Properties

Label 3364.1.j.f.2287.2
Level $3364$
Weight $1$
Character 3364.2287
Analytic conductor $1.679$
Analytic rank $0$
Dimension $12$
Projective image $D_{3}$
CM discriminant -116
Inner twists $24$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3364,1,Mod(571,3364)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3364, base_ring=CyclotomicField(14))
 
chi = DirichletCharacter(H, H._module([7, 12]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3364.571");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3364 = 2^{2} \cdot 29^{2} \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3364.j (of order \(14\), degree \(6\), not minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.67885470250\)
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: no (minimal twist has level 116)
Projective image: \(D_{3}\)
Projective field: Galois closure of 3.1.116.1

Embedding invariants

Embedding label 2287.2
Root \(-0.781831 - 0.623490i\) of defining polynomial
Character \(\chi\) \(=\) 3364.2287
Dual form 3364.1.j.f.2327.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.974928 + 0.222521i) q^{2} +(-0.433884 - 0.900969i) q^{3} +(0.900969 + 0.433884i) q^{4} +(-0.222521 + 0.974928i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(0.781831 + 0.623490i) q^{8} +O(q^{10})\) \(q+(0.974928 + 0.222521i) q^{2} +(-0.433884 - 0.900969i) q^{3} +(0.900969 + 0.433884i) q^{4} +(-0.222521 + 0.974928i) q^{5} +(-0.222521 - 0.974928i) q^{6} +(0.781831 + 0.623490i) q^{8} +(-0.433884 + 0.900969i) q^{10} +(-0.781831 + 0.623490i) q^{11} -1.00000i q^{12} +(0.623490 + 0.781831i) q^{13} +(0.974928 - 0.222521i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-0.867767 + 1.80194i) q^{19} +(-0.623490 + 0.781831i) q^{20} +(-0.900969 + 0.433884i) q^{22} +(0.222521 - 0.974928i) q^{24} +(0.433884 + 0.900969i) q^{26} +(-0.974928 - 0.222521i) q^{27} +1.00000 q^{30} +(-0.974928 - 0.222521i) q^{31} +(0.433884 + 0.900969i) q^{32} +(0.900969 + 0.433884i) q^{33} +(-1.24698 + 1.56366i) q^{38} +(0.433884 - 0.900969i) q^{39} +(-0.781831 + 0.623490i) q^{40} +(0.974928 - 0.222521i) q^{43} +(-0.974928 + 0.222521i) q^{44} +(0.781831 - 0.623490i) q^{47} +(0.433884 - 0.900969i) q^{48} +(0.623490 - 0.781831i) q^{49} +(0.222521 + 0.974928i) q^{52} +(0.222521 - 0.974928i) q^{53} +(-0.900969 - 0.433884i) q^{54} +(-0.433884 - 0.900969i) q^{55} +2.00000 q^{57} +(0.974928 + 0.222521i) q^{60} +(-0.900969 - 0.433884i) q^{62} +(0.222521 + 0.974928i) q^{64} +(-0.900969 + 0.433884i) q^{65} +(0.781831 + 0.623490i) q^{66} +(-1.56366 + 1.24698i) q^{76} +(0.623490 - 0.781831i) q^{78} +(0.781831 + 0.623490i) q^{79} +(-0.900969 + 0.433884i) q^{80} +(0.222521 + 0.974928i) q^{81} +1.00000 q^{86} -1.00000 q^{88} +(0.222521 + 0.974928i) q^{93} +(0.900969 - 0.433884i) q^{94} +(-1.56366 - 1.24698i) q^{95} +(0.623490 - 0.781831i) q^{96} +(0.781831 - 0.623490i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + 2 q^{4} - 2 q^{5} - 2 q^{6}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{13} - 2 q^{16} + 2 q^{20} - 2 q^{22} + 2 q^{24} + 12 q^{30} + 2 q^{33} + 4 q^{38} - 2 q^{49} + 2 q^{52} + 2 q^{53} - 2 q^{54} + 24 q^{57} - 2 q^{62} + 2 q^{64} - 2 q^{65} - 2 q^{78} - 2 q^{80} + 2 q^{81} + 12 q^{86} - 12 q^{88} + 2 q^{93} + 2 q^{94} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3364\mathbb{Z}\right)^\times\).

