Properties

Label 3100.1.t.b.2299.1
Level $3100$
Weight $1$
Character 3100.2299
Analytic conductor $1.547$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

Related objects

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3100,1,Mod(1699,3100)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3100, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 3, 2]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3100.1699");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3100 = 2^{2} \cdot 5^{2} \cdot 31 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3100.t (of order \(6\), degree \(2\), 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: \(1.54710153916\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{6})\)
Coefficient field: \(\Q(\zeta_{12})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{4} - x^{2} + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 124)
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.15376.1

Embedding invariants

Embedding label 2299.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 3100.2299
Dual form 3100.1.t.b.1699.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.866025 + 0.500000i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-0.866025 + 0.500000i) q^{13} +(-0.500000 + 0.866025i) q^{14} +1.00000 q^{16} +(0.866025 + 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{19} +(-0.500000 - 0.866025i) q^{21} +(-0.866025 + 0.500000i) q^{22} +(-0.500000 + 0.866025i) q^{24} +(-0.866025 + 0.500000i) q^{26} -1.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} -1.00000i q^{31} +1.00000 q^{32} -1.00000i q^{33} +(0.866025 + 0.500000i) q^{34} +(0.866025 + 0.500000i) q^{37} +(-0.866025 - 0.500000i) q^{38} -1.00000i q^{39} +(-0.500000 - 0.866025i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-0.500000 + 0.866025i) q^{43} +(-0.866025 + 0.500000i) q^{44} +(-0.500000 + 0.866025i) q^{48} +(-0.866025 + 0.500000i) q^{51} +(-0.866025 + 0.500000i) q^{52} +(-0.866025 + 0.500000i) q^{53} -1.00000 q^{54} +(-0.500000 + 0.866025i) q^{56} +(0.866025 - 0.500000i) q^{57} +(0.866025 + 0.500000i) q^{59} -1.00000i q^{62} +1.00000 q^{64} -1.00000i q^{66} +(0.500000 + 0.866025i) q^{67} +(0.866025 + 0.500000i) q^{68} +(0.866025 - 0.500000i) q^{71} +(0.866025 - 0.500000i) q^{73} +(0.866025 + 0.500000i) q^{74} +(-0.866025 - 0.500000i) q^{76} -1.00000i q^{77} -1.00000i q^{78} +(0.866025 + 0.500000i) q^{79} +(0.500000 - 0.866025i) q^{81} +(-0.500000 - 0.866025i) q^{82} +(0.500000 + 0.866025i) q^{83} +(-0.500000 - 0.866025i) q^{84} +(-0.500000 + 0.866025i) q^{86} +(-0.866025 + 0.500000i) q^{88} -1.00000i q^{91} +(0.866025 + 0.500000i) q^{93} +(-0.500000 + 0.866025i) q^{96} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{6} - 2 q^{7} + 4 q^{8} - 2 q^{12} - 2 q^{14} + 4 q^{16} - 2 q^{21} - 2 q^{24} - 4 q^{27} - 2 q^{28} + 4 q^{32} - 2 q^{41} - 2 q^{42} - 2 q^{43} - 2 q^{48} - 4 q^{54} - 2 q^{56} + 4 q^{64} + 2 q^{67} + 2 q^{81} - 2 q^{82} + 2 q^{83} - 2 q^{84} - 2 q^{86} - 2 q^{96}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3100\mathbb{Z}\right)^\times\).

