Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [48,22,Mod(47,48)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(48, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("48.47");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 48 = 2^{4} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 48.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(134.149125258\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 47.7 | ||
Character | \(\chi\) | \(=\) | 48.47 |
Dual form | 48.22.c.c.47.8 |
$q$-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 \(\left(\mathbb{Z}/48\mathbb{Z}\right)^\times\).
\(n\) | \(17\) | \(31\) | \(37\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | −66724.2 | − | 77512.8i | −0.652394 | − | 0.757880i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 3.35931e6i | − | 0.153839i | −0.997037 | − | 0.0769193i | \(-0.975492\pi\) | ||
0.997037 | − | 0.0769193i | \(-0.0245084\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 5.38569e8i | − | 0.720630i | −0.932831 | − | 0.360315i | \(-0.882669\pi\) | ||
0.932831 | − | 0.360315i | \(-0.117331\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.55613e9 | + | 1.03440e10i | −0.148764 | + | 0.988873i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10838e10 | −0.128844 | −0.0644219 | − | 0.997923i | \(-0.520520\pi\) | ||||
−0.0644219 | + | 0.997923i | \(0.520520\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.02798e11 | −0.206815 | −0.103407 | − | 0.994639i | \(-0.532975\pi\) | ||||
−0.103407 | + | 0.994639i | \(0.532975\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.60390e11 | + | 2.24147e11i | −0.116591 | + | 0.100363i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.33984e12i | 0.883025i | 0.897255 | + | 0.441513i | \(0.145558\pi\) | ||||
−0.897255 | + | 0.441513i | \(0.854442\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.47425e13i | − | 0.925827i | −0.886403 | − | 0.462914i | \(-0.846804\pi\) | ||
0.886403 | − | 0.462914i | \(-0.153196\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.17460e13 | + | 3.59356e13i | −0.546151 | + | 0.470134i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.19781e13 | 0.0602902 | 0.0301451 | − | 0.999546i | \(-0.490403\pi\) | ||||
0.0301451 | + | 0.999546i | \(0.490403\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65552e14 | 0.976334 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 9.05621e14 | − | 5.69572e14i | 0.846500 | − | 0.532389i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 1.07027e15i | − | 0.472405i | −0.971704 | − | 0.236202i | \(-0.924097\pi\) | ||
0.971704 | − | 0.236202i | \(-0.0759028\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.35099e15i | 0.515173i | 0.966255 | + | 0.257587i | \(0.0829273\pi\) | ||||
−0.966255 | + | 0.257587i | \(0.917073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.39554e14 | + | 8.59133e14i | 0.0840569 | + | 0.0976482i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.80922e15 | −0.110861 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.92214e15 | −0.339224 | −0.169612 | − | 0.985511i | \(-0.554252\pi\) | ||||
−0.169612 | + | 0.985511i | \(0.554252\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.85914e15 | + | 7.96820e15i | 0.134925 | + | 0.156741i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.00256e16i | 0.582052i | 0.956715 | + | 0.291026i | \(0.0939965\pi\) | ||||
−0.956715 | + | 0.291026i | \(0.906003\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.92100e16i | − | 0.206117i | −0.994675 | − | 0.103058i | \(-0.967137\pi\) | ||
0.994675 | − | 0.103058i | \(-0.0328628\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.47486e16 | + | 5.22752e15i | 0.152127 | + | 0.0228857i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.06543e17 | 1.68203 | 0.841016 | − | 0.541010i | \(-0.181958\pi\) | ||||
0.841016 | + | 0.541010i | \(0.181958\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.68489e17 | 0.480693 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.68932e17 | − | 4.89745e17i | 0.669227 | − | 0.576080i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.40099e18i | 1.10037i | 0.835043 | + | 0.550185i | \(0.185443\pi\) | ||||
−0.835043 | + | 0.550185i | \(0.814557\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.72338e16i | 0.0198212i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.91786e18 | + | 1.65092e18i | −0.701666 | + | 0.604004i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.94674e18 | 0.750577 | 0.375288 | − | 0.926908i | \(-0.377544\pi\) | ||||
0.375288 | + | 0.926908i | \(0.377544\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.60888e18 | 0.468264 | 0.234132 | − | 0.972205i | \(-0.424775\pi\) | ||||
0.234132 | + | 0.972205i | \(0.424775\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.57094e18 | + | 8.38082e17i | 0.712611 | + | 0.107204i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.45332e17i | 0.0318161i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.51456e18i | 0.101508i | 0.998711 | + | 0.0507542i | \(0.0161625\pi\) | ||||
−0.998711 | + | 0.0507542i | \(0.983837\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.99230e17 | − | 9.28459e17i | −0.0393329 | − | 0.0456927i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.03995e19 | 0.743716 | 0.371858 | − | 0.928290i | \(-0.378721\pi\) | ||||
0.371858 | + | 0.928290i | \(0.378721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.87616e19 | 0.510951 | 0.255475 | − | 0.966816i | \(-0.417768\pi\) | ||||
0.255475 | + | 0.966816i | \(0.417768\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −3.10636e19 | − | 3.60863e19i | −0.636954 | − | 0.739944i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.96937e18i | 0.0928487i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.90268e19i | 0.463744i | 0.972746 | + | 0.231872i | \(0.0744851\pi\) | ||||
−0.972746 | + | 0.231872i | \(0.925515\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.04576e20 | − | 3.21930e19i | −0.955738 | − | 0.294218i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.01616e20 | −1.42628 | −0.713141 | − | 0.701021i | \(-0.752728\pi\) | ||||
−0.713141 | + | 0.701021i | \(0.752728\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.46568e19 | 0.135843 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.29597e19 | + | 7.14129e19i | −0.358026 | + | 0.308194i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 3.22002e20i | − | 1.09462i | −0.836930 | − | 0.547310i | \(-0.815652\pi\) | ||
0.836930 | − | 0.547310i | \(-0.184348\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.53641e19i | 0.149037i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.82232e20 | − | 1.56868e20i | 0.390440 | − | 0.336096i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.31176e19 | −0.142428 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.24560e20 | −0.584569 | −0.292285 | − | 0.956331i | \(-0.594415\pi\) | ||||
−0.292285 | + | 0.956331i | \(0.594415\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.72477e19 | − | 1.14650e20i | 0.0191674 | − | 0.127410i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.28599e20i | 0.656318i | 0.944622 | + | 0.328159i | \(0.106428\pi\) | ||||
−0.944622 | + | 0.328159i | \(0.893572\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.10166e21i | − | 0.807714i | −0.914822 | − | 0.403857i | \(-0.867669\pi\) | ||
0.914822 | − | 0.403857i | \(-0.132331\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.20719e20 | + | 1.40238e20i | 0.0723248 | + | 0.0840191i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.86116e21 | 1.40609 | 0.703043 | − | 0.711148i | \(-0.251824\pi\) | ||||
