Properties

Label 3332.1.cc.b.1495.1
Level $3332$
Weight $1$
Character 3332.1495
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 1495.1
Root \(0.0747301 - 0.997204i\) of defining polynomial
Character \(\chi\) \(=\) 3332.1495
Dual form 3332.1.cc.b.2991.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.955573 - 0.294755i) q^{2} +(0.266948 + 0.680173i) q^{3} +(0.826239 - 0.563320i) q^{4} +(0.455573 + 0.571270i) q^{6} +(0.623490 - 0.781831i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.341678 - 0.317031i) q^{9} +O(q^{10})\) \(q+(0.955573 - 0.294755i) q^{2} +(0.266948 + 0.680173i) q^{3} +(0.826239 - 0.563320i) q^{4} +(0.455573 + 0.571270i) q^{6} +(0.623490 - 0.781831i) q^{7} +(0.623490 - 0.781831i) q^{8} +(0.341678 - 0.317031i) q^{9} +(-1.40097 - 1.29991i) q^{11} +(0.603718 + 0.411608i) q^{12} +(-0.425270 + 1.86323i) q^{13} +(0.365341 - 0.930874i) q^{14} +(0.365341 - 0.930874i) q^{16} +(0.0747301 - 0.997204i) q^{17} +(0.233052 - 0.403658i) q^{18} +(0.698220 + 0.215372i) q^{21} +(-1.72188 - 0.829215i) q^{22} +(-0.0332580 - 0.443797i) q^{23} +(0.698220 + 0.215372i) q^{24} +(0.955573 + 0.294755i) q^{25} +(0.142820 + 1.90580i) q^{26} +(0.965168 + 0.464800i) q^{27} +(0.0747301 - 0.997204i) q^{28} +(-0.623490 + 1.07992i) q^{31} +(0.0747301 - 0.997204i) q^{32} +(0.510177 - 1.29991i) q^{33} +(-0.222521 - 0.974928i) q^{34} +(0.103718 - 0.454418i) q^{36} +(-1.38084 + 0.208129i) q^{39} +0.730682 q^{42} +(-1.88980 - 0.284841i) q^{44} +(-0.162592 - 0.414278i) q^{46} +0.730682 q^{48} +(-0.222521 - 0.974928i) q^{49} +1.00000 q^{50} +(0.698220 - 0.215372i) q^{51} +(0.698220 + 1.77904i) q^{52} +(-1.63402 + 1.11406i) q^{53} +(1.05929 + 0.159662i) q^{54} +(-0.222521 - 0.974928i) q^{56} +(-0.277479 + 1.21572i) q^{62} +(-0.0348320 - 0.464800i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.104356 - 1.39254i) q^{66} +(-0.500000 - 0.866025i) q^{68} +(0.292981 - 0.141092i) q^{69} +(1.78181 + 0.858075i) q^{71} +(-0.0348320 - 0.464800i) q^{72} +(0.0546039 + 0.728639i) q^{75} +(-1.88980 + 0.284841i) q^{77} +(-1.25815 + 0.605893i) q^{78} +(0.733052 + 1.26968i) q^{79} +(-0.0236628 + 0.315758i) q^{81} +(0.698220 - 0.215372i) q^{84} +(-1.88980 + 0.284841i) q^{88} +(-0.535628 + 0.496990i) q^{89} +(1.19158 + 1.49419i) q^{91} +(-0.277479 - 0.347948i) q^{92} +(-0.900969 - 0.135799i) q^{93} +(0.698220 - 0.215372i) q^{96} +(-0.500000 - 0.866025i) q^{98} -0.890792 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{2} + 13 q^{3} + q^{4} - 5 q^{6} - 2 q^{7} - 2 q^{8} + 14 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{8}{21}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.955573 0.294755i 0.955573 0.294755i
\(3\) 0.266948 + 0.680173i 0.266948 + 0.680173i 1.00000 \(0\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(4\) 0.826239 0.563320i 0.826239 0.563320i
\(5\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(6\) 0.455573 + 0.571270i 0.455573 + 0.571270i
\(7\) 0.623490 0.781831i 0.623490 0.781831i
\(8\) 0.623490 0.781831i 0.623490 0.781831i
\(9\) 0.341678 0.317031i 0.341678 0.317031i
\(10\) 0 0
\(11\) −1.40097 1.29991i −1.40097 1.29991i −0.900969 0.433884i \(-0.857143\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(12\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(13\) −0.425270 + 1.86323i −0.425270 + 1.86323i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(14\) 0.365341 0.930874i 0.365341 0.930874i
\(15\) 0 0
\(16\) 0.365341 0.930874i 0.365341 0.930874i
\(17\) 0.0747301 0.997204i 0.0747301 0.997204i
\(18\) 0.233052 0.403658i 0.233052 0.403658i
\(19\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(20\) 0 0
\(21\) 0.698220 + 0.215372i 0.698220 + 0.215372i
\(22\) −1.72188 0.829215i −1.72188 0.829215i
\(23\) −0.0332580 0.443797i −0.0332580 0.443797i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(24\) 0.698220 + 0.215372i 0.698220 + 0.215372i
\(25\) 0.955573 + 0.294755i 0.955573 + 0.294755i
\(26\) 0.142820 + 1.90580i 0.142820 + 1.90580i
\(27\) 0.965168 + 0.464800i 0.965168 + 0.464800i
\(28\) 0.0747301 0.997204i 0.0747301 0.997204i
\(29\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(30\) 0 0
\(31\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(32\) 0.0747301 0.997204i 0.0747301 0.997204i
\(33\) 0.510177 1.29991i 0.510177 1.29991i
\(34\) −0.222521 0.974928i −0.222521 0.974928i
\(35\) 0 0
\(36\) 0.103718 0.454418i 0.103718 0.454418i
\(37\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(38\) 0 0
\(39\) −1.38084 + 0.208129i −1.38084 + 0.208129i
\(40\) 0 0
\(41\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(42\) 0.730682 0.730682
\(43\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(44\) −1.88980 0.284841i −1.88980 0.284841i
\(45\) 0 0
\(46\) −0.162592 0.414278i −0.162592 0.414278i
