Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,8,Mod(37,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.37");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.k (of order \(3\), degree \(2\), 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: | \(78.7210264220\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 89566 x^{14} - 207320 x^{13} + 5161603375 x^{12} - 17143558340 x^{11} + 178819626045814 x^{10} + \cdots + 34\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{13}\cdot 7^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 37.6 | ||
Root | \(62.2223 - 107.772i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.37 |
Dual form | 252.8.k.e.109.6 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 135.624 | − | 234.907i | 0.485223 | − | 0.840430i | −0.514633 | − | 0.857410i | \(-0.672072\pi\) |
0.999856 | + | 0.0169803i | \(0.00540526\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 87.0016 | + | 903.313i | 0.0958703 | + | 0.995394i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2753.41 | + | 4769.04i | 0.623729 | + | 1.08033i | 0.988785 | + | 0.149345i | \(0.0477164\pi\) |
−0.365056 | + | 0.930985i | \(0.618950\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8802.63 | 1.11125 | 0.555624 | − | 0.831434i | \(-0.312479\pi\) | ||||
0.555624 | + | 0.831434i | \(0.312479\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3420.94 | − | 5925.24i | −0.168878 | − | 0.292506i | 0.769147 | − | 0.639071i | \(-0.220681\pi\) |
−0.938026 | + | 0.346565i | \(0.887348\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13231.5 | − | 22917.6i | 0.442558 | − | 0.766533i | −0.555320 | − | 0.831636i | \(-0.687404\pi\) |
0.997879 | + | 0.0651034i | \(0.0207377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −41328.3 | + | 71582.8i | −0.708273 | + | 1.22676i | 0.257224 | + | 0.966352i | \(0.417192\pi\) |
−0.965497 | + | 0.260413i | \(0.916141\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2274.86 | + | 3940.17i | 0.0291182 | + | 0.0504342i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −233335. | −1.77659 | −0.888295 | − | 0.459274i | \(-0.848110\pi\) | ||||
−0.888295 | + | 0.459274i | \(0.848110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19823.7 | + | 34335.7i | 0.119514 | + | 0.207005i | 0.919575 | − | 0.392914i | \(-0.128533\pi\) |
−0.800061 | + | 0.599919i | \(0.795200\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 223994. | + | 102073.i | 0.883077 | + | 0.402415i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −115873. | + | 200699.i | −0.376078 | + | 0.651386i | −0.990488 | − | 0.137601i | \(-0.956061\pi\) |
0.614410 | + | 0.788987i | \(0.289394\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 403925. | 0.915287 | 0.457643 | − | 0.889136i | \(-0.348694\pi\) | ||||
0.457643 | + | 0.889136i | \(0.348694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −122932. | −0.235791 | −0.117895 | − | 0.993026i | \(-0.537615\pi\) | ||||
−0.117895 | + | 0.993026i | \(0.537615\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 52674.9 | − | 91235.6i | 0.0740050 | − | 0.128180i | −0.826648 | − | 0.562719i | \(-0.809755\pi\) |
0.900653 | + | 0.434539i | \(0.143089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −808404. | + | 157179.i | −0.981618 | + | 0.190857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −665248. | − | 1.15224e6i | −0.613788 | − | 1.06311i | −0.990596 | − | 0.136820i | \(-0.956312\pi\) |
0.376808 | − | 0.926291i | \(-0.377022\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.49371e6 | 1.21059 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 429413. | + | 743764.i | 0.272203 | + | 0.471469i | 0.969426 | − | 0.245385i | \(-0.0789145\pi\) |
−0.697223 | + | 0.716855i | \(0.745581\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 525507. | − | 910205.i | 0.296431 | − | 0.513434i | −0.678886 | − | 0.734244i | \(-0.737537\pi\) |
0.975317 | + | 0.220810i | \(0.0708701\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.19385e6 | − | 2.06780e6i | 0.539202 | − | 0.933926i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.21180e6 | + | 3.83096e6i | 0.898432 | + | 1.55613i | 0.829499 | + | 0.558508i | \(0.188626\pi\) |
0.0689321 | + | 0.997621i | \(0.478041\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −154446. | −0.0512121 | −0.0256060 | − | 0.999672i | \(-0.508152\pi\) | ||||
−0.0256060 | + | 0.999672i | \(0.508152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.07857e6 | + | 1.86813e6i | 0.324502 | + | 0.562054i | 0.981411 | − | 0.191916i | \(-0.0614700\pi\) |
−0.656910 | + | 0.753969i | \(0.728137\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.06838e6 | + | 2.90210e6i | −1.01556 | + | 0.724427i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −954414. | + | 1.65309e6i | −0.217792 | + | 0.377227i | −0.954133 | − | 0.299384i | \(-0.903219\pi\) |
0.736341 | + | 0.676611i | \(0.236552\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.56018e6 | 1.64327 | 0.821637 | − | 0.570012i | \(-0.193061\pi\) | ||||
0.821637 | + | 0.570012i | \(0.193061\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.85584e6 | −0.327774 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.54046e6 | + | 9.59637e6i | −0.833069 | + | 1.44292i | 0.0625233 | + | 0.998044i | \(0.480085\pi\) |
−0.895593 | + | 0.444875i | \(0.853248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 765843. | + | 7.95153e6i | 0.106536 | + | 1.10613i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.58900e6 | − | 6.21634e6i | −0.429478 | − | 0.743878i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.13502e6 | 0.126270 | 0.0631352 | − | 0.998005i | \(-0.479890\pi\) | ||||
0.0631352 | + | 0.998005i | \(0.479890\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.16132e6 | − | 7.20762e6i | −0.401889 | − | 0.696092i | 0.592065 | − | 0.805890i | \(-0.298313\pi\) |
−0.993954 | + | 0.109798i | \(0.964980\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.20374e6 | + | 9.01315e6i | −0.469230 | + | 0.812730i | −0.999381 | − | 0.0351731i | \(-0.988802\pi\) |