0.703043 | + | 0.711148i | \(0.251824\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.14210e20 | −0.248507 | −0.124254 | − | 0.992250i | \(-0.539654\pi\) | ||||
−0.124254 | + | 0.992250i | \(0.539654\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.62046e20 | + | 7.69093e20i | 0.221308 | + | 0.257091i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.66572e20i | − | 0.184724i | −0.995725 | − | 0.0923620i | \(-0.970558\pi\) | ||
0.995725 | − | 0.0923620i | \(-0.0294417\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 4.02383e19i | − | 0.00927496i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.59967e20 | − | 1.06334e21i | 0.0307666 | − | 0.204513i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.95301e21 | 0.636334 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.27740e21 | −0.983399 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.87762e21 | − | 3.33791e21i | 0.441125 | − | 0.379727i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 3.16578e21i | − | 0.304036i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.06323e21i | − | 0.655496i | −0.944765 | − | 0.327748i | \(-0.893710\pi\) | ||
0.944765 | − | 0.327748i | \(-0.106290\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.26415e21 | + | 1.94901e21i | −0.156212 | + | 0.134469i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.11320e21 | −0.300154 | −0.150077 | − | 0.988674i | \(-0.547952\pi\) | ||||
−0.150077 | + | 0.988674i | \(0.547952\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.33255e22 | −0.667179 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.91337e21 | − | 3.04226e21i | −0.0819020 | − | 0.130224i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 3.00101e22i | − | 1.10078i | −0.834907 | − | 0.550392i | \(-0.814478\pi\) | ||
0.834907 | − | 0.550392i | \(-0.185522\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.17753e22i | − | 0.370951i | −0.982649 | − | 0.185476i | \(-0.940617\pi\) | ||
0.982649 | − | 0.185476i | \(-0.0593826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.04711e22 | − | 4.70149e22i | −1.09735 | − | 1.27478i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.13939e21 | 0.0266468 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.59537e21 | −0.0726741 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.79147e22 | − | 2.08114e22i | −0.313601 | − | 0.364308i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 1.04192e23i | − | 1.58262i | −0.611415 | − | 0.791310i | \(-0.709400\pi\) | ||
0.611415 | − | 0.791310i | \(-0.290600\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.10277e22i | 0.277673i | 0.990315 | + | 0.138836i | \(0.0443362\pi\) | ||||
−0.990315 | + | 0.138836i | \(0.955664\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −7.59230e22 | − | 1.14217e22i | −0.873199 | − | 0.131363i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 7.89772e21 | 0.0792536 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.94849e23 | −1.70904 | −0.854521 | − | 0.519417i | \(-0.826149\pi\) | ||||
−0.854521 | + | 0.519417i | \(0.826149\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.08595e23 | − | 9.34799e22i | 0.833948 | − | 0.717874i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.45105e21i | − | 0.0434469i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 2.58356e23i | − | 1.52844i | −0.644956 | − | 0.764220i | \(-0.723124\pi\) | ||
0.644956 | − | 0.764220i | \(-0.276876\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.88610e21 | − | 2.48439e21i | 0.0150221 | − | 0.0129312i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.21326e23 | 1.47375 | 0.736874 | − | 0.676030i | \(-0.236301\pi\) | ||||
0.736874 | + | 0.676030i | \(0.236301\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.36497e23 | −0.957228 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.55935e23 | + | 3.85024e22i | 0.915525 | + | 0.137730i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.34693e23i | − | 1.37625i | −0.725591 | − | 0.688126i | \(-0.758434\pi\) | ||
0.725591 | − | 0.688126i | \(-0.241566\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 2.50732e23i | − | 0.703575i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.96618e23 | − | 2.28410e23i | −0.489672 | − | 0.568847i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.46180e23 | 1.20887 | 0.604435 | − | 0.796655i | \(-0.293399\pi\) | ||||
0.604435 | + | 0.796655i | \(0.293399\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −5.49682e23 | −1.08265 | −0.541323 | − | 0.840815i | \(-0.682076\pi\) | ||||
−0.541323 | + | 0.840815i | \(0.682076\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.74075e23 | − | 2.02222e23i | −0.305493 | − | 0.354888i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.33316e22i | 0.0521858i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 8.13530e22i | − | 0.113772i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.06754e23 | − | 4.87739e23i | −0.383655 | − | 0.610013i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.75346e23 | −0.420321 | −0.210160 | − | 0.977667i | \(-0.567399\pi\) | ||||
−0.210160 | + | 0.977667i | \(0.567399\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.23478e24 | −1.23947 | −0.619736 | − | 0.784810i | \(-0.712760\pi\) | ||||
−0.619736 | + | 0.784810i | \(0.712760\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.67677e22 | − | 2.30420e22i | 0.0241128 | − | 0.0207566i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 1.87914e24i | − | 1.52077i | −0.649472 | − | 0.760386i | \(-0.725010\pi\) | ||
0.649472 | − | 0.760386i | \(-0.274990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 1.12227e24i | − | 0.816843i | −0.912793 | − | 0.408421i | \(-0.866079\pi\) | ||
0.912793 | − | 0.408421i | \(-0.133921\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.17398e23 | − | 1.01058e23i | 0.0769312 | − | 0.0662235i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.76414e23 | −0.340429 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.68051e23 | 0.0895420 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.86395e22 | + | 1.23901e23i | −0.00896903 | + | 0.0596193i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.74239e23i | 0.119287i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.45410e23i | 0.135947i | 0.997687 | + | 0.0679734i | \(0.0216533\pi\) | ||||
−0.997687 | + | 0.0679734i | \(0.978347\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.36114e24 | − | 1.58122e24i | −0.485196 | − | 0.563647i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.81256e22 | −0.0317087 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.26617e24 | 0.371249 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.25185e24 | − | 1.45426e24i | −0.333341 | − | 0.387239i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 7.54524e23i | − | 0.182623i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.46788e24i | 0.983785i | 0.870656 | + | 0.491892i | \(0.163695\pi\) | ||||
−0.870656 | + | 0.491892i | \(0.836305\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.24458e23 | + | 4.81565e24i | −0.145244 | + | 0.965470i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.79434e23 | 0.105860 | 0.0529301 | − | 0.998598i | \(-0.483144\pi\) | ||||
0.0529301 | + | 0.998598i | \(0.483144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.40712e24 | 0.401075 | 0.200538 | − | 0.979686i | \(-0.435731\pi\) | ||||