\(47\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(48\) 0.730682 0.730682
\(49\) −0.222521 0.974928i −0.222521 0.974928i
\(50\) 1.00000 1.00000
\(51\) 0.698220 0.215372i 0.698220 0.215372i
\(52\) 0.698220 + 1.77904i 0.698220 + 1.77904i
\(53\) −1.63402 + 1.11406i −1.63402 + 1.11406i −0.733052 + 0.680173i \(0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(54\) 1.05929 + 0.159662i 1.05929 + 0.159662i
\(55\) 0 0
\(56\) −0.222521 0.974928i −0.222521 0.974928i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(60\) 0 0
\(61\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(62\) −0.277479 + 1.21572i −0.277479 + 1.21572i
\(63\) −0.0348320 0.464800i −0.0348320 0.464800i
\(64\) −0.222521 0.974928i −0.222521 0.974928i
\(65\) 0 0
\(66\) 0.104356 1.39254i 0.104356 1.39254i
\(67\) 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
\(69\) 0.292981 0.141092i 0.292981 0.141092i
\(70\) 0 0
\(71\) 1.78181 + 0.858075i 1.78181 + 0.858075i 0.955573 + 0.294755i \(0.0952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(72\) −0.0348320 0.464800i −0.0348320 0.464800i
\(73\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(74\) 0 0
\(75\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i
\(76\) 0 0
\(77\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(78\) −1.25815 + 0.605893i −1.25815 + 0.605893i
\(79\) 0.733052 + 1.26968i 0.733052 + 1.26968i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(80\) 0 0
\(81\) −0.0236628 + 0.315758i −0.0236628 + 0.315758i
\(82\) 0 0
\(83\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(84\) 0.698220 0.215372i 0.698220 0.215372i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(89\) −0.535628 + 0.496990i −0.535628 + 0.496990i −0.900969 0.433884i \(-0.857143\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(90\) 0 0
\(91\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(92\) −0.277479 0.347948i −0.277479 0.347948i
\(93\) −0.900969 0.135799i −0.900969 0.135799i
\(94\) 0 0
\(95\) 0 0
\(96\) 0.698220 0.215372i 0.698220 0.215372i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 0.866025i −0.500000 0.866025i
\(99\) −0.890792 −0.890792
\(100\) 0.955573 0.294755i 0.955573 0.294755i
\(101\) −0.162592 0.414278i −0.162592 0.414278i 0.826239 0.563320i \(-0.190476\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(102\) 0.603718 0.411608i 0.603718 0.411608i
\(103\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(104\) 1.19158 + 1.49419i 1.19158 + 1.49419i
\(105\) 0 0
\(106\) −1.23305 + 1.54620i −1.23305 + 1.54620i
\(107\) −1.21135 + 1.12397i −1.21135 + 1.12397i −0.222521 + 0.974928i \(0.571429\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(108\) 1.05929 0.159662i 1.05929 0.159662i
\(109\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.500000 0.866025i −0.500000 0.866025i
\(113\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.445396 + 0.771449i 0.445396 + 0.771449i
\(118\) 0 0
\(119\) −0.733052 0.680173i −0.733052 0.680173i
\(120\) 0 0
\(121\) 0.198220 + 2.64506i 0.198220 + 2.64506i
\(122\) 0 0
\(123\) 0 0
\(124\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i
\(125\) 0 0
\(126\) −0.170287 0.433884i −0.170287 0.433884i
\(127\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(128\) −0.500000 0.866025i −0.500000 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) −0.162592 + 0.414278i −0.162592 + 0.414278i −0.988831 0.149042i \(-0.952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(132\) −0.310737 1.36143i −0.310737 1.36143i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.733052 0.680173i −0.733052 0.680173i
\(137\) −0.722521 + 0.108903i −0.722521 + 0.108903i −0.500000 0.866025i \(-0.666667\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(138\) 0.238377 0.221181i 0.238377 0.221181i
\(139\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.95557 + 0.294755i 1.95557 + 0.294755i
\(143\) 3.01782 2.05751i 3.01782 2.05751i
\(144\) −0.170287 0.433884i −0.170287 0.433884i
\(145\) 0 0
\(146\) 0 0
\(147\) 0.603718 0.411608i 0.603718 0.411608i
\(148\) 0 0
\(149\) 0.698220 0.215372i 0.698220 0.215372i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(150\) 0.266948 + 0.680173i 0.266948 + 0.680173i
\(151\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(152\) 0 0
\(153\) −0.290611 0.364415i −0.290611 0.364415i
\(154\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(155\) 0 0
\(156\) −1.02366 + 0.949820i −1.02366 + 0.949820i
\(157\) 1.44973 0.218511i 1.44973 0.218511i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(158\) 1.07473 + 0.997204i 1.07473 + 0.997204i
\(159\) −1.19395 0.814021i −1.19395 0.814021i
\(160\) 0 0
\(161\) −0.367711 0.250701i −0.367711 0.250701i
\(162\) 0.0704598 + 0.308705i 0.0704598 + 0.308705i
