Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,9,Mod(127,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.127");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.g (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: | \(156.433386263\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 127.17 | ||
Character | \(\chi\) | \(=\) | 384.127 |
Dual form | 384.9.g.a.127.18 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | − 46.7654i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −425.597 | −0.680955 | −0.340477 | − | 0.940253i | \(-0.610589\pi\) | ||||
−0.340477 | + | 0.940253i | \(0.610589\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 584.708i | 0.243527i | 0.992559 | + | 0.121763i | \(0.0388549\pi\) | ||||
−0.992559 | + | 0.121763i | \(0.961145\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2187.00 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 24293.3i | 1.65927i | 0.558308 | + | 0.829634i | \(0.311451\pi\) | ||||
−0.558308 | + | 0.829634i | \(0.688549\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 23313.7 | 0.816277 | 0.408139 | − | 0.912920i | \(-0.366178\pi\) | ||||
0.408139 | + | 0.912920i | \(0.366178\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19903.2i | 0.393149i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −42504.3 | −0.508905 | −0.254453 | − | 0.967085i | \(-0.581895\pi\) | ||||
−0.254453 | + | 0.967085i | \(0.581895\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 122820.i | 0.942441i | 0.882016 | + | 0.471220i | \(0.156186\pi\) | ||||
−0.882016 | + | 0.471220i | \(0.843814\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 27344.1 | 0.140600 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 88938.3i | 0.317817i | 0.987293 | + | 0.158909i | \(0.0507976\pi\) | ||||
−0.987293 | + | 0.158909i | \(0.949202\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −209493. | −0.536301 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 102276.i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 333559. | 0.471608 | 0.235804 | − | 0.971801i | \(-0.424228\pi\) | ||||
0.235804 | + | 0.971801i | \(0.424228\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 522835.i | 0.566133i | 0.959100 | + | 0.283066i | \(0.0913517\pi\) | ||||
−0.959100 | + | 0.283066i | \(0.908648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.13609e6 | 0.957979 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 248850.i | − 0.165831i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 276058. | 0.147297 | 0.0736484 | − | 0.997284i | \(-0.476536\pi\) | ||||
0.0736484 | + | 0.997284i | \(0.476536\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − 1.09027e6i | − 0.471278i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.48281e6 | 0.524748 | 0.262374 | − | 0.964966i | \(-0.415495\pi\) | ||||
0.262374 | + | 0.964966i | \(0.415495\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 5.21926e6i | − 1.52663i | −0.646024 | − | 0.763317i | \(-0.723569\pi\) | ||||
0.646024 | − | 0.763317i | \(-0.276431\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 930780. | 0.226985 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.82942e6i | 0.989700i | 0.868978 | + | 0.494850i | \(0.164777\pi\) | ||||
−0.868978 | + | 0.494850i | \(0.835223\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.42292e6 | 0.940695 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.98773e6i | 0.293817i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.03784e7 | −1.31530 | −0.657651 | − | 0.753322i | \(-0.728450\pi\) | ||||
−0.657651 | + | 0.753322i | \(0.728450\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.03392e7i | − 1.12989i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.74371e6 | 0.544118 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.42321e7i | − 1.17452i | −0.809397 | − | 0.587262i | \(-0.800206\pi\) | ||||
0.809397 | − | 0.587262i | \(-0.199794\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.91381e6 | 0.499342 | 0.249671 | − | 0.968331i | \(-0.419678\pi\) | ||||
0.249671 | + | 0.968331i | \(0.419678\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.27876e6i | − 0.0811756i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −9.92223e6 | −0.555848 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.84110e6i | 0.190615i | 0.995448 | + | 0.0953074i | \(0.0303834\pi\) | ||||
−0.995448 | + | 0.0953074i | \(0.969617\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.15923e6 | 0.183492 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.13356e7i | 1.23312i | 0.787308 | + | 0.616559i | \(0.211474\pi\) | ||||
−0.787308 | + | 0.616559i | \(0.788526\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.39061e7 | −0.489681 | −0.244841 | − | 0.969563i | \(-0.578736\pi\) | ||||
−0.244841 | + | 0.969563i | \(0.578736\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.79700e6i | 0.309633i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.42045e7 | −0.404076 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 3.00456e7i | − 0.771387i | −0.922627 | − | 0.385693i | \(-0.873962\pi\) | ||||
0.922627 | − | 0.385693i | \(-0.126038\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.78297e6 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.11053e7i | − 0.655424i | −0.944778 | − | 0.327712i | \(-0.893722\pi\) | ||||
0.944778 | − | 0.327712i | \(-0.106278\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.80897e7 | 0.346541 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 1.55990e7i | − 0.272283i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.17019e7 | 0.186507 | 0.0932534 | − | 0.995642i | \(-0.470273\pi\) | ||||
0.0932534 | + | 0.995642i | \(0.470273\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.36317e7i | 0.198786i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.44506e7 | 0.326857 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 5.22717e7i | − 0.641759i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.92489e7 | 1.00813 | 0.504064 | − | 0.863666i | \(-0.331837\pi\) | ||||
0.504064 | + | 0.863666i | \(0.331837\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 5.31295e7i | − 0.553089i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.05738e8 | −1.97710 | −0.988551 | − | 0.150888i | \(-0.951787\pi\) | ||||
−0.988551 | + | 0.150888i | \(0.951787\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.65189e7i | − 0.591012i | −0.955341 | − | 0.295506i | \(-0.904512\pi\) | ||||
0.955341 | − | 0.295506i | \(-0.0954883\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.16376e7 | −0.0957424 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 3.48590e7i | − 0.265937i | −0.991120 | − | 0.132969i | \(-0.957549\pi\) | ||||
