Properties

Label 580.1.bd.a.507.1
Level $580$
Weight $1$
Character 580.507
Analytic conductor $0.289$
Analytic rank $0$
Dimension $12$
Projective image $D_{28}$
CM discriminant -4
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [580,1,Mod(127,580)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(580, base_ring=CyclotomicField(28))
 
chi = DirichletCharacter(H, H._module([14, 7, 25]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("580.127");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 580.bd (of order \(28\), degree \(12\), 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: \(12\)
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: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{28}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{28} - \cdots)\)

Embedding invariants

Embedding label 507.1
Root \(0.433884 + 0.900969i\) of defining polynomial
Character \(\chi\) \(=\) 580.507
Dual form 580.1.bd.a.143.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.623490 - 0.781831i) q^{2} +(-0.222521 - 0.974928i) q^{4} +(-0.433884 - 0.900969i) q^{5} +(-0.900969 - 0.433884i) q^{8} +(0.900969 + 0.433884i) q^{9} +O(q^{10})\) \(q+(0.623490 - 0.781831i) q^{2} +(-0.222521 - 0.974928i) q^{4} +(-0.433884 - 0.900969i) q^{5} +(-0.900969 - 0.433884i) q^{8} +(0.900969 + 0.433884i) q^{9} +(-0.974928 - 0.222521i) q^{10} +(-1.59842 - 0.559311i) q^{13} +(-0.900969 + 0.433884i) q^{16} +1.56366 q^{17} +(0.900969 - 0.433884i) q^{18} +(-0.781831 + 0.623490i) q^{20} +(-0.623490 + 0.781831i) q^{25} +(-1.43388 + 0.900969i) q^{26} +(0.433884 + 0.900969i) q^{29} +(-0.222521 + 0.974928i) q^{32} +(0.974928 - 1.22252i) q^{34} +(0.222521 - 0.974928i) q^{36} +(0.193096 - 0.400969i) q^{37} +1.00000i q^{40} +(0.752407 + 0.752407i) q^{41} -1.00000i q^{45} +(0.433884 - 0.900969i) q^{49} +(0.222521 + 0.974928i) q^{50} +(-0.189606 + 1.68280i) q^{52} +(0.222521 + 1.97493i) q^{53} +(0.974928 + 0.222521i) q^{58} +(0.119137 + 0.189606i) q^{61} +(0.623490 + 0.781831i) q^{64} +(0.189606 + 1.68280i) q^{65} +(-0.347948 - 1.52446i) q^{68} +(-0.623490 - 0.781831i) q^{72} +(-0.777479 - 0.974928i) q^{73} +(-0.193096 - 0.400969i) q^{74} +(0.781831 + 0.623490i) q^{80} +(0.623490 + 0.781831i) q^{81} +(1.05737 - 0.119137i) q^{82} +(-0.678448 - 1.40881i) q^{85} +(-1.87590 + 0.211363i) q^{89} +(-0.781831 - 0.623490i) q^{90} +(-1.90097 + 0.433884i) q^{97} +(-0.433884 - 0.900969i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q - 2 q^{2} - 2 q^{4} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q - 2 q^{2} - 2 q^{4} - 2 q^{8} + 2 q^{9} + 2 q^{13} - 2 q^{16} + 2 q^{18} + 2 q^{25} - 12 q^{26} - 2 q^{32} + 2 q^{36} - 2 q^{41} + 2 q^{50} + 2 q^{52} + 2 q^{53} + 2 q^{61} - 2 q^{64} - 2 q^{65} + 2 q^{72} - 10 q^{73} - 2 q^{81} - 2 q^{82} - 2 q^{89} - 14 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

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

\(n\) \(117\) \(291\) \(321\)
\(\chi(n)\) \(e\left(\frac{1}{4}\right)\) \(-1\) \(e\left(\frac{13}{28}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.623490 0.781831i 0.623490 0.781831i
\(3\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(4\) −0.222521 0.974928i −0.222521 0.974928i
\(5\) −0.433884 0.900969i −0.433884 0.900969i
\(6\) 0 0
\(7\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(8\) −0.900969 0.433884i −0.900969 0.433884i
\(9\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(10\) −0.974928 0.222521i −0.974928 0.222521i
\(11\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(12\) 0 0
\(13\) −1.59842 0.559311i −1.59842 0.559311i −0.623490 0.781831i \(-0.714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(17\) 1.56366 1.56366 0.781831 0.623490i \(-0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(18\) 0.900969 0.433884i 0.900969 0.433884i
\(19\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(20\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(24\) 0 0
\(25\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(26\) −1.43388 + 0.900969i −1.43388 + 0.900969i
\(27\) 0 0
\(28\) 0 0
\(29\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(30\) 0 0
\(31\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(32\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(33\) 0 0
\(34\) 0.974928 1.22252i 0.974928 1.22252i
