Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,9,Mod(197,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.197");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.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: | \(102.659409735\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 4002260 x^{14} + 6534459751956 x^{12} + \cdots + 19\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2^{32}\cdot 3^{37}\cdot 7^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.9 | ||
Root | \(221.696i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.197 |
Dual form | 252.9.c.a.197.8 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 221.696i | 0.354713i | 0.984147 | + | 0.177357i | \(0.0567546\pi\) | ||||
−0.984147 | + | 0.177357i | \(0.943245\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −907.493 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19481.4i | 1.33060i | 0.746574 | + | 0.665302i | \(0.231697\pi\) | ||||
−0.746574 | + | 0.665302i | \(0.768303\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19141.3 | −0.670191 | −0.335095 | − | 0.942184i | \(-0.608769\pi\) | ||||
−0.335095 | + | 0.942184i | \(0.608769\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 134659.i | − 1.61227i | −0.591729 | − | 0.806137i | \(-0.701554\pi\) | ||||
0.591729 | − | 0.806137i | \(-0.298446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −194587. | −1.49314 | −0.746570 | − | 0.665307i | \(-0.768301\pi\) | ||||
−0.746570 | + | 0.665307i | \(0.768301\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 42602.7i | 0.152239i | 0.997099 | + | 0.0761194i | \(0.0242530\pi\) | ||||
−0.997099 | + | 0.0761194i | \(0.975747\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 341476. | 0.874178 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 814906.i | 1.15217i | 0.817391 | + | 0.576084i | \(0.195420\pi\) | ||||
−0.817391 | + | 0.576084i | \(0.804580\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −203649. | −0.220514 | −0.110257 | − | 0.993903i | \(-0.535167\pi\) | ||||
−0.110257 | + | 0.993903i | \(0.535167\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 201187.i | − 0.134069i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.43832e6 | 0.767449 | 0.383725 | − | 0.923448i | \(-0.374641\pi\) | ||||
0.383725 | + | 0.923448i | \(0.374641\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 2.77633e6i | − 0.982507i | −0.871017 | − | 0.491253i | \(-0.836539\pi\) | ||||
0.871017 | − | 0.491253i | \(-0.163461\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.04485e6 | −1.47562 | −0.737810 | − | 0.675009i | \(-0.764140\pi\) | ||||
−0.737810 | + | 0.675009i | \(0.764140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 5.42366e6i | − 1.11148i | −0.831357 | − | 0.555739i | \(-0.812435\pi\) | ||||
0.831357 | − | 0.555739i | \(-0.187565\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 823543. | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.34818e7i | 1.70861i | 0.519772 | + | 0.854305i | \(0.326017\pi\) | ||||
−0.519772 | + | 0.854305i | \(0.673983\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.31894e6 | −0.471983 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 1.38302e7i | − 1.14135i | −0.821175 | − | 0.570676i | \(-0.806681\pi\) | ||||
0.821175 | − | 0.570676i | \(-0.193319\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.26176e7 | 1.63353 | 0.816766 | − | 0.576969i | \(-0.195765\pi\) | ||||
0.816766 | + | 0.576969i | \(0.195765\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 4.24355e6i | − 0.237726i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.91134e7 | 1.94100 | 0.970502 | − | 0.241091i | \(-0.0775054\pi\) | ||||
0.970502 | + | 0.241091i | \(0.0775054\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.02970e7i | 1.19225i | 0.802893 | + | 0.596123i | \(0.203293\pi\) | ||||
−0.802893 | + | 0.596123i | \(0.796707\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.42017e7 | −1.90863 | −0.954315 | − | 0.298802i | \(-0.903413\pi\) | ||||
−0.954315 | + | 0.298802i | \(0.903413\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.76792e7i | − 0.502921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.10178e7 | −0.539609 | −0.269804 | − | 0.962915i | \(-0.586959\pi\) | ||||
−0.269804 | + | 0.962915i | \(0.586959\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 1.30858e7i | − 0.275732i | −0.990451 | − | 0.137866i | \(-0.955976\pi\) | ||||
0.990451 | − | 0.137866i | \(-0.0440244\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.98533e7 | 0.571895 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − 1.78236e7i | − 0.284077i | −0.989861 | − | 0.142038i | \(-0.954634\pi\) | ||||
0.989861 | − | 0.142038i | \(-0.0453657\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.73706e7 | 0.253308 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 4.31392e7i | − 0.529636i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.89791e7 | 0.779167 | 0.389583 | − | 0.920991i | \(-0.372619\pi\) | ||||
0.389583 | + | 0.920991i | \(0.372619\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 1.90594e8i | − 1.83157i | −0.401670 | − | 0.915785i | \(-0.631570\pi\) | ||||
