Properties

Label 2783.1.f.a.390.1
Level $2783$
Weight $1$
Character 2783.390
Analytic conductor $1.389$
Analytic rank $0$
Dimension $4$
Projective image $D_{3}$
CM discriminant -23
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [2783,1,Mod(390,2783)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(2783, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([4, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("2783.390");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 2783 = 11^{2} \cdot 23 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 2783.f (of order \(10\), degree \(4\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.38889793016\)
Analytic rank: \(0\)
Dimension: \(4\)
Coefficient field: \(\Q(\zeta_{10})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{3} + x^{2} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 23)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.23.1
Artin image: $S_3\times C_{10}$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{30} - \cdots)\)

Embedding invariants

Embedding label 390.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 2783.390
Dual form 2783.1.f.a.735.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.309017 + 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{8} +O(q^{10})\) \(q+(0.309017 + 0.951057i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-0.309017 + 0.951057i) q^{6} +(0.809017 + 0.587785i) q^{8} +(0.309017 + 0.951057i) q^{13} +(-0.309017 + 0.951057i) q^{16} +1.00000 q^{23} +(0.309017 + 0.951057i) q^{24} +(-0.809017 - 0.587785i) q^{25} +(-0.809017 + 0.587785i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.809017 + 0.587785i) q^{29} +(-0.309017 - 0.951057i) q^{31} +(-0.309017 + 0.951057i) q^{39} +(-0.809017 - 0.587785i) q^{41} +(0.309017 + 0.951057i) q^{46} +(0.809017 + 0.587785i) q^{47} +(-0.809017 + 0.587785i) q^{48} +(0.309017 - 0.951057i) q^{49} +(0.309017 - 0.951057i) q^{50} +1.00000 q^{54} +(-0.809017 - 0.587785i) q^{58} +(-1.61803 + 1.17557i) q^{59} +(0.809017 - 0.587785i) q^{62} +(0.309017 + 0.951057i) q^{64} +(0.809017 + 0.587785i) q^{69} +(-0.309017 + 0.951057i) q^{71} +(-0.809017 + 0.587785i) q^{73} +(-0.309017 - 0.951057i) q^{75} -1.00000 q^{78} +(0.809017 - 0.587785i) q^{81} +(0.309017 - 0.951057i) q^{82} -1.00000 q^{87} +(0.309017 - 0.951057i) q^{93} +(-0.309017 + 0.951057i) q^{94} +1.00000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - q^{2} + q^{3} + q^{6} + q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - q^{2} + q^{3} + q^{6} + q^{8} - q^{13} + q^{16} + 4 q^{23} - q^{24} - q^{25} - q^{26} - q^{27} - q^{29} + q^{31} + q^{39} - q^{41} - q^{46} + q^{47} - q^{48} - q^{49} - q^{50} + 4 q^{54} - q^{58} - 2 q^{59} + q^{62} - q^{64} + q^{69} + q^{71} - q^{73} + q^{75} - 4 q^{78} + q^{81} - q^{82} - 4 q^{87} - q^{93} + q^{94} + 4 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2783\mathbb{Z}\right)^\times\).

