Properties

Label 1400.1.bs.c.741.1
Level $1400$
Weight $1$
Character 1400.741
Analytic conductor $0.699$
Analytic rank $0$
Dimension $8$
Projective image $D_{10}$
CM discriminant -56
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [1400,1,Mod(181,1400)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(1400, base_ring=CyclotomicField(10))
 
chi = DirichletCharacter(H, H._module([0, 5, 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("1400.181");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 1400.bs (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: \(0.698691017686\)
Analytic rank: \(0\)
Dimension: \(8\)
Relative dimension: \(2\) over \(\Q(\zeta_{10})\)
Coefficient field: \(\Q(\zeta_{20})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{10}\)
Projective field: Galois closure of 10.0.10504375000000000000.2

Embedding invariants

Embedding label 741.1
Root \(0.951057 - 0.309017i\) of defining polynomial
Character \(\chi\) \(=\) 1400.741
Dual form 1400.1.bs.c.461.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.587785 - 1.80902i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(0.587785 - 1.80902i) q^{6} -1.00000 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.11803 + 1.53884i) q^{9} +O(q^{10})\) \(q+(0.809017 + 0.587785i) q^{2} +(-0.587785 - 1.80902i) q^{3} +(0.309017 + 0.951057i) q^{4} +(-0.587785 + 0.809017i) q^{5} +(0.587785 - 1.80902i) q^{6} -1.00000 q^{7} +(-0.309017 + 0.951057i) q^{8} +(-2.11803 + 1.53884i) q^{9} +(-0.951057 + 0.309017i) q^{10} +(1.53884 - 1.11803i) q^{12} +(-1.53884 + 1.11803i) q^{13} +(-0.809017 - 0.587785i) q^{14} +(1.80902 + 0.587785i) q^{15} +(-0.809017 + 0.587785i) q^{16} -2.61803 q^{18} +(-0.951057 - 0.309017i) q^{20} +(0.587785 + 1.80902i) q^{21} +(-0.500000 - 0.363271i) q^{23} +1.90211 q^{24} +(-0.309017 - 0.951057i) q^{25} -1.90211 q^{26} +(2.48990 + 1.80902i) q^{27} +(-0.309017 - 0.951057i) q^{28} +(1.11803 + 1.53884i) q^{30} -1.00000 q^{32} +(0.587785 - 0.809017i) q^{35} +(-2.11803 - 1.53884i) q^{36} +(2.92705 + 2.12663i) q^{39} +(-0.587785 - 0.809017i) q^{40} +(-0.587785 + 1.80902i) q^{42} -2.61803i q^{45} +(-0.190983 - 0.587785i) q^{46} +(1.53884 + 1.11803i) q^{48} +1.00000 q^{49} +(0.309017 - 0.951057i) q^{50} +(-1.53884 - 1.11803i) q^{52} +(0.951057 + 2.92705i) q^{54} +(0.309017 - 0.951057i) q^{56} +(-0.951057 + 0.690983i) q^{59} +1.90211i q^{60} +(0.951057 + 0.690983i) q^{61} +(2.11803 - 1.53884i) q^{63} +(-0.809017 - 0.587785i) q^{64} -1.90211i q^{65} +(-0.363271 + 1.11803i) q^{69} +(0.951057 - 0.309017i) q^{70} +(0.500000 + 1.53884i) q^{71} +(-0.809017 - 2.48990i) q^{72} +(-1.53884 + 1.11803i) q^{75} +(1.11803 + 3.44095i) q^{78} +(-0.190983 - 0.587785i) q^{79} -1.00000i q^{80} +(1.00000 - 3.07768i) q^{81} +(0.363271 - 1.11803i) q^{83} +(-1.53884 + 1.11803i) q^{84} +(1.53884 - 2.11803i) q^{90} +(1.53884 - 1.11803i) q^{91} +(0.190983 - 0.587785i) q^{92} +(0.587785 + 1.80902i) q^{96} +(0.809017 + 0.587785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 8 q + 2 q^{2} - 2 q^{4} - 8 q^{7} + 2 q^{8} - 8 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 8 q + 2 q^{2} - 2 q^{4} - 8 q^{7} + 2 q^{8} - 8 q^{9} - 2 q^{14} + 10 q^{15} - 2 q^{16} - 12 q^{18} - 4 q^{23} + 2 q^{25} + 2 q^{28} - 8 q^{32} - 8 q^{36} + 10 q^{39} - 6 q^{46} + 8 q^{49} - 2 q^{50} - 2 q^{56} + 8 q^{63} - 2 q^{64} + 4 q^{71} - 2 q^{72} - 6 q^{79} + 8 q^{81} + 6 q^{92} + 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times\).

