Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3920,1,Mod(319,3920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3920, base_ring=CyclotomicField(42))
chi = DirichletCharacter(H, H._module([21, 0, 21, 16]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3920.319");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3920 = 2^{4} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3920.fc (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: | \(1.95633484952\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
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 | 1999.2 | ||
Root | \(0.149042 + 0.988831i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3920.1999 |
Dual form | 3920.1.fc.a.1759.2 |
$q$-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 \(\left(\mathbb{Z}/3920\mathbb{Z}\right)^\times\).
\(n\) | \(981\) | \(1471\) | \(3041\) | \(3137\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{17}{21}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 1.64786 | − | 1.12349i | 1.64786 | − | 1.12349i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.294755 | + | 0.955573i | −0.294755 | + | 0.955573i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.08786 | − | 2.77183i | 1.08786 | − | 2.77183i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.24349 | − | 1.55929i | −1.24349 | − | 1.55929i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.587862 | + | 1.90580i | 0.587862 | + | 1.90580i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.825886 | + | 0.766310i | −0.825886 | + | 0.766310i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.877681 | − | 3.84537i | −0.877681 | − | 3.84537i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.326239 | − | 1.42935i | 0.326239 | − | 1.42935i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.658322 | + | 0.317031i | 0.658322 | + | 0.317031i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.67738 | − | 0.807782i | 1.67738 | − | 0.807782i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.84537 | − | 0.877681i | −2.84537 | − | 0.877681i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.858075 | + | 0.129334i | 0.858075 | + | 0.129334i | 0.563320 | − | 0.826239i | \(-0.309524\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.57906 | + | 0.487076i | −1.57906 | + | 0.487076i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.32803 | + | 1.85654i | 2.32803 | + | 1.85654i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.866025 | + | 1.50000i | −0.866025 | + | 1.50000i | 1.00000i | \(0.5\pi\) | ||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.500000 | + | 2.19064i | −0.500000 | + | 2.19064i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.46200 | + | 1.35654i | −1.46200 | + | 1.35654i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.58375 | − | 3.32523i | −3.58375 | − | 3.32523i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.367554 | + | 0.460898i | 0.367554 | + | 0.460898i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.06826 | − | 2.72188i | −1.06826 | − | 2.72188i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.535628 | + | 1.36476i | −0.535628 | + | 1.36476i | 0.365341 | + | 0.930874i | \(0.380952\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.57906 | − | 1.07659i | 1.57906 | − | 1.07659i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.129436 | + | 1.72721i | 0.129436 | + | 1.72721i | 0.563320 | + | 0.826239i | \(0.309524\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.85654 | − | 0.728639i | 1.85654 | − | 0.728639i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.215372 | − | 0.548760i | 0.215372 | − | 0.548760i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.825886 | + | 0.766310i | 0.825886 | + | 0.766310i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.44100 | − | 0.217196i | 1.44100 | − | 0.217196i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.347948 | + | 1.52446i | −0.347948 | + | 1.52446i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.85654 | − | 3.21562i | 1.85654 | − | 3.21562i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.76903 | + | 1.16259i | −3.76903 | + | 1.16259i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.55929 | − | 0.750915i | 1.55929 | − | 0.750915i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.44973 | − | 0.218511i | −1.44973 | − | 0.218511i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.99441 | −1.99441 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1.88980 | + | 0.284841i | 1.88980 | + | 0.284841i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.488831 | − | 1.01507i | −0.488831 | − | 1.01507i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.61105 | + | 1.09839i | 1.61105 | + | 1.09839i | 0.930874 | + | 0.365341i | \(0.119048\pi\) |
