Properties

Label 580.1.y.c.399.1
Level $580$
Weight $1$
Character 580.399
Analytic conductor $0.289$
Analytic rank $0$
Dimension $12$
Projective image $D_{14}$
CM discriminant -20
Inner twists $8$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [580,1,Mod(179,580)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(580, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 7, 11]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("580.179");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 580.y (of order \(14\), degree \(6\), 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: \(0.289457707327\)
Analytic rank: \(0\)
Dimension: \(12\)
Relative dimension: \(2\) over \(\Q(\zeta_{14})\)
Coefficient field: \(\Q(\zeta_{28})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{10} + x^{8} - x^{6} + x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{14}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{14} + \cdots)\)

Embedding invariants

Embedding label 399.1
Root \(-0.781831 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 580.399
Dual form 580.1.y.c.439.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(-0.974928 + 0.222521i) q^{2} +(0.193096 - 0.400969i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-0.222521 - 0.974928i) q^{5} +(-0.0990311 + 0.433884i) q^{6} +(0.781831 + 0.376510i) q^{7} +(-0.781831 + 0.623490i) q^{8} +(0.500000 + 0.626980i) q^{9} +O(q^{10})\) \(q+(-0.974928 + 0.222521i) q^{2} +(0.193096 - 0.400969i) q^{3} +(0.900969 - 0.433884i) q^{4} +(-0.222521 - 0.974928i) q^{5} +(-0.0990311 + 0.433884i) q^{6} +(0.781831 + 0.376510i) q^{7} +(-0.781831 + 0.623490i) q^{8} +(0.500000 + 0.626980i) q^{9} +(0.433884 + 0.900969i) q^{10} -0.445042i q^{12} +(-0.846011 - 0.193096i) q^{14} +(-0.433884 - 0.0990311i) q^{15} +(0.623490 - 0.781831i) q^{16} +(-0.626980 - 0.500000i) q^{18} +(-0.623490 - 0.781831i) q^{20} +(0.301938 - 0.240787i) q^{21} +(0.433884 - 1.90097i) q^{23} +(0.0990311 + 0.433884i) q^{24} +(-0.900969 + 0.433884i) q^{25} +(0.781831 - 0.178448i) q^{27} +0.867767 q^{28} +(-0.900969 - 0.433884i) q^{29} +0.445042 q^{30} +(-0.433884 + 0.900969i) q^{32} +(0.193096 - 0.846011i) q^{35} +(0.722521 + 0.347948i) q^{36} +(0.781831 + 0.623490i) q^{40} +1.56366i q^{41} +(-0.240787 + 0.301938i) q^{42} +(-1.21572 - 0.277479i) q^{43} +(0.500000 - 0.626980i) q^{45} +1.94986i q^{46} +(1.40881 + 1.12349i) q^{47} +(-0.193096 - 0.400969i) q^{48} +(-0.153989 - 0.193096i) q^{49} +(0.781831 - 0.623490i) q^{50} +(-0.722521 + 0.347948i) q^{54} +(-0.846011 + 0.193096i) q^{56} +(0.974928 + 0.222521i) q^{58} +(-0.433884 + 0.0990311i) q^{60} +(0.154851 + 0.678448i) q^{63} +(0.222521 - 0.974928i) q^{64} +(-0.678448 - 0.541044i) q^{69} +0.867767i q^{70} +(-0.781831 - 0.178448i) q^{72} +0.445042i q^{75} +(-0.900969 - 0.433884i) q^{80} +(-0.0990311 + 0.433884i) q^{81} +(-0.347948 - 1.52446i) q^{82} +(-1.40881 + 0.678448i) q^{83} +(0.167563 - 0.347948i) q^{84} +1.24698 q^{86} +(-0.347948 + 0.277479i) q^{87} +(-0.846011 + 0.193096i) q^{89} +(-0.347948 + 0.722521i) q^{90} +(-0.433884 - 1.90097i) q^{92} +(-1.62349 - 0.781831i) q^{94} +(0.277479 + 0.347948i) q^{96} +(0.193096 + 0.153989i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} - 2 q^{5} - 10 q^{6} + 6 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} - 2 q^{5} - 10 q^{6} + 6 q^{9} - 2 q^{16} + 2 q^{20} - 14 q^{21} + 10 q^{24} - 2 q^{25} - 2 q^{29} + 4 q^{30} + 8 q^{36} + 6 q^{45} - 12 q^{49} - 8 q^{54} + 2 q^{64} - 2 q^{80} - 10 q^{81} - 4 q^{86} - 10 q^{94} + 4 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/580\mathbb{Z}\right)^\times\).

