Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1911,1,Mod(59,1911)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1911, base_ring=CyclotomicField(84))
chi = DirichletCharacter(H, H._module([42, 26, 77]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1911.59");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1911 = 3 \cdot 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 1911.ep (of order \(84\), degree \(24\), 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: | \(0.953713239142\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{84}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{84} - \cdots)\) |
Embedding invariants
Embedding label | 1055.1 | ||
Root | \(-0.294755 + 0.955573i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1911.1055 |
Dual form | 1911.1.ep.a.605.1 |
$q$-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 \(\left(\mathbb{Z}/1911\mathbb{Z}\right)^\times\).
\(n\) | \(638\) | \(1471\) | \(1522\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{42}\right)\) |
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 | 0.330279 | − | 0.943883i | \(-0.392857\pi\) | ||||
−0.330279 | + | 0.943883i | \(0.607143\pi\) | |||||||
\(3\) | −0.680173 | + | 0.733052i | −0.680173 | + | 0.733052i | ||||
\(4\) | −0.781831 | − | 0.623490i | −0.781831 | − | 0.623490i | ||||
\(5\) | 0 | 0 | −0.0373912 | − | 0.999301i | \(-0.511905\pi\) | ||||
0.0373912 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.997204 | + | 0.0747301i | 0.997204 | + | 0.0747301i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0747301 | − | 0.997204i | −0.0747301 | − | 0.997204i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | 0.757972 | − | 0.652287i | \(-0.226190\pi\) | ||||
−0.757972 | + | 0.652287i | \(0.773810\pi\) | |||||||
\(12\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | ||||
\(13\) | −0.930874 | − | 0.365341i | −0.930874 | − | 0.365341i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(17\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.392355 | − | 1.46429i | 0.392355 | − | 1.46429i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.997204 | + | 0.0747301i | −0.997204 | + | 0.0747301i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(28\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(29\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.0579571 | + | 0.216299i | −0.0579571 | + | 0.216299i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.563320 | + | 0.826239i | −0.563320 | + | 0.826239i | ||||
\(37\) | 0.205245 | − | 1.82160i | 0.205245 | − | 1.82160i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.900969 | − | 0.433884i | 0.900969 | − | 0.433884i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.884115 | − | 0.467269i | \(-0.845238\pi\) | ||||
0.884115 | + | 0.467269i | \(0.154762\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.587862 | − | 1.90580i | 0.587862 | − | 1.90580i | 0.222521 | − | 0.974928i | \(-0.428571\pi\) |
0.365341 | − | 0.930874i | \(-0.380952\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.652287 | − | 0.757972i | \(-0.726190\pi\) | ||||
0.652287 | + | 0.757972i | \(0.273810\pi\) | |||||||
\(48\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(49\) | 0.988831 | + | 0.149042i | 0.988831 | + | 0.149042i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(53\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.806531 | + | 1.28359i | 0.806531 | + | 1.28359i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.84095 | + | 0.722521i | 1.84095 | + | 0.722521i | 0.974928 | + | 0.222521i | \(0.0714286\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.00000i | − | 1.00000i | ||||||
\(64\) | 0.433884 | − | 0.900969i | 0.433884 | − | 0.900969i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.275400 | − | 1.02781i | −0.275400 | − | 1.02781i | −0.955573 | − | 0.294755i | \(-0.904762\pi\) |
0.680173 | − | 0.733052i | \(-0.261905\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.916562 | − | 0.399892i | \(-0.869048\pi\) | ||||
0.916562 | + | 0.399892i | \(0.130952\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.900198 | + | 0.774683i | 0.900198 | + | 0.774683i | 0.974928 | − | 0.222521i | \(-0.0714286\pi\) |
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.623490 | − | 0.781831i | 0.623490 | − | 0.781831i | ||||
\(76\) | −1.21972 | + | 0.900198i | −1.21972 | + | 0.900198i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.781831 | − | 1.35417i | 0.781831 | − | 1.35417i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.930874 | − | 0.365341i | \(-0.119048\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.988831 | + | 0.149042i | −0.988831 | + | 0.149042i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(84\) | 0.997204 | − | 0.0747301i | 0.997204 | − | 0.0747301i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.943883 | − | 0.330279i | \(-0.107143\pi\) | ||||
