Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,11,Mod(65,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.65");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.e (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(121.988592513\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 10188 x^{18} + 45921062 x^{16} + 120525675724 x^{14} + 203898078666673 x^{12} + \cdots + 53\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{176}\cdot 3^{47} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.6 | ||
Root | \(26.0163i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.65 |
Dual form | 192.11.e.k.65.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −168.749 | + | 174.851i | −0.694439 | + | 0.719552i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5349.27i | 1.71177i | 0.517170 | + | 0.855883i | \(0.326986\pi\) | ||||
−0.517170 | + | 0.855883i | \(0.673014\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −28157.9 | −1.67537 | −0.837684 | − | 0.546155i | \(-0.816091\pi\) | ||||
−0.837684 | + | 0.546155i | \(0.816091\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2096.84 | − | 59011.8i | −0.0355101 | − | 0.999369i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 178116.i | 1.10596i | 0.833194 | + | 0.552981i | \(0.186510\pi\) | ||||
−0.833194 | + | 0.552981i | \(0.813490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −450204. | −1.21253 | −0.606265 | − | 0.795262i | \(-0.707333\pi\) | ||||
−0.606265 | + | 0.795262i | \(0.707333\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −935326. | − | 902681.i | −1.23170 | − | 1.18872i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 1.63099e6i | − | 1.14870i | −0.818611 | − | 0.574348i | \(-0.805255\pi\) | ||
0.818611 | − | 0.574348i | \(-0.194745\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.37708e6 | 0.556150 | 0.278075 | − | 0.960559i | \(-0.410304\pi\) | ||||
0.278075 | + | 0.960559i | \(0.410304\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.75161e6 | − | 4.92344e6i | 1.16344 | − | 1.20551i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.19808e6i | − | 0.186143i | −0.995659 | − | 0.0930717i | \(-0.970331\pi\) | ||
0.995659 | − | 0.0930717i | \(-0.0296686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.88490e7 | −1.93014 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.06721e7 | + | 9.59152e6i | 0.743758 | + | 0.668449i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.50212e6i | − | 0.365758i | −0.983135 | − | 0.182879i | \(-0.941458\pi\) | ||
0.983135 | − | 0.182879i | \(-0.0585417\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.53697e7 | 1.23544 | 0.617722 | − | 0.786396i | \(-0.288056\pi\) | ||||
0.617722 | + | 0.786396i | \(0.288056\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.11438e7 | − | 3.00569e7i | −0.795797 | − | 0.768022i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 1.50624e8i | − | 2.86784i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.95516e7 | −0.714578 | −0.357289 | − | 0.933994i | \(-0.616299\pi\) | ||||
−0.357289 | + | 0.933994i | \(0.616299\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 7.59713e7 | − | 7.87187e7i | 0.842028 | − | 0.872479i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.90414e7i | − | 0.336981i | −0.985703 | − | 0.168491i | \(-0.946111\pi\) | ||
0.985703 | − | 0.168491i | \(-0.0538893\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.40453e8 | 0.955409 | 0.477705 | − | 0.878521i | \(-0.341469\pi\) | ||||
0.477705 | + | 0.878521i | \(0.341469\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.15670e8 | − | 1.12165e7i | 1.71069 | − | 0.0607850i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 75336.3i | 0.000328485i | 1.00000 | 0.000164242i | \(5.22800e-5\pi\) | |||||
−1.00000 | 0.000164242i | \(0.999948\pi\) | ||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.10393e8 | 1.80686 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.85180e8 | + | 2.75226e8i | 0.826547 | + | 0.797700i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 4.45933e8i | − | 1.06633i | −0.846012 | − | 0.533164i | \(-0.821003\pi\) | ||
0.846012 | − | 0.533164i | \(-0.178997\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.52791e8 | −1.89315 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.32381e8 | + | 2.40784e8i | −0.386212 | + | 0.400179i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 1.38477e8i | − | 0.193694i | −0.995299 | − | 0.0968471i | \(-0.969124\pi\) | ||
0.995299 | − | 0.0968471i | \(-0.0308758\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.60888e9 | −1.90491 | −0.952454 | − | 0.304682i | \(-0.901450\pi\) | ||||
−0.952454 | + | 0.304682i | \(0.901450\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.90425e7 | + | 1.66165e9i | 0.0594925 | + | 1.67431i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.40826e9i | − | 2.07557i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.71653e9 | −1.27139 | −0.635694 | − | 0.771941i | \(-0.719286\pi\) | ||||
−0.635694 | + | 0.771941i | \(0.719286\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.09486e8 | + | 2.02175e8i | 0.133940 | + | 0.129265i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.26776e9i | 1.25691i | 0.777844 | + | 0.628457i | \(0.216313\pi\) | ||||
−0.777844 | + | 0.628457i | \(0.783687\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.96508e8 | 0.143028 | 0.0715141 | − | 0.997440i | \(-0.477217\pi\) | ||||
0.0715141 | + | 0.997440i | \(0.477217\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.18075e9 | − | 3.29578e9i | 1.34036 | − | 1.38884i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.01538e9i | − | 1.85289i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.23007e9 | −1.69970 | −0.849849 | − | 0.527026i | \(-0.823307\pi\) | ||||
−0.849849 | + | 0.527026i | \(0.823307\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.47799e9 | + | 2.47476e8i | −0.997478 | + | 0.0709754i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.44213e8i | 0.188932i | 0.995528 | + | 0.0944662i | \(0.0301144\pi\) | ||||
−0.995528 | + | 0.0944662i | \(0.969886\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 8.72458e9 | 1.96630 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.31175e9 | + | 1.26597e9i | 0.263182 | + | 0.253997i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 1.07832e9i | − | 0.193106i | −0.995328 | − | 0.0965531i | \(-0.969218\pi\) | ||
0.995328 | − | 0.0965531i | \(-0.0307818\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.26768e10 | 2.03144 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −5.96859e9 | + | 6.18444e9i | −0.857940 | + | 0.888966i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.36638e9i | 0.951998i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.33891e9 | −0.854619 | −0.427310 | − | 0.904105i | \(-0.640539\pi\) | ||||
−0.427310 | + | 0.904105i | \(0.640539\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.05109e10 | − | 3.73480e8i | 1.10526 | − | 0.0392728i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.20616e10i | 1.14762i | 0.818987 | + | 0.573812i | \(0.194536\pi\) | ||||
−0.818987 | + | 0.573812i | \(0.805464\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.94813e9 | −0.685613 | −0.342806 | − | 0.939406i | \(-0.611377\pi\) | ||||
−0.342806 | + | 0.939406i | \(0.611377\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.63368e10 | + | 2.54176e10i | 2.06356 | + | 1.99154i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 2.62129e10i | − | 1.86895i | −0.356033 | − | 0.934473i | \(-0.615871\pi\) | ||
