Properties

Label 3025.1.bc.a.766.1
Level $3025$
Weight $1$
Character 3025.766
Analytic conductor $1.510$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -11
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3025,1,Mod(596,3025)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3025, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([6, 1]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3025.596");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3025 = 5^{2} \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3025.bc (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: \(1.50967166321\)
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: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 275)
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.47265625.1

Embedding invariants

Embedding label 766.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 3025.766
Dual form 3025.1.bc.a.1086.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q-1.61803 q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{5} +1.61803 q^{9} +O(q^{10})\) \(q-1.61803 q^{3} +(-0.809017 + 0.587785i) q^{4} +(-0.809017 + 0.587785i) q^{5} +1.61803 q^{9} +(1.30902 - 0.951057i) q^{12} +(1.30902 - 0.951057i) q^{15} +(0.309017 - 0.951057i) q^{16} +(0.309017 - 0.951057i) q^{20} +(-0.500000 - 0.363271i) q^{23} +(0.309017 - 0.951057i) q^{25} -1.00000 q^{27} +(1.30902 - 0.951057i) q^{31} +(-1.30902 + 0.951057i) q^{36} +(-1.61803 - 1.17557i) q^{37} +(-1.30902 + 0.951057i) q^{45} +2.00000 q^{47} +(-0.500000 + 1.53884i) q^{48} +(-0.809017 + 0.587785i) q^{49} +(-0.500000 + 1.53884i) q^{53} +(1.30902 + 0.951057i) q^{59} +(-0.500000 + 1.53884i) q^{60} +(0.309017 + 0.951057i) q^{64} +(0.190983 - 0.587785i) q^{67} +(0.809017 + 0.587785i) q^{69} +(1.30902 + 0.951057i) q^{71} +(-0.500000 + 1.53884i) q^{75} +(0.309017 + 0.951057i) q^{80} +(-0.500000 - 0.363271i) q^{89} +0.618034 q^{92} +(-2.11803 + 1.53884i) q^{93} +(-0.500000 + 1.53884i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{3} - q^{4} - q^{5} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{3} - q^{4} - q^{5} + 2 q^{9} + 3 q^{12} + 3 q^{15} - q^{16} - q^{20} - 2 q^{23} - q^{25} - 4 q^{27} + 3 q^{31} - 3 q^{36} - 2 q^{37} - 3 q^{45} + 8 q^{47} - 2 q^{48} - q^{49} - 2 q^{53} + 3 q^{59} - 2 q^{60} - q^{64} + 3 q^{67} + q^{69} + 3 q^{71} - 2 q^{75} - q^{80} - 2 q^{89} - 2 q^{92} - 4 q^{93} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3025\mathbb{Z}\right)^\times\).

\(n\) \(727\) \(2301\)
\(\chi(n)\) \(e\left(\frac{1}{5}\right)\) \(e\left(\frac{7}{10}\right)\)

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 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(3\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(5\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(6\) 0 0
\(7\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(8\) 0 0
\(9\) 1.61803 1.61803
\(10\) 0 0
\(11\) 0 0
\(12\) 1.30902 0.951057i 1.30902 0.951057i
\(13\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(14\) 0 0
\(15\) 1.30902 0.951057i 1.30902 0.951057i
\(16\) 0.309017 0.951057i 0.309017 0.951057i
\(17\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(18\) 0 0
\(19\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(20\) 0.309017 0.951057i 0.309017 0.951057i
\(21\) 0 0
\(22\) 0 0
\(23\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) 0 0
\(25\) 0.309017 0.951057i 0.309017 0.951057i
\(26\) 0 0
\(27\) −1.00000 −1.00000
\(28\) 0 0
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(32\) 0 0
\(33\) 0 0
\(34\) 0 0
\(35\) 0 0
\(36\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(37\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0 0
\(41\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(46\) 0 0
\(47\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(48\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(49\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(50\) 0 0
\(51\) 0 0
\(52\) 0 0
\(53\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0 0
\(59\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(60\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(61\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(65\) 0 0
\(66\) 0 0
\(67\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(68\) 0 0
\(69\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(70\) 0 0
\(71\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(72\) 0 0
\(73\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(74\) 0 0
\(75\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(80\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(81\) 0 0
\(82\) 0 0
\(83\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.618034 0.618034
\(93\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(101\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(102\) 0 0
\(103\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(108\) 0.809017 0.587785i 0.809017 0.587785i
\(109\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(110\) 0 0
\(111\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(112\) 0 0
\(113\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(114\) 0 0
\(115\) 0.618034 0.618034
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(125\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(126\) 0 0
\(127\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(128\) 0 0
