Properties

Label 3332.1.cc.b.2515.1
Level $3332$
Weight $1$
Character 3332.2515
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 2515.1
Root \(0.955573 - 0.294755i\) of defining polynomial
Character \(\chi\) \(=\) 3332.2515
Dual form 3332.1.cc.b.2447.1

$q$-expansion

comment: q-expansion
 
sage: f.q_expansion() # note that sage often uses an isomorphic number field
 
gp: mfcoefs(f, 20)
 
\(f(q)\) \(=\) \(q+(0.365341 + 0.930874i) q^{2} +(0.0111692 + 0.149042i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-0.134659 + 0.0648483i) q^{6} +(-0.900969 - 0.433884i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.966742 - 0.145713i) q^{9} +O(q^{10})\) \(q+(0.365341 + 0.930874i) q^{2} +(0.0111692 + 0.149042i) q^{3} +(-0.733052 + 0.680173i) q^{4} +(-0.134659 + 0.0648483i) q^{6} +(-0.900969 - 0.433884i) q^{7} +(-0.900969 - 0.433884i) q^{8} +(0.966742 - 0.145713i) q^{9} +(-0.722521 - 0.108903i) q^{11} +(-0.109562 - 0.101659i) q^{12} +(0.455573 - 0.571270i) q^{13} +(0.0747301 - 0.997204i) q^{14} +(0.0747301 - 0.997204i) q^{16} +(0.955573 - 0.294755i) q^{17} +(0.488831 + 0.846680i) q^{18} +(0.0546039 - 0.139129i) q^{21} +(-0.162592 - 0.712362i) q^{22} +(1.19158 + 0.367554i) q^{23} +(0.0546039 - 0.139129i) q^{24} +(0.365341 - 0.930874i) q^{25} +(0.698220 + 0.215372i) q^{26} +(0.0657731 + 0.288171i) q^{27} +(0.955573 - 0.294755i) q^{28} +(0.900969 + 1.56052i) q^{31} +(0.955573 - 0.294755i) q^{32} +(0.00816111 - 0.108903i) q^{33} +(0.623490 + 0.781831i) q^{34} +(-0.609562 + 0.764367i) q^{36} +(0.0902318 + 0.0615190i) q^{39} +0.149460 q^{42} +(0.603718 - 0.411608i) q^{44} +(0.0931869 + 1.24349i) q^{46} +0.149460 q^{48} +(0.623490 + 0.781831i) q^{49} +1.00000 q^{50} +(0.0546039 + 0.139129i) q^{51} +(0.0546039 + 0.728639i) q^{52} +(-1.21135 + 1.12397i) q^{53} +(-0.244221 + 0.166507i) q^{54} +(0.623490 + 0.781831i) q^{56} +(-1.12349 + 1.40881i) q^{62} +(-0.934227 - 0.288171i) q^{63} +(0.623490 + 0.781831i) q^{64} +(0.104356 - 0.0321896i) q^{66} +(-0.500000 + 0.866025i) q^{68} +(-0.0414721 + 0.181701i) q^{69} +(-0.367711 - 1.61105i) q^{71} +(-0.934227 - 0.288171i) q^{72} +(0.142820 + 0.0440542i) q^{75} +(0.603718 + 0.411608i) q^{77} +(-0.0243010 + 0.106470i) q^{78} +(0.988831 - 1.71271i) q^{79} +(0.892012 - 0.275149i) q^{81} +(0.0546039 + 0.139129i) q^{84} +(0.603718 + 0.411608i) q^{88} +(-0.147791 + 0.0222759i) q^{89} +(-0.658322 + 0.317031i) q^{91} +(-1.12349 + 0.541044i) q^{92} +(-0.222521 + 0.151712i) q^{93} +(0.0546039 + 0.139129i) q^{96} +(-0.500000 + 0.866025i) q^{98} -0.714360 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 12 q + q^{2} + 13 q^{3} + q^{4} - 5 q^{6} - 2 q^{7} - 2 q^{8} + 14 q^{9}+O(q^{10}) \) 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 \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(885\) \(1667\)
\(\chi(n)\) \(-1\) \(e\left(\frac{10}{21}\right)\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(3\) 0.0111692 + 0.149042i 0.0111692 + 0.149042i 1.00000 \(0\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(4\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(5\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(6\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(7\) −0.900969 0.433884i −0.900969 0.433884i
\(8\) −0.900969 0.433884i −0.900969 0.433884i
\(9\) 0.966742 0.145713i 0.966742 0.145713i
\(10\) 0 0
\(11\) −0.722521 0.108903i −0.722521 0.108903i −0.222521 0.974928i \(-0.571429\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(12\) −0.109562 0.101659i −0.109562 0.101659i
\(13\) 0.455573 0.571270i 0.455573 0.571270i −0.500000 0.866025i \(-0.666667\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(14\) 0.0747301 0.997204i 0.0747301 0.997204i
\(15\) 0 0
\(16\) 0.0747301 0.997204i 0.0747301 0.997204i
\(17\) 0.955573 0.294755i 0.955573 0.294755i
\(18\) 0.488831 + 0.846680i 0.488831 + 0.846680i
\(19\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(20\) 0 0
\(21\) 0.0546039 0.139129i 0.0546039 0.139129i
\(22\) −0.162592 0.712362i −0.162592 0.712362i
\(23\) 1.19158 + 0.367554i 1.19158 + 0.367554i 0.826239 0.563320i \(-0.190476\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(24\) 0.0546039 0.139129i 0.0546039 0.139129i
\(25\) 0.365341 0.930874i 0.365341 0.930874i
\(26\) 0.698220 + 0.215372i 0.698220 + 0.215372i
\(27\) 0.0657731 + 0.288171i 0.0657731 + 0.288171i
\(28\) 0.955573 0.294755i 0.955573 0.294755i
\(29\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(30\) 0 0
\(31\) 0.900969 + 1.56052i 0.900969 + 1.56052i 0.826239 + 0.563320i \(0.190476\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(32\) 0.955573 0.294755i 0.955573 0.294755i
\(33\) 0.00816111 0.108903i 0.00816111 0.108903i
\(34\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(35\) 0 0
\(36\) −0.609562 + 0.764367i −0.609562 + 0.764367i
\(37\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(38\) 0 0
\(39\) 0.0902318 + 0.0615190i 0.0902318 + 0.0615190i
\(40\) 0 0
\(41\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(42\) 0.149460 0.149460
\(43\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(44\) 0.603718 0.411608i 0.603718 0.411608i
\(45\) 0 0
\(46\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i
\(47\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(48\) 0.149460 0.149460
\(49\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(50\) 1.00000 1.00000