\(n\) \(351\) \(701\) \(801\) \(1177\)
\(\chi(n)\) \(1\) \(-1\) \(-1\) \(e\left(\frac{1}{5}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(3\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(4\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(5\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(6\) 0.587785 1.80902i 0.587785 1.80902i
\(7\) −1.00000 −1.00000
\(8\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(9\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(10\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(11\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(12\) 1.53884 1.11803i 1.53884 1.11803i
\(13\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(14\) −0.809017 0.587785i −0.809017 0.587785i
\(15\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(16\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(17\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(18\) −2.61803 −2.61803
\(19\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(20\) −0.951057 0.309017i −0.951057 0.309017i
\(21\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(22\) 0 0
\(23\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(24\) 1.90211 1.90211
\(25\) −0.309017 0.951057i −0.309017 0.951057i
\(26\) −1.90211 −1.90211
\(27\) 2.48990 + 1.80902i 2.48990 + 1.80902i
\(28\) −0.309017 0.951057i −0.309017 0.951057i
\(29\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(30\) 1.11803 + 1.53884i 1.11803 + 1.53884i
\(31\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(32\) −1.00000 −1.00000
\(33\) 0 0
\(34\) 0 0
\(35\) 0.587785 0.809017i 0.587785 0.809017i
\(36\) −2.11803 1.53884i −2.11803 1.53884i
\(37\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(38\) 0 0
\(39\) 2.92705 + 2.12663i 2.92705 + 2.12663i
\(40\) −0.587785 0.809017i −0.587785 0.809017i
\(41\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(42\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(43\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(44\) 0 0
\(45\) 2.61803i 2.61803i
\(46\) −0.190983 0.587785i −0.190983 0.587785i
\(47\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(48\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(49\) 1.00000 1.00000
\(50\) 0.309017 0.951057i 0.309017 0.951057i
\(51\) 0 0
\(52\) −1.53884 1.11803i −1.53884 1.11803i
\(53\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(54\) 0.951057 + 2.92705i 0.951057 + 2.92705i
\(55\) 0 0
\(56\) 0.309017 0.951057i 0.309017 0.951057i
\(57\) 0 0
\(58\) 0 0
\(59\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(60\) 1.90211i 1.90211i
\(61\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(62\) 0 0
\(63\) 2.11803 1.53884i 2.11803 1.53884i
\(64\) −0.809017 0.587785i −0.809017 0.587785i
\(65\) 1.90211i 1.90211i
\(66\) 0 0
\(67\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(68\) 0 0
\(69\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(70\) 0.951057 0.309017i 0.951057 0.309017i
\(71\) 0.500000 + 1.53884i 0.500000 + 1.53884i 0.809017 + 0.587785i \(0.200000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(72\) −0.809017 2.48990i −0.809017 2.48990i
\(73\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(74\) 0 0
\(75\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(76\) 0 0
\(77\) 0 0
\(78\) 1.11803 + 3.44095i 1.11803 + 3.44095i
\(79\) −0.190983 0.587785i −0.190983 0.587785i 0.809017 0.587785i \(-0.200000\pi\)
−1.00000 \(\pi\)
\(80\) 1.00000i 1.00000i
\(81\) 1.00000 3.07768i 1.00000 3.07768i
\(82\) 0 0
\(83\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(84\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(90\) 1.53884 2.11803i 1.53884 2.11803i
\(91\) 1.53884 1.11803i 1.53884 1.11803i
\(92\) 0.190983 0.587785i 0.190983 0.587785i
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(97\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(98\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(99\) 0 0
\(100\) 0.809017 0.587785i 0.809017 0.587785i
\(101\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(102\) 0 0
\(103\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(104\) −0.587785 1.80902i −0.587785 1.80902i
\(105\) −1.80902 0.587785i −1.80902 0.587785i
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) −0.951057 + 2.92705i −0.951057 + 2.92705i
\(109\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.809017 0.587785i 0.809017 0.587785i
\(113\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(114\) 0 0
\(115\) 0.587785 0.190983i 0.587785 0.190983i
\(116\) 0 0
\(117\) 1.53884 4.73607i 1.53884 4.73607i