\(35\) 0 0
\(36\) 0.222521 0.974928i 0.222521 0.974928i
\(37\) 0.193096 0.400969i 0.193096 0.400969i −0.781831 0.623490i \(-0.785714\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(38\) 0 0
\(39\) 0 0
\(40\) 1.00000i 1.00000i
\(41\) 0.752407 + 0.752407i 0.752407 + 0.752407i 0.974928 0.222521i \(-0.0714286\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(42\) 0 0
\(43\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(44\) 0 0
\(45\) 1.00000i 1.00000i
\(46\) 0 0
\(47\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(48\) 0 0
\(49\) 0.433884 0.900969i 0.433884 0.900969i
\(50\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(51\) 0 0
\(52\) −0.189606 + 1.68280i −0.189606 + 1.68280i
\(53\) 0.222521 + 1.97493i 0.222521 + 1.97493i 0.222521 + 0.974928i \(0.428571\pi\)
1.00000i \(0.5\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 0 0
\(57\) 0 0
\(58\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(59\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0.119137 + 0.189606i 0.119137 + 0.189606i 0.900969 0.433884i \(-0.142857\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(65\) 0.189606 + 1.68280i 0.189606 + 1.68280i
\(66\) 0 0
\(67\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(68\) −0.347948 1.52446i −0.347948 1.52446i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(72\) −0.623490 0.781831i −0.623490 0.781831i
\(73\) −0.777479 0.974928i −0.777479 0.974928i 0.222521 0.974928i \(-0.428571\pi\)
−1.00000 \(\pi\)
\(74\) −0.193096 0.400969i −0.193096 0.400969i
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) 0 0
\(79\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(80\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(81\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(82\) 1.05737 0.119137i 1.05737 0.119137i
\(83\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(84\) 0 0
\(85\) −0.678448 1.40881i −0.678448 1.40881i
\(86\) 0 0
\(87\) 0 0
\(88\) 0 0
\(89\) −1.87590 + 0.211363i −1.87590 + 0.211363i −0.974928 0.222521i \(-0.928571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(90\) −0.781831 0.623490i −0.781831 0.623490i
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) 0 0
\(95\) 0 0
\(96\) 0 0
\(97\) −1.90097 + 0.433884i −1.90097 + 0.433884i −0.900969 + 0.433884i \(0.857143\pi\)
−1.00000 \(\pi\)
\(98\) −0.433884 0.900969i −0.433884 0.900969i
\(99\) 0 0
\(100\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(101\) 0.656405 + 0.0739590i 0.656405 + 0.0739590i 0.433884 0.900969i \(-0.357143\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(102\) 0 0
\(103\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(104\) 1.19745 + 1.19745i 1.19745 + 1.19745i
\(105\) 0 0
\(106\) 1.68280 + 1.05737i 1.68280 + 1.05737i
\(107\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(108\) 0 0
\(109\) −0.433884 + 1.90097i −0.433884 + 1.90097i 1.00000i \(0.5\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0 0
\(113\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0.781831 0.623490i 0.781831 0.623490i
\(117\) −1.19745 1.19745i −1.19745 1.19745i
\(118\) 0 0
\(119\) 0 0
\(120\) 0 0
\(121\) −0.781831 0.623490i −0.781831 0.623490i
\(122\) 0.222521 + 0.0250721i 0.222521 + 0.0250721i
\(123\) 0 0
\(124\) 0 0
\(125\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(126\) 0 0
\(127\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(128\) 1.00000 1.00000
\(129\) 0 0
\(130\) 1.43388 + 0.900969i 1.43388 + 0.900969i
\(131\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −1.40881 0.678448i −1.40881 0.678448i
\(137\) −0.781831 0.376510i −0.781831 0.376510i 1.00000i \(-0.5\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(138\) 0 0
\(139\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0 0
\(143\) 0 0
\(144\) −1.00000 −1.00000
\(145\) 0.623490 0.781831i 0.623490 0.781831i
\(146\) −1.24698 −1.24698
\(147\) 0 0
\(148\) −0.433884 0.0990311i −0.433884 0.0990311i
\(149\) −0.277479 1.21572i −0.277479 1.21572i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(150\) 0 0
\(151\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(152\) 0 0
\(153\) 1.40881 + 0.678448i 1.40881 + 0.678448i
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) 0.867767i 0.867767i −0.900969 0.433884i \(-0.857143\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0.974928 0.222521i 0.974928 0.222521i