0.200538 | + | 0.979686i | \(0.435731\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.62703e23 | − | 3.98301e23i | 0.0703682 | − | 0.0605739i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.26681e25i | 1.75984i | 0.475122 | + | 0.879920i | \(0.342404\pi\) | ||||
−0.475122 | + | 0.879920i | \(0.657596\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 2.03757e24i | − | 0.258761i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.02508e24 | − | 2.60403e24i | 0.351463 | − | 0.302544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.20140e24 | 0.766018 | 0.383009 | − | 0.923745i | \(-0.374888\pi\) | ||||
0.383009 | + | 0.923745i | \(0.374888\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.59925e25 | 1.55861 | 0.779305 | − | 0.626645i | \(-0.215573\pi\) | ||||
0.779305 | + | 0.626645i | \(0.215573\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 4.48237e24 | + | 1.02540e25i | 0.400536 | + | 0.916281i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 9.01939e23i | − | 0.0739491i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.54349e24i | 0.191475i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.34527e25 | + | 1.56278e25i | 0.930497 | + | 1.08095i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.04461e25 | −0.664323 | −0.332162 | − | 0.943223i | \(-0.607778\pi\) | ||||
−0.332162 | + | 0.943223i | \(0.607778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.32763e23 | −0.00776802 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.64521e24 | − | 1.91122e24i | −0.0886234 | − | 0.102953i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.38723e25i | 1.18467i | 0.805692 | + | 0.592335i | \(0.201794\pi\) | ||||
−0.805692 | + | 0.592335i | \(0.798206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.34376e24i | 0.244455i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.10708e25 | + | 1.66548e24i | 0.467148 | + | 0.0702770i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.88198e25 | −1.90134 | −0.950672 | − | 0.310197i | \(-0.899605\pi\) | ||||
−0.950672 | + | 0.310197i | \(0.899605\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.70636e24 | 0.169279 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2.49593e25 | + | 2.14853e25i | −0.829590 | + | 0.714123i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 8.09476e23i | − | 0.0248774i | −0.999923 | − | 0.0124387i | \(-0.996041\pi\) | ||
0.999923 | − | 0.0124387i | \(-0.00395946\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.04241e25i | 1.14938i | 0.818372 | + | 0.574689i | \(0.194877\pi\) | ||||
−0.818372 | + | 0.574689i | \(0.805123\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.29143e24 | − | 3.69412e24i | 0.112952 | − | 0.0972307i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.16007e24 | −0.125795 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.50913e25 | 1.24465 | 0.622323 | − | 0.782761i | \(-0.286189\pi\) | ||||
0.622323 | + | 0.782761i | \(0.286189\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.43186e25 | − | 3.65844e24i | −0.509441 | − | 0.0766394i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 6.47626e24i | − | 0.125866i | −0.998018 | − | 0.0629330i | \(-0.979955\pi\) | ||
0.998018 | − | 0.0629330i | \(-0.0200454\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.84729e25i | − | 0.513658i | −0.966457 | − | 0.256829i | \(-0.917322\pi\) | ||
0.966457 | − | 0.256829i | \(-0.0826778\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.54595e24 | + | 6.44268e24i | 0.0929192 | + | 0.107943i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.69422e25 | 0.419444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.52187e25 | 0.220267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.83284e25 | + | 3.29089e25i | 0.381369 | + | 0.443033i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.97655e25i | 0.623474i | 0.950168 | + | 0.311737i | \(0.100911\pi\) | ||||
−0.950168 | + | 0.311737i | \(0.899089\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 9.89901e24i | − | 0.115468i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.00377e25 | + | 6.31300e24i | −0.109066 | + | 0.0685950i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.23133e24 | −0.0124689 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.57316e25 | −0.148534 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.64758e25 | − | 4.86152e25i | 0.497410 | − | 0.428178i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 8.76404e24i | − | 0.0720371i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 4.07188e25i | − | 0.312494i | −0.987718 | − | 0.156247i | \(-0.950060\pi\) | ||
0.987718 | − | 0.156247i | \(-0.0499396\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.53929e25 | + | 7.35075e25i | −0.612150 | + | 0.526948i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.17735e26 | 0.788720 | 0.394360 | − | 0.918956i | \(-0.370966\pi\) | ||||
0.394360 | + | 0.918956i | \(0.370966\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.96270e25 | −0.248185 | −0.124092 | − | 0.992271i | \(-0.539602\pi\) | ||||
−0.124092 | + | 0.992271i | \(0.539602\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.81538e24 | − | 1.87145e25i | 0.0164921 | − | 0.109627i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 1.71567e25i | − | 0.0940398i | −0.998894 | − | 0.0470199i | \(-0.985028\pi\) | ||
0.998894 | − | 0.0470199i | \(-0.0149724\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.18626e25i | 0.0608665i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.90908e26 | − | 2.21776e26i | −0.917322 | − | 1.06564i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.81606e26 | 0.817529 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.78581e25 | −0.201920 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.09827e25 | + | 4.76092e25i | 0.162125 | + | 0.188339i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 3.26665e26i | − | 1.21212i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 3.33714e26i | − | 1.16193i | −0.813928 | − | 0.580966i | \(-0.802675\pi\) | ||
0.813928 | − | 0.580966i | \(-0.197325\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.54401e25 | − | 1.02634e26i | 0.0504645 | − | 0.335450i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.08789e24 | 0.0156159 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.88797e26 | −0.832682 | −0.416341 | − | 0.909209i | \(-0.636688\pi\) | ||||
−0.416341 | + | 0.909209i | \(0.636688\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.16679e25 | + | 4.44764e25i | −0.139999 | + | 0.120513i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2.60578e25i | − | 0.0663769i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.45416e26i | − | 1.06703i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.11898e24 | + | 2.68486e24i | −0.00702931 | + | 0.00605093i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.15406e26 | −0.456876 | −0.228438 | − | 0.973558i | \(-0.573362\pi\) | ||||
−0.228438 | + | 0.973558i | \(0.573362\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −7.99890e26 | −1.59721 | −0.798607 | − | 0.601853i | \(-0.794429\pi\) | ||||
−0.798607 | + | 0.601853i | \(0.794429\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.30964e25 | + | 5.85511e25i | −0.175069 | + | 0.110106i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 9.63826e26i | − | 1.70751i | −0.520671 | − | 0.853757i | \(-0.674318\pi\) | ||