\(163\) 0.730682 1.86175i 0.730682 1.86175i 0.365341 0.930874i \(-0.380952\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i −0.500000 0.866025i \(-0.666667\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(168\) 0.603718 0.411608i 0.603718 0.411608i
\(169\) −2.38980 1.15087i −2.38980 1.15087i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(174\) 0 0
\(175\) 0.826239 0.563320i 0.826239 0.563320i
\(176\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(177\) 0 0
\(178\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(179\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(180\) 0 0
\(181\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(182\) 1.57906 + 1.07659i 1.57906 + 1.07659i
\(183\) 0 0
\(184\) −0.367711 0.250701i −0.367711 0.250701i
\(185\) 0 0
\(186\) −0.900969 + 0.135799i −0.900969 + 0.135799i
\(187\) −1.40097 + 1.29991i −1.40097 + 1.29991i
\(188\) 0 0
\(189\) 0.965168 0.464800i 0.965168 0.464800i
\(190\) 0 0
\(191\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(192\) 0.603718 0.411608i 0.603718 0.411608i
\(193\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.733052 0.680173i −0.733052 0.680173i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.851217 + 0.262566i −0.851217 + 0.262566i
\(199\) −0.722521 1.84095i −0.722521 1.84095i −0.500000 0.866025i \(-0.666667\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(200\) 0.826239 0.563320i 0.826239 0.563320i
\(201\) 0 0
\(202\) −0.277479 0.347948i −0.277479 0.347948i
\(203\) 0 0
\(204\) 0.455573 0.571270i 0.455573 0.571270i
\(205\) 0 0
\(206\) 0 0
\(207\) −0.152061 0.141092i −0.152061 0.141092i
\(208\) 1.57906 + 1.07659i 1.57906 + 1.07659i
\(209\) 0 0
\(210\) 0 0
\(211\) 0.400969 + 1.75676i 0.400969 + 1.75676i 0.623490 + 0.781831i \(0.285714\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(212\) −0.722521 + 1.84095i −0.722521 + 1.84095i
\(213\) −0.107988 + 1.44100i −0.107988 + 1.44100i
\(214\) −0.826239 + 1.43109i −0.826239 + 1.43109i
\(215\) 0 0
\(216\) 0.965168 0.464800i 0.965168 0.464800i
\(217\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 1.82624 + 0.563320i 1.82624 + 0.563320i
\(222\) 0 0
\(223\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(224\) −0.733052 0.680173i −0.733052 0.680173i
\(225\) 0.419945 0.202235i 0.419945 0.202235i
\(226\) 0 0
\(227\) 0.988831 1.71271i 0.988831 1.71271i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(228\) 0 0
\(229\) −0.658322 + 1.67738i −0.658322 + 1.67738i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(230\) 0 0
\(231\) −0.698220 1.20935i −0.698220 1.20935i
\(232\) 0 0
\(233\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(234\) 0.652997 + 0.605893i 0.652997 + 0.605893i
\(235\) 0 0
\(236\) 0 0
\(237\) −0.667917 + 0.837541i −0.667917 + 0.837541i
\(238\) −0.900969 0.433884i −0.900969 0.433884i
\(239\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(240\) 0 0
\(241\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(242\) 0.969059 + 2.46912i 0.969059 + 2.46912i
\(243\) 0.802576 0.247562i 0.802576 0.247562i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(252\) −0.290611 0.364415i −0.290611 0.364415i
\(253\) −0.530303 + 0.664979i −0.530303 + 0.664979i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.733052 0.680173i −0.733052 0.680173i
\(257\) −0.826239 0.563320i −0.826239 0.563320i 0.0747301 0.997204i \(-0.476190\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i
\(263\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(264\) −0.698220 1.20935i −0.698220 1.20935i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.481024 0.231649i −0.481024 0.231649i
\(268\) 0 0
\(269\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(270\) 0 0
\(271\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(272\) −0.900969 0.433884i −0.900969 0.433884i
\(273\) −0.698220 + 1.20935i −0.698220 + 1.20935i
\(274\) −0.658322 + 0.317031i −0.658322 + 0.317031i
\(275\) −0.955573 1.65510i −0.955573 1.65510i
\(276\) 0.162592 0.281618i 0.162592 0.281618i
\(277\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(278\) −0.535628 + 1.36476i −0.535628 + 1.36476i
\(279\) 0.129334 + 0.566649i 0.129334 + 0.566649i
\(280\) 0 0
\(281\) 0.222521 0.974928i 0.222521 0.974928i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(282\) 0 0
\(283\) −1.40097 1.29991i −1.40097 1.29991i −0.900969 0.433884i \(-0.857143\pi\)
−0.500000 0.866025i \(-0.666667\pi\)
\(284\) 1.95557 0.294755i 1.95557 0.294755i
\(285\) 0 0
\(286\) 2.27728 2.85562i 2.27728 2.85562i
\(287\) 0 0
\(288\) −0.290611 0.364415i −0.290611 0.364415i