0.356033 | − | 0.934473i | \(-0.384129\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.12947e9 | −0.268387 | −0.134194 | − | 0.990955i | \(-0.542844\pi\) | ||||
−0.134194 | + | 0.990955i | \(0.542844\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 8.36177e9 | − | 8.66416e9i | 0.496230 | − | 0.514176i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.12310e9i | − | 0.332337i | −0.986097 | − | 0.166169i | \(-0.946860\pi\) | ||
0.986097 | − | 0.166169i | \(-0.0531396\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.40887e9 | 0.318634 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.44004e8 | + | 2.65673e10i | 0.0430571 | + | 1.21177i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.59251e10i | 1.92449i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.78795e9 | −0.223151 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.82642e9 | + | 6.58817e9i | 0.242475 | + | 0.234013i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 4.85896e10i | − | 1.59218i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 5.47457e10 | 1.65704 | 0.828518 | − | 0.559963i | \(-0.189185\pi\) | ||||
0.828518 | + | 0.559963i | \(0.189185\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.37013e10 | + | 2.45584e10i | −0.663473 | + | 0.687466i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.62381e10i | 1.45772i | 0.684662 | + | 0.728861i | \(0.259950\pi\) | ||||
−0.684662 | + | 0.728861i | \(0.740050\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.87757e10 | −0.931756 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.13076e10 | + | 5.70880e10i | −1.14423 | + | 1.27314i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 6.26992e10i | − | 1.29915i | −0.760298 | − | 0.649575i | \(-0.774947\pi\) | ||
0.760298 | − | 0.649575i | \(-0.225053\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.97029e10 | 1.34331 | 0.671656 | − | 0.740863i | \(-0.265583\pi\) | ||||
0.671656 | + | 0.740863i | \(0.265583\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.31726e7 | − | 1.27129e7i | −0.000236362 | − | 0.000228112i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 8.01886e10i | − | 1.34101i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.01309e10 | 0.626093 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.61281e10 | + | 8.92428e10i | −1.25475 | + | 1.30013i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.56743e10i | 0.894260i | 0.894469 | + | 0.447130i | \(0.147554\pi\) | ||||
−0.894469 | + | 0.447130i | \(0.852446\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.21530e10 | 0.409578 | 0.204789 | − | 0.978806i | \(-0.434349\pi\) | ||||
0.204789 | + | 0.978806i | \(0.434349\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.62473e10 | + | 3.41991e9i | −1.14797 | + | 0.0407904i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.89202e11i | 2.11479i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.67081e10 | 1.01383 | 0.506914 | − | 0.861997i | \(-0.330786\pi\) | ||||
0.506914 | + | 0.861997i | \(0.330786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.79720e10 | + | 7.52506e10i | 0.767278 | + | 0.740499i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.37355e10i | 0.311859i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.50185e10 | −0.478157 | −0.239079 | − | 0.971000i | \(-0.576845\pi\) | ||||
−0.239079 | + | 0.971000i | \(0.576845\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.60782e11 | − | 1.66597e11i | 1.31467 | − | 1.36222i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.35753e11i | 1.04512i | 0.852602 | + | 0.522561i | \(0.175023\pi\) | ||||
−0.852602 | + | 0.522561i | \(0.824977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48252e10 | 0.470230 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.88752e9 | − | 8.12640e10i | −0.0197489 | − | 0.555799i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.42251e10i | 0.349921i | 0.984575 | + | 0.174961i | \(0.0559798\pi\) | ||||
−0.984575 | + | 0.174961i | \(0.944020\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.30750e11 | 3.23370 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.42128e10 | + | 2.33677e10i | 0.139373 | + | 0.134509i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.73734e10i | 0.529877i | 0.964265 | + | 0.264939i | \(0.0853517\pi\) | ||||
−0.964265 | + | 0.264939i | \(0.914648\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.86408e11 | −0.959561 | −0.479781 | − | 0.877389i | \(-0.659284\pi\) | ||||
−0.479781 | + | 0.877389i | \(0.659284\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.71496e11 | − | 2.81314e11i | 1.32284 | − | 1.37068i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.65065e11i | − | 1.22319i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.90505e11 | 1.27041 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.00504e11 | − | 2.70077e11i | −1.24607 | − | 1.11990i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.04353e11i | − | 0.410525i | −0.978707 | − | 0.205263i | \(-0.934195\pi\) | ||
0.978707 | − | 0.205263i | \(-0.0658048\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.12618e11 | 0.420555 | 0.210278 | − | 0.977642i | \(-0.432563\pi\) | ||||
0.210278 | + | 0.977642i | \(0.432563\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.21087e11 | + | 4.06391e11i | 1.49348 | + | 1.44135i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.09320e11i | 0.705472i | 0.935723 | + | 0.352736i | \(0.114749\pi\) | ||||
−0.935723 | + | 0.352736i | \(0.885251\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.51611e10 | 0.0485808 | 0.0242904 | − | 0.999705i | \(-0.492267\pi\) | ||||
0.0242904 | + | 0.999705i | \(0.492267\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.89663e11 | − | 3.00138e11i | 0.882901 | − | 0.914830i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.11244e11i | 0.612780i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.08843e11 | 0.576833 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −7.07010e10 | + | 2.51218e9i | −0.186026 | + | 0.00660997i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.45281e11i | 0.615080i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.66929e11 | −0.638238 | −0.319119 | − | 0.947715i | \(-0.603387\pi\) | ||||
−0.319119 | + | 0.947715i | \(0.603387\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.96521e11 | − | 3.82681e11i | −0.904415 | − | 0.872849i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 7.51322e11i | 1.63544i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.95938e11 | −2.06982 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −5.00352e10 | + | 5.18447e10i | −0.0993243 | + | 0.102916i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.34276e11i | 1.39283i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.57318e11 | −1.19193 | −0.595966 | − | 0.803010i | \(-0.703231\pi\) | ||||
−0.595966 | + | 0.803010i | \(0.703231\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.95234e10 | + | 1.11232e12i | 0.0685395 | + | 1.92892i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.05930e11i | 0.507566i | 0.967261 | + | 0.253783i | \(0.0816750\pi\) | ||||
−0.967261 | + | 0.253783i | \(0.918325\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.20549e11 | 0.667789 | 0.333895 | − | 0.942610i | \(-0.391637\pi\) | ||||
0.333895 | + | 0.942610i | \(0.391637\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.76945e11 | + | 8.46338e11i | 1.33325 | + | 1.28672i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 9.41814e10i | − | 0.137147i | −0.997646 | − | 0.0685734i | \(-0.978155\pi\) | ||
