Properties

Label 775.1.w.a.681.1
Level $775$
Weight $1$
Character 775.681
Analytic conductor $0.387$
Analytic rank $0$
Dimension $4$
Projective image $D_{5}$
CM discriminant -31
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [775,1,Mod(61,775)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(775, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([8, 5]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("775.61");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 775 = 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 775.w (of order \(10\), degree \(4\), 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: \(0.386775384791\)
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: yes
Projective image: \(D_{5}\)
Projective field: Galois closure of 5.1.375390625.1

Embedding invariants

Embedding label 681.1
Root \(0.809017 - 0.587785i\) of defining polynomial
Character \(\chi\) \(=\) 775.681
Dual form 775.1.w.a.371.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.190983 + 0.587785i) q^{2} +(0.500000 - 0.363271i) q^{4} +(0.309017 - 0.951057i) q^{5} -1.61803 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +O(q^{10})\) \(q+(0.190983 + 0.587785i) q^{2} +(0.500000 - 0.363271i) q^{4} +(0.309017 - 0.951057i) q^{5} -1.61803 q^{7} +(0.809017 + 0.587785i) q^{8} +(0.309017 - 0.951057i) q^{9} +0.618034 q^{10} +(-0.309017 - 0.951057i) q^{14} +0.618034 q^{18} +(1.30902 + 0.951057i) q^{19} +(-0.190983 - 0.587785i) q^{20} +(-0.809017 - 0.587785i) q^{25} +(-0.809017 + 0.587785i) q^{28} +(-0.809017 - 0.587785i) q^{31} +1.00000 q^{32} +(-0.500000 + 1.53884i) q^{35} +(-0.190983 - 0.587785i) q^{36} +(-0.309017 + 0.951057i) q^{38} +(0.809017 - 0.587785i) q^{40} +(-0.500000 + 1.53884i) q^{41} +(-0.809017 - 0.587785i) q^{45} +(-0.500000 + 0.363271i) q^{47} +1.61803 q^{49} +(0.190983 - 0.587785i) q^{50} +(-1.30902 - 0.951057i) q^{56} +(-0.500000 + 1.53884i) q^{59} +(0.190983 - 0.587785i) q^{62} +(-0.500000 + 1.53884i) q^{63} +(0.190983 + 0.587785i) q^{64} +(1.30902 + 0.951057i) q^{67} -1.00000 q^{70} +(-1.61803 + 1.17557i) q^{71} +(0.809017 - 0.587785i) q^{72} +1.00000 q^{76} +(-0.809017 - 0.587785i) q^{81} -1.00000 q^{82} +(0.190983 - 0.587785i) q^{90} +(-0.309017 - 0.224514i) q^{94} +(1.30902 - 0.951057i) q^{95} +(-0.500000 + 0.363271i) q^{97} +(0.309017 + 0.951057i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 3 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 3 q^{2} + 2 q^{4} - q^{5} - 2 q^{7} + q^{8} - q^{9} - 2 q^{10} + q^{14} - 2 q^{18} + 3 q^{19} - 3 q^{20} - q^{25} - q^{28} - q^{31} + 4 q^{32} - 2 q^{35} - 3 q^{36} + q^{38} + q^{40} - 2 q^{41} - q^{45} - 2 q^{47} + 2 q^{49} + 3 q^{50} - 3 q^{56} - 2 q^{59} + 3 q^{62} - 2 q^{63} + 3 q^{64} + 3 q^{67} - 4 q^{70} - 2 q^{71} + q^{72} + 4 q^{76} - q^{81} - 4 q^{82} + 3 q^{90} + q^{94} + 3 q^{95} - 2 q^{97} - q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).

