Properties

Label 799.1.e.b.234.4
Level $799$
Weight $1$
Character 799.234
Analytic conductor $0.399$
Analytic rank $0$
Dimension $8$
Projective image $D_{20}$
CM discriminant -47
Inner twists $4$

Related objects

Downloads

Learn more

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [799,1,Mod(140,799)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(799, base_ring=CyclotomicField(4))
 
chi = DirichletCharacter(H, H._module([3, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("799.140");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 799 = 17 \cdot 47 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 799.e (of order \(4\), degree \(2\), 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: \(0.398752945094\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(4\) over \(\Q(i)\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{20}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{20} - \cdots)\)

Embedding invariants

Embedding label 234.4
Root \(-0.587785 + 0.809017i\) of defining polynomial
Character \(\chi\) \(=\) 799.234
Dual form 799.1.e.b.140.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+0.618034i q^{2} +(-0.221232 - 0.221232i) q^{3} +0.618034 q^{4} +(0.136729 - 0.136729i) q^{6} +(0.642040 - 0.642040i) q^{7} +1.00000i q^{8} -0.902113i q^{9} +O(q^{10})\) \(q+0.618034i q^{2} +(-0.221232 - 0.221232i) q^{3} +0.618034 q^{4} +(0.136729 - 0.136729i) q^{6} +(0.642040 - 0.642040i) q^{7} +1.00000i q^{8} -0.902113i q^{9} +(-0.136729 - 0.136729i) q^{12} +(0.396802 + 0.396802i) q^{14} +(-0.809017 - 0.587785i) q^{17} +0.557537 q^{18} -0.284079 q^{21} +(0.221232 - 0.221232i) q^{24} +1.00000i q^{25} +(-0.420808 + 0.420808i) q^{27} +(0.396802 - 0.396802i) q^{28} +1.00000i q^{32} +(0.363271 - 0.500000i) q^{34} -0.557537i q^{36} +(0.221232 + 0.221232i) q^{37} -0.175571i q^{42} -1.00000 q^{47} +0.175571i q^{49} -0.618034 q^{50} +(0.0489435 + 0.309017i) q^{51} +1.90211i q^{53} +(-0.260074 - 0.260074i) q^{54} +(0.642040 + 0.642040i) q^{56} +0.618034i q^{59} +(1.26007 - 1.26007i) q^{61} +(-0.579192 - 0.579192i) q^{63} -0.618034 q^{64} +(-0.500000 - 0.363271i) q^{68} +(-1.39680 - 1.39680i) q^{71} +0.902113 q^{72} +(-0.136729 + 0.136729i) q^{74} +(0.221232 - 0.221232i) q^{75} +(-1.39680 + 1.39680i) q^{79} -0.715921 q^{81} -0.175571 q^{84} +0.618034 q^{89} -0.618034i q^{94} +(0.221232 - 0.221232i) q^{96} +(-1.26007 - 1.26007i) q^{97} -0.108509 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q - 2 q^{3} - 4 q^{4} + 4 q^{6} + 2 q^{7}+O(q^{10}) \) Copy content Toggle raw display \( 8 q - 2 q^{3} - 4 q^{4} + 4 q^{6} + 2 q^{7} - 4 q^{12} - 6 q^{14} - 2 q^{17} + 4 q^{18} + 4 q^{21} + 2 q^{24} - 6 q^{28} + 2 q^{37} - 8 q^{47} + 4 q^{50} + 8 q^{51} + 10 q^{54} + 2 q^{56} - 2 q^{61} - 8 q^{63} + 4 q^{64} - 4 q^{68} - 2 q^{71} - 8 q^{72} - 4 q^{74} + 2 q^{75} - 2 q^{79} - 12 q^{81} + 8 q^{84} - 4 q^{89} + 2 q^{96} + 2 q^{97} - 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/799\mathbb{Z}\right)^\times\).

\(n\) \(52\) \(377\)
\(\chi(n)\) \(-1\) \(e\left(\frac{1}{4}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).



Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(3\) −0.221232 0.221232i −0.221232 0.221232i 0.587785 0.809017i \(-0.300000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 0.618034 0.618034
\(5\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(6\) 0.136729 0.136729i 0.136729 0.136729i
\(7\) 0.642040 0.642040i 0.642040 0.642040i −0.309017 0.951057i \(-0.600000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(8\) 1.00000i 1.00000i
\(9\) 0.902113i 0.902113i
\(10\) 0 0
\(11\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(12\) −0.136729 0.136729i −0.136729 0.136729i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0.396802 + 0.396802i 0.396802 + 0.396802i
\(15\) 0 0
\(16\) 0 0
\(17\) −0.809017 0.587785i −0.809017 0.587785i
\(18\) 0.557537 0.557537
\(19\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(20\) 0 0
\(21\) −0.284079 −0.284079
\(22\) 0 0
\(23\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(24\) 0.221232 0.221232i 0.221232 0.221232i
\(25\) 1.00000i 1.00000i
\(26\) 0 0
\(27\) −0.420808 + 0.420808i −0.420808 + 0.420808i
\(28\) 0.396802 0.396802i 0.396802 0.396802i
\(29\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(30\) 0 0
\(31\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(32\) 1.00000i 1.00000i
\(33\) 0 0
\(34\) 0.363271 0.500000i 0.363271 0.500000i
\(35\) 0 0
\(36\) 0.557537i 0.557537i
\(37\) 0.221232 + 0.221232i 0.221232 + 0.221232i 0.809017 0.587785i \(-0.200000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(42\) 0.175571i 0.175571i
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) −1.00000 −1.00000
\(48\) 0 0
\(49\) 0.175571i 0.175571i
\(50\) −0.618034 −0.618034
\(51\) 0.0489435 + 0.309017i 0.0489435 + 0.309017i
\(52\) 0 0
\(53\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(54\) −0.260074 0.260074i −0.260074 0.260074i
\(55\) 0 0
\(56\) 0.642040 + 0.642040i 0.642040 + 0.642040i
\(57\) 0 0
\(58\) 0 0
\(59\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(60\) 0 0
\(61\) 1.26007 1.26007i 1.26007 1.26007i 0.309017 0.951057i \(-0.400000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(62\) 0 0
\(63\) −0.579192 0.579192i −0.579192 0.579192i
\(64\) −0.618034 −0.618034
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) −0.500000 0.363271i −0.500000 0.363271i
\(69\) 0 0
\(70\) 0 0
\(71\) −1.39680 1.39680i −1.39680 1.39680i −0.809017 0.587785i \(-0.800000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(72\) 0.902113 0.902113
\(73\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(74\) −0.136729 + 0.136729i −0.136729 + 0.136729i
\(75\) 0.221232 0.221232i 0.221232 0.221232i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) −1.39680 + 1.39680i −1.39680 + 1.39680i −0.587785 + 0.809017i \(0.700000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0 0
\(81\) −0.715921 −0.715921
\(82\) 0 0
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) −0.175571 −0.175571
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0.618034i 0.618034i
\(95\) 0 0
\(96\) 0.221232 0.221232i 0.221232 0.221232i
\(97\) −1.26007 1.26007i −1.26007 1.26007i −0.951057 0.309017i \(-0.900000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(98\) −0.108509 −0.108509
\(99\) 0 0
\(100\) 0.618034i 0.618034i
\(101\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(102\) −0.190983 + 0.0302487i −0.190983 + 0.0302487i
\(103\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) −1.17557 −1.17557
\(107\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(108\) −0.260074 + 0.260074i −0.260074 + 0.260074i
\(109\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(110\) 0 0
\(111\) 0.0978870i 0.0978870i
\(112\) 0 0
\(113\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.381966 −0.381966
\(119\) −0.896802 + 0.142040i −0.896802 + 0.142040i
\(120\) 0 0
\(121\) 1.00000i 1.00000i
\(122\) 0.778768 + 0.778768i 0.778768 + 0.778768i
\(123\) 0 0
\(124\) 0 0
\(125\) 0 0
\(126\) 0.357960 0.357960i 0.357960 0.357960i
\(127\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(128\) 0.618034i 0.618034i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.26007 1.26007i −1.26007 1.26007i −0.951057 0.309017i \(-0.900000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.587785 0.809017i 0.587785 0.809017i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0 0