\(n\) \(1937\) \(2301\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(3\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(4\) 0 0
\(5\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(6\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(7\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(8\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0
\(12\) 0 0
\(13\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(17\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(18\) 0 0
\(19\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 1.00000 1.00000
\(24\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(25\) −0.809017 0.587785i −0.809017 0.587785i
\(26\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(27\) 0.309017 0.951057i 0.309017 0.951057i
\(28\) 0 0
\(29\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(30\) 0 0
\(31\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0 0
\(39\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(40\) 0 0
\(41\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(47\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(48\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(49\) 0.309017 0.951057i 0.309017 0.951057i
\(50\) 0.309017 0.951057i 0.309017 0.951057i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 1.00000 1.00000
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) −0.809017 0.587785i −0.809017 0.587785i
\(59\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0 0
\(61\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(62\) 0.809017 0.587785i 0.809017 0.587785i
\(63\) 0 0
\(64\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(68\) 0 0
\(69\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(70\) 0 0
\(71\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(72\) 0 0
\(73\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(74\) 0 0
\(75\) −0.309017 0.951057i −0.309017 0.951057i
\(76\) 0 0
\(77\) 0 0
\(78\) −1.00000 −1.00000
\(79\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(80\) 0 0
\(81\) 0.809017 0.587785i 0.809017 0.587785i
\(82\) 0.309017 0.951057i 0.309017 0.951057i
\(83\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −1.00000 −1.00000
\(88\) 0 0
\(89\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.309017 0.951057i 0.309017 0.951057i
\(94\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(95\) 0 0
\(96\) 0 0
\(97\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) 1.00000 1.00000
\(99\) 0 0
\(100\) 0 0
\(101\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(102\) 0 0
\(103\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(104\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.61803 1.17557i −1.61803 1.17557i
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) −0.309017 0.951057i −0.309017 0.951057i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(128\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(129\) 0 0
\(130\) 0 0
\(131\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(138\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(139\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(140\) 0 0
\(141\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(142\) −1.00000 −1.00000
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) −0.809017 0.587785i −0.809017 0.587785i
\(147\) 0.809017 0.587785i 0.809017 0.587785i
\(148\) 0 0
\(149\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(150\) 0.809017 0.587785i 0.809017 0.587785i
\(151\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) 0 0
\(162\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(163\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(174\) −0.309017 0.951057i −0.309017 0.951057i
\(175\) 0 0
\(176\) 0 0
\(177\) −2.00000 −2.00000
\(178\) 0 0
\(179\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(180\) 0 0
\(181\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(185\) 0 0
\(186\) 1.00000 1.00000
