Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2320,1,Mod(239,2320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2320, base_ring=CyclotomicField(14))
chi = DirichletCharacter(H, H._module([7, 0, 7, 6]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2320.239");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2320 = 2^{4} \cdot 5 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 2320.cx (of order \(14\), degree \(6\), 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: | \(1.15783082931\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{14})\) |
Coefficient field: | \(\Q(\zeta_{28})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | yes |
Projective image: | \(D_{14}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
Embedding invariants
Embedding label | 239.2 | ||
Root | \(-0.433884 - 0.900969i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2320.239 |
Dual form | 2320.1.cx.c.1359.2 |
$q$-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 \(\left(\mathbb{Z}/2320\mathbb{Z}\right)^\times\).
\(n\) | \(321\) | \(581\) | \(1857\) | \(2031\) |
\(\chi(n)\) | \(e\left(\frac{3}{7}\right)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.75676 | + | 0.846011i | 1.75676 | + | 0.846011i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.781831 | − | 0.376510i | −0.781831 | − | 0.376510i | − | 1.00000i | \(-0.5\pi\) | |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.74698 | + | 2.19064i | 1.74698 | + | 2.19064i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.433884 | + | 1.90097i | −0.433884 | + | 1.90097i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.05496 | − | 1.32288i | −1.05496 | − | 1.32288i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.433884 | − | 1.90097i | 0.433884 | − | 1.90097i | − | 1.00000i | \(-0.5\pi\) | |
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.781831 | + | 3.42543i | 0.781831 | + | 3.42543i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.193096 | − | 0.846011i | 0.193096 | − | 0.846011i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.24698 | −1.24698 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.347948 | − | 1.52446i | 0.347948 | − | 1.52446i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.74698 | + | 2.19064i | −1.74698 | + | 2.19064i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.541044 | + | 0.678448i | −0.541044 | + | 0.678448i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.153989 | − | 0.193096i | −0.153989 | − | 0.193096i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.80194 | + | 0.867767i | 1.80194 | + | 0.867767i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.541044 | − | 2.37047i | −0.541044 | − | 2.37047i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.37047 | − | 2.97247i | 2.37047 | − | 2.97247i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.94986 | −1.94986 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.900969 | + | 3.94740i | −0.900969 | + | 3.94740i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.40881 | − | 0.678448i | 1.40881 | − | 0.678448i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.21572 | − | 1.52446i | −1.21572 | − | 1.52446i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.400969 | + | 1.75676i | 0.400969 | + | 1.75676i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.0990311 | − | 0.433884i | 0.0990311 | − | 0.433884i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
1.00000 | \(0\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.974928 | + | 1.22252i | −0.974928 | + | 1.22252i | 1.00000i | \(0.5\pi\) | ||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.05496 | − | 1.32288i | 1.05496 | − | 1.32288i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.21572 | − | 1.52446i | −1.21572 | − | 1.52446i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
−0.433884 | − | 0.900969i | \(-0.642857\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.12349 | + | 0.541044i | 1.12349 | + | 0.541044i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.94986 | 1.94986 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.19064 | − | 1.05496i | −2.19064 | − | 1.05496i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.541044 | − | 0.678448i | 0.541044 | − | 0.678448i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.90097 | − | 2.38374i | 1.90097 | − | 2.38374i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.16557 | + | 1.52446i | −3.16557 | + | 1.52446i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.52446 | + | 0.734141i | −1.52446 | + | 0.734141i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.107160 | − | 0.469501i | −0.107160 | − | 0.469501i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.62349 | + | 0.781831i | −1.62349 | + | 0.781831i | −0.623490 | + | 0.781831i | \(0.714286\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.05496 | + | 1.32288i | −1.05496 | + | 1.32288i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.974928 | − | 1.22252i | 0.974928 | − | 1.22252i | − | 1.00000i | \(-0.5\pi\) | |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.40881 | − | 0.678448i | −1.40881 | − | 0.678448i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.867767 | 0.867767 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.43143 | + | 3.04892i | 2.43143 | + | 3.04892i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.678448 | − | 2.97247i | 0.678448 | − | 2.97247i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.541044 | + | 0.678448i | 0.541044 | + | 0.678448i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.277479 | − | 1.21572i | −0.277479 | − | 1.21572i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 4.92233 | − | 2.37047i | 4.92233 | − | 2.37047i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.56366 | 1.56366 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.541044 | + | 0.678448i | 0.541044 | + | 0.678448i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.52446 | − | 1.21572i | −2.52446 | − | 1.21572i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.347948 | + | 1.52446i | 0.347948 | + | 1.52446i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.12349 | − | 0.541044i | −1.12349 | − | 0.541044i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.781831 | − | 0.376510i | −0.781831 | − | 0.376510i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.277479 | + | 0.347948i | 0.277479 | + | 0.347948i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2.73169 | + | 3.42543i | −2.73169 | + | 3.42543i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.153989 | − | 0.193096i | 0.153989 | − | 0.193096i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.04892 | 3.04892 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.623490 | − | 2.73169i | −0.623490 | − | 2.73169i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.193096 | + | 0.846011i | 0.193096 | + | 0.846011i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.781831 | + | 3.42543i | −0.781831 | + | 3.42543i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.277479 | + | 0.347948i | 0.277479 | + | 0.347948i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.277479 | + | 0.347948i | 0.277479 | + | 0.347948i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.75676 | − | 0.846011i | −1.75676 | − | 0.846011i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.781831 | − | 0.623490i | \(-0.785714\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.974928 | + | 0.469501i | 0.974928 | + | 0.469501i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.846011 | + | 1.06086i | −0.846011 | + | 1.06086i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.541044 | − | 0.678448i | 0.541044 | − | 0.678448i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.445042 | + | 1.94986i | −0.445042 | + | 1.94986i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.94986 | −1.94986 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −2.74698 | + | 1.32288i | −2.74698 | + | 1.32288i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.19064 | − | 1.05496i | 2.19064 | − | 1.05496i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.846011 | − | 3.70662i | −0.846011 | − | 3.70662i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.51597 | + | 1.90097i | 1.51597 | + | 1.90097i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.678448 | − | 0.326723i | 0.678448 | − | 0.326723i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.240787 | + | 1.05496i | 0.240787 | + | 1.05496i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.42543 | + | 1.64960i | 3.42543 | + | 1.64960i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.24698 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.433884 | − | 1.90097i | 0.433884 | − | 1.90097i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.781831 | − | 0.376510i | 0.781831 | − | 0.376510i | − | 1.00000i | \(-0.5\pi\) | |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.17845 | − | 2.73169i | −2.17845 | − | 2.73169i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.433884 | − | 1.90097i | −0.433884 | − | 1.90097i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.52446 | − | 0.734141i | 1.52446 | − | 0.734141i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.433884 | + | 1.90097i | −0.433884 | + | 1.90097i | 1.00000i | \(0.5\pi\) | ||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.94740 | − | 1.90097i | 3.94740 | − | 1.90097i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.445042 | 0.445042 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.400969 | + | 1.75676i | 0.400969 | + | 1.75676i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −4.04892 | −4.04892 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.62349 | − | 0.781831i | −1.62349 | − | 0.781831i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.974928 | + | 1.22252i | 0.974928 | + | 1.22252i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.277479 | − | 1.21572i | 0.277479 | − | 1.21572i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.43143 | −2.43143 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.08209 | − | 1.35690i | −1.08209 | − | 1.35690i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.21572 | − | 1.52446i | 1.21572 | − | 1.52446i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.153989 | − | 0.674671i | 0.153989 | − | 0.674671i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.62349 | + | 0.781831i | −1.62349 | + | 0.781831i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.51352 | −3.51352 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.400969 | + | 1.75676i | −0.400969 | + | 1.75676i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.12349 | − | 0.541044i | −1.12349 | − | 0.541044i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.56366 | −1.56366 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.40881 | − | 0.678448i | −1.40881 | − | 0.678448i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.97247 | + | 1.43147i | −2.97247 | + | 1.43147i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.193096 | − | 0.846011i | 0.193096 | − | 0.846011i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.74698 | − | 1.32288i | 2.74698 | − | 1.32288i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.90097 | − | 2.38374i | −1.90097 | − | 2.38374i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.40881 | + | 0.678448i | −1.40881 | + | 0.678448i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.445042 | 0.445042 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.433884 | − | 1.90097i | 0.433884 | − | 1.90097i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 0.777479 | − | 0.974928i | 0.777479 | − | 0.974928i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