\(n\) \(117\) \(291\) \(321\)
\(\chi(n)\) \(-1\) \(-1\) \(e\left(\frac{13}{14}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(3\) 0.193096 0.400969i 0.193096 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(4\) 0.900969 0.433884i 0.900969 0.433884i
\(5\) −0.222521 0.974928i −0.222521 0.974928i
\(6\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(7\) 0.781831 + 0.376510i 0.781831 + 0.376510i 0.781831 0.623490i \(-0.214286\pi\)
1.00000i \(0.5\pi\)
\(8\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(9\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(10\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(11\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(12\) 0.445042i 0.445042i
\(13\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(14\) −0.846011 0.193096i −0.846011 0.193096i
\(15\) −0.433884 0.0990311i −0.433884 0.0990311i
\(16\) 0.623490 0.781831i 0.623490 0.781831i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.626980 0.500000i −0.626980 0.500000i
\(19\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(20\) −0.623490 0.781831i −0.623490 0.781831i
\(21\) 0.301938 0.240787i 0.301938 0.240787i
\(22\) 0 0
\(23\) 0.433884 1.90097i 0.433884 1.90097i 1.00000i \(-0.5\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(24\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(25\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(26\) 0 0
\(27\) 0.781831 0.178448i 0.781831 0.178448i
\(28\) 0.867767 0.867767
\(29\) −0.900969 0.433884i −0.900969 0.433884i
\(30\) 0.445042 0.445042
\(31\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(32\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(33\) 0 0
\(34\) 0 0
\(35\) 0.193096 0.846011i 0.193096 0.846011i
\(36\) 0.722521 + 0.347948i 0.722521 + 0.347948i
\(37\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(41\) 1.56366i 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(42\) −0.240787 + 0.301938i −0.240787 + 0.301938i
\(43\) −1.21572 0.277479i −1.21572 0.277479i −0.433884 0.900969i \(-0.642857\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(44\) 0 0
\(45\) 0.500000 0.626980i 0.500000 0.626980i
\(46\) 1.94986i 1.94986i
\(47\) 1.40881 + 1.12349i 1.40881 + 1.12349i 0.974928 + 0.222521i \(0.0714286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(48\) −0.193096 0.400969i −0.193096 0.400969i
\(49\) −0.153989 0.193096i −0.153989 0.193096i
\(50\) 0.781831 0.623490i 0.781831 0.623490i
\(51\) 0 0
\(52\) 0 0
\(53\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(54\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(55\) 0 0
\(56\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(57\) 0 0
\(58\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i
\(61\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(62\) 0 0
\(63\) 0.154851 + 0.678448i 0.154851 + 0.678448i
\(64\) 0.222521 0.974928i 0.222521 0.974928i
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(68\) 0 0
\(69\) −0.678448 0.541044i −0.678448 0.541044i
\(70\) 0.867767i 0.867767i
\(71\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(72\) −0.781831 0.178448i −0.781831 0.178448i
\(73\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(74\) 0 0
\(75\) 0.445042i 0.445042i
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(80\) −0.900969 0.433884i −0.900969 0.433884i
\(81\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(82\) −0.347948 1.52446i −0.347948 1.52446i
\(83\) −1.40881 + 0.678448i −1.40881 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(84\) 0.167563 0.347948i 0.167563 0.347948i
\(85\) 0 0
\(86\) 1.24698 1.24698
\(87\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(88\) 0 0
\(89\) −0.846011 + 0.193096i −0.846011 + 0.193096i −0.623490 0.781831i \(-0.714286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(90\) −0.347948 + 0.722521i −0.347948 + 0.722521i
\(91\) 0 0
\(92\) −0.433884 1.90097i −0.433884 1.90097i
\(93\) 0 0
\(94\) −1.62349 0.781831i −1.62349 0.781831i
\(95\) 0 0
\(96\) 0.277479 + 0.347948i 0.277479 + 0.347948i
\(97\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(98\) 0.193096 + 0.153989i 0.193096 + 0.153989i
\(99\) 0 0
\(100\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(101\) −1.90097 0.433884i −1.90097 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
−1.00000 \(\pi\)
\(102\) 0 0
\(103\) −0.974928 + 1.22252i −0.974928 + 1.22252i 1.00000i \(0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(104\) 0 0
\(105\) −0.301938 0.240787i −0.301938 0.240787i
\(106\) 0 0
\(107\) 1.21572 + 1.52446i 1.21572 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(108\) 0.626980 0.500000i 0.626980 0.500000i
\(109\) 1.12349 + 0.541044i 1.12349 + 0.541044i 0.900969 0.433884i \(-0.142857\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.781831 0.376510i 0.781831 0.376510i
\(113\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(114\) 0 0
