Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,21,Mod(3,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 21, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.3");
S:= CuspForms(chi, 21);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 21 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.d (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: | \(20.2811012082\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} + 66008406614424 x^{16} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{153}\cdot 3^{15}\cdot 5^{4}\cdot 7^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.18 | ||
Root | \(-1372.90 + 1.21540e6i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.3 |
Dual form | 8.21.d.b.3.17 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 979.944 | + | 297.130i | 0.956976 | + | 0.290166i | ||||
\(3\) | −11837.6 | −0.200471 | −0.100235 | − | 0.994964i | \(-0.531960\pi\) | ||||
−0.100235 | + | 0.994964i | \(0.531960\pi\) | |||||||
\(4\) | 872004. | + | 582341.i | 0.831608 | + | 0.555364i | ||||
\(5\) | − | 4.86160e6i | − | 0.497827i | −0.968526 | − | 0.248914i | \(-0.919926\pi\) | ||
0.968526 | − | 0.248914i | \(-0.0800736\pi\) | |||||||
\(6\) | −1.16002e7 | − | 3.51730e6i | −0.191846 | − | 0.0581697i | ||||
\(7\) | − | 3.96260e8i | − | 1.40281i | −0.712762 | − | 0.701406i | \(-0.752556\pi\) | ||
0.712762 | − | 0.701406i | \(-0.247444\pi\) | |||||||
\(8\) | 6.81484e8 | + | 8.29760e8i | 0.634681 | + | 0.772774i | ||||
\(9\) | −3.34666e9 | −0.959812 | ||||||||
\(10\) | 1.44453e9 | − | 4.76409e9i | 0.144453 | − | 0.476409i | ||||
\(11\) | 2.78400e10 | 1.07335 | 0.536677 | − | 0.843788i | \(-0.319679\pi\) | ||||
0.536677 | + | 0.843788i | \(0.319679\pi\) | |||||||
\(12\) | −1.03224e10 | − | 6.89351e9i | −0.166713 | − | 0.111334i | ||||
\(13\) | − | 1.92255e11i | − | 1.39458i | −0.716788 | − | 0.697291i | \(-0.754388\pi\) | ||
0.716788 | − | 0.697291i | \(-0.245612\pi\) | |||||||
\(14\) | 1.17741e11 | − | 3.88312e11i | 0.407048 | − | 1.34246i | ||||
\(15\) | 5.75496e10i | 0.0997997i | ||||||||
\(16\) | 4.21269e11 | + | 1.01561e12i | 0.383142 | + | 0.923689i | ||||
\(17\) | 1.00761e12 | 0.499807 | 0.249904 | − | 0.968271i | \(-0.419601\pi\) | ||||
0.249904 | + | 0.968271i | \(0.419601\pi\) | |||||||
\(18\) | −3.27953e12 | − | 9.94391e11i | −0.918517 | − | 0.278505i | ||||
\(19\) | 9.04652e11 | 0.147552 | 0.0737761 | − | 0.997275i | \(-0.476495\pi\) | ||||
0.0737761 | + | 0.997275i | \(0.476495\pi\) | |||||||
\(20\) | 2.83111e12 | − | 4.23933e12i | 0.276475 | − | 0.413997i | ||||
\(21\) | 4.69076e12i | 0.281222i | ||||||||
\(22\) | 2.72817e13 | + | 8.27211e12i | 1.02717 | + | 0.311451i | ||||
\(23\) | − | 5.92847e13i | − | 1.43108i | −0.698571 | − | 0.715541i | \(-0.746180\pi\) | ||
0.698571 | − | 0.715541i | \(-0.253820\pi\) | |||||||
\(24\) | −8.06712e12 | − | 9.82235e12i | −0.127235 | − | 0.154918i | ||||
\(25\) | 7.17323e13 | 0.752168 | ||||||||
\(26\) | 5.71247e13 | − | 1.88399e14i | 0.404660 | − | 1.33458i | ||||
\(27\) | 8.08914e13 | 0.392884 | ||||||||
\(28\) | 2.30758e14 | − | 3.45540e14i | 0.779071 | − | 1.16659i | ||||
\(29\) | − | 4.75437e14i | − | 1.13009i | −0.825060 | − | 0.565045i | \(-0.808859\pi\) | ||
0.825060 | − | 0.565045i | \(-0.191141\pi\) | |||||||
\(30\) | −1.70997e13 | + | 5.63953e13i | −0.0289585 | + | 0.0955060i | ||||
\(31\) | 5.26254e14i | 0.642065i | 0.947068 | + | 0.321032i | \(0.104030\pi\) | ||||
−0.947068 | + | 0.321032i | \(0.895970\pi\) | |||||||
\(32\) | 1.11053e14 | + | 1.12041e15i | 0.0986351 | + | 0.995124i | ||||
\(33\) | −3.29559e14 | −0.215176 | ||||||||
\(34\) | 9.87399e14 | + | 2.99390e14i | 0.478304 | + | 0.145027i | ||||
\(35\) | −1.92645e15 | −0.698358 | ||||||||
\(36\) | −2.91830e15 | − | 1.94890e15i | −0.798187 | − | 0.533044i | ||||
\(37\) | 5.41855e15i | 1.12685i | 0.826167 | + | 0.563425i | \(0.190517\pi\) | ||||
−0.826167 | + | 0.563425i | \(0.809483\pi\) | |||||||
\(38\) | 8.86508e14 | + | 2.68799e14i | 0.141204 | + | 0.0428146i | ||||
\(39\) | 2.27584e15i | 0.279573i | ||||||||
\(40\) | 4.03396e15 | − | 3.31310e15i | 0.384708 | − | 0.315962i | ||||
\(41\) | −1.00310e16 | −0.747318 | −0.373659 | − | 0.927566i | \(-0.621897\pi\) | ||||
−0.373659 | + | 0.927566i | \(0.621897\pi\) | |||||||
\(42\) | −1.39376e15 | + | 4.59668e15i | −0.0816011 | + | 0.269123i | ||||
\(43\) | −2.73018e16 | −1.26330 | −0.631651 | − | 0.775253i | \(-0.717622\pi\) | ||||
−0.631651 | + | 0.775253i | \(0.717622\pi\) | |||||||
\(44\) | 2.42766e16 | + | 1.62124e16i | 0.892609 | + | 0.596102i | ||||
\(45\) | 1.62701e16i | 0.477821i | ||||||||
\(46\) | 1.76153e16 | − | 5.80957e16i | 0.415251 | − | 1.36951i | ||||
\(47\) | 5.52785e16i | 1.05094i | 0.850812 | + | 0.525470i | \(0.176111\pi\) | ||||
−0.850812 | + | 0.525470i | \(0.823889\pi\) | |||||||
\(48\) | −4.98681e15 | − | 1.20223e16i | −0.0768087 | − | 0.185172i | ||||
\(49\) | −7.72294e16 | −0.967880 | ||||||||
\(50\) | 7.02936e16 | + | 2.13138e16i | 0.719807 | + | 0.218253i | ||||
\(51\) | −1.19276e16 | −0.100197 | ||||||||
\(52\) | 1.11958e17 | − | 1.67647e17i | 0.774500 | − | 1.15975i | ||||
\(53\) | 1.63835e16i | 0.0936804i | 0.998902 | + | 0.0468402i | \(0.0149152\pi\) | ||||
−0.998902 | + | 0.0468402i | \(0.985085\pi\) | |||||||
\(54\) | 7.92691e16 | + | 2.40353e16i | 0.375981 | + | 0.114002i | ||||
\(55\) | − | 1.35347e17i | − | 0.534345i | ||||||
\(56\) | 3.28800e17 | − | 2.70044e17i | 1.08406 | − | 0.890338i | ||||
\(57\) | −1.07089e16 | −0.0295799 | ||||||||
\(58\) | 1.41266e17 | − | 4.65901e17i | 0.327913 | − | 1.08147i | ||||
\(59\) | −5.08001e17 | −0.993904 | −0.496952 | − | 0.867778i | \(-0.665548\pi\) | ||||
−0.496952 | + | 0.867778i | \(0.665548\pi\) | |||||||
\(60\) | −3.35135e16 | + | 5.01834e16i | −0.0554251 | + | 0.0829942i | ||||
\(61\) | 2.76180e17i | 0.387164i | 0.981084 | + | 0.193582i | \(0.0620105\pi\) | ||||
−0.981084 | + | 0.193582i | \(0.937990\pi\) | |||||||
\(62\) | −1.56366e17 | + | 5.15700e17i | −0.186305 | + | 0.614441i | ||||
\(63\) | 1.32614e18i | 1.34643i | ||||||||
\(64\) | −2.24081e17 | + | 1.13094e18i | −0.194359 | + | 0.980930i | ||||
\(65\) | −9.34666e17 | −0.694261 | ||||||||
\(66\) | −3.22949e17 | − | 9.79217e16i | −0.205918 | − | 0.0624367i | ||||
\(67\) | −7.08470e17 | −0.388663 | −0.194332 | − | 0.980936i | \(-0.562254\pi\) | ||||
−0.194332 | + | 0.980936i | \(0.562254\pi\) | |||||||
\(68\) | 8.78638e17 | + | 5.86772e17i | 0.415643 | + | 0.277575i | ||||
\(69\) | 7.01788e17i | 0.286890i | ||||||||
\(70\) | −1.88782e18 | − | 5.72407e17i | −0.668312 | − | 0.202640i | ||||
\(71\) | − | 2.20639e18i | − | 0.677795i | −0.940823 | − | 0.338898i | \(-0.889946\pi\) | ||
0.940823 | − | 0.338898i | \(-0.110054\pi\) | |||||||
\(72\) | −2.28069e18 | − | 2.77692e18i | −0.609174 | − | 0.741717i | ||||
\(73\) | 8.31823e18 | 1.93554 | 0.967770 | − | 0.251835i | \(-0.0810342\pi\) | ||||
0.967770 | + | 0.251835i | \(0.0810342\pi\) | |||||||
\(74\) | −1.61001e18 | + | 5.30988e18i | −0.326973 | + | 1.07837i | ||||
\(75\) | −8.49137e17 | −0.150787 | ||||||||
\(76\) | 7.88860e17 | + | 5.26816e17i | 0.122706 | + | 0.0819451i | ||||
\(77\) | − | 1.10319e19i | − | 1.50571i | ||||||
\(78\) | −6.76218e17 | + | 2.23019e18i | −0.0811224 | + | 0.267544i | ||||
\(79\) | − | 2.46057e18i | − | 0.259875i | −0.991522 | − | 0.129938i | \(-0.958522\pi\) | ||
0.991522 | − | 0.129938i | \(-0.0414777\pi\) | |||||||
\(80\) | 4.93747e18 | − | 2.04804e18i | 0.459838 | − | 0.190739i | ||||
\(81\) | 1.07115e19 | 0.881050 | ||||||||
\(82\) | −9.82981e18 | − | 2.98051e18i | −0.715166 | − | 0.216846i | ||||
\(83\) | 1.22709e19 | 0.790851 | 0.395425 | − | 0.918498i | \(-0.370597\pi\) | ||||
0.395425 | + | 0.918498i | \(0.370597\pi\) | |||||||
\(84\) | −2.73162e18 | + | 4.09036e18i | −0.156181 | + | 0.233867i | ||||
\(85\) | − | 4.89858e18i | − | 0.248818i | ||||||
\(86\) | −2.67543e19 | − | 8.11219e18i | −1.20895 | − | 0.366567i | ||||
\(87\) | 5.62802e18i | 0.226550i | ||||||||
\(88\) | 1.89725e19 | + | 2.31005e19i | 0.681238 | + | 0.829460i | ||||
\(89\) | 3.83975e19 | 1.23141 | 0.615706 | − | 0.787976i | \(-0.288871\pi\) | ||||
0.615706 | + | 0.787976i | \(0.288871\pi\) | |||||||
\(90\) | −4.83433e18 | + | 1.59438e19i | −0.138647 | + | 0.457263i | ||||
\(91\) | −7.61829e19 | −1.95634 | ||||||||
\(92\) | 3.45239e19 | − | 5.16965e19i | 0.794771 | − | 1.19010i | ||||
\(93\) | − | 6.22958e18i | − | 0.128715i | ||||||
\(94\) | −1.64249e19 | + | 5.41699e19i | −0.304947 | + | 1.00572i | ||||
\(95\) | − | 4.39805e18i | − | 0.0734555i | ||||||
\(96\) | −1.31460e18 | − | 1.32629e19i | −0.0197734 | − | 0.199493i | ||||
\(97\) | 2.89133e19 | 0.392085 | 0.196043 | − | 0.980595i | \(-0.437191\pi\) | ||||
0.196043 | + | 0.980595i | \(0.437191\pi\) | |||||||
\(98\) | −7.56804e19 | − | 2.29471e19i | −0.926239 | − | 0.280846i | ||||
\(99\) | −9.31710e19 | −1.03022 | ||||||||
\(100\) | 6.25508e19 | + | 4.17727e19i | 0.625508 | + | 0.417727i | ||||
\(101\) | 9.84179e19i | 0.890964i | 0.895291 | + | 0.445482i | \(0.146968\pi\) | ||||
−0.895291 | + | 0.445482i | \(0.853032\pi\) | |||||||
\(102\) | −1.16884e19 | − | 3.54406e18i | −0.0958858 | − | 0.0290736i | ||||
\(103\) | 2.53311e20i | 1.88487i | 0.334385 | + | 0.942436i | \(0.391471\pi\) | ||||
−0.334385 | + | 0.942436i | \(0.608529\pi\) | |||||||
\(104\) | 1.59525e20 | − | 1.31019e20i | 1.07770 | − | 0.885115i | ||||
\(105\) | 2.28046e19 | 0.140000 | ||||||||
\(106\) | −4.86803e18 | + | 1.60549e19i | −0.0271828 | + | 0.0896499i | ||||
\(107\) | −3.48945e20 | −1.77386 | −0.886931 | − | 0.461902i | \(-0.847167\pi\) | ||||
−0.886931 | + | 0.461902i | \(0.847167\pi\) | |||||||
\(108\) | 7.05376e19 | + | 4.71064e19i | 0.326726 | + | 0.218194i | ||||