\(n\) \(251\) \(652\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(3\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(4\) 0.500000 0.363271i 0.500000 0.363271i
\(5\) 0.309017 0.951057i 0.309017 0.951057i
\(6\) 0 0
\(7\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(8\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(9\) 0.309017 0.951057i 0.309017 0.951057i
\(10\) 0.618034 0.618034
\(11\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(12\) 0 0
\(13\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(14\) −0.309017 0.951057i −0.309017 0.951057i
\(15\) 0 0
\(16\) 0 0
\(17\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(18\) 0.618034 0.618034
\(19\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(20\) −0.190983 0.587785i −0.190983 0.587785i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(24\) 0 0
\(25\) −0.809017 0.587785i −0.809017 0.587785i
\(26\) 0 0
\(27\) 0 0
\(28\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(29\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(30\) 0 0
\(31\) −0.809017 0.587785i −0.809017 0.587785i
\(32\) 1.00000 1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(36\) −0.190983 0.587785i −0.190983 0.587785i
\(37\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(38\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(39\) 0 0
\(40\) 0.809017 0.587785i 0.809017 0.587785i
\(41\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) 0 0
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) −0.809017 0.587785i −0.809017 0.587785i
\(46\) 0 0
\(47\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) 0 0
\(49\) 1.61803 1.61803
\(50\) 0.190983 0.587785i 0.190983 0.587785i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.30902 0.951057i −1.30902 0.951057i
\(57\) 0 0
\(58\) 0 0
\(59\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(60\) 0 0
\(61\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(62\) 0.190983 0.587785i 0.190983 0.587785i
\(63\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(64\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(65\) 0 0
\(66\) 0 0
\(67\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) −1.00000 −1.00000
\(71\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(72\) 0.809017 0.587785i 0.809017 0.587785i
\(73\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 1.00000 1.00000
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(80\) 0 0
\(81\) −0.809017 0.587785i −0.809017 0.587785i
\(82\) −1.00000 −1.00000
\(83\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(90\) 0.190983 0.587785i 0.190983 0.587785i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −0.309017 0.224514i −0.309017 0.224514i
\(95\) 1.30902 0.951057i 1.30902 0.951057i
\(96\) 0 0
\(97\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(99\) 0 0
\(100\) −0.618034 −0.618034
\(101\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(102\) 0 0
\(103\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(104\) 0 0
\(105\) 0 0
\(106\) 0 0
\(107\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(108\) 0 0
\(109\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −1.00000 −1.00000
\(119\) 0 0
\(120\) 0 0
\(121\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.618034 −0.618034
\(125\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(126\) −1.00000 −1.00000
\(127\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(128\) 0.500000 0.363271i 0.500000 0.363271i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(132\) 0 0
\(133\) −2.11803 1.53884i −2.11803 1.53884i
\(134\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(135\) 0 0
\(136\) 0 0
\(137\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(138\) 0 0
\(139\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(140\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(141\) 0 0
\(142\) −1.00000 0.726543i −1.00000 0.726543i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) 0 0
\(148\) 0 0
\(149\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(150\) 0 0
\(151\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(152\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(153\) 0 0
\(154\) 0 0
\(155\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(156\) 0 0
\(157\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.309017 0.951057i 0.309017 0.951057i
\(161\) 0 0
\(162\) 0.190983 0.587785i 0.190983 0.587785i
\(163\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(164\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(168\) 0 0
\(169\) −0.809017 0.587785i −0.809017 0.587785i
\(170\) 0 0
\(171\) 1.30902 0.951057i 1.30902 0.951057i
\(172\) 0 0
\(173\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(174\) 0 0
\(175\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(176\) 0 0
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(180\) −0.618034 −0.618034
\(181\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(189\) 0 0
\(190\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(191\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(192\) 0 0
\(193\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(194\) −0.309017 0.224514i −0.309017 0.224514i
\(195\) 0 0
\(196\) 0.809017 0.587785i 0.809017 0.587785i
\(197\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(198\) 0 0
\(199\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) −0.309017 0.951057i −0.309017 0.951057i
\(201\) 0 0
\(202\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(203\) 0 0
\(204\) 0 0
\(205\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(206\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(207\) 0 0
\(208\) 0 0
\(209\) 0 0
\(210\) 0 0
\(211\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −0.309017 0.951057i −0.309017 0.951057i
\(215\) 0 0
\(216\) 0 0
