Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(73,252)]
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, 1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.73");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.z (of order \(6\), 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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - x^{9} + 1442 x^{8} + 59551 x^{7} + 2229058 x^{6} + 41253567 x^{5} + 582209889 x^{4} + \cdots + 63214027776 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{9}\cdot 7^{6} \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 145.3 | ||
Root | \(23.4172 - 40.5598i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.145 |
Dual form | 252.9.z.c.73.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
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 | ||||||||
\(5\) | −327.308 | − | 188.971i | −0.523693 | − | 0.302354i | 0.214751 | − | 0.976669i | \(-0.431106\pi\) |
−0.738444 | + | 0.674314i | \(0.764439\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −894.589 | + | 2228.12i | −0.372590 | + | 0.927996i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9669.77 | + | 16748.5i | 0.660459 | + | 1.14395i | 0.980495 | + | 0.196543i | \(0.0629714\pi\) |
−0.320037 | + | 0.947405i | \(0.603695\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 48446.7i | − | 1.69625i | −0.529793 | − | 0.848127i | \(-0.677731\pi\) | ||
0.529793 | − | 0.848127i | \(-0.322269\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4752.58 | + | 2743.90i | −0.0569028 | + | 0.0328529i | −0.528182 | − | 0.849131i | \(-0.677126\pi\) |
0.471279 | + | 0.881984i | \(0.343793\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −71330.2 | − | 41182.5i | −0.547342 | − | 0.316008i | 0.200707 | − | 0.979651i | \(-0.435676\pi\) |
−0.748049 | + | 0.663643i | \(0.769009\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 99846.4 | − | 172939.i | 0.356797 | − | 0.617990i | −0.630627 | − | 0.776086i | \(-0.717202\pi\) |
0.987424 | + | 0.158096i | \(0.0505355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −123892. | − | 214587.i | −0.317164 | − | 0.549344i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −729518. | −1.03144 | −0.515720 | − | 0.856757i | \(-0.672475\pi\) | ||||
−0.515720 | + | 0.856757i | \(0.672475\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −657851. | + | 379810.i | −0.712329 | + | 0.411263i | −0.811923 | − | 0.583765i | \(-0.801579\pi\) |
0.0995939 | + | 0.995028i | \(0.468246\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 713857. | − | 560229.i | 0.475706 | − | 0.373331i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.20997e6 | + | 2.09573e6i | −0.645606 | + | 1.11822i | 0.338555 | + | 0.940947i | \(0.390062\pi\) |
−0.984161 | + | 0.177276i | \(0.943271\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.65776e6i | 0.940547i | 0.882521 | + | 0.470274i | \(0.155845\pi\) | ||||
−0.882521 | + | 0.470274i | \(0.844155\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.43503e6 | 1.00475 | 0.502374 | − | 0.864651i | \(-0.332460\pi\) | ||||
0.502374 | + | 0.864651i | \(0.332460\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 3.34472e6 | + | 1.93107e6i | 0.685437 | + | 0.395738i | 0.801901 | − | 0.597458i | \(-0.203822\pi\) |
−0.116463 | + | 0.993195i | \(0.537156\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.16422e6 | − | 3.98650e6i | −0.722353 | − | 0.691525i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.43200e6 | + | 2.48030e6i | 0.181485 | + | 0.314341i | 0.942386 | − | 0.334526i | \(-0.108576\pi\) |
−0.760901 | + | 0.648868i | \(0.775243\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.30924e6i | − | 0.798770i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.34642e7 | − | 7.77355e6i | 1.11115 | − | 0.641522i | 0.172022 | − | 0.985093i | \(-0.444970\pi\) |
0.939127 | + | 0.343571i | \(0.111637\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.84904e6 | − | 5.10899e6i | −0.639112 | − | 0.368991i | 0.145161 | − | 0.989408i | \(-0.453630\pi\) |
−0.784272 | + | 0.620417i | \(0.786963\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.15504e6 | + | 1.58570e7i | −0.512869 | + | 0.888316i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.64879e6 | + | 6.31988e6i | 0.181071 | + | 0.313624i | 0.942246 | − | 0.334923i | \(-0.108710\pi\) |
−0.761174 | + | 0.648547i | \(0.775377\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.30195e7 | 1.69290 | 0.846451 | − | 0.532466i | \(-0.178735\pi\) | ||||
0.846451 | + | 0.532466i | \(0.178735\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.32896e7 | − | 7.67277e6i | 0.467973 | − | 0.270185i | −0.247418 | − | 0.968909i | \(-0.579582\pi\) |
0.715391 | + | 0.698724i | \(0.246249\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.59682e7 | + | 6.56234e6i | −1.30766 | + | 0.186679i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.11705e7 | + | 1.93479e7i | −0.286790 | + | 0.496735i | −0.973042 | − | 0.230629i | \(-0.925922\pi\) |
0.686252 | + | 0.727364i | \(0.259255\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 8.50228e7i | − | 1.79153i | −0.444533 | − | 0.895763i | \(-0.646630\pi\) | ||
0.444533 | − | 0.895763i | \(-0.353370\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.07408e6 | 0.0397328 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.69746e7 | + | 1.55738e7i | 0.429927 | + | 0.248219i | 0.699316 | − | 0.714813i | \(-0.253488\pi\) |
−0.269388 | + | 0.963032i | \(0.586821\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.07945e8 | + | 4.33399e7i | 1.57412 | + | 0.632008i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.55646e7 | + | 2.69587e7i | 0.191093 | + | 0.330983i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 9.56779e7i | − | 1.08075i | −0.841425 | − | 0.540375i | \(-0.818283\pi\) | ||
0.841425 | − | 0.540375i | \(-0.181717\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.66653e7 | − | 5.00362e7i | 0.832836 | − | 0.480838i | −0.0219866 | − | 0.999758i | \(-0.506999\pi\) |
0.854823 | + | 0.518920i | \(0.173666\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.69279e7 | − | 5.59614e7i | −0.861192 | − | 0.497209i | 0.00321926 | − | 0.999995i | \(-0.498975\pi\) |