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(192\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(193\) 0.309017 0.951057i 0.309017 0.951057i −0.669131 0.743145i \(-0.733333\pi\)
0.978148 0.207912i \(-0.0666667\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −0.309017 0.951057i −0.309017 0.951057i
\(201\) 0 0
\(202\) 1.61803 1.17557i 1.61803 1.17557i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −1.00000 −1.00000
\(209\) 0 0
\(210\) 0 0
\(211\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(212\) 0 0
\(213\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(214\) 0 0
\(215\) 0 0
\(216\) 0.809017 0.587785i 0.809017 0.587785i
\(217\) 0 0
\(218\) 0 0
\(219\) −1.00000 −1.00000
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(228\) 0 0
\(229\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −1.00000 −1.00000
\(233\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 0.809017 0.587785i 0.809017 0.587785i
\(247\) 0 0
\(248\) 0.309017 0.951057i 0.309017 0.951057i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000 1.00000
\(255\) 0 0
\(256\) 0 0
\(257\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(270\) 0 0
\(271\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(278\) −0.809017 0.587785i −0.809017 0.587785i
\(279\) 0 0
\(280\) 0 0
\(281\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(282\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(283\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.309017 0.951057i 0.309017 0.951057i
\(303\) 0.618034 1.90211i 0.618034 1.90211i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(312\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(313\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0.309017 0.951057i 0.309017 0.951057i
\(326\) 0.809017 0.587785i 0.809017 0.587785i
\(327\) 0 0
\(328\) −0.309017 0.951057i −0.309017 0.951057i
\(329\) 0 0
\(330\) 0 0
\(331\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.61803 1.17557i 1.61803 1.17557i
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(347\) −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i \(0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(348\) 0 0
\(349\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(350\) 0 0
\(351\) 1.00000 1.00000
\(352\) 0 0
\(353\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(354\) −0.618034 1.90211i −0.618034 1.90211i
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(359\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(360\) 0 0
\(361\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(368\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(377\) −0.809017 0.587785i −0.809017 0.587785i
\(378\) 0 0
\(379\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(380\) 0 0
\(381\) 0.809017 0.587785i 0.809017 0.587785i
\(382\) 0 0
\(383\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(384\) −1.00000 −1.00000
\(385\) 0 0
\(386\) 1.00000 1.00000
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.809017 0.587785i 0.809017 0.587785i
\(393\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(394\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.809017 0.587785i 0.809017 0.587785i
\(401\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(402\) 0 0
\(403\) 0.809017 0.587785i 0.809017 0.587785i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.00000 −1.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(422\) 1.61803 1.17557i 1.61803 1.17557i
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) −0.809017 0.587785i −0.809017 0.587785i
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(432\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(433\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) −0.309017 0.951057i −0.309017 0.951057i
\(439\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 0 0
\(443\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.618034 1.90211i 0.618034 1.90211i
\(447\) 0 0
\(448\) 0 0