\(51\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i
\(52\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i
\(53\) −1.21135 + 1.12397i −1.21135 + 1.12397i −0.222521 + 0.974928i \(0.571429\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(54\) −0.244221 + 0.166507i −0.244221 + 0.166507i
\(55\) 0 0
\(56\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(57\) 0 0
\(58\) 0 0
\(59\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(60\) 0 0
\(61\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(62\) −1.12349 + 1.40881i −1.12349 + 1.40881i
\(63\) −0.934227 0.288171i −0.934227 0.288171i
\(64\) 0.623490 + 0.781831i 0.623490 + 0.781831i
\(65\) 0 0
\(66\) 0.104356 0.0321896i 0.104356 0.0321896i
\(67\) 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
\(69\) −0.0414721 + 0.181701i −0.0414721 + 0.181701i
\(70\) 0 0
\(71\) −0.367711 1.61105i −0.367711 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(72\) −0.934227 0.288171i −0.934227 0.288171i
\(73\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(74\) 0 0
\(75\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(76\) 0 0
\(77\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(78\) −0.0243010 + 0.106470i −0.0243010 + 0.106470i
\(79\) 0.988831 1.71271i 0.988831 1.71271i 0.365341 0.930874i \(-0.380952\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(80\) 0 0
\(81\) 0.892012 0.275149i 0.892012 0.275149i
\(82\) 0 0
\(83\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(84\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i
\(85\) 0 0
\(86\) 0 0
\(87\) 0 0
\(88\) 0.603718 + 0.411608i 0.603718 + 0.411608i
\(89\) −0.147791 + 0.0222759i −0.147791 + 0.0222759i −0.222521 0.974928i \(-0.571429\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(90\) 0 0
\(91\) −0.658322 + 0.317031i −0.658322 + 0.317031i
\(92\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(93\) −0.222521 + 0.151712i −0.222521 + 0.151712i
\(94\) 0 0
\(95\) 0 0
\(96\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i
\(97\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(98\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(99\) −0.714360 −0.714360
\(100\) 0.365341 + 0.930874i 0.365341 + 0.930874i
\(101\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i 0.826239 + 0.563320i \(0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(102\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(103\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(104\) −0.658322 + 0.317031i −0.658322 + 0.317031i
\(105\) 0 0
\(106\) −1.48883 0.716983i −1.48883 0.716983i
\(107\) 1.44973 0.218511i 1.44973 0.218511i 0.623490 0.781831i \(-0.285714\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(108\) −0.244221 0.166507i −0.244221 0.166507i
\(109\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(113\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 0 0
\(117\) 0.357180 0.618654i 0.357180 0.618654i
\(118\) 0 0
\(119\) −0.988831 0.149042i −0.988831 0.149042i
\(120\) 0 0
\(121\) −0.445396 0.137386i −0.445396 0.137386i
\(122\) 0 0
\(123\) 0 0
\(124\) −1.72188 0.531130i −1.72188 0.531130i
\(125\) 0 0
\(126\) −0.0730607 0.974928i −0.0730607 0.974928i
\(127\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(128\) −0.500000 + 0.866025i −0.500000 + 0.866025i
\(129\) 0 0
\(130\) 0 0
\(131\) 0.0931869 1.24349i 0.0931869 1.24349i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(132\) 0.0680900 + 0.0853822i 0.0680900 + 0.0853822i
\(133\) 0 0
\(134\) 0 0
\(135\) 0 0
\(136\) −0.988831 0.149042i −0.988831 0.149042i
\(137\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i 0.623490 0.781831i \(-0.285714\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(138\) −0.184292 + 0.0277776i −0.184292 + 0.0277776i
\(139\) 1.78181 + 0.858075i 1.78181 + 0.858075i 0.955573 + 0.294755i \(0.0952381\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.36534 0.930874i 1.36534 0.930874i
\(143\) −0.391374 + 0.363142i −0.391374 + 0.363142i
\(144\) −0.0730607 0.974928i −0.0730607 0.974928i
\(145\) 0 0
\(146\) 0 0
\(147\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(148\) 0 0
\(149\) 0.0546039 + 0.139129i 0.0546039 + 0.139129i 0.955573 0.294755i \(-0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(150\) 0.0111692 + 0.149042i 0.0111692 + 0.149042i
\(151\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(152\) 0 0
\(153\) 0.880843 0.424191i 0.880843 0.424191i
\(154\) −0.162592 + 0.712362i −0.162592 + 0.712362i
\(155\) 0 0
\(156\) −0.107988 + 0.0162766i −0.107988 + 0.0162766i
\(157\) −1.63402 1.11406i −1.63402 1.11406i −0.900969 0.433884i \(-0.857143\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(158\) 1.95557 + 0.294755i 1.95557 + 0.294755i
\(159\) −0.181049 0.167989i −0.181049 0.167989i
\(160\) 0 0
\(161\) −0.914101 0.848162i −0.914101 0.848162i
\(162\) 0.582018 + 0.729827i 0.582018 + 0.729827i
\(163\) 0.149460 1.99441i 0.149460 1.99441i 0.0747301 0.997204i \(-0.476190\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(164\) 0 0
\(165\) 0 0
\(166\) 0 0
\(167\) −0.425270 + 1.86323i −0.425270 + 1.86323i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(168\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(169\) 0.103718 + 0.454418i 0.103718 + 0.454418i
\(170\) 0 0
\(171\) 0 0
\(172\) 0 0
\(173\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(174\) 0 0