0.520671 | − | 0.853757i | \(-0.325682\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 6.85283e25i | − | 0.114412i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −2.63761e26 | − | 3.06409e26i | −0.415140 | − | 0.482265i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.26259e26 | −0.632677 | −0.316339 | − | 0.948646i | \(-0.602454\pi\) | ||||
−0.316339 | + | 0.948646i | \(0.602454\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.02020e26 | 0.142844 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.85578e26 | + | 5.64092e26i | 0.641564 | + | 0.745299i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.30259e25i | − | 0.0786039i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 3.28445e26i | − | 0.386784i | −0.981122 | − | 0.193392i | \(-0.938051\pi\) | ||
0.981122 | − | 0.193392i | \(-0.0619489\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.17462e26 | − | 7.78461e25i | −0.575575 | − | 0.0865885i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.54530e26 | 0.792959 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 9.10674e26 | 0.904524 | 0.452262 | − | 0.891885i | \(-0.350617\pi\) | ||||
0.452262 | + | 0.891885i | \(0.350617\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.45389e26 | + | 2.11234e26i | −0.230423 | + | 0.198352i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.10022e26i | 0.0977003i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.08412e27i | − | 0.910677i | −0.890318 | − | 0.455339i | \(-0.849518\pi\) | ||
0.890318 | − | 0.455339i | \(-0.150482\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.25004e26 | + | 5.38012e26i | −0.496787 | + | 0.427642i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 8.00460e26 | 0.602216 | 0.301108 | − | 0.953590i | \(-0.402643\pi\) | ||||
0.301108 | + | 0.953590i | \(0.402643\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00530e25 | 0.0142837 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.02147e26 | + | 4.54545e25i | 0.203823 | + | 0.0306628i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.52183e27i | 1.61156i | 0.592218 | + | 0.805778i | \(0.298253\pi\) | ||||
−0.592218 | + | 0.805778i | \(0.701747\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.79175e25i | 0.0532377i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3.41174e26 | + | 3.96339e26i | 0.195819 | + | 0.227481i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.31103e26 | 0.0713418 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.36092e27 | 1.21838 | 0.609188 | − | 0.793026i | \(-0.291495\pi\) | ||||
0.609188 | + | 0.793026i | \(0.291495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 8.89134e26 | + | 1.03290e27i | 0.435263 | + | 0.505641i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.73414e26i | 0.359249i | 0.983735 | + | 0.179625i | \(0.0574883\pi\) | ||||
−0.983735 | + | 0.179625i | \(0.942512\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 2.41678e26i | − | 0.106545i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.08146e26 | + | 3.51303e26i | −0.0452621 | + | 0.147029i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.09975e26 | 0.0437070 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.53526e27 | 0.957035 | 0.478517 | − | 0.878078i | \(-0.341174\pi\) | ||||
0.478517 | + | 0.878078i | \(0.341174\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.32617e27 | + | 2.00240e27i | −0.834262 | + | 0.718144i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.58702e27i | − | 0.540888i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.77291e26i | 0.219417i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −9.12738e26 | + | 7.85698e26i | −0.281137 | + | 0.242007i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.48106e27 | −1.31260 | −0.656302 | − | 0.754498i | \(-0.727880\pi\) | ||||
−0.656302 | + | 0.754498i | \(0.727880\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.95661e27 | 1.10246 | 0.551228 | − | 0.834354i | \(-0.314159\pi\) | ||||
0.551228 | + | 0.834354i | \(0.314159\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −9.43858e26 | + | 6.27406e27i | −0.250226 | + | 1.66332i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.41708e27i | 0.862127i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.40506e27i | − | 0.337445i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.60250e25 | − | 8.83176e25i | −0.0173842 | − | 0.0201951i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.76889e27 | −1.25626 | −0.628132 | − | 0.778106i | \(-0.716180\pi\) | ||||
−0.628132 | + | 0.778106i | \(0.716180\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.74142e27 | 0.983524 | 0.491762 | − | 0.870730i | \(-0.336353\pi\) | ||||
0.491762 | + | 0.870730i | \(0.336353\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.39898e26 | + | 2.78687e26i | 0.0474121 | + | 0.0550783i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 2.96368e26i | − | 0.0558183i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 5.57774e27i | − | 1.00134i | −0.865639 | − | 0.500669i | \(-0.833087\pi\) | ||
0.865639 | − | 0.500669i | \(-0.166913\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.17803e26 | + | 2.77724e27i | −0.0715100 | + | 0.475344i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.92820e27 | 0.477927 | 0.238964 | − | 0.971028i | \(-0.423192\pi\) | ||||
0.238964 | + | 0.971028i | \(0.423192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.08170e27 | −0.168395 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8.07618e27 | + | 6.95209e27i | −1.19944 | + | 1.03249i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 9.39845e27i | 1.33189i | 0.745999 | + | 0.665947i | \(0.231972\pi\) | ||||
−0.745999 | + | 0.665947i | \(0.768028\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 5.54471e26i | − | 0.0749938i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.62991e27 | − | 1.40305e27i | 0.210443 | − | 0.181152i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.85985e26 | 0.0229276 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.76565e27 | 0.914234 | 0.457117 | − | 0.889407i | \(-0.348882\pi\) | ||||
0.457117 | + | 0.889407i | \(0.348882\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.18057e27 | + | 6.64711e27i | 0.470113 | + | 0.747480i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.60358e27i | − | 0.816881i | −0.912785 | − | 0.408440i | \(-0.866073\pi\) | ||
0.912785 | − | 0.408440i | \(-0.133927\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 1.13806e28i | − | 1.16833i | −0.811634 | − | 0.584166i | \(-0.801422\pi\) | ||
0.811634 | − | 0.584166i | \(-0.198578\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.26969e26 | − | 6.12174e26i | −0.0517045 | − | 0.0600647i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.98186e27 | 0.748647 | 0.374323 | − | 0.927298i | \(-0.377875\pi\) | ||||
0.374323 | + | 0.927298i | \(0.377875\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.15698e26 | 0.0731500 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.30012e28 | + | 1.51033e28i | 1.11497 | + | 1.29525i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.23757e26i | 0.0265569i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 1.15189e28i | − | 0.903916i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.44918e28 | − | 2.18012e27i | −1.08813 | − | 0.163696i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.21612e27 | −0.302963 | −0.151482 | − | 0.988460i | \(-0.548404\pi\) | ||||
−0.151482 | + | 0.988460i | \(0.548404\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.01998e27 | 0.0701566 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.00039e26 | + | 4.30441e26i | −0.0329275 | + | 0.0283445i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.42623e27i | 0.0899293i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 6.41939e27i | − | 0.387650i | −0.981036 | − | 0.193825i | \(-0.937911\pi\) | ||