1.00000 | \(0\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.40881 | − | 0.678448i | −1.40881 | − | 0.678448i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.80194 | −1.80194 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.56366 | 1.56366 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.52446 | + | 0.734141i | 1.52446 | + | 0.734141i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.52446 | − | 1.21572i | −2.52446 | − | 1.21572i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.21572 | − | 1.52446i | 1.21572 | − | 1.52446i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.62349 | − | 0.781831i | 1.62349 | − | 0.781831i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
1.00000 | \(0\) | |||||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0.541044 | + | 0.678448i | 0.541044 | + | 0.678448i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.277479 | + | 1.21572i | −0.277479 | + | 1.21572i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.40881 | + | 0.678448i | −1.40881 | + | 0.678448i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.24698 | + | 5.46337i | 1.24698 | + | 5.46337i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0.867767 | 0.867767 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.19064 | − | 2.74698i | 2.19064 | − | 2.74698i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.277479 | − | 0.347948i | 0.277479 | − | 0.347948i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.433884 | + | 1.90097i | 0.433884 | + | 1.90097i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.35690 | −1.35690 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.75676 | − | 0.846011i | −1.75676 | − | 0.846011i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.781831 | − | 0.623490i | \(-0.785714\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.12349 | + | 1.40881i | 1.12349 | + | 1.40881i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.433884 | + | 1.90097i | 0.433884 | + | 1.90097i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.376510 | + | 1.64960i | 0.376510 | + | 1.64960i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.541044 | − | 2.37047i | 0.541044 | − | 2.37047i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.85086 | 6.85086 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.347948 | − | 1.52446i | 0.347948 | − | 1.52446i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.781831 | + | 0.376510i | 0.781831 | + | 0.376510i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.400969 | − | 0.193096i | −0.400969 | − | 0.193096i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.433884 | + | 1.90097i | 0.433884 | + | 1.90097i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
1.00000i | \(0.500000\pi\) | |||||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.74698 | + | 1.32288i | 2.74698 | + | 1.32288i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.541044 | − | 0.678448i | −0.541044 | − | 0.678448i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −0.0990311 | + | 0.433884i | −0.0990311 | + | 0.433884i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.21572 | + | 1.52446i | −1.21572 | + | 1.52446i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.376510 | + | 1.64960i | 0.376510 | + | 1.64960i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.19064 | − | 2.74698i | −2.19064 | − | 2.74698i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.678448 | + | 2.97247i | −0.678448 | + | 2.97247i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.541044 | + | 0.678448i | −0.541044 | + | 0.678448i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.51597 | − | 1.90097i | −1.51597 | − | 1.90097i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.0990311 | − | 0.433884i | −0.0990311 | − | 0.433884i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.05496 | − | 1.32288i | −1.05496 | − | 1.32288i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.240787 | + | 0.301938i | −0.240787 | + | 0.301938i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.277479 | + | 0.347948i | −0.277479 | + | 0.347948i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.22252 | − | 0.588735i | 1.22252 | − | 0.588735i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.193096 | + | 0.846011i | 0.193096 | + | 0.846011i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.00000 | 1.00000 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.347948 | + | 1.52446i | 0.347948 | + | 1.52446i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.04892 | + | 1.94986i | −4.04892 | + | 1.94986i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.433884 | − | 