Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,9,Mod(79,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.79");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.l (of order \(4\), degree \(2\), not 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: | \(78.2166931317\) |
Analytic rank: | \(0\) |
Dimension: | \(64\) |
Relative dimension: | \(32\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 175.5 | ||
Character | \(\chi\) | \(=\) | 192.175 |
Dual form | 192.9.l.a.79.5 |
$q$-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 \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −33.0681 | + | 33.0681i | −0.408248 | + | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −384.834 | + | 384.834i | −0.615734 | + | 0.615734i | −0.944434 | − | 0.328700i | \(-0.893389\pi\) |
0.328700 | + | 0.944434i | \(0.393389\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1641.15 | −0.683528 | −0.341764 | − | 0.939786i | \(-0.611024\pi\) | ||||
−0.341764 | + | 0.939786i | \(0.611024\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 2187.00i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5395.29 | − | 5395.29i | −0.368506 | − | 0.368506i | 0.498426 | − | 0.866932i | \(-0.333911\pi\) |
−0.866932 | + | 0.498426i | \(0.833911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 31216.1 | + | 31216.1i | 1.09296 | + | 1.09296i | 0.995211 | + | 0.0977498i | \(0.0311645\pi\) |
0.0977498 | + | 0.995211i | \(0.468836\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 25451.5i | − | 0.502745i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −103035. | −1.23364 | −0.616821 | − | 0.787103i | \(-0.711580\pi\) | ||||
−0.616821 | + | 0.787103i | \(0.711580\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −143933. | + | 143933.i | −1.10445 | + | 1.10445i | −0.110584 | + | 0.993867i | \(0.535272\pi\) |
−0.993867 | + | 0.110584i | \(0.964728\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 54269.7 | − | 54269.7i | 0.279049 | − | 0.279049i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −322047. | −1.15082 | −0.575410 | − | 0.817865i | \(-0.695158\pi\) | ||||
−0.575410 | + | 0.817865i | \(0.695158\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 94430.7i | 0.241743i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 72320.0 | + | 72320.0i | 0.136083 | + | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −645577. | − | 645577.i | −0.912759 | − | 0.912759i | 0.0837291 | − | 0.996489i | \(-0.473317\pi\) |
−0.996489 | + | 0.0837291i | \(0.973317\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 611529.i | − | 0.662171i | −0.943601 | − | 0.331086i | \(-0.892585\pi\) | ||
0.943601 | − | 0.331086i | \(-0.107415\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 356824. | 0.300884 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 631570. | − | 631570.i | 0.420871 | − | 0.420871i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −486387. | + | 486387.i | −0.259523 | + | 0.259523i | −0.824860 | − | 0.565337i | \(-0.808746\pi\) |
0.565337 | + | 0.824860i | \(0.308746\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.06451e6 | −0.892399 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 852590.i | 0.301720i | 0.988555 | + | 0.150860i | \(0.0482043\pi\) | ||||
−0.988555 | + | 0.150860i | \(0.951796\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 821316. | + | 821316.i | 0.240235 | + | 0.240235i | 0.816947 | − | 0.576712i | \(-0.195665\pi\) |
−0.576712 | + | 0.816947i | \(0.695665\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 841632. | + | 841632.i | 0.205245 | + | 0.205245i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.87783e6i | 0.589758i | 0.955535 | + | 0.294879i | \(0.0952794\pi\) | ||||
−0.955535 | + | 0.294879i | \(0.904721\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.07143e6 | −0.532790 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.40717e6 | − | 3.40717e6i | 0.503632 | − | 0.503632i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.13734e6 | − | 4.13734e6i | 0.524345 | − | 0.524345i | −0.394536 | − | 0.918881i | \(-0.629094\pi\) |
0.918881 | + | 0.394536i | \(0.129094\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.15258e6 | 0.453803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 9.51920e6i | − | 0.901781i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.34276e7 | + | 1.34276e7i | 1.10813 | + | 1.10813i | 0.993396 | + | 0.114733i | \(0.0366013\pi\) |
0.114733 | + | 0.993396i | \(0.463399\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.49089e7 | − | 1.49089e7i | −1.07678 | − | 1.07678i | −0.996796 | − | 0.0799824i | \(-0.974514\pi\) |
−0.0799824 | − | 0.996796i | \(-0.525486\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.58919e6i | 0.227843i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −2.40260e7 | −1.34595 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.88490e6 | − | 2.88490e6i | 0.143163 | − | 0.143163i | −0.631893 | − | 0.775056i | \(-0.717722\pi\) |
0.775056 | + | 0.631893i | \(0.217722\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.06495e7 | − | 1.06495e7i | 0.469820 | − | 0.469820i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.41039e7 | 0.948535 | 0.474267 | − | 0.880381i | \(-0.342713\pi\) | ||||
0.474267 | + | 0.880381i | \(0.342713\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.84105e6i | 0.276111i | 0.990425 | + | 0.138055i | \(0.0440852\pi\) | ||||
−0.990425 | + | 0.138055i | \(0.955915\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.12264e6 | − | 3.12264e6i | −0.0986910 | − | 0.0986910i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 8.85448e6 | + | 8.85448e6i | 0.251884 | + | 0.251884i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.93662e7i | 1.52416i | 0.647482 | + | 0.762081i | \(0.275822\pi\) | ||||
−0.647482 | + | 0.762081i | \(0.724178\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −4.78297e6 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.14005e7 | − | 6.14005e7i | 1.29378 | − | 1.29378i | 0.361346 | − | 0.932432i | \(-0.382317\pi\) |
0.932432 | − | 0.361346i | \(-0.117683\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.96514e7 | − | 3.96514e7i | 0.759596 | − | 0.759596i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.26961e7 | 0.745265 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7.56364e7i | − | 1.20551i | −0.797926 | − | 0.602755i | \(-0.794070\pi\) | ||
0.797926 | − | 0.602755i | \(-0.205930\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.12302e7 | − | 5.12302e7i | −0.747069 | − | 0.747069i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.02221e7 | + | 2.02221e7i | 0.270330 | + | 0.270330i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 1.10781e8i | − | 1.36010i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.26587e8 | 1.42989 | 0.714943 | − | 0.699183i | \(-0.246453\pi\) | ||||
0.714943 | + | 0.699183i | \(0.246453\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.17995e7 | + | 1.17995e7i | −0.122835 | + | 0.122835i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.95367e7 | + | 1.95367e7i | −0.187744 | + | 0.187744i | −0.794720 | − | 0.606976i | \(-0.792382\pi\) |
0.606976 | + | 0.794720i | \(0.292382\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.15906e7 | −0.813771 | −0.406885 | − | 0.913479i | \(-0.633385\pi\) | ||||
−0.406885 | + | 0.913479i | \(0.633385\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.17697e7i | 0.343640i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.10695e7 | + | 3.10695e7i | 0.237028 | + | 0.237028i | 0.815618 | − | 0.578590i | \(-0.196397\pi\) |
−0.578590 | + | 0.815618i | \(0.696397\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.58824e8 | + | 1.58824e8i | 1.12515 | + | 1.12515i | 0.990955 | + | 0.134197i | \(0.0428455\pi\) |
