586 | ||||||||
\(797\) | − | 3.04943e52i | − | 1.81121i | −0.424122 | − | 0.905605i | \(-0.639417\pi\) | ||
0.424122 | − | 0.905605i | \(-0.360583\pi\) | |||||||
\(798\) | 5.83708e51 | + | 4.04636e52i | 0.338956 | + | 2.34970i | ||||
\(799\) | 1.58744e52 | 0.901272 | ||||||||
\(800\) | 1.16162e51i | 0.0644829i | ||||||||
\(801\) | −2.26325e51 | − | 7.68138e51i | −0.122842 | − | 0.416921i | ||||
\(802\) | 2.57442e52 | 1.36628 | ||||||||
\(803\) | 9.87444e51i | 0.512428i | ||||||||
\(804\) | −1.02492e51 | + | 1.47849e50i | −0.0520091 | + | 0.00750258i | ||||
\(805\) | 2.82242e52 | 1.40054 | ||||||||
\(806\) | − | 2.14820e50i | − | 0.0104242i | ||||||
\(807\) | −2.94583e51 | − | 2.04209e52i | −0.139792 | − | 0.969063i | ||||
\(808\) | −8.53830e51 | −0.396248 | ||||||||
\(809\) | − | 2.61039e51i | − | 0.118477i | −0.998244 | − | 0.0592383i | \(-0.981133\pi\) | ||
0.998244 | − | 0.0592383i | \(-0.0188672\pi\) | |||||||
\(810\) | 2.96345e52 | − | 1.91233e52i | 1.31543 | − | 0.848852i | ||||
\(811\) | 8.22781e51 | 0.357198 | 0.178599 | − | 0.983922i | \(-0.442844\pi\) | ||||
0.178599 | + | 0.983922i | \(0.442844\pi\) | |||||||
\(812\) | − | 3.47287e52i | − | 1.47462i | ||||||
\(813\) | −9.81176e51 | + | 1.41540e51i | −0.407490 | + | 0.0587825i | ||||
\(814\) | −5.57934e52 | −2.26643 | ||||||||
\(815\) | 3.82683e52i | 1.52055i | ||||||||
\(816\) | 2.52008e49 | + | 1.74696e50i | 0.000979473 | + | 0.00678986i | ||||
\(817\) | −3.24997e52 | −1.23561 | ||||||||
\(818\) | 5.01097e52i | 1.86364i | ||||||||
\(819\) | 2.41189e50 | − | 7.10643e49i | 0.00877500 | − | 0.00258548i | ||||
\(820\) | 1.77602e52 | 0.632119 | ||||||||
\(821\) | 3.51999e52i | 1.22565i | 0.790220 | + | 0.612823i | \(0.209966\pi\) | ||||
−0.790220 | + | 0.612823i | \(0.790034\pi\) | |||||||
\(822\) | 5.44087e50 | − | 7.84873e49i | 0.0185343 | − | 0.00267366i | ||||
\(823\) | −6.41580e51 | −0.213823 | −0.106911 | − | 0.994269i | \(-0.534096\pi\) | ||||
−0.106911 | + | 0.994269i | \(0.534096\pi\) | |||||||
\(824\) | − | 2.78851e52i | − | 0.909249i | ||||||
\(825\) | 4.09002e50 | + | 2.83527e51i | 0.0130483 | + | 0.0904530i | ||||
\(826\) | −9.64638e52 | −3.01109 | ||||||||
\(827\) | − | 1.85904e52i | − | 0.567792i | −0.958855 | − | 0.283896i | \(-0.908373\pi\) | ||
0.958855 | − | 0.283896i | \(-0.0916270\pi\) | |||||||
\(828\) | −1.58415e52 | − | 5.37652e52i | −0.473423 | − | 1.60678i | ||||
\(829\) | 5.08345e52 | 1.48654 | 0.743271 | − | 0.668991i | \(-0.233274\pi\) | ||||
0.743271 | + | 0.668991i | \(0.233274\pi\) | |||||||
\(830\) | 6.78627e52i | 1.94189i | ||||||||
\(831\) | 5.50424e52 | − | 7.94015e51i | 1.54127 | − | 0.222336i | ||||
\(832\) | −3.85241e50 | −0.0105563 | ||||||||
\(833\) | 4.09634e52i | 1.09846i | ||||||||
\(834\) | 8.39929e50 | + | 5.82252e51i | 0.0220421 | + | 0.152800i | ||||
\(835\) | −5.86342e52 | −1.50589 | ||||||||
\(836\) | − | 9.51711e52i | − | 2.39217i | ||||||