0.680173 | + | 0.733052i | \(0.261905\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.0663300 | + | 0.290611i | −0.0663300 | + | 0.290611i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.149042 | − | 0.988831i | 0.149042 | − | 0.988831i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.623490 | − | 0.781831i | −0.623490 | − | 0.781831i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.05484 | + | 2.57669i | −2.05484 | + | 2.57669i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.93323 | + | 0.294755i | 3.93323 | + | 0.294755i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.258149 | + | 3.44476i | 0.258149 | + | 3.44476i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.26968 | + | 0.733052i | 1.26968 | + | 0.733052i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.266948 | − | 0.680173i | 0.266948 | − | 0.680173i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.22563 | + | 3.12285i | 1.22563 | + | 3.12285i | ||||
\(208\) | 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 | ||||||||
\(215\) | −0.930874 | − | 1.61232i | −0.930874 | − | 1.61232i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.347948 | − | 1.52446i | −0.347948 | − | 1.52446i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.433884 | − | 0.900969i | \(-0.357143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.662592 | + | 2.90301i | −0.662592 | + | 2.90301i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −0.781831 | + | 1.35417i | −0.781831 | + | 1.35417i | 0.149042 | + | 0.988831i | \(0.452381\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.367711 | − | 0.250701i | −0.367711 | − | 0.250701i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.0648483 | − | 0.865341i | 0.0648483 | − | 0.865341i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.19158 | − | 0.367554i | −1.19158 | − | 0.367554i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.74116 | − | 0.865341i | −5.74116 | − | 0.865341i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.12349 | + | 0.346551i | 1.12349 | + | 0.346551i | ||||
\(250\) | 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 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.60700 | − | 2.45921i | −3.60700 | − | 2.45921i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.680173 | − | 1.17809i | 0.680173 | − | 1.17809i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.974928 | − | 0.222521i | \(-0.0714286\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.650653 | + | 2.85070i | 0.650653 | + | 2.85070i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.95557 | + | 0.294755i | −1.95557 | + | 0.294755i | −0.955573 | + | 0.294755i | \(0.904762\pi\) |
−1.00000 | \(1.00000\pi\) | |||||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.12349 | − | 1.40881i | 1.12349 | − | 1.40881i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.900969 | − | 0.433884i | \(-0.142857\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.317031 | + | 0.807782i | 0.317031 | + | 0.807782i | 0.997204 | + | 0.0747301i | \(0.0238095\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.496990 | + | 0.535628i | −0.496990 | + | 0.535628i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.277479 | + | 1.84095i | 0.277479 | + | 1.84095i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.39254 | − | 3.54812i | 1.39254 | − | 3.54812i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.603718 | + | 1.53825i | 0.603718 | + | 1.53825i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.185853 | − | 0.233052i | 0.185853 | − | 0.233052i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.15379 | + | 2.70077i | 2.15379 | + | 2.70077i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.67738 | − | 2.46026i | 1.67738 | − | 2.46026i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.261623 | − | 1.14625i | −0.261623 | − | 1.14625i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.64786 | + | 1.12349i | 1.64786 | + | 1.12349i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.376510 | + | 0.781831i | −0.376510 | + | 0.781831i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.56052 | + | 0.751509i | 1.56052 | + | 0.751509i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.781831 | − | 0.623490i | 0.781831 | − | 0.623490i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.22188 | + | 0.334895i | 2.22188 | + | 0.334895i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1.77904 | + | 0.548760i | 1.77904 | + | 0.548760i | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.658322 | + | 0.317031i | −0.658322 | + | 0.317031i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.443797 | + | 1.94440i | −0.443797 | + | 1.94440i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 0.294755 | − | 0.0444272i | 0.294755 | − | 0.0444272i | − | 1.00000i | \(-0.5\pi\) | |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.59492 | − | 1.47987i | 1.59492 | − | 1.47987i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.46200 | + | 1.35654i | 1.46200 | + | 1.35654i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.13935 | + | 2.90301i | 1.13935 | + | 2.90301i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.496990 | − | 1.26631i | 0.496990 | − | 1.26631i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.414278 | − | 5.52815i | −0.414278 | − | 5.52815i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.367711 | − | 0.250701i | 0.367711 | − | 0.250701i | −0.365341 | − | 0.930874i | \(-0.619048\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.0546039 | − | 0.139129i | 0.0546039 | − | 0.139129i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.04812 | + | 3.82222i | −3.04812 | + | 3.82222i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.44973 | − | 1.34515i | −1.44973 | − | 1.34515i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.623490 | − | 0.781831i | \(-0.714286\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.432142 | − | 0.400969i | 0.432142 | − | 0.400969i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.0332580 | − | 0.145713i | 0.0332580 | − | 0.145713i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.29196 | − | 2.23774i | 1.29196 | − | 2.23774i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.65248i | − | 1.65248i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.63444 | + | 1.26868i | −2.63444 | + | 1.26868i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.46026 | + | 1.67738i | −2.46026 | + | 1.67738i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.34515 | − | 0.202749i | −1.34515 | − | 0.202749i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.40097 | + | 0.432142i | 1.40097 | + | 0.432142i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.43414 | − | 1.65379i | 3.43414 | − | 1.65379i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 1.48883 | + | 0.716983i | 1.48883 | + | 0.716983i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.400969 | − | 1.75676i | 0.400969 | − | 1.75676i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.131178 | − | 0.574730i | −0.131178 | − | 0.574730i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.26968 | + | 1.17809i | −1.26968 | + | 1.17809i | −0.294755 | + | 0.955573i | \(0.595238\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.17809 | − | 1.26968i | −1.17809 | − | 1.26968i | ||||
\(470\) | 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 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.94594 | − | 1.12349i | −1.94594 | − | 1.12349i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.716983 | + | 0.488831i | −0.716983 | + | 0.488831i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.88881 | 3.88881 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.217196 | + | 0.553406i | 0.217196 | + | 0.553406i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.16078 | + | 1.45557i | −1.16078 | + | 1.45557i | −0.294755 | + | 0.955573i | \(0.595238\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.19158 | − | 1.49419i | −1.19158 | − | 1.49419i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.46200 | − | 1.35654i | −1.46200 | − | 1.35654i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.826239 | − | 1.43109i | −0.826239 | − | 1.43109i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.0747301 | − | 0.997204i | \(-0.476190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.71271 | − | 0.258149i | 1.71271 | − | 0.258149i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.222521 | − | 0.385418i | 0.222521 | − | 0.385418i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.61105 | − | 1.09839i | −1.61105 | − | 1.09839i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
−0.680173 | − | 0.733052i | \(-0.738095\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.865341 | − | 1.79690i | −0.865341 | − | 1.79690i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.0201262 | − | 0.268565i | 0.0201262 | − | 0.268565i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.563320 | − | 0.173761i | −0.563320 | − | 0.173761i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.147791 | − | 0.0222759i | −0.147791 | − | 0.0222759i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.90580 | − | 0.587862i | −1.90580 | − | 0.587862i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.01507 | + | 0.488831i | 1.01507 | + | 0.488831i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.367711 | + | 4.90676i | −0.367711 | + | 4.90676i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.34515 | − | 0.202749i | 1.34515 | − | 0.202749i | 0.563320 | − | 0.826239i | \(-0.309524\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.23383 | − | 2.44440i | 4.23383 | − | 2.44440i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.623490 | + | 1.07992i | 0.623490 | + | 1.07992i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.702449 | − | 0.880843i | 0.702449 | − | 0.880843i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −0.548760 | + | 0.215372i | −0.548760 | + | 0.215372i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.94986 | −1.94986 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.277479 | − | 0.347948i | 0.277479 | − | 0.347948i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.21562 | + | 4.03227i | 3.21562 | + | 4.03227i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.680173 | − | 1.17809i | −0.680173 | − | 1.17809i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.294755 | − | 0.955573i | \(-0.404762\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.91583 | − | 0.218511i | 2.91583 | − | 0.218511i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.324275 | − | 1.42074i | −0.324275 | − | 1.42074i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.67161 | + | 2.50326i | 3.67161 | + | 2.50326i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −1.14625 | − | 0.914101i | −1.14625 | − | 0.914101i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.54620 | + | 0.233052i | 1.54620 | + | 0.233052i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.142820 | − | 0.0440542i | −0.142820 | − | 0.0440542i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.40881 | − | 0.678448i | 1.40881 | − | 0.678448i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.34537 | − | 1.61105i | −3.34537 | − | 1.61105i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.0222759 | + | 0.297251i | −0.0222759 | + | 0.297251i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.88980 | − | 0.284841i | 1.88980 | − | 0.284841i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.825886 | + | 1.43048i | 0.825886 | + | 1.43048i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.28608 | − | 2.12117i | −2.28608 | − | 2.12117i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.44100 | + | 3.67161i | 1.44100 | + | 3.67161i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.233052 | + | 3.10986i | 0.233052 | + | 3.10986i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.246289 | + | 0.167917i | −0.246289 | + | 0.167917i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
0.433884 | + | 0.900969i | \(0.357143\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.887595 | −0.887595 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(692\) | 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 | ||||||||
\(701\) | −0.0931869 | − | 0.116853i | −0.0931869 | − | 0.116853i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −0.865341 | − | 1.49881i | −0.865341 | − | 1.49881i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0.563320 | + | 1.82624i | 0.563320 | + | 1.82624i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.40097 | + | 1.29991i | −1.40097 | + | 1.29991i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(710\) | 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 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.68862 | − | 0.385418i | −1.68862 | − | 0.385418i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.37650 | + | 0.733052i | −2.37650 | + | 0.733052i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.109562 | + | 1.46200i | −0.109562 | + | 1.46200i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.531130 | − | 0.255779i | −0.531130 | − | 0.255779i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −6.02815 | + | 2.90301i | −6.02815 | + | 2.90301i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0.149042 | + | 1.98883i | 0.149042 | + | 1.98883i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.268565 | − | 0.129334i | −0.268565 | − | 0.129334i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.142820 | − | 1.90580i | 0.142820 | − | 1.90580i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.67738 | − | 0.517402i | 1.67738 | − | 0.517402i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.460898 | + | 0.367554i | 0.460898 | + | 0.367554i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −0.914101 | + | 0.848162i | −0.914101 | + | 0.848162i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −0.997204 | + | 0.0747301i | −0.997204 | + | 0.0747301i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.777479 | + | 0.974928i | 0.777479 | + | 0.974928i | 1.00000 | \(0\) | ||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(774\) | 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 | ||||||||
\(783\) | −5.78270 | −5.78270 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.12397 | + | 0.766310i | −1.12397 | + | 0.766310i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.202749 | − | 2.70550i | −0.202749 | − | 2.70550i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 3.20018 | + | 2.96934i | 3.20018 | + | 2.96934i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.975699 | + | 0.563320i | −0.975699 | + | 0.563320i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.89135 | + | 2.68278i | −2.89135 | + | 2.68278i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | 0.365341 | − | 0.930874i | \(-0.380952\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.974928 | − | 1.68862i | 0.974928 | − | 1.68862i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.19158 | + | 0.367554i | −1.19158 | + | 0.367554i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.0222759 | + | 0.297251i | −0.0222759 | + | 0.297251i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.79690 | + | 0.865341i | −1.79690 | + | 0.865341i | −0.866025 | + | 0.500000i | \(0.833333\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 0.425270 | + | 0.131178i | 0.425270 | + | 0.131178i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.294755 | + | 0.0444272i | 0.294755 | + | 0.0444272i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.03563 | − | 0.498732i | −1.03563 | − | 0.498732i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.268565 | − | 3.58375i | 0.268565 | − | 3.58375i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.955573 | + | 0.294755i | −0.955573 | + | 0.294755i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.433884 | − | 0.900969i | −0.433884 | − | 0.900969i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.42996 | + | 0.974928i | 1.42996 | + | 0.974928i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) | ||||
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.217196 | + | 1.44100i | −0.217196 | + | 1.44100i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.866025 | − | 1.50000i | −0.866025 | − | 1.50000i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.24349 | + | 1.55929i | 1.24349 | + | 1.55929i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.997204 | − | 0.0747301i | −0.997204 | − | 0.0747301i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.00000 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.56366 | −1.56366 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0.0841939 | + | 1.12349i | 0.0841939 | + | 1.12349i | 0.866025 | + | 0.500000i | \(0.166667\pi\) |
−0.781831 | + | 0.623490i | \(0.785714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35417 | − | 0.781831i | −1.35417 | − | 0.781831i | ||||
\(890\) | 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 | ||||||||
\(903\) | 2.52554 | + | 2.72188i | 2.52554 | + | 2.72188i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.97213 | + | 0.297251i | −1.97213 | + | 0.297251i | −0.974928 | + | 0.222521i | \(0.928571\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.26631 | − | 5.54807i | −1.26631 | − | 5.54807i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.222521 | − | 0.974928i | \(-0.428571\pi\) | ||||
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.72305 | + | 1.85654i | 2.72305 | + | 1.85654i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.0444272 | − | 0.592840i | 0.0444272 | − | 0.592840i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.92833 | + | 1.52019i | 4.92833 | + | 1.52019i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1.63402 | + | 0.246289i | 1.63402 | + | 0.246289i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 0.900969 | − | 0.433884i | \(-0.142857\pi\) | ||||
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.0332580 | + | 0.443797i | −0.0332580 | + | 0.443797i | 0.955573 | + | 0.294755i | \(0.0952381\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.786643 | + | 0.242647i | −0.786643 | + | 0.242647i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 3.94426i | − | 3.94426i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.246289 | + | 0.167917i | 0.246289 | + | 0.167917i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −1.28677 | − | 1.19395i | −1.28677 | − | 1.19395i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.24349 | − | 1.55929i | 1.24349 | − | 1.55929i | 0.563320 | − | 0.826239i | \(-0.309524\pi\) |
0.680173 | − | 0.733052i | \(-0.261905\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.97766 | 2.97766 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −0.930874 | + | 0.634659i | −0.930874 | + | 0.634659i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.257945 | + | 1.71135i | 0.257945 | + | 1.71135i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −0.766310 | + | 1.95253i | −0.766310 | + | 1.95253i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(998\) | 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 | 3920.1.fc.a.1999.2 | yes | 24 | |
4.3 | odd | 2 | inner | 3920.1.fc.a.1999.1 | yes | 24 | |
5.4 | even | 2 | inner | 3920.1.fc.a.1999.1 | yes | 24 | |
20.19 | odd | 2 | CM | 3920.1.fc.a.1999.2 | yes | 24 | |
49.44 | even | 21 | inner | 3920.1.fc.a.1759.2 | yes | 24 | |
196.191 | odd | 42 | inner | 3920.1.fc.a.1759.1 | ✓ | 24 | |
245.44 | even | 42 | inner | 3920.1.fc.a.1759.1 | ✓ | 24 | |
980.779 | odd | 42 | inner | 3920.1.fc.a.1759.2 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3920.1.fc.a.1759.1 | ✓ | 24 | 196.191 | odd | 42 | inner | |
3920.1.fc.a.1759.1 | ✓ | 24 | 245.44 | even | 42 | inner | |
3920.1.fc.a.1759.2 | yes | 24 | 49.44 | even | 21 | inner | |
3920.1.fc.a.1759.2 | yes | 24 | 980.779 | odd | 42 | inner | |
3920.1.fc.a.1999.1 | yes | 24 | 4.3 | odd | 2 | inner | |
3920.1.fc.a.1999.1 | yes | 24 | 5.4 | even | 2 | inner | |
3920.1.fc.a.1999.2 | yes | 24 | 1.1 | even | 1 | trivial | |
3920.1.fc.a.1999.2 | yes | 24 | 20.19 | odd | 2 | CM |