Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,37,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, 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("4.3");
S:= CuspForms(chi, 37);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 37 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(32.8365034637\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + \cdots + 51\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{240}\cdot 3^{24}\cdot 5^{6}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.16 | ||
Root | \(1.85096e7i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.37.b.b.3.15 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 261200. | + | 22229.7i | 0.996398 | + | 0.0847997i | ||||
\(3\) | 2.96154e8i | 0.764425i | 0.924074 | + | 0.382213i | \(0.124838\pi\) | ||||
−0.924074 | + | 0.382213i | \(0.875162\pi\) | |||||||
\(4\) | 6.77312e10 | + | 1.16128e10i | 0.985618 | + | 0.168989i | ||||
\(5\) | 1.46296e12 | 0.383506 | 0.191753 | − | 0.981443i | \(-0.438583\pi\) | ||||
0.191753 | + | 0.981443i | \(0.438583\pi\) | |||||||
\(6\) | −6.58343e12 | + | 7.73554e13i | −0.0648231 | + | 0.761672i | ||||
\(7\) | − | 2.38729e15i | − | 1.46602i | −0.680216 | − | 0.733012i | \(-0.738114\pi\) | ||
0.680216 | − | 0.733012i | \(-0.261886\pi\) | |||||||
\(8\) | 1.74332e16 | + | 4.53891e15i | 0.967738 | + | 0.251960i | ||||
\(9\) | 6.23874e16 | 0.415654 | ||||||||
\(10\) | 3.82125e17 | + | 3.25212e16i | 0.382125 | + | 0.0325212i | ||||
\(11\) | − | 1.01014e19i | − | 1.81683i | −0.418065 | − | 0.908417i | \(-0.637292\pi\) | ||
0.418065 | − | 0.908417i | \(-0.362708\pi\) | |||||||
\(12\) | −3.43918e18 | + | 2.00589e19i | −0.129179 | + | 0.753432i | ||||
\(13\) | −4.81295e19 | −0.427988 | −0.213994 | − | 0.976835i | \(-0.568647\pi\) | ||||
−0.213994 | + | 0.976835i | \(0.568647\pi\) | |||||||
\(14\) | 5.30689e19 | − | 6.23561e20i | 0.124318 | − | 1.46074i | ||||
\(15\) | 4.33261e20i | 0.293162i | ||||||||
\(16\) | 4.45265e21 | + | 1.57310e21i | 0.942886 | + | 0.333116i | ||||
\(17\) | 1.19657e22 | 0.850858 | 0.425429 | − | 0.904992i | \(-0.360123\pi\) | ||||
0.425429 | + | 0.904992i | \(0.360123\pi\) | |||||||
\(18\) | 1.62956e22 | + | 1.38686e21i | 0.414156 | + | 0.0352473i | ||||
\(19\) | − | 1.66265e22i | − | 0.159674i | −0.996808 | − | 0.0798371i | \(-0.974560\pi\) | ||
0.996808 | − | 0.0798371i | \(-0.0254400\pi\) | |||||||
\(20\) | 9.90879e22 | + | 1.69891e22i | 0.377990 | + | 0.0648081i | ||||
\(21\) | 7.07007e23 | 1.12067 | ||||||||
\(22\) | 2.24553e23 | − | 2.63850e24i | 0.154067 | − | 1.81029i | ||||
\(23\) | 2.63389e24i | 0.811888i | 0.913898 | + | 0.405944i | \(0.133057\pi\) | ||||
−0.913898 | + | 0.405944i | \(0.866943\pi\) | |||||||
\(24\) | −1.34422e24 | + | 5.16292e24i | −0.192605 | + | 0.739763i | ||||
\(25\) | −1.24117e25 | −0.852923 | ||||||||
\(26\) | −1.25714e25 | − | 1.06991e24i | −0.426446 | − | 0.0362932i | ||||
\(27\) | 6.29274e25i | 1.08216i | ||||||||
\(28\) | 2.77232e25 | − | 1.61694e26i | 0.247741 | − | 1.44494i | ||||
\(29\) | 1.36780e26 | 0.649920 | 0.324960 | − | 0.945728i | \(-0.394649\pi\) | ||||
0.324960 | + | 0.945728i | \(0.394649\pi\) | |||||||
\(30\) | −9.63129e24 | + | 1.13168e26i | −0.0248600 | + | 0.292106i | ||||
\(31\) | − | 4.52800e26i | − | 0.647733i | −0.946103 | − | 0.323866i | \(-0.895017\pi\) | ||
0.946103 | − | 0.323866i | \(-0.104983\pi\) | |||||||
\(32\) | 1.12806e27 | + | 5.09874e26i | 0.911241 | + | 0.411873i | ||||
\(33\) | 2.99159e27 | 1.38883 | ||||||||
\(34\) | 3.12544e27 | + | 2.65994e26i | 0.847793 | + | 0.0721525i | ||||
\(35\) | − | 3.49251e27i | − | 0.562229i | ||||||
\(36\) | 4.22557e27 | + | 7.24493e26i | 0.409676 | + | 0.0702407i | ||||
\(37\) | 5.31006e27 | 0.314390 | 0.157195 | − | 0.987568i | \(-0.449755\pi\) | ||||
0.157195 | + | 0.987568i | \(0.449755\pi\) | |||||||
\(38\) | 3.69602e26 | − | 4.34283e27i | 0.0135403 | − | 0.159099i | ||||
\(39\) | − | 1.42538e28i | − | 0.327165i | ||||||
\(40\) | 2.55041e28 | + | 6.64024e27i | 0.371133 | + | 0.0966282i | ||||
\(41\) | 1.73682e29 | 1.62048 | 0.810241 | − | 0.586097i | \(-0.199336\pi\) | ||||
0.810241 | + | 0.586097i | \(0.199336\pi\) | |||||||
\(42\) | 1.84670e29 | + | 1.57166e28i | 1.11663 | + | 0.0950322i | ||||
\(43\) | 2.26096e29i | 0.895079i | 0.894264 | + | 0.447539i | \(0.147700\pi\) | ||||
−0.894264 | + | 0.447539i | \(0.852300\pi\) | |||||||
\(44\) | 1.17306e29 | − | 6.84183e29i | 0.307024 | − | 1.79070i | ||||
\(45\) | 9.12702e28 | 0.159406 | ||||||||
\(46\) | −5.85506e28 | + | 6.87970e29i | −0.0688478 | + | 0.808963i | ||||
\(47\) | − | 1.08183e30i | − | 0.863768i | −0.901929 | − | 0.431884i | \(-0.857849\pi\) | ||
0.901929 | − | 0.431884i | \(-0.142151\pi\) | |||||||
\(48\) | −4.65879e29 | + | 1.31867e30i | −0.254643 | + | 0.720766i | ||||
\(49\) | −3.04744e30 | −1.14923 | ||||||||
\(50\) | −3.24192e30 | − | 2.75908e29i | −0.849851 | − | 0.0723277i | ||||
\(51\) | 3.54369e30i | 0.650418i | ||||||||
\(52\) | −3.25987e30 | − | 5.58919e29i | −0.421832 | − | 0.0723250i | ||||
\(53\) | −1.23762e31 | −1.13664 | −0.568319 | − | 0.822808i | \(-0.692406\pi\) | ||||
−0.568319 | + | 0.822808i | \(0.692406\pi\) | |||||||
\(54\) | −1.39886e30 | + | 1.64366e31i | −0.0917670 | + | 1.07826i | ||||
\(55\) | − | 1.47780e31i | − | 0.696767i | ||||||
\(56\) | 1.08357e31 | − | 4.16182e31i | 0.369379 | − | 1.41873i | ||||
\(57\) | 4.92399e30 | 0.122059 | ||||||||
\(58\) | 3.57270e31 | + | 3.04059e30i | 0.647579 | + | 0.0551131i | ||||
\(59\) | 9.54768e31i | 1.27222i | 0.771599 | + | 0.636109i | \(0.219457\pi\) | ||||
−0.771599 | + | 0.636109i | \(0.780543\pi\) | |||||||
\(60\) | −5.03138e30 | + | 2.93453e31i | −0.0495410 | + | 0.288945i | ||||
\(61\) | −5.38786e31 | −0.393985 | −0.196992 | − | 0.980405i | \(-0.563117\pi\) | ||||
−0.196992 | + | 0.980405i | \(0.563117\pi\) | |||||||
\(62\) | 1.00656e31 | − | 1.18271e32i | 0.0549276 | − | 0.645400i | ||||
\(63\) | − | 1.48937e32i | − | 0.609358i | ||||||
\(64\) | 2.83315e32 | + | 1.58255e32i | 0.873032 | + | 0.487662i | ||||
\(65\) | −7.04115e31 | −0.164136 | ||||||||
\(66\) | 7.81401e32 | + | 6.65022e31i | 1.38383 | + | 0.117773i | ||||
\(67\) | − | 6.26685e32i | − | 0.846647i | −0.905979 | − | 0.423324i | \(-0.860863\pi\) | ||
0.905979 | − | 0.423324i | \(-0.139137\pi\) | |||||||
\(68\) | 8.10450e32 | + | 1.38955e32i | 0.838621 | + | 0.143785i | ||||
\(69\) | −7.80036e32 | −0.620628 | ||||||||
\(70\) | 7.76377e31 | − | 9.12244e32i | 0.0476769 | − | 0.560204i | ||||
\(71\) | 2.83770e33i | 1.34994i | 0.737843 | + | 0.674972i | \(0.235844\pi\) | ||||
−0.737843 | + | 0.674972i | \(0.764156\pi\) | |||||||
\(72\) | 1.08761e33 | + | 2.83171e32i | 0.402244 | + | 0.104728i | ||||
\(73\) | −6.34742e33 | −1.83141 | −0.915705 | − | 0.401851i | \(-0.868367\pi\) | ||||
−0.915705 | + | 0.401851i | \(0.868367\pi\) | |||||||
\(74\) | 1.38699e33 | + | 1.18041e32i | 0.313258 | + | 0.0266602i | ||||
\(75\) | − | 3.67577e33i | − | 0.651996i | ||||||
\(76\) | 1.93080e32 | − | 1.12613e33i | 0.0269831 | − | 0.157378i | ||||
\(77\) | −2.41151e34 | −2.66352 | ||||||||
\(78\) | 3.16857e32 | − | 3.72308e33i | 0.0277435 | − | 0.325986i | ||||
\(79\) | 2.21307e34i | 1.54066i | 0.637645 | + | 0.770330i | \(0.279909\pi\) | ||||
−0.637645 | + | 0.770330i | \(0.720091\pi\) | |||||||
\(80\) | 6.51405e33 | + | 2.30138e33i | 0.361602 | + | 0.127752i | ||||
\(81\) | −9.27220e33 | −0.411578 | ||||||||
\(82\) | 4.53656e34 | + | 3.86089e33i | 1.61464 | + | 0.137416i | ||||
\(83\) | − | 6.15416e34i | − | 1.76102i | −0.474031 | − | 0.880508i | \(-0.657201\pi\) | ||
0.474031 | − | 0.880508i | \(-0.342799\pi\) | |||||||
\(84\) | 4.78864e34 | + | 8.21033e33i | 1.10455 | + | 0.189380i | ||||
\(85\) | 1.75053e34 | 0.326309 | ||||||||
\(86\) | −5.02606e33 | + | 5.90563e34i | −0.0759024 | + | 0.891855i | ||||
\(87\) | 4.05081e34i | 0.496816i | ||||||||
\(88\) | 4.58495e34 | − | 1.76101e35i | 0.457770 | − | 1.75822i | ||||
\(89\) | −8.78919e34 | −0.716026 | −0.358013 | − | 0.933717i | \(-0.616546\pi\) | ||||
−0.358013 | + | 0.933717i | \(0.616546\pi\) | |||||||
\(90\) | 2.38398e34 | + | 2.02891e33i | 0.158831 | + | 0.0135176i | ||||
\(91\) | 1.14899e35i | 0.627440i | ||||||||
\(92\) | −3.05868e34 | + | 1.78396e35i | −0.137200 | + | 0.800211i | ||||
\(93\) | 1.34099e35 | 0.495144 | ||||||||
\(94\) | 2.40488e34 | − | 2.82573e35i | 0.0732473 | − | 0.860657i | ||||
\(95\) | − | 2.43238e34i | − | 0.0612360i | ||||||
\(96\) | −1.51001e35 | + | 3.34080e35i | −0.314846 | + | 0.696576i | ||||
\(97\) | 1.81673e35 | 0.314340 | 0.157170 | − | 0.987572i | \(-0.449763\pi\) | ||||
0.157170 | + | 0.987572i | \(0.449763\pi\) | |||||||
\(98\) | −7.95991e35 | − | 6.77438e34i | −1.14509 | − | 0.0974541i | ||||
\(99\) | − | 6.30203e35i | − | 0.755174i | ||||||
\(100\) | −8.40656e35 | − | 1.44134e35i | −0.840656 | − | 0.144134i | ||||
\(101\) | 5.19200e35 | 0.434060 | 0.217030 | − | 0.976165i | \(-0.430363\pi\) | ||||
0.217030 | + | 0.976165i | \(0.430363\pi\) | |||||||
\(102\) | −7.87753e34 | + | 9.25611e35i | −0.0551552 | + | 0.648075i | ||||
\(103\) | 7.57511e35i | 0.444958i | 0.974937 | + | 0.222479i | \(0.0714149\pi\) | ||||
−0.974937 | + | 0.222479i | \(0.928585\pi\) | |||||||
\(104\) | −8.39052e35 | − | 2.18455e35i | −0.414180 | − | 0.107836i | ||||
\(105\) | 1.03432e36 | 0.429782 | ||||||||
\(106\) | −3.23266e36 | − | 2.75120e35i | −1.13254 | − | 0.0963866i | ||||
\(107\) | − | 1.18309e36i | − | 0.350034i | −0.984565 | − | 0.175017i | \(-0.944002\pi\) | ||
0.984565 | − | 0.175017i | \(-0.0559980\pi\) | |||||||
\(108\) | −7.30764e35 | + | 4.26215e36i | −0.182873 | + | 1.06660i | ||||
