Properties

Label 3332.1.cc.a.135.1
Level $3332$
Weight $1$
Character 3332.135
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 135.1
Root \(-0.988831 - 0.149042i\) of defining polynomial
Character \(\chi\) \(=\) 3332.135
Dual form 3332.1.cc.a.543.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.826239 - 0.563320i) q^{2} +(-1.07473 + 0.997204i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.326239 + 1.42935i) q^{6} +(0.222521 + 0.974928i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.0858993 - 1.14625i) q^{9} +O(q^{10})\) \(q+(0.826239 - 0.563320i) q^{2} +(-1.07473 + 0.997204i) q^{3} +(0.365341 - 0.930874i) q^{4} +(-0.326239 + 1.42935i) q^{6} +(0.222521 + 0.974928i) q^{7} +(-0.222521 - 0.974928i) q^{8} +(0.0858993 - 1.14625i) q^{9} +(-0.123490 - 1.64786i) q^{11} +(0.535628 + 1.36476i) q^{12} +(-1.48883 - 0.716983i) q^{13} +(0.733052 + 0.680173i) q^{14} +(-0.733052 - 0.680173i) q^{16} +(-0.988831 - 0.149042i) q^{17} +(-0.574730 - 0.995462i) q^{18} +(-1.21135 - 0.825886i) q^{21} +(-1.03030 - 1.29196i) q^{22} +(-1.78181 + 0.268565i) q^{23} +(1.21135 + 0.825886i) q^{24} +(0.826239 + 0.563320i) q^{25} +(-1.63402 + 0.246289i) q^{26} +(0.136622 + 0.171318i) q^{27} +(0.988831 + 0.149042i) q^{28} +(-0.222521 - 0.385418i) q^{31} +(-0.988831 - 0.149042i) q^{32} +(1.77597 + 1.64786i) q^{33} +(-0.900969 + 0.433884i) q^{34} +(-1.03563 - 0.498732i) q^{36} +(2.31507 - 0.714104i) q^{39} -1.46610 q^{42} +(-1.57906 - 0.487076i) q^{44} +(-1.32091 + 1.22563i) q^{46} +1.46610 q^{48} +(-0.900969 + 0.433884i) q^{49} +1.00000 q^{50} +(1.21135 - 0.825886i) q^{51} +(-1.21135 + 1.12397i) q^{52} +(0.698220 - 1.77904i) q^{53} +(0.209389 + 0.0645880i) q^{54} +(0.900969 - 0.433884i) q^{56} +(-0.400969 - 0.193096i) q^{62} +(1.13662 - 0.171318i) q^{63} +(-0.900969 + 0.433884i) q^{64} +(2.39564 + 0.361085i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(1.64715 - 2.06546i) q^{69} +(-1.19158 - 1.49419i) q^{71} +(-1.13662 + 0.171318i) q^{72} +(-1.44973 + 0.218511i) q^{75} +(1.57906 - 0.487076i) q^{77} +(1.51053 - 1.89415i) q^{78} +(0.0747301 - 0.129436i) q^{79} +(0.818951 + 0.123437i) q^{81} +(-1.21135 + 0.825886i) q^{84} +(-1.57906 + 0.487076i) q^{88} +(-0.109562 + 1.46200i) q^{89} +(0.367711 - 1.61105i) q^{91} +(-0.400969 + 1.75676i) q^{92} +(0.623490 + 0.192321i) q^{93} +(1.21135 - 0.825886i) q^{96} +(-0.500000 + 0.866025i) q^{98} -1.89946 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{2} - 13 q^{3} + q^{4} + 5 q^{6} + 2 q^{7} - 2 q^{8} + 14 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{16}{21}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.826239 0.563320i 0.826239 0.563320i
\(3\) −1.07473 + 0.997204i −1.07473 + 0.997204i −0.0747301 + 0.997204i \(0.523810\pi\)
−1.00000 \(1.00000\pi\)
\(4\) 0.365341 0.930874i 0.365341 0.930874i
\(5\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(6\) −0.326239 + 1.42935i −0.326239 + 1.42935i
\(7\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(8\) −0.222521 0.974928i −0.222521 0.974928i
\(9\) 0.0858993 1.14625i 0.0858993 1.14625i
\(10\) 0 0
\(11\) −0.123490 1.64786i −0.123490 1.64786i −0.623490 0.781831i \(-0.714286\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(12\) 0.535628 + 1.36476i 0.535628 + 1.36476i
\(13\) −1.48883 0.716983i −1.48883 0.716983i −0.500000 0.866025i \(-0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(14\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(15\) 0 0
\(16\) −0.733052 0.680173i −0.733052 0.680173i
\(17\) −0.988831 0.149042i −0.988831 0.149042i
\(18\) −0.574730 0.995462i −0.574730 0.995462i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) −1.21135 0.825886i −1.21135 0.825886i
\(22\) −1.03030 1.29196i −1.03030 1.29196i
\(23\) −1.78181 + 0.268565i −1.78181 + 0.268565i −0.955573 0.294755i \(-0.904762\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(24\) 1.21135 + 0.825886i 1.21135 + 0.825886i
\(25\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(26\) −1.63402 + 0.246289i −1.63402 + 0.246289i
\(27\) 0.136622 + 0.171318i 0.136622 + 0.171318i
\(28\) 0.988831 + 0.149042i 0.988831 + 0.149042i
\(29\) 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 \(-0.238095\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(32\) −0.988831 0.149042i −0.988831 0.149042i
\(33\) 1.77597 + 1.64786i 1.77597 + 1.64786i
\(34\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(35\) 0 0
\(36\) −1.03563 0.498732i −1.03563 0.498732i
\(37\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(38\) 0 0
\(39\) 2.31507 0.714104i 2.31507 0.714104i
\(40\) 0 0
\(41\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(42\) −1.46610 −1.46610
\(43\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(44\) −1.57906 0.487076i −1.57906 0.487076i
\(45\) 0 0