0.530151 | + | 0.847903i | \(0.322135\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −7.54590e6 | + | 1.30699e7i | −0.595481 | + | 1.03140i | 0.397998 | + | 0.917386i | \(0.369705\pi\) |
−0.993479 | + | 0.114017i | \(0.963628\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.33676e7 | + | 2.31534e7i | 0.988694 | + | 1.71247i | 0.624205 | + | 0.781261i | \(0.285423\pi\) |
0.364489 | + | 0.931208i | \(0.381244\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −54643.3 | −0.00356256 | −0.00178128 | − | 0.999998i | \(-0.500567\pi\) | ||||
−0.00178128 | + | 0.999998i | \(0.500567\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.12102e7 | + | 1.94167e7i | 0.687340 | + | 1.19051i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.05472e6 | − | 3.60568e6i | 0.274968 | − | 0.196143i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.41890e6 | + | 9.38582e6i | −0.278075 | + | 0.481641i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.24253e7 | 1.02696 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.99538e7 | 1.29760 | 0.648798 | − | 0.760961i | \(-0.275272\pi\) | ||||
0.648798 | + | 0.760961i | \(0.275272\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.29309e7 | − | 3.97174e7i | 0.891191 | − | 1.54359i | 0.0527416 | − | 0.998608i | \(-0.483204\pi\) |
0.838449 | − | 0.544980i | \(-0.183463\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.18529e7 | + | 9.95828e6i | 0.805431 | + | 0.367032i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.37558e7 | − | 2.38257e7i | −0.457049 | − | 0.791631i | 0.541755 | − | 0.840537i | \(-0.317760\pi\) |
−0.998803 | + | 0.0489051i | \(0.984427\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.41540e7 | 0.447021 | 0.223510 | − | 0.974702i | \(-0.428248\pi\) | ||||
0.223510 | + | 0.974702i | \(0.428248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.42372e7 | + | 4.19801e7i | 0.693117 | + | 1.20051i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.16458e7 | + | 5.48121e7i | −0.862041 | + | 1.49310i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.57625e7 | + | 2.73014e7i | −0.390367 | + | 0.676135i | −0.992498 | − | 0.122262i | \(-0.960985\pi\) |
0.602131 | + | 0.798397i | \(0.294319\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.45008e6 | − | 9.43982e6i | −0.128820 | − | 0.223123i | 0.794400 | − | 0.607396i | \(-0.207786\pi\) |
−0.923220 | + | 0.384272i | \(0.874452\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.07543e7 | 0.231964 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.48305e7 | + | 7.76486e7i | 0.924537 | + | 1.60135i | 0.792304 | + | 0.610127i | \(0.208881\pi\) |
0.132233 | + | 0.991219i | \(0.457785\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.82573e7 | − | 3.11046e7i | −1.28902 | − | 0.587400i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.56018e7 | + | 7.89846e7i | −0.824755 | + | 1.42852i | 0.0773509 | + | 0.997004i | \(0.475354\pi\) |
−0.902106 | + | 0.431514i | \(0.857980\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.72822e7 | −0.785579 | −0.392789 | − | 0.919628i | \(-0.628490\pi\) | ||||
−0.392789 | + | 0.919628i | \(0.628490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.47378e7 | 0.234872 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.07168e7 | − | 1.85621e7i | 0.157364 | − | 0.272562i | −0.776553 | − | 0.630051i | \(-0.783034\pi\) |
0.933917 | + | 0.357489i | \(0.116367\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.36129e6 | + | 2.39771e6i | −0.0474103 | + | 0.0338192i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.11093e7 | + | 3.65624e7i | 0.275099 | + | 0.476485i | 0.970160 | − | 0.242465i | \(-0.0779561\pi\) |
−0.695061 | + | 0.718951i | \(0.744623\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.62466e6 | 0.0579702 | 0.0289851 | − | 0.999580i | \(-0.490772\pi\) | ||||
0.0289851 | + | 0.999580i | \(0.490772\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.14304e7 | + | 5.44390e7i | 0.364963 | + | 0.632134i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.88385e7 | − | 3.26292e7i | 0.210669 | − | 0.364889i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.94101e7 | + | 1.54863e8i | −0.928474 | + | 1.60816i | −0.142597 | + | 0.989781i | \(0.545545\pi\) |
−0.785877 | + | 0.618383i | \(0.787788\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.05863e7 | + | 3.56566e7i | 0.206124 | + | 0.357017i | 0.950490 | − | 0.310754i | \(-0.100582\pi\) |
−0.744366 | + | 0.667771i | \(0.767248\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.97492e7 | 0.836370 | 0.418185 | − | 0.908362i | \(-0.362666\pi\) | ||||
0.418185 | + | 0.908362i | \(0.362666\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.51247e7 | − | 2.61968e7i | −0.136051 | − | 0.235647i | 0.789948 | − | 0.613174i | \(-0.210108\pi\) |
−0.925998 | + | 0.377527i | \(0.876774\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.03005e7 | − | 2.10775e8i | −0.170322 | − | 1.76841i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.47819e7 | − | 9.48850e7i | 0.444118 | − | 0.769235i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.45726e8 | 1.10415 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.15724e7 | 0.304661 | 0.152331 | − | 0.988330i | \(-0.451322\pi\) | ||||
0.152331 | + | 0.988330i | \(0.451322\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.66726e7 | + | 2.88777e7i | −0.114411 | + | 0.198166i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.92912e7 | + | 2.08943e7i | −0.194593 | + | 0.138809i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.01133e7 | − | 5.21577e7i | −0.187666 | − | 0.325047i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.48057e7 | 0.0894052 | 0.0447026 | − | 0.999000i | \(-0.485766\pi\) | ||||
0.0447026 | + | 0.999000i | \(0.485766\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −9.63163e7 | − | 1.66825e8i | −0.546524 | − | 0.946607i | −0.998509 | − | 0.0545820i | \(-0.982617\pi\) |
