Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3528,1,Mod(397,3528)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3528, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([0, 21, 0, 29]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3528.397");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3528 = 2^{3} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3528.fb (of order \(42\), degree \(12\), 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: | \(1.76070136457\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{42})\) |
Coefficient field: | \(\Q(\zeta_{84})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{24} + x^{22} - x^{18} - x^{16} + x^{12} - x^{8} - x^{6} + x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{42}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{42} - \cdots)\) |
Embedding invariants
Embedding label | 2413.1 | ||
Root | \(0.930874 - 0.365341i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3528.2413 |
Dual form | 3528.1.fb.a.829.1 |
$q$-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 \(\left(\mathbb{Z}/3528\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) | \(1765\) | \(2647\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{11}{42}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.563320 | − | 0.826239i | −0.563320 | − | 0.826239i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.365341 | + | 0.930874i | −0.365341 | + | 0.930874i | ||||
\(5\) | −1.90580 | − | 0.587862i | −1.90580 | − | 0.587862i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.930874 | − | 0.365341i | \(-0.880952\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(8\) | 0.974928 | − | 0.222521i | 0.974928 | − | 0.222521i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.587862 | + | 1.90580i | 0.587862 | + | 1.90580i | ||||
\(11\) | 0.728639 | − | 0.0546039i | 0.728639 | − | 0.0546039i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(14\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(17\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 1.24349 | − | 1.55929i | 1.24349 | − | 1.55929i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.455573 | − | 0.571270i | −0.455573 | − | 0.571270i | ||||
\(23\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.46026 | + | 1.67738i | 2.46026 | + | 1.67738i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.0747301 | + | 0.997204i | −0.0747301 | + | 0.997204i | ||||
\(29\) | 1.29196 | + | 1.03030i | 1.29196 | + | 1.03030i | 0.997204 | + | 0.0747301i | \(0.0238095\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.17809 | + | 0.680173i | −1.17809 | + | 0.680173i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(32\) | −0.149042 | + | 0.988831i | −0.149042 | + | 0.988831i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.99441 | −1.99441 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.98883 | − | 0.149042i | −1.98883 | − | 0.149042i | ||||
\(41\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(44\) | −0.215372 | + | 0.698220i | −0.215372 | + | 0.698220i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(50\) | − | 2.97766i | − | 2.97766i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.930874 | − | 0.365341i | −0.930874 | − | 0.365341i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.42074 | − | 0.324275i | −1.42074 | − | 0.324275i | ||||
\(56\) | 0.866025 | − | 0.500000i | 0.866025 | − | 0.500000i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.123490 | − | 1.64786i | 0.123490 | − | 1.64786i | ||||
\(59\) | 1.65510 | − | 0.510531i | 1.65510 | − | 0.510531i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0 | 0 | 0.930874 | − | 0.365341i | \(-0.119048\pi\) | ||||
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(62\) | 1.22563 | + | 0.590232i | 1.22563 | + | 0.590232i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.12349 | + | 1.64786i | 1.12349 | + | 1.64786i | ||||
\(71\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.09839 | − | 1.61105i | 1.09839 | − | 1.61105i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.733052 | − | 0.680173i | \(-0.238095\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.680173 | − | 0.266948i | 0.680173 | − | 0.266948i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.955573 | − | 1.65510i | 0.955573 | − | 1.65510i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.733052 | − | 0.680173i | \(-0.238095\pi\) | |||||||
\(80\) | 0.997204 | + | 1.72721i | 0.997204 | + | 1.72721i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.01507 | + | 0.488831i | −1.01507 | + | 0.488831i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.698220 | − | 0.215372i | 0.698220 | − | 0.215372i | ||||
\(89\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.298085i | 0.298085i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(98\) | −0.930874 | − | 0.365341i | −0.930874 | − | 0.365341i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.46026 | + | 1.67738i | −2.46026 | + | 1.67738i | ||||