\(837\) | −3.64479e52 | + | 1.67070e52i | −0.896633 | + | 0.410998i | ||||
\(838\) | 3.19600e52 | 0.769511 | ||||||||
\(839\) | − | 4.29155e50i | − | 0.0101134i | −0.999987 | − | 0.00505672i | \(-0.998390\pi\) | ||
0.999987 | − | 0.00505672i | \(-0.00160961\pi\) | |||||||
\(840\) | 5.84296e52 | − | 8.42877e51i | 1.34774 | − | 0.194418i | ||||
\(841\) | 2.56184e52 | 0.578395 | ||||||||
\(842\) | − | 2.62808e52i | − | 0.580793i | ||||||
\(843\) | −4.97667e49 | − | 3.44991e50i | −0.00107657 | − | 0.00746297i | ||||
\(844\) | −3.43453e52 | −0.727284 | ||||||||
\(845\) | − | 4.66503e52i | − | 0.967017i | ||||||
\(846\) | −6.04968e52 | + | 1.78249e52i | −1.22762 | + | 0.361709i | ||||
\(847\) | 6.97682e52 | 1.38598 | ||||||||
\(848\) | 5.24075e50i | 0.0101922i | ||||||||
\(849\) | 7.28508e52 | − | 1.05091e52i | 1.38706 | − | 0.200091i | ||||
\(850\) | 6.41567e51 | 0.119592 | ||||||||
\(851\) | − | 5.62162e52i | − | 1.02596i | ||||||
\(852\) | 1.10320e52 | + | 7.64754e52i | 0.197124 | + | 1.36650i | ||||
\(853\) | −2.57721e52 | −0.450887 | −0.225443 | − | 0.974256i | \(-0.572383\pi\) | ||||
−0.225443 | + | 0.974256i | \(0.572383\pi\) | |||||||
\(854\) | 2.67559e52i | 0.458329i | ||||||||
\(855\) | 1.70536e52 | + | 5.78790e52i | 0.286039 | + | 0.970802i | ||||
\(856\) | 5.60826e52 | 0.921086 | ||||||||
\(857\) | 5.20144e52i | 0.836505i | 0.908331 | + | 0.418252i | \(0.137357\pi\) | ||||
−0.908331 | + | 0.418252i | \(0.862643\pi\) | |||||||
\(858\) | −9.36793e50 | + | 1.35137e50i | −0.0147527 | + | 0.00212816i | ||||
\(859\) | −5.54657e52 | −0.855357 | −0.427678 | − | 0.903931i | \(-0.640668\pi\) | ||||
−0.427678 | + | 0.903931i | \(0.640668\pi\) | |||||||
\(860\) | 1.22535e53i | 1.85050i | ||||||||
\(861\) | −5.45597e51 | − | 3.78217e52i | −0.0806891 | − | 0.559350i | ||||
\(862\) | 4.11851e52 | 0.596498 | ||||||||
\(863\) | − | 2.75559e52i | − | 0.390859i | −0.980718 | − | 0.195430i | \(-0.937390\pi\) | ||
0.980718 | − | 0.195430i | \(-0.0626101\pi\) | |||||||
\(864\) | 2.98495e52 | + | 6.51196e52i | 0.414657 | + | 0.904616i | ||||
\(865\) | −7.76906e51 | −0.105701 | ||||||||
\(866\) | − | 1.02533e53i | − | 1.36628i | ||||||
\(867\) | −2.27286e52 | + | 3.27872e51i | −0.296640 | + | 0.0427918i | ||||
\(868\) | −1.75230e53 | −2.24003 | ||||||||
\(869\) | − | 3.22056e52i | − | 0.403251i | ||||||
\(870\) | −1.18337e52 | − | 8.20333e52i | −0.145136 | − | 1.00611i | ||||
\(871\) | −1.76188e49 | −0.000211665 | ||||||||
\(872\) | − | 3.16431e52i | − | 0.372376i | ||||||
\(873\) | −1.78836e52 | + | 5.26925e51i | −0.206157 | + | 0.0607424i | ||||
\(874\) | 1.55059e53 | 1.75102 | ||||||||
\(875\) | − | 1.30432e53i | − | 1.44291i | ||||||
\(876\) | −5.37793e52 | + | 7.75793e51i | −0.582829 | + | 0.0840760i | ||||
\(877\) | 4.40882e52 | 0.468091 | 0.234045 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234045 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(878\) | 2.04133e53i | 2.12330i | ||||||||