−0.943883 | + | 0.330279i | \(0.892857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.900969 | − | 0.433884i | −0.900969 | − | 0.433884i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.119137 | − | 0.189606i | −0.119137 | − | 0.189606i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.26012 | + | 0.337649i | −1.26012 | + | 0.337649i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.826239 | + | 0.563320i | 0.826239 | + | 0.563320i | ||||
\(101\) | 0 | 0 | −0.733052 | − | 0.680173i | \(-0.761905\pi\) | ||||
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.109562 | + | 0.101659i | 0.109562 | + | 0.101659i | 0.733052 | − | 0.680173i | \(-0.238095\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(108\) | −0.222521 | − | 0.974928i | −0.222521 | − | 0.974928i | ||||
\(109\) | 0.918245 | − | 0.173741i | 0.918245 | − | 0.173741i | 0.294755 | − | 0.955573i | \(-0.404762\pi\) |
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.19572 | + | 1.38946i | 1.19572 | + | 1.38946i | ||||
\(112\) | 0.149042 | + | 0.988831i | 0.149042 | + | 0.988831i | ||||
\(113\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.294755 | + | 0.955573i | −0.294755 | + | 0.955573i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.149042 | − | 0.988831i | 0.149042 | − | 0.988831i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.180173 | − | 0.132974i | 0.180173 | − | 0.132974i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.53825 | − | 0.603718i | −1.53825 | − | 0.603718i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
−0.974928 | + | 0.222521i | \(0.928571\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.997204 | + | 1.72721i | 0.997204 | + | 1.72721i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.294755 | − | 0.955573i | \(-0.404762\pi\) | ||||
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.500684 | − | 1.43087i | 0.500684 | − | 1.43087i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.32624 | + | 1.42935i | −1.32624 | + | 1.42935i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0.955573 | − | 0.294755i | 0.955573 | − | 0.294755i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.781831 | + | 0.623490i | −0.781831 | + | 0.623490i | ||||
\(148\) | −1.29621 | + | 1.29621i | −1.29621 | + | 1.29621i | ||||
\(149\) | 0 | 0 | 0.982566 | − | 0.185912i | \(-0.0595238\pi\) | ||||
−0.982566 | + | 0.185912i | \(0.940476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.392253 | − | 0.531484i | −0.392253 | − | 0.531484i | 0.563320 | − | 0.826239i | \(-0.309524\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.974928 | − | 0.222521i | −0.974928 | − | 0.222521i | ||||
\(157\) | −0.925270 | − | 0.997204i | −0.925270 | − | 0.997204i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.0747301 | + | 0.00279620i | 0.0747301 | + | 0.00279620i | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.399892 | − | 0.916562i | \(-0.630952\pi\) | ||||
0.399892 | + | 0.916562i | \(0.369048\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.48952 | − | 0.281831i | −1.48952 | − | 0.281831i | ||||
\(172\) | −1.64786 | + | 1.12349i | −1.64786 | + | 1.12349i | ||||
\(173\) | 0 | 0 | −0.988831 | − | 0.149042i | \(-0.952381\pi\) | ||||
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.00000 | −1.00000 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.32091 | + | 0.636119i | 1.32091 | + | 0.636119i | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.78181 | + | 0.858075i | −1.78181 | + | 0.858075i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.733052 | + | 0.680173i | 0.733052 | + | 0.680173i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.955573 | − | 0.294755i | \(-0.0952381\pi\) | ||||
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(192\) | 0.365341 | + | 0.930874i | 0.365341 | + | 0.930874i | ||||
\(193\) | 0.0747301 | + | 1.99720i | 0.0747301 | + | 1.99720i | 0.0747301 | + | 0.997204i | \(0.476190\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.680173 | − | 0.733052i | −0.680173 | − | 0.733052i | ||||
\(197\) | 0 | 0 | −0.965926 | − | 0.258819i | \(-0.916667\pi\) | ||||
0.965926 | + | 0.258819i | \(0.0833333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.250701 | + | 1.09839i | −0.250701 | + | 1.09839i | 0.680173 | + | 0.733052i | \(0.261905\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.940755 | + | 0.497204i | 0.940755 | + | 0.497204i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.149042 | − | 0.988831i | 0.149042 | − | 0.988831i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.139129 | + | 1.85654i | 0.139129 | + | 1.85654i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0739590 | + | 0.211363i | −0.0739590 | + | 0.211363i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.18017 | + | 0.132974i | −1.18017 | + | 0.132974i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.18017 | − | 1.59908i | −1.18017 | − | 1.59908i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.149042 | + | 0.988831i | 0.149042 | + | 0.988831i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(228\) | 0.169732 | − | 1.50641i | 0.169732 | − | 1.50641i | ||||