\(109\) | − | 4.36494e20i | − | 1.84380i | −0.387429 | − | 0.921899i | \(-0.626637\pi\) | ||
0.387429 | − | 0.921899i | \(-0.373363\pi\) | |||||||
\(110\) | 4.02156e19 | − | 1.32632e20i | 0.155049 | − | 0.511356i | ||||
\(111\) | − | 6.41426e19i | − | 0.225900i | ||||||
\(112\) | 4.02444e20 | − | 1.66932e20i | 1.29576 | − | 0.537477i | ||||
\(113\) | 5.39787e20 | 1.59015 | 0.795075 | − | 0.606511i | \(-0.207431\pi\) | ||||
0.795075 | + | 0.606511i | \(0.207431\pi\) | |||||||
\(114\) | −1.04941e19 | − | 3.18193e18i | −0.0283072 | − | 0.00858307i | ||||
\(115\) | −2.88218e20 | −0.712432 | ||||||||
\(116\) | 2.76866e20 | − | 4.14583e20i | 0.627611 | − | 0.939791i | ||||
\(117\) | 6.43411e20i | 1.33854i | ||||||||
\(118\) | −4.97813e20 | − | 1.50942e20i | −0.951143 | − | 0.288397i | ||||
\(119\) | − | 3.99274e20i | − | 0.701135i | ||||||
\(120\) | −4.77523e19 | + | 3.92191e19i | −0.0771226 | + | 0.0633410i | ||||
\(121\) | 1.02318e20 | 0.152089 | ||||||||
\(122\) | −8.20614e19 | + | 2.70641e20i | −0.112342 | + | 0.370506i | ||||
\(123\) | 1.18743e20 | 0.149815 | ||||||||
\(124\) | −3.06459e20 | + | 4.58896e20i | −0.356579 | + | 0.533946i | ||||
\(125\) | − | 8.12371e20i | − | 0.872277i | ||||||
\(126\) | −3.94037e20 | + | 1.29955e21i | −0.390689 | + | 1.28851i | ||||
\(127\) | 1.10768e21i | 1.01479i | 0.861713 | + | 0.507396i | \(0.169392\pi\) | ||||
−0.861713 | + | 0.507396i | \(0.830608\pi\) | |||||||
\(128\) | −5.55622e20 | + | 1.04167e21i | −0.470630 | + | 0.882331i | ||||
\(129\) | 3.23188e20 | 0.253255 | ||||||||
\(130\) | −9.15920e20 | − | 2.77717e20i | −0.664392 | − | 0.201451i | ||||
\(131\) | −2.07719e20 | −0.139561 | −0.0697804 | − | 0.997562i | \(-0.522230\pi\) | ||||
−0.0697804 | + | 0.997562i | \(0.522230\pi\) | |||||||
\(132\) | −2.87377e20 | − | 1.91916e20i | −0.178942 | − | 0.119501i | ||||
\(133\) | − | 3.58477e20i | − | 0.206988i | ||||||
\(134\) | −6.94261e20 | − | 2.10508e20i | −0.371942 | − | 0.112777i | ||||
\(135\) | − | 3.93261e20i | − | 0.195589i | ||||||
\(136\) | 6.86669e20 | + | 8.36073e20i | 0.317218 | + | 0.386238i | ||||
\(137\) | 7.35146e20 | 0.315622 | 0.157811 | − | 0.987469i | \(-0.449556\pi\) | ||||
0.157811 | + | 0.987469i | \(0.449556\pi\) | |||||||
\(138\) | −2.08522e20 | + | 6.87713e20i | −0.0832456 | + | 0.274547i | ||||
\(139\) | 3.82935e21 | 1.42225 | 0.711127 | − | 0.703064i | \(-0.248185\pi\) | ||||
0.711127 | + | 0.703064i | \(0.248185\pi\) | |||||||
\(140\) | −1.67988e21 | − | 1.12185e21i | −0.580760 | − | 0.387843i | ||||
\(141\) | − | 6.54364e20i | − | 0.210683i | ||||||
\(142\) | 6.55584e20 | − | 2.16214e21i | 0.196673 | − | 0.648634i | ||||
\(143\) | − | 5.35239e21i | − | 1.49688i | ||||||
\(144\) | −1.40984e21 | − | 3.39889e21i | −0.367744 | − | 0.886568i | ||||
\(145\) | −2.31138e21 | −0.562590 | ||||||||
\(146\) | 8.15140e21 | + | 2.47159e21i | 1.85227 | + | 0.561628i | ||||
\(147\) | 9.14209e20 | 0.194031 | ||||||||
\(148\) | −3.15545e21 | + | 4.72500e21i | −0.625811 | + | 0.937097i | ||||
\(149\) | 3.97915e21i | 0.737781i | 0.929473 | + | 0.368891i | \(0.120262\pi\) | ||||
−0.929473 | + | 0.368891i | \(0.879738\pi\) | |||||||
\(150\) | −8.32107e20 | − | 2.52304e20i | −0.144300 | − | 0.0437534i | ||||
\(151\) | 3.56951e21i | 0.579215i | 0.957146 | + | 0.289607i | \(0.0935247\pi\) | ||||
−0.957146 | + | 0.289607i | \(0.906475\pi\) | |||||||
\(152\) | 6.16506e20 | + | 7.50644e20i | 0.0936486 | + | 0.114024i | ||||
\(153\) | −3.37212e21 | −0.479721 | ||||||||
\(154\) | 3.27790e21 | − | 1.08106e22i | 0.436907 | − | 1.44093i | ||||
\(155\) | 2.55844e21 | 0.319637 | ||||||||
\(156\) | −1.32531e21 | + | 1.98454e21i | −0.155265 | + | 0.232495i | ||||
\(157\) | 8.79447e20i | 0.0966525i | 0.998832 | + | 0.0483263i | \(0.0153887\pi\) | ||||
−0.998832 | + | 0.0483263i | \(0.984611\pi\) | |||||||
\(158\) | 7.31109e20 | − | 2.41122e21i | 0.0754069 | − | 0.248694i | ||||
\(159\) | − | 1.93941e20i | − | 0.0187802i | ||||||
\(160\) | 5.44698e21 | − | 5.39896e20i | 0.495400 | − | 0.0491033i | ||||
\(161\) | −2.34921e22 | −2.00754 | ||||||||
\(162\) | 1.04967e22 | + | 3.18271e21i | 0.843144 | + | 0.255651i | ||||
\(163\) | 5.56367e21 | 0.420228 | 0.210114 | − | 0.977677i | \(-0.432616\pi\) | ||||
0.210114 | + | 0.977677i | \(0.432616\pi\) | |||||||
\(164\) | −8.74707e21 | − | 5.84146e21i | −0.621475 | − | 0.415033i | ||||
\(165\) | 1.60218e21i | 0.107120i | ||||||||
\(166\) | 1.20248e22 | + | 3.64604e21i | 0.756826 | + | 0.229478i | ||||
\(167\) | 1.51638e22i | 0.898759i | 0.893341 | + | 0.449379i | \(0.148355\pi\) | ||||
−0.893341 | + | 0.449379i | \(0.851645\pi\) | |||||||
\(168\) | −3.89220e21 | + | 3.19667e21i | −0.217321 | + | 0.178487i | ||||
\(169\) | −1.79570e22 | −0.944860 | ||||||||
\(170\) | 1.45552e21 | − | 4.80034e21i | 0.0721984 | − | 0.238113i | ||||
\(171\) | −3.02756e21 | −0.141622 | ||||||||
\(172\) | −2.38073e22 | − | 1.58990e22i | −1.05057 | − | 0.701592i | ||||
\(173\) | 4.65103e22i | 1.93682i | 0.249370 | + | 0.968408i | \(0.419777\pi\) | ||||
−0.249370 | + | 0.968408i | \(0.580223\pi\) | |||||||
\(174\) | −1.67225e21 | + | 5.51515e21i | −0.0657370 | + | 0.216803i | ||||
\(175\) | − | 2.84246e22i | − | 1.05515i | ||||||
\(176\) | 1.17282e22 | + | 2.82745e22i | 0.411247 | + | 0.991446i | ||||
\(177\) | 6.01351e21 | 0.199249 | ||||||||
\(178\) | 3.76274e22 | + | 1.14091e22i | 1.17843 | + | 0.357314i | ||||
\(179\) | 2.15790e22 | 0.639001 | 0.319500 | − | 0.947586i | \(-0.396485\pi\) | ||||
0.319500 | + | 0.947586i | \(0.396485\pi\) | |||||||
\(180\) | −9.47474e21 | + | 1.41876e22i | −0.265364 | + | 0.397359i | ||||
\(181\) | − | 6.42549e22i | − | 1.70263i | −0.524654 | − | 0.851316i | \(-0.675805\pi\) | ||
0.524654 | − | 0.851316i | \(-0.324195\pi\) | |||||||
\(182\) | −7.46550e22 | − | 2.26362e22i | −1.87217 | − | 0.567662i | ||||
\(183\) | − | 3.26931e21i | − | 0.0776149i | ||||||
\(184\) | 4.91921e22 | − | 4.04016e22i | 1.10590 | − | 0.908281i | ||||
\(185\) | 2.63428e22 | 0.560977 | ||||||||
\(186\) | 1.85099e21 | − | 6.10464e21i | 0.0373487 | − | 0.123177i | ||||
\(187\) | 2.80519e22 | 0.536470 | ||||||||
\(188\) | −3.21910e22 | + | 4.82031e22i | −0.583654 | + | 0.873970i | ||||
\(189\) | − | 3.20540e22i | − | 0.551143i | ||||||
\(190\) | 1.30679e21 | − | 4.30985e21i | 0.0213143 | − | 0.0702952i | ||||
\(191\) | − | 6.88101e21i | − | 0.106492i | −0.998581 | − | 0.0532462i | \(-0.983043\pi\) | ||
0.998581 | − | 0.0532462i | \(-0.0169568\pi\) | |||||||
\(192\) | 2.65258e21 | − | 1.33875e22i | 0.0389633 | − | 0.196648i | ||||
\(193\) | 1.13196e23 | 1.57854 | 0.789272 | − | 0.614044i | \(-0.210458\pi\) | ||||
0.789272 | + | 0.614044i | \(0.210458\pi\) | |||||||
\(194\) | 2.83334e22 | + | 8.59101e21i | 0.375216 | + | 0.113770i | ||||
\(195\) | 1.10642e22 | 0.139179 | ||||||||
\(196\) | −6.73443e22 | − | 4.49738e22i | −0.804897 | − | 0.537526i | ||||
\(197\) | − | 1.59402e22i | − | 0.181064i | −0.995894 | − | 0.0905320i | \(-0.971143\pi\) | ||
0.995894 | − | 0.0905320i | \(-0.0288567\pi\) | |||||||
\(198\) | −9.13024e22 | − | 2.76839e22i | −0.985894 | − | 0.298934i | ||||
\(199\) | − | 5.88531e22i | − | 0.604280i | −0.953264 | − | 0.302140i | \(-0.902299\pi\) | ||
0.953264 | − | 0.302140i | \(-0.0977010\pi\) | |||||||
\(200\) | 4.88844e22 | + | 5.95206e22i | 0.477387 | + | 0.581256i | ||||
\(201\) | 8.38658e21 | 0.0779155 | ||||||||
\(202\) | −2.92429e22 | + | 9.64440e22i | −0.258527 | + | 0.852632i | ||||
\(203\) | −1.88396e23 | −1.58530 | ||||||||
\(204\) | −1.04010e22 | − | 6.94596e21i | −0.0833243 | − | 0.0556456i | ||||
\(205\) | 4.87667e22i | 0.372036i | ||||||||
\(206\) | −7.52663e22 | + | 2.48231e23i | −0.546926 | + | 1.80378i | ||||
\(207\) | 1.98406e23i | 1.37357i | ||||||||
\(208\) | 1.95256e23 | − | 8.09912e22i | 1.28816 | − | 0.534324i | ||||
\(209\) | 2.51856e22 | 0.158376 | ||||||||
\(210\) | 2.23472e22 | + | 6.77591e21i | 0.133977 | + | 0.0406233i | ||||
\(211\) | −1.31609e23 | −0.752424 | −0.376212 | − | 0.926534i | \(-0.622773\pi\) | ||||
−0.376212 | + | 0.926534i | \(0.622773\pi\) | |||||||
\(212\) | −9.54080e21 | + | 1.42865e22i | −0.0520267 | + | 0.0779053i | ||||
\(213\) | 2.61183e22i | 0.135878i | ||||||||
\(214\) | −3.41947e23 | − | 1.03682e23i | −1.69754 | − | 0.514714i | ||||
\(215\) | 1.32730e23i | 0.628906i | ||||||||
\(216\) | 5.51262e22 | + | 6.71205e22i | 0.249356 | + | 0.303611i | ||||
\(217\) | 2.08533e23 | 0.900696 | ||||||||
\(218\) | 1.29695e23 | − | 4.27740e23i | 0.535007 | − | 1.76447i | ||||
\(219\) | −9.84677e22 | −0.388019 | ||||||||
\(220\) | 7.88181e22 | − | 1.18023e23i | 0.296756 | − | 0.444365i | ||||
\(221\) | − | 1.93718e23i | − | 0.697022i | ||||||
\(222\) | 1.90587e22 | − | 6.28561e22i | 0.0655485 | − | 0.216181i | ||||
\(223\) | − | 2.37547e23i | − | 0.781090i | −0.920584 | − | 0.390545i | \(-0.872287\pi\) | ||
0.920584 | − | 0.390545i | \(-0.127713\pi\) | |||||||
\(224\) | 4.43973e23 | − | 4.40059e22i | 1.39597 | − | 0.138366i | ||||
\(225\) | −2.40063e23 | −0.721939 | ||||||||
\(226\) | 5.28961e23 | + | 1.60387e23i | 1.52174 | + | 0.461407i | ||||
\(227\) | −3.05009e23 | −0.839564 | −0.419782 | − | 0.907625i | \(-0.637893\pi\) | ||||
−0.419782 | + | 0.907625i | \(0.637893\pi\) | |||||||
\(228\) | −9.33820e21 | − | 6.23623e21i | −0.0245988 | − | 0.0164276i | ||||
\(229\) | 2.03839e23i | 0.513963i | 0.966416 | + | 0.256981i | \(0.0827279\pi\) | ||||
−0.966416 | + | 0.256981i | \(0.917272\pi\) | |||||||
\(230\) | −2.82438e23 | − | 8.56383e22i | −0.681781 | − | 0.206723i | ||||
\(231\) | 1.30591e23i | 0.301851i | ||||||||
\(232\) | 3.94498e23 | − | 3.24003e23i | 0.873304 | − | 0.717247i | ||||
\(233\) | 1.55544e23 | 0.329834 | 0.164917 | − | 0.986307i | \(-0.447264\pi\) | ||||