\(n\) \(1551\) \(1801\) \(2977\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 1.00000
\(3\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(4\) 1.00000 1.00000
\(5\) 0 0
\(6\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(7\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) 0 0
\(11\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(12\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(13\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(14\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(15\) 0 0
\(16\) 1.00000 1.00000
\(17\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(18\) 0 0
\(19\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(20\) 0 0
\(21\) −0.500000 0.866025i −0.500000 0.866025i
\(22\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(23\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(24\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(25\) 0 0
\(26\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(27\) −1.00000 −1.00000
\(28\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(29\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 1.00000i 1.00000i
\(32\) 1.00000 1.00000
\(33\) 1.00000i 1.00000i
\(34\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(38\) −0.866025 0.500000i −0.866025 0.500000i
\(39\) 1.00000i 1.00000i
\(40\) 0 0
\(41\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(42\) −0.500000 0.866025i −0.500000 0.866025i
\(43\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(44\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(45\) 0 0
\(46\) 0 0
\(47\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(48\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(49\) 0 0
\(50\) 0 0
\(51\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(52\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(53\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(54\) −1.00000 −1.00000
\(55\) 0 0
\(56\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(57\) 0.866025 0.500000i 0.866025 0.500000i
\(58\) 0 0
\(59\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(60\) 0 0
\(61\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(62\) 1.00000i 1.00000i
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 1.00000i 1.00000i
\(67\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(69\) 0 0
\(70\) 0 0
\(71\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 0 0
\(73\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(74\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(75\) 0 0
\(76\) −0.866025 0.500000i −0.866025 0.500000i
\(77\) 1.00000i 1.00000i
\(78\) 1.00000i 1.00000i
\(79\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) −0.500000 0.866025i −0.500000 0.866025i
\(83\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(84\) −0.500000 0.866025i −0.500000 0.866025i
\(85\) 0 0
\(86\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(87\) 0 0
\(88\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(89\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(90\) 0 0
\(91\) 1.00000i 1.00000i
\(92\) 0 0
\(93\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(94\) 0 0
\(95\) 0 0
\(96\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(103\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(104\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(105\) 0 0
\(106\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(107\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(108\) −1.00000 −1.00000
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(112\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(113\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(114\) 0.866025 0.500000i 0.866025 0.500000i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(119\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(120\) 0 0
\(121\) 0 0
\(122\) 0 0
\(123\) 1.00000 1.00000
\(124\) 1.00000i 1.00000i
\(125\) 0 0
\(126\) 0 0
\(127\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(128\) 1.00000 1.00000
\(129\) −0.500000 0.866025i −0.500000 0.866025i
\(130\) 0 0
\(131\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(132\) 1.00000i 1.00000i
\(133\) 0.866025 0.500000i 0.866025 0.500000i
\(134\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(135\) 0 0
\(136\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(137\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(138\) 0 0
\(139\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 0.866025 0.500000i 0.866025 0.500000i
\(143\) 0.500000 0.866025i 0.500000 0.866025i
\(144\) 0 0
\(145\) 0 0
\(146\) 0.866025 0.500000i 0.866025 0.500000i
\(147\) 0 0
\(148\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(149\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(150\) 0 0
\(151\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) −0.866025 0.500000i −0.866025 0.500000i
\(153\) 0 0
\(154\) 1.00000i 1.00000i
\(155\) 0 0
\(156\) 1.00000i 1.00000i