−0.864411 | + | 0.502785i | \(0.832309\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.73411e7 | + | 1.51279e8i | −0.666321 | + | 1.15410i | 0.312605 | + | 0.949883i | \(0.398798\pi\) |
−0.978925 | + | 0.204218i | \(0.934535\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.12720e8 | + | 1.95236e8i | 0.798535 | + | 1.38310i | 0.920570 | + | 0.390577i | \(0.127725\pi\) |
−0.122035 | + | 0.992526i | \(0.538942\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.21183e8 | 1.35655 | 0.678277 | − | 0.734806i | \(-0.262727\pi\) | ||||
0.678277 | + | 0.734806i | \(0.262727\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.53611e7 | + | 3.77362e7i | −0.373704 | + | 0.215758i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.86213e6 | − | 1.30440e7i | −0.00928588 | − | 0.0650462i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.98296e7 | + | 1.38269e8i | −0.372411 | + | 0.645035i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.41282e8i | 0.988292i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.34179e8 | 1.66899 | 0.834495 | − | 0.551016i | \(-0.185760\pi\) | ||||
0.834495 | + | 0.551016i | \(0.185760\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.33866e8 | + | 7.72876e7i | 0.454554 | + | 0.262437i | 0.709752 | − | 0.704452i | \(-0.248807\pi\) |
−0.255198 | + | 0.966889i | \(0.582141\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.55571e8 | − | 1.22091e8i | 0.497189 | − | 0.390190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.70378e8 | − | 4.68308e8i | −0.767519 | − | 1.32938i | −0.938905 | − | 0.344178i | \(-0.888158\pi\) |
0.171386 | − | 0.985204i | \(-0.445176\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 4.03527e8i | − | 1.08097i | −0.841354 | − | 0.540484i | \(-0.818241\pi\) | ||
0.841354 | − | 0.540484i | \(-0.181759\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 8.11411e8 | − | 4.68469e8i | 1.94043 | − | 1.12031i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.38777e8 | + | 1.37858e8i | 0.540158 | + | 0.311860i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.20512e8 | − | 7.28348e8i | 0.853166 | − | 1.47773i | −0.0251707 | − | 0.999683i | \(-0.508013\pi\) |
0.878336 | − | 0.478043i | \(-0.158654\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.71087e8 | + | 2.96331e8i | 0.329085 | + | 0.569992i | 0.982331 | − | 0.187154i | \(-0.0599264\pi\) |
−0.653246 | + | 0.757146i | \(0.726593\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2.87093e8 | 0.497389 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.37023e8 | − | 2.52315e8i | 0.719292 | − | 0.415284i | −0.0951999 | − | 0.995458i | \(-0.530349\pi\) |
0.814492 | + | 0.580175i | \(0.197016\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.96007e8 | + | 3.77179e8i | 0.440554 | + | 0.561363i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.08409e8 | − | 5.34179e8i | 0.436894 | − | 0.756723i | −0.560554 | − | 0.828118i | \(-0.689412\pi\) |
0.997448 | + | 0.0713951i | \(0.0227451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.27129e9i | 1.63448i | 0.576300 | + | 0.817239i | \(0.304496\pi\) | ||||
−0.576300 | + | 0.817239i | \(0.695504\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.53135e9 | −1.87728 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.10198e9 | + | 6.36226e8i | 1.23023 | + | 0.710276i | 0.967079 | − | 0.254478i | \(-0.0819036\pi\) |
0.263155 | + | 0.964754i | \(0.415237\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.88959e8 | − | 8.40787e7i | 0.627961 | − | 0.0896466i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1.01757e9 | + | 1.76248e9i | 0.991175 | + | 1.71677i | 0.610387 | + | 0.792103i | \(0.291014\pi\) |
0.380788 | + | 0.924662i | \(0.375653\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.83706e8i | 0.916539i | 0.888813 | + | 0.458269i | \(0.151531\pi\) | ||||
−0.888813 | + | 0.458269i | \(0.848469\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7.92066e8 | − | 4.57299e8i | 0.676199 | − | 0.390404i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.19128e7 | − | 5.30659e7i | −0.0751639 | − | 0.0433959i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.66014e8 | − | 2.87545e8i | 0.124742 | − | 0.216059i | −0.796890 | − | 0.604124i | \(-0.793523\pi\) |
0.921632 | + | 0.388065i | \(0.126857\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.85509e8 | + | 4.94516e8i | 0.205774 | + | 0.356411i | 0.950379 | − | 0.311094i | \(-0.100696\pi\) |
−0.744605 | + | 0.667505i | \(0.767362\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.79680e8 | 0.384878 | 0.192439 | − | 0.981309i | \(-0.438360\pi\) | ||||
0.192439 | + | 0.981309i | \(0.438360\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.30497e8 | − | 3.06282e8i | 0.338275 | − | 0.195303i | −0.321234 | − | 0.947000i | \(-0.604098\pi\) |
0.659509 | + | 0.751697i | \(0.270764\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.52619e8 | − | 1.62545e9i | 0.384304 | − | 0.957172i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.02241e8 | − | 8.69907e8i | 0.284378 | − | 0.492558i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1.59290e9i | − | 0.834841i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.96142e8 | −0.149407 | −0.0747034 | − | 0.997206i | \(-0.523801\pi\) | ||||
−0.0747034 | + | 0.997206i | \(0.523801\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.12431e9 | − | 6.49123e8i | −0.526179 | − | 0.303790i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.57756e8 | − | 1.80554e9i | −0.116244 | − | 0.814271i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.32933e8 | + | 2.30247e8i | 0.0557268 | + | 0.0965216i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.61451e9i | 0.652862i | 0.945221 | + | 0.326431i | \(0.105846\pi\) | ||||
−0.945221 | + | 0.326431i | \(0.894154\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.24050e7 | − | 5.33501e7i | 0.0348010 | − | 0.0200924i | −0.482499 | − | 0.875897i | \(-0.660271\pi\) |
0.517300 | + | 0.855804i | \(0.326937\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.19529e9 | + | 2.42215e9i | 1.52553 | + | 0.880763i | 0.999542 | + | 0.0302696i | \(0.00963658\pi\) |