\(879\) | −4.18164e51 | − | 2.89878e52i | −0.0426135 | − | 0.295403i | ||||
\(880\) | −8.22013e50 | −0.00820711 | ||||||||
\(881\) | − | 3.15747e52i | − | 0.308868i | −0.988003 | − | 0.154434i | \(-0.950645\pi\) | ||
0.988003 | − | 0.154434i | \(-0.0493554\pi\) | |||||||
\(882\) | −4.59964e52 | − | 1.56110e53i | −0.440849 | − | 1.49622i | ||||
\(883\) | −1.34500e53 | −1.26308 | −0.631540 | − | 0.775343i | \(-0.717577\pi\) | ||||
−0.631540 | + | 0.775343i | \(0.717577\pi\) | |||||||
\(884\) | 1.31093e51i | 0.0120625i | ||||||||
\(885\) | −1.40914e53 | + | 2.03275e52i | −1.27050 | + | 0.183276i | ||||
\(886\) | 8.93783e52 | 0.789633 | ||||||||
\(887\) | 1.43899e53i | 1.24575i | 0.782321 | + | 0.622876i | \(0.214036\pi\) | ||||
−0.782321 | + | 0.622876i | \(0.785964\pi\) | |||||||
\(888\) | −1.67882e52 | − | 1.16379e53i | −0.142420 | − | 0.987279i | ||||
\(889\) | −2.06466e53 | −1.71639 | ||||||||
\(890\) | − | 8.35247e52i | − | 0.680448i | ||||||
\(891\) | 9.57845e52 | + | 1.48433e53i | 0.764710 | + | 1.18504i | ||||
\(892\) | 1.70314e53 | 1.33255 | ||||||||
\(893\) | − | 1.07898e53i | − | 0.827349i | ||||||
\(894\) | −2.44308e53 | + | 3.52426e52i | −1.83595 | + | 0.264846i | ||||
\(895\) | 2.11567e53 | 1.55824 | ||||||||
\(896\) | 3.14965e53i | 2.27362i | ||||||||
\(897\) | −1.36161e50 | − | 9.43892e50i | −0.000963362 | − | 0.00667819i | ||||
\(898\) | 4.30549e53 | 2.98572 | ||||||||
\(899\) | 9.42225e52i | 0.640443i | ||||||||
\(900\) | −1.51204e52 | + | 4.45510e51i | −0.100739 | + | 0.0296820i | ||||
\(901\) | −2.95684e53 | −1.93100 | ||||||||
\(902\) | 1.43845e53i | 0.920823i | ||||||||
\(903\) | 2.60947e53 | − | 3.76429e52i | 1.63747 | − | 0.236213i | ||||
\(904\) | 3.99419e52 | 0.245696 | ||||||||
\(905\) | 6.08911e52i | 0.367181i | ||||||||
\(906\) | −1.47342e52 | − | 1.02140e53i | −0.0871002 | − | 0.603793i | ||||
\(907\) | 2.72180e53 | 1.57734 | 0.788671 | − | 0.614816i | \(-0.210770\pi\) | ||||
0.788671 | + | 0.614816i | \(0.210770\pi\) | |||||||
\(908\) | − | 3.52997e53i | − | 2.00552i | ||||||
\(909\) | 2.00090e52 | + | 6.79097e52i | 0.111449 | + | 0.378253i | ||||
\(910\) | 2.62260e51 | 0.0143215 | ||||||||
\(911\) | 9.26197e52i | 0.495876i | 0.968776 | + | 0.247938i | \(0.0797529\pi\) | ||||
−0.968776 | + | 0.247938i | \(0.920247\pi\) | |||||||
\(912\) | 1.18741e51 | − | 1.71290e50i | 0.00623295 | − | 0.000899135i | ||||
\(913\) | −3.39910e53 | −1.74940 | ||||||||
\(914\) | − | 5.53068e53i | − | 2.79092i | ||||||
\(915\) | 5.63819e51 | + | 3.90848e52i | 0.0278972 | + | 0.193388i | ||||
\(916\) | −3.49258e53 | −1.69445 | ||||||||
\(917\) | − | 2.34841e52i | − | 0.111719i | ||||||
\(918\) | 3.59658e53 | − | 1.64860e53i | 1.67773 | − | 0.769035i | ||||
\(919\) | −4.91601e52 | −0.224871 | −0.112436 | − | 0.993659i | \(-0.535865\pi\) | ||||
−0.112436 | + | 0.993659i | \(0.535865\pi\) | |||||||
