Properties

Label 3325.1.bc.a.3051.1
Level $3325$
Weight $1$
Character 3325.3051
Analytic conductor $1.659$
Analytic rank $0$
Dimension $4$
Projective image $A_{4}$
CM/RM no
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3325,1,Mod(2876,3325)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3325, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([0, 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("3325.2876");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3325 = 5^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3325.bc (of order \(6\), degree \(2\), 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: \(1.65939116700\)
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: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 133)
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.17689.1

Embedding invariants

Embedding label 3051.1
Root \(0.866025 - 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 3325.3051
Dual form 3325.1.bc.a.2876.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.866025 + 0.500000i) q^{6} +1.00000i q^{7} +1.00000 q^{8} +(0.866025 - 0.500000i) q^{13} +(0.866025 + 0.500000i) q^{14} +(0.500000 - 0.866025i) q^{16} +(-0.866025 - 0.500000i) q^{17} +1.00000i q^{19} +(0.500000 - 0.866025i) q^{21} +(0.500000 + 0.866025i) q^{23} +(-0.866025 - 0.500000i) q^{24} -1.00000i q^{26} +1.00000i q^{27} +(0.500000 + 0.866025i) q^{29} +(-0.866025 + 0.500000i) q^{34} +(0.866025 + 0.500000i) q^{38} -1.00000 q^{39} +(0.866025 + 0.500000i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(0.500000 - 0.866025i) q^{43} +1.00000 q^{46} +(0.866025 - 0.500000i) q^{47} +(-0.866025 + 0.500000i) q^{48} -1.00000 q^{49} +(0.500000 + 0.866025i) q^{51} +(-0.500000 - 0.866025i) q^{53} +(0.866025 + 0.500000i) q^{54} +1.00000i q^{56} +(0.500000 - 0.866025i) q^{57} +1.00000 q^{58} +(-0.866025 - 0.500000i) q^{59} +(0.866025 - 0.500000i) q^{61} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{67} -1.00000i q^{69} +(0.500000 - 0.866025i) q^{71} +(0.866025 + 0.500000i) q^{73} +(-0.500000 + 0.866025i) q^{78} +(-0.500000 + 0.866025i) q^{79} +(0.500000 - 0.866025i) q^{81} +(0.866025 - 0.500000i) q^{82} +(-0.500000 - 0.866025i) q^{86} -1.00000i q^{87} +(0.866025 - 0.500000i) q^{89} +(0.500000 + 0.866025i) q^{91} -1.00000i q^{94} +(-0.866025 - 0.500000i) q^{97} +(-0.500000 + 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q + 2 q^{2} + 4 q^{8}+O(q^{10}) \) Copy content Toggle raw display \( 4 q + 2 q^{2} + 4 q^{8} + 2 q^{16} + 2 q^{21} + 2 q^{23} + 2 q^{29} - 4 q^{39} - 2 q^{42} + 2 q^{43} + 4 q^{46} - 4 q^{49} + 2 q^{51} - 2 q^{53} + 2 q^{57} + 4 q^{58} + 4 q^{64} + 2 q^{67} + 2 q^{71} - 2 q^{78} - 2 q^{79} + 2 q^{81} - 2 q^{86} + 2 q^{91} - 2 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3325\mathbb{Z}\right)^\times\).