0.981036 | − | 0.193825i | \(-0.0620894\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.00259e28 | + | 1.72386e28i | −1.15837 | + | 0.997145i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.36908e28 | 0.758704 | 0.379352 | − | 0.925252i | \(-0.376147\pi\) | ||||
0.379352 | + | 0.925252i | \(0.376147\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.85561e27 | 0.417145 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −3.85145e26 | − | 5.79405e25i | −0.0196006 | − | 0.00294868i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 1.09865e28i | − | 0.535943i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 3.87160e28i | − | 1.81065i | −0.424718 | − | 0.905326i | \(-0.639627\pi\) | ||
0.424718 | − | 0.905326i | \(-0.360373\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.14402e28 | − | 2.49069e28i | −0.961464 | − | 1.11692i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 8.82865e27 | 0.379691 | 0.189846 | − | 0.981814i | \(-0.439201\pi\) | ||||
0.189846 | + | 0.981814i | \(0.439201\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.44759e27 | 0.100967 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.57801e28 | + | 1.83316e28i | 0.624490 | + | 0.725464i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.32243e28i | − | 0.502153i | −0.967967 | − | 0.251077i | \(-0.919215\pi\) | ||
0.967967 | − | 0.251077i | \(-0.0807846\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 1.01044e28i | − | 0.368206i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.40926e28 | − | 2.24073e28i | −0.492900 | − | 0.783713i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.70083e27 | −0.124258 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.72278e27 | −0.216719 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.36943e28 | + | 2.90045e28i | −1.04303 | + | 0.897859i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.45445e28i | − | 1.62164i | −0.585295 | − | 0.810820i | \(-0.699021\pi\) | ||
0.585295 | − | 0.810820i | \(-0.300979\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.79200e28i | − | 1.65410i | −0.562130 | − | 0.827049i | \(-0.690018\pi\) | ||
0.562130 | − | 0.827049i | \(-0.309982\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.94350e28 | + | 1.67299e28i | −0.533225 | + | 0.459008i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.72559e28 | −0.454911 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.93281e28 | −0.996365 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −4.58550e27 | + | 3.04809e28i | −0.111659 | + | 0.742225i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 5.14255e27i | − | 0.120377i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 9.61151e27i | − | 0.216310i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.64434e28 | − | 4.23360e28i | −0.788659 | − | 0.916178i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.97587e27 | −0.0619343 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.05578e28 | 0.611718 | 0.305859 | − | 0.952077i | \(-0.401056\pi\) | ||||
0.305859 | + | 0.952077i | \(0.401056\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.66771e28 | + | 4.26074e28i | 0.706312 | + | 0.820516i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 2.06332e27i | 0.0382300i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 7.14206e28i | − | 1.27338i | −0.771121 | − | 0.636688i | \(-0.780304\pi\) | ||
0.771121 | − | 0.636688i | \(-0.219696\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.05975e27 | + | 2.69861e28i | −0.0696610 | + | 0.463054i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.64811e28 | −0.437365 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.10186e28 | 0.334188 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.58362e27 | − | 2.22402e27i | 0.0395506 | − | 0.0340457i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.93564e28i | 0.580145i | 0.957005 | + | 0.290072i | \(0.0936794\pi\) | ||||
−0.957005 | + | 0.290072i | \(0.906321\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.00275e27i | 0.0426280i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.30590e27 | + | 5.42821e27i | −0.0862258 | + | 0.0742244i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.33412e29 | 1.75734 | 0.878669 | − | 0.477431i | \(-0.158432\pi\) | ||||
0.878669 | + | 0.477431i | \(0.158432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.23922e27 | −0.0284177 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.73382e28 | + | 5.63214e28i | −0.212022 | + | 0.688733i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.93784e27i | − | 0.0228370i | −0.999935 | − | 0.0114185i | \(-0.996365\pi\) | ||
0.999935 | − | 0.0114185i | \(-0.00363470\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 1.02725e29i | − | 1.16680i | −0.812183 | − | 0.583402i | \(-0.801721\pi\) | ||
0.812183 | − | 0.583402i | \(-0.198279\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.50446e28 | + | 2.90941e28i | 0.274215 | + | 0.318553i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.57644e27 | 0.0588633 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.55640e29 | 1.58408 | 0.792038 | − | 0.610472i | \(-0.209020\pi\) | ||||
0.792038 | + | 0.610472i | \(0.209020\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.23894e28 | + | 9.57110e28i | 0.808624 | + | 0.939371i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.08584e29i | 1.02782i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 1.55282e28i | − | 0.141776i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.57210e27 | − | 5.37381e26i | −0.0314621 | − | 0.00473310i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.21099e27 | 0.0527790 | 0.0263895 | − | 0.999652i | \(-0.491599\pi\) | ||||
0.0263895 | + | 0.999652i | \(0.491599\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.81693e28 | 0.476962 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.45658e29 | + | 1.25384e29i | −1.15256 | + | 0.992142i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1.08708e29i | 0.830207i | 0.909774 | + | 0.415104i | \(0.136255\pi\) | ||||
−0.909774 | + | 0.415104i | \(0.863745\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 1.32794e28i | − | 0.0978927i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.69900e28 | + | 7.48823e28i | −0.619069 | + | 0.532903i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.09707e29 | −1.44089 | −0.720445 | − | 0.693512i | \(-0.756063\pi\) | ||||
−0.720445 | + | 0.693512i | \(0.756063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.73455e26 | −0.00645853 | −0.00322927 | − | 0.999995i | \(-0.501028\pi\) | ||||
−0.00322927 | + | 0.999995i | \(0.501028\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.56666e28 | − | 2.35685e27i | −0.100379 | − | 0.0151008i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.44471e28i | 0.151285i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.06415e29i | 1.23384i | 0.787024 | + | 0.616922i | \(0.211621\pi\) | ||||
−0.787024 | + | 0.616922i | \(0.788379\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.84608e28 | + | 4.46795e28i | 0.222094 | + | 0.258004i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.23517e28 | −0.347869 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.35444e29 | 1.80836 | 0.904181 | − | 0.427149i | \(-0.140482\pi\) | ||||