\(n\) \(1683\) \(2525\)
\(\chi(n)\) \(-1\) \(e\left(\frac{4}{7}\right)\)

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
\(3\) −0.433884 0.900969i −0.433884 0.900969i −0.997204 0.0747301i \(-0.976190\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(4\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(5\) −0.222521 + 0.974928i −0.222521 + 0.974928i 0.733052 + 0.680173i \(0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(6\) −0.222521 0.974928i −0.222521 0.974928i
\(7\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(8\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(9\) 0 0
\(10\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(11\) −0.781831 + 0.623490i −0.781831 + 0.623490i −0.930874 0.365341i \(-0.880952\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(12\) 1.00000i 1.00000i
\(13\) 0.623490 + 0.781831i 0.623490 + 0.781831i 0.988831 0.149042i \(-0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(14\) 0 0
\(15\) 0.974928 0.222521i 0.974928 0.222521i
\(16\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(17\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −0.867767 + 1.80194i −0.867767 + 1.80194i −0.433884 + 0.900969i \(0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(20\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(21\) 0 0
\(22\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(23\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(24\) 0.222521 0.974928i 0.222521 0.974928i
\(25\) 0 0
\(26\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(27\) −0.974928 0.222521i −0.974928 0.222521i
\(28\) 0 0
\(29\) 0 0
\(30\) 1.00000 1.00000
\(31\) −0.974928 0.222521i −0.974928 0.222521i −0.294755 0.955573i \(-0.595238\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(32\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(33\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(34\) 0 0
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(38\) −1.24698 + 1.56366i −1.24698 + 1.56366i
\(39\) 0.433884 0.900969i 0.433884 0.900969i
\(40\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(41\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(42\) 0 0
\(43\) 0.974928 0.222521i 0.974928 0.222521i 0.294755 0.955573i \(-0.404762\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(44\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(45\) 0 0
\(46\) 0 0
\(47\) 0.781831 0.623490i 0.781831 0.623490i −0.149042 0.988831i \(-0.547619\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(48\) 0.433884 0.900969i 0.433884 0.900969i
\(49\) 0.623490 0.781831i 0.623490 0.781831i
\(50\) 0 0
\(51\) 0 0
\(52\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(53\) 0.222521 0.974928i 0.222521 0.974928i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(54\) −0.900969 0.433884i −0.900969 0.433884i
\(55\) −0.433884 0.900969i −0.433884 0.900969i
\(56\) 0 0
\(57\) 2.00000 2.00000
\(58\) 0 0
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(61\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(62\) −0.900969 0.433884i −0.900969 0.433884i
\(63\) 0 0
\(64\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(65\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(66\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(67\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(68\) 0 0
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(72\) 0 0
\(73\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) −1.56366 + 1.24698i −1.56366 + 1.24698i
\(77\) 0 0
\(78\) 0.623490 0.781831i 0.623490 0.781831i
\(79\) 0.781831 + 0.623490i 0.781831 + 0.623490i 0.930874 0.365341i \(-0.119048\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(80\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(81\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(82\) 0 0
\(83\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 1.00000 1.00000
\(87\) 0 0
\(88\) −1.00000 −1.00000
\(89\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(94\) 0.900969 0.433884i 0.900969 0.433884i
\(95\) −1.56366 1.24698i −1.56366 1.24698i
\(96\) 0.623490 0.781831i 0.623490 0.781831i
\(97\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(98\) 0.781831 0.623490i 0.781831 0.623490i
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(102\) 0 0
\(103\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(104\) 1.00000i 1.00000i
\(105\) 0 0
\(106\) 0.433884 0.900969i 0.433884 0.900969i
\(107\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(108\) −0.781831 0.623490i −0.781831 0.623490i
\(109\) −0.900969 + 0.433884i −0.900969 + 0.433884i −0.826239 0.563320i \(-0.809524\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(110\) −0.222521 0.974928i −0.222521 0.974928i
\(111\) 0 0
\(112\) 0 0
\(113\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(114\) 1.94986 + 0.445042i 1.94986 + 0.445042i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0 0
\(119\) 0 0
\(120\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(121\) 0 0
\(122\) 0 0
\(123\) 0 0
\(124\) −0.781831 0.623490i −0.781831 0.623490i
\(125\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(126\) 0 0
\(127\) 1.56366 1.24698i 1.56366 1.24698i 0.781831 0.623490i \(-0.214286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(128\) 1.00000i 1.00000i
\(129\) −0.623490 0.781831i −0.623490 0.781831i
\(130\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(131\) 1.94986 0.445042i 1.94986 0.445042i 0.974928 0.222521i \(-0.0714286\pi\)