\(118\) −1.17557 −1.17557
\(119\) 0 0
\(120\) −1.11803 + 1.53884i −1.11803 + 1.53884i
\(121\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(122\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(126\) 2.61803 2.61803
\(127\) −1.61803 1.17557i −1.61803 1.17557i −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 0.587785i \(-0.800000\pi\)
\(128\) −0.309017 0.951057i −0.309017 0.951057i
\(129\) 0 0
\(130\) 1.11803 1.53884i 1.11803 1.53884i
\(131\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −2.92705 + 0.951057i −2.92705 + 0.951057i
\(136\) 0 0
\(137\) −1.61803 + 1.17557i −1.61803 + 1.17557i −0.809017 + 0.587785i \(0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(138\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(139\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(140\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(141\) 0 0
\(142\) −0.500000 + 1.53884i −0.500000 + 1.53884i
\(143\) 0 0
\(144\) 0.809017 2.48990i 0.809017 2.48990i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.587785 1.80902i −0.587785 1.80902i
\(148\) 0 0
\(149\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(150\) −1.90211 −1.90211
\(151\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) −1.11803 + 3.44095i −1.11803 + 3.44095i
\(157\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(158\) 0.190983 0.587785i 0.190983 0.587785i
\(159\) 0 0
\(160\) 0.587785 0.809017i 0.587785 0.809017i
\(161\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(162\) 2.61803 1.90211i 2.61803 1.90211i
\(163\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.951057 0.690983i 0.951057 0.690983i
\(167\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(168\) −1.90211 −1.90211
\(169\) 0.809017 2.48990i 0.809017 2.48990i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(174\) 0 0
\(175\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(176\) 0 0
\(177\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(178\) 0 0
\(179\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(180\) 2.48990 0.809017i 2.48990 0.809017i
\(181\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(182\) 1.90211 1.90211
\(183\) 0.690983 2.12663i 0.690983 2.12663i
\(184\) 0.500000 0.363271i 0.500000 0.363271i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −2.48990 1.80902i −2.48990 1.80902i
\(190\) 0 0
\(191\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(192\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(193\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(194\) 0 0
\(195\) −3.44095 + 1.11803i −3.44095 + 1.11803i
\(196\) 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 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(200\) 1.00000 1.00000
\(201\) 0 0
\(202\) −1.53884 1.11803i −1.53884 1.11803i
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 1.61803 1.61803
\(208\) 0.587785 1.80902i 0.587785 1.80902i
\(209\) 0 0
\(210\) −1.11803 1.53884i −1.11803 1.53884i
\(211\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(212\) 0 0
\(213\) 2.48990 1.80902i 2.48990 1.80902i
\(214\) 0 0
\(215\) 0 0
\(216\) −2.48990 + 1.80902i −2.48990 + 1.80902i
\(217\) 0 0
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(224\) 1.00000 1.00000
\(225\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(226\) −1.61803 −1.61803
\(227\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(228\) 0 0
\(229\) 0.363271 + 1.11803i 0.363271 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(230\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(231\) 0 0
\(232\) 0 0
\(233\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(234\) 4.02874 2.92705i 4.02874 2.92705i
\(235\) 0 0
\(236\) −0.951057 0.690983i −0.951057 0.690983i
\(237\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(238\) 0 0
\(239\) −0.500000 0.363271i −0.500000 0.363271i 0.309017 0.951057i \(-0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(240\) −1.80902 + 0.587785i −1.80902 + 0.587785i
\(241\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(242\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(243\) −3.07768 −3.07768
\(244\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(245\) −0.587785 + 0.809017i −0.587785 + 0.809017i
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) −2.23607 −2.23607
\(250\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(251\) −1.17557 −1.17557 −0.587785 0.809017i \(-0.700000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(252\) 2.11803 + 1.53884i 2.11803 + 1.53884i
\(253\) 0 0
\(254\) −0.618034 1.90211i −0.618034 1.90211i