0.904181 | + | 0.427149i | \(0.140482\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.12131e28 | − | 1.30261e28i | −0.0584167 | − | 0.0678621i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.58509e28i | − | 0.381915i | −0.981598 | − | 0.190957i | \(-0.938841\pi\) | ||
0.981598 | − | 0.190957i | \(-0.0611592\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 1.69637e29i | − | 0.825599i | −0.910822 | − | 0.412800i | \(-0.864551\pi\) | ||
0.910822 | − | 0.412800i | \(-0.135449\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.08476e28 | − | 6.82241e27i | 0.0510356 | − | 0.0320978i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.73420e29 | −0.788815 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.11358e29 | 0.929561 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.12571e28 | − | 1.82984e28i | 0.0904054 | − | 0.0778222i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 7.28269e28i | − | 0.299544i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.18428e29i | 1.66461i | 0.554318 | + | 0.832305i | \(0.312979\pi\) | ||||
−0.554318 | + | 0.832305i | \(0.687021\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.67737e28 | − | 2.30472e28i | 0.103031 | − | 0.0886908i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.70869e28 | −0.100841 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.76003e28 | −0.0994144 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.17442e28 | + | 2.11012e29i | −0.110638 | + | 0.735440i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.30463e29i | 0.777306i | 0.921384 | + | 0.388653i | \(0.127060\pi\) | ||||
−0.921384 | + | 0.388653i | \(0.872940\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.90657e29i | − | 1.27521i | −0.770365 | − | 0.637603i | \(-0.779926\pi\) | ||
0.770365 | − | 0.637603i | \(-0.220074\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.54735e27 | + | 7.60599e27i | 0.0206866 | + | 0.0240314i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.10310e29 | −0.643229 | −0.321615 | − | 0.946871i | \(-0.604226\pi\) | ||||
−0.321615 | + | 0.946871i | \(0.604226\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.26609e28 | −0.0967072 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.44843e28 | − | 9.81446e28i | −0.242201 | − | 0.281362i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.73996e28i | 0.103819i | 0.998652 | + | 0.0519096i | \(0.0165308\pi\) | ||||
−0.998652 | + | 0.0519096i | \(0.983469\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.71768e28i | 0.0461753i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.91954e28 | + | 1.94069e29i | −0.0760112 | + | 0.505265i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.10909e29 | 1.28839 | 0.644195 | − | 0.764862i | \(-0.277193\pi\) | ||||
0.644195 | + | 0.764862i | \(0.277193\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.57481e29 | −1.11753 | −0.558763 | − | 0.829327i | \(-0.688724\pi\) | ||||
−0.558763 | + | 0.829327i | \(0.688724\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.84853e28 | + | 5.03450e28i | −0.138406 | + | 0.119142i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.47646e28i | 0.102638i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.28198e28i | − | 0.0284814i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.46318e29 | − | 2.98115e29i | 0.745591 | − | 0.641815i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.89162e28 | −0.0603329 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.21002e29 | −0.851386 | −0.425693 | − | 0.904868i | \(-0.639970\pi\) | ||||
−0.425693 | + | 0.904868i | \(0.639970\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.21614e29 | − | 2.65165e29i | 0.826466 | − | 0.519789i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 9.75613e28i | − | 0.185394i | −0.995694 | − | 0.0926972i | \(-0.970451\pi\) | ||
0.995694 | − | 0.0926972i | \(-0.0295489\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.28655e29i | 0.421258i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3.86622e28 | − | 4.49136e28i | −0.0690625 | − | 0.0802293i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.90606e29 | 1.54265 | 0.771326 | − | 0.636440i | \(-0.219594\pi\) | ||||
0.771326 | + | 0.636440i | \(0.219594\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.00813e29 | −0.169343 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.60613e29 | − | 1.86583e29i | −0.261659 | − | 0.303967i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1.44020e29i | − | 0.227573i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 4.37221e29i | − | 0.670165i | −0.942189 | − | 0.335082i | \(-0.891236\pi\) | ||
0.942189 | − | 0.335082i | \(-0.108764\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −6.17469e28 | − | 9.28910e27i | −0.0918155 | − | 0.0138126i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.95570e28 | −0.0570667 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.67180e29 | −0.513966 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9.81938e29 | − | 8.45266e29i | 1.33375 | − | 1.14811i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 1.09604e30i | − | 1.44473i | −0.691514 | − | 0.722363i | \(-0.743056\pi\) | ||
0.691514 | − | 0.722363i | \(-0.256944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2.45498e29i | 0.314063i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.57938e29 | + | 1.35955e29i | −0.196110 | + | 0.168814i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.92401e29 | 0.472962 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.48518e29 | −0.758816 | −0.379408 | − | 0.925229i | \(-0.623872\pi\) | ||||
−0.379408 | + | 0.925229i | \(0.623872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.03692e29 | − | 6.07307e28i | −0.458584 | − | 0.0689886i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.81605e28i | 0.0310599i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 3.82758e27i | − | 0.00409931i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −4.80507e29 | − | 5.58201e29i | −0.499745 | − | 0.580549i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.11310e30 | −1.12430 | −0.562149 | − | 0.827036i | \(-0.690025\pi\) | ||||
−0.562149 | + | 0.827036i | \(0.690025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.93321e29 | −0.582062 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.06709e30 | − | 1.23962e30i | −1.01683 | − | 1.18124i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 4.98267e29i | − | 0.461225i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.24390e30i | 1.11860i | 0.828966 | + | 0.559299i | \(0.188930\pi\) | ||||
−0.828966 | + | 0.559299i | \(0.811070\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 4.95737e29 | − | 1.03163e30i | 0.433124 | − | 0.901334i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.14397e29 | 0.182006 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.82256e30 | −1.50346 | −0.751729 | − | 0.659473i | \(-0.770780\pi\) | ||||
−0.751729 | + | 0.659473i | \(0.770780\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.99118e28 | + | 6.01811e28i | −0.0560446 | + | 0.0482440i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 1.67871e28i | − | 0.0130787i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.87087e29i | 0.293118i | 0.989202 | + | 0.146559i | \(0.0468198\pi\) | ||||
−0.989202 | + | 0.146559i | \(0.953180\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.97153e29 | − | 1.69712e29i | 0.145115 | − | 0.124917i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.65148e29 | −0.118166 | −0.0590828 | − | 0.998253i | \(-0.518818\pi\) | ||||