\(175\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(176\) −0.162592 + 0.712362i −0.162592 + 0.712362i
\(177\) 0 0
\(178\) −0.0747301 0.129436i −0.0747301 0.129436i
\(179\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(180\) 0 0
\(181\) 0 0 −0.623490 0.781831i \(-0.714286\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(182\) −0.535628 0.496990i −0.535628 0.496990i
\(183\) 0 0
\(184\) −0.914101 0.848162i −0.914101 0.848162i
\(185\) 0 0
\(186\) −0.222521 0.151712i −0.222521 0.151712i
\(187\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(188\) 0 0
\(189\) 0.0657731 0.288171i 0.0657731 0.288171i
\(190\) 0 0
\(191\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(192\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(193\) 0 0 −0.0747301 0.997204i \(-0.523810\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(194\) 0 0
\(195\) 0 0
\(196\) −0.988831 0.149042i −0.988831 0.149042i
\(197\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(198\) −0.260985 0.664979i −0.260985 0.664979i
\(199\) 0.123490 + 1.64786i 0.123490 + 1.64786i 0.623490 + 0.781831i \(0.285714\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(200\) −0.733052 + 0.680173i −0.733052 + 0.680173i
\(201\) 0 0
\(202\) −1.12349 + 0.541044i −1.12349 + 0.541044i
\(203\) 0 0
\(204\) −0.134659 0.0648483i −0.134659 0.0648483i
\(205\) 0 0
\(206\) 0 0
\(207\) 1.20551 + 0.181701i 1.20551 + 0.181701i
\(208\) −0.535628 0.496990i −0.535628 0.496990i
\(209\) 0 0
\(210\) 0 0
\(211\) −0.277479 0.347948i −0.277479 0.347948i 0.623490 0.781831i \(-0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(212\) 0.123490 1.64786i 0.123490 1.64786i
\(213\) 0.236007 0.0727985i 0.236007 0.0727985i
\(214\) 0.733052 + 1.26968i 0.733052 + 1.26968i
\(215\) 0 0
\(216\) 0.0657731 0.288171i 0.0657731 0.288171i
\(217\) −0.134659 1.79690i −0.134659 1.79690i
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 0.266948 0.680173i 0.266948 0.680173i
\(222\) 0 0
\(223\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(224\) −0.988831 0.149042i −0.988831 0.149042i
\(225\) 0.217550 0.953150i 0.217550 0.953150i
\(226\) 0 0
\(227\) −0.826239 1.43109i −0.826239 1.43109i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(228\) 0 0
\(229\) −0.0332580 + 0.443797i −0.0332580 + 0.443797i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(230\) 0 0
\(231\) −0.0546039 + 0.0945768i −0.0546039 + 0.0945768i
\(232\) 0 0
\(233\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(234\) 0.706381 + 0.106470i 0.706381 + 0.106470i
\(235\) 0 0
\(236\) 0 0
\(237\) 0.266310 + 0.128248i 0.266310 + 0.128248i
\(238\) −0.222521 0.974928i −0.222521 0.974928i
\(239\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(240\) 0 0
\(241\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(242\) −0.0348320 0.464800i −0.0348320 0.464800i
\(243\) 0.158960 + 0.405024i 0.158960 + 0.405024i
\(244\) 0 0
\(245\) 0 0
\(246\) 0 0
\(247\) 0 0
\(248\) −0.134659 1.79690i −0.134659 1.79690i
\(249\) 0 0
\(250\) 0 0
\(251\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(252\) 0.880843 0.424191i 0.880843 0.424191i
\(253\) −0.820914 0.395331i −0.820914 0.395331i
\(254\) 0 0
\(255\) 0 0
\(256\) −0.988831 0.149042i −0.988831 0.149042i
\(257\) 0.733052 + 0.680173i 0.733052 + 0.680173i 0.955573 0.294755i \(-0.0952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0 0
\(261\) 0 0
\(262\) 1.19158 0.367554i 1.19158 0.367554i
\(263\) 0 0 −0.500000 0.866025i \(-0.666667\pi\)
0.500000 + 0.866025i \(0.333333\pi\)
\(264\) −0.0546039 + 0.0945768i −0.0546039 + 0.0945768i
\(265\) 0 0
\(266\) 0 0
\(267\) −0.00497075 0.0217783i −0.00497075 0.0217783i
\(268\) 0 0
\(269\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(270\) 0 0
\(271\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(272\) −0.222521 0.974928i −0.222521 0.974928i
\(273\) −0.0546039 0.0945768i −0.0546039 0.0945768i
\(274\) −0.0332580 + 0.145713i −0.0332580 + 0.145713i
\(275\) −0.365341 + 0.632789i −0.365341 + 0.632789i
\(276\) −0.0931869 0.161404i −0.0931869 0.161404i
\(277\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(278\) −0.147791 + 1.97213i −0.147791 + 1.97213i
\(279\) 1.09839 + 1.37734i 1.09839 + 1.37734i
\(280\) 0 0
\(281\) −0.623490 + 0.781831i −0.623490 + 0.781831i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(282\) 0 0
\(283\) −0.722521 0.108903i −0.722521 0.108903i −0.222521 0.974928i \(-0.571429\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(284\) 1.36534 + 0.930874i 1.36534 + 0.930874i
\(285\) 0 0
\(286\) −0.481024 0.231649i −0.481024 0.231649i
\(287\) 0 0
\(288\) 0.880843 0.424191i 0.880843 0.424191i
\(289\) 0.826239 0.563320i 0.826239 0.563320i
\(290\) 0 0
\(291\) 0 0
\(292\) 0 0
\(293\) −1.97766 −1.97766 −0.988831 0.149042i \(-0.952381\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(294\) −0.134659 0.0648483i −0.134659 0.0648483i
\(295\) 0 0
\(296\) 0 0
\(297\) −0.0161399 0.215372i −0.0161399 0.215372i
\(298\) −0.109562 + 0.101659i −0.109562 + 0.101659i
\(299\) 0.752824 0.513267i 0.752824 0.513267i
\(300\) −0.134659 + 0.0648483i −0.134659 + 0.0648483i
\(301\) 0 0
\(302\) 0 0
\(303\) −0.184292 + 0.0277776i −0.184292 + 0.0277776i
\(304\) 0 0
\(305\) 0 0
\(306\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(307\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(308\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(309\) 0 0