\(255\) 0 0
\(256\) 0.309017 0.951057i 0.309017 0.951057i
\(257\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.80902 0.587785i 1.80902 0.587785i
\(261\) 0 0
\(262\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(263\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(270\) −2.92705 0.951057i −2.92705 0.951057i
\(271\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(272\) 0 0
\(273\) −2.92705 2.12663i −2.92705 2.12663i
\(274\) −2.00000 −2.00000
\(275\) 0 0
\(276\) −1.17557 −1.17557
\(277\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.587785 + 0.809017i 0.587785 + 0.809017i
\(281\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(282\) 0 0
\(283\) −0.587785 + 1.80902i −0.587785 + 1.80902i 1.00000i \(0.5\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(284\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) 2.11803 1.53884i 2.11803 1.53884i
\(289\) −0.809017 0.587785i −0.809017 0.587785i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(294\) 0.587785 1.80902i 0.587785 1.80902i
\(295\) 1.17557i 1.17557i
\(296\) 0 0
\(297\) 0 0
\(298\) 0 0
\(299\) 1.17557 1.17557
\(300\) −1.53884 1.11803i −1.53884 1.11803i
\(301\) 0 0
\(302\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(303\) 1.11803 + 3.44095i 1.11803 + 3.44095i
\(304\) 0 0
\(305\) −1.11803 + 0.363271i −1.11803 + 0.363271i
\(306\) 0 0
\(307\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(312\) −2.92705 + 2.12663i −2.92705 + 2.12663i
\(313\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(314\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(315\) 2.61803i 2.61803i
\(316\) 0.500000 0.363271i 0.500000 0.363271i
\(317\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.951057 0.309017i 0.951057 0.309017i
\(321\) 0 0
\(322\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(323\) 0 0
\(324\) 3.23607 3.23607
\(325\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(326\) 0 0
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(332\) 1.17557 1.17557
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) −1.53884 1.11803i −1.53884 1.11803i
\(337\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(338\) 2.11803 1.53884i 2.11803 1.53884i
\(339\) 2.48990 + 1.80902i 2.48990 + 1.80902i
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) −0.690983 0.951057i −0.690983 0.951057i
\(346\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(347\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(348\) 0 0
\(349\) −1.90211 −1.90211 −0.951057 0.309017i \(-0.900000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(350\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(351\) −5.85410 −5.85410
\(352\) 0 0
\(353\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(354\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(355\) −1.53884 0.500000i −1.53884 0.500000i
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.500000 + 0.363271i −0.500000 + 0.363271i −0.809017 0.587785i \(-0.800000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(360\) 2.48990 + 0.809017i 2.48990 + 0.809017i
\(361\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(362\) 0.951057 0.690983i 0.951057 0.690983i
\(363\) 1.53884 1.11803i 1.53884 1.11803i
\(364\) 1.53884 + 1.11803i 1.53884 + 1.11803i
\(365\) 0 0
\(366\) 1.80902 1.31433i 1.80902 1.31433i
\(367\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(368\) 0.618034 0.618034
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(374\) 0 0
\(375\) 1.90211i 1.90211i
\(376\) 0 0
\(377\) 0 0
\(378\) −0.951057 2.92705i −0.951057 2.92705i
\(379\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(380\) 0 0
\(381\) −1.17557 + 3.61803i −1.17557 + 3.61803i
\(382\) 0.618034 0.618034
\(383\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(384\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(385\) 0 0
\(386\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(390\) −3.44095 1.11803i −3.44095 1.11803i
\(391\) 0 0
\(392\) −0.309017 + 0.951057i −0.309017 + 0.951057i
\(393\) 2.23607 2.23607
\(394\) 0 0
\(395\) 0.587785 + 0.190983i 0.587785 + 0.190983i
\(396\) 0 0
\(397\) 0.587785 + 1.80902i 0.587785 + 1.80902i 0.587785 + 0.809017i \(0.300000\pi\)
1.00000i \(0.5\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(401\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.587785 1.80902i −0.587785 1.80902i
\(405\) 1.90211 + 2.61803i 1.90211 + 2.61803i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(410\) 0 0
\(411\) 3.07768 + 2.23607i 3.07768 + 2.23607i
\(412\) 0 0
\(413\) 0.951057 0.690983i 0.951057 0.690983i