\(139\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(140\) 0 0
\(141\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(142\) 0.863271 0.863271i 0.863271 0.863271i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0.0388418 0.0388418i 0.0388418 0.0388418i
\(148\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(149\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(150\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 0 0
\(153\) −0.530249 + 0.729825i −0.530249 + 0.729825i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(158\) −0.863271 0.863271i −0.863271 0.863271i
\(159\) 0.420808 0.420808i 0.420808 0.420808i
\(160\) 0 0
\(161\) 0 0
\(162\) 0.442463i 0.442463i
\(163\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(168\) 0.284079i 0.284079i
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.642040 + 0.642040i 0.642040 + 0.642040i 0.951057 0.309017i \(-0.100000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(174\) 0 0
\(175\) 0.642040 + 0.642040i 0.642040 + 0.642040i
\(176\) 0 0
\(177\) 0.136729 0.136729i 0.136729 0.136729i
\(178\) 0.381966i 0.381966i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(182\) 0 0
\(183\) −0.557537 −0.557537
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.618034 −0.618034
\(189\) 0.540350i 0.540350i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(193\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(194\) 0.778768 0.778768i 0.778768 0.778768i
\(195\) 0 0
\(196\) 0.108509i 0.108509i
\(197\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(198\) 0 0
\(199\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(200\) −1.00000 −1.00000
\(201\) 0 0
\(202\) 0.726543i 0.726543i
\(203\) 0 0
\(204\) 0.0302487 + 0.190983i 0.0302487 + 0.190983i
\(205\) 0 0
\(206\) 0.726543i 0.726543i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(212\) 1.17557i 1.17557i
\(213\) 0.618034i 0.618034i
\(214\) 0 0
\(215\) 0 0
\(216\) −0.420808 0.420808i −0.420808 0.420808i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0.0604975 0.0604975
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0.642040 + 0.642040i 0.642040 + 0.642040i
\(225\) 0.902113 0.902113
\(226\) 0 0
\(227\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.381966i 0.381966i
\(237\) 0.618034 0.618034
\(238\) −0.0877853 0.554254i −0.0877853 0.554254i
\(239\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(240\) 0 0
\(241\) 0.221232 + 0.221232i 0.221232 + 0.221232i 0.809017 0.587785i \(-0.200000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(242\) 0.618034 0.618034
\(243\) 0.579192 + 0.579192i 0.579192 + 0.579192i
\(244\) 0.778768 0.778768i 0.778768 0.778768i
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(252\) −0.357960 0.357960i −0.357960 0.357960i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −1.00000 −1.00000
\(257\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 0.284079 0.284079
\(260\) 0 0
\(261\) 0 0
\(262\) 0.778768 0.778768i 0.778768 0.778768i
\(263\) 0.618034i 0.618034i 0.951057 + 0.309017i \(0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.136729 0.136729i −0.136729 0.136729i
\(268\) 0 0
\(269\) 1.00000 + 1.00000i 1.00000 + 1.00000i 1.00000 \(0\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(282\) −0.136729 + 0.136729i −0.136729 + 0.136729i
\(283\) −0.642040 + 0.642040i −0.642040 + 0.642040i −0.951057 0.309017i \(-0.900000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(284\) −0.863271 0.863271i −0.863271 0.863271i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0.902113 0.902113
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0.557537i 0.557537i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0.0240055 + 0.0240055i 0.0240055 + 0.0240055i
\(295\) 0 0
\(296\) −0.221232 + 0.221232i −0.221232 + 0.221232i
\(297\) 0 0
\(298\) 0.726543i 0.726543i
\(299\) 0 0
\(300\) 0.136729 0.136729i 0.136729 0.136729i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.260074 0.260074i −0.260074 0.260074i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.451057 0.327712i −0.451057 0.327712i
\(307\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(308\) 0 0
