Properties

Label 201.1.g.a.29.2
Level $201$
Weight $1$
Character 201.29
Analytic conductor $0.100$
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] = [201,1,Mod(29,201)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(201, base_ring=CyclotomicField(6))
 
chi = DirichletCharacter(H, H._module([3, 4]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("201.29");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 201 = 3 \cdot 67 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 201.g (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: \(0.100312067539\)
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: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(A_{4}\)
Projective field: Galois closure of 4.0.40401.1
Artin image: $\SL(2,3):C_2$
Artin field: Galois closure of \(\mathbb{Q}[x]/(x^{16} - \cdots)\)

Embedding invariants

Embedding label 29.2
Root \(-0.866025 + 0.500000i\) of defining polynomial
Character \(\chi\) \(=\) 201.29
Dual form 201.1.g.a.104.2

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\) \(q+(0.866025 + 0.500000i) q^{2} +1.00000i q^{3} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000i q^{8} -1.00000 q^{9} +(-0.866025 + 0.500000i) q^{11} +(-0.500000 + 0.866025i) q^{13} -1.00000i q^{14} +(0.500000 - 0.866025i) q^{16} +(0.866025 + 0.500000i) q^{17} +(-0.866025 - 0.500000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(0.866025 - 0.500000i) q^{21} -1.00000 q^{22} +(-0.866025 - 0.500000i) q^{23} +1.00000 q^{24} +1.00000 q^{25} +(-0.866025 + 0.500000i) q^{26} -1.00000i q^{27} +(-0.866025 + 0.500000i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-0.500000 - 0.866025i) q^{33} +(0.500000 + 0.866025i) q^{34} +(-0.500000 + 0.866025i) q^{37} +(0.866025 - 0.500000i) q^{38} +(-0.866025 - 0.500000i) q^{39} +(0.866025 - 0.500000i) q^{41} +1.00000 q^{42} +(-0.500000 - 0.866025i) q^{46} +(-0.866025 + 0.500000i) q^{47} +(0.866025 + 0.500000i) q^{48} +(0.866025 + 0.500000i) q^{50} +(-0.500000 + 0.866025i) q^{51} +(0.500000 - 0.866025i) q^{54} +(-0.866025 + 0.500000i) q^{56} +(0.866025 + 0.500000i) q^{57} -1.00000 q^{58} +(-0.500000 + 0.866025i) q^{61} +1.00000i q^{62} +(0.500000 + 0.866025i) q^{63} -1.00000 q^{64} -1.00000i q^{66} -1.00000 q^{67} +(0.500000 - 0.866025i) q^{69} +(0.866025 - 0.500000i) q^{71} +1.00000i q^{72} +(0.500000 - 0.866025i) q^{73} +(-0.866025 + 0.500000i) q^{74} +1.00000i q^{75} +(0.866025 + 0.500000i) q^{77} +(-0.500000 - 0.866025i) q^{78} +(-0.500000 - 0.866025i) q^{79} +1.00000 q^{81} +1.00000 q^{82} +(0.866025 + 0.500000i) q^{83} +(-0.500000 - 0.866025i) q^{87} +(0.500000 + 0.866025i) q^{88} -2.00000i q^{89} +1.00000 q^{91} +(-0.866025 + 0.500000i) q^{93} -1.00000 q^{94} +(-0.500000 + 0.866025i) q^{97} +(0.866025 - 0.500000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4 q - 2 q^{6} - 2 q^{7} - 4 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 4 q - 2 q^{6} - 2 q^{7} - 4 q^{9} - 2 q^{13} + 2 q^{16} + 2 q^{19} - 4 q^{22} + 4 q^{24} + 4 q^{25} + 2 q^{31} - 2 q^{33} + 2 q^{34} - 2 q^{37} + 4 q^{42} - 2 q^{46} - 2 q^{51} + 2 q^{54} - 4 q^{58} - 2 q^{61} + 2 q^{63} - 4 q^{64} - 4 q^{67} + 2 q^{69} + 2 q^{73} - 2 q^{78} - 2 q^{79} + 4 q^{81} + 4 q^{82} - 2 q^{87} + 2 q^{88} + 4 q^{91} - 4 q^{94} - 2 q^{97}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/201\mathbb{Z}\right)^\times\).