−0.0590828 | + | 0.998253i | \(0.518818\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.50012e29 | −0.243468 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.13740e29 | − | 2.08551e30i | 0.212180 | − | 1.41041i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 1.54093e30i | − | 1.01327i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.67639e30i | 1.07191i | 0.844248 | + | 0.535953i | \(0.180048\pi\) | ||||
−0.844248 | + | 0.535953i | \(0.819952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 6.97006e29 | + | 8.09706e29i | 0.433400 | + | 0.503477i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.06385e28 | 0.0427168 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.60704e30 | 0.945195 | 0.472597 | − | 0.881278i | \(-0.343317\pi\) | ||||
0.472597 | + | 0.881278i | \(0.343317\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.85847e27 | + | 1.02908e28i | 0.00506781 | + | 0.00588723i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.22744e28i | − | 0.0123956i | −0.999981 | − | 0.00619779i | \(-0.998027\pi\) | ||
0.999981 | − | 0.00619779i | \(-0.00197283\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.30795e29i | 0.179082i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.83691e28 | + | 2.55049e29i | −0.0202086 | + | 0.134332i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.02920e29 | −0.155230 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.43319e29 | −0.171187 | −0.0855937 | − | 0.996330i | \(-0.527279\pi\) | ||||
−0.0855937 | + | 0.996330i | \(0.527279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.85041e30 | − | 1.59286e30i | 0.897837 | − | 0.772871i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.61088e30i | 1.70501i | 0.522715 | + | 0.852507i | \(0.324919\pi\) | ||||
−0.522715 | + | 0.852507i | \(0.675081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.09451e30i | 0.502981i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.14210e29 | − | 3.56558e29i | 0.185268 | − | 0.159481i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.23776e30 | 0.538879 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.26103e29 | −0.0958232 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.09596e29 | − | 9.69259e29i | −0.251503 | − | 0.399891i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.54560e29i | 0.262917i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.41302e29i | 0.133476i | 0.997771 | + | 0.0667381i | \(0.0212592\pi\) | ||||
−0.997771 | + | 0.0667381i | \(0.978741\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.25746e30 | + | 3.78416e30i | 1.24043 | + | 1.44099i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.58995e29 | −0.133118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.68189e29 | −0.0968439 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.14028e29 | − | 3.64804e29i | −0.110437 | − | 0.128293i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.68234e30i | 0.918759i | 0.888240 | + | 0.459379i | \(0.151928\pi\) | ||||
−0.888240 | + | 0.459379i | \(0.848072\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.45193e30i | 1.48528i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.33077e30 | + | 5.01076e29i | 1.08244 | + | 0.162840i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.07949e29 | −0.0658328 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.16711e28 | −0.00668381 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6.27448e28 | + | 5.40116e28i | −0.0188541 | + | 0.0162299i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 3.53882e30i | − | 1.03609i | −0.855352 | − | 0.518046i | \(-0.826659\pi\) | ||
0.855352 | − | 0.518046i | \(-0.173341\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.99263e30i | 0.853755i | 0.904309 | + | 0.426878i | \(0.140387\pi\) | ||||
−0.904309 | + | 0.426878i | \(0.859613\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.13339e30 | − | 2.69727e30i | 0.871091 | − | 0.749847i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.67897e29 | −0.235133 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.22728e29 | −0.190828 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.72684e29 | − | 8.61536e28i | −0.147378 | − | 0.0221714i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 5.35892e30i | 1.34423i | 0.740446 | + | 0.672116i | \(0.234614\pi\) | ||||
−0.740446 | + | 0.672116i | \(0.765386\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.16207e30i | 0.773168i | 0.922254 | + | 0.386584i | \(0.126345\pi\) | ||||
−0.922254 | + | 0.386584i | \(0.873655\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.44301e29 | + | 3.99971e29i | 0.0820676 | + | 0.0953372i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.29159e29 | 0.0764889 | 0.0382444 | − | 0.999268i | \(-0.487823\pi\) | ||||
0.0382444 | + | 0.999268i | \(0.487823\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.48817e30 | 0.337155 | 0.168578 | − | 0.985688i | \(-0.446083\pi\) | ||||
0.168578 | + | 0.985688i | \(0.446083\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.67592e30 | − | 4.27029e30i | −0.811999 | − | 0.943292i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.97067e30i | 0.424464i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 1.07943e30i | − | 0.226719i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.33906e30 | + | 2.12911e30i | 0.274273 | + | 0.436094i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7.74493e30 | −1.54709 | −0.773547 | − | 0.633739i | \(-0.781519\pi\) | ||||
−0.773547 | + | 0.633739i | \(0.781519\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.98736e30 | 0.776834 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.01994e29 | + | 4.32123e29i | −0.0953913 | + | 0.0821142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 7.94467e29i | 0.147259i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.91938e30i | 0.708667i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.20702e30 | + | 1.89983e30i | −0.389291 | + | 0.335108i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.18849e29 | −0.0204519 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.25888e29 | 0.0379253 | 0.0189626 | − | 0.999820i | \(-0.493964\pi\) | ||||
0.0189626 | + | 0.999820i | \(0.493964\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.29342e29 | − | 8.59765e29i | 0.0211882 | − | 0.140843i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 5.81104e30i | − | 0.928871i | −0.885607 | − | 0.464435i | \(-0.846257\pi\) | ||
0.885607 | − | 0.464435i | \(-0.153743\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.98116e29i | 0.155687i | 0.996966 | + | 0.0778436i | \(0.0248035\pi\) | ||||
−0.996966 | + | 0.0778436i | \(0.975197\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.79770e30 | − | 2.08837e30i | −0.273642 | − | 0.317888i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.39637e30 | −0.207438 | −0.103719 | − | 0.994607i | \(-0.533074\pi\) | ||||
−0.103719 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.46027e30 | −0.211721 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.01545e30 | − | 1.17964e30i | −0.143701 | − | 0.166936i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 4.32564e29i | − | 0.0597506i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1.55695e29i | − | 0.0209934i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.60669e29 | − | 4.39163e30i | 0.0869630 | − | 0.578065i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.70499e30 | −0.219098 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.19505e29 | 0.0400850 | 0.0200425 | − | 0.999799i | \(-0.493620\pi\) | ||||
