Properties

Label 3332.1.cc.b.2923.1
Level $3332$
Weight $1$
Character 3332.2923
Analytic conductor $1.663$
Analytic rank $0$
Dimension $12$
Projective image $D_{21}$
CM discriminant -68
Inner twists $4$

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Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms
 
[N,k,chi] = [3332,1,Mod(135,3332)]
 
mf = mfinit([N,k,chi],0)
 
lf = mfeigenbasis(mf)
 
from sage.modular.dirichlet import DirichletCharacter
 
H = DirichletGroup(3332, base_ring=CyclotomicField(42))
 
chi = DirichletCharacter(H, H._module([21, 32, 21]))
 
N = Newforms(chi, 1, names="a")
 
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
 
chi := DirichletCharacter("3332.135");
 
S:= CuspForms(chi, 1);
 
N := Newforms(S);
 
Level: \( N \) \(=\) \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight: \( k \) \(=\) \( 1 \)
Character orbit: \([\chi]\) \(=\) 3332.cc (of order \(42\), degree \(12\), minimal)

Newform invariants

comment: select newform
 
sage: f = N[0] # Warning: the index may be different
 
gp: f = lf[1] \\ Warning: the index may be different
 
Self dual: no
Analytic conductor: \(1.66288462209\)
Analytic rank: \(0\)
Dimension: \(12\)
Coefficient field: \(\Q(\zeta_{21})\)
comment: defining polynomial
 
gp: f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{12} - x^{11} + x^{9} - x^{8} + x^{6} - x^{4} + x^{3} - x + 1 \) Copy content Toggle raw display
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Projective image: \(D_{21}\)
Projective field: Galois closure of \(\mathbb{Q}[x]/(x^{21} + \cdots)\)