\(161\) 0 0
\(162\) 1.00000 1.00000
\(163\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(164\) 0.566116 0.900969i 0.566116 0.900969i
\(165\) 0 0
\(166\) 0 0
\(167\) 0 0 −0.532032 0.846724i \(-0.678571\pi\)
0.532032 + 0.846724i \(0.321429\pi\)
\(168\) 0 0
\(169\) 1.46028 + 1.16453i 1.46028 + 1.16453i
\(170\) −1.52446 0.347948i −1.52446 0.347948i
\(171\) 0 0
\(172\) 0 0
\(173\) 0.158342 + 0.158342i 0.158342 + 0.158342i 0.781831 0.623490i \(-0.214286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 0 0
\(177\) 0 0
\(178\) −1.00435 + 1.59842i −1.00435 + 1.59842i
\(179\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(180\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(181\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) −0.445042 −0.445042
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) 0 0
\(190\) 0 0
\(191\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(192\) 0 0
\(193\) −1.75676 + 0.400969i −1.75676 + 0.400969i −0.974928 0.222521i \(-0.928571\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(194\) −0.846011 + 1.75676i −0.846011 + 1.75676i
\(195\) 0 0
\(196\) −0.974928 0.222521i −0.974928 0.222521i
\(197\) −0.0739590 + 0.656405i −0.0739590 + 0.656405i 0.900969 + 0.433884i \(0.142857\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(198\) 0 0
\(199\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(200\) 0.900969 0.433884i 0.900969 0.433884i
\(201\) 0 0
\(202\) 0.467085 0.467085i 0.467085 0.467085i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.351438 1.00435i 0.351438 1.00435i
\(206\) 0 0
\(207\) 0 0
\(208\) 1.68280 0.189606i 1.68280 0.189606i
\(209\) 0 0
\(210\) 0 0
\(211\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(212\) 1.87590 0.656405i 1.87590 0.656405i
\(213\) 0 0
\(214\) 0 0
\(215\) 0 0
\(216\) 0 0
\(217\) 0 0
\(218\) 1.21572 + 1.52446i 1.21572 + 1.52446i
\(219\) 0 0
\(220\) 0 0
\(221\) −2.49939 0.874573i −2.49939 0.874573i
\(222\) 0 0
\(223\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(224\) 0 0
\(225\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(226\) −1.12349 1.40881i −1.12349 1.40881i
\(227\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(228\) 0 0
\(229\) −1.05737 1.68280i −1.05737 1.68280i −0.623490 0.781831i \(-0.714286\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 1.00000i 1.00000i
\(233\) −1.33485 + 1.33485i −1.33485 + 1.33485i −0.433884 + 0.900969i \(0.642857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(234\) −1.68280 + 0.189606i −1.68280 + 0.189606i
\(235\) 0 0
\(236\) 0 0
\(237\) 0 0
\(238\) 0 0
\(239\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(240\) 0 0
\(241\) −0.541044 + 1.12349i −0.541044 + 1.12349i 0.433884 + 0.900969i \(0.357143\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(242\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(243\) 0 0
\(244\) 0.158342 0.158342i 0.158342 0.158342i
\(245\) −1.00000 −1.00000
\(246\) 0 0
\(247\) 0 0
\(248\) 0 0
\(249\) 0 0
\(250\) 0.781831 0.623490i 0.781831 0.623490i
\(251\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0 0
\(255\) 0 0
\(256\) 0.623490 0.781831i 0.623490 0.781831i
\(257\) 0.566116 0.900969i 0.566116 0.900969i −0.433884 0.900969i \(-0.642857\pi\)
1.00000 \(0\)
\(258\) 0 0
\(259\) 0 0
\(260\) 1.59842 0.559311i 1.59842 0.559311i
\(261\) 1.00000i 1.00000i
\(262\) 0 0
\(263\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(264\) 0 0
\(265\) 1.68280 1.05737i 1.68280 1.05737i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) −1.78183 + 0.623490i −1.78183 + 0.623490i −0.781831 + 0.623490i \(0.785714\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(272\) −1.40881 + 0.678448i −1.40881 + 0.678448i
\(273\) 0 0
\(274\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(275\) 0 0
\(276\) 0 0
\(277\) −0.211363 0.0739590i −0.211363 0.0739590i 0.222521 0.974928i \(-0.428571\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 1.75676 + 0.846011i 1.75676 + 0.846011i 0.974928 + 0.222521i \(0.0714286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(282\) 0 0
\(283\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(289\) 1.44504 1.44504
\(290\) −0.222521 0.974928i −0.222521 0.974928i
\(291\) 0 0
\(292\) −0.777479 + 0.974928i −0.777479 + 0.974928i