0.134197 | + | 0.990955i | \(0.457154\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.21678e7i | − | 0.211899i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.60534e8 | 0.984586 | 0.492293 | − | 0.870430i | \(-0.336159\pi\) | ||||
0.492293 | + | 0.870430i | \(0.336159\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23934e8 | − | 1.23934e8i | 0.708599 | − | 0.708599i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 6.82695e7 | − | 6.82695e7i | 0.364320 | − | 0.364320i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.69096e8 | 0.843228 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 1.56140e8i | − | 0.728407i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.81935e7 | − | 2.81935e7i | −0.123177 | − | 0.123177i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.86666e8 | − | 1.86666e8i | −0.764583 | − | 0.764583i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 3.99089e7i | − | 0.153411i | −0.997054 | − | 0.0767053i | \(-0.975560\pi\) | ||
0.997054 | − | 0.0767053i | \(-0.0244401\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.43187e7 | −0.196151 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.54455e8 | − | 1.54455e8i | 0.524464 | − | 0.524464i | −0.394453 | − | 0.918916i | \(-0.629066\pi\) |
0.918916 | + | 0.394453i | \(0.129066\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.36216e8 | − | 2.36216e8i | 0.754923 | − | 0.754923i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.56623e7 | −0.167582 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.36175e8i | 0.386557i | 0.981144 | + | 0.193279i | \(0.0619121\pi\) | ||||
−0.981144 | + | 0.193279i | \(0.938088\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.58060e8 | − | 1.58060e8i | −0.423412 | − | 0.423412i | 0.462965 | − | 0.886377i | \(-0.346786\pi\) |
−0.886377 | + | 0.462965i | \(0.846786\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.51645e7 | − | 9.51645e7i | −0.240768 | − | 0.240768i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3.36840e8i | − | 0.805525i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.96880e8 | 1.12403 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.01566e8 | − | 1.01566e8i | 0.217511 | − | 0.217511i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 8.48839e7 | − | 8.48839e7i | 0.172219 | − | 0.172219i | −0.615735 | − | 0.787953i | \(-0.711141\pi\) |
0.787953 | + | 0.615735i | \(0.211141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.18564e8 | −0.420407 | −0.210204 | − | 0.977658i | \(-0.567413\pi\) | ||||
−0.210204 | + | 0.977658i | \(0.567413\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.25338e8i | 0.411214i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.35337e8 | + | 2.35337e8i | 0.407722 | + | 0.407722i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.95758e8 | − | 4.95758e8i | −0.815964 | − | 0.815964i | 0.169557 | − | 0.985520i | \(-0.445766\pi\) |
−0.985520 | + | 0.169557i | \(0.945766\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.73628e8i | 0.428126i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.28527e8 | 0.786617 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.97042e8 | − | 4.97042e8i | 0.704113 | − | 0.704113i | −0.261178 | − | 0.965291i | \(-0.584111\pi\) |
0.965291 | + | 0.261178i | \(0.0841109\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.37318e8 | + | 1.37318e8i | −0.185264 | + | 0.185264i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −9.42688e8 | −1.21200 | −0.605999 | − | 0.795465i | \(-0.707226\pi\) | ||||
−0.605999 | + | 0.795465i | \(0.707226\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.13315e9i | 1.38913i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.14782e8 | + | 3.14782e8i | 0.368150 | + | 0.368150i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.41416e8 | − | 3.41416e8i | −0.381153 | − | 0.381153i | 0.490364 | − | 0.871518i | \(-0.336864\pi\) |
−0.871518 | + | 0.490364i | \(0.836864\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1.54975e8i | − | 0.165238i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.88051e8 | −0.904784 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.79686e8 | − | 3.79686e8i | 0.369839 | − | 0.369839i | −0.497580 | − | 0.867418i | \(-0.665778\pi\) |
0.867418 | + | 0.497580i | \(0.165778\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.22061e9 | − | 1.22061e9i | 1.13727 | − | 1.13727i | 0.148334 | − | 0.988937i | \(-0.452609\pi\) |
0.988937 | − | 0.148334i | \(-0.0473910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.86019e8 | 0.879186 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 3.74357e8i | − | 0.319594i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.55904e8 | + | 5.55904e8i | 0.454604 | + | 0.454604i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.18688e8 | − | 1.18688e8i | −0.0930163 | − | 0.0930163i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.77560e8i | 0.133417i | 0.997773 | + | 0.0667086i | \(0.0212498\pi\) | ||||
−0.997773 | + | 0.0667086i | \(0.978750\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.45722e9 | 1.05026 | 0.525128 | − | 0.851023i | \(-0.324017\pi\) | ||||
0.525128 | + | 0.851023i | \(0.324017\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 7.94494e8 | − | 7.94494e8i | 0.549481 | − | 0.549481i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.53284e8 | + | 4.53284e8i | −0.300958 | + | 0.300958i | −0.841388 | − | 0.540431i | \(-0.818261\pi\) |
0.540431 | + | 0.841388i | \(0.318261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.22382e8 | −0.333101 | −0.166551 | − | 0.986033i | \(-0.553263\pi\) | ||||
−0.166551 | + | 0.986033i | \(0.553263\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.90796e8i | 0.116892i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.05949e9 | + | 1.05949e9i | 0.623896 | + | 0.623896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.28106e8 | − | 3.28106e8i | −0.185780 | − | 0.185780i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.04316e8i | 0.383607i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.55312e9 | 0.813993 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.04066e9 | + | 2.04066e9i | −1.02954 | + | 1.02954i | −0.0299864 | + | 0.999550i | \(0.509546\pi\) |
−0.999550 | + | 0.0299864i | \(0.990454\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.97069e8 | + | 7.97069e8i | −0.387238 | + | 0.387238i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.32141e8 | −0.295842 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.00361e9i | 0.452612i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.59289e8 | − | 2.59289e8i | −0.112722 | − | 0.112722i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.21635e9 | − | 3.21635e9i | −1.34832 | − | 1.34832i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.77778e9i | 1.52763i | 0.645437 | + | 0.763814i | \(0.276675\pi\) | ||||
−0.645437 | + | 0.763814i | \(0.723325\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.06520e8 | 0.0805809 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.90321e9 | − | 2.90321e9i | 1.09339 | − | 1.09339i | 0.0982251 | − | 0.995164i | \(-0.468683\pi\) |
0.995164 | − | 0.0982251i | \(-0.0313165\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.11959e9 | + | 3.11959e9i | −1.13437 | + | 1.13437i | −0.144932 | + | 0.989442i | \(0.546296\pi\) |
−0.989442 | + | 0.144932i | \(0.953704\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.85602e8 | −0.205662 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.02496e8i | 0.272282i | 0.990689 | + | 0.136141i | \(0.0434700\pi\) | ||||