\(157\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(158\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(159\) 1.00000i 1.00000i
\(160\) 0 0
\(161\) 0 0
\(162\) 0.500000 0.866025i 0.500000 0.866025i
\(163\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(164\) −0.500000 0.866025i −0.500000 0.866025i
\(165\) 0 0
\(166\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(167\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(168\) −0.500000 0.866025i −0.500000 0.866025i
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(173\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(177\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(178\) 0 0
\(179\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(182\) 1.00000i 1.00000i
\(183\) 0 0
\(184\) 0 0
\(185\) 0 0
\(186\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(187\) −1.00000 −1.00000
\(188\) 0 0
\(189\) 0.500000 0.866025i 0.500000 0.866025i
\(190\) 0 0
\(191\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(192\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(193\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0 0
\(197\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(198\) 0 0
\(199\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(200\) 0 0
\(201\) −1.00000 −1.00000
\(202\) 0 0
\(203\) 0 0
\(204\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(205\) 0 0
\(206\) −0.500000 0.866025i −0.500000 0.866025i
\(207\) 0 0
\(208\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(209\) 1.00000 1.00000
\(210\) 0 0
\(211\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(212\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(213\) 1.00000i 1.00000i
\(214\) 0.500000 0.866025i 0.500000 0.866025i
\(215\) 0 0
\(216\) −1.00000 −1.00000
\(217\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(218\) 0 0
\(219\) 1.00000i 1.00000i
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(223\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(224\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(225\) 0 0
\(226\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(227\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(228\) 0.866025 0.500000i 0.866025 0.500000i
\(229\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(232\) 0 0
\(233\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(237\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(238\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(239\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(242\) 0 0
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) 1.00000 1.00000
\(247\) 1.00000 1.00000
\(248\) 1.00000i 1.00000i
\(249\) −1.00000 −1.00000
\(250\) 0 0
\(251\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 0.500000 0.866025i 0.500000 0.866025i
\(255\) 0 0
\(256\) 1.00000 1.00000
\(257\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) −0.500000 0.866025i −0.500000 0.866025i
\(259\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(260\) 0 0
\(261\) 0 0
\(262\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(263\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(264\) 1.00000i 1.00000i
\(265\) 0 0
\(266\) 0.866025 0.500000i 0.866025 0.500000i
\(267\) 0 0
\(268\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(269\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(272\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(273\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(274\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(278\) 0 0
\(279\) 0 0
\(280\) 0 0
\(281\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(282\) 0 0
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0.866025 0.500000i 0.866025 0.500000i
\(285\) 0 0
\(286\) 0.500000 0.866025i 0.500000 0.866025i
\(287\) 1.00000 1.00000
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0 0
\(292\) 0.866025 0.500000i 0.866025 0.500000i
\(293\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(297\) 0.866025 0.500000i 0.866025 0.500000i
\(298\) 0.500000 0.866025i 0.500000 0.866025i
\(299\) 0 0
\(300\) 0 0
\(301\) −0.500000 0.866025i −0.500000 0.866025i
\(302\) 2.00000i 2.00000i
\(303\) 0 0
\(304\) −0.866025 0.500000i −0.866025 0.500000i
\(305\) 0 0
\(306\) 0 0
\(307\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(308\) 1.00000i 1.00000i
\(309\) 1.00000 1.00000
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) 1.00000i 1.00000i
\(313\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(314\) 0 0
\(315\) 0 0
\(316\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(317\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(318\) 1.00000i 1.00000i
\(319\) 0 0
\(320\) 0 0
\(321\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(322\) 0 0
\(323\) −0.500000 0.866025i −0.500000 0.866025i
\(324\) 0.500000 0.866025i 0.500000 0.866025i
\(325\) 0 0
\(326\) 0 0
\(327\) 0 0
\(328\) −0.500000 0.866025i −0.500000 0.866025i
\(329\) 0 0
\(330\) 0 0
\(331\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(332\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(333\) 0 0