\(293\) 1.90097 + 0.433884i 1.90097 + 0.433884i 1.00000 \(0\)
0.900969 + 0.433884i \(0.142857\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −0.347948 + 0.277479i −0.347948 + 0.277479i
\(297\) 0 0
\(298\) −1.12349 0.541044i −1.12349 0.541044i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) 0 0
\(305\) 0.119137 0.189606i 0.119137 0.189606i
\(306\) 1.40881 0.678448i 1.40881 0.678448i
\(307\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(312\) 0 0
\(313\) −0.222521 0.0250721i −0.222521 0.0250721i 1.00000i \(-0.5\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(314\) −0.678448 0.541044i −0.678448 0.541044i
\(315\) 0 0
\(316\) 0 0
\(317\) 0.974928 + 0.777479i 0.974928 + 0.777479i 0.974928 0.222521i \(-0.0714286\pi\)
1.00000i \(0.5\pi\)
\(318\) 0 0
\(319\) 0 0
\(320\) 0.433884 0.900969i 0.433884 0.900969i
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) 0.623490 0.781831i 0.623490 0.781831i
\(325\) 1.43388 0.900969i 1.43388 0.900969i
\(326\) 0 0
\(327\) 0 0
\(328\) −0.351438 1.00435i −0.351438 1.00435i
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(332\) 0 0
\(333\) 0.347948 0.277479i 0.347948 0.277479i
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0.846011 + 1.75676i 0.846011 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(338\) 1.82094 0.415617i 1.82094 0.415617i
\(339\) 0 0
\(340\) −1.22252 + 0.974928i −1.22252 + 0.974928i
\(341\) 0 0
\(342\) 0 0
\(343\) 0 0
\(344\) 0 0
\(345\) 0 0
\(346\) 0.222521 0.0250721i 0.222521 0.0250721i
\(347\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(348\) 0 0
\(349\) 1.24698i 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 0 0
\(353\) 1.05737 0.119137i 1.05737 0.119137i 0.433884 0.900969i \(-0.357143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.623490 + 1.78183i 0.623490 + 1.78183i
\(357\) 0 0
\(358\) 0 0
\(359\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(360\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(361\) −0.433884 0.900969i −0.433884 0.900969i
\(362\) −1.12349 1.40881i −1.12349 1.40881i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.541044 + 1.12349i −0.541044 + 1.12349i
\(366\) 0 0
\(367\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(368\) 0 0
\(369\) 0.351438 + 1.00435i 0.351438 + 1.00435i
\(370\) −0.277479 + 0.347948i −0.277479 + 0.347948i
\(371\) 0 0
\(372\) 0 0
\(373\) 1.59842 + 1.00435i 1.59842 + 1.00435i 0.974928 + 0.222521i \(0.0714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0 0
\(377\) −0.189606 1.68280i −0.189606 1.68280i
\(378\) 0 0
\(379\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.781831 + 1.62349i −0.781831 + 1.62349i
\(387\) 0 0
\(388\) 0.846011 + 1.75676i 0.846011 + 1.75676i
\(389\) −0.158342 + 0.158342i −0.158342 + 0.158342i −0.781831 0.623490i \(-0.785714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(393\) 0 0
\(394\) 0.467085 + 0.467085i 0.467085 + 0.467085i
\(395\) 0 0
\(396\) 0 0
\(397\) 0.656405 + 1.87590i 0.656405 + 1.87590i 0.433884 + 0.900969i \(0.357143\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0.222521 0.974928i 0.222521 0.974928i
\(401\) 0.277479 0.347948i 0.277479 0.347948i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(402\) 0 0
\(403\) 0 0
\(404\) −0.0739590 0.656405i −0.0739590 0.656405i
\(405\) 0.433884 0.900969i 0.433884 0.900969i
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) −1.59842 + 1.00435i −1.59842 + 1.00435i −0.623490 + 0.781831i \(0.714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(410\) −0.566116 0.900969i −0.566116 0.900969i
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) 0.900969 1.43388i 0.900969 1.43388i
\(417\) 0 0
\(418\) 0 0
\(419\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(420\) 0 0
\(421\) 0.158342 1.40532i 0.158342 1.40532i −0.623490 0.781831i \(-0.714286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(422\) 0 0
\(423\) 0 0
\(424\) 0.656405 1.87590i 0.656405 1.87590i
\(425\) −0.974928 + 1.22252i −0.974928 + 1.22252i
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(432\) 0 0
\(433\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1.94986 1.94986
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(440\) 0 0
\(441\) 0.781831 0.623490i 0.781831 0.623490i
\(442\) −2.24211 + 1.40881i −2.24211 + 1.40881i