0.991120 | − | 0.132969i | \(-0.0424510\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.19465e8 | −1.55475 | −0.777373 | − | 0.629041i | \(-0.783448\pi\) | ||||
−0.777373 | + | 0.629041i | \(0.783448\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 1.29100e7i | − 0.0850419i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.36984e7 | 0.390674 | 0.195337 | − | 0.980736i | \(-0.437420\pi\) | ||||
0.195337 | + | 0.980736i | \(0.437420\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 3.78519e7i | − 0.216419i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.09871e7 | −0.272092 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 2.48526e7i | − 0.123932i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.75808e8 | −1.75317 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 6.93443e7i | − 0.302964i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.55408e8 | 1.04615 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.48584e8i | 1.33996i | 0.742377 | + | 0.669982i | \(0.233698\pi\) | ||||
−0.742377 | + | 0.669982i | \(0.766302\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.44081e8 | −0.881403 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.97297e8i | 1.68862i | 0.535858 | + | 0.844308i | \(0.319988\pi\) | ||||
−0.535858 | + | 0.844308i | \(0.680012\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.18138e7 | −0.229510 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 4.35283e7i | − 0.131050i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.23148e8 | 0.349579 | 0.174789 | − | 0.984606i | \(-0.444076\pi\) | ||||
0.174789 | + | 0.984606i | \(0.444076\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 4.32112e8i | − 1.15754i | −0.815490 | − | 0.578772i | \(-0.803532\pi\) | ||||
0.815490 | − | 0.578772i | \(-0.196468\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.25850e8 | 0.571404 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.66368e8i | 1.35442i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.41962e8 | −0.321144 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 2.53605e8i | − 0.543110i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.85179e8 | 0.578593 | 0.289296 | − | 0.957240i | \(-0.406579\pi\) | ||||
0.289296 | + | 0.957240i | \(0.406579\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.67567e8i | 0.322316i | 0.986929 | + | 0.161158i | \(0.0515228\pi\) | ||||
−0.986929 | + | 0.161158i | \(0.948477\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.29569e7 | 0.169635 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.22517e8i | − 0.385511i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.13988e8 | −0.187613 | −0.0938063 | − | 0.995590i | \(-0.529903\pi\) | ||||
−0.0938063 | + | 0.995590i | \(0.529903\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.85348e8i | 0.759390i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.20030e7 | −0.0773971 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 9.50214e7i | − 0.134608i | −0.997733 | − | 0.0673040i | \(-0.978560\pi\) | ||||
0.997733 | − | 0.0673040i | \(-0.0214397\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.83515e8 | −0.652340 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.54182e8i | 0.326798i | 0.986560 | + | 0.163399i | \(0.0522458\pi\) | ||||
−0.986560 | + | 0.163399i | \(0.947754\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.72202e8 | −0.333691 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 2.68607e8i | − 0.314147i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.79172e8 | −1.09314 | −0.546569 | − | 0.837414i | \(-0.684066\pi\) | ||||
−0.546569 | + | 0.837414i | \(0.684066\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 1.22492e8i | − 0.130604i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.65571e8 | −0.678112 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 6.36115e8i | − 0.619617i | −0.950799 | − | 0.309809i | \(-0.899735\pi\) | ||||
0.950799 | − | 0.309809i | \(-0.100265\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.09761e9 | 1.02267 | 0.511333 | − | 0.859383i | \(-0.329152\pi\) | ||||
0.511333 | + | 0.859383i | \(0.329152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 3.23327e8i | − 0.288295i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.17489e8 | −0.100302 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 1.03257e9i | − 0.844410i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.98015e7 | −0.0468668 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.54416e9i | 1.16027i | 0.814521 | + | 0.580134i | \(0.197000\pi\) | ||||
−0.814521 | + | 0.580134i | \(0.803000\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.52519e9 | −1.09924 | −0.549622 | − | 0.835413i | \(-0.685228\pi\) | ||||
−0.549622 | + | 0.835413i | \(0.685228\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.64017e8i | 0.320919i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.71469e9 | −1.80242 | −0.901209 | − | 0.433386i | \(-0.857319\pi\) | ||||
−0.901209 | + | 0.433386i | \(0.857319\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.01061e9i | 0.644426i | 0.946667 | + | 0.322213i | \(0.104427\pi\) | ||||
−0.946667 | + | 0.322213i | \(0.895573\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.79630e8 | 0.110051 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.95035e8i | 0.114849i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.31080e8 | −0.357330 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 1.94508e8i | − 0.105939i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −2.98370e9 | −1.56376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 3.42535e8i | − 0.172812i | −0.996260 | − | 0.0864062i | \(-0.972462\pi\) | ||||
0.996260 | − | 0.0864062i | \(-0.0275383\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.46542e9 | 0.711941 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.22130e9i | 1.03957i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.05706e8 | −0.137869 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.50324e8i | 0.282718i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.90932e8 | −0.415408 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.37197e8i | 0.257664i | 0.991666 | + | 0.128832i | \(0.0411228\pi\) | ||||
−0.991666 | + | 0.128832i | \(0.958877\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.58160e8 | 0.178767 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 2.70397e9i | − 1.01835i | −0.860662 | − | 0.509176i | \(-0.829950\pi\) | ||||
0.860662 | − | 0.509176i | \(-0.170050\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.13967e9 | −1.50530 | −0.752652 | − | 0.658419i | \(-0.771226\pi\) | ||||
−0.752652 | + | 0.658419i | \(0.771226\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.64279e8i | 0.233294i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.40816e9 | −1.15637 | −0.578185 | − | 0.815906i | \(-0.696239\pi\) | ||||