0.164917 | + | 0.986307i | \(0.447264\pi\) | |||||||
\(234\) | −1.91177e23 | + | 6.30507e23i | −0.388398 | + | 1.28095i | ||||
\(235\) | 2.68742e23 | 0.523187 | ||||||||
\(236\) | −4.42979e23 | − | 2.95830e23i | −0.826538 | − | 0.551978i | ||||
\(237\) | 2.91272e22i | 0.0520973i | ||||||||
\(238\) | 1.18636e23 | − | 3.91266e23i | 0.203446 | − | 0.670970i | ||||
\(239\) | 1.59701e23i | 0.262620i | 0.991341 | + | 0.131310i | \(0.0419184\pi\) | ||||
−0.991341 | + | 0.131310i | \(0.958082\pi\) | |||||||
\(240\) | −5.84477e22 | + | 2.42439e22i | −0.0921839 | + | 0.0382375i | ||||
\(241\) | −3.71550e22 | −0.0562143 | −0.0281072 | − | 0.999605i | \(-0.508948\pi\) | ||||
−0.0281072 | + | 0.999605i | \(0.508948\pi\) | |||||||
\(242\) | 1.00266e23 | + | 3.04017e22i | 0.145546 | + | 0.0441310i | ||||
\(243\) | −4.08849e23 | −0.569509 | ||||||||
\(244\) | −1.60831e23 | + | 2.40830e23i | −0.215017 | + | 0.321968i | ||||
\(245\) | 3.75458e23i | 0.481837i | ||||||||
\(246\) | 1.16361e23 | + | 3.52820e22i | 0.143370 | + | 0.0434713i | ||||
\(247\) | − | 1.73924e23i | − | 0.205774i | ||||||
\(248\) | −4.36665e23 | + | 3.58634e23i | −0.496171 | + | 0.407506i | ||||
\(249\) | −1.45258e23 | −0.158542 | ||||||||
\(250\) | 2.41380e23 | − | 7.96078e23i | 0.253105 | − | 0.834749i | ||||
\(251\) | 1.22841e24 | 1.23768 | 0.618838 | − | 0.785519i | \(-0.287604\pi\) | ||||
0.618838 | + | 0.785519i | \(0.287604\pi\) | |||||||
\(252\) | −7.72268e23 | + | 1.15640e24i | −0.747761 | + | 1.11971i | ||||
\(253\) | − | 1.65049e24i | − | 1.53606i | ||||||
\(254\) | −3.29125e23 | + | 1.08546e24i | −0.294458 | + | 0.971132i | ||||
\(255\) | 5.79874e22i | 0.0498806i | ||||||||
\(256\) | −8.53990e23 | + | 8.55689e23i | −0.706404 | + | 0.707809i | ||||
\(257\) | −1.13022e24 | −0.899150 | −0.449575 | − | 0.893242i | \(-0.648425\pi\) | ||||
−0.449575 | + | 0.893242i | \(0.648425\pi\) | |||||||
\(258\) | 3.16706e23 | + | 9.60287e22i | 0.242359 | + | 0.0734859i | ||||
\(259\) | 2.14715e24 | 1.58076 | ||||||||
\(260\) | −8.15033e23 | − | 5.44295e23i | −0.577353 | − | 0.385568i | ||||
\(261\) | 1.59112e24i | 1.08467i | ||||||||
\(262\) | −2.03553e23 | − | 6.17196e22i | −0.133556 | − | 0.0404958i | ||||
\(263\) | − | 1.73822e24i | − | 1.09786i | −0.835868 | − | 0.548930i | \(-0.815035\pi\) | ||
0.835868 | − | 0.548930i | \(-0.184965\pi\) | |||||||
\(264\) | −2.24589e23 | − | 2.73455e23i | −0.136568 | − | 0.166282i | ||||
\(265\) | 7.96501e22 | 0.0466367 | ||||||||
\(266\) | 1.06514e23 | − | 3.51287e23i | 0.0600608 | − | 0.198083i | ||||
\(267\) | −4.54534e23 | −0.246862 | ||||||||
\(268\) | −6.17789e23 | − | 4.12571e23i | −0.323215 | − | 0.215849i | ||||
\(269\) | 1.91524e24i | 0.965383i | 0.875790 | + | 0.482691i | \(0.160341\pi\) | ||||
−0.875790 | + | 0.482691i | \(0.839659\pi\) | |||||||
\(270\) | 1.16850e23 | − | 3.85374e23i | 0.0567531 | − | 0.187174i | ||||
\(271\) | − | 2.24447e23i | − | 0.105056i | −0.998619 | − | 0.0525280i | \(-0.983272\pi\) | ||
0.998619 | − | 0.0525280i | \(-0.0167279\pi\) | |||||||
\(272\) | 4.24475e23 | + | 1.02333e24i | 0.191497 | + | 0.461667i | ||||
\(273\) | 9.01821e23 | 0.392188 | ||||||||
\(274\) | 7.20402e23 | + | 2.18434e23i | 0.302043 | + | 0.0915829i | ||||
\(275\) | 1.99703e24 | 0.807342 | ||||||||
\(276\) | −4.08680e23 | + | 6.11962e23i | −0.159328 | + | 0.238580i | ||||
\(277\) | − | 3.22736e24i | − | 1.21353i | −0.794883 | − | 0.606763i | \(-0.792468\pi\) | ||
0.794883 | − | 0.606763i | \(-0.207532\pi\) | |||||||
\(278\) | 3.75255e24 | + | 1.13781e24i | 1.36106 | + | 0.412689i | ||||
\(279\) | − | 1.76119e24i | − | 0.616261i | ||||||
\(280\) | −1.31285e24 | − | 1.59849e24i | −0.443235 | − | 0.539673i | ||||
\(281\) | −4.13828e24 | −1.34821 | −0.674104 | − | 0.738636i | \(-0.735470\pi\) | ||||
−0.674104 | + | 0.738636i | \(0.735470\pi\) | |||||||
\(282\) | 1.94431e23 | − | 6.41240e23i | 0.0611329 | − | 0.201618i | ||||
\(283\) | 1.84766e24 | 0.560735 | 0.280368 | − | 0.959893i | \(-0.409544\pi\) | ||||
0.280368 | + | 0.959893i | \(0.409544\pi\) | |||||||
\(284\) | 1.28487e24 | − | 1.92398e24i | 0.376423 | − | 0.563660i | ||||
\(285\) | 5.20623e22i | 0.0147257i | ||||||||
\(286\) | 1.59035e24 | − | 5.24504e24i | 0.434344 | − | 1.43248i | ||||
\(287\) | 3.97488e24i | 1.04835i | ||||||||
\(288\) | −3.71657e23 | − | 3.74963e24i | −0.0946711 | − | 0.955131i | ||||
\(289\) | −3.04896e24 | −0.750193 | ||||||||
\(290\) | −2.26502e24 | − | 6.86781e23i | −0.538385 | − | 0.163244i | ||||
\(291\) | −3.42264e23 | −0.0786015 | ||||||||
\(292\) | 7.25353e24 | + | 4.84404e24i | 1.60961 | + | 1.07493i | ||||
\(293\) | 3.50629e22i | 0.00751919i | 0.999993 | + | 0.00375960i | \(0.00119672\pi\) | ||||
−0.999993 | + | 0.00375960i | \(0.998803\pi\) | |||||||
\(294\) | 8.95874e23 | + | 2.71639e23i | 0.185684 | + | 0.0563013i | ||||
\(295\) | 2.46970e24i | 0.494793i | ||||||||
\(296\) | −4.49610e24 | + | 3.69266e24i | −0.870800 | + | 0.715190i | ||||
\(297\) | 2.25202e24 | 0.421704 | ||||||||
\(298\) | −1.18232e24 | + | 3.89934e24i | −0.214079 | + | 0.706039i | ||||
\(299\) | −1.13978e25 | −1.99576 | ||||||||
\(300\) | −7.40451e23 | − | 4.94487e23i | −0.125396 | − | 0.0837419i | ||||
\(301\) | 1.08186e25i | 1.77217i | ||||||||
\(302\) | −1.06061e24 | + | 3.49792e24i | −0.168068 | + | 0.554295i | ||||
\(303\) | − | 1.16503e24i | − | 0.178612i | ||||||
\(304\) | 3.81102e23 | + | 9.18771e23i | 0.0565335 | + | 0.136292i | ||||
\(305\) | 1.34268e24 | 0.192741 | ||||||||
\(306\) | −3.30449e24 | − | 1.00196e24i | −0.459081 | − | 0.139199i | ||||
\(307\) | −8.38314e24 | −1.12726 | −0.563628 | − | 0.826028i | \(-0.690595\pi\) | ||||
−0.563628 | + | 0.826028i | \(0.690595\pi\) | |||||||
\(308\) | 6.42432e24 | − | 9.61984e24i | 0.836219 | − | 1.25216i | ||||
\(309\) | − | 2.99859e24i | − | 0.377861i | ||||||
\(310\) | 2.50712e24 | + | 7.60188e23i | 0.305885 | + | 0.0927478i | ||||
\(311\) | 7.29114e24i | 0.861374i | 0.902501 | + | 0.430687i | \(0.141729\pi\) | ||||
−0.902501 | + | 0.430687i | \(0.858271\pi\) | |||||||
\(312\) | −1.88840e24 | + | 1.55094e24i | −0.216046 | + | 0.177440i | ||||
\(313\) | 7.51935e24 | 0.833177 | 0.416588 | − | 0.909095i | \(-0.363226\pi\) | ||||
0.416588 | + | 0.909095i | \(0.363226\pi\) | |||||||
\(314\) | −2.61310e23 | + | 8.61809e23i | −0.0280453 | + | 0.0924942i | ||||
\(315\) | 6.44718e24 | 0.670292 | ||||||||
\(316\) | 1.43289e24 | − | 2.14563e24i | 0.144325 | − | 0.216114i | ||||
\(317\) | − | 7.43530e24i | − | 0.725615i | −0.931864 | − | 0.362807i | \(-0.881818\pi\) | ||
0.931864 | − | 0.362807i | \(-0.118182\pi\) | |||||||
\(318\) | 5.76257e22 | − | 1.90052e23i | 0.00544936 | − | 0.0179722i | ||||
\(319\) | − | 1.32362e25i | − | 1.21299i | ||||||
\(320\) | 5.49815e24 | + | 1.08939e24i | 0.488334 | + | 0.0967574i | ||||
\(321\) | 4.13067e24 | 0.355607 | ||||||||
\(322\) | −2.30210e25 | − | 6.98022e24i | −1.92117 | − | 0.582519i | ||||
\(323\) | 9.11535e23 | 0.0737476 | ||||||||
\(324\) | 9.34048e24 | + | 6.23775e24i | 0.732688 | + | 0.489303i | ||||
\(325\) | − | 1.37909e25i | − | 1.04896i | ||||||
\(326\) | 5.45209e24 | + | 1.65313e24i | 0.402149 | + | 0.121936i | ||||
\(327\) | 5.16704e24i | 0.369627i | ||||||||
\(328\) | −6.83596e24 | − | 8.32332e24i | −0.474309 | − | 0.577508i | ||||
\(329\) | 2.19046e25 | 1.47427 | ||||||||
\(330\) | −4.76056e23 | + | 1.57005e24i | −0.0310827 | + | 0.102512i | ||||
\(331\) | −7.67940e22 | −0.00486460 | −0.00243230 | − | 0.999997i | \(-0.500774\pi\) | ||||
−0.00243230 | + | 0.999997i | \(0.500774\pi\) | |||||||
\(332\) | 1.07002e25 | + | 7.14583e24i | 0.657678 | + | 0.439210i | ||||
\(333\) | − | 1.81340e25i | − | 1.08156i | ||||||
\(334\) | −4.50562e24 | + | 1.48597e25i | −0.260789 | + | 0.860091i | ||||
\(335\) | 3.44430e24i | 0.193487i | ||||||||
\(336\) | −4.76396e24 | + | 1.97607e24i | −0.259762 | + | 0.107748i | ||||
\(337\) | 1.40411e25 | 0.743196 | 0.371598 | − | 0.928394i | \(-0.378810\pi\) | ||||
0.371598 | + | 0.928394i | \(0.378810\pi\) | |||||||
\(338\) | −1.75969e25 | − | 5.33557e24i | −0.904209 | − | 0.274166i | ||||
\(339\) | −6.38978e24 | −0.318778 | ||||||||
\(340\) | 2.85265e24 | − | 4.27158e24i | 0.138184 | − | 0.206919i | ||||
\(341\) | 1.46509e25i | 0.689163i | ||||||||
\(342\) | −2.96684e24 | − | 8.99578e23i | −0.135529 | − | 0.0410940i | ||||
\(343\) | − | 1.01557e24i | − | 0.0450579i | ||||||
\(344\) | −1.86058e25 | − | 2.26540e25i | −0.801794 | − | 0.976247i | ||||
\(345\) | 3.41181e24 | 0.142822 | ||||||||
\(346\) | −1.38196e25 | + | 4.55775e25i | −0.561998 | + | 1.85349i | ||||
\(347\) | 4.44481e24 | 0.175614 | 0.0878068 | − | 0.996138i | \(-0.472014\pi\) | ||||
0.0878068 | + | 0.996138i | \(0.472014\pi\) | |||||||
\(348\) | −3.27743e24 | + | 4.90766e24i | −0.125817 | + | 0.188400i | ||||
\(349\) | 3.02572e25i | 1.12869i | 0.825539 | + | 0.564346i | \(0.190871\pi\) | ||||
−0.825539 | + | 0.564346i | \(0.809129\pi\) | |||||||
\(350\) | 8.44580e24 | − | 2.78545e25i | 0.306168 | − | 1.00975i | ||||
\(351\) | − | 1.55518e25i | − | 0.547910i | ||||||
\(352\) | 3.09173e24 | + | 3.11922e25i | 0.105870 | + | 1.06812i | ||||
\(353\) | −3.47498e25 | −1.15666 | −0.578329 | − | 0.815804i | \(-0.696295\pi\) | ||||
−0.578329 | + | 0.815804i | \(0.696295\pi\) | |||||||
\(354\) | 5.89290e24 | + | 1.78679e24i | 0.190676 | + | 0.0578151i | ||||
\(355\) | −1.07266e25 | −0.337425 | ||||||||
\(356\) | 3.34828e25 | + | 2.23605e25i | 1.02405 | + | 0.683881i | ||||
\(357\) | 4.72644e24i | 0.140557i | ||||||||
\(358\) | 2.11462e25 | + | 6.41177e24i | 0.611509 | + | 0.185416i | ||||
\(359\) | − | 1.38151e25i | − | 0.388516i | −0.980950 | − | 0.194258i | \(-0.937770\pi\) | ||
0.980950 | − | 0.194258i | \(-0.0622300\pi\) | |||||||