\(229\) | −0.328735 | + | 0.173741i | −0.328735 | + | 0.173741i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.149042 | − | 0.988831i | \(-0.547619\pi\) | ||||
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.460898 | + | 1.49419i | 0.460898 | + | 1.49419i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | −0.846724 | − | 0.532032i | \(-0.821429\pi\) | ||||
0.846724 | + | 0.532032i | \(0.178571\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.189606 | + | 1.68280i | 0.189606 | + | 1.68280i | 0.623490 | + | 0.781831i | \(0.285714\pi\) |
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.563320 | − | 0.826239i | 0.563320 | − | 0.826239i | ||||
\(244\) | −0.988831 | − | 1.71271i | −0.988831 | − | 1.71271i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.900198 | + | 1.21972i | −0.900198 | + | 1.21972i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(252\) | −0.623490 | + | 0.781831i | −0.623490 | + | 0.781831i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.900969 | + | 0.433884i | −0.900969 | + | 0.433884i | ||||
\(257\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.340799 | − | 1.80117i | 0.340799 | − | 1.80117i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −0.425511 | + | 0.975281i | −0.425511 | + | 0.975281i | ||||
\(269\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.197979 | + | 1.75711i | 0.197979 | + | 1.75711i | 0.563320 | + | 0.826239i | \(0.309524\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.930874 | − | 0.365341i | 0.930874 | − | 0.365341i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.460898 | + | 0.367554i | −0.460898 | + | 0.367554i | −0.826239 | − | 0.563320i | \(-0.809524\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.220025 | + | 0.0416310i | 0.220025 | + | 0.0416310i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.0222759 | − | 0.297251i | 0.0222759 | − | 0.297251i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.222521 | + | 0.974928i | −0.222521 | + | 0.974928i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.609587 | − | 1.15339i | 0.609587 | − | 1.15339i | ||||
\(292\) | −0.220796 | − | 1.16694i | −0.220796 | − | 1.16694i | ||||
\(293\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.974928 | + | 0.222521i | −0.974928 | + | 0.222521i | ||||
\(301\) | 0.728639 | − | 1.85654i | 0.728639 | − | 1.85654i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.51488 | + | 0.0566829i | 1.51488 | + | 0.0566829i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 0.623490 | − | 1.78183i | 0.623490 | − | 1.78183i | − | 1.00000i | \(-0.5\pi\) | |
0.623490 | − | 0.781831i | \(-0.285714\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.149042 | + | 0.0111692i | −0.149042 | + | 0.0111692i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.365341 | − | 0.930874i | \(-0.380952\pi\) | ||||
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.632789 | + | 0.365341i | 0.632789 | + | 0.365341i | 0.781831 | − | 0.623490i | \(-0.214286\pi\) |
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.45557 | + | 0.571270i | −1.45557 | + | 0.571270i | ||||
\(317\) | 0 | 0 | −0.916562 | − | 0.399892i | \(-0.869048\pi\) | ||||
0.916562 | + | 0.399892i | \(0.130952\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(325\) | 0.955573 | + | 0.294755i | 0.955573 | + | 0.294755i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.497204 | + | 0.791295i | −0.497204 | + | 0.791295i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.785841 | − | 1.80117i | −0.785841 | − | 1.80117i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
−0.222521 | − | 0.974928i | \(-0.571429\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.83184 | − | 0.0685427i | −1.83184 | − | 0.0685427i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(337\) | −1.86323 | + | 0.425270i | −1.86323 | + | 0.425270i | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0.974928 | + | 0.222521i | 0.974928 | + | 0.222521i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0734787 | − | 1.96376i | 0.0734787 | − | 1.96376i | −0.149042 | − | 0.988831i | \(-0.547619\pi\) |
0.222521 | − | 0.974928i | \(-0.428571\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | −0.467269 | − | 0.884115i | \(-0.654762\pi\) | ||||
0.467269 | + | 0.884115i | \(0.345238\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.467269 | − | 0.884115i | \(-0.654762\pi\) | ||||
0.467269 | + | 0.884115i | \(0.345238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.12417 | − | 0.649042i | −1.12417 | − | 0.649042i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(364\) | 0.433884 | + | 0.900969i | 0.433884 | + | 0.900969i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.332083 | − | 0.487076i | −0.332083 | − | 0.487076i | 0.623490 | − | 0.781831i | \(-0.285714\pi\) |