0.401670 | − | 0.915785i | \(-0.368430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.00729e7 | −0.178345 | −0.0891727 | − | 0.996016i | \(-0.528422\pi\) | ||||
−0.0891727 | + | 0.996016i | \(0.528422\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.00201e7i | 0.0764427i | 0.999269 | + | 0.0382214i | \(0.0121692\pi\) | ||||
−0.999269 | + | 0.0382214i | \(0.987831\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.41310e8 | 1.00107 | 0.500537 | − | 0.865715i | \(-0.333136\pi\) | ||||
0.500537 | + | 0.865715i | \(0.333136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 2.29538e8i | − 1.40780i | −0.710299 | − | 0.703901i | \(-0.751440\pi\) | ||||
0.710299 | − | 0.703901i | \(-0.248560\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.44484e6 | −0.0540012 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.22202e8i | 0.609382i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.65165e8 | −0.770508 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.62304e8i | 0.664796i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.60959e8 | 1.77193 | 0.885967 | − | 0.463748i | \(-0.153496\pi\) | ||||
0.885967 | + | 0.463748i | \(0.153496\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 3.50919e8i | − 1.19158i | −0.803141 | − | 0.595788i | \(-0.796840\pi\) | ||||
0.803141 | − | 0.595788i | \(-0.203160\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.76587e8 | 0.564354 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.62021e8i | − 0.743796i | −0.928274 | − | 0.371898i | \(-0.878707\pi\) | ||||
0.928274 | − | 0.371898i | \(-0.121293\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.38052e8 | 0.905576 | 0.452788 | − | 0.891618i | \(-0.350430\pi\) | ||||
0.452788 | + | 0.891618i | \(0.350430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 3.72899e8i | − 0.891759i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.80661e8 | −0.408689 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 7.73781e8i | − 1.56990i | −0.619557 | − | 0.784952i | \(-0.712688\pi\) | ||||
0.619557 | − | 0.784952i | \(-0.287312\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.78380e8 | −0.727814 | −0.363907 | − | 0.931435i | \(-0.618557\pi\) | ||||
−0.363907 | + | 0.931435i | \(0.618557\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.51482e7i | − 0.0782192i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.38439e8 | 1.21539 | 0.607695 | − | 0.794170i | \(-0.292094\pi\) | ||||
0.607695 | + | 0.794170i | \(0.292094\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 3.86616e7i | − 0.0575409i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.26252e9 | 1.78850 | 0.894250 | − | 0.447567i | \(-0.147709\pi\) | ||||
0.894250 | + | 0.447567i | \(0.147709\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 6.70075e8i | − 0.861505i | −0.902470 | − | 0.430752i | \(-0.858248\pi\) | ||||
0.902470 | − | 0.430752i | \(-0.141752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.49341e8 | −0.550845 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.97871e8i | 0.220902i | 0.993882 | + | 0.110451i | \(0.0352294\pi\) | ||||
−0.993882 | + | 0.110451i | \(0.964771\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.09887e8 | −0.330408 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 1.26692e9i | − 1.23406i | −0.786938 | − | 0.617031i | \(-0.788335\pi\) | ||||
0.786938 | − | 0.617031i | \(-0.211665\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.41676e8 | 0.877379 | 0.438689 | − | 0.898639i | \(-0.355443\pi\) | ||||
0.438689 | + | 0.898639i | \(0.355443\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.18870e8i | 0.272224i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.62334e9 | 2.14530 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 3.87580e8i | − 0.291225i | −0.989342 | − | 0.145612i | \(-0.953485\pi\) | ||||
0.989342 | − | 0.145612i | \(-0.0465152\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.95489e8 | 0.429185 | 0.214593 | − | 0.976704i | \(-0.431158\pi\) | ||||
0.214593 | + | 0.976704i | \(0.431158\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.92777e9i | − 1.27994i | −0.768400 | − | 0.639970i | \(-0.778947\pi\) | ||||
0.768400 | − | 0.639970i | \(-0.221053\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.50314e9 | −0.958491 | −0.479246 | − | 0.877681i | \(-0.659090\pi\) | ||||
−0.479246 | + | 0.877681i | \(0.659090\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 7.39521e8i | − 0.435478i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.15501e8 | 0.348508 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 3.79083e9i | − 1.98678i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.59815e9 | −1.31079 | −0.655397 | − | 0.755285i | \(-0.727499\pi\) | ||||
−0.655397 | + | 0.755285i | \(0.727499\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 1.11842e9i | − 0.523422i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.84810e8 | 0.0833464 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.57755e9i | 1.08053i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.32831e9 | −0.537130 | −0.268565 | − | 0.963262i | \(-0.586549\pi\) | ||||