\(360\) | −1.35003e25 | + | 1.10878e25i | −0.369247 | + | 0.303264i | ||||
\(361\) | −3.67716e25 | −0.978228 | ||||||||
\(362\) | 1.90921e25 | − | 6.29662e25i | 0.494045 | − | 1.62938i | ||||
\(363\) | −1.21120e24 | −0.0304894 | ||||||||
\(364\) | −6.64318e25 | − | 4.43644e25i | −1.62690 | − | 1.08648i | ||||
\(365\) | − | 4.04399e25i | − | 0.963565i | ||||||
\(366\) | 9.71409e23 | − | 3.20374e24i | 0.0225212 | − | 0.0742756i | ||||
\(367\) | 8.35212e25i | 1.88424i | 0.335277 | + | 0.942120i | \(0.391170\pi\) | ||||
−0.335277 | + | 0.942120i | \(0.608830\pi\) | |||||||
\(368\) | 6.02100e25 | − | 2.49749e25i | 1.32188 | − | 0.548308i | ||||
\(369\) | 3.35703e25 | 0.717285 | ||||||||
\(370\) | 2.58145e25 | + | 7.82724e24i | 0.536842 | + | 0.162776i | ||||
\(371\) | 6.49213e24 | 0.131416 | ||||||||
\(372\) | 3.62774e24 | − | 5.43222e24i | 0.0714836 | − | 0.107040i | ||||
\(373\) | 5.09653e25i | 0.977656i | 0.872380 | + | 0.488828i | \(0.162575\pi\) | ||||
−0.872380 | + | 0.488828i | \(0.837425\pi\) | |||||||
\(374\) | 2.74892e25 | + | 8.33504e24i | 0.513389 | + | 0.155665i | ||||
\(375\) | 9.61652e24i | 0.174866i | ||||||||
\(376\) | −4.58679e25 | + | 3.76714e25i | −0.812139 | + | 0.667012i | ||||
\(377\) | −9.14051e25 | −1.57600 | ||||||||
\(378\) | 9.52420e24 | − | 3.14111e25i | 0.159923 | − | 0.527431i | ||||
\(379\) | 2.21704e25 | 0.362562 | 0.181281 | − | 0.983431i | \(-0.441976\pi\) | ||||
0.181281 | + | 0.983431i | \(0.441976\pi\) | |||||||
\(380\) | 2.56117e24 | − | 3.83512e24i | 0.0407945 | − | 0.0610862i | ||||
\(381\) | − | 1.31123e25i | − | 0.203436i | ||||||
\(382\) | 2.04455e24 | − | 6.74301e24i | 0.0309005 | − | 0.101911i | ||||
\(383\) | − | 1.03560e26i | − | 1.52477i | −0.647126 | − | 0.762383i | \(-0.724029\pi\) | ||
0.647126 | − | 0.762383i | \(-0.275971\pi\) | |||||||
\(384\) | 6.57722e24 | − | 1.23309e25i | 0.0943474 | − | 0.176881i | ||||
\(385\) | −5.36326e25 | −0.749586 | ||||||||
\(386\) | 1.10925e26 | + | 3.36338e25i | 1.51063 | + | 0.458039i | ||||
\(387\) | 9.13698e25 | 1.21253 | ||||||||
\(388\) | 2.52125e25 | + | 1.68374e25i | 0.326061 | + | 0.217750i | ||||
\(389\) | 7.82150e25i | 0.985812i | 0.870082 | + | 0.492906i | \(0.164065\pi\) | ||||
−0.870082 | + | 0.492906i | \(0.835935\pi\) | |||||||
\(390\) | 1.08423e25 | + | 3.28750e24i | 0.133191 | + | 0.0403850i | ||||
\(391\) | − | 5.97358e25i | − | 0.715265i | ||||||
\(392\) | −5.26306e25 | − | 6.40818e25i | −0.614295 | − | 0.747953i | ||||
\(393\) | 2.45889e24 | 0.0279778 | ||||||||
\(394\) | 4.73631e24 | − | 1.56205e25i | 0.0525386 | − | 0.173274i | ||||
\(395\) | −1.19623e25 | −0.129373 | ||||||||
\(396\) | −8.12455e25 | − | 5.42573e25i | −0.856737 | − | 0.572145i | ||||
\(397\) | − | 6.91197e25i | − | 0.710718i | −0.934730 | − | 0.355359i | \(-0.884359\pi\) | ||
0.934730 | − | 0.355359i | \(-0.115641\pi\) | |||||||
\(398\) | 1.74870e25 | − | 5.76727e25i | 0.175341 | − | 0.578282i | ||||
\(399\) | 4.24350e24i | 0.0414950i | ||||||||
\(400\) | 3.02186e25 | + | 7.28518e25i | 0.288187 | + | 0.694769i | ||||
\(401\) | 9.67081e24 | 0.0899537 | 0.0449768 | − | 0.998988i | \(-0.485679\pi\) | ||||
0.0449768 | + | 0.998988i | \(0.485679\pi\) | |||||||
\(402\) | 8.21837e24 | + | 2.49190e24i | 0.0745633 | + | 0.0226084i | ||||
\(403\) | 1.01175e26 | 0.895412 | ||||||||
\(404\) | −5.73128e25 | + | 8.58208e25i | −0.494809 | + | 0.740933i | ||||
\(405\) | − | 5.20750e25i | − | 0.438611i | ||||||
\(406\) | −1.84618e26 | − | 5.59782e25i | −1.51710 | − | 0.460001i | ||||
\(407\) | 1.50853e26i | 1.20951i | ||||||||
\(408\) | −8.12850e24 | − | 9.89708e24i | −0.0635929 | − | 0.0774293i | ||||
\(409\) | 3.70175e25 | 0.282601 | 0.141301 | − | 0.989967i | \(-0.454872\pi\) | ||||
0.141301 | + | 0.989967i | \(0.454872\pi\) | |||||||
\(410\) | −1.44900e25 | + | 4.77886e25i | −0.107952 | + | 0.356029i | ||||
\(411\) | −8.70235e24 | −0.0632730 | ||||||||
\(412\) | −1.47513e26 | + | 2.20888e26i | −1.04679 | + | 1.56747i | ||||
\(413\) | 2.01300e26i | 1.39426i | ||||||||
\(414\) | −5.89522e25 | + | 1.94426e26i | −0.398563 | + | 1.31447i | ||||
\(415\) | − | 5.96560e25i | − | 0.393707i | ||||||
\(416\) | 2.15404e26 | − | 2.13505e25i | 1.38778 | − | 0.137555i | ||||
\(417\) | −4.53302e25 | −0.285120 | ||||||||
\(418\) | 2.46804e25 | + | 7.48338e24i | 0.151562 | + | 0.0459552i | ||||
\(419\) | −1.11094e26 | −0.666118 | −0.333059 | − | 0.942906i | \(-0.608081\pi\) | ||||
−0.333059 | + | 0.942906i | \(0.608081\pi\) | |||||||
\(420\) | 1.98857e25 | + | 1.32800e25i | 0.116425 | + | 0.0777510i | ||||
\(421\) | − | 2.76341e26i | − | 1.57988i | −0.613183 | − | 0.789941i | \(-0.710111\pi\) | ||
0.613183 | − | 0.789941i | \(-0.289889\pi\) | |||||||
\(422\) | −1.28970e26 | − | 3.91051e25i | −0.720052 | − | 0.218328i | ||||
\(423\) | − | 1.84998e26i | − | 1.00870i | ||||||
\(424\) | −1.35944e25 | + | 1.11651e25i | −0.0723938 | + | 0.0594572i | ||||
\(425\) | 7.22781e25 | 0.375939 | ||||||||
\(426\) | −7.76053e24 | + | 2.55945e25i | −0.0394271 | + | 0.130032i | ||||
\(427\) | 1.09439e26 | 0.543118 | ||||||||
\(428\) | −3.04282e26 | − | 2.03205e26i | −1.47516 | − | 0.985138i | ||||
\(429\) | 6.33593e25i | 0.300080i | ||||||||
\(430\) | −3.94382e25 | + | 1.30068e26i | −0.182487 | + | 0.601849i | ||||
\(431\) | 2.45142e26i | 1.10827i | 0.832427 | + | 0.554134i | \(0.186950\pi\) | ||||
−0.832427 | + | 0.554134i | \(0.813050\pi\) | |||||||
\(432\) | 3.40771e25 | + | 8.21539e25i | 0.150531 | + | 0.362903i | ||||
\(433\) | 3.48165e26 | 1.50282 | 0.751409 | − | 0.659837i | \(-0.229375\pi\) | ||||
0.751409 | + | 0.659837i | \(0.229375\pi\) | |||||||
\(434\) | 2.04351e26 | + | 6.19615e25i | 0.861944 | + | 0.261351i | ||||
\(435\) | 2.73612e25 | 0.112783 | ||||||||
\(436\) | 2.54189e26 | − | 3.80625e26i | 1.02398 | − | 1.53332i | ||||
\(437\) | − | 5.36321e25i | − | 0.211159i | ||||||
\(438\) | −9.64928e25 | − | 2.92577e25i | −0.371325 | − | 0.112590i | ||||
\(439\) | − | 1.66012e26i | − | 0.624445i | −0.950009 | − | 0.312223i | \(-0.898927\pi\) | ||
0.950009 | − | 0.312223i | \(-0.101073\pi\) | |||||||
\(440\) | 1.12306e26 | − | 9.22368e25i | 0.412928 | − | 0.339139i | ||||
\(441\) | 2.58460e26 | 0.928983 | ||||||||
\(442\) | 5.75593e25 | − | 1.89833e26i | 0.202252 | − | 0.667034i | ||||
\(443\) | −5.32389e26 | −1.82891 | −0.914454 | − | 0.404689i | \(-0.867380\pi\) | ||||
−0.914454 | + | 0.404689i | \(0.867380\pi\) | |||||||
\(444\) | 3.73528e25 | − | 5.59326e25i | 0.125457 | − | 0.187860i | ||||
\(445\) | − | 1.86673e26i | − | 0.613031i | ||||||
\(446\) | 7.05823e25 | − | 2.32783e26i | 0.226646 | − | 0.747485i | ||||
\(447\) | − | 4.71035e25i | − | 0.147903i | ||||||
\(448\) | 4.48144e26 | + | 8.87943e25i | 1.37606 | + | 0.272650i | ||||
\(449\) | −2.32273e26 | −0.697487 | −0.348743 | − | 0.937218i | \(-0.613391\pi\) | ||||
−0.348743 | + | 0.937218i | \(0.613391\pi\) | |||||||
\(450\) | −2.35249e26 | − | 7.13300e25i | −0.690879 | − | 0.209482i | ||||
\(451\) | −2.79263e26 | −0.802137 | ||||||||
\(452\) | 4.70697e26 | + | 3.14340e26i | 1.32238 | + | 0.883112i | ||||
\(453\) | − | 4.22544e25i | − | 0.116115i | ||||||
\(454\) | −2.98891e26 | − | 9.06272e25i | −0.803442 | − | 0.243613i | ||||
\(455\) | 3.70370e26i | 0.973918i | ||||||||
\(456\) | −7.29794e24 | − | 8.88581e24i | −0.0187738 | − | 0.0228586i | ||||
\(457\) | 5.64579e25 | 0.142090 | 0.0710449 | − | 0.997473i | \(-0.477367\pi\) | ||||
0.0710449 | + | 0.997473i | \(0.477367\pi\) | |||||||
\(458\) | −6.05665e25 | + | 1.99750e26i | −0.149134 | + | 0.491850i | ||||
\(459\) | 8.15069e25 | 0.196366 | ||||||||
\(460\) | −2.51328e26 | − | 1.67841e26i | −0.592464 | − | 0.395659i | ||||
\(461\) | 4.09880e26i | 0.945469i | 0.881205 | + | 0.472735i | \(0.156733\pi\) | ||||
−0.881205 | + | 0.472735i | \(0.843267\pi\) | |||||||
\(462\) | −3.88024e25 | + | 1.27972e26i | −0.0875869 | + | 0.288864i | ||||
\(463\) | 4.96909e26i | 1.09766i | 0.835935 | + | 0.548829i | \(0.184926\pi\) | ||||
−0.835935 | + | 0.548829i | \(0.815074\pi\) | |||||||
\(464\) | 4.82857e26 | − | 2.00287e26i | 1.04385 | − | 0.432985i | ||||
\(465\) | −3.02857e25 | −0.0640779 | ||||||||
\(466\) | 1.52425e26 | + | 4.62169e25i | 0.315643 | + | 0.0957064i | ||||
\(467\) | −6.59837e26 | −1.33742 | −0.668710 | − | 0.743523i | \(-0.733153\pi\) | ||||
−0.668710 | + | 0.743523i | \(0.733153\pi\) | |||||||
\(468\) | −3.74685e26 | + | 5.61057e26i | −0.743374 | + | 1.11314i | ||||
\(469\) | 2.80738e26i | 0.545221i | ||||||||
\(470\) | 2.63352e26 | + | 7.98512e25i | 0.500677 | + | 0.151811i | ||||
\(471\) | − | 1.04105e25i | − | 0.0193760i | ||||||
\(472\) | −3.46195e26 | − | 4.21519e26i | −0.630812 | − | 0.768063i | ||||
\(473\) | −7.60084e26 | −1.35597 | ||||||||
\(474\) | −8.65456e24 | + | 2.85430e25i | −0.0151169 | + | 0.0498559i | ||||
\(475\) | 6.48928e25 | 0.110984 | ||||||||
\(476\) | 2.32514e26 | − | 3.48169e26i | 0.389385 | − | 0.583069i | ||||
\(477\) | − | 5.48300e25i | − | 0.0899155i | ||||||
\(478\) | −4.74519e25 | + | 1.56498e26i | −0.0762034 | + | 0.251321i | ||||
\(479\) | − | 3.67403e26i | − | 0.577813i | −0.957357 | − | 0.288906i | \(-0.906708\pi\) | ||
0.957357 | − | 0.288906i | \(-0.0932916\pi\) | |||||||
\(480\) | −6.44791e25 | + | 6.39107e24i | −0.0993131 | + | 0.00984376i | ||||
\(481\) | 1.04174e27 | 1.57148 | ||||||||
\(482\) | −3.64098e25 | − | 1.10399e25i | −0.0537958 | − | 0.0163115i | ||||
\(483\) | 2.78090e26 | 0.402452 | ||||||||
\(484\) | 8.92216e25 | + | 5.95839e25i | 0.126478 | + | 0.0844647i | ||||
\(485\) | − | 1.40565e26i | − | 0.195191i | ||||||
\(486\) | −4.00649e26 | − | 1.21481e26i | −0.545007 | − | 0.165252i | ||||
\(487\) | − | 8.25813e26i | − | 1.10051i | −0.834998 | − | 0.550253i | \(-0.814531\pi\) | ||