\(449\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) −0.309017 0.951057i −0.309017 0.951057i
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(462\) 0 0
\(463\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(464\) −0.309017 0.951057i −0.309017 0.951057i
\(465\) 0 0
\(466\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(467\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −2.00000 −2.00000
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0.309017 0.951057i 0.309017 0.951057i
\(479\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(488\) 0 0
\(489\) 0.309017 0.951057i 0.309017 0.951057i
\(490\) 0 0
\(491\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.00000 1.00000
\(497\) 0 0
\(498\) 0 0
\(499\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(500\) 0 0
\(501\) 0.618034 1.90211i 0.618034 1.90211i
\(502\) 0 0
\(503\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.809017 + 0.587785i 0.809017 + 0.587785i 0.913545 0.406737i \(-0.133333\pi\)
−0.104528 + 0.994522i \(0.533333\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(513\) 0 0
\(514\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(520\) 0 0
\(521\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(522\) 0 0
\(523\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 1.00000 1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0.309017 0.951057i 0.309017 0.951057i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(538\) −1.00000 −1.00000
\(539\) 0 0
\(540\) 0 0
\(541\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(542\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(543\) 0 0
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(553\) 0 0
\(554\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(569\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) −0.809017 0.587785i −0.809017 0.587785i
\(576\) 0 0
\(577\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(578\) 0.309017 0.951057i 0.309017 0.951057i
\(579\) 0.809017 0.587785i 0.809017 0.587785i
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) −1.00000 −1.00000
\(585\) 0 0
\(586\) 0 0
\(587\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(592\) 0 0
\(593\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(599\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(600\) 0.309017 0.951057i 0.309017 0.951057i
\(601\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 2.00000 2.00000
\(607\) −0.618034 1.90211i −0.618034 1.90211i −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 0.951057i \(-0.600000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(612\) 0 0
\(613\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(614\) −0.618034 1.90211i −0.618034 1.90211i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) 0 0
\(621\) 0.309017 0.951057i 0.309017 0.951057i
\(622\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(623\) 0 0
\(624\) −0.809017 0.587785i −0.809017 0.587785i
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(632\) 0 0
\(633\) 0.618034 1.90211i 0.618034 1.90211i
\(634\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(635\) 0 0
\(636\) 0 0
\(637\) 1.00000 1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(648\) 1.00000 1.00000
\(649\) 0 0
\(650\) 1.00000 1.00000
\(651\) 0 0
\(652\) 0 0
\(653\) 0.809017 0.587785i 0.809017 0.587785i −0.104528 0.994522i \(-0.533333\pi\)
0.913545 + 0.406737i \(0.133333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0.809017 0.587785i 0.809017 0.587785i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(662\) −0.309017 0.951057i −0.309017 0.951057i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(668\) 0 0
\(669\) −0.618034 1.90211i −0.618034 1.90211i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(674\) 0 0
\(675\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(676\) 0 0
\(677\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −2.00000 −2.00000
\(695\) 0 0
\(696\) −0.809017 0.587785i −0.809017 0.587785i