−0.268565 | + | 0.963262i | \(0.586549\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.87981e9i | 0.707964i | 0.935252 | + | 0.353982i | \(0.115173\pi\) | ||||
−0.935252 | + | 0.353982i | \(0.884827\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.36880e7 | −0.0195225 | −0.00976125 | − | 0.999952i | \(-0.503107\pi\) | ||||
−0.00976125 | + | 0.999952i | \(0.503107\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.03976e9i | 0.352784i | 0.984320 | + | 0.176392i | \(0.0564426\pi\) | ||||
−0.984320 | + | 0.176392i | \(0.943557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.20240e9 | 0.394256 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 2.06002e9i | − 0.631364i | −0.948865 | − | 0.315682i | \(-0.897767\pi\) | ||||
0.948865 | − | 0.315682i | \(-0.102233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5.91153e9 | 1.75239 | 0.876197 | − | 0.481954i | \(-0.160073\pi\) | ||||
0.876197 | + | 0.481954i | \(0.160073\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.82576e8i | 0.0506733i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.72466e9 | 1.00069 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.27398e9i | 1.58070i | 0.612658 | + | 0.790348i | \(0.290100\pi\) | ||||
−0.612658 | + | 0.790348i | \(0.709900\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.29959e8 | −0.202570 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.16469e9i | 0.954663i | 0.878723 | + | 0.477331i | \(0.158396\pi\) | ||||
−0.878723 | + | 0.477331i | \(0.841604\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.30527e9 | −0.290069 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5.30124e9i | − 1.10804i | −0.832504 | − | 0.554019i | \(-0.813094\pi\) | ||||
0.832504 | − | 0.554019i | \(-0.186906\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.98885e9 | −0.606067 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 6.25848e9i | − 1.19525i | −0.801775 | − | 0.597626i | \(-0.796111\pi\) | ||||
0.801775 | − | 0.597626i | \(-0.203889\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.62468e9 | −0.301226 | −0.150613 | − | 0.988593i | \(-0.548125\pi\) | ||||
−0.150613 | + | 0.988593i | \(0.548125\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.65242e9i | 1.16319i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.99114e9 | −0.508063 | −0.254032 | − | 0.967196i | \(-0.581757\pi\) | ||||
−0.254032 | + | 0.967196i | \(0.581757\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 2.36189e9i | − 0.378822i | −0.981898 | − | 0.189411i | \(-0.939342\pi\) | ||||
0.981898 | − | 0.189411i | \(-0.0606579\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.63475e9 | −1.03438 | −0.517188 | − | 0.855872i | \(-0.673021\pi\) | ||||
−0.517188 | + | 0.855872i | \(0.673021\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.51950e9i | 0.371353i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.11572e10 | −1.59943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.55688e9i | 0.889665i | 0.895614 | + | 0.444833i | \(0.146737\pi\) | ||||
−0.895614 | + | 0.444833i | \(0.853263\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.06609e9 | 0.404853 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 8.15471e8i | − 0.102029i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.57816e9 | 0.557732 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.01423e9i | 0.579436i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.12109e10 | 1.26208 | 0.631042 | − | 0.775749i | \(-0.282628\pi\) | ||||
0.631042 | + | 0.775749i | \(0.282628\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.89689e8i | 0.0844140i | 0.999109 | + | 0.0422070i | \(0.0134389\pi\) | ||||
−0.999109 | + | 0.0422070i | \(0.986561\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.75039e9 | −0.182371 | −0.0911857 | − | 0.995834i | \(-0.529066\pi\) | ||||
−0.0911857 | + | 0.995834i | \(0.529066\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 1.03386e8i | − 0.0102383i | −0.999987 | − | 0.00511913i | \(-0.998371\pi\) | ||||
0.999987 | − | 0.00511913i | \(-0.00162948\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.58755e10 | −1.53308 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.62029e10i | 2.40735i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.53630e9 | −0.585866 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.92193e9i | 0.420099i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.71555e10 | −1.42919 | −0.714596 | − | 0.699538i | \(-0.753389\pi\) | ||||
−0.714596 | + | 0.699538i | \(0.753389\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.67128e9i | 0.688500i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.46235e9 | 0.268443 | 0.134221 | − | 0.990951i | \(-0.457147\pi\) | ||||
0.134221 | + | 0.990951i | \(0.457147\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 3.96737e9i | − 0.293417i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −7.47359e8 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.02435e9i | 0.622441i | 0.950338 | + | 0.311220i | \(0.100738\pi\) | ||||
−0.950338 | + | 0.311220i | \(0.899262\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.16999e10 | −0.788646 | −0.394323 | − | 0.918972i | \(-0.629021\pi\) | ||||