\(309\) 0.260074 + 0.260074i 0.260074 + 0.260074i
\(310\) 0 0
\(311\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(312\) 0 0
\(313\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(314\) 1.17557i 1.17557i
\(315\) 0 0
\(316\) −0.863271 + 0.863271i −0.863271 + 0.863271i
\(317\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(318\) 0.260074 + 0.260074i 0.260074 + 0.260074i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.442463 −0.442463
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) −0.642040 + 0.642040i −0.642040 + 0.642040i
\(330\) 0 0
\(331\) 0.618034i 0.618034i −0.951057 0.309017i \(-0.900000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(332\) 0 0
\(333\) 0.199576 0.199576i 0.199576 0.199576i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.642040 + 0.642040i 0.642040 + 0.642040i 0.951057 0.309017i \(-0.100000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) 0.618034i 0.618034i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0.754763 + 0.754763i 0.754763 + 0.754763i
\(344\) 0 0
\(345\) 0 0
\(346\) −0.396802 + 0.396802i −0.396802 + 0.396802i
\(347\) 0.221232 0.221232i 0.221232 0.221232i −0.587785 0.809017i \(-0.700000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) −0.396802 + 0.396802i −0.396802 + 0.396802i
\(351\) 0 0
\(352\) 0 0
\(353\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(354\) 0.0845030 + 0.0845030i 0.0845030 + 0.0845030i
\(355\) 0 0
\(356\) 0.381966 0.381966
\(357\) 0.229825 + 0.166977i 0.229825 + 0.166977i
\(358\) 0 0
\(359\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 0 0
\(363\) −0.221232 + 0.221232i −0.221232 + 0.221232i
\(364\) 0 0
\(365\) 0 0
\(366\) 0.344577i 0.344577i
\(367\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.22123 + 1.22123i 1.22123 + 1.22123i
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 1.00000i 1.00000i
\(377\) 0 0
\(378\) −0.333955 −0.333955
\(379\) −0.642040 0.642040i −0.642040 0.642040i 0.309017 0.951057i \(-0.400000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(384\) 0.136729 0.136729i 0.136729 0.136729i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.778768 0.778768i −0.778768 0.778768i
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.175571 −0.175571
\(393\) 0.557537i 0.557537i
\(394\) 0.618034 + 0.618034i 0.618034 + 0.618034i
\(395\) 0 0
\(396\) 0 0
\(397\) 1.39680 1.39680i 1.39680 1.39680i 0.587785 0.809017i \(-0.300000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.221232 0.221232i 0.221232 0.221232i −0.587785 0.809017i \(-0.700000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.726543 0.726543
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −0.309017 + 0.0489435i −0.309017 + 0.0489435i
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −0.726543 −0.726543
\(413\) 0.396802 + 0.396802i 0.396802 + 0.396802i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(420\) 0 0
\(421\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(422\) 0 0
\(423\) 0.902113i 0.902113i
\(424\) −1.90211 −1.90211
\(425\) 0.587785 0.809017i 0.587785 0.809017i
\(426\) −0.381966 −0.381966
\(427\) 1.61803i 1.61803i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 1.26007 1.26007i 1.26007 1.26007i 0.309017 0.951057i \(-0.400000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(432\) 0 0
\(433\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(440\) 0 0
\(441\) 0.158384 0.158384
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0.0604975i 0.0604975i
\(445\) 0 0
\(446\) 0 0
\(447\) −0.260074 0.260074i −0.260074 0.260074i
\(448\) −0.396802 + 0.396802i −0.396802 + 0.396802i
\(449\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(450\) 0.557537i 0.557537i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 1.17557i 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(458\) 0 0
\(459\) 0.587785 0.0930960i 0.587785 0.0930960i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0.420808 + 0.420808i 0.420808 + 0.420808i
\(472\) −0.618034 −0.618034
\(473\) 0 0
\(474\) 0.381966i 0.381966i
\(475\) 0 0
\(476\) −0.554254 + 0.0877853i −0.554254 + 0.0877853i
\(477\) 1.71592 1.71592
\(478\) 1.00000i 1.00000i