\(n\) \(876\) \(2376\) \(2927\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(3\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(4\) 0 0
\(5\) 0 0
\(6\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(7\) 1.00000i 1.00000i
\(8\) 1.00000 1.00000
\(9\) 0 0
\(10\) 0 0
\(11\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(12\) 0 0
\(13\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(14\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.500000 0.866025i
\(17\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(18\) 0 0
\(19\) 1.00000i 1.00000i
\(20\) 0 0
\(21\) 0.500000 0.866025i 0.500000 0.866025i
\(22\) 0 0
\(23\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(24\) −0.866025 0.500000i −0.866025 0.500000i
\(25\) 0 0
\(26\) 1.00000i 1.00000i
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(30\) 0 0
\(31\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(32\) 0 0
\(33\) 0 0
\(34\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(35\) 0 0
\(36\) 0 0
\(37\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(38\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(39\) −1.00000 −1.00000
\(40\) 0 0
\(41\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(42\) −0.500000 0.866025i −0.500000 0.866025i
\(43\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(44\) 0 0
\(45\) 0 0
\(46\) 1.00000 1.00000
\(47\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(48\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(49\) −1.00000 −1.00000
\(50\) 0 0
\(51\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(52\) 0 0
\(53\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(54\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(55\) 0 0
\(56\) 1.00000i 1.00000i
\(57\) 0.500000 0.866025i 0.500000 0.866025i
\(58\) 1.00000 1.00000
\(59\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 0 0
\(61\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(62\) 0 0
\(63\) 0 0
\(64\) 1.00000 1.00000
\(65\) 0 0
\(66\) 0 0
\(67\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) 0 0
\(69\) 1.00000i 1.00000i
\(70\) 0 0
\(71\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(72\) 0 0
\(73\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(74\) 0 0
\(75\) 0 0
\(76\) 0 0
\(77\) 0 0
\(78\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(79\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(80\) 0 0
\(81\) 0.500000 0.866025i 0.500000 0.866025i
\(82\) 0.866025 0.500000i 0.866025 0.500000i
\(83\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −0.500000 0.866025i −0.500000 0.866025i
\(87\) 1.00000i 1.00000i
\(88\) 0 0
\(89\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(90\) 0 0
\(91\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(92\) 0 0
\(93\) 0 0
\(94\) 1.00000i 1.00000i
\(95\) 0 0
\(96\) 0 0
\(97\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) 0 0
\(100\) 0 0
\(101\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) 1.00000 1.00000
\(103\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(104\) 0.866025 0.500000i 0.866025 0.500000i
\(105\) 0 0
\(106\) −1.00000 −1.00000
\(107\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(108\) 0 0
\(109\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) −0.500000 0.866025i −0.500000 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 0 0
\(118\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(119\) 0.500000 0.866025i 0.500000 0.866025i
\(120\) 0 0
\(121\) −1.00000 −1.00000
\(122\) 1.00000i 1.00000i
\(123\) −0.500000 0.866025i −0.500000 0.866025i
\(124\) 0 0
\(125\) 0 0
\(126\) 0 0
\(127\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) 0.500000 0.866025i 0.500000 0.866025i
\(129\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(130\) 0 0
\(131\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(132\) 0 0
\(133\) −1.00000 −1.00000
\(134\) 1.00000 1.00000
\(135\) 0 0
\(136\) −0.866025 0.500000i −0.866025 0.500000i
\(137\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(138\) −0.866025 0.500000i −0.866025 0.500000i
\(139\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(140\) 0 0
\(141\) −1.00000 −1.00000
\(142\) −0.500000 0.866025i −0.500000 0.866025i
\(143\) 0 0
\(144\) 0 0
\(145\) 0 0
\(146\) 0.866025 0.500000i 0.866025 0.500000i
\(147\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(148\) 0 0
\(149\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(150\) 0 0