Embedding invariants

Embedding label 2923.1
Root \(0.365341 + 0.930874i\) of defining polynomial
Character \(\chi\) \(=\) 3332.2923
Dual form 3332.1.cc.b.611.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.0747301 + 0.997204i) q^{2} +(1.82624 + 0.563320i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-0.425270 + 1.86323i) q^{6} +(-0.222521 - 0.974928i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(2.19158 + 1.49419i) q^{9} +O(q^{10})\) \(q+(0.0747301 + 0.997204i) q^{2} +(1.82624 + 0.563320i) q^{3} +(-0.988831 + 0.149042i) q^{4} +(-0.425270 + 1.86323i) q^{6} +(-0.222521 - 0.974928i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(2.19158 + 1.49419i) q^{9} +(0.123490 - 0.0841939i) q^{11} +(-1.88980 - 0.284841i) q^{12} +(-0.134659 - 0.0648483i) q^{13} +(0.955573 - 0.294755i) q^{14} +(0.955573 - 0.294755i) q^{16} +(0.365341 + 0.930874i) q^{17} +(-1.32624 + 2.29711i) q^{18} +(0.142820 - 1.90580i) q^{21} +(0.0931869 + 0.116853i) q^{22} +(-0.658322 + 1.67738i) q^{23} +(0.142820 - 1.90580i) q^{24} +(0.0747301 - 0.997204i) q^{25} +(0.0546039 - 0.139129i) q^{26} +(1.96906 + 2.46912i) q^{27} +(0.365341 + 0.930874i) q^{28} +(0.222521 - 0.385418i) q^{31} +(0.365341 + 0.930874i) q^{32} +(0.272950 - 0.0841939i) q^{33} +(-0.900969 + 0.433884i) q^{34} +(-2.38980 - 1.15087i) q^{36} +(-0.209389 - 0.194285i) q^{39} +1.91115 q^{42} +(-0.109562 + 0.101659i) q^{44} +(-1.72188 - 0.531130i) q^{46} +1.91115 q^{48} +(-0.900969 + 0.433884i) q^{49} +1.00000 q^{50} +(0.142820 + 1.90580i) q^{51} +(0.142820 + 0.0440542i) q^{52} +(1.44973 - 0.218511i) q^{53} +(-2.31507 + 2.14807i) q^{54} +(-0.900969 + 0.433884i) q^{56} +(0.400969 + 0.193096i) q^{62} +(0.969059 - 2.46912i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(0.104356 + 0.265895i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(-2.14715 + 2.69244i) q^{69} +(-0.914101 - 1.14625i) q^{71} +(0.969059 - 2.46912i) q^{72} +(0.698220 - 1.77904i) q^{75} +(-0.109562 - 0.101659i) q^{77} +(0.178094 - 0.223322i) q^{78} +(-0.826239 - 1.43109i) q^{79} +(1.23601 + 3.14929i) q^{81} +(0.142820 + 1.90580i) q^{84} +(-0.109562 - 0.101659i) q^{88} +(1.57906 + 1.07659i) q^{89} +(-0.0332580 + 0.145713i) q^{91} +(0.400969 - 1.75676i) q^{92} +(0.623490 - 0.578514i) q^{93} +(0.142820 + 1.90580i) q^{96} +(-0.500000 - 0.866025i) q^{98} +0.396440 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{2} + 13 q^{3} + q^{4} - 5 q^{6} - 2 q^{7} - 2 q^{8} + 14 q^{9}+O(q^{10}) \) Copy content Toggle raw display \( 12 q + q^{2} + 13 q^{3} + q^{4} - 5 q^{6} - 2 q^{7} - 2 q^{8} + 14 q^{9} - 8 q^{11} - q^{12} - 5 q^{13} + q^{14} + q^{16} + q^{17} - 7 q^{18} - q^{21} + 2 q^{22} + 2 q^{23} - q^{24} + q^{25} - q^{26} + 12 q^{27} + q^{28} + 2 q^{31} + q^{32} - 6 q^{33} - 2 q^{34} - 7 q^{36} - 6 q^{39} + 2 q^{42} - q^{44} + 2 q^{46} + 2 q^{48} - 2 q^{49} + 12 q^{50} - q^{51} - q^{52} - q^{53} - 6 q^{54} - 2 q^{56} - 4 q^{62} - 2 q^{64} + 15 q^{66} - 6 q^{68} - 3 q^{69} + 2 q^{71} - q^{75} - q^{77} - 9 q^{78} - q^{79} + 13 q^{81} - q^{84} - q^{88} - q^{89} + 2 q^{91} - 4 q^{92} - 2 q^{93} - q^{96} - 6 q^{98} - 14 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{2}{21}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(3\) 1.82624 + 0.563320i 1.82624 + 0.563320i 1.00000 \(0\)
0.826239 + 0.563320i \(0.190476\pi\)
\(4\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(5\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(6\) −0.425270 + 1.86323i −0.425270 + 1.86323i
\(7\) −0.222521 0.974928i −0.222521 0.974928i
\(8\) −0.222521 0.974928i −0.222521 0.974928i
\(9\) 2.19158 + 1.49419i 2.19158 + 1.49419i
\(10\) 0 0
\(11\) 0.123490 0.0841939i 0.123490 0.0841939i −0.500000 0.866025i \(-0.666667\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(12\) −1.88980 0.284841i −1.88980 0.284841i
\(13\) −0.134659 0.0648483i −0.134659 0.0648483i 0.365341 0.930874i \(-0.380952\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0.955573 0.294755i 0.955573 0.294755i
\(15\) 0 0
\(16\) 0.955573 0.294755i 0.955573 0.294755i
\(17\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(18\) −1.32624 + 2.29711i −1.32624 + 2.29711i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) 0.142820 1.90580i 0.142820 1.90580i
\(22\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i
\(23\) −0.658322 + 1.67738i −0.658322 + 1.67738i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(24\) 0.142820 1.90580i 0.142820 1.90580i
\(25\) 0.0747301 0.997204i 0.0747301 0.997204i
\(26\) 0.0546039 0.139129i 0.0546039 0.139129i
\(27\) 1.96906 + 2.46912i 1.96906 + 2.46912i
\(28\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(29\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(30\) 0 0
\(31\) 0.222521 0.385418i 0.222521 0.385418i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(32\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(33\) 0.272950 0.0841939i 0.272950 0.0841939i
\(34\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(35\) 0 0
\(36\) −2.38980 1.15087i −2.38980 1.15087i
\(37\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(38\) 0 0
\(39\) −0.209389 0.194285i −0.209389 0.194285i
\(40\) 0 0
\(41\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(42\) 1.91115 1.91115
\(43\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(45\) 0 0
\(46\) −1.72188 0.531130i −1.72188 0.531130i
\(47\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(48\) 1.91115 1.91115