\(109\) | 5.99820e36 | 1.27158 | 0.635791 | − | 0.771861i | \(-0.280674\pi\) | ||||
0.635791 | + | 0.771861i | \(0.280674\pi\) | |||||||
\(110\) | 3.28511e35 | − | 3.86001e36i | 0.0590856 | − | 0.694257i | ||||
\(111\) | 1.57260e36i | 0.240328i | ||||||||
\(112\) | 3.75545e36 | − | 1.06298e37i | 0.488357 | − | 1.38229i | ||||
\(113\) | 1.38128e37 | 1.53063 | 0.765314 | − | 0.643657i | \(-0.222584\pi\) | ||||
0.765314 | + | 0.643657i | \(0.222584\pi\) | |||||||
\(114\) | 1.28615e36 | + | 1.09459e35i | 0.121619 | + | 0.0103506i | ||||
\(115\) | 3.85327e36i | 0.311364i | ||||||||
\(116\) | 9.26430e36 | + | 1.58840e36i | 0.640573 | + | 0.109829i | ||||
\(117\) | −3.00268e36 | −0.177895 | ||||||||
\(118\) | −2.12242e36 | + | 2.49385e37i | −0.107884 | + | 1.26764i | ||||
\(119\) | − | 2.85656e37i | − | 1.24738i | ||||||
\(120\) | −1.96653e36 | + | 7.55314e36i | −0.0738650 | + | 0.283704i | ||||
\(121\) | −7.11266e37 | −2.30089 | ||||||||
\(122\) | −1.40731e37 | − | 1.19771e36i | −0.392566 | − | 0.0334098i | ||||
\(123\) | 5.14365e37i | 1.23874i | ||||||||
\(124\) | 5.25828e36 | − | 3.06687e37i | 0.109459 | − | 0.638417i | ||||
\(125\) | −3.94466e37 | −0.710607 | ||||||||
\(126\) | 3.31083e36 | − | 3.89023e37i | 0.0516734 | − | 0.607163i | ||||
\(127\) | − | 3.83191e37i | − | 0.518739i | −0.965778 | − | 0.259369i | \(-0.916485\pi\) | ||
0.965778 | − | 0.259369i | \(-0.0835147\pi\) | |||||||
\(128\) | 7.04839e37 | + | 4.76343e37i | 0.828534 | + | 0.559939i | ||||
\(129\) | −6.69594e37 | −0.684221 | ||||||||
\(130\) | −1.83915e37 | − | 1.56523e36i | −0.163545 | − | 0.0139187i | ||||
\(131\) | 7.43704e37i | 0.576125i | 0.957612 | + | 0.288062i | \(0.0930111\pi\) | ||||
−0.957612 | + | 0.288062i | \(0.906989\pi\) | |||||||
\(132\) | 2.02624e38 | + | 3.47407e37i | 1.36886 | + | 0.234697i | ||||
\(133\) | −3.96922e37 | −0.234086 | ||||||||
\(134\) | 1.39310e37 | − | 1.63690e38i | 0.0717955 | − | 0.843598i | ||||
\(135\) | 9.20602e37i | 0.415015i | ||||||||
\(136\) | 2.08600e38 | + | 5.43112e37i | 0.823408 | + | 0.214382i | ||||
\(137\) | 6.29514e37 | 0.217788 | 0.108894 | − | 0.994053i | \(-0.465269\pi\) | ||||
0.108894 | + | 0.994053i | \(0.465269\pi\) | |||||||
\(138\) | −2.03745e38 | − | 1.73400e37i | −0.618392 | − | 0.0526291i | ||||
\(139\) | − | 5.21959e38i | − | 1.39114i | −0.718459 | − | 0.695569i | \(-0.755152\pi\) | ||
0.718459 | − | 0.695569i | \(-0.244848\pi\) | |||||||
\(140\) | 4.05579e37 | − | 2.36552e38i | 0.0950103 | − | 0.554143i | ||||
\(141\) | 3.20388e38 | 0.660286 | ||||||||
\(142\) | −6.30813e37 | + | 7.41206e38i | −0.114475 | + | 1.34508i | ||||
\(143\) | 4.86178e38i | 0.777583i | ||||||||
\(144\) | 2.77789e38 | + | 9.81414e37i | 0.391914 | + | 0.138461i | ||||
\(145\) | 2.00104e38 | 0.249248 | ||||||||
\(146\) | −1.65794e39 | − | 1.41101e38i | −1.82481 | − | 0.155303i | ||||
\(147\) | − | 9.02512e38i | − | 0.878498i | ||||||
\(148\) | 3.59657e38 | + | 6.16648e37i | 0.309868 | + | 0.0531283i | ||||
\(149\) | 1.11386e39 | 0.850113 | 0.425056 | − | 0.905167i | \(-0.360254\pi\) | ||||
0.425056 | + | 0.905167i | \(0.360254\pi\) | |||||||
\(150\) | 8.17113e37 | − | 9.60109e38i | 0.0552891 | − | 0.649648i | ||||
\(151\) | 2.20582e39i | 1.32430i | 0.749372 | + | 0.662149i | \(0.230355\pi\) | ||||
−0.749372 | + | 0.662149i | \(0.769645\pi\) | |||||||
\(152\) | 7.54660e37 | − | 2.89853e38i | 0.0402315 | − | 0.154523i | ||||
\(153\) | 7.46508e38 | 0.353662 | ||||||||
\(154\) | −6.29886e39 | − | 5.36073e38i | −2.65393 | − | 0.225866i | ||||
\(155\) | − | 6.62428e38i | − | 0.248409i | ||||||
\(156\) | 1.65526e38 | − | 9.65423e38i | 0.0552871 | − | 0.322459i | ||||
\(157\) | −2.97211e39 | −0.884853 | −0.442427 | − | 0.896805i | \(-0.645882\pi\) | ||||
−0.442427 | + | 0.896805i | \(0.645882\pi\) | |||||||
\(158\) | −4.91959e38 | + | 5.78052e39i | −0.130648 | + | 1.53511i | ||||
\(159\) | − | 3.66527e39i | − | 0.868875i | ||||||
\(160\) | 1.65031e39 | + | 7.45925e38i | 0.349466 | + | 0.157956i | ||||
\(161\) | 6.28786e39 | 1.19025 | ||||||||
\(162\) | −2.42190e39 | − | 2.06119e38i | −0.410096 | − | 0.0349017i | ||||
\(163\) | 5.14197e39i | 0.779386i | 0.920945 | + | 0.389693i | \(0.127419\pi\) | ||||
−0.920945 | + | 0.389693i | \(0.872581\pi\) | |||||||
\(164\) | 1.17636e40 | + | 2.01693e39i | 1.59718 | + | 0.273843i | ||||
\(165\) | 4.37657e39 | 0.532626 | ||||||||
\(166\) | 1.36805e39 | − | 1.60747e40i | 0.149334 | − | 1.75467i | ||||
\(167\) | − | 8.78588e39i | − | 0.860773i | −0.902645 | − | 0.430387i | \(-0.858377\pi\) | ||
0.902645 | − | 0.430387i | \(-0.141623\pi\) | |||||||
\(168\) | 1.23254e40 | + | 3.20904e39i | 1.08451 | + | 0.282363i | ||||
\(169\) | −1.03298e40 | −0.816827 | ||||||||
\(170\) | 4.57238e39 | + | 3.89139e38i | 0.325134 | + | 0.0276709i | ||||
\(171\) | − | 1.03728e39i | − | 0.0663692i | ||||||
\(172\) | −2.62561e39 | + | 1.53138e40i | −0.151258 | + | 0.882206i | ||||
\(173\) | −1.25353e40 | −0.650585 | −0.325292 | − | 0.945613i | \(-0.605463\pi\) | ||||
−0.325292 | + | 0.945613i | \(0.605463\pi\) | |||||||
\(174\) | −9.00484e38 | + | 1.05807e40i | −0.0421298 | + | 0.495026i | ||||
\(175\) | 2.96303e40i | 1.25041i | ||||||||
\(176\) | 1.58906e40 | − | 4.49782e40i | 0.605217 | − | 1.71307i | ||||
\(177\) | −2.82758e40 | −0.972516 | ||||||||
\(178\) | −2.29573e40 | − | 1.95381e39i | −0.713447 | − | 0.0607188i | ||||
\(179\) | 4.92645e39i | 0.138414i | 0.997602 | + | 0.0692070i | \(0.0220469\pi\) | ||||
−0.997602 | + | 0.0692070i | \(0.977953\pi\) | |||||||
\(180\) | 6.18184e39 | + | 1.05990e39i | 0.157113 | + | 0.0269377i | ||||
\(181\) | −7.14294e40 | −1.64310 | −0.821548 | − | 0.570140i | \(-0.806889\pi\) | ||||
−0.821548 | + | 0.570140i | \(0.806889\pi\) | |||||||
\(182\) | −2.55418e39 | + | 3.00117e40i | −0.0532068 | + | 0.625180i | ||||
\(183\) | − | 1.59564e40i | − | 0.301172i | ||||||
\(184\) | −1.19550e40 | + | 4.59171e40i | −0.204563 | + | 0.785694i | ||||
\(185\) | 7.76841e39 | 0.120570 | ||||||||
\(186\) | 3.50265e40 | + | 2.98098e39i | 0.493360 | + | 0.0419880i | ||||
\(187\) | − | 1.20871e41i | − | 1.54587i | ||||||
\(188\) | 1.25631e40 | − | 7.32735e40i | 0.145967 | − | 0.851345i | ||||
\(189\) | 1.50226e41 | 1.58648 | ||||||||
\(190\) | 5.40712e38 | − | 6.35338e39i | 0.00519280 | − | 0.0610155i | ||||
\(191\) | 1.55729e41i | 1.36072i | 0.732876 | + | 0.680362i | \(0.238178\pi\) | ||||
−0.732876 | + | 0.680362i | \(0.761822\pi\) | |||||||
\(192\) | −4.68680e40 | + | 8.39050e40i | −0.372782 | + | 0.667368i | ||||
\(193\) | 9.98102e40 | 0.723008 | 0.361504 | − | 0.932371i | \(-0.382263\pi\) | ||||
0.361504 | + | 0.932371i | \(0.382263\pi\) | |||||||
\(194\) | 4.74531e40 | + | 4.03855e39i | 0.313208 | + | 0.0266560i | ||||
\(195\) | − | 2.08527e40i | − | 0.125470i | ||||||
\(196\) | −2.06407e41 | − | 3.53893e40i | −1.13270 | − | 0.194206i | ||||
\(197\) | 1.02224e41 | 0.511871 | 0.255935 | − | 0.966694i | \(-0.417617\pi\) | ||||
0.255935 | + | 0.966694i | \(0.417617\pi\) | |||||||
\(198\) | 1.40092e40 | − | 1.64609e41i | 0.0640385 | − | 0.752454i | ||||
\(199\) | 8.08444e40i | 0.337516i | 0.985657 | + | 0.168758i | \(0.0539757\pi\) | ||||
−0.985657 | + | 0.168758i | \(0.946024\pi\) | |||||||
\(200\) | −2.16375e41 | − | 5.63354e40i | −0.825406 | − | 0.214903i | ||||
\(201\) | 1.85595e41 | 0.647199 | ||||||||
\(202\) | 1.35615e41 | + | 1.15417e40i | 0.432497 | + | 0.0368082i | ||||
\(203\) | − | 3.26535e41i | − | 0.952799i | ||||||
\(204\) | −4.11522e40 | + | 2.40018e41i | −0.109913 | + | 0.641063i | ||||
\(205\) | 2.54089e41 | 0.621464 | ||||||||
\(206\) | −1.68393e40 | + | 1.97862e41i | −0.0377323 | + | 0.443355i | ||||
\(207\) | 1.64321e41i | 0.337464i | ||||||||
\(208\) | −2.14304e41 | − | 7.57124e40i | −0.403543 | − | 0.142570i | ||||
\(209\) | −1.67951e41 | −0.290102 | ||||||||
\(210\) | 2.70165e41 | + | 2.29927e40i | 0.428234 | + | 0.0364454i | ||||
\(211\) | 5.10879e40i | 0.0743420i | 0.999309 | + | 0.0371710i | \(0.0118346\pi\) | ||||
−0.999309 | + | 0.0371710i | \(0.988165\pi\) | |||||||
\(212\) | −8.38255e41 | − | 1.43723e41i | −1.12029 | − | 0.192079i | ||||
\(213\) | −8.40396e41 | −1.03193 | ||||||||
\(214\) | 2.62998e40 | − | 3.09023e41i | 0.0296828 | − | 0.348773i | ||||
\(215\) | 3.30770e41i | 0.343268i | ||||||||
\(216\) | −2.85622e41 | + | 1.09703e42i | −0.272661 | + | 1.04725i | ||||
\(217\) | −1.08097e42 | −0.949592 | ||||||||
\(218\) | 1.56673e42 | + | 1.33339e41i | 1.26700 | + | 0.107830i | ||||
\(219\) | − | 1.87981e42i | − | 1.39998i | ||||||
\(220\) | 1.71614e41 | − | 1.00093e42i | 0.117746 | − | 0.686746i | ||||
\(221\) | −5.75903e41 | −0.364157 | ||||||||
\(222\) | −3.49584e40 | + | 4.10762e41i | −0.0203797 | + | 0.239462i | ||||
\(223\) | 3.14384e42i | 1.69033i | 0.534503 | + | 0.845167i | \(0.320499\pi\) | ||||
−0.534503 | + | 0.845167i | \(0.679501\pi\) | |||||||
\(224\) | 1.21722e42 | − | 2.69302e42i | 0.603816 | − | 1.33590i | ||||
\(225\) | −7.74331e41 | −0.354521 | ||||||||
\(226\) | 3.60790e42 | + | 3.07055e41i | 1.52512 | + | 0.129797i | ||||
\(227\) | 2.54173e42i | 0.992347i | 0.868223 | + | 0.496174i | \(0.165262\pi\) | ||||
−0.868223 | + | 0.496174i | \(0.834738\pi\) | |||||||
\(228\) | 3.33508e41 | + | 5.71814e40i | 0.120304 | + | 0.0206266i | ||||
\(229\) | 3.08692e42 | 1.02917 | 0.514585 | − | 0.857440i | \(-0.327946\pi\) | ||||
0.514585 | + | 0.857440i | \(0.327946\pi\) | |||||||
\(230\) | −8.56571e40 | + | 1.00647e42i | −0.0264036 | + | 0.310242i | ||||
\(231\) | − | 7.14179e42i | − | 2.03606i | ||||||
\(232\) | 2.38452e42 | + | 6.20834e41i | 0.628952 | + | 0.163754i | ||||
\(233\) | 7.31206e41 | 0.178498 | 0.0892489 | − | 0.996009i | \(-0.471553\pi\) | ||||