\(310\) 0 0
\(311\) −0.955573 + 0.294755i −0.955573 + 0.294755i −0.733052 0.680173i \(-0.761905\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(312\) −0.0546039 0.0945768i −0.0546039 0.0945768i
\(313\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(314\) 0.440071 1.92808i 0.440071 1.92808i
\(315\) 0 0
\(316\) 0.440071 + 1.92808i 0.440071 + 1.92808i
\(317\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(318\) 0.0902318 0.229907i 0.0902318 0.229907i
\(319\) 0 0
\(320\) 0 0
\(321\) 0.0487597 + 0.213630i 0.0487597 + 0.213630i
\(322\) 0.455573 1.16078i 0.455573 1.16078i
\(323\) 0 0
\(324\) −0.466742 + 0.808421i −0.466742 + 0.808421i
\(325\) −0.365341 0.632789i −0.365341 0.632789i
\(326\) 1.91115 0.589510i 1.91115 0.589510i
\(327\) 0 0
\(328\) 0 0
\(329\) 0 0
\(330\) 0 0
\(331\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(332\) 0 0
\(333\) 0 0
\(334\) −1.88980 + 0.284841i −1.88980 + 0.284841i
\(335\) 0 0
\(336\) −0.134659 0.0648483i −0.134659 0.0648483i
\(337\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(338\) −0.385113 + 0.262566i −0.385113 + 0.262566i
\(339\) 0 0
\(340\) 0 0
\(341\) −0.481024 1.22563i −0.481024 1.22563i
\(342\) 0 0
\(343\) −0.222521 0.974928i −0.222521 0.974928i
\(344\) 0 0
\(345\) 0 0
\(346\) 0 0
\(347\) 0.326239 0.302705i 0.326239 0.302705i −0.500000 0.866025i \(-0.666667\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(348\) 0 0
\(349\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(350\) −0.900969 0.433884i −0.900969 0.433884i
\(351\) 0.194588 + 0.0937086i 0.194588 + 0.0937086i
\(352\) −0.722521 + 0.108903i −0.722521 + 0.108903i
\(353\) −0.826239 0.563320i −0.826239 0.563320i 0.0747301 0.997204i \(-0.476190\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) 0.0931869 0.116853i 0.0931869 0.116853i
\(357\) 0.0111692 0.149042i 0.0111692 0.149042i
\(358\) 0 0
\(359\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(360\) 0 0
\(361\) −0.500000 0.866025i −0.500000 0.866025i
\(362\) 0 0
\(363\) 0.0155017 0.0679173i 0.0155017 0.0679173i
\(364\) 0.266948 0.680173i 0.266948 0.680173i
\(365\) 0 0
\(366\) 0 0
\(367\) −0.535628 + 1.36476i −0.535628 + 1.36476i 0.365341 + 0.930874i \(0.380952\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(368\) 0.455573 1.16078i 0.455573 1.16078i
\(369\) 0 0
\(370\) 0 0
\(371\) 1.57906 0.487076i 1.57906 0.487076i
\(372\) 0.0599289 0.262566i 0.0599289 0.262566i
\(373\) −0.365341 + 0.632789i −0.365341 + 0.632789i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(374\) −0.365341 0.632789i −0.365341 0.632789i
\(375\) 0 0
\(376\) 0 0
\(377\) 0 0
\(378\) 0.292280 0.0440542i 0.292280 0.0440542i
\(379\) −0.623490 + 0.781831i −0.623490 + 0.781831i −0.988831 0.149042i \(-0.952381\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 0 0
\(383\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(384\) −0.134659 0.0648483i −0.134659 0.0648483i
\(385\) 0 0
\(386\) 0 0
\(387\) 0 0
\(388\) 0 0
\(389\) 0.142820 + 1.90580i 0.142820 + 1.90580i 0.365341 + 0.930874i \(0.380952\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(390\) 0 0
\(391\) 1.24698 1.24698
\(392\) −0.222521 0.974928i −0.222521 0.974928i
\(393\) 0.186374 0.186374
\(394\) 0 0
\(395\) 0 0
\(396\) 0.523663 0.485888i 0.523663 0.485888i
\(397\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(398\) −1.48883 + 0.716983i −1.48883 + 0.716983i
\(399\) 0 0
\(400\) −0.900969 0.433884i −0.900969 0.433884i
\(401\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(402\) 0 0
\(403\) 1.30194 + 0.196236i 1.30194 + 0.196236i
\(404\) −0.914101 0.848162i −0.914101 0.848162i
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) 0.0111692 0.149042i 0.0111692 0.149042i
\(409\) 1.57906 0.487076i 1.57906 0.487076i 0.623490 0.781831i \(-0.285714\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(410\) 0 0
\(411\) −0.0111692 + 0.0193456i −0.0111692 + 0.0193456i
\(412\) 0 0
\(413\) 0 0
\(414\) 0.271281 + 1.18856i 0.271281 + 1.18856i
\(415\) 0 0
\(416\) 0.266948 0.680173i 0.266948 0.680173i
\(417\) −0.107988 + 0.275149i −0.107988 + 0.275149i
\(418\) 0 0
\(419\) 0.440071 + 1.92808i 0.440071 + 1.92808i 0.365341 + 0.930874i \(0.380952\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(420\) 0 0
\(421\) 0.400969 1.75676i 0.400969 1.75676i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(422\) 0.222521 0.385418i 0.222521 0.385418i
\(423\) 0 0
\(424\) 1.57906 0.487076i 1.57906 0.487076i
\(425\) 0.0747301 0.997204i 0.0747301 0.997204i
\(426\) 0.153989 + 0.193096i 0.153989 + 0.193096i
\(427\) 0 0
\(428\) −0.914101 + 1.14625i −0.914101 + 1.14625i
\(429\) −0.0584948 0.0542752i −0.0584948 0.0542752i
\(430\) 0 0
\(431\) −0.826239 0.563320i −0.826239 0.563320i 0.0747301 0.997204i \(-0.476190\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(432\) 0.292280 0.0440542i 0.292280 0.0440542i
\(433\) −1.12349 0.541044i −1.12349 0.541044i −0.222521 0.974928i \(-0.571429\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(434\) 1.62349 0.781831i 1.62349 0.781831i
\(435\) 0 0
\(436\) 0 0
\(437\) 0 0
\(438\) 0 0
\(439\) −0.722521 1.84095i −0.722521 1.84095i −0.500000 0.866025i \(-0.666667\pi\)
−0.222521 0.974928i \(-0.571429\pi\)
\(440\) 0 0
\(441\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(442\) 0.730682 0.730682