\(289\) −0.988831 0.149042i −0.988831 0.149042i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.46610 −1.46610 −0.733052 0.680173i \(-0.761905\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(294\) 0.455573 0.571270i 0.455573 0.571270i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.747972 1.90580i −0.747972 1.90580i
\(298\) 0.603718 0.411608i 0.603718 0.411608i
\(299\) 0.841040 + 0.126766i 0.841040 + 0.126766i
\(300\) 0.455573 + 0.571270i 0.455573 + 0.571270i
\(301\) 0 0
\(302\) 0 0
\(303\) 0.238377 0.221181i 0.238377 0.221181i
\(304\) 0 0
\(305\) 0 0
\(306\) −0.385113 0.262566i −0.385113 0.262566i
\(307\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(308\) −1.40097 + 1.29991i −1.40097 + 1.29991i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i 0.826239 + 0.563320i \(0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(312\) −0.698220 + 1.20935i −0.698220 + 1.20935i
\(313\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(314\) 1.32091 0.636119i 1.32091 0.636119i
\(315\) 0 0
\(316\) 1.32091 + 0.636119i 1.32091 + 0.636119i
\(317\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(318\) −1.38084 0.425934i −1.38084 0.425934i
\(319\) 0 0
\(320\) 0 0
\(321\) −1.08786 0.523887i −1.08786 0.523887i
\(322\) −0.425270 0.131178i −0.425270 0.131178i
\(323\) 0 0
\(324\) 0.158322 + 0.274221i 0.158322 + 0.274221i
\(325\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(326\) 0.149460 1.99441i 0.149460 1.99441i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(335\) 0 0
\(336\) 0.455573 0.571270i 0.455573 0.571270i
\(337\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(338\) −2.62285 0.395331i −2.62285 0.395331i
\(339\) 0 0
\(340\) 0 0
\(341\) 2.27728 0.702449i 2.27728 0.702449i
\(342\) 0 0
\(343\) −0.900969 0.433884i −0.900969 0.433884i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) −1.48883 + 1.01507i −1.48883 + 1.01507i −0.500000 + 0.866025i \(0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(348\) 0 0
\(349\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(350\) 0.623490 0.781831i 0.623490 0.781831i
\(351\) −1.27649 + 1.60066i −1.27649 + 1.60066i
\(352\) −1.40097 + 1.29991i −1.40097 + 1.29991i
\(353\) 0.988831 0.149042i 0.988831 0.149042i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −0.162592 + 0.712362i −0.162592 + 0.712362i
\(357\) 0.266948 0.680173i 0.266948 0.680173i
\(358\) 0 0
\(359\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(360\) 0 0
\(361\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(362\) 0 0
\(363\) −1.74618 + 0.840918i −1.74618 + 0.840918i
\(364\) 1.82624 + 0.563320i 1.82624 + 0.563320i
\(365\) 0 0
\(366\) 0 0
\(367\) 1.57906 + 0.487076i 1.57906 + 0.487076i 0.955573 0.294755i \(-0.0952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(368\) −0.425270 0.131178i −0.425270 0.131178i
\(369\) 0 0
\(370\) 0 0
\(371\) −0.147791 + 1.97213i −0.147791 + 1.97213i
\(372\) −0.820914 + 0.395331i −0.820914 + 0.395331i
\(373\) −0.955573 1.65510i −0.955573 1.65510i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(374\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.785286 0.728639i 0.785286 0.728639i
\(379\) 0.222521 0.974928i 0.222521 0.974928i −0.733052 0.680173i \(-0.761905\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(384\) 0.455573 0.571270i 0.455573 0.571270i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i 0.955573 0.294755i \(-0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(390\) 0 0
\(391\) −0.445042 −0.445042
\(392\) −0.900969 0.433884i −0.900969 0.433884i
\(393\) −0.325184 −0.325184
\(394\) 0 0
\(395\) 0 0
\(396\) −0.736007 + 0.501801i −0.736007 + 0.501801i
\(397\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(398\) −1.23305 1.54620i −1.23305 1.54620i
\(399\) 0 0
\(400\) 0.623490 0.781831i 0.623490 0.781831i
\(401\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(402\) 0 0
\(403\) −1.74698 1.62096i −1.74698 1.62096i
\(404\) −0.367711 0.250701i −0.367711 0.250701i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.266948 0.680173i 0.266948 0.680173i
\(409\) −0.147791 + 1.97213i −0.147791 + 1.97213i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(410\) 0 0
\(411\) −0.266948 0.462368i −0.266948 0.462368i
\(412\) 0 0
\(413\) 0 0
\(414\) −0.186893 0.0900030i −0.186893 0.0900030i
\(415\) 0 0
\(416\) 1.82624 + 0.563320i 1.82624 + 0.563320i
\(417\) −1.02366 0.315758i −1.02366 0.315758i
\(418\) 0 0
\(419\) 1.32091 + 0.636119i 1.32091 + 0.636119i 0.955573 0.294755i \(-0.0952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(420\) 0 0
\(421\) −1.12349 + 0.541044i −1.12349 + 0.541044i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(422\) 0.900969 + 1.56052i 0.900969 + 1.56052i
\(423\) 0 0
\(424\) −0.147791 + 1.97213i −0.147791 + 1.97213i
\(425\) 0.365341 0.930874i 0.365341 0.930874i
\(426\) 0.321552 + 1.40881i 0.321552 + 1.40881i
\(427\) 0 0