\(n\) \(68\) \(136\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(3\) 1.00000i 1.00000i
\(4\) 0 0
\(5\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(6\) −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 \(\pi\)
\(8\) 1.00000i 1.00000i
\(9\) −1.00000 −1.00000
\(10\) 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 0
\(13\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(14\) 1.00000i 1.00000i
\(15\) 0 0
\(16\) 0.500000 0.866025i 0.500000 0.866025i
\(17\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(18\) −0.866025 0.500000i −0.866025 0.500000i
\(19\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(20\) 0 0
\(21\) 0.866025 0.500000i 0.866025 0.500000i
\(22\) −1.00000 −1.00000
\(23\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 1.00000 1.00000
\(25\) 1.00000 1.00000
\(26\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(27\) 1.00000i 1.00000i
\(28\) 0 0
\(29\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(30\) 0 0
\(31\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(32\) 0 0
\(33\) −0.500000 0.866025i −0.500000 0.866025i
\(34\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(35\) 0 0
\(36\) 0 0
\(37\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(38\) 0.866025 0.500000i 0.866025 0.500000i
\(39\) −0.866025 0.500000i −0.866025 0.500000i
\(40\) 0 0
\(41\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(42\) 1.00000 1.00000
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) −0.500000 0.866025i −0.500000 0.866025i
\(47\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(48\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(49\) 0 0
\(50\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(51\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(52\) 0 0
\(53\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(54\) 0.500000 0.866025i 0.500000 0.866025i
\(55\) 0 0
\(56\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(57\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(58\) −1.00000 −1.00000
\(59\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(60\) 0 0
\(61\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(62\) 1.00000i 1.00000i
\(63\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(64\) −1.00000 −1.00000
\(65\) 0 0
\(66\) 1.00000i 1.00000i
\(67\) −1.00000 −1.00000
\(68\) 0 0
\(69\) 0.500000 0.866025i 0.500000 0.866025i
\(70\) 0 0
\(71\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(72\) 1.00000i 1.00000i
\(73\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(74\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(75\) 1.00000i 1.00000i
\(76\) 0 0
\(77\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(78\) −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
\(81\) 1.00000 1.00000
\(82\) 1.00000 1.00000
\(83\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 0 0
\(87\) −0.500000 0.866025i −0.500000 0.866025i
\(88\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(89\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(90\) 0 0
\(91\) 1.00000 1.00000
\(92\) 0 0
\(93\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(94\) −1.00000 −1.00000
\(95\) 0 0
\(96\) 0 0
\(97\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(98\) 0 0
\(99\) 0.866025 0.500000i 0.866025 0.500000i
\(100\) 0 0
\(101\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(102\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(103\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(104\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(105\) 0 0
\(106\) 0 0
\(107\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) −0.866025 0.500000i −0.866025 0.500000i
\(112\) −1.00000 −1.00000
\(113\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(114\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(115\) 0 0
\(116\) 0 0
\(117\) 0.500000 0.866025i 0.500000 0.866025i
\(118\) 0 0
\(119\) 1.00000i 1.00000i
\(120\) 0 0
\(121\) 0 0
\(122\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(123\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(124\) 0 0
\(125\) 0 0
\(126\) 1.00000i 1.00000i
\(127\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(128\) −0.866025 0.500000i −0.866025 0.500000i
\(129\) 0 0
\(130\) 0 0
\(131\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(132\) 0 0
\(133\) −1.00000 −1.00000
\(134\) −0.866025 0.500000i −0.866025 0.500000i
\(135\) 0 0
\(136\) 0.500000 0.866025i 0.500000 0.866025i
\(137\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(138\) 0.866025 0.500000i 0.866025 0.500000i
\(139\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(140\) 0 0