\(443\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 0 0
\(447\) −0.0201262 + 0.00969225i −0.0201262 + 0.00969225i
\(448\) −0.222521 0.974928i −0.222521 0.974928i
\(449\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(450\) 0.966742 0.145713i 0.966742 0.145713i
\(451\) 0 0
\(452\) 0 0
\(453\) 0 0
\(454\) 1.03030 1.29196i 1.03030 1.29196i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.0931869 1.24349i 0.0931869 1.24349i −0.733052 0.680173i \(-0.761905\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(458\) −0.425270 + 0.131178i −0.425270 + 0.131178i
\(459\) 0.147791 + 0.255981i 0.147791 + 0.255981i
\(460\) 0 0
\(461\) −0.367711 + 1.61105i −0.367711 + 1.61105i 0.365341 + 0.930874i \(0.380952\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(462\) −0.107988 0.0162766i −0.107988 0.0162766i
\(463\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(464\) 0 0
\(465\) 0 0
\(466\) 0 0
\(467\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(468\) 0.158960 + 0.696449i 0.158960 + 0.696449i
\(469\) 0 0
\(470\) 0 0
\(471\) 0.147791 0.255981i 0.147791 0.255981i
\(472\) 0 0
\(473\) 0 0
\(474\) −0.0220888 + 0.294755i −0.0220888 + 0.294755i
\(475\) 0 0
\(476\) 0.826239 0.563320i 0.826239 0.563320i
\(477\) −1.00729 + 1.26310i −1.00729 + 1.26310i
\(478\) 0 0
\(479\) −1.23305 0.185853i −1.23305 0.185853i −0.500000 0.866025i \(-0.666667\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(480\) 0 0
\(481\) 0 0
\(482\) 0 0
\(483\) 0.116202 0.145713i 0.116202 0.145713i
\(484\) 0.419945 0.202235i 0.419945 0.202235i
\(485\) 0 0
\(486\) −0.318951 + 0.295943i −0.318951 + 0.295943i
\(487\) −0.0747301 0.997204i −0.0747301 0.997204i −0.900969 0.433884i \(-0.857143\pi\)
0.826239 0.563320i \(-0.190476\pi\)
\(488\) 0 0
\(489\) 0.298920 0.298920
\(490\) 0 0
\(491\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(492\) 0 0
\(493\) 0 0
\(494\) 0 0
\(495\) 0 0
\(496\) 1.62349 0.781831i 1.62349 0.781831i
\(497\) −0.367711 + 1.61105i −0.367711 + 1.61105i
\(498\) 0 0
\(499\) 1.95557 0.294755i 1.95557 0.294755i 0.955573 0.294755i \(-0.0952381\pi\)
1.00000 \(0\)
\(500\) 0 0
\(501\) −0.282450 0.0425725i −0.282450 0.0425725i
\(502\) 0 0
\(503\) −0.914101 + 1.14625i −0.914101 + 1.14625i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(504\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(505\) 0 0
\(506\) 0.0680900 0.908598i 0.0680900 0.908598i
\(507\) −0.0665690 + 0.0205338i −0.0665690 + 0.0205338i
\(508\) 0 0
\(509\) −0.623490 + 1.07992i −0.623490 + 1.07992i 0.365341 + 0.930874i \(0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −0.222521 0.974928i −0.222521 0.974928i
\(513\) 0 0
\(514\) −0.365341 + 0.930874i −0.365341 + 0.930874i
\(515\) 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 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(524\) 0.777479 + 0.974928i 0.777479 + 0.974928i
\(525\) −0.109562 0.101659i −0.109562 0.101659i
\(526\) 0 0
\(527\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(528\) −0.107988 0.0162766i −0.107988 0.0162766i
\(529\) 0.458528 + 0.312619i 0.458528 + 0.312619i
\(530\) 0 0
\(531\) 0 0
\(532\) 0 0
\(533\) 0 0
\(534\) 0.0184568 0.0125836i 0.0184568 0.0125836i
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 0 0
\(539\) −0.365341 0.632789i −0.365341 0.632789i
\(540\) 0 0
\(541\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) 0.826239 0.563320i 0.826239 0.563320i
\(545\) 0 0
\(546\) 0.0680900 0.0853822i 0.0680900 0.0853822i
\(547\) −1.72188 0.829215i −1.72188 0.829215i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 0.680173i \(-0.761905\pi\)
\(548\) −0.147791 + 0.0222759i −0.147791 + 0.0222759i
\(549\) 0 0
\(550\) −0.722521 0.108903i −0.722521 0.108903i
\(551\) 0 0
\(552\) 0.116202 0.145713i 0.116202 0.145713i
\(553\) −1.63402 + 1.11406i −1.63402 + 1.11406i
\(554\) 0 0
\(555\) 0 0
\(556\) −1.88980 + 0.582926i −1.88980 + 0.582926i
\(557\) −0.826239 1.43109i −0.826239 1.43109i −0.900969 0.433884i \(-0.857143\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(558\) −0.880843 + 1.52566i −0.880843 + 1.52566i
\(559\) 0 0
\(560\) 0 0
\(561\) −0.0243010 0.106470i −0.0243010 0.106470i
\(562\) −0.955573 0.294755i −0.955573 0.294755i
\(563\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −0.162592 0.712362i −0.162592 0.712362i
\(567\) −0.923058 0.139129i −0.923058 0.139129i
\(568\) −0.367711 + 1.61105i −0.367711 + 1.61105i
\(569\) −0.365341 + 0.632789i −0.365341 + 0.632789i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(570\) 0 0
\(571\) −1.72188 + 0.531130i −1.72188 + 0.531130i −0.988831 0.149042i \(-0.952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(572\) 0.0398981 0.532403i 0.0398981 0.532403i
\(573\) 0 0
\(574\) 0 0
\(575\) 0.777479 0.974928i 0.777479 0.974928i
\(576\) 0.716677 + 0.664979i 0.716677 + 0.664979i
\(577\) 1.44973 + 0.218511i 1.44973 + 0.218511i 0.826239 0.563320i \(-0.190476\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(578\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(579\) 0 0
\(580\) 0 0
\(581\) 0 0
\(582\) 0 0
\(583\) 0.997630 0.680173i 0.997630 0.680173i
\(584\) 0 0
\(585\) 0 0
\(586\) −0.722521 1.84095i −0.722521 1.84095i
\(587\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(588\) 0.0111692 0.149042i 0.0111692 0.149042i
\(589\) 0 0
\(590\) 0 0
\(591\) 0 0
\(592\) 0 0