\(46\) −1.32091 + 1.22563i −1.32091 + 1.22563i
\(47\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(48\) 1.46610 1.46610
\(49\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(50\) 1.00000 1.00000
\(51\) 1.21135 0.825886i 1.21135 0.825886i
\(52\) −1.21135 + 1.12397i −1.21135 + 1.12397i
\(53\) 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(54\) 0.209389 + 0.0645880i 0.209389 + 0.0645880i
\(55\) 0 0
\(56\) 0.900969 0.433884i 0.900969 0.433884i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(60\) 0 0
\(61\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(62\) −0.400969 0.193096i −0.400969 0.193096i
\(63\) 1.13662 0.171318i 1.13662 0.171318i
\(64\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(65\) 0 0
\(66\) 2.39564 + 0.361085i 2.39564 + 0.361085i
\(67\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(68\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(69\) 1.64715 2.06546i 1.64715 2.06546i
\(70\) 0 0
\(71\) −1.19158 1.49419i −1.19158 1.49419i −0.826239 0.563320i \(-0.809524\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(72\) −1.13662 + 0.171318i −1.13662 + 0.171318i
\(73\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(74\) 0 0
\(75\) −1.44973 + 0.218511i −1.44973 + 0.218511i
\(76\) 0 0
\(77\) 1.57906 0.487076i 1.57906 0.487076i
\(78\) 1.51053 1.89415i 1.51053 1.89415i
\(79\) 0.0747301 0.129436i 0.0747301 0.129436i −0.826239 0.563320i \(-0.809524\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(80\) 0 0
\(81\) 0.818951 + 0.123437i 0.818951 + 0.123437i
\(82\) 0 0
\(83\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(84\) −1.21135 + 0.825886i −1.21135 + 0.825886i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −1.57906 + 0.487076i −1.57906 + 0.487076i
\(89\) −0.109562 + 1.46200i −0.109562 + 1.46200i 0.623490 + 0.781831i \(0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(90\) 0 0
\(91\) 0.367711 1.61105i 0.367711 1.61105i
\(92\) −0.400969 + 1.75676i −0.400969 + 1.75676i
\(93\) 0.623490 + 0.192321i 0.623490 + 0.192321i
\(94\) 0 0
\(95\) 0 0
\(96\) 1.21135 0.825886i 1.21135 0.825886i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) −1.89946 −1.89946
\(100\) 0.826239 0.563320i 0.826239 0.563320i
\(101\) 1.32091 1.22563i 1.32091 1.22563i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(102\) 0.535628 1.36476i 0.535628 1.36476i
\(103\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(104\) −0.367711 + 1.61105i −0.367711 + 1.61105i
\(105\) 0 0
\(106\) −0.425270 1.86323i −0.425270 1.86323i
\(107\) −0.0546039 + 0.728639i −0.0546039 + 0.728639i 0.900969 + 0.433884i \(0.142857\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(108\) 0.209389 0.0645880i 0.209389 0.0645880i
\(109\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(110\) 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
\(117\) −0.949729 + 1.64498i −0.949729 + 1.64498i
\(118\) 0 0
\(119\) −0.0747301 0.997204i −0.0747301 0.997204i
\(120\) 0 0
\(121\) −1.71135 + 0.257945i −1.71135 + 0.257945i
\(122\) 0 0
\(123\) 0 0
\(124\) −0.440071 + 0.0663300i −0.440071 + 0.0663300i
\(125\) 0 0
\(126\) 0.842614 0.781831i 0.842614 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
\(131\) −1.32091 1.22563i −1.32091 1.22563i −0.955573 0.294755i \(-0.904762\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(132\) 2.18278 1.05117i 2.18278 1.05117i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(137\) −1.40097 + 0.432142i −1.40097 + 0.432142i −0.900969 0.433884i \(-0.857143\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) 0.197424 2.63444i 0.197424 2.63444i
\(139\) 0.0332580 + 0.145713i 0.0332580 + 0.145713i 0.988831 0.149042i \(-0.0476190\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1.82624 0.563320i −1.82624 0.563320i
\(143\) −0.997630 + 2.54192i −0.997630 + 2.54192i
\(144\) −0.842614 + 0.781831i −0.842614 + 0.781831i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.535628 1.36476i 0.535628 1.36476i
\(148\) 0 0
\(149\) −1.21135 + 0.825886i −1.21135 + 0.825886i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(150\) −1.07473 + 0.997204i −1.07473 + 0.997204i
\(151\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(152\) 0 0
\(153\) −0.255779 + 1.12064i −0.255779 + 1.12064i
\(154\) 1.03030 1.29196i 1.03030 1.29196i
\(155\) 0 0
\(156\) 0.181049 2.41593i 0.181049 2.41593i
\(157\) 0.142820 0.0440542i 0.142820 0.0440542i −0.222521 0.974928i \(-0.571429\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(158\) −0.0111692 0.149042i −0.0111692 0.149042i
\(159\) 1.02366 + 2.60825i 1.02366 + 2.60825i
\(160\) 0 0
\(161\) −0.658322 1.67738i −0.658322 1.67738i
\(162\) 0.746184 0.359343i 0.746184 0.359343i
\(163\) 1.46610 + 1.36035i 1.46610 + 1.36035i 0.733052 + 0.680173i \(0.238095\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) 1.23305 1.54620i 1.23305 1.54620i 0.500000 0.866025i \(-0.333333\pi\)