\(414\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(415\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(416\) 1.53884 1.11803i 1.53884 1.11803i
\(417\) 0 0
\(418\) 0 0
\(419\) 0.587785 1.80902i 0.587785 1.80902i 1.00000i \(-0.5\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(420\) 1.90211i 1.90211i
\(421\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0 0
\(425\) 0 0
\(426\) 3.07768 3.07768
\(427\) −0.951057 0.690983i −0.951057 0.690983i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(432\) −3.07768 −3.07768
\(433\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(434\) 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
\(441\) −2.11803 + 1.53884i −2.11803 + 1.53884i
\(442\) 0 0
\(443\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0 0
\(448\) 0.809017 + 0.587785i 0.809017 + 0.587785i
\(449\) 0.618034 0.618034 0.309017 0.951057i \(-0.400000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(450\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(451\) 0 0
\(452\) −1.30902 0.951057i −1.30902 0.951057i
\(453\) −0.363271 1.11803i −0.363271 1.11803i
\(454\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(455\) 1.90211i 1.90211i
\(456\) 0 0
\(457\) 1.61803 1.61803 0.809017 0.587785i \(-0.200000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(458\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(459\) 0 0
\(460\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(461\) 0 0 0.587785 0.809017i \(-0.300000\pi\)
−0.587785 + 0.809017i \(0.700000\pi\)
\(462\) 0 0
\(463\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(467\) 0 0 −0.951057 0.309017i \(-0.900000\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(468\) 4.97980 4.97980
\(469\) 0 0
\(470\) 0 0
\(471\) −0.690983 2.12663i −0.690983 2.12663i
\(472\) −0.363271 1.11803i −0.363271 1.11803i
\(473\) 0 0
\(474\) −1.17557 −1.17557
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) −0.190983 0.587785i −0.190983 0.587785i
\(479\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(480\) −1.80902 0.587785i −1.80902 0.587785i
\(481\) 0 0
\(482\) 0 0
\(483\) 0.363271 1.11803i 0.363271 1.11803i
\(484\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(485\) 0 0
\(486\) −2.48990 1.80902i −2.48990 1.80902i
\(487\) 1.30902 0.951057i 1.30902 0.951057i 0.309017 0.951057i \(-0.400000\pi\)
1.00000 \(0\)
\(488\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(489\) 0 0
\(490\) −0.951057 + 0.309017i −0.951057 + 0.309017i
\(491\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) −0.500000 1.53884i −0.500000 1.53884i
\(498\) −1.80902 1.31433i −1.80902 1.31433i
\(499\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(500\) 1.00000i 1.00000i
\(501\) 0 0
\(502\) −0.951057 0.690983i −0.951057 0.690983i
\(503\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(504\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(505\) 1.11803 1.53884i 1.11803 1.53884i
\(506\) 0 0
\(507\) −4.97980 −4.97980
\(508\) 0.618034 1.90211i 0.618034 1.90211i
\(509\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.809017 0.587785i 0.809017 0.587785i
\(513\) 0 0
\(514\) 0 0
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0.690983 2.12663i 0.690983 2.12663i
\(520\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(521\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(522\) 0 0
\(523\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(524\) −1.17557 −1.17557
\(525\) 1.53884 1.11803i 1.53884 1.11803i
\(526\) 0.618034 0.618034
\(527\) 0 0
\(528\) 0 0
\(529\) −0.190983 0.587785i −0.190983 0.587785i
\(530\) 0 0
\(531\) 0.951057 2.92705i 0.951057 2.92705i
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0.951057 0.690983i 0.951057 0.690983i
\(539\) 0 0
\(540\) −1.80902 2.48990i −1.80902 2.48990i
\(541\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(542\) 0 0
\(543\) −2.23607 −2.23607
\(544\) 0 0
\(545\) 0 0
\(546\) −1.11803 3.44095i −1.11803 3.44095i
\(547\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(548\) −1.61803 1.17557i −1.61803 1.17557i
\(549\) −3.07768 −3.07768
\(550\) 0 0
\(551\) 0 0
\(552\) −0.951057 0.690983i −0.951057 0.690983i
\(553\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 1.00000i 1.00000i
\(561\) 0 0
\(562\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(563\) −1.53884 + 1.11803i −1.53884 + 1.11803i −0.587785 + 0.809017i \(0.700000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(564\) 0 0
\(565\) 1.61803i 1.61803i
\(566\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(567\) −1.00000 + 3.07768i −1.00000 + 3.07768i