\(920\) | − | 2.23906e53i | − | 1.00435i | ||||||
\(921\) | 1.20597e53 | − | 1.73968e52i | 0.530474 | − | 0.0765236i | ||||
\(922\) | −3.51780e53 | −1.51745 | ||||||||
\(923\) | 1.31465e51i | 0.00556134i | ||||||||
\(924\) | 1.10232e53 | + | 7.64148e53i | 0.457313 | + | 3.17017i | ||||
\(925\) | −1.58097e52 | −0.0643239 | ||||||||
\(926\) | 5.87087e53i | 2.34264i | ||||||||
\(927\) | −2.21785e53 | + | 6.53472e52i | −0.867956 | + | 0.255736i | ||||
\(928\) | 1.68342e53 | 0.646145 | ||||||||
\(929\) | − | 3.55083e53i | − | 1.33674i | −0.743829 | − | 0.668370i | \(-0.766992\pi\) | ||
0.743829 | − | 0.668370i | \(-0.233008\pi\) | |||||||
\(930\) | −4.13915e53 | + | 5.97093e52i | −1.52833 | + | 0.220470i | ||||
\(931\) | 2.78428e53 | 1.00837 | ||||||||
\(932\) | 2.21271e53i | 0.786030i | ||||||||
\(933\) | −1.98910e52 | − | 1.37888e53i | −0.0693087 | − | 0.480459i | ||||
\(934\) | −1.53748e53 | −0.525491 | ||||||||
\(935\) | − | 4.63781e53i | − | 1.55490i | ||||||
\(936\) | −5.63762e50 | − | 1.91338e51i | −0.00185409 | − | 0.00629269i | ||||
\(937\) | 3.78210e53 | 1.22017 | 0.610085 | − | 0.792336i | \(-0.291135\pi\) | ||||
0.610085 | + | 0.792336i | \(0.291135\pi\) | |||||||
\(938\) | 2.32393e52i | 0.0735482i | ||||||||
\(939\) | 2.23848e53 | − | 3.22912e52i | 0.694979 | − | 0.100254i | ||||
\(940\) | −4.06813e53 | −1.23906 | ||||||||
\(941\) | 6.46499e53i | 1.93177i | 0.258976 | + | 0.965884i | \(0.416615\pi\) | ||||
−0.258976 | + | 0.965884i | \(0.583385\pi\) | |||||||
\(942\) | −3.21190e52 | − | 2.22654e53i | −0.0941555 | − | 0.652701i | ||||
\(943\) | −1.44935e53 | −0.416833 | ||||||||
\(944\) | 2.83075e51i | 0.00798739i | ||||||||
\(945\) | −2.03965e53 | − | 4.44970e53i | −0.564655 | − | 1.23185i | ||||
\(946\) | −9.92443e53 | −2.69566 | ||||||||
\(947\) | 2.47742e53i | 0.660236i | 0.943940 | + | 0.330118i | \(0.107089\pi\) | ||||
−0.943940 | + | 0.330118i | \(0.892911\pi\) | |||||||
\(948\) | 1.75402e53 | − | 2.53026e52i | 0.458652 | − | 0.0661629i | ||||
\(949\) | −9.24492e50 | −0.00237198 | ||||||||
\(950\) | − | 4.36072e52i | − | 0.109783i | ||||||
\(951\) | −5.53764e52 | − | 3.83879e53i | −0.136797 | − | 0.948297i | ||||
\(952\) | 6.62238e53 | 1.60527 | ||||||||
\(953\) | 2.63848e53i | 0.627598i | 0.949489 | + | 0.313799i | \(0.101602\pi\) | ||||
−0.949489 | + | 0.313799i | \(0.898398\pi\) | |||||||
\(954\) | 1.12684e54 | − | 3.32013e53i | 2.63021 | − | 0.774970i | ||||
\(955\) | 3.08337e53 | 0.706262 | ||||||||
\(956\) | − | 6.37463e53i | − | 1.43289i | ||||||
\(957\) | 4.10888e53 | − | 5.92727e52i | 0.906376 | − | 0.130749i | ||||
\(958\) | 7.67573e53 | 1.66165 | ||||||||
\(959\) | − | 7.62941e51i | − | 0.0162090i | ||||||
\(960\) | 1.07078e53 | + | 7.42282e53i | 0.223264 | + | 1.54770i | ||||
\(961\) | −1.32580e52 | −0.0271305 | ||||||||
\(962\) | − | 5.22364e51i | − | 0.0104911i | ||||||