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0.809017 0.587785i 0.809017 0.587785i
\(136\) 0 0
\(137\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(138\) 0 0
\(139\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(140\) 0 0
\(141\) −3.23607 −3.23607
\(142\) 0 0
\(143\) 0 0
\(144\) 0.500000 1.53884i 0.500000 1.53884i
\(145\) 0 0
\(146\) 0 0
\(147\) 1.30902 0.951057i 1.30902 0.951057i
\(148\) 2.00000 2.00000
\(149\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(150\) 0 0
\(151\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(156\) 0 0
\(157\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(158\) 0 0
\(159\) 0.809017 2.48990i 0.809017 2.48990i
\(160\) 0 0
\(161\) 0 0
\(162\) 0 0
\(163\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(168\) 0 0
\(169\) 1.00000 1.00000
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) −2.11803 1.53884i −2.11803 1.53884i
\(178\) 0 0
\(179\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) 0.500000 1.53884i 0.500000 1.53884i
\(181\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 2.00000 2.00000
\(186\) 0 0
\(187\) 0 0
\(188\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(189\) 0 0
\(190\) 0 0
\(191\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(192\) −0.500000 1.53884i −0.500000 1.53884i
\(193\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.309017 0.951057i 0.309017 0.951057i
\(197\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(198\) 0 0
\(199\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(200\) 0 0
\(201\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) −0.809017 0.587785i −0.809017 0.587785i
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(212\) −0.500000 1.53884i −0.500000 1.53884i
\(213\) −2.11803 1.53884i −2.11803 1.53884i
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(224\) 0 0
\(225\) 0.500000 1.53884i 0.500000 1.53884i
\(226\) 0 0
\(227\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(228\) 0 0
\(229\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 0 0
\(235\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(236\) −1.61803 −1.61803
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) −0.500000 1.53884i −0.500000 1.53884i
\(241\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(242\) 0 0
\(243\) 1.00000 1.00000
\(244\) 0 0
\(245\) 0.309017 0.951057i 0.309017 0.951057i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) −0.809017 0.587785i −0.809017 0.587785i
\(257\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0 0
\(263\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(264\) 0 0
\(265\) −0.500000 1.53884i −0.500000 1.53884i
\(266\) 0 0
\(267\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(268\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(269\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(270\) 0 0
\(271\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −1.00000 −1.00000
\(277\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) 0 0
\(279\) 2.11803 1.53884i 2.11803 1.53884i
\(280\) 0 0
\(281\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(282\) 0 0
\(283\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(284\) −1.61803 −1.61803
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 0 0
\(289\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(290\) 0 0
\(291\) 0.809017 2.48990i 0.809017 2.48990i
\(292\) 0 0
\(293\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(294\) 0 0
\(295\) −1.61803 −1.61803
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 0 0
\(300\) −0.500000 1.53884i −0.500000 1.53884i
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0.809017 0.587785i 0.809017 0.587785i
\(310\) 0 0
\(311\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(312\) 0 0
\(313\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0 0
\(317\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(318\) 0 0
\(319\) 0 0
\(320\) −0.809017 0.587785i −0.809017 0.587785i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0 0
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(332\) 0 0
\(333\) −2.61803 1.90211i −2.61803 1.90211i
\(334\) 0 0
\(335\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(336\) 0 0
\(337\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(338\) 0 0
\(339\) −0.309017 0.951057i −0.309017 0.951057i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) −1.00000 −1.00000
\(346\) 0 0
\(347\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(348\) 0 0
\(349\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(354\) 0 0
\(355\) −1.61803 −1.61803
\(356\) 0.618034 0.618034
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(360\) 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
\(367\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(368\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0.809017 2.48990i 0.809017 2.48990i
\(373\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(374\) 0 0
\(375\) −0.500000 1.53884i −0.500000 1.53884i
\(376\) 0 0
\(377\) 0 0
\(378\) 0 0
\(379\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) −0.500000 1.53884i −0.500000 1.53884i
\(389\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.809017 0.587785i −0.809017 0.587785i
\(401\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(412\) 0.190983 0.587785i 0.190983 0.587785i
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(422\) 0 0
\(423\) 3.23607 3.23607