\(141\) −0.500000 0.866025i −0.500000 0.866025i
\(142\) 1.00000 1.00000
\(143\) 1.00000i 1.00000i
\(144\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(145\) 0 0
\(146\) 0.866025 0.500000i 0.866025 0.500000i
\(147\) 0 0
\(148\) 0 0
\(149\) 2.00000i 2.00000i 1.00000i \(-0.5\pi\)
1.00000i \(-0.5\pi\)
\(150\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(151\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(152\) −0.866025 0.500000i −0.866025 0.500000i
\(153\) −0.866025 0.500000i −0.866025 0.500000i
\(154\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(155\) 0 0
\(156\) 0 0
\(157\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(158\) 1.00000i 1.00000i
\(159\) 0 0
\(160\) 0 0
\(161\) 1.00000i 1.00000i
\(162\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(163\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(167\) −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
\(171\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(172\) 0 0
\(173\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(174\) 1.00000i 1.00000i
\(175\) −0.500000 0.866025i −0.500000 0.866025i
\(176\) 1.00000i 1.00000i
\(177\) 0 0
\(178\) 1.00000 1.73205i 1.00000 1.73205i
\(179\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
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 \(\pi\)
\(182\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(183\) −0.866025 0.500000i −0.866025 0.500000i
\(184\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(185\) 0 0
\(186\) −1.00000 −1.00000
\(187\) −1.00000 −1.00000
\(188\) 0 0
\(189\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(190\) 0 0
\(191\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(192\) 1.00000i 1.00000i
\(193\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(194\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(195\) 0 0
\(196\) 0 0
\(197\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(198\) 1.00000 1.00000
\(199\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(200\) 1.00000i 1.00000i
\(201\) 1.00000i 1.00000i
\(202\) 1.00000 1.00000
\(203\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(204\) 0 0
\(205\) 0 0
\(206\) 1.00000i 1.00000i
\(207\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(208\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(209\) 1.00000i 1.00000i
\(210\) 0 0
\(211\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(212\) 0 0
\(213\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(214\) 0 0
\(215\) 0 0
\(216\) −1.00000 −1.00000
\(217\) 0.500000 0.866025i 0.500000 0.866025i
\(218\) 0 0
\(219\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(220\) 0 0
\(221\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(222\) −0.500000 0.866025i −0.500000 0.866025i
\(223\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(224\) 0 0
\(225\) −1.00000 −1.00000
\(226\) −1.00000 −1.00000
\(227\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(228\) 0 0
\(229\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(230\) 0 0
\(231\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(232\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(233\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(234\) 0.866025 0.500000i 0.866025 0.500000i
\(235\) 0 0
\(236\) 0 0
\(237\) 0.866025 0.500000i 0.866025 0.500000i
\(238\) 0.500000 0.866025i 0.500000 0.866025i
\(239\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(240\) 0 0
\(241\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(242\) 0 0
\(243\) 1.00000i 1.00000i
\(244\) 0 0
\(245\) 0 0
\(246\) 1.00000i 1.00000i
\(247\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(248\) 0.866025 0.500000i 0.866025 0.500000i
\(249\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(250\) 0 0
\(251\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(252\) 0 0
\(253\) 1.00000 1.00000
\(254\) 1.00000i 1.00000i
\(255\) 0 0
\(256\) 0 0
\(257\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(258\) 0 0
\(259\) 1.00000 1.00000
\(260\) 0 0
\(261\) 0.866025 0.500000i 0.866025 0.500000i
\(262\) 0 0
\(263\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(264\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(265\) 0 0
\(266\) −0.866025 0.500000i −0.866025 0.500000i
\(267\) 2.00000 2.00000
\(268\) 0 0
\(269\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 0.866025 0.500000i 0.866025 0.500000i
\(273\) 1.00000i 1.00000i
\(274\) 0 0
\(275\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(276\) 0 0
\(277\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(278\) 0 0