\(963\) | −1.31426e53 | − | 4.46055e53i | −0.259065 | − | 0.879256i | ||||
\(964\) | 2.02451e53 | 0.391682 | ||||||||
\(965\) | 7.39656e53i | 1.40455i | ||||||||
\(966\) | −1.24500e54 | + | 1.79597e53i | −2.32049 | + | 0.334743i | ||||
\(967\) | −4.09707e53 | −0.749543 | −0.374772 | − | 0.927117i | \(-0.622279\pi\) | ||||
−0.374772 | + | 0.927117i | \(0.622279\pi\) | |||||||
\(968\) | − | 5.53480e53i | − | 0.993907i | ||||||
\(969\) | 9.66420e52 | + | 6.69938e53i | 0.170348 | + | 1.18088i | ||||
\(970\) | −1.94460e53 | −0.336464 | ||||||||
\(971\) | 5.74857e53i | 0.976369i | 0.872740 | + | 0.488185i | \(0.162341\pi\) | ||||
−0.872740 | + | 0.488185i | \(0.837659\pi\) | |||||||
\(972\) | −7.33159e53 | + | 6.38290e53i | −1.22238 | + | 1.06420i | ||||
\(973\) | 8.16457e52 | 0.133630 | ||||||||
\(974\) | 1.34742e54i | 2.16492i | ||||||||
\(975\) | −2.65451e50 | + | 3.82927e49i | −0.000418699 | + | 6.03994e-5i | ||||
\(976\) | 7.85155e50 | 0.00121579 | ||||||||
\(977\) | − | 1.05474e54i | − | 1.60340i | −0.597725 | − | 0.801701i | \(-0.703929\pi\) | ||
0.597725 | − | 0.801701i | \(-0.296071\pi\) | |||||||
\(978\) | −2.43511e53 | − | 1.68806e54i | −0.363428 | − | 2.51934i | ||||
\(979\) | 4.18358e53 | 0.612999 | ||||||||
\(980\) | − | 1.04977e54i | − | 1.51016i | ||||||
\(981\) | −2.51674e53 | + | 7.41537e52i | −0.355465 | + | 0.104735i | ||||
\(982\) | −3.70004e53 | −0.513097 | ||||||||
\(983\) | 6.28170e53i | 0.855290i | 0.903947 | + | 0.427645i | \(0.140657\pi\) | ||||
−0.903947 | + | 0.427645i | \(0.859343\pi\) | |||||||
\(984\) | −3.00044e53 | + | 4.32829e52i | −0.401119 | + | 0.0578634i | ||||
\(985\) | 5.75030e53 | 0.754812 | ||||||||
\(986\) | − | 9.29761e53i | − | 1.19836i | ||||||
\(987\) | 1.24974e53 | + | 8.66338e53i | 0.158165 | + | 1.09642i | ||||
\(988\) | 8.91037e51 | 0.0110731 | ||||||||
\(989\) | − | 9.99964e53i | − | 1.22026i | ||||||
\(990\) | 5.20764e53 | + | 1.76745e54i | 0.624033 | + | 2.11794i | ||||
\(991\) | −5.20787e53 | −0.612822 | −0.306411 | − | 0.951899i | \(-0.599128\pi\) | ||||
−0.306411 | + | 0.951899i | \(0.599128\pi\) | |||||||
\(992\) | − | 8.49404e53i | − | 0.981531i | ||||||
\(993\) | −1.64223e54 | + | 2.36900e53i | −1.86358 | + | 0.268831i | ||||
\(994\) | 1.73403e54 | 1.93242 | ||||||||
\(995\) | − | 1.53522e54i | − | 1.68017i | ||||||
\(996\) | −2.67053e53 | − | 1.85126e54i | −0.287032 | − | 1.98975i | ||||
\(997\) | 3.78042e53 | 0.399049 | 0.199525 | − | 0.979893i | \(-0.436060\pi\) | ||||
0.199525 | + | 0.979893i | \(0.436060\pi\) | |||||||
\(998\) | 2.86585e54i | 2.97100i | ||||||||
\(999\) | −8.86280e53 | + | 4.06253e53i | −0.902386 | + | 0.413635i |
(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 | 3.37.b.b.2.2 | ✓ | 10 | |
3.2 | odd | 2 | inner | 3.37.b.b.2.9 | yes | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.37.b.b.2.2 | ✓ | 10 | 1.1 | even | 1 | trivial | |
3.37.b.b.2.9 | yes | 10 | 3.2 | odd | 2 | inner |