\(568\) −1.61803 −1.61803
\(569\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(570\) 0 0
\(571\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(572\) 0 0
\(573\) −0.951057 0.690983i −0.951057 0.690983i
\(574\) 0 0
\(575\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(576\) 2.61803 2.61803
\(577\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(578\) −0.309017 0.951057i −0.309017 0.951057i
\(579\) −0.951057 2.92705i −0.951057 2.92705i
\(580\) 0 0
\(581\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 2.92705 + 4.02874i 2.92705 + 4.02874i
\(586\) 0 0
\(587\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(588\) 1.53884 1.11803i 1.53884 1.11803i
\(589\) 0 0
\(590\) 0.690983 0.951057i 0.690983 0.951057i
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) 0 0
\(598\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(599\) −0.618034 −0.618034 −0.309017 0.951057i \(-0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(600\) −0.587785 1.80902i −0.587785 1.80902i
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0.190983 + 0.587785i 0.190983 + 0.587785i
\(605\) −0.951057 0.309017i −0.951057 0.309017i
\(606\) −1.11803 + 3.44095i −1.11803 + 3.44095i
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −1.11803 0.363271i −1.11803 0.363271i
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) −0.190983 + 0.587785i −0.190983 + 0.587785i 0.809017 + 0.587785i \(0.200000\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0.363271 1.11803i 0.363271 1.11803i −0.587785 0.809017i \(-0.700000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(620\) 0 0
\(621\) −0.587785 1.80902i −0.587785 1.80902i
\(622\) 0 0
\(623\) 0 0
\(624\) −3.61803 −3.61803
\(625\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.363271 + 1.11803i 0.363271 + 1.11803i
\(629\) 0 0
\(630\) −1.53884 + 2.11803i −1.53884 + 2.11803i
\(631\) 0.500000 1.53884i 0.500000 1.53884i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(632\) 0.618034 0.618034
\(633\) 0 0
\(634\) 0 0
\(635\) 1.90211 0.618034i 1.90211 0.618034i
\(636\) 0 0
\(637\) −1.53884 + 1.11803i −1.53884 + 1.11803i
\(638\) 0 0
\(639\) −3.42705 2.48990i −3.42705 2.48990i
\(640\) 0.951057 + 0.309017i 0.951057 + 0.309017i
\(641\) 0.500000 0.363271i 0.500000 0.363271i −0.309017 0.951057i \(-0.600000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(642\) 0 0
\(643\) 1.17557 1.17557 0.587785 0.809017i \(-0.300000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(644\) −0.190983 + 0.587785i −0.190983 + 0.587785i
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(648\) 2.61803 + 1.90211i 2.61803 + 1.90211i
\(649\) 0 0
\(650\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(654\) 0 0
\(655\) −0.690983 0.951057i −0.690983 0.951057i
\(656\) 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
\(661\) 0.951057 + 0.690983i 0.951057 + 0.690983i 0.951057 0.309017i \(-0.100000\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.951057 + 0.690983i 0.951057 + 0.690983i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) −0.587785 1.80902i −0.587785 1.80902i
\(673\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(674\) 0.618034 0.618034
\(675\) 0.951057 2.92705i 0.951057 2.92705i
\(676\) 2.61803 2.61803
\(677\) −0.951057 0.690983i −0.951057 0.690983i 1.00000i \(-0.5\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(678\) 0.951057 + 2.92705i 0.951057 + 2.92705i
\(679\) 0 0
\(680\) 0 0
\(681\) 1.11803 3.44095i 1.11803 3.44095i
\(682\) 0 0
\(683\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(684\) 0 0
\(685\) 2.00000i 2.00000i
\(686\) −0.809017 0.587785i −0.809017 0.587785i
\(687\) 1.80902 1.31433i 1.80902 1.31433i
\(688\) 0 0
\(689\) 0 0
\(690\) 1.17557i 1.17557i
\(691\) 1.53884 1.11803i 1.53884 1.11803i 0.587785 0.809017i \(-0.300000\pi\)
0.951057 0.309017i \(-0.100000\pi\)
\(692\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.53884 1.11803i −1.53884 1.11803i
\(699\) 3.07768 3.07768
\(700\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(701\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(702\) −4.73607 3.44095i −4.73607 3.44095i
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0 0
\(707\) 1.90211 1.90211
\(708\) −0.690983 + 2.12663i −0.690983 + 2.12663i
\(709\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(710\) −0.951057 1.30902i −0.951057 1.30902i
\(711\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) −0.363271 + 1.11803i −0.363271 + 1.11803i
\(718\) −0.618034 −0.618034