−0.578185 | + | 0.815906i | \(0.696239\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 2.05539e9i | − 0.673941i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.40509e9 | −0.445360 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.63879e9i | 0.808748i | 0.914594 | + | 0.404374i | \(0.132511\pi\) | ||||
−0.914594 | + | 0.404374i | \(0.867489\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.91684e9 | −0.568223 | −0.284111 | − | 0.958791i | \(-0.591699\pi\) | ||||
−0.284111 | + | 0.958791i | \(0.591699\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 2.23677e8i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.30798e9 | −0.640570 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.86338e9i | 0.769293i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.45465e9 | −0.378409 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 4.44444e9i | − 1.11975i | −0.828576 | − | 0.559877i | \(-0.810848\pi\) | ||||
0.828576 | − | 0.559877i | \(-0.189152\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.16061e9 | −0.527344 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 8.45971e8i | − 0.200076i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.46470e9 | −0.335749 | −0.167875 | − | 0.985808i | \(-0.553690\pi\) | ||||
−0.167875 | + | 0.985808i | \(0.553690\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.61413e8i | 0.0358708i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.29494e8 | −0.157203 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5.24355e9i | − 1.09598i | −0.836485 | − | 0.547990i | \(-0.815393\pi\) | ||||
0.836485 | − | 0.547990i | \(-0.184607\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.41700e9 | 0.895661 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 5.47242e8i | − 0.107680i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.77476e9 | −0.338946 | −0.169473 | − | 0.985535i | \(-0.554207\pi\) | ||||
−0.169473 | + | 0.985535i | \(0.554207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 1.01882e9i | − 0.188895i | −0.995530 | − | 0.0944475i | \(-0.969892\pi\) | ||||
0.995530 | − | 0.0944475i | \(-0.0301085\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.37492e8 | 0.114769 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.08927e9i | − 0.889867i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.10632e10 | −1.87914 | −0.939572 | − | 0.342350i | \(-0.888777\pi\) | ||||
−0.939572 | + | 0.342350i | \(0.888777\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 1.14344e9i | − 0.188711i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.73642e8 | −0.0278503 | −0.0139252 | − | 0.999903i | \(-0.504433\pi\) | ||||
−0.0139252 | + | 0.999903i | \(0.504433\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 1.19880e10i | − 1.86897i | −0.356007 | − | 0.934483i | \(-0.615862\pi\) | ||||
0.356007 | − | 0.934483i | \(-0.384138\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.44451e9 | −0.370520 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.67013e8i | 0.127790i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.16914e9 | −0.741015 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 4.17376e9i | − 0.582043i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.84249e9 | 0.385681 | 0.192840 | − | 0.981230i | \(-0.438230\pi\) | ||||
0.192840 | + | 0.981230i | \(0.438230\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.05715e9i | 0.799798i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.48462e9 | −0.319326 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.07348e9i | 0.259427i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.05174e9 | 0.371777 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.62141e9i | 1.14148i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.94249e9 | −0.340029 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 2.31641e9i | − 0.260773i | −0.991463 | − | 0.130386i | \(-0.958378\pi\) | ||||
0.991463 | − | 0.130386i | \(-0.0416218\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.11078e9 | −0.341221 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.91506e9i | 0.632292i | 0.948711 | + | 0.316146i | \(0.102389\pi\) | ||||
−0.948711 | + | 0.316146i | \(0.897611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.46268e9 | 0.360774 | 0.180387 | − | 0.983596i | \(-0.442265\pi\) | ||||
0.180387 | + | 0.983596i | \(0.442265\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.44235e8i | 0.0552769i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.25563e10 | 1.24344 | 0.621718 | − | 0.783241i | \(-0.286435\pi\) | ||||
0.621718 | + | 0.783241i | \(0.286435\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.10327e9i | 0.782524i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.63019e9 | −0.153539 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.22037e9i | − 0.479613i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.88405e9 | −0.437770 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.02634e10i | 0.897632i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.82380e9 | −0.241019 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.31223e9i | 0.692477i | 0.938146 | + | 0.346239i | \(0.112541\pi\) | ||||
−0.938146 | + | 0.346239i | \(0.887459\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.03739e8 | −0.0490990 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 1.63476e9i | − 0.129800i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.36914e10 | −1.06152 | −0.530758 | − | 0.847523i | \(-0.678093\pi\) | ||||
−0.530758 | + | 0.847523i | \(0.678093\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 2.97888e9i | − 0.225556i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.27014e10 | −0.939366 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.54155e9i | 0.472611i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.77016e9 | −0.124950 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 5.70122e9i | 0.393233i | 0.980480 | + | 0.196617i | \(0.0629954\pi\) | ||||
−0.980480 | + | 0.196617i | \(0.937005\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.21129e9 | 0.486084 | 0.243042 | − | 0.970016i | \(-0.421855\pi\) | ||||
0.243042 | + | 0.970016i | \(0.421855\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.38443e9i | 0.157093i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.06540e9 | −0.326223 | −0.163112 | − | 0.986608i | \(-0.552153\pi\) | ||||
−0.163112 | + | 0.986608i | \(0.552153\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.33363e10i | − 0.839698i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.16224e9 | −0.0715523 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.28030e10i | 0.770785i | 0.922753 | + | 0.385392i | \(0.125934\pi\) | ||||