−0.990689 | + | 0.136141i | \(0.956530\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.10749e9 | − | 1.10749e9i | −0.363134 | − | 0.363134i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.96313e9 | − | 1.96313e9i | −0.622237 | − | 0.622237i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.81741e9i | 0.557009i | 0.960435 | + | 0.278504i | \(0.0898386\pi\) | ||||
−0.960435 | + | 0.278504i | \(0.910161\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.03588e9 | −0.899945 | −0.449972 | − | 0.893042i | \(-0.648566\pi\) | ||||
−0.449972 | + | 0.893042i | \(0.648566\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.58164e8 | − | 1.58164e8i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.18199e9 | − | 1.18199e9i | 0.328057 | − | 0.328057i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.98605e9 | −2.41424 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.06080e9i | 1.05637i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.76988e9 | − | 2.76988e9i | −0.697856 | − | 0.697856i | 0.266092 | − | 0.963948i | \(-0.414267\pi\) |
−0.963948 | + | 0.266092i | \(0.914267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.73754e9 | + | 1.73754e9i | 0.424084 | + | 0.424084i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.62239e9i | 0.620207i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.22766e9 | −1.65678 | −0.828391 | − | 0.560151i | \(-0.810743\pi\) | ||||
−0.828391 | + | 0.560151i | \(0.810743\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.98234e8 | − | 7.98234e8i | 0.177391 | − | 0.177391i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.41188e9 | + | 1.41188e9i | −0.304253 | + | 0.304253i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.44090e9 | −0.510183 | −0.255092 | − | 0.966917i | \(-0.582106\pi\) | ||||
−0.255092 | + | 0.966917i | \(0.582106\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.18437e9i | 0.645715i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.50115e9 | + | 2.50115e9i | 0.492148 | + | 0.492148i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.52011e9 | − | 2.52011e9i | −0.481294 | − | 0.481294i | 0.424251 | − | 0.905545i | \(-0.360538\pi\) |
−0.905545 | + | 0.424251i | \(0.860538\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.26633e9i | 0.605596i | 0.953055 | + | 0.302798i | \(0.0979208\pi\) | ||||
−0.953055 | + | 0.302798i | \(0.902079\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.38817e9 | 0.609979 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.09481e8 | − | 5.09481e8i | 0.0890835 | − | 0.0890835i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.51461e8 | + | 1.51461e8i | −0.0257266 | + | 0.0257266i | −0.719853 | − | 0.694126i | \(-0.755791\pi\) |
0.694126 | + | 0.719853i | \(0.255791\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.33741e9 | −0.220724 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.66129e9i | 1.38918i | 0.719408 | + | 0.694588i | \(0.244413\pi\) | ||||
−0.719408 | + | 0.694588i | \(0.755587\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.50915e9 | + | 4.50915e9i | 0.702990 | + | 0.702990i | 0.965051 | − | 0.262061i | \(-0.0844023\pi\) |
−0.262061 | + | 0.965051i | \(0.584402\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.66331e9 | + | 3.66331e9i | 0.555257 | + | 0.555257i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 1.39923e9i | − | 0.206234i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.64046e9 | 0.521873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.18598e9 | + | 4.18598e9i | −0.583748 | + | 0.583748i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7.35696e9 | − | 7.35696e9i | 0.998224 | − | 0.998224i | −0.00177487 | − | 0.999998i | \(-0.500565\pi\) |
0.999998 | + | 0.00177487i | \(0.000564961\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.03348e10 | −1.36463 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 7.80375e8i | − | 0.100295i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.00530e10 | − | 1.00530e10i | −1.25780 | − | 1.25780i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.34790e9 | − | 1.34790e9i | −0.164207 | − | 0.164207i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1.29208e9i | − | 0.153292i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.14749e10 | 1.32602 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00075e10 | − | 1.00075e10i | 1.12660 | − | 1.12660i | 0.135878 | − | 0.990726i | \(-0.456614\pi\) |
0.990726 | − | 0.135878i | \(-0.0433856\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.02873e9 | − | 3.02873e9i | 0.332220 | − | 0.332220i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.28626e9 | −0.351286 | −0.175643 | − | 0.984454i | \(-0.556200\pi\) | ||||
−0.175643 | + | 0.984454i | \(0.556200\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.64826e10i | 1.71731i | 0.512558 | + | 0.858653i | \(0.328698\pi\) | ||||
−0.512558 | + | 0.858653i | \(0.671302\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.38124e9 | − | 1.38124e9i | −0.140290 | − | 0.140290i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −3.61075e9 | − | 3.61075e9i | −0.357569 | − | 0.357569i | 0.505347 | − | 0.862916i | \(-0.331365\pi\) |
−0.862916 | + | 0.505347i | \(0.831365\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.96616e9i | 0.672714i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.05482e9 | −0.193533 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.48302e10 | − | 1.48302e10i | 1.36250 | − | 1.36250i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.94775e9 | + | 2.94775e9i | −0.264215 | + | 0.264215i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.05040e10 | −0.918683 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 4.72295e9i | − | 0.403116i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.14455e9 | + | 5.14455e9i | 0.428584 | + | 0.428584i | 0.888146 | − | 0.459562i | \(-0.151994\pi\) |
−0.459562 | + | 0.888146i | \(0.651994\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.06373e9 | + | 1.06373e9i | 0.0865075 | + | 0.0865075i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.22041e9i | 0.176301i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.55489e10 | 1.20553 | 0.602767 | − | 0.797917i | \(-0.294065\pi\) | ||||
0.602767 | + | 0.797917i | \(0.294065\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.30856e9 | + | 5.30856e9i | −0.401955 | + | 0.401955i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.29938e9 | + | 3.29938e9i | −0.244014 | + | 0.244014i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.45016e10 | 1.04770 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.19656e9i | 0.578569i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.31648e10 | + | 1.31648e10i | 0.908019 | + | 0.908019i | 0.996112 | − | 0.0880935i | \(-0.0280774\pi\) |
−0.0880935 | + | 0.996112i | \(0.528077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.71698e10 | − | 1.71698e10i | −1.15735 | − | 1.15735i | −0.985044 | − | 0.172301i | \(-0.944880\pi\) |
−0.172301 | − | 0.985044i | \(-0.555120\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.51509e9i | 0.297466i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.92630e10 | −1.24058 | −0.620291 | − | 0.784372i | \(-0.712985\pi\) | ||||
−0.620291 | + | 0.784372i | \(0.712985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −9.27599e9 | + | 9.27599e9i | −0.584045 | + | 0.584045i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −5.59168e9 | + | 5.59168e9i | −0.344247 | + | 0.344247i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.02815e10 | 0.618981 | 0.309491 | − | 0.950903i | \(-0.399842\pi\) | ||||