\(719\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(720\) 1.53884 + 2.11803i 1.53884 + 2.11803i
\(721\) 0 0
\(722\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(723\) 0 0
\(724\) 1.17557 1.17557
\(725\) 0 0
\(726\) 1.90211 1.90211
\(727\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(728\) 0.587785 + 1.80902i 0.587785 + 1.80902i
\(729\) 0.809017 + 2.48990i 0.809017 + 2.48990i
\(730\) 0 0
\(731\) 0 0
\(732\) 2.23607 2.23607
\(733\) −0.363271 + 1.11803i −0.363271 + 1.11803i 0.587785 + 0.809017i \(0.300000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(734\) 0 0
\(735\) 1.80902 + 0.587785i 1.80902 + 0.587785i
\(736\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −1.61803 −1.61803 −0.809017 0.587785i \(-0.800000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0.951057 + 2.92705i 0.951057 + 2.92705i
\(748\) 0 0
\(749\) 0 0
\(750\) 1.11803 1.53884i 1.11803 1.53884i
\(751\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(752\) 0 0
\(753\) 0.690983 + 2.12663i 0.690983 + 2.12663i
\(754\) 0 0
\(755\) −0.363271 + 0.500000i −0.363271 + 0.500000i
\(756\) 0.951057 2.92705i 0.951057 2.92705i
\(757\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(762\) −3.07768 + 2.23607i −3.07768 + 2.23607i
\(763\) 0 0
\(764\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(765\) 0 0
\(766\) 0 0
\(767\) 0.690983 2.12663i 0.690983 2.12663i
\(768\) −1.90211 −1.90211
\(769\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(773\) 1.53884 + 1.11803i 1.53884 + 1.11803i 0.951057 + 0.309017i \(0.100000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) −2.12663 2.92705i −2.12663 2.92705i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(785\) −0.690983 + 0.951057i −0.690983 + 0.951057i
\(786\) 1.80902 + 1.31433i 1.80902 + 1.31433i
\(787\) 0 0 −0.587785 0.809017i \(-0.700000\pi\)
0.587785 + 0.809017i \(0.300000\pi\)
\(788\) 0 0
\(789\) −0.951057 0.690983i −0.951057 0.690983i
\(790\) 0.363271 + 0.500000i 0.363271 + 0.500000i
\(791\) 1.30902 0.951057i 1.30902 0.951057i
\(792\) 0 0
\(793\) −2.23607 −2.23607
\(794\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(795\) 0 0
\(796\) 0 0
\(797\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(801\) 0 0
\(802\) −1.61803 1.17557i −1.61803 1.17557i
\(803\) 0 0
\(804\) 0 0
\(805\) −0.587785 + 0.190983i −0.587785 + 0.190983i
\(806\) 0 0
\(807\) −2.23607 −2.23607
\(808\) 0.587785 1.80902i 0.587785 1.80902i
\(809\) 1.61803 1.17557i 1.61803 1.17557i 0.809017 0.587785i \(-0.200000\pi\)
0.809017 0.587785i \(-0.200000\pi\)
\(810\) 3.23607i 3.23607i
\(811\) −1.53884 1.11803i −1.53884 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
−0.587785 0.809017i \(-0.700000\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) 0 0
\(819\) −1.53884 + 4.73607i −1.53884 + 4.73607i
\(820\) 0 0
\(821\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(822\) 1.17557 + 3.61803i 1.17557 + 3.61803i
\(823\) −1.30902 0.951057i −1.30902 0.951057i −0.309017 0.951057i \(-0.600000\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 1.17557 1.17557
\(827\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(828\) 0.500000 + 1.53884i 0.500000 + 1.53884i
\(829\) 0 0 0.951057 0.309017i \(-0.100000\pi\)
−0.951057 + 0.309017i \(0.900000\pi\)
\(830\) 1.17557i 1.17557i
\(831\) 0 0
\(832\) 1.90211 1.90211
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 1.53884 1.11803i 1.53884 1.11803i
\(839\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(840\) 1.11803 1.53884i 1.11803 1.53884i
\(841\) −0.809017 + 0.587785i −0.809017 + 0.587785i
\(842\) 0 0
\(843\) 3.07768 3.07768
\(844\) 0 0
\(845\) 1.53884 + 2.11803i 1.53884 + 2.11803i
\(846\) 0 0
\(847\) −0.309017 0.951057i −0.309017 0.951057i
\(848\) 0 0
\(849\) 3.61803 3.61803
\(850\) 0 0
\(851\) 0 0
\(852\) 2.48990 + 1.80902i 2.48990 + 1.80902i
\(853\) −0.363271 1.11803i −0.363271 1.11803i −0.951057 0.309017i \(-0.900000\pi\)
0.587785 0.809017i \(-0.300000\pi\)
\(854\) −0.363271 1.11803i −0.363271 1.11803i
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0 0
\(859\) −0.951057 + 0.690983i −0.951057 + 0.690983i −0.951057 0.309017i \(-0.900000\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −1.30902 + 0.951057i −1.30902 + 0.951057i
\(863\) −1.30902 + 0.951057i −1.30902 + 0.951057i −0.309017 + 0.951057i \(0.600000\pi\)
−1.00000 \(\pi\)
\(864\) −2.48990 1.80902i −2.48990 1.80902i
\(865\) −1.11803 + 0.363271i −1.11803 + 0.363271i
\(866\) 0 0
\(867\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) −0.951057 0.309017i −0.951057 0.309017i
\(876\) 0 0
\(877\) 0 0 −0.809017 0.587785i \(-0.800000\pi\)