\(479\) −0.642040 0.642040i −0.642040 0.642040i 0.309017 0.951057i \(-0.400000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) −0.136729 + 0.136729i −0.136729 + 0.136729i
\(483\) 0 0
\(484\) 0.618034i 0.618034i
\(485\) 0 0
\(486\) −0.357960 + 0.357960i −0.357960 + 0.357960i
\(487\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(488\) 1.26007 + 1.26007i 1.26007 + 1.26007i
\(489\) 0 0
\(490\) 0 0
\(491\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −1.79360 −1.79360
\(498\) 0 0
\(499\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) 0.726543i 0.726543i
\(503\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(504\) 0.579192 0.579192i 0.579192 0.579192i
\(505\) 0 0
\(506\) 0 0
\(507\) −0.221232 0.221232i −0.221232 0.221232i
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0.175571i 0.175571i
\(519\) 0.284079i 0.284079i
\(520\) 0 0
\(521\) 0.642040 0.642040i 0.642040 0.642040i −0.309017 0.951057i \(-0.600000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(522\) 0 0
\(523\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(524\) −0.778768 0.778768i −0.778768 0.778768i
\(525\) 0.284079i 0.284079i
\(526\) −0.381966 −0.381966
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000i 1.00000i
\(530\) 0 0
\(531\) 0.557537 0.557537
\(532\) 0 0
\(533\) 0 0
\(534\) 0.0845030 0.0845030i 0.0845030 0.0845030i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.618034 + 0.618034i −0.618034 + 0.618034i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.642040 + 0.642040i 0.642040 + 0.642040i 0.951057 0.309017i \(-0.100000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(542\) 0.726543i 0.726543i
\(543\) 0 0
\(544\) 0.587785 0.809017i 0.587785 0.809017i
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(548\) 0 0
\(549\) −1.13673 1.13673i −1.13673 1.13673i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 1.79360i 1.79360i
\(554\) −0.863271 + 0.863271i −0.863271 + 0.863271i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(564\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(565\) 0 0
\(566\) −0.396802 0.396802i −0.396802 0.396802i
\(567\) −0.459650 + 0.459650i −0.459650 + 0.459650i
\(568\) 1.39680 1.39680i 1.39680 1.39680i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) −1.39680 + 1.39680i −1.39680 + 1.39680i −0.587785 + 0.809017i \(0.700000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.557537i 0.557537i
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) −0.344577 −0.344577
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(588\) 0.0240055 0.0240055i 0.0240055 0.0240055i
\(589\) 0 0
\(590\) 0 0
\(591\) −0.442463 −0.442463
\(592\) 0 0
\(593\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.726543 0.726543
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(600\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(601\) −1.26007 + 1.26007i −1.26007 + 1.26007i −0.309017 + 0.951057i \(0.600000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.160734 0.160734i 0.160734 0.160734i
\(607\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.327712 + 0.451057i −0.327712 + 0.451057i
\(613\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0.726543i 0.726543i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.39680 1.39680i −1.39680 1.39680i −0.809017 0.587785i \(-0.800000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(618\) −0.160734 + 0.160734i −0.160734 + 0.160734i
\(619\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0.396802 0.396802i 0.396802 0.396802i
\(624\) 0 0
\(625\) −1.00000 −1.00000
\(626\) 0 0
\(627\) 0 0
\(628\) −1.17557 −1.17557
\(629\) −0.0489435 0.309017i −0.0489435 0.309017i
\(630\) 0 0
\(631\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(632\) −1.39680 1.39680i −1.39680 1.39680i
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0.260074 0.260074i 0.260074 0.260074i
\(637\) 0 0
\(638\) 0 0
\(639\) −1.26007 + 1.26007i −1.26007 + 1.26007i
\(640\) 0 0
\(641\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(642\) 0 0
\(643\) −1.26007 1.26007i −1.26007 1.26007i −0.951057 0.309017i \(-0.900000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(648\) 0.715921i 0.715921i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) −0.221232 + 0.221232i −0.221232 + 0.221232i −0.809017 0.587785i \(-0.800000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) −0.396802 0.396802i −0.396802 0.396802i