0.733052 0.680173i \(-0.238095\pi\)
\(168\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(169\) 1.07906 + 1.35310i 1.07906 + 1.35310i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(174\) 0 0
\(175\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(176\) −1.03030 + 1.29196i −1.03030 + 1.29196i
\(177\) 0 0
\(178\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(179\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(180\) 0 0
\(181\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(182\) −0.603718 1.53825i −0.603718 1.53825i
\(183\) 0 0
\(184\) 0.658322 + 1.67738i 0.658322 + 1.67738i
\(185\) 0 0
\(186\) 0.623490 0.192321i 0.623490 0.192321i
\(187\) −0.123490 + 1.64786i −0.123490 + 1.64786i
\(188\) 0 0
\(189\) −0.136622 + 0.171318i −0.136622 + 0.171318i
\(190\) 0 0
\(191\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(192\) 0.535628 1.36476i 0.535628 1.36476i
\(193\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −1.56941 + 1.07000i −1.56941 + 1.07000i
\(199\) 1.40097 1.29991i 1.40097 1.29991i 0.500000 0.866025i \(-0.333333\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(200\) 0.365341 0.930874i 0.365341 0.930874i
\(201\) 0 0
\(202\) 0.400969 1.75676i 0.400969 1.75676i
\(203\) 0 0
\(204\) −0.326239 1.42935i −0.326239 1.42935i
\(205\) 0 0
\(206\) 0 0
\(207\) 0.154785 + 2.06546i 0.154785 + 2.06546i
\(208\) 0.603718 + 1.53825i 0.603718 + 1.53825i
\(209\) 0 0
\(210\) 0 0
\(211\) 1.12349 0.541044i 1.12349 0.541044i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(212\) −1.40097 1.29991i −1.40097 1.29991i
\(213\) 2.77064 + 0.417607i 2.77064 + 0.417607i
\(214\) 0.365341 + 0.632789i 0.365341 + 0.632789i
\(215\) 0 0
\(216\) 0.136622 0.171318i 0.136622 0.171318i
\(217\) 0.326239 0.302705i 0.326239 0.302705i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.36534 + 0.930874i 1.36534 + 0.930874i
\(222\) 0 0
\(223\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(224\) −0.0747301 0.997204i −0.0747301 0.997204i
\(225\) 0.716677 0.898684i 0.716677 0.898684i
\(226\) 0 0
\(227\) 0.955573 + 1.65510i 0.955573 + 1.65510i 0.733052 + 0.680173i \(0.238095\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(228\) 0 0
\(229\) −0.914101 0.848162i −0.914101 0.848162i 0.0747301 0.997204i \(-0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(230\) 0 0
\(231\) −1.21135 + 2.09812i −1.21135 + 2.09812i
\(232\) 0 0
\(233\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(234\) 0.141947 + 1.89415i 0.141947 + 1.89415i
\(235\) 0 0
\(236\) 0 0
\(237\) 0.0487597 + 0.213630i 0.0487597 + 0.213630i
\(238\) −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 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(242\) −1.26868 + 1.17716i −1.26868 + 1.17716i
\(243\) −1.18429 + 0.807437i −1.18429 + 0.807437i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.326239 + 0.302705i −0.326239 + 0.302705i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(252\) 0.255779 1.12064i 0.255779 1.12064i
\(253\) 0.662592 + 2.90301i 0.662592 + 2.90301i
\(254\) 0 0
\(255\) 0 0
\(256\) 0.0747301 + 0.997204i 0.0747301 + 0.997204i
\(257\) −0.365341 0.930874i −0.365341 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −1.78181 0.268565i −1.78181 0.268565i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) 1.21135 2.09812i 1.21135 2.09812i
\(265\) 0 0
\(266\) 0 0
\(267\) −1.34017 1.68052i −1.34017 1.68052i
\(268\) 0 0
\(269\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(270\) 0 0
\(271\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(272\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(273\) 1.21135 + 2.09812i 1.21135 + 2.09812i
\(274\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(275\) 0.826239 1.43109i 0.826239 1.43109i
\(276\) −1.32091 2.28789i −1.32091 2.28789i
\(277\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(278\) 0.109562 + 0.101659i 0.109562 + 0.101659i
\(279\) −0.460898 + 0.221957i −0.460898 + 0.221957i
\(280\) 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 1.64786i −0.123490 1.64786i −0.623490 0.781831i \(-0.714286\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(284\) −1.82624 + 0.563320i −1.82624 + 0.563320i
\(285\) 0 0
\(286\) 0.607634 + 2.66222i 0.607634 + 2.66222i
\(287\) 0 0
\(288\) −0.255779 + 1.12064i −0.255779 + 1.12064i
\(289\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) 0.149460 0.149460 0.0747301 0.997204i \(-0.476190\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(294\) −0.326239 1.42935i −0.326239 1.42935i
\(295\) 0 0
\(296\) 0 0
\(297\) 0.265436 0.246289i 0.265436 0.246289i
\(298\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(299\) 2.84537 + 0.877681i 2.84537 + 0.877681i