\(49\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(50\) 1.00000 1.00000
\(51\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(52\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(53\) 1.44973 0.218511i 1.44973 0.218511i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(54\) −2.31507 + 2.14807i −2.31507 + 2.14807i
\(55\) 0 0
\(56\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(60\) 0 0
\(61\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(62\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(63\) 0.969059 2.46912i 0.969059 2.46912i
\(64\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(65\) 0 0
\(66\) 0.104356 + 0.265895i 0.104356 + 0.265895i
\(67\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(68\) −0.500000 0.866025i −0.500000 0.866025i
\(69\) −2.14715 + 2.69244i −2.14715 + 2.69244i
\(70\) 0 0
\(71\) −0.914101 1.14625i −0.914101 1.14625i −0.988831 0.149042i \(-0.952381\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(72\) 0.969059 2.46912i 0.969059 2.46912i
\(73\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(74\) 0 0
\(75\) 0.698220 1.77904i 0.698220 1.77904i
\(76\) 0 0
\(77\) −0.109562 0.101659i −0.109562 0.101659i
\(78\) 0.178094 0.223322i 0.178094 0.223322i
\(79\) −0.826239 1.43109i −0.826239 1.43109i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(80\) 0 0
\(81\) 1.23601 + 3.14929i 1.23601 + 3.14929i
\(82\) 0 0
\(83\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(84\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −0.109562 0.101659i −0.109562 0.101659i
\(89\) 1.57906 + 1.07659i 1.57906 + 1.07659i 0.955573 + 0.294755i \(0.0952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(90\) 0 0
\(91\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i
\(92\) 0.400969 1.75676i 0.400969 1.75676i
\(93\) 0.623490 0.578514i 0.623490 0.578514i
\(94\) 0 0
\(95\) 0 0
\(96\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 0.866025i −0.500000 0.866025i
\(99\) 0.396440 0.396440
\(100\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(101\) −1.72188 0.531130i −1.72188 0.531130i −0.733052 0.680173i \(-0.761905\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(102\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(103\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(104\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i
\(105\) 0 0
\(106\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(107\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(108\) −2.31507 2.14807i −2.31507 2.14807i
\(109\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.500000 0.866025i
\(113\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) −0.198220 0.343327i −0.198220 0.343327i
\(118\) 0 0
\(119\) 0.826239 0.563320i 0.826239 0.563320i
\(120\) 0 0
\(121\) −0.357180 + 0.910080i −0.357180 + 0.910080i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.162592 + 0.414278i −0.162592 + 0.414278i
\(125\) 0 0
\(126\) 2.53464 + 0.781831i 2.53464 + 0.781831i
\(127\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) −1.72188 + 0.531130i −1.72188 + 0.531130i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(132\) −0.257353 + 0.123935i −0.257353 + 0.123935i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.826239 0.563320i 0.826239 0.563320i
\(137\) −1.40097 1.29991i −1.40097 1.29991i −0.900969 0.433884i \(-0.857143\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(138\) −2.84537 1.93994i −2.84537 1.93994i
\(139\) −0.367711 1.61105i −0.367711 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.07473 0.997204i 1.07473 0.997204i
\(143\) −0.0220888 + 0.00332936i −0.0220888 + 0.00332936i
\(144\) 2.53464 + 0.781831i 2.53464 + 0.781831i
\(145\) 0 0
\(146\) 0 0
\(147\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(148\) 0 0
\(149\) 0.142820 + 1.90580i 0.142820 + 1.90580i 0.365341 + 0.930874i \(0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(150\) 1.82624 + 0.563320i 1.82624 + 0.563320i
\(151\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(152\) 0 0
\(153\) −0.590232 + 2.58597i −0.590232 + 2.58597i
\(154\) 0.0931869 0.116853i 0.0931869 0.116853i
\(155\) 0 0
\(156\) 0.236007 + 0.160907i 0.236007 + 0.160907i
\(157\) −1.21135 1.12397i −1.21135 1.12397i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(158\) 1.36534 0.930874i 1.36534 0.930874i
\(159\) 2.77064 + 0.417607i 2.77064 + 0.417607i
\(160\) 0 0
\(161\) 1.78181 + 0.268565i 1.78181 + 0.268565i
\(162\) −3.04812 + 1.46790i −3.04812 + 1.46790i
\(163\) 1.91115 0.589510i 1.91115 0.589510i 0.955573 0.294755i \(-0.0952381\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 0.455573 0.571270i 0.455573 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(168\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(169\) −0.609562 0.764367i −0.609562 0.764367i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(174\) 0 0
\(175\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(176\) 0.0931869 0.116853i 0.0931869 0.116853i
\(177\) 0 0
\(178\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(179\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(180\) 0 0
\(181\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) −0.147791 0.0222759i −0.147791 0.0222759i
\(183\) 0 0
\(184\) 1.78181 + 0.268565i 1.78181 + 0.268565i
\(185\) 0 0
\(186\) 0.623490 + 0.578514i 0.623490 + 0.578514i
\(187\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i