\(659\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(660\) 0 0
\(661\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(662\) 0.381966 0.381966
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.123345 + 0.123345i 0.123345 + 0.123345i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.284079i 0.284079i
\(673\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(674\) −0.396802 + 0.396802i −0.396802 + 0.396802i
\(675\) −0.420808 0.420808i −0.420808 0.420808i
\(676\) 0.618034 0.618034
\(677\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(678\) 0 0
\(679\) −1.61803 −1.61803
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.26007 1.26007i −1.26007 1.26007i −0.951057 0.309017i \(-0.900000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.466469 + 0.466469i −0.466469 + 0.466469i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(692\) 0.396802 + 0.396802i 0.396802 + 0.396802i
\(693\) 0 0
\(694\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0.396802 + 0.396802i 0.396802 + 0.396802i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1.17557i 1.17557i
\(707\) 0.754763 0.754763i 0.754763 0.754763i
\(708\) 0.0845030 0.0845030i 0.0845030 0.0845030i
\(709\) 0.642040 + 0.642040i 0.642040 + 0.642040i 0.951057 0.309017i \(-0.100000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0 0
\(711\) 1.26007 + 1.26007i 1.26007 + 1.26007i
\(712\) 0.618034i 0.618034i
\(713\) 0 0
\(714\) −0.103198 + 0.142040i −0.103198 + 0.142040i
\(715\) 0 0
\(716\) 0 0
\(717\) −0.357960 0.357960i −0.357960 0.357960i
\(718\) 0 0
\(719\) 1.26007 + 1.26007i 1.26007 + 1.26007i 0.951057 + 0.309017i \(0.100000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0 0
\(721\) −0.754763 + 0.754763i −0.754763 + 0.754763i
\(722\) 0.618034i 0.618034i
\(723\) 0.0978870i 0.0978870i
\(724\) 0 0
\(725\) 0 0
\(726\) −0.136729 0.136729i −0.136729 0.136729i
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) 0.459650i 0.459650i
\(730\) 0 0
\(731\) 0 0
\(732\) −0.344577 −0.344577
\(733\) 1.61803i 1.61803i −0.587785 0.809017i \(-0.700000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 1.90211i 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −0.754763 + 0.754763i −0.754763 + 0.754763i
\(743\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(752\) 0 0
\(753\) 0.260074 + 0.260074i 0.260074 + 0.260074i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.333955i 0.333955i
\(757\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(758\) 0.396802 0.396802i 0.396802 0.396802i
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.726543 0.726543
\(767\) 0 0
\(768\) 0.221232 + 0.221232i 0.221232 + 0.221232i
\(769\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 1.61803i 1.61803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.26007 1.26007i 1.26007 1.26007i
\(777\) −0.0628473 0.0628473i −0.0628473 0.0628473i
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) −0.344577 −0.344577
\(787\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(788\) 0.618034 0.618034i 0.618034 0.618034i
\(789\) 0.136729 0.136729i 0.136729 0.136729i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0.863271 + 0.863271i 0.863271 + 0.863271i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(798\) 0 0
\(799\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(800\) −1.00000 −1.00000
\(801\) 0.557537i 0.557537i
\(802\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0.442463i 0.442463i
\(808\) 1.17557i 1.17557i
\(809\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(810\) 0 0
\(811\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(812\) 0 0
\(813\) −0.260074 0.260074i −0.260074 0.260074i
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(822\) 0 0
\(823\) −1.00000 + 1.00000i −1.00000 + 1.00000i 1.00000i \(0.5\pi\)
−1.00000 \(\pi\)
\(824\) 1.17557i 1.17557i
\(825\) 0 0
\(826\) −0.245237 + 0.245237i −0.245237 + 0.245237i
\(827\) −1.26007 + 1.26007i −1.26007 + 1.26007i −0.309017 + 0.951057i \(0.600000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0.618034i 0.618034i
\(832\) 0 0
\(833\) 0.103198 0.142040i 0.103198 0.142040i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(840\) 0 0