\(443\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(444\) 0 0
\(445\) 1.00435 + 1.59842i 1.00435 + 1.59842i
\(446\) 0 0
\(447\) 0 0
\(448\) 0 0
\(449\) 0.222521 1.97493i 0.222521 1.97493i 1.00000i \(-0.5\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(450\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(451\) 0 0
\(452\) −1.80194 −1.80194
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0 0
\(457\) 0.351438 + 0.559311i 0.351438 + 0.559311i 0.974928 0.222521i \(-0.0714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(458\) −1.97493 0.222521i −1.97493 0.222521i
\(459\) 0 0
\(460\) 0 0
\(461\) 1.19745 0.752407i 1.19745 0.752407i 0.222521 0.974928i \(-0.428571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(462\) 0 0
\(463\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(464\) −0.781831 0.623490i −0.781831 0.623490i
\(465\) 0 0
\(466\) 0.211363 + 1.87590i 0.211363 + 1.87590i
\(467\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(468\) −0.900969 + 1.43388i −0.900969 + 1.43388i
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) 0 0
\(473\) 0 0
\(474\) 0 0
\(475\) 0 0
\(476\) 0 0
\(477\) −0.656405 + 1.87590i −0.656405 + 1.87590i
\(478\) 0 0
\(479\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(480\) 0 0
\(481\) −0.532915 + 0.532915i −0.532915 + 0.532915i
\(482\) 0.541044 + 1.12349i 0.541044 + 1.12349i
\(483\) 0 0
\(484\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(485\) 1.21572 + 1.52446i 1.21572 + 1.52446i
\(486\) 0 0
\(487\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(488\) −0.0250721 0.222521i −0.0250721 0.222521i
\(489\) 0 0
\(490\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(491\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(492\) 0 0
\(493\) 0.678448 + 1.40881i 0.678448 + 1.40881i
\(494\) 0 0
\(495\) 0 0
\(496\) 0 0
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(500\) 1.00000i 1.00000i
\(501\) 0 0
\(502\) 0 0
\(503\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(504\) 0 0
\(505\) −0.218169 0.623490i −0.218169 0.623490i
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) 0.193096 + 0.400969i 0.193096 + 0.400969i 0.974928 0.222521i \(-0.0714286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.222521 0.974928i −0.222521 0.974928i
\(513\) 0 0
\(514\) −0.351438 1.00435i −0.351438 1.00435i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0.559311 1.59842i 0.559311 1.59842i
\(521\) 1.80194i 1.80194i 0.433884 + 0.900969i \(0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(522\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(523\) 0 0 0.707107 0.707107i \(-0.250000\pi\)
−0.707107 + 0.707107i \(0.750000\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0 0
\(527\) 0 0
\(528\) 0 0
\(529\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(530\) 0.222521 1.97493i 0.222521 1.97493i
\(531\) 0 0
\(532\) 0 0
\(533\) −0.781831 1.62349i −0.781831 1.62349i
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) −0.623490 + 1.78183i −0.623490 + 1.78183i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.900969 0.566116i −0.900969 0.566116i 1.00000i \(-0.5\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.347948 + 1.52446i −0.347948 + 1.52446i
\(545\) 1.90097 0.433884i 1.90097 0.433884i
\(546\) 0 0
\(547\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(548\) −0.193096 + 0.846011i −0.193096 + 0.846011i
\(549\) 0.0250721 + 0.222521i 0.0250721 + 0.222521i
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) −0.189606 + 0.119137i −0.189606 + 0.119137i
\(555\) 0 0
\(556\) 0 0
\(557\) −1.05737 0.119137i −1.05737 0.119137i −0.433884 0.900969i \(-0.642857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(558\) 0 0
\(559\) 0 0
\(560\) 0 0
\(561\) 0 0
\(562\) 1.75676 0.846011i 1.75676 0.846011i
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0.351438 1.00435i 0.351438 1.00435i −0.623490 0.781831i \(-0.714286\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(570\) 0 0
\(571\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(577\) 0.433884 + 0.0990311i 0.433884 + 0.0990311i 0.433884 0.900969i \(-0.357143\pi\)
1.00000i \(0.5\pi\)
\(578\) 0.900969 1.12978i 0.900969 1.12978i
\(579\) 0 0
\(580\) −0.900969 0.433884i −0.900969 0.433884i
\(581\) 0 0
\(582\) 0 0
\(583\) 0 0