0.997646 | − | 0.0685734i | \(-0.0218447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.02994e8 | −0.000562289 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.82567e11 | − | 9.14483e11i | 1.18034 | − | 1.22302i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.04683e12i | 1.34241i | 0.741270 | + | 0.671207i | \(0.234224\pi\) | ||||
−0.741270 | + | 0.671207i | \(0.765776\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.83352e11 | 0.594536 | 0.297268 | − | 0.954794i | \(-0.403925\pi\) | ||||
0.297268 | + | 0.954794i | \(0.403925\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 5.43635e11 | − | 6.49892e11i | 0.641617 | − | 0.767025i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.73023e12i | 3.09292i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.19968e11 | −0.674348 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.30126e11 | − | 1.25585e11i | −0.135947 | − | 0.131202i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 1.46442e10i | − | 0.0146993i | −0.999973 | − | 0.00734967i | \(-0.997661\pi\) | ||
0.999973 | − | 0.00734967i | \(-0.00233949\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.13398e11 | 0.205867 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.47226e12 | + | 1.52550e12i | −1.36547 | + | 1.41486i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.85667e11i | − | 0.165604i | −0.996566 | − | 0.0828018i | \(-0.973613\pi\) | ||
0.996566 | − | 0.0828018i | \(-0.0263869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.39527e12 | 1.19718 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.42714e11 | + | 1.57307e10i | −0.365528 | + | 0.0129881i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2.37088e12i | − | 1.88422i | −0.335311 | − | 0.942108i | \(-0.608841\pi\) | ||
0.335311 | − | 0.942108i | \(-0.391159\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.38542e12 | 1.82530 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.88545e11 | + | 1.81964e11i | 0.138950 | + | 0.134100i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 2.10863e12i | − | 1.49706i | −0.663103 | − | 0.748528i | \(-0.730761\pi\) | ||
0.663103 | − | 0.748528i | \(-0.269239\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.03984e9 | 0.00481633 | 0.00240817 | − | 0.999997i | \(-0.499233\pi\) | ||||
0.00240817 | + | 0.999997i | \(0.499233\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.13919e12 | + | 2.21655e12i | −1.41071 | + | 1.46172i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 3.35732e12i | − | 2.13466i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.66329e11 | −0.347272 | −0.173636 | − | 0.984810i | \(-0.555552\pi\) | ||||
−0.173636 | + | 0.984810i | \(0.555552\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.41645e10 | − | 2.08723e12i | −0.0438708 | − | 1.23467i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 2.59975e12i | − | 1.48388i | −0.670465 | − | 0.741942i | \(-0.733905\pi\) | ||
0.670465 | − | 0.741942i | \(-0.266095\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.69836e12 | 0.935617 | 0.467808 | − | 0.883830i | \(-0.345044\pi\) | ||||
0.467808 | + | 0.883830i | \(0.345044\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.28802e12 | − | 1.24307e12i | −0.685012 | − | 0.661104i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.09932e12i | 0.564568i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.44120e11 | −0.319505 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.23843e12 | − | 1.28322e12i | 0.593481 | − | 0.614943i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 5.67611e11i | 0.262853i | 0.991326 | + | 0.131426i | \(0.0419557\pi\) | ||||
−0.991326 | + | 0.131426i | \(0.958044\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.40749e11 | 0.331559 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.70840e12 | + | 1.90088e12i | −0.739279 | + | 0.822567i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 5.39382e11i | 0.225705i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.95487e12 | −1.60066 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.10899e12 | − | 2.03538e12i | −0.825775 | − | 0.796954i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.60632e12i | − | 3.26076i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.77370e12 | −1.01711 | −0.508555 | − | 0.861030i | \(-0.669820\pi\) | ||||
−0.508555 | + | 0.861030i | \(0.669820\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.34124e12 | − | 1.38974e12i | 0.476116 | − | 0.493334i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.17799e12i | 1.09232i | 0.837681 | + | 0.546161i | \(0.183911\pi\) | ||||
−0.837681 | + | 0.546161i | \(0.816089\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.55843e12 | 1.18450 | 0.592252 | − | 0.805752i | \(-0.298239\pi\) | ||||
0.592252 | + | 0.805752i | \(0.298239\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −8.88860e12 | + | 3.15834e11i | −2.86603 | + | 0.101837i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3.35804e12i | − | 1.04904i | −0.851400 | − | 0.524518i | \(-0.824246\pi\) | ||
0.851400 | − | 0.524518i | \(-0.175754\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.33625e12 | 0.404515 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.58336e12 | + | 4.42340e12i | 1.34480 | + | 1.29787i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 2.24600e12i | − | 0.638847i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.48591e12 | 2.34036 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.96842e11 | − | 7.22043e11i | 0.186378 | − | 0.193119i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 2.12131e9i | − | 0.000550333i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.34093e12 | −0.337493 | −0.168747 | − | 0.985659i | \(-0.553972\pi\) | ||||
−0.168747 | + | 0.985659i | \(0.553972\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.03902e11 | + | 2.92413e12i | 0.0253747 | + | 0.714127i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 9.18220e12i | − | 2.17632i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.61536e12 | −1.75203 | −0.876014 | − | 0.482285i | \(-0.839807\pi\) | ||||
−0.876014 | + | 0.482285i | \(0.839807\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.07063e12 | + | 1.03326e12i | 0.239134 | + | 0.230788i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.29992e12i | 1.36635i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.41769e12 | −1.35179 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.08149e12 | + | 1.12060e12i | −0.221272 | + | 0.229274i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.04512e12i | 0.804052i | 0.915628 | + | 0.402026i | \(0.131694\pi\) | ||||
−0.915628 | + | 0.402026i | \(0.868306\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.58213e12 | 1.46441 | 0.732207 | − | 0.681082i | \(-0.238490\pi\) | ||||
0.732207 | + | 0.681082i | \(0.238490\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.80463e12 | − | 4.31814e12i | −0.901829 | − | 0.810515i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.96340e12i | 0.723093i | 0.932354 | + | 0.361547i | \(0.117751\pi\) | ||||
−0.932354 | + | 0.361547i | \(0.882249\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.21309e13 | −2.15154 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −8.03006e12 | − | 7.74980e12i | −1.38477 | − | 1.33644i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.40340e12i | − | 1.57693i | −0.615079 | − | 0.788465i | \(-0.710876\pi\) | ||