\(188\) 0 0
\(189\) 1.96906 2.46912i 1.96906 2.46912i
\(190\) 0 0
\(191\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(192\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(193\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.826239 0.563320i 0.826239 0.563320i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) 0.0296260 + 0.395331i 0.0296260 + 0.395331i
\(199\) −1.40097 0.432142i −1.40097 0.432142i −0.500000 0.866025i \(-0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(200\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(201\) 0 0
\(202\) 0.400969 1.75676i 0.400969 1.75676i
\(203\) 0 0
\(204\) −0.425270 1.86323i −0.425270 1.86323i
\(205\) 0 0
\(206\) 0 0
\(207\) −3.94909 + 2.69244i −3.94909 + 2.69244i
\(208\) −0.147791 0.0222759i −0.147791 0.0222759i
\(209\) 0 0
\(210\) 0 0
\(211\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(212\) −1.40097 + 0.432142i −1.40097 + 0.432142i
\(213\) −1.02366 2.60825i −1.02366 2.60825i
\(214\) 0.988831 1.71271i 0.988831 1.71271i
\(215\) 0 0
\(216\) 1.96906 2.46912i 1.96906 2.46912i
\(217\) −0.425270 0.131178i −0.425270 0.131178i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.0111692 0.149042i 0.0111692 0.149042i
\(222\) 0 0
\(223\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) 0.826239 0.563320i 0.826239 0.563320i
\(225\) 1.65379 2.07379i 1.65379 2.07379i
\(226\) 0 0
\(227\) 0.733052 1.26968i 0.733052 1.26968i −0.222521 0.974928i \(-0.571429\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(228\) 0 0
\(229\) 1.19158 0.367554i 1.19158 0.367554i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(230\) 0 0
\(231\) −0.142820 0.247372i −0.142820 0.247372i
\(232\) 0 0
\(233\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(234\) 0.327554 0.223322i 0.327554 0.223322i
\(235\) 0 0
\(236\) 0 0
\(237\) −0.702749 3.07894i −0.702749 3.07894i
\(238\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(239\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(240\) 0 0
\(241\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(242\) −0.934227 0.288171i −0.934227 0.288171i
\(243\) 0.247176 + 3.29834i 0.247176 + 3.29834i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.425270 0.131178i −0.425270 0.131178i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(252\) −0.590232 + 2.58597i −0.590232 + 2.58597i
\(253\) 0.0599289 + 0.262566i 0.0599289 + 0.262566i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.826239 0.563320i 0.826239 0.563320i
\(257\) 0.988831 + 0.149042i 0.988831 + 0.149042i 0.623490 0.781831i \(-0.285714\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.658322 1.67738i −0.658322 1.67738i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −0.142820 0.247372i −0.142820 0.247372i
\(265\) 0 0
\(266\) 0 0
\(267\) 2.27728 + 2.85562i 2.27728 + 2.85562i
\(268\) 0 0
\(269\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(270\) 0 0
\(271\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(272\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(273\) −0.142820 + 0.247372i −0.142820 + 0.247372i
\(274\) 1.19158 1.49419i 1.19158 1.49419i
\(275\) −0.0747301 0.129436i −0.0747301 0.129436i
\(276\) 1.72188 2.98239i 1.72188 2.98239i
\(277\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(278\) 1.57906 0.487076i 1.57906 0.487076i
\(279\) 1.06356 0.512184i 1.06356 0.512184i
\(280\) 0 0
\(281\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(282\) 0 0
\(283\) 0.123490 0.0841939i 0.123490 0.0841939i −0.500000 0.866025i \(-0.666667\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(284\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(285\) 0 0
\(286\) −0.00497075 0.0217783i −0.00497075 0.0217783i
\(287\) 0 0
\(288\) −0.590232 + 2.58597i −0.590232 + 2.58597i
\(289\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 1.65248 1.65248 0.826239 0.563320i \(-0.190476\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(294\) −0.425270 1.86323i −0.425270 1.86323i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.451044 + 0.139129i 0.451044 + 0.139129i
\(298\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(299\) 0.197424 0.183183i 0.197424 0.183183i
\(300\) −0.425270 + 1.86323i −0.425270 + 1.86323i
\(301\) 0 0
\(302\) 0 0
\(303\) −2.84537 1.93994i −2.84537 1.93994i
\(304\) 0 0
\(305\) 0 0
\(306\) −2.62285 0.395331i −2.62285 0.395331i
\(307\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(308\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.365341 0.930874i −0.365341 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(312\) −0.142820 + 0.247372i −0.142820 + 0.247372i
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 1.03030 1.29196i 1.03030 1.29196i
\(315\) 0 0
\(316\) 1.03030 + 1.29196i 1.03030 + 1.29196i
\(317\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(318\) −0.209389 + 2.79410i −0.209389 + 2.79410i
\(319\) 0 0
\(320\) 0 0
\(321\) −2.35654 2.95501i −2.35654 2.95501i
\(322\) −0.134659 + 1.79690i −0.134659 + 1.79690i
\(323\) 0 0
\(324\) −1.69158 2.92990i −1.69158 2.92990i
\(325\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(326\) 0.730682 + 1.86175i 0.730682 + 1.86175i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(335\) 0 0
\(336\) −0.425270 1.86323i −0.425270 1.86323i
\(337\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) 0.716677 0.664979i 0.716677 0.664979i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.00497075 0.0663300i −0.00497075 0.0663300i