0.0892489 | + | 0.996009i | \(0.471553\pi\) | |||||||
\(234\) | −7.84298e41 | − | 6.67487e40i | −0.177254 | − | 0.0150854i | ||||
\(235\) | − | 1.58267e42i | − | 0.331260i | ||||||
\(236\) | −1.10875e42 | + | 6.46675e42i | −0.214990 | + | 1.25392i | ||||
\(237\) | −6.55409e42 | −1.17772 | ||||||||
\(238\) | 6.35006e41 | − | 7.46133e42i | 0.105777 | − | 1.24289i | ||||
\(239\) | 3.35689e42i | 0.518532i | 0.965806 | + | 0.259266i | \(0.0834806\pi\) | ||||
−0.965806 | + | 0.259266i | \(0.916519\pi\) | |||||||
\(240\) | −6.81562e41 | + | 1.92916e42i | −0.0976570 | + | 0.276418i | ||||
\(241\) | 2.11826e42 | 0.281626 | 0.140813 | − | 0.990036i | \(-0.455028\pi\) | ||||
0.140813 | + | 0.990036i | \(0.455028\pi\) | |||||||
\(242\) | −1.85782e43 | − | 1.58113e42i | −2.29260 | − | 0.195115i | ||||
\(243\) | 6.69907e42i | 0.767541i | ||||||||
\(244\) | −3.64926e42 | − | 6.25682e41i | −0.388319 | − | 0.0665789i | ||||
\(245\) | −4.45828e42 | −0.440735 | ||||||||
\(246\) | −1.14342e42 | + | 1.34352e43i | −0.105045 | + | 1.23428i | ||||
\(247\) | 8.00224e41i | 0.0683386i | ||||||||
\(248\) | 2.05522e42 | − | 7.89376e42i | 0.163203 | − | 0.626836i | ||||
\(249\) | 1.82258e43 | 1.34617 | ||||||||
\(250\) | −1.03034e43 | − | 8.76888e41i | −0.708047 | − | 0.0602593i | ||||
\(251\) | − | 1.09661e43i | − | 0.701336i | −0.936500 | − | 0.350668i | \(-0.885955\pi\) | ||
0.936500 | − | 0.350668i | \(-0.114045\pi\) | |||||||
\(252\) | 1.72958e42 | − | 1.00877e43i | 0.102975 | − | 0.600595i | ||||
\(253\) | 2.66061e43 | 1.47507 | ||||||||
\(254\) | 8.51824e41 | − | 1.00089e43i | 0.0439889 | − | 0.516870i | ||||
\(255\) | 5.18427e42i | 0.249439i | ||||||||
\(256\) | 1.73515e43 | + | 1.40089e43i | 0.778067 | + | 0.628181i | ||||
\(257\) | −5.04919e42 | −0.211070 | −0.105535 | − | 0.994416i | \(-0.533655\pi\) | ||||
−0.105535 | + | 0.994416i | \(0.533655\pi\) | |||||||
\(258\) | −1.74898e43 | − | 1.48849e42i | −0.681757 | − | 0.0580218i | ||||
\(259\) | − | 1.26767e43i | − | 0.460903i | ||||||
\(260\) | −4.76905e42 | − | 8.17675e41i | −0.161775 | − | 0.0277371i | ||||
\(261\) | 8.53337e42 | 0.270142 | ||||||||
\(262\) | −1.65323e42 | + | 1.94255e43i | −0.0488552 | + | 0.574050i | ||||
\(263\) | 2.22021e43i | 0.612620i | 0.951932 | + | 0.306310i | \(0.0990943\pi\) | ||||
−0.951932 | + | 0.306310i | \(0.900906\pi\) | |||||||
\(264\) | 5.21529e43 | + | 1.35785e43i | 1.34403 | + | 0.349931i | ||||
\(265\) | −1.81059e43 | −0.435907 | ||||||||
\(266\) | −1.03676e43 | − | 8.82348e41i | −0.233243 | − | 0.0198505i | ||||
\(267\) | − | 2.60296e43i | − | 0.547349i | ||||||
\(268\) | 7.27757e42 | − | 4.24461e43i | 0.143074 | − | 0.834471i | ||||
\(269\) | −2.41057e43 | −0.443178 | −0.221589 | − | 0.975140i | \(-0.571124\pi\) | ||||
−0.221589 | + | 0.975140i | \(0.571124\pi\) | |||||||
\(270\) | −2.04648e42 | + | 2.40461e43i | −0.0351932 | + | 0.413521i | ||||
\(271\) | − | 4.83064e43i | − | 0.777244i | −0.921397 | − | 0.388622i | \(-0.872951\pi\) | ||
0.921397 | − | 0.388622i | \(-0.127049\pi\) | |||||||
\(272\) | 5.32791e43 | + | 1.88232e43i | 0.802262 | + | 0.283435i | ||||
\(273\) | −3.40279e43 | −0.479631 | ||||||||
\(274\) | 1.64429e43 | + | 1.39939e42i | 0.217004 | + | 0.0184684i | ||||
\(275\) | 1.25376e44i | 1.54962i | ||||||||
\(276\) | −5.28327e43 | − | 9.05841e42i | −0.611702 | − | 0.104879i | ||||
\(277\) | −1.00881e44 | −1.09439 | −0.547196 | − | 0.837005i | \(-0.684305\pi\) | ||||
−0.547196 | + | 0.837005i | \(0.684305\pi\) | |||||||
\(278\) | 1.16030e43 | − | 1.36336e44i | 0.117968 | − | 1.38613i | ||||
\(279\) | − | 2.82490e43i | − | 0.269233i | ||||||
\(280\) | 1.58522e43 | − | 6.08857e43i | 0.141659 | − | 0.544090i | ||||
\(281\) | −1.08851e44 | −0.912261 | −0.456130 | − | 0.889913i | \(-0.650765\pi\) | ||||
−0.456130 | + | 0.889913i | \(0.650765\pi\) | |||||||
\(282\) | 8.36853e43 | + | 7.12214e42i | 0.657908 | + | 0.0559921i | ||||
\(283\) | 2.09138e44i | 1.54268i | 0.636421 | + | 0.771342i | \(0.280414\pi\) | ||||
−0.636421 | + | 0.771342i | \(0.719586\pi\) | |||||||
\(284\) | −3.29536e43 | + | 1.92201e44i | −0.228125 | + | 1.33053i | ||||
\(285\) | 7.20360e42 | 0.0468104 | ||||||||
\(286\) | −1.08076e43 | + | 1.26990e44i | −0.0659388 | + | 0.774782i | ||||
\(287\) | − | 4.14629e44i | − | 2.37567i | ||||||
\(288\) | 7.03768e43 | + | 3.18097e43i | 0.378761 | + | 0.171196i | ||||
\(289\) | −5.45926e43 | −0.276040 | ||||||||
\(290\) | 5.22672e43 | + | 4.44826e42i | 0.248350 | + | 0.0211362i | ||||
\(291\) | 5.38033e43i | 0.240290i | ||||||||
\(292\) | −4.29918e44 | − | 7.37113e43i | −1.80507 | − | 0.309487i | ||||
\(293\) | 1.29240e44 | 0.510246 | 0.255123 | − | 0.966909i | \(-0.417884\pi\) | ||||
0.255123 | + | 0.966909i | \(0.417884\pi\) | |||||||
\(294\) | 2.00626e43 | − | 2.35736e44i | 0.0744964 | − | 0.875334i | ||||
\(295\) | 1.39679e44i | 0.487903i | ||||||||
\(296\) | 9.25715e43 | + | 2.41019e43i | 0.304247 | + | 0.0792137i | ||||
\(297\) | 6.35658e44 | 1.96611 | ||||||||
\(298\) | 2.90939e44 | + | 2.47607e43i | 0.847051 | + | 0.0720893i | ||||
\(299\) | − | 1.26768e44i | − | 0.347478i | ||||||
\(300\) | 4.26860e43 | − | 2.48964e44i | 0.110180 | − | 0.642619i | ||||
\(301\) | 5.39758e44 | 1.31221 | ||||||||
\(302\) | −4.90349e43 | + | 5.76160e44i | −0.112300 | + | 1.31953i | ||||
\(303\) | 1.53763e44i | 0.331807i | ||||||||
\(304\) | 2.61550e43 | − | 7.40318e43i | 0.0531901 | − | 0.150555i | ||||
\(305\) | −7.88222e43 | −0.151096 | ||||||||
\(306\) | 1.94988e44 | + | 1.65947e43i | 0.352388 | + | 0.0299905i | ||||
\(307\) | − | 5.37830e44i | − | 0.916546i | −0.888812 | − | 0.458273i | \(-0.848468\pi\) | ||
0.888812 | − | 0.458273i | \(-0.151532\pi\) | |||||||
\(308\) | −1.63335e45 | − | 2.80044e44i | −2.62522 | − | 0.450105i | ||||
\(309\) | −2.24340e44 | −0.340137 | ||||||||
\(310\) | 1.47256e43 | − | 1.73026e44i | 0.0210651 | − | 0.247515i | ||||
\(311\) | 1.27143e45i | 1.71635i | 0.513353 | + | 0.858177i | \(0.328403\pi\) | ||||
−0.513353 | + | 0.858177i | \(0.671597\pi\) | |||||||
\(312\) | 6.46965e43 | − | 2.48489e44i | 0.0824324 | − | 0.316610i | ||||
\(313\) | −1.55517e44 | −0.187059 | −0.0935296 | − | 0.995616i | \(-0.529815\pi\) | ||||
−0.0935296 | + | 0.995616i | \(0.529815\pi\) | |||||||
\(314\) | −7.76315e44 | − | 6.60693e43i | −0.881666 | − | 0.0750353i | ||||
\(315\) | − | 2.17889e44i | − | 0.233693i | ||||||
\(316\) | −2.56999e44 | + | 1.49894e45i | −0.260354 | + | 1.51850i | ||||
\(317\) | −1.28628e45 | −1.23103 | −0.615515 | − | 0.788125i | \(-0.711052\pi\) | ||||
−0.615515 | + | 0.788125i | \(0.711052\pi\) | |||||||
\(318\) | 8.14779e43 | − | 9.57367e44i | 0.0736804 | − | 0.865745i | ||||
\(319\) | − | 1.38168e45i | − | 1.18080i | ||||||
\(320\) | 4.14479e44 | + | 2.31521e44i | 0.334813 | + | 0.187021i | ||||
\(321\) | 3.50377e44 | 0.267575 | ||||||||
\(322\) | 1.64239e45 | + | 1.39777e44i | 1.18596 | + | 0.100933i | ||||
\(323\) | − | 1.98947e44i | − | 0.135860i | ||||||
\(324\) | −6.28017e44 | − | 1.07676e44i | −0.405659 | − | 0.0695520i | ||||
\(325\) | 5.97368e44 | 0.365041 | ||||||||
\(326\) | −1.14305e44 | + | 1.34308e45i | −0.0660918 | + | 0.776579i | ||||
\(327\) | 1.77639e45i | 0.972030i | ||||||||
\(328\) | 3.02783e45 | + | 7.88324e44i | 1.56820 | + | 0.408297i | ||||
\(329\) | −2.58264e45 | −1.26630 | ||||||||
\(330\) | 1.14316e45 | + | 9.72899e43i | 0.530708 | + | 0.0451666i | ||||
\(331\) | − | 9.60496e44i | − | 0.422271i | −0.977457 | − | 0.211136i | \(-0.932284\pi\) | ||
0.977457 | − | 0.211136i | \(-0.0677162\pi\) | |||||||
\(332\) | 7.14671e44 | − | 4.16829e45i | 0.297592 | − | 1.73569i | ||||
\(333\) | 3.31281e44 | 0.130677 | ||||||||
\(334\) | 1.95308e44 | − | 2.29487e45i | 0.0729933 | − | 0.857673i | ||||
\(335\) | − | 9.16814e44i | − | 0.324694i | ||||||
\(336\) | 3.14806e45 | + | 1.11219e45i | 1.05666 | + | 0.373312i | ||||
\(337\) | 2.40643e45 | 0.765658 | 0.382829 | − | 0.923819i | \(-0.374950\pi\) | ||||
0.382829 | + | 0.923819i | \(0.374950\pi\) | |||||||
\(338\) | −2.69813e45 | − | 2.29628e44i | −0.813884 | − | 0.0692667i | ||||
\(339\) | 4.09072e45i | 1.17005i | ||||||||
\(340\) | 1.18566e45 | + | 2.03286e44i | 0.321616 | + | 0.0551425i | ||||
\(341\) | −4.57394e45 | −1.17682 | ||||||||
\(342\) | 2.30585e43 | − | 2.70938e44i | 0.00562809 | − | 0.0661301i | ||||
\(343\) | 9.44676e44i | 0.218771i | ||||||||
\(344\) | −1.02623e45 | + | 3.94159e45i | −0.225524 | + | 0.866202i | ||||
\(345\) | −1.14116e45 | −0.238014 | ||||||||
\(346\) | −3.27421e45 | − | 2.78656e44i | −0.648242 | − | 0.0551694i | ||||
\(347\) | − | 5.95983e45i | − | 1.12022i | −0.828418 | − | 0.560110i | \(-0.810759\pi\) | ||
0.828418 | − | 0.560110i | \(-0.189241\pi\) | |||||||
\(348\) | −4.70413e44 | + | 2.74366e45i | −0.0839562 | + | 0.489670i | ||||
\(349\) | 3.96150e45 | 0.671432 | 0.335716 | − | 0.941963i | \(-0.391022\pi\) | ||||
0.335716 | + | 0.941963i | \(0.391022\pi\) | |||||||
\(350\) | −6.58674e44 | + | 7.73943e45i | −0.106034 | + | 1.24590i | ||||
\(351\) | − | 3.02867e45i | − | 0.463152i | ||||||
\(352\) | 5.15047e45 | − | 1.13951e46i | 0.748305 | − | 1.65557i | ||||
\(353\) | −3.77639e45 | −0.521353 | −0.260677 | − | 0.965426i | \(-0.583946\pi\) | ||||
−0.260677 | + | 0.965426i | \(0.583946\pi\) | |||||||
\(354\) | −7.38564e45 | − | 6.28565e44i | −0.969013 | − | 0.0824691i | ||||
\(355\) | 4.15144e45i | 0.517712i | ||||||||
\(356\) | −5.95302e45 | − | 1.02067e45i | −0.705728 | − | 0.121000i | ||||
\(357\) | 8.45983e45 | 0.953528 | ||||||||
\(358\) | −1.09514e44 | + | 1.28679e45i | −0.0117375 | + | 0.137915i | ||||
\(359\) | 8.40831e45i | 0.857054i | 0.903529 | + | 0.428527i | \(0.140967\pi\) | ||||
−0.903529 | + | 0.428527i | \(0.859033\pi\) | |||||||