0.974928 0.222521i \(-0.0714286\pi\)
\(132\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(133\) 0 0
\(134\) 0 0
\(135\) 0.433884 0.900969i 0.433884 0.900969i
\(136\) 0 0
\(137\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(138\) 0 0
\(139\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(140\) 0 0
\(141\) −0.900969 0.433884i −0.900969 0.433884i
\(142\) 0 0
\(143\) −0.974928 0.222521i −0.974928 0.222521i
\(144\) 0 0
\(145\) 0 0
\(146\) 0 0
\(147\) −0.974928 0.222521i −0.974928 0.222521i
\(148\) 0 0
\(149\) −0.900969 0.433884i −0.900969 0.433884i −0.0747301 0.997204i \(-0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(150\) 0 0
\(151\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(152\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.433884 0.900969i 0.433884 0.900969i
\(156\) 0.781831 0.623490i 0.781831 0.623490i
\(157\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(158\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(159\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(160\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(161\) 0 0
\(162\) 1.00000i 1.00000i
\(163\) 0.781831 0.623490i 0.781831 0.623490i −0.149042 0.988831i \(-0.547619\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(164\) 0 0
\(165\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(166\) 0 0
\(167\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(168\) 0 0
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(173\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.974928 0.222521i −0.974928 0.222521i
\(177\) 0 0
\(178\) 0 0
\(179\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(180\) 0 0
\(181\) 0.900969 0.433884i 0.900969 0.433884i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 1.00000i 1.00000i
\(187\) 0 0
\(188\) 0.974928 0.222521i 0.974928 0.222521i
\(189\) 0 0
\(190\) −1.24698 1.56366i −1.24698 1.56366i
\(191\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(192\) 0.781831 0.623490i 0.781831 0.623490i
\(193\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(194\) 0 0
\(195\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(196\) 0.900969 0.433884i 0.900969 0.433884i
\(197\) −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(198\) 0 0
\(199\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 0 0
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(209\) −0.445042 1.94986i −0.445042 1.94986i
\(210\) 0 0
\(211\) −0.781831 0.623490i −0.781831 0.623490i 0.149042 0.988831i \(-0.452381\pi\)
−0.930874 + 0.365341i \(0.880952\pi\)
\(212\) 0.623490 0.781831i 0.623490 0.781831i
\(213\) 0 0
\(214\) 0 0
\(215\) 1.00000i 1.00000i
\(216\) −0.623490 0.781831i −0.623490 0.781831i
\(217\) 0 0
\(218\) −0.974928 + 0.222521i −0.974928 + 0.222521i
\(219\) 0 0
\(220\) 1.00000i 1.00000i
\(221\) 0 0
\(222\) 0 0
\(223\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(228\) 1.80194 + 0.867767i 1.80194 + 0.867767i
\(229\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0 0
\(233\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(234\) 0 0
\(235\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(236\) 0 0
\(237\) 0.222521 0.974928i 0.222521 0.974928i
\(238\) 0 0
\(239\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(240\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(241\) 0.623490 0.781831i 0.623490 0.781831i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(246\) 0 0
\(247\) −1.94986 + 0.445042i −1.94986 + 0.445042i
\(248\) −0.623490 0.781831i −0.623490 0.781831i
\(249\) 0 0
\(250\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(251\) 0.433884 0.900969i 0.433884 0.900969i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.80194 0.867767i 1.80194 0.867767i
\(255\) 0 0
\(256\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(257\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(258\) −0.433884 0.900969i −0.433884 0.900969i
\(259\) 0 0
\(260\) −1.00000 −1.00000
\(261\) 0 0
\(262\) 2.00000 2.00000
\(263\) −0.974928 0.222521i −0.974928 0.222521i −0.294755 0.955573i \(-0.595238\pi\)
−0.680173 + 0.733052i \(0.738095\pi\)
\(264\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(265\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(266\) 0 0
\(267\) 0 0
\(268\) 0 0
\(269\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(270\) 0.623490 0.781831i 0.623490 0.781831i
\(271\) −0.433884 + 0.900969i −0.433884 + 0.900969i 0.563320 + 0.826239i \(0.309524\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(272\) 0 0
\(273\) 0 0
\(274\) 0 0
\(275\) 0 0
\(276\) 0 0
\(277\) 1.24698 + 1.56366i 1.24698 + 1.56366i 0.623490 + 0.781831i \(0.285714\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) −0.623490 + 0.781831i −0.623490 + 0.781831i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(282\) −0.781831 0.623490i −0.781831 0.623490i
\(283\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(284\) 0 0
\(285\) −0.445042 + 1.94986i −0.445042 + 1.94986i
\(286\) −0.900969 0.433884i −0.900969 0.433884i
\(287\) 0 0
\(288\) 0 0
\(289\) −1.00000 −1.00000
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(294\) −0.900969 0.433884i −0.900969 0.433884i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.900969 0.433884i 0.900969 0.433884i
\(298\) −0.781831 0.623490i −0.781831 0.623490i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) 0 0
\(303\) 0 0