\(151\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(152\) 1.00000i 1.00000i
\(153\) 0 0
\(154\) 0 0
\(155\) 0 0
\(156\) 0 0
\(157\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(158\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(159\) 1.00000i 1.00000i
\(160\) 0 0
\(161\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(162\) −0.500000 0.866025i −0.500000 0.866025i
\(163\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(168\) 0.500000 0.866025i 0.500000 0.866025i
\(169\) 0 0
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(174\) −0.866025 0.500000i −0.866025 0.500000i
\(175\) 0 0
\(176\) 0 0
\(177\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(178\) 1.00000i 1.00000i
\(179\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(180\) 0 0
\(181\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(182\) 1.00000 1.00000
\(183\) −1.00000 −1.00000
\(184\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(185\) 0 0
\(186\) 0 0
\(187\) 0 0
\(188\) 0 0
\(189\) −1.00000 −1.00000
\(190\) 0 0
\(191\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(192\) −0.866025 0.500000i −0.866025 0.500000i
\(193\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(194\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(195\) 0 0
\(196\) 0 0
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(200\) 0 0
\(201\) 1.00000i 1.00000i
\(202\) 1.00000i 1.00000i
\(203\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(204\) 0 0
\(205\) 0 0
\(206\) 0 0
\(207\) 0 0
\(208\) 1.00000i 1.00000i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(212\) 0 0
\(213\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(214\) 0 0
\(215\) 0 0
\(216\) 1.00000i 1.00000i
\(217\) 0 0
\(218\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(219\) −0.500000 0.866025i −0.500000 0.866025i
\(220\) 0 0
\(221\) −1.00000 −1.00000
\(222\) 0 0
\(223\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 0 0
\(227\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(228\) 0 0
\(229\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(233\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(234\) 0 0
\(235\) 0 0
\(236\) 0 0
\(237\) 0.866025 0.500000i 0.866025 0.500000i
\(238\) −0.500000 0.866025i −0.500000 0.866025i
\(239\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(240\) 0 0
\(241\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(242\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(243\) 0 0
\(244\) 0 0
\(245\) 0 0
\(246\) −1.00000 −1.00000
\(247\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(248\) 0 0
\(249\) 0 0
\(250\) 0 0
\(251\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) 1.00000 1.00000
\(255\) 0 0
\(256\) 0 0
\(257\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) 1.00000i 1.00000i
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(263\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(267\) −1.00000 −1.00000
\(268\) 0 0
\(269\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 0 0
\(271\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(272\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(273\) 1.00000i 1.00000i
\(274\) −1.00000 −1.00000
\(275\) 0 0
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 1.00000i 1.00000i
\(279\) 0 0
\(280\) 0 0
\(281\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(282\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(283\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(292\) 0 0
\(293\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(294\) 0.866025 0.500000i 0.866025 0.500000i
\(295\) 0 0
\(296\) 0 0
\(297\) 0 0
\(298\) −0.500000 0.866025i −0.500000 0.866025i
\(299\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(300\) 0 0
\(301\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(302\) 0 0
\(303\) −1.00000 −1.00000
\(304\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(305\) 0 0
\(306\) 0 0
\(307\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −1.00000 −1.00000
\(313\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(314\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(315\) 0 0
\(316\) 0 0
\(317\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(318\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(319\) 0 0
\(320\) 0 0
\(321\) 0 0
\(322\) 1.00000i 1.00000i
\(323\) 0.500000 0.866025i 0.500000 0.866025i
\(324\) 0 0
\(325\) 0 0