\(279\) −0.500000 0.866025i −0.500000 0.866025i
\(280\) 0 0
\(281\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(282\) 1.00000i 1.00000i
\(283\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0.500000 0.866025i 0.500000 0.866025i
\(287\) −0.866025 0.500000i −0.866025 0.500000i
\(288\) 0 0
\(289\) 0 0
\(290\) 0 0
\(291\) −0.866025 0.500000i −0.866025 0.500000i
\(292\) 0 0
\(293\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(297\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(298\) 1.00000 1.73205i 1.00000 1.73205i
\(299\) 0.866025 0.500000i 0.866025 0.500000i
\(300\) 0 0
\(301\) 0 0
\(302\) 0.866025 0.500000i 0.866025 0.500000i
\(303\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(304\) −0.500000 0.866025i −0.500000 0.866025i
\(305\) 0 0
\(306\) −0.500000 0.866025i −0.500000 0.866025i
\(307\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(308\) 0 0
\(309\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(310\) 0 0
\(311\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(312\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 0.866025 0.500000i 0.866025 0.500000i
\(315\) 0 0
\(316\) 0 0
\(317\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(318\) 0 0
\(319\) 0.500000 0.866025i 0.500000 0.866025i
\(320\) 0 0
\(321\) 0 0
\(322\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(323\) 0.866025 0.500000i 0.866025 0.500000i
\(324\) 0 0
\(325\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(326\) 1.00000i 1.00000i
\(327\) 0 0
\(328\) −0.500000 0.866025i −0.500000 0.866025i
\(329\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(330\) 0 0
\(331\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(332\) 0 0
\(333\) 0.500000 0.866025i 0.500000 0.866025i
\(334\) −1.00000 −1.00000
\(335\) 0 0
\(336\) 1.00000i 1.00000i
\(337\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(338\) 0 0
\(339\) −0.500000 0.866025i −0.500000 0.866025i
\(340\) 0 0
\(341\) −0.866025 0.500000i −0.866025 0.500000i
\(342\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(343\) −1.00000 −1.00000
\(344\) 0 0
\(345\) 0 0
\(346\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(347\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(348\) 0 0
\(349\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(350\) 1.00000i 1.00000i
\(351\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(352\) 0 0
\(353\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0 0
\(357\) 1.00000 1.00000
\(358\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(359\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(360\) 0 0
\(361\) 0 0
\(362\) 1.00000i 1.00000i
\(363\) 0 0
\(364\) 0 0
\(365\) 0 0
\(366\) −0.500000 0.866025i −0.500000 0.866025i
\(367\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(368\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(369\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(370\) 0 0
\(371\) 0 0
\(372\) 0 0
\(373\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(374\) −0.866025 0.500000i −0.866025 0.500000i
\(375\) 0 0
\(376\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(377\) 1.00000i 1.00000i
\(378\) −1.00000 −1.00000
\(379\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(380\) 0 0
\(381\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(382\) −0.500000 0.866025i −0.500000 0.866025i
\(383\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(384\) 0.500000 0.866025i 0.500000 0.866025i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(390\) 0 0
\(391\) −0.500000 0.866025i −0.500000 0.866025i
\(392\) 0 0
\(393\) 0 0
\(394\) 1.00000 1.00000
\(395\) 0 0
\(396\) 0 0
\(397\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(398\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(399\) 1.00000i 1.00000i
\(400\) 0.500000 0.866025i 0.500000 0.866025i
\(401\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(402\) 0.500000 0.866025i 0.500000 0.866025i
\(403\) −1.00000 −1.00000
\(404\) 0 0
\(405\) 0 0
\(406\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(407\) 1.00000i 1.00000i
\(408\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(409\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 0 0
\(413\) 0 0
\(414\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(415\) 0 0
\(416\) 0 0
\(417\) 0 0
\(418\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(419\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(420\) 0 0
\(421\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(422\) 0.866025 0.500000i 0.866025 0.500000i
\(423\) 0.866025 0.500000i 0.866025 0.500000i