0.525985 | + | 0.850494i | \(0.323697\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.88395e8 | − | 1.19234e9i | 0.233568 | − | 0.404552i | −0.725287 | − | 0.688446i | \(-0.758293\pi\) |
0.958856 | + | 0.283894i | \(0.0916264\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.29835e8 | − | 1.26411e9i | −0.239306 | − | 0.414490i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.43290e9 | −0.745647 | −0.372824 | − | 0.927902i | \(-0.621610\pi\) | ||||
−0.372824 | + | 0.927902i | \(0.621610\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.63518e7 | + | 4.40817e7i | −0.0226335 | + | 0.0130674i | −0.511274 | − | 0.859418i | \(-0.670826\pi\) |
0.488641 | + | 0.872485i | \(0.337493\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.09648e8 | + | 2.09173e9i | 0.169206 | + | 0.580553i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.99516e9 | + | 3.45571e9i | −0.536030 | + | 0.928431i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.17652e8i | 0.0548362i | 0.999624 | + | 0.0274181i | \(0.00872854\pi\) | ||||
−0.999624 | + | 0.0274181i | \(0.991271\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.86197e9 | 0.942598 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.91538e8 | − | 5.72465e8i | −0.227288 | − | 0.131225i | 0.382032 | − | 0.924149i | \(-0.375224\pi\) |
−0.609320 | + | 0.792924i | \(0.708558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3.58711e9 | − | 4.57077e9i | −0.797160 | − | 1.01576i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.63387e9 | + | 4.56199e9i | 0.550517 | + | 0.953524i | 0.998237 | + | 0.0593498i | \(0.0189027\pi\) |
−0.447720 | + | 0.894174i | \(0.647764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 1.08243e9i | − | 0.219491i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.99560e9 | + | 3.46156e9i | −1.14505 | + | 0.661093i | −0.947675 | − | 0.319236i | \(-0.896574\pi\) |
−0.197371 | + | 0.980329i | \(0.563240\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.03483e9 | − | 5.97462e8i | −0.191864 | − | 0.110773i | 0.400991 | − | 0.916082i | \(-0.368666\pi\) |
−0.592855 | + | 0.805309i | \(0.701999\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.39602e9 | − | 4.15002e9i | 0.418947 | − | 0.725638i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.25716e8 | + | 9.10566e8i | 0.0892960 | + | 0.154665i | 0.907214 | − | 0.420670i | \(-0.138205\pi\) |
−0.817918 | + | 0.575335i | \(0.804872\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.39931e9 | 0.224434 | 0.112217 | − | 0.993684i | \(-0.464205\pi\) | ||||
0.112217 | + | 0.993684i | \(0.464205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.63101e9 | − | 4.98311e9i | 1.34560 | − | 0.776882i | 0.357976 | − | 0.933731i | \(-0.383467\pi\) |
0.987623 | + | 0.156849i | \(0.0501335\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5.92181e9 | − | 2.37760e9i | −0.872824 | − | 0.350439i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.47282e9 | + | 6.01510e9i | −0.497841 | + | 0.862287i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 9.23400e9i | − | 1.25291i | −0.779458 | − | 0.626454i | \(-0.784506\pi\) | ||
0.779458 | − | 0.626454i | \(-0.215494\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.87592e9 | −0.775867 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.37833e9 | − | 4.83723e9i | −1.04827 | − | 0.605218i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.07294e9 | + | 7.65366e9i | −0.374359 | + | 0.932402i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.93091e9 | + | 3.34443e9i | 0.223132 | + | 0.386476i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.40040e8i | − | 0.0157652i | −0.999969 | − | 0.00788259i | \(-0.997491\pi\) | ||
0.999969 | − | 0.00788259i | \(-0.00250913\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.15689e9 | + | 3.55468e9i | −0.658143 | + | 0.379979i | −0.791569 | − | 0.611080i | \(-0.790735\pi\) |
0.133426 | + | 0.991059i | \(0.457402\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.86699e8 | − | 3.96466e8i | −0.0715466 | − | 0.0413075i | 0.463800 | − | 0.885940i | \(-0.346486\pi\) |
−0.535347 | + | 0.844633i | \(0.679819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.37244e9 | + | 1.45015e10i | −0.829115 | + | 1.43607i | 0.0696182 | + | 0.997574i | \(0.477822\pi\) |
−0.898733 | + | 0.438496i | \(0.855511\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.05427e9 | − | 1.22184e10i | −0.681223 | − | 1.17991i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.52003e8 | 0.0415271 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.03961e10 | + | 6.00216e9i | −0.931826 | + | 0.537990i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.29481e9 | + | 5.72491e9i | −0.622630 | + | 0.488635i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.81682e9 | + | 1.18071e10i | −0.567897 | + | 0.983627i | 0.428876 | + | 0.903363i | \(0.358910\pi\) |
−0.996774 | + | 0.0802640i | \(0.974424\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.75806e9i | − | 0.218990i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.81834e10 | −1.40979 | −0.704897 | − | 0.709309i | \(-0.749007\pi\) | ||||
−0.704897 | + | 0.709309i | \(0.749007\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.27225e10 | − | 7.34536e9i | −0.940927 | − | 0.543245i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.26077e10 | − | 5.71210e9i | 0.910874 | − | 0.412685i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −6.16239e8 | − | 1.06736e9i | −0.0425041 | − | 0.0736193i | 0.843991 | − | 0.536358i | \(-0.180200\pi\) |
−0.886495 | + | 0.462738i | \(0.846867\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 1.23418e10i | − | 0.831910i | −0.909385 | − | 0.415955i | \(-0.863447\pi\) | ||
0.909385 | − | 0.415955i | \(-0.136553\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.51638e10 | − | 8.75484e9i | 0.976585 | − | 0.563831i | 0.0753473 | − | 0.997157i | \(-0.475993\pi\) |
0.901237 | + | 0.433326i | \(0.142660\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.40806e10 | − | 8.12945e9i | −0.886561 | − | 0.511856i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.45738e8 | + | 4.25631e8i | −0.0147943 | + | 0.0256245i | −0.873328 | − | 0.487133i | \(-0.838043\pi\) |