0.309491 | + | 0.950903i | \(0.399842\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 2.44500e10i | − | 1.43962i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.16327e9 | + | 5.16327e9i | 0.297371 | + | 0.297371i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.01750e9 | − | 3.01750e9i | −0.170011 | − | 0.170011i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 2.39423e10i | − | 1.31978i | −0.751361 | − | 0.659891i | \(-0.770602\pi\) | ||
0.751361 | − | 0.659891i | \(-0.229398\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.86461e9 | 0.100573 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.78999e9 | + | 6.78999e9i | −0.358404 | + | 0.358404i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.92293e9 | + | 5.92293e9i | −0.305986 | + | 0.305986i | −0.843350 | − | 0.537364i | \(-0.819420\pi\) |
0.537364 | + | 0.843350i | \(0.319420\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.23454e10 | 0.624280 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.03048e10i | − | 1.99522i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.10426e10 | + | 1.10426e10i | 0.535200 | + | 0.535200i | 0.922115 | − | 0.386916i | \(-0.126460\pi\) |
−0.386916 | + | 0.922115i | \(0.626460\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.31971e9 | + | 1.31971e9i | 0.0626296 | + | 0.0626296i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.10277e10i | − | 1.44196i | −0.692954 | − | 0.720982i | \(-0.743691\pi\) | ||
0.692954 | − | 0.720982i | \(-0.256309\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.81501e9 | −0.310187 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.79622e9 | − | 1.79622e9i | 0.0800784 | − | 0.0800784i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.10968e10 | − | 3.10968e10i | 1.35805 | − | 1.35805i | 0.481738 | − | 0.876315i | \(-0.340006\pi\) |
0.876315 | − | 0.481738i | \(-0.159994\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31821e10 | 1.41970 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.02150e10i | 0.428223i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −2.28461e10 | − | 2.28461e10i | −0.938479 | − | 0.938479i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.64482e10 | + | 1.64482e10i | 0.662151 | + | 0.662151i | 0.955887 | − | 0.293736i | \(-0.0948985\pi\) |
−0.293736 | + | 0.955887i | \(0.594899\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.56224e10i | 0.616392i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.28798e10 | 1.27160 | 0.635802 | − | 0.771852i | \(-0.280670\pi\) | ||||
0.635802 | + | 0.771852i | \(0.280670\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.90895e10 | − | 1.90895e10i | 0.723727 | − | 0.723727i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.84065e9 | − | 1.84065e9i | 0.0684149 | − | 0.0684149i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.24840e9 | 0.191271 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 6.27386e9i | − | 0.224203i | −0.993697 | − | 0.112102i | \(-0.964242\pi\) | ||
0.993697 | − | 0.112102i | \(-0.0357582\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4.50304e9 | − | 4.50304e9i | −0.157811 | − | 0.157811i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2.20367e10 | − | 2.20367e10i | −0.757437 | − | 0.757437i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.72580e10i | 1.59325i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.04535e10 | 0.345714 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.37482e9 | − | 7.37482e9i | 0.239274 | − | 0.239274i | −0.577276 | − | 0.816549i | \(-0.695884\pi\) |
0.816549 | + | 0.577276i | \(0.195884\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.59972e10 | + | 3.59972e10i | −1.14588 | + | 1.14588i | −0.158529 | + | 0.987354i | \(0.550675\pi\) |
−0.987354 | + | 0.158529i | \(0.949325\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.29382e9 | 0.196586 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 9.72967e9i | − | 0.298224i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.44677e10 | + | 2.44677e10i | 0.736008 | + | 0.736008i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.11386e10 | + | 1.11386e10i | 0.328854 | + | 0.328854i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.58757e10i | − | 1.32946i | −0.747086 | − | 0.664728i | \(-0.768548\pi\) | ||
0.747086 | − | 0.664728i | \(-0.231452\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.70715e10 | −1.33908 | −0.669540 | − | 0.742776i | \(-0.733509\pi\) | ||||
−0.669540 | + | 0.742776i | \(0.733509\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.64309e10 | + | 1.64309e10i | −0.458885 | + | 0.458885i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.63532e10 | − | 4.63532e10i | 1.27102 | − | 1.27102i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.94691e10 | −0.524188 | −0.262094 | − | 0.965042i | \(-0.584413\pi\) | ||||
−0.262094 | + | 0.965042i | \(0.584413\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.71721e9i | 0.177597i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.47090e10 | − | 4.47090e10i | −1.16086 | − | 1.16086i | −0.984288 | − | 0.176573i | \(-0.943499\pi\) |
−0.176573 | − | 0.984288i | \(-0.556501\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.91075e10 | + | 2.91075e10i | 0.742274 | + | 0.742274i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.61390e9i | 0.140616i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 4.98537e10 | 1.22663 | 0.613313 | − | 0.789840i | \(-0.289837\pi\) | ||||
0.613313 | + | 0.789840i | \(0.289837\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.59997e9 | − | 4.59997e9i | 0.111186 | − | 0.111186i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.22749e9 | − | 7.22749e9i | 0.171631 | − | 0.171631i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.94303e10 | 0.919992 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 2.08818e10i | − | 0.478743i | −0.970928 | − | 0.239372i | \(-0.923059\pi\) | ||
0.970928 | − | 0.239372i | \(-0.0769415\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.45149e9 | − | 7.45149e9i | −0.167877 | − | 0.167877i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.14710e10 | + | 4.14710e10i | 0.918206 | + | 0.918206i | 0.996899 | − | 0.0786924i | \(-0.0250745\pi\) |
−0.0786924 | + | 0.996899i | \(0.525075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 5.47650e10i | − | 1.19173i | −0.803083 | − | 0.595867i | \(-0.796809\pi\) | ||
0.803083 | − | 0.595867i | \(-0.203191\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.55643e10 | −0.332903 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −3.98156e10 | + | 3.98156e10i | −0.837117 | + | 0.837117i | −0.988478 | − | 0.151362i | \(-0.951634\pi\) |
0.151362 | + | 0.988478i | \(0.451634\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.73455e9 | + | 4.73455e9i | −0.0978560 | + | 0.0978560i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3.27875e10 | 0.666232 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 8.86248e9i | − | 0.177056i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.35917e10 | − | 1.35917e10i | −0.266993 | − | 0.266993i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −9.04835e9 | − | 9.04835e9i | −0.174782 | − | 0.174782i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 4.13653e10i | − | 0.785767i | −0.919588 | − | 0.392884i | \(-0.871478\pi\) | ||
0.919588 | − | 0.392884i | \(-0.128522\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.03662e10 | −0.567296 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.74774e10 | + | 1.74774e10i | −0.321135 | + | 0.321135i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.87149e10 | + | 4.87149e10i | −0.880430 | + | 0.880430i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.75043e10 | −0.666753 | −0.333377 | − | 0.942794i | \(-0.608188\pi\) | ||||