\(304\) −1.94986 + 0.445042i −1.94986 + 0.445042i
\(305\) 0 0
\(306\) 0 0
\(307\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.623490 0.781831i 0.623490 0.781831i
\(311\) −1.56366 1.24698i −1.56366 1.24698i −0.781831 0.623490i \(-0.785714\pi\)
−0.781831 0.623490i \(-0.785714\pi\)
\(312\) 0.900969 0.433884i 0.900969 0.433884i
\(313\) 0.222521 + 0.974928i 0.222521 + 0.974928i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(317\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(318\) −1.00000 −1.00000
\(319\) 0 0
\(320\) −1.00000 −1.00000
\(321\) 0 0
\(322\) 0 0
\(323\) 0 0
\(324\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(325\) 0 0
\(326\) 0.900969 0.433884i 0.900969 0.433884i
\(327\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(328\) 0 0
\(329\) 0 0
\(330\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(331\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0 0
\(335\) 0 0
\(336\) 0 0
\(337\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0.900969 0.433884i 0.900969 0.433884i
\(342\) 0 0
\(343\) 0 0
\(344\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(345\) 0 0
\(346\) −1.94986 0.445042i −1.94986 0.445042i
\(347\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(348\) 0 0
\(349\) −1.00000 −1.00000 −0.500000 0.866025i \(-0.666667\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(350\) 0 0
\(351\) −0.433884 0.900969i −0.433884 0.900969i
\(352\) −0.900969 0.433884i −0.900969 0.433884i
\(353\) 0.445042 1.94986i 0.445042 1.94986i 0.222521 0.974928i \(-0.428571\pi\)
0.222521 0.974928i \(-0.428571\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 0 0
\(358\) 0 0
\(359\) −0.781831 + 0.623490i −0.781831 + 0.623490i −0.930874 0.365341i \(-0.880952\pi\)
0.149042 + 0.988831i \(0.452381\pi\)
\(360\) 0 0
\(361\) −1.87047 2.34549i −1.87047 2.34549i
\(362\) 0.974928 0.222521i 0.974928 0.222521i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) 0 0
\(367\) −0.867767 + 1.80194i −0.867767 + 1.80194i −0.433884 + 0.900969i \(0.642857\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 0 0
\(372\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(373\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(374\) 0 0
\(375\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(376\) 1.00000 1.00000
\(377\) 0 0
\(378\) 0 0
\(379\) 1.94986 + 0.445042i 1.94986 + 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(380\) −0.867767 1.80194i −0.867767 1.80194i
\(381\) −1.80194 0.867767i −1.80194 0.867767i
\(382\) 0.445042 1.94986i 0.445042 1.94986i
\(383\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(384\) 0.900969 0.433884i 0.900969 0.433884i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(390\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(391\) 0 0
\(392\) 0.974928 0.222521i 0.974928 0.222521i
\(393\) −1.24698 1.56366i −1.24698 1.56366i
\(394\) 2.00000i 2.00000i
\(395\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(396\) 0 0
\(397\) −0.623490 + 0.781831i −0.623490 + 0.781831i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(398\) 0 0
\(399\) 0 0
\(400\) 0 0
\(401\) 0.222521 0.974928i 0.222521 0.974928i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(402\) 0 0
\(403\) −0.433884 0.900969i −0.433884 0.900969i
\(404\) 0 0
\(405\) −1.00000 −1.00000
\(406\) 0 0
\(407\) 0 0
\(408\) 0 0
\(409\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(417\) 0 0
\(418\) 2.00000i 2.00000i
\(419\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(420\) 0 0
\(421\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(422\) −0.623490 0.781831i −0.623490 0.781831i
\(423\) 0 0
\(424\) 0.781831 0.623490i 0.781831 0.623490i
\(425\) 0 0
\(426\) 0 0
\(427\) 0 0
\(428\) 0 0
\(429\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(430\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(431\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(432\) −0.433884 0.900969i −0.433884 0.900969i
\(433\) 0 0 −0.974928 0.222521i \(-0.928571\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00000 −1.00000
\(437\) 0 0
\(438\) 0 0
\(439\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(440\) 0.222521 0.974928i 0.222521 0.974928i
\(441\) 0 0
\(442\) 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 0
\(446\) 0 0
\(447\) 1.00000i 1.00000i
\(448\) 0 0
\(449\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 1.56366 + 1.24698i 1.56366 + 1.24698i
\(457\) 1.80194 0.867767i 1.80194 0.867767i 0.900969 0.433884i \(-0.142857\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(458\) 0 0
\(459\) 0 0
\(460\) 0 0
\(461\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(464\) 0 0
\(465\) −1.00000 −1.00000
\(466\) −0.974928 0.222521i −0.974928 0.222521i
\(467\) −0.433884 0.900969i −0.433884 0.900969i −0.997204 0.0747301i \(-0.976190\pi\)
0.563320 0.826239i \(-0.309524\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(471\) 0 0
\(472\) 0 0
\(473\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(474\) 0.433884 0.900969i 0.433884 0.900969i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.974928 + 0.222521i −0.974928 + 0.222521i −0.680173 0.733052i \(-0.738095\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(480\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(481\) 0 0
\(482\) 0.781831 0.623490i 0.781831 0.623490i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(488\) 0 0
\(489\) −0.900969 0.433884i −0.900969 0.433884i