\(326\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(327\) 0.866025 0.500000i 0.866025 0.500000i
\(328\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(329\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(330\) 0 0
\(331\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 1.00000i 1.00000i
\(335\) 0 0
\(336\) −0.500000 0.866025i −0.500000 0.866025i
\(337\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) 0 0
\(340\) 0 0
\(341\) 0 0
\(342\) 0 0
\(343\) 1.00000i 1.00000i
\(344\) 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 1.00000 \(0\)
−1.00000 \(\pi\)
\(350\) 0 0
\(351\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(352\) 0 0
\(353\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 1.00000 1.00000
\(355\) 0 0
\(356\) 0 0
\(357\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(358\) 0 0
\(359\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) −1.00000 −1.00000
\(362\) 1.00000i 1.00000i
\(363\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(364\) 0 0
\(365\) 0 0
\(366\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(367\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(368\) 1.00000 1.00000
\(369\) 0 0
\(370\) 0 0
\(371\) 0.866025 0.500000i 0.866025 0.500000i
\(372\) 0 0
\(373\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) 0.866025 0.500000i 0.866025 0.500000i
\(377\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(378\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(379\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(380\) 0 0
\(381\) 1.00000i 1.00000i
\(382\) 0 0
\(383\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(384\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(385\) 0 0
\(386\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(387\) 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
\(391\) 1.00000i 1.00000i
\(392\) −1.00000 −1.00000
\(393\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(398\) 1.00000i 1.00000i
\(399\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(400\) 0 0
\(401\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(402\) −0.866025 0.500000i −0.866025 0.500000i
\(403\) 0 0
\(404\) 0 0
\(405\) 0 0
\(406\) 1.00000i 1.00000i
\(407\) 0 0
\(408\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(409\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(410\) 0 0
\(411\) 1.00000i 1.00000i
\(412\) 0 0
\(413\) 0.500000 0.866025i 0.500000 0.866025i
\(414\) 0 0
\(415\) 0 0
\(416\) 0 0
\(417\) −1.00000 −1.00000
\(418\) 0 0
\(419\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(420\) 0 0
\(421\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(422\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(423\) 0 0
\(424\) −0.500000 0.866025i −0.500000 0.866025i
\(425\) 0 0
\(426\) 1.00000i 1.00000i
\(427\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(428\) 0 0
\(429\) 0 0
\(430\) 0 0
\(431\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(432\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(433\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 0 0
\(437\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(438\) −1.00000 −1.00000
\(439\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(443\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0.866025 0.500000i 0.866025 0.500000i
\(447\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(448\) 1.00000i 1.00000i
\(449\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(450\) 0 0
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0 0
\(455\) 0 0
\(456\) 0.500000 0.866025i 0.500000 0.866025i
\(457\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(458\) 0 0
\(459\) 0.500000 0.866025i 0.500000 0.866025i
\(460\) 0 0
\(461\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(462\) 0 0
\(463\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(464\) 1.00000 1.00000
\(465\) 0 0
\(466\) −0.500000 0.866025i −0.500000 0.866025i
\(467\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(468\) 0 0
\(469\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(470\) 0 0
\(471\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(472\) −0.866025 0.500000i −0.866025 0.500000i
\(473\) 0 0
\(474\) 1.00000i 1.00000i
\(475\) 0 0
\(476\) 0 0
\(477\) 0 0
\(478\) 0 0
\(479\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 1.00000i 1.00000i
\(483\) 1.00000 1.00000
\(484\) 0 0
\(485\) 0 0
\(486\) 0 0