\(697\) 0 0
\(698\) 0.309017 0.951057i 0.309017 0.951057i
\(699\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(700\) 0 0
\(701\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(702\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) −0.309017 0.951057i −0.309017 0.951057i
\(707\) 0 0
\(708\) 0 0
\(709\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −0.309017 0.951057i −0.309017 0.951057i
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.309017 0.951057i −0.309017 0.951057i
\(718\) 0 0
\(719\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(723\) 0 0
\(724\) 0 0
\(725\) 1.00000 1.00000
\(726\) 0 0
\(727\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(728\) 0 0
\(729\) −0.809017 0.587785i −0.809017 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(744\) 0.809017 0.587785i 0.809017 0.587785i
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(752\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(753\) 0 0
\(754\) 0.309017 0.951057i 0.309017 0.951057i
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.309017 + 0.951057i 0.309017 + 0.951057i 0.978148 + 0.207912i \(0.0666667\pi\)
−0.669131 + 0.743145i \(0.733333\pi\)
\(762\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) −1.61803 1.17557i −1.61803 1.17557i
\(768\) 0 0
\(769\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(770\) 0 0
\(771\) 1.00000 1.00000
\(772\) 0 0
\(773\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(774\) 0 0
\(775\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(784\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(785\) 0 0
\(786\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(787\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.309017 0.951057i −0.309017 0.951057i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(807\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(808\) 0.618034 1.90211i 0.618034 1.90211i
\(809\) −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i \(0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(810\) 0 0
\(811\) −0.809017 0.587785i −0.809017 0.587785i 0.104528 0.994522i \(-0.466667\pi\)
−0.913545 + 0.406737i \(0.866667\pi\)
\(812\) 0 0
\(813\) 2.00000 2.00000
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(819\) 0 0
\(820\) 0 0
\(821\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(822\) 0 0
\(823\) −0.309017 0.951057i −0.309017 0.951057i −0.978148 0.207912i \(-0.933333\pi\)
0.669131 0.743145i \(-0.266667\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(828\) 0 0
\(829\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(830\) 0 0
\(831\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(832\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(833\) 0 0
\(834\) −0.309017 0.951057i −0.309017 0.951057i
\(835\) 0 0
\(836\) 0 0
\(837\) −1.00000 −1.00000
\(838\) 0 0
\(839\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i \(0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(858\) 0 0
\(859\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) −0.309017 0.951057i −0.309017 0.951057i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 1.61803 + 1.17557i 1.61803 + 1.17557i 0.809017 + 0.587785i \(0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(878\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(887\) −0.809017 + 0.587785i −0.809017 + 0.587785i −0.913545 0.406737i \(-0.866667\pi\)
0.104528 + 0.994522i \(0.466667\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(898\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(899\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0.809017 0.587785i 0.809017 0.587785i
\(907\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(920\) 0 0
\(921\) −1.61803 1.17557i −1.61803 1.17557i
\(922\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(923\) −1.00000 −1.00000
\(924\) 0 0
\(925\) 0 0
\(926\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(927\) 0 0
\(928\) 0 0