\(360\) | 1.59113e45 | + | 4.14267e44i | 0.154263 | + | 0.0401638i | ||||
\(361\) | 1.05661e46 | 0.974504 | ||||||||
\(362\) | −1.86574e46 | − | 1.58786e45i | −1.63718 | − | 0.139334i | ||||
\(363\) | − | 2.10644e46i | − | 1.75886i | ||||||
\(364\) | −1.33430e45 | + | 7.78226e45i | −0.106030 | + | 0.618416i | ||||
\(365\) | −9.28601e45 | −0.702357 | ||||||||
\(366\) | 3.54706e44 | − | 4.16780e45i | 0.0255393 | − | 0.300087i | ||||
\(367\) | 8.59773e45i | 0.589379i | 0.955593 | + | 0.294689i | \(0.0952162\pi\) | ||||
−0.955593 | + | 0.294689i | \(0.904784\pi\) | |||||||
\(368\) | −4.14336e45 | + | 1.17278e46i | −0.270453 | + | 0.765517i | ||||
\(369\) | 1.08355e46 | 0.673559 | ||||||||
\(370\) | 2.02911e45 | + | 1.72690e44i | 0.120136 | + | 0.0102243i | ||||
\(371\) | 2.95457e46i | 1.66634i | ||||||||
\(372\) | 9.08265e45 | + | 1.55726e45i | 0.488022 | + | 0.0836736i | ||||
\(373\) | 2.05825e46 | 1.05375 | 0.526876 | − | 0.849942i | \(-0.323363\pi\) | ||||
0.526876 | + | 0.849942i | \(0.323363\pi\) | |||||||
\(374\) | 2.68693e45 | − | 3.15714e46i | 0.131089 | − | 1.54030i | ||||
\(375\) | − | 1.16823e46i | − | 0.543206i | ||||||
\(376\) | 4.91032e45 | − | 1.88597e46i | 0.217635 | − | 0.835901i | ||||
\(377\) | −6.58318e45 | −0.278158 | ||||||||
\(378\) | 3.92391e46 | + | 3.33949e45i | 1.58076 | + | 0.134533i | ||||
\(379\) | − | 2.71367e46i | − | 1.04244i | −0.853422 | − | 0.521221i | \(-0.825477\pi\) | ||
0.853422 | − | 0.521221i | \(-0.174523\pi\) | |||||||
\(380\) | 2.82468e44 | − | 1.64748e45i | 0.0103482 | − | 0.0603553i | ||||
\(381\) | 1.13484e46 | 0.396537 | ||||||||
\(382\) | −3.46183e45 | + | 4.06765e46i | −0.115389 | + | 1.35582i | ||||
\(383\) | − | 2.21749e46i | − | 0.705152i | −0.935783 | − | 0.352576i | \(-0.885306\pi\) | ||
0.935783 | − | 0.352576i | \(-0.114694\pi\) | |||||||
\(384\) | −1.41071e46 | + | 2.08741e46i | −0.428031 | + | 0.633353i | ||||
\(385\) | −3.52794e46 | −1.02148 | ||||||||
\(386\) | 2.60704e46 | + | 2.21875e45i | 0.720404 | + | 0.0613109i | ||||
\(387\) | 1.41056e46i | 0.372043i | ||||||||
\(388\) | 1.23050e46 | + | 2.10974e45i | 0.309820 | + | 0.0531199i | ||||
\(389\) | −6.09024e46 | −1.46400 | −0.732001 | − | 0.681303i | \(-0.761414\pi\) | ||||
−0.732001 | + | 0.681303i | \(0.761414\pi\) | |||||||
\(390\) | 4.63549e44 | − | 5.44671e45i | 0.0106398 | − | 0.125018i | ||||
\(391\) | 3.15163e46i | 0.690801i | ||||||||
\(392\) | −5.31267e46 | − | 1.38321e46i | −1.11215 | − | 0.289559i | ||||
\(393\) | −2.20251e46 | −0.440405 | ||||||||
\(394\) | 2.67008e46 | + | 2.27241e45i | 0.510027 | + | 0.0434065i | ||||
\(395\) | 3.23763e46i | 0.590852i | ||||||||
\(396\) | 7.31842e45 | − | 4.26844e46i | 0.127616 | − | 0.744313i | ||||
\(397\) | −8.96756e46 | −1.49433 | −0.747163 | − | 0.664641i | \(-0.768585\pi\) | ||||
−0.747163 | + | 0.664641i | \(0.768585\pi\) | |||||||
\(398\) | −1.79715e45 | + | 2.11166e46i | −0.0286213 | + | 0.336301i | ||||
\(399\) | − | 1.17550e46i | − | 0.178942i | ||||||
\(400\) | −5.52648e46 | − | 1.95248e46i | −0.804209 | − | 0.284123i | ||||
\(401\) | 3.36429e46 | 0.468052 | 0.234026 | − | 0.972230i | \(-0.424810\pi\) | ||||
0.234026 | + | 0.972230i | \(0.424810\pi\) | |||||||
\(402\) | 4.84774e46 | + | 4.12573e45i | 0.644868 | + | 0.0548823i | ||||
\(403\) | 2.17931e46i | 0.277222i | ||||||||
\(404\) | 3.51660e46 | + | 6.02937e45i | 0.427817 | + | 0.0733512i | ||||
\(405\) | −1.35649e46 | −0.157843 | ||||||||
\(406\) | 7.25879e45 | − | 8.52909e46i | 0.0807971 | − | 0.949367i | ||||
\(407\) | − | 5.36393e46i | − | 0.571195i | ||||||
\(408\) | −1.60845e46 | + | 6.17779e46i | −0.163879 | + | 0.629434i | ||||
\(409\) | 6.55074e46 | 0.638661 | 0.319331 | − | 0.947643i | \(-0.396542\pi\) | ||||
0.319331 | + | 0.947643i | \(0.396542\pi\) | |||||||
\(410\) | 6.63680e46 | + | 5.64833e45i | 0.619226 | + | 0.0527000i | ||||
\(411\) | 1.86433e46i | 0.166483i | ||||||||
\(412\) | −8.79683e45 | + | 5.13071e46i | −0.0751928 | + | 0.438559i | ||||
\(413\) | 2.27931e47 | 1.86510 | ||||||||
\(414\) | −3.65282e45 | + | 4.29207e46i | −0.0286169 | + | 0.336249i | ||||
\(415\) | − | 9.00329e46i | − | 0.675360i | ||||||
\(416\) | −5.42931e46 | − | 2.45400e46i | −0.390000 | − | 0.176277i | ||||
\(417\) | 1.54580e47 | 1.06342 | ||||||||
\(418\) | −4.38688e46 | − | 3.73351e45i | −0.289057 | − | 0.0246005i | ||||
\(419\) | 3.50715e46i | 0.221361i | 0.993856 | + | 0.110681i | \(0.0353031\pi\) | ||||
−0.993856 | + | 0.110681i | \(0.964697\pi\) | |||||||
\(420\) | 7.00558e46 | + | 1.20114e46i | 0.423601 | + | 0.0726283i | ||||
\(421\) | 4.57681e46 | 0.265146 | 0.132573 | − | 0.991173i | \(-0.457676\pi\) | ||||
0.132573 | + | 0.991173i | \(0.457676\pi\) | |||||||
\(422\) | −1.13567e45 | + | 1.33442e46i | −0.00630418 | + | 0.0740742i | ||||
\(423\) | − | 6.74925e46i | − | 0.359028i | ||||||
\(424\) | −2.15757e47 | − | 5.61745e46i | −1.09997 | − | 0.286387i | ||||
\(425\) | −1.48514e47 | −0.725717 | ||||||||
\(426\) | −2.19511e47 | − | 1.86818e46i | −1.02822 | − | 0.0875076i | ||||
\(427\) | 1.28624e47i | 0.577591i | ||||||||
\(428\) | 1.37390e46 | − | 8.01321e46i | 0.0591517 | − | 0.345000i | ||||
\(429\) | −1.43984e47 | −0.594404 | ||||||||
\(430\) | −7.35292e45 | + | 8.63970e46i | −0.0291090 | + | 0.342032i | ||||
\(431\) | − | 1.74245e47i | − | 0.661561i | −0.943708 | − | 0.330780i | \(-0.892688\pi\) | ||
0.943708 | − | 0.330780i | \(-0.107312\pi\) | |||||||
\(432\) | −9.89910e46 | + | 2.80194e47i | −0.360486 | + | 1.02035i | ||||
\(433\) | 2.39178e47 | 0.835486 | 0.417743 | − | 0.908565i | \(-0.362821\pi\) | ||||
0.417743 | + | 0.908565i | \(0.362821\pi\) | |||||||
\(434\) | −2.82348e47 | − | 2.40296e46i | −0.946172 | − | 0.0805252i | ||||
\(435\) | 5.92617e46i | 0.190532i | ||||||||
\(436\) | 4.06265e47 | + | 6.96560e46i | 1.25329 | + | 0.214883i | ||||
\(437\) | 4.37922e46 | 0.129638 | ||||||||
\(438\) | 4.17878e46 | − | 4.91007e47i | 0.118718 | − | 1.39493i | ||||
\(439\) | 4.04214e47i | 1.10217i | 0.834448 | + | 0.551087i | \(0.185787\pi\) | ||||
−0.834448 | + | 0.551087i | \(0.814213\pi\) | |||||||
\(440\) | 6.70760e46 | − | 2.57628e47i | 0.175557 | − | 0.674287i | ||||
\(441\) | −1.90122e47 | −0.477680 | ||||||||
\(442\) | −1.50426e47 | − | 1.28022e46i | −0.362845 | − | 0.0308804i | ||||
\(443\) | 6.19474e46i | 0.143468i | 0.997424 | + | 0.0717341i | \(0.0228533\pi\) | ||||
−0.997424 | + | 0.0717341i | \(0.977147\pi\) | |||||||
\(444\) | −1.82623e46 | + | 1.06514e47i | −0.0406126 | + | 0.236871i | ||||
\(445\) | −1.28582e47 | −0.274600 | ||||||||
\(446\) | −6.98867e46 | + | 8.21169e47i | −0.143340 | + | 1.68424i | ||||
\(447\) | 3.29873e47i | 0.649848i | ||||||||
\(448\) | 3.77802e47 | − | 6.76357e47i | 0.714925 | − | 1.27989i | ||||
\(449\) | −5.94487e47 | −1.08071 | −0.540354 | − | 0.841438i | \(-0.681710\pi\) | ||||
−0.540354 | + | 0.841438i | \(0.681710\pi\) | |||||||
\(450\) | −2.02255e47 | − | 1.72132e46i | −0.353244 | − | 0.0300633i | ||||
\(451\) | − | 1.75443e48i | − | 2.94415i | ||||||
\(452\) | 9.35557e47 | + | 1.60405e47i | 1.50862 | + | 0.258659i | ||||
\(453\) | −6.53263e47 | −1.01233 | ||||||||
\(454\) | −5.65019e46 | + | 6.63899e47i | −0.0841508 | + | 0.988773i | ||||
\(455\) | 1.68093e47i | 0.240627i | ||||||||
\(456\) | 8.58410e46 | + | 2.23496e46i | 0.118121 | + | 0.0307540i | ||||
\(457\) | 2.64756e47 | 0.350231 | 0.175116 | − | 0.984548i | \(-0.443970\pi\) | ||||
0.175116 | + | 0.984548i | \(0.443970\pi\) | |||||||
\(458\) | 8.06303e47 | + | 6.86214e46i | 1.02546 | + | 0.0872733i | ||||
\(459\) | 7.52970e47i | 0.920766i | ||||||||
\(460\) | −4.47472e46 | + | 2.60986e47i | −0.0526169 | + | 0.306886i | ||||
\(461\) | 6.93782e47 | 0.784524 | 0.392262 | − | 0.919854i | \(-0.371693\pi\) | ||||
0.392262 | + | 0.919854i | \(0.371693\pi\) | |||||||
\(462\) | 1.58760e47 | − | 1.86543e48i | 0.172658 | − | 2.02873i | ||||
\(463\) | 1.29767e48i | 1.35740i | 0.734417 | + | 0.678698i | \(0.237456\pi\) | ||||
−0.734417 | + | 0.678698i | \(0.762544\pi\) | |||||||
\(464\) | 6.09036e47 | + | 2.15169e47i | 0.612800 | + | 0.216499i | ||||
\(465\) | 1.96181e47 | 0.189891 | ||||||||
\(466\) | 1.90991e47 | + | 1.62545e46i | 0.177855 | + | 0.0151366i | ||||
\(467\) | − | 6.13925e47i | − | 0.550062i | −0.961435 | − | 0.275031i | \(-0.911312\pi\) | ||
0.961435 | − | 0.275031i | \(-0.0886881\pi\) | |||||||
\(468\) | −2.03375e47 | − | 3.48695e46i | −0.175336 | − | 0.0300622i | ||||
\(469\) | −1.49608e48 | −1.24121 | ||||||||
\(470\) | 3.51824e46 | − | 4.13393e47i | 0.0280908 | − | 0.330067i | ||||
\(471\) | − | 8.80203e47i | − | 0.676404i | ||||||
\(472\) | −4.33360e47 | + | 1.66447e48i | −0.320548 | + | 1.23117i | ||||
\(473\) | 2.28390e48 | 1.62621 | ||||||||
\(474\) | −1.71193e48 | − | 1.45696e47i | −1.17348 | − | 0.0998703i | ||||
\(475\) | 2.06362e47i | 0.136190i | ||||||||
\(476\) | 3.31727e47 | − | 1.93478e48i | 0.210793 | − | 1.22944i | ||||
\(477\) | −7.72120e47 | −0.472448 | ||||||||
\(478\) | −7.46229e46 | + | 8.76820e47i | −0.0439713 | + | 0.516664i | ||||
\(479\) | − | 2.23667e47i | − | 0.126929i | −0.997984 | − | 0.0634646i | \(-0.979785\pi\) | ||
0.997984 | − | 0.0634646i | \(-0.0202150\pi\) | |||||||
\(480\) | −2.20909e47 | + | 4.88746e47i | −0.120745 | + | 0.267141i | ||||
\(481\) | −2.55571e47 | −0.134555 | ||||||||
\(482\) | 5.53290e47 | + | 4.70884e46i | 0.280612 | + | 0.0238818i | ||||
\(483\) | 1.86218e48i | 0.909855i | ||||||||
\(484\) | −4.81748e48 | − | 8.25979e47i | −2.26780 | − | 0.388824i | ||||
\(485\) | 2.65781e47 | 0.120551 | ||||||||
\(486\) | −1.48919e47 | + | 1.74979e48i | −0.0650872 | + | 0.764776i | ||||