0.615079 | − | 0.788465i | \(-0.289124\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.23471e12 | −0.690698 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.76708e11 | − | 1.01203e12i | 0.154964 | − | 0.160568i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.58610e12i | 0.244831i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.67351e12 | 0.401562 | 0.200781 | − | 0.979636i | \(-0.435652\pi\) | ||||
0.200781 | + | 0.979636i | \(0.435652\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.30390e12 | + | 8.18633e10i | −0.336769 | + | 0.0119662i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.25566e13i | 1.78649i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.52230e12 | −1.04185 | −0.520927 | − | 0.853602i | \(-0.674413\pi\) | ||||
−0.520927 | + | 0.853602i | \(0.674413\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.49595e12 | + | 8.19943e12i | 1.14566 | + | 1.10567i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.37749e12i | 0.443493i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.82171e12 | −0.616602 | −0.308301 | − | 0.951289i | \(-0.599760\pi\) | ||||
−0.308301 | + | 0.951289i | \(0.599760\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.23827e12 | + | 9.57236e12i | −1.15071 | + | 1.19232i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.52117e11i | 0.0305920i | 0.999883 | + | 0.0152960i | \(0.00486906\pi\) | ||||
−0.999883 | + | 0.0152960i | \(0.995131\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.68286e13 | 3.17172 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.94507e11 | − | 8.28839e12i | −0.0339267 | − | 0.954806i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.39301e12i | 0.605457i | 0.953077 | + | 0.302729i | \(0.0978976\pi\) | ||||
−0.953077 | + | 0.302729i | \(0.902102\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.95406e12 | −0.213822 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.83330e12 | − | 9.49010e12i | −1.04891 | − | 1.01230i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2.79770e13i | − | 2.90949i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.66288e12 | 0.878435 | 0.439218 | − | 0.898381i | \(-0.355256\pi\) | ||||
0.439218 | + | 0.898381i | \(0.355256\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.54335e12 | − | 6.77998e12i | 0.647047 | − | 0.670447i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5.59724e12i | − | 0.539824i | −0.962885 | − | 0.269912i | \(-0.913005\pi\) | ||
0.962885 | − | 0.269912i | \(-0.0869947\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.59236e13 | −1.49801 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.32382e12 | − | 1.86047e13i | −0.121493 | − | 1.70745i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 8.82595e12i | − | 0.790295i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.38459e12 | 0.208352 | 0.104176 | − | 0.994559i | \(-0.466779\pi\) | ||||
0.104176 | + | 0.994559i | \(0.466779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.09630e13 | + | 1.05804e13i | 0.934805 | + | 0.902179i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.89921e12i | 0.324509i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.98099e12 | −0.323408 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.17623e13 | + | 1.21876e13i | −0.932848 | + | 0.966583i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 9.44038e12i | − | 0.731004i | −0.930811 | − | 0.365502i | \(-0.880897\pi\) | ||
0.930811 | − | 0.365502i | \(-0.119103\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.89623e12 | −0.521436 | −0.260718 | − | 0.965415i | \(-0.583959\pi\) | ||||
−0.260718 | + | 0.965415i | \(0.583959\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.44573e9 | − | 1.57968e8i | 0.000328278 | − | 1.16645e-5i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.07425e13i | 2.21715i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.53027e13 | 3.19142 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.40211e13 | + | 1.35317e13i | 0.964928 | + | 0.931250i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.36918e12i | 0.0920604i | 0.998940 | + | 0.0460302i | \(0.0146570\pi\) | ||||
−0.998940 | + | 0.0460302i | \(0.985343\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.62027e12 | −0.434947 | −0.217474 | − | 0.976066i | \(-0.569782\pi\) | ||||
−0.217474 | + | 0.976066i | \(0.569782\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.77203e12 | + | 7.01693e12i | −0.434783 | + | 0.450506i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.64986e12i | − | 0.103524i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.25660e13 | −0.770679 | −0.385339 | − | 0.922775i | \(-0.625916\pi\) | ||||
−0.385339 | + | 0.922775i | \(0.625916\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.07021e12 | − | 3.01192e13i | −0.0641618 | − | 1.80572i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.42122e13i | 0.832997i | 0.909136 | + | 0.416499i | \(0.136743\pi\) | ||||
−0.909136 | + | 0.416499i | \(0.863257\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.76820e12 | 0.330553 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1.14832e13 | − | 1.10824e13i | −0.643467 | − | 0.621009i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.33640e12i | 0.128031i | 0.997949 | + | 0.0640154i | \(0.0203907\pi\) | ||||
−0.997949 | + | 0.0640154i | \(0.979609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.95390e12 | 0.372688 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −5.42577e12 | + | 5.62199e12i | −0.284427 | + | 0.294713i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.78116e13i | 3.47734i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.00514e13 | 1.50759 | 0.753797 | − | 0.657108i | \(-0.228220\pi\) | ||||
0.753797 | + | 0.657108i | \(0.228220\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.56436e13 | − | 1.74061e13i | 0.767846 | − | 0.854352i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 3.81933e12i | − | 0.183435i | −0.995785 | − | 0.0917176i | \(-0.970764\pi\) | ||
0.995785 | − | 0.0917176i | \(-0.0292357\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.23279e11 | 0.0198940 | 0.00994700 | − | 0.999951i | \(-0.496834\pi\) | ||||
0.00994700 | + | 0.999951i | \(0.496834\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.30822e13 | − | 3.19276e13i | −1.52170 | − | 1.46859i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.30173e12i | 0.148647i | 0.997234 | + | 0.0743236i | \(0.0236798\pi\) | ||||
−0.997234 | + | 0.0743236i | \(0.976320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.83340e13 | 2.13004 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1.63193e13 | + | 1.69095e13i | −0.704041 | + | 0.729502i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.50170e13i | 1.05665i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.59567e13 | −1.07345 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.63153e13 | + | 9.35049e11i | −1.06566 | + | 0.0378654i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.64798e12i | 0.382612i | 0.981530 | + | 0.191306i | \(0.0612723\pi\) | ||||
−0.981530 | + | 0.191306i | \(0.938728\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.23084e13 | 0.866447 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.89869e12 | − | 5.69282e12i | −0.224399 | − | 0.216567i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 3.92578e13i | − | 1.46291i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.19673e13 | 0.801923 | 0.400962 | − | 0.916095i | \(-0.368676\pi\) | ||||