0.858533 | + | 0.512758i | \(0.171376\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.09978e9 | − | 8.83308e9i | −0.300278 | − | 0.520096i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5.79973e9 | −0.326766 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.21943e9 | − | 1.85874e9i | 0.177466 | − | 0.102460i | −0.408636 | − | 0.912698i | \(-0.633995\pi\) |
0.586102 | + | 0.810238i | \(0.300662\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.80747e9 | + | 9.71821e8i | −0.359327 | + | 0.0512969i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.50275e9 | − | 7.79900e9i | 0.232618 | − | 0.402906i | −0.725960 | − | 0.687737i | \(-0.758604\pi\) |
0.958578 | + | 0.284831i | \(0.0919376\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.53427e10i | 1.74958i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.72072e9 | 0.0833974 | 0.0416987 | − | 0.999130i | \(-0.486723\pi\) | ||||
0.0416987 | + | 0.999130i | \(0.486723\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.02302e10 | − | 5.90640e9i | −0.475432 | − | 0.274491i | 0.243079 | − | 0.970007i | \(-0.421843\pi\) |
−0.718511 | + | 0.695516i | \(0.755176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.62859e10 | + | 6.53877e9i | 0.741255 | + | 0.297614i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.12760e10 | − | 1.95307e10i | −0.492445 | − | 0.852940i | 0.507517 | − | 0.861642i | \(-0.330563\pi\) |
−0.999962 | + | 0.00870164i | \(0.997230\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.09588e9i | 0.0468872i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 7.31239e9 | − | 4.22181e9i | 0.300380 | − | 0.173424i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.50595e10 | + | 1.44681e10i | 1.00881 | + | 0.582438i | 0.910844 | − | 0.412751i | \(-0.135432\pi\) |
0.0979687 | + | 0.995189i | \(0.468765\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.68401e10 | − | 2.91679e10i | 0.651280 | − | 1.12805i | −0.331533 | − | 0.943444i | \(-0.607566\pi\) |
0.982813 | − | 0.184606i | \(-0.0591008\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.84006e10 | + | 3.18707e10i | 0.697607 | + | 1.20829i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.68005e10 | −1.70558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.44482e10 | + | 1.41152e10i | −0.873683 | + | 0.504421i | −0.868570 | − | 0.495566i | \(-0.834961\pi\) |
−0.00511242 | + | 0.999987i | \(0.501627\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.27548e9 | + | 3.69539e10i | 0.181327 | + | 1.27017i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.60669e10 | + | 2.78286e10i | −0.541675 | + | 0.938209i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.39616e10i | 0.777426i | 0.921359 | + | 0.388713i | \(0.127080\pi\) | ||||
−0.921359 | + | 0.388713i | \(0.872920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.62773e9 | 0.0836474 | 0.0418237 | − | 0.999125i | \(-0.486683\pi\) | ||||
0.0418237 | + | 0.999125i | \(0.486683\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.17761e9 | + | 6.79896e8i | 0.0360950 | + | 0.0208395i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.92997e10 | − | 1.51463e10i | 0.580549 | − | 0.455610i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.51439e10 | − | 2.62300e10i | −0.438863 | − | 0.760132i | 0.558739 | − | 0.829343i | \(-0.311285\pi\) |
−0.997602 | + | 0.0692109i | \(0.977952\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.52520e10i | − | 1.00284i | −0.865204 | − | 0.501420i | \(-0.832811\pi\) | ||
0.865204 | − | 0.501420i | \(-0.167189\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.42441e10 | + | 8.22385e9i | −0.390580 | + | 0.225502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.83835e9 | − | 3.94812e9i | −0.184117 | − | 0.106300i | 0.405109 | − | 0.914269i | \(-0.367234\pi\) |
−0.589225 | + | 0.807969i | \(0.700567\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.09947e10 | − | 5.36844e10i | 0.804771 | − | 1.39390i | −0.111675 | − | 0.993745i | \(-0.535622\pi\) |
0.916446 | − | 0.400159i | \(-0.131045\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.88601e9 | − | 1.01949e10i | −0.150100 | − | 0.259981i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 3.41615e10 | 0.840526 | 0.420263 | − | 0.907402i | \(-0.361938\pi\) | ||||
0.420263 | + | 0.907402i | \(0.361938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.45136e10 | + | 2.57000e10i | −1.07594 | + | 0.621192i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.71413e10 | − | 3.45840e10i | −0.633263 | − | 0.806919i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.83643e10 | − | 6.64489e10i | 0.879554 | − | 1.52343i | 0.0277221 | − | 0.999616i | \(-0.491175\pi\) |
0.851832 | − | 0.523816i | \(-0.175492\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 1.69291e10i | − | 0.374826i | −0.982281 | − | 0.187413i | \(-0.939990\pi\) | ||
0.982281 | − | 0.187413i | \(-0.0600103\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.31514e10 | 0.286185 | 0.143093 | − | 0.989709i | \(-0.454295\pi\) | ||||
0.143093 | + | 0.989709i | \(0.454295\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.04029e10 | + | 1.75531e10i | 0.639215 | + | 0.369051i | 0.784312 | − | 0.620367i | \(-0.213016\pi\) |
−0.145097 | + | 0.989417i | \(0.546349\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.73456e10 | + | 2.47623e9i | −0.358507 | + | 0.0511799i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.32160e10 | + | 5.75318e10i | 0.663594 | + | 1.14938i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.04088e10i | 0.400906i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.02789e10 | − | 1.74815e10i | 0.575172 | − | 0.332076i | −0.184040 | − | 0.982919i | \(-0.558918\pi\) |
0.759213 | + | 0.650843i | \(0.225584\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01531e11 | + | 5.86191e10i | 1.89679 | + | 1.09511i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.80804e10 | + | 3.13162e10i | −0.326769 | + | 0.565981i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4.13971e10 | − | 7.17018e10i | −0.735959 | − | 1.27472i | −0.954301 | − | 0.298846i | \(-0.903398\pi\) |