\(428\) −0.367711 + 1.61105i −0.367711 + 1.61105i
\(429\) 2.20507 + 1.50339i 2.20507 + 1.50339i
\(430\) 0 0
\(431\) 0.988831 0.149042i 0.988831 0.149042i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(432\) 0.785286 0.728639i 0.785286 0.728639i
\(433\) −0.277479 + 0.347948i −0.277479 + 0.347948i −0.900969 0.433884i \(-0.857143\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(434\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −1.40097 + 0.432142i −1.40097 + 0.432142i −0.900969 0.433884i \(-0.857143\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(440\) 0 0
\(441\) −0.385113 0.262566i −0.385113 0.262566i
\(442\) 1.91115 1.91115
\(443\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) 0.332879 + 0.417417i 0.332879 + 0.417417i
\(448\) −0.900969 0.433884i −0.900969 0.433884i
\(449\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(450\) 0.341678 0.317031i 0.341678 0.317031i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 0.440071 1.92808i 0.440071 1.92808i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.162592 + 0.414278i −0.162592 + 0.414278i −0.988831 0.149042i \(-0.952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(458\) −0.134659 + 1.79690i −0.134659 + 1.79690i
\(459\) 0.535628 0.927735i 0.535628 0.927735i
\(460\) 0 0
\(461\) 1.78181 0.858075i 1.78181 0.858075i 0.826239 0.563320i \(-0.190476\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(462\) −1.02366 0.949820i −1.02366 0.949820i
\(463\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(468\) 0.802576 + 0.386500i 0.802576 + 0.386500i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.535628 + 0.927735i 0.535628 + 0.927735i
\(472\) 0 0
\(473\) 0 0
\(474\) −0.391374 + 0.997204i −0.391374 + 0.997204i
\(475\) 0 0
\(476\) −0.988831 0.149042i −0.988831 0.149042i
\(477\) −0.205119 + 0.898684i −0.205119 + 0.898684i
\(478\) 0 0
\(479\) 0.326239 + 0.302705i 0.326239 + 0.302705i 0.826239 0.563320i \(-0.190476\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0.0723603 0.317031i 0.0723603 0.317031i
\(484\) 1.65379 + 2.07379i 1.65379 + 2.07379i
\(485\) 0 0
\(486\) 0.693950 0.473127i 0.693950 0.473127i
\(487\) −0.365341 0.930874i −0.365341 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(488\) 0 0
\(489\) 1.46136 1.46136
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(497\) 1.78181 0.858075i 1.78181 0.858075i
\(498\) 0 0
\(499\) 1.07473 0.997204i 1.07473 0.997204i 0.0747301 0.997204i \(-0.476190\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) −0.0800550 0.0742802i −0.0800550 0.0742802i
\(502\) 0 0
\(503\) −0.367711 + 1.61105i −0.367711 + 1.61105i 0.365341 + 0.930874i \(0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(504\) −0.385113 0.262566i −0.385113 0.262566i
\(505\) 0 0
\(506\) −0.310737 + 0.791745i −0.310737 + 0.791745i
\(507\) 0.144836 1.93270i 0.144836 1.93270i
\(508\) 0 0
\(509\) 0.222521 + 0.385418i 0.222521 + 0.385418i 0.955573 0.294755i \(-0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.900969 0.433884i −0.900969 0.433884i
\(513\) 0 0
\(514\) −0.955573 0.294755i −0.955573 0.294755i
\(515\) 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 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(524\) 0.0990311 + 0.433884i 0.0990311 + 0.433884i
\(525\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(526\) 0 0
\(527\) 1.03030 + 0.702449i 1.03030 + 0.702449i
\(528\) −1.02366 0.949820i −1.02366 0.949820i
\(529\) 0.792981 0.119523i 0.792981 0.119523i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) −0.527933 0.0795731i −0.527933 0.0795731i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(540\) 0 0
\(541\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −0.988831 0.149042i −0.988831 0.149042i
\(545\) 0 0
\(546\) −0.310737 + 1.36143i −0.310737 + 1.36143i
\(547\) 0.0931869 0.116853i 0.0931869 0.116853i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(548\) −0.535628 + 0.496990i −0.535628 + 0.496990i
\(549\) 0 0
\(550\) −1.40097 1.29991i −1.40097 1.29991i
\(551\) 0 0
\(552\) 0.0723603 0.317031i 0.0723603 0.317031i
\(553\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(554\) 0 0
\(555\) 0 0
\(556\) −0.109562 + 1.46200i −0.109562 + 1.46200i
\(557\) 0.988831 1.71271i 0.988831 1.71271i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(558\) 0.290611 + 0.503353i 0.290611 + 0.503353i
\(559\) 0 0
\(560\) 0 0
\(561\) −1.25815 0.605893i −1.25815 0.605893i
\(562\) −0.0747301 0.997204i −0.0747301 0.997204i
\(563\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −1.72188 0.829215i −1.72188 0.829215i
\(567\) 0.232116 + 0.215372i 0.232116 + 0.215372i
\(568\) 1.78181 0.858075i 1.78181 0.858075i
\(569\) −0.955573 1.65510i −0.955573 1.65510i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(570\) 0 0