−0.333377 | + | 0.942794i | \(0.608188\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.28725e10i | 0.574906i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.37271e10 | + | 3.37271e10i | 0.580300 | + | 0.580300i | 0.934986 | − | 0.354686i | \(-0.115412\pi\) |
−0.354686 | + | 0.934986i | \(0.615412\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.65171e10 | + | 6.65171e10i | 1.12602 | + | 1.12602i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 9.08170e9i | − | 0.151268i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.95581e10 | −0.648350 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.51104e10 | + | 2.51104e10i | −0.404997 | + | 0.404997i | −0.879990 | − | 0.474992i | \(-0.842451\pi\) |
0.474992 | + | 0.879990i | \(0.342451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.11729e10 | − | 3.11729e10i | 0.494796 | − | 0.494796i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.44447e10 | −1.00673 | −0.503367 | − | 0.864073i | \(-0.667906\pi\) | ||||
−0.503367 | + | 0.864073i | \(0.667906\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 1.50368e10i | − | 0.231201i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.74712e10 | − | 3.74712e10i | −0.567109 | − | 0.567109i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.53752e10 | + | 1.53752e10i | 0.229061 | + | 0.229061i | 0.812300 | − | 0.583240i | \(-0.198215\pi\) |
−0.583240 | + | 0.812300i | \(0.698215\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.28683e10i | − | 0.188729i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.08185e10 | −0.300594 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.52472e10 | − | 3.52472e10i | 0.501066 | − | 0.501066i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.55268e10 | − | 1.55268e10i | 0.217329 | − | 0.217329i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.25800e10 | 0.311210 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 9.02387e10i | − | 1.22473i | −0.790574 | − | 0.612367i | \(-0.790218\pi\) | ||
0.790574 | − | 0.612367i | \(-0.209782\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.84379e10 | + | 4.84379e10i | 0.647409 | + | 0.647409i | 0.952366 | − | 0.304957i | \(-0.0986421\pi\) |
−0.304957 | + | 0.952366i | \(0.598642\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.12473e9 | + | 5.12473e9i | 0.0674580 | + | 0.0674580i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.30089e10i | 0.816883i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.54030e10 | 0.324387 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.93662e10 | − | 2.93662e10i | 0.369376 | − | 0.369376i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.66145e10 | + | 2.66145e10i | −0.329769 | + | 0.329769i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.39132e10 | −0.291893 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.51110e10i | 0.301972i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.65713e10 | + | 1.65713e10i | 0.196336 | + | 0.196336i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.79797e10 | + | 3.79797e10i | 0.443367 | + | 0.443367i | 0.893142 | − | 0.449775i | \(-0.148496\pi\) |
−0.449775 | + | 0.893142i | \(0.648496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.07268e10i | 0.928578i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.22242e11 | −1.38559 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.14985e11 | + | 1.14985e11i | −1.28438 | + | 1.28438i | −0.346230 | + | 0.938150i | \(0.612538\pi\) |
−0.938150 | + | 0.346230i | \(0.887462\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.26058e10 | + | 3.26058e10i | −0.358926 | + | 0.358926i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.85840e11 | 2.01620 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 9.74289e10i | − | 1.04181i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.23793e10 | + | 1.23793e10i | 0.130474 | + | 0.130474i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.72576e10 | − | 6.72576e10i | −0.698748 | − | 0.698748i | 0.265392 | − | 0.964141i | \(-0.414499\pi\) |
−0.964141 | + | 0.265392i | \(0.914499\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12765e10i | 0.525135i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.67654e10 | −0.371183 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.11194e10 | + | 7.11194e10i | −0.707872 | + | 0.707872i | −0.966087 | − | 0.258216i | \(-0.916866\pi\) |
0.258216 | + | 0.966087i | \(0.416866\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.17790e10 | + | 6.17790e10i | −0.606243 | + | 0.606243i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.84957e9 | 0.0759475 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.10524e11i | 1.05440i | 0.849740 | + | 0.527202i | \(0.176759\pi\) | ||||
−0.849740 | + | 0.527202i | \(0.823241\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.00791e11 | − | 1.00791e11i | −0.948153 | − | 0.948153i | 0.0505672 | − | 0.998721i | \(-0.483897\pi\) |
−0.998721 | + | 0.0505672i | \(0.983897\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −5.87158e9 | − | 5.87158e9i | −0.0544673 | − | 0.0544673i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.04111e10i | − | 0.278202i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.37265e10 | 0.304276 | 0.152138 | − | 0.988359i | \(-0.451384\pi\) | ||||
0.152138 | + | 0.988359i | \(0.451384\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.81874e10 | + | 4.81874e10i | −0.428765 | + | 0.428765i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.00767e11 | + | 1.00767e11i | −0.884333 | + | 0.884333i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.46443e10 | −0.386448 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 5.25448e10i | 0.448649i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.03937e11 | − | 1.03937e11i | −0.875424 | − | 0.875424i | 0.117633 | − | 0.993057i | \(-0.462469\pi\) |
−0.993057 | + | 0.117633i | \(0.962469\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.80193e10 | + | 8.80193e10i | 0.731336 | + | 0.731336i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 2.99785e10i | − | 0.245731i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.66969e11 | −1.35026 | −0.675131 | − | 0.737698i | \(-0.735913\pi\) | ||||
−0.675131 | + | 0.737698i | \(0.735913\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.50738e10 | + | 6.50738e10i | −0.519205 | + | 0.519205i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.72742e10 | − | 1.72742e10i | 0.135988 | − | 0.135988i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.70800e10 | 0.521058 | 0.260529 | − | 0.965466i | \(-0.416103\pi\) | ||||
0.260529 | + | 0.965466i | \(0.416103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.69694e11i | − | 1.30067i | −0.759646 | − | 0.650337i | \(-0.774628\pi\) | ||
0.759646 | − | 0.650337i | \(-0.225372\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6.30927e9 | − | 6.30927e9i | −0.0477211 | − | 0.0477211i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.00882e10 | + | 6.00882e10i | 0.448505 | + | 0.448505i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.42708e11i | − | 1.05122i | −0.850725 | − | 0.525611i | \(-0.823837\pi\) | ||
0.850725 | − | 0.525611i | \(-0.176163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.00706e10 | −0.509409 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.98346e10 | + | 8.98346e10i | −0.644583 | + | 0.644583i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.31736e10 | + | 1.31736e10i | −0.0932957 | + | 0.0932957i | −0.752214 | − | 0.658919i | \(-0.771014\pi\) |
0.658919 | + | 0.752214i | \(0.271014\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.16997e10 | 0.151688 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.15813e11i | 0.799130i | 0.916705 | + | 0.399565i | \(0.130839\pi\) | ||||