0.834998 | − | 0.550253i | \(-0.185469\pi\) | |||||||
\(488\) | −2.29163e26 | + | 1.88212e26i | −0.299190 | + | 0.245725i | ||||
\(489\) | −6.58604e25 | −0.0842434 | ||||||||
\(490\) | −1.11560e26 | + | 3.67928e26i | −0.139813 | + | 0.461107i | ||||
\(491\) | 3.79623e26 | 0.466163 | 0.233082 | − | 0.972457i | \(-0.425119\pi\) | ||||
0.233082 | + | 0.972457i | \(0.425119\pi\) | |||||||
\(492\) | 1.03544e26 | + | 6.91488e25i | 0.124588 | + | 0.0832020i | ||||
\(493\) | − | 4.79054e26i | − | 0.564827i | ||||||
\(494\) | 5.16780e25 | − | 1.70436e26i | 0.0597085 | − | 0.196921i | ||||
\(495\) | 4.52960e26i | 0.512871i | ||||||||
\(496\) | −5.34468e26 | + | 2.21695e26i | −0.593068 | + | 0.246002i | ||||
\(497\) | −8.74302e26 | −0.950819 | ||||||||
\(498\) | −1.42344e26 | − | 4.31603e25i | −0.151721 | − | 0.0460036i | ||||
\(499\) | 1.58664e27 | 1.65757 | 0.828784 | − | 0.559568i | \(-0.189033\pi\) | ||||
0.828784 | + | 0.559568i | \(0.189033\pi\) | |||||||
\(500\) | 4.73077e26 | − | 7.08391e26i | 0.484431 | − | 0.725392i | ||||
\(501\) | − | 1.79503e26i | − | 0.180175i | ||||||
\(502\) | 1.20378e27 | + | 3.64998e26i | 1.18443 | + | 0.359131i | ||||
\(503\) | 1.42295e27i | 1.37249i | 0.727372 | + | 0.686244i | \(0.240742\pi\) | ||||
−0.727372 | + | 0.686244i | \(0.759258\pi\) | |||||||
\(504\) | −1.10038e27 | + | 9.03746e26i | −1.04049 | + | 0.854557i | ||||
\(505\) | 4.78468e26 | 0.443547 | ||||||||
\(506\) | 4.90410e26 | − | 1.61739e27i | 0.445712 | − | 1.46997i | ||||
\(507\) | 2.12568e26 | 0.189417 | ||||||||
\(508\) | −6.45047e26 | + | 9.65901e26i | −0.563579 | + | 0.843909i | ||||
\(509\) | − | 9.54843e26i | − | 0.818001i | −0.912534 | − | 0.409001i | \(-0.865877\pi\) | ||
0.912534 | − | 0.409001i | \(-0.134123\pi\) | |||||||
\(510\) | −1.72298e25 | + | 5.68244e25i | −0.0144737 | + | 0.0477346i | ||||
\(511\) | − | 3.29618e27i | − | 2.71520i | ||||||
\(512\) | −1.09111e27 | + | 5.84781e26i | −0.881394 | + | 0.472382i | ||||
\(513\) | 7.31786e25 | 0.0579710 | ||||||||
\(514\) | −1.10755e27 | − | 3.35823e26i | −0.860466 | − | 0.260903i | ||||
\(515\) | 1.23150e27 | 0.938342 | ||||||||
\(516\) | 2.81821e26 | + | 1.88205e26i | 0.210609 | + | 0.140649i | ||||
\(517\) | 1.53896e27i | 1.12803i | ||||||||
\(518\) | 2.10409e27 | + | 6.37983e26i | 1.51275 | + | 0.458682i | ||||
\(519\) | − | 5.50570e26i | − | 0.388275i | ||||||
\(520\) | −6.36960e26 | − | 7.75549e26i | −0.440635 | − | 0.536507i | ||||
\(521\) | −3.59622e26 | −0.244044 | −0.122022 | − | 0.992527i | \(-0.538938\pi\) | ||||
−0.122022 | + | 0.992527i | \(0.538938\pi\) | |||||||
\(522\) | −4.72770e26 | + | 1.55921e27i | −0.314735 | + | 1.03801i | ||||
\(523\) | −4.12832e26 | −0.269623 | −0.134811 | − | 0.990871i | \(-0.543043\pi\) | ||||
−0.134811 | + | 0.990871i | \(0.543043\pi\) | |||||||
\(524\) | −1.81132e26 | − | 1.20963e26i | −0.116060 | − | 0.0775071i | ||||
\(525\) | 3.36479e26i | 0.211526i | ||||||||
\(526\) | 5.16477e26 | − | 1.70336e27i | 0.318562 | − | 1.05063i | ||||
\(527\) | 5.30258e26i | 0.320908i | ||||||||
\(528\) | −1.38833e26 | − | 3.34702e26i | −0.0824430 | − | 0.198756i | ||||
\(529\) | −1.79852e27 | −1.04800 | ||||||||
\(530\) | 7.80526e25 | + | 2.36664e25i | 0.0446302 | + | 0.0135324i | ||||
\(531\) | 1.70011e27 | 0.953961 | ||||||||
\(532\) | 2.08756e26 | − | 3.12593e26i | 0.114954 | − | 0.172133i | ||||
\(533\) | 1.92851e27i | 1.04220i | ||||||||
\(534\) | −4.45418e26 | − | 1.35056e26i | −0.236241 | − | 0.0716309i | ||||
\(535\) | 1.69643e27i | 0.883077i | ||||||||
\(536\) | −4.82811e26 | − | 5.87860e26i | −0.246677 | − | 0.300349i | ||||
\(537\) | −2.55443e26 | −0.128101 | ||||||||
\(538\) | −5.69074e26 | + | 1.87682e27i | −0.280121 | + | 0.923849i | ||||
\(539\) | −2.15007e27 | −1.03888 | ||||||||
\(540\) | 2.29012e26 | − | 3.42925e26i | 0.108623 | − | 0.162653i | ||||
\(541\) | − | 1.95235e27i | − | 0.909045i | −0.890735 | − | 0.454523i | \(-0.849810\pi\) | ||
0.890735 | − | 0.454523i | \(-0.150190\pi\) | |||||||
\(542\) | 6.66899e25 | − | 2.19946e26i | 0.0304837 | − | 0.100536i | ||||
\(543\) | 7.60623e26i | 0.341327i | ||||||||
\(544\) | 1.11898e26 | + | 1.12893e27i | 0.0492985 | + | 0.497370i | ||||
\(545\) | −2.12206e27 | −0.917894 | ||||||||
\(546\) | 8.83734e26 | + | 2.67958e26i | 0.375314 | + | 0.113799i | ||||
\(547\) | −8.12726e26 | −0.338899 | −0.169450 | − | 0.985539i | \(-0.554199\pi\) | ||||
−0.169450 | + | 0.985539i | \(0.554199\pi\) | |||||||
\(548\) | 6.41050e26 | + | 4.28106e26i | 0.262474 | + | 0.175285i | ||||
\(549\) | − | 9.24281e26i | − | 0.371604i | ||||||
\(550\) | 1.95698e27 | + | 5.93377e26i | 0.772608 | + | 0.234263i | ||||
\(551\) | − | 4.30105e26i | − | 0.166747i | ||||||
\(552\) | −5.82316e26 | + | 4.78257e26i | −0.221701 | + | 0.182084i | ||||
\(553\) | −9.75025e26 | −0.364556 | ||||||||
\(554\) | 9.58944e26 | − | 3.16263e27i | 0.352124 | − | 1.16132i | ||||
\(555\) | −3.11835e26 | −0.112459 | ||||||||
\(556\) | 3.33921e27 | + | 2.22999e27i | 1.18276 | + | 0.789868i | ||||
\(557\) | 4.65269e27i | 1.61865i | 0.587364 | + | 0.809323i | \(0.300166\pi\) | ||||
−0.587364 | + | 0.809323i | \(0.699834\pi\) | |||||||
\(558\) | 5.23303e26 | − | 1.72587e27i | 0.178818 | − | 0.589747i | ||||
\(559\) | 5.24891e27i | 1.76178i | ||||||||
\(560\) | −8.11556e26 | − | 1.95652e27i | −0.267571 | − | 0.645066i | ||||
\(561\) | −3.32066e26 | −0.107546 | ||||||||
\(562\) | −4.05529e27 | − | 1.22961e27i | −1.29020 | − | 0.391204i | ||||
\(563\) | −1.62681e27 | −0.508455 | −0.254228 | − | 0.967144i | \(-0.581821\pi\) | ||||
−0.254228 | + | 0.967144i | \(0.581821\pi\) | |||||||
\(564\) | 3.81063e26 | − | 5.70608e26i | 0.117005 | − | 0.175205i | ||||
\(565\) | − | 2.62423e27i | − | 0.791621i | ||||||
\(566\) | 1.81060e27 | + | 5.48995e26i | 0.536610 | + | 0.162706i | ||||
\(567\) | − | 4.24454e27i | − | 1.23595i | ||||||
\(568\) | 1.83077e27 | − | 1.50362e27i | 0.523782 | − | 0.430184i | ||||
\(569\) | 3.69001e27 | 1.03730 | 0.518651 | − | 0.854986i | \(-0.326435\pi\) | ||||
0.518651 | + | 0.854986i | \(0.326435\pi\) | |||||||
\(570\) | −1.54693e25 | + | 5.10182e25i | −0.00427289 | + | 0.0140921i | ||||
\(571\) | 3.77393e26 | 0.102431 | 0.0512156 | − | 0.998688i | \(-0.483690\pi\) | ||||
0.0512156 | + | 0.998688i | \(0.483690\pi\) | |||||||
\(572\) | 3.11692e27 | − | 4.66730e27i | 0.831313 | − | 1.24482i | ||||
\(573\) | 8.14546e25i | 0.0213486i | ||||||||
\(574\) | −1.18105e27 | + | 3.89516e27i | −0.304194 | + | 1.00324i | ||||
\(575\) | − | 4.25263e27i | − | 1.07641i | ||||||
\(576\) | 7.49922e26 | − | 3.78485e27i | 0.186548 | − | 0.941508i | ||||
\(577\) | 5.96875e27 | 1.45923 | 0.729617 | − | 0.683856i | \(-0.239698\pi\) | ||||
0.729617 | + | 0.683856i | \(0.239698\pi\) | |||||||
\(578\) | −2.98781e27 | − | 9.05936e26i | −0.717917 | − | 0.217680i | ||||
\(579\) | −1.33996e27 | −0.316451 | ||||||||
\(580\) | −2.01553e27 | − | 1.34601e27i | −0.467854 | − | 0.312442i | ||||
\(581\) | − | 4.86245e27i | − | 1.10941i | ||||||
\(582\) | −3.35399e26 | − | 1.01697e26i | −0.0752198 | − | 0.0228075i | ||||
\(583\) | 4.56118e26i | 0.100552i | ||||||||
\(584\) | 5.66874e27 | + | 6.90213e27i | 1.22845 | + | 1.49574i | ||||
\(585\) | 3.12801e27 | 0.666360 | ||||||||
\(586\) | −1.04182e25 | + | 3.43596e25i | −0.00218181 | + | 0.00719569i | ||||
\(587\) | −5.25622e27 | −1.08216 | −0.541081 | − | 0.840970i | \(-0.681985\pi\) | ||||
−0.541081 | + | 0.840970i | \(0.681985\pi\) | |||||||
\(588\) | 7.97194e26 | + | 5.32381e26i | 0.161358 | + | 0.107758i | ||||
\(589\) | 4.76077e26i | 0.0947380i | ||||||||
\(590\) | −7.33820e26 | + | 2.42016e27i | −0.143572 | + | 0.473505i | ||||
\(591\) | 1.88694e26i | 0.0362980i | ||||||||
\(592\) | −5.50312e27 | + | 2.28267e27i | −1.04086 | + | 0.431744i | ||||
\(593\) | 2.01007e27 | 0.373821 | 0.186911 | − | 0.982377i | \(-0.440153\pi\) | ||||
0.186911 | + | 0.982377i | \(0.440153\pi\) | |||||||
\(594\) | 2.20685e27 | + | 6.69142e26i | 0.403561 | + | 0.122364i | ||||
\(595\) | −1.94111e27 | −0.349044 | ||||||||
\(596\) | −2.31722e27 | + | 3.46983e27i | −0.409737 | + | 0.613545i | ||||
\(597\) | 6.96678e26i | 0.121140i | ||||||||
\(598\) | −1.11692e28 | − | 3.38662e27i | −1.90990 | − | 0.579102i | ||||
\(599\) | 5.36055e27i | 0.901448i | 0.892663 | + | 0.450724i | \(0.148834\pi\) | ||||
−0.892663 | + | 0.450724i | \(0.851166\pi\) | |||||||
\(600\) | −5.78673e26 | − | 7.04580e26i | −0.0957020 | − | 0.116525i | ||||
\(601\) | 6.55184e25 | 0.0106566 | 0.00532830 | − | 0.999986i | \(-0.498304\pi\) | ||||
0.00532830 | + | 0.999986i | \(0.498304\pi\) | |||||||
\(602\) | −3.21453e27 | + | 1.06016e28i | −0.514225 | + | 1.69593i | ||||
\(603\) | 2.37101e27 | 0.373044 | ||||||||
\(604\) | −2.07867e27 | + | 3.11263e27i | −0.321675 | + | 0.481679i | ||||
\(605\) | − | 4.97428e26i | − | 0.0757141i | ||||||
\(606\) | 3.46165e26 | − | 1.14166e27i | 0.0518271 | − | 0.170928i | ||||
\(607\) | 8.75457e27i | 1.28928i | 0.764485 | + | 0.644641i | \(0.222993\pi\) | ||||
−0.764485 | + | 0.644641i | \(0.777007\pi\) | |||||||
\(608\) | 1.00465e26 | + | 1.01358e27i | 0.0145538 | + | 0.146833i | ||||
\(609\) | 2.23016e27 | 0.317806 | ||||||||
\(610\) | 1.31575e27 | + | 3.98949e26i | 0.184448 | + | 0.0559267i | ||||
\(611\) | 1.06276e28 | 1.46562 | ||||||||
\(612\) | −2.94050e27 | − | 1.96372e27i | −0.398939 | − | 0.266419i | ||||
\(613\) | − | 3.98007e27i | − | 0.531234i | −0.964079 | − | 0.265617i | \(-0.914424\pi\) | ||
0.964079 | − | 0.265617i | \(-0.0855756\pi\) | |||||||
\(614\) | −8.21500e27 | − | 2.49088e27i | −1.07876 | − | 0.327091i | ||||
\(615\) | − | 5.77279e26i | − | 0.0745822i | ||||||
\(616\) | 9.15381e27 | − | 7.51805e27i | 1.16358 | − | 0.955648i | ||||