0.400962 | + | 0.916095i | \(0.368676\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.28429e12 | − | 9.62005e12i | 0.332051 | − | 0.344059i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.28264e13i | 1.50074i | 0.661021 | + | 0.750368i | \(0.270123\pi\) | ||||
−0.661021 | + | 0.750368i | \(0.729877\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.22359e13 | −0.420146 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.99785e12 | + | 5.62259e13i | 0.0672258 | + | 1.89195i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 6.38554e13i | − | 2.10579i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.94645e13 | 1.59879 | 0.799394 | − | 0.600808i | \(-0.205154\pi\) | ||||
0.799394 | + | 0.600808i | \(0.205154\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.37366e13 | − | 2.29081e13i | −0.752020 | − | 0.725773i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.19508e12i | 0.254515i | 0.991870 | + | 0.127257i | \(0.0406174\pi\) | ||||
−0.991870 | + | 0.127257i | \(0.959383\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.45210e13 | −1.96446 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.09392e13 | + | 1.13348e13i | −0.326546 | + | 0.338355i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 6.27293e13i | − | 1.83604i | −0.396538 | − | 0.918018i | \(-0.629789\pi\) | ||
0.396538 | − | 0.918018i | \(-0.370211\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.34904e12 | −0.239625 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.46964e13 | + | 1.32083e13i | 0.413641 | + | 0.371758i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 4.25167e13i | − | 1.17361i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.34186e10 | −0.000363291 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.48132e12 | − | 9.15041e12i | −0.251786 | − | 0.242999i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.82197e13i | 1.77714i | 0.458742 | + | 0.888570i | \(0.348300\pi\) | ||||
−0.458742 | + | 0.888570i | \(0.651700\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.20501e13 | 1.33019 | 0.665094 | − | 0.746760i | \(-0.268392\pi\) | ||||
0.665094 | + | 0.746760i | \(0.268392\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −8.95632e13 | + | 9.28022e13i | −2.24560 | + | 2.32681i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 5.76875e13i | − | 1.41915i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.99911e13 | 0.965351 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.17175e12 | + | 2.90363e11i | −0.193572 | + | 0.00687810i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.75766e13i | 0.408600i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.40220e14 | 3.19920 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.70258e13 | − | 1.64316e13i | −0.381274 | − | 0.367967i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 9.09092e13i | 1.99832i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.97274e13 | 1.93615 | 0.968074 | − | 0.250664i | \(-0.0806490\pi\) | ||||
0.968074 | + | 0.250664i | \(0.0806490\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.14562e13 | − | 3.25937e13i | 0.666356 | − | 0.690454i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 2.20896e13i | − | 0.459416i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.14970e13 | 1.45999 | 0.729997 | − | 0.683450i | \(-0.239521\pi\) | ||||
0.729997 | + | 0.683450i | \(0.239521\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3.37356e12 | + | 9.49428e13i | 0.0676435 | + | 1.90371i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 1.03310e13i | − | 0.203416i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.47268e14 | 2.84762 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.63469e13 | + | 4.47293e13i | 0.880148 | + | 0.849430i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 3.15650e13i | − | 0.588748i | −0.955690 | − | 0.294374i | \(-0.904889\pi\) | ||
0.955690 | − | 0.294374i | \(-0.0951112\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.32326e13 | −1.15846 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.90223e13 | + | 5.07951e13i | −0.882225 | + | 0.914129i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.62866e13i | − | 0.464721i | −0.972630 | − | 0.232360i | \(-0.925355\pi\) | ||
0.972630 | − | 0.232360i | \(-0.0746449\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.27541e13 | 0.568883 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.79330e13 | − | 6.96841e12i | 1.67114 | − | 0.118910i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.15953e13i | 1.20039i | 0.799853 | + | 0.600196i | \(0.204911\pi\) | ||||
−0.799853 | + | 0.600196i | \(0.795089\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.82970e13 | −1.45467 | −0.727337 | − | 0.686281i | \(-0.759242\pi\) | ||||
−0.727337 | + | 0.686281i | \(0.759242\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.82463e13 | + | 1.76095e13i | 0.295394 | + | 0.285085i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.25827e13i | 0.359283i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.49027e13 | −0.858449 | −0.429225 | − | 0.903198i | \(-0.641213\pi\) | ||||
−0.429225 | + | 0.903198i | \(0.641213\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.90042e13 | + | 1.96915e13i | −0.292050 | + | 0.302611i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.09555e13i | − | 0.316531i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.94280e13 | 1.17932 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.42116e14 | + | 5.04973e12i | −2.07426 | + | 0.0737036i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 3.24821e13i | − | 0.466073i | −0.972468 | − | 0.233037i | \(-0.925134\pi\) | ||
0.972468 | − | 0.233037i | \(-0.0748662\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.87070e13 | 0.687092 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.65999e13 | − | 3.53225e13i | −0.507624 | − | 0.489907i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.39408e13i | 0.735603i | 0.929904 | + | 0.367802i | \(0.119889\pi\) | ||||
−0.929904 | + | 0.367802i | \(0.880111\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.45666e14 | −3.29428 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.55841e12 | + | 2.65093e12i | −0.0337364 | + | 0.0349564i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.22481e13i | 0.418186i | 0.977896 | + | 0.209093i | \(0.0670512\pi\) | ||||
−0.977896 | + | 0.209093i | \(0.932949\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.59568e13 | 0.458573 | 0.229286 | − | 0.973359i | \(-0.426361\pi\) | ||||
0.229286 | + | 0.973359i | \(0.426361\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.59929e12 | + | 1.01296e14i | 0.0451471 | + | 1.27059i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 3.09613e13i | − | 0.381981i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.98176e13 | −0.725915 | −0.362957 | − | 0.931806i | \(-0.618233\pi\) | ||||
−0.362957 | + | 0.931806i | \(0.618233\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.69363e13 | − | 3.56472e13i | −0.440927 | − | 0.425538i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 3.39167e10i | − | 0.000398298i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −5.00692e12 | −0.0578454 | −0.0289227 | − | 0.999582i | \(-0.509208\pi\) | ||||
−0.0289227 | + | 0.999582i | \(0.509208\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.52419e13 | + | 3.65164e13i | −0.400575 | + | 0.415061i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 1.77476e14i | − | 1.98479i | −0.123095 | − | 0.992395i | \(-0.539282\pi\) | ||