0.451985 | − | 0.892025i | \(-0.350716\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.58823e7 | − | 2.75090e7i | 0.0873956 | − | 0.151374i | −0.819014 | − | 0.573774i | \(-0.805479\pi\) |
0.906409 | + | 0.422400i | \(0.138812\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.65294e6 | + | 4.59502e6i | −0.0137398 | + | 0.0237981i | −0.872814 | − | 0.488054i | \(-0.837707\pi\) |
0.859074 | + | 0.511852i | \(0.171040\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.42879e7 | − | 2.47474e7i | −0.0718178 | − | 0.124392i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.84527e7 | −0.276957 | −0.138478 | − | 0.990365i | \(-0.544221\pi\) | ||||
−0.138478 | + | 0.990365i | \(0.544221\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.49460e8 | − | 2.58872e8i | −0.687803 | − | 1.19131i | −0.972547 | − | 0.232707i | \(-0.925242\pi\) |
0.284743 | − | 0.958604i | \(-0.408092\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.27163e7 | + | 2.11217e8i | −0.315901 | + | 0.917589i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.16472e8 | − | 2.01735e8i | 0.491792 | − | 0.851808i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.54841e8 | 1.01721 | 0.508606 | − | 0.860999i | \(-0.330161\pi\) | ||||
0.508606 | + | 0.860999i | \(0.330161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.55175e8 | −1.76708 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.67755e8 | − | 2.90560e8i | 0.616467 | − | 1.06775i | −0.373659 | − | 0.927566i | \(-0.621897\pi\) |
0.990125 | − | 0.140185i | \(-0.0447698\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.91375e8 | − | 8.72088e7i | −0.684440 | − | 0.311897i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.52202e8 | − | 2.63622e8i | −0.515912 | − | 0.893585i | −0.999829 | − | 0.0184718i | \(-0.994120\pi\) |
0.483918 | − | 0.875114i | \(-0.339213\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.60894e8 | −1.19129 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.75579e8 | + | 4.77317e8i | 0.863204 | + | 1.49511i | 0.868819 | + | 0.495129i | \(0.164879\pi\) |
−0.00561523 | + | 0.999984i | \(0.501787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.05360e8 | − | 5.28899e8i | 0.932008 | − | 1.61429i | 0.152124 | − | 0.988361i | \(-0.451389\pi\) |
0.779884 | − | 0.625924i | \(-0.215278\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.25272e7 | + | 2.16978e7i | −0.0363237 | + | 0.0629146i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.96395e7 | − | 1.55260e8i | −0.253408 | − | 0.438915i | 0.711054 | − | 0.703137i | \(-0.248218\pi\) |
−0.964462 | + | 0.264222i | \(0.914885\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.22014e8 | −0.328048 | −0.164024 | − | 0.986456i | \(-0.552447\pi\) | ||||
−0.164024 | + | 0.986456i | \(0.552447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.24497e8 | − | 2.15635e8i | −0.326518 | − | 0.565546i | 0.655300 | − | 0.755368i | \(-0.272542\pi\) |
−0.981818 | + | 0.189823i | \(0.939209\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.51421e7 | + | 3.64871e8i | 0.0877488 | + | 0.911071i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.81764e8 | − | 3.14824e8i | 0.442960 | − | 0.767229i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4.74504e8 | −1.10205 | −0.551027 | − | 0.834487i | \(-0.685764\pi\) | ||||
−0.551027 | + | 0.834487i | \(0.685764\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.32954e8 | 0.528316 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.63798e8 | + | 6.30117e8i | −0.787067 | + | 1.36324i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.06953e7 | − | 1.11046e8i | −0.0226053 | − | 0.234705i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.42543e8 | − | 2.46891e8i | −0.287670 | − | 0.498260i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 3.83066e8 | 0.755595 | 0.377798 | − | 0.925888i | \(-0.376682\pi\) | ||||
0.377798 | + | 0.925888i | \(0.376682\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.36877e8 | − | 4.10282e8i | −0.446540 | − | 0.773431i | 0.551618 | − | 0.834097i | \(-0.314011\pi\) |
−0.998158 | + | 0.0606664i | \(0.980677\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.10694e8 | + | 1.91728e8i | −0.204042 | + | 0.353411i | −0.949827 | − | 0.312776i | \(-0.898741\pi\) |
0.745785 | + | 0.666187i | \(0.232075\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.36623e8 | − | 4.09843e8i | 0.417205 | − | 0.722620i | −0.578452 | − | 0.815716i | \(-0.696343\pi\) |
0.995657 | + | 0.0930963i | \(0.0296764\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.42466e8 | − | 1.11278e9i | −1.10811 | − | 1.91930i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.81056e8 | −0.298954 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.00248e7 | + | 3.46839e7i | 0.0323575 | + | 0.0560449i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 8.69970e7 | + | 3.96442e7i | 0.134685 | + | 0.0613754i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.58900e7 | + | 7.94838e7i | −0.0695537 | + | 0.120471i | −0.898705 | − | 0.438554i | \(-0.855491\pi\) |
0.829151 | + | 0.559024i | \(0.188824\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.19989e9 | 1.74376 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.12466e8 | 0.587061 | 0.293530 | − | 0.955950i | \(-0.405170\pi\) | ||||
0.293530 | + | 0.955950i | \(0.405170\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.09166e8 | + | 1.89080e8i | −0.149089 | + | 0.258230i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.12315e8 | − | 7.16567e8i | −0.284086 | − | 0.958799i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.94162e8 | + | 8.55913e8i | 0.634916 | + | 1.09971i | 0.986533 | + | 0.163562i | \(0.0522985\pi\) |
−0.351617 | + | 0.936144i | \(0.614368\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.13371e9 | −1.42762 | −0.713812 | − | 0.700337i | \(-0.753033\pi\) | ||||
−0.713812 | + | 0.700337i | \(0.753033\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.88180e8 | − | 1.01876e9i | −0.711703 | − | 1.23271i | −0.964217 | − | 0.265113i | \(-0.914591\pi\) |