0.208947i | 0.433884 | − | 0.208947i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.974928 | + | 1.22252i | −0.974928 | + | 1.22252i | 1.00000i | \(0.5\pi\) | ||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.12349 | − | 1.40881i | −1.12349 | − | 1.40881i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.94740 | + | 1.90097i | 3.94740 | + | 1.90097i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.376510 | + | 1.64960i | 0.376510 | + | 1.64960i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.674671 | − | 0.846011i | −0.674671 | − | 0.846011i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.781831 | − | 3.42543i | 0.781831 | − | 3.42543i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.376510 | + | 1.64960i | −0.376510 | + | 1.64960i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.14795 | + | 3.94740i | −3.14795 | + | 3.94740i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.52446 | − | 0.734141i | −1.52446 | − | 0.734141i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.193096 | + | 0.846011i | 0.193096 | + | 0.846011i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.400969 | + | 0.193096i | 0.400969 | + | 0.193096i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.40881 | + | 0.678448i | 1.40881 | + | 0.678448i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −0.777479 | − | 0.974928i | −0.777479 | − | 0.974928i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.541044 | − | 0.678448i | 0.541044 | − | 0.678448i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −0.193096 | + | 0.846011i | −0.193096 | + | 0.846011i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.445042 | 0.445042 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.347948 | − | 1.52446i | 0.347948 | − | 1.52446i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.193096 | + | 0.846011i | 0.193096 | + | 0.846011i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.193096 | + | 0.846011i | −0.193096 | + | 0.846011i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.37047 | − | 2.97247i | −2.37047 | − | 2.97247i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.31551 | + | 1.64960i | 1.31551 | + | 1.64960i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.40881 | + | 0.678448i | 1.40881 | + | 0.678448i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.75676 | + | 0.846011i | 1.75676 | + | 0.846011i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.193096 | + | 0.846011i | 0.193096 | + | 0.846011i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.777479 | + | 0.974928i | −0.777479 | + | 0.974928i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.867767 | 0.867767 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.678448 | + | 0.326723i | −0.678448 | + | 0.326723i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.38374 | + | 1.14795i | −2.38374 | + | 1.14795i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.0990311 | + | 0.433884i | −0.0990311 | + | 0.433884i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.974928 | + | 1.22252i | 0.974928 | + | 1.22252i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.12349 | − | 0.541044i | 1.12349 | − | 0.541044i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.43143 | + | 3.04892i | −2.43143 | + | 3.04892i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.42543 | − | 1.64960i | −3.42543 | − | 1.64960i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.38129 | −4.38129 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0.445042 | 0.445042 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.277479 | + | 0.347948i | −0.277479 | + | 0.347948i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.541044 | + | 2.37047i | −0.541044 | + | 2.37047i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 3.04892 | 3.04892 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1.75676 | − | 0.846011i | 1.75676 | − | 0.846011i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.21572 | − | 5.32640i | 1.21572 | − | 5.32640i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.40881 | + | 0.678448i | −1.40881 | + | 0.678448i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.777479 | + | 3.40636i | 0.777479 | + | 3.40636i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.46828 | 1.46828 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.74698 | − | 1.32288i | −2.74698 | − | 1.32288i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(998\) | 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 | 2320.1.cx.c.239.2 | yes | 12 | |
4.3 | odd | 2 | inner | 2320.1.cx.c.239.1 | ✓ | 12 | |
5.4 | even | 2 | inner | 2320.1.cx.c.239.1 | ✓ | 12 | |
20.19 | odd | 2 | CM | 2320.1.cx.c.239.2 | yes | 12 | |
29.25 | even | 7 | inner | 2320.1.cx.c.1359.2 | yes | 12 | |
116.83 | odd | 14 | inner | 2320.1.cx.c.1359.1 | yes | 12 | |
145.54 | even | 14 | inner | 2320.1.cx.c.1359.1 | yes | 12 | |
580.199 | odd | 14 | inner | 2320.1.cx.c.1359.2 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2320.1.cx.c.239.1 | ✓ | 12 | 4.3 | odd | 2 | inner | |
2320.1.cx.c.239.1 | ✓ | 12 | 5.4 | even | 2 | inner | |
2320.1.cx.c.239.2 | yes | 12 | 1.1 | even | 1 | trivial | |
2320.1.cx.c.239.2 | yes | 12 | 20.19 | odd | 2 | CM | |
2320.1.cx.c.1359.1 | yes | 12 | 116.83 | odd | 14 | inner | |
2320.1.cx.c.1359.1 | yes | 12 | 145.54 | even | 14 | inner | |
2320.1.cx.c.1359.2 | yes | 12 | 29.25 | even | 7 | inner | |
2320.1.cx.c.1359.2 | yes | 12 | 580.199 | odd | 14 | inner |