\(487\) | − | 2.09873e48i | − | 0.883967i | −0.897023 | − | 0.441984i | \(-0.854275\pi\) | ||
0.897023 | − | 0.441984i | \(-0.145725\pi\) | |||||||
\(488\) | −9.39278e47 | − | 2.44550e47i | −0.381274 | − | 0.0992684i | ||||
\(489\) | −1.52282e48 | −0.595783 | ||||||||
\(490\) | −1.16450e48 | − | 9.91064e46i | −0.439148 | − | 0.0373742i | ||||
\(491\) | 9.13688e47i | 0.332148i | 0.986113 | + | 0.166074i | \(0.0531090\pi\) | ||||
−0.986113 | + | 0.166074i | \(0.946891\pi\) | |||||||
\(492\) | −5.97322e47 | + | 3.48385e48i | −0.209332 | + | 1.22092i | ||||
\(493\) | 1.63667e48 | 0.552990 | ||||||||
\(494\) | −1.77888e46 | + | 2.09018e47i | −0.00579510 | + | 0.0680925i | ||||
\(495\) | − | 9.21961e47i | − | 0.289614i | ||||||
\(496\) | 7.12299e47 | − | 2.01616e48i | 0.215770 | − | 0.610738i | ||||
\(497\) | 6.77442e48 | 1.97905 | ||||||||
\(498\) | 4.76058e48 | + | 4.05155e47i | 1.34132 | + | 0.114155i | ||||
\(499\) | − | 3.32131e47i | − | 0.0902609i | −0.998981 | − | 0.0451304i | \(-0.985630\pi\) | ||
0.998981 | − | 0.0451304i | \(-0.0143703\pi\) | |||||||
\(500\) | −2.67176e48 | − | 4.58086e47i | −0.700387 | − | 0.120084i | ||||
\(501\) | 2.60197e48 | 0.657997 | ||||||||
\(502\) | 2.43774e47 | − | 2.86435e48i | 0.0594731 | − | 0.698810i | ||||
\(503\) | − | 3.11350e48i | − | 0.732868i | −0.930444 | − | 0.366434i | \(-0.880579\pi\) | ||
0.930444 | − | 0.366434i | \(-0.119421\pi\) | |||||||
\(504\) | 6.76011e47 | − | 2.59645e48i | 0.153534 | − | 0.589699i | ||||
\(505\) | 7.59568e47 | 0.166465 | ||||||||
\(506\) | 6.94950e48 | + | 5.91446e47i | 1.46975 | + | 0.125085i | ||||
\(507\) | − | 3.05920e48i | − | 0.624403i | ||||||
\(508\) | 4.44993e47 | − | 2.59540e48i | 0.0876609 | − | 0.511278i | ||||
\(509\) | −6.15463e48 | −1.17026 | −0.585129 | − | 0.810940i | \(-0.698956\pi\) | ||||
−0.585129 | + | 0.810940i | \(0.698956\pi\) | |||||||
\(510\) | −1.15245e47 | + | 1.35413e48i | −0.0211524 | + | 0.248541i | ||||
\(511\) | 1.51531e49i | 2.68489i | ||||||||
\(512\) | 4.22079e48 | + | 4.04484e48i | 0.721995 | + | 0.691898i | ||||
\(513\) | 1.04626e48 | 0.172793 | ||||||||
\(514\) | −1.31885e48 | − | 1.12242e47i | −0.210309 | − | 0.0178986i | ||||
\(515\) | 1.10821e48i | 0.170644i | ||||||||
\(516\) | −4.53523e48 | − | 7.77586e47i | −0.674381 | − | 0.115626i | ||||
\(517\) | −1.09280e49 | −1.56932 | ||||||||
\(518\) | 2.81799e47 | − | 3.31115e48i | 0.0390845 | − | 0.459243i | ||||
\(519\) | − | 3.71237e48i | − | 0.497324i | ||||||
\(520\) | −1.22750e48 | − | 3.19591e47i | −0.158840 | − | 0.0413557i | ||||
\(521\) | −5.37366e48 | −0.671725 | −0.335862 | − | 0.941911i | \(-0.609028\pi\) | ||||
−0.335862 | + | 0.941911i | \(0.609028\pi\) | |||||||
\(522\) | 2.22892e48 | + | 1.89695e47i | 0.269169 | + | 0.0229079i | ||||
\(523\) | − | 1.04564e49i | − | 1.21998i | −0.792411 | − | 0.609988i | \(-0.791174\pi\) | ||
0.792411 | − | 0.609988i | \(-0.208826\pi\) | |||||||
\(524\) | −8.63649e47 | + | 5.03719e48i | −0.0973585 | + | 0.567839i | ||||
\(525\) | −8.77513e48 | −0.955842 | ||||||||
\(526\) | −4.93547e47 | + | 5.79919e48i | −0.0519500 | + | 0.610413i | ||||
\(527\) | − | 5.41807e48i | − | 0.551129i | ||||||
\(528\) | 1.33205e49 | + | 4.70606e48i | 1.30951 | + | 0.462643i | ||||
\(529\) | 3.58716e48 | 0.340839 | ||||||||
\(530\) | −4.72925e48 | − | 4.02489e47i | −0.434337 | − | 0.0369648i | ||||
\(531\) | 5.95655e48i | 0.528802i | ||||||||
\(532\) | −2.68840e48 | − | 4.60938e47i | −0.230720 | − | 0.0395579i | ||||
\(533\) | −8.35921e48 | −0.693546 | ||||||||
\(534\) | 5.78630e47 | − | 6.79891e48i | 0.0464150 | − | 0.545377i | ||||
\(535\) | − | 1.73081e48i | − | 0.134240i | ||||||
\(536\) | 2.84446e48 | − | 1.09251e49i | 0.213321 | − | 0.819332i | ||||
\(537\) | −1.45899e48 | −0.105807 | ||||||||
\(538\) | −6.29640e48 | − | 5.35863e47i | −0.441582 | − | 0.0375814i | ||||
\(539\) | 3.07836e49i | 2.08796i | ||||||||
\(540\) | −1.06908e48 | + | 6.23535e48i | −0.0701329 | + | 0.409047i | ||||
\(541\) | 1.77918e49 | 1.12894 | 0.564468 | − | 0.825455i | \(-0.309081\pi\) | ||||
0.564468 | + | 0.825455i | \(0.309081\pi\) | |||||||
\(542\) | 1.07384e48 | − | 1.26176e49i | 0.0659100 | − | 0.774444i | ||||
\(543\) | − | 2.11541e49i | − | 1.25602i | ||||||
\(544\) | 1.34980e49 | + | 6.10099e48i | 0.775337 | + | 0.350445i | ||||
\(545\) | 8.77513e48 | 0.487659 | ||||||||
\(546\) | −8.88808e48 | − | 7.56431e47i | −0.477904 | − | 0.0406726i | ||||
\(547\) | − | 3.11538e48i | − | 0.162084i | −0.996711 | − | 0.0810419i | \(-0.974175\pi\) | ||
0.996711 | − | 0.0810419i | \(-0.0258248\pi\) | |||||||
\(548\) | 4.26377e48 | + | 7.31042e47i | 0.214656 | + | 0.0368038i | ||||
\(549\) | −3.36135e48 | −0.163761 | ||||||||
\(550\) | −2.78707e48 | + | 3.27481e49i | −0.131407 | + | 1.54404i | ||||
\(551\) | − | 2.27417e48i | − | 0.103776i | ||||||
\(552\) | −1.35985e49 | − | 3.54051e48i | −0.600605 | − | 0.156373i | ||||
\(553\) | 5.28324e49 | 2.25865 | ||||||||
\(554\) | −2.63500e49 | − | 2.24255e48i | −1.09045 | − | 0.0928041i | ||||
\(555\) | 2.30065e48i | 0.0921671i | ||||||||
\(556\) | 6.06141e48 | − | 3.53529e49i | 0.235086 | − | 1.37113i | ||||
\(557\) | −2.68438e49 | −1.00798 | −0.503988 | − | 0.863711i | \(-0.668134\pi\) | ||||
−0.503988 | + | 0.863711i | \(0.668134\pi\) | |||||||
\(558\) | 6.27968e47 | − | 7.37864e48i | 0.0228309 | − | 0.268263i | ||||
\(559\) | − | 1.08819e49i | − | 0.383083i | ||||||
\(560\) | 5.49406e48 | − | 1.55509e49i | 0.187288 | − | 0.530118i | ||||
\(561\) | 3.57964e49 | 1.18170 | ||||||||
\(562\) | −2.84319e49 | − | 2.41973e48i | −0.908975 | − | 0.0773595i | ||||
\(563\) | 5.69125e48i | 0.176221i | 0.996111 | + | 0.0881103i | \(0.0280828\pi\) | ||||
−0.996111 | + | 0.0881103i | \(0.971917\pi\) | |||||||
\(564\) | 2.17002e49 | + | 3.72060e48i | 0.650790 | + | 0.111581i | ||||
\(565\) | 2.02076e49 | 0.587005 | ||||||||
\(566\) | −4.64908e48 | + | 5.46267e49i | −0.130819 | + | 1.53713i | ||||
\(567\) | 2.21355e49i | 0.603384i | ||||||||
\(568\) | −1.28801e49 | + | 4.94702e49i | −0.340132 | + | 1.30639i | ||||
\(569\) | −1.13238e49 | −0.289714 | −0.144857 | − | 0.989453i | \(-0.546272\pi\) | ||||
−0.144857 | + | 0.989453i | \(0.546272\pi\) | |||||||
\(570\) | 1.88158e48 | + | 1.60134e47i | 0.0466418 | + | 0.00396951i | ||||
\(571\) | − | 4.77390e49i | − | 1.14663i | −0.819335 | − | 0.573315i | \(-0.805657\pi\) | ||
0.819335 | − | 0.573315i | \(-0.194343\pi\) | |||||||
\(572\) | −5.64589e48 | + | 3.29294e49i | −0.131403 | + | 0.766399i | ||||
\(573\) | −4.61199e49 | −1.04017 | ||||||||
\(574\) | 9.21709e48 | − | 1.08301e50i | 0.201456 | − | 2.36711i | ||||
\(575\) | − | 3.26909e49i | − | 0.692478i | ||||||
\(576\) | 1.76753e49 | + | 9.87315e48i | 0.362879 | + | 0.202699i | ||||
\(577\) | 4.06405e49 | 0.808714 | 0.404357 | − | 0.914601i | \(-0.367495\pi\) | ||||
0.404357 | + | 0.914601i | \(0.367495\pi\) | |||||||
\(578\) | −1.42596e49 | − | 1.21358e48i | −0.275046 | − | 0.0234081i | ||||
\(579\) | 2.95592e49i | 0.552686i | ||||||||
\(580\) | 1.35533e49 | + | 2.32377e48i | 0.245664 | + | 0.0421201i | ||||
\(581\) | −1.46918e50 | −2.58169 | ||||||||
\(582\) | −1.19603e48 | + | 1.40534e49i | −0.0203765 | + | 0.239424i | ||||
\(583\) | 1.25018e50i | 2.06508i | ||||||||
\(584\) | −1.10656e50 | − | 2.88103e49i | −1.77232 | − | 0.461442i | ||||
\(585\) | −4.39279e48 | −0.0682236 | ||||||||
\(586\) | 3.37575e49 | + | 2.87297e48i | 0.508409 | + | 0.0432688i | ||||
\(587\) | − | 5.94523e49i | − | 0.868326i | −0.900834 | − | 0.434163i | \(-0.857044\pi\) | ||
0.900834 | − | 0.434163i | \(-0.142956\pi\) | |||||||
\(588\) | 1.04807e49 | − | 6.11282e49i | 0.148456 | − | 0.865864i | ||||
\(589\) | −7.52846e48 | −0.103426 | ||||||||
\(590\) | −3.10502e48 | + | 3.64840e49i | −0.0413741 | + | 0.486146i | ||||
\(591\) | 3.02740e49i | 0.391287i | ||||||||
\(592\) | 2.36439e49 | + | 8.35325e48i | 0.296434 | + | 0.104728i | ||||
\(593\) | −1.47365e49 | −0.179230 | −0.0896148 | − | 0.995976i | \(-0.528564\pi\) | ||||
−0.0896148 | + | 0.995976i | \(0.528564\pi\) | |||||||
\(594\) | 1.66034e50 | + | 1.41305e49i | 1.95903 | + | 0.166725i | ||||
\(595\) | − | 4.17903e49i | − | 0.478377i | ||||||
\(596\) | 7.54428e49 | + | 1.29350e49i | 0.837886 | + | 0.143659i | ||||
\(597\) | −2.39424e49 | −0.258006 | ||||||||
\(598\) | 2.81801e48 | − | 3.31117e49i | 0.0294660 | − | 0.346226i | ||||
\(599\) | 2.00221e49i | 0.203154i | 0.994828 | + | 0.101577i | \(0.0323889\pi\) | ||||
−0.994828 | + | 0.101577i | \(0.967611\pi\) | |||||||
\(600\) | 1.66840e49 | − | 6.40804e49i | 0.164277 | − | 0.630961i | ||||
\(601\) | 1.56279e50 | 1.49334 | 0.746670 | − | 0.665195i | \(-0.231651\pi\) | ||||
0.746670 | + | 0.665195i | \(0.231651\pi\) | |||||||
\(602\) | 1.40985e50 | + | 1.19987e49i | 1.30748 | + | 0.111275i | ||||
\(603\) | − | 3.90972e49i | − | 0.351912i | ||||||
\(604\) | −2.56158e49 | + | 1.49403e50i | −0.223791 | + | 1.30525i | ||||
\(605\) | −1.04055e50 | −0.882404 | ||||||||
\(606\) | −3.41812e48 | + | 4.01629e49i | −0.0281371 | + | 0.330611i | ||||
\(607\) | − | 1.63488e50i | − | 1.30644i | −0.757168 | − | 0.653220i | \(-0.773418\pi\) | ||
0.757168 | − | 0.653220i | \(-0.226582\pi\) | |||||||
\(608\) | 8.47740e48 | − | 1.87557e49i | 0.0657655 | − | 0.145502i | ||||
\(609\) | 9.67047e49 | 0.728344 | ||||||||
\(610\) | −2.05883e49 | − | 1.75220e48i | −0.150551 | − | 0.0128129i | ||||
\(611\) | 5.20679e49i | 0.369682i | ||||||||
\(612\) | 5.05619e49 | + | 8.66905e48i | 0.348576 | + | 0.0597649i | ||||
\(613\) | −9.89772e49 | −0.662593 | −0.331296 | − | 0.943527i | \(-0.607486\pi\) | ||||
−0.331296 | + | 0.943527i | \(0.607486\pi\) | |||||||
\(614\) | 1.19558e49 | − | 1.40481e50i | 0.0777228 | − | 0.913244i | ||||