0.252514 | − | 0.967593i | \(-0.418743\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.09466e7 | + | 3.62805e7i | −0.0248493 | + | 0.0430402i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.65381e8 | − | 6.32858e8i | 0.416788 | − | 0.721898i | −0.578827 | − | 0.815451i | \(-0.696489\pi\) |
0.995614 | + | 0.0935532i | \(0.0298225\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.67926e7 | + | 1.67650e8i | 0.108285 | + | 0.187555i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.85118e8 | 0.629822 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.06230e8 | + | 5.30405e8i | 0.323382 | + | 0.560114i | 0.981184 | − | 0.193077i | \(-0.0618468\pi\) |
−0.657802 | + | 0.753191i | \(0.728513\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.82959e8 | − | 7.01174e8i | 0.999371 | − | 0.712882i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.75024e8 | + | 4.76356e8i | −0.274404 | + | 0.475281i | −0.969985 | − | 0.243167i | \(-0.921814\pi\) |
0.695581 | + | 0.718448i | \(0.255147\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.05396e9 | −1.97423 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.77173e8 | 0.167171 | 0.0835853 | − | 0.996501i | \(-0.473363\pi\) | ||||
0.0835853 | + | 0.996501i | \(0.473363\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.41656e8 | − | 2.45356e8i | 0.128837 | − | 0.223152i | −0.794389 | − | 0.607409i | \(-0.792209\pi\) |
0.923226 | + | 0.384257i | \(0.125542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.29955e8 | + | 1.34929e9i | 0.116060 | + | 1.20501i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.25354e8 | + | 1.25635e9i | 0.624779 | + | 1.08215i | 0.988584 | + | 0.150673i | \(0.0481442\pi\) |
−0.363805 | + | 0.931475i | \(0.618523\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.65527e8 | 0.478448 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.58882e8 | + | 4.48398e8i | 0.211355 | + | 0.366078i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.93238e8 | + | 1.02752e9i | −0.475842 | + | 0.824182i | −0.999617 | − | 0.0276745i | \(-0.991190\pi\) |
0.523775 | + | 0.851856i | \(0.324523\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.92674e8 | − | 5.06926e8i | 0.226662 | − | 0.392590i | −0.730155 | − | 0.683282i | \(-0.760552\pi\) |
0.956817 | + | 0.290692i | \(0.0938854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.74501e8 | + | 3.02245e8i | 0.132810 | + | 0.230034i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.27619e9 | −0.938283 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.05156e9 | + | 1.82135e9i | 0.759978 | + | 1.31632i | 0.942861 | + | 0.333187i | \(0.108124\pi\) |
−0.182882 | + | 0.983135i | \(0.558543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.34492e8 | + | 4.52603e8i | −0.443201 | + | 0.316149i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.16096e9 | − | 2.01085e9i | 0.797353 | − | 1.38106i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.71830e9 | −1.80530 | −0.902648 | − | 0.430380i | \(-0.858380\pi\) | ||||
−0.902648 | + | 0.430380i | \(0.858380\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.29822e8 | 0.346053 | 0.173027 | − | 0.984917i | \(-0.444645\pi\) | ||||
0.173027 | + | 0.984917i | \(0.444645\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.55643e7 | − | 2.69582e7i | 0.00983488 | − | 0.0170345i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.67919e8 | + | 3.95508e8i | 0.539488 | + | 0.245843i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.01224e8 | + | 1.75325e8i | 0.0608995 | + | 0.105481i | 0.894868 | − | 0.446331i | \(-0.147270\pi\) |
−0.833968 | + | 0.551812i | \(0.813936\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.56435e8 | −0.388584 | −0.194292 | − | 0.980944i | \(-0.562241\pi\) | ||||
−0.194292 | + | 0.980944i | \(0.562241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.09367e9 | + | 1.89429e9i | 0.626904 | + | 1.08583i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.19575e8 | − | 7.26724e8i | 0.236692 | − | 0.409962i | −0.723071 | − | 0.690774i | \(-0.757270\pi\) |
0.959763 | + | 0.280811i | \(0.0906035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.11299e7 | + | 1.05880e8i | −0.0334072 | + | 0.0578630i | −0.882246 | − | 0.470789i | \(-0.843969\pi\) |
0.848838 | + | 0.528652i | \(0.177303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.50284e9 | + | 2.60299e9i | 0.808448 | + | 1.40027i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.95736e9 | 1.02049 | 0.510244 | − | 0.860030i | \(-0.329555\pi\) | ||||
0.510244 | + | 0.860030i | \(0.329555\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.11217e9 | + | 1.92633e9i | 0.570891 | + | 0.988812i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97174e9 | + | 8.98515e8i | 0.981318 | + | 0.447183i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.37930e9 | + | 2.38901e9i | −0.676007 | + | 1.17088i | 0.300167 | + | 0.953887i | \(0.402958\pi\) |
−0.976174 | + | 0.216991i | \(0.930376\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.05133e9 | −0.499788 | −0.249894 | − | 0.968273i | \(-0.580396\pi\) | ||||
−0.249894 | + | 0.968273i | \(0.580396\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.67036e9 | 0.782127 | 0.391063 | − | 0.920364i | \(-0.372107\pi\) | ||||
0.391063 | + | 0.920364i | \(0.372107\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.73863e8 | − | 1.51357e9i | 0.397040 | − | 0.687693i | −0.596319 | − | 0.802747i | \(-0.703371\pi\) |
0.993359 | + | 0.115054i | \(0.0367041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.26812e9 | + | 2.33125e9i | −1.46283 | + | 1.04348i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.38483e8 | − | 5.86269e8i | −0.147070 | − | 0.254732i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.20399e8 | 0.0515460 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −9.61974e8 | − | 1.66619e9i | −0.399935 | − | 0.692707i | 0.593783 | − | 0.804625i | \(-0.297634\pi\) |