\(617\) | −1.86653e27 | −0.233445 | −0.116722 | − | 0.993165i | \(-0.537239\pi\) | ||||
−0.116722 | + | 0.993165i | \(0.537239\pi\) | |||||||
\(618\) | 8.90971e26 | − | 2.93845e27i | 0.109642 | − | 0.361605i | ||||
\(619\) | −1.35625e28 | −1.64223 | −0.821114 | − | 0.570764i | \(-0.806647\pi\) | ||||
−0.821114 | + | 0.570764i | \(0.806647\pi\) | |||||||
\(620\) | 2.23097e27 | + | 1.48988e27i | 0.265813 | + | 0.177515i | ||||
\(621\) | − | 4.79563e27i | − | 0.562250i | ||||||
\(622\) | −2.16642e27 | + | 7.14491e27i | −0.249941 | + | 0.824314i | ||||
\(623\) | − | 1.52154e28i | − | 1.72744i | ||||||
\(624\) | −2.31135e27 | + | 9.58740e26i | −0.258238 | + | 0.107116i | ||||
\(625\) | 2.89150e27 | 0.317924 | ||||||||
\(626\) | 7.36854e27 | + | 2.23422e27i | 0.797330 | + | 0.241759i | ||||
\(627\) | −2.98136e26 | −0.0317497 | ||||||||
\(628\) | −5.12138e26 | + | 7.66881e26i | −0.0536773 | + | 0.0803770i | ||||
\(629\) | 5.45978e27i | 0.563208i | ||||||||
\(630\) | 6.31787e27 | + | 1.91565e27i | 0.641454 | + | 0.194496i | ||||
\(631\) | − | 1.05880e28i | − | 1.05808i | −0.848597 | − | 0.529040i | \(-0.822552\pi\) | ||
0.848597 | − | 0.529040i | \(-0.177448\pi\) | |||||||
\(632\) | 2.04168e27 | − | 1.67684e27i | 0.200825 | − | 0.164938i | ||||
\(633\) | 1.55794e27 | 0.150839 | ||||||||
\(634\) | 2.20925e27 | − | 7.28618e27i | 0.210549 | − | 0.694396i | ||||
\(635\) | 5.38509e27 | 0.505191 | ||||||||
\(636\) | 1.12940e26 | − | 1.69118e26i | 0.0104298 | − | 0.0156177i | ||||
\(637\) | 1.48477e28i | 1.34979i | ||||||||
\(638\) | 3.93286e27 | − | 1.29707e28i | 0.351967 | − | 1.16080i | ||||
\(639\) | 7.38402e27i | 0.650556i | ||||||||
\(640\) | 5.06419e27 | + | 2.70121e27i | 0.439248 | + | 0.234292i | ||||
\(641\) | −4.49180e27 | −0.383566 | −0.191783 | − | 0.981437i | \(-0.561427\pi\) | ||||
−0.191783 | + | 0.981437i | \(0.561427\pi\) | |||||||
\(642\) | 4.04783e27 | + | 1.22735e27i | 0.340308 | + | 0.103185i | ||||
\(643\) | 9.22634e27 | 0.763694 | 0.381847 | − | 0.924225i | \(-0.375288\pi\) | ||||
0.381847 | + | 0.924225i | \(0.375288\pi\) | |||||||
\(644\) | −2.04852e28 | − | 1.36804e28i | −1.66948 | − | 1.11491i | ||||
\(645\) | − | 1.57121e27i | − | 0.126077i | ||||||
\(646\) | 8.93253e26 | + | 2.70844e26i | 0.0705748 | + | 0.0213990i | ||||
\(647\) | 9.33398e27i | 0.726146i | 0.931761 | + | 0.363073i | \(0.118272\pi\) | ||||
−0.931761 | + | 0.363073i | \(0.881728\pi\) | |||||||
\(648\) | 7.29972e27 | + | 8.88798e27i | 0.559186 | + | 0.680852i | ||||
\(649\) | −1.41428e28 | −1.06681 | ||||||||
\(650\) | 4.09769e27 | − | 1.35143e28i | 0.304372 | − | 1.00383i | ||||
\(651\) | −2.46853e27 | −0.180563 | ||||||||
\(652\) | 4.85154e27 | + | 3.23995e27i | 0.349465 | + | 0.233380i | ||||
\(653\) | − | 1.60220e28i | − | 1.13654i | −0.822842 | − | 0.568270i | \(-0.807613\pi\) | ||
0.822842 | − | 0.568270i | \(-0.192387\pi\) | |||||||
\(654\) | −1.53528e27 | + | 5.06341e27i | −0.107253 | + | 0.353725i | ||||
\(655\) | 1.00985e27i | 0.0694772i | ||||||||
\(656\) | −4.22575e27 | − | 1.01876e28i | −0.286329 | − | 0.690290i | ||||
\(657\) | −2.78382e28 | −1.85775 | ||||||||
\(658\) | 2.14653e28 | + | 6.50852e27i | 1.41084 | + | 0.427783i | ||||
\(659\) | 2.39029e28 | 1.54738 | 0.773688 | − | 0.633566i | \(-0.218410\pi\) | ||||
0.773688 | + | 0.633566i | \(0.218410\pi\) | |||||||
\(660\) | −9.33016e26 | + | 1.39711e27i | −0.0594908 | + | 0.0890822i | ||||
\(661\) | 1.77129e28i | 1.11243i | 0.831037 | + | 0.556217i | \(0.187748\pi\) | ||||
−0.831037 | + | 0.556217i | \(0.812252\pi\) | |||||||
\(662\) | −7.52538e25 | − | 2.28178e25i | −0.00465531 | − | 0.00141154i | ||||
\(663\) | 2.29315e27i | 0.139732i | ||||||||
\(664\) | 8.36240e27 | + | 1.01819e28i | 0.501938 | + | 0.611149i | ||||
\(665\) | −1.74277e27 | −0.103044 | ||||||||
\(666\) | 5.38816e27 | − | 1.77703e28i | 0.313833 | − | 1.03503i | ||||
\(667\) | −2.81862e28 | −1.61725 | ||||||||
\(668\) | −8.83050e27 | + | 1.32229e28i | −0.499138 | + | 0.747415i | ||||
\(669\) | 2.81198e27i | 0.156586i | ||||||||
\(670\) | −1.02340e27 | + | 3.37522e27i | −0.0561434 | + | 0.185163i | ||||
\(671\) | 7.68887e27i | 0.415564i | ||||||||
\(672\) | −5.25557e27 | + | 5.20924e26i | −0.279851 | + | 0.0277384i | ||||
\(673\) | −2.07760e27 | −0.108996 | −0.0544981 | − | 0.998514i | \(-0.517356\pi\) | ||||
−0.0544981 | + | 0.998514i | \(0.517356\pi\) | |||||||
\(674\) | 1.37595e28 | + | 4.17204e27i | 0.711221 | + | 0.215650i | ||||
\(675\) | 5.80253e27 | 0.295515 | ||||||||
\(676\) | −1.56586e28 | − | 1.04571e28i | −0.785753 | − | 0.524741i | ||||
\(677\) | 6.05106e26i | 0.0299188i | 0.999888 | + | 0.0149594i | \(0.00476191\pi\) | ||||
−0.999888 | + | 0.0149594i | \(0.995238\pi\) | |||||||
\(678\) | −6.26162e27 | − | 1.89859e27i | −0.305063 | − | 0.0924986i | ||||
\(679\) | − | 1.14572e28i | − | 0.550022i | ||||||
\(680\) | 4.06465e27 | − | 3.33831e27i | 0.192280 | − | 0.157920i | ||||
\(681\) | 3.61057e27 | 0.168308 | ||||||||
\(682\) | −4.35323e27 | + | 1.43571e28i | −0.199971 | + | 0.659512i | ||||
\(683\) | −2.09376e27 | −0.0947809 | −0.0473904 | − | 0.998876i | \(-0.515090\pi\) | ||||
−0.0473904 | + | 0.998876i | \(0.515090\pi\) | |||||||
\(684\) | −2.64004e27 | − | 1.76307e27i | −0.117774 | − | 0.0786519i | ||||
\(685\) | − | 3.57398e27i | − | 0.157126i | ||||||
\(686\) | 3.01757e26 | − | 9.95206e26i | 0.0130743 | − | 0.0431193i | ||||
\(687\) | − | 2.41296e27i | − | 0.103034i | ||||||
\(688\) | −1.15014e28 | − | 2.77279e28i | −0.484025 | − | 1.16690i | ||||
\(689\) | 3.14981e27 | 0.130645 | ||||||||
\(690\) | 3.34338e27 | + | 1.01375e27i | 0.136677 | + | 0.0414420i | ||||
\(691\) | 2.96337e28 | 1.19400 | 0.597002 | − | 0.802240i | \(-0.296358\pi\) | ||||
0.597002 | + | 0.802240i | \(0.296358\pi\) | |||||||
\(692\) | −2.70849e28 | + | 4.05572e28i | −1.07564 | + | 1.61067i | ||||
\(693\) | 3.69199e28i | 1.44520i | ||||||||
\(694\) | 4.35566e27 | + | 1.32069e27i | 0.168058 | + | 0.0509571i | ||||
\(695\) | − | 1.86168e28i | − | 0.708037i | ||||||
\(696\) | −4.66991e27 | + | 3.83541e27i | −0.175072 | + | 0.143787i | ||||
\(697\) | −1.01073e28 | −0.373515 | ||||||||
\(698\) | −8.99033e27 | + | 2.96504e28i | −0.327508 | + | 1.08013i | ||||
\(699\) | −1.84127e27 | −0.0661219 | ||||||||
\(700\) | 1.65528e28 | − | 2.47864e28i | 0.585992 | − | 0.877471i | ||||
\(701\) | − | 2.48058e28i | − | 0.865713i | −0.901463 | − | 0.432856i | \(-0.857506\pi\) | ||
0.901463 | − | 0.432856i | \(-0.142494\pi\) | |||||||
\(702\) | 4.62090e27 | − | 1.52399e28i | 0.158985 | − | 0.524337i | ||||
\(703\) | 4.90191e27i | 0.166269i | ||||||||
\(704\) | −6.23843e27 | + | 3.14853e28i | −0.208616 | + | 1.05289i | ||||
\(705\) | −3.18126e27 | −0.104884 | ||||||||
\(706\) | −3.40528e28 | − | 1.03252e28i | −1.10689 | − | 0.335622i | ||||
\(707\) | 3.89990e28 | 1.24986 | ||||||||
\(708\) | 5.24380e27 | + | 3.50191e27i | 0.165697 | + | 0.110655i | ||||
\(709\) | − | 3.39191e28i | − | 1.05677i | −0.849003 | − | 0.528387i | \(-0.822797\pi\) | ||
0.849003 | − | 0.528387i | \(-0.177203\pi\) | |||||||
\(710\) | −1.05114e28 | − | 3.18718e27i | −0.322908 | − | 0.0979092i | ||||
\(711\) | 8.23468e27i | 0.249431i | ||||||||
\(712\) | 2.61673e28 | + | 3.18607e28i | 0.781554 | + | 0.951603i | ||||
\(713\) | 3.11989e28 | 0.918847 | ||||||||
\(714\) | −1.40437e27 | + | 4.63165e27i | −0.0407848 | + | 0.134510i | ||||
\(715\) | −2.60211e28 | −0.745188 | ||||||||
\(716\) | 1.88170e28 | + | 1.25663e28i | 0.531398 | + | 0.354878i | ||||
\(717\) | − | 1.89047e27i | − | 0.0526476i | ||||||
\(718\) | 4.10488e27 | − | 1.35380e28i | 0.112734 | − | 0.371801i | ||||
\(719\) | − | 4.82927e28i | − | 1.30795i | −0.756515 | − | 0.653977i | \(-0.773099\pi\) | ||
0.756515 | − | 0.653977i | \(-0.226901\pi\) | |||||||
\(720\) | −1.65240e28 | + | 6.85409e27i | −0.441358 | + | 0.183073i | ||||
\(721\) | 1.00377e29 | 2.64412 | ||||||||
\(722\) | −3.60341e28 | − | 1.09259e28i | −0.936141 | − | 0.283848i | ||||
\(723\) | 4.39826e26 | 0.0112693 | ||||||||
\(724\) | 3.74183e28 | − | 5.60305e28i | 0.945580 | − | 1.41592i | ||||
\(725\) | − | 3.41042e28i | − | 0.850017i | ||||||
\(726\) | −1.18690e27 | − | 3.59882e26i | −0.0291776 | − | 0.00884697i | ||||
\(727\) | 3.90810e28i | 0.947593i | 0.880634 | + | 0.473797i | \(0.157117\pi\) | ||||
−0.880634 | + | 0.473797i | \(0.842883\pi\) | |||||||
\(728\) | −5.19174e28 | − | 6.32135e28i | −1.24165 | − | 1.51181i | ||||
\(729\) | −3.25089e28 | −0.766880 | ||||||||
\(730\) | 1.20159e28 | − | 3.96288e28i | 0.279594 | − | 0.922109i | ||||
\(731\) | −2.75095e28 | −0.631407 | ||||||||
\(732\) | 1.90385e27 | − | 2.85085e27i | 0.0431045 | − | 0.0645451i | ||||
\(733\) | − | 2.46670e28i | − | 0.550905i | −0.961315 | − | 0.275452i | \(-0.911172\pi\) | ||
0.961315 | − | 0.275452i | \(-0.0888277\pi\) | |||||||
\(734\) | −2.48166e28 | + | 8.18461e28i | −0.546742 | + | 1.80317i | ||||
\(735\) | − | 4.44452e27i | − | 0.0965942i | ||||||
\(736\) | 6.64232e28 | − | 6.58376e27i | 1.42410 | − | 0.141155i | ||||
\(737\) | −1.97238e28 | −0.417173 | ||||||||
\(738\) | 3.28970e28 | + | 9.97474e27i | 0.686424 | + | 0.208131i | ||||
\(739\) | −3.59103e28 | −0.739221 | −0.369611 | − | 0.929187i | \(-0.620509\pi\) | ||||
−0.369611 | + | 0.929187i | \(0.620509\pi\) | |||||||
\(740\) | 2.29710e28 | + | 1.53405e28i | 0.466513 | + | 0.311546i | ||||
\(741\) | 2.05884e27i | 0.0412516i | ||||||||
\(742\) | 6.36192e27 | + | 1.92900e27i | 0.125762 | + | 0.0381324i | ||||
\(743\) | 4.29533e28i | 0.837739i | 0.908046 | + | 0.418869i | \(0.137574\pi\) | ||||
−0.908046 | + | 0.418869i | \(0.862426\pi\) | |||||||
\(744\) | 5.16905e27 | − | 4.24536e27i | 0.0994676 | − | 0.0816930i | ||||
\(745\) | 1.93450e28 | 0.367288 | ||||||||
\(746\) | −1.51433e28 | + | 4.99431e28i | −0.283682 | + | 0.935594i | ||||