\(115\) −1.94986 −1.94986
\(116\) −1.00000 −1.00000
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.400969 0.193096i 0.400969 0.193096i
\(121\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(122\) 0 0
\(123\) 0.626980 + 0.301938i 0.626980 + 0.301938i
\(124\) 0 0
\(125\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(126\) −0.301938 0.626980i −0.301938 0.626980i
\(127\) −1.40881 1.12349i −1.40881 1.12349i −0.974928 0.222521i \(-0.928571\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(128\) 1.00000i 1.00000i
\(129\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(130\) 0 0
\(131\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) −0.347948 0.722521i −0.347948 0.722521i
\(136\) 0 0
\(137\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(138\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(139\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(140\) −0.193096 0.846011i −0.193096 0.846011i
\(141\) 0.722521 0.347948i 0.722521 0.347948i
\(142\) 0 0
\(143\) 0 0
\(144\) 0.801938 0.801938
\(145\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(146\) 0 0
\(147\) −0.107160 + 0.0244587i −0.107160 + 0.0244587i
\(148\) 0 0
\(149\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(150\) −0.0990311 0.433884i −0.0990311 0.433884i
\(151\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(152\) 0 0
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(161\) 1.05496 1.32288i 1.05496 1.32288i
\(162\) 0.445042i 0.445042i
\(163\) 0.974928 + 0.777479i 0.974928 + 0.777479i 0.974928 0.222521i \(-0.0714286\pi\)
1.00000i \(0.5\pi\)
\(164\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(165\) 0 0
\(166\) 1.22252 0.974928i 1.22252 0.974928i
\(167\) −1.40881 0.678448i −1.40881 0.678448i −0.433884 0.900969i \(-0.642857\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(168\) −0.0859360 + 0.376510i −0.0859360 + 0.376510i
\(169\) −0.222521 0.974928i −0.222521 0.974928i
\(170\) 0 0
\(171\) 0 0
\(172\) −1.21572 + 0.277479i −1.21572 + 0.277479i
\(173\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(174\) 0.277479 0.347948i 0.277479 0.347948i
\(175\) −0.867767 −0.867767
\(176\) 0 0
\(177\) 0 0
\(178\) 0.781831 0.376510i 0.781831 0.376510i
\(179\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(180\) 0.178448 0.781831i 0.178448 0.781831i
\(181\) −0.400969 0.193096i −0.400969 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0.846011 + 1.75676i 0.846011 + 1.75676i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 1.75676 + 0.400969i 1.75676 + 0.400969i
\(189\) 0.678448 + 0.154851i 0.678448 + 0.154851i
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −0.347948 0.277479i −0.347948 0.277479i
\(193\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.222521 0.107160i −0.222521 0.107160i
\(197\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(198\) 0 0
\(199\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(200\) 0.433884 0.900969i 0.433884 0.900969i
\(201\) 0 0
\(202\) 1.94986 1.94986
\(203\) −0.541044 0.678448i −0.541044 0.678448i
\(204\) 0 0
\(205\) 1.52446 0.347948i 1.52446 0.347948i
\(206\) 0.678448 1.40881i 0.678448 1.40881i
\(207\) 1.40881 0.678448i 1.40881 0.678448i
\(208\) 0 0
\(209\) 0 0
\(210\) 0.347948 + 0.167563i 0.347948 + 0.167563i
\(211\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(212\) 0 0
\(213\) 0 0
\(214\) −1.52446 1.21572i −1.52446 1.21572i
\(215\) 1.24698i 1.24698i
\(216\) −0.500000 + 0.626980i −0.500000 + 0.626980i
\(217\) 0 0
\(218\) −1.21572 0.277479i −1.21572 0.277479i
\(219\) 0 0
\(220\) 0 0
\(221\) 0 0
\(222\) 0 0
\(223\) 0.541044 + 0.678448i 0.541044 + 0.678448i 0.974928 0.222521i \(-0.0714286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(224\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(225\) −0.722521 0.347948i −0.722521 0.347948i
\(226\) 0 0
\(227\) 0.347948 + 1.52446i 0.347948 + 1.52446i 0.781831 + 0.623490i \(0.214286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(228\) 0 0
\(229\) 0.678448 1.40881i 0.678448 1.40881i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(230\) 1.90097 0.433884i 1.90097 0.433884i
\(231\) 0 0
\(232\) 0.974928 0.222521i 0.974928 0.222521i
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0.781831 1.62349i 0.781831 1.62349i
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(240\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(241\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(242\) −0.433884 0.900969i −0.433884 0.900969i
\(243\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(244\) 0 0
\(245\) −0.153989 + 0.193096i −0.153989 + 0.193096i
\(246\) −0.678448 0.154851i −0.678448 0.154851i
\(247\) 0 0
\(248\) 0 0
\(249\) 0.695895i 0.695895i
\(250\) −0.781831 0.623490i −0.781831 0.623490i
\(251\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(252\) 0.433884 + 0.544073i 0.433884 + 0.544073i