−0.955573 | + | 0.294755i | \(0.904762\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.0250721 | + | 0.222521i | −0.0250721 | + | 0.222521i | ||||
\(373\) | 0.433884 | + | 0.751509i | 0.433884 | + | 0.751509i | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.85486 | − | 0.350958i | 1.85486 | − | 0.350958i | 0.866025 | − | 0.500000i | \(-0.166667\pi\) |
0.988831 | + | 0.149042i | \(0.0476190\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.48883 | − | 0.716983i | 1.48883 | − | 0.716983i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.652287 | − | 0.757972i | \(-0.273810\pi\) | ||||
−0.652287 | + | 0.757972i | \(0.726190\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.94440 | − | 0.443797i | −1.94440 | − | 0.443797i | ||||
\(388\) | 1.19572 | + | 0.521689i | 1.19572 | + | 0.521689i | ||||
\(389\) | 0 | 0 | −0.294755 | − | 0.955573i | \(-0.595238\pi\) | ||||
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.751927 | + | 1.42271i | −0.751927 | + | 1.42271i | 0.149042 | + | 0.988831i | \(0.452381\pi\) |
−0.900969 | + | 0.433884i | \(0.857143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.708353 | + | 1.34027i | 0.708353 | + | 1.34027i | ||||
\(400\) | −0.294755 | − | 0.955573i | −0.294755 | − | 0.955573i | ||||
\(401\) | 0 | 0 | −0.330279 | − | 0.943883i | \(-0.607143\pi\) | ||||
0.330279 | + | 0.943883i | \(0.392857\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.132974 | − | 0.180173i | 0.132974 | − | 0.180173i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.0895474 | − | 0.794755i | 0.0895474 | − | 0.794755i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.955573 | − | 0.294755i | \(-0.0952381\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.0222759 | − | 0.147791i | −0.0222759 | − | 0.147791i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.145713 | − | 1.94440i | −0.145713 | − | 1.94440i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.149042 | − | 0.988831i | \(-0.452381\pi\) | ||||
−0.149042 | + | 0.988831i | \(0.547619\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.68280 | + | 0.189606i | 1.68280 | + | 0.189606i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.78181 | + | 0.858075i | 1.78181 | + | 0.858075i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | 0.884115 | − | 0.467269i | \(-0.154762\pi\) | ||||
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(432\) | −0.433884 | + | 0.900969i | −0.433884 | + | 0.900969i | ||||
\(433\) | 0.636119 | + | 0.590232i | 0.636119 | + | 0.590232i | 0.930874 | − | 0.365341i | \(-0.119048\pi\) |
−0.294755 | + | 0.955573i | \(0.595238\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.826239 | − | 0.436680i | −0.826239 | − | 0.436680i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.72188 | + | 0.829215i | −1.72188 | + | 0.829215i | −0.733052 | + | 0.680173i | \(0.761905\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.0747301 | − | 0.997204i | 0.0747301 | − | 0.997204i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(444\) | −0.0685427 | − | 1.83184i | −0.0685427 | − | 1.83184i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(449\) | 0 | 0 | −0.0373912 | − | 0.999301i | \(-0.511905\pi\) | ||||
0.0373912 | + | 0.999301i | \(0.488095\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.656405 | + | 0.0739590i | 0.656405 | + | 0.0739590i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.68280 | + | 1.05737i | 1.68280 | + | 1.05737i | 0.900969 | + | 0.433884i | \(0.142857\pi\) |
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.804598 | − | 0.593820i | \(-0.797619\pi\) | ||||
0.804598 | + | 0.593820i | \(0.202381\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.75711 | − | 0.197979i | 1.75711 | − | 0.197979i | 0.826239 | − | 0.563320i | \(-0.190476\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(468\) | 0.826239 | − | 0.563320i | 0.826239 | − | 0.563320i | ||||
\(469\) | −0.197822 | − | 1.04551i | −0.197822 | − | 1.04551i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.36035 | 1.36035 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.281831 | + | 1.48952i | −0.281831 | + | 1.48952i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.652287 | − | 0.757972i | \(-0.726190\pi\) | ||||
0.652287 | + | 0.757972i | \(0.273810\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.856562 | + | 1.62069i | −0.856562 | + | 1.62069i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.425511 | + | 0.677197i | 0.425511 | + | 0.677197i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.0528791 | + | 0.0528791i | −0.0528791 | + | 0.0528791i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.223772 | − | 0.00837297i | −0.223772 | − | 0.00837297i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.299168 | − | 1.58114i | 0.299168 | − | 1.58114i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.733052 | − | 0.680173i | \(-0.238095\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.997204 | − | 0.0747301i | \(-0.976190\pi\) | ||||