\(747\) | −4.10664e28 | −0.759068 | ||||||||
\(748\) | 2.44613e28 | + | 1.63357e28i | 0.446133 | + | 0.297936i | ||||
\(749\) | 1.38273e29i | 2.48839i | ||||||||
\(750\) | −2.85735e27 | + | 9.42364e27i | −0.0507401 | + | 0.167343i | ||||
\(751\) | − | 1.61560e28i | − | 0.283096i | −0.989931 | − | 0.141548i | \(-0.954792\pi\) | ||
0.989931 | − | 0.141548i | \(-0.0452080\pi\) | |||||||
\(752\) | −5.61413e28 | + | 2.32872e28i | −0.970742 | + | 0.402660i | ||||
\(753\) | −1.45414e28 | −0.248118 | ||||||||
\(754\) | −8.95719e28 | − | 2.71592e28i | −1.50820 | − | 0.457302i | ||||
\(755\) | 1.73535e28 | 0.288349 | ||||||||
\(756\) | 1.86664e28 | − | 2.79512e28i | 0.306085 | − | 0.458335i | ||||
\(757\) | − | 3.24624e28i | − | 0.525317i | −0.964889 | − | 0.262659i | \(-0.915401\pi\) | ||
0.964889 | − | 0.262659i | \(-0.0845993\pi\) | |||||||
\(758\) | 2.17258e28 | + | 6.58750e27i | 0.346963 | + | 0.105203i | ||||
\(759\) | 1.95378e28i | 0.307934i | ||||||||
\(760\) | 3.64933e27 | − | 2.99720e27i | 0.0567645 | − | 0.0466208i | ||||
\(761\) | 2.94459e27 | 0.0452042 | 0.0226021 | − | 0.999745i | \(-0.492805\pi\) | ||||
0.0226021 | + | 0.999745i | \(0.492805\pi\) | |||||||
\(762\) | 3.89604e27 | − | 1.28493e28i | 0.0590301 | − | 0.194683i | ||||
\(763\) | −1.72965e29 | −2.58650 | ||||||||
\(764\) | 4.00710e27 | − | 6.00027e27i | 0.0591420 | − | 0.0885599i | ||||
\(765\) | 1.63939e28i | 0.238818i | ||||||||
\(766\) | 3.07707e28 | − | 1.01483e29i | 0.442435 | − | 1.45916i | ||||
\(767\) | 9.76658e28i | 1.38608i | ||||||||
\(768\) | 1.01092e28 | − | 1.01293e28i | 0.141613 | − | 0.141895i | ||||
\(769\) | 2.27487e28 | 0.314553 | 0.157277 | − | 0.987555i | \(-0.449729\pi\) | ||||
0.157277 | + | 0.987555i | \(0.449729\pi\) | |||||||
\(770\) | −5.25569e28 | − | 1.59358e28i | −0.717336 | − | 0.217504i | ||||
\(771\) | 1.33791e28 | 0.180253 | ||||||||
\(772\) | 9.87070e28 | + | 6.59184e28i | 1.31273 | + | 0.876665i | ||||
\(773\) | − | 4.97514e28i | − | 0.653147i | −0.945172 | − | 0.326573i | \(-0.894106\pi\) | ||
0.945172 | − | 0.326573i | \(-0.105894\pi\) | |||||||
\(774\) | 8.95373e28 | + | 2.71487e28i | 1.16036 | + | 0.351835i | ||||
\(775\) | 3.77494e28i | 0.482940i | ||||||||
\(776\) | 1.97040e28 | + | 2.39911e28i | 0.248849 | + | 0.302993i | ||||
\(777\) | −2.54171e28 | −0.316895 | ||||||||
\(778\) | −2.32400e28 | + | 7.66463e28i | −0.286049 | + | 0.943399i | ||||
\(779\) | −9.07456e27 | −0.110268 | ||||||||
\(780\) | 9.64802e27 | + | 6.44313e27i | 0.115742 | + | 0.0772949i | ||||
\(781\) | − | 6.14259e28i | − | 0.727514i | ||||||
\(782\) | 1.77493e28 | − | 5.85377e28i | 0.207546 | − | 0.684492i | ||||
\(783\) | − | 3.84588e28i | − | 0.443995i | ||||||
\(784\) | −3.25344e28 | − | 7.84347e28i | −0.370836 | − | 0.894021i | ||||
\(785\) | 4.27552e27 | 0.0481163 | ||||||||
\(786\) | 2.40958e27 | + | 7.30611e26i | 0.0267741 | + | 0.00811821i | ||||
\(787\) | 1.07675e29 | 1.18132 | 0.590662 | − | 0.806919i | \(-0.298867\pi\) | ||||
0.590662 | + | 0.806919i | \(0.298867\pi\) | |||||||
\(788\) | 9.28264e27 | − | 1.38999e28i | 0.100556 | − | 0.150574i | ||||
\(789\) | 2.05763e28i | 0.220089i | ||||||||
\(790\) | −1.17224e28 | − | 3.55436e27i | −0.123807 | − | 0.0375396i | ||||
\(791\) | − | 2.13896e29i | − | 2.23068i | ||||||
\(792\) | −6.34946e28 | − | 7.73096e28i | −0.653860 | − | 0.796125i | ||||
\(793\) | 5.30971e28 | 0.539931 | ||||||||
\(794\) | 2.05375e28 | − | 6.77335e28i | 0.206226 | − | 0.680140i | ||||
\(795\) | −9.42864e26 | −0.00934928 | ||||||||
\(796\) | 3.42725e28 | − | 5.13201e28i | 0.335595 | − | 0.502524i | ||||
\(797\) | − | 5.01741e27i | − | 0.0485173i | −0.999706 | − | 0.0242586i | \(-0.992277\pi\) | ||
0.999706 | − | 0.0242586i | \(-0.00772252\pi\) | |||||||
\(798\) | −1.26087e27 | + | 4.15839e27i | −0.0120404 | + | 0.0397097i | ||||
\(799\) | 5.56991e28i | 0.525267i | ||||||||
\(800\) | 7.96611e27 | + | 8.03696e28i | 0.0741902 | + | 0.748500i | ||||
\(801\) | −1.28503e29 | −1.18192 | ||||||||
\(802\) | 9.47685e27 | + | 2.87349e27i | 0.0860836 | + | 0.0261015i | ||||
\(803\) | 2.31580e29 | 2.07752 | ||||||||
\(804\) | 7.31313e27 | + | 4.88385e27i | 0.0647952 | + | 0.0432715i | ||||
\(805\) | 1.14209e29i | 0.999408i | ||||||||
\(806\) | 9.91459e28 | + | 3.00621e28i | 0.856888 | + | 0.259818i | ||||
\(807\) | − | 2.26718e28i | − | 0.193531i | ||||||
\(808\) | −8.16632e28 | + | 6.70702e28i | −0.688514 | + | 0.565478i | ||||
\(809\) | 3.71760e28 | 0.309583 | 0.154792 | − | 0.987947i | \(-0.450529\pi\) | ||||
0.154792 | + | 0.987947i | \(0.450529\pi\) | |||||||
\(810\) | 1.54730e28 | − | 5.10306e28i | 0.127270 | − | 0.419740i | ||||
\(811\) | −1.24910e29 | −1.01482 | −0.507408 | − | 0.861706i | \(-0.669396\pi\) | ||||
−0.507408 | + | 0.861706i | \(0.669396\pi\) | |||||||
\(812\) | −1.64282e29 | − | 1.09711e29i | −1.31835 | − | 0.880420i | ||||
\(813\) | 2.65691e27i | 0.0210606i | ||||||||
\(814\) | −4.48228e28 | + | 1.47827e29i | −0.350958 | + | 1.15747i | ||||
\(815\) | − | 2.70483e28i | − | 0.209201i | ||||||
\(816\) | −5.02475e27 | − | 1.21138e28i | −0.0383896 | − | 0.0925505i | ||||
\(817\) | −2.46987e28 | −0.186403 | ||||||||
\(818\) | 3.62751e28 | + | 1.09990e28i | 0.270443 | + | 0.0820012i | ||||
\(819\) | 2.54958e29 | 1.87771 | ||||||||
\(820\) | −2.83988e28 | + | 4.25247e28i | −0.206615 | + | 0.309388i | ||||
\(821\) | − | 8.98034e28i | − | 0.645448i | −0.946493 | − | 0.322724i | \(-0.895401\pi\) | ||
0.946493 | − | 0.322724i | \(-0.104599\pi\) | |||||||
\(822\) | −8.52782e27 | − | 2.58573e27i | −0.0605508 | − | 0.0183597i | ||||
\(823\) | 5.34245e28i | 0.374751i | 0.982288 | + | 0.187375i | \(0.0599980\pi\) | ||||
−0.982288 | + | 0.187375i | \(0.940002\pi\) | |||||||
\(824\) | −2.10187e29 | + | 1.72627e29i | −1.45658 | + | 1.19629i | ||||
\(825\) | −2.36400e28 | −0.161848 | ||||||||
\(826\) | −5.98123e28 | + | 1.97263e29i | −0.404567 | + | 1.33427i | ||||
\(827\) | −8.05212e28 | −0.538090 | −0.269045 | − | 0.963128i | \(-0.586708\pi\) | ||||
−0.269045 | + | 0.963128i | \(0.586708\pi\) | |||||||
\(828\) | −1.15540e29 | + | 1.73010e29i | −0.762830 | + | 1.14227i | ||||
\(829\) | − | 1.27468e29i | − | 0.831485i | −0.909482 | − | 0.415742i | \(-0.863522\pi\) | ||
0.909482 | − | 0.415742i | \(-0.136478\pi\) | |||||||
\(830\) | 1.77256e28 | − | 5.84596e28i | 0.114240 | − | 0.376769i | ||||
\(831\) | 3.82041e28i | 0.243276i | ||||||||
\(832\) | 2.17428e29 | + | 4.30807e28i | 1.36799 | + | 0.271050i | ||||
\(833\) | −7.78169e28 | −0.483754 | ||||||||
\(834\) | −4.44211e28 | − | 1.34690e28i | −0.272853 | − | 0.0827321i | ||||
\(835\) | 7.37203e28 | 0.447427 | ||||||||
\(836\) | 2.19619e28 | + | 1.46666e28i | 0.131706 | + | 0.0879561i | ||||
\(837\) | 4.25695e28i | 0.252257i | ||||||||
\(838\) | −1.08866e29 | − | 3.30094e28i | −0.637460 | − | 0.193285i | ||||
\(839\) | − | 1.20820e29i | − | 0.699067i | −0.936924 | − | 0.349533i | \(-0.886340\pi\) | ||
0.936924 | − | 0.349533i | \(-0.113660\pi\) | |||||||
\(840\) | 1.55409e28 | + | 1.89223e28i | 0.0888555 | + | 0.108189i | ||||
\(841\) | −4.90457e28 | −0.277103 | ||||||||
\(842\) | 8.21092e28 | − | 2.70799e29i | 0.458428 | − | 1.51191i | ||||
\(843\) | 4.89873e28 | 0.270276 | ||||||||
\(844\) | −1.14764e29 | − | 7.66416e28i | −0.625721 | − | 0.417869i | ||||
\(845\) | 8.72998e28i | 0.470377i | ||||||||
\(846\) | 5.49685e28 | − | 1.81288e29i | 0.292692 | − | 0.965306i | ||||
\(847\) | − | 4.05444e28i | − | 0.213352i | ||||||
\(848\) | −1.66392e28 | + | 6.90188e27i | −0.0865316 | + | 0.0358929i | ||||
\(849\) | −2.18718e28 | −0.112411 | ||||||||
\(850\) | 7.08284e28 | + | 2.14760e28i | 0.359765 | + | 0.109085i | ||||
\(851\) | 3.21237e29 | 1.61261 | ||||||||
\(852\) | −1.52098e28 | + | 2.27753e28i | −0.0754617 | + | 0.112997i | ||||
\(853\) | 2.92906e29i | 1.43628i | 0.695901 | + | 0.718138i | \(0.255005\pi\) | ||||
−0.695901 | + | 0.718138i | \(0.744995\pi\) | |||||||
\(854\) | 1.07244e29 | + | 3.25176e28i | 0.519751 | + | 0.157594i | ||||
\(855\) | 1.47188e28i | 0.0705035i | ||||||||
\(856\) | −2.37801e29 | − | 2.89541e29i | −1.12584 | − | 1.37079i | ||||
\(857\) | −1.78476e29 | −0.835162 | −0.417581 | − | 0.908640i | \(-0.637122\pi\) | ||||
−0.417581 | + | 0.908640i | \(0.637122\pi\) | |||||||
\(858\) | −1.88259e28 | + | 6.20886e28i | −0.0870731 | + | 0.287170i | ||||
\(859\) | −3.54007e29 | −1.61838 | −0.809189 | − | 0.587549i | \(-0.800093\pi\) | ||||
−0.809189 | + | 0.587549i | \(0.800093\pi\) | |||||||
\(860\) | −7.72944e28 | + | 1.15741e29i | −0.349272 | + | 0.523003i | ||||
\(861\) | − | 4.70530e28i | − | 0.210163i | ||||||
\(862\) | −7.28390e28 | + | 2.40225e29i | −0.321581 | + | 1.06059i | ||||
\(863\) | − | 5.98519e28i | − | 0.261198i | −0.991435 | − | 0.130599i | \(-0.958310\pi\) | ||
0.991435 | − | 0.130599i | \(-0.0416900\pi\) | |||||||
\(864\) | 8.98326e27 | + | 9.06315e28i | 0.0387522 | + | 0.390969i | ||||
\(865\) | 2.26115e29 | 0.964201 | ||||||||
\(866\) | 3.41182e29 | + | 1.03450e29i | 1.43816 | + | 0.436066i | ||||
\(867\) | 3.60923e28 | 0.150392 | ||||||||
\(868\) | 1.81842e29 | + | 1.21437e29i | 0.749025 | + | 0.500214i | ||||
\(869\) | − | 6.85024e28i | − | 0.278938i | ||||||
\(870\) | 2.68124e28 | + | 8.12982e27i | 0.107930 | + | 0.0327257i | ||||
\(871\) | 1.36207e29i | 0.542023i | ||||||||
\(872\) | 3.62185e29 | − | 2.97464e29i | 1.42484 | − | 1.17022i | ||||
\(873\) | −9.67629e28 | −0.376328 | ||||||||
\(874\) | 1.59357e28 | − | 5.25564e28i | 0.0612712 | − | 0.202074i | ||||
\(875\) | −3.21910e29 | −1.22364 | ||||||||
\(876\) | −8.58642e28 | − | 5.73418e28i | −0.322679 | − | 0.215492i | ||||
\(877\) | − | 1.41241e29i | − | 0.524765i | −0.964964 | − | 0.262383i | \(-0.915492\pi\) | ||