0.123095 | − | 0.992395i | \(-0.460718\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.46484e13 | −0.161189 | −0.0805946 | − | 0.996747i | \(-0.525682\pi\) | ||||
−0.0805946 | + | 0.996747i | \(0.525682\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.14914e13 | − | 1.27861e13i | 0.124427 | − | 0.138446i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.03631e13i | 0.323524i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.58462e13 | 0.795305 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.28876e13 | − | 4.13907e13i | −0.442582 | − | 0.427135i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.08180e13i | 0.820833i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.18554e13 | −0.518379 | −0.259189 | − | 0.965827i | \(-0.583455\pi\) | ||||
−0.259189 | + | 0.965827i | \(0.583455\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.50438e13 | − | 4.66728e13i | 0.443217 | − | 0.459246i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.92850e14i | 2.83646i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.29781e14 | −2.19087 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.33825e14 | − | 4.75512e12i | 1.25612 | − | 0.0446331i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.58207e14i | 1.46196i | 0.682396 | + | 0.730982i | \(0.260938\pi\) | ||||
−0.682396 | + | 0.730982i | \(0.739062\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.36125e14 | 1.23846 | 0.619231 | − | 0.785209i | \(-0.287444\pi\) | ||||
0.619231 | + | 0.785209i | \(0.287444\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.31369e14 | − | 1.26784e14i | −1.17678 | − | 1.13571i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 9.00820e13i | − | 0.794541i | −0.917702 | − | 0.397271i | \(-0.869957\pi\) | ||
0.917702 | − | 0.397271i | \(-0.130043\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.46649e13 | 0.214218 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.68063e14 | − | 1.74141e14i | 1.43737 | − | 1.48935i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 3.05209e13i | − | 0.257059i | −0.991706 | − | 0.128529i | \(-0.958974\pi\) | ||
0.991706 | − | 0.128529i | \(-0.0410256\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00833e14 | −2.49528 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.21728e11 | − | 1.74974e13i | −0.00507895 | − | 0.142938i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1.37676e14i | − | 1.10773i | −0.832608 | − | 0.553863i | \(-0.813153\pi\) | ||
0.832608 | − | 0.553863i | \(-0.186847\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.75218e13 | 0.455854 | 0.227927 | − | 0.973678i | \(-0.426805\pi\) | ||||
0.227927 | + | 0.973678i | \(0.426805\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.28389e14 | − | 1.23908e14i | −1.00221 | − | 0.967235i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2.07422e14i | − | 1.59495i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.98817e12 | −0.0680835 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.10922e14 | − | 1.14933e14i | 0.827723 | − | 0.857657i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 2.86567e14i | − | 2.10676i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.10871e13 | 0.587322 | 0.293661 | − | 0.955910i | \(-0.405126\pi\) | ||||
0.293661 | + | 0.955910i | \(0.405126\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.01159e14 | − | 1.80791e14i | −1.43556 | − | 1.29020i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.40518e13i | 0.309756i | 0.987934 | + | 0.154878i | \(0.0494985\pi\) | ||||
−0.987934 | + | 0.154878i | \(0.950501\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.06648e14 | 1.43180 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.34922e13 | − | 5.16253e13i | −0.365220 | − | 0.352474i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 2.80952e14i | − | 1.89029i | −0.326654 | − | 0.945144i | \(-0.605921\pi\) | ||
0.326654 | − | 0.945144i | \(-0.394079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.35395e14 | 2.22384 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −7.09671e13 | + | 7.35335e13i | −0.463739 | + | 0.480509i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.00761e14i | 1.29295i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.40745e14 | −0.893393 | −0.446697 | − | 0.894686i | \(-0.647400\pi\) | ||||
−0.446697 | + | 0.894686i | \(0.647400\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.95966e14 | + | 1.05164e13i | −1.85172 | + | 0.0657964i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.72860e14i | 2.29944i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.36759e13 | −0.387089 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.64677e13 | + | 1.58930e13i | 0.0986842 | + | 0.0952400i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.11816e13i | 0.184208i | 0.995749 | + | 0.0921040i | \(0.0293592\pi\) | ||||
−0.995749 | + | 0.0921040i | \(0.970641\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.82367e13 | −0.397412 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.80047e10 | − | 7.04640e10i | 0.000390475 | − | 0.000404596i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 3.39631e14i | − | 1.92269i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.26220e14 | 1.82087 | 0.910436 | − | 0.413651i | \(-0.135747\pi\) | ||||
0.910436 | + | 0.413651i | \(0.135747\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.09666e13 | + | 3.08636e14i | 0.0603565 | + | 1.69863i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.23759e13i | − | 0.229970i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.28950e14 | 2.29550 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.83039e14 | − | 1.76651e14i | −0.965936 | − | 0.932224i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 2.80158e14i | − | 1.45801i | −0.684511 | − | 0.729003i | \(-0.739984\pi\) | ||
0.684511 | − | 0.729003i | \(-0.260016\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.23803e14 | 1.14865 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −8.15649e13 | + | 8.45146e13i | −0.412869 | + | 0.427799i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.41408e14i | 0.705965i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.09502e14 | −0.539202 | −0.269601 | − | 0.962972i | \(-0.586892\pi\) | ||||
−0.269601 | + | 0.962972i | \(0.586892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.18968e13 | + | 2.04723e14i | 0.106351 | + | 0.994329i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 2.29077e14i | − | 1.09748i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.14955e14 | 0.543262 | 0.271631 | − | 0.962401i | \(-0.412437\pi\) | ||||
0.271631 | + | 0.962401i | \(0.412437\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.77383e14 | − | 4.60722e14i | −2.22552 | − | 2.14784i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 3.05742e14i | − | 1.40611i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.62362e14 | −0.736651 | −0.368325 | − | 0.929697i | \(-0.620069\pi\) | ||||
−0.368325 | + | 0.929697i | \(0.620069\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.04619e14 | − | 1.08402e14i | 0.468294 | − | 0.485229i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.87172e13i | 0.347636i | 0.984778 | + | 0.173818i | \(0.0556105\pi\) | ||||
−0.984778 | + | 0.173818i | \(0.944389\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.51309e14 | −1.53076 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.39173e13 | − | 1.56049e12i | 0.188813 | − | 0.00670901i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.38102e14i | 3.13117i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.16911e14 | 0.907990 | 0.453995 | − | 0.891004i | \(-0.349998\pi\) | ||||