\(300\) −0.326239 + 1.42935i −0.326239 + 1.42935i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.197424 + 2.63444i −0.197424 + 2.63444i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.419945 + 1.07000i 0.419945 + 1.07000i
\(307\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(308\) 0.123490 1.64786i 0.123490 1.64786i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.988831 0.149042i −0.988831 0.149042i −0.365341 0.930874i \(-0.619048\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(312\) −1.21135 2.09812i −1.21135 2.09812i
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0.0931869 0.116853i 0.0931869 0.116853i
\(315\) 0 0
\(316\) −0.0931869 0.116853i −0.0931869 0.116853i
\(317\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(318\) 2.31507 + 1.57839i 2.31507 + 1.57839i
\(319\) 0 0
\(320\) 0 0
\(321\) −0.667917 0.837541i −0.667917 0.837541i
\(322\) −1.48883 1.01507i −1.48883 1.01507i
\(323\) 0 0
\(324\) 0.414101 0.717244i 0.414101 0.717244i
\(325\) −0.826239 1.43109i −0.826239 1.43109i
\(326\) 1.97766 + 0.298085i 1.97766 + 0.298085i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) 0.147791 1.97213i 0.147791 1.97213i
\(335\) 0 0
\(336\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(337\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(338\) 1.65379 + 0.510127i 1.65379 + 0.510127i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.607634 + 0.414278i −0.607634 + 0.414278i
\(342\) 0 0
\(343\) −0.623490 0.781831i −0.623490 0.781831i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −0.455573 + 1.16078i −0.455573 + 1.16078i 0.500000 + 0.866025i \(0.333333\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(348\) 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
\(351\) −0.0805743 0.353019i −0.0805743 0.353019i
\(352\) −0.123490 + 1.64786i −0.123490 + 1.64786i
\(353\) −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 1.32091 + 0.636119i 1.32091 + 0.636119i
\(357\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(358\) 0 0
\(359\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) 0 0
\(363\) 1.58202 1.98379i 1.58202 1.98379i
\(364\) −1.36534 0.930874i −1.36534 0.930874i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.603718 0.411608i −0.603718 0.411608i 0.222521 0.974928i \(-0.428571\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(368\) 1.48883 + 1.01507i 1.48883 + 1.01507i
\(369\) 0 0
\(370\) 0 0
\(371\) 1.88980 + 0.284841i 1.88980 + 0.284841i
\(372\) 0.406813 0.510127i 0.406813 0.510127i
\(373\) −0.826239 + 1.43109i −0.826239 + 1.43109i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(374\) 0.826239 + 1.43109i 0.826239 + 1.43109i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) −0.0163752 + 0.218511i −0.0163752 + 0.218511i
\(379\) −0.900969 0.433884i −0.900969 0.433884i −0.0747301 0.997204i \(-0.523810\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(384\) −0.326239 1.42935i −0.326239 1.42935i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 1.44973 1.34515i 1.44973 1.34515i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(390\) 0 0
\(391\) 1.80194 1.80194
\(392\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(393\) 2.64183 2.64183
\(394\) 0 0
\(395\) 0 0
\(396\) −0.693950 + 1.76815i −0.693950 + 1.76815i
\(397\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(398\) 0.425270 1.86323i 0.425270 1.86323i
\(399\) 0 0
\(400\) −0.222521 0.974928i −0.222521 0.974928i
\(401\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(402\) 0 0
\(403\) 0.0549581 + 0.733365i 0.0549581 + 0.733365i
\(404\) −0.658322 1.67738i −0.658322 1.67738i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −1.07473 0.997204i −1.07473 0.997204i
\(409\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(410\) 0 0
\(411\) 1.07473 1.86149i 1.07473 1.86149i
\(412\) 0 0
\(413\) 0 0
\(414\) 1.29141 + 1.61937i 1.29141 + 1.61937i
\(415\) 0 0
\(416\) 1.36534 + 0.930874i 1.36534 + 0.930874i
\(417\) −0.181049 0.123437i −0.181049 0.123437i
\(418\) 0 0
\(419\) −0.0931869 0.116853i −0.0931869 0.116853i 0.733052 0.680173i \(-0.238095\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(420\) 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
\(424\) −1.88980 0.284841i −1.88980 0.284841i
\(425\) −0.733052 0.680173i −0.733052 0.680173i
\(426\) 2.52446 1.21572i 2.52446 1.21572i
\(427\) 0 0
\(428\) 0.658322 + 0.317031i 0.658322 + 0.317031i
\(429\) −1.46263 3.72672i −1.46263 3.72672i
\(430\) 0 0
\(431\) 0.955573 0.294755i 0.955573 0.294755i 0.222521 0.974928i \(-0.428571\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(432\) 0.0163752 0.218511i 0.0163752 0.218511i
\(433\) 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 + 0.0841939i −0.123490 + 0.0841939i −0.623490 0.781831i \(-0.714286\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(440\) 0 0