\(424\) 0 0
\(425\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(426\) 1.00000i 1.00000i
\(427\) 1.00000 1.00000
\(428\) 0 0
\(429\) 1.00000 1.00000
\(430\) 0 0
\(431\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(432\) −0.866025 0.500000i −0.866025 0.500000i
\(433\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(434\) 0.866025 0.500000i 0.866025 0.500000i
\(435\) 0 0
\(436\) 0 0
\(437\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(438\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(439\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(440\) 0 0
\(441\) 0 0
\(442\) −1.00000 −1.00000
\(443\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 2.00000 2.00000
\(448\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(449\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(450\) −0.866025 0.500000i −0.866025 0.500000i
\(451\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(452\) 0 0
\(453\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(454\) 1.00000 1.00000
\(455\) 0 0
\(456\) 0.500000 0.866025i 0.500000 0.866025i
\(457\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(458\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(459\) 0.500000 0.866025i 0.500000 0.866025i
\(460\) 0 0
\(461\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(462\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(463\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(464\) 1.00000i 1.00000i
\(465\) 0 0
\(466\) −1.00000 −1.00000
\(467\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(468\) 0 0
\(469\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(470\) 0 0
\(471\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(472\) 0 0
\(473\) 0 0
\(474\) 1.00000 1.00000
\(475\) 0.500000 0.866025i 0.500000 0.866025i
\(476\) 0 0
\(477\) 0 0
\(478\) 1.00000 1.00000
\(479\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(480\) 0 0
\(481\) −0.500000 0.866025i −0.500000 0.866025i
\(482\) 0 0
\(483\) −1.00000 −1.00000
\(484\) 0 0
\(485\) 0 0
\(486\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(487\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(488\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(489\) 0.866025 0.500000i 0.866025 0.500000i
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) −1.00000 −1.00000
\(494\) 1.00000i 1.00000i
\(495\) 0 0
\(496\) 1.00000 1.00000
\(497\) −0.866025 0.500000i −0.866025 0.500000i
\(498\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(499\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) −0.500000 0.866025i −0.500000 0.866025i
\(502\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(503\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(504\) 0.866025 0.500000i 0.866025 0.500000i
\(505\) 0 0
\(506\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(507\) 0 0
\(508\) 0 0
\(509\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(510\) 0 0
\(511\) −1.00000 −1.00000
\(512\) 1.00000i 1.00000i
\(513\) −0.866025 0.500000i −0.866025 0.500000i
\(514\) −1.00000 −1.00000
\(515\) 0 0
\(516\) 0 0
\(517\) 0.500000 0.866025i 0.500000 0.866025i
\(518\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(519\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(520\) 0 0
\(521\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(522\) 1.00000 1.00000
\(523\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(524\) 0 0
\(525\) 0.866025 0.500000i 0.866025 0.500000i
\(526\) 0 0
\(527\) 1.00000i 1.00000i
\(528\) −1.00000 −1.00000
\(529\) 0 0
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 1.00000i 1.00000i
\(534\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(535\) 0 0
\(536\) 1.00000i 1.00000i
\(537\) −2.00000 −2.00000
\(538\) −1.00000 + 1.73205i −1.00000 + 1.73205i
\(539\) 0 0
\(540\) 0 0
\(541\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(542\) 0 0
\(543\) 0.866025 0.500000i 0.866025 0.500000i
\(544\) 0 0
\(545\) 0 0
\(546\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(547\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(548\) 0 0
\(549\) 0.500000 0.866025i 0.500000 0.866025i
\(550\) −1.00000 −1.00000
\(551\) 1.00000i 1.00000i
\(552\) −0.866025 0.500000i −0.866025 0.500000i
\(553\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(554\) 0 0
\(555\) 0 0
\(556\) 0 0
\(557\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(558\) 1.00000i 1.00000i
\(559\) 0 0
\(560\) 0 0
\(561\) 1.00000i 1.00000i
\(562\) −0.500000 0.866025i −0.500000 0.866025i
\(563\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0 0
\(567\) −0.500000 0.866025i −0.500000 0.866025i