\(253\) 0 0
\(254\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(255\) 0 0
\(256\) −0.222521 0.974928i −0.222521 0.974928i
\(257\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(258\) 0.240787 0.500000i 0.240787 0.500000i
\(259\) 0 0
\(260\) 0 0
\(261\) −0.178448 0.781831i −0.178448 0.781831i
\(262\) 0 0
\(263\) 1.75676 0.400969i 1.75676 0.400969i 0.781831 0.623490i \(-0.214286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) −0.0859360 + 0.376510i −0.0859360 + 0.376510i
\(268\) 0 0
\(269\) −1.52446 + 1.21572i −1.52446 + 1.21572i −0.623490 + 0.781831i \(0.714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(270\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(271\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) −0.846011 0.193096i −0.846011 0.193096i
\(277\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(281\) 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i \(-0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(282\) −0.626980 + 0.500000i −0.626980 + 0.500000i
\(283\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.588735 + 1.22252i −0.588735 + 1.22252i
\(288\) −0.781831 + 0.178448i −0.781831 + 0.178448i
\(289\) −1.00000 −1.00000
\(290\) 1.00000i 1.00000i
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(294\) 0.0990311 0.0476909i 0.0990311 0.0476909i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −1.40881 + 1.12349i −1.40881 + 1.12349i
\(299\) 0 0
\(300\) 0.193096 + 0.400969i 0.193096 + 0.400969i
\(301\) −0.846011 0.674671i −0.846011 0.674671i
\(302\) 0 0
\(303\) −0.541044 + 0.678448i −0.541044 + 0.678448i
\(304\) 0 0
\(305\) 0 0
\(306\) 0 0
\(307\) 0.445042i 0.445042i −0.974928 0.222521i \(-0.928571\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(308\) 0 0
\(309\) 0.301938 + 0.626980i 0.301938 + 0.626980i
\(310\) 0 0
\(311\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(312\) 0 0
\(313\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) 0 0
\(315\) 0.626980 0.301938i 0.626980 0.301938i
\(316\) 0 0
\(317\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 0.846011 0.193096i 0.846011 0.193096i
\(322\) −0.734141 + 1.52446i −0.734141 + 1.52446i
\(323\) 0 0
\(324\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(325\) 0 0
\(326\) −1.12349 0.541044i −1.12349 0.541044i
\(327\) 0.433884 0.346011i 0.433884 0.346011i
\(328\) −0.974928 1.22252i −0.974928 1.22252i
\(329\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(333\) 0 0
\(334\) 1.52446 + 0.347948i 1.52446 + 0.347948i
\(335\) 0 0
\(336\) 0.386193i 0.386193i
\(337\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(338\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) −0.240787 1.05496i −0.240787 1.05496i
\(344\) 1.12349 0.541044i 1.12349 0.541044i
\(345\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(346\) 0 0
\(347\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(348\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(349\) 1.24698 1.24698 0.623490 0.781831i \(-0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(350\) 0.846011 0.193096i 0.846011 0.193096i
\(351\) 0 0
\(352\) 0 0
\(353\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(360\) 0.801938i 0.801938i
\(361\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(362\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i
\(363\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.781831 1.62349i −0.781831 1.62349i −0.781831 0.623490i \(-0.785714\pi\)
1.00000i \(-0.5\pi\)
\(368\) −1.21572 1.52446i −1.21572 1.52446i
\(369\) −0.980386 + 0.781831i −0.980386 + 0.781831i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0 0
\(375\) 0.433884 0.0990311i 0.433884 0.0990311i
\(376\) −1.80194 −1.80194
\(377\) 0 0
\(378\) −0.695895 −0.695895
\(379\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(380\) 0 0
\(381\) −0.722521 + 0.347948i −0.722521 + 0.347948i
\(382\) 0 0
\(383\) 0.433884 1.90097i 0.433884 1.90097i 1.00000i \(-0.5\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(384\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(385\) 0 0
\(386\) 0 0
\(387\) −0.433884 0.900969i −0.433884 0.900969i
\(388\) 0 0
\(389\) 1.94986i 1.94986i −0.222521 0.974928i \(-0.571429\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0.240787 + 0.0549581i 0.240787 + 0.0549581i
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(401\) −0.400969 1.75676i −0.400969 1.75676i −0.623490 0.781831i \(-0.714286\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −1.90097 + 0.433884i −1.90097 + 0.433884i
\(405\) 0.445042 0.445042
\(406\) 0.678448 + 0.541044i 0.678448 + 0.541044i
\(407\) 0 0
\(408\) 0 0
\(409\) 0.376510 0.781831i 0.376510 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
1.00000 \(0\)
\(410\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(411\) 0 0
\(412\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(413\) 0 0