\(487\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(488\) 0.866025 0.500000i 0.866025 0.500000i
\(489\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(490\) 0 0
\(491\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 1.00000i 1.00000i
\(494\) 1.00000 1.00000
\(495\) 0 0
\(496\) 0 0
\(497\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(498\) 0 0
\(499\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) 1.00000 1.00000
\(502\) 1.00000i 1.00000i
\(503\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 0 0
\(508\) 0 0
\(509\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(510\) 0 0
\(511\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(512\) 1.00000 1.00000
\(513\) −1.00000 −1.00000
\(514\) 1.00000i 1.00000i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) −0.500000 0.866025i −0.500000 0.866025i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 0 0
\(523\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(524\) 0 0
\(525\) 0 0
\(526\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(527\) 0 0
\(528\) 0 0
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.00000 1.00000
\(534\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(535\) 0 0
\(536\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(537\) 0 0
\(538\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(539\) 0 0
\(540\) 0 0
\(541\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(542\) 0.866025 0.500000i 0.866025 0.500000i
\(543\) 1.00000 1.00000
\(544\) 0 0
\(545\) 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 0
\(549\) 0 0
\(550\) 0 0
\(551\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(552\) 1.00000i 1.00000i
\(553\) −0.866025 0.500000i −0.866025 0.500000i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(558\) 0 0
\(559\) 1.00000i 1.00000i
\(560\) 0 0
\(561\) 0 0
\(562\) −1.00000 −1.00000
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.866025 0.500000i 0.866025 0.500000i
\(567\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(568\) 0.500000 0.866025i 0.500000 0.866025i
\(569\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(570\) 0 0
\(571\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(572\) 0 0
\(573\) 0 0
\(574\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(575\) 0 0
\(576\) 0 0
\(577\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0.866025 0.500000i 0.866025 0.500000i
\(580\) 0 0
\(581\) 0 0
\(582\) 1.00000 1.00000
\(583\) 0 0
\(584\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(585\) 0 0
\(586\) −1.73205 1.00000i −1.73205 1.00000i
\(587\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 0 0
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 0 0
\(597\) −1.00000 −1.00000
\(598\) 0.866025 0.500000i 0.866025 0.500000i
\(599\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(600\) 0 0
\(601\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(602\) 0.866025 0.500000i 0.866025 0.500000i
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(607\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 1.00000 1.00000
\(610\) 0 0
\(611\) 0.500000 0.866025i 0.500000 0.866025i
\(612\) 0 0
\(613\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(614\) 0.866025 0.500000i 0.866025 0.500000i
\(615\) 0 0
\(616\) 0 0
\(617\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(618\) 0 0
\(619\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(622\) 0 0
\(623\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(624\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(625\) 0 0
\(626\) 1.00000i 1.00000i
\(627\) 0 0
\(628\) 0 0
\(629\) 0 0
\(630\) 0 0
\(631\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(632\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(633\) 0.866025 0.500000i 0.866025 0.500000i
\(634\) −1.00000 −1.00000
\(635\) 0 0
\(636\) 0 0
\(637\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(642\) 0 0
\(643\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −0.500000 0.866025i −0.500000 0.866025i
\(647\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(648\) 0.500000 0.866025i 0.500000 0.866025i
\(649\) 0 0
\(650\) 0 0
\(651\) 0 0
\(652\) 0 0
\(653\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(654\) 1.00000i 1.00000i
\(655\) 0 0
\(656\) 0.866025 0.500000i 0.866025 0.500000i
\(657\) 0 0
\(658\) 1.00000 1.00000
\(659\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(660\) 0 0
\(661\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(662\) 0 0