\(841\) 1.00000i 1.00000i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) −0.557537 −0.557537
\(847\) −0.642040 0.642040i −0.642040 0.642040i
\(848\) 0 0
\(849\) 0.284079 0.284079
\(850\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(851\) 0 0
\(852\) 0.381966i 0.381966i
\(853\) 1.39680 + 1.39680i 1.39680 + 1.39680i 0.809017 + 0.587785i \(0.200000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(854\) 1.00000 1.00000
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(858\) 0 0
\(859\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.778768 + 0.778768i 0.778768 + 0.778768i
\(863\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(864\) −0.420808 0.420808i −0.420808 0.420808i
\(865\) 0 0
\(866\) 0 0
\(867\) 0.142040 0.278768i 0.142040 0.278768i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −1.13673 + 1.13673i −1.13673 + 1.13673i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(878\) 0.618034 0.618034i 0.618034 0.618034i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(882\) 0.0978870i 0.0978870i
\(883\) 1.90211 1.90211 0.951057 0.309017i \(-0.100000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(888\) 0.0978870 0.0978870
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0.160734 0.160734i 0.160734 0.160734i
\(895\) 0 0
\(896\) 0.396802 + 0.396802i 0.396802 + 0.396802i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.557537 0.557537
\(901\) 1.11803 1.53884i 1.11803 1.53884i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.00000 1.00000i 1.00000 1.00000i 1.00000i \(-0.5\pi\)
1.00000 \(0\)
\(908\) 0 0
\(909\) 1.06050i 1.06050i
\(910\) 0 0
\(911\) 1.26007 1.26007i 1.26007 1.26007i 0.309017 0.951057i \(-0.400000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.726543 0.726543
\(915\) 0 0
\(916\) 0 0
\(917\) −1.61803 −1.61803
\(918\) 0.0575365 + 0.363271i 0.0575365 + 0.363271i
\(919\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −0.260074 0.260074i −0.260074 0.260074i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −0.221232 + 0.221232i −0.221232 + 0.221232i
\(926\) 0 0
\(927\) 1.06050i 1.06050i
\(928\) 0 0
\(929\) 0.221232 0.221232i 0.221232 0.221232i −0.587785 0.809017i \(-0.700000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 1.26007 1.26007i 1.26007 1.26007i 0.309017 0.951057i \(-0.400000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(942\) −0.260074 + 0.260074i −0.260074 + 0.260074i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −1.00000 1.00000i −1.00000 1.00000i 1.00000i \(-0.5\pi\)
−1.00000 \(\pi\)
\(948\) 0.381966 0.381966
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −0.142040 0.896802i −0.142040 0.896802i
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 1.06050i 1.06050i
\(955\) 0 0
\(956\) 1.00000 1.00000
\(957\) 0 0
\(958\) 0.396802 0.396802i 0.396802 0.396802i
\(959\) 0 0
\(960\) 0 0
\(961\) 1.00000i 1.00000i
\(962\) 0 0
\(963\) 0 0
\(964\) 0.136729 + 0.136729i 0.136729 + 0.136729i
\(965\) 0 0
\(966\) 0 0
\(967\) 1.90211i 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(968\) 1.00000 1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0.357960 + 0.357960i 0.357960 + 0.357960i
\(973\) 0 0
\(974\) −0.618034 0.618034i −0.618034 0.618034i
\(975\) 0 0
\(976\) 0 0
\(977\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 1.17557 1.17557
\(983\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0.284079 0.284079
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.26007 + 1.26007i 1.26007 + 1.26007i 0.951057 + 0.309017i \(0.100000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(992\) 0 0
\(993\) −0.136729 + 0.136729i −0.136729 + 0.136729i
\(994\) 1.10851i 1.10851i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(998\) 0 0
\(999\) −0.186192 −0.186192
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (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 799.1.e.b.234.4 yes 8
17.4 even 4 inner 799.1.e.b.140.2 8
47.46 odd 2 CM 799.1.e.b.234.4 yes 8
799.140 odd 4 inner 799.1.e.b.140.2 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
799.1.e.b.140.2 8 17.4 even 4 inner
799.1.e.b.140.2 8 799.140 odd 4 inner
799.1.e.b.234.4 yes 8 1.1 even 1 trivial
799.1.e.b.234.4 yes 8 47.46 odd 2 CM