\(217\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(218\) 1.23607 1.23607
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(224\) −1.61803 −1.61803
\(225\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(226\) 0.381966 0.381966
\(227\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(228\) 0 0
\(229\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(234\) 0 0
\(235\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(236\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(240\) 0 0
\(241\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(242\) −0.500000 0.363271i −0.500000 0.363271i
\(243\) 0 0
\(244\) 0 0
\(245\) 0.500000 1.53884i 0.500000 1.53884i
\(246\) 0 0
\(247\) 0 0
\(248\) −0.309017 0.951057i −0.309017 0.951057i
\(249\) 0 0
\(250\) −0.500000 0.363271i −0.500000 0.363271i
\(251\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(252\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(257\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 0.118034 0.363271i 0.118034 0.363271i
\(263\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0.500000 1.53884i 0.500000 1.53884i
\(267\) 0 0
\(268\) 1.00000 1.00000
\(269\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(270\) 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
\(276\) 0 0
\(277\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(278\) 0 0
\(279\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(280\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(281\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(282\) 0 0
\(283\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(284\) −0.381966 + 1.17557i −0.381966 + 1.17557i
\(285\) 0 0
\(286\) 0 0
\(287\) 0.809017 2.48990i 0.809017 2.48990i
\(288\) 0.309017 0.951057i 0.309017 0.951057i
\(289\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(294\) 0 0
\(295\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(296\) 0 0
\(297\) 0 0
\(298\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −0.500000 0.363271i −0.500000 0.363271i
\(311\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(312\) 0 0
\(313\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(314\) −0.309017 0.951057i −0.309017 0.951057i
\(315\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(316\) 0 0
\(317\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.618034 0.618034
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.618034 −0.618034
\(325\) 0 0
\(326\) 1.23607 1.23607
\(327\) 0 0
\(328\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(329\) 0.809017 0.587785i 0.809017 0.587785i
\(330\) 0 0
\(331\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 1.30902 0.951057i 1.30902 0.951057i
\(336\) 0 0
\(337\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(338\) 0.190983 0.587785i 0.190983 0.587785i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(347\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(348\) 0 0
\(349\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(350\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(354\) 0 0
\(355\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(360\) −0.309017 0.951057i −0.309017 0.951057i
\(361\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(362\) 0 0
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(368\) 0 0
\(369\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −0.618034 −0.618034
\(377\) 0 0
\(378\) 0 0
\(379\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(380\) 0.309017 0.951057i 0.309017 0.951057i
\(381\) 0 0
\(382\) 1.23607 1.23607
\(383\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 0.381966 + 1.17557i 0.381966 + 1.17557i
\(387\) 0 0
\(388\) −0.118034 + 0.363271i −0.118034 + 0.363271i
\(389\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) 0.309017 0.224514i 0.309017 0.224514i
\(405\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(410\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(411\) 0 0
\(412\) 0.309017 0.951057i 0.309017 0.951057i
\(413\) 0.809017 2.48990i 0.809017 2.48990i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(420\) 0 0
\(421\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(422\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(423\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(429\) 0 0
\(430\) 0 0
\(431\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(432\) 0 0
\(433\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(434\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(435\) 0 0
\(436\) −0.381966 1.17557i −0.381966 1.17557i
\(437\) 0 0
\(438\) 0 0
\(439\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(440\) 0 0
\(441\) 0.500000 1.53884i 0.500000 1.53884i
\(442\) 0 0
\(443\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) −0.309017 0.951057i −0.309017 0.951057i
\(449\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(450\) −0.500000 0.363271i −0.500000 0.363271i
\(451\) 0 0
\(452\) −0.118034 0.363271i −0.118034 0.363271i
\(453\) 0 0
\(454\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(462\) 0 0
\(463\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(467\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(468\) 0 0
\(469\) −2.11803 1.53884i −2.11803 1.53884i
\(470\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(471\) 0 0
\(472\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(473\) 0 0
\(474\) 0 0
\(475\) −0.500000 1.53884i −0.500000 1.53884i
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0 0
\(484\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(485\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(486\) 0 0
\(487\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 1.00000 1.00000
\(491\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 2.61803 1.90211i 2.61803 1.90211i
\(498\) 0 0