\(663\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(668\) 0 0
\(669\) −0.500000 0.866025i −0.500000 0.866025i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(674\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(675\) 0 0
\(676\) 0 0
\(677\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(678\) 0 0
\(679\) 0.500000 0.866025i 0.500000 0.866025i
\(680\) 0 0
\(681\) 0 0
\(682\) 0 0
\(683\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.866025 0.500000i −0.866025 0.500000i
\(687\) 0 0
\(688\) −0.500000 0.866025i −0.500000 0.866025i
\(689\) −0.866025 0.500000i −0.866025 0.500000i
\(690\) 0 0
\(691\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(692\) 0 0
\(693\) 0 0
\(694\) −0.500000 0.866025i −0.500000 0.866025i
\(695\) 0 0
\(696\) 1.00000i 1.00000i
\(697\) −0.500000 0.866025i −0.500000 0.866025i
\(698\) 0 0
\(699\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(700\) 0 0
\(701\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(702\) 1.00000 1.00000
\(703\) 0 0
\(704\) 0 0
\(705\) 0 0
\(706\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(707\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(708\) 0 0
\(709\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 0.866025 0.500000i 0.866025 0.500000i
\(713\) 0 0
\(714\) 1.00000i 1.00000i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(719\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(723\) 1.00000 1.00000
\(724\) 0 0
\(725\) 0 0
\(726\) 0.866025 0.500000i 0.866025 0.500000i
\(727\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(728\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(729\) −1.00000 −1.00000
\(730\) 0 0
\(731\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(732\) 0 0
\(733\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(734\) 1.00000i 1.00000i
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 0 0
\(739\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(740\) 0 0
\(741\) 1.00000i 1.00000i
\(742\) 1.00000i 1.00000i
\(743\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) 0 0
\(747\) 0 0
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(752\) 1.00000i 1.00000i
\(753\) 1.00000 1.00000
\(754\) 0.866025 0.500000i 0.866025 0.500000i
\(755\) 0 0
\(756\) 0 0
\(757\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(758\) 0 0
\(759\) 0 0
\(760\) 0 0
\(761\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(762\) −0.866025 0.500000i −0.866025 0.500000i
\(763\) −0.866025 0.500000i −0.866025 0.500000i
\(764\) 0 0
\(765\) 0 0
\(766\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(767\) −1.00000 −1.00000
\(768\) 0 0
\(769\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(770\) 0 0
\(771\) −1.00000 −1.00000
\(772\) 0 0
\(773\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −0.866025 0.500000i −0.866025 0.500000i
\(777\) 0 0
\(778\) −1.00000 −1.00000
\(779\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(780\) 0 0
\(781\) 0 0
\(782\) −0.866025 0.500000i −0.866025 0.500000i
\(783\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(784\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(785\) 0 0
\(786\) 1.00000 1.00000
\(787\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(788\) 0 0
\(789\) 0.866025 0.500000i 0.866025 0.500000i
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 0.500000 0.866025i 0.500000 0.866025i
\(794\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(795\) 0 0
\(796\) 0 0
\(797\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(798\) 0.866025 0.500000i 0.866025 0.500000i
\(799\) −1.00000 −1.00000
\(800\) 0 0
\(801\) 0 0
\(802\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0 0
\(807\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(808\) 0.866025 0.500000i 0.866025 0.500000i
\(809\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(810\) 0 0
\(811\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(812\) 0 0
\(813\) −0.500000 0.866025i −0.500000 0.866025i
\(814\) 0 0
\(815\) 0 0
\(816\) 1.00000 1.00000
\(817\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(818\) 1.00000i 1.00000i
\(819\) 0 0
\(820\) 0 0
\(821\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(822\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(823\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(824\) 0 0
\(825\) 0 0
\(826\) −0.500000 0.866025i −0.500000 0.866025i
\(827\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(828\) 0 0