0.218342 | − | 0.975872i | \(-0.429935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.23248e10 | 1.07235 | 0.536173 | − | 0.844108i | \(-0.319870\pi\) | ||||
0.536173 | + | 0.844108i | \(0.319870\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.46709e9 | − | 2.00173e9i | 0.0586918 | − | 0.0338857i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.84848e10 | + | 9.58525e10i | −0.630759 | + | 1.57101i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.15575e9 | − | 1.23941e10i | 0.115412 | − | 0.199900i | −0.802532 | − | 0.596609i | \(-0.796514\pi\) |
0.917945 | + | 0.396709i | \(0.129848\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.69313e10i | − | 1.20180i | −0.799325 | − | 0.600899i | \(-0.794809\pi\) | ||
0.799325 | − | 0.600899i | \(-0.205191\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.78217e10 | −0.581534 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.47817e10 | + | 4.31752e10i | 1.11410 | + | 0.643226i | 0.939888 | − | 0.341482i | \(-0.110929\pi\) |
0.174212 | + | 0.984708i | \(0.444262\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.20708e9 | + | 3.64748e10i | 0.0763679 | + | 0.534946i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.11502e10 | + | 3.66332e10i | 0.300667 | + | 0.520770i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.46921e10i | 1.04547i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.35013e10 | − | 2.51155e10i | 0.590407 | − | 0.340872i | −0.174851 | − | 0.984595i | \(-0.555944\pi\) |
0.765259 | + | 0.643723i | \(0.222611\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.93369e10 | + | 2.27112e10i | 0.525767 | + | 0.303552i | 0.739291 | − | 0.673386i | \(-0.235161\pi\) |
−0.213524 | + | 0.976938i | \(0.568494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.08433e9 | − | 3.61016e9i | 0.0270223 | − | 0.0468041i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.92169e10 | + | 3.32846e10i | 0.245392 | + | 0.425031i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.28760e11 | 1.59541 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.71749e10 | − | 3.30099e10i | 0.697895 | − | 0.402930i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.65010e10 | − | 1.08293e11i | 0.313984 | − | 1.28306i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.94658e10 | + | 5.10362e10i | −0.343976 | + | 0.595784i | −0.985167 | − | 0.171597i | \(-0.945107\pi\) |
0.641191 | + | 0.767381i | \(0.278441\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.52032e10i | − | 0.965762i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.83691e10 | 1.09878 | 0.549388 | − | 0.835567i | \(-0.314861\pi\) | ||||
0.549388 | + | 0.835567i | \(0.314861\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.20366e10 | + | 3.00434e10i | 0.564551 | + | 0.325943i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.31163e10 | − | 4.21976e10i | −0.354113 | − | 0.451219i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.69551e10 | + | 9.86492e10i | 0.591714 | + | 1.02488i | 0.994002 | + | 0.109366i | \(0.0348820\pi\) |
−0.402287 | + | 0.915514i | \(0.631785\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.66416e11i | − | 1.70431i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8.01740e10 | + | 4.62885e10i | −0.797995 | + | 0.460723i | −0.842770 | − | 0.538275i | \(-0.819076\pi\) |
0.0447747 | + | 0.998997i | \(0.485743\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23949e10 | − | 4.17972e10i | −0.710418 | − | 0.410160i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 4.57486e8 | − | 7.92389e8i | 0.00436444 | − | 0.00755943i | −0.863835 | − | 0.503775i | \(-0.831944\pi\) |
0.868199 | + | 0.496216i | \(0.165277\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.01821e10 | − | 8.69179e10i | −0.472068 | − | 0.817645i | 0.527421 | − | 0.849604i | \(-0.323159\pi\) |
−0.999489 | + | 0.0319584i | \(0.989826\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.94807e10 | −0.452652 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.75665e10 | − | 5.63301e10i | 0.880233 | − | 0.508203i | 0.00949770 | − | 0.999955i | \(-0.496977\pi\) |
0.870735 | + | 0.491752i | \(0.163643\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.89441e11 | + | 7.60605e10i | 1.66253 | + | 0.667505i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.76943e10 | + | 4.79680e10i | −0.239727 | + | 0.415219i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 1.51553e10i | − | 0.127647i | −0.997961 | − | 0.0638236i | \(-0.979671\pi\) | ||
0.997961 | − | 0.0638236i | \(-0.0203295\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.25662e10 | 0.519850 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −7.22390e10 | − | 4.17072e10i | −0.584189 | − | 0.337281i | 0.178608 | − | 0.983920i | \(-0.442841\pi\) |
−0.762796 | + | 0.646639i | \(0.776174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85545e9 | + | 4.62129e9i | −0.0148041 | + | 0.0368719i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.83703e10 | + | 3.18183e10i | 0.142695 | + | 0.247155i | 0.928511 | − | 0.371306i | \(-0.121090\pi\) |
−0.785816 | + | 0.618461i | \(0.787756\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.77240e10i | 0.442444i | 0.975223 | + | 0.221222i | \(0.0710046\pi\) | ||||
−0.975223 | + | 0.221222i | \(0.928995\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.22577e10 | − | 3.01710e10i | 0.390058 | − | 0.225200i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.58050e10 | − | 2.64455e10i | −0.337410 | − | 0.194804i | 0.321716 | − | 0.946836i | \(-0.395740\pi\) |
−0.659126 | + | 0.752032i | \(0.729074\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.35541e10 | − | 1.62040e11i | 0.671271 | − | 1.16268i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.82662e10 | + | 1.70202e11i | 0.695925 | + | 1.20538i | 0.969868 | + | 0.243632i | \(0.0783388\pi\) |
−0.273943 | + | 0.961746i | \(0.588328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.78844e11 | −1.23405 | −0.617027 | − | 0.786942i | \(-0.711663\pi\) | ||||
−0.617027 | + | 0.786942i | \(0.711663\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.70567e9 | − | 2.13947e9i | 0.0252408 | − | 0.0145728i | −0.487326 | − | 0.873220i | \(-0.662028\pi\) |