\(568\) −0.500000 0.866025i −0.500000 0.866025i
\(569\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(570\) 0 0
\(571\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(572\) 0 0
\(573\) 0.500000 0.866025i 0.500000 0.866025i
\(574\) −0.500000 0.866025i −0.500000 0.866025i
\(575\) −0.866025 0.500000i −0.866025 0.500000i
\(576\) 1.00000 1.00000
\(577\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(578\) 0 0
\(579\) 0 0
\(580\) 0 0
\(581\) 1.00000i 1.00000i
\(582\) −0.500000 0.866025i −0.500000 0.866025i
\(583\) 0 0
\(584\) −0.866025 0.500000i −0.866025 0.500000i
\(585\) 0 0
\(586\) 0 0
\(587\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(588\) 0 0
\(589\) 1.00000 1.00000
\(590\) 0 0
\(591\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(592\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(593\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(594\) 1.00000i 1.00000i
\(595\) 0 0
\(596\) 0 0
\(597\) −0.866025 0.500000i −0.866025 0.500000i
\(598\) 1.00000 1.00000
\(599\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(600\) 1.00000 1.00000
\(601\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(602\) 0 0
\(603\) 1.00000 1.00000
\(604\) 0 0
\(605\) 0 0
\(606\) 1.00000i 1.00000i
\(607\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(610\) 0 0
\(611\) 1.00000i 1.00000i
\(612\) 0 0
\(613\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(614\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(615\) 0 0
\(616\) 0.500000 0.866025i 0.500000 0.866025i
\(617\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(618\) −1.00000 −1.00000
\(619\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(622\) 0 0
\(623\) −1.73205 + 1.00000i −1.73205 + 1.00000i
\(624\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(625\) 1.00000 1.00000
\(626\) 0 0
\(627\) −1.00000 −1.00000
\(628\) 0 0
\(629\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(630\) 0 0
\(631\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(632\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(633\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(634\) −0.500000 0.866025i −0.500000 0.866025i
\(635\) 0 0
\(636\) 0 0
\(637\) 0 0
\(638\) 0.866025 0.500000i 0.866025 0.500000i
\(639\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(640\) 0 0
\(641\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(642\) 0 0
\(643\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 1.00000 1.00000
\(647\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(648\) 1.00000i 1.00000i
\(649\) 0 0
\(650\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(651\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(652\) 0 0
\(653\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 1.00000i 1.00000i
\(657\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(658\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(659\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(660\) 0 0
\(661\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(662\) 1.00000i 1.00000i
\(663\) −0.500000 0.866025i −0.500000 0.866025i
\(664\) 0.500000 0.866025i 0.500000 0.866025i
\(665\) 0 0
\(666\) 0.866025 0.500000i 0.866025 0.500000i
\(667\) 1.00000 1.00000
\(668\) 0 0
\(669\) 0 0
\(670\) 0 0
\(671\) 1.00000i 1.00000i
\(672\) 0 0
\(673\) 2.00000 2.00000 1.00000 \(0\)
1.00000 \(0\)
\(674\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(675\) 1.00000i 1.00000i
\(676\) 0 0
\(677\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(678\) 1.00000i 1.00000i
\(679\) 1.00000 1.00000
\(680\) 0 0
\(681\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(682\) −0.500000 0.866025i −0.500000 0.866025i
\(683\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.866025 0.500000i −0.866025 0.500000i
\(687\) −0.866025 0.500000i −0.866025 0.500000i
\(688\) 0 0
\(689\) 0 0
\(690\) 0 0
\(691\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(692\) 0 0
\(693\) −0.866025 0.500000i −0.866025 0.500000i
\(694\) −1.00000 −1.00000
\(695\) 0 0
\(696\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(697\) 1.00000 1.00000
\(698\) 0 0
\(699\) −0.500000 0.866025i −0.500000 0.866025i
\(700\) 0 0
\(701\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(702\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(703\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(704\) 0.866025 0.500000i 0.866025 0.500000i
\(705\) 0 0
\(706\) −0.500000 0.866025i −0.500000 0.866025i
\(707\) −0.866025 0.500000i −0.866025 0.500000i
\(708\) 0 0
\(709\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(710\) 0 0