−0.922753 | + | 0.385392i | \(0.874066\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.89886e9 | 0.111805 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.75748e10i | 1.01219i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.91839e9 | 0.333451 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 3.57832e10i | − 1.97249i | −0.165290 | − | 0.986245i | \(-0.552856\pi\) | ||||
0.165290 | − | 0.986245i | \(-0.447144\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −3.24291e9 | −0.174916 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 6.06832e9i | − 0.320312i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.68848e10 | −1.90552 | −0.952758 | − | 0.303731i | \(-0.901768\pi\) | ||||
−0.952758 | + | 0.303731i | \(0.901768\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 1.19442e10i | − 0.603996i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.77650e9 | 0.384963 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.95039e9i | − 0.0945290i | −0.998882 | − | 0.0472645i | \(-0.984950\pi\) | ||||
0.998882 | − | 0.0472645i | \(-0.0150504\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.63017e10 | 0.773629 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 1.97660e10i | − 0.918592i | −0.888283 | − | 0.459296i | \(-0.848102\pi\) | ||||
0.888283 | − | 0.459296i | \(-0.151898\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.04539e9 | 0.275158 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.14145e10i | 0.508878i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.83144e8 | 0.00799823 | 0.00399911 | − | 0.999992i | \(-0.498727\pi\) | ||||
0.00399911 | + | 0.999992i | \(0.498727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 3.78026e9i | − 0.161739i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.32563e10 | 0.974923 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.27873e10i | 0.525279i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.20182e9 | 0.289921 | 0.144961 | − | 0.989437i | \(-0.453694\pi\) | ||||
0.144961 | + | 0.989437i | \(0.453694\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.35840e9i | 0.132507i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.54914e10 | −1.37260 | −0.686302 | − | 0.727316i | \(-0.740767\pi\) | ||||
−0.686302 | + | 0.727316i | \(0.740767\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.21892e10i | 0.462121i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.03562e9 | −0.0756616 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.70637e9i | 0.244405i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4.66917e9 | 0.166858 | 0.0834289 | − | 0.996514i | \(-0.473413\pi\) | ||||
0.0834289 | + | 0.996514i | \(0.473413\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 5.75906e9i | − 0.201829i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.32165e9 | 0.286028 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.32383e10i | 0.446314i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.02079e10 | −0.668308 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.47311e10i | 1.12684i | 0.826170 | + | 0.563421i | \(0.190515\pi\) | ||||
−0.826170 | + | 0.563421i | \(0.809485\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.19134e10 | 1.65254 | 0.826269 | − | 0.563276i | \(-0.190459\pi\) | ||||
0.826269 | + | 0.563276i | \(0.190459\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 1.05619e10i | − 0.329900i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.90433e9 | 0.272926 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.04256e9i | 0.121603i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.64864e10 | 0.781976 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.31069e10i | 1.82881i | 0.404806 | + | 0.914403i | \(0.367339\pi\) | ||||
−0.404806 | + | 0.914403i | \(0.632661\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.71812e10 | 0.773245 | 0.386622 | − | 0.922238i | \(-0.373642\pi\) | ||||
0.386622 | + | 0.922238i | \(0.373642\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.63889e9i | 0.185412i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.09234e10 | −0.299524 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 3.44182e10i | − 0.926681i | −0.886180 | − | 0.463340i | \(-0.846651\pi\) | ||||
0.886180 | − | 0.463340i | \(-0.153349\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.18599e10 | −0.313565 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 2.24571e10i | − 0.583093i | −0.956557 | − | 0.291547i | \(-0.905830\pi\) | ||||
0.956557 | − | 0.291547i | \(-0.0941699\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.98027e9 | −0.127003 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 1.33365e10i | − 0.334051i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.00449e10 | −0.985284 | −0.492642 | − | 0.870232i | \(-0.663969\pi\) | ||||
−0.492642 | + | 0.870232i | \(0.663969\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.60225e10i | 0.870698i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.83635e9 | 0.186089 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 5.80161e9i | − 0.135364i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.33836e10 | 1.91168 | 0.955841 | − | 0.293883i | \(-0.0949477\pi\) | ||||
0.955841 | + | 0.293883i | \(0.0949477\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 4.34716e9i | − 0.0979389i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.16433e10 | 1.14343 | 0.571715 | − | 0.820452i | \(-0.306278\pi\) | ||||
0.571715 | + | 0.820452i | \(0.306278\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.77439e10i | − 1.03895i | −0.854486 | − | 0.519475i | \(-0.826128\pi\) | ||||
0.854486 | − | 0.519475i | \(-0.173872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.04061e10 | −0.222575 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.33765e10i | 0.491488i | 0.969335 | + | 0.245744i | \(0.0790322\pi\) | ||||
−0.969335 | + | 0.245744i | \(0.920968\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.24592e9 | −0.0464198 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.33071e9i | 0.108318i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.26793e11 | 2.53310 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 2.57298e10i | − 0.505432i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.26975e10 | 0.438434 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 5.12753e10i | − 0.974017i | −0.873397 | − | 0.487008i | \(-0.838088\pi\) | ||||
0.873397 | − | 0.487008i | \(-0.161912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.43594e9 | 0.120235 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.43194e9i | 0.0446852i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.79840e10 | −0.686490 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 8.40950e10i | − 1.49505i | −0.664236 | − | 0.747523i | \(-0.731243\pi\) | ||||