\(342\) 0 0
\(343\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.23305 + 0.185853i −1.23305 + 0.185853i −0.733052 0.680173i \(-0.761905\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(348\) 0 0
\(349\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(350\) −0.222521 0.974928i −0.222521 0.974928i
\(351\) −0.105033 0.460180i −0.105033 0.460180i
\(352\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i
\(353\) 0.733052 + 0.680173i 0.733052 + 0.680173i 0.955573 0.294755i \(-0.0952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −1.72188 0.829215i −1.72188 0.829215i
\(357\) 1.82624 0.563320i 1.82624 0.563320i
\(358\) 0 0
\(359\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 0 0
\(363\) −1.16496 + 1.46082i −1.16496 + 1.46082i
\(364\) 0.0111692 0.149042i 0.0111692 0.149042i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.147791 + 1.97213i −0.147791 + 1.97213i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(368\) −0.134659 + 1.79690i −0.134659 + 1.79690i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.535628 1.36476i −0.535628 1.36476i
\(372\) −0.530303 + 0.664979i −0.530303 + 0.664979i
\(373\) −0.0747301 0.129436i −0.0747301 0.129436i 0.826239 0.563320i \(-0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 2.60937 + 1.77904i 2.60937 + 1.77904i
\(379\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(384\) −0.425270 1.86323i −0.425270 1.86323i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i \(-0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(390\) 0 0
\(391\) −1.80194 −1.80194
\(392\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(393\) −3.44377 −3.44377
\(394\) 0 0
\(395\) 0 0
\(396\) −0.392012 + 0.0590863i −0.392012 + 0.0590863i
\(397\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(398\) 0.326239 1.42935i 0.326239 1.42935i
\(399\) 0 0
\(400\) −0.222521 0.974928i −0.222521 0.974928i
\(401\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(402\) 0 0
\(403\) −0.0549581 + 0.0374698i −0.0549581 + 0.0374698i
\(404\) 1.78181 + 0.268565i 1.78181 + 0.268565i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 1.82624 0.563320i 1.82624 0.563320i
\(409\) −0.535628 1.36476i −0.535628 1.36476i −0.900969 0.433884i \(-0.857143\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(410\) 0 0
\(411\) −1.82624 3.16314i −1.82624 3.16314i
\(412\) 0 0
\(413\) 0 0
\(414\) −2.98003 3.73684i −2.98003 3.73684i
\(415\) 0 0
\(416\) 0.0111692 0.149042i 0.0111692 0.149042i
\(417\) 0.236007 3.14929i 0.236007 3.14929i
\(418\) 0 0
\(419\) 1.03030 + 1.29196i 1.03030 + 1.29196i 0.955573 + 0.294755i \(0.0952381\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(420\) 0 0
\(421\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(422\) −0.623490 1.07992i −0.623490 1.07992i
\(423\) 0 0
\(424\) −0.535628 1.36476i −0.535628 1.36476i
\(425\) 0.955573 0.294755i 0.955573 0.294755i
\(426\) 2.52446 1.21572i 2.52446 1.21572i
\(427\) 0 0
\(428\) 1.78181 + 0.858075i 1.78181 + 0.858075i
\(429\) −0.0422150 0.00636289i −0.0422150 0.00636289i
\(430\) 0 0
\(431\) 0.733052 + 0.680173i 0.733052 + 0.680173i 0.955573 0.294755i \(-0.0952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(432\) 2.60937 + 1.77904i 2.60937 + 1.77904i
\(433\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(434\) 0.0990311 0.433884i 0.0990311 0.433884i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) 0.123490 + 1.64786i 0.123490 + 1.64786i 0.623490 + 0.781831i \(0.285714\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −2.62285 0.395331i −2.62285 0.395331i
\(442\) 0.149460 0.149460
\(443\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.812753 + 3.56090i −0.812753 + 3.56090i
\(448\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(449\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(450\) 2.19158 + 1.49419i 2.19158 + 1.49419i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.32091 + 0.636119i 1.32091 + 0.636119i
\(455\) 0 0
\(456\) 0 0
\(457\) −1.72188 + 0.531130i −1.72188 + 0.531130i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(458\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(459\) −1.57906 + 2.73502i −1.57906 + 2.73502i
\(460\) 0 0
\(461\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(462\) 0.236007 0.160907i 0.236007 0.160907i
\(463\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(468\) 0.247176 + 0.309949i 0.247176 + 0.309949i
\(469\) 0 0
\(470\) 0 0
\(471\) −1.57906 2.73502i −1.57906 2.73502i
\(472\) 0 0
\(473\) 0 0
\(474\) 3.01782 0.930874i 3.01782 0.930874i
\(475\) 0 0
\(476\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(477\) 3.50369 + 1.68729i 3.50369 + 1.68729i
\(478\) 0 0
\(479\) −1.48883 + 1.01507i −1.48883 + 1.01507i −0.500000 + 0.866025i \(0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 3.10273 + 1.49419i 3.10273 + 1.49419i
\(484\) 0.217550 0.953150i 0.217550 0.953150i
\(485\) 0 0
\(486\) −3.27064 + 0.492970i −3.27064 + 0.492970i
\(487\) −0.955573 0.294755i −0.955573 0.294755i −0.222521 0.974928i \(-0.571429\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(488\) 0 0
\(489\) 3.82229 3.82229
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.0990311 0.433884i 0.0990311 0.433884i
\(497\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(498\) 0 0
\(499\) 1.36534 + 0.930874i 1.36534 + 0.930874i 1.00000 \(0\)