\(441\) 0.419945 + 1.07000i 0.419945 + 1.07000i
\(442\) 1.65248 1.65248
\(443\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.478300 2.09557i 0.478300 2.09557i
\(448\) −0.623490 0.781831i −0.623490 0.781831i
\(449\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(450\) 0.0858993 1.14625i 0.0858993 1.14625i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.72188 + 0.829215i 1.72188 + 0.829215i
\(455\) 0 0
\(456\) 0 0
\(457\) 1.32091 + 1.22563i 1.32091 + 1.22563i 0.955573 + 0.294755i \(0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(458\) −1.23305 0.185853i −1.23305 0.185853i
\(459\) −0.109562 0.189767i −0.109562 0.189767i
\(460\) 0 0
\(461\) 1.19158 1.49419i 1.19158 1.49419i 0.365341 0.930874i \(-0.380952\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(462\) 0.181049 + 2.41593i 0.181049 + 2.41593i
\(463\) 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 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(468\) 1.18429 + 1.48506i 1.18429 + 1.48506i
\(469\) 0 0
\(470\) 0 0
\(471\) −0.109562 + 0.189767i −0.109562 + 0.189767i
\(472\) 0 0
\(473\) 0 0
\(474\) 0.160629 + 0.149042i 0.160629 + 0.149042i
\(475\) 0 0
\(476\) −0.955573 0.294755i −0.955573 0.294755i
\(477\) −1.97924 0.953150i −1.97924 0.953150i
\(478\) 0 0
\(479\) 0.134659 + 1.79690i 0.134659 + 1.79690i 0.500000 + 0.866025i \(0.333333\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 2.38020 + 1.14625i 2.38020 + 1.14625i
\(484\) −0.385113 + 1.68729i −0.385113 + 1.68729i
\(485\) 0 0
\(486\) −0.523663 + 1.33427i −0.523663 + 1.33427i
\(487\) −0.733052 + 0.680173i −0.733052 + 0.680173i −0.955573 0.294755i \(-0.904762\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(488\) 0 0
\(489\) −2.93221 −2.93221
\(490\) 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
\(497\) 1.19158 1.49419i 1.19158 1.49419i
\(498\) 0 0
\(499\) −0.0111692 + 0.149042i −0.0111692 + 0.149042i 0.988831 + 0.149042i \(0.0476190\pi\)
−1.00000 \(\pi\)
\(500\) 0 0
\(501\) 0.216677 + 2.89135i 0.216677 + 2.89135i
\(502\) 0 0
\(503\) 0.658322 + 0.317031i 0.658322 + 0.317031i 0.733052 0.680173i \(-0.238095\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(504\) −0.419945 1.07000i −0.419945 1.07000i
\(505\) 0 0
\(506\) 2.18278 + 2.02532i 2.18278 + 2.02532i
\(507\) −2.50902 0.378174i −2.50902 0.378174i
\(508\) 0 0
\(509\) 0.900969 1.56052i 0.900969 1.56052i 0.0747301 0.997204i \(-0.476190\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(513\) 0 0
\(514\) −0.826239 0.563320i −0.826239 0.563320i
\(515\) 0 0
\(516\) 0 0
\(517\) 0 0
\(518\) 0 0
\(519\) 0 0
\(520\) 0 0
\(521\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(522\) 0 0
\(523\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(524\) −1.62349 + 0.781831i −1.62349 + 0.781831i
\(525\) −0.535628 1.36476i −0.535628 1.36476i
\(526\) 0 0
\(527\) 0.162592 + 0.414278i 0.162592 + 0.414278i
\(528\) −0.181049 2.41593i −0.181049 2.41593i
\(529\) 2.14715 0.662309i 2.14715 0.662309i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −2.05397 0.633565i −2.05397 0.633565i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) 0.826239 + 1.43109i 0.826239 + 1.43109i
\(540\) 0 0
\(541\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(545\) 0 0
\(546\) 2.18278 + 1.05117i 2.18278 + 1.05117i
\(547\) −0.440071 1.92808i −0.440071 1.92808i −0.365341 0.930874i \(-0.619048\pi\)
−0.0747301 0.997204i \(-0.523810\pi\)
\(548\) −0.109562 + 1.46200i −0.109562 + 1.46200i
\(549\) 0 0
\(550\) −0.123490 1.64786i −0.123490 1.64786i
\(551\) 0 0
\(552\) −2.38020 1.14625i −2.38020 1.14625i
\(553\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(554\) 0 0
\(555\) 0 0
\(556\) 0.147791 + 0.0222759i 0.147791 + 0.0222759i
\(557\) −0.955573 1.65510i −0.955573 1.65510i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(558\) −0.255779 + 0.443022i −0.255779 + 0.443022i
\(559\) 0 0
\(560\) 0 0
\(561\) −1.51053 1.89415i −1.51053 1.89415i
\(562\) 0.988831 0.149042i 0.988831 0.149042i
\(563\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.03030 1.29196i −1.03030 1.29196i
\(567\) 0.0618916 + 0.825886i 0.0618916 + 0.825886i
\(568\) −1.19158 + 1.49419i −1.19158 + 1.49419i
\(569\) −0.826239 + 1.43109i −0.826239 + 1.43109i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(570\) 0 0
\(571\) −0.440071 0.0663300i −0.440071 0.0663300i −0.0747301 0.997204i \(-0.523810\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(572\) 2.00173 + 1.85734i 2.00173 + 1.85734i
\(573\) 0 0
\(574\) 0 0
\(575\) −1.62349 0.781831i −1.62349 0.781831i
\(576\) 0.419945 + 1.07000i 0.419945 + 1.07000i
\(577\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(578\) 0.955573 0.294755i 0.955573 0.294755i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) −3.01782 0.930874i −3.01782 0.930874i