\(829\) 2.00000i 2.00000i 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
\(833\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(834\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(835\) 0 0
\(836\) 0 0
\(837\) 0 0
\(838\) 0 0
\(839\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) −0.500000 0.866025i −0.500000 0.866025i
\(843\) 1.00000i 1.00000i
\(844\) 0 0
\(845\) 0 0
\(846\) 0 0
\(847\) 1.00000i 1.00000i
\(848\) −1.00000 −1.00000
\(849\) −0.500000 0.866025i −0.500000 0.866025i
\(850\) 0 0
\(851\) 0 0
\(852\) 0 0
\(853\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(854\) 1.00000 1.00000
\(855\) 0 0
\(856\) 0 0
\(857\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(858\) 0 0
\(859\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(860\) 0 0
\(861\) 0.866025 0.500000i 0.866025 0.500000i
\(862\) −1.00000 −1.00000
\(863\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 1.00000i 1.00000i
\(867\) 0 0
\(868\) 0 0
\(869\) 0 0
\(870\) 0 0
\(871\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(872\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(873\) 0 0
\(874\) 1.00000i 1.00000i
\(875\) 0 0
\(876\) 0 0
\(877\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(878\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(879\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0 0
\(883\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(884\) 0 0
\(885\) 0 0
\(886\) 1.00000 1.00000
\(887\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(888\) 0 0
\(889\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(890\) 0 0
\(891\) 0 0
\(892\) 0 0
\(893\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(894\) 1.00000i 1.00000i
\(895\) 0 0
\(896\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(897\) −0.500000 0.866025i −0.500000 0.866025i
\(898\) 0 0
\(899\) 0 0
\(900\) 0 0
\(901\) 1.00000i 1.00000i
\(902\) 0 0
\(903\) −0.500000 0.866025i −0.500000 0.866025i
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(908\) 0 0
\(909\) 0 0
\(910\) 0 0
\(911\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(912\) −0.500000 0.866025i −0.500000 0.866025i
\(913\) 0 0
\(914\) 0 0
\(915\) 0 0
\(916\) 0 0
\(917\) 0.500000 0.866025i 0.500000 0.866025i
\(918\) −0.500000 0.866025i −0.500000 0.866025i
\(919\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(920\) 0 0
\(921\) −0.500000 0.866025i −0.500000 0.866025i
\(922\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(923\) 1.00000i 1.00000i
\(924\) 0 0
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 1.00000i 1.00000i
\(932\) 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 \(0.166667\pi\)
\(938\) 1.00000i 1.00000i
\(939\) 1.00000 1.00000
\(940\) 0 0
\(941\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(942\) 1.00000 1.00000
\(943\) 1.00000i 1.00000i
\(944\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(945\) 0 0
\(946\) 0 0
\(947\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(948\) 0 0
\(949\) 1.00000 1.00000
\(950\) 0 0
\(951\) 1.00000i 1.00000i
\(952\) 0.500000 0.866025i 0.500000 0.866025i
\(953\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 1.00000i 1.00000i
\(959\) 0.866025 0.500000i 0.866025 0.500000i
\(960\) 0 0
\(961\) 1.00000 1.00000
\(962\) 0 0
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) 0.500000 0.866025i 0.500000 0.866025i
\(967\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(968\) −1.00000 −1.00000
\(969\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(970\) 0 0
\(971\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(974\) 0 0
\(975\) 0 0
\(976\) 1.00000i 1.00000i
\(977\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(978\) 1.73205 1.00000i 1.73205 1.00000i
\(979\) 0 0
\(980\) 0 0
\(981\) 0 0
\(982\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(983\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(984\) −0.500000 0.866025i −0.500000 0.866025i
\(985\) 0 0
\(986\) −0.866025 0.500000i −0.866025 0.500000i
\(987\) 1.00000i 1.00000i
\(988\) 0 0
\(989\) 1.00000 1.00000
\(990\) 0 0
\(991\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(992\) 0 0
\(993\) 0 0
\(994\) 0.866025 0.500000i 0.866025 0.500000i
\(995\) 0 0
\(996\) 0 0
\(997\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(998\) −0.500000 0.866025i −0.500000 0.866025i
\(999\) 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 3325.1.bc.a.3051.1 4