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.997204 | + | 0.0747301i | −0.997204 | + | 0.0747301i | ||||
\(508\) | 0.826239 | + | 1.43109i | 0.826239 | + | 1.43109i | ||||
\(509\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.839789 | + | 0.839789i | 0.839789 | + | 0.839789i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.21972 | − | 0.900198i | 1.21972 | − | 0.900198i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.297251 | − | 1.97213i | 0.297251 | − | 1.97213i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.81507 | + | 0.414278i | −1.81507 | + | 0.414278i | −0.988831 | − | 0.149042i | \(-0.952381\pi\) |
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0.680173 | − | 0.733052i | 0.680173 | − | 0.733052i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.28359 | + | 0.806531i | −1.28359 | + | 0.806531i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.281831 | + | 0.242536i | −0.281831 | + | 0.242536i | −0.781831 | − | 0.623490i | \(-0.785714\pi\) |
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.36476 | + | 0.535628i | −1.36476 | + | 0.535628i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.162592 | + | 0.712362i | −0.162592 | + | 0.712362i | 0.826239 | + | 0.563320i | \(0.190476\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.582926 | − | 1.88980i | 0.582926 | − | 1.88980i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.880843 | − | 1.29196i | 0.880843 | − | 1.29196i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.92808 | − | 0.290611i | 1.92808 | − | 0.290611i | ||||
\(557\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.24349 | + | 1.55929i | −1.24349 | + | 1.55929i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.900969 | − | 0.433884i | \(-0.857143\pi\) | ||||
0.900969 | + | 0.433884i | \(0.142857\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.997204 | + | 0.0747301i | −0.997204 | + | 0.0747301i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.680173 | − | 0.266948i | −0.680173 | − | 0.266948i | − | 1.00000i | \(-0.5\pi\) | |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.930874 | − | 0.365341i | −0.930874 | − | 0.365341i | ||||
\(577\) | 0.371563 | + | 1.96376i | 0.371563 | + | 1.96376i | 0.222521 | + | 0.974928i | \(0.428571\pi\) |
0.149042 | + | 0.988831i | \(0.452381\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.51488 | − | 1.30366i | −1.51488 | − | 1.30366i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(588\) | 1.00000 | 1.00000 | ||||||||
\(589\) | 0.293984 | + | 0.169732i | 0.293984 | + | 0.169732i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.82160 | − | 0.205245i | 1.82160 | − | 0.205245i | ||||
\(593\) | 0 | 0 | 0.999301 | − | 0.0373912i | \(-0.0119048\pi\) | ||||
−0.999301 | + | 0.0373912i | \(0.988095\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.634659 | − | 0.930874i | −0.634659 | − | 0.930874i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.826239 | − | 0.563320i | \(-0.809524\pi\) | ||||
0.826239 | + | 0.563320i | \(0.190476\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.563320 | − | 0.826239i | 0.563320 | − | 0.826239i | −0.433884 | − | 0.900969i | \(-0.642857\pi\) |
0.997204 | + | 0.0747301i | \(0.0238095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.00435 | + | 0.351438i | −1.00435 | + | 0.351438i | ||||
\(604\) | −0.0246991 | + | 0.660096i | −0.0246991 | + | 0.660096i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50000 | − | 0.866025i | 1.50000 | − | 0.866025i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
1.00000 | \(0\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.299168 | + | 1.58114i | −0.299168 | + | 1.58114i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 0.593820 | − | 0.804598i | \(-0.297619\pi\) | ||||
−0.593820 | + | 0.804598i | \(0.702381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.86603 | + | 0.500000i | 1.86603 | + | 0.500000i | 1.00000 | \(0\) | ||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0.623490 | + | 0.781831i | 0.623490 | + | 0.781831i | ||||
\(625\) | 0.988831 | − | 0.149042i | 0.988831 | − | 0.149042i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.101659 | + | 1.35654i | 0.101659 | + | 1.35654i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.373714 | + | 0.707101i | 0.373714 | + | 0.707101i | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) |
−0.623490 | + | 0.781831i | \(0.714286\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.45557 | − | 1.16078i | −1.45557 | − | 1.16078i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.866025 | − | 0.500000i | −0.866025 | − | 0.500000i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.781831 | − | 0.623490i | \(-0.785714\pi\) | ||||