\(101\) | 1.14625 | − | 1.06356i | 1.14625 | − | 1.06356i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.460898 | − | 1.49419i | 0.460898 | − | 1.49419i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(107\) | 1.90580 | + | 0.142820i | 1.90580 | + | 0.142820i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(110\) | 0.532403 | + | 1.35654i | 0.532403 | + | 1.35654i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(113\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.43109 | + | 0.826239i | −1.43109 | + | 0.826239i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.35417 | − | 1.07992i | −1.35417 | − | 1.07992i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.460898 | + | 0.0694692i | −0.460898 | + | 0.0694692i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.202749 | − | 1.34515i | −0.202749 | − | 1.34515i | ||||
\(125\) | −2.45921 | − | 3.08375i | −2.45921 | − | 3.08375i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.914101 | + | 1.14625i | −0.914101 | + | 1.14625i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.432142 | + | 0.400969i | 0.432142 | + | 0.400969i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.294755 | − | 0.955573i | \(-0.595238\pi\) | ||||
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(140\) | 0.728639 | − | 1.85654i | 0.728639 | − | 1.85654i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.85654 | − | 2.72305i | −1.85654 | − | 2.72305i | ||||
\(146\) | −1.94986 | −1.94986 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.250701 | + | 0.367711i | 0.250701 | + | 0.367711i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.365341 | − | 0.930874i | 0.365341 | − | 0.930874i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.988831 | − | 0.149042i | \(-0.0476190\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.603718 | − | 0.411608i | −0.603718 | − | 0.411608i | ||||
\(155\) | 2.64506 | − | 0.603718i | 2.64506 | − | 0.603718i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | −0.294755 | − | 0.955573i | \(-0.595238\pi\) | ||||
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(158\) | −1.90580 | + | 0.142820i | −1.90580 | + | 0.142820i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.865341 | − | 1.79690i | 0.865341 | − | 1.79690i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.975699 | + | 0.563320i | 0.975699 | + | 0.563320i | ||||
\(167\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −0.858075 | + | 0.129334i | −0.858075 | + | 0.129334i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.84537 | + | 0.877681i | 2.84537 | + | 0.877681i | ||||
\(176\) | −0.571270 | − | 0.455573i | −0.571270 | − | 0.455573i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.268565 | − | 1.78181i | 0.268565 | − | 1.78181i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | −0.433884 | − | 0.900969i | \(-0.642857\pi\) | ||||
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.294755 | − | 0.955573i | \(-0.404762\pi\) | ||||
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.40097 | + | 1.29991i | −1.40097 | + | 1.29991i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(194\) | 0.246289 | − | 0.167917i | 0.246289 | − | 0.167917i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(197\) | − | 1.24698i | − | 1.24698i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.32624 | + | 1.42935i | 1.32624 | + | 1.42935i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(200\) | 2.77183 | + | 1.08786i | 2.77183 | + | 1.08786i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.52446 | − | 0.347948i | −1.52446 | − | 0.347948i | ||||
\(203\) | 1.53825 | + | 0.603718i | 1.53825 | + | 0.603718i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.49419 | + | 0.460898i | −1.49419 | + | 0.460898i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(212\) | 0.680173 | − | 0.733052i | 0.680173 | − | 0.733052i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.955573 | − | 1.65510i | −0.955573 | − | 1.65510i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.925270 | + | 0.997204i | −0.925270 | + | 0.997204i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.820914 | − | 1.20406i | 0.820914 | − | 1.20406i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.233052 | − | 0.185853i | 0.233052 | − | 0.185853i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(224\) | 0.149042 | + | 0.988831i | 0.149042 | + | 0.988831i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.930874 | + | 1.61232i | 0.930874 | + | 1.61232i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0 | 0 | 0.680173 | − | 0.733052i | \(-0.261905\pi\) | ||||
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.48883 | + | 0.716983i | 1.48883 | + | 0.716983i | ||||
\(233\) | 0 | 0 | 0.930874 | − | 0.365341i | \(-0.119048\pi\) | ||||