\(490\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(491\) 0.974928 + 0.222521i 0.974928 + 0.222521i 0.680173 0.733052i \(-0.261905\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) −2.00000 −2.00000
\(495\) 0 0
\(496\) −0.433884 0.900969i −0.433884 0.900969i
\(497\) 0 0
\(498\) 0 0
\(499\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(500\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(501\) 0 0
\(502\) 0.623490 0.781831i 0.623490 0.781831i
\(503\) −0.433884 + 0.900969i −0.433884 + 0.900969i 0.563320 + 0.826239i \(0.309524\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 1.94986 0.445042i 1.94986 0.445042i
\(509\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(513\) 1.24698 1.56366i 1.24698 1.56366i
\(514\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(515\) 0 0
\(516\) −0.222521 0.974928i −0.222521 0.974928i
\(517\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(518\) 0 0
\(519\) 0.867767 + 1.80194i 0.867767 + 1.80194i
\(520\) −0.974928 0.222521i −0.974928 0.222521i
\(521\) 1.00000 1.00000 0.500000 0.866025i \(-0.333333\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(524\) 1.94986 + 0.445042i 1.94986 + 0.445042i
\(525\) 0 0
\(526\) −0.900969 0.433884i −0.900969 0.433884i
\(527\) 0 0
\(528\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(529\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(530\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 1.00000i 1.00000i
\(540\) 0.781831 0.623490i 0.781831 0.623490i
\(541\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(542\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(543\) −0.781831 0.623490i −0.781831 0.623490i
\(544\) 0 0
\(545\) −0.222521 0.974928i −0.222521 0.974928i
\(546\) 0 0
\(547\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(548\) 0 0
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) 0 0
\(554\) 0.867767 + 1.80194i 0.867767 + 1.80194i
\(555\) 0 0
\(556\) 0 0
\(557\) 0.445042 + 1.94986i 0.445042 + 1.94986i 0.222521 + 0.974928i \(0.428571\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(558\) 0 0
\(559\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(560\) 0 0
\(561\) 0 0
\(562\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(563\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(564\) −0.623490 0.781831i −0.623490 0.781831i
\(565\) 0 0
\(566\) 0 0
\(567\) 0 0
\(568\) 0 0
\(569\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(570\) −0.867767 + 1.80194i −0.867767 + 1.80194i
\(571\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(572\) −0.781831 0.623490i −0.781831 0.623490i
\(573\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(578\) −0.974928 0.222521i −0.974928 0.222521i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(584\) 0 0
\(585\) 0 0
\(586\) 0 0
\(587\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(588\) −0.781831 0.623490i −0.781831 0.623490i
\(589\) 1.24698 1.56366i 1.24698 1.56366i
\(590\) 0 0
\(591\) −1.56366 + 1.24698i −1.56366 + 1.24698i
\(592\) 0 0
\(593\) 0.623490 + 0.781831i 0.623490 + 0.781831i 0.988831 0.149042i \(-0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(594\) 0.974928 0.222521i 0.974928 0.222521i
\(595\) 0 0
\(596\) −0.623490 0.781831i −0.623490 0.781831i
\(597\) 0 0
\(598\) 0 0
\(599\) 0.433884 0.900969i 0.433884 0.900969i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(600\) 0 0
\(601\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0 0
\(607\) 0.974928 + 0.222521i 0.974928 + 0.222521i 0.680173 0.733052i \(-0.261905\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(608\) −2.00000 −2.00000
\(609\) 0 0
\(610\) 0 0
\(611\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(612\) 0 0
\(613\) −0.900969 0.433884i −0.900969 0.433884i −0.0747301 0.997204i \(-0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(614\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(615\) 0 0
\(616\) 0 0
\(617\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(618\) 0 0
\(619\) −0.433884 + 0.900969i −0.433884 + 0.900969i 0.563320 + 0.826239i \(0.309524\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(620\) 0.781831 0.623490i 0.781831 0.623490i
\(621\) 0 0
\(622\) −1.24698 1.56366i −1.24698 1.56366i
\(623\) 0 0
\(624\) 0.974928 0.222521i 0.974928 0.222521i
\(625\) −0.623490 0.781831i −0.623490 0.781831i
\(626\) 1.00000i 1.00000i
\(627\) −1.56366 + 1.24698i −1.56366 + 1.24698i
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(632\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(633\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(634\) 0 0
\(635\) 0.867767 + 1.80194i 0.867767 + 1.80194i
\(636\) −0.974928 0.222521i −0.974928 0.222521i
\(637\) 1.00000 1.00000
\(638\) 0 0
\(639\) 0 0
\(640\) −0.974928 0.222521i −0.974928 0.222521i
\(641\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(642\) 0 0
\(643\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(644\) 0 0
\(645\) 0.900969 0.433884i 0.900969 0.433884i
\(646\) 0 0
\(647\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(648\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0.974928 0.222521i 0.974928 0.222521i
\(653\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(654\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(655\) 2.00000i 2.00000i
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0.781831 + 0.623490i 0.781831 + 0.623490i 0.930874 0.365341i \(-0.119048\pi\)