0.964964 | − | 0.262383i | \(-0.0845083\pi\) | |||||||
\(878\) | 4.93271e28 | − | 1.62682e29i | 0.181193 | − | 0.597579i | ||||
\(879\) | − | 4.15060e26i | − | 0.00150738i | ||||||
\(880\) | 1.37459e29 | − | 5.70176e28i | 0.493569 | − | 0.204730i | ||||
\(881\) | −2.59025e29 | −0.919564 | −0.459782 | − | 0.888032i | \(-0.652073\pi\) | ||||
−0.459782 | + | 0.888032i | \(0.652073\pi\) | |||||||
\(882\) | 2.53276e29 | + | 7.67962e28i | 0.889015 | + | 0.269559i | ||||
\(883\) | −2.78860e29 | −0.967785 | −0.483892 | − | 0.875127i | \(-0.660777\pi\) | ||||
−0.483892 | + | 0.875127i | \(0.660777\pi\) | |||||||
\(884\) | 1.12810e29 | − | 1.68923e29i | 0.387101 | − | 0.579649i | ||||
\(885\) | − | 2.92352e28i | − | 0.0991914i | ||||||
\(886\) | −5.21712e29 | − | 1.58189e29i | −1.75022 | − | 0.530687i | ||||
\(887\) | 2.60662e29i | 0.864652i | 0.901717 | + | 0.432326i | \(0.142307\pi\) | ||||
−0.901717 | + | 0.432326i | \(0.857693\pi\) | |||||||
\(888\) | 5.32229e28 | − | 4.37121e28i | 0.174570 | − | 0.143375i | ||||
\(889\) | 4.38929e29 | 1.42356 | ||||||||
\(890\) | 5.54662e28 | − | 1.82929e29i | 0.177881 | − | 0.586656i | ||||
\(891\) | 2.98209e29 | 0.945678 | ||||||||
\(892\) | 1.38333e29 | − | 2.07142e29i | 0.433789 | − | 0.649561i | ||||
\(893\) | 5.00079e28i | 0.155069i | ||||||||
\(894\) | 1.39959e28 | − | 4.61588e28i | 0.0429165 | − | 0.141540i | ||||
\(895\) | − | 1.04908e29i | − | 0.318112i | ||||||
\(896\) | 4.12773e29 | + | 2.20170e29i | 1.23774 | + | 0.660205i | ||||
\(897\) | 1.34922e29 | 0.400091 | ||||||||
\(898\) | −2.27615e29 | − | 6.90153e28i | −0.667478 | − | 0.202387i | ||||
\(899\) | 2.50201e29 | 0.725591 | ||||||||
\(900\) | −2.09336e29 | − | 1.39799e29i | −0.600370 | − | 0.400939i | ||||
\(901\) | 1.65082e28i | 0.0468221i | ||||||||
\(902\) | −2.73662e29 | − | 8.29775e28i | −0.767626 | − | 0.232753i | ||||
\(903\) | − | 1.28066e29i | − | 0.355269i | ||||||
\(904\) | 3.67856e29 | + | 4.47894e29i | 1.00924 | + | 1.22883i | ||||
\(905\) | −3.12381e29 | −0.847617 | ||||||||
\(906\) | 1.25550e28 | − | 4.14070e28i | 0.0336927 | − | 0.111120i | ||||
\(907\) | −6.98026e29 | −1.85267 | −0.926337 | − | 0.376697i | \(-0.877060\pi\) | ||||
−0.926337 | + | 0.376697i | \(0.877060\pi\) | |||||||
\(908\) | −2.65969e29 | − | 1.77619e29i | −0.698187 | − | 0.466263i | ||||
\(909\) | − | 3.29371e29i | − | 0.855158i | ||||||
\(910\) | −1.10048e29 | + | 3.62942e29i | −0.282598 | + | 0.932016i | ||||
\(911\) | 5.98350e29i | 1.51975i | 0.650071 | + | 0.759873i | \(0.274739\pi\) | ||||
−0.650071 | + | 0.759873i | \(0.725261\pi\) | |||||||
\(912\) | −4.51133e27 | − | 1.08760e28i | −0.0113333 | − | 0.0273226i | ||||
\(913\) | 3.41622e29 | 0.848863 | ||||||||
\(914\) | 5.53256e28 | + | 1.67753e28i | 0.135977 | + | 0.0412296i | ||||
\(915\) | −1.58941e28 | −0.0386388 | ||||||||
\(916\) | −1.18704e29 | + | 1.77748e29i | −0.285436 | + | 0.427415i | ||||
\(917\) | 8.23107e28i | 0.195778i | ||||||||
\(918\) | 7.98721e28 | + | 2.42181e28i | 0.187918 | + | 0.0569788i | ||||
\(919\) | 1.14274e29i | 0.265946i | 0.991120 | + | 0.132973i | \(0.0424524\pi\) | ||||
−0.991120 | + | 0.132973i | \(0.957548\pi\) | |||||||
\(920\) | −1.96416e29 | − | 2.39152e29i | −0.452167 | − | 0.550549i | ||||
\(921\) | 9.92361e28 | 0.225982 | ||||||||
\(922\) | −1.21788e29 | + | 4.01659e29i | −0.274343 | + | 0.904792i | ||||
\(923\) | −4.24189e29 | −0.945241 | ||||||||
\(924\) | −7.60484e28 | + | 1.13876e29i | −0.167637 | + | 0.251022i | ||||
\(925\) | 3.88685e29i | 0.847580i | ||||||||
\(926\) | −1.47646e29 | + | 4.86943e29i | −0.318503 | + | 1.05043i | ||||
\(927\) | − | 8.47745e29i | − | 1.80912i | ||||||
\(928\) | 5.32684e29 | − | 5.27988e28i | 1.12458 | − | 0.111467i | ||||
\(929\) | 7.98293e28 | 0.166727 | 0.0833633 | − | 0.996519i | \(-0.473434\pi\) | ||||
0.0833633 | + | 0.996519i | \(0.473434\pi\) | |||||||
\(930\) | −2.96783e28 | − | 8.99878e27i | −0.0613210 | − | 0.0185932i | ||||
\(931\) | −6.98657e28 | −0.142813 | ||||||||
\(932\) | 1.35635e29 | + | 9.05798e28i | 0.274292 | + | 0.183178i | ||||
\(933\) | − | 8.63095e28i | − | 0.172680i | ||||||
\(934\) | −6.46603e29 | − | 1.96057e29i | −1.27988 | − | 0.388074i | ||||
\(935\) | − | 1.36377e29i | − | 0.267070i | ||||||
\(936\) | −5.33877e29 | + | 4.38474e29i | −1.03439 | + | 0.849544i | ||||
\(937\) | 1.00786e30 | 1.93200 | 0.965998 | − | 0.258548i | \(-0.0832440\pi\) | ||||
0.965998 | + | 0.258548i | \(0.0832440\pi\) | |||||||
\(938\) | −8.34157e28 | + | 2.75108e29i | −0.158205 | + | 0.521764i | ||||
\(939\) | −8.90110e28 | −0.167027 | ||||||||
\(940\) | 2.34344e29 | + | 1.56499e29i | 0.435086 | + | 0.290559i | ||||
\(941\) | 7.65693e29i | 1.40656i | 0.710912 | + | 0.703281i | \(0.248282\pi\) | ||||
−0.710912 | + | 0.703281i | \(0.751718\pi\) | |||||||
\(942\) | 3.09328e27 | − | 1.02017e28i | 0.00562225 | − | 0.0185424i | ||||
\(943\) | 5.94685e29i | 1.06947i | ||||||||
\(944\) | −2.14005e29 | − | 5.15930e29i | −0.380807 | − | 0.918059i | ||||
\(945\) | −1.55834e29 | −0.274374 | ||||||||
\(946\) | −7.44840e29 | − | 2.25844e29i | −1.29763 | − | 0.393456i | ||||
\(947\) | 5.26248e29 | 0.907174 | 0.453587 | − | 0.891212i | \(-0.350144\pi\) | ||||
0.453587 | + | 0.891212i | \(0.350144\pi\) | |||||||
\(948\) | −1.69620e28 | + | 2.53990e28i | −0.0289330 | + | 0.0433245i | ||||
\(949\) | − | 1.59922e30i | − | 2.69927i | ||||||
\(950\) | 6.35913e28 | + | 1.92816e28i | 0.106209 | + | 0.0322038i | ||||
\(951\) | 8.80160e28i | 0.145464i | ||||||||
\(952\) | 3.31302e29 | − | 2.72099e29i | 0.541819 | − | 0.444997i | ||||
\(953\) | −7.28169e27 | −0.0117843 | −0.00589214 | − | 0.999983i | \(-0.501876\pi\) | ||||
−0.00589214 | + | 0.999983i | \(0.501876\pi\) | |||||||
\(954\) | 1.62916e28 | − | 5.37303e28i | 0.0260904 | − | 0.0860470i | ||||
\(955\) | −3.34527e28 | −0.0530148 | ||||||||
\(956\) | −9.30003e28 | + | 1.39260e29i | −0.145850 | + | 0.218397i | ||||
\(957\) | 1.56684e29i | 0.243168i | ||||||||
\(958\) | 1.09166e29 | − | 3.60034e29i | 0.167662 | − | 0.552953i | ||||
\(959\) | − | 2.91309e29i | − | 0.442759i | ||||||
\(960\) | −6.50848e28 | − | 1.28958e28i | −0.0978966 | − | 0.0193970i | ||||
\(961\) | 3.94847e29 | 0.587753 | ||||||||
\(962\) | 1.02085e30 | + | 3.09533e29i | 1.50387 | + | 0.455991i | ||||
\(963\) | 1.16780e30 | 1.70257 | ||||||||
\(964\) | −3.23993e28 | − | 2.16369e28i | −0.0467483 | − | 0.0312194i | ||||
\(965\) | − | 5.50311e29i | − | 0.785842i | ||||||
\(966\) | 2.72513e29 | + | 8.26289e28i | 0.385137 | + | 0.116778i | ||||
\(967\) | − | 4.20930e29i | − | 0.588769i | −0.955687 | − | 0.294384i | \(-0.904885\pi\) | ||
0.955687 | − | 0.294384i | \(-0.0951146\pi\) | |||||||
\(968\) | 6.97280e28 | + | 8.48992e28i | 0.0965280 | + | 0.117530i | ||||
\(969\) | −1.07904e28 | −0.0147842 | ||||||||
\(970\) | 4.17660e28 | − | 1.37746e29i | 0.0566377 | − | 0.186793i | ||||
\(971\) | −8.64643e29 | −1.16050 | −0.580249 | − | 0.814439i | \(-0.697045\pi\) | ||||
−0.580249 | + | 0.814439i | \(0.697045\pi\) | |||||||
\(972\) | −3.56518e29 | − | 2.38090e29i | −0.473608 | − | 0.316285i | ||||
\(973\) | − | 1.51742e30i | − | 1.99515i | ||||||
\(974\) | 2.45374e29 | − | 8.09251e29i | 0.319329 | − | 1.05316i | ||||
\(975\) | 1.63251e29i | 0.210286i | ||||||||
\(976\) | −2.80491e29 | + | 1.16346e29i | −0.357619 | + | 0.148339i | ||||
\(977\) | −1.01193e30 | −1.27704 | −0.638519 | − | 0.769606i | \(-0.720453\pi\) | ||||
−0.638519 | + | 0.769606i | \(0.720453\pi\) | |||||||
\(978\) | −6.45395e28 | − | 1.95691e28i | −0.0806190 | − | 0.0244446i | ||||
\(979\) | 1.06899e30 | 1.32174 | ||||||||
\(980\) | −2.18645e29 | + | 3.27401e29i | −0.267595 | + | 0.400700i | ||||
\(981\) | 1.46080e30i | 1.76970i | ||||||||
\(982\) | 3.72010e29 | + | 1.12797e29i | 0.446107 | + | 0.135265i | ||||
\(983\) | − | 2.24923e28i | − | 0.0266992i | −0.999911 | − | 0.0133496i | \(-0.995751\pi\) | ||
0.999911 | − | 0.0133496i | \(-0.00424944\pi\) | |||||||
\(984\) | 8.09213e28 | + | 9.85280e28i | 0.0950849 | + | 0.115773i | ||||
\(985\) | −7.74949e28 | −0.0901386 | ||||||||
\(986\) | 1.42341e29 | − | 4.69446e29i | 0.163893 | − | 0.540526i | ||||
\(987\) | −2.59298e29 | −0.295548 | ||||||||
\(988\) | 1.01283e29 | − | 1.51662e29i | 0.114279 | − | 0.171123i | ||||
\(989\) | 1.61858e30i | 1.80789i | ||||||||
\(990\) | −1.34588e29 | + | 4.43875e29i | −0.148818 | + | 0.490805i | ||||
\(991\) | − | 5.02722e29i | − | 0.550290i | −0.961403 | − | 0.275145i | \(-0.911274\pi\) | ||
0.961403 | − | 0.275145i | \(-0.0887259\pi\) | |||||||
\(992\) | −5.89620e29 | + | 5.84423e28i | −0.638934 | + | 0.0633301i | ||||
\(993\) | 9.09055e26 | 0.000975209 | ||||||||
\(994\) | −8.56767e29 | − | 2.59781e29i | −0.909911 | − | 0.275895i | ||||
\(995\) | −2.86120e29 | −0.300827 | ||||||||
\(996\) | −1.26665e29 | − | 8.45894e28i | −0.131845 | − | 0.0880486i | ||||
\(997\) | 1.53860e30i | 1.58553i | 0.609527 | + | 0.792766i | \(0.291360\pi\) | ||||
−0.609527 | + | 0.792766i | \(0.708640\pi\) | |||||||
\(998\) | 1.55481e30 | + | 4.71437e29i | 1.58625 | + | 0.480970i | ||||
\(999\) | 4.38314e29i | 0.442722i |
(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 | 8.21.d.b.3.18 | yes | 18 | |
3.2 | odd | 2 | 72.21.b.b.19.1 | 18 | |||
4.3 | odd | 2 | 32.21.d.b.15.9 | 18 | |||
8.3 | odd | 2 | inner | 8.21.d.b.3.17 | ✓ | 18 | |
8.5 | even | 2 | 32.21.d.b.15.10 | 18 | |||
24.11 | even | 2 | 72.21.b.b.19.2 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.21.d.b.3.17 | ✓ | 18 | 8.3 | odd | 2 | inner | |
8.21.d.b.3.18 | yes | 18 | 1.1 | even | 1 | trivial | |
32.21.d.b.15.9 | 18 | 4.3 | odd | 2 | |||
32.21.d.b.15.10 | 18 | 8.5 | even | 2 | |||
72.21.b.b.19.1 | 18 | 3.2 | odd | 2 | |||
72.21.b.b.19.2 | 18 | 24.11 | even | 2 |