0.781831 | + | 0.623490i | \(0.214286\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.0349435 | + | 0.0661163i | 0.0349435 | + | 0.0661163i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.955573 | − | 0.294755i | \(-0.904762\pi\) | ||||
0.955573 | + | 0.294755i | \(0.0952381\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.104635 | − | 0.197979i | −0.104635 | − | 0.197979i | ||||
\(652\) | −0.0566829 | − | 0.0487796i | −0.0566829 | − | 0.0487796i | ||||
\(653\) | 0 | 0 | −0.222521 | − | 0.974928i | \(-0.571429\pi\) | ||||
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.705245 | − | 0.955573i | 0.705245 | − | 0.955573i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.365341 | − | 0.930874i | \(-0.619048\pi\) | ||||
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.262919 | − | 1.38956i | 0.262919 | − | 1.38956i | −0.563320 | − | 0.826239i | \(-0.690476\pi\) |
0.826239 | − | 0.563320i | \(-0.190476\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.97493 | + | 0.222521i | 1.97493 | + | 0.222521i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.766310 | − | 1.12397i | 0.766310 | − | 1.12397i | −0.222521 | − | 0.974928i | \(-0.571429\pi\) |
0.988831 | − | 0.149042i | \(-0.0476190\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.826239 | − | 0.563320i | −0.826239 | − | 0.563320i | ||||
\(676\) | −0.149042 | − | 0.988831i | −0.149042 | − | 0.988831i | ||||
\(677\) | 0 | 0 | −0.563320 | − | 0.826239i | \(-0.690476\pi\) | ||||
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.28183 | + | 0.242536i | −1.28183 | + | 0.242536i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.846724 | − | 0.532032i | \(-0.178571\pi\) | ||||
−0.846724 | + | 0.532032i | \(0.821429\pi\) | |||||||
\(684\) | 0.988831 | + | 1.14904i | 0.988831 | + | 1.14904i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.0962349 | − | 0.359154i | 0.0962349 | − | 0.359154i | ||||
\(688\) | 1.98883 | + | 0.149042i | 1.98883 | + | 0.149042i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.438297 | − | 0.275400i | 0.438297 | − | 0.275400i | −0.294755 | − | 0.955573i | \(-0.595238\pi\) |
0.733052 | + | 0.680173i | \(0.238095\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0.781831 | + | 0.623490i | 0.781831 | + | 0.623490i | ||||
\(701\) | 0 | 0 | 0.433884 | − | 0.900969i | \(-0.357143\pi\) | ||||
−0.433884 | + | 0.900969i | \(0.642857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.58682 | − | 1.01525i | −2.58682 | − | 1.01525i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.220796 | + | 0.299168i | 0.220796 | + | 0.299168i | 0.900969 | − | 0.433884i | \(-0.142857\pi\) |
−0.680173 | + | 0.733052i | \(0.738095\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.40881 | − | 0.678448i | −1.40881 | − | 0.678448i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.733052 | − | 0.680173i | \(-0.238095\pi\) | ||||
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.101659 | + | 0.109562i | 0.101659 | + | 0.109562i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.36254 | − | 1.00560i | −1.36254 | − | 1.00560i | ||||
\(724\) | −0.636119 | − | 1.32091i | −0.636119 | − | 1.32091i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.222521 | + | 0.974928i | 0.222521 | + | 0.974928i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.92808 | + | 0.440071i | 1.92808 | + | 0.440071i | ||||
\(733\) | −0.500684 | + | 0.430874i | −0.500684 | + | 0.430874i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.365341 | + | 0.930874i | \(0.380952\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.707101 | − | 1.62069i | 0.707101 | − | 1.62069i | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) |
0.781831 | − | 0.623490i | \(-0.214286\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.281831 | − | 1.48952i | −0.281831 | − | 1.48952i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.467269 | − | 0.884115i | \(-0.345238\pi\) | ||||
−0.467269 | + | 0.884115i | \(0.654762\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.09839 | + | 0.250701i | −1.09839 | + | 0.250701i | −0.733052 | − | 0.680173i | \(-0.761905\pi\) |
−0.365341 | + | 0.930874i | \(0.619048\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.149042 | − | 0.988831i | −0.149042 | − | 0.988831i | ||||
\(757\) | −1.92808 | − | 0.290611i | −1.92808 | − | 0.290611i | −0.930874 | − | 0.365341i | \(-0.880952\pi\) |
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.804598 | − | 0.593820i | \(-0.202381\pi\) | ||||
−0.804598 | + | 0.593820i | \(0.797619\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.928661 | − | 0.104635i | 0.928661 | − | 0.104635i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0.294755 | − | 0.955573i | 0.294755 | − | 0.955573i | ||||
\(769\) | −0.337649 | + | 0.392355i | −0.337649 | + | 0.392355i | −0.900969 | − | 0.433884i | \(-0.857143\pi\) |