\(584\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(585\) −0.559311 + 1.59842i −0.559311 + 1.59842i
\(586\) 1.52446 1.21572i 1.52446 1.21572i
\(587\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0.445042i 0.445042i
\(593\) −1.87590 0.656405i −1.87590 0.656405i −0.974928 0.222521i \(-0.928571\pi\)
−0.900969 0.433884i \(-0.857143\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(597\) 0 0
\(598\) 0 0
\(599\) 0 0 0.532032 0.846724i \(-0.321429\pi\)
−0.532032 + 0.846724i \(0.678571\pi\)
\(600\) 0 0
\(601\) −1.33485 + 0.467085i −1.33485 + 0.467085i −0.900969 0.433884i \(-0.857143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(606\) 0 0
\(607\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) −0.0739590 0.211363i −0.0739590 0.211363i
\(611\) 0 0
\(612\) 0.347948 1.52446i 0.347948 1.52446i
\(613\) 0.566116 0.900969i 0.566116 0.900969i −0.433884 0.900969i \(-0.642857\pi\)
1.00000 \(0\)
\(614\) 0 0
\(615\) 0 0
\(616\) 0 0
\(617\) 0.376510 0.781831i 0.376510 0.781831i −0.623490 0.781831i \(-0.714286\pi\)
1.00000 \(0\)
\(618\) 0 0
\(619\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 0 0
\(625\) −0.222521 0.974928i −0.222521 0.974928i
\(626\) −0.158342 + 0.158342i −0.158342 + 0.158342i
\(627\) 0 0
\(628\) −0.846011 + 0.193096i −0.846011 + 0.193096i
\(629\) 0.301938 0.626980i 0.301938 0.626980i
\(630\) 0 0
\(631\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) 1.21572 0.277479i 1.21572 0.277479i
\(635\) 0 0
\(636\) 0 0
\(637\) −1.19745 + 1.19745i −1.19745 + 1.19745i
\(638\) 0 0
\(639\) 0 0
\(640\) −0.433884 0.900969i −0.433884 0.900969i
\(641\) −0.752407 1.19745i −0.752407 1.19745i −0.974928 0.222521i \(-0.928571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(642\) 0 0
\(643\) 0 0 0.993712 0.111964i \(-0.0357143\pi\)
−0.993712 + 0.111964i \(0.964286\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.943883 0.330279i \(-0.107143\pi\)
−0.943883 + 0.330279i \(0.892857\pi\)
\(648\) −0.222521 0.974928i −0.222521 0.974928i
\(649\) 0 0
\(650\) 0.189606 1.68280i 0.189606 1.68280i
\(651\) 0 0
\(652\) 0 0
\(653\) 0.277479 + 0.347948i 0.277479 + 0.347948i 0.900969 0.433884i \(-0.142857\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00435 0.351438i −1.00435 0.351438i
\(657\) −0.277479 1.21572i −0.277479 1.21572i
\(658\) 0 0
\(659\) 0 0 −0.330279 0.943883i \(-0.607143\pi\)
0.330279 + 0.943883i \(0.392857\pi\)
\(660\) 0 0
\(661\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(662\) 0 0
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0.445042i 0.445042i
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 0.0739590 0.656405i 0.0739590 0.656405i −0.900969 0.433884i \(-0.857143\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(674\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(675\) 0 0
\(676\) 0.810394 1.68280i 0.810394 1.68280i
\(677\) 0.846011 0.193096i 0.846011 0.193096i 0.222521 0.974928i \(-0.428571\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 1.56366i 1.56366i
\(681\) 0 0
\(682\) 0 0
\(683\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(684\) 0 0
\(685\) 0.867767i 0.867767i
\(686\) 0 0
\(687\) 0 0
\(688\) 0 0
\(689\) 0.748917 3.28122i 0.748917 3.28122i
\(690\) 0 0
\(691\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(692\) 0.119137 0.189606i 0.119137 0.189606i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 1.17651 + 1.17651i 1.17651 + 1.17651i
\(698\) −0.974928 0.777479i −0.974928 0.777479i
\(699\) 0 0
\(700\) 0 0
\(701\) −1.22252 0.974928i −1.22252 0.974928i −0.222521 0.974928i \(-0.571429\pi\)
−1.00000 \(\pi\)
\(702\) 0 0
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 0.566116 0.900969i 0.566116 0.900969i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.781831 0.376510i 0.781831 0.376510i 1.00000i \(-0.5\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 1.78183 + 0.623490i 1.78183 + 0.623490i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(720\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(721\) 0 0
\(722\) −0.974928 0.222521i −0.974928 0.222521i
\(723\) 0 0
\(724\) −1.80194 −1.80194
\(725\) −0.974928 0.222521i −0.974928 0.222521i
\(726\) 0 0
\(727\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(728\) 0 0
\(729\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(730\) 0.541044 + 1.12349i 0.541044 + 1.12349i