0.512567 | + | 0.858647i | \(0.328695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −5.88315e10 | + | 4.61705e10i | −0.390533 | + | 0.306487i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.79992e9 | + | 4.84961e9i | −0.0183496 | + | 0.0317824i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1.32802e10i | − | 0.0848400i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.52207e10 | −0.474482 | −0.237241 | − | 0.971451i | \(-0.576243\pi\) | ||||
−0.237241 | + | 0.971451i | \(0.576243\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.42110e11 | − | 8.20474e10i | −0.874038 | − | 0.504626i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.93133e11 | + | 2.01743e11i | −1.17300 | + | 1.22529i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.42255e10 | + | 4.19597e10i | 0.143496 | + | 0.248542i | 0.928811 | − | 0.370554i | \(-0.120832\pi\) |
−0.785315 | + | 0.619097i | \(0.787499\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 9.91856e10i | − | 0.580236i | −0.956991 | − | 0.290118i | \(-0.906305\pi\) | ||
0.956991 | − | 0.290118i | \(-0.0936946\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.08123e10 | + | 6.24247e9i | −0.0617021 | + | 0.0356237i | −0.530534 | − | 0.847664i | \(-0.678008\pi\) |
0.468832 | + | 0.883288i | \(0.344675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.60391e11 | + | 1.50337e11i | 1.46773 | + | 0.847397i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.02174e11 | + | 1.76970e11i | −0.561936 | + | 0.973302i | 0.435391 | + | 0.900241i | \(0.356610\pi\) |
−0.997327 | + | 0.0730610i | \(0.976723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.92103e10 | − | 5.05937e10i | −0.158698 | − | 0.274873i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2.69754e11 | −1.43030 | −0.715149 | − | 0.698973i | \(-0.753641\pi\) | ||||
−0.715149 | + | 0.698973i | \(0.753641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.16400e11 | − | 6.72037e10i | 0.609745 | − | 0.352036i | −0.163121 | − | 0.986606i | \(-0.552156\pi\) |
0.772866 | + | 0.634570i | \(0.218823\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −7.39912e10 | + | 1.05628e10i | −0.378350 | + | 0.0540125i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.28397e10 | + | 1.26162e11i | −0.368015 | + | 0.637420i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.97611e11i | − | 0.974814i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.85348e11 | −0.903499 | −0.451750 | − | 0.892145i | \(-0.649200\pi\) | ||||
−0.451750 | + | 0.892145i | \(0.649200\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.28495e11 | + | 1.31922e11i | 1.08773 | + | 0.628003i | 0.932972 | − | 0.359950i | \(-0.117206\pi\) |
0.154760 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.13182e11 | + | 8.55925e10i | 1.00293 | + | 0.402677i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2.06407e11 | − | 3.57507e11i | −0.948509 | − | 1.64287i | −0.748568 | − | 0.663059i | \(-0.769258\pi\) |
−0.199942 | − | 0.979808i | \(-0.564075\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.04375e11i | 0.928250i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.20163e11 | − | 6.93759e10i | 0.533203 | − | 0.307845i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.41227e11 | − | 1.97007e11i | −1.49669 | − | 0.864113i | −0.496694 | − | 0.867926i | \(-0.665453\pi\) |
−0.999993 | + | 0.00381313i | \(0.998786\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −7.62550e10 | + | 1.32078e11i | −0.326835 | + | 0.566096i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.29264e9 | − | 1.26312e10i | −0.0308997 | − | 0.0535198i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −2.63008e11 | −1.08917 | −0.544587 | − | 0.838704i | \(-0.683314\pi\) | ||||
−0.544587 | + | 0.838704i | \(0.683314\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.72615e11 | − | 9.96592e10i | 0.706735 | − | 0.408034i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.39568e10 | + | 2.37862e11i | 0.135909 | + | 0.952024i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.26127e11 | − | 3.91664e11i | 0.894886 | − | 1.54999i | 0.0609414 | − | 0.998141i | \(-0.480590\pi\) |
0.833945 | − | 0.551848i | \(-0.186077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.51691e11i | 0.586950i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.54109e11 | −1.35492 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.41212e11 | + | 1.39264e11i | 0.902574 | + | 0.521102i | 0.878035 | − | 0.478597i | \(-0.158855\pi\) |
0.0245399 | + | 0.999699i | \(0.492188\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.11399e11 | − | 1.65904e11i | 0.782280 | − | 0.613927i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 9.03815e10 | + | 1.56545e11i | 0.327135 | + | 0.566615i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.13459e11i | 0.406165i | 0.979162 | + | 0.203083i | \(0.0650960\pi\) | ||||
−0.979162 | + | 0.203083i | \(0.934904\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.63253e10 | + | 9.42540e9i | −0.0571730 | + | 0.0330088i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.59122e11 | − | 2.07339e11i | −1.24402 | − | 0.718234i | −0.274108 | − | 0.961699i | \(-0.588382\pi\) |
−0.969910 | + | 0.243465i | \(0.921716\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.05659e10 | + | 1.22224e11i | −0.239180 | + | 0.414272i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.59283e10 | − | 4.49092e10i | −0.0869354 | − | 0.150577i | 0.819279 | − | 0.573395i | \(-0.194374\pi\) |
−0.906214 | + | 0.422819i | \(0.861041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.16614e11 | −1.03890 | −0.519451 | − | 0.854500i | \(-0.673863\pi\) | ||||
−0.519451 | + | 0.854500i | \(0.673863\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.75274e11 | + | 1.58930e11i | −0.893594 | + | 0.515917i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.58933e11 | − | 3.29939e11i | −0.822737 | − | 1.04835i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.00643e11 | − | 1.74319e11i | 0.316392 | − | 0.548006i | −0.663341 | − | 0.748318i | \(-0.730862\pi\) |