−0.993717 | + | 0.111918i | \(0.964301\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.01999e9 | + | 1.76668e9i | −0.417916 | + | 0.723851i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.53935e8 | − | 2.66624e8i | 0.0612692 | − | 0.106121i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.71220e9 | + | 2.96562e9i | 0.671743 | + | 1.16349i | 0.977409 | + | 0.211355i | \(0.0677875\pi\) |
−0.305666 | + | 0.952139i | \(0.598879\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.92888e9 | −1.11665 | −0.558325 | − | 0.829622i | \(-0.688556\pi\) | ||||
−0.558325 | + | 0.829622i | \(0.688556\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.98225e8 | + | 1.38257e9i | 0.300028 | + | 0.519663i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.34370e7 | − | 1.39513e8i | −0.00490972 | − | 0.0509762i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.54754e9 | − | 2.68042e9i | 0.557559 | − | 0.965721i | −0.440140 | − | 0.897929i | \(-0.645071\pi\) |
0.997699 | − | 0.0677918i | \(-0.0215953\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.54605e9 | 0.892029 | 0.446014 | − | 0.895026i | \(-0.352843\pi\) | ||||
0.446014 | + | 0.895026i | \(0.352843\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.25750e9 | −0.780023 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1.01304e8 | + | 1.75463e8i | −0.0340496 | + | 0.0589757i | −0.882548 | − | 0.470222i | \(-0.844174\pi\) |
0.848498 | + | 0.529198i | \(0.177507\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.59367e9 | + | 1.13681e9i | −0.528355 | + | 0.376891i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.41150e9 | + | 2.44480e9i | 0.455362 | + | 0.788710i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.80141e8 | 0.184636 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.74740e9 | − | 4.75864e9i | −0.851119 | − | 1.47418i | −0.880199 | − | 0.474604i | \(-0.842591\pi\) |
0.0290803 | − | 0.999577i | \(-0.490742\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.84283e9 | − | 3.19187e9i | 0.563286 | − | 0.975640i | −0.433921 | − | 0.900951i | \(-0.642870\pi\) |
0.997207 | − | 0.0746890i | \(-0.0237964\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.35632e8 | − | 2.34921e8i | 0.0403668 | − | 0.0699173i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.71365e9 | − | 2.96813e9i | −0.503301 | − | 0.871743i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.55560e9 | 1.01711 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.04681e9 | + | 3.54518e9i | 0.577882 | + | 1.00092i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.97546e9 | − | 3.42253e9i | −0.818452 | − | 0.941428i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.06594e8 | + | 1.22386e9i | −0.191858 | + | 0.332308i | −0.945866 | − | 0.324557i | \(-0.894785\pi\) |
0.754008 | + | 0.656865i | \(0.228118\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 7.25188e9 | 1.91895 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.40167e9 | 1.41115 | 0.705574 | − | 0.708637i | \(-0.250689\pi\) | ||||
0.705574 | + | 0.708637i | \(0.250689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.08736e9 | + | 5.34747e9i | −0.786244 | + | 1.36181i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.57630e9 | − | 7.18312e8i | −0.396369 | − | 0.180624i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.85131e9 | − | 4.93861e9i | −0.699118 | − | 1.21091i | −0.968772 | − | 0.247951i | \(-0.920243\pi\) |
0.269654 | − | 0.962957i | \(-0.413091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.08213e9 | −0.262022 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.78880e9 | + | 4.83035e9i | 0.658626 | + | 1.14077i | 0.980972 | + | 0.194151i | \(0.0621952\pi\) |
−0.322346 | + | 0.946622i | \(0.604471\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.41094e6 | + | 1.28361e7i | −0.00172864 | + | 0.00299408i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.19424e9 | + | 2.06848e9i | −0.271767 | + | 0.470714i | −0.969314 | − | 0.245824i | \(-0.920941\pi\) |
0.697547 | + | 0.716539i | \(0.254275\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.78817e9 | − | 4.82925e9i | −0.626747 | − | 1.08556i | −0.988200 | − | 0.153168i | \(-0.951053\pi\) |
0.361453 | − | 0.932390i | \(-0.382281\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.76065e8 | −0.0824946 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.88721e9 | + | 6.73285e9i | 0.842409 | + | 1.45909i | 0.887853 | + | 0.460128i | \(0.152196\pi\) |
−0.0454440 | + | 0.998967i | \(0.514470\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.44750e8 | + | 7.73252e9i | 0.157541 | + | 1.63570i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.66340e9 | − | 6.34519e9i | 0.765675 | − | 1.32619i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.89217e8 | −0.120238 | −0.0601190 | − | 0.998191i | \(-0.519148\pi\) | ||||
−0.0601190 | + | 0.998191i | \(0.519148\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.04919e9 | 0.211568 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −8.58290e8 | + | 1.48660e9i | −0.169022 | + | 0.292754i | −0.938076 | − | 0.346429i | \(-0.887394\pi\) |
0.769054 | + | 0.639183i | \(0.220727\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.61461e8 | − | 1.67641e9i | −0.0314238 | − | 0.326265i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.84213e9 | − | 6.65477e9i | −0.730430 | − | 1.26514i | −0.956700 | − | 0.291076i | \(-0.905987\pi\) |
0.226270 | − | 0.974065i | \(-0.427347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.01577e10 | −1.90869 | −0.954344 | − | 0.298709i | \(-0.903444\pi\) | ||||
−0.954344 | + | 0.298709i | \(0.903444\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.46986e9 | + | 2.54588e9i | 0.269857 | + | 0.467406i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.12929e9 | − | 1.95598e9i | 0.204948 | − | 0.354981i | −0.745168 | − | 0.666877i | \(-0.767631\pi\) |
0.950116 | + | 0.311896i | \(0.100964\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.63678e8 | − | 8.03113e8i | 0.0822379 | − | 0.142440i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.16951e9 | − | 5.48975e9i | −0.555752 | − | 0.962590i | −0.997845 | − | 0.0656207i | \(-0.979097\pi\) |