−0.916705 | + | 0.399565i | \(0.869161\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.00573e11 | + | 1.00573e11i | 0.685047 | + | 0.685047i | 0.961133 | − | 0.276086i | \(-0.0890374\pi\) |
−0.276086 | + | 0.961133i | \(0.589037\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.32904e10 | − | 2.32904e10i | −0.156607 | − | 0.156607i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.24131e11i | 0.824000i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.06784e11 | 0.699818 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −5.13589e10 | + | 5.13589e10i | −0.332311 | + | 0.332311i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.01149e10 | − | 5.01149e10i | 0.320158 | − | 0.320158i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.57349e11 | −1.62333 | −0.811663 | − | 0.584126i | \(-0.801438\pi\) | ||||
−0.811663 | + | 0.584126i | \(0.801438\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.34962e11i | − | 0.840613i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.53583e10 | + | 1.53583e10i | 0.0944602 | + | 0.0944602i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9.58779e10 | − | 9.58779e10i | −0.582319 | − | 0.582319i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 5.27152e10i | − | 0.316178i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.55257e10 | −0.328899 | −0.164449 | − | 0.986386i | \(-0.552585\pi\) | ||||
−0.164449 | + | 0.986386i | \(0.552585\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.24970e11 | − | 2.24970e11i | 1.31608 | − | 1.31608i | 0.399223 | − | 0.916854i | \(-0.369280\pi\) |
0.916854 | − | 0.399223i | \(-0.130720\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.09037e10 | − | 2.09037e10i | 0.120777 | − | 0.120777i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.46421e10 | 0.425958 | 0.212979 | − | 0.977057i | \(-0.431683\pi\) | ||||
0.212979 | + | 0.977057i | \(0.431683\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.44892e11i | − | 0.816704i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.31875e10 | − | 3.31875e10i | −0.184778 | − | 0.184778i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.00441e11 | − | 1.00441e11i | −0.552407 | − | 0.552407i | 0.374728 | − | 0.927135i | \(-0.377736\pi\) |
−0.927135 | + | 0.374728i | \(0.877736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.18879e11i | 0.645861i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.71484e10 | 0.0920368 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6.06155e10 | + | 6.06155e10i | −0.321397 | + | 0.321397i | −0.849303 | − | 0.527906i | \(-0.822977\pi\) |
0.527906 | + | 0.849303i | \(0.322977\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.53142e11 | + | 2.53142e11i | −1.32605 | + | 1.32605i | −0.417258 | + | 0.908788i | \(0.637009\pi\) |
−0.908788 | + | 0.417258i | \(0.862991\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.12717e11 | 1.10090 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.81808e11i | 0.929664i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.07906e11 | + | 2.07906e11i | 1.05042 | + | 1.05042i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.24924e11 | − | 1.24924e11i | −0.623651 | − | 0.623651i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.60876e11i | 0.793598i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.93933e11 | 0.945347 | 0.472674 | − | 0.881238i | \(-0.343289\pi\) | ||||
0.472674 | + | 0.881238i | \(0.343289\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.82922e9 | + | 6.82922e9i | −0.0328970 | + | 0.0328970i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.34311e11 | − | 2.34311e11i | 1.11542 | − | 1.11542i | 0.123015 | − | 0.992405i | \(-0.460744\pi\) |
0.992405 | − | 0.123015i | \(-0.0392563\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.07748e11 | −0.977366 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.92007e11i | 0.892749i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.09474e11 | + | 1.09474e11i | 0.503071 | + | 0.503071i | 0.912391 | − | 0.409320i | \(-0.134234\pi\) |
−0.409320 | + | 0.912391i | \(0.634234\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.24046e10 | − | 5.24046e10i | −0.238017 | − | 0.238017i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.06318e11i | − | 0.926212i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.58303e11 | 1.14618 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.91786e11 | − | 1.91786e11i | 0.841212 | − | 0.841212i | −0.147805 | − | 0.989017i | \(-0.547221\pi\) |
0.989017 | + | 0.147805i | \(0.0472208\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.93648e10 | − | 1.93648e10i | 0.0839613 | − | 0.0839613i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.21654e11 | 0.521419 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 8.78466e10i | − | 0.372215i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.65370e10 | − | 2.65370e10i | −0.111159 | − | 0.111159i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.59629e10 | + | 6.59629e10i | 0.273167 | + | 0.273167i | 0.830374 | − | 0.557207i | \(-0.188127\pi\) |
−0.557207 | + | 0.830374i | \(0.688127\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.40014e11i | − | 0.573260i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 7.32451e10 | 0.296498 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.20627e10 | − | 3.20627e10i | 0.128328 | − | 0.128328i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.04133e10 | − | 7.04133e10i | 0.278657 | − | 0.278657i | −0.553916 | − | 0.832573i | \(-0.686867\pi\) |
0.832573 | + | 0.553916i | \(0.186867\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.29834e11 | 0.508054 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.96941e11i | 0.762040i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.29627e11 | + | 1.29627e11i | 0.495989 | + | 0.495989i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.00984e10 | − | 6.00984e10i | −0.227398 | − | 0.227398i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 3.04136e11i | − | 1.13803i | −0.822328 | − | 0.569014i | \(-0.807325\pi\) | ||
0.822328 | − | 0.569014i | \(-0.192675\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.50314e11 | 0.556235 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00391e11 | − | 1.00391e11i | 0.367401 | − | 0.367401i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.09623e10 | − | 6.09623e10i | 0.220653 | − | 0.220653i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.32769e11 | −1.19125 | −0.595627 | − | 0.803261i | \(-0.703097\pi\) | ||||
−0.595627 | + | 0.803261i | \(0.703097\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.04604e10i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.46243e10 | − | 8.46243e10i | −0.296364 | − | 0.296364i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.26829e11 | + | 2.26829e11i | 0.785748 | + | 0.785748i | 0.980794 | − | 0.195046i | \(-0.0624857\pi\) |
−0.195046 | + | 0.980794i | \(0.562486\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.81723e10i | 0.267857i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.11298e10 | −0.105513 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.61160e11 | − | 2.61160e11i | 0.875646 | − | 0.875646i | −0.117434 | − | 0.993081i | \(-0.537467\pi\) |
0.993081 | + | 0.117434i | \(0.0374669\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.97152e11 | − | 2.97152e11i | 0.985611 | − | 0.985611i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.26105e11 | −0.741918 | −0.370959 | − | 0.928649i | \(-0.620971\pi\) | ||||