\(334\) 0.500000 0.866025i 0.500000 0.866025i
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.500000 0.866025i
\(337\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(338\) 0 0
\(339\) 1.00000i 1.00000i
\(340\) 0 0
\(341\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(342\) 0 0
\(343\) −1.00000 −1.00000
\(344\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(345\) 0 0
\(346\) 0.866025 0.500000i 0.866025 0.500000i
\(347\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 0 0
\(351\) 0.866025 0.500000i 0.866025 0.500000i
\(352\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(353\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(354\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(355\) 0 0
\(356\) 0 0
\(357\) 1.00000i 1.00000i
\(358\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(359\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) −0.500000 0.866025i −0.500000 0.866025i
\(363\) 0 0
\(364\) 1.00000i 1.00000i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) 0 0
\(371\) 1.00000i 1.00000i
\(372\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(373\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(374\) −1.00000 −1.00000
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.500000 0.866025i 0.500000 0.866025i
\(379\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(382\) 0.866025 0.500000i 0.866025 0.500000i
\(383\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(384\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(385\) 0 0
\(386\) −0.866025 0.500000i −0.866025 0.500000i
\(387\) 0 0
\(388\) 0 0
\(389\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(394\) 0.866025 0.500000i 0.866025 0.500000i
\(395\) 0 0
\(396\) 0 0
\(397\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(399\) 1.00000i 1.00000i
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) −1.00000 −1.00000
\(403\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) −1.00000 −1.00000
\(408\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(409\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(410\) 0 0
\(411\) 1.00000i 1.00000i
\(412\) −0.500000 0.866025i −0.500000 0.866025i
\(413\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(414\) 0 0
\(415\) 0 0
\(416\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(417\) 0 0
\(418\) 1.00000 1.00000
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(422\) −0.866025 0.500000i −0.866025 0.500000i
\(423\) 0 0
\(424\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(425\) 0 0
\(426\) 1.00000i 1.00000i
\(427\) 0 0
\(428\) 0.500000 0.866025i 0.500000 0.866025i
\(429\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(430\) 0 0
\(431\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(432\) −1.00000 −1.00000
\(433\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(434\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 1.00000i 1.00000i
\(439\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.00000 −1.00000
\(443\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(444\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(445\) 0 0
\(446\) 0.500000 0.866025i 0.500000 0.866025i
\(447\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(448\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(449\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(450\) 0 0
\(451\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(452\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(453\) −1.73205 1.00000i −1.73205 1.00000i
\(454\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(455\) 0 0
\(456\) 0.866025 0.500000i 0.866025 0.500000i
\(457\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(458\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(459\) −0.866025 0.500000i −0.866025 0.500000i
\(460\) 0 0
\(461\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(462\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(468\) 0 0
\(469\) −1.00000 −1.00000
\(470\) 0 0
\(471\) 0 0
\(472\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(473\) 1.00000i 1.00000i
\(474\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(475\) 0 0
\(476\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(477\) 0 0
\(478\) 0.866025 0.500000i 0.866025 0.500000i
\(479\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −1.00000 −1.00000
\(482\) 0.500000 0.866025i 0.500000 0.866025i
\(483\) 0 0
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(488\) 0 0
\(489\) 0 0
\(490\) 0 0
\(491\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(492\) 1.00000 1.00000
\(493\) 0 0
\(494\) 1.00000 1.00000
\(495\) 0 0
\(496\) 1.00000i 1.00000i
\(497\) 1.00000i 1.00000i
\(498\) −1.00000 −1.00000
\(499\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(500\) 0 0
\(501\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(502\) −0.866025 0.500000i −0.866025 0.500000i
\(503\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0.500000 0.866025i 0.500000 0.866025i