0.664236 | − | 0.747523i | \(-0.268757\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.44371e9 | −0.0777160 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.45788e10i | 1.11113i | 0.831474 | + | 0.555564i | \(0.187497\pi\) | ||||
−0.831474 | + | 0.555564i | \(0.812503\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.41777e10 | −0.240004 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.26118e10i | 0.376629i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.83222e10 | −0.300298 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 9.33890e10i | − 1.50624i | −0.657885 | − | 0.753119i | \(-0.728549\pi\) | ||||
0.657885 | − | 0.753119i | \(-0.271451\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.18869e10 | 0.188677 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 7.08092e10i | − 1.10616i | −0.833128 | − | 0.553080i | \(-0.813452\pi\) | ||||
0.833128 | − | 0.553080i | \(-0.186548\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.75614e10 | 1.34632 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.27296e10i | 0.192657i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.13904e10 | 1.36154 | 0.680769 | − | 0.732498i | \(-0.261646\pi\) | ||||
0.680769 | + | 0.732498i | \(0.261646\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 8.13101e9i | − 0.119251i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.25615e10 | −0.181373 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.83102e10i | 0.402452i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.17323e11 | −1.64218 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 4.57914e10i | 0.631123i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.08647e11 | 1.47458 | 0.737289 | − | 0.675577i | \(-0.236105\pi\) | ||||
0.737289 | + | 0.675577i | \(0.236105\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 4.66215e10i | − 0.623131i | −0.950225 | − | 0.311566i | \(-0.899147\pi\) | ||||
0.950225 | − | 0.311566i | \(-0.100853\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.72838e9 | −0.0754041 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 2.22227e10i | − 0.288108i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.04010e10 | 0.898992 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.11257e10i | 0.391508i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 3.45699e10 | 0.428340 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.48359e10i | 0.181091i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.97482e10 | −0.357736 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.31741e11i | 1.56086i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.67851e11 | 1.95945 | 0.979726 | − | 0.200340i | \(-0.0642046\pi\) | ||||
0.979726 | + | 0.200340i | \(0.0642046\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 5.13301e10i | − 0.590436i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.34035e10 | 1.05871 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.61757e10i | 0.404080i | 0.979377 | + | 0.202040i | \(0.0647571\pi\) | ||||
−0.979377 | + | 0.202040i | \(0.935243\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.51205e10 | −0.166447 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.09677e10i | 0.444462i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.75679e10 | 0.187853 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.49443e9i | 0.0579097i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 5.93877e10 | 0.616986 | 0.308493 | − | 0.951227i | \(-0.400175\pi\) | ||||
0.308493 | + | 0.951227i | \(0.400175\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 1.21680e11i | − 1.24616i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.82886e10 | −0.487521 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.66243e10i | 0.563598i | 0.959473 | + | 0.281799i | \(0.0909311\pi\) | ||||
−0.959473 | + | 0.281799i | \(0.909069\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.71098e10 | −0.266031 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.79664e9i | 0.0270585i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −4.58266e10 | −0.437188 | −0.218594 | − | 0.975816i | \(-0.570147\pi\) | ||||
−0.218594 | + | 0.975816i | \(0.570147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 5.45678e10i | − 0.513325i | −0.966501 | − | 0.256662i | \(-0.917377\pi\) | ||||
0.966501 | − | 0.256662i | \(-0.0826228\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 7.22132e10 | 0.669881 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 1.86319e10i | − 0.170446i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.69500e11 | −1.52921 | −0.764604 | − | 0.644500i | \(-0.777066\pi\) | ||||
−0.764604 | + | 0.644500i | \(0.777066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.13260e10i | 0.634649i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.81875e10 | 0.159613 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 2.52125e11i | − 2.18244i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.16999e10 | 0.185283 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 5.05989e10i | 0.426175i | 0.977033 | + | 0.213088i | \(0.0683520\pi\) | ||||
−0.977033 | + | 0.213088i | \(0.931648\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.42145e10 | −0.533546 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.26953e11i | 1.04063i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.12289e10 | −0.252544 | −0.126272 | − | 0.991996i | \(-0.540301\pi\) | ||||
−0.126272 | + | 0.991996i | \(0.540301\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.05772e10i | 0.0843922i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4.72617e10 | 0.372059 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − 2.49376e10i | − 0.193708i | −0.995299 | − | 0.0968538i | \(-0.969122\pi\) | ||||
0.995299 | − | 0.0968538i | \(-0.0308779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.02149e11 | 1.54944 | 0.774719 | − | 0.632305i | \(-0.217891\pi\) | ||||
0.774719 | + | 0.632305i | \(0.217891\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8.40049e9i | − 0.0635382i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.59942e11 | 1.19383 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.86515e11i | 1.37391i | 0.726699 | + | 0.686956i | \(0.241054\pi\) | ||||
−0.726699 | + | 0.686956i | \(0.758946\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.12088e9 | 0.0663082 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.12592e11i | 0.807870i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.64658e11 | −1.87432 | −0.937159 | − | 0.348904i | \(-0.886554\pi\) | ||||
−0.937159 | + | 0.348904i | \(0.886554\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.95127e10i | 0.206304i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.71229e11 | −1.87152 | −0.935761 | − | 0.352634i | \(-0.885286\pi\) | ||||