5.2 odd 4 3325.1.bi.a.524.2 4
5.3 odd 4 3325.1.bi.b.524.1 4
5.4 even 2 133.1.m.a.125.2 yes 4
7.6 odd 2 inner 3325.1.bc.a.3051.2 4
15.14 odd 2 1197.1.ci.c.1189.2 4
19.7 even 3 inner 3325.1.bc.a.2876.2 4
20.19 odd 2 2128.1.cy.a.657.1 4
35.4 even 6 931.1.k.a.68.1 4
35.9 even 6 931.1.t.a.619.1 4
35.13 even 4 3325.1.bi.a.524.1 4
35.19 odd 6 931.1.t.a.619.2 4
35.24 odd 6 931.1.k.a.68.2 4
35.27 even 4 3325.1.bi.b.524.2 4
35.34 odd 2 133.1.m.a.125.1 yes 4
95.4 even 18 2527.1.y.e.62.1 12
95.7 odd 12 3325.1.bi.a.349.1 4
95.9 even 18 2527.1.y.e.2050.2 12
95.14 odd 18 2527.1.y.d.1833.2 12
95.24 even 18 2527.1.y.e.1833.1 12
95.29 odd 18 2527.1.y.d.2050.1 12
95.34 odd 18 2527.1.y.d.62.2 12
95.44 even 18 2527.1.y.e.776.2 12
95.49 even 6 2527.1.d.e.1084.1 2
95.54 even 18 2527.1.y.e.1182.2 12
95.59 odd 18 2527.1.y.d.2400.2 12
95.64 even 6 133.1.m.a.83.1 4
95.69 odd 6 2527.1.m.d.1014.2 4
95.74 even 18 2527.1.y.e.2400.1 12
95.79 odd 18 2527.1.y.d.1182.1 12
95.83 odd 12 3325.1.bi.b.349.2 4
95.84 odd 6 2527.1.d.b.1084.2 2
95.89 odd 18 2527.1.y.d.776.1 12
95.94 odd 2 2527.1.m.d.790.1 4
105.104 even 2 1197.1.ci.c.1189.1 4
133.83 odd 6 inner 3325.1.bc.a.2876.1 4
140.139 even 2 2128.1.cy.a.657.2 4
285.254 odd 6 1197.1.ci.c.748.1 4
380.159 odd 6 2128.1.cy.a.881.2 4
665.34 even 18 2527.1.y.d.62.1 12
665.69 even 6 2527.1.m.d.1014.1 4
665.83 even 12 3325.1.bi.a.349.2 4
665.104 odd 18 2527.1.y.e.2050.1 12
665.139 odd 18 2527.1.y.e.776.1 12
665.159 odd 6 931.1.k.a.178.2 4
665.174 even 18 2527.1.y.d.1182.2 12
665.244 odd 18 2527.1.y.e.1182.1 12
665.254 even 6 931.1.k.a.178.1 4
665.279 even 18 2527.1.y.d.776.2 12
665.314 even 18 2527.1.y.d.2050.2 12
665.349 odd 6 133.1.m.a.83.2 yes 4
665.384 odd 18 2527.1.y.e.62.2 12
665.444 odd 6 931.1.t.a.558.1 4
665.454 odd 18 2527.1.y.e.2400.2 12
665.482 even 12 3325.1.bi.b.349.1 4
665.489 even 18 2527.1.y.d.1833.1 12
665.524 odd 6 2527.1.d.e.1084.2 2
665.559 even 6 2527.1.d.b.1084.1 2
665.594 odd 18 2527.1.y.e.1833.2 12
665.629 even 18 2527.1.y.d.2400.1 12
665.634 even 6 931.1.t.a.558.2 4
665.664 even 2 2527.1.m.d.790.2 4
1995.1679 even 6 1197.1.ci.c.748.2 4
2660.1679 even 6 2128.1.cy.a.881.1 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
133.1.m.a.83.1 4 95.64 even 6
133.1.m.a.83.2 yes 4 665.349 odd 6
133.1.m.a.125.1 yes 4 35.34 odd 2
133.1.m.a.125.2 yes 4 5.4 even 2
931.1.k.a.68.1 4 35.4 even 6
931.1.k.a.68.2 4 35.24 odd 6
931.1.k.a.178.1 4 665.254 even 6
931.1.k.a.178.2 4 665.159 odd 6
931.1.t.a.558.1 4 665.444 odd 6
931.1.t.a.558.2 4 665.634 even 6
931.1.t.a.619.1 4 35.9 even 6
931.1.t.a.619.2 4 35.19 odd 6
1197.1.ci.c.748.1 4 285.254 odd 6
1197.1.ci.c.748.2 4 1995.1679 even 6
1197.1.ci.c.1189.1 4 105.104 even 2
1197.1.ci.c.1189.2 4 15.14 odd 2
2128.1.cy.a.657.1 4 20.19 odd 2
2128.1.cy.a.657.2 4 140.139 even 2
2128.1.cy.a.881.1 4 2660.1679 even 6
2128.1.cy.a.881.2 4 380.159 odd 6
2527.1.d.b.1084.1 2 665.559 even 6
2527.1.d.b.1084.2 2 95.84 odd 6
2527.1.d.e.1084.1 2 95.49 even 6
2527.1.d.e.1084.2 2 665.524 odd 6
2527.1.m.d.790.1 4 95.94 odd 2
2527.1.m.d.790.2 4 665.664 even 2
2527.1.m.d.1014.1 4 665.69 even 6
2527.1.m.d.1014.2 4 95.69 odd 6
2527.1.y.d.62.1 12 665.34 even 18
2527.1.y.d.62.2 12 95.34 odd 18
2527.1.y.d.776.1 12 95.89 odd 18
2527.1.y.d.776.2 12 665.279 even 18
2527.1.y.d.1182.1 12 95.79 odd 18
2527.1.y.d.1182.2 12 665.174 even 18
2527.1.y.d.1833.1 12 665.489 even 18
2527.1.y.d.1833.2 12 95.14 odd 18
2527.1.y.d.2050.1 12 95.29 odd 18
2527.1.y.d.2050.2 12 665.314 even 18
2527.1.y.d.2400.1 12 665.629 even 18
2527.1.y.d.2400.2 12 95.59 odd 18
2527.1.y.e.62.1 12 95.4 even 18
2527.1.y.e.62.2 12 665.384 odd 18
2527.1.y.e.776.1 12 665.139 odd 18
2527.1.y.e.776.2 12 95.44 even 18
2527.1.y.e.1182.1 12 665.244 odd 18
2527.1.y.e.1182.2 12 95.54 even 18
2527.1.y.e.1833.1 12 95.24 even 18
2527.1.y.e.1833.2 12 665.594 odd 18
2527.1.y.e.2050.1 12 665.104 odd 18
2527.1.y.e.2050.2 12 95.9 even 18
2527.1.y.e.2400.1 12 95.74 even 18
2527.1.y.e.2400.2 12 665.454 odd 18
3325.1.bc.a.2876.1 4 133.83 odd 6 inner
3325.1.bc.a.2876.2 4 19.7 even 3 inner
3325.1.bc.a.3051.1 4 1.1 even 1 trivial
3325.1.bc.a.3051.2 4 7.6 odd 2 inner
3325.1.bi.a.349.1 4 95.7 odd 12
3325.1.bi.a.349.2 4 665.83 even 12
3325.1.bi.a.524.1 4 35.13 even 4
3325.1.bi.a.524.2 4 5.2 odd 4
3325.1.bi.b.349.1 4 665.482 even 12
3325.1.bi.b.349.2 4 95.83 odd 12
3325.1.bi.b.524.1 4 5.3 odd 4
3325.1.bi.b.524.2 4 35.27 even 4