\(509\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) 1.00000i 1.00000i
\(512\) 1.00000 1.00000
\(513\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(514\) 0.866025 0.500000i 0.866025 0.500000i
\(515\) 0 0
\(516\) −0.500000 0.866025i −0.500000 0.866025i
\(517\) 0 0
\(518\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(519\) 1.00000i 1.00000i
\(520\) 0 0
\(521\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(524\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(525\) 0 0
\(526\) 0 0
\(527\) 0.500000 0.866025i 0.500000 0.866025i
\(528\) 1.00000i 1.00000i
\(529\) −1.00000 −1.00000
\(530\) 0 0
\(531\) 0 0
\(532\) 0.866025 0.500000i 0.866025 0.500000i
\(533\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(534\) 0 0
\(535\) 0 0
\(536\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(537\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(538\) −0.500000 0.866025i −0.500000 0.866025i
\(539\) 0 0
\(540\) 0 0
\(541\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(542\) 0 0
\(543\) 1.00000 1.00000
\(544\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(545\) 0 0
\(546\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(547\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(548\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(549\) 0 0
\(550\) 0 0
\(551\) 0 0
\(552\) 0 0
\(553\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 1.00000i 1.00000i
\(560\) 0 0
\(561\) 0.500000 0.866025i 0.500000 0.866025i
\(562\) 2.00000 2.00000
\(563\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(568\) 0.866025 0.500000i 0.866025 0.500000i
\(569\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(570\) 0 0
\(571\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(572\) 0.500000 0.866025i 0.500000 0.866025i
\(573\) 1.00000i 1.00000i
\(574\) 1.00000 1.00000
\(575\) 0 0
\(576\) 0 0
\(577\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(578\) 0 0
\(579\) 0.866025 0.500000i 0.866025 0.500000i
\(580\) 0 0
\(581\) −1.00000 −1.00000
\(582\) 0 0
\(583\) 0.500000 0.866025i 0.500000 0.866025i
\(584\) 0.866025 0.500000i 0.866025 0.500000i
\(585\) 0 0
\(586\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(587\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(588\) 0 0
\(589\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(590\) 0 0
\(591\) 1.00000i 1.00000i
\(592\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(593\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(594\) 0.866025 0.500000i 0.866025 0.500000i
\(595\) 0 0
\(596\) 0.500000 0.866025i 0.500000 0.866025i
\(597\) 1.00000i 1.00000i
\(598\) 0 0
\(599\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(600\) 0 0
\(601\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(602\) −0.500000 0.866025i −0.500000 0.866025i
\(603\) 0 0
\(604\) 2.00000i 2.00000i
\(605\) 0 0
\(606\) 0 0
\(607\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(608\) −0.866025 0.500000i −0.866025 0.500000i
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0 0
\(613\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(614\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(615\) 0 0
\(616\) 1.00000i 1.00000i
\(617\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(618\) 1.00000 1.00000
\(619\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 0 0
\(623\) 0 0
\(624\) 1.00000i 1.00000i
\(625\) 0 0
\(626\) −0.866025 0.500000i −0.866025 0.500000i
\(627\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(628\) 0 0
\(629\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(630\) 0 0
\(631\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(632\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(633\) 0.866025 0.500000i 0.866025 0.500000i
\(634\) −0.866025 0.500000i −0.866025 0.500000i
\(635\) 0 0
\(636\) 1.00000i 1.00000i
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(642\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.500000 0.866025i −0.500000 0.866025i
\(647\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(648\) 0.500000 0.866025i 0.500000 0.866025i
\(649\) −1.00000 −1.00000
\(650\) 0 0
\(651\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(652\) 0 0
\(653\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −0.500000 0.866025i −0.500000 0.866025i
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(662\) 0.866025 0.500000i 0.866025 0.500000i
\(663\) 0.500000 0.866025i 0.500000 0.866025i
\(664\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) 0.500000 0.866025i 0.500000 0.866025i
\(669\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(670\) 0 0
\(671\) 0 0
\(672\) −0.500000 0.866025i −0.500000 0.866025i
\(673\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(674\) 2.00000i 2.00000i
\(675\) 0 0
\(676\) 0 0
\(677\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(678\) 1.00000i 1.00000i
\(679\) 0 0
\(680\) 0 0
\(681\) −1.00000 −1.00000
\(682\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(683\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −1.00000