0.979732 | + | 0.200311i | \(0.0641953\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 1.29322e11i | − | 0.398001i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.64675e10 | −0.141503 | −0.0707515 | − | 0.997494i | \(-0.522540\pi\) | ||||
−0.0707515 | + | 0.997494i | \(0.522540\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.01663e11 | − | 5.86953e10i | −0.303128 | − | 0.175011i | 0.340719 | − | 0.940165i | \(-0.389329\pi\) |
−0.643847 | + | 0.765154i | \(0.722663\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.35847e11 | + | 7.64966e10i | −1.58104 | + | 0.225706i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.76603e11 | − | 6.52295e11i | −1.08818 | − | 1.88479i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 3.16824e11i | − | 0.905967i | −0.891519 | − | 0.452984i | \(-0.850360\pi\) | ||
0.891519 | − | 0.452984i | \(-0.149640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.18087e10 | − | 2.99118e10i | 0.145106 | − | 0.0837769i | −0.425689 | − | 0.904869i | \(-0.639968\pi\) |
0.570795 | + | 0.821092i | \(0.306635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.63005e11 | + | 9.41110e10i | 0.451850 | + | 0.260876i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.09453e11 | − | 1.89579e11i | 0.297221 | − | 0.514801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.15989e11 | + | 7.20514e11i | 1.11809 | + | 1.93659i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.90721e11 | −0.502251 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.91607e11 | + | 1.10624e11i | −0.499473 | + | 0.288371i | −0.728496 | − | 0.685050i | \(-0.759780\pi\) |
0.229023 | + | 0.973421i | \(0.426447\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.97868e11 | + | 4.92821e11i | −0.505439 | + | 1.25888i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.47514e11 | + | 4.28707e11i | −0.625903 | + | 1.08410i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 2.22900e11i | − | 0.552429i | −0.961096 | − | 0.276215i | \(-0.910920\pi\) | ||
0.961096 | − | 0.276215i | \(-0.0890800\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.11947e10 | −0.0520044 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.57015e11 | + | 1.48388e11i | 0.618154 | + | 0.356891i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.56095e10 | − | 1.79391e11i | −0.0609842 | − | 0.427185i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.60307e11 | + | 4.50865e11i | 0.607703 | + | 1.05257i | 0.991618 | + | 0.129204i | \(0.0412422\pi\) |
−0.383915 | + | 0.923368i | \(0.625424\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 7.42722e11i | − | 1.71689i | −0.512904 | − | 0.858446i | \(-0.671430\pi\) | ||
0.512904 | − | 0.858446i | \(-0.328570\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2.01889e11 | + | 1.16561e11i | −0.457597 | + | 0.264194i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.45022e11 | − | 1.41463e11i | −0.549941 | − | 0.317509i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.95281e11 | + | 3.38237e11i | −0.429821 | + | 0.744472i | −0.996857 | − | 0.0792213i | \(-0.974757\pi\) |
0.567036 | + | 0.823693i | \(0.308090\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.11169e11 | + | 5.38960e11i | 0.678261 | + | 1.17478i | 0.975504 | + | 0.219980i | \(0.0705993\pi\) |
−0.297244 | + | 0.954802i | \(0.596067\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.76465e11 | −1.01861 | −0.509307 | − | 0.860585i | \(-0.670098\pi\) | ||||
−0.509307 | + | 0.860585i | \(0.670098\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.95189e11 | + | 3.43632e11i | −1.26019 | + | 0.727572i | −0.973111 | − | 0.230335i | \(-0.926018\pi\) |
−0.287080 | + | 0.957907i | \(0.592685\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.07294e10 | + | 7.51995e9i | 0.0638225 | + | 0.0156183i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.40238e11 | − | 4.16104e11i | 0.494191 | − | 0.855964i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 2.54247e11i | − | 0.513106i | −0.966530 | − | 0.256553i | \(-0.917413\pi\) | ||
0.966530 | − | 0.256553i | \(-0.0825868\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.19496e10 | 0.0638677 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.01224e11 | + | 2.89382e11i | 0.983116 | + | 0.567602i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.36665e11 | − | 3.01564e11i | −0.459833 | − | 0.585929i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.41622e11 | + | 4.18502e11i | 0.460701 | + | 0.797957i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.25449e11i | 0.614733i | 0.951591 | + | 0.307367i | \(0.0994478\pi\) | ||||
−0.951591 | + | 0.307367i | \(0.900552\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 5.78614e11 | − | 3.34063e11i | 1.07267 | − | 0.619305i | 0.143759 | − | 0.989613i | \(-0.454081\pi\) |
0.928909 | + | 0.370307i | \(0.120748\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.40365e11 | + | 4.85185e11i | 1.54346 | + | 0.891116i | 0.998617 | + | 0.0525777i | \(0.0167437\pi\) |
0.544842 | + | 0.838539i | \(0.316590\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.65239e11 | + | 2.86202e11i | −0.297899 | + | 0.515976i | −0.975655 | − | 0.219311i | \(-0.929619\pi\) |
0.677756 | + | 0.735287i | \(0.262952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.40457e11 | − | 4.16484e11i | −0.429510 | − | 0.743933i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.32065e11 | −0.757652 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.06177e11 | − | 1.76772e11i | 0.531986 | − | 0.307142i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.37605e11 | − | 2.15848e11i | −0.917131 | − | 0.368228i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.99474e11 | − | 5.18704e11i | 0.506244 | − | 0.876841i | −0.493729 | − | 0.869616i | \(-0.664367\pi\) |
0.999974 | − | 0.00722558i | \(-0.00229999\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 2.08291e11i | − | 0.345754i | −0.984943 | − | 0.172877i | \(-0.944694\pi\) | ||
0.984943 | − | 0.172877i | \(-0.0553064\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.84994e11 | −1.29129 | −0.645645 | − | 0.763638i | \(-0.723411\pi\) | ||||