0.563320 | + | 0.826239i | \(0.309524\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.18681 | − | 1.60807i | 1.18681 | − | 1.60807i | ||||
\(773\) | 0 | 0 | −0.943883 | − | 0.330279i | \(-0.892857\pi\) | ||||
0.943883 | + | 0.330279i | \(0.107143\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.0416310 | − | 0.220025i | 0.0416310 | − | 0.220025i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.08855 | + | 1.47493i | 1.08855 | + | 1.47493i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0747301 | + | 0.997204i | 0.0747301 | + | 0.997204i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.425511 | + | 0.677197i | 0.425511 | + | 0.677197i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.44973 | − | 1.34515i | −1.44973 | − | 1.34515i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.880843 | − | 0.702449i | 0.880843 | − | 0.702449i | ||||
\(797\) | 0 | 0 | 0.0747301 | − | 0.997204i | \(-0.476190\pi\) | ||||
−0.0747301 | + | 0.997204i | \(0.523810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.425511 | − | 0.975281i | −0.425511 | − | 0.975281i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.826239 | − | 0.563320i | \(-0.190476\pi\) | ||||
−0.826239 | + | 0.563320i | \(0.809524\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.98603 | − | 0.223772i | 1.98603 | − | 0.223772i | 0.988831 | − | 0.149042i | \(-0.0476190\pi\) |
0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.42271 | − | 1.05001i | −1.42271 | − | 1.05001i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.55999 | − | 1.60855i | −2.55999 | − | 1.60855i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.365341 | + | 0.930874i | −0.365341 | + | 0.930874i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.993712 | − | 0.111964i | \(-0.964286\pi\) | ||||
0.993712 | + | 0.111964i | \(0.0357143\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.846011 | + | 0.193096i | −0.846011 | + | 0.193096i | −0.623490 | − | 0.781831i | \(-0.714286\pi\) |
−0.222521 | + | 0.974928i | \(0.571429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.680173 | − | 1.73305i | −0.680173 | − | 1.73305i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.0440542 | − | 0.587862i | 0.0440542 | − | 0.587862i | ||||
\(832\) | −0.733052 | + | 0.680173i | −0.733052 | + | 0.680173i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.180173 | + | 0.132974i | −0.180173 | + | 0.132974i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.884115 | − | 0.467269i | \(-0.154762\pi\) | ||||
−0.884115 | + | 0.467269i | \(0.845238\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.733052 | − | 0.680173i | −0.733052 | − | 0.680173i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.04876 | − | 1.53825i | 1.04876 | − | 1.53825i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.222521 | − | 0.974928i | 0.222521 | − | 0.974928i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0.202749 | + | 0.218511i | 0.202749 | + | 0.218511i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.656405 | + | 0.0739590i | 0.656405 | + | 0.0739590i | 0.433884 | − | 0.900969i | \(-0.357143\pi\) |
0.222521 | + | 0.974928i | \(0.428571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.0747301 | − | 0.997204i | \(-0.523810\pi\) | ||||
0.0747301 | + | 0.997204i | \(0.476190\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.53825 | + | 0.603718i | −1.53825 | + | 0.603718i | −0.974928 | − | 0.222521i | \(-0.928571\pi\) |
−0.563320 | + | 0.826239i | \(0.690476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.258819 | − | 0.965926i | \(-0.583333\pi\) | ||||
0.258819 | + | 0.965926i | \(0.416667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −0.563320 | − | 0.826239i | −0.563320 | − | 0.826239i | ||||
\(868\) | 0.189606 | − | 0.119137i | 0.189606 | − | 0.119137i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.119137 | + | 1.05737i | −0.119137 | + | 1.05737i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.430874 | + | 1.23137i | 0.430874 | + | 1.23137i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.00560 | + | 0.631863i | 1.00560 | + | 0.631863i | ||||
\(877\) | −0.882094 | + | 1.66900i | −0.882094 | + | 1.66900i | −0.149042 | + | 0.988831i | \(0.547619\pi\) |
−0.733052 | + | 0.680173i | \(0.761905\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1.46610i | − | 1.46610i | −0.680173 | − | 0.733052i | \(-0.738095\pi\) | ||
0.680173 | − | 0.733052i | \(-0.261905\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.974928 | − | 0.222521i | \(-0.928571\pi\) | ||||
0.974928 | + | 0.222521i | \(0.0714286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.48883 | − | 0.716983i | −1.48883 | − | 0.716983i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.0743122 | + | 1.98603i | −0.0743122 | + | 1.98603i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.865341 | + | 1.79690i | 0.865341 | + | 1.79690i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.07659 | + | 1.57906i | 1.07659 | + | 1.57906i | 0.781831 | + | 0.623490i | \(0.214286\pi\) |