\(584\) 0 0
\(585\) 0 0
\(586\) 0.123490 0.0841939i 0.123490 0.0841939i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) −1.07473 0.997204i −1.07473 0.997204i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) 0.698220 + 0.215372i 0.698220 + 0.215372i 0.623490 0.781831i \(-0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(594\) 0.0805743 0.353019i 0.0805743 0.353019i
\(595\) 0 0
\(596\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(597\) −0.209389 + 2.79410i −0.209389 + 2.79410i
\(598\) 2.84537 0.877681i 2.84537 0.877681i
\(599\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(600\) 0.535628 + 1.36476i 0.535628 + 1.36476i
\(601\) 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
\(606\) 1.32091 + 2.28789i 1.32091 + 2.28789i
\(607\) −0.500000 + 0.866025i −0.500000 + 0.866025i 0.500000 + 0.866025i \(0.333333\pi\)
−1.00000 \(\pi\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) 0.949729 + 0.647514i 0.949729 + 0.647514i
\(613\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.826239 1.43109i −0.826239 1.43109i
\(617\) 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 \(-0.333333\pi\)
−1.00000 \(\pi\)
\(620\) 0 0
\(621\) −0.289444 0.268565i −0.289444 0.268565i
\(622\) −0.900969 + 0.433884i −0.900969 + 0.433884i
\(623\) −1.44973 + 0.218511i −1.44973 + 0.218511i
\(624\) −2.18278 1.05117i −2.18278 1.05117i
\(625\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(626\) 0 0
\(627\) 0 0
\(628\) 0.0111692 0.149042i 0.0111692 0.149042i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(632\) −0.142820 0.0440542i −0.142820 0.0440542i
\(633\) −0.667917 + 1.70182i −0.667917 + 1.70182i
\(634\) 0 0
\(635\) 0 0
\(636\) 2.80194 2.80194
\(637\) 1.65248 1.65248
\(638\) 0 0
\(639\) −1.81507 + 1.23749i −1.81507 + 1.23749i
\(640\) 0 0
\(641\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(642\) −1.02366 0.315758i −1.02366 0.315758i
\(643\) −0.440071 + 1.92808i −0.440071 + 1.92808i −0.0747301 + 0.997204i \(0.523810\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(644\) −1.80194 −1.80194
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(648\) −0.0618916 0.825886i −0.0618916 0.825886i
\(649\) 0 0
\(650\) −1.48883 0.716983i −1.48883 0.716983i
\(651\) −0.0487597 + 0.650653i −0.0487597 + 0.650653i
\(652\) 1.80194 0.867767i 1.80194 0.867767i
\(653\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(654\) 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
\(661\) −0.367711 0.250701i −0.367711 0.250701i 0.365341 0.930874i \(-0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(662\) 0 0
\(663\) −2.39564 + 0.361085i −2.39564 + 0.361085i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.988831 1.71271i −0.988831 1.71271i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(673\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(674\) 0 0
\(675\) 0.0163752 + 0.218511i 0.0163752 + 0.218511i
\(676\) 1.65379 0.510127i 1.65379 0.510127i
\(677\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) −2.67746 0.825886i −2.67746 0.825886i
\(682\) −0.268680 + 0.684585i −0.268680 + 0.684585i
\(683\) 1.40097 1.29991i 1.40097 1.29991i 0.500000 0.866025i \(-0.333333\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.955573 0.294755i −0.955573 0.294755i
\(687\) 1.82820 1.82820
\(688\) 0 0
\(689\) −2.31507 + 2.14807i −2.31507 + 2.14807i
\(690\) 0 0
\(691\) 0.425270 + 0.131178i 0.425270 + 0.131178i 0.500000 0.866025i \(-0.333333\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(692\) 0 0
\(693\) −0.422669 1.85183i −0.422669 1.85183i
\(694\) 0.277479 + 1.21572i 0.277479 + 1.21572i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(699\) 0 0
\(700\) 0.733052 + 0.680173i 0.733052 + 0.680173i
\(701\) −1.72188 + 0.829215i −1.72188 + 0.829215i −0.733052 + 0.680173i \(0.761905\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(702\) −0.265436 0.246289i −0.265436 0.246289i
\(703\) 0 0
\(704\) 0.826239 + 1.43109i 0.826239 + 1.43109i
\(705\) 0 0
\(706\) −0.623490 + 0.781831i −0.623490 + 0.781831i
\(707\) 1.48883 + 1.01507i 1.48883 + 1.01507i
\(708\) 0 0
\(709\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(710\) 0 0
\(711\) −0.141947 0.0967776i −0.141947 0.0967776i
\(712\) 1.44973 0.218511i 1.44973 0.218511i
\(713\) 0.500000 + 0.626980i 0.500000 + 0.626980i
\(714\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 1.21135 + 1.12397i 1.21135 + 1.12397i 0.988831 + 0.149042i \(0.0476190\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.900969 0.433884i −0.900969 0.433884i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0.189617 2.53026i 0.189617 2.53026i
\(727\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(728\) −1.65248 −1.65248