\(414\) −1.22252 + 0.974928i −1.22252 + 0.974928i
\(415\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(416\) 0 0
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(420\) −0.376510 0.0859360i −0.376510 0.0859360i
\(421\) −1.52446 0.347948i −1.52446 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(422\) 0 0
\(423\) 1.44504i 1.44504i
\(424\) 0 0
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 1.75676 + 0.846011i 1.75676 + 0.846011i
\(429\) 0 0
\(430\) −0.277479 1.21572i −0.277479 1.21572i
\(431\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(432\) 0.347948 0.722521i 0.347948 0.722521i
\(433\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(434\) 0 0
\(435\) 0.347948 + 0.277479i 0.347948 + 0.277479i
\(436\) 1.24698 1.24698
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(440\) 0 0
\(441\) 0.0440730 0.193096i 0.0440730 0.193096i
\(442\) 0 0
\(443\) 1.56366 1.24698i 1.56366 1.24698i 0.781831 0.623490i \(-0.214286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(444\) 0 0
\(445\) 0.376510 + 0.781831i 0.376510 + 0.781831i
\(446\) −0.678448 0.541044i −0.678448 0.541044i
\(447\) 0.801938i 0.801938i
\(448\) 0.541044 0.678448i 0.541044 0.678448i
\(449\) 0.846011 + 0.193096i 0.846011 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(450\) 0.781831 + 0.178448i 0.781831 + 0.178448i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) −0.678448 1.40881i −0.678448 1.40881i
\(455\) 0 0
\(456\) 0 0
\(457\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(458\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(459\) 0 0
\(460\) −1.75676 + 0.846011i −1.75676 + 0.846011i
\(461\) −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i \(0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(462\) 0 0
\(463\) −1.56366 −1.56366 −0.781831 0.623490i \(-0.785714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(464\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(465\) 0 0
\(466\) 0 0
\(467\) 0.541044 1.12349i 0.541044 1.12349i −0.433884 0.900969i \(-0.642857\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(480\) 0.277479 0.347948i 0.277479 0.347948i
\(481\) 0 0
\(482\) 0.347948 + 0.277479i 0.347948 + 0.277479i
\(483\) −0.326723 0.678448i −0.326723 0.678448i
\(484\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(485\) 0 0
\(486\) −0.900969 0.433884i −0.900969 0.433884i
\(487\) −0.193096 + 0.846011i −0.193096 + 0.846011i 0.781831 + 0.623490i \(0.214286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(488\) 0 0
\(489\) 0.500000 0.240787i 0.500000 0.240787i
\(490\) 0.107160 0.222521i 0.107160 0.222521i
\(491\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(492\) 0.695895 0.695895
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) −0.154851 0.678448i −0.154851 0.678448i
\(499\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(500\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(501\) −0.544073 + 0.433884i −0.544073 + 0.433884i
\(502\) 0 0
\(503\) 0.541044 + 1.12349i 0.541044 + 1.12349i 0.974928 + 0.222521i \(0.0714286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(504\) −0.544073 0.433884i −0.544073 0.433884i
\(505\) 1.94986i 1.94986i
\(506\) 0 0
\(507\) −0.433884 0.0990311i −0.433884 0.0990311i
\(508\) −1.75676 0.400969i −1.75676 0.400969i
\(509\) −0.777479 + 0.974928i −0.777479 + 0.974928i 0.222521 + 0.974928i \(0.428571\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(513\) 0 0
\(514\) 0 0
\(515\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(516\) −0.123490 + 0.541044i −0.123490 + 0.541044i
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 1.80194 1.80194 0.900969 0.433884i \(-0.142857\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(522\) 0.347948 + 0.722521i 0.347948 + 0.722521i
\(523\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(524\) 0 0
\(525\) −0.167563 + 0.347948i −0.167563 + 0.347948i
\(526\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(527\) 0 0
\(528\) 0 0
\(529\) −2.52446 1.21572i −2.52446 1.21572i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.386193i 0.386193i
\(535\) 1.21572 1.52446i 1.21572 1.52446i
\(536\) 0 0
\(537\) 0 0
\(538\) 1.21572 1.52446i 1.21572 1.52446i
\(539\) 0 0
\(540\) −0.626980 0.500000i −0.626980 0.500000i
\(541\) 0.376510 + 0.781831i 0.376510 + 0.781831i 1.00000 \(0\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(542\) 0 0
\(543\) −0.154851 + 0.123490i −0.154851 + 0.123490i
\(544\) 0 0
\(545\) 0.277479 1.21572i 0.277479 1.21572i
\(546\) 0 0
\(547\) 1.40881 0.678448i 1.40881 0.678448i 0.433884 0.900969i \(-0.357143\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0.867767 0.867767
\(553\) 0 0
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) −0.541044 0.678448i −0.541044 0.678448i
\(561\) 0 0
\(562\) −0.347948 0.277479i −0.347948 0.277479i