−0.149042 + 0.988831i \(0.547619\pi\)
\(660\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(661\) −0.445042 1.94986i −0.445042 1.94986i −0.222521 0.974928i \(-0.571429\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(662\) 0.222521 0.974928i 0.222521 0.974928i
\(663\) 0 0
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −0.222521 0.974928i −0.222521 0.974928i −0.955573 0.294755i \(-0.904762\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(674\) 0 0
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0 0
\(682\) 0.974928 0.222521i 0.974928 0.222521i
\(683\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0 0
\(687\) 0 0
\(688\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(689\) 0.900969 0.433884i 0.900969 0.433884i
\(690\) 0 0
\(691\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(692\) −1.80194 0.867767i −1.80194 0.867767i
\(693\) 0 0
\(694\) 0 0
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −0.974928 0.222521i −0.974928 0.222521i
\(699\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(700\) 0 0
\(701\) −0.222521 + 0.974928i −0.222521 + 0.974928i 0.733052 + 0.680173i \(0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(702\) −0.222521 0.974928i −0.222521 0.974928i
\(703\) 0 0
\(704\) −0.781831 0.623490i −0.781831 0.623490i
\(705\) 0.623490 0.781831i 0.623490 0.781831i
\(706\) 0.867767 1.80194i 0.867767 1.80194i
\(707\) 0 0
\(708\) 0 0
\(709\) 0.623490 + 0.781831i 0.623490 + 0.781831i 0.988831 0.149042i \(-0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 0 0
\(715\) 0.433884 0.900969i 0.433884 0.900969i
\(716\) 0 0
\(717\) 0 0
\(718\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(719\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −1.30165 2.70291i −1.30165 2.70291i
\(723\) −0.974928 0.222521i −0.974928 0.222521i
\(724\) 1.00000 1.00000
\(725\) 0 0
\(726\) 0 0
\(727\) 1.94986 + 0.445042i 1.94986 + 0.445042i 0.974928 + 0.222521i \(0.0714286\pi\)
0.974928 + 0.222521i \(0.0714286\pi\)
\(728\) 0 0
\(729\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) 0 0 −0.781831 0.623490i \(-0.785714\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(734\) −1.24698 + 1.56366i −1.24698 + 1.56366i
\(735\) 0.433884 0.900969i 0.433884 0.900969i
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.974928 0.222521i 0.974928 0.222521i 0.294755 0.955573i \(-0.404762\pi\)
0.680173 + 0.733052i \(0.261905\pi\)
\(740\) 0 0
\(741\) 1.24698 + 1.56366i 1.24698 + 1.56366i
\(742\) 0 0
\(743\) −1.56366 + 1.24698i −1.56366 + 1.24698i −0.781831 + 0.623490i \(0.785714\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(744\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(745\) 0.623490 0.781831i 0.623490 0.781831i
\(746\) 0.781831 + 0.623490i 0.781831 + 0.623490i
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(751\) −0.867767 1.80194i −0.867767 1.80194i −0.433884 0.900969i \(-0.642857\pi\)
−0.433884 0.900969i \(-0.642857\pi\)
\(752\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(753\) −1.00000 −1.00000
\(754\) 0 0
\(755\) 0 0
\(756\) 0 0
\(757\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(758\) 1.80194 + 0.867767i 1.80194 + 0.867767i
\(759\) 0 0
\(760\) −0.445042 1.94986i −0.445042 1.94986i
\(761\) −1.80194 + 0.867767i −1.80194 + 0.867767i −0.900969 + 0.433884i \(0.857143\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(762\) −1.56366 1.24698i −1.56366 1.24698i
\(763\) 0 0
\(764\) 0.867767 1.80194i 0.867767 1.80194i
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.974928 0.222521i 0.974928 0.222521i
\(769\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(770\) 0 0
\(771\) 1.00000i 1.00000i
\(772\) 0 0
\(773\) 0 0 0.433884 0.900969i \(-0.357143\pi\)
−0.433884 + 0.900969i \(0.642857\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 0 0
\(778\) 0 0
\(779\) 0 0
\(780\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(781\) 0 0
\(782\) 0 0
\(783\) 0 0
\(784\) 1.00000 1.00000
\(785\) 0 0
\(786\) −0.867767 1.80194i −0.867767 1.80194i
\(787\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(788\) 0.445042 1.94986i 0.445042 1.94986i
\(789\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(790\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(791\) 0 0
\(792\) 0 0
\(793\) 0 0
\(794\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(795\) 1.00000i 1.00000i
\(796\) 0 0
\(797\) 0 0 0.974928 0.222521i \(-0.0714286\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0.433884 0.900969i 0.433884 0.900969i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −0.222521 0.974928i −0.222521 0.974928i
\(807\) 0 0
\(808\) 0 0
\(809\) 0 0 −0.433884 0.900969i \(-0.642857\pi\)
0.433884 + 0.900969i \(0.357143\pi\)
\(810\) −0.974928 0.222521i −0.974928 0.222521i
\(811\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(812\) 0 0
\(813\) 1.00000 1.00000
\(814\) 0 0
\(815\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(816\) 0 0
\(817\) −0.445042 + 1.94986i −0.445042 + 1.94986i
\(818\) 0 0
\(819\) 0 0
\(820\) 0 0
\(821\) 0.623490 0.781831i 0.623490 0.781831i −0.365341 0.930874i \(-0.619048\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(822\) 0 0
\(823\) 1.56366 1.24698i 1.56366 1.24698i 0.781831 0.623490i \(-0.214286\pi\)
0.781831 0.623490i \(-0.214286\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) 0 0
\(827\) −0.974928 + 0.222521i −0.974928 + 0.222521i −0.680173 0.733052i \(-0.738095\pi\)