\(729\) 0.283323 1.24132i 0.283323 1.24132i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.826239 + 0.563320i −0.826239 + 0.563320i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(734\) −0.730682 −0.730682
\(735\) 0 0
\(736\) 1.80194 1.80194
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.72188 0.829215i 1.72188 0.829215i
\(743\) −0.326239 1.42935i −0.326239 1.42935i −0.826239 0.563320i \(-0.809524\pi\)
0.500000 0.866025i \(-0.333333\pi\)
\(744\) 0.0487597 0.650653i 0.0487597 0.650653i
\(745\) 0 0
\(746\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(747\) 0 0
\(748\) 1.48883 + 0.716983i 1.48883 + 0.716983i
\(749\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(750\) 0 0
\(751\) 0.109562 + 0.101659i 0.109562 + 0.101659i 0.733052 0.680173i \(-0.238095\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.109562 + 0.189767i 0.109562 + 0.189767i
\(757\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(758\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(759\) −3.60700 2.45921i −3.60700 2.45921i
\(760\) 0 0
\(761\) 1.95557 0.294755i 1.95557 0.294755i 0.955573 0.294755i \(-0.0952381\pi\)
1.00000 \(0\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) −1.07473 0.997204i −1.07473 0.997204i
\(769\) 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
\(771\) 1.32091 + 0.636119i 1.32091 + 0.636119i
\(772\) 0 0
\(773\) −0.147791 1.97213i −0.147791 1.97213i −0.222521 0.974928i \(-0.571429\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(774\) 0 0
\(775\) 0.0332580 0.443797i 0.0332580 0.443797i
\(776\) 0 0
\(777\) 0 0
\(778\) 0.440071 1.92808i 0.440071 1.92808i
\(779\) 0 0
\(780\) 0 0
\(781\) −2.31507 + 2.14807i −2.31507 + 2.14807i
\(782\) 1.48883 1.01507i 1.48883 1.01507i
\(783\) 0 0
\(784\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(785\) 0 0
\(786\) 2.18278 1.48819i 2.18278 1.48819i
\(787\) 0.914101 0.848162i 0.914101 0.848162i −0.0747301 0.997204i \(-0.523810\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.422669 + 1.85183i 0.422669 + 1.85183i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −0.698220 1.77904i −0.698220 1.77904i
\(797\) −1.72188 0.829215i −1.72188 0.829215i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) −0.733052 0.680173i −0.733052 0.680173i
\(801\) 1.66641 + 0.251170i 1.66641 + 0.251170i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0.458528 + 0.574976i 0.458528 + 0.574976i
\(807\) 0 0
\(808\) −1.48883 1.01507i −1.48883 1.01507i
\(809\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(810\) 0 0
\(811\) −1.19158 1.49419i −1.19158 1.49419i −0.826239 0.563320i \(-0.809524\pi\)
−0.365341 0.930874i \(-0.619048\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) −1.44973 0.218511i −1.44973 0.218511i
\(817\) 0 0
\(818\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(819\) −1.81507 0.559875i −1.81507 0.559875i
\(820\) 0 0
\(821\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(822\) −0.160629 2.14345i −0.160629 2.14345i
\(823\) 1.40097 0.432142i 1.40097 0.432142i 0.500000 0.866025i \(-0.333333\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(824\) 0 0
\(825\) 0.539102 + 2.36196i 0.539102 + 2.36196i
\(826\) 0 0
\(827\) 0.162592 0.712362i 0.162592 0.712362i −0.826239 0.563320i \(-0.809524\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(828\) 1.97924 + 0.610513i 1.97924 + 0.610513i
\(829\) 0.266948 0.680173i 0.266948 0.680173i −0.733052 0.680173i \(-0.761905\pi\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.65248 1.65248
\(833\) 0.955573 0.294755i 0.955573 0.294755i
\(834\) −0.219124 −0.219124
\(835\) 0 0
\(836\) 0 0
\(837\) 0.0356278 0.0907783i 0.0356278 0.0907783i
\(838\) −0.142820 0.0440542i −0.142820 0.0440542i
\(839\) 0.277479 1.21572i 0.277479 1.21572i −0.623490 0.781831i \(-0.714286\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(840\) 0 0
\(841\) −0.222521 0.974928i −0.222521 0.974928i
\(842\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i
\(843\) −1.40097 + 0.432142i −1.40097 + 0.432142i
\(844\) −0.0931869 1.24349i −0.0931869 1.24349i
\(845\) 0 0
\(846\) 0 0
\(847\) −0.632289 1.61105i −0.632289 1.61105i
\(848\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(849\) 1.77597 + 1.64786i 1.77597 + 1.64786i
\(850\) −0.988831 0.149042i −0.988831 0.149042i
\(851\) 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 0.108903i 0.722521 0.108903i
\(857\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(858\) −3.30782 2.25523i −3.30782 2.25523i
\(859\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.623490 0.781831i 0.623490 0.781831i
\(863\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(864\) −0.109562 0.189767i −0.109562 0.189767i
\(865\) 0 0
\(866\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(867\) −1.32091 + 0.636119i −1.32091 + 0.636119i