−0.370959 | + | 0.928649i | \(0.620971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.53324e10i | 0.212082i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.34283e11 | − | 1.34283e11i | −0.431259 | − | 0.431259i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.09898e10 | − | 5.09898e10i | −0.162015 | − | 0.162015i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 2.89023e11i | − | 0.908599i | −0.890849 | − | 0.454299i | \(-0.849890\pi\) | ||
0.890849 | − | 0.454299i | \(-0.150110\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.83189e11 | 0.569797 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.41108e10 | − | 8.41108e10i | 0.258859 | − | 0.258859i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.76966e10 | − | 9.76966e10i | 0.297506 | − | 0.297506i | −0.542530 | − | 0.840036i | \(-0.682534\pi\) |
0.840036 | + | 0.542530i | \(0.182534\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.14914e11 | −0.346263 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.87097e11i | 1.75054i | 0.483638 | + | 0.875268i | \(0.339315\pi\) | ||||
−0.483638 | + | 0.875268i | \(0.660685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.60655e11 | − | 2.60655e11i | −0.769072 | − | 0.769072i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −8.67175e10 | − | 8.67175e10i | −0.253199 | − | 0.253199i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 8.38314e11i | 2.42228i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.78377e10 | −0.0796028 | −0.0398014 | − | 0.999208i | \(-0.512673\pi\) | ||||
−0.0398014 | + | 0.999208i | \(0.512673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.39005e11 | − | 2.39005e11i | 0.676378 | − | 0.676378i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.61024e11 | − | 2.61024e11i | 0.731075 | − | 0.731075i | −0.239758 | − | 0.970833i | \(-0.577068\pi\) |
0.970833 | + | 0.239758i | \(0.0770680\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.77471e10 | 0.160075 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.27922e10i | 0.144839i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.22716e11 | − | 1.22716e11i | −0.333235 | − | 0.333235i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.30047e11 | − | 1.30047e11i | −0.349541 | − | 0.349541i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 9.33763e10i | − | 0.248422i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.81569e11 | 1.00483 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.28668e11 | − | 1.28668e11i | 0.335406 | − | 0.335406i | −0.519229 | − | 0.854635i | \(-0.673781\pi\) |
0.854635 | + | 0.519229i | \(0.173781\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 8.07158e10 | − | 8.07158e10i | 0.208282 | − | 0.208282i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.63460e11 | −0.672991 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.30794e11i | − | 2.35375i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.05301e11 | − | 1.05301e11i | −0.263612 | − | 0.263612i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3.04188e11 | + | 3.04188e11i | 0.753892 | + | 0.753892i | 0.975203 | − | 0.221311i | \(-0.0710336\pi\) |
−0.221311 | + | 0.975203i | \(0.571034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 2.96518e11i | − | 0.727551i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.65417e11 | −0.401837 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.23048e10 | − | 4.23048e10i | 0.101748 | − | 0.101748i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.03395e11 | + | 2.03395e11i | −0.484347 | + | 0.484347i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.66671e11 | 0.392975 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.38359e11i | 0.556464i | 0.960514 | + | 0.278232i | \(0.0897484\pi\) | ||||
−0.960514 | + | 0.278232i | \(0.910252\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.90694e11 | + | 3.90694e11i | 0.903137 | + | 0.903137i | 0.995706 | − | 0.0925691i | \(-0.0295079\pi\) |
−0.0925691 | + | 0.995706i | \(0.529508\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.08011e11 | − | 1.08011e11i | −0.247234 | − | 0.247234i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3.82557e11i | 0.867093i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.36429e11 | −0.530656 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.12040e11 | + | 1.12040e11i | −0.249023 | + | 0.249023i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.98722e11 | + | 4.98722e11i | −1.09771 | + | 1.09771i | −0.103027 | + | 0.994679i | \(0.532853\pi\) |
−0.994679 | + | 0.103027i | \(0.967147\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.41917e11 | −0.527311 | −0.263656 | − | 0.964617i | \(-0.584928\pi\) | ||||
−0.263656 | + | 0.964617i | \(0.584928\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.36952e10i | 0.0727364i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −2.56152e11 | − | 2.56152e11i | −0.547615 | − | 0.547615i | 0.378135 | − | 0.925750i | \(-0.376565\pi\) |
−0.925750 | + | 0.378135i | \(0.876565\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.12961e11 | − | 5.12961e11i | −1.08609 | − | 1.08609i | −0.995927 | − | 0.0901650i | \(-0.971261\pi\) |
−0.0901650 | − | 0.995927i | \(-0.528739\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1.00171e10i | − | 0.0210057i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.16465e11 | 0.657272 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.62778e11 | − | 3.62778e11i | 0.746269 | − | 0.746269i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.42258e10 | − | 4.42258e10i | 0.0901101 | − | 0.0901101i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.60064e11 | 0.323032 | 0.161516 | − | 0.986870i | \(-0.448362\pi\) | ||||
0.161516 | + | 0.986870i | \(0.448362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.33294e11i | 0.666260i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −2.86413e11 | − | 2.86413e11i | −0.567129 | − | 0.567129i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.36076e11 | − | 4.36076e11i | −0.855333 | − | 0.855333i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.56250e11i | 0.497886i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.98218e11 | −0.573989 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.56639e11 | − | 1.56639e11i | 0.298664 | − | 0.298664i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.58588e10 | − | 9.58588e10i | 0.181066 | − | 0.181066i | −0.610754 | − | 0.791820i | \(-0.709134\pi\) |
0.791820 | + | 0.610754i | \(0.209134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.42277e11 | −0.453366 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 2.38708e11i | − | 0.442531i | −0.975214 | − | 0.221265i | \(-0.928981\pi\) | ||
0.975214 | − | 0.221265i | \(-0.0710187\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.68287e11 | + | 3.68287e11i | 0.676417 | + | 0.676417i | 0.959187 | − | 0.282771i | \(-0.0912536\pi\) |
−0.282771 | + | 0.959187i | \(0.591254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.62698e10 | + | 4.62698e10i | 0.0841948 | + | 0.0841948i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.95499e11i | 1.07359i | 0.843713 | + | 0.536794i | \(0.180365\pi\) | ||||
−0.843713 | + | 0.536794i | \(0.819635\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.62777e11 | 0.469378 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.20383e11 | + | 1.20383e11i | −0.213054 | + | 0.213054i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 3.20298e11 | − | 3.20298e11i | 0.561663 | − | 0.561663i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.80110e11 | 0.312944 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 2.76845e11i | − | 0.476629i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 3.06347e11 | + | 3.06347e11i | 0.522614 | + | 0.522614i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.72863e11 | + | 2.72863e11i | 0.461260 | + | 0.461260i | 0.899068 | − | 0.437808i | \(-0.144245\pi\) |