−0.394323 | + | 0.918972i | \(0.629021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2.18232e10i | 1.40546i | 0.711456 | + | 0.702731i | \(0.248036\pi\) | ||||
−0.711456 | + | 0.702731i | \(0.751964\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.71672e9 | −0.422906 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 4.38983e9i | − 0.264283i | −0.991231 | − | 0.132142i | \(-0.957815\pi\) | ||||
0.991231 | − | 0.132142i | \(-0.0421854\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.08807e10 | 1.22947 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.20163e10i | − 0.677017i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.80399e10 | −1.54565 | −0.772826 | − | 0.634618i | \(-0.781158\pi\) | ||||
−0.772826 | + | 0.634618i | \(0.781158\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 1.22346e10i | − 0.645794i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.38135e10 | 1.23023 | 0.615117 | − | 0.788436i | \(-0.289109\pi\) | ||||
0.615117 | + | 0.788436i | \(0.289109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 1.55984e10i | − 0.772172i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.46006e10 | −0.707644 | −0.353822 | − | 0.935313i | \(-0.615118\pi\) | ||||
−0.353822 | + | 0.935313i | \(0.615118\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.86050e10i | 0.864639i | 0.901721 | + | 0.432319i | \(0.142305\pi\) | ||||
−0.901721 | + | 0.432319i | \(0.857695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.91941e9 | 0.178393 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.88545e10i | 1.26013i | 0.776542 | + | 0.630065i | \(0.216972\pi\) | ||||
−0.776542 | + | 0.630065i | \(0.783028\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.73682e9 | 0.245451 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 4.65956e9i | − 0.191406i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.40951e10 | −0.567421 | −0.283711 | − | 0.958910i | \(-0.591566\pi\) | ||||
−0.283711 | + | 0.958910i | \(0.591566\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.40495e10i | 0.543354i | 0.962388 | + | 0.271677i | \(0.0875783\pi\) | ||||
−0.962388 | + | 0.271677i | \(0.912422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.89811e9 | 0.147786 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.80205e10i | 1.02117i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.92375e9 | −0.0687474 | −0.0343737 | − | 0.999409i | \(-0.510944\pi\) | ||||
−0.0343737 | + | 0.999409i | \(0.510944\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.25508e10i | 0.431391i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.90107e9 | 0.0978060 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 8.86258e9i | − 0.287544i | −0.989611 | − | 0.143772i | \(-0.954077\pi\) | ||||
0.989611 | − | 0.143772i | \(-0.0459232\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.06857e9 | −0.225011 | −0.112505 | − | 0.993651i | \(-0.535888\pi\) | ||||
−0.112505 | + | 0.993651i | \(0.535888\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 4.59827e10i | − 1.40942i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.05253e10 | −0.617417 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.15168e10i | 0.623546i | 0.950157 | + | 0.311773i | \(0.100923\pi\) | ||||
−0.950157 | + | 0.311773i | \(0.899077\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.27339e10 | −0.362250 | −0.181125 | − | 0.983460i | \(-0.557974\pi\) | ||||
−0.181125 | + | 0.983460i | \(0.557974\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.28995e9i | − 0.227314i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.14824e10 | 1.65536 | 0.827681 | − | 0.561199i | \(-0.189660\pi\) | ||||
0.827681 | + | 0.561199i | \(0.189660\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 1.95753e10i | − 0.508269i | −0.967169 | − | 0.254135i | \(-0.918209\pi\) | ||||
0.967169 | − | 0.254135i | \(-0.0817906\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.95142e9 | 0.100766 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 5.91515e10i | − 1.45539i | −0.685899 | − | 0.727697i | \(-0.740591\pi\) | ||||
0.685899 | − | 0.727697i | \(-0.259409\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.40867e10 | 1.30733 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.85099e9i | 0.0898518i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.05670e10 | −0.242262 | −0.121131 | − | 0.992637i | \(-0.538652\pi\) | ||||
−0.121131 | + | 0.992637i | \(0.538652\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 1.94330e10i | − 0.430265i | −0.976585 | − | 0.215132i | \(-0.930982\pi\) | ||||
0.976585 | − | 0.215132i | \(-0.0690183\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.45181e10 | 1.18636 | 0.593180 | − | 0.805070i | \(-0.297872\pi\) | ||||
0.593180 | + | 0.805070i | \(0.297872\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.48698e10i | 1.36388i | 0.731410 | + | 0.681938i | \(0.238863\pi\) | ||||
−0.731410 | + | 0.681938i | \(0.761137\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.54951e10 | −0.733631 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.82807e10i | − 1.96347i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.64469e10 | −1.30527 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.58840e10i | 0.681647i | 0.940127 | + | 0.340823i | \(0.110706\pi\) | ||||