\(868\) −0.162592 0.414278i −0.162592 0.414278i
\(869\) −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 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(878\) −0.0546039 + 0.139129i −0.0546039 + 0.139129i
\(879\) −0.160629 + 0.149042i −0.160629 + 0.149042i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) 0.949729 + 0.647514i 0.949729 + 0.647514i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 1.36534 0.930874i 1.36534 0.930874i
\(885\) 0 0
\(886\) 0 0
\(887\) −1.57906 0.487076i −1.57906 0.487076i −0.623490 0.781831i \(-0.714286\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.102274 1.36476i 0.102274 1.36476i
\(892\) 0 0
\(893\) 0 0
\(894\) −0.785286 2.00088i −0.785286 2.00088i
\(895\) 0 0
\(896\) −0.955573 0.294755i −0.955573 0.294755i
\(897\) −3.93323 + 1.89415i −3.93323 + 1.89415i
\(898\) 0 0
\(899\) 0 0
\(900\) −0.574730 0.995462i −0.574730 0.995462i
\(901\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 0.367711 + 0.250701i 0.367711 + 0.250701i 0.733052 0.680173i \(-0.238095\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(908\) 1.88980 0.284841i 1.88980 0.284841i
\(909\) −1.29141 1.61937i −1.29141 1.61937i
\(910\) 0 0
\(911\) 1.12349 1.40881i 1.12349 1.40881i 0.222521 0.974928i \(-0.428571\pi\)
0.900969 0.433884i \(-0.142857\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.78181 + 0.268565i 1.78181 + 0.268565i
\(915\) 0 0
\(916\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(917\) 0.900969 1.56052i 0.900969 1.56052i
\(918\) −0.197424 0.0950744i −0.197424 0.0950744i
\(919\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 0.142820 1.90580i 0.142820 1.90580i
\(923\) 0.702749 + 3.07894i 0.702749 + 3.07894i
\(924\) 1.51053 + 1.89415i 1.51053 + 1.89415i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) 1.21135 0.825886i 1.21135 0.825886i
\(934\) 0 0
\(935\) 0 0
\(936\) 1.81507 + 0.559875i 1.81507 + 0.559875i
\(937\) 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 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(942\) 0.0163752 + 0.218511i 0.0163752 + 0.218511i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.733052 0.680173i −0.733052 0.680173i 0.222521 0.974928i \(-0.428571\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(948\) 0.216677 + 0.0326588i 0.216677 + 0.0326588i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −0.955573 + 0.294755i −0.955573 + 0.294755i
\(953\) −1.23305 1.54620i −1.23305 1.54620i −0.733052 0.680173i \(-0.761905\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(954\) −2.17225 + 0.327414i −2.17225 + 0.327414i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 1.12349 + 1.40881i 1.12349 + 1.40881i
\(959\) −0.733052 1.26968i −0.733052 1.26968i
\(960\) 0 0
\(961\) 0.400969 0.694498i 0.400969 0.694498i
\(962\) 0 0
\(963\) 0.830509 + 0.125179i 0.830509 + 0.125179i
\(964\) 0 0
\(965\) 0 0
\(966\) 2.61232 0.393744i 2.61232 0.393744i
\(967\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(968\) 0.632289 + 1.61105i 0.632289 + 1.61105i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(972\) 0.318951 + 1.39742i 0.318951 + 1.39742i
\(973\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(974\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(975\) 2.31507 + 0.714104i 2.31507 + 0.714104i
\(976\) 0 0
\(977\) 1.32091 1.22563i 1.32091 1.22563i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(978\) −2.42270 + 1.65177i −2.42270 + 1.65177i
\(979\) 2.42270 2.42270
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 1.21135 1.12397i 1.21135 1.12397i 0.222521 0.974928i \(-0.428571\pi\)
0.988831 0.149042i \(-0.0476190\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) 0.147791 + 1.97213i 0.147791 + 1.97213i 0.222521 + 0.974928i \(0.428571\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(992\) 0.162592 + 0.414278i 0.162592 + 0.414278i
\(993\) 0 0
\(994\) 0.142820 1.90580i 0.142820 1.90580i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(998\) 0.0747301 + 0.129436i 0.0747301 + 0.129436i
\(999\) 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.a.135.1 12
4.3 odd 2 3332.1.cc.b.135.1 yes 12
17.16 even 2 3332.1.cc.b.135.1 yes 12
49.4 even 21 inner 3332.1.cc.a.543.1 yes 12
68.67 odd 2 CM 3332.1.cc.a.135.1 12
196.151 odd 42 3332.1.cc.b.543.1 yes 12
833.543 even 42 3332.1.cc.b.543.1 yes 12
3332.543 odd 42 inner 3332.1.cc.a.543.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.1.cc.a.135.1 12 1.1 even 1 trivial
3332.1.cc.a.135.1 12 68.67 odd 2 CM
3332.1.cc.a.543.1 yes 12 49.4 even 21 inner
3332.1.cc.a.543.1 yes 12 3332.543 odd 42 inner
3332.1.cc.b.135.1 yes 12 4.3 odd 2
3332.1.cc.b.135.1 yes 12 17.16 even 2
3332.1.cc.b.543.1 yes 12 196.151 odd 42
3332.1.cc.b.543.1 yes 12 833.543 even 42