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(433\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(440\) 0 0
\(441\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(442\) 0 0
\(443\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) −3.23607 −3.23607
\(445\) 0.618034 0.618034
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) −0.500000 0.363271i −0.500000 0.363271i
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(461\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(462\) 0 0
\(463\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(464\) 0 0
\(465\) 0.809017 2.48990i 0.809017 2.48990i
\(466\) 0 0
\(467\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(478\) 0 0
\(479\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) 0 0
\(485\) −0.500000 1.53884i −0.500000 1.53884i
\(486\) 0 0
\(487\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(488\) 0 0
\(489\) 2.61803 2.61803
\(490\) 0 0
\(491\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) −0.500000 1.53884i −0.500000 1.53884i
\(497\) 0 0
\(498\) 0 0
\(499\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(500\) −0.809017 0.587785i −0.809017 0.587785i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) −1.61803 −1.61803
\(508\) 0 0
\(509\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0 0
\(515\) 0.190983 0.587785i 0.190983 0.587785i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.190983 0.587785i −0.190983 0.587785i
\(530\) 0 0
\(531\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) −1.00000 −1.00000
\(538\) 0 0
\(539\) 0 0
\(540\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(541\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) −1.00000 3.07768i −1.00000 3.07768i
\(544\) 0 0
\(545\) 0 0
\(546\) 0 0
\(547\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(548\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) −3.23607 −3.23607
\(556\) 0 0
\(557\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0 0
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 2.61803 1.90211i 2.61803 1.90211i
\(565\) −0.500000 0.363271i −0.500000 0.363271i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(572\) 0 0
\(573\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(574\) 0 0
\(575\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(576\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(577\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(588\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.00000 −1.00000
\(598\) 0 0
\(599\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(600\) 0 0
\(601\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(602\) 0 0
\(603\) 0.309017 0.951057i 0.309017 0.951057i
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(618\) 0 0
\(619\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(620\) −0.500000 1.53884i −0.500000 1.53884i
\(621\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.809017 0.587785i −0.809017 0.587785i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(629\) 0 0
\(630\) 0 0
\(631\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) 0 0
\(636\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(637\) 0 0
\(638\) 0 0
\(639\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(640\) 0 0
\(641\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(642\) 0 0
\(643\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(648\) 0 0
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.30902 0.951057i 1.30902 0.951057i
\(653\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(660\) 0 0
\(661\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 0 0
\(675\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(676\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(684\) 0 0
\(685\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(686\) 0 0
\(687\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 2.61803 1.90211i 2.61803 1.90211i
\(706\) 0 0
\(707\) 0 0
\(708\) 2.61803 2.61803
\(709\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) −1.00000 −1.00000
\(714\) 0 0
\(715\) 0 0
\(716\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(717\) 0 0
\(718\) 0 0
\(719\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(720\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(721\) 0 0
\(722\) 0 0
\(723\) 0 0
\(724\) −1.61803 1.17557i −1.61803 1.17557i
\(725\) 0 0
\(726\) 0 0
\(727\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(728\) 0 0
\(729\) −1.61803 −1.61803
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 0 0
\(735\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(752\) 0.618034 1.90211i 0.618034 1.90211i
\(753\) −2.11803 1.53884i −2.11803 1.53884i
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0.618034 0.618034
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(769\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(770\) 0 0
\(771\) −0.309017 0.951057i −0.309017 0.951057i
\(772\) 0 0
\(773\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(774\) 0 0
\(775\) −0.500000 1.53884i −0.500000 1.53884i
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(785\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(786\) 0 0
\(787\) 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 0
\(795\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(796\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(797\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) −0.809017 0.587785i −0.809017 0.587785i