\(563\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(564\) 0.500000 0.626980i 0.500000 0.626980i
\(565\) 0 0
\(566\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(567\) −0.240787 + 0.301938i −0.240787 + 0.301938i
\(568\) 0 0
\(569\) 1.52446 + 1.21572i 1.52446 + 1.21572i 0.900969 + 0.433884i \(0.142857\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(570\) 0 0
\(571\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.301938 1.32288i 0.301938 1.32288i
\(575\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(576\) 0.722521 0.347948i 0.722521 0.347948i
\(577\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(578\) 0.974928 0.222521i 0.974928 0.222521i
\(579\) 0 0
\(580\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(581\) −1.35690 −1.35690
\(582\) 0 0
\(583\) 0 0
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) −1.75676 0.846011i −1.75676 0.846011i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(588\) −0.0859360 + 0.0685317i −0.0859360 + 0.0685317i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1.12349 1.40881i 1.12349 1.40881i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(600\) −0.277479 0.347948i −0.277479 0.347948i
\(601\) 0.678448 0.541044i 0.678448 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(602\) 0.974928 + 0.469501i 0.974928 + 0.469501i
\(603\) 0 0
\(604\) 0 0
\(605\) 0.900969 0.433884i 0.900969 0.433884i
\(606\) 0.376510 0.781831i 0.376510 0.781831i
\(607\) 0.433884 0.0990311i 0.433884 0.0990311i 1.00000i \(-0.5\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(608\) 0 0
\(609\) −0.376510 + 0.0859360i −0.376510 + 0.0859360i
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(614\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(615\) 0.154851 0.678448i 0.154851 0.678448i
\(616\) 0 0
\(617\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(618\) −0.433884 0.544073i −0.433884 0.544073i
\(619\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(620\) 0 0
\(621\) 1.56366i 1.56366i
\(622\) 0 0
\(623\) −0.734141 0.167563i −0.734141 0.167563i
\(624\) 0 0
\(625\) 0.623490 0.781831i 0.623490 0.781831i
\(626\) 0 0
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) −0.544073 + 0.433884i −0.544073 + 0.433884i
\(631\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 0 0
\(635\) −0.781831 + 1.62349i −0.781831 + 1.62349i
\(636\) 0 0
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0.974928 0.222521i 0.974928 0.222521i
\(641\) 0.846011 1.75676i 0.846011 1.75676i 0.222521 0.974928i \(-0.428571\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(642\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(643\) 0.433884 + 1.90097i 0.433884 + 1.90097i 0.433884 + 0.900969i \(0.357143\pi\)
1.00000i \(0.500000\pi\)
\(644\) 0.376510 1.64960i 0.376510 1.64960i
\(645\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(646\) 0 0
\(647\) 0.541044 + 0.678448i 0.541044 + 0.678448i 0.974928 0.222521i \(-0.0714286\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(648\) −0.193096 0.400969i −0.193096 0.400969i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 1.21572 + 0.277479i 1.21572 + 0.277479i
\(653\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(654\) −0.346011 + 0.433884i −0.346011 + 0.433884i
\(655\) 0 0
\(656\) 1.22252 + 0.974928i 1.22252 + 0.974928i
\(657\) 0 0
\(658\) −0.974928 1.22252i −0.974928 1.22252i
\(659\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(660\) 0 0
\(661\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i 0.900969 + 0.433884i \(0.142857\pi\)
−1.00000 \(\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0.678448 1.40881i 0.678448 1.40881i
\(665\) 0 0
\(666\) 0 0
\(667\) −1.21572 + 1.52446i −1.21572 + 1.52446i
\(668\) −1.56366 −1.56366
\(669\) 0.376510 0.0859360i 0.376510 0.0859360i
\(670\) 0 0
\(671\) 0 0
\(672\) 0.0859360 + 0.376510i 0.0859360 + 0.376510i
\(673\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(674\) 0 0
\(675\) −0.626980 + 0.500000i −0.626980 + 0.500000i
\(676\) −0.623490 0.781831i −0.623490 0.781831i
\(677\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.678448 + 0.154851i 0.678448 + 0.154851i
\(682\) 0 0
\(683\) −0.541044 + 0.678448i −0.541044 + 0.678448i −0.974928 0.222521i \(-0.928571\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.469501 + 0.974928i 0.469501 + 0.974928i
\(687\) −0.433884 0.544073i −0.433884 0.544073i
\(688\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(689\) 0 0
\(690\) 0.193096 0.846011i 0.193096 0.846011i
\(691\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0.0990311 0.433884i 0.0990311 0.433884i
\(697\) 0 0
\(698\) −1.21572 + 0.277479i −1.21572 + 0.277479i
\(699\) 0 0
\(700\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(701\) −0.0990311 0.433884i −0.0990311 0.433884i 0.900969 0.433884i \(-0.142857\pi\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) −0.500000 0.626980i −0.500000 0.626980i