\(929\) −0.309017 + 0.951057i −0.309017 + 0.951057i 0.669131 + 0.743145i \(0.266667\pi\)
−0.978148 + 0.207912i \(0.933333\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(942\) 0 0
\(943\) −0.809017 0.587785i −0.809017 0.587785i
\(944\) −0.618034 1.90211i −0.618034 1.90211i
\(945\) 0 0
\(946\) 0 0
\(947\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(948\) 0 0
\(949\) −0.809017 0.587785i −0.809017 0.587785i
\(950\) 0 0
\(951\) −0.618034 + 1.90211i −0.618034 + 1.90211i
\(952\) 0 0
\(953\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(975\) 0.809017 0.587785i 0.809017 0.587785i
\(976\) 0 0
\(977\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(978\) 1.00000 1.00000
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −0.809017 0.587785i −0.809017 0.587785i
\(983\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(984\) 0.309017 0.951057i 0.309017 0.951057i
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(992\) 0 0
\(993\) −0.809017 0.587785i −0.809017 0.587785i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(998\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(999\) 0 0
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 2783.1.f.a.390.1 4
11.2 odd 10 2783.1.f.c.735.1 4
11.3 even 5 2783.1.d.b.1816.1 1
11.4 even 5 inner 2783.1.f.a.850.1 4
11.5 even 5 inner 2783.1.f.a.2138.1 4
11.6 odd 10 2783.1.f.c.2138.1 4
11.7 odd 10 2783.1.f.c.850.1 4
11.8 odd 10 23.1.b.a.22.1 1
11.9 even 5 inner 2783.1.f.a.735.1 4
11.10 odd 2 2783.1.f.c.390.1 4
23.22 odd 2 CM 2783.1.f.a.390.1 4
33.8 even 10 207.1.d.a.91.1 1
44.19 even 10 368.1.f.a.321.1 1
55.8 even 20 575.1.c.a.574.2 2
55.19 odd 10 575.1.d.a.551.1 1
55.52 even 20 575.1.c.a.574.1 2
77.19 even 30 1127.1.f.a.459.1 2
77.30 odd 30 1127.1.f.b.459.1 2
77.41 even 10 1127.1.d.b.344.1 1
77.52 even 30 1127.1.f.a.275.1 2
77.74 odd 30 1127.1.f.b.275.1 2
88.19 even 10 1472.1.f.a.321.1 1
88.85 odd 10 1472.1.f.b.321.1 1
99.41 even 30 1863.1.f.a.298.1 2
99.52 odd 30 1863.1.f.b.919.1 2
99.74 even 30 1863.1.f.a.919.1 2
99.85 odd 30 1863.1.f.b.298.1 2
132.107 odd 10 3312.1.c.a.2161.1 1
143.8 even 20 3887.1.c.a.3886.1 2
143.19 even 60 3887.1.j.e.3403.2 4
143.30 odd 30 3887.1.h.a.3357.1 2
143.41 even 60 3887.1.j.e.2851.1 4
143.63 even 60 3887.1.j.e.2851.2 4
143.74 odd 30 3887.1.h.c.3357.1 2
143.85 even 60 3887.1.j.e.3403.1 4
143.96 even 20 3887.1.c.a.3886.2 2
143.107 odd 30 3887.1.h.c.22.1 2
143.129 odd 10 3887.1.d.b.2874.1 1
143.140 odd 30 3887.1.h.a.22.1 2
253.8 odd 110 529.1.d.a.28.1 10
253.19 even 110 529.1.d.a.352.1 10
253.30 even 110 529.1.d.a.411.1 10
253.41 odd 110 529.1.d.a.274.1 10
253.52 odd 110 529.1.d.a.263.1 10
253.63 even 110 529.1.d.a.263.1 10
253.68 even 10 2783.1.f.c.735.1 4
253.74 even 110 529.1.d.a.274.1 10
253.85 odd 110 529.1.d.a.411.1 10
253.91 odd 10 2783.1.d.b.1816.1 1
253.96 odd 110 529.1.d.a.352.1 10
253.107 even 110 529.1.d.a.28.1 10
253.114 odd 10 inner 2783.1.f.a.850.1 4
253.118 odd 110 529.1.d.a.359.1 10
253.129 even 110 529.1.d.a.195.1 10
253.137 odd 10 inner 2783.1.f.a.2138.1 4
253.140 odd 110 529.1.d.a.42.1 10
253.151 odd 110 529.1.d.a.130.1 10
253.160 even 10 2783.1.f.c.2138.1 4
253.173 odd 110 529.1.d.a.63.1 10
253.183 even 10 2783.1.f.c.850.1 4
253.195 even 110 529.1.d.a.63.1 10
253.206 even 10 23.1.b.a.22.1 1
253.217 even 110 529.1.d.a.130.1 10
253.228 even 110 529.1.d.a.42.1 10
253.229 odd 10 inner 2783.1.f.a.735.1 4
253.239 odd 110 529.1.d.a.195.1 10
253.250 even 110 529.1.d.a.359.1 10
253.252 even 2 2783.1.f.c.390.1 4
759.206 odd 10 207.1.d.a.91.1 1
1012.459 odd 10 368.1.f.a.321.1 1
1265.459 even 10 575.1.d.a.551.1 1
1265.712 odd 20 575.1.c.a.574.1 2
1265.1218 odd 20 575.1.c.a.574.2 2
1771.206 odd 30 1127.1.f.a.275.1 2
1771.459 even 30 1127.1.f.b.275.1 2
1771.712 odd 30 1127.1.f.a.459.1 2
1771.965 odd 10 1127.1.d.b.344.1 1
1771.1724 even 30 1127.1.f.b.459.1 2
2024.459 odd 10 1472.1.f.a.321.1 1
2024.965 even 10 1472.1.f.b.321.1 1
2277.965 odd 30 1863.1.f.a.919.1 2