−0.940127 | + | 0.340823i | \(0.889294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.75314e10 | −0.514337 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.52924e10i | 0.276381i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.43804e10 | −1.50012 | −0.750060 | − | 0.661370i | \(-0.769975\pi\) | ||||
−0.750060 | + | 0.661370i | \(0.769975\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 7.79053e10i | − 1.34042i | −0.742172 | − | 0.670210i | \(-0.766204\pi\) | ||||
0.742172 | − | 0.670210i | \(-0.233796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.09734e11 | 1.85761 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 2.74943e10i | − 0.450627i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.86613e10 | −0.462268 | −0.231134 | − | 0.972922i | \(-0.574244\pi\) | ||||
−0.231134 | + | 0.972922i | \(0.574244\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 2.24664e10i | − 0.350963i | −0.984483 | − | 0.175481i | \(-0.943852\pi\) | ||||
0.984483 | − | 0.175481i | \(-0.0561482\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.22538e10 | 0.649682 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 1.20669e11i | − 1.79773i | −0.438227 | − | 0.898864i | \(-0.644393\pi\) | ||||
0.438227 | − | 0.898864i | \(-0.355607\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.91877e10 | 0.721394 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 4.45008e9i | − 0.0632615i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.05660e11 | 1.47894 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 4.64705e10i | − 0.630705i | −0.948975 | − | 0.315353i | \(-0.897877\pi\) | ||||
0.948975 | − | 0.315353i | \(-0.102123\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.55571e10 | 0.341590 | 0.170795 | − | 0.985307i | \(-0.445366\pi\) | ||||
0.170795 | + | 0.985307i | \(0.445366\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.74231e10i | 0.355529i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.64960e10 | 0.976823 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5.31426e10i | 0.658467i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.22141e9 | −0.0271152 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.60438e10i | 0.190086i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.38276e11 | 1.61421 | 0.807104 | − | 0.590410i | \(-0.201034\pi\) | ||||
0.807104 | + | 0.590410i | \(0.201034\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.13278e10i | 0.355094i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.33492e9 | 0.0707606 | 0.0353803 | − | 0.999374i | \(-0.488736\pi\) | ||||
0.0353803 | + | 0.999374i | \(0.488736\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 1.58571e11i | − 1.72035i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.90735e10 | 0.203953 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8.12825e10i | − 0.844455i | −0.906490 | − | 0.422227i | \(-0.861248\pi\) | ||||
0.906490 | − | 0.422227i | \(-0.138752\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.65651e10 | 0.988947 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 6.53719e10i | 0.650665i | 0.945600 | + | 0.325332i | \(0.105476\pi\) | ||||
−0.945600 | + | 0.325332i | \(0.894524\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.08877e10 | 0.499366 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 5.59552e10i | − 0.533815i | −0.963722 | − | 0.266908i | \(-0.913998\pi\) | ||||
0.963722 | − | 0.266908i | \(-0.0860019\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.07046e11 | −1.00699 | −0.503496 | − | 0.863997i | \(-0.667953\pi\) | ||||
−0.503496 | + | 0.863997i | \(0.667953\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.45478e10i | 0.133084i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.68411e10 | −0.873688 | −0.436844 | − | 0.899537i | \(-0.643904\pi\) | ||||
−0.436844 | + | 0.899537i | \(0.643904\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.18753e10i | 0.104217i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.62643e11 | −2.27348 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 1.19009e11i | − 1.00236i | −0.865342 | − | 0.501182i | \(-0.832899\pi\) | ||||
0.865342 | − | 0.501182i | \(-0.167101\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.96276e10 | 0.329258 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 1.43498e11i | − 1.16045i | −0.814456 | − | 0.580226i | \(-0.802964\pi\) | ||||
0.814456 | − | 0.580226i | \(-0.197036\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.70916e10 | −0.216156 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.87645e11i | 1.45757i | 0.684741 | + | 0.728787i | \(0.259915\pi\) | ||||
−0.684741 | + | 0.728787i | \(0.740085\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.22645e10 | −0.247302 | −0.123651 | − | 0.992326i | \(-0.539460\pi\) | ||||
−0.123651 | + | 0.992326i | \(0.539460\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 3.66165e10i | − 0.273310i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.80704e10 | 0.354097 | 0.177049 | − | 0.984202i | \(-0.443345\pi\) | ||||