−0.935761 | + | 0.352634i | \(0.885286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.76820e10i | 0.597239i | 0.954372 | + | 0.298619i | \(0.0965261\pi\) | ||||
−0.954372 | + | 0.298619i | \(0.903474\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.09625e9 | −0.0611640 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.84217e9i | 0.0454194i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.68678e10 | −0.176080 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.39534e11i | 0.902838i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.17337e10 | −0.0749602 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 1.73981e11i | − 1.09745i | −0.836003 | − | 0.548724i | \(-0.815114\pi\) | ||||
0.836003 | − | 0.548724i | \(-0.184886\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.60188e10 | −0.0997733 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.48356e11i | − 0.912455i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.26428e11 | 0.767868 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 6.85310e10i | − 0.411040i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.11172e11 | −1.25085 | −0.625424 | − | 0.780285i | \(-0.715074\pi\) | ||||
−0.625424 | + | 0.780285i | \(0.715074\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 2.30983e11i | − 1.35125i | −0.737245 | − | 0.675626i | \(-0.763873\pi\) | ||||
0.737245 | − | 0.675626i | \(-0.236127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.03880e11 | 0.600195 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.25708e11i | 1.28804i | 0.765007 | + | 0.644022i | \(0.222735\pi\) | ||||
−0.765007 | + | 0.644022i | \(0.777265\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.45746e11 | 1.94885 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.42965e10i | 0.0795984i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.78919e11 | −0.984019 | −0.492009 | − | 0.870590i | \(-0.663737\pi\) | ||||
−0.492009 | + | 0.870590i | \(0.663737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − 2.11648e11i | − 1.14987i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.04126e10 | 0.163227 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 9.19117e10i | − 0.487337i | −0.969859 | − | 0.243668i | \(-0.921649\pi\) | ||||
0.969859 | − | 0.243668i | \(-0.0783508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.04482e11 | −1.07115 | −0.535573 | − | 0.844489i | \(-0.679904\pi\) | ||||
−0.535573 | + | 0.844489i | \(0.679904\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.63413e10i | 0.239836i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.05637e10 | 0.156286 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.96662e10i | 0.149885i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.97988e10 | 0.148763 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.67959e11i | 0.828542i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.26000e11 | 1.58912 | 0.794561 | − | 0.607184i | \(-0.207701\pi\) | ||||
0.794561 | + | 0.607184i | \(0.207701\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 2.14260e10i | − 0.103211i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.18596e11 | 0.564565 | 0.282282 | − | 0.959331i | \(-0.408908\pi\) | ||||
0.282282 | + | 0.959331i | \(0.408908\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.21846e10i | 0.245506i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.26452e11 | −0.587946 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1.72598e11i | − 0.793148i | −0.918003 | − | 0.396574i | \(-0.870199\pi\) | ||||
0.918003 | − | 0.396574i | \(-0.129801\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.24114e10 | −0.238047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.93593e11i | 0.869087i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.41958e11 | −1.07365 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.45326e11i | 0.637428i | 0.947851 | + | 0.318714i | \(0.103251\pi\) | ||||
−0.947851 | + | 0.318714i | \(0.896749\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.10653e10 | 0.134692 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.83905e11i | 0.788234i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.30259e10 | −0.267047 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.59384e11i | 0.667630i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.46244e11 | 1.43387 | 0.716935 | − | 0.697140i | \(-0.245544\pi\) | ||||
0.716935 | + | 0.697140i | \(0.245544\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.39054e10i | 0.138819i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.61209e10 | −0.389100 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1.20297e11i | − 0.481478i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.96735e9 | 0.0354878 | 0.0177439 | − | 0.999843i | \(-0.494352\pi\) | ||||
0.0177439 | + | 0.999843i | \(0.494352\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 6.57097e10i | 0.257129i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −4.65001e10 | −0.179927 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 2.41044e11i | − 0.922300i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.23404e11 | 0.466931 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 9.39298e10i | − 0.351470i | −0.984438 | − | 0.175735i | \(-0.943770\pi\) | ||||
0.984438 | − | 0.175735i | \(-0.0562301\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.88942e10 | 0.143927 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 8.96419e10i | 0.328064i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.98782e10 | −0.252924 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.29456e11i | 0.821412i | 0.911768 | + | 0.410706i | \(0.134718\pi\) | ||||
−0.911768 | + | 0.410706i | \(0.865282\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.04604e10 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.21841e11i | 0.776912i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.44865e11 | −1.54103 | −0.770516 | − | 0.637420i | \(-0.780002\pi\) | ||||
−0.770516 | + | 0.637420i | \(0.780002\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1.07933e11i | 0.369833i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.33132e10 | −0.316281 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 5.10990e11i | − 1.71330i | −0.515895 | − | 0.856652i | \(-0.672541\pi\) | ||||
0.515895 | − | 0.856652i | \(-0.327459\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.33907e11 | 0.444152 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.87724e11i | 1.27224i | 0.771592 | + | 0.636118i | \(0.219461\pi\) | ||||