\(706\) 0 0
\(707\) −1.32288 1.05496i −1.32288 1.05496i
\(708\) 0 0
\(709\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.541044 0.678448i 0.541044 0.678448i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(720\) −0.178448 0.781831i −0.178448 0.781831i
\(721\) −1.22252 + 0.588735i −1.22252 + 0.588735i
\(722\) 0.433884 0.900969i 0.433884 0.900969i
\(723\) −0.193096 + 0.0440730i −0.193096 + 0.0440730i
\(724\) −0.445042 −0.445042
\(725\) 1.00000 1.00000
\(726\) −0.445042 −0.445042
\(727\) −1.21572 + 0.277479i −1.21572 + 0.277479i −0.781831 0.623490i \(-0.785714\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(734\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(735\) 0.0476909 + 0.0990311i 0.0476909 + 0.0990311i
\(736\) 1.52446 + 1.21572i 1.52446 + 1.21572i
\(737\) 0 0
\(738\) 0.781831 0.980386i 0.781831 0.980386i
\(739\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0 0
\(743\) −0.974928 0.777479i −0.974928 0.777479i 1.00000i \(-0.5\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(744\) 0 0
\(745\) −1.12349 1.40881i −1.12349 1.40881i
\(746\) 0 0
\(747\) −1.12978 0.544073i −1.12978 0.544073i
\(748\) 0 0
\(749\) 0.376510 + 1.64960i 0.376510 + 1.64960i
\(750\) −0.400969 + 0.193096i −0.400969 + 0.193096i
\(751\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(752\) 1.75676 0.400969i 1.75676 0.400969i
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.678448 0.154851i 0.678448 0.154851i
\(757\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 0.400969 + 0.193096i 0.400969 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(762\) 0.626980 0.500000i 0.626980 0.500000i
\(763\) 0.674671 + 0.846011i 0.674671 + 0.846011i
\(764\) 0 0
\(765\) 0 0
\(766\) 1.94986i 1.94986i
\(767\) 0 0
\(768\) −0.433884 0.0990311i −0.433884 0.0990311i
\(769\) 0.846011 + 0.193096i 0.846011 + 0.193096i 0.623490 0.781831i \(-0.285714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0 0
\(773\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(774\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0.433884 + 1.90097i 0.433884 + 1.90097i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −0.781831 0.178448i −0.781831 0.178448i
\(784\) −0.246980 −0.246980
\(785\) 0 0
\(786\) 0 0
\(787\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(788\) 0 0
\(789\) 0.178448 0.781831i 0.178448 0.781831i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 1.00000i 1.00000i
\(801\) −0.544073 0.433884i −0.544073 0.433884i
\(802\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(803\) 0 0
\(804\) 0 0
\(805\) −1.52446 0.734141i −1.52446 0.734141i
\(806\) 0 0
\(807\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(808\) 1.75676 0.846011i 1.75676 0.846011i
\(809\) 0.846011 1.75676i 0.846011 1.75676i 0.222521 0.974928i \(-0.428571\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(810\) −0.433884 + 0.0990311i −0.433884 + 0.0990311i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) −0.781831 0.376510i −0.781831 0.376510i
\(813\) 0 0
\(814\) 0 0
\(815\) 0.541044 1.12349i 0.541044 1.12349i
\(816\) 0 0
\(817\) 0 0
\(818\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(819\) 0 0
\(820\) 1.22252 0.974928i 1.22252 0.974928i
\(821\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(822\) 0 0
\(823\) 1.40881 + 1.12349i 1.40881 + 1.12349i 0.974928 + 0.222521i \(0.0714286\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(824\) 1.56366i 1.56366i
\(825\) 0 0
\(826\) 0 0
\(827\) −1.75676 0.400969i −1.75676 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(828\) 0.974928 1.22252i 0.974928 1.22252i
\(829\) 1.94986i 1.94986i 0.222521 + 0.974928i \(0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(830\) −1.22252 0.974928i −1.22252 0.974928i
\(831\) 0 0
\(832\) 0 0
\(833\) 0 0
\(834\) 0 0
\(835\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(840\) 0.386193 0.386193
\(841\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(842\) 1.56366 1.56366
\(843\) 0.193096 0.0440730i 0.193096 0.0440730i
\(844\) 0 0
\(845\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(846\) −0.321552 1.40881i −0.321552 1.40881i
\(847\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(848\) 0 0
\(849\) −0.678448 + 0.541044i −0.678448 + 0.541044i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.90097 0.433884i −1.90097 0.433884i
\(857\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(858\) 0 0
\(859\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(860\) 0.541044 + 1.12349i 0.541044 + 1.12349i
\(861\) 0.376510 + 0.472129i 0.376510 + 0.472129i
\(862\) 0 0
\(863\) −1.40881 0.678448i −1.40881 0.678448i −0.433884 0.900969i \(-0.642857\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(864\) −0.178448 + 0.781831i −0.178448 + 0.781831i
\(865\) 0 0
\(866\) 0 0
\(867\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(868\) 0 0