0.177049 | + | 0.984202i | \(0.443345\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.03816e11i | 0.744902i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.76119e11 | 1.24728 | 0.623640 | − | 0.781712i | \(-0.285653\pi\) | ||||
0.623640 | + | 0.781712i | \(0.285653\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 8.55999e10i | − 0.590653i | −0.955396 | − | 0.295327i | \(-0.904572\pi\) | ||||
0.955396 | − | 0.295327i | \(-0.0954285\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −7.64495e10 | −0.520729 | −0.260365 | − | 0.965510i | \(-0.583843\pi\) | ||||
−0.260365 | + | 0.965510i | \(0.583843\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.61748e10i | 0.107371i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.74070e10 | 0.638367 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 1.93683e11i | − 1.23734i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.98446e10 | −0.125177 | −0.0625885 | − | 0.998039i | \(-0.519936\pi\) | ||||
−0.0625885 | + | 0.998039i | \(0.519936\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.02193e11i | 0.628529i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.57637e10 | −0.0957415 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.72891e11i | 1.61643i | 0.588888 | + | 0.808214i | \(0.299566\pi\) | ||||
−0.588888 | + | 0.808214i | \(0.700434\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.55006e10 | −0.266179 | −0.133089 | − | 0.991104i | \(-0.542490\pi\) | ||||
−0.133089 | + | 0.991104i | \(0.542490\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 9.73260e10i | − 0.555408i | −0.960667 | − | 0.277704i | \(-0.910427\pi\) | ||||
0.960667 | − | 0.277704i | \(-0.0895734\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.69431e11 | 1.51869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.60986e11i | − 0.885392i | −0.896672 | − | 0.442696i | \(-0.854022\pi\) | ||||
0.896672 | − | 0.442696i | \(-0.145978\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.77973e10 | 0.422668 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.02994e11i | 1.07632i | 0.842843 | + | 0.538160i | \(0.180880\pi\) | ||||
−0.842843 | + | 0.538160i | \(0.819120\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.97091e11 | −1.55627 | −0.778133 | − | 0.628099i | \(-0.783833\pi\) | ||||
−0.778133 | + | 0.628099i | \(0.783833\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.91485e10i | 0.200184i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.47172e10 | −0.175405 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.40623e11i | 2.17359i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.16935e10 | 0.105747 | 0.0528737 | − | 0.998601i | \(-0.483162\pi\) | ||||
0.0528737 | + | 0.998601i | \(0.483162\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 1.42130e10i | − 0.0676596i | −0.999428 | − | 0.0338298i | \(-0.989230\pi\) | ||||
0.999428 | − | 0.0338298i | \(-0.0107704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.25980e10 | −0.294497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.61548e9i | 0.0349957i | 0.999847 | + | 0.0174978i | \(0.00557002\pi\) | ||||
−0.999847 | + | 0.0174978i | \(0.994430\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.80890e10 | 0.263834 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 2.58059e11i | − 1.14509i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.09041e11 | −0.478273 | −0.239136 | − | 0.970986i | \(-0.576864\pi\) | ||||
−0.239136 | + | 0.970986i | \(0.576864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.49448e10i | 0.321220i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.73857e11 | −1.58407 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 3.22792e11i | − 1.33675i | −0.743823 | − | 0.668376i | \(-0.766990\pi\) | ||||
0.743823 | − | 0.668376i | \(-0.233010\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.79880e11 | −1.14591 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.72962e11i | 0.692268i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.28670e11 | −0.509205 | −0.254602 | − | 0.967046i | \(-0.581945\pi\) | ||||
−0.254602 | + | 0.967046i | \(0.581945\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 8.67600e9i | − 0.0335708i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.26702e10 | 0.316319 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.19347e11i | 0.446577i | 0.974752 | + | 0.223288i | \(0.0716792\pi\) | ||||
−0.974752 | + | 0.223288i | \(0.928321\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82160e10 | 0.0674082 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.78271e11i | 1.00720i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.26145e11 | −0.451578 | −0.225789 | − | 0.974176i | \(-0.572496\pi\) | ||||
−0.225789 | + | 0.974176i | \(0.572496\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.79333e11i | 2.37910i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.14006e10 | −0.0741327 | −0.0370664 | − | 0.999313i | \(-0.511801\pi\) | ||||
−0.0370664 | + | 0.999313i | \(0.511801\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7.61984e11i | 2.58271i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 9.32712e9 | 0.0312730 | 0.0156365 | − | 0.999878i | \(-0.495023\pi\) | ||||