\(802\) 0 0
\(803\) 0 0
\(804\) −0.309017 0.951057i −0.309017 0.951057i
\(805\) 0 0
\(806\) 0 0
\(807\) −0.309017 0.951057i −0.309017 0.951057i
\(808\) 0 0
\(809\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(810\) 0 0
\(811\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 1.30902 0.951057i 1.30902 0.951057i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(822\) 0 0
\(823\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(828\) 1.00000 1.00000
\(829\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(838\) 0 0
\(839\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(840\) 0 0
\(841\) 0.309017 0.951057i 0.309017 0.951057i
\(842\) 0 0
\(843\) 0 0
\(844\) 0 0
\(845\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(846\) 0 0
\(847\) 0 0
\(848\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(849\) 0 0
\(850\) 0 0
\(851\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(852\) 2.61803 2.61803
\(853\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 0 0
\(867\) 1.30902 0.951057i 1.30902 0.951057i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(882\) 0 0
\(883\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(884\) 0 0
\(885\) 2.61803 2.61803
\(886\) 0 0
\(887\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(893\) 0 0
\(894\) 0 0
\(895\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) −1.61803 1.17557i −1.61803 1.17557i
\(906\) 0 0
\(907\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) −1.61803 + 1.17557i −1.61803 + 1.17557i
\(926\) 0 0
\(927\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(928\) 0 0
\(929\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0.809017 0.587785i 0.809017 0.587785i
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(938\) 0 0
\(939\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(940\) 0.618034 1.90211i 0.618034 1.90211i
\(941\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 1.30902 0.951057i 1.30902 0.951057i
\(945\) 0 0
\(946\) 0 0
\(947\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(952\) 0 0
\(953\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(954\) 0 0
\(955\) 0.618034 0.618034
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(961\) 0.500000 1.53884i 0.500000 1.53884i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0 0
\(967\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(972\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(981\) 0 0
\(982\) 0 0
\(983\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(992\) 0 0
\(993\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(994\) 0 0
\(995\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(996\) 0 0
\(997\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(998\) 0 0
\(999\) 1.61803 + 1.17557i 1.61803 + 1.17557i
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 3025.1.bc.a.766.1 4
11.2 odd 10 3025.1.w.a.941.1 4
11.3 even 5 3025.1.m.a.1691.1 4
11.4 even 5 3025.1.u.a.3016.1 4
11.5 even 5 275.1.v.a.241.1 yes 4
11.6 odd 10 275.1.v.a.241.1 yes 4
11.7 odd 10 3025.1.u.a.3016.1 4
11.8 odd 10 3025.1.m.a.1691.1 4
11.9 even 5 3025.1.w.a.941.1 4
11.10 odd 2 CM 3025.1.bc.a.766.1 4
25.11 even 5 3025.1.m.a.161.1 4
33.5 odd 10 2475.1.bu.a.1891.1 4
33.17 even 10 2475.1.bu.a.1891.1 4
55.17 even 20 1375.1.s.b.549.1 8
55.27 odd 20 1375.1.s.b.549.1 8
55.28 even 20 1375.1.s.b.549.2 8
55.38 odd 20 1375.1.s.b.549.2 8
55.39 odd 10 1375.1.v.a.76.1 4
55.49 even 10 1375.1.v.a.76.1 4
275.27 odd 20 1375.1.s.b.824.2 8
275.36 even 5 inner 3025.1.bc.a.1086.1 4
275.39 odd 10 1375.1.v.a.1176.1 4
275.61 odd 10 275.1.v.a.186.1 4
275.86 even 5 3025.1.u.a.336.1 4
275.127 even 20 1375.1.s.b.824.2 8
275.136 even 5 3025.1.w.a.2411.1 4
275.148 odd 20 1375.1.s.b.824.1 8
275.161 odd 10 3025.1.w.a.2411.1 4
275.186 odd 10 3025.1.m.a.161.1 4
275.211 odd 10 3025.1.u.a.336.1 4
275.214 even 10 1375.1.v.a.1176.1 4
275.236 even 5 275.1.v.a.186.1 4
275.248 even 20 1375.1.s.b.824.1 8
275.261 odd 10 inner 3025.1.bc.a.1086.1 4
825.236 odd 10 2475.1.bu.a.2386.1 4
825.611 even 10 2475.1.bu.a.2386.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
275.1.v.a.186.1 4 275.61 odd 10
275.1.v.a.186.1 4 275.236 even 5
275.1.v.a.241.1 yes 4 11.5 even 5
275.1.v.a.241.1 yes 4 11.6 odd 10
1375.1.s.b.549.1 8 55.17 even 20
1375.1.s.b.549.1 8 55.27 odd 20
1375.1.s.b.549.2 8 55.28 even 20
1375.1.s.b.549.2 8 55.38 odd 20
1375.1.s.b.824.1 8 275.148 odd 20
1375.1.s.b.824.1 8 275.248 even 20
1375.1.s.b.824.2 8 275.27 odd 20
1375.1.s.b.824.2 8 275.127 even 20
1375.1.v.a.76.1 4 55.39 odd 10
1375.1.v.a.76.1 4 55.49 even 10
1375.1.v.a.1176.1 4 275.39 odd 10
1375.1.v.a.1176.1 4 275.214 even 10
2475.1.bu.a.1891.1 4 33.5 odd 10
2475.1.bu.a.1891.1 4 33.17 even 10
2475.1.bu.a.2386.1 4 825.236 odd 10
2475.1.bu.a.2386.1 4 825.611 even 10
3025.1.m.a.161.1 4 25.11 even 5
3025.1.m.a.161.1 4 275.186 odd 10
3025.1.m.a.1691.1 4 11.3 even 5
3025.1.m.a.1691.1 4 11.8 odd 10
3025.1.u.a.336.1 4 275.86 even 5
3025.1.u.a.336.1 4 275.211 odd 10
3025.1.u.a.3016.1 4 11.4 even 5
3025.1.u.a.3016.1 4 11.7 odd 10
3025.1.w.a.941.1 4 11.2 odd 10
3025.1.w.a.941.1 4 11.9 even 5
3025.1.w.a.2411.1 4 275.136 even 5
3025.1.w.a.2411.1 4 275.161 odd 10
3025.1.bc.a.766.1 4 1.1 even 1 trivial
3025.1.bc.a.766.1 4 11.10 odd 2 CM
3025.1.bc.a.1086.1 4 275.36 even 5 inner
3025.1.bc.a.1086.1 4 275.261 odd 10 inner