−0.294755 + 0.955573i \(0.595238\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0.867767 1.80194i 0.867767 1.80194i
\(832\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0.445042 1.94986i 0.445042 1.94986i
\(837\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(838\) 0 0
\(839\) 0.974928 + 0.222521i 0.974928 + 0.222521i 0.680173 0.733052i \(-0.261905\pi\)
0.294755 + 0.955573i \(0.404762\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) 0 0
\(843\) 0.974928 + 0.222521i 0.974928 + 0.222521i
\(844\) −0.433884 0.900969i −0.433884 0.900969i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) 0.900969 0.433884i 0.900969 0.433884i
\(849\) 0 0
\(850\) 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
\(856\) 0 0
\(857\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(858\) 1.00000i 1.00000i
\(859\) 0.781831 0.623490i 0.781831 0.623490i −0.149042 0.988831i \(-0.547619\pi\)
0.930874 + 0.365341i \(0.119048\pi\)
\(860\) −0.433884 + 0.900969i −0.433884 + 0.900969i
\(861\) 0 0
\(862\) 0 0
\(863\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(864\) −0.222521 0.974928i −0.222521 0.974928i
\(865\) 0.445042 1.94986i 0.445042 1.94986i
\(866\) 0 0
\(867\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(868\) 0 0
\(869\) −1.00000 −1.00000
\(870\) 0 0
\(871\) 0 0
\(872\) −0.974928 0.222521i −0.974928 0.222521i
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0.900969 0.433884i 0.900969 0.433884i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(878\) 0 0
\(879\) 0 0
\(880\) 0.433884 0.900969i 0.433884 0.900969i
\(881\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(882\) 0 0
\(883\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.24698 + 1.56366i 1.24698 + 1.56366i
\(887\) 1.00000i 1.00000i 0.866025 + 0.500000i \(0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.781831 0.623490i −0.781831 0.623490i
\(892\) 0 0
\(893\) 0.445042 + 1.94986i 0.445042 + 1.94986i
\(894\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(895\) 0 0
\(896\) 0 0
\(897\) 0 0
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 0 0
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(906\) 0 0
\(907\) 1.56366 + 1.24698i 1.56366 + 1.24698i 0.781831 + 0.623490i \(0.214286\pi\)
0.781831 + 0.623490i \(0.214286\pi\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 1.00000i 1.00000i −0.866025 0.500000i \(-0.833333\pi\)
0.866025 0.500000i \(-0.166667\pi\)
\(912\) 1.24698 + 1.56366i 1.24698 + 1.56366i
\(913\) 0 0
\(914\) 1.94986 0.445042i 1.94986 0.445042i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0 0
\(919\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(920\) 0 0
\(921\) 0.900969 0.433884i 0.900969 0.433884i
\(922\) 0 0
\(923\) 0 0
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(930\) −0.974928 0.222521i −0.974928 0.222521i
\(931\) 0.867767 + 1.80194i 0.867767 + 1.80194i
\(932\) −0.900969 0.433884i −0.900969 0.433884i
\(933\) −0.445042 + 1.94986i −0.445042 + 1.94986i
\(934\) −0.222521 0.974928i −0.222521 0.974928i
\(935\) 0 0
\(936\) 0 0
\(937\) −1.24698 + 1.56366i −1.24698 + 1.56366i −0.623490 + 0.781831i \(0.714286\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(938\) 0 0
\(939\) 0.781831 0.623490i 0.781831 0.623490i
\(940\) 1.00000i 1.00000i
\(941\) 0.623490 + 0.781831i 0.623490 + 0.781831i 0.988831 0.149042i \(-0.0476190\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) −0.781831 + 0.623490i −0.781831 + 0.623490i
\(947\) 0.433884 0.900969i 0.433884 0.900969i −0.563320 0.826239i \(-0.690476\pi\)
0.997204 0.0747301i \(-0.0238095\pi\)
\(948\) 0.623490 0.781831i 0.623490 0.781831i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0 0
\(953\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(954\) 0 0
\(955\) 1.94986 + 0.445042i 1.94986 + 0.445042i
\(956\) 0 0
\(957\) 0 0
\(958\) −1.00000 −1.00000
\(959\) 0 0
\(960\) 0.433884 + 0.900969i 0.433884 + 0.900969i
\(961\) 0 0
\(962\) 0 0
\(963\) 0 0
\(964\) 0.900969 0.433884i 0.900969 0.433884i
\(965\) 0 0
\(966\) 0 0
\(967\) −0.433884 + 0.900969i −0.433884 + 0.900969i 0.563320 + 0.826239i \(0.309524\pi\)
−0.997204 + 0.0747301i \(0.976190\pi\)
\(968\) 0 0
\(969\) 0 0
\(970\) 0 0
\(971\) −1.94986 + 0.445042i −1.94986 + 0.445042i −0.974928 + 0.222521i \(0.928571\pi\)
−0.974928 + 0.222521i \(0.928571\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) 0 0
\(975\) 0 0
\(976\) 0 0
\(977\) −0.623490 + 0.781831i −0.623490 + 0.781831i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(978\) −0.781831 0.623490i −0.781831 0.623490i
\(979\) 0 0
\(980\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(981\) 0 0
\(982\) 0.900969 + 0.433884i 0.900969 + 0.433884i
\(983\) 0.433884 + 0.900969i 0.433884 + 0.900969i 0.997204 + 0.0747301i \(0.0238095\pi\)
−0.563320 + 0.826239i \(0.690476\pi\)
\(984\) 0 0
\(985\) 2.00000 2.00000
\(986\) 0 0
\(987\) 0 0
\(988\) −1.94986 0.445042i −1.94986 0.445042i
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(992\) −0.222521 0.974928i −0.222521 0.974928i
\(993\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(994\) 0 0
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.781831 0.623490i \(-0.214286\pi\)
−0.781831 + 0.623490i \(0.785714\pi\)
\(998\) 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 3364.1.j.f.2287.2 12
4.3 odd 2 inner 3364.1.j.f.2287.1 12
29.2 odd 28 3364.1.h.b.651.1 6
29.3 odd 28 3364.1.h.b.2719.1 6