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.129436 | + | 1.72721i | −0.129436 | + | 1.72721i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.04876 | − | 0.411608i | −1.04876 | − | 0.411608i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(242\) | 0.317031 | + | 0.341678i | 0.317031 | + | 0.341678i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.90580 | + | 0.587862i | −1.90580 | + | 0.587862i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −0.997204 | + | 0.925270i | −0.997204 | + | 0.925270i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.16259 | + | 3.76903i | −1.16259 | + | 3.76903i | ||||
\(251\) | −0.302705 | + | 1.32624i | −0.302705 | + | 1.32624i | 0.563320 | + | 0.826239i | \(0.309524\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 1.46200 | + | 0.109562i | 1.46200 | + | 0.109562i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(257\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0878620 | − | 0.582926i | 0.0878620 | − | 0.582926i | ||||
\(263\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.55929 | + | 1.24349i | 1.55929 | + | 1.24349i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.930874 | + | 0.634659i | 0.930874 | + | 0.634659i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.0444272 | + | 0.294755i | 0.0444272 | + | 0.294755i | 1.00000 | \(0\) | ||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.88423 | + | 1.08786i | 1.88423 | + | 1.08786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.94440 | + | 0.443797i | −1.94440 | + | 0.443797i | ||||
\(281\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | ||||
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(290\) | −1.20406 | + | 3.06789i | −1.20406 | + | 3.06789i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.09839 | + | 1.61105i | 1.09839 | + | 1.61105i | ||||
\(293\) | 0.298085 | 0.298085 | 0.149042 | − | 0.988831i | \(-0.452381\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.45442 | −3.45442 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.162592 | − | 0.414278i | 0.162592 | − | 0.414278i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(308\) | 0.730682i | 0.730682i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.98883 | − | 1.84537i | −1.98883 | − | 1.84537i | ||||
\(311\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.510531 | − | 0.294755i | −0.510531 | − | 0.294755i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.19158 | + | 1.49419i | 1.19158 | + | 1.49419i | ||||
\(317\) | −0.294755 | − | 1.95557i | −0.294755 | − | 1.95557i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.997630 | + | 0.680173i | 0.997630 | + | 0.680173i | ||||
\(320\) | −1.97213 | + | 0.297251i | −1.97213 | + | 0.297251i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(332\) | −0.0841939 | − | 1.12349i | −0.0841939 | − | 1.12349i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(338\) | −0.294755 | + | 0.955573i | −0.294755 | + | 0.955573i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.821265 | + | 0.559929i | −0.821265 | + | 0.559929i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.590232 | + | 0.636119i | 0.590232 | + | 0.636119i | ||||
\(347\) | −1.67738 | − | 0.658322i | −1.67738 | − | 0.658322i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(350\) | −0.877681 | − | 2.84537i | −0.877681 | − | 2.84537i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.0546039 | + | 0.728639i | −0.0546039 | + | 0.728639i | ||||
\(353\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.62349 | + | 0.781831i | −1.62349 | + | 0.781831i | ||||
\(359\) | 0 | 0 | 0.680173 | − | 0.733052i | \(-0.261905\pi\) | ||||
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.04039 | + | 2.42463i | −3.04039 | + | 2.42463i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.975699 | − | 1.43109i | 0.975699 | − | 1.43109i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.997204 | − | 0.0747301i | −0.997204 | − | 0.0747301i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.45320 | + | 0.108903i | −1.45320 | + | 0.108903i | ||||
\(386\) | 1.86323 | + | 0.425270i | 1.86323 | + | 0.425270i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −0.277479 | − | 0.108903i | −0.277479 | − | 0.108903i | ||||
\(389\) | 1.22563 | + | 1.32091i | 1.22563 | + | 1.32091i | 0.930874 | + | 0.365341i | \(0.119048\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0.680173 | − | 0.733052i | 0.680173 | − | 0.733052i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.03030 | + | 0.702449i | −1.03030 | + | 0.702449i | ||||
\(395\) | −2.79410 | + | 2.59255i | −2.79410 | + | 2.59255i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | 0.294755 | − | 0.955573i | \(-0.404762\pi\) | ||||
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(398\) | 0.433884 | − | 1.90097i | 0.433884 | − | 1.90097i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.662592 | − | 2.90301i | −0.662592 | − | 2.90301i | ||||