\(687\) −0.500000 0.866025i −0.500000 0.866025i
\(688\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(689\) 0.500000 0.866025i 0.500000 0.866025i
\(690\) 0 0
\(691\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(692\) 0.866025 0.500000i 0.866025 0.500000i
\(693\) 0 0
\(694\) 0.500000 0.866025i 0.500000 0.866025i
\(695\) 0 0
\(696\) 0 0
\(697\) 1.00000i 1.00000i
\(698\) 0 0
\(699\) 0 0
\(700\) 0 0
\(701\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(702\) 0.866025 0.500000i 0.866025 0.500000i
\(703\) −0.500000 0.866025i −0.500000 0.866025i
\(704\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(705\) 0 0
\(706\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(707\) 0 0
\(708\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(709\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0 0
\(713\) 0 0
\(714\) 1.00000i 1.00000i
\(715\) 0 0
\(716\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(717\) 1.00000i 1.00000i
\(718\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(719\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) 0 0
\(721\) 1.00000 1.00000
\(722\) 0 0
\(723\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(724\) −0.500000 0.866025i −0.500000 0.866025i
\(725\) 0 0
\(726\) 0 0
\(727\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(728\) 1.00000i 1.00000i
\(729\) 1.00000 1.00000
\(730\) 0 0
\(731\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(732\) 0 0
\(733\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(734\) −0.500000 0.866025i −0.500000 0.866025i
\(735\) 0 0
\(736\) 0 0
\(737\) −0.866025 0.500000i −0.866025 0.500000i
\(738\) 0 0
\(739\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(740\) 0 0
\(741\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(742\) 1.00000i 1.00000i
\(743\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(744\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(745\) 0 0
\(746\) 2.00000i 2.00000i
\(747\) 0 0
\(748\) −1.00000 −1.00000
\(749\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(750\) 0 0
\(751\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(752\) 0 0
\(753\) 0.866025 0.500000i 0.866025 0.500000i
\(754\) 0 0
\(755\) 0 0
\(756\) 0.500000 0.866025i 0.500000 0.866025i
\(757\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(758\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(759\) 0 0
\(760\) 0 0
\(761\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(762\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(763\) 0 0
\(764\) 0.866025 0.500000i 0.866025 0.500000i
\(765\) 0 0
\(766\) −0.500000 0.866025i −0.500000 0.866025i
\(767\) −1.00000 −1.00000
\(768\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(769\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(770\) 0 0
\(771\) 1.00000i 1.00000i
\(772\) −0.866025 0.500000i −0.866025 0.500000i
\(773\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 0 0
\(777\) 1.00000i 1.00000i
\(778\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(779\) 1.00000i 1.00000i
\(780\) 0 0
\(781\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 0 0
\(786\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(787\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(788\) 0.866025 0.500000i 0.866025 0.500000i
\(789\) 0 0
\(790\) 0 0
\(791\) 1.00000i 1.00000i
\(792\) 0 0
\(793\) 0 0
\(794\) −0.866025 0.500000i −0.866025 0.500000i
\(795\) 0 0
\(796\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(797\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(798\) 1.00000i 1.00000i
\(799\) 0 0
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(804\) −1.00000 −1.00000
\(805\) 0 0
\(806\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(807\) 1.00000 1.00000
\(808\) 0 0
\(809\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) −1.00000 −1.00000
\(815\) 0 0
\(816\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(817\) 0.866025 0.500000i 0.866025 0.500000i
\(818\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(819\) 0 0
\(820\) 0 0
\(821\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(822\) 1.00000i 1.00000i
\(823\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(824\) −0.500000 0.866025i −0.500000 0.866025i
\(825\) 0 0
\(826\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(827\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(828\) 0 0
\(829\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 1.00000 1.00000
\(837\) 1.00000i 1.00000i
\(838\) 0 0
\(839\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(840\) 0 0
\(841\) −1.00000 −1.00000
\(842\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(843\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(844\) −0.866025 0.500000i −0.866025 0.500000i
\(845\) 0 0
\(846\) 0 0
\(847\) 0 0
\(848\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(849\) 0 0
\(850\) 0 0
\(851\) 0 0
\(852\) 1.00000i 1.00000i
\(853\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.500000 0.866025i 0.500000 0.866025i