\(711\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(712\) −2.00000 −2.00000
\(713\) 1.00000i 1.00000i
\(714\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(715\) 0 0
\(716\) 0 0
\(717\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(718\) 0 0
\(719\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(720\) 0 0
\(721\) 0.500000 0.866025i 0.500000 0.866025i
\(722\) 0 0
\(723\) 0 0
\(724\) 0 0
\(725\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(726\) 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 0
\(732\) 0 0
\(733\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(734\) 1.00000i 1.00000i
\(735\) 0 0
\(736\) 0 0
\(737\) 0.866025 0.500000i 0.866025 0.500000i
\(738\) −1.00000 −1.00000
\(739\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(740\) 0 0
\(741\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(742\) 0 0
\(743\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(744\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(745\) 0 0
\(746\) 1.00000i 1.00000i
\(747\) −0.866025 0.500000i −0.866025 0.500000i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(752\) 1.00000i 1.00000i
\(753\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(754\) 0.500000 0.866025i 0.500000 0.866025i
\(755\) 0 0
\(756\) 0 0
\(757\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(758\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(759\) 1.00000i 1.00000i
\(760\) 0 0
\(761\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(762\) −1.00000 −1.00000
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(767\) 0 0
\(768\) 0 0
\(769\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(770\) 0 0
\(771\) −0.500000 0.866025i −0.500000 0.866025i
\(772\) 0 0
\(773\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(774\) 0 0
\(775\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(776\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(777\) 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
\(782\) 1.00000i 1.00000i
\(783\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(784\) 0 0
\(785\) 0 0
\(786\) 0 0
\(787\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(792\) −0.500000 0.866025i −0.500000 0.866025i
\(793\) −0.500000 0.866025i −0.500000 0.866025i
\(794\) 0 0
\(795\) 0 0
\(796\) 0 0
\(797\) 0.866025 0.500000i 0.866025 0.500000i 1.00000i \(-0.5\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(798\) 0.500000 0.866025i 0.500000 0.866025i
\(799\) −1.00000 −1.00000
\(800\) 0 0
\(801\) 2.00000i 2.00000i
\(802\) 0 0
\(803\) 1.00000i 1.00000i
\(804\) 0 0
\(805\) 0 0
\(806\) −0.866025 0.500000i −0.866025 0.500000i
\(807\) −2.00000 −2.00000
\(808\) −0.500000 0.866025i −0.500000 0.866025i
\(809\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(810\) 0 0
\(811\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0.500000 0.866025i 0.500000 0.866025i
\(815\) 0 0
\(816\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(817\) 0 0
\(818\) 1.00000i 1.00000i
\(819\) −1.00000 −1.00000
\(820\) 0 0
\(821\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(822\) 0 0
\(823\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(824\) 0.866025 0.500000i 0.866025 0.500000i
\(825\) −0.500000 0.866025i −0.500000 0.866025i
\(826\) 0 0
\(827\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(828\) 0 0
\(829\) −2.00000 −2.00000 −1.00000 \(\pi\)
−1.00000 \(\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.500000 0.866025i 0.500000 0.866025i
\(833\) 0 0
\(834\) 0 0
\(835\) 0 0
\(836\) 0 0
\(837\) 0.866025 0.500000i 0.866025 0.500000i
\(838\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(839\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(840\) 0 0
\(841\) 0 0
\(842\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(843\) 0.500000 0.866025i 0.500000 0.866025i
\(844\) 0 0
\(845\) 0 0
\(846\) 1.00000 1.00000
\(847\) 0 0
\(848\) 0 0
\(849\) 0 0
\(850\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(851\) 0.866025 0.500000i 0.866025 0.500000i
\(852\) 0 0
\(853\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(854\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(855\) 0 0
\(856\) 0 0
\(857\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(858\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(859\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(860\) 0 0
\(861\) 0.500000 0.866025i 0.500000 0.866025i
\(862\) 1.00000 1.00000
\(863\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 1.00000i 1.00000i
\(867\) 0 0
\(868\) 0 0
\(869\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(870\) 0 0