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(501\) 0 0
\(502\) 0 0
\(503\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(504\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(505\) 0.190983 0.587785i 0.190983 0.587785i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0 0
\(513\) 0 0
\(514\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(515\) −0.500000 1.53884i −0.500000 1.53884i
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(522\) 0 0
\(523\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(524\) −0.381966 −0.381966
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(530\) 0 0
\(531\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(532\) −1.61803 −1.61803
\(533\) 0 0
\(534\) 0 0
\(535\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(536\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(537\) 0 0
\(538\) 0 0
\(539\) 0 0
\(540\) 0 0
\(541\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0 0
\(545\) −1.61803 1.17557i −1.61803 1.17557i
\(546\) 0 0
\(547\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) −0.500000 0.363271i −0.500000 0.363271i
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 0.381966 1.17557i 0.381966 1.17557i
\(563\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(564\) 0 0
\(565\) −0.500000 0.363271i −0.500000 0.363271i
\(566\) 0.381966 1.17557i 0.381966 1.17557i
\(567\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(568\) −2.00000 −2.00000
\(569\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(570\) 0 0
\(571\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 1.61803 1.61803
\(575\) 0 0
\(576\) 0.618034 0.618034
\(577\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(578\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) −0.309017 0.951057i −0.309017 0.951057i
\(587\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(588\) 0 0
\(589\) −0.500000 1.53884i −0.500000 1.53884i
\(590\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(591\) 0 0
\(592\) 0 0
\(593\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0.309017 0.224514i 0.309017 0.224514i
\(597\) 0 0
\(598\) 0 0
\(599\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 1.30902 0.951057i 1.30902 0.951057i
\(604\) 0 0
\(605\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(606\) 0 0
\(607\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(608\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(614\) 0.118034 + 0.363271i 0.118034 + 0.363271i
\(615\) 0 0
\(616\) 0 0
\(617\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(618\) 0 0
\(619\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(620\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(621\) 0 0
\(622\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(623\) 0 0
\(624\) 0 0
\(625\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(626\) 0 0
\(627\) 0 0
\(628\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(629\) 0 0
\(630\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(631\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0.118034 0.363271i 0.118034 0.363271i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0.618034 + 1.90211i 0.618034 + 1.90211i
\(640\) −0.190983 0.587785i −0.190983 0.587785i
\(641\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(648\) −0.309017 0.951057i −0.309017 0.951057i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) −0.381966 1.17557i −0.381966 1.17557i
\(653\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(654\) 0 0
\(655\) −0.500000 + 0.363271i −0.500000 + 0.363271i
\(656\) 0 0
\(657\) 0 0
\(658\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(659\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(660\) 0 0
\(661\) 0.618034 + 1.90211i 0.618034 + 1.90211i 0.309017 + 0.951057i \(0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(671\) 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 0
\(676\) −0.618034 −0.618034
\(677\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(678\) 0 0
\(679\) 0.809017 0.587785i 0.809017 0.587785i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(684\) 0.309017 0.951057i 0.309017 0.951057i
\(685\) 0 0
\(686\) −0.190983 0.587785i −0.190983 0.587785i
\(687\) 0 0
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.190983 0.587785i 0.190983 0.587785i −0.809017 0.587785i \(-0.800000\pi\)
1.00000 \(0\)
\(692\) 1.00000 + 0.726543i 1.00000 + 0.726543i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.309017 0.951057i −0.309017 0.951057i
\(699\) 0 0
\(700\) 1.00000 1.00000
\(701\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) −1.00000 −1.00000
\(708\) 0 0
\(709\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(710\) −1.00000 + 0.726543i −1.00000 + 0.726543i
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0.381966 0.381966
\(719\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(720\) 0 0
\(721\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(722\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0 0
\(727\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(728\) 0 0
\(729\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(739\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0.190983 0.587785i 0.190983 0.587785i
\(746\) 0.809017 0.587785i 0.809017 0.587785i
\(747\) 0 0
\(748\) 0 0
\(749\) 2.61803 2.61803
\(750\) 0 0
\(751\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(759\) 0 0
\(760\) 1.61803 1.61803
\(761\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(762\) 0 0
\(763\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(764\) −0.381966 1.17557i −0.381966 1.17557i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 1.00000 0.726543i 1.00000 0.726543i
\(773\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(774\) 0 0
\(775\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(776\) −0.618034 −0.618034