0.442093 | − | 0.896969i | \(-0.354236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.51460e9 | −1.11658 | −0.558290 | − | 0.829646i | \(-0.688542\pi\) | ||||
−0.558290 | + | 0.829646i | \(0.688542\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.99392e9 | − | 8.64972e9i | −0.846299 | − | 1.46583i | −0.884488 | − | 0.466563i | \(-0.845492\pi\) |
0.0381887 | − | 0.999271i | \(-0.487841\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.15055e9 | − | 4.16987e9i | −1.51614 | − | 0.690899i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.86368e9 | − | 4.96005e9i | 0.469186 | − | 0.812654i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.58558e9 | 0.254046 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.90293e8 | −0.109378 | −0.0546891 | − | 0.998503i | \(-0.517417\pi\) | ||||
−0.0546891 | + | 0.998503i | \(0.517417\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.06245e9 | − | 7.03637e9i | 0.629622 | − | 1.09054i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.11609e9 | + | 1.38359e9i | −1.09082 | + | 0.212090i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.03158e8 | + | 6.98291e8i | 0.0604606 | + | 0.104721i | 0.894671 | − | 0.446725i | \(-0.147410\pi\) |
−0.834211 | + | 0.551446i | \(0.814076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.24540e9 | −1.07479 | −0.537395 | − | 0.843331i | \(-0.680592\pi\) | ||||
−0.537395 | + | 0.843331i | \(0.680592\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 5.06148e9 | + | 8.76675e9i | 0.734705 | + | 1.27255i | 0.954853 | + | 0.297079i | \(0.0960126\pi\) |
−0.220148 | + | 0.975466i | \(0.570654\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.36469e9 | + | 4.09577e9i | −0.339562 | + | 0.588138i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −5.23757e9 | + | 9.07174e9i | −0.736095 | + | 1.27495i | 0.218146 | + | 0.975916i | \(0.429999\pi\) |
−0.954241 | + | 0.299038i | \(0.903334\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.21994e9 | − | 1.07733e10i | −0.864852 | − | 1.49797i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.86587e9 | 0.798424 | 0.399212 | − | 0.916859i | \(-0.369284\pi\) | ||||
0.399212 | + | 0.916859i | \(0.369284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.88047e9 | + | 6.72116e9i | 0.522611 | + | 0.905189i | 0.999654 | + | 0.0263091i | \(0.00837541\pi\) |
−0.477043 | + | 0.878880i | \(0.658291\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.30305e9 | − | 3.78282e9i | 0.699278 | − | 0.498816i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.64335e9 | − | 1.67028e10i | 1.25831 | − | 2.17946i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.78774e9 | 0.739571 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.37850e9 | 0.427239 | 0.213620 | − | 0.976917i | \(-0.431475\pi\) | ||||
0.213620 | + | 0.976917i | \(0.431475\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7.21681e9 | − | 1.24999e10i | 0.893891 | − | 1.54827i | 0.0587208 | − | 0.998274i | \(-0.481298\pi\) |
0.835171 | − | 0.549991i | \(-0.185369\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.87483e7 | + | 1.02528e9i | 0.0121056 | + | 0.125689i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49427e9 | + | 2.58816e9i | 0.179456 | + | 0.310827i | 0.941694 | − | 0.336470i | \(-0.109233\pi\) |
−0.762238 | + | 0.647296i | \(0.775900\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.46243e9 | −0.887081 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.85594e9 | − | 1.01428e10i | −0.682070 | − | 1.18138i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.72440e9 | − | 9.91495e9i | 0.660019 | − | 1.14319i | −0.320591 | − | 0.947218i | \(-0.603881\pi\) |
0.980610 | − | 0.195969i | \(-0.0627852\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.91962e9 | − | 3.32488e9i | 0.216904 | − | 0.375690i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38180e9 | − | 2.39335e9i | −0.154572 | − | 0.267727i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.77015e9 | 0.303732 | 0.151866 | − | 0.988401i | \(-0.451472\pi\) | ||||
0.151866 | + | 0.988401i | \(0.451472\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.06635e9 | + | 5.31107e9i | 0.332873 | + | 0.576552i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.14869e9 | − | 4.38605e9i | 0.654357 | − | 0.466773i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9.01249e8 | − | 1.56101e9i | 0.0949692 | − | 0.164492i | −0.814627 | − | 0.579986i | \(-0.803058\pi\) |
0.909596 | + | 0.415494i | \(0.136391\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.27713e9 | −0.338595 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.31486e10 | 1.34526 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.56454e9 | + | 7.90602e9i | −0.457979 | + | 0.793244i | −0.998854 | − | 0.0478595i | \(-0.984760\pi\) |
0.540875 | + | 0.841103i | \(0.318093\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.59442e9 | − | 3.91645e9i | −0.853972 | − | 0.389152i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.30805e8 | − | 9.19381e8i | −0.0517311 | − | 0.0896009i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.21081e10 | −1.16871 | −0.584354 | − | 0.811499i | \(-0.698652\pi\) | ||||
−0.584354 | + | 0.811499i | \(0.698652\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.20544e8 | + | 7.28404e8i | 0.0398200 | + | 0.0689702i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.82100e9 | − | 1.18143e10i | 0.639711 | − | 1.10801i | −0.345785 | − | 0.938314i | \(-0.612387\pi\) |
0.985496 | − | 0.169699i | \(-0.0542795\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.21800e10 | + | 2.10964e10i | −1.12076 | + | 1.94121i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.37583e9 | − | 4.11506e9i | −0.216551 | − | 0.375077i | 0.737200 | − | 0.675674i | \(-0.236147\pi\) |
−0.953751 | + | 0.300597i | \(0.902814\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.47115e9 | −0.399907 | −0.199953 | − | 0.979805i | \(-0.564079\pi\) | ||||