\(615\) | 7.52495e49i | 0.475063i | ||||||||
\(616\) | −4.20404e50 | − | 1.09456e50i | −2.57759 | − | 0.671101i | ||||
\(617\) | 1.30487e50 | 0.777022 | 0.388511 | − | 0.921444i | \(-0.372990\pi\) | ||||
0.388511 | + | 0.921444i | \(0.372990\pi\) | |||||||
\(618\) | −5.85976e49 | − | 4.98702e48i | −0.338912 | − | 0.0288436i | ||||
\(619\) | 2.95569e49i | 0.166046i | 0.996548 | + | 0.0830228i | \(0.0264574\pi\) | ||||
−0.996548 | + | 0.0830228i | \(0.973543\pi\) | |||||||
\(620\) | 7.69265e48 | − | 4.48670e49i | 0.0419784 | − | 0.244837i | ||||
\(621\) | −1.65744e50 | −0.878594 | ||||||||
\(622\) | −2.82637e49 | + | 3.32098e50i | −0.145546 | + | 1.71017i | ||||
\(623\) | 2.09824e50i | 1.04971i | ||||||||
\(624\) | 2.24225e49 | − | 6.34670e49i | 0.108984 | − | 0.308479i | ||||
\(625\) | 1.22905e50 | 0.580401 | ||||||||
\(626\) | −4.06209e49 | − | 3.45710e48i | −0.186385 | − | 0.0158626i | ||||
\(627\) | − | 4.97395e49i | − | 0.221761i | ||||||
\(628\) | −2.01304e50 | − | 3.45145e49i | −0.872127 | − | 0.149530i | ||||
\(629\) | 6.35386e49 | 0.267501 | ||||||||
\(630\) | 4.84361e48 | − | 5.69125e49i | 0.0198171 | − | 0.232851i | ||||
\(631\) | − | 1.95097e50i | − | 0.775751i | −0.921712 | − | 0.387876i | \(-0.873209\pi\) | ||
0.921712 | − | 0.387876i | \(-0.126791\pi\) | |||||||
\(632\) | −1.00449e50 | + | 3.85809e50i | −0.388185 | + | 1.49095i | ||||
\(633\) | −1.51299e49 | −0.0568289 | ||||||||
\(634\) | −3.35976e50 | − | 2.85937e49i | −1.22660 | − | 0.104391i | ||||
\(635\) | − | 5.60593e49i | − | 0.198939i | ||||||
\(636\) | 4.25640e49 | − | 2.48253e50i | 0.146830 | − | 0.856379i | ||||
\(637\) | 1.46672e50 | 0.491855 | ||||||||
\(638\) | 3.07144e49 | − | 3.60895e50i | 0.100131 | − | 1.17654i | ||||
\(639\) | 1.77037e50i | 0.561109i | ||||||||
\(640\) | 1.03115e50 | + | 6.96871e49i | 0.317748 | + | 0.214740i | ||||
\(641\) | 2.40479e50 | 0.720498 | 0.360249 | − | 0.932856i | \(-0.382692\pi\) | ||||
0.360249 | + | 0.932856i | \(0.382692\pi\) | |||||||
\(642\) | 9.15185e49 | + | 7.78880e48i | 0.266611 | + | 0.0226903i | ||||
\(643\) | 3.65575e50i | 1.03557i | 0.855511 | + | 0.517785i | \(0.173243\pi\) | ||||
−0.855511 | + | 0.517785i | \(0.826757\pi\) | |||||||
\(644\) | 4.25884e50 | + | 7.30197e49i | 1.17313 | + | 0.201138i | ||||
\(645\) | −9.79588e49 | −0.262403 | ||||||||
\(646\) | 4.42254e48 | − | 5.19649e49i | 0.0115209 | − | 0.135371i | ||||
\(647\) | − | 7.82816e50i | − | 1.98327i | −0.129059 | − | 0.991637i | \(-0.541196\pi\) | ||
0.129059 | − | 0.991637i | \(-0.458804\pi\) | |||||||
\(648\) | −1.61644e50 | − | 4.20857e49i | −0.398300 | − | 0.103701i | ||||
\(649\) | 9.64454e50 | 2.31141 | ||||||||
\(650\) | 1.56032e50 | + | 1.32793e49i | 0.363726 | + | 0.0309553i | ||||
\(651\) | − | 3.20133e50i | − | 0.725893i | ||||||
\(652\) | −5.97127e49 | + | 3.48272e50i | −0.131707 | + | 0.768177i | ||||
\(653\) | −7.97111e50 | −1.71034 | −0.855169 | − | 0.518350i | \(-0.826547\pi\) | ||||
−0.855169 | + | 0.518350i | \(0.826547\pi\) | |||||||
\(654\) | −3.94888e49 | + | 4.63993e50i | −0.0824278 | + | 0.968528i | ||||
\(655\) | 1.08801e50i | 0.220947i | ||||||||
\(656\) | 7.73343e50 | + | 2.73218e50i | 1.52793 | + | 0.539809i | ||||
\(657\) | −3.95999e50 | −0.761232 | ||||||||
\(658\) | −6.74586e50 | − | 5.74115e49i | −1.26174 | − | 0.107382i | ||||
\(659\) | 7.45713e50i | 1.35717i | 0.734522 | + | 0.678585i | \(0.237407\pi\) | ||||
−0.734522 | + | 0.678585i | \(0.762593\pi\) | |||||||
\(660\) | 2.96430e50 | + | 5.08242e49i | 0.524966 | + | 0.0900077i | ||||
\(661\) | −3.41956e50 | −0.589310 | −0.294655 | − | 0.955604i | \(-0.595205\pi\) | ||||
−0.294655 | + | 0.955604i | \(0.595205\pi\) | |||||||
\(662\) | 2.13516e49 | − | 2.50881e50i | 0.0358085 | − | 0.420750i | ||||
\(663\) | − | 1.70556e50i | − | 0.278371i | ||||||
\(664\) | 2.79332e50 | − | 1.07287e51i | 0.443706 | − | 1.70420i | ||||
\(665\) | −5.80681e49 | −0.0897735 | ||||||||
\(666\) | 8.65305e49 | + | 7.36429e48i | 0.130207 | + | 0.0110814i | ||||
\(667\) | 3.60264e50i | 0.527662i | ||||||||
\(668\) | 1.02029e50 | − | 5.95078e50i | 0.145461 | − | 0.848394i | ||||
\(669\) | −9.31060e50 | −1.29213 | ||||||||
\(670\) | 2.03805e49 | − | 2.39472e50i | 0.0275340 | − | 0.323525i | ||||
\(671\) | 5.44252e50i | 0.715805i | ||||||||
\(672\) | 7.97548e50 | + | 3.60484e50i | 1.02120 | + | 0.461572i | ||||
\(673\) | 8.55644e50 | 1.06665 | 0.533325 | − | 0.845911i | \(-0.320942\pi\) | ||||
0.533325 | + | 0.845911i | \(0.320942\pi\) | |||||||
\(674\) | 6.28559e50 | + | 5.34943e49i | 0.762900 | + | 0.0649276i | ||||
\(675\) | − | 7.81034e50i | − | 0.923001i | ||||||
\(676\) | −6.99647e50 | − | 1.19958e50i | −0.805079 | − | 0.138034i | ||||
\(677\) | −8.83947e50 | −0.990444 | −0.495222 | − | 0.868766i | \(-0.664913\pi\) | ||||
−0.495222 | + | 0.868766i | \(0.664913\pi\) | |||||||
\(678\) | −9.09356e49 | + | 1.06849e51i | −0.0992201 | + | 1.16584i | ||||
\(679\) | − | 4.33708e50i | − | 0.460831i | ||||||
\(680\) | 3.05174e50 | + | 7.94550e49i | 0.315782 | + | 0.0822169i | ||||
\(681\) | −7.52743e50 | −0.758575 | ||||||||
\(682\) | −1.19471e51 | − | 1.01677e50i | −1.17258 | − | 0.0997943i | ||||
\(683\) | 1.05574e50i | 0.100922i | 0.998726 | + | 0.0504608i | \(0.0160690\pi\) | ||||
−0.998726 | + | 0.0504608i | \(0.983931\pi\) | |||||||
\(684\) | 1.20457e49 | − | 7.02563e49i | 0.0112156 | − | 0.0654147i | ||||
\(685\) | 9.20953e49 | 0.0835232 | ||||||||
\(686\) | −2.09999e49 | + | 2.46749e50i | −0.0185517 | + | 0.217983i | ||||
\(687\) | 9.14204e50i | 0.786723i | ||||||||
\(688\) | −3.55672e50 | + | 1.00673e51i | −0.298165 | + | 0.843957i | ||||
\(689\) | 5.95661e50 | 0.486467 | ||||||||
\(690\) | −2.98071e50 | − | 2.53677e49i | −0.237157 | − | 0.0201836i | ||||
\(691\) | − | 4.73080e50i | − | 0.366716i | −0.983046 | − | 0.183358i | \(-0.941303\pi\) | ||
0.983046 | − | 0.183358i | \(-0.0586967\pi\) | |||||||
\(692\) | −8.49029e50 | − | 1.45570e50i | −0.641228 | − | 0.109941i | ||||
\(693\) | −1.50448e51 | −1.10710 | ||||||||
\(694\) | 1.32485e50 | − | 1.55671e51i | 0.0949943 | − | 1.11618i | ||||
\(695\) | − | 7.63605e50i | − | 0.533510i | ||||||
\(696\) | −1.83862e50 | + | 7.06186e50i | −0.125178 | + | 0.480787i | ||||
\(697\) | 2.07822e51 | 1.37880 | ||||||||
\(698\) | 1.03474e51 | + | 8.80631e49i | 0.669013 | + | 0.0569372i | ||||
\(699\) | 2.16550e50i | 0.136448i | ||||||||
\(700\) | −3.44091e50 | + | 2.00689e51i | −0.211304 | + | 1.23242i | ||||
\(701\) | 1.72691e51 | 1.03358 | 0.516791 | − | 0.856112i | \(-0.327127\pi\) | ||||
0.516791 | + | 0.856112i | \(0.327127\pi\) | |||||||
\(702\) | 6.73265e49 | − | 7.91087e50i | 0.0392752 | − | 0.461484i | ||||
\(703\) | − | 8.82876e49i | − | 0.0502000i | ||||||
\(704\) | 1.59861e51 | − | 2.86189e51i | 0.886002 | − | 1.58615i | ||||
\(705\) | 4.68714e50 | 0.253224 | ||||||||
\(706\) | −9.86392e50 | − | 8.39482e49i | −0.519475 | − | 0.0442106i | ||||
\(707\) | − | 1.23948e51i | − | 0.636343i | ||||||
\(708\) | −1.91516e51 | − | 3.28362e50i | −0.958529 | − | 0.164344i | ||||
\(709\) | 3.74194e51 | 1.82585 | 0.912924 | − | 0.408130i | \(-0.133819\pi\) | ||||
0.912924 | + | 0.408130i | \(0.133819\pi\) | |||||||
\(710\) | −9.22854e49 | + | 1.08435e51i | −0.0439018 | + | 0.515847i | ||||
\(711\) | 1.38067e51i | 0.640381i | ||||||||
\(712\) | −1.53224e51 | − | 3.98933e50i | −0.692925 | − | 0.180410i | ||||
\(713\) | 1.19262e51 | 0.525886 | ||||||||
\(714\) | 2.20970e51 | + | 1.88060e50i | 0.950094 | + | 0.0808589i | ||||
\(715\) | 7.11258e50i | 0.298208i | ||||||||
\(716\) | −5.72099e49 | + | 3.33674e50i | −0.0233904 | + | 0.136423i | ||||
\(717\) | −9.94158e50 | −0.396379 | ||||||||
\(718\) | −1.86914e50 | + | 2.19625e51i | −0.0726780 | + | 0.853967i | ||||
\(719\) | 3.21231e50i | 0.121814i | 0.998143 | + | 0.0609070i | \(0.0193993\pi\) | ||||
−0.998143 | + | 0.0609070i | \(0.980601\pi\) | |||||||
\(720\) | 4.06394e50 | + | 1.43577e50i | 0.150301 | + | 0.0531006i | ||||
\(721\) | 1.80840e51 | 0.652319 | ||||||||
\(722\) | 2.75985e51 | + | 2.34881e50i | 0.970994 | + | 0.0826377i | ||||
\(723\) | 6.27332e50i | 0.215282i | ||||||||
\(724\) | −4.83800e51 | − | 8.29496e50i | −1.61946 | − | 0.277664i | ||||
\(725\) | −1.69767e51 | −0.554332 | ||||||||
\(726\) | 4.68257e50 | − | 5.50202e51i | 0.149151 | − | 1.75252i | ||||
\(727\) | − | 2.83677e51i | − | 0.881464i | −0.897639 | − | 0.440732i | \(-0.854719\pi\) | ||
0.897639 | − | 0.440732i | \(-0.145281\pi\) | |||||||
\(728\) | −5.21517e50 | + | 2.00306e51i | −0.158090 | + | 0.607198i | ||||
\(729\) | −3.37566e51 | −0.998306 | ||||||||
\(730\) | −2.42550e51 | − | 2.06426e50i | −0.699827 | − | 0.0595596i | ||||
\(731\) | 2.70540e51i | 0.761585i | ||||||||
\(732\) | 1.85298e50 | − | 1.08074e51i | 0.0508946 | − | 0.296841i | ||||
\(733\) | −4.57843e51 | −1.22700 | −0.613500 | − | 0.789695i | \(-0.710239\pi\) | ||||
−0.613500 | + | 0.789695i | \(0.710239\pi\) | |||||||
\(734\) | −1.91125e50 | + | 2.24572e51i | −0.0499792 | + | 0.587256i | ||||
\(735\) | − | 1.32034e51i | − | 0.336909i | ||||||
\(736\) | −1.34295e51 | + | 2.97119e51i | −0.334395 | + | 0.739825i | ||||
\(737\) | −6.33042e51 | −1.53822 | ||||||||
\(738\) | 2.83024e51 | + | 2.40871e50i | 0.671133 | + | 0.0571176i | ||||
\(739\) | − | 1.18843e51i | − | 0.275026i | −0.990500 | − | 0.137513i | \(-0.956089\pi\) | ||
0.990500 | − | 0.137513i | \(-0.0439108\pi\) | |||||||
\(740\) | 5.26163e50 | + | 9.02130e49i | 0.118836 | + | 0.0203750i | ||||
\(741\) | −2.36990e50 | −0.0522398 | ||||||||
\(742\) | −6.56792e50 | + | 7.71732e51i | −0.141305 | + | 1.66034i | ||||
\(743\) | − | 1.36253e51i | − | 0.286119i | −0.989714 | − | 0.143059i | \(-0.954306\pi\) | ||