\(871\) 0.500000 0.866025i 0.500000 0.866025i
\(872\) 0 0
\(873\) 0.500000 0.866025i 0.500000 0.866025i
\(874\) −1.00000 −1.00000
\(875\) 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
\(879\) 0 0
\(880\) 0 0
\(881\) −0.866025 0.500000i −0.866025 0.500000i 1.00000i \(-0.5\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(882\) 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 \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(888\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(889\) 0.500000 0.866025i 0.500000 0.866025i
\(890\) 0 0
\(891\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(892\) 0 0
\(893\) 1.00000i 1.00000i
\(894\) 1.73205 + 1.00000i 1.73205 + 1.00000i
\(895\) 0 0
\(896\) 1.00000i 1.00000i
\(897\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(898\) −1.00000 −1.00000
\(899\) −0.866025 0.500000i −0.866025 0.500000i
\(900\) 0 0
\(901\) 0 0
\(902\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(903\) 0 0
\(904\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(905\) 0 0
\(906\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(907\) −0.500000 0.866025i −0.500000 0.866025i 0.500000 0.866025i \(-0.333333\pi\)
−1.00000 \(\pi\)
\(908\) 0 0
\(909\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(910\) 0 0
\(911\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(912\) 0.866025 0.500000i 0.866025 0.500000i
\(913\) −1.00000 −1.00000
\(914\) 1.00000i 1.00000i
\(915\) 0 0
\(916\) 0 0
\(917\) 0 0
\(918\) 0.866025 0.500000i 0.866025 0.500000i
\(919\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(920\) 0 0
\(921\) −0.866025 0.500000i −0.866025 0.500000i
\(922\) 0 0
\(923\) 1.00000i 1.00000i
\(924\) 0 0
\(925\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(926\) 0.866025 0.500000i 0.866025 0.500000i
\(927\) −0.500000 0.866025i −0.500000 0.866025i
\(928\) 0 0
\(929\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 0 0
\(934\) −0.500000 0.866025i −0.500000 0.866025i
\(935\) 0 0
\(936\) −0.866025 0.500000i −0.866025 0.500000i
\(937\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(938\) 1.00000i 1.00000i
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(942\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(943\) −1.00000 −1.00000
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(948\) 0 0
\(949\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(950\) 0.866025 0.500000i 0.866025 0.500000i
\(951\) 0.500000 0.866025i 0.500000 0.866025i
\(952\) −1.00000 −1.00000
\(953\) 2.00000i 2.00000i 1.00000i \(0.5\pi\)
1.00000i \(0.5\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 0 0
\(957\) 0.866025 + 0.500000i 0.866025 + 0.500000i
\(958\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(959\) 0 0
\(960\) 0 0
\(961\) 0 0
\(962\) 1.00000i 1.00000i
\(963\) 0 0
\(964\) 0 0
\(965\) 0 0
\(966\) −0.866025 0.500000i −0.866025 0.500000i
\(967\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(968\) 0 0
\(969\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(970\) 0 0
\(971\) −0.866025 + 0.500000i −0.866025 + 0.500000i −0.866025 0.500000i \(-0.833333\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) 0 0
\(974\) −0.866025 + 0.500000i −0.866025 + 0.500000i
\(975\) −0.866025 0.500000i −0.866025 0.500000i
\(976\) 0.500000 + 0.866025i 0.500000 + 0.866025i
\(977\) 0.866025 + 0.500000i 0.866025 + 0.500000i 0.866025 0.500000i \(-0.166667\pi\)
1.00000i \(0.5\pi\)
\(978\) 1.00000 1.00000
\(979\) 1.00000 + 1.73205i 1.00000 + 1.73205i
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(984\) 0.866025 0.500000i 0.866025 0.500000i
\(985\) 0 0
\(986\) −0.866025 0.500000i −0.866025 0.500000i
\(987\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(992\) 0 0
\(993\) 0.866025 0.500000i 0.866025 0.500000i
\(994\) −0.500000 0.866025i −0.500000 0.866025i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 1.00000i \(-0.5\pi\)
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 201.1.g.a.29.2 yes 4
3.2 odd 2 inner 201.1.g.a.29.1 4
4.3 odd 2 3216.1.bb.b.833.1 4
12.11 even 2 3216.1.bb.b.833.2 4
67.37 even 3 inner 201.1.g.a.104.1 yes 4
201.104 odd 6 inner 201.1.g.a.104.2 yes 4
268.171 odd 6 3216.1.bb.b.305.1 4
804.707 even 6 3216.1.bb.b.305.2 4
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
201.1.g.a.29.1 4 3.2 odd 2 inner
201.1.g.a.29.2 yes 4 1.1 even 1 trivial
201.1.g.a.104.1 yes 4 67.37 even 3 inner
201.1.g.a.104.2 yes 4 201.104 odd 6 inner
3216.1.bb.b.305.1 4 268.171 odd 6
3216.1.bb.b.305.2 4 804.707 even 6
3216.1.bb.b.833.1 4 4.3 odd 2
3216.1.bb.b.833.2 4 12.11 even 2