0.0156365 | + | 0.999878i | \(0.495023\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 5.47858e11i | − 1.79768i | −0.438275 | − | 0.898841i | \(-0.644410\pi\) | ||||
0.438275 | − | 0.898841i | \(-0.355590\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.71544e11 | 0.556866 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 9.09315e9i | − 0.0288926i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.25787e10 | −0.102418 | −0.0512088 | − | 0.998688i | \(-0.516307\pi\) | ||||
−0.0512088 | + | 0.998688i | \(0.516307\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.38853e10i | − 0.258165i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.83680e11 | 0.559342 | 0.279671 | − | 0.960096i | \(-0.409775\pi\) | ||||
0.279671 | + | 0.960096i | \(0.409775\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 1.15436e11i | − 0.344194i | −0.985080 | − | 0.172097i | \(-0.944946\pi\) | ||||
0.985080 | − | 0.172097i | \(-0.0550543\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.28238e11 | −0.378371 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.64728e11i | 0.764924i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.80169e11 | 0.515198 | 0.257599 | − | 0.966252i | \(-0.417069\pi\) | ||||
0.257599 | + | 0.966252i | \(0.417069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.65686e11i | 1.86445i | 0.361874 | + | 0.932227i | \(0.382137\pi\) | ||||
−0.361874 | + | 0.932227i | \(0.617863\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.95413e10 | −0.192768 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 5.40239e11i | 1.46702i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.90227e11 | −1.58641 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.63709e11i | 0.431115i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.36920e11 | 1.13895 | 0.569473 | − | 0.822010i | \(-0.307147\pi\) | ||||
0.569473 | + | 0.822010i | \(0.307147\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.08304e11i | 0.532099i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.32931e11 | −1.09478 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 3.59644e11i | − 0.891333i | −0.895199 | − | 0.445667i | \(-0.852967\pi\) | ||||
0.895199 | − | 0.445667i | \(-0.147033\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.30343e11 | −1.79201 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.05592e12i | − 2.53963i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.57112e9 | 0.0204105 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 4.25571e11i | − 0.993522i | −0.867887 | − | 0.496761i | \(-0.834523\pi\) | ||||
0.867887 | − | 0.496761i | \(-0.165477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.09416e11 | −0.252929 | −0.126465 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126465 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.79896e11i | 0.634405i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.81665e11 | 2.20331 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 6.79455e11i | − 1.49551i | −0.663977 | − | 0.747753i | \(-0.731133\pi\) | ||||
0.663977 | − | 0.747753i | \(-0.268867\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7.80059e11 | −1.70031 | −0.850155 | − | 0.526533i | \(-0.823492\pi\) | ||||
−0.850155 | + | 0.526533i | \(0.823492\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6.01868e11i | 1.28671i | 0.765569 | + | 0.643353i | \(0.222457\pi\) | ||||
−0.765569 | + | 0.643353i | \(0.777543\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.26918e11 | 0.268722 | 0.134361 | − | 0.990932i | \(-0.457102\pi\) | ||||
0.134361 | + | 0.990932i | \(0.457102\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 1.10897e11i | − 0.230325i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.48553e11 | 0.305587 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 8.99511e11i | 1.81534i | 0.419682 | + | 0.907671i | \(0.362142\pi\) | ||||
−0.419682 | + | 0.907671i | \(0.637858\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.63826e11 | −0.327490 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 9.96170e10i | − 0.195392i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.49886e11 | 0.291225 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.12764e10i | 0.116836i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.68583e11 | 0.696209 | 0.348105 | − | 0.937456i | \(-0.386825\pi\) | ||||
0.348105 | + | 0.937456i | \(0.386825\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 2.55843e11i | − 0.474297i | −0.971473 | − | 0.237148i | \(-0.923787\pi\) | ||||
0.971473 | − | 0.237148i | \(-0.0762127\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.52059e11 | −0.279279 | −0.139640 | − | 0.990202i | \(-0.544594\pi\) | ||||
−0.139640 | + | 0.990202i | \(0.544594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.82719e11i | 1.59140i | 0.605691 | + | 0.795700i | \(0.292897\pi\) | ||||
−0.605691 | + | 0.795700i | \(0.707103\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.38673e10 | −0.0783567 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 4.09456e11i | − 0.718006i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.48682e11 | −1.30084 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 1.47289e11i | − 0.251269i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.67630e11 | −1.12859 | −0.564297 | − | 0.825572i | \(-0.690853\pi\) | ||||