0.0200425 | + | 0.999799i | \(0.493620\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.85747e30 | − | 3.32056e30i | 0.472519 | − | 0.406751i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 5.17345e30i | 0.618776i | 0.950936 | + | 0.309388i | \(0.100124\pi\) | ||||
−0.950936 | + | 0.309388i | \(0.899876\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.69512e30i | 0.548352i | 0.961679 | + | 0.274176i | \(0.0884051\pi\) | ||||
−0.961679 | + | 0.274176i | \(0.911595\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7.67300e29 | + | 6.60503e29i | −0.0875106 | + | 0.0753304i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.10473e31 | 1.23043 | 0.615215 | − | 0.788359i | \(-0.289069\pi\) | ||||
0.615215 | + | 0.788359i | \(0.289069\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.34261e30 | −0.472370 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.15909e30 | + | 3.56820e29i | 0.123141 | + | 0.0379082i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 1.50074e31i | − | 1.55727i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.83479e30i | − | 0.185971i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.21597e28 | + | 9.54441e28i | 0.00813463 | + | 0.00944993i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.51620e30 | 0.243370 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.02830e31 | −0.971654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 1.04968e30 | + | 1.21940e30i | 0.0969025 | + | 0.112571i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.84655e30i | 0.166553i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.08940e31i | − | 0.960092i | −0.877243 | − | 0.480046i | \(-0.840620\pi\) | ||
0.877243 | − | 0.480046i | \(-0.159380\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.53660e30 | − | 1.13379e30i | −0.649015 | − | 0.0976367i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.98401e31 | 1.66956 | 0.834778 | − | 0.550586i | \(-0.185596\pi\) | ||||
0.834778 | + | 0.550586i | \(0.185596\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.23466e30 | 0.183768 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.79326e29 | + | 5.84773e29i | −0.0545955 | + | 0.0469966i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.75381e30i | 0.216300i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 2.28095e31i | − | 1.75107i | −0.483155 | − | 0.875535i | \(-0.660509\pi\) | ||
0.483155 | − | 0.875535i | \(-0.339491\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.15623e30 | + | 2.71692e30i | −0.236833 | + | 0.203869i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.09704e30 | −0.153811 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.61927e30 | −0.331196 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.13955e31 | + | 1.71433e30i | 0.798726 | + | 0.120159i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.79281e31i | 1.22848i | 0.789118 | + | 0.614241i | \(0.210538\pi\) | ||||
−0.789118 | + | 0.614241i | \(0.789462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 6.64308e30i | − | 0.445039i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −7.85580e30 | − | 9.12601e30i | −0.514556 | − | 0.597755i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.73290e29 | −0.0175026 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.61944e31 | −1.01414 | −0.507070 | − | 0.861905i | \(-0.669272\pi\) | ||||
−0.507070 | + | 0.861905i | \(0.669272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.64408e30 | + | 3.07160e30i | 0.161914 | + | 0.188094i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 3.23862e31i | − | 1.93940i | −0.244290 | − | 0.969702i | \(-0.578555\pi\) | ||
0.244290 | − | 0.969702i | \(-0.421445\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.99212e29i | 0.0350920i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.63847e30 | + | 1.03048e30i | −0.0938435 | + | 0.0590210i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 2.43921e29 | 0.0136639 | 0.00683194 | − | 0.999977i | \(-0.497825\pi\) | ||||
0.00683194 | + | 0.999977i | \(0.497825\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.92866e30 | −0.105672 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.32987e30 | + | 1.14477e30i | −0.0712709 | + | 0.0613510i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 3.54176e31i | − | 1.85671i | −0.371699 | − | 0.928353i | \(-0.621225\pi\) | ||
0.371699 | − | 0.928353i | \(-0.378775\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.26090e30i | 0.0646616i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.19504e29 | − | 7.91523e29i | 0.0461295 | − | 0.0397089i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.61625e31 | −0.793257 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.52983e31 | 0.734596 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4.45232e30 | + | 2.95957e31i | −0.209175 | + | 1.39044i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.14800e30i | 0.190679i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 2.46691e31i | − | 1.10962i | −0.831977 | − | 0.554811i | \(-0.812791\pi\) | ||
0.831977 | − | 0.554811i | \(-0.187209\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.21175e31 | − | 1.40768e31i | −0.533351 | − | 0.619589i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.25722e31 | −0.972235 | −0.486118 | − | 0.873893i | \(-0.661587\pi\) | ||||
−0.486118 | + | 0.873893i | \(0.661587\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.34182e30 | −0.267319 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.19329e30 | + | 3.70961e30i | 0.131732 | + | 0.153031i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 2.32937e31i | 0.940471i | 0.882541 | + | 0.470235i | \(0.155831\pi\) | ||||
−0.882541 | + | 0.470235i | \(0.844169\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.56899e30i | 0.141035i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.55790e29 | − | 6.35337e30i | 0.0369690 | − | 0.245742i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.85194e30 | 0.183697 | 0.0918487 | − | 0.995773i | \(-0.470722\pi\) | ||||
0.0918487 | + | 0.995773i | \(0.470722\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.31262e30 | −0.233953 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.53208e31 | + | 2.17965e31i | −0.918643 | + | 0.790781i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 3.49881e29i | − | 0.0124268i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.92717e31i | − | 1.71326i | −0.515927 | − | 0.856632i | \(-0.672552\pi\) | ||
0.515927 | − | 0.856632i | \(-0.327448\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.58671e31 | + | 2.22668e31i | −0.880605 | + | 0.758037i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −3.77004e30 | −0.125662 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.46075e31 | 1.45582 | 0.727911 | − | 0.685671i | \(-0.240491\pi\) | ||||
0.727911 | + | 0.685671i | \(0.240491\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.98569e30 | + | 5.65137e30i | −0.287153 | + | 0.180599i |
(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 | 48.22.c.c.47.7 | ✓ | 28 | |
3.2 | odd | 2 | inner | 48.22.c.c.47.21 | yes | 28 | |
4.3 | odd | 2 | inner | 48.22.c.c.47.22 | yes | 28 | |
12.11 | even | 2 | inner | 48.22.c.c.47.8 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.22.c.c.47.7 | ✓ | 28 | 1.1 | even | 1 | trivial | |
48.22.c.c.47.8 | yes | 28 | 12.11 | even | 2 | inner | |
48.22.c.c.47.21 | yes | 28 | 3.2 | odd | 2 | inner | |
48.22.c.c.47.22 | yes | 28 | 4.3 | odd | 2 | inner |