\(869\) 0 0
\(870\) −0.400969 0.193096i −0.400969 0.193096i
\(871\) 0 0
\(872\) −1.21572 + 0.277479i −1.21572 + 0.277479i
\(873\) 0 0
\(874\) 0 0
\(875\) 0.193096 + 0.846011i 0.193096 + 0.846011i
\(876\) 0 0
\(877\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 1.22252 + 0.974928i 1.22252 + 0.974928i 1.00000 \(0\)
0.222521 + 0.974928i \(0.428571\pi\)
\(882\) 0.198062i 0.198062i
\(883\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) −1.24698 + 1.56366i −1.24698 + 1.56366i
\(887\) 1.80194i 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(888\) 0 0
\(889\) −0.678448 1.40881i −0.678448 1.40881i
\(890\) −0.541044 0.678448i −0.541044 0.678448i
\(891\) 0 0
\(892\) 0.781831 + 0.376510i 0.781831 + 0.376510i
\(893\) 0 0
\(894\) 0.178448 + 0.781831i 0.178448 + 0.781831i
\(895\) 0 0
\(896\) −0.376510 + 0.781831i −0.376510 + 0.781831i
\(897\) 0 0
\(898\) −0.867767 −0.867767
\(899\) 0 0
\(900\) −0.801938 −0.801938
\(901\) 0 0
\(902\) 0 0
\(903\) −0.433884 + 0.208947i −0.433884 + 0.208947i
\(904\) 0 0
\(905\) −0.0990311 + 0.433884i −0.0990311 + 0.433884i
\(906\) 0 0
\(907\) 0.974928 0.777479i 0.974928 0.777479i 1.00000i \(-0.5\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(908\) 0.974928 + 1.22252i 0.974928 + 1.22252i
\(909\) −0.678448 1.40881i −0.678448 1.40881i
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 1.56366i 1.56366i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(920\) 1.52446 1.21572i 1.52446 1.21572i
\(921\) −0.178448 0.0859360i −0.178448 0.0859360i
\(922\) 0.347948 1.52446i 0.347948 1.52446i
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 1.52446 0.347948i 1.52446 0.347948i
\(927\) −1.25396 −1.25396
\(928\) 0.781831 0.623490i 0.781831 0.623490i
\(929\) −0.445042 −0.445042 −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(935\) 0 0
\(936\) 0 0
\(937\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 1.80194i 1.80194i
\(941\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(942\) 0 0
\(943\) 2.97247 + 0.678448i 2.97247 + 0.678448i
\(944\) 0 0
\(945\) 0.695895i 0.695895i
\(946\) 0 0
\(947\) 0.193096 + 0.400969i 0.193096 + 0.400969i 0.974928 0.222521i \(-0.0714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(948\) 0 0
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) −0.193096 + 0.400969i −0.193096 + 0.400969i
\(961\) 0.900969 0.433884i 0.900969 0.433884i
\(962\) 0 0
\(963\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(964\) −0.400969 0.193096i −0.400969 0.193096i
\(965\) 0 0
\(966\) 0.469501 + 0.588735i 0.469501 + 0.588735i
\(967\) −0.541044 1.12349i −0.541044 1.12349i −0.974928 0.222521i \(-0.928571\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(968\) −0.781831 0.623490i −0.781831 0.623490i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(972\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(973\) 0 0
\(974\) 0.867767i 0.867767i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(978\) −0.433884 + 0.346011i −0.433884 + 0.346011i
\(979\) 0 0
\(980\) −0.0549581 + 0.240787i −0.0549581 + 0.240787i
\(981\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(982\) 0 0
\(983\) −0.867767 + 1.80194i −0.867767 + 1.80194i −0.433884 + 0.900969i \(0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(984\) −0.678448 + 0.154851i −0.678448 + 0.154851i
\(985\) 0 0
\(986\) 0 0
\(987\) 0.695895 0.695895
\(988\) 0 0
\(989\) −1.05496 + 2.19064i −1.05496 + 2.19064i
\(990\) 0 0
\(991\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0.301938 + 0.626980i 0.301938 + 0.626980i
\(997\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(998\) 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 580.1.y.c.399.1 12
4.3 odd 2 inner 580.1.y.c.399.2 yes 12
5.2 odd 4 2900.1.be.a.51.1 6
5.3 odd 4 2900.1.be.b.51.1 6
5.4 even 2 inner 580.1.y.c.399.2 yes 12
20.3 even 4 2900.1.be.a.51.1 6
20.7 even 4 2900.1.be.b.51.1 6
20.19 odd 2 CM 580.1.y.c.399.1 12
29.4 even 14 inner 580.1.y.c.439.1 yes 12
116.91 odd 14 inner 580.1.y.c.439.2 yes 12
145.4 even 14 inner 580.1.y.c.439.2 yes 12
145.33 odd 28 2900.1.be.a.1251.1 6
145.62 odd 28 2900.1.be.b.1251.1 6
580.207 even 28 2900.1.be.a.1251.1 6
580.323 even 28 2900.1.be.b.1251.1 6
580.439 odd 14 inner 580.1.y.c.439.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.1.y.c.399.1 12 1.1 even 1 trivial
580.1.y.c.399.1 12 20.19 odd 2 CM
580.1.y.c.399.2 yes 12 4.3 odd 2 inner
580.1.y.c.399.2 yes 12 5.4 even 2 inner
580.1.y.c.439.1 yes 12 29.4 even 14 inner
580.1.y.c.439.1 yes 12 580.439 odd 14 inner
580.1.y.c.439.2 yes 12 116.91 odd 14 inner
580.1.y.c.439.2 yes 12 145.4 even 14 inner
2900.1.be.a.51.1 6 5.2 odd 4
2900.1.be.a.51.1 6 20.3 even 4
2900.1.be.a.1251.1 6 145.33 odd 28
2900.1.be.a.1251.1 6 580.207 even 28
2900.1.be.b.51.1 6 5.3 odd 4
2900.1.be.b.51.1 6 20.7 even 4
2900.1.be.b.1251.1 6 145.62 odd 28
2900.1.be.b.1251.1 6 580.323 even 28