0.453995 | + | 0.891004i | \(0.349998\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.56056e12 | + | 2.47119e12i | 0.0105769 | + | 0.0102078i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.71995e14i | 0.701102i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.18882e14 | −1.28277 | −0.641387 | − | 0.767217i | \(-0.721641\pi\) | ||||
−0.641387 | + | 0.767217i | \(0.721641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.60106e13 | + | 3.73129e13i | −0.142962 | + | 0.148132i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1.03295e14i | − | 0.404720i | −0.979311 | − | 0.202360i | \(-0.935139\pi\) | ||
0.979311 | − | 0.202360i | \(-0.0648610\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.16277e14 | 0.449648 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.82940e13 | − | 5.14853e14i | −0.0698235 | − | 1.96506i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.23428e13i | 0.234860i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.32731e14 | −1.60911 | −0.804556 | − | 0.593877i | \(-0.797597\pi\) | ||||
−0.804556 | + | 0.593877i | \(0.797597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.24642e13 | + | 3.13311e13i | 0.119160 | + | 0.115002i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.82569e14i | − | 0.661499i | −0.943719 | − | 0.330749i | \(-0.892699\pi\) | ||
0.943719 | − | 0.330749i | \(-0.107301\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.66685e14 | −2.38458 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.35450e14 | + | 2.43965e14i | −0.831368 | + | 0.861434i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 5.37631e13i | − | 0.187412i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.03925e14 | −1.39010 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 7.19567e13 | − | 8.00635e13i | 0.244491 | − | 0.272036i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 5.17317e14i | 1.73544i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.59519e14 | −0.859599 | −0.429799 | − | 0.902924i | \(-0.641416\pi\) | ||||
−0.429799 | + | 0.902924i | \(0.641416\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.14551e14 | + | 4.00082e14i | 1.35579 | + | 1.30847i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.72414e14i | 0.556787i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.24324e14 | 2.30976 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.02536e14 | + | 4.17093e14i | −1.26756 | + | 1.31340i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 4.01181e14i | − | 1.24752i | −0.781615 | − | 0.623762i | \(-0.785604\pi\) | ||
0.781615 | − | 0.623762i | \(-0.214396\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.22872e11 | 0.000377329 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.36334e13 | + | 2.26105e12i | −0.192984 | + | 0.00685722i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.28128e13i | 0.158184i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.80460e14 | −0.533829 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 3.68696e14 | + | 3.55828e14i | 1.07721 | + | 1.03961i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.58715e14i | − | 1.03516i | −0.855635 | − | 0.517580i | \(-0.826833\pi\) | ||
0.855635 | − | 0.517580i | \(-0.173167\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.70575e14 | −0.486197 | −0.243099 | − | 0.970002i | \(-0.578164\pi\) | ||||
−0.243099 | + | 0.970002i | \(0.578164\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.18796e12 | + | 1.23092e12i | −0.00334465 | + | 0.00346560i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 2.94309e14i | − | 0.818493i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.93416e14 | 0.531350 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.65812e13 | − | 7.48081e14i | −0.0721365 | − | 2.03015i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.41602e14i | 1.45199i | 0.687699 | + | 0.725996i | \(0.258621\pi\) | ||||
−0.687699 | + | 0.725996i | \(0.741379\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.00889e14 | 1.59146 | 0.795728 | − | 0.605654i | \(-0.207088\pi\) | ||||
0.795728 | + | 0.605654i | \(0.207088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 5.87031e14 | + | 5.66543e14i | 1.53600 | + | 1.48239i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.42677e14i | 1.66137i | 0.556746 | + | 0.830683i | \(0.312050\pi\) | ||||
−0.556746 | + | 0.830683i | \(0.687950\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.94214e14 | −0.751433 | −0.375716 | − | 0.926735i | \(-0.622603\pi\) | ||||
−0.375716 | + | 0.926735i | \(0.622603\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.55673e13 | − | 9.90233e13i | 0.241159 | − | 0.249881i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 8.32443e14i | − | 2.07553i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.26179e14 | −1.78900 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.77470e14 | + | 3.39249e14i | 0.918871 | + | 0.825832i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 3.32908e14i | − | 0.800783i | −0.916344 | − | 0.400391i | \(-0.868874\pi\) | ||
0.916344 | − | 0.400391i | \(-0.131126\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.64425e14 | 0.866221 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.54569e14 | + | 4.38704e14i | 1.06773 | + | 1.03047i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.46768e14i | 0.804924i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.62977e14 | 0.373859 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.86596e14 | + | 2.96960e14i | −0.649728 | + | 0.673225i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.93670e13i | 0.133014i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.59443e14 | 0.795948 | 0.397974 | − | 0.917397i | \(-0.369713\pi\) | ||||
0.397974 | + | 0.917397i | \(0.369713\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.34703e14 | − | 1.54461e13i | 0.951398 | − | 0.0338056i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.64547e14i | 0.572267i | 0.958190 | + | 0.286133i | \(0.0923700\pi\) | ||||
−0.958190 | + | 0.286133i | \(0.907630\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.74692e14 | 1.87021 | 0.935103 | − | 0.354376i | \(-0.115307\pi\) | ||||
0.935103 | + | 0.354376i | \(0.115307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.92218e14 | − | 1.85509e14i | −0.406236 | − | 0.392057i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.64635e14i | 0.970639i | 0.874337 | + | 0.485320i | \(0.161297\pi\) | ||||
−0.874337 | + | 0.485320i | \(0.838703\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.90065e14 | −0.598983 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.08694e14 | − | 1.12625e14i | 0.221876 | − | 0.229900i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 9.31560e14i | − | 1.87980i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.72790e14 | 1.54160 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.53885e13 | + | 4.33082e14i | 0.0303476 | + | 0.854080i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.36818e15i | 2.66750i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.09510e14 | 0.596591 | 0.298295 | − | 0.954474i | \(-0.403582\pi\) | ||||
0.298295 | + | 0.954474i | \(0.403582\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.92474e13 | − | 9.57835e13i | −0.189136 | − | 0.182535i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 3.87713e14i | − | 0.730518i | −0.930906 | − | 0.365259i | \(-0.880980\pi\) | ||