0.365341 + 0.930874i \(0.380952\pi\)
\(500\) 0 0
\(501\) 1.15379 0.786643i 1.15379 0.786643i
\(502\) 0 0
\(503\) 1.78181 + 0.858075i 1.78181 + 0.858075i 0.955573 + 0.294755i \(0.0952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(504\) −2.62285 0.395331i −2.62285 0.395331i
\(505\) 0 0
\(506\) −0.257353 + 0.0793829i −0.257353 + 0.0793829i
\(507\) −0.682623 1.73929i −0.682623 1.73929i
\(508\) 0 0
\(509\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(513\) 0 0
\(514\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(522\) 0 0
\(523\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(524\) 1.62349 0.781831i 1.62349 0.781831i
\(525\) −1.88980 0.284841i −1.88980 0.284841i
\(526\) 0 0
\(527\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i
\(528\) 0.236007 0.160907i 0.236007 0.160907i
\(529\) −1.64715 1.52833i −1.64715 1.52833i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −2.67746 + 2.48432i −2.67746 + 2.48432i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(540\) 0 0
\(541\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(545\) 0 0
\(546\) −0.257353 0.123935i −0.257353 0.123935i
\(547\) −0.162592 0.712362i −0.162592 0.712362i −0.988831 0.149042i \(-0.952381\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(548\) 1.57906 + 1.07659i 1.57906 + 1.07659i
\(549\) 0 0
\(550\) 0.123490 0.0841939i 0.123490 0.0841939i
\(551\) 0 0
\(552\) 3.10273 + 1.49419i 3.10273 + 1.49419i
\(553\) −1.21135 + 1.12397i −1.21135 + 1.12397i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.603718 + 1.53825i 0.603718 + 1.53825i
\(557\) 0.733052 1.26968i 0.733052 1.26968i −0.222521 0.974928i \(-0.571429\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(558\) 0.590232 + 1.02231i 0.590232 + 1.02231i
\(559\) 0 0
\(560\) 0 0
\(561\) 0.178094 + 0.223322i 0.178094 + 0.223322i
\(562\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(563\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i
\(567\) 2.79530 1.90580i 2.79530 1.90580i
\(568\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(569\) −0.0747301 0.129436i −0.0747301 0.129436i 0.826239 0.563320i \(-0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) −0.162592 0.414278i −0.162592 0.414278i 0.826239 0.563320i \(-0.190476\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(572\) 0.0213459 0.00658434i 0.0213459 0.00658434i
\(573\) 0 0
\(574\) 0 0
\(575\) 1.62349 + 0.781831i 1.62349 + 0.781831i
\(576\) −2.62285 0.395331i −2.62285 0.395331i
\(577\) −1.63402 + 1.11406i −1.63402 + 1.11406i −0.733052 + 0.680173i \(0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) −0.733052 0.680173i −0.733052 0.680173i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.160629 0.149042i 0.160629 0.149042i
\(584\) 0 0
\(585\) 0 0
\(586\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 1.82624 0.563320i 1.82624 0.563320i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 1.44973 1.34515i 1.44973 1.34515i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(594\) −0.105033 + 0.460180i −0.105033 + 0.460180i
\(595\) 0 0
\(596\) −0.425270 1.86323i −0.425270 1.86323i
\(597\) −2.31507 1.57839i −2.31507 1.57839i
\(598\) 0.197424 + 0.183183i 0.197424 + 0.183183i
\(599\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(600\) −1.88980 0.284841i −1.88980 0.284841i
\(601\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 1.72188 2.98239i 1.72188 2.98239i
\(607\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.198220 2.64506i 0.198220 2.64506i
\(613\) 0.0546039 0.728639i 0.0546039 0.728639i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(617\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(618\) 0 0
\(619\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) −5.43792 + 1.67738i −5.43792 + 1.67738i
\(622\) 0.900969 0.433884i 0.900969 0.433884i
\(623\) 0.698220 1.77904i 0.698220 1.77904i
\(624\) −0.257353 0.123935i −0.257353 0.123935i
\(625\) −0.988831 0.149042i −0.988831 0.149042i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.36534 + 0.930874i 1.36534 + 0.930874i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) −1.21135 + 1.12397i −1.21135 + 1.12397i
\(633\) −2.35654 + 0.355192i −2.35654 + 0.355192i
\(634\) 0 0
\(635\) 0 0
\(636\) −2.80194 −2.80194
\(637\) 0.149460 0.149460
\(638\) 0 0
\(639\) −0.290611 3.87793i −0.290611 3.87793i
\(640\) 0 0
\(641\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(642\) 2.77064 2.57078i 2.77064 2.57078i
\(643\) −0.162592 + 0.712362i −0.162592 + 0.712362i 0.826239 + 0.563320i \(0.190476\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(644\) −1.80194 −1.80194
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(648\) 2.79530 1.90580i 2.79530 1.90580i
\(649\) 0 0
\(650\) −0.134659 0.0648483i −0.134659 0.0648483i
\(651\) −0.702749 0.479126i −0.702749 0.479126i
\(652\) −1.80194 + 0.867767i −1.80194 + 0.867767i
\(653\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(660\) 0 0
\(661\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(662\) 0 0
\(663\) 0.104356 0.265895i 0.104356 0.265895i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 1.82624 0.563320i 1.82624 0.563320i
\(673\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) 2.60937 1.77904i 2.60937 1.77904i
\(676\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(677\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 2.05397 1.90580i 2.05397 1.90580i