\(401\) | 0 | 0 | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) | ||||
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0.571270 | + | 1.45557i | 0.571270 | + | 1.45557i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.367711 | − | 1.61105i | −0.367711 | − | 1.61105i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.258149 | − | 1.71271i | 0.258149 | − | 1.71271i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.22252 | + | 0.974928i | 1.22252 | + | 0.974928i | ||||
\(413\) | 1.43109 | − | 0.975699i | 1.43109 | − | 0.975699i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.22188 | − | 0.334895i | 2.22188 | − | 0.334895i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.541044 | − | 0.678448i | −0.541044 | − | 0.678448i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −0.829215 | + | 1.72188i | −0.829215 | + | 1.72188i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.294755 | − | 0.955573i | \(-0.595238\pi\) | ||||
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.846011 | − | 0.193096i | 0.846011 | − | 0.193096i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(434\) | 1.34515 | + | 0.202749i | 1.34515 | + | 0.202749i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.04876 | + | 1.53825i | 1.04876 | + | 1.53825i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(440\) | −1.45728 | −1.45728 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1.11406 | + | 1.63402i | 1.11406 | + | 1.63402i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.284841 | − | 0.0878620i | −0.284841 | − | 0.0878620i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.733052 | − | 0.680173i | 0.733052 | − | 0.680173i | ||||
\(449\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.807782 | − | 1.67738i | 0.807782 | − | 1.67738i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.21135 | − | 1.12397i | −1.21135 | − | 1.12397i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.21572 | + | 1.52446i | −1.21572 | + | 1.52446i | −0.433884 | + | 0.900969i | \(0.642857\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.12349 | + | 1.40881i | 1.12349 | + | 1.40881i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(464\) | −0.246289 | − | 1.63402i | −0.246289 | − | 1.63402i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.54620 | + | 0.233052i | −1.54620 | + | 0.233052i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.250701 | + | 1.09839i | 0.250701 | + | 1.09839i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.103718 | − | 0.454418i | 0.103718 | − | 0.454418i | ||||
\(485\) | 0.175233 | − | 0.568090i | 0.175233 | − | 0.568090i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.07473 | + | 0.997204i | −1.07473 | + | 0.997204i | −0.0747301 | + | 0.997204i | \(0.523810\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.55929 | + | 1.24349i | 1.55929 | + | 1.24349i | ||||
\(491\) | − | 0.149460i | − | 0.149460i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) | ||
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.32624 | + | 0.302705i | 1.32624 | + | 0.302705i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(500\) | 3.76903 | − | 1.16259i | 3.76903 | − | 1.16259i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.26631 | − | 0.496990i | 1.26631 | − | 0.496990i | ||||
\(503\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.80974 | + | 1.35310i | −2.80974 | + | 1.35310i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −0.733052 | − | 1.26968i | −0.733052 | − | 1.26968i | ||||
\(509\) | −0.866025 | + | 1.50000i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.574730 | − | 1.86323i | 0.574730 | − | 1.86323i | ||||
\(512\) | 0.781831 | − | 0.623490i | 0.781831 | − | 0.623490i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.75676 | + | 2.57669i | −1.75676 | + | 2.57669i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0 | 0 | 0.680173 | − | 0.733052i | \(-0.261905\pi\) | ||||
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(524\) | −0.531130 | + | 0.255779i | −0.531130 | + | 0.255779i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.955573 | + | 0.294755i | −0.955573 | + | 0.294755i | ||||
\(530\) | 0.149042 | − | 1.98883i | 0.149042 | − | 1.98883i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.54812 | − | 1.39254i | −3.54812 | − | 1.39254i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 1.12664i | − | 1.12664i | ||||||