−0.771592 | + | 0.636118i | \(0.780539\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.21371e11 | −0.393995 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.80273e10i | 0.218475i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.03823e10 | 0.0647629 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 4.16206e8i | − 0.00130842i | −1.00000 | 0.000654212i | \(-0.999792\pi\) | |||||
1.00000 | 0.000654212i | \(-0.000208242\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.07846e11 | −0.646490 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 7.13161e10i | − 0.219482i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −3.02639e11 | −0.921596 | −0.460798 | − | 0.887505i | \(-0.652437\pi\) | ||||
−0.460798 | + | 0.887505i | \(0.652437\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.01042e11i | 0.304462i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.33821e11 | −0.995348 | −0.497674 | − | 0.867364i | \(-0.665812\pi\) | ||||
−0.497674 | + | 0.867364i | \(0.665812\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 1.28323e11i | − 0.378622i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.95621e10 | −0.115514 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 3.31804e11i | − 0.958738i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.15184e11 | −1.18723 | −0.593615 | − | 0.804749i | \(-0.702300\pi\) | ||||
−0.593615 | + | 0.804749i | \(0.702300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.84971e10i | 0.193845i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.71927e10 | −0.188193 | −0.0940967 | − | 0.995563i | \(-0.529996\pi\) | ||||
−0.0940967 | + | 0.995563i | \(0.529996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 1.09530e11i | − 0.303617i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.54856e9 | 0.0207100 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.82119e11i | 0.494544i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.61247e11 | −2.04607 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.41151e10i | 0.0907610i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 4.85130e10 | 0.127756 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 7.23571e11i | − 1.88618i | −0.332542 | − | 0.943088i | \(-0.607906\pi\) | ||||
0.332542 | − | 0.943088i | \(-0.392094\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −2.45217e11 | −0.632765 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.72450e10i | 0.0951397i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.61186e11 | 0.407601 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 2.06563e11i | − 0.517110i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.83695e11 | −0.703101 | −0.351550 | − | 0.936169i | \(-0.614345\pi\) | ||||
−0.351550 | + | 0.936169i | \(0.614345\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 2.05271e11i | − 0.503664i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.55920e10 | −0.0621690 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 3.37825e11i | − 0.812513i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.21323e10 | 0.0527039 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 8.29974e10i | 0.195691i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 4.24107e11 | 0.990105 | 0.495053 | − | 0.868863i | \(-0.335149\pi\) | ||||
0.495053 | + | 0.868863i | \(0.335149\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 8.29372e11i | − 1.91719i | −0.284768 | − | 0.958597i | \(-0.591916\pi\) | ||||
0.284768 | − | 0.958597i | \(-0.408084\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.76455e10 | −0.109059 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.04408e10i | 0.0916619i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 6.41028e11 | 1.43876 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 2.98126e10i | − 0.0662618i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.59588e11 | −0.791466 | −0.395733 | − | 0.918366i | \(-0.629509\pi\) | ||||
−0.395733 | + | 0.918366i | \(0.629509\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 5.69282e11i | − 1.24088i | −0.784256 | − | 0.620438i | \(-0.786955\pi\) | ||||
0.784256 | − | 0.620438i | \(-0.213045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.38002e11 | −0.513765 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.99528e11i | 1.06792i | 0.845510 | + | 0.533959i | \(0.179296\pi\) | ||||
−0.845510 | + | 0.533959i | \(0.820704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −5.89395e11 | −1.24792 | −0.623962 | − | 0.781455i | \(-0.714478\pi\) | ||||
−0.623962 | + | 0.781455i | \(0.714478\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.17373e11i | 1.08492i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.30497e11 | −0.478725 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 1.08179e11i | − 0.222535i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.34734e10 | −0.108952 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.66218e11i | 0.537266i | 0.963243 | + | 0.268633i | \(0.0865719\pi\) | ||||
−0.963243 | + | 0.268633i | \(0.913428\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3.88985e11 | −0.777586 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.12044e9i | 0.0160794i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.15848e11 | 0.227229 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 2.19738e11i | − 0.426944i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.60624e11 | −1.07905 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.45522e10i | 0.0468135i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.44334e10 | −0.0839293 | −0.0419647 | − | 0.999119i | \(-0.513362\pi\) | ||||
−0.0419647 | + | 0.999119i | \(0.513362\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.14318e11i | 0.213920i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.92427e11 | −0.727504 | −0.363752 | − | 0.931496i | \(-0.618504\pi\) | ||||
−0.363752 | + | 0.931496i | \(0.618504\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 5.05227e11i | − 0.927928i | −0.885854 | − | 0.463964i | \(-0.846427\pi\) | ||||
0.885854 | − | 0.463964i | \(-0.153573\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.05462e10 | 0.0737798 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.89803e11i | 0.883036i | 0.897252 | + | 0.441518i | \(0.145560\pi\) | ||||
−0.897252 | + | 0.441518i | \(0.854440\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.16732e11 | 0.744377 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.41737e11i | 0.427825i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.29907e11 | 1.27994 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.95503e10i | 0.155594i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.95187e11 | −0.336043 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.49339e11i | 0.254766i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.35062e11 | −0.735449 | −0.367725 | − | 0.929935i | \(-0.619863\pi\) | ||||