\(777\) 0 0
\(778\) 0 0
\(779\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(786\) 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
\(791\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(792\) 0 0
\(793\) 0 0
\(794\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.809017 0.587785i −0.809017 0.587785i
\(801\) 0 0
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(809\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(810\) −0.500000 0.363271i −0.500000 0.363271i
\(811\) −0.500000 1.53884i −0.500000 1.53884i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) −1.61803 1.17557i −1.61803 1.17557i
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) 0 0
\(820\) 1.00000 1.00000
\(821\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(822\) 0 0
\(823\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(824\) 1.61803 1.61803
\(825\) 0 0
\(826\) 1.61803 1.61803
\(827\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(828\) 0 0
\(829\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0.118034 0.363271i 0.118034 0.363271i
\(839\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(840\) 0 0
\(841\) 0.309017 0.951057i 0.309017 0.951057i
\(842\) −0.309017 0.224514i −0.309017 0.224514i
\(843\) 0 0
\(844\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(845\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(846\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(847\) 1.30902 0.951057i 1.30902 0.951057i
\(848\) 0 0
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(854\) 0 0
\(855\) −0.500000 1.53884i −0.500000 1.53884i
\(856\) −1.30902 0.951057i −1.30902 0.951057i
\(857\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(858\) 0 0
\(859\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(863\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(864\) 0 0
\(865\) 2.00000 2.00000
\(866\) 0 0
\(867\) 0 0
\(868\) 1.00000 1.00000
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.61803 1.17557i 1.61803 1.17557i
\(873\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(874\) 0 0
\(875\) 1.30902 0.951057i 1.30902 0.951057i
\(876\) 0 0
\(877\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(878\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(882\) 1.00000 1.00000
\(883\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −0.309017 0.951057i −0.309017 0.951057i
\(887\) 0.618034 1.90211i 0.618034 1.90211i 0.309017 0.951057i \(-0.400000\pi\)
0.309017 0.951057i \(-0.400000\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) −1.00000 −1.00000
\(894\) 0 0
\(895\) 0 0
\(896\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0.500000 0.363271i 0.500000 0.363271i
\(905\) 0 0
\(906\) 0 0
\(907\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(908\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(909\) 0.190983 0.587785i 0.190983 0.587785i
\(910\) 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
\(917\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(918\) 0 0
\(919\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) −0.500000 1.53884i −0.500000 1.53884i
\(928\) 0 0
\(929\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(930\) 0 0
\(931\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(932\) 1.00000 1.00000
\(933\) 0 0
\(934\) 0.381966 1.17557i 0.381966 1.17557i
\(935\) 0 0
\(936\) 0 0
\(937\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(938\) 0.500000 1.53884i 0.500000 1.53884i
\(939\) 0 0
\(940\) 0.309017 + 0.224514i 0.309017 + 0.224514i
\(941\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0.809017 0.587785i 0.809017 0.587785i
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(954\) 0 0
\(955\) −1.61803 1.17557i −1.61803 1.17557i
\(956\) 0 0
\(957\) 0 0
\(958\) −0.309017 0.224514i −0.309017 0.224514i
\(959\) 0 0
\(960\) 0 0
\(961\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(962\) 0 0
\(963\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(964\) 0 0
\(965\) 0.618034 1.90211i 0.618034 1.90211i
\(966\) 0 0
\(967\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) −0.309017 + 0.224514i −0.309017 + 0.224514i
\(971\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(972\) 0 0
\(973\) 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
\(981\) −1.61803 1.17557i −1.61803 1.17557i
\(982\) 0 0
\(983\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(992\) −0.809017 0.587785i −0.809017 0.587785i
\(993\) 0 0
\(994\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(995\) 0 0
\(996\) 0 0
\(997\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(998\) 0 0
\(999\) 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 775.1.w.a.681.1 yes 4
5.2 odd 4 3875.1.z.c.3099.1 8
5.3 odd 4 3875.1.z.c.3099.2 8
5.4 even 2 3875.1.w.a.526.1 4
25.3 odd 20 3875.1.z.c.774.1 8
25.4 even 10 3875.1.w.a.2851.1 4
25.21 even 5 inner 775.1.w.a.371.1 4
25.22 odd 20 3875.1.z.c.774.2 8
31.30 odd 2 CM 775.1.w.a.681.1 yes 4
155.92 even 4 3875.1.z.c.3099.1 8
155.123 even 4 3875.1.z.c.3099.2 8
155.154 odd 2 3875.1.w.a.526.1 4
775.154 odd 10 3875.1.w.a.2851.1 4
775.247 even 20 3875.1.z.c.774.2 8
775.278 even 20 3875.1.z.c.774.1 8
775.371 odd 10 inner 775.1.w.a.371.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
775.1.w.a.371.1 4 25.21 even 5 inner
775.1.w.a.371.1 4 775.371 odd 10 inner
775.1.w.a.681.1 yes 4 1.1 even 1 trivial
775.1.w.a.681.1 yes 4 31.30 odd 2 CM
3875.1.w.a.526.1 4 5.4 even 2
3875.1.w.a.526.1 4 155.154 odd 2
3875.1.w.a.2851.1 4 25.4 even 10
3875.1.w.a.2851.1 4 775.154 odd 10
3875.1.z.c.774.1 8 25.3 odd 20
3875.1.z.c.774.1 8 775.278 even 20
3875.1.z.c.774.2 8 25.22 odd 20
3875.1.z.c.774.2 8 775.247 even 20
3875.1.z.c.3099.1 8 5.2 odd 4
3875.1.z.c.3099.1 8 155.92 even 4
3875.1.z.c.3099.2 8 5.3 odd 4
3875.1.z.c.3099.2 8 155.123 even 4