\(593\) −1.21135 + 0.825886i −1.21135 + 0.825886i −0.988831 0.149042i \(-0.952381\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(594\) 0.194588 0.0937086i 0.194588 0.0937086i
\(595\) 0 0
\(596\) −0.134659 0.0648483i −0.134659 0.0648483i
\(597\) −0.244221 + 0.0368104i −0.244221 + 0.0368104i
\(598\) 0.752824 + 0.513267i 0.752824 + 0.513267i
\(599\) 0 0 −0.988831 0.149042i \(-0.952381\pi\)
0.988831 + 0.149042i \(0.0476190\pi\)
\(600\) −0.109562 0.101659i −0.109562 0.101659i
\(601\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 0 0
\(605\) 0 0
\(606\) −0.0931869 0.161404i −0.0931869 0.161404i
\(607\) 0.500000 0.866025i 0.500000 0.866025i −0.500000 0.866025i \(-0.666667\pi\)
1.00000 \(0\)
\(608\) 0 0
\(609\) 0 0
\(610\) 0 0
\(611\) 0 0
\(612\) −0.357180 + 0.910080i −0.357180 + 0.910080i
\(613\) 0.698220 1.77904i 0.698220 1.77904i 0.0747301 0.997204i \(-0.476190\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(614\) 0 0
\(615\) 0 0
\(616\) −0.365341 0.632789i −0.365341 0.632789i
\(617\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(618\) 0 0
\(619\) 0.500000 + 0.866025i 0.500000 + 0.866025i 1.00000 \(0\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(620\) 0 0
\(621\) −0.0275443 + 0.367554i −0.0275443 + 0.367554i
\(622\) −0.623490 0.781831i −0.623490 0.781831i
\(623\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(624\) 0.0680900 0.0853822i 0.0680900 0.0853822i
\(625\) −0.733052 0.680173i −0.733052 0.680173i
\(626\) 0 0
\(627\) 0 0
\(628\) 1.95557 0.294755i 1.95557 0.294755i
\(629\) 0 0
\(630\) 0 0
\(631\) 0 0 0.900969 0.433884i \(-0.142857\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(632\) −1.63402 + 1.11406i −1.63402 + 1.11406i
\(633\) 0.0487597 0.0452424i 0.0487597 0.0452424i
\(634\) 0 0
\(635\) 0 0
\(636\) 0.246980 0.246980
\(637\) 0.730682 0.730682
\(638\) 0 0
\(639\) −0.590232 1.50389i −0.590232 1.50389i
\(640\) 0 0
\(641\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(642\) −0.181049 + 0.123437i −0.181049 + 0.123437i
\(643\) −1.72188 + 0.829215i −1.72188 + 0.829215i −0.733052 + 0.680173i \(0.761905\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(644\) 1.24698 1.24698
\(645\) 0 0
\(646\) 0 0
\(647\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(648\) −0.923058 0.139129i −0.923058 0.139129i
\(649\) 0 0
\(650\) 0.455573 0.571270i 0.455573 0.571270i
\(651\) 0.266310 0.0401398i 0.266310 0.0401398i
\(652\) 1.24698 + 1.56366i 1.24698 + 1.56366i
\(653\) 0 0 0.0747301 0.997204i \(-0.476190\pi\)
−0.0747301 + 0.997204i \(0.523810\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 0 0
\(657\) 0 0
\(658\) 0 0
\(659\) 0 0 −0.222521 0.974928i \(-0.571429\pi\)
0.222521 + 0.974928i \(0.428571\pi\)
\(660\) 0 0
\(661\) −0.658322 + 1.67738i −0.658322 + 1.67738i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(662\) 0 0
\(663\) 0.104356 + 0.0321896i 0.104356 + 0.0321896i
\(664\) 0 0
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −0.955573 1.65510i −0.955573 1.65510i
\(669\) 0 0
\(670\) 0 0
\(671\) 0 0
\(672\) 0.0111692 0.149042i 0.0111692 0.149042i
\(673\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(674\) 0 0
\(675\) 0.292280 + 0.0440542i 0.292280 + 0.0440542i
\(676\) −0.385113 0.262566i −0.385113 0.262566i
\(677\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0 0
\(681\) 0.204064 0.139129i 0.204064 0.139129i
\(682\) 0.965168 0.895545i 0.965168 0.895545i
\(683\) 0.123490 + 1.64786i 0.123490 + 1.64786i 0.623490 + 0.781831i \(0.285714\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 0.826239 0.563320i 0.826239 0.563320i
\(687\) −0.0665160 −0.0665160
\(688\) 0 0
\(689\) 0.0902318 + 1.20406i 0.0902318 + 1.20406i
\(690\) 0 0
\(691\) −1.48883 + 1.01507i −1.48883 + 1.01507i −0.500000 + 0.866025i \(0.666667\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(692\) 0 0
\(693\) 0.643616 + 0.309949i 0.643616 + 0.309949i
\(694\) 0.400969 + 0.193096i 0.400969 + 0.193096i
\(695\) 0 0
\(696\) 0 0
\(697\) 0 0
\(698\) 0.326239 + 0.302705i 0.326239 + 0.302705i
\(699\) 0 0
\(700\) 0.0747301 0.997204i 0.0747301 0.997204i
\(701\) 1.03030 + 1.29196i 1.03030 + 1.29196i 0.955573 + 0.294755i \(0.0952381\pi\)
0.0747301 + 0.997204i \(0.476190\pi\)
\(702\) −0.0161399 + 0.215372i −0.0161399 + 0.215372i
\(703\) 0 0
\(704\) −0.365341 0.632789i −0.365341 0.632789i
\(705\) 0 0
\(706\) 0.222521 0.974928i 0.222521 0.974928i
\(707\) 0.455573 1.16078i 0.455573 1.16078i
\(708\) 0 0
\(709\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(710\) 0 0
\(711\) 0.706381 1.79983i 0.706381 1.79983i
\(712\) 0.142820 + 0.0440542i 0.142820 + 0.0440542i
\(713\) 0.500000 + 2.19064i 0.500000 + 2.19064i
\(714\) 0.142820 0.0440542i 0.142820 0.0440542i
\(715\) 0 0
\(716\) 0 0
\(717\) 0 0
\(718\) 0 0
\(719\) 0.0546039 0.728639i 0.0546039 0.728639i −0.900969 0.433884i \(-0.857143\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 0.623490 0.781831i 0.623490 0.781831i
\(723\) 0 0
\(724\) 0 0
\(725\) 0 0
\(726\) 0.0688859 0.0103829i 0.0688859 0.0103829i
\(727\) 0 0 −0.900969 0.433884i \(-0.857143\pi\)
0.900969 + 0.433884i \(0.142857\pi\)
\(728\) 0.730682 0.730682
\(729\) 0.782450 0.376808i 0.782450 0.376808i
\(730\) 0 0
\(731\) 0 0
\(732\) 0 0
\(733\) −0.365341 0.930874i −0.365341 0.930874i −0.988831 0.149042i \(-0.952381\pi\)
0.623490 0.781831i \(-0.285714\pi\)
\(734\) −1.46610 −1.46610