−0.199953 | + | 0.979805i | \(0.564079\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.27554e9 | + | 7.40545e9i | 0.378830 | + | 0.656152i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.24627e10 | − | 5.67921e9i | −1.08374 | − | 0.493857i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.08632e9 | − | 1.22739e10i | 0.610494 | − | 1.05741i | −0.380663 | − | 0.924714i | \(-0.624304\pi\) |
0.991157 | − | 0.132693i | \(-0.0423623\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.95664e9 | −0.250026 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.37310e10 | −1.15045 | −0.575223 | − | 0.817997i | \(-0.695085\pi\) | ||||
−0.575223 | + | 0.817997i | \(0.695085\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.17090e8 | + | 5.49216e8i | −0.0260817 | + | 0.0451749i | −0.878772 | − | 0.477242i | \(-0.841636\pi\) |
0.852690 | + | 0.522417i | \(0.174970\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.97518e10 | + | 1.40895e10i | −1.60979 | + | 1.14831i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.77996e9 | + | 6.54709e9i | 0.302485 | + | 0.523919i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.38079e9 | 0.664573 | 0.332287 | − | 0.943178i | \(-0.392180\pi\) | ||||
0.332287 | + | 0.943178i | \(0.392180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.91233e9 | − | 6.77635e9i | −0.304654 | − | 0.527676i | 0.672530 | − | 0.740070i | \(-0.265207\pi\) |
−0.977184 | + | 0.212393i | \(0.931874\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.01925e7 | + | 1.56218e8i | −0.00696008 | + | 0.0120552i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.34452e9 | − | 9.25698e9i | 0.405068 | − | 0.701598i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.25252e8 | − | 7.36559e8i | −0.0319425 | − | 0.0553260i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.43203e10 | 1.79443 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.28524e10 | + | 2.22609e10i | 0.939878 | + | 1.62792i | 0.765696 | + | 0.643202i | \(0.222395\pi\) |
0.174181 | + | 0.984714i | \(0.444272\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.75406e6 | − | 4.93600e7i | −0.000341544 | − | 0.00354615i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.62585e9 | − | 8.01220e9i | 0.329409 | − | 0.570552i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.31351e10 | −1.61870 | −0.809352 | − | 0.587324i | \(-0.800182\pi\) | ||||
−0.809352 | + | 0.587324i | \(0.800182\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.20790e8 | −0.0499914 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.93947e9 | + | 1.02875e10i | −0.404802 | + | 0.701138i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.65640e10 | + | 1.18156e10i | −1.11913 | + | 0.798308i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.55541e9 | + | 1.65504e10i | 0.634497 | + | 1.09898i | 0.986622 | + | 0.163027i | \(0.0521259\pi\) |
−0.352125 | + | 0.935953i | \(0.614541\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.86864e9 | −0.188844 | −0.0944219 | − | 0.995532i | \(-0.530100\pi\) | ||||
−0.0944219 | + | 0.995532i | \(0.530100\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.23694e10 | + | 2.14244e10i | 0.800380 | + | 1.38630i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.62658e9 | + | 2.81731e9i | −0.104351 | + | 0.180741i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.05325e10 | − | 1.82429e10i | 0.664250 | − | 1.15051i | −0.315239 | − | 0.949012i | \(-0.602085\pi\) |
0.979488 | − | 0.201502i | \(-0.0645821\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.06065e10 | + | 1.83710e10i | 0.663243 | + | 1.14877i | 0.979758 | + | 0.200184i | \(0.0641539\pi\) |
−0.316515 | + | 0.948588i | \(0.602513\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.41630e10 | −0.870735 | −0.435368 | − | 0.900253i | \(-0.643382\pi\) | ||||
−0.435368 | + | 0.900253i | \(0.643382\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.10354e10 | + | 1.91138e10i | 0.672738 | + | 1.16522i | 0.977125 | + | 0.212667i | \(0.0682150\pi\) |
−0.304387 | + | 0.952548i | \(0.598452\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.69683e9 | + | 4.25229e9i | 0.221601 | + | 0.254897i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.41259e9 | + | 1.11069e10i | −0.381180 | + | 0.660224i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.97333e8 | 0.0115354 | 0.00576771 | − | 0.999983i | \(-0.498164\pi\) | ||||
0.00576771 | + | 0.999983i | \(0.498164\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.71954e10 | 2.15627 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.99880e9 | − | 3.46203e9i | 0.113965 | − | 0.197393i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.94978e9 | − | 4.07838e9i | −0.506081 | − | 0.230620i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.57771e9 | − | 1.65891e10i | −0.532732 | − | 0.922718i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.85016e10 | −1.57234 | −0.786171 | − | 0.618009i | \(-0.787940\pi\) | ||||
−0.786171 | + | 0.618009i | \(0.787940\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −8.52798e9 | − | 1.47709e10i | −0.462821 | − | 0.801630i | 0.536279 | − | 0.844041i | \(-0.319830\pi\) |
−0.999100 | + | 0.0424108i | \(0.986496\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.70608e8 | − | 6.41913e8i | 0.0199498 | − | 0.0345541i | −0.855878 | − | 0.517178i | \(-0.826983\pi\) |
0.875828 | + | 0.482623i | \(0.160316\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.07828e10 | − | 1.86764e10i | 0.571078 | − | 0.989136i | −0.425378 | − | 0.905016i | \(-0.639859\pi\) |
0.996456 | − | 0.0841198i | \(-0.0268078\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.90691e9 | − | 5.03492e9i | −0.152713 | − | 0.264506i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.05116e10 | −0.543373 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.94697e10 | + | 3.37225e10i | 0.998380 | + | 1.72924i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.95104e9 | + | 2.02571e10i | 0.0984550 | + | 1.02223i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.91711e10 | − | 3.32053e10i | 0.959728 | − | 1.66230i | 0.236570 | − | 0.971614i | \(-0.423977\pi\) |