−0.645645 | + | 0.763638i | \(0.723411\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 4.11593e11 | + | 2.37634e11i | 0.664927 | + | 0.383896i | 0.794152 | − | 0.607720i | \(-0.207916\pi\) |
−0.129225 | + | 0.991615i | \(0.541249\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.88412e11 | + | 9.67402e11i | −0.621849 | + | 1.54882i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1.59053e11 | − | 2.75488e11i | −0.250113 | − | 0.433208i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 7.69163e11i | − | 1.19874i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 4.79914e11 | − | 2.77078e11i | 0.734724 | − | 0.424193i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.36114e10 | − | 7.85856e9i | −0.0206540 | − | 0.0119246i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.85892e11 | − | 3.21975e11i | 0.277119 | − | 0.479985i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.01929e11 | + | 5.22956e11i | 0.446144 | + | 0.772745i | 0.998131 | − | 0.0611081i | \(-0.0194634\pi\) |
−0.551987 | + | 0.833853i | \(0.686130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5.64766e10 | −0.0819965 | −0.0409982 | − | 0.999159i | \(-0.513054\pi\) | ||||
−0.0409982 | + | 0.999159i | \(0.513054\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.42401e12 | − | 8.22151e11i | 2.04941 | − | 1.18323i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.91961e11 | + | 2.29129e11i | −0.412903 | + | 0.324043i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.53883e10 | + | 6.12943e10i | −0.0496132 | + | 0.0859327i | −0.889766 | − | 0.456418i | \(-0.849132\pi\) |
0.840152 | + | 0.542351i | \(0.182466\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2.08415e12i | − | 2.87159i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.99623e11 | 0.819052 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.88996e11 | + | 3.97792e11i | 0.925026 | + | 0.534064i | 0.885235 | − | 0.465144i | \(-0.153998\pi\) |
0.0397908 | + | 0.999208i | \(0.487331\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32861e11 | + | 4.55851e11i | 0.176847 | + | 0.606770i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.00559e10 | + | 3.47378e10i | 0.0262419 | + | 0.0454523i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.34401e11i | 1.21220i | 0.795388 | + | 0.606101i | \(0.207267\pi\) | ||||
−0.795388 | + | 0.606101i | \(0.792733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.21783e12 | + | 7.03113e11i | −1.55320 | + | 0.896741i | −0.555322 | + | 0.831636i | \(0.687405\pi\) |
−0.997878 | + | 0.0651050i | \(0.979262\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.59631e11 | + | 2.65368e11i | 0.581249 | + | 0.335584i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.50197e10 | − | 7.79763e10i | 0.0559760 | − | 0.0969534i | −0.836680 | − | 0.547693i | \(-0.815506\pi\) |
0.892656 | + | 0.450739i | \(0.148840\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.71720e11 | − | 6.43838e11i | −0.458302 | − | 0.793802i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.15644e11 | 0.746376 | 0.373188 | − | 0.927756i | \(-0.378265\pi\) | ||||
0.373188 | + | 0.927756i | \(0.378265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.08675e11 | + | 6.27438e10i | −0.130653 | + | 0.0754323i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.28532e12 | − | 1.83490e11i | 1.51963 | − | 0.216940i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.37934e11 | + | 2.38908e11i | −0.161725 | + | 0.280116i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.15812e11i | − | 0.248866i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.52860e11 | 0.517914 | 0.258957 | − | 0.965889i | \(-0.416621\pi\) | ||||
0.258957 | + | 0.965889i | \(0.416621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.65973e10 | + | 4.99970e10i | 0.0974154 | + | 0.0562428i | 0.547916 | − | 0.836533i | \(-0.315421\pi\) |
−0.450501 | + | 0.892776i | \(0.648755\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.99105e11 | + | 3.60991e11i | 1.00313 | + | 0.402758i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.56681e11 | + | 7.90994e11i | 0.501227 | + | 0.868151i | 0.999999 | + | 0.00141736i | \(0.000451159\pi\) |
−0.498772 | + | 0.866733i | \(0.666216\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.02380e11i | 0.655753i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.08072e11 | − | 4.66541e11i | 0.865438 | − | 0.499661i | −0.000391493 | − | 1.00000i | \(-0.500125\pi\) |
0.865830 | + | 0.500339i | \(0.166791\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.89734e11 | − | 1.09543e11i | −0.201558 | − | 0.116370i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.42976e11 | − | 5.94051e11i | 0.358491 | − | 0.620924i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.26833e11 | − | 1.43212e12i | −0.857280 | − | 1.48485i | −0.874513 | − | 0.485002i | \(-0.838819\pi\) |
0.0172326 | − | 0.999852i | \(-0.494514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.31515e11 | −0.236203 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.26012e11 | − | 5.34633e11i | 0.937208 | − | 0.541097i | 0.0481238 | − | 0.998841i | \(-0.484676\pi\) |
0.889084 | + | 0.457744i | \(0.151342\pi\) | |||||||
\(998\) | 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 | 252.9.z.c.145.3 | 10 | ||
3.2 | odd | 2 | 28.9.h.a.5.2 | ✓ | 10 | ||
7.3 | odd | 6 | inner | 252.9.z.c.73.3 | 10 | ||
12.11 | even | 2 | 112.9.s.b.33.4 | 10 | |||
21.2 | odd | 6 | 196.9.b.a.97.3 | 10 | |||
21.5 | even | 6 | 196.9.b.a.97.8 | 10 | |||
21.11 | odd | 6 | 196.9.h.a.129.4 | 10 | |||
21.17 | even | 6 | 28.9.h.a.17.2 | yes | 10 | ||
21.20 | even | 2 | 196.9.h.a.117.4 | 10 | |||
84.59 | odd | 6 | 112.9.s.b.17.4 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
28.9.h.a.5.2 | ✓ | 10 | 3.2 | odd | 2 | ||
28.9.h.a.17.2 | yes | 10 | 21.17 | even | 6 | ||
112.9.s.b.17.4 | 10 | 84.59 | odd | 6 | |||
112.9.s.b.33.4 | 10 | 12.11 | even | 2 | |||
196.9.b.a.97.3 | 10 | 21.2 | odd | 6 | |||
196.9.b.a.97.8 | 10 | 21.5 | even | 6 | |||
196.9.h.a.117.4 | 10 | 21.20 | even | 2 | |||
196.9.h.a.129.4 | 10 | 21.11 | odd | 6 | |||
252.9.z.c.73.3 | 10 | 7.3 | odd | 6 | inner | ||
252.9.z.c.145.3 | 10 | 1.1 | even | 1 | trivial |