\(735\) 0 0
\(736\) 1.24698 1.24698
\(737\) 0 0
\(738\) 0 0
\(739\) 0 0 0.733052 0.680173i \(-0.238095\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.03030 + 1.29196i 1.03030 + 1.29196i
\(743\) −0.134659 0.0648483i −0.134659 0.0648483i 0.365341 0.930874i \(-0.380952\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(744\) 0.266310 0.0401398i 0.266310 0.0401398i
\(745\) 0 0
\(746\) −0.722521 0.108903i −0.722521 0.108903i
\(747\) 0 0
\(748\) 0.455573 0.571270i 0.455573 0.571270i
\(749\) −1.40097 0.432142i −1.40097 0.432142i
\(750\) 0 0
\(751\) −0.147791 + 1.97213i −0.147791 + 1.97213i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(752\) 0 0
\(753\) 0 0
\(754\) 0 0
\(755\) 0 0
\(756\) 0.147791 + 0.255981i 0.147791 + 0.255981i
\(757\) 0.222521 + 0.974928i 0.222521 + 0.974928i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(758\) −0.955573 0.294755i −0.955573 0.294755i
\(759\) 0.0497521 0.126766i 0.0497521 0.126766i
\(760\) 0 0
\(761\) 1.82624 + 0.563320i 1.82624 + 0.563320i 1.00000 \(0\)
0.826239 + 0.563320i \(0.190476\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 0 0
\(765\) 0 0
\(766\) 0 0
\(767\) 0 0
\(768\) 0.0111692 0.149042i 0.0111692 0.149042i
\(769\) −0.623490 0.781831i −0.623490 0.781831i 0.365341 0.930874i \(-0.380952\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(770\) 0 0
\(771\) −0.0931869 + 0.116853i −0.0931869 + 0.116853i
\(772\) 0 0
\(773\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(774\) 0 0
\(775\) 1.78181 0.268565i 1.78181 0.268565i
\(776\) 0 0
\(777\) 0 0
\(778\) −1.72188 + 0.829215i −1.72188 + 0.829215i
\(779\) 0 0
\(780\) 0 0
\(781\) 0.0902318 + 1.20406i 0.0902318 + 1.20406i
\(782\) 0.455573 + 1.16078i 0.455573 + 1.16078i
\(783\) 0 0
\(784\) 0.826239 0.563320i 0.826239 0.563320i
\(785\) 0 0
\(786\) 0.0680900 + 0.173490i 0.0680900 + 0.173490i
\(787\) −0.0332580 0.443797i −0.0332580 0.443797i −0.988831 0.149042i \(-0.952381\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0.643616 + 0.309949i 0.643616 + 0.309949i
\(793\) 0 0
\(794\) 0 0
\(795\) 0 0
\(796\) −1.21135 1.12397i −1.21135 1.12397i
\(797\) 1.03030 1.29196i 1.03030 1.29196i 0.0747301 0.997204i \(-0.476190\pi\)
0.955573 0.294755i \(-0.0952381\pi\)
\(798\) 0 0
\(799\) 0 0
\(800\) 0.0747301 0.997204i 0.0747301 0.997204i
\(801\) −0.139630 + 0.0430701i −0.139630 + 0.0430701i
\(802\) 0 0
\(803\) 0 0
\(804\) 0 0
\(805\) 0 0
\(806\) 0.292981 + 1.28363i 0.292981 + 1.28363i
\(807\) 0 0
\(808\) 0.455573 1.16078i 0.455573 1.16078i
\(809\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(810\) 0 0
\(811\) −0.367711 1.61105i −0.367711 1.61105i −0.733052 0.680173i \(-0.761905\pi\)
0.365341 0.930874i \(-0.380952\pi\)
\(812\) 0 0
\(813\) 0 0
\(814\) 0 0
\(815\) 0 0
\(816\) 0.142820 0.0440542i 0.142820 0.0440542i
\(817\) 0 0
\(818\) 1.03030 + 1.29196i 1.03030 + 1.29196i
\(819\) −0.590232 + 0.402413i −0.590232 + 0.402413i
\(820\) 0 0
\(821\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(822\) −0.0220888 0.00332936i −0.0220888 0.00332936i
\(823\) 0.123490 + 0.0841939i 0.123490 + 0.0841939i 0.623490 0.781831i \(-0.285714\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(824\) 0 0
\(825\) −0.0983929 0.0473835i −0.0983929 0.0473835i
\(826\) 0 0
\(827\) 1.32091 0.636119i 1.32091 0.636119i 0.365341 0.930874i \(-0.380952\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(828\) −1.00729 + 0.686757i −1.00729 + 0.686757i
\(829\) 1.07473 0.997204i 1.07473 0.997204i 0.0747301 0.997204i \(-0.476190\pi\)
1.00000 \(0\)
\(830\) 0 0
\(831\) 0 0
\(832\) 0.730682 0.730682
\(833\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(834\) −0.295582 −0.295582
\(835\) 0 0
\(836\) 0 0
\(837\) −0.390438 + 0.362273i −0.390438 + 0.362273i
\(838\) −1.63402 + 1.11406i −1.63402 + 1.11406i
\(839\) 0.400969 0.193096i 0.400969 0.193096i −0.222521 0.974928i \(-0.571429\pi\)
0.623490 + 0.781831i \(0.285714\pi\)
\(840\) 0 0
\(841\) −0.900969 0.433884i −0.900969 0.433884i
\(842\) 1.78181 0.268565i 1.78181 0.268565i
\(843\) −0.123490 0.0841939i −0.123490 0.0841939i
\(844\) 0.440071 + 0.0663300i 0.440071 + 0.0663300i
\(845\) 0 0
\(846\) 0 0
\(847\) 0.341678 + 0.317031i 0.341678 + 0.317031i
\(848\) 1.03030 + 1.29196i 1.03030 + 1.29196i
\(849\) 0.00816111 0.108903i 0.00816111 0.108903i
\(850\) 0.955573 0.294755i 0.955573 0.294755i
\(851\) 0 0
\(852\) −0.123490 + 0.213891i −0.123490 + 0.213891i
\(853\) 0 0 0.222521 0.974928i \(-0.428571\pi\)
−0.222521 + 0.974928i \(0.571429\pi\)
\(854\) 0 0
\(855\) 0 0
\(856\) −1.40097 0.432142i −1.40097 0.432142i
\(857\) 0 0 0.365341 0.930874i \(-0.380952\pi\)
−0.365341 + 0.930874i \(0.619048\pi\)
\(858\) 0.0291528 0.0742802i 0.0291528 0.0742802i
\(859\) 0 0 −0.955573 0.294755i \(-0.904762\pi\)
0.955573 + 0.294755i \(0.0952381\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) 0.222521 0.974928i 0.222521 0.974928i
\(863\) 0 0 0.500000 0.866025i \(-0.333333\pi\)
−0.500000 + 0.866025i \(0.666667\pi\)
\(864\) 0.147791 + 0.255981i 0.147791 + 0.255981i
\(865\) 0 0
\(866\) 0.0931869 1.24349i 0.0931869 1.24349i
\(867\) 0.0931869 + 0.116853i 0.0931869 + 0.116853i
\(868\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(869\) −0.900969 + 1.12978i −0.900969 + 1.12978i
\(870\) 0 0
\(871\) 0 0
\(872\) 0 0
\(873\) 0 0
\(874\) 0 0
\(875\) 0 0
\(876\) 0 0
\(877\) 0 0 0.826239 0.563320i \(-0.190476\pi\)