\(857\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(858\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(859\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(862\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(863\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(864\) −1.00000 −1.00000
\(865\) 0 0
\(866\) 0 0
\(867\) 0 0
\(868\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(869\) −1.00000 −1.00000
\(870\) 0 0
\(871\) −0.866025 0.500000i −0.866025 0.500000i
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 1.00000i 1.00000i
\(877\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(878\) 0.866025 0.500000i 0.866025 0.500000i
\(879\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(880\) 0 0
\(881\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(882\) 0 0
\(883\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(884\) −1.00000 −1.00000
\(885\) 0 0
\(886\) −0.500000 0.866025i −0.500000 0.866025i
\(887\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(888\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(889\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(890\) 0 0
\(891\) 1.00000i 1.00000i
\(892\) 0.500000 0.866025i 0.500000 0.866025i
\(893\) 0 0
\(894\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(895\) 0 0
\(896\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(897\) 0 0
\(898\) 2.00000 2.00000
\(899\) 0 0
\(900\) 0 0
\(901\) −1.00000 −1.00000
\(902\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(903\) 1.00000 1.00000
\(904\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(905\) 0 0
\(906\) −1.73205 1.00000i −1.73205 1.00000i
\(907\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(908\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(909\) 0 0
\(910\) 0 0
\(911\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(912\) 0.866025 0.500000i 0.866025 0.500000i
\(913\) −0.866025 0.500000i −0.866025 0.500000i
\(914\) 0 0
\(915\) 0 0
\(916\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(917\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(918\) −0.866025 0.500000i −0.866025 0.500000i
\(919\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(920\) 0 0
\(921\) −0.500000 0.866025i −0.500000 0.866025i
\(922\) 0 0
\(923\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(924\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) 0 0
\(935\) 0 0
\(936\) 0 0
\(937\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(938\) −1.00000 −1.00000
\(939\) 0.866025 0.500000i 0.866025 0.500000i
\(940\) 0 0
\(941\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(942\) 0 0
\(943\) 0 0
\(944\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(945\) 0 0
\(946\) 1.00000i 1.00000i
\(947\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(948\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(949\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(950\) 0 0
\(951\) 0.866025 0.500000i 0.866025 0.500000i
\(952\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(953\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0.866025 0.500000i 0.866025 0.500000i
\(957\) 0 0
\(958\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(959\) 1.00000i 1.00000i
\(960\) 0 0
\(961\) −1.00000 −1.00000
\(962\) −1.00000 −1.00000
\(963\) 0 0
\(964\) 0.500000 0.866025i 0.500000 0.866025i
\(965\) 0 0
\(966\) 0 0
\(967\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(968\) 0 0
\(969\) 1.00000 1.00000
\(970\) 0 0
\(971\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.500000 0.866025i −0.500000 0.866025i
\(975\) 0 0
\(976\) 0 0
\(977\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(978\) 0 0
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(983\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(984\) 1.00000 1.00000
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 1.00000 1.00000
\(989\) 0 0
\(990\) 0 0
\(991\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(992\) 1.00000i 1.00000i
\(993\) 1.00000i 1.00000i
\(994\) 1.00000i 1.00000i
\(995\) 0 0
\(996\) −1.00000 −1.00000
\(997\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(998\) −0.866025 0.500000i −0.866025 0.500000i
\(999\) −0.866025 0.500000i −0.866025 0.500000i
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 3100.1.t.b.2299.1 4
4.3 odd 2 3100.1.t.a.2299.2 4
5.2 odd 4 124.1.i.a.67.2 yes 4
5.3 odd 4 3100.1.z.a.2051.1 4
5.4 even 2 3100.1.t.a.2299.1 4
15.2 even 4 1116.1.x.a.811.1 4
20.3 even 4 3100.1.z.a.2051.2 4
20.7 even 4 124.1.i.a.67.1 4
20.19 odd 2 inner 3100.1.t.b.2299.2 4
31.25 even 3 inner 3100.1.t.b.1699.2 4
40.27 even 4 1984.1.s.a.191.2 4
40.37 odd 4 1984.1.s.a.191.1 4
60.47 odd 4 1116.1.x.a.811.2 4
124.87 odd 6 3100.1.t.a.1699.1 4
155.2 odd 20 3844.1.n.e.547.1 16
155.7 odd 60 3844.1.n.e.1299.1 16
155.12 even 60 3844.1.n.f.3727.1 16
155.17 even 60 3844.1.n.f.3615.2 16
155.22 even 60 3844.1.l.c.1335.2 8
155.27 even 20 3844.1.n.f.235.1 16
155.37 even 12 3844.1.i.d.2443.2 4