29.4 even 14 inner 3364.1.j.f.1415.2 12
29.5 even 14 inner 3364.1.j.f.1031.2 12
29.6 even 14 3364.1.b.a.1683.2 2
29.7 even 7 inner 3364.1.j.f.2327.1 12
29.8 odd 28 3364.1.h.a.63.1 6
29.9 even 14 inner 3364.1.j.f.1619.1 12
29.10 odd 28 3364.1.h.a.267.1 6
29.11 odd 28 3364.1.h.b.1111.1 6
29.12 odd 4 3364.1.h.a.2759.1 6
29.13 even 14 inner 3364.1.j.f.571.1 12
29.14 odd 28 116.1.d.a.115.1 1
29.15 odd 28 116.1.d.b.115.1 yes 1
29.16 even 7 inner 3364.1.j.f.571.2 12
29.17 odd 4 3364.1.h.b.2759.1 6
29.18 odd 28 3364.1.h.a.1111.1 6
29.19 odd 28 3364.1.h.b.267.1 6
29.20 even 7 inner 3364.1.j.f.1619.2 12
29.21 odd 28 3364.1.h.b.63.1 6
29.22 even 14 inner 3364.1.j.f.2327.2 12
29.23 even 7 3364.1.b.a.1683.1 2
29.24 even 7 inner 3364.1.j.f.1031.1 12
29.25 even 7 inner 3364.1.j.f.1415.1 12
29.26 odd 28 3364.1.h.a.2719.1 6
29.27 odd 28 3364.1.h.a.651.1 6
29.28 even 2 inner 3364.1.j.f.2287.1 12
87.14 even 28 1044.1.g.b.811.1 1
87.44 even 28 1044.1.g.a.811.1 1
116.3 even 28 3364.1.h.a.2719.1 6
116.7 odd 14 inner 3364.1.j.f.2327.2 12
116.11 even 28 3364.1.h.a.1111.1 6
116.15 even 28 116.1.d.a.115.1 1
116.19 even 28 3364.1.h.a.267.1 6
116.23 odd 14 3364.1.b.a.1683.2 2
116.27 even 28 3364.1.h.b.651.1 6
116.31 even 28 3364.1.h.a.651.1 6
116.35 odd 14 3364.1.b.a.1683.1 2
116.39 even 28 3364.1.h.b.267.1 6
116.43 even 28 116.1.d.b.115.1 yes 1
116.47 even 28 3364.1.h.b.1111.1 6
116.51 odd 14 inner 3364.1.j.f.2327.1 12
116.55 even 28 3364.1.h.b.2719.1 6
116.63 odd 14 inner 3364.1.j.f.1031.1 12
116.67 odd 14 inner 3364.1.j.f.1619.2 12
116.71 odd 14 inner 3364.1.j.f.571.2 12
116.75 even 4 3364.1.h.a.2759.1 6
116.79 even 28 3364.1.h.a.63.1 6
116.83 odd 14 inner 3364.1.j.f.1415.2 12
116.91 odd 14 inner 3364.1.j.f.1415.1 12
116.95 even 28 3364.1.h.b.63.1 6
116.99 even 4 3364.1.h.b.2759.1 6
116.103 odd 14 inner 3364.1.j.f.571.1 12
116.107 odd 14 inner 3364.1.j.f.1619.1 12
116.111 odd 14 inner 3364.1.j.f.1031.2 12
116.115 odd 2 CM 3364.1.j.f.2287.2 12
145.14 odd 28 2900.1.g.d.2551.1 1
145.43 even 28 2900.1.e.b.2899.2 2
145.44 odd 28 2900.1.g.a.2551.1 1
145.72 even 28 2900.1.e.b.2899.1 2
145.73 even 28 2900.1.e.a.2899.1 2
145.102 even 28 2900.1.e.a.2899.2 2
232.43 even 28 1856.1.h.c.1855.1 1
232.101 odd 28 1856.1.h.a.1855.1 1
232.131 even 28 1856.1.h.a.1855.1 1
232.189 odd 28 1856.1.h.c.1855.1 1
348.131 odd 28 1044.1.g.b.811.1 1
348.275 odd 28 1044.1.g.a.811.1 1
580.43 odd 28 2900.1.e.a.2899.1 2
580.159 even 28 2900.1.g.a.2551.1 1
580.247 odd 28 2900.1.e.b.2899.1 2
580.363 odd 28 2900.1.e.b.2899.2 2
580.479 even 28 2900.1.g.d.2551.1 1
580.507 odd 28 2900.1.e.a.2899.2 2
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
116.1.d.a.115.1 1 29.14 odd 28
116.1.d.a.115.1 1 116.15 even 28
116.1.d.b.115.1 yes 1 29.15 odd 28
116.1.d.b.115.1 yes 1 116.43 even 28
1044.1.g.a.811.1 1 87.44 even 28
1044.1.g.a.811.1 1 348.275 odd 28
1044.1.g.b.811.1 1 87.14 even 28
1044.1.g.b.811.1 1 348.131 odd 28
1856.1.h.a.1855.1 1 232.101 odd 28
1856.1.h.a.1855.1 1 232.131 even 28
1856.1.h.c.1855.1 1 232.43 even 28
1856.1.h.c.1855.1 1 232.189 odd 28
2900.1.e.a.2899.1 2 145.73 even 28
2900.1.e.a.2899.1 2 580.43 odd 28
2900.1.e.a.2899.2 2 145.102 even 28
2900.1.e.a.2899.2 2 580.507 odd 28
2900.1.e.b.2899.1 2 145.72 even 28
2900.1.e.b.2899.1 2 580.247 odd 28
2900.1.e.b.2899.2 2 145.43 even 28
2900.1.e.b.2899.2 2 580.363 odd 28
2900.1.g.a.2551.1 1 145.44 odd 28
2900.1.g.a.2551.1 1 580.159 even 28
2900.1.g.d.2551.1 1 145.14 odd 28
2900.1.g.d.2551.1 1 580.479 even 28
3364.1.b.a.1683.1 2 29.23 even 7
3364.1.b.a.1683.1 2 116.35 odd 14
3364.1.b.a.1683.2 2 29.6 even 14
3364.1.b.a.1683.2 2 116.23 odd 14
3364.1.h.a.63.1 6 29.8 odd 28
3364.1.h.a.63.1 6 116.79 even 28
3364.1.h.a.267.1 6 29.10 odd 28
3364.1.h.a.267.1 6 116.19 even 28
3364.1.h.a.651.1 6 29.27 odd 28
3364.1.h.a.651.1 6 116.31 even 28
3364.1.h.a.1111.1 6 29.18 odd 28
3364.1.h.a.1111.1 6 116.11 even 28
3364.1.h.a.2719.1 6 29.26 odd 28
3364.1.h.a.2719.1 6 116.3 even 28
3364.1.h.a.2759.1 6 29.12 odd 4
3364.1.h.a.2759.1 6 116.75 even 4
3364.1.h.b.63.1 6 29.21 odd 28
3364.1.h.b.63.1 6 116.95 even 28
3364.1.h.b.267.1 6 29.19 odd 28
3364.1.h.b.267.1 6 116.39 even 28
3364.1.h.b.651.1 6 29.2 odd 28
3364.1.h.b.651.1 6 116.27 even 28
3364.1.h.b.1111.1 6 29.11 odd 28
3364.1.h.b.1111.1 6 116.47 even 28
3364.1.h.b.2719.1 6 29.3 odd 28
3364.1.h.b.2719.1 6 116.55 even 28
3364.1.h.b.2759.1 6 29.17 odd 4
3364.1.h.b.2759.1 6 116.99 even 4
3364.1.j.f.571.1 12 29.13 even 14 inner
3364.1.j.f.571.1 12 116.103 odd 14 inner
3364.1.j.f.571.2 12 29.16 even 7 inner
3364.1.j.f.571.2 12 116.71 odd 14 inner
3364.1.j.f.1031.1 12 29.24 even 7 inner
3364.1.j.f.1031.1 12 116.63 odd 14 inner
3364.1.j.f.1031.2 12 29.5 even 14 inner
3364.1.j.f.1031.2 12 116.111 odd 14 inner
3364.1.j.f.1415.1 12 29.25 even 7 inner
3364.1.j.f.1415.1 12 116.91 odd 14 inner
3364.1.j.f.1415.2 12 29.4 even 14 inner
3364.1.j.f.1415.2 12 116.83 odd 14 inner
3364.1.j.f.1619.1 12 29.9 even 14 inner
3364.1.j.f.1619.1 12 116.107 odd 14 inner
3364.1.j.f.1619.2 12 29.20 even 7 inner
3364.1.j.f.1619.2 12 116.67 odd 14 inner
3364.1.j.f.2287.1 12 4.3 odd 2 inner
3364.1.j.f.2287.1 12 29.28 even 2 inner
3364.1.j.f.2287.2 12 1.1 even 1 trivial
3364.1.j.f.2287.2 12 116.115 odd 2 CM
3364.1.j.f.2327.1 12 29.7 even 7 inner
3364.1.j.f.2327.1 12 116.51 odd 14 inner
3364.1.j.f.2327.2 12 29.22 even 14 inner
3364.1.j.f.2327.2 12 116.7 odd 14 inner