\(571\) 0.0931869 1.24349i 0.0931869 1.24349i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(572\) 1.33440 3.40000i 1.33440 3.40000i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.0990311 0.433884i 0.0990311 0.433884i
\(576\) −0.385113 0.262566i −0.385113 0.262566i
\(577\) −1.21135 1.12397i −1.21135 1.12397i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(578\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 3.73738 + 0.563320i 3.73738 + 0.563320i
\(584\) 0 0
\(585\) 0 0
\(586\) −1.40097 + 0.432142i −1.40097 + 0.432142i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.266948 0.680173i 0.266948 0.680173i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.63402 0.246289i −1.63402 0.246289i −0.733052 0.680173i \(-0.761905\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(594\) −1.27649 1.60066i −1.27649 1.60066i
\(595\) 0 0
\(596\) 0.455573 0.571270i 0.455573 0.571270i
\(597\) 1.05929 0.982878i 1.05929 0.982878i
\(598\) 0.841040 0.126766i 0.841040 0.126766i
\(599\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(600\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(601\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) 0.162592 0.281618i 0.162592 0.281618i
\(607\) 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
\(612\) −0.445396 0.137386i −0.445396 0.137386i
\(613\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i 0.365341 0.930874i \(-0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(617\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(618\) 0 0
\(619\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(620\) 0 0
\(621\) 0.174178 0.443797i 0.174178 0.443797i
\(622\) 0.222521 + 0.974928i 0.222521 + 0.974928i
\(623\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i
\(624\) −0.310737 + 1.36143i −0.310737 + 1.36143i
\(625\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.07473 0.997204i 1.07473 0.997204i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(632\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(633\) −1.08786 + 0.741692i −1.08786 + 0.741692i
\(634\) 0 0
\(635\) 0 0
\(636\) −1.44504 −1.44504
\(637\) 1.91115 1.91115
\(638\) 0 0
\(639\) 0.880843 0.271704i 0.880843 0.271704i
\(640\) 0 0
\(641\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(642\) −1.19395 0.179959i −1.19395 0.179959i
\(643\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i 0.826239 0.563320i \(-0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(644\) −0.445042 −0.445042
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(648\) 0.232116 + 0.215372i 0.232116 + 0.215372i
\(649\) 0 0
\(650\) −0.425270 + 1.86323i −0.425270 + 1.86323i
\(651\) −0.667917 + 0.619736i −0.667917 + 0.619736i
\(652\) −0.445042 1.94986i −0.445042 1.94986i
\(653\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(660\) 0 0
\(661\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(662\) 0 0
\(663\) 0.104356 + 1.39254i 0.104356 + 1.39254i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.0747301 + 0.129436i −0.0747301 + 0.129436i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.266948 0.680173i 0.266948 0.680173i
\(673\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(674\) 0 0
\(675\) 0.785286 + 0.728639i 0.785286 + 0.728639i
\(676\) −2.62285 + 0.395331i −2.62285 + 0.395331i
\(677\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 1.42890 + 0.215372i 1.42890 + 0.215372i
\(682\) 1.96906 1.34248i 1.96906 1.34248i
\(683\) −0.722521 1.84095i −0.722521 1.84095i −0.500000 0.866025i \(-0.666667\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −0.988831 0.149042i −0.988831 0.149042i
\(687\) −1.31664 −1.31664
\(688\) 0 0
\(689\) −1.38084 3.51833i −1.38084 3.51833i
\(690\) 0 0
\(691\) −1.23305 0.185853i −1.23305 0.185853i −0.500000 0.866025i \(-0.666667\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(692\) 0 0
\(693\) −0.555400 + 0.696449i −0.555400 + 0.696449i
\(694\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) −1.48883 1.01507i −1.48883 1.01507i
\(699\) 0 0
\(700\) 0.365341 0.930874i 0.365341 0.930874i
\(701\) 0.440071 + 1.92808i 0.440071 + 1.92808i 0.365341 + 0.930874i \(0.380952\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(702\) −0.747972 + 1.90580i −0.747972 + 1.90580i
\(703\) 0 0
\(704\) −0.955573 + 1.65510i −0.955573 + 1.65510i
\(705\) 0 0
\(706\) 0.900969 0.433884i 0.900969 0.433884i
\(707\) −0.425270 0.131178i −0.425270 0.131178i
\(708\) 0 0
\(709\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(710\) 0 0
\(711\) 0.652997 + 0.201423i 0.652997 + 0.201423i
\(712\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i
\(713\) 0.500000 + 0.240787i 0.500000 + 0.240787i