\(539\) | 0.571270 | − | 0.455573i | 0.571270 | − | 0.455573i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(542\) | 0.218511 | − | 0.202749i | 0.218511 | − | 0.202749i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.162592 | − | 2.16964i | −0.162592 | − | 2.16964i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.425270 | − | 1.86323i | 0.425270 | − | 1.86323i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0.129436 | − | 0.0747301i | 0.129436 | − | 0.0747301i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1.46200 | + | 1.35654i | 1.46200 | + | 1.35654i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.487076 | − | 0.332083i | −0.487076 | − | 0.332083i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.35654 | + | 0.101659i | −1.35654 | + | 0.101659i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(578\) | −0.294755 | − | 0.955573i | −0.294755 | − | 0.955573i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.21308 | − | 0.733365i | 3.21308 | − | 0.733365i | ||||
\(581\) | −0.825886 | + | 0.766310i | −0.825886 | + | 0.766310i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.698220 | − | 0.215372i | −0.698220 | − | 0.215372i | ||||
\(584\) | 0.712362 | − | 1.81507i | 0.712362 | − | 1.81507i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.167917 | − | 0.246289i | −0.167917 | − | 0.246289i | ||||
\(587\) | 1.86175 | 1.86175 | 0.930874 | − | 0.365341i | \(-0.119048\pi\) | ||||
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 1.94594 | + | 2.85417i | 1.94594 | + | 2.85417i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.433884 | + | 0.0990311i | −0.433884 | + | 0.0990311i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | ||||
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.590232 | + | 1.22563i | −0.590232 | + | 1.22563i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(605\) | 0.919218 | + | 0.138550i | 0.919218 | + | 0.138550i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.61232 | + | 0.930874i | 1.61232 | + | 0.930874i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.603718 | − | 0.411608i | 0.603718 | − | 0.411608i | ||||
\(617\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(620\) | −0.404364 | + | 2.68278i | −0.404364 | + | 2.68278i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.78608 | + | 4.55086i | 1.78608 | + | 4.55086i | ||||
\(626\) | 0.0440542 | + | 0.587862i | 0.0440542 | + | 0.587862i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.440071 | + | 1.92808i | −0.440071 | + | 1.92808i | −0.0747301 | + | 0.997204i | \(0.523810\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(632\) | 0.563320 | − | 1.82624i | 0.563320 | − | 1.82624i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1.44973 | + | 1.34515i | −1.44973 | + | 1.34515i | ||||
\(635\) | 2.41593 | − | 1.64715i | 2.41593 | − | 1.64715i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1.20744i | − | 1.20744i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.35654 | + | 1.46200i | 1.35654 | + | 1.46200i | ||||
\(641\) | 0 | 0 | −0.930874 | − | 0.365341i | \(-0.880952\pi\) | ||||
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.17809 | − | 0.462368i | 1.17809 | − | 0.462368i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.101659 | − | 0.109562i | 0.101659 | − | 0.109562i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.587862 | − | 1.01821i | −0.587862 | − | 1.01821i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0.974928 | − | 0.777479i | 0.974928 | − | 0.777479i | − | 1.00000i | \(-0.5\pi\) | |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0 | 0 | 0.563320 | − | 0.826239i | \(-0.309524\pi\) | ||||
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.880843 | + | 0.702449i | −0.880843 | + | 0.702449i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.658322 | + | 0.317031i | 0.658322 | + | 0.317031i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(674\) | −0.930874 | + | 0.365341i | −0.930874 | + | 0.365341i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(677\) | 0.139129 | − | 1.85654i | 0.139129 | − | 1.85654i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.0878620 | + | 0.284841i | 0.0878620 | + | 0.284841i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.925270 | + | 0.363142i | 0.925270 | + | 0.363142i | ||||
\(683\) | 0.101659 | + | 0.109562i | 0.101659 | + | 0.109562i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −0.997204 | − | 0.0747301i | −0.997204 | − | 0.0747301i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | 0.294755 | − | 0.955573i | \(-0.404762\pi\) | ||||
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(692\) | 0.193096 | − | 0.846011i | 0.193096 | − | 0.846011i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.400969 | + | 1.75676i | 0.400969 | + | 1.75676i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.85654 | + | 2.32803i | −1.85654 | + | 2.32803i | ||||
\(701\) | −0.636119 | − | 1.32091i | −0.636119 | − | 1.32091i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
0.294755 | − | 0.955573i | \(-0.404762\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.632789 | − | 0.365341i | 0.632789 | − | 0.365341i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.781831 | − | 1.35417i | 0.781831 | − | 1.35417i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.56052 | + | 0.900969i | 1.56052 | + | 0.900969i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 1.56366i | − | 1.56366i | ||||||