0.723158 | − | 0.690683i | \(-0.242690\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.03208e10 | 1.00121 | 0.500605 | − | 0.865676i | \(-0.333111\pi\) | ||||
0.500605 | + | 0.865676i | \(0.333111\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.54529e10 | 1.24415 | 0.622077 | − | 0.782956i | \(-0.286289\pi\) | ||||
0.622077 | + | 0.782956i | \(0.286289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.37821e10 | − | 2.38713e10i | 0.663105 | − | 1.14853i | −0.316691 | − | 0.948529i | \(-0.602572\pi\) |
0.979795 | − | 0.200002i | \(-0.0640950\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.60603e9 | + | 2.70577e10i | 0.124401 | + | 1.29162i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.39393e9 | − | 2.41436e9i | −0.0655030 | − | 0.113455i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.14517e10 | 0.533937 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −4.62557e9 | − | 8.01173e9i | −0.212328 | − | 0.367762i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.55155e9 | + | 7.88352e9i | −0.207311 | + | 0.359073i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.27214e8 | − | 1.08637e9i | 0.0281284 | − | 0.0487199i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.18519e9 | − | 7.24896e9i | −0.186247 | − | 0.322589i | 0.757749 | − | 0.652546i | \(-0.226299\pi\) |
−0.943996 | + | 0.329957i | \(0.892966\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.69466e10 | −1.61905 | −0.809526 | − | 0.587085i | \(-0.800276\pi\) | ||||
−0.809526 | + | 0.587085i | \(0.800276\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.35697e10 | + | 4.08238e10i | 1.02496 | + | 1.77528i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.78723e10 | + | 1.72583e10i | 1.62192 | + | 0.739102i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.32414e9 | − | 4.02553e9i | 0.0987774 | − | 0.171087i | −0.812401 | − | 0.583099i | \(-0.801840\pi\) |
0.911179 | + | 0.412011i | \(0.135173\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.35953e9 | −0.0569093 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.05438e9 | −0.0438029 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.94340e10 | + | 3.36606e10i | −0.795256 | + | 1.37742i | 0.127421 | + | 0.991849i | \(0.459330\pi\) |
−0.922677 | + | 0.385575i | \(0.874003\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.09421e9 | + | 2.06064e10i | −0.288124 | + | 0.836908i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.10989e9 | − | 8.85059e9i | −0.204442 | − | 0.354105i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.56802e10 | −1.41690 | −0.708448 | − | 0.705763i | \(-0.750604\pi\) | ||||
−0.708448 | + | 0.705763i | \(0.750604\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.53266e9 | − | 6.11875e9i | −0.138210 | − | 0.239386i | 0.788609 | − | 0.614895i | \(-0.210801\pi\) |
−0.926819 | + | 0.375508i | \(0.877468\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.66936e10 | + | 2.89141e10i | −0.648273 | + | 1.12284i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.83189e9 | − | 1.01011e10i | 0.223144 | − | 0.386496i | −0.732617 | − | 0.680641i | \(-0.761701\pi\) |
0.955761 | + | 0.294145i | \(0.0950347\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.49423e9 | + | 1.64445e10i | 0.360602 | + | 0.624581i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.29165e10 | 0.857675 | 0.428837 | − | 0.903382i | \(-0.358923\pi\) | ||||
0.428837 | + | 0.903382i | \(0.358923\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.42523e10 | + | 4.20062e10i | 0.901033 | + | 1.56063i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.03253e10 | − | 1.44986e10i | 0.744168 | − | 0.530837i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.29703e10 | − | 2.24653e10i | 0.471433 | − | 0.816545i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.11680e10 | 0.400064 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.42924e9 | 0.0863928 | 0.0431964 | − | 0.999067i | \(-0.486246\pi\) | ||||
0.0431964 | + | 0.999067i | \(0.486246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.48392e10 | + | 4.30227e10i | −0.870703 | + | 1.50810i | −0.00943237 | + | 0.999956i | \(0.503002\pi\) |
−0.861271 | + | 0.508146i | \(0.830331\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.23142e9 | + | 1.27855e10i | 0.0428560 | + | 0.444962i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.26462e9 | + | 1.43147e10i | 0.283525 | + | 0.491080i | 0.972250 | − | 0.233942i | \(-0.0751627\pi\) |
−0.688725 | + | 0.725022i | \(0.741829\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.10206e10 | −2.07844 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.02453e10 | − | 1.77454e10i | −0.344023 | − | 0.595864i | 0.641153 | − | 0.767413i | \(-0.278456\pi\) |
−0.985176 | + | 0.171548i | \(0.945123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.21721e10 | − | 2.10827e10i | 0.405826 | − | 0.702911i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.08059e9 | − | 8.79985e9i | 0.167004 | − | 0.289260i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.87248e10 | − | 3.24322e10i | −0.611165 | − | 1.05857i | −0.991044 | − | 0.133533i | \(-0.957368\pi\) |
0.379879 | − | 0.925036i | \(-0.375966\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.20508e9 | −0.264060 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.57909e9 | − | 2.73507e9i | −0.0504632 | − | 0.0874049i | 0.839690 | − | 0.543065i | \(-0.182736\pi\) |
−0.890154 | + | 0.455661i | \(0.849403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 252.8.k.e.37.6 | yes | 16 | |
3.2 | odd | 2 | inner | 252.8.k.e.37.3 | ✓ | 16 | |
7.4 | even | 3 | inner | 252.8.k.e.109.6 | yes | 16 | |
21.11 | odd | 6 | inner | 252.8.k.e.109.3 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.8.k.e.37.3 | ✓ | 16 | 3.2 | odd | 2 | inner | |
252.8.k.e.37.6 | yes | 16 | 1.1 | even | 1 | trivial | |
252.8.k.e.109.3 | yes | 16 | 21.11 | odd | 6 | inner | |
252.8.k.e.109.6 | yes | 16 | 7.4 | even | 3 | inner |