\(714\) 0.0546039 0.728639i 0.0546039 0.728639i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −0.222521 + 0.974928i −0.222521 + 0.974928i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) −1.42074 + 1.31825i −1.42074 + 1.31825i
\(727\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(728\) 1.91115 1.91115
\(729\) 0.580055 + 0.727366i 0.580055 + 0.727366i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(734\) 1.65248 1.65248
\(735\) 0 0
\(736\) −0.445042 −0.445042
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 0.440071 + 1.92808i 0.440071 + 1.92808i
\(743\) 0.455573 0.571270i 0.455573 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(744\) −0.667917 + 0.619736i −0.667917 + 0.619736i
\(745\) 0 0
\(746\) −1.40097 1.29991i −1.40097 1.29991i
\(747\) 0 0
\(748\) −0.425270 + 1.86323i −0.425270 + 1.86323i
\(749\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(750\) 0 0
\(751\) −0.535628 + 1.36476i −0.535628 + 1.36476i 0.365341 + 0.930874i \(0.380952\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.535628 0.927735i 0.535628 0.927735i
\(757\) 0.900969 + 0.433884i 0.900969 + 0.433884i 0.826239 0.563320i \(-0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(758\) −0.0747301 0.997204i −0.0747301 0.997204i
\(759\) −0.593864 0.183183i −0.593864 0.183183i
\(760\) 0 0
\(761\) 0.0111692 + 0.149042i 0.0111692 + 0.149042i 1.00000 \(0\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.266948 0.680173i 0.266948 0.680173i
\(769\) 0.222521 + 0.974928i 0.222521 + 0.974928i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(770\) 0 0
\(771\) 0.162592 0.712362i 0.162592 0.712362i
\(772\) 0 0
\(773\) −0.109562 0.101659i −0.109562 0.101659i 0.623490 0.781831i \(-0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(774\) 0 0
\(775\) −0.914101 + 0.848162i −0.914101 + 0.848162i
\(776\) 0 0
\(777\) 0 0
\(778\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i
\(779\) 0 0
\(780\) 0 0
\(781\) −1.38084 3.51833i −1.38084 3.51833i
\(782\) −0.425270 + 0.131178i −0.425270 + 0.131178i
\(783\) 0 0
\(784\) −0.988831 0.149042i −0.988831 0.149042i
\(785\) 0 0
\(786\) −0.310737 + 0.0958497i −0.310737 + 0.0958497i
\(787\) −0.658322 1.67738i −0.658322 1.67738i −0.733052 0.680173i \(-0.761905\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) −0.555400 + 0.696449i −0.555400 + 0.696449i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −1.63402 1.11406i −1.63402 1.11406i
\(797\) 0.440071 1.92808i 0.440071 1.92808i 0.0747301 0.997204i \(-0.476190\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.365341 0.930874i 0.365341 0.930874i
\(801\) −0.0254511 + 0.339621i −0.0254511 + 0.339621i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) −2.14715 1.03401i −2.14715 1.03401i
\(807\) 0 0
\(808\) −0.425270 0.131178i −0.425270 0.131178i
\(809\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(810\) 0 0
\(811\) 1.78181 + 0.858075i 1.78181 + 0.858075i 0.955573 + 0.294755i \(0.0952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0.0546039 0.728639i 0.0546039 0.728639i
\(817\) 0 0
\(818\) 0.440071 + 1.92808i 0.440071 + 1.92808i
\(819\) 0.880843 + 0.132766i 0.880843 + 0.132766i
\(820\) 0 0
\(821\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(822\) −0.391374 0.363142i −0.391374 0.363142i
\(823\) −0.722521 + 0.108903i −0.722521 + 0.108903i −0.500000 0.866025i \(-0.666667\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(824\) 0 0
\(825\) 0.870666 1.09178i 0.870666 1.09178i
\(826\) 0 0
\(827\) 1.03030 + 1.29196i 1.03030 + 1.29196i 0.955573 + 0.294755i \(0.0952381\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(828\) −0.205119 0.0309167i −0.205119 0.0309167i
\(829\) 1.36534 0.930874i 1.36534 0.930874i 0.365341 0.930874i \(-0.380952\pi\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 1.91115 1.91115
\(833\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(834\) −1.07126 −1.07126
\(835\) 0 0
\(836\) 0 0
\(837\) −1.10372 + 0.752502i −1.10372 + 0.752502i
\(838\) 1.44973 + 0.218511i 1.44973 + 0.218511i
\(839\) −1.12349 1.40881i −1.12349 1.40881i −0.900969 0.433884i \(-0.857143\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(840\) 0 0
\(841\) 0.623490 0.781831i 0.623490 0.781831i
\(842\) −0.914101 + 0.848162i −0.914101 + 0.848162i
\(843\) 0.722521 0.108903i 0.722521 0.108903i
\(844\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(845\) 0 0
\(846\) 0 0
\(847\) 2.19158 + 1.49419i 2.19158 + 1.49419i
\(848\) 0.440071 + 1.92808i 0.440071 + 1.92808i
\(849\) 0.510177 1.29991i 0.510177 1.29991i
\(850\) 0.0747301 0.997204i 0.0747301 0.997204i
\(851\) 0 0
\(852\) 0.722521 + 1.25144i 0.722521 + 1.25144i
\(853\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) 0.123490 + 1.64786i 0.123490 + 1.64786i