0.930906 | − | 0.365259i | \(-0.119020\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.34305e14 | −0.622786 | −0.311393 | − | 0.950281i | \(-0.600796\pi\) | ||||
−0.311393 | + | 0.950281i | \(0.600796\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.25000e14 | + | 1.29521e14i | −0.230247 | + | 0.238574i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 4.02259e14i | − | 0.732636i | −0.930490 | − | 0.366318i | \(-0.880618\pi\) | ||
0.930490 | − | 0.366318i | \(-0.119382\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.54153e15 | −2.77614 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.40795e13 | − | 6.19486e14i | −0.0784961 | − | 1.10317i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.03744e11i | 0.000182687i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −5.20876e14 | −0.907025 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.43115e13 | − | 9.10199e13i | −0.162406 | − | 0.156738i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 2.65348e14i | − | 0.451874i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.27311e14 | −1.22489 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.67379e14 | − | 6.91513e14i | 1.11156 | − | 1.15176i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 9.97148e14i | − | 1.64254i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.22073e14 | −0.198877 | −0.0994383 | − | 0.995044i | \(-0.531705\pi\) | ||||
−0.0994383 | + | 0.995044i | \(0.531705\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.11779e14 | − | 2.52913e13i | 1.14690 | − | 0.0407522i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 8.78434e14i | − | 1.39997i | −0.714160 | − | 0.699983i | \(-0.753191\pi\) | ||
0.714160 | − | 0.699983i | \(-0.246809\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.32556e14 | −0.208952 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.50483e15 | + | 1.45230e15i | 2.34628 | + | 2.26440i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 1.58355e15i | − | 2.44222i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.50552e14 | 0.992440 | 0.496220 | − | 0.868197i | \(-0.334721\pi\) | ||||
0.496220 | + | 0.868197i | \(0.334721\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.68058e14 | − | 4.84985e14i | 0.706320 | − | 0.731863i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1.02096e15i | − | 1.52405i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.34001e14 | 1.37924 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.66659e13 | + | 4.69033e14i | 0.0243462 | + | 0.685180i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.32678e14i | 0.480779i | 0.970676 | + | 0.240390i | \(0.0772752\pi\) | ||||
−0.970676 | + | 0.240390i | \(0.922725\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.02853e14 | 1.00488 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.55675e14 | − | 5.36281e14i | −0.785982 | − | 0.758550i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.55399e15i | 2.17465i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.20052e14 | −0.443121 | −0.221561 | − | 0.975147i | \(-0.571115\pi\) | ||||
−0.221561 | + | 0.975147i | \(0.571115\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.00480e14 | + | 6.22196e14i | −0.822566 | + | 0.852313i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.14134e14i | 1.23897i | 0.785007 | + | 0.619487i | \(0.212659\pi\) | ||||
−0.785007 | + | 0.619487i | \(0.787341\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.67748e13 | −0.0627268 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.44471e15 | − | 1.60748e15i | 1.91700 | − | 2.13298i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 6.50116e14i | − | 0.853573i | −0.904352 | − | 0.426787i | \(-0.859646\pi\) | ||
0.904352 | − | 0.426787i | \(-0.140354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.33489e14 | −0.173426 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.87158e14 | + | 5.66665e14i | 0.754835 | + | 0.728490i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 2.90513e14i | 0.369574i | 0.982779 | + | 0.184787i | \(0.0591595\pi\) | ||||
−0.982779 | + | 0.184787i | \(0.940840\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.58214e14 | 0.702723 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.25490e14 | + | 2.33645e14i | −0.280911 | + | 0.291069i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.76548e15i | 2.17655i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.31389e14 | 0.526322 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.54687e15 | + | 5.49643e13i | −1.86777 | + | 0.0663665i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.02426e14i | 0.719892i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.49279e13 | −0.0767890 | −0.0383945 | − | 0.999263i | \(-0.512224\pi\) | ||||
−0.0383945 | + | 0.999263i | \(0.512224\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.92716e14 | + | 3.79009e14i | 0.459684 | + | 0.443640i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.14450e15i | 1.32593i | 0.748652 | + | 0.662963i | \(0.230702\pi\) | ||||
−0.748652 | + | 0.662963i | \(0.769298\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.96269e15 | −2.25054 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.43199e15 | + | 1.48377e15i | −1.62523 | + | 1.68401i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.42540e15i | 1.60127i | 0.599151 | + | 0.800636i | \(0.295505\pi\) | ||||
−0.599151 | + | 0.800636i | \(0.704495\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.92066e14 | 0.213568 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.65882e12 | + | 2.43687e14i | 0.00953046 | + | 0.268218i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 8.80673e14i | 0.959504i | 0.877404 | + | 0.479752i | \(0.159273\pi\) | ||||
−0.877404 | + | 0.479752i | \(0.840727\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.11971e15 | −1.20760 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.70914e11 | + | 3.57969e11i | 0.000395993 | + | 0.000382172i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1.68275e14i | − | 0.177843i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.31440e14 | −0.346766 | −0.173383 | − | 0.984854i | \(-0.555470\pi\) | ||||
−0.173383 | + | 0.984854i | \(0.555470\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.26279e14 | − | 2.34462e14i | 0.234368 | − | 0.242844i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.11007e13i | 0.0831590i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.53229e14 | 0.460089 | 0.230044 | − | 0.973180i | \(-0.426113\pi\) | ||||
0.230044 | + | 0.973180i | \(0.426113\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.28821e14 | − | 4.75275e14i | −0.531473 | − | 0.477659i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 192.11.e.k.65.6 | 20 | ||
3.2 | odd | 2 | inner | 192.11.e.k.65.5 | 20 | ||
4.3 | odd | 2 | inner | 192.11.e.k.65.15 | 20 | ||
8.3 | odd | 2 | 96.11.e.a.65.6 | yes | 20 | ||
8.5 | even | 2 | 96.11.e.a.65.15 | yes | 20 | ||
12.11 | even | 2 | inner | 192.11.e.k.65.16 | 20 | ||
24.5 | odd | 2 | 96.11.e.a.65.16 | yes | 20 | ||
24.11 | even | 2 | 96.11.e.a.65.5 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
96.11.e.a.65.5 | ✓ | 20 | 24.11 | even | 2 | ||
96.11.e.a.65.6 | yes | 20 | 8.3 | odd | 2 | ||
96.11.e.a.65.15 | yes | 20 | 8.5 | even | 2 | ||
96.11.e.a.65.16 | yes | 20 | 24.5 | odd | 2 | ||
192.11.e.k.65.5 | 20 | 3.2 | odd | 2 | inner | ||
192.11.e.k.65.6 | 20 | 1.1 | even | 1 | trivial | ||
192.11.e.k.65.15 | 20 | 4.3 | odd | 2 | inner | ||
192.11.e.k.65.16 | 20 | 12.11 | even | 2 | inner |