\(682\) 0.0657731 0.00991370i 0.0657731 0.00991370i
\(683\) −1.40097 0.432142i −1.40097 0.432142i −0.500000 0.866025i \(-0.666667\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(687\) 2.38316 2.38316
\(688\) 0 0
\(689\) −0.209389 0.0645880i −0.209389 0.0645880i
\(690\) 0 0
\(691\) 0.326239 0.302705i 0.326239 0.302705i −0.500000 0.866025i \(-0.666667\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(692\) 0 0
\(693\) −0.0882162 0.386500i −0.0882162 0.386500i
\(694\) −0.277479 1.21572i −0.277479 1.21572i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.23305 0.185853i −1.23305 0.185853i
\(699\) 0 0
\(700\) 0.955573 0.294755i 0.955573 0.294755i
\(701\) 1.32091 0.636119i 1.32091 0.636119i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(702\) 0.451044 0.139129i 0.451044 0.139129i
\(703\) 0 0
\(704\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(705\) 0 0
\(706\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(707\) −0.134659 + 1.79690i −0.134659 + 1.79690i
\(708\) 0 0
\(709\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(710\) 0 0
\(711\) 0.327554 4.37090i 0.327554 4.37090i
\(712\) 0.698220 1.77904i 0.698220 1.77904i
\(713\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(714\) 0.698220 + 1.77904i 0.698220 + 1.77904i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.142820 0.0440542i 0.142820 0.0440542i −0.222521 0.974928i \(-0.571429\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.900969 0.433884i −0.900969 0.433884i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −1.54379 1.05254i −1.54379 1.05254i
\(727\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(728\) 0.149460 0.149460
\(729\) −0.653793 + 2.86445i −0.653793 + 2.86445i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.0747301 0.997204i −0.0747301 0.997204i −0.900969 0.433884i \(-0.857143\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(734\) −1.97766 −1.97766
\(735\) 0 0
\(736\) −1.80194 −1.80194
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.32091 0.636119i 1.32091 0.636119i
\(743\) −0.425270 1.86323i −0.425270 1.86323i −0.500000 0.866025i \(-0.666667\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(744\) −0.702749 0.479126i −0.702749 0.479126i
\(745\) 0 0
\(746\) 0.123490 0.0841939i 0.123490 0.0841939i
\(747\) 0 0
\(748\) −0.134659 0.0648483i −0.134659 0.0648483i
\(749\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(750\) 0 0
\(751\) 1.57906 0.487076i 1.57906 0.487076i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) −1.57906 + 2.73502i −1.57906 + 2.73502i
\(757\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(758\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(759\) −0.0384640 + 0.513267i −0.0384640 + 0.513267i
\(760\) 0 0
\(761\) 0.266948 0.680173i 0.266948 0.680173i −0.733052 0.680173i \(-0.761905\pi\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 1.82624 0.563320i 1.82624 0.563320i
\(769\) 0.900969 0.433884i 0.900969 0.433884i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(770\) 0 0
\(771\) 1.72188 + 0.829215i 1.72188 + 0.829215i
\(772\) 0 0
\(773\) 0.603718 0.411608i 0.603718 0.411608i −0.222521 0.974928i \(-0.571429\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(774\) 0 0
\(775\) −0.367711 0.250701i −0.367711 0.250701i
\(776\) 0 0
\(777\) 0 0
\(778\) −0.162592 + 0.712362i −0.162592 + 0.712362i
\(779\) 0 0
\(780\) 0 0
\(781\) −0.209389 0.0645880i −0.209389 0.0645880i
\(782\) −0.134659 1.79690i −0.134659 1.79690i
\(783\) 0 0
\(784\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(785\) 0 0
\(786\) −0.257353 3.43414i −0.257353 3.43414i
\(787\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.0882162 0.386500i −0.0882162 0.386500i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(797\) 1.32091 + 0.636119i 1.32091 + 0.636119i 0.955573 0.294755i \(-0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.955573 0.294755i 0.955573 0.294755i
\(801\) 1.85201 + 4.71885i 1.85201 + 4.71885i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −0.0414721 0.0520043i −0.0414721 0.0520043i
\(807\) 0 0
\(808\) −0.134659 + 1.79690i −0.134659 + 1.79690i
\(809\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(810\) 0 0
\(811\) −0.914101 1.14625i −0.914101 1.14625i −0.988831 0.149042i \(-0.952381\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0.698220 + 1.77904i 0.698220 + 1.77904i
\(817\) 0 0
\(818\) 1.32091 0.636119i 1.32091 0.636119i
\(819\) −0.290611 + 0.269648i −0.290611 + 0.269648i
\(820\) 0 0
\(821\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(822\) 3.01782 2.05751i 3.01782 2.05751i
\(823\) −1.40097 1.29991i −1.40097 1.29991i −0.900969 0.433884i \(-0.857143\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(824\) 0 0
\(825\) −0.0635609 0.278479i −0.0635609 0.278479i
\(826\) 0 0
\(827\) 0.440071 1.92808i 0.440071 1.92808i 0.0747301 0.997204i \(-0.476190\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(828\) 3.50369 3.25095i 3.50369 3.25095i
\(829\) 1.95557 0.294755i 1.95557 0.294755i 0.955573 0.294755i \(-0.0952381\pi\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.149460 0.149460
\(833\) −0.733052 0.680173i −0.733052 0.680173i
\(834\) 3.15813 3.15813
\(835\) 0 0
\(836\) 0 0
\(837\) 1.38980 0.209479i 1.38980 0.209479i
\(838\) −1.21135 + 1.12397i −1.21135 + 1.12397i
\(839\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(840\) 0 0
\(841\) −0.222521 0.974928i −0.222521 0.974928i