\(857\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(858\) 2.55023 + 0.786643i 2.55023 + 0.786643i
\(859\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.900969 0.433884i 0.900969 0.433884i
\(863\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(864\) 0.535628 0.927735i 0.535628 0.927735i
\(865\) 0 0
\(866\) −0.162592 + 0.414278i −0.162592 + 0.414278i
\(867\) −0.162592 0.712362i −0.162592 0.712362i
\(868\) 1.03030 + 0.702449i 1.03030 + 0.702449i
\(869\) 0.623490 2.73169i 0.623490 2.73169i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(878\) −1.21135 + 0.825886i −1.21135 + 0.825886i
\(879\) −0.391374 0.997204i −0.391374 0.997204i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.445396 0.137386i −0.445396 0.137386i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 1.82624 0.563320i 1.82624 0.563320i
\(885\) 0 0
\(886\) 0 0
\(887\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) 0.443608 0.411608i 0.443608 0.411608i
\(892\) 0 0
\(893\) 0 0
\(894\) 0.441126 + 0.300754i 0.441126 + 0.300754i
\(895\) 0 0
\(896\) −0.988831 0.149042i −0.988831 0.149042i
\(897\) 0.138291 + 0.605893i 0.138291 + 0.605893i
\(898\) 0 0
\(899\) 0 0
\(900\) 0.233052 0.403658i 0.233052 0.403658i
\(901\) 0.988831 + 1.71271i 0.988831 + 1.71271i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(908\) −0.147791 1.97213i −0.147791 1.97213i
\(909\) −0.186893 0.0900030i −0.186893 0.0900030i
\(910\) 0 0
\(911\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i
\(915\) 0 0
\(916\) 0.400969 + 1.75676i 0.400969 + 1.75676i
\(917\) 0.222521 + 0.385418i 0.222521 + 0.385418i
\(918\) 0.238377 1.04440i 0.238377 1.04440i
\(919\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 1.44973 1.34515i 1.44973 1.34515i
\(923\) −2.35654 + 2.95501i −2.35654 + 2.95501i
\(924\) −1.25815 0.605893i −1.25815 0.605893i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.698220 + 0.215372i −0.698220 + 0.215372i
\(934\) 0 0
\(935\) 0 0
\(936\) 0.880843 + 0.132766i 0.880843 + 0.132766i
\(937\) 0.777479 + 0.974928i 0.777479 + 0.974928i 1.00000 \(0\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(942\) 0.785286 + 0.728639i 0.785286 + 0.728639i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.365341 + 0.930874i −0.365341 + 0.930874i 0.623490 + 0.781831i \(0.285714\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(948\) −0.0800550 + 1.06826i −0.0800550 + 1.06826i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) −0.988831 + 0.149042i −0.988831 + 0.149042i
\(953\) −0.134659 0.0648483i −0.134659 0.0648483i 0.365341 0.930874i \(-0.380952\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(954\) 0.0688859 + 0.919218i 0.0688859 + 0.919218i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(959\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(960\) 0 0
\(961\) −0.277479 0.480608i −0.277479 0.480608i
\(962\) 0 0
\(963\) −0.0575591 + 0.768072i −0.0575591 + 0.768072i
\(964\) 0 0
\(965\) 0 0
\(966\) −0.0243010 0.324275i −0.0243010 0.324275i
\(967\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(968\) 2.19158 + 1.49419i 2.19158 + 1.49419i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(972\) 0.523663 0.656652i 0.523663 0.656652i
\(973\) 0.326239 + 1.42935i 0.326239 + 1.42935i
\(974\) −0.623490 0.781831i −0.623490 0.781831i
\(975\) −1.38084 0.208129i −1.38084 0.208129i
\(976\) 0 0
\(977\) −0.162592 0.414278i −0.162592 0.414278i 0.826239 0.563320i \(-0.190476\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(978\) 1.39644 0.430745i 1.39644 0.430745i
\(979\) 1.39644 1.39644
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.698220 + 1.77904i 0.698220 + 1.77904i 0.623490 + 0.781831i \(0.285714\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −0.109562 0.101659i −0.109562 0.101659i 0.623490 0.781831i \(-0.285714\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(992\) 1.03030 + 0.702449i 1.03030 + 0.702449i
\(993\) 0 0
\(994\) 1.44973 1.34515i 1.44973 1.34515i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(998\) 0.733052 1.26968i 0.733052 1.26968i
\(999\) 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.1495.1 yes 12
4.3 odd 2 3332.1.cc.a.1495.1 12
17.16 even 2 3332.1.cc.a.1495.1 12
49.2 even 21 inner 3332.1.cc.b.2991.1 yes 12
68.67 odd 2 CM 3332.1.cc.b.1495.1 yes 12
196.51 odd 42 3332.1.cc.a.2991.1 yes 12
833.492 even 42 3332.1.cc.a.2991.1 yes 12
3332.2991 odd 42 inner 3332.1.cc.b.2991.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.1.cc.a.1495.1 12 4.3 odd 2
3332.1.cc.a.1495.1 12 17.16 even 2
3332.1.cc.a.2991.1 yes 12 196.51 odd 42
3332.1.cc.a.2991.1 yes 12 833.492 even 42
3332.1.cc.b.1495.1 yes 12 1.1 even 1 trivial
3332.1.cc.b.1495.1 yes 12 68.67 odd 2 CM
3332.1.cc.b.2991.1 yes 12 49.2 even 21 inner
3332.1.cc.b.2991.1 yes 12 3332.2991 odd 42 inner