0.809017 + 0.587785i \(0.200000\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(882\) −2.61803 −2.61803
\(883\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(884\) 0 0
\(885\) −2.12663 + 0.690983i −2.12663 + 0.690983i
\(886\) 0 0
\(887\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(888\) 0 0
\(889\) 1.61803 + 1.17557i 1.61803 + 1.17557i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0.309017 + 0.951057i 0.309017 + 0.951057i
\(897\) −0.690983 2.12663i −0.690983 2.12663i
\(898\) 0.500000 + 0.363271i 0.500000 + 0.363271i
\(899\) 0 0
\(900\) −0.809017 + 2.48990i −0.809017 + 2.48990i
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) −0.500000 1.53884i −0.500000 1.53884i
\(905\) 0.690983 + 0.951057i 0.690983 + 0.951057i
\(906\) 0.363271 1.11803i 0.363271 1.11803i
\(907\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(908\) −0.587785 + 1.80902i −0.587785 + 1.80902i
\(909\) 4.02874 2.92705i 4.02874 2.92705i
\(910\) −1.11803 + 1.53884i −1.11803 + 1.53884i
\(911\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.30902 + 0.951057i 1.30902 + 0.951057i
\(915\) 1.31433 + 1.80902i 1.31433 + 1.80902i
\(916\) −0.951057 + 0.690983i −0.951057 + 0.690983i
\(917\) 0.363271 1.11803i 0.363271 1.11803i
\(918\) 0 0
\(919\) −0.618034 + 1.90211i −0.618034 + 1.90211i −0.309017 + 0.951057i \(0.600000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(920\) 0.618034i 0.618034i
\(921\) 0 0
\(922\) 0 0
\(923\) −2.48990 1.80902i −2.48990 1.80902i
\(924\) 0 0
\(925\) 0 0
\(926\) −1.61803 −1.61803
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) −1.61803 −1.61803
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 4.02874 + 2.92705i 4.02874 + 2.92705i
\(937\) 0 0 0.809017 0.587785i \(-0.200000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0.951057 0.690983i 0.951057 0.690983i 1.00000i \(-0.5\pi\)
0.951057 + 0.309017i \(0.100000\pi\)
\(942\) 0.690983 2.12663i 0.690983 2.12663i
\(943\) 0 0
\(944\) 0.363271 1.11803i 0.363271 1.11803i
\(945\) 2.92705 0.951057i 2.92705 0.951057i
\(946\) 0 0
\(947\) 0 0 −0.309017 0.951057i \(-0.600000\pi\)
0.309017 + 0.951057i \(0.400000\pi\)
\(948\) −0.951057 0.690983i −0.951057 0.690983i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.190983 + 0.587785i 0.190983 + 0.587785i 1.00000 \(0\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(954\) 0 0
\(955\) 0.618034i 0.618034i
\(956\) 0.190983 0.587785i 0.190983 0.587785i
\(957\) 0 0
\(958\) 0 0
\(959\) 1.61803 1.17557i 1.61803 1.17557i
\(960\) −1.11803 1.53884i −1.11803 1.53884i
\(961\) −0.809017 0.587785i −0.809017 0.587785i
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) −0.951057 + 1.30902i −0.951057 + 1.30902i
\(966\) 0.951057 0.690983i 0.951057 0.690983i
\(967\) −0.500000 + 1.53884i −0.500000 + 1.53884i 0.309017 + 0.951057i \(0.400000\pi\)
−0.809017 + 0.587785i \(0.800000\pi\)
\(968\) −1.00000 −1.00000
\(969\) 0 0
\(970\) 0 0
\(971\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(972\) −0.951057 2.92705i −0.951057 2.92705i
\(973\) 0 0
\(974\) 1.61803 1.61803
\(975\) 1.11803 3.44095i 1.11803 3.44095i
\(976\) −1.17557 −1.17557
\(977\) 1.30902 + 0.951057i 1.30902 + 0.951057i 1.00000 \(0\)
0.309017 + 0.951057i \(0.400000\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) −0.951057 0.309017i −0.951057 0.309017i
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 0.309017 0.951057i \(-0.400000\pi\)
−0.309017 + 0.951057i \(0.600000\pi\)
\(984\) 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 \(0.600000\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.500000 1.53884i 0.500000 1.53884i
\(995\) 0 0
\(996\) −0.690983 2.12663i −0.690983 2.12663i
\(997\) −0.587785 1.80902i −0.587785 1.80902i −0.587785 0.809017i \(-0.700000\pi\)
1.00000i \(-0.5\pi\)
\(998\) 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 1400.1.bs.c.741.1 yes 8
7.6 odd 2 inner 1400.1.bs.c.741.2 yes 8
8.5 even 2 inner 1400.1.bs.c.741.2 yes 8
25.11 even 5 inner 1400.1.bs.c.461.1 8
56.13 odd 2 CM 1400.1.bs.c.741.1 yes 8
175.111 odd 10 inner 1400.1.bs.c.461.2 yes 8
200.61 even 10 inner 1400.1.bs.c.461.2 yes 8
1400.461 odd 10 inner 1400.1.bs.c.461.1 8
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
1400.1.bs.c.461.1 8 25.11 even 5 inner
1400.1.bs.c.461.1 8 1400.461 odd 10 inner
1400.1.bs.c.461.2 yes 8 175.111 odd 10 inner
1400.1.bs.c.461.2 yes 8 200.61 even 10 inner
1400.1.bs.c.741.1 yes 8 1.1 even 1 trivial
1400.1.bs.c.741.1 yes 8 56.13 odd 2 CM
1400.1.bs.c.741.2 yes 8 7.6 odd 2 inner
1400.1.bs.c.741.2 yes 8 8.5 even 2 inner