\(722\) | 0.433884 | − | 0.900969i | 0.433884 | − | 0.900969i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.45035 | + | 4.70191i | 1.45035 | + | 4.70191i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.09839 | + | 0.250701i | −1.09839 | + | 0.250701i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.71604 | + | 1.14625i | 3.71604 | + | 1.14625i | ||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.563320 | − | 0.826239i | \(-0.690476\pi\) | ||||
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(734\) | −1.73205 | −1.73205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(743\) | 0 | 0 | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.261623 | − | 0.848162i | −0.261623 | − | 0.848162i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.86323 | − | 0.425270i | 1.86323 | − | 0.425270i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.535628 | + | 0.496990i | 0.535628 | + | 0.496990i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.24349 | + | 1.55929i | −1.24349 | + | 1.55929i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.255779 | + | 0.531130i | 0.255779 | + | 0.531130i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(770\) | 0.908598 | + | 1.13935i | 0.908598 | + | 1.13935i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −0.698220 | − | 1.77904i | −0.698220 | − | 1.77904i | ||||
\(773\) | −0.116853 | − | 1.55929i | −0.116853 | − | 1.55929i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
0.563320 | − | 0.826239i | \(-0.309524\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.03932 | − | 0.302705i | −4.03932 | − | 0.302705i | ||||
\(776\) | 0.0663300 | + | 0.290611i | 0.0663300 | + | 0.290611i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | ||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.988831 | − | 0.149042i | −0.988831 | − | 0.149042i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0 | 0 | −0.680173 | − | 0.733052i | \(-0.738095\pi\) | ||||
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(788\) | 1.16078 | + | 0.455573i | 1.16078 | + | 0.455573i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.71604 | + | 0.848162i | 3.71604 | + | 0.848162i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.81507 | + | 0.712362i | −1.81507 | + | 0.712362i | ||||
\(797\) | 0.268565 | + | 0.129334i | 0.268565 | + | 0.129334i | 0.563320 | − | 0.826239i | \(-0.309524\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.02532 | + | 2.18278i | −2.02532 | + | 2.18278i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.712362 | − | 1.23385i | 0.712362 | − | 1.23385i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.880843 | − | 1.29196i | 0.880843 | − | 1.29196i | ||||
\(809\) | 0 | 0 | 0.563320 | − | 0.826239i | \(-0.309524\pi\) | ||||
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(812\) | −1.12397 | + | 1.21135i | −1.12397 | + | 1.21135i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −1.56052 | + | 0.751509i | −1.56052 | + | 0.751509i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.77904 | + | 0.698220i | −1.77904 | + | 0.698220i | −0.781831 | + | 0.623490i | \(0.785714\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.425270 | − | 0.131178i | 0.425270 | − | 0.131178i | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(824\) | 0.116853 | − | 1.55929i | 0.116853 | − | 1.55929i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.61232 | − | 0.632789i | −1.61232 | − | 0.632789i | ||||
\(827\) | −0.145713 | − | 0.0332580i | −0.145713 | − | 0.0332580i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0 | 0 | −0.930874 | − | 0.365341i | \(-0.880952\pi\) | ||||
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(830\) | −1.52833 | − | 1.64715i | −1.52833 | − | 1.64715i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.255779 | + | 0.829215i | −0.255779 | + | 0.829215i | ||||
\(839\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.385113 | + | 1.68729i | 0.385113 | + | 1.68729i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.728639 | + | 1.85654i | 0.728639 | + | 1.85654i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.419945 | + | 0.202235i | −0.419945 | + | 0.202235i | ||||
\(848\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.88980 | − | 0.284841i | 1.88980 | − | 0.284841i | ||||
\(857\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.71135 | + | 0.257945i | 1.71135 | + | 0.257945i | ||||
\(866\) | −0.636119 | − | 0.590232i | −0.636119 | − | 0.590232i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.590232 | − | 1.22563i | −0.590232 | − | 1.22563i | ||||