0.294755 | + | 0.955573i | \(0.404762\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | −0.623490 | − | 0.781831i | \(-0.714286\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(912\) | −1.07193 | + | 1.07193i | −1.07193 | + | 1.07193i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.365341 | + | 0.0691263i | 0.365341 | + | 0.0691263i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.496990 | + | 1.26631i | −0.496990 | + | 1.26631i | 0.433884 | + | 0.900969i | \(0.357143\pi\) |
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.882094 | + | 1.66900i | 0.882094 | + | 1.66900i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.0685427 | + | 1.83184i | −0.0685427 | + | 1.83184i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.0931869 | − | 0.116853i | 0.0931869 | − | 0.116853i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.185912 | − | 0.982566i | \(-0.559524\pi\) | ||||
0.185912 | + | 0.982566i | \(0.440476\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.606214 | − | 1.38946i | 0.606214 | − | 1.38946i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.61105 | − | 0.367711i | 1.61105 | − | 0.367711i | 0.680173 | − | 0.733052i | \(-0.261905\pi\) |
0.930874 | + | 0.365341i | \(0.119048\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.698220 | + | 0.215372i | −0.698220 | + | 0.215372i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.999301 | − | 0.0373912i | \(-0.988095\pi\) | ||||
0.999301 | + | 0.0373912i | \(0.0119048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.532032 | − | 0.846724i | \(-0.321429\pi\) | ||||
−0.532032 | + | 0.846724i | \(0.678571\pi\) | |||||||
\(948\) | 0.571270 | − | 1.45557i | 0.571270 | − | 1.45557i | ||||
\(949\) | −0.554947 | − | 1.05001i | −0.554947 | − | 1.05001i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.930874 | − | 0.365341i | \(-0.119048\pi\) | ||||
−0.930874 | + | 0.365341i | \(0.880952\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.822599 | + | 0.474928i | 0.822599 | + | 0.474928i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0.900969 | − | 1.43388i | 0.900969 | − | 1.43388i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.649042 | − | 1.85486i | 0.649042 | − | 1.85486i | 0.149042 | − | 0.988831i | \(-0.452381\pi\) |
0.500000 | − | 0.866025i | \(-0.333333\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.997204 | − | 0.0747301i | \(-0.0238095\pi\) | ||||
−0.997204 | + | 0.0747301i | \(0.976190\pi\) | |||||||
\(972\) | −0.955573 | + | 0.294755i | −0.955573 | + | 0.294755i | ||||
\(973\) | −1.42935 | + | 1.32624i | −1.42935 | + | 1.32624i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(976\) | −0.294755 | + | 1.95557i | −0.294755 | + | 1.95557i | ||||
\(977\) | 0 | 0 | 0.999301 | − | 0.0373912i | \(-0.0119048\pi\) | ||||
−0.999301 | + | 0.0373912i | \(0.988095\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −0.241876 | − | 0.902694i | −0.241876 | − | 0.902694i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.467269 | − | 0.884115i | \(-0.345238\pi\) | ||||
−0.467269 | + | 0.884115i | \(0.654762\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.46429 | − | 0.392355i | 1.46429 | − | 0.392355i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −0.0111692 | + | 0.149042i | −0.0111692 | + | 0.149042i | 0.988831 | + | 0.149042i | \(0.0476190\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1.85486 | + | 0.649042i | 1.85486 | + | 0.649042i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.35417 | + | 1.07992i | −1.35417 | + | 1.07992i | −0.365341 | + | 0.930874i | \(0.619048\pi\) |
−0.988831 | + | 0.149042i | \(0.952381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.29621 | − | 1.29621i | 1.29621 | − | 1.29621i |
(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 | 1911.1.ep.a.1055.1 | yes | 24 | |
3.2 | odd | 2 | CM | 1911.1.ep.a.1055.1 | yes | 24 | |
13.7 | odd | 12 | 1911.1.ea.a.761.1 | ✓ | 24 | ||
39.20 | even | 12 | 1911.1.ea.a.761.1 | ✓ | 24 | ||
49.17 | odd | 42 | 1911.1.ea.a.899.1 | yes | 24 | ||
147.17 | even | 42 | 1911.1.ea.a.899.1 | yes | 24 | ||
637.605 | even | 84 | inner | 1911.1.ep.a.605.1 | yes | 24 | |
1911.605 | odd | 84 | inner | 1911.1.ep.a.605.1 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1911.1.ea.a.761.1 | ✓ | 24 | 13.7 | odd | 12 | ||
1911.1.ea.a.761.1 | ✓ | 24 | 39.20 | even | 12 | ||
1911.1.ea.a.899.1 | yes | 24 | 49.17 | odd | 42 | ||
1911.1.ea.a.899.1 | yes | 24 | 147.17 | even | 42 | ||
1911.1.ep.a.605.1 | yes | 24 | 637.605 | even | 84 | inner | |
1911.1.ep.a.605.1 | yes | 24 | 1911.605 | odd | 84 | inner | |
1911.1.ep.a.1055.1 | yes | 24 | 1.1 | even | 1 | trivial | |
1911.1.ep.a.1055.1 | yes | 24 | 3.2 | odd | 2 | CM |