2277.1471 even 30 1863.1.f.b.298.1 2
2277.1724 odd 30 1863.1.f.a.298.1 2
2277.2230 even 30 1863.1.f.b.919.1 2
3036.2483 even 10 3312.1.c.a.2161.1 1
3289.206 odd 60 3887.1.j.e.2851.2 4
3289.459 even 30 3887.1.h.a.3357.1 2
3289.712 even 30 3887.1.h.a.22.1 2
3289.965 even 30 3887.1.h.c.22.1 2
3289.1218 even 30 3887.1.h.c.3357.1 2
3289.1471 odd 60 3887.1.j.e.2851.1 4
3289.1724 odd 20 3887.1.c.a.3886.1 2
3289.2230 odd 60 3887.1.j.e.3403.1 4
3289.2736 odd 60 3887.1.j.e.3403.2 4
3289.2989 even 10 3887.1.d.b.2874.1 1
3289.3242 odd 20 3887.1.c.a.3886.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
23.1.b.a.22.1 1 11.8 odd 10
23.1.b.a.22.1 1 253.206 even 10
207.1.d.a.91.1 1 33.8 even 10
207.1.d.a.91.1 1 759.206 odd 10
368.1.f.a.321.1 1 44.19 even 10
368.1.f.a.321.1 1 1012.459 odd 10
529.1.d.a.28.1 10 253.8 odd 110
529.1.d.a.28.1 10 253.107 even 110
529.1.d.a.42.1 10 253.140 odd 110
529.1.d.a.42.1 10 253.228 even 110
529.1.d.a.63.1 10 253.173 odd 110
529.1.d.a.63.1 10 253.195 even 110
529.1.d.a.130.1 10 253.151 odd 110
529.1.d.a.130.1 10 253.217 even 110
529.1.d.a.195.1 10 253.129 even 110
529.1.d.a.195.1 10 253.239 odd 110
529.1.d.a.263.1 10 253.52 odd 110
529.1.d.a.263.1 10 253.63 even 110
529.1.d.a.274.1 10 253.41 odd 110
529.1.d.a.274.1 10 253.74 even 110
529.1.d.a.352.1 10 253.19 even 110
529.1.d.a.352.1 10 253.96 odd 110
529.1.d.a.359.1 10 253.118 odd 110
529.1.d.a.359.1 10 253.250 even 110
529.1.d.a.411.1 10 253.30 even 110
529.1.d.a.411.1 10 253.85 odd 110
575.1.c.a.574.1 2 55.52 even 20
575.1.c.a.574.1 2 1265.712 odd 20
575.1.c.a.574.2 2 55.8 even 20
575.1.c.a.574.2 2 1265.1218 odd 20
575.1.d.a.551.1 1 55.19 odd 10
575.1.d.a.551.1 1 1265.459 even 10
1127.1.d.b.344.1 1 77.41 even 10
1127.1.d.b.344.1 1 1771.965 odd 10
1127.1.f.a.275.1 2 77.52 even 30
1127.1.f.a.275.1 2 1771.206 odd 30
1127.1.f.a.459.1 2 77.19 even 30
1127.1.f.a.459.1 2 1771.712 odd 30
1127.1.f.b.275.1 2 77.74 odd 30
1127.1.f.b.275.1 2 1771.459 even 30
1127.1.f.b.459.1 2 77.30 odd 30
1127.1.f.b.459.1 2 1771.1724 even 30
1472.1.f.a.321.1 1 88.19 even 10
1472.1.f.a.321.1 1 2024.459 odd 10
1472.1.f.b.321.1 1 88.85 odd 10
1472.1.f.b.321.1 1 2024.965 even 10
1863.1.f.a.298.1 2 99.41 even 30
1863.1.f.a.298.1 2 2277.1724 odd 30
1863.1.f.a.919.1 2 99.74 even 30
1863.1.f.a.919.1 2 2277.965 odd 30
1863.1.f.b.298.1 2 99.85 odd 30
1863.1.f.b.298.1 2 2277.1471 even 30
1863.1.f.b.919.1 2 99.52 odd 30
1863.1.f.b.919.1 2 2277.2230 even 30
2783.1.d.b.1816.1 1 11.3 even 5
2783.1.d.b.1816.1 1 253.91 odd 10
2783.1.f.a.390.1 4 1.1 even 1 trivial
2783.1.f.a.390.1 4 23.22 odd 2 CM
2783.1.f.a.735.1 4 11.9 even 5 inner
2783.1.f.a.735.1 4 253.229 odd 10 inner
2783.1.f.a.850.1 4 11.4 even 5 inner
2783.1.f.a.850.1 4 253.114 odd 10 inner
2783.1.f.a.2138.1 4 11.5 even 5 inner
2783.1.f.a.2138.1 4 253.137 odd 10 inner
2783.1.f.c.390.1 4 11.10 odd 2
2783.1.f.c.390.1 4 253.252 even 2
2783.1.f.c.735.1 4 11.2 odd 10
2783.1.f.c.735.1 4 253.68 even 10
2783.1.f.c.850.1 4 11.7 odd 10
2783.1.f.c.850.1 4 253.183 even 10
2783.1.f.c.2138.1 4 11.6 odd 10
2783.1.f.c.2138.1 4 253.160 even 10
3312.1.c.a.2161.1 1 132.107 odd 10
3312.1.c.a.2161.1 1 3036.2483 even 10
3887.1.c.a.3886.1 2 143.8 even 20
3887.1.c.a.3886.1 2 3289.1724 odd 20
3887.1.c.a.3886.2 2 143.96 even 20
3887.1.c.a.3886.2 2 3289.3242 odd 20
3887.1.d.b.2874.1 1 143.129 odd 10
3887.1.d.b.2874.1 1 3289.2989 even 10
3887.1.h.a.22.1 2 143.140 odd 30
3887.1.h.a.22.1 2 3289.712 even 30
3887.1.h.a.3357.1 2 143.30 odd 30
3887.1.h.a.3357.1 2 3289.459 even 30
3887.1.h.c.22.1 2 143.107 odd 30
3887.1.h.c.22.1 2 3289.965 even 30
3887.1.h.c.3357.1 2 143.74 odd 30
3887.1.h.c.3357.1 2 3289.1218 even 30
3887.1.j.e.2851.1 4 143.41 even 60
3887.1.j.e.2851.1 4 3289.1471 odd 60
3887.1.j.e.2851.2 4 143.63 even 60
3887.1.j.e.2851.2 4 3289.206 odd 60
3887.1.j.e.3403.1 4 143.85 even 60
3887.1.j.e.3403.1 4 3289.2230 odd 60
3887.1.j.e.3403.2 4 143.19 even 60
3887.1.j.e.3403.2 4 3289.2736 odd 60