0.989714 | − | 0.143059i | \(-0.0456940\pi\) | |||||||
\(744\) | 2.33777e51 | + | 6.08661e50i | 0.479169 | + | 0.124756i | ||||
\(745\) | 1.62953e51 | 0.326023 | ||||||||
\(746\) | 5.37613e51 | + | 4.57543e50i | 1.04996 | + | 0.0893578i | ||||
\(747\) | − | 3.83942e51i | − | 0.731973i | ||||||
\(748\) | 1.40365e51 | − | 8.18672e51i | 0.261234 | − | 1.52364i | ||||
\(749\) | −2.82439e51 | −0.513158 | ||||||||
\(750\) | 2.59694e50 | − | 3.05141e51i | 0.0460637 | − | 0.541250i | ||||
\(751\) | 9.12443e51i | 1.58011i | 0.613037 | + | 0.790054i | \(0.289948\pi\) | ||||
−0.613037 | + | 0.790054i | \(0.710052\pi\) | |||||||
\(752\) | 1.70182e51 | − | 4.81701e51i | 0.287735 | − | 0.814434i | ||||
\(753\) | 3.24766e51 | 0.536119 | ||||||||
\(754\) | −1.71952e51 | − | 1.46342e50i | −0.277156 | − | 0.0235877i | ||||
\(755\) | 3.22703e51i | 0.507876i | ||||||||
\(756\) | 1.01750e52 | + | 1.74455e51i | 1.56366 | + | 0.268096i | ||||
\(757\) | 1.02914e52 | 1.54436 | 0.772181 | − | 0.635403i | \(-0.219166\pi\) | ||||
0.772181 | + | 0.635403i | \(0.219166\pi\) | |||||||
\(758\) | 6.03242e50 | − | 7.08810e51i | 0.0883987 | − | 1.03869i | ||||
\(759\) | 7.87949e51i | 1.12758i | ||||||||
\(760\) | 1.10404e50 | − | 4.24042e50i | 0.0154290 | − | 0.0592604i | ||||
\(761\) | −6.32974e51 | −0.863898 | −0.431949 | − | 0.901898i | \(-0.642174\pi\) | ||||
−0.431949 | + | 0.901898i | \(0.642174\pi\) | |||||||
\(762\) | 2.96419e51 | + | 2.52271e50i | 0.395109 | + | 0.0336262i | ||||
\(763\) | − | 1.43195e52i | − | 1.86417i | ||||||
\(764\) | −1.80846e51 | + | 1.05477e52i | −0.229947 | + | 1.34115i | ||||
\(765\) | 1.09211e51 | 0.135632 | ||||||||
\(766\) | 4.92941e50 | − | 5.79207e51i | 0.0597967 | − | 0.702612i | ||||
\(767\) | − | 4.59525e51i | − | 0.544494i | ||||||
\(768\) | −4.14880e51 | + | 5.13871e51i | −0.480198 | + | 0.594774i | ||||
\(769\) | −2.74311e51 | −0.310148 | −0.155074 | − | 0.987903i | \(-0.549562\pi\) | ||||
−0.155074 | + | 0.987903i | \(0.549562\pi\) | |||||||
\(770\) | −9.21498e51 | − | 7.84253e50i | −1.01780 | − | 0.0866210i | ||||
\(771\) | − | 1.49534e51i | − | 0.161347i | ||||||
\(772\) | 6.76026e51 | + | 1.15908e51i | 0.712610 | + | 0.122180i | ||||
\(773\) | −8.35558e51 | −0.860490 | −0.430245 | − | 0.902712i | \(-0.641573\pi\) | ||||
−0.430245 | + | 0.902712i | \(0.641573\pi\) | |||||||
\(774\) | −3.13563e50 | + | 3.68437e51i | −0.0315491 | + | 0.370703i | ||||
\(775\) | 5.62000e51i | 0.552466i | ||||||||
\(776\) | 3.16715e51 | + | 8.24599e50i | 0.304199 | + | 0.0792012i | ||||
\(777\) | 3.75425e51 | 0.352326 | ||||||||
\(778\) | −1.59077e52 | − | 1.35385e51i | −1.45873 | − | 0.124147i | ||||
\(779\) | − | 2.88771e51i | − | 0.258749i | ||||||
\(780\) | 2.42158e50 | − | 1.41237e51i | 0.0212029 | − | 0.123665i | ||||
\(781\) | 2.86649e52 | 2.45263 | ||||||||
\(782\) | −7.00598e50 | + | 8.23204e51i | −0.0585798 | + | 0.688313i | ||||
\(783\) | 8.60724e51i | 0.703319i | ||||||||
\(784\) | −1.35692e52 | − | 4.79392e51i | −1.08359 | − | 0.382826i | ||||
\(785\) | −4.34808e51 | −0.339346 | ||||||||
\(786\) | −5.75295e51 | − | 4.89612e50i | −0.438818 | − | 0.0373462i | ||||
\(787\) | 1.35932e52i | 1.01339i | 0.862125 | + | 0.506696i | \(0.169133\pi\) | ||||
−0.862125 | + | 0.506696i | \(0.830867\pi\) | |||||||
\(788\) | 6.92374e51 | + | 1.18711e51i | 0.504509 | + | 0.0865003i | ||||
\(789\) | −6.57525e51 | −0.468302 | ||||||||
\(790\) | −7.19716e50 | + | 8.45667e51i | −0.0501041 | + | 0.588724i | ||||
\(791\) | − | 3.29752e52i | − | 2.24394i | ||||||
\(792\) | 2.86043e51 | − | 1.09865e52i | 0.190274 | − | 0.730810i | ||||
\(793\) | 2.59315e51 | 0.168621 | ||||||||
\(794\) | −2.34233e52 | − | 1.99347e51i | −1.48894 | − | 0.126718i | ||||
\(795\) | − | 5.36213e51i | − | 0.333219i | ||||||
\(796\) | −9.38831e50 | + | 5.47569e51i | −0.0570364 | + | 0.332662i | ||||
\(797\) | 8.02228e51 | 0.476484 | 0.238242 | − | 0.971206i | \(-0.423429\pi\) | ||||
0.238242 | + | 0.971206i | \(0.423429\pi\) | |||||||
\(798\) | 2.61311e50 | − | 3.07041e51i | 0.0151742 | − | 0.178297i | ||||
\(799\) | − | 1.29448e52i | − | 0.734944i | ||||||
\(800\) | −1.40011e52 | − | 6.32839e51i | −0.777219 | − | 0.351296i | ||||
\(801\) | −5.48335e51 | −0.297619 | ||||||||
\(802\) | 8.78751e51 | + | 7.47872e50i | 0.466366 | + | 0.0396907i | ||||
\(803\) | 6.41181e52i | 3.32737i | ||||||||
\(804\) | 1.25706e52 | + | 2.15528e51i | 0.637891 | + | 0.109369i | ||||
\(805\) | 9.19888e51 | 0.456467 | ||||||||
\(806\) | −4.84454e50 | + | 5.69234e51i | −0.0235083 | + | 0.276223i | ||||
\(807\) | − | 7.13900e51i | − | 0.338777i | ||||||
\(808\) | 9.05132e51 | + | 2.35660e51i | 0.420056 | + | 0.109366i | ||||
\(809\) | −2.33922e52 | −1.06169 | −0.530844 | − | 0.847469i | \(-0.678125\pi\) | ||||
−0.530844 | + | 0.847469i | \(0.678125\pi\) | |||||||
\(810\) | −3.54314e51 | − | 3.01543e50i | −0.157274 | − | 0.0133850i | ||||
\(811\) | − | 2.42897e52i | − | 1.05450i | −0.849710 | − | 0.527250i | \(-0.823223\pi\) | ||
0.849710 | − | 0.527250i | \(-0.176777\pi\) | |||||||
\(812\) | 3.79199e51 | − | 2.21166e52i | 0.161012 | − | 0.939096i | ||||
\(813\) | 1.43061e52 | 0.594145 | ||||||||
\(814\) | 1.19239e51 | − | 1.40106e52i | 0.0484371 | − | 0.569137i | ||||
\(815\) | 7.52249e51i | 0.298899i | ||||||||
\(816\) | −5.57457e51 | + | 1.57788e52i | −0.216665 | + | 0.613270i | ||||
\(817\) | 3.75918e51 | 0.142921 | ||||||||
\(818\) | 1.71105e52 | + | 1.45621e51i | 0.636361 | + | 0.0541583i | ||||
\(819\) | 7.16827e51i | 0.260798i | ||||||||
\(820\) | 1.72097e52 | + | 2.95069e51i | 0.612526 | + | 0.105020i | ||||
\(821\) | 1.13894e52 | 0.396575 | 0.198288 | − | 0.980144i | \(-0.436462\pi\) | ||||
0.198288 | + | 0.980144i | \(0.436462\pi\) | |||||||
\(822\) | −4.14436e50 | + | 4.86963e51i | −0.0141177 | + | 0.165883i | ||||
\(823\) | − | 1.13918e52i | − | 0.379659i | −0.981817 | − | 0.189830i | \(-0.939206\pi\) | ||
0.981817 | − | 0.189830i | \(-0.0607936\pi\) | |||||||
\(824\) | −3.43827e51 | + | 1.32059e52i | −0.112112 | + | 0.430603i | ||||
\(825\) | −3.71306e52 | −1.18457 | ||||||||
\(826\) | 5.95356e52 | + | 5.06685e51i | 1.85838 | + | 0.158160i | ||||
\(827\) | − | 4.85397e51i | − | 0.148251i | −0.997249 | − | 0.0741255i | \(-0.976383\pi\) | ||
0.997249 | − | 0.0741255i | \(-0.0236165\pi\) | |||||||
\(828\) | −1.90823e51 | + | 1.11297e52i | −0.0570276 | + | 0.332611i | ||||
\(829\) | 3.03027e51 | 0.0886135 | 0.0443067 | − | 0.999018i | \(-0.485892\pi\) | ||||
0.0443067 | + | 0.999018i | \(0.485892\pi\) | |||||||
\(830\) | 2.00141e51 | − | 2.35166e52i | 0.0572704 | − | 0.672928i | ||||
\(831\) | − | 2.98763e52i | − | 0.836581i | ||||||
\(832\) | −1.36358e52 | − | 7.61676e51i | −0.373647 | − | 0.208713i | ||||
\(833\) | −3.64647e52 | −0.977829 | ||||||||
\(834\) | 4.03764e52 | + | 3.43628e51i | 1.05959 | + | 0.0901778i | ||||
\(835\) | − | 1.28534e52i | − | 0.330112i | ||||||
\(836\) | −1.13755e52 | − | 1.95039e51i | −0.285929 | − | 0.0490239i | ||||
\(837\) | 2.84935e52 | 0.700952 | ||||||||
\(838\) | −7.79631e50 | + | 9.16067e51i | −0.0187714 | + | 0.220564i | ||||
\(839\) | 4.55576e51i | 0.107361i | 0.998558 | + | 0.0536804i | \(0.0170952\pi\) | ||||
−0.998558 | + | 0.0536804i | \(0.982905\pi\) | |||||||
\(840\) | 1.80316e52 | + | 4.69469e51i | 0.415916 | + | 0.108288i | ||||
\(841\) | −2.55834e52 | −0.577604 | ||||||||
\(842\) | 1.19546e52 | + | 1.01741e51i | 0.264191 | + | 0.0224843i | ||||
\(843\) | − | 3.22367e52i | − | 0.697355i | ||||||
\(844\) | −5.93274e50 | + | 3.46025e51i | −0.0125629 | + | 0.0732728i | ||||
\(845\) | −1.51120e52 | −0.313258 | ||||||||
\(846\) | 1.50034e51 | − | 1.76290e52i | 0.0304455 | − | 0.357735i | ||||
\(847\) | 1.69800e53i | 3.37316i | ||||||||
\(848\) | −5.51070e52 | − | 1.94690e52i | −1.07172 | − | 0.378633i | ||||
\(849\) | −6.19370e52 | −1.17927 | ||||||||
\(850\) | −3.87919e52 | − | 3.30143e51i | −0.723103 | − | 0.0615406i | ||||
\(851\) | 1.39861e52i | 0.255249i | ||||||||
\(852\) | −5.69210e52 | − | 9.75936e51i | −1.01709 | − | 0.174385i | ||||
\(853\) | −3.80014e52 | −0.664840 | −0.332420 | − | 0.943132i | \(-0.607865\pi\) | ||||
−0.332420 | + | 0.943132i | \(0.607865\pi\) | |||||||
\(854\) | −2.85928e51 | + | 3.35966e52i | −0.0489796 | + | 0.575511i | ||||
\(855\) | − | 1.51750e51i | − | 0.0254530i | ||||||
\(856\) | 5.36994e51 | − | 2.06251e52i | 0.0881946 | − | 0.338741i | ||||
\(857\) | −1.39613e52 | −0.224528 | −0.112264 | − | 0.993678i | \(-0.535810\pi\) | ||||
−0.112264 | + | 0.993678i | \(0.535810\pi\) | |||||||
\(858\) | −3.76085e52 | − | 3.20072e51i | −0.592263 | − | 0.0504053i | ||||
\(859\) | − | 6.39064e52i | − | 0.985525i | −0.870164 | − | 0.492762i | \(-0.835987\pi\) | ||
0.870164 | − | 0.492762i | \(-0.164013\pi\) | |||||||
\(860\) | −3.84116e51 | + | 2.24034e52i | −0.0580084 | + | 0.338331i | ||||
\(861\) | 1.22794e53 | 1.81602 | ||||||||
\(862\) | 3.87342e51 | − | 4.55128e52i | 0.0561002 | − | 0.659178i | ||||
\(863\) | − | 1.26060e53i | − | 1.78807i | −0.447997 | − | 0.894035i | \(-0.647862\pi\) | ||
0.447997 | − | 0.894035i | \(-0.352138\pi\) | |||||||
\(864\) | −3.20851e52 | + | 7.09860e52i | −0.445713 | + | 0.986110i | ||||
\(865\) | −1.83386e52 | −0.249503 | ||||||||
\(866\) | 6.24733e52 | + | 5.31687e51i | 0.832477 | + | 0.0708490i | ||||
\(867\) | − | 1.61678e52i | − | 0.211012i | ||||||
\(868\) | −7.32151e52 | − | 1.25531e52i | −0.935935 | − | 0.160470i | ||||
\(869\) | 2.23552e53 | 2.79912 | ||||||||
\(870\) | −1.31737e51 | + | 1.54791e52i | −0.0161570 | + | 0.189845i | ||||
\(871\) | 3.01620e52i | 0.362355i | ||||||||
\(872\) | 1.04568e53 | + | 2.72253e52i | 1.23056 | + | 0.320388i | ||||