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(734\) 0 0
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 1.00435 + 0.351438i 1.00435 + 0.351438i
\(739\) 0 0 0.111964 0.993712i \(-0.464286\pi\)
−0.111964 + 0.993712i \(0.535714\pi\)
\(740\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(741\) 0 0
\(742\) 0 0
\(743\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(744\) 0 0
\(745\) −0.974928 + 0.777479i −0.974928 + 0.777479i
\(746\) 1.78183 0.623490i 1.78183 0.623490i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) −1.43388 0.900969i −1.43388 0.900969i
\(755\) 0 0
\(756\) 0 0
\(757\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) −0.193096 + 0.846011i −0.193096 + 0.846011i 0.781831 + 0.623490i \(0.214286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 1.56366i 1.56366i
\(766\) 0 0
\(767\) 0 0
\(768\) 0 0
\(769\) −0.656405 0.0739590i −0.656405 0.0739590i −0.222521 0.974928i \(-0.571429\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.781831 + 1.62349i 0.781831 + 1.62349i
\(773\) 1.75676 0.400969i 1.75676 0.400969i 0.781831 0.623490i \(-0.214286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.90097 + 0.433884i 1.90097 + 0.433884i
\(777\) 0 0
\(778\) 0.0250721 + 0.222521i 0.0250721 + 0.222521i
\(779\) 0 0
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000i 1.00000i
\(785\) −0.781831 + 0.376510i −0.781831 + 0.376510i
\(786\) 0 0
\(787\) 0 0 −0.846724 0.532032i \(-0.821429\pi\)
0.846724 + 0.532032i \(0.178571\pi\)
\(788\) 0.656405 0.0739590i 0.656405 0.0739590i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) −0.0843826 0.369704i −0.0843826 0.369704i
\(794\) 1.87590 + 0.656405i 1.87590 + 0.656405i
\(795\) 0 0
\(796\) 0 0
\(797\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.623490 0.781831i −0.623490 0.781831i
\(801\) −1.78183 0.623490i −1.78183 0.623490i
\(802\) −0.0990311 0.433884i −0.0990311 0.433884i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0 0
\(808\) −0.559311 0.351438i −0.559311 0.351438i
\(809\) −0.900969 1.43388i −0.900969 1.43388i −0.900969 0.433884i \(-0.857143\pi\)
1.00000i \(-0.5\pi\)
\(810\) −0.433884 0.900969i −0.433884 0.900969i
\(811\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0 0
\(817\) 0 0
\(818\) −0.211363 + 1.87590i −0.211363 + 1.87590i
\(819\) 0 0
\(820\) −1.05737 0.119137i −1.05737 0.119137i
\(821\) −0.678448 + 1.40881i −0.678448 + 1.40881i 0.222521 + 0.974928i \(0.428571\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(822\) 0 0
\(823\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(828\) 0 0
\(829\) −1.19745 1.19745i −1.19745 1.19745i −0.974928 0.222521i \(-0.928571\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −0.559311 1.59842i −0.559311 1.59842i
\(833\) 0.678448 1.40881i 0.678448 1.40881i
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) 0 0 −0.111964 0.993712i \(-0.535714\pi\)
0.111964 + 0.993712i \(0.464286\pi\)
\(840\) 0 0
\(841\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(842\) −1.00000 1.00000i −1.00000 1.00000i
\(843\) 0 0
\(844\) 0 0
\(845\) 0.415617 1.82094i 0.415617 1.82094i
\(846\) 0 0
\(847\) 0 0
\(848\) −1.05737 1.68280i −1.05737 1.68280i
\(849\) 0 0
\(850\) 0.347948 + 1.52446i 0.347948 + 1.52446i
\(851\) 0 0
\(852\) 0 0
\(853\) 0.867767 0.867767 0.433884 0.900969i \(-0.357143\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0 0
\(857\) 1.33485 + 0.467085i 1.33485 + 0.467085i 0.900969 0.433884i \(-0.142857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(858\) 0 0
\(859\) 0 0 0.330279 0.943883i \(-0.392857\pi\)
−0.330279 + 0.943883i \(0.607143\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.846724 0.532032i \(-0.178571\pi\)
−0.846724 + 0.532032i \(0.821429\pi\)
\(864\) 0 0
\(865\) 0.0739590 0.211363i 0.0739590 0.211363i
\(866\) 0 0
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) 1.21572 1.52446i 1.21572 1.52446i
\(873\) −1.90097 0.433884i −1.90097 0.433884i
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) −1.19745 + 0.752407i −1.19745 + 0.752407i −0.974928 0.222521i \(-0.928571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0 0
\(881\) 0.656405 1.87590i 0.656405 1.87590i 0.222521 0.974928i \(-0.428571\pi\)
0.433884 0.900969i \(-0.357143\pi\)
\(882\) 1.00000i 1.00000i
\(883\) 0 0 −0.943883 0.330279i \(-0.892857\pi\)