\(869\) | 0.605893 | − | 1.25815i | 0.605893 | − | 1.25815i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.25890 | − | 2.22188i | −3.25890 | − | 2.22188i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(878\) | 0.680173 | − | 1.73305i | 0.680173 | − | 1.73305i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.820914 | + | 1.20406i | 0.820914 | + | 1.20406i | ||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.722521 | − | 1.84095i | 0.722521 | − | 1.84095i | ||||
\(887\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.0878620 | + | 0.284841i | 0.0878620 | + | 0.284841i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.55929 | + | 3.23790i | −1.55929 | + | 3.23790i | ||||
\(896\) | −0.974928 | − | 0.222521i | −0.974928 | − | 0.222521i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.22283 | − | 0.335038i | −2.22283 | − | 0.335038i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(908\) | −1.84095 | + | 0.277479i | −1.84095 | + | 0.277479i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.712926 | + | 0.411608i | −0.712926 | + | 0.411608i | ||||
\(914\) | −0.246289 | + | 1.63402i | −0.246289 | + | 1.63402i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.531130 | + | 0.255779i | 0.531130 | + | 0.255779i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.455573 | + | 1.16078i | 0.455573 | + | 1.16078i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.94440 | + | 0.145713i | 1.94440 | + | 0.145713i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0.531130 | − | 1.72188i | 0.531130 | − | 1.72188i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.21135 | + | 1.12397i | −1.21135 | + | 1.12397i | ||||
\(929\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.06356 | + | 1.14625i | 1.06356 | + | 1.14625i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.32624 | − | 0.302705i | −1.32624 | − | 0.302705i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.284841 | − | 0.0878620i | 0.284841 | − | 0.0878620i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −1.56052 | − | 0.751509i | −1.56052 | − | 0.751509i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.302705 | − | 0.326239i | 0.302705 | − | 0.326239i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.781831 | − | 0.623490i | \(-0.214286\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.425270 | − | 0.736589i | 0.425270 | − | 0.736589i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.766310 | − | 0.825886i | 0.766310 | − | 0.825886i | ||||
\(965\) | 3.43414 | − | 1.65379i | 3.43414 | − | 1.65379i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.72188 | − | 0.829215i | −1.72188 | − | 0.829215i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.733052 | − | 0.680173i | \(-0.761905\pi\) | |||||||
\(968\) | −0.433884 | + | 0.170287i | −0.433884 | + | 0.170287i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.568090 | + | 0.175233i | −0.568090 | + | 0.175233i | ||||
\(971\) | −0.101659 | + | 1.35654i | −0.101659 | + | 1.35654i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.42935 | + | 0.326239i | 1.42935 | + | 0.326239i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | −0.680173 | − | 0.733052i | \(-0.738095\pi\) | ||||
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0.149042 | − | 1.98883i | 0.149042 | − | 1.98883i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.123490 | + | 0.0841939i | −0.123490 | + | 0.0841939i | ||||
\(983\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.733052 | + | 2.37650i | −0.733052 | + | 2.37650i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.0546039 | + | 0.728639i | 0.0546039 | + | 0.728639i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(992\) | −0.496990 | − | 1.26631i | −0.496990 | − | 1.26631i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.68729 | − | 3.50369i | −1.68729 | − | 3.50369i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | 0.149042 | − | 0.988831i | \(-0.452381\pi\) | ||||
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(998\) | 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 | 3528.1.fb.a.2413.1 | yes | 24 | |
3.2 | odd | 2 | inner | 3528.1.fb.a.2413.2 | yes | 24 | |
8.5 | even | 2 | inner | 3528.1.fb.a.2413.2 | yes | 24 | |
24.5 | odd | 2 | CM | 3528.1.fb.a.2413.1 | yes | 24 | |
49.45 | odd | 42 | inner | 3528.1.fb.a.829.2 | yes | 24 | |
147.143 | even | 42 | inner | 3528.1.fb.a.829.1 | ✓ | 24 | |
392.45 | odd | 42 | inner | 3528.1.fb.a.829.1 | ✓ | 24 | |
1176.437 | even | 42 | inner | 3528.1.fb.a.829.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3528.1.fb.a.829.1 | ✓ | 24 | 147.143 | even | 42 | inner | |
3528.1.fb.a.829.1 | ✓ | 24 | 392.45 | odd | 42 | inner | |
3528.1.fb.a.829.2 | yes | 24 | 49.45 | odd | 42 | inner | |
3528.1.fb.a.829.2 | yes | 24 | 1176.437 | even | 42 | inner | |
3528.1.fb.a.2413.1 | yes | 24 | 1.1 | even | 1 | trivial | |
3528.1.fb.a.2413.1 | yes | 24 | 24.5 | odd | 2 | CM | |
3528.1.fb.a.2413.2 | yes | 24 | 3.2 | odd | 2 | inner | |
3528.1.fb.a.2413.2 | yes | 24 | 8.5 | even | 2 | inner |