−0.564297 | + | 0.825572i | \(0.690853\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 9.80883e11i | − 1.62822i | −0.580709 | − | 0.814111i | \(-0.697225\pi\) | ||||
0.580709 | − | 0.814111i | \(-0.302775\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.60537e11 | 0.922065 | 0.461033 | − | 0.887383i | \(-0.347479\pi\) | ||||
0.461033 | + | 0.887383i | \(0.347479\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 5.43060e11i | − 0.877311i | −0.898655 | − | 0.438655i | \(-0.855455\pi\) | ||||
0.898655 | − | 0.438655i | \(-0.144545\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.18317e11 | −0.669728 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.05538e12i | 1.65959i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.80871e11 | 0.437739 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.65955e11i | − 0.254069i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.81544e12 | 2.75475 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.08766e11i | 0.311218i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.56480e11 | −0.231222 | −0.115611 | − | 0.993295i | \(-0.536883\pi\) | ||||
−0.115611 | + | 0.993295i | \(0.536883\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.05213e12i | − 1.52755i | −0.645483 | − | 0.763775i | \(-0.723344\pi\) | ||||
0.645483 | − | 0.763775i | \(-0.276656\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.54929e11 | 0.366891 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.18457e11i | 0.450374i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.04578e12 | 1.46615 | 0.733077 | − | 0.680146i | \(-0.238084\pi\) | ||||
0.733077 | + | 0.680146i | \(0.238084\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 5.79924e11i | − 0.799033i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.91153e11 | 0.670888 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 1.30474e12i | − 1.75171i | −0.482578 | − | 0.875853i | \(-0.660300\pi\) | ||||
0.482578 | − | 0.875853i | \(-0.339700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.60251e11 | −0.213306 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 5.81583e11i | 0.760966i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.72155e11 | −1.00172 | −0.500860 | − | 0.865528i | \(-0.666983\pi\) | ||||
−0.500860 | + | 0.865528i | \(0.666983\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.85580e11i | 0.236686i | 0.992973 | + | 0.118343i | \(0.0377582\pi\) | ||||
−0.992973 | + | 0.118343i | \(0.962242\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.18279e11 | 0.149576 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 4.65591e11i | 0.578902i | 0.957193 | + | 0.289451i | \(0.0934727\pi\) | ||||
−0.957193 | + | 0.289451i | \(0.906527\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.03749e12 | 1.27915 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 3.01476e11i | − 0.365495i | −0.983160 | − | 0.182748i | \(-0.941501\pi\) | ||||
0.983160 | − | 0.182748i | \(-0.0584991\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.59249e10 | 0.103301 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.37782e11i | 0.281128i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.11418e11 | −0.951374 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.32017e11i | 0.152238i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.13827e11 | 0.930735 | 0.465368 | − | 0.885118i | \(-0.345922\pi\) | ||||
0.465368 | + | 0.885118i | \(0.345922\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 1.34616e12i | − 1.51433i | −0.653225 | − | 0.757164i | \(-0.726584\pi\) | ||||
0.653225 | − | 0.757164i | \(-0.273416\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.06780e11 | −0.342275 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.92037e11i | 0.979050i | 0.871989 | + | 0.489525i | \(0.162830\pi\) | ||||
−0.871989 | + | 0.489525i | \(0.837170\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.47229e11 | 0.377994 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 3.53170e11i | − 0.378242i | −0.981954 | − | 0.189121i | \(-0.939436\pi\) | ||||
0.981954 | − | 0.189121i | \(-0.0605638\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.27377e11 | 0.454011 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2.14924e11i | − 0.224647i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.61424e11 | 0.789463 | 0.394732 | − | 0.918796i | \(-0.370838\pi\) | ||||
0.394732 | + | 0.918796i | \(0.370838\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.33241e11i | − 0.339990i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.57737e12 | −1.59644 | −0.798221 | − | 0.602365i | \(-0.794225\pi\) | ||||
−0.798221 | + | 0.602365i | \(0.794225\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 252.9.c.a.197.9 | yes | 16 | |
3.2 | odd | 2 | inner | 252.9.c.a.197.8 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.9.c.a.197.8 | ✓ | 16 | 3.2 | odd | 2 | inner | |
252.9.c.a.197.9 | yes | 16 | 1.1 | even | 1 | trivial |