−0.437808 | + | 0.899068i | \(0.644245\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.86561e11i | 0.815046i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −4.80491e11 | −0.797594 | −0.398797 | − | 0.917039i | \(-0.630572\pi\) | ||||
−0.398797 | + | 0.917039i | \(0.630572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.86314e11 | − | 4.86314e11i | 0.799970 | − | 0.799970i | −0.183121 | − | 0.983090i | \(-0.558620\pi\) |
0.983090 | + | 0.183121i | \(0.0586199\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.41752e11 | − | 3.41752e11i | 0.557106 | − | 0.557106i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.96631e11 | 0.802304 | 0.401152 | − | 0.916011i | \(-0.368610\pi\) | ||||
0.401152 | + | 0.916011i | \(0.368610\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.54966e10i | 0.104860i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.58055e10 | + | 2.58055e10i | 0.0409451 | + | 0.0409451i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −4.14216e11 | − | 4.14216e11i | −0.651359 | − | 0.651359i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.92232e11i | 0.455445i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 6.64869e11 | 1.02699 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.94789e11 | + | 3.94789e11i | −0.604403 | + | 0.604403i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.26290e11 | + | 4.26290e11i | −0.646854 | + | 0.646854i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.91452e10 | 0.134075 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.39467e11i | 1.40051i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.21265e11 | + | 7.21265e11i | 1.06578 | + | 1.06578i | 0.997679 | + | 0.0680965i | \(0.0216926\pi\) |
0.0680965 | + | 0.997679i | \(0.478307\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.27268e10 | + | 4.27268e10i | 0.0625813 | + | 0.0625813i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.20871e12i | − | 1.75489i | −0.479679 | − | 0.877444i | \(-0.659247\pi\) | ||
0.479679 | − | 0.877444i | \(-0.340753\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.62548e11 | −0.953529 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.79453e11 | + | 3.79453e11i | −0.541345 | + | 0.541345i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.53483e11 | + | 2.53483e11i | −0.358485 | + | 0.358485i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.04154e11 | −0.566610 | −0.283305 | − | 0.959030i | \(-0.591431\pi\) | ||||
−0.283305 | + | 0.959030i | \(0.591431\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.61857e11i | 0.919868i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.52428e11 | + | 7.52428e11i | 1.03671 | + | 1.03671i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.59299e10 | − | 4.59299e10i | −0.0627377 | − | 0.0627377i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2.00309e11i | 0.271257i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.91794e11 | −0.526011 | −0.263005 | − | 0.964794i | \(-0.584714\pi\) | ||||
−0.263005 | + | 0.964794i | \(0.584714\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.42080e11 | − | 4.42080e11i | 0.588441 | − | 0.588441i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.08671e11 | − | 1.08671e11i | 0.143412 | − | 0.143412i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −4.27862e11 | −0.559831 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.60556e11i | − | 1.11640i | −0.829705 | − | 0.558201i | \(-0.811492\pi\) | ||
0.829705 | − | 0.558201i | \(-0.188508\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.45047e11 | − | 5.45047e11i | −0.701087 | − | 0.701087i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.22516e11 | − | 1.22516e11i | −0.156256 | − | 0.156256i | 0.624650 | − | 0.780905i | \(-0.285242\pi\) |
−0.780905 | + | 0.624650i | \(0.785242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.74574e11i | − | 0.347226i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.13502e10 | 0.114547 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −7.27477e11 | + | 7.27477e11i | −0.904523 | + | 0.904523i | −0.995823 | − | 0.0913008i | \(-0.970898\pi\) |
0.0913008 | + | 0.995823i | \(0.470898\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.44767e11 | + | 2.44767e11i | −0.301778 | + | 0.301778i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.38801e11 | 0.291954 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 8.98115e10i | − | 0.108883i | −0.998517 | − | 0.0544415i | \(-0.982662\pi\) | ||
0.998517 | − | 0.0544415i | \(-0.0173378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −6.83311e10 | − | 6.83311e10i | −0.0821495 | − | 0.0821495i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.30358e11 | − | 2.30358e11i | −0.274634 | − | 0.274634i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 2.23483e11i | − | 0.264223i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.78923e11 | 0.561529 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6.79491e10 | − | 6.79491e10i | 0.0790093 | − | 0.0790093i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.60787e11 | + | 5.60787e11i | −0.646679 | + | 0.646679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −8.82093e11 | −1.00881 | −0.504404 | − | 0.863468i | \(-0.668288\pi\) | ||||
−0.504404 | + | 0.863468i | \(0.668288\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 9.80811e11i | 1.11247i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −9.08166e10 | − | 9.08166e10i | −0.102162 | − | 0.102162i | 0.654178 | − | 0.756340i | \(-0.273015\pi\) |
−0.756340 | + | 0.654178i | \(0.773015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.59400e11 | + | 2.59400e11i | 0.289414 | + | 0.289414i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1.94953e11i | − | 0.215731i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.04854e11 | 0.444345 | 0.222172 | − | 0.975007i | \(-0.428685\pi\) | ||||
0.222172 | + | 0.975007i | \(0.428685\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.08081e11 | + | 4.08081e11i | −0.444238 | + | 0.444238i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.47349e11 | − | 3.47349e11i | 0.375051 | − | 0.375051i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.80835e11 | −0.407870 | −0.203935 | − | 0.978984i | \(-0.565373\pi\) | ||||
−0.203935 | + | 0.978984i | \(0.565373\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.48878e11i | − | 0.370620i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.56179e11 | + | 1.56179e11i | 0.164571 | + | 0.164571i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.64502e11 | − | 2.64502e11i | −0.276467 | − | 0.276467i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.19820e11i | 0.435280i | 0.976029 | + | 0.217640i | \(0.0698358\pi\) | ||||
−0.976029 | + | 0.217640i | \(0.930164\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.40241e11 | −0.349937 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.01030e11 | − | 2.01030e11i | 0.205102 | − | 0.205102i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.83409e11 | + | 4.83409e11i | −0.489254 | + | 0.489254i | −0.908071 | − | 0.418817i | \(-0.862445\pi\) |
0.418817 | + | 0.908071i | \(0.362445\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.03510e10 | −0.0706331 |
(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 | 192.9.l.a.175.5 | 64 | ||
4.3 | odd | 2 | 48.9.l.a.19.32 | ✓ | 64 | ||
16.5 | even | 4 | 48.9.l.a.43.32 | yes | 64 | ||
16.11 | odd | 4 | inner | 192.9.l.a.79.5 | 64 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.9.l.a.19.32 | ✓ | 64 | 4.3 | odd | 2 | ||
48.9.l.a.43.32 | yes | 64 | 16.5 | even | 4 | ||
192.9.l.a.79.5 | 64 | 16.11 | odd | 4 | inner | ||
192.9.l.a.175.5 | 64 | 1.1 | even | 1 | trivial |