\(842\) −0.367711 0.250701i −0.367711 0.250701i
\(843\) 1.40097 + 1.29991i 1.40097 + 1.29991i
\(844\) 1.03030 0.702449i 1.03030 0.702449i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.966742 + 0.145713i 0.966742 + 0.145713i
\(848\) 1.32091 0.636119i 1.32091 0.636119i
\(849\) 0.272950 0.0841939i 0.272950 0.0841939i
\(850\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(851\) 0 0
\(852\) 1.40097 + 2.42655i 1.40097 + 2.42655i
\(853\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(857\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(858\) 0.00319036 0.0425725i 0.00319036 0.0425725i
\(859\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(863\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(864\) −1.57906 + 2.73502i −1.57906 + 2.73502i
\(865\) 0 0
\(866\) −1.72188 + 0.531130i −1.72188 + 0.531130i
\(867\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(868\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i
\(869\) −0.222521 0.107160i −0.222521 0.107160i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(878\) −1.63402 + 0.246289i −1.63402 + 0.246289i
\(879\) 3.01782 + 0.930874i 3.01782 + 0.930874i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.198220 2.64506i 0.198220 2.64506i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0.0111692 + 0.149042i 0.0111692 + 0.149042i
\(885\) 0 0
\(886\) 0 0
\(887\) −0.109562 + 0.101659i −0.109562 + 0.101659i −0.733052 0.680173i \(-0.761905\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.417786 + 0.284841i 0.417786 + 0.284841i
\(892\) 0 0
\(893\) 0 0
\(894\) −3.61168 0.544374i −3.61168 0.544374i
\(895\) 0 0
\(896\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(897\) 0.463734 0.223322i 0.463734 0.223322i
\(898\) 0 0
\(899\) 0 0
\(900\) −1.32624 + 2.29711i −1.32624 + 2.29711i
\(901\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(908\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(909\) −2.98003 3.73684i −2.98003 3.73684i
\(910\) 0 0
\(911\) −1.12349 + 1.40881i −1.12349 + 1.40881i −0.222521 + 0.974928i \(0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.658322 1.67738i −0.658322 1.67738i
\(915\) 0 0
\(916\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(917\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(918\) −2.84537 1.37026i −2.84537 1.37026i
\(919\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.21135 0.825886i −1.21135 0.825886i
\(923\) 0.0487597 + 0.213630i 0.0487597 + 0.213630i
\(924\) 0.178094 + 0.223322i 0.178094 + 0.223322i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.142820 1.90580i −0.142820 1.90580i
\(934\) 0 0
\(935\) 0 0
\(936\) −0.290611 + 0.269648i −0.290611 + 0.269648i
\(937\) 0.0990311 0.433884i 0.0990311 0.433884i −0.900969 0.433884i \(-0.857143\pi\)
1.00000 \(0\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(942\) 2.60937 1.77904i 2.60937 1.77904i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(948\) 1.15379 + 2.93982i 1.15379 + 2.93982i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −0.733052 0.680173i −0.733052 0.680173i
\(953\) 0.455573 + 0.571270i 0.455573 + 0.571270i 0.955573 0.294755i \(-0.0952381\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) −1.42074 + 3.61999i −1.42074 + 3.61999i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −1.12349 1.40881i −1.12349 1.40881i
\(959\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(960\) 0 0
\(961\) 0.400969 + 0.694498i 0.400969 + 0.694498i
\(962\) 0 0
\(963\) −1.91647 4.88309i −1.91647 4.88309i
\(964\) 0 0
\(965\) 0 0
\(966\) −1.25815 + 3.20571i −1.25815 + 3.20571i
\(967\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(968\) 0.966742 + 0.145713i 0.966742 + 0.145713i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(972\) −0.736007 3.22466i −0.736007 3.22466i
\(973\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(974\) 0.222521 0.974928i 0.222521 0.974928i
\(975\) −0.209389 + 0.194285i −0.209389 + 0.194285i
\(976\) 0 0
\(977\) −1.72188 0.531130i −1.72188 0.531130i −0.733052 0.680173i \(-0.761905\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(978\) 0.285640 + 3.81160i 0.285640 + 3.81160i
\(979\) 0.285640 0.285640
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i 0.365341 0.930874i \(-0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.603718 0.411608i 0.603718 0.411608i −0.222521 0.974928i \(-0.571429\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(992\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i
\(993\) 0 0
\(994\) −1.21135 0.825886i −1.21135 0.825886i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(998\) −0.826239 + 1.43109i −0.826239 + 1.43109i
\(999\) 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 3332.1.cc.b.2923.1 yes 12
4.3 odd 2 3332.1.cc.a.2923.1 yes 12
17.16 even 2 3332.1.cc.a.2923.1 yes 12
49.23 even 21 inner 3332.1.cc.b.611.1 yes 12
68.67 odd 2 CM 3332.1.cc.b.2923.1 yes 12
196.23 odd 42 3332.1.cc.a.611.1 12
833.611 even 42 3332.1.cc.a.611.1 12
3332.611 odd 42 inner 3332.1.cc.b.611.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.1.cc.a.611.1 12 196.23 odd 42
3332.1.cc.a.611.1 12 833.611 even 42
3332.1.cc.a.2923.1 yes 12 4.3 odd 2
3332.1.cc.a.2923.1 yes 12 17.16 even 2
3332.1.cc.b.611.1 yes 12 49.23 even 21 inner
3332.1.cc.b.611.1 yes 12 3332.611 odd 42 inner
3332.1.cc.b.2923.1 yes 12 1.1 even 1 trivial
3332.1.cc.b.2923.1 yes 12 68.67 odd 2 CM