0.943883 + 0.330279i \(0.107143\pi\)
\(884\) −0.296480 + 2.63133i −0.296480 + 2.63133i
\(885\) 0 0
\(886\) 0 0
\(887\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 1.87590 + 0.211363i 1.87590 + 0.211363i
\(891\) 0 0
\(892\) 0 0
\(893\) 0 0
\(894\) 0 0
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) −1.40532 1.40532i −1.40532 1.40532i
\(899\) 0 0
\(900\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(901\) 0.347948 + 3.08812i 0.347948 + 3.08812i
\(902\) 0 0
\(903\) 0 0
\(904\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(905\) −1.75676 + 0.400969i −1.75676 + 0.400969i
\(906\) 0 0
\(907\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(908\) 0 0
\(909\) 0.559311 + 0.351438i 0.559311 + 0.351438i
\(910\) 0 0
\(911\) 0 0 −0.707107 0.707107i \(-0.750000\pi\)
0.707107 + 0.707107i \(0.250000\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 0.656405 + 0.0739590i 0.656405 + 0.0739590i
\(915\) 0 0
\(916\) −1.40532 + 1.40532i −1.40532 + 1.40532i
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.158342 1.40532i 0.158342 1.40532i
\(923\) 0 0
\(924\) 0 0
\(925\) 0.193096 + 0.400969i 0.193096 + 0.400969i
\(926\) 0 0
\(927\) 0 0
\(928\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(929\) 1.94986i 1.94986i 0.222521 + 0.974928i \(0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 1.59842 + 1.00435i 1.59842 + 1.00435i
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0.559311 + 1.59842i 0.559311 + 1.59842i
\(937\) 0.623490 0.218169i 0.623490 0.218169i 1.00000i \(-0.5\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(948\) 0 0
\(949\) 0.697449 + 1.99319i 0.697449 + 1.99319i
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.900969 + 0.566116i 0.900969 + 0.566116i 0.900969 0.433884i \(-0.142857\pi\)
1.00000i \(0.5\pi\)
\(954\) 1.05737 + 1.68280i 1.05737 + 1.68280i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0 0
\(959\) 0 0
\(960\) 0 0
\(961\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(962\) 0.0843826 + 0.748917i 0.0843826 + 0.748917i
\(963\) 0 0
\(964\) 1.21572 + 0.277479i 1.21572 + 0.277479i
\(965\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(966\) 0 0
\(967\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(968\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(969\) 0 0
\(970\) 1.94986 1.94986
\(971\) 0 0 −0.993712 0.111964i \(-0.964286\pi\)
0.993712 + 0.111964i \(0.0357143\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) −0.189606 0.119137i −0.189606 0.119137i
\(977\) −0.623490 1.78183i −0.623490 1.78183i −0.623490 0.781831i \(-0.714286\pi\)
1.00000i \(-0.5\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(981\) −1.21572 + 1.52446i −1.21572 + 1.52446i
\(982\) 0 0
\(983\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(984\) 0 0
\(985\) 0.623490 0.218169i 0.623490 0.218169i
\(986\) 1.52446 + 0.347948i 1.52446 + 0.347948i
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) −1.62349 + 0.781831i −1.62349 + 0.781831i −0.623490 + 0.781831i \(0.714286\pi\)
−1.00000 \(1.00000\pi\)
\(998\) 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.bd.a.507.1 yes 12
4.3 odd 2 CM 580.1.bd.a.507.1 yes 12
5.2 odd 4 2900.1.cg.b.43.1 12
5.3 odd 4 580.1.bm.a.43.1 yes 12
5.4 even 2 2900.1.bx.c.507.1 12
20.3 even 4 580.1.bm.a.43.1 yes 12
20.7 even 4 2900.1.cg.b.43.1 12
20.19 odd 2 2900.1.bx.c.507.1 12
29.27 odd 28 580.1.bm.a.27.1 yes 12
116.27 even 28 580.1.bm.a.27.1 yes 12
145.27 even 28 2900.1.bx.c.143.1 12
145.114 odd 28 2900.1.cg.b.607.1 12
145.143 even 28 inner 580.1.bd.a.143.1 12
580.27 odd 28 2900.1.bx.c.143.1 12
580.143 odd 28 inner 580.1.bd.a.143.1 12
580.259 even 28 2900.1.cg.b.607.1 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
580.1.bd.a.143.1 12 145.143 even 28 inner
580.1.bd.a.143.1 12 580.143 odd 28 inner
580.1.bd.a.507.1 yes 12 1.1 even 1 trivial
580.1.bd.a.507.1 yes 12 4.3 odd 2 CM
580.1.bm.a.27.1 yes 12 29.27 odd 28
580.1.bm.a.27.1 yes 12 116.27 even 28
580.1.bm.a.43.1 yes 12 5.3 odd 4
580.1.bm.a.43.1 yes 12 20.3 even 4
2900.1.bx.c.143.1 12 145.27 even 28
2900.1.bx.c.143.1 12 580.27 odd 28
2900.1.bx.c.507.1 12 5.4 even 2
2900.1.bx.c.507.1 12 20.19 odd 2
2900.1.cg.b.43.1 12 5.2 odd 4
2900.1.cg.b.43.1 12 20.7 even 4
2900.1.cg.b.607.1 12 145.114 odd 28
2900.1.cg.b.607.1 12 580.259 even 28