−0.367725 | + | 0.929935i | \(0.619863\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 1.32930e11i | − 0.222673i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.66566e11 | −1.27247 | −0.636233 | − | 0.771497i | \(-0.719508\pi\) | ||||
−0.636233 | + | 0.771497i | \(0.719508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.00425e11i | 0.658686i | 0.944210 | + | 0.329343i | \(0.106827\pi\) | ||||
−0.944210 | + | 0.329343i | \(0.893173\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.83265e11 | 0.461763 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.09803e11i | 0.338936i | 0.985536 | + | 0.169468i | \(0.0542049\pi\) | ||||
−0.985536 | + | 0.169468i | \(0.945795\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.03820e11 | −0.326317 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.16194e11i | 0.184363i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.93149e11 | −0.932734 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.70728e11i | 0.421931i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.69671e10 | 0.149780 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.74397e11i | 0.266993i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.41125e11 | 0.669365 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 1.42716e11i | − 0.214645i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −4.67139e11 | −0.696389 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 6.37382e11i | − 0.941826i | −0.882180 | − | 0.470913i | \(-0.843925\pi\) | ||||
0.882180 | − | 0.470913i | \(-0.156075\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.49949e11 | 0.659034 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 8.99658e11i | 1.30618i | 0.757279 | + | 0.653091i | \(0.226528\pi\) | ||||
−0.757279 | + | 0.653091i | \(0.773472\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.55652e11 | 1.08752 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.37607e11i | 0.196316i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.90774e11 | −0.411223 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 5.06013e11i | − 0.709413i | −0.934978 | − | 0.354707i | \(-0.884581\pi\) | ||||
0.934978 | − | 0.354707i | \(-0.115419\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.08328e11 | −0.150557 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 7.30549e11i | 1.00657i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.78321e10 | −0.0789955 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.45477e11i | 0.197004i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.05701e12 | 1.41912 | 0.709558 | − | 0.704647i | \(-0.248895\pi\) | ||||
0.709558 | + | 0.704647i | \(0.248895\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.66042e11i | 0.886549i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.76620e11 | 0.365054 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.39459e11i | 0.575005i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.81575e11 | −1.01394 | −0.506970 | − | 0.861964i | \(-0.669235\pi\) | ||||
−0.506970 | + | 0.861964i | \(0.669235\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 1.61933e11i | − 0.208293i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.91580e11 | −1.13711 | −0.568554 | − | 0.822646i | \(-0.692497\pi\) | ||||
−0.568554 | + | 0.822646i | \(0.692497\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.31879e11i | 0.166774i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.54513e10 | 0.0319141 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 9.28543e11i | − 1.15452i | −0.816560 | − | 0.577261i | \(-0.804121\pi\) | ||||
0.816560 | − | 0.577261i | \(-0.195879\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.24202e11 | −0.399716 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 5.87199e11i | − 0.717898i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.14427e12 | −1.38725 | −0.693626 | − | 0.720335i | \(-0.743988\pi\) | ||||
−0.693626 | + | 0.720335i | \(0.743988\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 6.57189e11i | − 0.790090i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.78952e11 | 0.451790 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.20057e10i | 0.0851319i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.79534e11 | 0.679494 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.62365e10i | 0.0886458i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.49115e11 | 0.748536 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.31974e11i | 0.265297i | 0.991163 | + | 0.132649i | \(0.0423482\pi\) | ||||
−0.991163 | + | 0.132649i | \(0.957652\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.44132e11 | −0.276905 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 6.93765e11i | − 0.780433i | −0.920723 | − | 0.390216i | \(-0.872400\pi\) | ||||
0.920723 | − | 0.390216i | \(-0.127600\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.52659e11 | 0.281893 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.28404e11i | 0.252747i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.39487e12 | 1.53093 | 0.765465 | − | 0.643477i | \(-0.222509\pi\) | ||||
0.765465 | + | 0.643477i | \(0.222509\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.84277e11i | 0.309465i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.79970e11 | 0.518248 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.19018e12i | 1.27467i | 0.770588 | + | 0.637334i | \(0.219963\pi\) | ||||
−0.770588 | + | 0.637334i | \(0.780037\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.15536e12 | 1.22736 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.32056e11i | 0.139152i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.64192e11 | 0.485191 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − 1.51631e12i | − 1.57215i | −0.618131 | − | 0.786075i | \(-0.712110\pi\) | ||||
0.618131 | − | 0.786075i | \(-0.287890\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.88725e11 | 0.399802 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 4.30114e11i | − 0.438825i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.43870e11 | −0.854073 | −0.427036 | − | 0.904234i | \(-0.640442\pi\) | ||||
−0.427036 | + | 0.904234i | \(0.640442\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.82341e10i | 0.0283473i |
(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 | 384.9.g.a.127.17 | ✓ | 32 | |
4.3 | odd | 2 | inner | 384.9.g.a.127.18 | yes | 32 | |
8.3 | odd | 2 | 384.9.g.b.127.15 | yes | 32 | ||
8.5 | even | 2 | 384.9.g.b.127.16 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.9.g.a.127.17 | ✓ | 32 | 1.1 | even | 1 | trivial | |
384.9.g.a.127.18 | yes | 32 | 4.3 | odd | 2 | inner | |
384.9.g.b.127.15 | yes | 32 | 8.3 | odd | 2 | ||
384.9.g.b.127.16 | yes | 32 | 8.5 | even | 2 |