155.42 even 60 3844.1.l.c.3271.1 8
155.47 odd 20 3844.1.n.e.1807.2 16
155.52 even 60 3844.1.l.c.531.1 8
155.57 even 12 3844.1.b.c.1923.2 2
155.67 odd 12 3844.1.b.d.1923.2 2
155.72 odd 60 3844.1.l.d.531.1 8
155.77 even 20 3844.1.n.f.1807.2 16
155.82 odd 60 3844.1.l.d.3271.1 8
155.87 odd 12 124.1.i.a.87.2 yes 4
155.92 even 4 3844.1.i.d.439.2 4
155.97 odd 20 3844.1.n.e.235.1 16
155.102 odd 60 3844.1.l.d.1335.2 8
155.107 odd 60 3844.1.n.e.3615.2 16
155.112 odd 60 3844.1.n.e.3727.1 16
155.117 even 60 3844.1.n.f.1299.1 16
155.118 odd 12 3100.1.z.a.1451.1 4
155.122 even 20 3844.1.n.f.547.1 16
155.127 even 60 3844.1.n.f.3331.2 16
155.132 odd 20 3844.1.n.e.3699.2 16
155.137 even 60 3844.1.l.c.3511.2 8
155.142 odd 60 3844.1.l.d.3511.2 8
155.147 even 20 3844.1.n.f.3699.2 16
155.149 even 6 3100.1.t.a.1699.2 4
155.152 odd 60 3844.1.n.e.3331.2 16
465.242 even 12 1116.1.x.a.955.1 4
620.7 even 60 3844.1.n.e.1299.2 16
620.27 odd 20 3844.1.n.f.235.2 16
620.47 even 20 3844.1.n.e.1807.1 16
620.67 even 12 3844.1.b.d.1923.1 2
620.87 even 12 124.1.i.a.87.1 yes 4
620.107 even 60 3844.1.n.e.3615.1 16
620.127 odd 60 3844.1.n.f.3331.1 16
620.147 odd 20 3844.1.n.f.3699.1 16
620.167 odd 60 3844.1.n.f.3727.2 16
620.207 odd 60 3844.1.l.c.531.2 8
620.227 even 60 3844.1.l.d.531.2 8
620.247 odd 4 3844.1.i.d.439.1 4
620.267 even 60 3844.1.n.e.3727.2 16
620.287 even 20 3844.1.n.e.3699.1 16
620.307 even 60 3844.1.n.e.3331.1 16
620.327 odd 60 3844.1.n.f.3615.1 16
620.347 odd 12 3844.1.i.d.2443.1 4
620.367 odd 12 3844.1.b.c.1923.1 2
620.387 odd 20 3844.1.n.f.1807.1 16
620.407 even 20 3844.1.n.e.235.2 16
620.427 odd 60 3844.1.n.f.1299.2 16
620.447 odd 60 3844.1.l.c.3511.1 8
620.459 odd 6 inner 3100.1.t.b.1699.1 4
620.467 even 20 3844.1.n.e.547.2 16
620.487 odd 60 3844.1.l.c.1335.1 8
620.507 odd 60 3844.1.l.c.3271.2 8
620.547 even 60 3844.1.l.d.3271.2 8
620.567 even 60 3844.1.l.d.1335.1 8
620.583 even 12 3100.1.z.a.1451.2 4
620.587 odd 20 3844.1.n.f.547.2 16
620.607 even 60 3844.1.l.d.3511.1 8
1240.397 odd 12 1984.1.s.a.831.2 4
1240.707 even 12 1984.1.s.a.831.1 4
1860.707 odd 12 1116.1.x.a.955.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
124.1.i.a.67.1 4 20.7 even 4
124.1.i.a.67.2 yes 4 5.2 odd 4
124.1.i.a.87.1 yes 4 620.87 even 12
124.1.i.a.87.2 yes 4 155.87 odd 12
1116.1.x.a.811.1 4 15.2 even 4
1116.1.x.a.811.2 4 60.47 odd 4
1116.1.x.a.955.1 4 465.242 even 12
1116.1.x.a.955.2 4 1860.707 odd 12
1984.1.s.a.191.1 4 40.37 odd 4
1984.1.s.a.191.2 4 40.27 even 4
1984.1.s.a.831.1 4 1240.707 even 12
1984.1.s.a.831.2 4 1240.397 odd 12
3100.1.t.a.1699.1 4 124.87 odd 6
3100.1.t.a.1699.2 4 155.149 even 6
3100.1.t.a.2299.1 4 5.4 even 2
3100.1.t.a.2299.2 4 4.3 odd 2
3100.1.t.b.1699.1 4 620.459 odd 6 inner
3100.1.t.b.1699.2 4 31.25 even 3 inner
3100.1.t.b.2299.1 4 1.1 even 1 trivial
3100.1.t.b.2299.2 4 20.19 odd 2 inner
3100.1.z.a.1451.1 4 155.118 odd 12
3100.1.z.a.1451.2 4 620.583 even 12
3100.1.z.a.2051.1 4 5.3 odd 4
3100.1.z.a.2051.2 4 20.3 even 4
3844.1.b.c.1923.1 2 620.367 odd 12
3844.1.b.c.1923.2 2 155.57 even 12
3844.1.b.d.1923.1 2 620.67 even 12
3844.1.b.d.1923.2 2 155.67 odd 12
3844.1.i.d.439.1 4 620.247 odd 4
3844.1.i.d.439.2 4 155.92 even 4
3844.1.i.d.2443.1 4 620.347 odd 12
3844.1.i.d.2443.2 4 155.37 even 12
3844.1.l.c.531.1 8 155.52 even 60
3844.1.l.c.531.2 8 620.207 odd 60
3844.1.l.c.1335.1 8 620.487 odd 60
3844.1.l.c.1335.2 8 155.22 even 60
3844.1.l.c.3271.1 8 155.42 even 60
3844.1.l.c.3271.2 8 620.507 odd 60
3844.1.l.c.3511.1 8 620.447 odd 60
3844.1.l.c.3511.2 8 155.137 even 60
3844.1.l.d.531.1 8 155.72 odd 60
3844.1.l.d.531.2 8 620.227 even 60
3844.1.l.d.1335.1 8 620.567 even 60
3844.1.l.d.1335.2 8 155.102 odd 60
3844.1.l.d.3271.1 8 155.82 odd 60
3844.1.l.d.3271.2 8 620.547 even 60
3844.1.l.d.3511.1 8 620.607 even 60
3844.1.l.d.3511.2 8 155.142 odd 60
3844.1.n.e.235.1 16 155.97 odd 20
3844.1.n.e.235.2 16 620.407 even 20
3844.1.n.e.547.1 16 155.2 odd 20
3844.1.n.e.547.2 16 620.467 even 20
3844.1.n.e.1299.1 16 155.7 odd 60
3844.1.n.e.1299.2 16 620.7 even 60
3844.1.n.e.1807.1 16 620.47 even 20
3844.1.n.e.1807.2 16 155.47 odd 20
3844.1.n.e.3331.1 16 620.307 even 60
3844.1.n.e.3331.2 16 155.152 odd 60
3844.1.n.e.3615.1 16 620.107 even 60
3844.1.n.e.3615.2 16 155.107 odd 60
3844.1.n.e.3699.1 16 620.287 even 20
3844.1.n.e.3699.2 16 155.132 odd 20
3844.1.n.e.3727.1 16 155.112 odd 60
3844.1.n.e.3727.2 16 620.267 even 60
3844.1.n.f.235.1 16 155.27 even 20
3844.1.n.f.235.2 16 620.27 odd 20
3844.1.n.f.547.1 16 155.122 even 20
3844.1.n.f.547.2 16 620.587 odd 20
3844.1.n.f.1299.1 16 155.117 even 60
3844.1.n.f.1299.2 16 620.427 odd 60
3844.1.n.f.1807.1 16 620.387 odd 20
3844.1.n.f.1807.2 16 155.77 even 20
3844.1.n.f.3331.1 16 620.127 odd 60
3844.1.n.f.3331.2 16 155.127 even 60
3844.1.n.f.3615.1 16 620.327 odd 60
3844.1.n.f.3615.2 16 155.17 even 60
3844.1.n.f.3699.1 16 620.147 odd 20
3844.1.n.f.3699.2 16 155.147 even 20
3844.1.n.f.3727.1 16 155.12 even 60
3844.1.n.f.3727.2 16 620.167 odd 60