\(873\) | 1.13341e52 | 0.130657 | ||||||||
\(874\) | 1.14385e52 | + | 9.73489e50i | 0.129171 | + | 0.0109932i | ||||
\(875\) | 9.41707e52i | 1.04177i | ||||||||
\(876\) | 2.18299e52 | − | 1.27322e53i | 0.236580 | − | 1.37984i | ||||
\(877\) | −4.36515e52 | −0.463454 | −0.231727 | − | 0.972781i | \(-0.574438\pi\) | ||||
−0.231727 | + | 0.972781i | \(0.574438\pi\) | |||||||
\(878\) | −8.98557e51 | + | 1.05581e53i | −0.0934640 | + | 1.09820i | ||||
\(879\) | 3.82750e52i | 0.390045i | ||||||||
\(880\) | 2.32472e52 | − | 6.58013e52i | 0.232104 | − | 0.656971i | ||||
\(881\) | 1.95340e53 | 1.91084 | 0.955420 | − | 0.295249i | \(-0.0954026\pi\) | ||||
0.955420 | + | 0.295249i | \(0.0954026\pi\) | |||||||
\(882\) | −4.96598e52 | − | 4.22636e51i | −0.475960 | − | 0.0405072i | ||||
\(883\) | − | 9.53989e52i | − | 0.895882i | −0.894063 | − | 0.447941i | \(-0.852157\pi\) | ||
0.894063 | − | 0.447941i | \(-0.147843\pi\) | |||||||
\(884\) | −3.90066e52 | − | 6.68785e51i | −0.358920 | − | 0.0615383i | ||||
\(885\) | −4.13664e52 | −0.372966 | ||||||||
\(886\) | −1.37707e51 | + | 1.61806e52i | −0.0121661 | + | 0.142951i | ||||
\(887\) | − | 1.15695e53i | − | 1.00159i | −0.865567 | − | 0.500793i | \(-0.833042\pi\) | ||
0.865567 | − | 0.500793i | \(-0.166958\pi\) | |||||||
\(888\) | −7.13788e51 | + | 2.74154e52i | −0.0605530 | + | 0.232574i | ||||
\(889\) | −9.14790e52 | −0.760484 | ||||||||
\(890\) | −3.35857e52 | − | 2.85835e51i | −0.273611 | − | 0.0232860i | ||||
\(891\) | 9.36627e52i | 0.747770i | ||||||||
\(892\) | −3.65088e52 | + | 2.12936e53i | −0.285647 | + | 1.66602i | ||||
\(893\) | −1.79870e52 | −0.137922 | ||||||||
\(894\) | −7.33300e51 | + | 8.61628e52i | −0.0551069 | + | 0.647507i | ||||
\(895\) | 7.20720e51i | 0.0530826i | ||||||||
\(896\) | 1.13717e53 | − | 1.68266e53i | 0.820884 | − | 1.21465i | ||||
\(897\) | 3.75428e52 | 0.265621 | ||||||||
\(898\) | −1.55280e53 | − | 1.32153e52i | −1.07682 | − | 0.0916437i | ||||
\(899\) | − | 6.19342e52i | − | 0.420975i | ||||||
\(900\) | −5.24464e52 | − | 8.99216e51i | −0.349422 | − | 0.0599099i | ||||
\(901\) | −1.48090e53 | −0.967118 | ||||||||
\(902\) | 3.90006e52 | − | 4.58258e53i | 0.249663 | − | 2.93354i | ||||
\(903\) | 1.59852e53i | 1.00308i | ||||||||
\(904\) | 2.40802e53 | + | 6.26950e52i | 1.48125 | + | 0.385657i | ||||
\(905\) | −1.04498e53 | −0.630137 | ||||||||
\(906\) | −1.70632e53 | − | 1.45219e52i | −1.00868 | − | 0.0858450i | ||||
\(907\) | 4.07057e52i | 0.235898i | 0.993020 | + | 0.117949i | \(0.0376319\pi\) | ||||
−0.993020 | + | 0.117949i | \(0.962368\pi\) | |||||||
\(908\) | −2.95166e52 | + | 1.72154e53i | −0.167695 | + | 0.978075i | ||||
\(909\) | 3.23915e52 | 0.180419 | ||||||||
\(910\) | −3.73666e51 | + | 4.39059e52i | −0.0204051 | + | 0.239760i | ||||
\(911\) | 2.29061e53i | 1.22637i | 0.789940 | + | 0.613184i | \(0.210112\pi\) | ||||
−0.789940 | + | 0.613184i | \(0.789888\pi\) | |||||||
\(912\) | 2.19248e52 | + | 7.74592e51i | 0.115088 | + | 0.0406599i | ||||
\(913\) | −6.21660e53 | −3.19948 | ||||||||
\(914\) | 6.91543e52 | + | 5.88546e51i | 0.348970 | + | 0.0296995i | ||||
\(915\) | − | 2.33435e52i | − | 0.115501i | ||||||
\(916\) | 2.09081e53 | + | 3.58478e52i | 1.01437 | + | 0.173918i | ||||
\(917\) | 1.77544e53 | 0.844613 | ||||||||
\(918\) | −1.67383e52 | + | 1.96676e53i | −0.0780807 | + | 0.917450i | ||||
\(919\) | − | 3.40869e53i | − | 1.55922i | −0.626263 | − | 0.779612i | \(-0.715416\pi\) | ||
0.626263 | − | 0.779612i | \(-0.284584\pi\) | |||||||
\(920\) | −1.74896e52 | + | 6.71748e52i | −0.0784512 | + | 0.301318i | ||||
\(921\) | 1.59281e53 | 0.700631 | ||||||||
\(922\) | 1.81216e53 | + | 1.54226e52i | 0.781698 | + | 0.0665274i | ||||
\(923\) | − | 1.36577e53i | − | 0.577760i | ||||||
\(924\) | 8.29363e52 | − | 4.83722e53i | 0.344072 | − | 2.00678i | ||||
\(925\) | −6.59067e52 | −0.268151 | ||||||||
\(926\) | −2.88469e52 | + | 3.38951e53i | −0.115107 | + | 1.35251i | ||||
\(927\) | 4.72592e52i | 0.184948i | ||||||||
\(928\) | 1.54297e53 | + | 6.97408e52i | 0.592234 | + | 0.267685i | ||||
\(929\) | 1.64652e53 | 0.619845 | 0.309923 | − | 0.950762i | \(-0.399697\pi\) | ||||
0.309923 | + | 0.950762i | \(0.399697\pi\) | |||||||
\(930\) | 5.12424e52 | + | 4.36105e51i | 0.189207 | + | 0.0161027i | ||||
\(931\) | 5.06682e52i | 0.183502i | ||||||||
\(932\) | 4.95254e52 | + | 8.49135e51i | 0.175931 | + | 0.0301641i | ||||
\(933\) | −3.76541e53 | −1.31203 | ||||||||
\(934\) | 1.36474e52 | − | 1.60357e53i | 0.0466451 | − | 0.548081i | ||||
\(935\) | − | 1.76829e53i | − | 0.592850i | ||||||
\(936\) | −5.23463e52 | − | 1.36289e52i | −0.172155 | − | 0.0448223i | ||||
\(937\) | 2.22858e53 | 0.718978 | 0.359489 | − | 0.933149i | \(-0.382951\pi\) | ||||
0.359489 | + | 0.933149i | \(0.382951\pi\) | |||||||
\(938\) | −3.90776e53 | − | 3.32575e52i | −1.23673 | − | 0.105254i | ||||
\(939\) | − | 4.60569e52i | − | 0.142993i | ||||||
\(940\) | 1.83792e52 | − | 1.07196e53i | 0.0559792 | − | 0.326496i | ||||
\(941\) | 6.08820e52 | 0.181918 | 0.0909590 | − | 0.995855i | \(-0.471007\pi\) | ||||
0.0909590 | + | 0.995855i | \(0.471007\pi\) | |||||||
\(942\) | 1.95667e52 | − | 2.29909e53i | 0.0573589 | − | 0.673968i | ||||
\(943\) | 4.57457e53i | 1.31565i | ||||||||
\(944\) | −1.50194e53 | + | 4.25125e53i | −0.423797 | + | 1.19956i | ||||
\(945\) | 2.19775e53 | 0.608423 | ||||||||
\(946\) | 5.96554e53 | + | 5.07705e52i | 1.62035 | + | 0.137902i | ||||
\(947\) | 2.99009e53i | 0.796865i | 0.917198 | + | 0.398432i | \(0.130446\pi\) | ||||
−0.917198 | + | 0.398432i | \(0.869554\pi\) | |||||||
\(948\) | −4.43916e53 | − | 7.61113e52i | −1.16078 | − | 0.199021i | ||||
\(949\) | 3.05498e53 | 0.783821 | ||||||||
\(950\) | −4.58738e51 | + | 5.39017e52i | −0.0115489 | + | 0.135699i | ||||
\(951\) | − | 3.80937e53i | − | 0.941031i | ||||||
\(952\) | 1.29657e53 | − | 4.97991e53i | 0.314290 | − | 1.20714i | ||||
\(953\) | −1.22357e52 | −0.0291044 | −0.0145522 | − | 0.999894i | \(-0.504632\pi\) | ||||
−0.0145522 | + | 0.999894i | \(0.504632\pi\) | |||||||
\(954\) | −2.01677e53 | − | 1.71640e52i | −0.470746 | − | 0.0400634i | ||||
\(955\) | 2.27826e53i | 0.521846i | ||||||||
\(956\) | −3.89829e52 | + | 2.27366e53i | −0.0876259 | + | 0.511074i | ||||
\(957\) | 4.09190e53 | 0.902632 | ||||||||
\(958\) | 4.97205e51 | − | 5.84216e52i | 0.0107636 | − | 0.126472i | ||||
\(959\) | − | 1.50283e53i | − | 0.319283i | ||||||
\(960\) | −6.85660e52 | + | 1.22750e53i | −0.142964 | + | 0.255940i | ||||
\(961\) | 2.83648e53 | 0.580442 | ||||||||
\(962\) | −6.67551e52 | − | 5.68127e51i | −0.134070 | − | 0.0114102i | ||||
\(963\) | − | 7.38100e52i | − | 0.145493i | ||||||
\(964\) | 1.43472e53 | + | 2.45990e52i | 0.277576 | + | 0.0475916i | ||||
\(965\) | 1.46018e53 | 0.277278 | ||||||||
\(966\) | −4.13957e52 | + | 4.86400e53i | −0.0771555 | + | 0.906578i | ||||
\(967\) | − | 3.40345e53i | − | 0.622648i | −0.950304 | − | 0.311324i | \(-0.899228\pi\) | ||
0.950304 | − | 0.311324i | \(-0.100772\pi\) | |||||||
\(968\) | −1.23996e54 | − | 3.22837e53i | −2.22665 | − | 0.579731i | ||||
\(969\) | 5.89190e52 | 0.103855 | ||||||||
\(970\) | 6.94219e52 | + | 5.90824e51i | 0.120117 | + | 0.0102227i | ||||
\(971\) | − | 5.73814e53i | − | 0.974597i | −0.873235 | − | 0.487299i | \(-0.837982\pi\) | ||
0.873235 | − | 0.487299i | \(-0.162018\pi\) | |||||||
\(972\) | −7.77950e52 | + | 4.53736e53i | −0.129706 | + | 0.756502i | ||||
\(973\) | −1.24607e54 | −2.03944 | ||||||||
\(974\) | 4.66543e52 | − | 5.48189e53i | 0.0749602 | − | 0.880783i | ||||
\(975\) | 1.76913e53i | 0.279046i | ||||||||
\(976\) | −2.39903e53 | − | 8.47563e52i | −0.371483 | − | 0.131243i | ||||
\(977\) | 1.42018e53 | 0.215894 | 0.107947 | − | 0.994157i | \(-0.465572\pi\) | ||||
0.107947 | + | 0.994157i | \(0.465572\pi\) | |||||||
\(978\) | −3.97759e53 | − | 3.38518e52i | −0.593637 | − | 0.0505222i | ||||
\(979\) | 8.87836e53i | 1.30090i | ||||||||
\(980\) | −3.01965e53 | − | 5.17732e52i | −0.434397 | − | 0.0744792i | ||||
\(981\) | 3.74212e53 | 0.528538 | ||||||||
\(982\) | −2.03111e52 | + | 2.38655e53i | −0.0281660 | + | 0.330951i | ||||
\(983\) | 9.93520e53i | 1.35274i | 0.736564 | + | 0.676368i | \(0.236447\pi\) | ||||
−0.736564 | + | 0.676368i | \(0.763553\pi\) | |||||||
\(984\) | −2.33466e53 | + | 8.96703e53i | −0.312112 | + | 1.19877i | ||||
\(985\) | 1.49549e53 | 0.196305 | ||||||||
\(986\) | 4.27498e53 | + | 3.63828e52i | 0.550998 | + | 0.0468934i | ||||
\(987\) | − | 7.64860e53i | − | 0.967995i | ||||||
\(988\) | −9.29284e51 | + | 5.42001e52i | −0.0115484 | + | 0.0673558i | ||||
\(989\) | −5.95512e53 | −0.726703 | ||||||||
\(990\) | 2.04950e52 | − | 2.40816e53i | 0.0245592 | − | 0.288570i | ||||
\(991\) | − | 1.52144e54i | − | 1.79031i | −0.445754 | − | 0.895156i | \(-0.647064\pi\) | ||
0.445754 | − | 0.895156i | \(-0.352936\pi\) | |||||||
\(992\) | 2.30871e53 | − | 5.10787e53i | 0.266784 | − | 0.590241i | ||||
\(993\) | 2.84455e53 | 0.322795 | ||||||||
\(994\) | 1.76948e54 | + | 1.50594e53i | 1.97192 | + | 0.167823i | ||||
\(995\) | 1.18272e53i | 0.129440i | ||||||||
\(996\) | 1.23446e54 | + | 2.11653e53i | 1.32681 | + | 0.227487i | ||||
\(997\) | −1.38403e54 | −1.46095 | −0.730473 | − | 0.682942i | \(-0.760700\pi\) | ||||
−0.730473 | + | 0.682942i | \(0.760700\pi\) | |||||||
\(998\) | 7.38319e51 | − | 8.67525e52i | 0.00765410 | − | 0.0899358i | ||||
\(999\) | 3.34149e53i | 0.340221i |
(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 | 4.37.b.b.3.16 | yes | 16 | |
4.3 | odd | 2 | inner | 4.37.b.b.3.15 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.37.b.b.3.15 | ✓ | 16 | 4.3 | odd | 2 | inner | |
4.37.b.b.3.16 | yes | 16 | 1.1 | even | 1 | trivial |