−0.826239 + 0.563320i \(0.809524\pi\)
\(878\) 1.44973 1.34515i 1.44973 1.34515i
\(879\) −0.0220888 0.294755i −0.0220888 0.294755i
\(880\) 0 0
\(881\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(882\) −0.357180 + 0.910080i −0.357180 + 0.910080i
\(883\) 0 0 1.00000 \(0\)
−1.00000 \(\pi\)
\(884\) 0.266948 + 0.680173i 0.266948 + 0.680173i
\(885\) 0 0
\(886\) 0 0
\(887\) 0.603718 0.411608i 0.603718 0.411608i −0.222521 0.974928i \(-0.571429\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(888\) 0 0
\(889\) 0 0
\(890\) 0 0
\(891\) −0.674462 + 0.101659i −0.674462 + 0.101659i
\(892\) 0 0
\(893\) 0 0
\(894\) −0.0163752 0.0151939i −0.0163752 0.0151939i
\(895\) 0 0
\(896\) 0.826239 0.563320i 0.826239 0.563320i
\(897\) 0.0849068 + 0.106470i 0.0849068 + 0.106470i
\(898\) 0 0
\(899\) 0 0
\(900\) 0.488831 + 0.846680i 0.488831 + 0.846680i
\(901\) −0.826239 + 1.43109i −0.826239 + 1.43109i
\(902\) 0 0
\(903\) 0 0
\(904\) 0 0
\(905\) 0 0
\(906\) 0 0
\(907\) −0.658322 + 1.67738i −0.658322 + 1.67738i 0.0747301 + 0.997204i \(0.476190\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(908\) 1.57906 + 0.487076i 1.57906 + 0.487076i
\(909\) 0.271281 + 1.18856i 0.271281 + 1.18856i
\(910\) 0 0
\(911\) −0.277479 + 1.21572i −0.277479 + 1.21572i 0.623490 + 0.781831i \(0.285714\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(912\) 0 0
\(913\) 0 0
\(914\) 1.19158 0.367554i 1.19158 0.367554i
\(915\) 0 0
\(916\) −0.277479 0.347948i −0.277479 0.347948i
\(917\) −0.623490 + 1.07992i −0.623490 + 1.07992i
\(918\) −0.184292 + 0.231095i −0.184292 + 0.231095i
\(919\) 0 0 −0.733052 0.680173i \(-0.761905\pi\)
0.733052 + 0.680173i \(0.238095\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.63402 + 0.246289i −1.63402 + 0.246289i
\(923\) −1.08786 0.523887i −1.08786 0.523887i
\(924\) −0.0243010 0.106470i −0.0243010 0.106470i
\(925\) 0 0
\(926\) 0 0
\(927\) 0 0
\(928\) 0 0
\(929\) 0 0 −0.365341 0.930874i \(-0.619048\pi\)
0.365341 + 0.930874i \(0.380952\pi\)
\(930\) 0 0
\(931\) 0 0
\(932\) 0 0
\(933\) −0.0546039 0.139129i −0.0546039 0.139129i
\(934\) 0 0
\(935\) 0 0
\(936\) −0.590232 + 0.402413i −0.590232 + 0.402413i
\(937\) 1.62349 0.781831i 1.62349 0.781831i 0.623490 0.781831i \(-0.285714\pi\)
1.00000 \(0\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) 0 0 −0.826239 0.563320i \(-0.809524\pi\)
0.826239 + 0.563320i \(0.190476\pi\)
\(942\) 0.292280 + 0.0440542i 0.292280 + 0.0440542i
\(943\) 0 0
\(944\) 0 0
\(945\) 0 0
\(946\) 0 0
\(947\) −0.0747301 + 0.997204i −0.0747301 + 0.997204i 0.826239 + 0.563320i \(0.190476\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(948\) −0.282450 + 0.0871242i −0.282450 + 0.0871242i
\(949\) 0 0
\(950\) 0 0
\(951\) 0 0
\(952\) 0.826239 + 0.563320i 0.826239 + 0.563320i
\(953\) −0.425270 1.86323i −0.425270 1.86323i −0.500000 0.866025i \(-0.666667\pi\)
0.0747301 0.997204i \(-0.476190\pi\)
\(954\) −1.54379 0.476196i −1.54379 0.476196i
\(955\) 0 0
\(956\) 0 0
\(957\) 0 0
\(958\) −0.277479 1.21572i −0.277479 1.21572i
\(959\) −0.0747301 0.129436i −0.0747301 0.129436i
\(960\) 0 0
\(961\) −1.12349 + 1.94594i −1.12349 + 1.94594i
\(962\) 0 0
\(963\) 1.36967 0.422488i 1.36967 0.422488i
\(964\) 0 0
\(965\) 0 0
\(966\) 0.178094 + 0.0549346i 0.178094 + 0.0549346i
\(967\) 0 0 0.623490 0.781831i \(-0.285714\pi\)
−0.623490 + 0.781831i \(0.714286\pi\)
\(968\) 0.341678 + 0.317031i 0.341678 + 0.317031i
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 0.988831 0.149042i \(-0.0476190\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(972\) −0.392012 0.188783i −0.392012 0.188783i
\(973\) −1.23305 1.54620i −1.23305 1.54620i
\(974\) 0.900969 0.433884i 0.900969 0.433884i
\(975\) 0.0902318 0.0615190i 0.0902318 0.0615190i
\(976\) 0 0
\(977\) 0.0931869 + 1.24349i 0.0931869 + 1.24349i 0.826239 + 0.563320i \(0.190476\pi\)
−0.733052 + 0.680173i \(0.761905\pi\)
\(978\) 0.109208 + 0.278257i 0.109208 + 0.278257i
\(979\) 0.109208 0.109208
\(980\) 0 0
\(981\) 0 0
\(982\) 0 0
\(983\) 0.0546039 + 0.728639i 0.0546039 + 0.728639i 0.955573 + 0.294755i \(0.0952381\pi\)
−0.900969 + 0.433884i \(0.857143\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 0 0
\(987\) 0 0
\(988\) 0 0
\(989\) 0 0
\(990\) 0 0
\(991\) −1.88980 0.284841i −1.88980 0.284841i −0.900969 0.433884i \(-0.857143\pi\)
−0.988831 + 0.149042i \(0.952381\pi\)
\(992\) 1.32091 + 1.22563i 1.32091 + 1.22563i
\(993\) 0 0
\(994\) −1.63402 + 0.246289i −1.63402 + 0.246289i
\(995\) 0 0
\(996\) 0 0
\(997\) 0 0 0.955573 0.294755i \(-0.0952381\pi\)
−0.955573 + 0.294755i \(0.904762\pi\)
\(998\) 0.988831 + 1.71271i 0.988831 + 1.71271i
\(999\) 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.2515.1 yes 12
4.3 odd 2 3332.1.cc.a.2515.1 yes 12
17.16 even 2 3332.1.cc.a.2515.1 yes 12
49.46 even 21 inner 3332.1.cc.b.2447.1 yes 12
68.67 odd 2 CM 3332.1.cc.b.2515.1 yes 12
196.95 odd 42 3332.1.cc.a.2447.1 12
833.781 even 42 3332.1.cc.a.2447.1 12
3332.2447 odd 42 inner 3332.1.cc.b.2447.1 yes 12
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
3332.1.cc.a.2447.1 12 196.95 odd 42
3332.1.cc.a.2447.1 12 833.781 even 42
3332.1.cc.a.2515.1 yes 12 4.3 odd 2
3332.1.cc.a.2515.1 yes 12 17.16 even 2
3332.1.cc.b.2447.1 yes 12 49.46 even 21 inner
3332.1.cc.b.2447.1 yes 12 3332.2447 odd 42 inner
3332.1.cc.b.2515.1 yes 12 1.1 even 1 trivial
3332.1.cc.b.2515.1 yes 12 68.67 odd 2 CM